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b/research/lean-contribution-archive/README.md @@ -0,0 +1,31 @@ +# Contribution checkpoints + +The current delivery uses one cumulative `review.patch` from public base +`db0e57bc7f36b5ac0fc844ad7ce1396165ee6647`, generated by +[`../lean-external-review/export_review.py`](../lean-external-review/export_review.py). +See the [review guide](../lean-external-review/README.md) for delivery, +build instructions and the supported patch application order. + +Five superseded per-task patch copies were retired during the privacy/reference +cleanup. Some embedded outdated commit citations; editing those copies would +also change their historical manifest and receipt bindings. They are no longer +part of the supported delivery. All corresponding Lean source directories, +required dependencies, source snapshots, proof receipts, notices and reviews +remain included. + +The neutral-author development checkpoints are: + +| Checkpoint | Commit | +| --- | --- | +| Obstruction and whole-residual hosting | `58d2b198f62d5b51d6b84ba511f2c630095e94b0` | +| Source invocation diagnostic | `a7f9ceebc83cb1aed29ab07202ae82bdf39100a2` | +| Task A: multiple-host framework | `13611a8958fc71046a83d8431d2bd6335e6a3e2f` | +| Task B: concrete source invocation | `f7330c5f5b1c5e85f91a98c95e8efc0e27c03490` | + +These identify historical source snapshots. Current reproduction uses the +complete review checkout and its own manifest. Earlier snapshots may retain +outdated documentation references; this table does not assert that previously +published Git objects have been removed by GitHub. + +Prepared with substantial OpenAI Codex assistance. Source-specific attribution +and the bounded mathematical claims remain unchanged. diff --git a/research/lean-external-review/DRAFT-PR.md b/research/lean-external-review/DRAFT-PR.md new file mode 100644 index 0000000000..cd0bd82e47 --- /dev/null +++ b/research/lean-external-review/DRAFT-PR.md @@ -0,0 +1,73 @@ +Title: Check one literal PR442 invocation with multi-host Lean certificates + +Upstream has incorporated #442 and the #509/#516 abstract stream-model +results. This contribution checks concrete obligations for one literal PR442 +R747 invocation (stage 2, replica 0, pair 0 at +`4e16d001d505d4f21dd2bcfc44591f9be4c279bd`). + +Task A generalizes the hosting contract to multiple hosts and recovers the +single-host theorems. Task B connects its 19,002-instruction word to that +contract, with Lean certificates for scalar endpoints, concrete ownership, +coordinate identities and COPY/ERASE guards, for arbitrary dirty Boolean +helpers and one explicitly clean, restored private temporary. + +Merged #516 already proves abstract realization for arbitrary global state +under hypotheses. The contribution here is checking selected concrete +invocation obligations in Lean; it is not the first arbitrary-state theorem. +The [overlap review](research/lean-external-review/MERGED-OVERLAP.md) covers +incorporated #509/#516 and draft #528. + +Main declarations include `MultiHosting.multi_hosting`, +`MultiHosting.SingleHost.whole_hosting_recovered`, +`MultiHosting.SingleHost.physical_whole_hosting_recovered`, +`SourceInvocation.actualContract`, `selected_call_completion`, +`selected_native_completion`, `selected_native_realization`, and +`selected_temporary_restoration` (the latter names are in `SourceInvocation`). + +Fresh Task B replay in progress; receipt will be added to this PR. + +Task A passed fresh: six modules, zero reuse, 21 axiom reports. Task B is +building all 52 modules from a new empty directory without `--resume`, with +931 planned axiom reports including `actualContract`. No final Task B PASS +is claimed. Reproduce after the [dependency setup](research/lean-external-review/README.md): + +```sh +python3 research/lean-external-review/reproduce.py \ + --allow-pending-task-b \ + --lean /path/to/lean-4.33.0-linux/bin/lean \ + --mathlib /path/to/mathlib4 \ + --build-dir /tmp/review-task-b-fresh \ + --receipt-dir /tmp/review-receipts-fresh +``` + +The base is `db0e57bc7f36b5ac0fc844ad7ce1396165ee6647`. The package uses +Lean 4.33.0 / Mathlib `db584cd6d46c92f209a44c0f1c829460d327499d`; +upstream #509/#516 use 4.21.0 / `308445d7985027f538e281e18df29ca16ede2ba3`. +No port is included. + +Scope limits: + +- One complete invocation; cross-invocation disjointness is not exercised. +- Pending ranges 15..21 and 1..28 are hand-supplied. Lean checks target-mask + containment; nothing binds them to the source schedule. +- Explicit input embeddings, an invertible chart and `2 ≠ 0`; extraction is + externally checked Python. Original-bank outputs remain auxiliary state. +- No full sweep, later scheduling, global-allocation equivalence, costs, + all-size compilation, analytic transfer or κ result. PR448's gain remains + unestablished. PR493 → PR472 → PR442 is provenance only. + +Original construction and predecessor credits remain in the source notices. +Prepared with substantial OpenAI Codex assistance. The human participant +initiated and coordinated the effort and does not claim independent derivation +or personal checking of the mathematics. Agent reviews are not human audits. + +No attribution requested; please don't add this account to CONTRIBUTORS. + +Questions for maintainers: + +1. Do the literal source binding, slot isometries, native operations and private + initialization faithfully represent this invocation? +2. Is retaining all host/data/exterior outputs with explicit auxiliary bank + outputs the right boundary for later scheduling proofs? +3. Where should these concrete certificates integrate with #509/#516 and #528? +4. Is a standalone Lean 4.33 package acceptable, or is a 4.21 port required? diff --git a/research/lean-external-review/MERGED-OVERLAP.md b/research/lean-external-review/MERGED-OVERLAP.md new file mode 100644 index 0000000000..2b529fd675 --- /dev/null +++ b/research/lean-external-review/MERGED-OVERLAP.md @@ -0,0 +1,136 @@ +# Overlap with the incorporated formal packages + +This bounded source review was made on 2026-10-12 against upstream main +`db0e57bc7f36b5ac0fc844ad7ce1396165ee6647`. It read the +[integration review][integration], its [exact-head record][integration-record], +the [review ledger][ledger], the merged #442/#509/#516 sources, Task A/B, +and draft #528's README and endpoint theorem. It did not rebuild the other +contributors' Lean packages, rerun their Python checks, or search every open +contribution. It makes no global novelty claim. + +The integration record pins #442 to +`4e16d001d505d4f21dd2bcfc44591f9be4c279bd`, #509 to +`7b9c720ecc9f483c383e7cd9c2ab81f06ee5df59`, and #516 to +`1c6b6ff9366a94e1f86a6c5d661a7df75c6ff814`. Thus the incorporated #442 +construction is the exact version selected by Task B. The batch also +incorporates #484 and #520; it leaves the selected conditional #531/#523/#493 +result unchanged. Incorporation does not establish a full multiplication +theorem. + +## What Task B adds, and what it does not + +The merged packages already prove general conjugation, physical realization, +helper endpoint, and scheduling lemmas. Task B's additional result is the +Lean verification of the embedded **19,002-instruction R747 invocation** +(#442, stage 2, replica 0, pair 0, forward), including its concrete labels, +Boolean scalar behavior, ownership, coordinate transformations, and clean +temporary guards. It uses its own replay and hosting definitions; it is +not an existing direct instantiation of `LemmaA.lemmaA_streams`. + +| Obligation | Incorporated #509/#516 | Task B's selected invocation | +| --- | --- | --- | +| Labels and exact recipes | `LemmaG.Stream.conj_matrix` assumes `RecipesExact` and `WellLabelled`. #484/#509 instance checks supply emitted-word evidence outside Lean. | `SourceFramed.actual_valid`, `SourceMoveGeometry.actual_matrix_run`, and the top-level matrix-realization theorems connect the literal trace to its gauges and matrix operators in Lean. | +| Scalar endpoint | `row_unit`, `row_pair`, and `LemmaA.family_endpoint` assume the relevant scalar row. The #484 application uses Python scalar replay. | `SourceMatrix.arbitrary_dirty_payloads` proves the complete literal normalized endpoint for all 987 live Boolean-valued input streams, including all 747 dirty helpers. | +| Ownership and charts | `realize_run` assumes an injective owner map. `lemmaA_streams` derives injectivity from assumed nonempty, disjoint footprints. #516 checks concrete owners in Python. | `SourceInvocation.oldOwner_injective` and `newOwner_injective`, with `ParentOwnership` and the geometry modules, discharge the chosen original/relocated layouts. The native bridge proves the common-coordinate interpretation. | +| Other invocations and scheduling | `commute_of_disjoint`, `whole_invocation`, `defer`, and `async_window` prove abstract consequences of support, disjointness, or commutation assumptions. Concrete windows and blocks are externally checked. | The multi-host application has the singleton list `[event]`. It checks many hosts within one complete call; cross-invocation residual disjointness is vacuous. It proves no later schedule or window correctness. | +| Arbitrary dirty state | `conj_matrix`, `realize_run`, and `lemmaA_streams` already quantify over arbitrary input functions/global states under their hypotheses. The concrete #484 endpoint application requires empty private registers. | The selected live helpers and retained exterior have arbitrary, possibly correlated Boolean payloads. Its designated private temporary starts blank and is restored; the original bank outputs are returned as actual outputs. | + +The source declarations behind the left column are +[`conj_matrix` and the row lemmas][lemma-g], +[`realize_run`, `family_endpoint`, and `endpoint_indep`][realize], +[`lemmaA_streams`][streams], and the +[`Schedule` support/interleaving theorems][schedule]. The merged +[instance-check descriptions][lemma-g-readme] and +[owner/window checks][lemma-a-readme] identify the external boundary. +The right column is collected in +[`SourceInvocation.lean`](../lean-multi-host-source/SourceInvocation.lean), +with the scalar endpoint in +[`SourceEndpoint.lean`](../lean-multi-host-source/SourceEndpoint.lean). + +Accordingly, the proposed description that the merged results “offer no +arbitrary-workspace theorem” is too broad. They **do** have universal abstract +state theorems. Nor does Task B prove all their concrete scheduling hypotheses. +The defensible distinction is that Task B discharges the listed local +obligations in Lean for one literal word, within the stated state model. +Its coordinate geometry is parameterized by a field with `2 ≠ 0` and an +invertible cover map; the data payloads in this instance are Boolean. +Neither contribution supplies unrestricted dirty initialization of every +register kind or a complete physical-machine theorem. In particular, #509's +copy/clear event semantics directly overwrite/clear a value; Task B separately +checks its concrete COPY/ERASE legality guards. + +Task B's comparison uses explicit old/new input embeddings, assigning defaults +to slots unused by a layout. It is not equality on arbitrary complete global +allocations. Source JSON parsing and extraction remain an external provenance +boundary, checked by `check_sources.py`; Lean checks the embedded literals. +The pending ranges **15..21 and 1..28 are hand-supplied** in `pendingTag`. +`tag_pending_contains` proves target-mask containment only. Nothing binds +these ranges to the source schedule. The singleton completion is visible in +[`PhysicalSourceConnection.lean`](../lean-multi-host-source/PhysicalSourceConnection.lean). +The full cover sweep, later child execution, costs, all-size compilation, +analytic transfer, and κ remain outside Task B. + +## Draft #528 + +GitHub's read-only API check at 2026-10-12 02:33 UTC found +[#528](https://github.com/CrocSwap/integer-mult-bounds/pull/528) open and draft, +head `df5bbdbf837df908ce2324ed880141918a19db5d`, with no merge recorded. +Its `CurrentMain.PR516CompleteBankEndpoint.full_state_endpoint` combines +#516's helper endpoint and rest-independence theorems with an exact complete +state split. It is explicitly universal over the helper and **all other +physical families**, with no clean-helper or clean-rest premise. + +Its [theorem][pr528-theorem] still takes owner injectivity, the actual word's +execution equality, recipes, labels, a complete helper unit row, a zero +off-diagonal helper column, and the bank-operator identification as hypotheses. +Its [README][pr528-readme] explicitly says that no selected finite witness or +physical word was newly checked. This overlaps Task A's abstract endpoint and +composition concerns. Task B supplies concrete local source evidence in a +different model, but is not yet an adapter satisfying #528's premises; its +clean temporary and common input embeddings must be respected in any such +connection. Nothing here proves the all-replica partition, sweep order, or +global boundary premises of that proposed connection. + +## Toolchain and provenance + +The incorporated packages pin Lean **4.21.0** and Mathlib +`308445d7985027f538e281e18df29ca16ede2ba3`. Task A/B pin Lean **4.33.0**; +Task B pins Mathlib `db584cd6d46c92f209a44c0f1c829460d327499d`. +The package stays independently reproducible at its existing pins. No shared +Lake dependency or source compatibility with 4.21.0 has been established. + +A port has not been attempted. An initial compatibility check could take a +few hours; a working estimate for a complete port and recorded replay is +**several focused engineering days**, plus build time. This is a planning +estimate, not a measured result. Task A has six replay modules; Task B has +52, including about 6.6 MB of local Lean source dominated by literal +certificates. Likely work includes core/Mathlib API and tactic compatibility, +kernel-reduction performance, and updating the runner's version/dependency +checks and receipts. A failed large certificate replay could materially +increase that estimate. Choosing a maintained standalone 4.33 package versus +a 4.21 port needs maintainer guidance. + +PR493's [explicit inherited-assumption statement][pr493-readme] and +[NOTICE attribution through PR472][pr493-notice] establish the +PR493 → PR472 → PR442 lineage. They establish **provenance only**: the +selected R747 proof does not transfer to a PR493 invocation. + +Credit remains with DaysSky for #442, DreamingOfClouds for #484/#509/#516, +James Chang (`jamesyc`) for #528 and its reused endpoint machinery, and the +predecessors named in their retained notices, including Jacob Sussman's E8 +construction. This review and the local verification contribution were +prepared with substantial AI assistance. + +[integration]: https://github.com/CrocSwap/integer-mult-bounds/blob/db0e57bc7f36b5ac0fc844ad7ce1396165ee6647/docs/research/community-formal-20261012-review.md +[integration-record]: https://github.com/CrocSwap/integer-mult-bounds/blob/db0e57bc7f36b5ac0fc844ad7ce1396165ee6647/docs/research/community-formal-20261012-integration.json +[ledger]: https://github.com/CrocSwap/integer-mult-bounds/blob/db0e57bc7f36b5ac0fc844ad7ce1396165ee6647/docs/research/pr-ledger.md +[lemma-g]: https://github.com/CrocSwap/integer-mult-bounds/blob/db0e57bc7f36b5ac0fc844ad7ce1396165ee6647/research/e8-lemma-g-lean/LemmaG/Stream.lean#L294 +[realize]: https://github.com/CrocSwap/integer-mult-bounds/blob/db0e57bc7f36b5ac0fc844ad7ce1396165ee6647/research/e8-lemma-a-lean/LemmaA/Realize.lean#L70 +[streams]: https://github.com/CrocSwap/integer-mult-bounds/blob/db0e57bc7f36b5ac0fc844ad7ce1396165ee6647/research/e8-lemma-a-lean/LemmaA/Streams.lean#L62 +[schedule]: https://github.com/CrocSwap/integer-mult-bounds/blob/db0e57bc7f36b5ac0fc844ad7ce1396165ee6647/research/e8-lemma-a-lean/LemmaA/Schedule.lean#L40 +[lemma-g-readme]: https://github.com/CrocSwap/integer-mult-bounds/blob/db0e57bc7f36b5ac0fc844ad7ce1396165ee6647/research/e8-lemma-g-lean/README.md +[lemma-a-readme]: https://github.com/CrocSwap/integer-mult-bounds/blob/db0e57bc7f36b5ac0fc844ad7ce1396165ee6647/research/e8-lemma-a-lean/README.md +[pr528-theorem]: https://github.com/CrocSwap/integer-mult-bounds/blob/df5bbdbf837df908ce2324ed880141918a19db5d/research/lean-complete-bank-endpoint/PR516CompleteBankEndpoint.lean#L48 +[pr528-readme]: https://github.com/CrocSwap/integer-mult-bounds/blob/df5bbdbf837df908ce2324ed880141918a19db5d/research/lean-complete-bank-endpoint/README.md +[pr493-readme]: https://github.com/CrocSwap/integer-mult-bounds/blob/c3a9a436b84fe44fdc223a5784d84736d1c2d3c7/research/e8-bit-carrier-skeleton/README.md#L147 +[pr493-notice]: https://github.com/CrocSwap/integer-mult-bounds/blob/c3a9a436b84fe44fdc223a5784d84736d1c2d3c7/research/e8-bit-carrier-skeleton/NOTICE.md#L42 diff --git a/research/lean-external-review/PRIVACY-AND-PROVENANCE.md b/research/lean-external-review/PRIVACY-AND-PROVENANCE.md new file mode 100644 index 0000000000..f3d58442c8 --- /dev/null +++ b/research/lean-external-review/PRIVACY-AND-PROVENANCE.md @@ -0,0 +1,66 @@ +# Identity, historical evidence, and source provenance + +The new review branch starts at upstream +`db0e57bc7f36b5ac0fc844ad7ce1396165ee6647`. Contribution commits use +`AI-assisted verification contributor `. +The human participant initiated and coordinated the AI-assisted effort; no +independent human derivation or checking of the mathematics is claimed. + +## Limits of the earlier privacy cleanup + +The previous public checkpoint is +`377012d9e1d350c29fc47669e82415249429f60c`. Its metadata rewrite replaced +personal Git author/committer fields and its later cleanup removed obsolete +commit citations from then-current files. That did not erase old objects: +unauthenticated checks still retrieved an old identifying commit through both +the fork and upstream repository URLs. Historical snapshots and diffs retain +references. No GitHub removal is claimed. + +A private Support request was prepared but not submitted. Eligibility for +GitHub's [sensitive-data removal process](https://docs.github.com/en/authentication/keeping-your-account-and-data-secure/removing-sensitive-data-from-a-repository) +requires GitHub's assessment. Copies, clones, and other references may remain. +The public account and required upstream attribution are still visible. +No old identifying commit IDs or personal Git identity are repeated here. + +## Current versus historical verification + +The current fresh-build receipts belong under `validation/`; their status is +reported in [VALIDATION.md](VALIDATION.md). They must match the current +manifests directly. Task B's receipt is pending until the ongoing fresh run +succeeds. The permanent inventory now includes `actualContract`. + +The old metadata-reanchoring helper and receipt were retired from this new +delivery. Their [historical record](https://github.com/cheesegrader/integer-mult-bounds/blob/377012d9e1d350c29fc47669e82415249429f60c/research/lean-external-review/validation/metadata-reanchor.json) +explains citation substitutions in older copies; it is not current proof +verification. Original Task A/B `replay-result.json` files remain unchanged as +historical context. In older regression receipts, original log hashes identify +pre-substitution bytes, not the published copies. No new claim relies on those +old log hashes or on the earlier missing external-library fingerprints. + +Authored reproduction instructions use portable paths. Machine paths in raw +historical execution records describe those runs and are not prerequisites. +Required local sources and dependencies remain included; the supported delivery +uses one cumulative patch from the new upstream base. + +## PR493 → PR472 → PR442 is provenance only + +At PR493 commit `c3a9a436b84fe44fdc223a5784d84736d1c2d3c7`: + +- The [README](https://github.com/CrocSwap/integer-mult-bounds/blob/c3a9a436b84fe44fdc223a5784d84736d1c2d3c7/research/e8-bit-carrier-skeleton/README.md#L147-L152) + explicitly lists “whole-call correlated-helper hosting (#442)” among inherited assumptions. +- The [NOTICE](https://github.com/CrocSwap/integer-mult-bounds/blob/c3a9a436b84fe44fdc223a5784d84736d1c2d3c7/research/e8-bit-carrier-skeleton/NOTICE.md#L42-L48) + names PR472 as the intermediary carrying PR442's `hosting_core.py`. +- The [source map](https://github.com/CrocSwap/integer-mult-bounds/blob/c3a9a436b84fe44fdc223a5784d84736d1c2d3c7/research/e8-bit-carrier-skeleton/SOURCE-pr472.json#L40-L43) + pins that source file's Git blob. + +The checked `hosting_core.py` bytes match at that PR493 commit, PR472 +`259c68488b7aa8a14cf3fcae7fc499381c9bf729`, and PR442 +`4e16d001d505d4f21dd2bcfc44591f9be4c279bd`: Git blob +`68b536daa9e6546c0aa046934bf840aaa3c3fde3`, SHA-256 +`d8b90cd5d152df3c7c351230863d9e61816ad5e1f21d69bea1a86a5daad559a3`. + +This establishes the interface's source lineage. It does not transfer the +selected R747 invocation proof to a PR493 word, ownership map, coordinate +system, or schedule. The current merged-work comparison is in +[MERGED-OVERLAP.md](MERGED-OVERLAP.md); it supersedes the earlier overlap snapshot +for current integration context. diff --git a/research/lean-external-review/README.md b/research/lean-external-review/README.md new file mode 100644 index 0000000000..765ebc1d6b --- /dev/null +++ b/research/lean-external-review/README.md @@ -0,0 +1,161 @@ +# External review: one literal PR442 R747 invocation + +This package contains Task A (a multi-host contract with exact single-host +recovery) and Task B (its connection to one literal PR442 forward invocation). +The contribution is prepared on a new local branch based on upstream +`db0e57bc7f36b5ac0fc844ad7ce1396165ee6647`. This snapshot is prepared for +a draft PR. The earlier public branch is unchanged. + +The human participant initiated and coordinated this AI-assisted verification +effort and does not claim independent derivation or personal checking of the +mathematics. Codex agents developed the proofs, ran checks, and prepared reviews. +Agent reviews are not human audits. + +## Scope and review entry points + +- [Task A](../lean-multi-host-framework/README.md): abstract multi-host completion + and exact recovery of the previous single-host theorem. +- [Task B](../lean-multi-host-source/README.md) and its + [statement review](../lean-multi-host-source/EXTERNAL-CLAIM-REVIEW.md): literal + endpoint, ownership, coordinate transformations and chronological clean-work guards. +- [Validation](VALIDATION.md): current receipts and fresh-versus-historical evidence. +- [Merged-work comparison](MERGED-OVERLAP.md), [draft PR](DRAFT-PR.md), and + [privacy/provenance](PRIVACY-AND-PROVENANCE.md). + +The selected invocation is stage 2, replica 0, pair 0 at PR442 commit +`4e16d001d505d4f21dd2bcfc44591f9be4c279bd`: 19,002 events, 987 live +Boolean payload streams, and one explicitly initialized clean private temporary. +The statements quantify over arbitrary dirty helper payloads, an address field +with `2 ≠ 0`, and an invertible invocation chart. The comparison retains every +affected host/data stream and the exterior of the active owners. Actual +old-bank outputs are threaded as auxiliary state. + +The multi-host theorem is applied to **one complete invocation**; +cross-invocation disjointness is not exercised. The remaining pending-coordinate +ranges 15..21 and 1..28 are hand-supplied. Lean checks that they contain the +target masks; nothing binds those choices to the source schedule. Completion +performs the remaining pending swaps immediately. + +Python extraction is reproducibly checked, not a formally verified compiler. +The local input embeddings are explicit. No full cover sweep, later recursive +schedule, arbitrary global allocation equivalence, physical cost bill, all-size +compiler, analytic transfer, or κ result is proved. PR448's split-helper gain +remains unestablished. + +## Delivery and patch order + +The new branch is `lean/pr442-invocation-review`. Its final commit is recorded +in an exported `delivery.json`; embedding that commit's own hash in a tracked +file would be circular. The historical public checkpoint +[`377012d`](https://github.com/cheesegrader/integer-mult-bounds/tree/377012d9e1d350c29fc47669e82415249429f60c) +does not contain this new validation. + +**Apply only the supplied cumulative `review.patch**, once, to this exact base: + +```sh +git clone https://github.com/CrocSwap/integer-mult-bounds.git review-checkout +cd review-checkout +git checkout --detach db0e57bc7f36b5ac0fc844ad7ce1396165ee6647 +git apply --check /absolute/path/to/review.patch +git apply /absolute/path/to/review.patch +python3 research/lean-external-review/verify_package.py --allow-pending-task-b +``` + +Alternatively, unpack the supplied `integer-mult-lean-review.tar.gz`, enter +`integer-mult-lean-review/`, and run `sha256sum -c SHA256SUMS` followed by the +same package check. This archive already contains the complete sources; do not +apply the patch inside it. No private checkout or historical commit is needed. +The explicit pending option reports `PENDING_TASK_B` while the fresh build is +unfinished; it does not assert a Task B proof PASS. + +Both routes include all local dependencies, particularly +`research/lean-whole-residual-hosting/CoordinateSwap.lean`, `Hosting.lean`, +and `PhysicalHosting.lean`. Task A builds six modules. Task B builds 50 own +modules plus `CoordinateSwap` and `MultiHosting`, for 52 total. + +## Install the public dependencies + +The Linux x86-64 commands require Git, Python 3.12, venv/pip, curl, tar, zstd +and a normal build environment. Lean and Mathlib are external public +dependencies; their binaries are not bundled. + +```sh +python3 -m venv /tmp/lean-review-python +/tmp/lean-review-python/bin/python -m pip install -r research/lean-external-review/requirements.txt + +mkdir -p /tmp/lean-review-deps +curl -fL https://github.com/leanprover/lean4/releases/download/v4.33.0/lean-4.33.0-linux.tar.zst \ + -o /tmp/lean-review-deps/lean-4.33.0-linux.tar.zst +echo '4b3fb03c29a1e0a253fb1d11f9bae3725f19a0dc6fc09b3ea16d2c9df3349e2c /tmp/lean-review-deps/lean-4.33.0-linux.tar.zst' | sha256sum -c - +tar --zstd -xf /tmp/lean-review-deps/lean-4.33.0-linux.tar.zst -C /tmp/lean-review-deps +export PATH="/tmp/lean-review-deps/lean-4.33.0-linux/bin:$PATH" +lean --githash +# Expected: d8b18978322de05a8f3dba51ef03cf5461676c17 + +git clone https://github.com/leanprover-community/mathlib4.git /tmp/lean-review-deps/mathlib4 +git -C /tmp/lean-review-deps/mathlib4 checkout --detach db584cd6d46c92f209a44c0f1c829460d327499d +cmp research/lean-multi-host-source/mathlib-lake-manifest.json /tmp/lean-review-deps/mathlib4/lake-manifest.json +``` + +From that Mathlib checkout, obtain the manifest-pinned dependencies and build +the required library targets: + +```sh +lake build Mathlib.Data.Matrix.Mul Mathlib.Algebra.BigOperators.Fin \ + Mathlib.Tactic.FieldSimp Mathlib.Tactic.Ring Mathlib.Tactic.NormNum +``` + +Mathlib's official cache is optional. A source build works without that cache. +No project-specific compiled artifact is required. + +Upstream's incorporated #509/#516 packages use Lean 4.21.0 and Mathlib +`308445d7985027f538e281e18df29ca16ede2ba3`. This package uses Lean 4.33.0 +and Mathlib `db584cd6d46c92f209a44c0f1c829460d327499d`; the environments +must remain separate. See the [port estimate](MERGED-OVERLAP.md). No port is included. + +## Reproduce both tasks fresh + +From the review root after dependency setup: + +```sh +/tmp/lean-review-python/bin/python research/lean-external-review/reproduce.py \ + --allow-pending-task-b \ + --lean /tmp/lean-review-deps/lean-4.33.0-linux/bin/lean \ + --mathlib /tmp/lean-review-deps/mathlib4 \ + --build-dir /tmp/lean-review-task-b-fresh \ + --receipt-dir /tmp/lean-review-receipts-fresh +``` + +The last two paths must be new. The command checks package integrity, regenerates +source literals, freshly compiles Task A and Task B, and audits the named +declarations with `lean -t 0`. Task A audits 21 declarations. Task B audits +931, including `SourceInvocation.actualContract`. It records installed +toolchain/library fingerprints and requires them to remain unchanged during +execution. Only standard Lean axioms are accepted. +The pending flag permits reproduction from this snapshot while its packaged +Task B receipt is absent. It does not enable reuse or bypass an invalid receipt. + +The current validation uses no resume option. An interrupted future build may +use the runner's separately documented resume facility; its receipt must say +resumed and must not replace this package's fresh-evidence claim. Historical +receipts remain context only. Current receipt hashes must match current +manifests directly; no metadata-reanchoring exception is used. + +## Export and validate a committed package + +From a clean, committed Git checkout: + +```sh +python3 research/lean-external-review/export_review.py --allow-pending-task-b \ + --output-dir /tmp/lean-review-delivery +python3 research/lean-external-review/validate_delivery.py \ + --allow-pending-task-b \ + --delivery-dir /tmp/lean-review-delivery \ + --receipt /tmp/lean-review-delivery/delivery-validation.json +``` + +The exporter creates one cumulative patch, a portable archive, exact commit IDs, +and checksums. The validator checks the extracted package, regenerates source +literals, and requires isolated patch application to reproduce the committed +tree. These are delivery checks, separate from Lean compilation. Neither +command pushes, publishes, or opens a pull request. diff --git a/research/lean-external-review/VALIDATION.md b/research/lean-external-review/VALIDATION.md new file mode 100644 index 0000000000..bc058b5069 --- /dev/null +++ b/research/lean-external-review/VALIDATION.md @@ -0,0 +1,87 @@ +# Validation on the current upstream base + +Exact upstream base: `db0e57bc7f36b5ac0fc844ad7ce1396165ee6647`. +Local review branch: `lean/pr442-invocation-review`. +The previous branch remains at `377012d9e1d350c29fc47669e82415249429f60c`. + +All 75 included Lean source files are byte-for-byte unchanged from that prior +contribution. The permanent Task B declaration inventory now additionally names +`SourceInvocation.actualContract`, bringing it to 931 entries. No proof was +edited to pass a build. + +## Current build status + +**Fresh Task B replay in progress; receipt will be added to this PR.** + +| Check | Current result | Evidence | +| --- | --- | --- | +| Task A | PASS: six modules freshly compiled, zero reused; 21 axiom reports | [fresh receipt](validation/task-a.json), [log](validation/task-a.log) | +| Task B | IN PROGRESS: new empty build directory, no resume; no final receipt yet | [run metadata](validation/run-metadata.json) | +| Source extraction | PASS: six input hashes and all 19,002 events in order | [source receipt](validation/source-binding.json) | +| Package and delivery | Integrity can be checked with Task B explicitly pending; this is not a Task B proof PASS | [package receipt](package-validation.json) and exported delivery receipt | + +Task A started on 2026-10-12 and completed with `lean -t 0`. Task B started +after Task A passed. Both use Lean 4.33.0 at +`d8b18978322de05a8f3dba51ef03cf5461676c17`; Task B uses Mathlib +`db584cd6d46c92f209a44c0f1c829460d327499d` and its pinned manifest. + +The unchanged Task B runner fingerprints the installed Lean distribution, +Mathlib, all eight manifest dependencies, and their artifacts before compilation, +then requires an identical fingerprint afterward. Its completed fresh receipt +will bind the current manifest, every module's source and artifacts, ordered +local dependency hashes, and all 931 axiom reports. No final Task B receipt or +fresh PASS is claimed while that run is incomplete. + +Task A accepts only `propext` and `Quot.sound`; Task B additionally permits +`Classical.choice`. These reports are transitive axiom inventories; a count +of named reports is not a count of new mathematical ideas. + +## Integrity checks while Task B runs + +```sh +python3 research/lean-external-review/verify_package.py --allow-pending-task-b +python3 research/lean-multi-host-source/check_sources.py +``` + +The explicit pending option checks the package, manifested sources, source +binding and fresh Task A evidence but reports `PENDING_TASK_B`. It cannot +convert a missing or invalid Task B result into proof success. Without that +option the verifier requires a matching fresh Task B receipt. Once the run +finishes, its receipt will be installed and the ordinary strict command rerun. + +Current evidence is directly bound to current manifests. The earlier +metadata-reanchoring helper and receipt are no longer part of this delivery's +verification path. Original `replay-result.json` files and older review +receipts remain historical context; their 930-entry Task B inventories and +legacy reuse do not establish the current 931-entry result. + +The old Task B compilation did not fingerprint its installed external libraries. +A successful current fresh build will provide those hashes for the new run. +It will not repair the historical receipt or authenticate earlier library bytes. +No project compiled module is reused in the current run. Installed public +Lean/Mathlib dependencies are fingerprinted; rebuilding Mathlib itself is not +claimed by the project replay. + +## Delivery and review limits + +The exporter creates one patch from the exact upstream base above. Validation +unpacks the archive, checks file hashes and source regeneration, then applies +that patch to an isolated base tree and requires the committed result tree. +While Task B is running, delivery validation also uses the explicit pending +option and reports that missing final proof result. + +The historical `make gen4-bank-verify` PASS and timed-out `make verify` sweep +were on the older base. They have not been rerun on this upstream base and are +not current integration evidence. No upstream generator or `upstream/` input +was changed. + +See [MERGED-OVERLAP.md](MERGED-OVERLAP.md) for the incorporated #442/#509/#516 +comparison, draft #528, and the toolchain mismatch. The current changes do not +prove source scheduling of the hand-supplied pending ranges or exercise +cross-invocation disjointness. Full cover sweeps, later scheduling, global +allocation equivalence, costs, all-size compilation, analytic transfer and κ +remain outside scope. + +This is ready to inspect as a draft with its missing Task B receipt explicitly +identified. The build continues independently; its result will be added to the +same PR when available. diff --git a/research/lean-external-review/export_review.py b/research/lean-external-review/export_review.py new file mode 100644 index 0000000000..e908cff6cb --- /dev/null +++ b/research/lean-external-review/export_review.py @@ -0,0 +1,106 @@ +#!/usr/bin/env python3 +"""Export a committed review snapshot and one cumulative public-base patch.""" +import argparse +import gzip +import hashlib +import io +import json +from pathlib import Path +import subprocess +import sys +import tarfile + +ROOT = Path(__file__).resolve().parents[2] +BASE = 'db0e57bc7f36b5ac0fc844ad7ce1396165ee6647' +PREFIXES = ['research/' + name for name in [ + 'lean-whole-residual-hosting', 'lean-multi-host-framework', + 'lean-multi-host-source', 'lean-external-review', + 'lean-single-stream-obstruction', 'lean-source-invocation-audit', + 'lean-contribution-archive', +]] +ROOT_FILES = ['LICENSE', 'NOTICE', 'CONTRIBUTING.md'] + + +def git(*args): + return subprocess.check_output(['git', *args], cwd=ROOT) + + +def digest(blob): + return hashlib.sha256(blob).hexdigest() + + +def main(): + p = argparse.ArgumentParser(description=__doc__) + p.add_argument('--output-dir', required=True, type=Path) + p.add_argument('--allow-pending-task-b', action='store_true', + help='export an explicitly unfinished package while the fresh Task B replay runs') + a = p.parse_args() + out = a.output_dir.resolve() + if out.is_relative_to(ROOT): + raise RuntimeError('Export outside the repository to avoid recursive packaging') + if git('status', '--porcelain').strip(): + raise RuntimeError('Commit the package first; working tree must be clean') + verify_command = [sys.executable, 'research/lean-external-review/verify_package.py'] + if a.allow_pending_task_b: + verify_command.append('--allow-pending-task-b') + validation = json.loads(subprocess.check_output(verify_command, cwd=ROOT)) + out.mkdir(parents=True, exist_ok=False) + head = git('rev-parse', 'HEAD').decode().strip() + subprocess.run(['git', 'merge-base', '--is-ancestor', BASE, head], cwd=ROOT, check=True) + package = json.loads((ROOT / 'research/lean-external-review/package-manifest.json').read_text()) + if package['base_commit'] != BASE: + raise RuntimeError('Package manifest and export base differ') + patch = git('diff', '--binary', '--full-index', BASE, head, '--', *ROOT_FILES, *PREFIXES) + (out / 'review.patch').write_bytes(patch) + raw_archive = git('archive', '--format=tar', head, *ROOT_FILES, *PREFIXES) + entries = {} + with tarfile.open(fileobj=io.BytesIO(raw_archive)) as archive: + for member in archive: + if member.isfile(): + entries[member.name] = archive.extractfile(member).read() + elif not member.isdir(): + raise RuntimeError('Unsupported archive member: ' + member.name) + entries['review.patch'] = patch + metadata = { + 'base_commit': BASE, 'review_commit': head, + 'validation_status': validation['status'], + 'task_b_verified': validation['task_b_verified'], + 'historical_task_a_commit': '13611a8958fc71046a83d8431d2bd6335e6a3e2f', + 'historical_task_b_commit': 'f7330c5f5b1c5e85f91a98c95e8efc0e27c03490', + 'patch_order': ['review.patch'], + 'patch_sha256': digest(patch), + 'source_manifest_sha256': digest(entries['research/lean-external-review/package-manifest.json']), + 'scope': 'All local review sources and dependencies; Lean/Mathlib are installed from pinned public sources.', + } + if validation['status'] == 'PENDING_TASK_B': + metadata['task_b_notice'] = validation['task_b_notice'] + entries['delivery.json'] = (json.dumps(metadata, indent=2) + '\n').encode() + entries['START-HERE.txt'] = ( + ('Fresh Task B replay in progress; receipt will be added to this PR.\n' + if validation['status'] == 'PENDING_TASK_B' else '') + + 'Read research/lean-external-review/README.md.\n' + 'This archive already contains the final review sources; do not apply review.patch here.\n' + 'Alternative: apply review.patch once to a clean public repository at ' + BASE + '.\n' + 'Use only review.patch; superseded per-task patch copies are not part of this delivery.\n' + 'Verify SHA256SUMS with: sha256sum -c SHA256SUMS\n' + 'No private checkout, unpublished commit, or prebuilt local Lean artifact is required.\n' + ).encode() + entries['SHA256SUMS'] = ''.join(f'{digest(blob)} {name}\n' + for name, blob in sorted(entries.items())).encode() + # Stable metadata makes repeated exports of the same commit byte-identical. + with (out / 'integer-mult-lean-review.tar.gz').open('wb') as raw: + with gzip.GzipFile(fileobj=raw, mode='wb', mtime=0, filename='') as gz: + with tarfile.open(fileobj=gz, mode='w') as archive: + for name, blob in sorted(entries.items()): + info = tarfile.TarInfo('integer-mult-lean-review/' + name) + info.size, info.mode, info.mtime = len(blob), 0o644, 0 + archive.addfile(info, io.BytesIO(blob)) + (out / 'delivery.json').write_bytes(entries['delivery.json']) + files = ['review.patch', 'integer-mult-lean-review.tar.gz', 'delivery.json'] + (out / 'SHA256SUMS').write_text(''.join(f'{digest((out / name).read_bytes())} {name}\n' + for name in files)) + print(json.dumps({'status': 'EXPORTED', 'validation_status': validation['status'], 'commit': head, 'output': str(out)})) + + +if __name__ == '__main__': + main() diff --git a/research/lean-external-review/package-manifest.json b/research/lean-external-review/package-manifest.json new file mode 100644 index 0000000000..0088d7023a --- /dev/null +++ b/research/lean-external-review/package-manifest.json @@ -0,0 +1,264 @@ +{ + "base_commit": "db0e57bc7f36b5ac0fc844ad7ce1396165ee6647", + "validation_status": "PENDING_TASK_B", + "historical_task_a_commit": "13611a8958fc71046a83d8431d2bd6335e6a3e2f", + "historical_task_b_commit": "f7330c5f5b1c5e85f91a98c95e8efc0e27c03490", + "excluded_from_recursive_hash": [ + "research/lean-external-review/package-manifest.json", + "research/lean-external-review/package-validation.json" + ], + 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"PENDING_TASK_B", + "completed_utc": "2026-10-12T02:39:44.505633+00:00", + "manifest_sha256": "06750464e1c2b65d460af064b52e655e1079cfc93c3fd0c7762cd7537542316b", + "files_checked": 252, + "task_b_verified": false, + "task_b_notice": "Fresh Task B replay in progress; receipt will be added to this PR.", + "task_a_modules": 6, + "task_b_modules": 52, + "task_a_theorem_closures": 21, + "task_b_planned_audit_declarations": 931, + "task_a_replay_mode": "fresh", + "task_b_replay_mode": "pending", + "task_a_receipt_sha256": "d1749aa810f710795aed4a5c88ec8ed5aedcce6616887defdddc686f1d5c1459", + "task_b_receipt_sha256": null, + "scope": "Inventory, manifested sources and available fresh receipt bindings; PENDING_TASK_B means Task B verification is unfinished. This verifier does not run Lean or authenticate build provenance." +} diff --git a/research/lean-external-review/reproduce.py b/research/lean-external-review/reproduce.py new file mode 100644 index 0000000000..db19a60a02 --- /dev/null +++ b/research/lean-external-review/reproduce.py @@ -0,0 +1,48 @@ +#!/usr/bin/env python3 +"""Reproduce Task A and Task B from the portable sources (fresh by default).""" +import argparse +import json +from pathlib import Path +import subprocess +import sys + +ROOT = Path(__file__).resolve().parents[2] + + +def main(): + p = argparse.ArgumentParser(description=__doc__) + p.add_argument('--lean', type=Path, required=True) + p.add_argument('--mathlib', type=Path, required=True) + p.add_argument('--build-dir', type=Path, required=True) + p.add_argument('--receipt-dir', type=Path, required=True) + p.add_argument('--allow-pending-task-b', action='store_true', + help='accept an explicitly pending package inventory before building Task B fresh') + p.add_argument('--resume', action='store_true', + help='resume an environment-bound build made by the current runner') + a = p.parse_args() + out = a.receipt_dir.resolve() + out.mkdir(parents=True, exist_ok=False) + lean, mathlib, build = map(lambda p: str(p.resolve()), (a.lean, a.mathlib, a.build_dir)) + commands = [ + ['research/lean-external-review/verify_package.py', '--receipt', str(out / 'inventory.json')] + + (['--allow-pending-task-b'] if a.allow_pending_task_b else []), + ['research/lean-multi-host-source/check_sources.py', '--receipt', str(out / 'source-binding.json')], + ['research/lean-multi-host-framework/replay.py', '--lean', lean, + '--receipt', str(out / 'task-a.json')], + ['research/lean-multi-host-source/replay.py', '--lean', lean, '--mathlib', mathlib, + '--build-dir', build, '--receipt', str(out / 'task-b.json')] + (['--resume'] if a.resume else []), + ] + for i, args in enumerate(commands): + command = [sys.executable, *args] + print('Running ' + args[0], flush=True) + with (out / f'{i + 1}.log').open('w') as log: + result = subprocess.run(command, cwd=ROOT, stdout=log, stderr=subprocess.STDOUT) + if result.returncode: + print(f'FAILED: see {out / f"{i + 1}.log"}', file=sys.stderr) + raise SystemExit(result.returncode) + print(json.dumps({'status': 'PASS', 'receipts': str(out), 'task_a': 'fresh', + 'task_b': 'resumed' if a.resume else 'fresh'})) + + +if __name__ == '__main__': + main() diff --git a/research/lean-external-review/requirements.txt b/research/lean-external-review/requirements.txt new file mode 100644 index 0000000000..de9542d36e --- /dev/null +++ b/research/lean-external-review/requirements.txt @@ -0,0 +1,2 @@ +sympy==1.14.0 +mpmath==1.3.0 diff --git a/research/lean-external-review/validate_delivery.py b/research/lean-external-review/validate_delivery.py new file mode 100644 index 0000000000..03ab0cd6fa --- /dev/null +++ b/research/lean-external-review/validate_delivery.py @@ -0,0 +1,109 @@ +#!/usr/bin/env python3 +"""Check an exported archive and apply its patch in an isolated public-base tree. + +Requires a Git checkout containing the pinned public base and delivery commit. +Fresh proof reproduction is a separate command; this checks delivery integrity. +""" +import argparse +from datetime import datetime, timezone +import hashlib +import json +from pathlib import Path +import subprocess +import sys +import tarfile +import tempfile + +ROOT = Path(__file__).resolve().parents[2] + + +def run(command, cwd): + return subprocess.check_output(command, cwd=cwd, stderr=subprocess.STDOUT) + + +def sha(path): + return hashlib.sha256(path.read_bytes()).hexdigest() + + +def require(ok, message): + if not ok: + raise RuntimeError(message) + + +def checksums(root): + count = 0 + for line in (root / 'SHA256SUMS').read_text().splitlines(): + digest, name = line.split(' ', 1) + path = (root / name).resolve(strict=True) + require(path.is_relative_to(root.resolve()), 'Checksum path escapes delivery') + require(sha(path) == digest, 'Delivery digest mismatch: ' + name) + count += 1 + return count + + +def main(): + p = argparse.ArgumentParser(description=__doc__) + p.add_argument('--delivery-dir', required=True, type=Path) + p.add_argument('--receipt', required=True, type=Path) + p.add_argument('--allow-pending-task-b', action='store_true', + help='check delivery integrity while reporting Task B verification as unfinished') + a = p.parse_args() + delivery = a.delivery_dir.resolve() + verify_command = [sys.executable, 'research/lean-external-review/verify_package.py'] + if a.allow_pending_task_b: + verify_command.append('--allow-pending-task-b') + outer_count = checksums(delivery) + metadata = json.loads((delivery / 'delivery.json').read_text()) + base, head = metadata['base_commit'], metadata['review_commit'] + require(sha(delivery / 'review.patch') == metadata['patch_sha256'], 'Patch metadata mismatch') + with tempfile.TemporaryDirectory(prefix='lean-review-delivery-') as tmp: + work = Path(tmp) + with tarfile.open(delivery / 'integer-mult-lean-review.tar.gz') as archive: + archive.extractall(work, filter='data') + snapshot = work / 'integer-mult-lean-review' + inner_count = checksums(snapshot) + require((snapshot / 'delivery.json').read_bytes() == (delivery / 'delivery.json').read_bytes(), + 'Archive/external delivery metadata differ') + require((snapshot / 'review.patch').read_bytes() == (delivery / 'review.patch').read_bytes(), + 'Archive/external patches differ') + inventory = json.loads(run(verify_command, snapshot)) + source_binding = json.loads(run([sys.executable, 'research/lean-multi-host-source/check_sources.py'], snapshot)) + baseline = work / 'public-base' + baseline.mkdir() + archive_path = work / 'base.tar' + run(['git', 'archive', '--format=tar', '--output=' + str(archive_path), base], ROOT) + with tarfile.open(archive_path) as archive: + archive.extractall(baseline, filter='data') + run(['git', 'init', '--quiet'], baseline) + run(['git', 'add', '--force', '.'], baseline) + before = run(['git', 'write-tree'], baseline).decode().strip() + require(before == run(['git', 'rev-parse', base + '^{tree}'], ROOT).decode().strip(), + 'Extracted baseline does not match exact public-base tree') + run(['git', 'apply', '--check', '--index', str(delivery / 'review.patch')], baseline) + run(['git', 'apply', '--index', str(delivery / 'review.patch')], baseline) + after = run(['git', 'write-tree'], baseline).decode().strip() + require(after == run(['git', 'rev-parse', head + '^{tree}'], ROOT).decode().strip(), + 'Applied patch does not reconstruct delivery commit tree') + patched_inventory = json.loads(run(verify_command, baseline)) + require(inventory['status'] == patched_inventory['status'] == metadata['validation_status'], + 'Delivery/archive/patch validation status mismatch') + require(inventory['task_b_verified'] == metadata['task_b_verified'], + 'Delivery Task B verification status mismatch') + require(inventory['manifest_sha256'] == patched_inventory['manifest_sha256'], + 'Archive/patch inventory divergence') + receipt = { + 'status': inventory['status'], 'delivery_integrity': 'PASS', 'completed_utc': datetime.now(timezone.utc).isoformat(), + 'base_commit': base, 'review_commit': head, 'base_tree': before, 'result_tree': after, + 'outer_checksums_verified': outer_count, 'archive_checksums_verified': inner_count, + 'archive_inventory': inventory, 'archive_source_binding': source_binding, + 'patch_inventory': patched_inventory, + 'artifacts_sha256': {name: sha(delivery / name) for name in + ['review.patch', 'integer-mult-lean-review.tar.gz', 'delivery.json']}, + 'scope': 'Fresh isolated patch application, archive inventory and source regeneration; not a new Lean compilation. PENDING_TASK_B means Task B verification is unfinished.', + } + a.receipt.write_text(json.dumps(receipt, indent=2) + '\n') + print(json.dumps({'status': inventory['status'], 'delivery_integrity': 'PASS', 'commit': head, 'receipt': str(a.receipt)})) + + +if __name__ == '__main__': + main() diff --git a/research/lean-external-review/validation/run-metadata.json b/research/lean-external-review/validation/run-metadata.json new file mode 100644 index 0000000000..de7e79435e --- /dev/null +++ b/research/lean-external-review/validation/run-metadata.json @@ -0,0 +1,32 @@ +{ + "upstream_base_commit": "db0e57bc7f36b5ac0fc844ad7ce1396165ee6647", + "task_a": { + "script_sha256": "43f3faf3530d065ad03db10f20978258a2ac1721c4b4581340ae1000e9c82727", + "receipt": "task-a.json", + "mode": "fresh", + "status": "PASS" + }, + "task_b": { + "script_sha256": "17a5ab55a0253358461725d360f85ee11c1a4887a162e7e814d029b0c6934583", + "receipt": "task-b.json", + "mode": "fresh", + "status": "running", + "build_directory_empty_at_start": true, + "resume_used": false, + "notice": "Fresh Task B replay in progress; receipt will be added to this PR.", + "started_utc": "2026-10-12T02:34:05.784041+00:00" + }, + "source_binding": { + "script_sha256": "ae0edd46c8f3452ea0dc2ee17625e949691b8195ccf7fe95f66406c8f6fcdb24", + "receipt": "source-binding.json", + "mode": "fresh regeneration", + "status": "PASS" + }, + "lean_release_archive_sha256": "4b3fb03c29a1e0a253fb1d11f9bae3725f19a0dc6fc09b3ea16d2c9df3349e2c", + "scope": "Fresh Task A complete; Task B fresh compilation running, no final result yet. Lean proof sources unchanged.", + "validation_commands": { + "task_a": "python3 research/lean-multi-host-framework/replay.py --lean /path/to/lean-4.33.0-linux/bin/lean --receipt /tmp/review-receipts/task-a.json", + "task_b": "python3 research/lean-multi-host-source/replay.py --lean /path/to/lean-4.33.0-linux/bin/lean --mathlib /path/to/mathlib4 --build-dir /tmp/review-task-b-fresh --receipt /tmp/review-receipts/task-b.json", + "source_binding": "python3 research/lean-multi-host-source/check_sources.py --receipt /tmp/review-receipts/source-binding.json" + } +} diff --git a/research/lean-external-review/validation/source-binding.json b/research/lean-external-review/validation/source-binding.json new file mode 100644 index 0000000000..7776d181d6 --- /dev/null +++ b/research/lean-external-review/validation/source-binding.json @@ -0,0 +1,7 @@ +{ + "status": "PASS", + "literal_events_in_order": 19002, + "live_roles": 987, + "source_input_hashes_checked": 6, + "scope": "Reproducible extraction; mathematical certificates are checked separately by Lean." +} diff --git a/research/lean-external-review/validation/task-a.json b/research/lean-external-review/validation/task-a.json new file mode 100644 index 0000000000..aa0b3d5b3f --- /dev/null +++ b/research/lean-external-review/validation/task-a.json @@ -0,0 +1,80 @@ +{ + "status": "PASS", + "task": "A only; no source endpoint contract supplied", + "lean": "Lean (version 4.33.0, x86_64-unknown-linux-gnu, commit d8b18978322de05a8f3dba51ef03cf5461676c17, Release)", + "lean_commit": "d8b18978322de05a8f3dba51ef03cf5461676c17", + "trust_level": 0, + "completed_utc": "2026-10-12T02:34:05.776099+00:00", + "manifest_sha256": "a6980854c10012d84a54040e83d89e5e23ac90510193c3d85a2ef32b74d06d18", + "toolchain": { + "sha256": "db7eaae92e952071be1978009f110250320e7f6f024615f017b3ca8a4525de93", + "files": 17505, + "bytes": 3255938837, + "lean_binary_sha256": "e8baaa71855a616dc351028f3ad2200051b0671f423a1696a100e809302d5550", + "meaning": "Current installed compiler, libraries, and source bytes; not archive-origin attestation." + }, + "replay_mode": "fresh", + "fresh_modules_compiled": 6, + "reused_modules": 0, + "source_sha256": { + "CoordinateSwap": "74d47e67dad5e8d548e69b008de19b65cfd138d3be71cf80d0b6c6990cf65841", + "Hosting": "102084fe6a003ab54e3b1eace36ccd9d872857eb4fc9b0770de3d6f7961af1f9", + "PhysicalHosting": "edd25772ad9c7cbae66a65bd9bc5cb00b98cf79e0e44913df4ff5f940525bc48", + "MultiHosting": "dc6188687ac8e089c64bf5ab7cd4c8c1a83f378d3c46bb1265a1b6ad43d199d6", + "SingleHostRecovery": "24590ece7ec72ad5edcdefc9d7f45acffa6dbccd644c95104ab8f2685fbaaf5d", + "MultiHostControls": "4321a232d7e36e0f4417a01ce951c601afde1b283c42c0b8ad24372e25fbc94d" + }, + "axioms": { + "MultiHosting.base_commutes": [ + "propext", + "Quot.sound" + ], + "MultiHosting.runBase_commutes": [ + "propext", + "Quot.sound" + ], + "MultiHosting.delay_residuals": [ + "propext", + "Quot.sound" + ], + "MultiHosting.multi_hosting": [ + "propext", + "Quot.sound" + ], + "MultiHosting.multi_hosting_in_context": [ + "propext", + "Quot.sound" + ], + "MultiHosting.PhysicalImplementations.original_projection": [], + "MultiHosting.PhysicalImplementations.relocated_projection": [], + "MultiHosting.physical_multi_hosting": [ + "propext", + "Quot.sound" + ], + "MultiHosting.physical_multi_hosting_in_context": [ + "propext", + "Quot.sound" + ], + "MultiHosting.SingleHost.collapse_embed": [], + "MultiHosting.SingleHost.embed_collapse": [ + "Quot.sound" + ], + "MultiHosting.SingleHost.collapse_onHosts": [], + "MultiHosting.SingleHost.collapse_base": [], + "MultiHosting.SingleHost.collapse_hosted": [], + "MultiHosting.SingleHost.collapse_runBase": [], + "MultiHosting.SingleHost.collapse_runHosted": [], + "MultiHosting.SingleHost.residuals_event": [], + "MultiHosting.SingleHost.whole_hosting_recovered": [ + "propext", + "Quot.sound" + ], + "MultiHosting.SingleHost.physical_whole_hosting_recovered": [ + "propext", + "Quot.sound" + ], + "MultiHosting.Controls.mixing_does_not_commute": [], + "MultiHosting.Controls.alias_breaks_refinement": [] + }, + "proved_boundary_inequalities": 2 +} diff --git a/research/lean-external-review/validation/task-a.log b/research/lean-external-review/validation/task-a.log new file mode 100644 index 0000000000..1316c1a1f3 --- /dev/null +++ b/research/lean-external-review/validation/task-a.log @@ -0,0 +1 @@ +{"status": "PASS", "compiled_modules": 6, "theorem_closures": 21, "proved_boundary_inequalities": 2} diff --git a/research/lean-external-review/verify_package.py b/research/lean-external-review/verify_package.py new file mode 100644 index 0000000000..8e80af6ed9 --- /dev/null +++ b/research/lean-external-review/verify_package.py @@ -0,0 +1,254 @@ +#!/usr/bin/env python3 +"""Check the portable review inventory and the A/B proof/receipt source bindings.""" +import argparse +from datetime import datetime, timezone +import hashlib +import json +from pathlib import Path +import re + +ROOT = Path(__file__).resolve().parents[2] +HERE = Path(__file__).resolve().parent +BASE = 'db0e57bc7f36b5ac0fc844ad7ce1396165ee6647' +DIRECTORIES = [ + 'lean-whole-residual-hosting', 'lean-multi-host-framework', + 'lean-multi-host-source', 'lean-external-review', + 'lean-single-stream-obstruction', 'lean-source-invocation-audit', + 'lean-contribution-archive', +] +# Avoid a circular digest. The delivery SHA256SUMS covers both files. +EXCLUDED = {'research/lean-external-review/package-manifest.json', + 'research/lean-external-review/package-validation.json'} +ROOT_FILES = ['LICENSE', 'NOTICE', 'CONTRIBUTING.md'] + + +def sha(path): + return hashlib.sha256(path.read_bytes()).hexdigest() + + +def require(ok, message): + if not ok: + raise RuntimeError(message) + + +def inventory(): + files = [ROOT / name for name in ROOT_FILES] + for name in DIRECTORIES: + files.extend(p for p in (ROOT / 'research' / name).rglob('*') + if p.is_file() and '__pycache__' not in p.parts and p.suffix != '.pyc') + require(all(not p.is_symlink() for p in files), 'Symlink in review sources') + return {str(p.relative_to(ROOT)): sha(p) for p in sorted(files) + if str(p.relative_to(ROOT)) not in EXCLUDED} + + +def object_sha(value): + return hashlib.sha256(json.dumps(value, sort_keys=True, separators=(',', ':')).encode()).hexdigest() + + +def digest_string(value): + return isinstance(value, str) and re.fullmatch(r'[0-9a-f]{64}', value) is not None + + +def footprint(record, label): + require(digest_string(record['sha256']), label + ': invalid fingerprint') + require(type(record['files']) is int and record['files'] >= 0 and + type(record['bytes']) is int and record['bytes'] >= 0, + label + ': invalid footprint counts') + + +def audit_inventory(receipt, names, allowed, label): + require(list(receipt['axioms']) == names, label + ': axiom inventory mismatch') + require(all(isinstance(axioms, list) and set(axioms) <= allowed + for axioms in receipt['axioms'].values()), label + ': unexpected axioms') + + +def bindings(allow_pending_task_b=False): + # Only these fresh receipts establish the current build claim. Original + # replay-result.json and archived review receipts remain inventory-covered + # historical evidence; neither they nor a metadata reanchor authorize reuse. + a = ROOT / 'research/lean-multi-host-framework' + b = ROOT / 'research/lean-multi-host-source' + ma = json.loads((a / 'proof-manifest.json').read_text()) + mb = json.loads((b / 'proof-manifest.json').read_text()) + current_a = json.loads((HERE / 'validation/task-a.json').read_text()) + task_b_receipt = HERE / 'validation/task-b.json' + current_b = json.loads(task_b_receipt.read_text()) if task_b_receipt.exists() else None + receipts = [('Task A', current_a, a)] + if current_b is not None: + receipts.append(('Task B', current_b, b)) + for label, receipt, directory in receipts: + require(receipt['status'] == 'PASS', label + ': fresh replay failed') + require(receipt['trust_level'] == 0, label + ': replay was not at trust level zero') + require(receipt['replay_mode'] == 'fresh' and receipt['reused_modules'] == 0, + label + ': current receipt is not a fully fresh build') + require(receipt['manifest_sha256'] == sha(directory / 'proof-manifest.json'), + label + ': fresh receipt/current manifest mismatch') + require(receipt['lean_commit'] == ma['lean_commit'] == mb['lean_commit'], + label + ': Lean pin mismatch') + require(receipt['lean'].startswith('Lean (version 4.33.0,'), + label + ': wrong Lean version') + require(current_a['fresh_modules_compiled'] == len(ma['sha256']), + 'Task A fresh module count mismatch') + require(current_a['source_sha256'] == ma['sha256'], 'Task A receipt/source mismatch') + audit_inventory(current_a, ma['theorems'], {'propext', 'Quot.sound'}, 'Task A') + footprint(current_a['toolchain'], 'Task A toolchain') + require(digest_string(current_a['toolchain']['lean_binary_sha256']), + 'Task A compiler fingerprint is invalid') + for name, digest in ma['sha256'].items(): + parent = a if name not in {'CoordinateSwap', 'Hosting', 'PhysicalHosting'} else a.parent / 'lean-whole-residual-hosting' + require(sha(parent / (name + '.lean')) == digest, 'Task A source mismatch: ' + name) + + module_names = [module['module'] for module in mb['modules']] + require(len(set(module_names)) == len(module_names), 'Duplicate Task B module') + require('SourceInvocation.actualContract' in mb['audit_declarations'], + 'Task B actualContract is absent from the permanent axiom inventory') + # A pending package still binds every manifested source and its import + # graph. It makes no claim that the pending Lean replay has succeeded. + prior_sources = set() + for module in mb['modules']: + name = module['module'] + source = (b / module['source']).resolve() + require(source.is_relative_to(ROOT), 'Dependency outside delivery: ' + name) + require(sha(source) == module['sha256'], 'Task B manifested source mismatch: ' + name) + code = re.sub(r'--[^\n]*', '', re.sub(r'/\-[\s\S]*?\-/', '', source.read_text())) + require(re.findall(r'^import (\S+)$', code, re.M) == module['imports'], + 'Task B manifested import mismatch: ' + name) + require(all(dep in prior_sources or dep == 'Std' or dep.startswith('Mathlib.') + for dep in module['imports']), 'Unordered or unmanifested dependency: ' + name) + prior_sources.add(name) + versions = json.loads((b / 'source-versions.json').read_text()) + require(versions['mathlib']['commit'] == mb['mathlib_commit'], + 'Mathlib pin mismatch') + require(versions['lean']['commit'] == mb['lean_commit'], 'Source version Lean mismatch') + require(json.loads((HERE / 'validation/source-binding.json').read_text())['status'] == 'PASS', + 'Source binding receipt failed') + run = json.loads((HERE / 'validation/run-metadata.json').read_text()) + require(run['upstream_base_commit'] == BASE, 'Run metadata upstream base mismatch') + for key, script, mode in [('task_a', a / 'replay.py', 'fresh'), + ('task_b', b / 'replay.py', 'fresh'), + ('source_binding', b / 'check_sources.py', 'fresh regeneration')]: + require(run[key]['script_sha256'] == sha(script) and run[key]['mode'] == mode, + 'Current runner metadata mismatch: ' + key) + if current_b is None: + require(allow_pending_task_b, + 'Fresh Task B receipt is absent; --allow-pending-task-b reports an explicitly unfinished package') + require(run['task_b'].get('status') == 'running', + 'Pending Task B requires run metadata explicitly marked running') + return {'status': 'PENDING_TASK_B', 'task_b_verified': False, + 'task_b_notice': 'Fresh Task B replay in progress; receipt will be added to this PR.', + 'task_a_modules': len(ma['sha256']), 'task_b_modules': len(module_names), + 'task_a_theorem_closures': len(ma['theorems']), + 'task_b_planned_audit_declarations': len(mb['audit_declarations']), + 'task_a_replay_mode': 'fresh', 'task_b_replay_mode': 'pending', + 'task_a_receipt_sha256': sha(HERE / 'validation/task-a.json'), + 'task_b_receipt_sha256': None} + require(current_a['lean'] == current_b['lean'], 'Task A/B compiler version mismatch') + require(current_b['mathlib_commit'] == mb['mathlib_commit'], 'Task B receipt Mathlib pin mismatch') + require(list(current_b['modules']) == module_names, 'Task B module inventory mismatch') + require(current_b['fresh_modules_compiled'] == len(module_names) and + current_b['fresh_module_names'] == module_names and + current_b['reused_module_names'] == [] and current_b['legacy_module_names'] == [] and + current_b['legacy_reused_modules'] == 0, + 'Task B fresh/reuse inventory mismatch') + require(current_b['historical_external_environment'] == 'fingerprinted_at_compile', + 'Task B compile environment was not fingerprinted') + require('SourceInvocation.actualContract' in mb['audit_declarations'], + 'Task B actualContract is absent from the permanent axiom inventory') + audit_inventory(current_b, mb['audit_declarations'], + {'propext', 'Quot.sound', 'Classical.choice'}, 'Task B') + + external = current_b['external_environment'] + components = external['components'] + require(components['schema'] == 1 and object_sha(components) == external['sha256'], + 'Task B external environment fingerprint mismatch') + footprint(components['toolchain'], 'Task B toolchain') + require(all(current_a['toolchain'][key] == components['toolchain'][key] + for key in ['sha256', 'files', 'bytes']) and + current_a['toolchain']['lean_binary_sha256'] == components['lean_binary_sha256'] and + digest_string(components['lean_binary_sha256']), + 'Task A/B toolchain footprint mismatch') + lake_manifest = json.loads((b / 'mathlib-lake-manifest.json').read_text()) + expected_dependencies = {'Mathlib': mb['mathlib_commit']} + for package in lake_manifest['packages']: + require(package['type'] == 'git' and not package.get('subDir'), + 'Unsupported external dependency layout: ' + package['name']) + expected_dependencies[package['name']] = package['rev'] + dependencies = components['dependencies'] + require(set(dependencies) == set(expected_dependencies), + 'External dependency inventory mismatch') + for name, commit in expected_dependencies.items(): + require(dependencies[name]['commit'] == commit, 'External dependency pin mismatch: ' + name) + for key in ['tracked_sources', 'build_artifacts', 'lake_configuration_artifacts']: + footprint(dependencies[name][key], name + '/' + key) + allowed_search = {name + '/.lake/build/lib/lean' for name in dependencies} | {'toolchain/lib/lean'} + search = components['library_search_order'] + require(set(search) <= allowed_search and len(set(search)) == len(search) and + 'Mathlib/.lake/build/lib/lean' in search, 'Unexpected external library search order') + + prior = {} + for module in mb['modules']: + name = module['module'] + record = current_b['modules'][name] + source = (b / module['source']).resolve() + require(source.is_relative_to(ROOT), 'Dependency outside delivery: ' + name) + require(sha(source) == module['sha256'] == record['sha256'], + 'Task B source/receipt mismatch: ' + name) + require(record['environment_sha256'] == external['sha256'] and + record['historical_external_environment'] == 'fingerprinted_at_compile' and + 'legacy_receipt' not in record, 'Task B module lacks fresh environment binding: ' + name) + artifacts = record['artifacts'] + require(artifacts.get('.olean') == record['olean_sha256'] and + set(artifacts) <= {'.olean', '.olean.private', '.olean.server', '.ir', '.ir.sig', '.so'} and + all(digest_string(digest) for digest in artifacts.values()), + 'Task B artifact fingerprint mismatch: ' + name) + local = [dep for dep in module['imports'] if dep in prior] + require(all(dep in prior or dep == 'Std' or dep.startswith('Mathlib.') + for dep in module['imports']), 'Unordered or unmanifested dependency: ' + name) + require(record['dependency_hashes'] == {dep: prior[dep]['olean_sha256'] for dep in local}, + 'Task B dependency olean binding mismatch: ' + name) + require(record['dependency_artifacts'] == {dep: prior[dep]['artifacts'] for dep in local}, + 'Task B dependency artifact binding mismatch: ' + name) + require(record['dependency_source_sha256'] == {dep: prior[dep]['sha256'] for dep in local}, + 'Task B dependency source binding mismatch: ' + name) + prior[name] = record + + return {'status': 'PASS', 'task_b_verified': True, 'task_a_modules': len(ma['sha256']), 'task_b_modules': len(module_names), + 'task_a_theorem_closures': len(ma['theorems']), + 'task_b_theorem_closures': len(mb['audit_declarations']), + 'task_a_replay_mode': 'fresh', 'task_b_replay_mode': 'fresh', + 'task_a_receipt_sha256': sha(HERE / 'validation/task-a.json'), + 'task_b_receipt_sha256': sha(HERE / 'validation/task-b.json')} + + +def main(): + p = argparse.ArgumentParser(description=__doc__) + p.add_argument('--write-manifest', action='store_true', + help='for package preparation only; reviewers should omit this') + p.add_argument('--receipt', type=Path) + p.add_argument('--allow-pending-task-b', action='store_true', + help='allow an absent Task B receipt only when explicitly marked running; result is PENDING_TASK_B') + args = p.parse_args() + files = inventory() + counts = bindings(allow_pending_task_b=args.allow_pending_task_b) + manifest_path = HERE / 'package-manifest.json' + if args.write_manifest: + manifest_path.write_text(json.dumps({ + 'base_commit': BASE, 'validation_status': counts['status'], + 'historical_task_a_commit': '13611a8958fc71046a83d8431d2bd6335e6a3e2f', + 'historical_task_b_commit': 'f7330c5f5b1c5e85f91a98c95e8efc0e27c03490', + 'excluded_from_recursive_hash': sorted(EXCLUDED), 'sha256': files, + }, indent=2) + '\n') + expected = json.loads(manifest_path.read_text()) + require(expected['base_commit'] == BASE, 'Package manifest upstream base mismatch') + require(expected['validation_status'] == counts['status'], 'Package validation status mismatch') + require(files == expected['sha256'], 'Package inventory differs from package-manifest.json') + result = {'status': counts['status'], 'completed_utc': datetime.now(timezone.utc).isoformat(), + 'manifest_sha256': sha(manifest_path), 'files_checked': len(files), **counts, + 'scope': 'Inventory, manifested sources and available fresh receipt bindings; PENDING_TASK_B means Task B verification is unfinished. This verifier does not run Lean or authenticate build provenance.'} + if args.receipt: + args.receipt.write_text(json.dumps(result, indent=2) + '\n') + print(json.dumps(result)) + + +if __name__ == '__main__': + main() diff --git a/research/lean-multi-host-framework/MultiHostControls.lean b/research/lean-multi-host-framework/MultiHostControls.lean new file mode 100644 index 0000000000..c8f3b6d9fb --- /dev/null +++ b/research/lean-multi-host-framework/MultiHostControls.lean @@ -0,0 +1,59 @@ +import MultiHosting + +/-! +Boundary controls for the multi-host framework. Apache-2.0. +Prepared with substantial OpenAI Codex assistance. + +These small models are not source providers. They show why retaining every +host does not permit arbitrary host mixing, and why distinct abstract host +indices must refine to distinct physical streams. +-/ +namespace MultiHosting.Controls +open WholeHosting + +def full : Mask Unit := fun _ => true +def firstOnly : HostMask Bool Unit := fun h _ => !h +def both : HostMask Bool Unit := fun _ => full +def address : Address Unit Bool := fun _ => (false, true) +def value : Stream Unit Bool Bool := fun a => (a ()).1 + +def initial : MultiHosting.WindowState Bool Unit Bool Bool Unit := + (fun h => if h then fun _ => false else value, ()) + +/-- A genuine cross-host XOR, outside the product endpoint interface. -/ +def mixHosts (s : MultiHosting.WindowState Bool Unit Bool Bool Unit) : + MultiHosting.WindowState Bool Unit Bool Bool Unit := + (fun h => if h then fun a => s.1 true a ^^ s.1 false a else s.1 false, s.2) + +theorem mixing_does_not_commute : + mixHosts (onHosts firstOnly initial) ≠ onHosts firstOnly (mixHosts initial) := by + intro equality + have observation := congrArg + (fun s : MultiHosting.WindowState Bool Unit Bool Bool Unit => s.1 true address) + equality + change true = false at observation + cases observation + +/-- An invalid ownership interpretation: both abstract hosts are views of +the same physical stream. A source owner-injectivity proof must exclude it. -/ +def aliasedView (s : Stream Unit Bool Bool) : + MultiHosting.WindowState Bool Unit Bool Bool Unit := (fun _ => s, ()) + +def aliasedPhysicalRun (s : Stream Unit Bool Bool) : Stream Unit Bool Bool := + bitAction full (bitAction full s) + +/-- Each nominal host receives one residual in the abstract endpoint, but +the actual aliased stream receives both, so the abstract endpoint is wrong. -/ +theorem alias_breaks_refinement : + onHosts both (aliasedView value) ≠ aliasedView (aliasedPhysicalRun value) := by + intro equality + have observation := congrArg + (fun s : MultiHosting.WindowState Bool Unit Bool Bool Unit => s.1 false address) + equality + change true = false at observation + cases observation + +end MultiHosting.Controls + +#print axioms MultiHosting.Controls.mixing_does_not_commute +#print axioms MultiHosting.Controls.alias_breaks_refinement diff --git a/research/lean-multi-host-framework/MultiHosting.lean b/research/lean-multi-host-framework/MultiHosting.lean new file mode 100644 index 0000000000..b2928e0560 --- /dev/null +++ b/research/lean-multi-host-framework/MultiHosting.lean @@ -0,0 +1,223 @@ +import CoordinateSwap + +/-! +Whole residual hosting on all affected physical streams. Apache-2.0. +Prepared with substantial OpenAI Codex assistance. + +`H` indexes distinct physical streams, not merely source family labels. +Each stream has a fixed coordinate chart throughout the window. Source +ownership and chart transport must establish this interpretation; they are +not consequences of the abstract product type. `R` contains all remaining +retained outputs, including scratch whose restoration is to be compared. +The complete endpoint contracts quantify over arbitrary stream contents, +retained state and auxiliary dirt; no independence or initialization is +assumed. Source refinement remains a separate obligation. +-/ +namespace MultiHosting +open WholeHosting + +abbrev HostMask (H : Type h) (ι : Type u) := H → Mask ι +abbrev WindowState (H : Type h) (ι : Type u) (K : Type v) (A : Type w) (R : Type z) := + (H → Stream ι K A) × R + +/-- One complete invocation endpoint in fixed charts for every host. `other` +cannot depend on any host, although a physical implementation may temporarily +read them if its complete endpoint satisfies the universal contract. -/ +structure WindowEvent (H : Type h) (ι : Type u) (R : Type z) where + idle : HostMask H ι + residual : HostMask H ι + other : R → R + +def onHosts {H ι K A R} (masks : HostMask H ι) + (s : WindowState H ι K A R) : WindowState H ι K A R := + (fun h => bitAction (masks h) (s.1 h), s.2) + +def WindowEvent.base {H ι K A R} (e : WindowEvent H ι R) + (s : WindowState H ι K A R) : WindowState H ι K A R := + (fun h => bitAction (e.idle h) (s.1 h), e.other s.2) + +def WindowEvent.hosted {H ι K A R} (e : WindowEvent H ι R) + (s : WindowState H ι K A R) : WindowState H ι K A R := + onHosts e.residual (e.base s) + +def runBase {H ι K A R} : + List (WindowEvent H ι R) → WindowState H ι K A R → WindowState H ι K A R + | [], s => s + | e :: es, s => runBase es (e.base s) + +def runHosted {H ι K A R} : + List (WindowEvent H ι R) → WindowState H ι K A R → WindowState H ι K A R + | [], s => s + | e :: es, s => runHosted es (e.hosted s) + +def residuals {H ι R} (events : List (WindowEvent H ι R)) (h : H) : List (Mask ι) := + events.map (fun e => e.residual h) + +def masksUnion {H ι R} (events : List (WindowEvent H ι R)) : HostMask H ι := + fun h => maskUnion (residuals events h) + +def remainders {H ι R} (pending : HostMask H ι) + (events : List (WindowEvent H ι R)) : HostMask H ι := + fun h => remainderMask (pending h) (masksUnion events h) + +def allOnHosts {H ι K A R} (events : List (WindowEvent H ι R)) + (s : WindowState H ι K A R) : WindowState H ι K A R := + (fun h => bitFactors (residuals events h) (s.1 h), s.2) + +theorem base_commutes {H ι K A R} (e : WindowEvent H ι R) (p : HostMask H ι) + (s : WindowState H ι K A R) : e.base (onHosts p s) = onHosts p (e.base s) := by + apply Prod.ext + · funext h + exact bitAction_commute (p h) (e.idle h) (s.1 h) + · rfl + +theorem runBase_commutes {H ι K A R} (events : List (WindowEvent H ι R)) + (p : HostMask H ι) (s : WindowState H ι K A R) : + runBase events (onHosts p s) = onHosts p (runBase events s) := by + induction events generalizing s with + | nil => rfl + | cons e es ih => + change runBase es (e.base (onHosts p s)) = onHosts p (runBase es (e.base s)) + rw [base_commutes, ih] + +/-- Simultaneously move the residual on every host to the end. This permits +several hosts to change during the same complete invocation. -/ +theorem delay_residuals {H ι K A R} (events : List (WindowEvent H ι R)) + (s : WindowState H ι K A R) : + runHosted events s = allOnHosts events (runBase events s) := by + induction events generalizing s with + | nil => rfl + | cons e es ih => + change runHosted es (onHosts e.residual (e.base s)) = + allOnHosts (e :: es) (runBase es (e.base s)) + rw [ih, runBase_commutes] + rfl + +/-- Each physical host has its own disjoint-mask and pending-subset +obligations. The equality covers every host and all of `R` on every input. +It does not by itself prove that a source program implements these endpoints. -/ +theorem multi_hosting {H ι K A R} (events : List (WindowEvent H ι R)) + (pending : HostMask H ι) + (hd : ∀ h, DisjointMasks (residuals events h)) + (hs : ∀ h, MaskSubset (masksUnion events h) (pending h)) + (s : WindowState H ι K A R) : + onHosts (remainders pending events) (runHosted events s) = + onHosts pending (runBase events s) := by + rw [delay_residuals] + apply Prod.ext + · funext h + exact bitFactors_complete (pending h) (residuals events h) (hd h) (hs h) + ((runBase events s).1 h) + · rfl + +theorem multi_hosting_in_context {H ι K A R X Y} + (events : List (WindowEvent H ι R)) (pending : HostMask H ι) + (hd : ∀ h, DisjointMasks (residuals events h)) + (hs : ∀ h, MaskSubset (masksUnion events h) (pending h)) + (before : X → WindowState H ι K A R) + (after : WindowState H ι K A R → Y) (x : X) : + after (onHosts (remainders pending events) (runHosted events (before x))) = + after (onHosts pending (runBase events (before x))) := + congrArg after (multi_hosting events pending hd hs (before x)) + +/-- `B` and `C` may be different auxiliary layouts. All semantically relevant +outputs must remain in the host family or `R`; this type grants no permission +to omit a changed output. Auxiliary outputs require a separate scope or +restoration argument before later code can ignore or reuse them. -/ +structure PhysicalContract {H ι K A R} (e : WindowEvent H ι R) + (B : Type b) (C : Type c) where + original : (WindowState H ι K A R × B) → (WindowState H ι K A R × B) + relocated : (WindowState H ι K A R × C) → (WindowState H ι K A R × C) + original_retained : ∀ s bank, (original (s, bank)).1 = e.base s + relocated_retained : ∀ s bank, (relocated (s, bank)).1 = e.hosted s + +/-- Actual auxiliary outputs, including arbitrary changed dirt, feed the +next invocation. No resetting or replacing the bank between calls occurs. -/ +inductive PhysicalImplementations {H ι K A R} (B : Type b) (C : Type c) : + List (WindowEvent H ι R) → Type _ where + | nil : PhysicalImplementations (K := K) (A := A) B C [] + | cons {e es} (contract : PhysicalContract (K := K) (A := A) e B C) + (rest : PhysicalImplementations (K := K) (A := A) B C es) : + PhysicalImplementations (K := K) (A := A) B C (e :: es) + +def PhysicalImplementations.runOriginal {H ι K A R B C} + {events : List (WindowEvent H ι R)} : + PhysicalImplementations (K := K) (A := A) B C events → + (WindowState H ι K A R × B) → (WindowState H ι K A R × B) + | .nil, s => s + | .cons contract rest, s => rest.runOriginal (contract.original s) + +def PhysicalImplementations.runRelocated {H ι K A R B C} + {events : List (WindowEvent H ι R)} : + PhysicalImplementations (K := K) (A := A) B C events → + (WindowState H ι K A R × C) → (WindowState H ι K A R × C) + | .nil, s => s + | .cons contract rest, s => rest.runRelocated (contract.relocated s) + +theorem PhysicalImplementations.original_projection {H ι K A R B C} + {events : List (WindowEvent H ι R)} + (program : PhysicalImplementations (K := K) (A := A) B C events) + (state : WindowState H ι K A R × B) : + (program.runOriginal state).1 = runBase events state.1 := by + induction program generalizing state with + | nil => rfl + | cons contract rest ih => + change (rest.runOriginal (contract.original state)).1 = runBase _ state.1 + rw [ih] + change runBase _ (contract.original (state.1, state.2)).1 = _ + rw [contract.original_retained] + rfl + +theorem PhysicalImplementations.relocated_projection {H ι K A R B C} + {events : List (WindowEvent H ι R)} + (program : PhysicalImplementations (K := K) (A := A) B C events) + (state : WindowState H ι K A R × C) : + (program.runRelocated state).1 = runHosted events state.1 := by + induction program generalizing state with + | nil => rfl + | cons contract rest ih => + change (rest.runRelocated (contract.relocated state)).1 = runHosted _ state.1 + rw [ih] + change runHosted _ (contract.relocated (state.1, state.2)).1 = _ + rw [contract.relocated_retained] + rfl + +theorem physical_multi_hosting {H ι K A R B C} + {events : List (WindowEvent H ι R)} + (program : PhysicalImplementations (K := K) (A := A) B C events) + (pending : HostMask H ι) + (hd : ∀ h, DisjointMasks (residuals events h)) + (hs : ∀ h, MaskSubset (masksUnion events h) (pending h)) + (s : WindowState H ι K A R) (oldBank : B) (newBank : C) : + onHosts (remainders pending events) (program.runRelocated (s, newBank)).1 = + onHosts pending (program.runOriginal (s, oldBank)).1 := by + rw [program.original_projection, program.relocated_projection] + exact multi_hosting events pending hd hs s + +theorem physical_multi_hosting_in_context {H ι K A R B C X Y} + {events : List (WindowEvent H ι R)} + (program : PhysicalImplementations (K := K) (A := A) B C events) + (pending : HostMask H ι) + (hd : ∀ h, DisjointMasks (residuals events h)) + (hs : ∀ h, MaskSubset (masksUnion events h) (pending h)) + (originalInput : X → WindowState H ι K A R × B) + (relocatedInput : X → WindowState H ι K A R × C) + (sameRetained : ∀ x, (originalInput x).1 = (relocatedInput x).1) + (observe : WindowState H ι K A R → Y) (x : X) : + observe (onHosts (remainders pending events) + (program.runRelocated (relocatedInput x)).1) = + observe (onHosts pending (program.runOriginal (originalInput x)).1) := by + rw [program.original_projection, program.relocated_projection, sameRetained x] + exact congrArg observe (multi_hosting events pending hd hs (relocatedInput x).1) + +end MultiHosting + +#print axioms MultiHosting.base_commutes +#print axioms MultiHosting.runBase_commutes +#print axioms MultiHosting.delay_residuals +#print axioms MultiHosting.multi_hosting +#print axioms MultiHosting.multi_hosting_in_context +#print axioms MultiHosting.PhysicalImplementations.original_projection +#print axioms MultiHosting.PhysicalImplementations.relocated_projection +#print axioms MultiHosting.physical_multi_hosting +#print axioms MultiHosting.physical_multi_hosting_in_context diff --git a/research/lean-multi-host-framework/README.md b/research/lean-multi-host-framework/README.md new file mode 100644 index 0000000000..d95bd09ac9 --- /dev/null +++ b/research/lean-multi-host-framework/README.md @@ -0,0 +1,51 @@ +# Multiple-host residual hosting (Task A) + +This package proves the abstract multiple-host generalization and recovers the +previous single-host theorem exactly. **It does not establish a physical source +invocation.** That separate obligation is tracked in `../lean-multi-host-source`. + +`MultiHosting.lean` retains every selected physical stream and all remaining +observed state. Residuals may act on several hosts during one invocation. The +pending-mask containment and disjointness conditions are checked per host. The +physical adapter quantifies over arbitrary dirty auxiliary inputs and threads +actual auxiliary outputs through subsequent invocations. + +`SingleHostRecovery.lean` defines inverse embeddings for a singleton host and +derives the exact previous operator theorem from `MultiHosting.multi_hosting`. +It also recovers the previous physical theorem using its projection lemmas. +`MultiHostControls.lean` proves that cross-host mixing and aliased physical +owners can invalidate a proposed source refinement. + +The endpoint contracts remain premises. A host denotes a distinct physical +stream, including its cover owner, with a fixed coordinate chart. Any output +whose equality or restoration matters must be retained. This work supplies no +new bound and does not assume PR448's missing split interface. + +## Build + +Use official Lean 4.33.0; no Mathlib is needed for Task A: + +```sh +python3 research/lean-multi-host-framework/replay.py \ + --lean /path/to/lean-4.33.0-linux/bin/lean \ + --receipt /tmp/multi-host-framework-replay.json +``` + +The offline replay checks source hashes, builds all six modules from source in +a fresh temporary directory with `lean -t 0`, audits all 21 new named theorem +closures, and requires only `propext` and `Quot.sound` (or no axioms). The three +unchanged dependencies are from `../lean-whole-residual-hosting`. The two +boundary inequalities are checked proofs, not merely failed test executions. + +See `REVIEW.md`, `replay-result.json`, `proof-manifest.json`, and +`overlap-audit.json` for review, validation, and exact source versions. + +Apache-2.0, following the repository license. Prepared with substantial OpenAI +Codex assistance; the existing WholeHosting authorship and source attribution +are retained in the sibling package and unchanged dependencies. + +The [external-review delivery](../lean-external-review/README.md) includes all +three WholeHosting dependencies and both tasks in one patch from the public +base, with a portable source archive and fresh reproduction command. The +human contributor initiated and coordinated the AI-assisted effort; they do +not claim independent derivation or personal checking of the mathematics. diff --git a/research/lean-multi-host-framework/REVIEW.md b/research/lean-multi-host-framework/REVIEW.md new file mode 100644 index 0000000000..bcde081d90 --- /dev/null +++ b/research/lean-multi-host-framework/REVIEW.md @@ -0,0 +1,69 @@ +# Independent review of Task A: multi-host framework + +Reviewed 2026-10-11 by a separate Codex agent. The reviewer did not write the +new framework or singleton recovery. No external publication occurred. + +**Verdict:** the abstract multi-host extension and exact singleton recovery are +sound. A fresh independent Lean4.33.0 build of both new modules and their three +dependencies passed. `framework-independent-build.json` contains source hashes +and compiler output. This completes the abstract compatibility review only; +no actual source invocation or physical-provider contract is discharged here. + +`MultiHosting.WindowState` retains a function from physical-host indices to +whole streams together with all remaining retained state R. The H index is +explicitly a distinct physical stream, including its cover owner when needed, +and must not silently identify all streams with the same source-family label. +The common coefficient/address/payload types do not force all streams to have +the same actual physical chart, but a fixed chart for each stream throughout +the window must be established by source refinement. + +Each event has a coordinate-mask action on every host and the same `other` +function on R. The pointwise commuting proof correctly permits multiple hosts +to change in one complete invocation and requires disjoint residual masks and +pending containment separately for every host. The theorem does not discard +any host or any part of R. Arbitrary input correlations are allowed because the +identity holds on every state, and no independence of input values is assumed. + +The physical adapter permits distinct auxiliary layouts and quantifies over +every original/relocated bank input. It threads actual bank outputs through +successive calls. It compares only retained outputs. Its documentation correctly +requires any component whose equality/restoration matters to stay retained; +auxiliary outputs need a separate continuation scope/restoration argument. + +`SingleHostRecovery.embed` and `collapse` are inverse on all retained state. +The recovered old operator statement genuinely follows by applying the new +`multi_hosting` theorem and collapsing the singleton-host state. The old +physical theorem is recovered using the old adapter's projection lemmas plus +that new derivation, not by invoking the old whole-hosting theorem. Thus this +is an exact conservative extension, not merely an analogous statement. + +No logical defect, dropped-state shortcut, initialization assumption, or new +axiom was found. The supplied complete endpoint contracts remain genuine +premises. In particular, an active-pair operation that reads/mixes a selected +host cannot be hidden inside `other : R → R`. For a shared window, every +selected host must have the stipulated independent coordinate action at every +complete event. Wider source schedules may require separate windows or a more +general commutation interface. + +Task B remains separate: instantiate concrete distinct owner streams, actual +coordinate/frame transformations, all scratch conventions, and the universal +arbitrary-dirt endpoint of the emitted source word. The new abstract theorem +alone does not count as that source proof. + +Reviewed hashes: + +- MultiHosting.lean: `dc6188687ac8e089c64bf5ab7cd4c8c1a83f378d3c46bb1265a1b6ad43d199d6` +- SingleHostRecovery.lean: `24590ece7ec72ad5edcdefc9d7f45acffa6dbccd644c95104ab8f2685fbaaf5d` + +Two checked negative controls in `MultiHostControls.lean` target source refinement: + +- `mixing_does_not_commute` retains both hosts but applies an actual XOR between them; moving a residual past that mix changes the result. +- `alias_breaks_refinement` maps two nominal hosts onto one physical stream; the abstract one-residual-per-host action disagrees with the two sequential physical actions. + +Both statements compiled in the independent build and use no axioms. Each is +a proved inequality, so replacing `≠` by `=` produces a false statement that +can be rejected by the corresponding theorem. They are small boundary models, +not claims about the actual source owner map. The source address coordinates +are Bool only for these abstract controls; no prime-admission claim is made. + +MultiHostControls.lean SHA256: `4321a232d7e36e0f4417a01ce951c601afde1b283c42c0b8ad24372e25fbc94d` diff --git a/research/lean-multi-host-framework/SingleHostRecovery.lean b/research/lean-multi-host-framework/SingleHostRecovery.lean new file mode 100644 index 0000000000..9c4cce9da4 --- /dev/null +++ b/research/lean-multi-host-framework/SingleHostRecovery.lean @@ -0,0 +1,142 @@ +import MultiHosting +import PhysicalHosting + +/-! +Exact recovery of the previous one-host theorems from `MultiHosting`. +Apache-2.0. Prepared with substantial OpenAI Codex assistance. + +The singleton embedding keeps the entire retained state. Its inverse shows +that the multi-host theorem specializes to the old theorem without dropping +any observations. The proof below calls the new `multi_hosting` theorem, +not the old `WholeHosting.whole_hosting` theorem. The physical corollary +uses the old adapter's independently proved projection lemmas, which thread +actual auxiliary-bank outputs and quantify over every dirty input. + +This compatibility result supplies no source-program endpoint contract. +-/ +namespace MultiHosting.SingleHost + +def embed {ι K A R} (s : WholeHosting.WindowState ι K A R) : + MultiHosting.WindowState Unit ι K A R := + (fun _ => s.1, s.2) + +def collapse {ι K A R} (s : MultiHosting.WindowState Unit ι K A R) : + WholeHosting.WindowState ι K A R := + (s.1 (), s.2) + +theorem collapse_embed {ι K A R} (s : WholeHosting.WindowState ι K A R) : + collapse (embed s) = s := by + rfl + +theorem embed_collapse {ι K A R} (s : MultiHosting.WindowState Unit ι K A R) : + embed (collapse s) = s := by + apply Prod.ext + · funext h + cases h + rfl + · rfl + +def event {ι R} (e : WholeHosting.WindowEvent ι R) : + MultiHosting.WindowEvent Unit ι R := + { idle := fun _ => e.idle + residual := fun _ => e.residual + other := e.other } + +theorem collapse_onHosts {ι K A R} (p : MultiHosting.HostMask Unit ι) + (s : MultiHosting.WindowState Unit ι K A R) : + collapse (MultiHosting.onHosts p s) = WholeHosting.onHost (p ()) (collapse s) := by + rfl + +theorem collapse_base {ι K A R} (e : WholeHosting.WindowEvent ι R) + (s : MultiHosting.WindowState Unit ι K A R) : + collapse ((event e).base s) = e.base (collapse s) := by + rfl + +theorem collapse_hosted {ι K A R} (e : WholeHosting.WindowEvent ι R) + (s : MultiHosting.WindowState Unit ι K A R) : + collapse ((event e).hosted s) = e.hosted (collapse s) := by + rfl + +theorem collapse_runBase {ι K A R} (events : List (WholeHosting.WindowEvent ι R)) + (s : MultiHosting.WindowState Unit ι K A R) : + collapse (MultiHosting.runBase (events.map event) s) = + WholeHosting.runBase events (collapse s) := by + induction events generalizing s with + | nil => rfl + | cons e es ih => + change collapse (MultiHosting.runBase (es.map event) ((event e).base s)) = _ + rw [ih, collapse_base] + rfl + +theorem collapse_runHosted {ι K A R} (events : List (WholeHosting.WindowEvent ι R)) + (s : MultiHosting.WindowState Unit ι K A R) : + collapse (MultiHosting.runHosted (events.map event) s) = + WholeHosting.runHosted events (collapse s) := by + induction events generalizing s with + | nil => rfl + | cons e es ih => + change collapse (MultiHosting.runHosted (es.map event) ((event e).hosted s)) = _ + rw [ih, collapse_hosted] + rfl + +theorem residuals_event {ι R} (events : List (WholeHosting.WindowEvent ι R)) (h : Unit) : + MultiHosting.residuals (events.map event) h = WholeHosting.residuals events := by + induction events with + | nil => rfl + | cons e es ih => + change e.residual :: MultiHosting.residuals (es.map event) h = + e.residual :: WholeHosting.residuals es + rw [ih] + +/-- The exact statement of `WholeHosting.whole_hosting`, derived from the +multi-host theorem by an invertible singleton-host change of state space. -/ +theorem whole_hosting_recovered {ι K A R} (events : List (WholeHosting.WindowEvent ι R)) + (pending : WholeHosting.Mask ι) + (hd : WholeHosting.DisjointMasks (WholeHosting.residuals events)) + (hs : WholeHosting.MaskSubset (WholeHosting.maskUnion (WholeHosting.residuals events)) pending) + (s : WholeHosting.WindowState ι K A R) : + WholeHosting.onHost + (WholeHosting.remainderMask pending (WholeHosting.maskUnion (WholeHosting.residuals events))) + (WholeHosting.runHosted events s) = + WholeHosting.onHost pending (WholeHosting.runBase events s) := by + have hd' : ∀ h, WholeHosting.DisjointMasks (MultiHosting.residuals (events.map event) h) := by + intro h + simpa only [residuals_event] using hd + have hs' : ∀ h, WholeHosting.MaskSubset + (MultiHosting.masksUnion (events.map event) h) pending := by + intro h + simpa only [MultiHosting.masksUnion, residuals_event] using hs + have equality := MultiHosting.multi_hosting (events.map event) (fun _ => pending) hd' hs' (embed s) + have projected := congrArg collapse equality + simpa only [collapse_onHosts, MultiHosting.remainders, MultiHosting.masksUnion, + residuals_event, collapse_runHosted, collapse_runBase, collapse_embed] using projected + +/-- The exact previous physical theorem also follows. No auxiliary output +is reset between invocations; the existing projection lemmas establish that +the actual original and relocated banks are threaded through each word. -/ +theorem physical_whole_hosting_recovered {ι K A R B C} + {events : List (WholeHosting.WindowEvent ι R)} + (program : WholeHosting.PhysicalImplementations (K := K) (A := A) B C events) + (pending : WholeHosting.Mask ι) + (hd : WholeHosting.DisjointMasks (WholeHosting.residuals events)) + (hs : WholeHosting.MaskSubset (WholeHosting.maskUnion (WholeHosting.residuals events)) pending) + (s : WholeHosting.WindowState ι K A R) (oldBank : B) (newBank : C) : + WholeHosting.onHost + (WholeHosting.remainderMask pending (WholeHosting.maskUnion (WholeHosting.residuals events))) + (program.runRelocated (s, newBank)).1 = + WholeHosting.onHost pending (program.runOriginal (s, oldBank)).1 := by + rw [program.original_projection, program.relocated_projection] + exact whole_hosting_recovered events pending hd hs s + +end MultiHosting.SingleHost + +#print axioms MultiHosting.SingleHost.collapse_embed +#print axioms MultiHosting.SingleHost.embed_collapse +#print axioms MultiHosting.SingleHost.collapse_onHosts +#print axioms MultiHosting.SingleHost.collapse_base +#print axioms MultiHosting.SingleHost.collapse_hosted +#print axioms MultiHosting.SingleHost.collapse_runBase +#print axioms MultiHosting.SingleHost.collapse_runHosted +#print axioms MultiHosting.SingleHost.residuals_event +#print axioms MultiHosting.SingleHost.whole_hosting_recovered +#print axioms MultiHosting.SingleHost.physical_whole_hosting_recovered diff --git a/research/lean-multi-host-framework/framework-independent-build.json b/research/lean-multi-host-framework/framework-independent-build.json new file mode 100644 index 0000000000..f8b29bf2c2 --- /dev/null +++ b/research/lean-multi-host-framework/framework-independent-build.json @@ -0,0 +1,41 @@ +{ + "build_dir": "/tmp/session4-framework-review-_pzkdssb", + "results": [ + { + "module": "CoordinateSwap", + "sha256": "74d47e67dad5e8d548e69b008de19b65cfd138d3be71cf80d0b6c6990cf65841", + "exit_code": 0, + "log": "'WholeHosting.swapAddress_involution' depends on axioms: [propext, Quot.sound]\n'WholeHosting.swapAddress_commute' depends on axioms: [propext, Quot.sound]\n'WholeHosting.swapAddress_disjoint_union' depends on axioms: [propext, Quot.sound]\n'WholeHosting.bitAction_involution' depends on axioms: [propext, Quot.sound]\n'WholeHosting.bitAction_commute' depends on axioms: [propext, Quot.sound]\n'WholeHosting.bitAction_disjoint_comp' depends on axioms: [propext, Quot.sound]\n'WholeHosting.bitAction_complete' depends on axioms: [propext, Quot.sound]\n'WholeHosting.bitFactors_union' depends on axioms: [propext, Quot.sound]\n'WholeHosting.bitFactors_complete' depends on axioms: [propext, Quot.sound]\n" + }, + { + "module": "Hosting", + "sha256": "102084fe6a003ab54e3b1eace36ccd9d872857eb4fc9b0770de3d6f7961af1f9", + "exit_code": 0, + "log": "'WholeHosting.base_commutes' depends on axioms: [propext, Quot.sound]\n'WholeHosting.runBase_commutes' depends on axioms: [propext, Quot.sound]\n'WholeHosting.delay_residuals' depends on axioms: [propext, Quot.sound]\n'WholeHosting.whole_hosting' depends on axioms: [propext, Quot.sound]\n'WholeHosting.whole_hosting_in_context' depends on axioms: [propext, Quot.sound]\n'WholeHosting.Implementations.original_eq' does not depend on any axioms\n'WholeHosting.Implementations.relocated_eq' does not depend on any axioms\n'WholeHosting.implementation_whole_hosting' depends on axioms: [propext, Quot.sound]\n" + }, + { + "module": "PhysicalHosting", + "sha256": "edd25772ad9c7cbae66a65bd9bc5cb00b98cf79e0e44913df4ff5f940525bc48", + "exit_code": 0, + "log": "'WholeHosting.PhysicalImplementations.original_projection' does not depend on any axioms\n'WholeHosting.PhysicalImplementations.relocated_projection' does not depend on any axioms\n'WholeHosting.physical_whole_hosting' depends on axioms: [propext, Quot.sound]\n'WholeHosting.physical_hosting_in_context' depends on axioms: [propext, Quot.sound]\n" + }, + { + "module": "MultiHosting", + "sha256": "dc6188687ac8e089c64bf5ab7cd4c8c1a83f378d3c46bb1265a1b6ad43d199d6", + "exit_code": 0, + "log": "'MultiHosting.base_commutes' depends on axioms: [propext, Quot.sound]\n'MultiHosting.runBase_commutes' depends on axioms: [propext, Quot.sound]\n'MultiHosting.delay_residuals' depends on axioms: [propext, Quot.sound]\n'MultiHosting.multi_hosting' depends on axioms: [propext, Quot.sound]\n'MultiHosting.multi_hosting_in_context' depends on axioms: [propext, Quot.sound]\n'MultiHosting.PhysicalImplementations.original_projection' does not depend on any axioms\n'MultiHosting.PhysicalImplementations.relocated_projection' does not depend on any axioms\n'MultiHosting.physical_multi_hosting' depends on axioms: [propext, Quot.sound]\n'MultiHosting.physical_multi_hosting_in_context' depends on axioms: [propext, Quot.sound]\n" + }, + { + "module": 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Missing source-specific matrix identities and emitted Trace still supplied.", + "verification": "source read only in this audit; not rebuilt" + }, + { + "repository_commit": "12a4934d15006e8c10f9b2264f13f8f341be802b", + "path": "research/machine-transfer-verification/full-transfer/localization/LocalizedAddressGauges.lean", + "sha256": "916af51a79becb7e21afc3fe5f3b963c4ea724020d4a0343d848352f25f3cbc5", + "lines": [ + 13, + 28, + 41, + 58 + ], + "scope": "Actual modular gauges and nested transport from rational projector identities plus prime eligibility. No modular matrix identity need be assumed separately once source rational identities are bound.", + "verification": "source read only in this audit; not rebuilt" + }, + { + "repository_commit": "12a4934d15006e8c10f9b2264f13f8f341be802b", + "path": "research/machine-transfer-verification/full-transfer/localization/EligibleLocalization.lean", + "sha256": "7c2525b8f30ddd26f5d9469972a8f9823c6b20805575d801c5c5755dea993c28", + "lines": [ + 21, + 45, + 67, + 87, + 93, + 115 + ], + "scope": "Finite rational table localization, numerator exceptions via reciprocal entries, eligible prime powers and eligible odd prime existence. 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No concrete finite graph, frame assignment or source Trace instantiated.", + "verification": "source read only in this audit; not rebuilt" + }, + { + "repository_commit": "12a4934d15006e8c10f9b2264f13f8f341be802b", + "path": "research/machine-transfer-verification/full-transfer/framed/TensorStageFrames.lean", + "sha256": "799c559518b6beccd32b24f3bc2bd5f096e9adffc8a9d26e9163ecfd83dc5fba", + "lines": [ + 17, + 21, + 51, + 98, + 120, + 152 + ], + "scope": "Exact ambient matrix/tensor identities for different two-stage geometry, not PR442 exterior-block geometry.", + "verification": "source read only in this audit; not rebuilt" + }, + { + "repository_commit": "12a4934d15006e8c10f9b2264f13f8f341be802b", + "path": "research/ranked-pair-verification/lean/DirtyWrapper.lean", + "sha256": "3ee3ee58cdb31bfa29c09c5f25b07f123b06988bdc7af8fcbc4062ba2780e30f", + "lines": [ + 148, + 189 + ], + "scope": "Existing generic arbitrary-dirty XOR wrapper; not actual R747 source/frame/owner instantiation.", + "verification": "source read only in this audit; not rebuilt" + }, + { + "repository": "jacobalansussman/wht-power-saving-lean", + "repository_commit": "9c94857bbaee886f8649edee0bc2d3c738f9555e", + "path": "Work/GFrame/Labels/GCarrier.lean", + "sha256": "fd613748598bcf50b9f564abaada1e9869a372b2b32c111487f0d983e54e5044", + "lines": [ + 72, + 113, + 142, + 156 + ], + "scope": "Dirty helper endpoint from generalized clean GRoute; complete source/certificate is a premise.", + "verification": "source read only; local Jacob checkout requests Lean4.34.1 while contribution uses Lean4.33.0" + }, + { + "repository": "jacobalansussman/wht-power-saving-lean", + "repository_commit": "9c94857bbaee886f8649edee0bc2d3c738f9555e", + "path": "Work/GCert/Chain/InvThm.lean", + "sha256": "ade7e7873da75ca63a4b5ce2f562dde9c12bfbb69d87d7ae831039ff790e5adb", + "lines": [ + 34, + 82, + 86, + 151 + ], + "scope": "Actual labelled complex/general-frame invocation certificate engine, not the different R747 bit source word.", + "verification": "source read only; local Jacob checkout requests Lean4.34.1 while contribution uses Lean4.33.0" + }, + { + "repository": "jacobalansussman/wht-power-saving-lean", + "repository_commit": "9c94857bbaee886f8649edee0bc2d3c738f9555e", + "path": "Work/GFrame/Engine/Adapt.lean", + "sha256": "feec0a3828867968a5c7c2c30b86ed70449abc3c660a60ada67203a75bae2ef7", + "lines": [ + 24, + 33, + 108, + 138 + ], + "scope": "Real address-permutation action and row transport in family-130 RAM model; no PR442 owner occurrence map.", + "verification": "source read only; local Jacob checkout requests Lean4.34.1 while contribution uses Lean4.33.0" + }, + { + "repository": "jacobalansussman/wht-power-saving-lean", + "repository_commit": "9c94857bbaee886f8649edee0bc2d3c738f9555e", + "path": "Work/GFrame/Engine/Letters.lean", + "sha256": "34906dbf5ae16b5174db00b4881a5cc1d2e583b8c8806db6523a5e2f86565f09", + "lines": [ + 31, + 39, + 151, + 159 + ], + "scope": "Actual additive address-permutation letter semantics and generalized word execution, not assumed local wrapper.", + "verification": "source read only; local Jacob checkout requests Lean4.34.1 while contribution uses Lean4.33.0" + } + ], + "actual_source_simplification": { + "source_commit": "4e16d001d505d4f21dd2bcfc44591f9be4c279bd", + "states_sha256": "40c063fd3d7b63c735f762097e692b5c36f618c60e8ed257de9e5f92be11b48e", + "frames_sha256": "884480e45865a9d9d57f5f7198844a64271b046bc95e9820efbefb9e10878330", + "helper_registers": [ + 240, + 986 + ], + "entrance_frames": [ + { + "frame": 0, + "helpers": 637, + "entrance_rank": 0, + "coordinate_axes": [] + }, + { + "frame": 2, + "helpers": 23, + "entrance_rank": 1, + "coordinate_axes": [ + 0 + ] + }, + { + "frame": 3, + "helpers": 17, + "entrance_rank": 1, + "coordinate_axes": [ + 1 + ] + }, + { + "frame": 4, + "helpers": 16, + "entrance_rank": 1, + "coordinate_axes": [ + 2 + ] + }, + { + "frame": 5, + "helpers": 3, + "entrance_rank": 1, + "coordinate_axes": [ + 3 + ] + }, + { + "frame": 6, + "helpers": 19, + "entrance_rank": 1, + "coordinate_axes": [ + 4 + ] + }, + { + "frame": 7, + "helpers": 18, + "entrance_rank": 1, + "coordinate_axes": [ + 5 + ] + }, + { + "frame": 9, + "helpers": 8, + "entrance_rank": 1, + "coordinate_axes": [ + 7 + ] + }, + { + "frame": 458, + "helpers": 1, + "entrance_rank": 4, + "coordinate_axes": [ + 0, + 1, + 2, + 3 + ] + }, + { + "frame": 460, + "helpers": 1, + "entrance_rank": 4, + "coordinate_axes": [ + 0, + 1, + 6, + 7 + ] + }, + { + "frame": 462, + "helpers": 1, + "entrance_rank": 4, + "coordinate_axes": [ + 0, + 2, + 5, + 7 + ] + }, + { + "frame": 464, + "helpers": 1, + "entrance_rank": 4, + "coordinate_axes": [ + 0, + 3, + 5, + 6 + ] + }, + { + "frame": 470, + "helpers": 1, + "entrance_rank": 4, + "coordinate_axes": [ + 2, + 3, + 6, + 7 + ] + }, + { + "frame": 471, + "helpers": 1, + "entrance_rank": 4, + "coordinate_axes": [ + 4, + 5, + 6, + 7 + ] + } + ], + "finding": "Every helper entrance is span of distinct coordinate vectors2e_i. Residual I\u2212P_E has literal complement-coordinate support. Helper route onto an allocated residual interval can therefore use a coordinate permutation plus the prescribed pending-child chart; no arbitrary square-root isometry is needed for these endpoint subspaces.", + "limitation": "Intermediate source frame projectors and their physical instruction realization remain necessary. Exact source owner chart must still be constructed and linked to emitted selectors; scalar rank alone is insufficient." + }, + "review_constraints": [ + "All affected retained host streams must appear in the multi-host state; independent banks may differ but all compared scratch/output components stay retained.", + "Pointwise host masks must share an actual address chart within a window. Different family charts require explicit encodings, not rank equality.", + "Task A product maps require rest not read host inputs, or a more general proved commutation contract. Actual active-pair operations may mix retained data and cannot silently be put in independent rest.", + "Task B must quantify over arbitrary correlated dirty inputs, keep source blank-temporary preconditions explicit, and prove actual source owner injectivity and finite-field frame realization.", + "Returning to a theorem with supplied complete-call endpoint assumptions would repeat earlier conditional work and would not complete Task B." + ], + "bounded_conclusion": "No new Lean multi-host theorem or actual PR442 R747 source provider was identified in this bounded audit. All154 Lean blobs in each of PR473477506507 are byte-identical to main. This is not an exhaustive novelty search of all repositories, branches, discussions or mathematical literature.", + "evidence_files": [ + { + "path": "/workspace/audit/session4/upstream-raw.json", + "sha256": "1e920f0b447b71daf0d3be3565b1e4e3d2c1e8a0898e1cee8f3f69e66cb4ccc1" + }, + { + "path": "/workspace/audit/session4/new-work-raw.json", + "sha256": "25116dc0603be07ae11120f1c3cdd1f71fb06be98f42a8361a35ae2bf5c39d1f" + }, + { + "path": "/workspace/audit/session4/new-work-lean-diff.json", + "sha256": "c7dc54b272616a1df38debd1b320d576a2737f8f4e4455df0136b30c461808b4" + } + ] +} diff --git a/research/lean-multi-host-framework/proof-manifest.json b/research/lean-multi-host-framework/proof-manifest.json new file mode 100644 index 0000000000..03b3c25382 --- /dev/null +++ b/research/lean-multi-host-framework/proof-manifest.json @@ -0,0 +1,56 @@ +{ + "source_base_commit": "a7f9ceebc83cb1aed29ab07202ae82bdf39100a2", + "lean_commit": "d8b18978322de05a8f3dba51ef03cf5461676c17", + "sha256": { + "CoordinateSwap": "74d47e67dad5e8d548e69b008de19b65cfd138d3be71cf80d0b6c6990cf65841", + "Hosting": "102084fe6a003ab54e3b1eace36ccd9d872857eb4fc9b0770de3d6f7961af1f9", + "PhysicalHosting": "edd25772ad9c7cbae66a65bd9bc5cb00b98cf79e0e44913df4ff5f940525bc48", + "MultiHosting": "dc6188687ac8e089c64bf5ab7cd4c8c1a83f378d3c46bb1265a1b6ad43d199d6", + "SingleHostRecovery": "24590ece7ec72ad5edcdefc9d7f45acffa6dbccd644c95104ab8f2685fbaaf5d", + "MultiHostControls": "4321a232d7e36e0f4417a01ce951c601afde1b283c42c0b8ad24372e25fbc94d" + }, + "imports": { + "CoordinateSwap": [ + "Std" + ], + "Hosting": [ + "CoordinateSwap" + ], + "PhysicalHosting": [ + "Hosting" + ], + "MultiHosting": [ + "CoordinateSwap" + ], + "SingleHostRecovery": [ + "MultiHosting", + "PhysicalHosting" + ], + "MultiHostControls": [ + "MultiHosting" + ] + }, + "theorems": [ + "MultiHosting.base_commutes", + "MultiHosting.runBase_commutes", + "MultiHosting.delay_residuals", + "MultiHosting.multi_hosting", + "MultiHosting.multi_hosting_in_context", + "MultiHosting.PhysicalImplementations.original_projection", + "MultiHosting.PhysicalImplementations.relocated_projection", + "MultiHosting.physical_multi_hosting", + "MultiHosting.physical_multi_hosting_in_context", + "MultiHosting.SingleHost.collapse_embed", + "MultiHosting.SingleHost.embed_collapse", + "MultiHosting.SingleHost.collapse_onHosts", + "MultiHosting.SingleHost.collapse_base", + "MultiHosting.SingleHost.collapse_hosted", + "MultiHosting.SingleHost.collapse_runBase", + "MultiHosting.SingleHost.collapse_runHosted", + "MultiHosting.SingleHost.residuals_event", + "MultiHosting.SingleHost.whole_hosting_recovered", + "MultiHosting.SingleHost.physical_whole_hosting_recovered", + "MultiHosting.Controls.mixing_does_not_commute", + "MultiHosting.Controls.alias_breaks_refinement" + ] +} diff --git a/research/lean-multi-host-framework/replay-result.json b/research/lean-multi-host-framework/replay-result.json new file mode 100644 index 0000000000..71ee4e002a --- /dev/null +++ b/research/lean-multi-host-framework/replay-result.json @@ -0,0 +1,68 @@ +{ + "status": "PASS", + "task": "A only; no source endpoint contract supplied", + "lean": "Lean (version 4.33.0, x86_64-unknown-linux-gnu, commit d8b18978322de05a8f3dba51ef03cf5461676c17, Release)", + "trust_level": 0, + "fresh_modules_compiled": 6, + "source_sha256": { + "CoordinateSwap": "74d47e67dad5e8d548e69b008de19b65cfd138d3be71cf80d0b6c6990cf65841", + "Hosting": "102084fe6a003ab54e3b1eace36ccd9d872857eb4fc9b0770de3d6f7961af1f9", + "PhysicalHosting": "edd25772ad9c7cbae66a65bd9bc5cb00b98cf79e0e44913df4ff5f940525bc48", + "MultiHosting": "dc6188687ac8e089c64bf5ab7cd4c8c1a83f378d3c46bb1265a1b6ad43d199d6", + "SingleHostRecovery": "24590ece7ec72ad5edcdefc9d7f45acffa6dbccd644c95104ab8f2685fbaaf5d", + "MultiHostControls": "4321a232d7e36e0f4417a01ce951c601afde1b283c42c0b8ad24372e25fbc94d" + }, + "axioms": { + "MultiHosting.base_commutes": [ + "propext", + "Quot.sound" + ], + "MultiHosting.runBase_commutes": [ + "propext", + "Quot.sound" + ], + "MultiHosting.delay_residuals": [ + "propext", + "Quot.sound" + ], + "MultiHosting.multi_hosting": [ + "propext", + "Quot.sound" + ], + "MultiHosting.multi_hosting_in_context": [ + "propext", + "Quot.sound" + ], + "MultiHosting.PhysicalImplementations.original_projection": [], + "MultiHosting.PhysicalImplementations.relocated_projection": [], + "MultiHosting.physical_multi_hosting": [ + "propext", + "Quot.sound" + ], + "MultiHosting.physical_multi_hosting_in_context": [ + "propext", + "Quot.sound" + ], + "MultiHosting.SingleHost.collapse_embed": [], + "MultiHosting.SingleHost.embed_collapse": [ + "Quot.sound" + ], + "MultiHosting.SingleHost.collapse_onHosts": [], + "MultiHosting.SingleHost.collapse_base": [], + "MultiHosting.SingleHost.collapse_hosted": [], + "MultiHosting.SingleHost.collapse_runBase": [], + "MultiHosting.SingleHost.collapse_runHosted": [], + "MultiHosting.SingleHost.residuals_event": [], + "MultiHosting.SingleHost.whole_hosting_recovered": [ + "propext", + "Quot.sound" + ], + "MultiHosting.SingleHost.physical_whole_hosting_recovered": [ + "propext", + "Quot.sound" + ], + "MultiHosting.Controls.mixing_does_not_commute": [], + "MultiHosting.Controls.alias_breaks_refinement": [] + }, + "proved_boundary_inequalities": 2 +} diff --git a/research/lean-multi-host-framework/replay.py b/research/lean-multi-host-framework/replay.py new file mode 100644 index 0000000000..c7b4026b2c --- /dev/null +++ b/research/lean-multi-host-framework/replay.py @@ -0,0 +1,119 @@ +#!/usr/bin/env python3 +"""Fresh offline Lean kernel replay of Task A, independent of Task B.""" +import argparse +from datetime import datetime, timezone +import hashlib +import json +import os +from pathlib import Path +import re +import subprocess +import tempfile + +ROOT = Path(__file__).resolve().parent +DEPS = ['CoordinateSwap', 'Hosting', 'PhysicalHosting'] +MODULES = DEPS + ['MultiHosting', 'SingleHostRecovery', 'MultiHostControls'] + + +def require(ok, message): + if not ok: + raise RuntimeError(message) + + + +def sha256_file(path): + digest = hashlib.sha256() + with path.open('rb') as stream: + for block in iter(lambda: stream.read(1024 * 1024), b''): + digest.update(block) + return digest.hexdigest() + + +def toolchain_snapshot(lean, env): + prefix = Path(subprocess.check_output([str(lean), '--print-prefix'], env=env, + text=True, timeout=30).strip()).resolve(strict=True) + require(lean == prefix / 'bin' / 'lean', 'Compiler is outside its reported toolchain prefix') + records = [(str(p.relative_to(prefix)), p.stat().st_size, sha256_file(p)) + for p in sorted(prefix.rglob('*')) if p.is_file()] + digest = hashlib.sha256(json.dumps(records, separators=(',', ':')).encode()).hexdigest() + return {'sha256': digest, 'files': len(records), 'bytes': sum(r[1] for r in records), + 'lean_binary_sha256': sha256_file(lean), + 'meaning': 'Current installed compiler, libraries, and source bytes; not archive-origin attestation.'} + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--lean', required=True, type=Path) + parser.add_argument('--receipt', type=Path) + args = parser.parse_args() + lean = args.lean.resolve(strict=True) + env = dict(os.environ) + env.pop('LEAN_PATH', None) + env.pop('LEAN_SRC_PATH', None) + env.pop('LEAN_SYSROOT', None) + version = subprocess.check_output([str(lean), '--version'], env=env, + text=True, timeout=30).strip() + require(version.startswith('Lean (version 4.33.0,'), 'Lean 4.33.0 required') + manifest_bytes = (ROOT / 'proof-manifest.json').read_bytes() + manifest = json.loads(manifest_bytes) + revision = subprocess.check_output([str(lean), '--githash'], env=env, text=True, timeout=30).strip() + require(revision == manifest['lean_commit'], 'Wrong Lean revision') + toolchain = toolchain_snapshot(lean, env) + sources = {} + for module in MODULES: + source_dir = ROOT.parent / 'lean-whole-residual-hosting' if module in DEPS else ROOT + source = (source_dir / (module + '.lean')).read_bytes() + require(hashlib.sha256(source).hexdigest() == manifest['sha256'][module], + 'Source mismatch: ' + module) + code = re.sub(r'--[^\n]*', '', re.sub(r'/\-[\s\S]*?\-/', '', source.decode())) + require(not re.search(r'\b(sorry|admit|native_decide|unsafe|axiom|opaque)\b', code), + 'Proof escape: ' + module) + imports = re.findall(r'^import (\S+)$', code, re.M) + require(imports == manifest['imports'][module], 'Import mismatch: ' + module) + require(all(x == 'Std' or x in MODULES[:MODULES.index(module)] for x in imports), + 'Unlisted dependency: ' + module) + sources[module] = source + reports = {} + with tempfile.TemporaryDirectory(prefix='multi-host-framework-') as tmp: + build = Path(tmp) + env['LEAN_PATH'] = str(build) + for module, source in sources.items(): + (build / (module + '.lean')).write_bytes(source) + for module in MODULES: + result = subprocess.run([str(lean), '-t', '0', '-o', module + '.olean', + module + '.lean'], cwd=build, env=env, + text=True, stdout=subprocess.PIPE, + stderr=subprocess.STDOUT, timeout=90) + require(result.returncode == 0 and 'warning:' not in result.stdout, + module + '\n' + result.stdout) + if module in DEPS: + continue + for line in result.stdout.splitlines(): + match = re.fullmatch(r"'([^']+)' does not depend on any axioms", line) + if match: + name, axioms = match[1], [] + else: + match = re.fullmatch(r"'([^']+)' depends on axioms: \[([^]]*)\]", line) + require(match is not None, 'Unexpected output: ' + line) + name, axioms = match[1], match[2].split(', ') + require(name not in reports, 'Duplicate axiom report: ' + name) + require(set(axioms) <= {'propext', 'Quot.sound'}, 'Unexpected axioms: ' + line) + reports[name] = axioms + require(list(reports) == manifest['theorems'], 'Theorem inventory mismatch') + require(toolchain_snapshot(lean, env) == toolchain, 'Toolchain changed during replay') + receipt = {'status': 'PASS', 'task': 'A only; no source endpoint contract supplied', + 'lean': version, 'lean_commit': revision, 'trust_level': 0, + 'completed_utc': datetime.now(timezone.utc).isoformat(), + 'manifest_sha256': hashlib.sha256(manifest_bytes).hexdigest(), + 'toolchain': toolchain, 'replay_mode': 'fresh', + 'fresh_modules_compiled': len(MODULES), 'reused_modules': 0, + 'source_sha256': manifest['sha256'], 'axioms': reports, + 'proved_boundary_inequalities': 2} + if args.receipt: + args.receipt.write_text(json.dumps(receipt, indent=2) + '\n') + print(json.dumps({'status': 'PASS', 'compiled_modules': len(MODULES), + 'theorem_closures': len(reports), 'proved_boundary_inequalities': 2})) + + +if __name__ == '__main__': + main() diff --git a/research/lean-multi-host-source/AddressPairs.lean b/research/lean-multi-host-source/AddressPairs.lean new file mode 100644 index 0000000000..5f7ace043d --- /dev/null +++ b/research/lean-multi-host-source/AddressPairs.lean @@ -0,0 +1,45 @@ +import FramedReplay +import CoordinateSwap + +/-! Explicit conversion between the source's pair of address vectors and +the hosting framework's vector of coordinate pairs. -/ +namespace AddressPairs + +abbrev Vectors (ι : Type) (K : Type) := (ι → K) × (ι → K) + +def join (p : Vectors ι K) : WholeHosting.Address ι K := fun i => (p.1 i, p.2 i) +def split (a : WholeHosting.Address ι K) : Vectors ι K := + (fun i => (a i).1, fun i => (a i).2) + +theorem split_join (p : Vectors ι K) : split (join p) = p := rfl +theorem join_split (a : WholeHosting.Address ι K) : join (split a) = a := rfl + +def gauge (g : FramedReplay.Gauge (Vectors ι K)) : + FramedReplay.Gauge (WholeHosting.Address ι K) where + forward a := join (g.forward (split a)) + inverse a := join (g.inverse (split a)) + inverse_forward a := by simp only [split_join, g.inverse_forward, join_split] + forward_inverse a := by simp only [split_join, g.forward_inverse, join_split] + +theorem relative_gauge (g h : FramedReplay.Gauge (Vectors ι K)) + (a : WholeHosting.Address ι K) : + (gauge g).forward ((gauge h).inverse a) = join (g.forward (h.inverse (split a))) := by + simp only [gauge, split_join] + +def swapVectors (mask : WholeHosting.Mask ι) (p : Vectors ι K) : Vectors ι K := + (fun i => if mask i then p.2 i else p.1 i, + fun i => if mask i then p.1 i else p.2 i) + +theorem join_swap (mask : WholeHosting.Mask ι) (p : Vectors ι K) : + join (swapVectors mask p) = WholeHosting.swapAddress mask (join p) := by + funext i + cases hm : mask i <;> simp [join, swapVectors, WholeHosting.swapAddress, hm] + +theorem relative_coordinate (g h : FramedReplay.Gauge (Vectors ι K)) + (mask : WholeHosting.Mask ι) + (hrel : ∀ p, g.forward (h.inverse p) = swapVectors mask p) + (a : WholeHosting.Address ι K) : + (gauge g).forward ((gauge h).inverse a) = WholeHosting.swapAddress mask a := by + rw [relative_gauge, hrel, join_swap, join_split] + +end AddressPairs diff --git a/research/lean-multi-host-source/BUILD.md b/research/lean-multi-host-source/BUILD.md new file mode 100644 index 0000000000..6e29799b1e --- /dev/null +++ b/research/lean-multi-host-source/BUILD.md @@ -0,0 +1,130 @@ +# Reproducing the source-invocation work + +Task A has its own independent replay in `../lean-multi-host-framework`. +This directory concerns Task B. A successful build certifies the statements +actually present in the Lean files; consult `README.md` for the precise scope +of the source connection and any remaining obligations. + +## Versions + +- Lean 4.33.0, commit `d8b18978322de05a8f3dba51ef03cf5461676c17`. +- Mathlib tag v4.33.0, commit `db584cd6d46c92f209a44c0f1c829460d327499d`. +- Mathlib dependencies: exact commits in `mathlib-lake-manifest.json`. +- Repository sources and compressed input snapshots: `source-versions.json`. + +The original generated source bytes are included under `inputs/`. Their raw +and compressed SHA-256 hashes are checked. These files are deterministic +replay artifacts from pinned PR442 and its inherited supplier, not new source +algorithms or a revised claimed bound. + +To regenerate the upstream snapshots separately from the supplied inputs, +make a second public checkout and explicitly fetch the pinned PR head: + +```sh +git clone --no-checkout https://github.com/CrocSwap/integer-mult-bounds.git /tmp/pr442-source-review +git -C /tmp/pr442-source-review fetch origin 4e16d001d505d4f21dd2bcfc44591f9be4c279bd +git -C /tmp/pr442-source-review checkout --detach 4e16d001d505d4f21dd2bcfc44591f9be4c279bd +``` + +Follow that checkout's own producer requirements and run +`python3 -B research/idle-axis-hosting/verify.py OUTPUT` in that checkout. +This larger upstream replay is optional for the packaged Lean reproduction; +the six required snapshots are already included. Each original path beneath `OUTPUT` is recorded in +`source-versions.json`. Compare the uncompressed hashes before regenerating +this package's Lean literals. The earlier +`../lean-source-invocation-audit/SOURCE-INSPECTION.md` documents the inherited +record format and the exact call selection. + +## Library preparation + +Install the official Lean toolchain and put its `bin` directory first in PATH. +Clone Mathlib and check out the exact commit above. From that checkout, build: + +```sh +lake build Mathlib.Data.Matrix.Mul \ + Mathlib.Algebra.BigOperators.Fin \ + Mathlib.Tactic.FieldSimp Mathlib.Tactic.Ring Mathlib.Tactic.NormNum +``` + +Mathlib's official `lake exe cache get` can supply the same library artifacts +when available. In this session the configured proxy refused the official +Azure cache endpoint, so the required library modules were built from source. +For writable cache storage use `MATHLIB_CACHE_DIR`; changing HOME is unnecessary. + +## Source binding and proof replay + +The source-binding checker uses Python 3 and SymPy (tested with Python 3.12 and +SymPy 1.14). SymPy constructs integer witnesses. Their mathematical validity +is checked by Lean, independently of the witness computation. + +```sh +python3 research/lean-multi-host-source/check_sources.py \ + --receipt /tmp/source-binding.json + +python3 research/lean-multi-host-source/replay.py \ + --lean /path/to/lean-4.33.0-linux/bin/lean \ + --mathlib /path/to/mathlib4 \ + --build-dir /tmp/multi-host-source-fresh \ + --receipt /tmp/multi-host-source-replay.json +``` + +The build directory must not already exist. Every local module is copied +from the manifested source and compiled afresh with `lean -t 0`. The replay +records compiler output, source hashes, elapsed times, and transitive axiom +closures for the permanent inventory of 931 declarations: the original +930 named theorem declarations plus `SourceInvocation.actualContract`. +The latter is a constructed definition whose transitive axioms are audited +explicitly. Only Lean/Mathlib's standard `propext`, `Quot.sound`, and +`Classical.choice` are accepted; project axioms, `sorry`, `admit`, and +`native_decide` are forbidden. The finite computations use kernel reduction. + +Large matrix certificates can take tens of minutes. If a retained build is +interrupted, the same command with `--resume` reuses only this script's +successful builds whose source, dependency, and compiled-artifact hashes +still match. Current builds also bind the installed toolchain, clean pinned +Mathlib/dependency sources, library artifacts, companion local artifacts, +and library search order. Changed modules and their dependents are rebuilt. The final +axiom audit is always rerun. The default per-module timeout is two hours; +`--module-timeout` adjusts it without changing a theorem or its proof. + +The following describes the historical resumed validation, not the current +fresh reproduction. The first completed build recorded Lean/Mathlib revisions but no byte hashes +for the installed Lean distribution, Mathlib or its eight manifest dependencies +(named in [EXTERNAL-BUILD-REVIEW.md](EXTERNAL-BUILD-REVIEW.md)). +Default resume rejects that legacy cache. For the packaging validation only, +an explicit `--allow-legacy-resume --legacy-receipt PATH --legacy-commit COMMIT` +was used together with `--resume`, anchoring each retained local source, +dependency and `.olean` hash to the successful receipt committed at +`f7330c5f5b1c5e85f91a98c95e8efc0e27c03490`. The current external environment +was checked and fingerprinted, but its historical bytes cannot be recovered +from that old receipt. Thus the reported Task B PASS checks retained local +artifacts and reruns their axiom audit; it cannot establish which external +library bytes were used for the original compilation. The new receipt labels +this limitation and reports fresh, reused and legacy-reused module counts +separately. This is not a +fresh 52-module recompilation or a `leanchecker --fresh` run. The legacy +option requires that historical Git receipt; fresh reproduction does not. +The fresh command above resolves the missing record for a new run: it compiles +all 52 local modules against the prepared pinned libraries and records the +actual toolchain/library hashes before and after the build. It creates new +verification evidence rather than filling in the historical receipt. + +Those historical receipts covered 930 named theorem declarations. They do +not certify the current 931-declaration inventory. No Lean proof source was +changed to add the `actualContract` audit entry. + +The portable delivery and one-command fresh reproduction of both tasks are +documented in [`../lean-external-review/README.md`](../lean-external-review/README.md). +Its validation notes and `EXTERNAL-BUILD-REVIEW.md` describe the exact checks +used for this delivery, while the original `replay-result.json` remains unchanged. + +The JSON parser and extraction scripts are a reproducible provenance boundary, +not a formally verified JSON parser. `check_sources.py` independently compares +the chronological normalized event list with the pinned template, verifies all +input hashes, and re-renders the generated certificates. The Lean statements +apply to the embedded literal data. Changing a generator cannot make a false +matrix identity pass the Lean kernel. + +After intentional changes to local Lean sources, run `update_manifest.py` in +this directory and review its changed inventory before replaying. Reproduction +of the committed sources does not require regenerating the manifest. diff --git a/research/lean-multi-host-source/EXTERNAL-BUILD-REVIEW.md b/research/lean-multi-host-source/EXTERNAL-BUILD-REVIEW.md new file mode 100644 index 0000000000..1203f0fca8 --- /dev/null +++ b/research/lean-multi-host-source/EXTERNAL-BUILD-REVIEW.md @@ -0,0 +1,142 @@ +# External build and retained-cache review + +Reviewed on 2026-10-12 against committed contribution +`f7330c5f5b1c5e85f91a98c95e8efc0e27c03490`, with the runner fixes described +below. No mathematical statement or Lean proof was changed in this review. + +The retained Task B build can be reused with an explicit historical-provenance +qualification. It cannot honestly be described as a new 52-module compilation. +An outside reviewer should use the fresh build documented in [BUILD.md](BUILD.md). + +## Findings and implemented fixes + +The previous Task B runner checked manifested source bytes, copied source bytes, +local `.olean` hashes, direct local dependency hashes, and the Lean and Mathlib +commit identifiers. Its mutable progress file was the only resume anchor. It +did not record byte hashes for the installed Lean 4.33.0 distribution (including +Lean/Std libraries), Mathlib's compiled artifacts, or those of its eight manifest +dependencies: plausible, LeanSearchClient, importGraph, proofwidgets, aesop, Qq, +batteries, and Cli. Exact dependency revisions are in `mathlib-lake-manifest.json`. +Its summary also counted reused modules as fresh. Task A always compiled fresh, +but checked only the Lean version prefix rather than the exact recorded compiler +commit. + +Both runners now check the exact compiler commit and snapshot the actual installed +toolchain bytes before and after validation. Task B additionally checks clean +tracked Mathlib and dependency sources at every pinned Git revision, hashes all +their `.lake/build` artifacts and Lake configuration artifacts, and records the +ordered external library search paths. These hashes include companion object, +IR, native, and trace files; they do not rely on `.hash` sidecars. An unexpected +library search root is rejected. A resumed local build rejects unmanifested +`.olean`, `.olean.private`, `.olean.server`, `.ir`, `.ir.sig`, and `.so` files, +including nested paths, and symlinked subdirectories that could shadow library +imports. + +New cache entries bind the source, local object and companion files, dependency +objects and companions, dependency source hashes, and current external snapshot. +The receipt reports fresh, reused, and legacy-reused module counts separately. +Task A remains fresh-only. + +Historical entries lack an external snapshot. The default resume policy rejects +their reuse. The explicit legacy option requires the old successful receipt to +match the bytes committed at a specified Git commit. Each reused historical +module must match that receipt's source hash, object hash, ordered dependency +hashes, recorded duration, and compiler output. Extra unrecorded companion files +prevent legacy reuse. A current environment snapshot is recorded separately; +`historical_external_environment` remains `unrecorded`, including on subsequent +explicit resumes. No new snapshot retrospectively certifies the old environment. + +This limits the final Task B PASS: it establishes that the 52 reused local +modules match the old successful receipt and that their 930-declaration axiom +audit passes now; it does not establish the external-library bytes used for +their original compilation. The documented fresh reproduction resolves this +for a new run by recompiling all 52 local modules and recording the installed +toolchain/library hashes before and after compilation. Use new build/receipt +directories, the pinned public dependency setup, and no resume options. +The resulting new receipt does not retrospectively repair the old one. + +The snapshot observes current bytes and clean pinned source checkouts. It does +not itself prove that every external compiled object was produced from those +sources, or authenticate a downloaded compiler archive. The dependency setup +and archive verification records supply those separate reproducibility steps. + +## Existing artifacts and honest reuse + +The old committed successful Task B receipt completed at +`2026-10-11T23:59:17.947059+00:00`, with 52 module records, 930 audited declarations, +and 2,756.5 seconds of accumulated module compilation time. Its SHA-256 is +`462fefd26aec066a37714a115e74dac08e1cef4b8b756ea3ff1c71f63699078e`. +Those durations describe the historical compilation, not the new resume run. + +| Historical artifact group | Objects | Runner progress | Use | +| --- | ---: | --- | --- | +| Complete Task B cache | 52 | 52 records | Complete historical cache; source, object, and dependency checks passed | +| Partial framed replay | 27 | None | Partial development artifacts | +| Framework review | 6 | None | Earlier framework review | +| Independent review | 6 | None | Earlier independent review | +| Frame-geometry model | 5 | None | Development model; not validation of the actual source certificate | +| Separate component builds | 1–18 each | None | Intermediate scalar, ownership, native, frame, and bridge builds | +| Earlier contribution build | 7 | None | Earlier contribution build | + +Only the first directory supplies the complete old runner record. The other +directories should not be silently adopted as a coherent replay cache. The +read-only check of all 52 cached modules and their committed receipt is saved in +[retained-cache.json](review-receipts/external-build/retained-cache.json). + +To preserve the historical directory, copy it to a new directory before resuming. +The recorded review used a separate copy. Exact historical locations are +preserved only in the linked evidence. After preserving the original committed +receipt as `old-task-b.json`, an illustrative local reuse command has this form; +these placeholders are not the command that produced the historical receipt: + +```sh +python3 research/lean-multi-host-source/replay.py \ + --lean /path/to/lean-4.33.0-linux/bin/lean \ + --mathlib /path/to/mathlib4 \ + --build-dir /path/to/copied-historical-cache \ + --resume --allow-legacy-resume \ + --legacy-receipt old-task-b.json \ + --legacy-commit f7330c5f5b1c5e85f91a98c95e8efc0e27c03490 \ + --receipt /tmp/task-b-resume.json +``` + +The old receipt can be recovered with `git show` at the exact commit above and +path `research/lean-multi-host-source/replay-result.json`. The runner verifies +that committed content itself. Reviewers without historical artifacts should +omit all resume options and choose a new build directory. + +## Checks and limits + +The full current external snapshot passed in 6.27 seconds. It covers the +17,505-file, 3,255,938,837-byte installed Lean distribution, Mathlib, and all eight +actual pinned dependency checkouts. The snapshot digest is +`4af0e99cf6f50d5aa306da33e7957bf99e1c81ccb35619d14cc7e78cad437559`; +the exact component hashes and revisions are in +[environment.json](review-receipts/external-build/environment.json). +The compiler is Lean commit `d8b18978322de05a8f3dba51ef03cf5461676c17`; +Mathlib is `db584cd6d46c92f209a44c0f1c829460d327499d`. + +Both Python scripts passed syntax compilation. Sixteen focused reuse-policy +checks and eight artifact-inventory checks passed, including the real retained +inventory and committed ordered receipt. Their record is +[reuse-policy-checks.json](review-receipts/external-build/reuse-policy-checks.json). +The committed [check_reuse_policy.py](review-receipts/external-build/check_reuse_policy.py) +repeats 22 self-contained fixture checks: rejected unapproved legacy reuse, +altered source/object/dependency bytes, altered dependency companion/source +hashes, changed external environment, unrecorded companions, shadow libraries, +and symlinked search subtrees. Its fixture bytes are explicitly not Lean proofs. +The two additional original checks inspected the actual repository receipt and +retained build. No full Task B rebuild was launched for these policy checks. + +The final validation receipts are +[Task A](../lean-external-review/validation/task-a.json) and +[Task B](../lean-external-review/validation/task-b.json). Task A recompiles its six +modules. Task B's receipt distinguishes all historical modules reused from any +newly compiled modules and reruns the 930-declaration axiom inventory through +`lean -t 0`. The inventory permits only the documented standard axioms. + +This final inventory is not a `leanchecker --fresh` rechecking of every constant +in the complete imported Lean/Std/Mathlib environment. Lean's supplied checker +supports that broader operation, but it was not run here. The record therefore +states exactly which modules were compiled earlier, which artifacts were +reused, what was hashed now, and what audit was rerun now. diff --git a/research/lean-multi-host-source/EXTERNAL-CLAIM-REVIEW.md b/research/lean-multi-host-source/EXTERNAL-CLAIM-REVIEW.md new file mode 100644 index 0000000000..091e563c62 --- /dev/null +++ b/research/lean-multi-host-source/EXTERNAL-CLAIM-REVIEW.md @@ -0,0 +1,189 @@ +# External claim review + +Reviewed 2026-10-12 against local contribution commit +`f7330c5f5b1c5e85f91a98c95e8efc0e27c03490`, including Task A at +`13611a8958fc71046a83d8431d2bd6335e6a3e2f`. The selected algorithm source is +PR442 `4e16d001d505d4f21dd2bcfc44591f9be4c279bd`. + +**Verdict:** the statements support a checked abstract multi-host theorem +and a concrete connection for one selected source invocation. They do not +support a verification of the complete algorithm, a resource saving or an +integer-multiplication bound. No unresolved mathematical mismatch was found +between the final entry theorem and that bounded claim. The source-extraction +and continuation boundaries below are essential parts of the claim. + +This is a Codex agent review, not an independent human audit. The reviewer +also developed frame/raw refinement modules and `SourceDataBehavior.lean`, +and helped debug `PhysicalSourceConnection.lean`; the ownership, geometry, +comparison and final connection were reviewed across agents. The requesting +contributor initiated and coordinated the AI effort. Codex agents developed +the proofs, ran automated checks and produced written reviews. This report +does not represent the contributor as having personally derived the +mathematics or independently checked the proofs. + +## Task A: what is proved and what remains a premise + +[`MultiHosting.multi_hosting`](../lean-multi-host-framework/MultiHosting.lean) +proves the retained-state equality for an arbitrary list of complete events +on multiple host streams. Every event must have the specified independent +coordinate-mask action on each host and an `other : R → R` action on the +remaining retained state. Residual masks must be pairwise disjoint and lie +inside the pending mask, separately for each host. Arbitrary input +correlations are allowed; a mathematical dependence of `other` on a host +is not allowed by this interface. + +`MultiHosting.physical_multi_hosting` transfers this identity to original +and relocated execution functions supplied through `PhysicalContract`. +Those contracts universally quantify over dirty auxiliary inputs and are +genuine premises of Task A. Actual auxiliary outputs feed subsequent calls. +The resulting equality compares retained outputs; it does not assert that +auxiliary outputs are restored or interchangeable. + +[`MultiHosting.SingleHost.whole_hosting_recovered`](../lean-multi-host-framework/SingleHostRecovery.lean) +derives the previous one-host operator statement by inverse singleton +embeddings. `physical_whole_hosting_recovered` derives the corresponding +physical statement using the preceding projection lemmas. Neither recovery +discharges a source-program endpoint premise. The two theorems in +`MultiHostControls.lean` are checked inequalities demonstrating the +cross-host mixing and physical-aliasing boundaries. + +The abstract product type does not itself prove that its host indices +denote distinct physical streams or that their coordinate charts match a +source program. Task B supplies these interpretations for the selected call. + +## Task B: concrete checked statements + +All entry declarations below are in [`SourceInvocation.lean`](SourceInvocation.lean). +They concern stage 2, replica 0, pair 0, forward orientation: 19,002 events, +240 data roles, 747 helper roles and one designated private role. + +| Declaration | Exact claim | +| --- | --- | +| `actualContract` | Constructs `MultiHosting.PhysicalContract` from the old and hosted execution folds and their explicit input/output layouts. Its endpoint obligations are proved, rather than passed as additional provider hypotheses. | +| `selected_call_completion` | Equates all retained outputs after the hosted call plus remaining pending swaps with the old call plus full pending swaps. Its single event is the complete 19,002-instruction invocation. | +| `selected_native_completion` | Gives the same equality for native instruction executions, read in the fixed retained coordinate charts. | +| `selected_native_realization` | Identifies each complete raw execution with its native execution through one shared cover-chart extension. | +| `selected_matrix_realization`, `selected_original_matrix_realization` | Identify the active-role gathers of both complete execution folds with the certified matrix word. Exterior preservation is supplied separately by the raw/native refinement results. | +| `selected_data_formula` | Gives the common old/new data endpoint, preserving the actual port charts and unequal entrance/exit frame pullbacks. | +| `selected_native_clean`, `selected_temporary_restoration` | Prove chronological COPY blankness and ERASE equality along those native runs, and return each layout's designated private row blank. | + +The following dependencies are substantive parts of that source connection: + +- `SourceMatrix.arbitrary_dirty_payloads` and `actual_payload_clean` interpret + the complete embedded word on every Boolean-valued input stream. They + follow from the checked symbolic matrix execution, not sampled payloads. +- `SourceFrameTrace.scalar_word` and `route_projection` connect the scalar, + frame and finite-role event lists. Actual indices are checked below 988; + the other 36 binary-tree leaves are inaccessible representation padding. +- `SelectedGeometry.helper_relative` supplies the actual helper endpoint + geometry. `SourceMoveGeometry.actual_matrix_run` uses checked membership + of actual MOVE pairs in the projector table to identify the complete + word's MOVE and COPY matrix operators. The stage-2 exterior factor is + included and cancelled in the proofs. +- The source and parent ownership modules prove injectivity of actual + family-and-cover-function keys. A family label alone is not treated as + a distinct physical stream. The port and slot charts are concrete choices + constructed from the source descriptors. +- `SourceInvocation.owner_overlap_data`, `old_common_cover` and + `new_common_cover` construct one native convention for both layouts. + `initialized_native_host_input`, `initialized_native_data_input` and + `initialized_native_tail_input` prove equality of retained native inputs + after private-row preparation. This closes an earlier review finding in + which two different inactive-owner cover extensions were used. +- `oldResult_framed` includes the actual old-bank outputs, through + `oldRaw_bank`. They are not replaced by their inputs. The final hosting + equality then compares the retained projection, as its contract specifies. + +## Parameters, resources and external boundary + +The concrete entry theorem accepts a field `K`, the condition `(2 : K) ≠ 0`, +an invertible invocation chart `d`, arbitrary retained state and arbitrary +old-bank payloads. It does not take geometry, owner injectivity, clean-work +guards or an endpoint-equality theorem as extra hypotheses. These parameters +are inhabited, for example by rational addresses and identity `d`. + +The allowed initial states include one designated clean private stream in +each layout. `SourceRaw.initial` constructs that permitted initial state; +it is not an instruction that erases an arbitrary dirty temporary for free. +All 987 original live roles may be dirty. The old auxiliary layout has its +747 independent input streams, while the relocated layout has no separate +helper-bank argument. No physical cost conclusion follows from these types. + +The compared retained state consists of all 747 affected host streams, +all 240 active data streams and arbitrary exterior payloads outside the +union of the active owner images. The explicit embeddings assign defaults +to slots unused by a layout. Thus the theorem is not equality for arbitrary +complete global allocations. `SourceRaw.other_payload_preserved` and +`SourceRawGuards.native_other_preserved` separately establish preservation +of arbitrary exterior payloads for their respective executions. + +The source-to-literal connection is external to Lean. `check_sources.py` +checks pinned input hashes, reconstructs binary records, compares normalized +events and regenerates certificate sources using Python/SymPy. Lean proves +the mathematical claims about those embedded literals; it does not verify +the JSON parser, Python producer or extraction program. This boundary must +accompany the phrase “actual source invocation.” + +The native ADD model is same-address Boolean XOR. Every actual source ADD +has coefficient `+1`; its separate phase field is an exporter annotation, +not another multiplier. The checked frame metadata and native-coordinate +refinement do not introduce the missing split-stream interface discussed +in PR448. Its advertised gain remains unestablished. + +## What is not established + +The multi-host theorem is applied to a singleton list containing the entire +19,002-instruction invocation. Its pairwise-disjointness condition between +separate events is therefore vacuous; cross-invocation disjointness is not +exercised. Owner injectivity within this selected invocation is proved and +does not establish disjointness across invocations. + +The pending-coordinate ranges 15..21 and 1..28 (half-open `[15,22)` and +`[1,29)`) are hand-supplied in `PhysicalSourceConnection.pendingTag`. +`tag_pending_contains` checks only the target-mask containment needed by +the completion theorem. Nothing in Lean or the source-extraction check +binds those ranges to the source schedule. The pending-mask completion is +applied immediately after this invocation. There is no proof here that +these operations occupy the required later positions in the full recursive +child schedule. There is also no complete +cover sweep, reverse-orientation theorem for the selected invocation, +all-size source compiler, fixed-tape implementation, physical cost bill, +register-saving theorem, analytic transfer or new κ bound. A continuation +that observes or reuses auxiliary outputs needs its own scope/restoration +argument. The two mutation controls concern one corrupted next checkpoint +and a dirty-private first-COPY state, not full corrupted-program replays. + +## Validation evidence and wording review + +At the original review, all then-current Task B manifested source hashes +matched the manifest, whose hash matched the stored PASS replay receipt: 52 source-built +modules, `lean -t 0`, and 930 named theorem axiom closures. Task A's six +source hashes also matched its PASS receipt and 21 named theorem checks. +The Task B receipt completed at 2026-10-11 23:59:17 UTC with only `propext`, +`Quot.sound` and `Classical.choice`. Generated finite checkpoint declarations +account for much of the count; it is not a count of independent mathematical +ideas. This review inspected those receipts and hashes; it did not repeat +the full approximately 46-minute package build. See [VALIDATION.md](VALIDATION.md) +for the hash-checked resume history and [BUILD.md](BUILD.md) for reproduction. +The current permanent inventory adds `SourceInvocation.actualContract`, a +constructed definition, to those 930 named theorem declarations. That +931-declaration inventory requires its own recorded audit; the historical +receipt is not evidence that the added declaration was audited. Current +fresh-build evidence is recorded separately in +[`../lean-external-review/VALIDATION.md`](../lean-external-review/VALIDATION.md). + +The README's substantive claim boundary agrees with the statements. Three +wording refinements were requested and verified in the updated README: the +native bridge is described as proved rather than a future requirement; +cleanliness is attributed to the named proved theorems; and the +matrix-realization equalities are described as active-role gathers of +complete folds, with exterior preservation separate. The updated notice +also explicitly distinguishes the human contributor's coordination from +the agents' proof development, checks and reviews. Packaging-only dependency relocation +does not change these mathematical claims, but its source manifests and +reproduction evidence must continue to match the distributed files. + +Existing generic transport and completion work, including PR397, Jacob +Sussman's repository, PR509 and PR513, is credited in the overlap review. +The useful checked addition is the selected concrete supplier obligation; +no exhaustive novelty claim is made for the supporting algebra. diff --git a/research/lean-multi-host-source/EXTERNAL-OVERLAP-REVIEW.md b/research/lean-multi-host-source/EXTERNAL-OVERLAP-REVIEW.md new file mode 100644 index 0000000000..31e8213923 --- /dev/null +++ b/research/lean-multi-host-source/EXTERNAL-OVERLAP-REVIEW.md @@ -0,0 +1,157 @@ +# Bounded upstream overlap refresh + +Snapshot: **2026-10-12 00:15:23 UTC**, compared with the previous audit at +2026-10-11 23:26:21 UTC. The selected target remains the one PR442 +stage-2, replica-0, forward R747 invocation. + +The new PR516 materially overlaps with generic stream realization, +ownership, and completion reasoning. It does **not** supply the concrete +PR442 bit-word, frame, owner-function, and clean-private certificates pursued +here. No newer work resolving that exact obligation was found within this +bounded refresh. This is not a global novelty or priority claim. + +## Exact pins and unchanged sources + +All seven requested heads are unchanged from the previous review. + +| Source | Exact head | Commit time or PR last-update time (UTC) | +| --- | --- | --- | +| main | `12a4934d15006e8c10f9b2264f13f8f341be802b` | 2026-10-10 14:13:23 | +| PR397 | `cb6455fa1e9af68be47c33948d3d1a6f0717a5e4` | 2026-10-11 18:03:59 | +| PR442 | `4e16d001d505d4f21dd2bcfc44591f9be4c279bd` | 2026-10-11 13:18:56 | +| PR448 | `359022bcd71143e45d48def0dd005bf67f339aa7` | 2026-10-11 21:15:56 | +| PR509 | `7b9c720ecc9f483c383e7cd9c2ab81f06ee5df59` | 2026-10-11 22:50:52 | +| PR513 | `005dd3f4e3cba8d1761abc4ab391aaf6d14d6f73` | 2026-10-11 23:10:56 | +| [Jacob Sussman's repository](https://github.com/jacobalansussman/wht-power-saving-lean) | `9c94857bbaee886f8649edee0bc2d3c738f9555e` | 2026-10-11 00:24:08 | + +Main's complete, untruncated tree still contains 154 Lean blobs. The +previous statement reviews of PR397's indexed scalar bridge, PR509's +generic conjugation/row interpretation, PR513's sequential completed-bank +bindings, and Sussman's linked Lean work therefore remain applicable. +Their existing generic results should continue to be credited. + +PR448 has two issue comments, no submitted reviews, and no review comments +at this snapshot. The latest discussion is still the author's +[comment 6113842081](https://github.com/CrocSwap/integer-mult-bounds/pull/448#issuecomment-6113842081), +updated 2026-10-11 21:15:52 UTC. It explicitly says that the split action +"presupposes that one local register can be read and written across two +streams" and that "The hub never states a multi-stream register interface." +It further acknowledges that a second register requires paying its frame +chain and that the advertised gains are not established. This refresh +found no subsequent interface repair. No claim in this contribution relies +on that split action or gain. + +## Recent-PR screen + +The API query requested all states, sorted by most recent update, with +100 results on page 1. The oldest returned update was 2026-10-11 11:55:14 UTC, +earlier than the prior audit cutoff. Eight PRs were updated after the cutoff. +Their full recursive trees were inspected; none was truncated. + +| PR | Exact current head | Last update on 2026-10-11 UTC | Lean comparison | +| --- | --- | --- | --- | +| 516 | `1c6b6ff9366a94e1f86a6c5d661a7df75c6ff814` | 23:58:28 | Six new Lean files beyond PR509; material generic overlap | +| 520 | `6077fa76950facbce11ec2f04dfbc93493114a44` | 23:57:03 | Same 154 Lean path/blob entries as main | +| 519 | `ffd3c48a80ba8b579dc300e785e387fe8acddfef` | 23:51:04 | Three new automatic-width counting modules | +| 518 | `e0a071dce251eeca96d446f73147048cfebbd5c7` | 23:50:50 | Same 154 Lean path/blob entries as main | +| 475 | `5996e33ecad6a0ccd578aec58831457829d75575` | 23:50:07 | Same 154 Lean path/blob entries as main | +| 511 | `9a20ad04be54b1c0fa26bd4ceb689f9ea220eab5` | 23:47:23 | All 158 Lean entries identical to previously reviewed `79f7c03c7f820ab89955b75ef239cbaccc627e6e` | +| 517 | `65518fcff5a7bd490365273ae5469a82aac14853` | 23:44:12 | Same 154 Lean path/blob entries as main | +| 515 | `6590606e733768f6a7004b3f55ae35f988ba515f` | 23:35:02 | All 203 Lean entries identical to its PR504 predecessor `35057a6d70f23480f4e960327d41ecac31ad5cb0` | + +The titles, descriptions and relevant new source files were reviewed. +PR520's allocator and PR515/517/518's constructions do not add a new Lean +instantiation of this obligation. PR515's additional Lean blobs relative +to main are inherited; comparing only its count with main would have +misclassified them as new work. + +## PR516: substantial generic overlap, concrete target still distinct + +PR516, by DreamingOfClouds with disclosed Claude assistance, proves the +realization part of Lemma A for the PR484 complex construction. It is stacked +on PR509; all six Lemma G Lean blobs are unchanged. All 18 files of its new +`research/e8-lemma-a-lean/` subtree were fetched at the exact head and matched +their Git blob hashes. All 17 entries in its SHA-256 manifest also matched. + +The important exposed interfaces are: + +- [`realize_run`](https://github.com/CrocSwap/integer-mult-bounds/blob/1c6b6ff9366a94e1f86a6c5d661a7df75c6ff814/research/e8-lemma-a-lean/LemmaA/Realize.lean#L70) + proves that a complete physical event fold, read through supplied charts, + equals the local run when the owner function is injective. + `realize_untouched` also preserves every unit outside that image. +- [`streamOwner_injective_of_disjoint`](https://github.com/CrocSwap/integer-mult-bounds/blob/1c6b6ff9366a94e1f86a6c5d661a7df75c6ff814/research/e8-lemma-a-lean/LemmaA/Streams.lean#L32) + derives injection of `(family,d*σ⁻¹)` from supplied nonempty, disjoint + footprints of group elements. `sweep_unique` proves the generic + right-multiplication bijection. +- [`lemmaA_streams`](https://github.com/CrocSwap/integer-mult-bounds/blob/1c6b6ff9366a94e1f86a6c5d661a7df75c6ff814/research/e8-lemma-a-lean/LemmaA/Streams.lean#L62) + takes the word, labels, exact recipes, well-labelledness, a unit helper + endpoint row, and a tensor-factorization equation as arguments. Its + conclusion identifies that helper's full stream action through its chart. +- [`lemmaA_piece` and `lemmaA_async`](https://github.com/CrocSwap/integer-mult-bounds/blob/1c6b6ff9366a94e1f86a6c5d661a7df75c6ff814/research/e8-lemma-a-lean/LemmaA/Tensor.lean#L115) + additionally require the off-diagonal helper column to vanish and, for + deferred completion, intervening actions to commute. These formalize + meaningful complete-invocation and scheduling principles. + +These results overlap with the generic foundations used here. This +contribution must not present physical gather/scatter induction, abstract +owner-group cancellation, helper independence from unit rows, spectator +preservation, or commuting completion as new discoveries. + +The instance boundary remains different. PR516's `PROOF.md` explicitly +says that it proves an abstract theorem in PR442's stream model and +inherits the assertion that this model describes the machine. Its instance +tables concern PR484's complex words and a replay of PR505. The owner and +window hypotheses are checked by Python; atomicity is partly checked as a +declared `loop_order`, with the asynchronous structural audit delegated to +PR505. The words, actual scalar endpoints, route functions, and matrices +are not embedded as the concrete PR442 R747 certificates in Lean. + +In particular, the new six Lean files contain no literal 19,002-event R747 +word, checked 987-row symbolic endpoint, actual nine COPY/nine ERASE +clean-private trajectory, 944-frame table, concrete 747-host address +isometries, original 172-family ownership certificate, or common native +cover connection for the old/new selected call. Those are the additional +obligations of this package. PR516 therefore does not replace them. + +This assessment is a source review. PR516 advertises a Lean 4.21/Mathlib +build and standard-axiom reports, but this refresh did not independently +rebuild it or execute its Python instance checks. Its disclosed PR505 +template-hash discrepancy is not treated as either a proof of failure of +the abstract theorem or a successful reproduction by this audit. + +## PR519 and integration implications + +All 16 files in PR519's new package were fetched and Git-hash checked; +its 15 `SHA256SUMS` entries matched. Its +[`count_run`](https://github.com/CrocSwap/integer-mult-bounds/blob/ffd3c48a80ba8b579dc300e785e387fe8acddfef/research/lean-automatic-width-count/BinaryAutomaticWidthCount.lean#L141) +and `counter_value` theorems concern a ten-state machine allocating counter +width and counting an input word. They do not discharge an address-frame, +dirty-helper, stream-owner, or R747 source-invocation obligation. Its build +was not rerun here. + +The selected contribution remains useful if its final coherent kernel replay +passes. Integration should cite PR516 alongside PR509 and PR513, describe +the result as discharging concrete source premises, and keep full-cover +scheduling, global allocation/cost, compiler, and κ claims out of scope. +No change of target or import of an external proof package is required by +this refresh. + +## Evidence and limits + +New evidence is confined to +[`review-receipts/external-overlap/`](review-receipts/external-overlap/). +`summary.json` records the pins and findings; `requests.json` records URLs, +retrieval timestamps and hashes; `tree-screen.json` and +`incremental-comparison.json` record the Lean path/blob comparisons. +Complete tree responses are compressed without changing their decoded +bytes. `files.json` records the 34 exact fetched package files and their +Git/SHA-256 hashes; the source copies under `raw/` are review evidence, +not imports or additions to the proof dependency closure. + +Repository contribution instructions and the contribution-review index were +read. The refresh used public HTTPS GET requests only: no publication, +comments, push, PR creation, external verifier execution, or git-ref changes. +Its search boundary is the requested exact heads, PR448's current discussion, +the latest 100 updated PRs, and the changed Lean subtrees described above. +Historical branches, all external repositories, and updates after the stated +snapshot were not exhaustively searched. diff --git a/research/lean-multi-host-source/EXTERNAL-REPOSITORY-CHECKS.md b/research/lean-multi-host-source/EXTERNAL-REPOSITORY-CHECKS.md new file mode 100644 index 0000000000..3fa78d934d --- /dev/null +++ b/research/lean-multi-host-source/EXTERNAL-REPOSITORY-CHECKS.md @@ -0,0 +1,40 @@ +# Repository baseline checks for external review + +The baseline repository sweep is **INCOMPLETE_TIMEOUT**; the independently run selected gen4 target is **PASS**. These checks supplement the standalone Lean replay receipts. They do not establish a larger bound or formalize the full multiplication theorem. + +Both commands used isolated `git archive` copies of commit `f7330c5f5b1c5e85f91a98c95e8efc0e27c03490`. They did not run in the working repository: the Makefile warns that its verification groups regenerate shared outputs. No generator or mathematical source was edited, and no environment fix was needed. All 20 tracked `upstream/` files in each archive still match their pinned Git blobs. + +| Command | Isolated archive | Limit | Elapsed | Result | +| --- | --- | --- | --- | --- | +| `make verify` | Full-sweep archive | 600 s | 600.715 s | INCOMPLETE_TIMEOUT; process exit -15 | +| `make gen4-bank-verify` | Selected-check archive | 600 s | 402.189 s | PASS; process exit 0 | + +The full sweep completed `verify-community`, `verify-producers`, `verify-partial-gauge`, `verify-three-stage-cover`, `verify-paired-cube`, then reached `verify-recycled-bit`. A supervisor sent SIGTERM at the agreed ten-minute limit. Any resulting Make “Terminated”/“Error” lines are interruption reports; the unfinished sweep is not a pass. The independent selected check used a second archive and its own ten-minute budget. + +The original full-sweep runner automatically attempted a selected-target fallback after interruption. The supervisor cancelled that duplicate promptly; its separate log and process receipt are preserved. It is not the independent selected check reported above. + +The selected verifier passed all nine stages: banks, bit, complex, finite, math, primes, raw, scalar, and virtual. Its complete [verification report](review-receipts/external-repository/gen4-verification.json) records unchanged inputs and the stage-omission negative controls. + +Selected-target final progress: + +```text +00:30:42 UTC banks PASS 78.3s +00:30:42 UTC Checking every complex source label and paid child. +00:30:43 UTC Deriving both complex scalar words and temporary lifetimes. +00:30:47 UTC Merging scalar events, exact frames and all final climbs. +00:31:30 UTC Recomputing complex cover, router, precision and row inequalities. +00:31:30 UTC complex PASS 48.1s +00:31:31 UTC math PASS 0.7s +00:31:31 UTC finite PASS 0.2s +``` + +Environment: Python 3.12.14, SymPy 1.14.0, GNU Make 4.4.1, Git 2.52.0, GCC/G++ 14.2.0, pdfTeX 1.40.26; Linux x86_64. The selected verifier's required Python/SymPy versions were already available. + +Evidence: [summary](review-receipts/external-repository/summary.json), [full-run receipt](review-receipts/external-repository/receipt.json), [selected-run receipt](review-receipts/external-repository/selected-receipt.json), [supervisor decisions](review-receipts/external-repository/supervisor-receipt.json), [full log](review-receipts/external-repository/verify.log), and [selected log](review-receipts/external-repository/gen4-bank-verify-isolated.log). The summary records log hashes, generated selected-stage artifacts, and the `upstream/` comparison. + +These are historical checks. Commit citations in some evidence copies were +subsequently replaced after the Git identity rewrite. Recorded log hashes still +identify the original bytes; the separate +[historical metadata record](https://github.com/cheesegrader/integer-mult-bounds/blob/377012d9e1d350c29fc47669e82415249429f60c/research/lean-external-review/validation/metadata-reanchor.json) +binds them to the published log copies. No repository checks were rerun for +that metadata correction. diff --git a/research/lean-multi-host-source/EndpointInterpretation.lean b/research/lean-multi-host-source/EndpointInterpretation.lean new file mode 100644 index 0000000000..fbf325c0e2 --- /dev/null +++ b/research/lean-multi-host-source/EndpointInterpretation.lean @@ -0,0 +1,56 @@ +import TreeReplay + +/-! +Interpretation of the checked endpoint matrix of the selected bit invocation. +Roles 0..986 are arbitrary dirty inputs; role 987 is the clean temporary. +Rows 120..239 receive rows 0..119 by XOR, and every other row is retained. +This file states the formulas independently of the generated certificate. +-/ +namespace SourceMatrix +set_option maxRecDepth 100000 +open TreeReplay +open LinearReplay (evalRow evalRow_zero evalRow_xor evalRow_shift_basis) + +def endpointRow (i : Nat) : Nat := + if i < 987 then + if 120 ≤ i ∧ i < 240 then (1 <<< i) ^^^ (1 <<< (i - 120)) else 1 <<< i + else 0 + +def endpointValue (u : Nat → Bool) (i : Nat) : Bool := + if i < 987 then + if 120 ≤ i ∧ i < 240 then u i ^^ u (i - 120) else u i + else false + +theorem evalRow_endpoint (u : Nat → Bool) (i : Nat) : + evalRow 987 u (endpointRow i) = endpointValue u i := by + unfold endpointRow endpointValue + by_cases h : i < 987 + · by_cases htarget : 120 ≤ i ∧ i < 240 + · have hsource : i - 120 < 987 := by omega + simp [h, htarget, evalRow_xor, evalRow_shift_basis, hsource] + · simp [h, htarget, evalRow_shift_basis] + · simp [h] + +theorem evalRows_endpoint (u : Nat → Bool) : + evalRows 987 u (Tree.tabulate 10 endpointRow) = Tree.tabulate 10 (endpointValue u) := by + simp only [evalRows, Tree.map_tabulate] + have hf : (fun i => evalRow 987 u (endpointRow i)) = endpointValue u := + funext (evalRow_endpoint u) + exact congrArg (Tree.tabulate 10) hf + +def endpointPayload {X : Type u} (input : Nat → X → Bool) (i : Nat) : X → Bool := + if i < 987 then + if 120 ≤ i ∧ i < 240 then fun x => input i x ^^ input (i - 120) x else input i + else fun _ => false + +theorem evalPayloadRows_endpoint {X : Type u} (input : Nat → X → Bool) : + evalPayloadRows 987 input (Tree.tabulate 10 endpointRow) = + Tree.tabulate 10 (endpointPayload input) := by + simp only [evalPayloadRows, Tree.map_tabulate] + apply congrArg (Tree.tabulate 10) + funext i x + by_cases h : i < 987 <;> by_cases ht : 120 ≤ i ∧ i < 240 <;> + simpa [Function.comp_apply, endpointValue, endpointPayload, h, ht] using + evalRow_endpoint (fun j => input j x) i + +end SourceMatrix diff --git a/research/lean-multi-host-source/FrameData.lean b/research/lean-multi-host-source/FrameData.lean new file mode 100644 index 0000000000..3f37406c50 --- /dev/null +++ b/research/lean-multi-host-source/FrameData.lean @@ -0,0 +1,11528 @@ +import Std + +/-! +Literal PR442 inherited frame rows, with independently checked integer +witnesses. Apache-2.0. Prepared with substantial OpenAI Codex assistance. +The balanced lookup stores proofs alongside each frame; no native_decide, +external solver axiom, or sampled field arithmetic is used. + +frames.json SHA-256: 884480e45865a9d9d57f5f7198844a64271b046bc95e9820efbefb9e10878330 +GLOBAL-TEMPLATE.json.gz SHA-256: 6e18a9ce240229c34556ba43fd6ec28f83200dfcf85e5584d4a670aeb605aeb0 +-/ +namespace FrameGeometry +set_option maxRecDepth 100000 +set_option maxHeartbeats 0 + +abbrev IntMatrix8 := Fin 8 → Fin 8 → Int +def entry (a : Array (Array Int)) : IntMatrix8 := + fun i j => (a.getD i.val #[]).getD j.val 0 + +def dot8 (a b : IntMatrix8) (i j : Fin 8) : Int := + a i 0 * b 0 j + (a i 1 * b 1 j + (a i 2 * b 2 j + + (a i 3 * b 3 j + (a i 4 * b 4 j + (a i 5 * b 5 j + + (a i 6 * b 6 j + (a i 7 * b 7 j + 0))))))) + +structure FrameDatum where + dimension : Nat + scaled : Array (Array Int) + /-- Exactly the source's B rows followed by its A rows. -/ + stack : Array (Array Int) + /-- Untrusted witness for 256 times the inverse of stack. -/ + inverse256 : Array (Array Int) + +def ValidFrame (d : FrameDatum) : Prop := + d.dimension ≤ 8 ∧ + (∀ i j : Fin 8, dot8 (entry d.scaled) (entry d.scaled) i j = 4 * entry d.scaled i j) ∧ + (∀ i j : Fin 8, entry d.scaled i j = entry d.scaled j i) ∧ + (∀ i j : Fin 8, dot8 (entry d.scaled) (fun a b => entry d.stack b a) i j = + if j.val < d.dimension then 4 * entry d.stack j i else 0) ∧ + (∀ i j : Fin 8, dot8 (entry d.stack) (entry d.inverse256) i j = + if i = j then 256 else 0) ∧ + (∀ i j : Fin 8, dot8 (entry d.inverse256) (entry d.stack) i j = + if i = j then 256 else 0) + +instance (d : FrameDatum) : Decidable (ValidFrame d) := by + unfold ValidFrame + infer_instance + +abbrev CertifiedFrame := { d : FrameDatum // ValidFrame d } + +def certified0 : CertifiedFrame := + ⟨{ dimension := 0, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[256, 0, 0, 0, 0, 0, 0, 0], #[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified1 : CertifiedFrame := + ⟨{ dimension := 8, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified2 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified3 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified4 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified5 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 0, 2, 0, 0, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified6 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified7 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 0, 0, 0, 2, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified8 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 0, 0, 0, 0, 2, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified9 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[128, 0, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified10 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[0, 1, 1, 0, 1, 0, 0, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 1, 0, 1, 0, 0, 1]], + stack := #[#[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, -1, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, -1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[64, 0, -64, 0, -64, 0, 0, -64], #[64, 0, 192, 0, -64, 0, 0, -64], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 0, -64, 0, 192, 0, 0, -64], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 0, -64, 0, -64, 0, 0, 192]] }, by decide⟩ + +def certified11 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[0, 1, 1, 0, 1, 0, 0, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -1, -1, 0, -1, 0, 0, 1]], + stack := #[#[0, 1, 1, 0, 1, 0, 0, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, -1, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[64, 0, -64, 0, -64, 0, 0, 64], #[64, 0, 192, 0, -64, 0, 0, 64], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 0, -64, 0, 192, 0, 0, 64], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 0, 64, 0, 64, 0, 0, 192]] }, by decide⟩ + +def certified12 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 1, 0, -1, 0, 0, 1], #[0, 1, 1, 0, -1, 0, 0, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -1, -1, 0, 1, 0, 0, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 1, 0, -1, 0, 0, 1]], + stack := #[#[0, 1, 1, 0, -1, 0, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 1, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, -1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[64, 0, -64, 0, 64, 0, 0, -64], #[64, 0, 192, 0, 64, 0, 0, -64], #[0, 0, 0, 256, 0, 0, 0, 0], #[-64, 0, 64, 0, 192, 0, 0, 64], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 0, -64, 0, 64, 0, 0, 192]] }, by decide⟩ + +def certified13 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 1, 0, -1, 0, 0, -1], #[0, 1, 1, 0, -1, 0, 0, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -1, -1, 0, 1, 0, 0, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -1, -1, 0, 1, 0, 0, 1]], + stack := #[#[0, 1, 1, 0, -1, 0, 0, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 1, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[64, 0, -64, 0, 64, 0, 0, 64], #[64, 0, 192, 0, 64, 0, 0, 64], #[0, 0, 0, 256, 0, 0, 0, 0], #[-64, 0, 64, 0, 192, 0, 0, -64], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 0, 64, 0, -64, 0, 0, 192]] }, by decide⟩ + +def certified14 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, -1, 0, 1, 0, 0, 1], #[0, -1, 1, 0, -1, 0, 0, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, -1, 0, 1, 0, 0, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, -1, 0, 1, 0, 0, 1]], + stack := #[#[0, 1, -1, 0, 1, 0, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, -1, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, -1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[64, 0, 64, 0, -64, 0, 0, -64], #[-64, 0, 192, 0, 64, 0, 0, 64], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 0, 64, 0, 192, 0, 0, -64], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 0, 64, 0, -64, 0, 0, 192]] }, by decide⟩ + +def certified15 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, -1, 0, 1, 0, 0, -1], #[0, -1, 1, 0, -1, 0, 0, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, -1, 0, 1, 0, 0, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 1, 0, -1, 0, 0, 1]], + stack := #[#[0, 1, -1, 0, 1, 0, 0, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, -1, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[64, 0, 64, 0, -64, 0, 0, 64], #[-64, 0, 192, 0, 64, 0, 0, -64], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 0, 64, 0, 192, 0, 0, 64], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 0, -64, 0, 64, 0, 0, 192]] }, by decide⟩ + +def certified16 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, -1, 0, -1, 0, 0, 1], #[0, -1, 1, 0, 1, 0, 0, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 1, 0, 1, 0, 0, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, -1, 0, -1, 0, 0, 1]], + stack := #[#[0, 1, -1, 0, -1, 0, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 1, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, -1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[64, 0, 64, 0, 64, 0, 0, -64], #[-64, 0, 192, 0, -64, 0, 0, 64], #[0, 0, 0, 256, 0, 0, 0, 0], #[-64, 0, -64, 0, 192, 0, 0, 64], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 0, 64, 0, 64, 0, 0, 192]] }, by decide⟩ + +def certified17 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, -1, 0, -1, 0, 0, -1], #[0, -1, 1, 0, 1, 0, 0, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 1, 0, 1, 0, 0, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 1, 0, 1, 0, 0, 1]], + stack := #[#[0, 1, -1, 0, -1, 0, 0, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 1, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[64, 0, 64, 0, 64, 0, 0, 64], #[-64, 0, 192, 0, -64, 0, 0, -64], #[0, 0, 0, 256, 0, 0, 0, 0], #[-64, 0, -64, 0, 192, 0, 0, -64], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 0, -64, 0, -64, 0, 0, 192]] }, by decide⟩ + +def certified18 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 0, 1, 0, 1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 0, 1, 0, 1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 0, 1, 0, 1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 0, 1, 0, 1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 0, 1, 0, 1, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[-1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[-1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[-1, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 0, -64, 0, -64, 0, -64, 0], #[0, 256, 0, 0, 0, 0, 0, 0], #[64, 0, 192, 0, -64, 0, -64, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 0, -64, 0, 192, 0, -64, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 0, -64, 0, -64, 0, 192, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified19 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 0, 1, 0, 1, 0, -1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 0, 1, 0, 1, 0, -1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 0, 1, 0, 1, 0, -1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 0, -1, 0, -1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 0, 1, 0, 1, 0, -1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[-1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[-1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 0, -64, 0, -64, 0, 64, 0], #[0, 256, 0, 0, 0, 0, 0, 0], #[64, 0, 192, 0, -64, 0, 64, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 0, -64, 0, 192, 0, 64, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 0, 64, 0, 64, 0, 192, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified20 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 0, 1, 0, -1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 0, 1, 0, -1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 0, -1, 0, 1, 0, -1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 0, 1, 0, -1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 0, 1, 0, -1, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[-1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[-1, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 0, -64, 0, 64, 0, -64, 0], #[0, 256, 0, 0, 0, 0, 0, 0], #[64, 0, 192, 0, 64, 0, -64, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[-64, 0, 64, 0, 192, 0, 64, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 0, -64, 0, 64, 0, 192, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified21 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 0, 1, 0, -1, 0, -1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 0, 1, 0, -1, 0, -1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 0, -1, 0, 1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 0, -1, 0, 1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 0, 1, 0, -1, 0, -1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[-1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 0, -64, 0, 64, 0, 64, 0], #[0, 256, 0, 0, 0, 0, 0, 0], #[64, 0, 192, 0, 64, 0, 64, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[-64, 0, 64, 0, 192, 0, -64, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 0, 64, 0, -64, 0, 192, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified22 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 0, -1, 0, 1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 0, 1, 0, -1, 0, -1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 0, -1, 0, 1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 0, -1, 0, 1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 0, -1, 0, 1, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[-1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[-1, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 0, 64, 0, -64, 0, -64, 0], #[0, 256, 0, 0, 0, 0, 0, 0], #[-64, 0, 192, 0, 64, 0, 64, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 0, 64, 0, 192, 0, -64, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 0, 64, 0, -64, 0, 192, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified23 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 0, -1, 0, 1, 0, -1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 0, 1, 0, -1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 0, -1, 0, 1, 0, -1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 0, 1, 0, -1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 0, -1, 0, 1, 0, -1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[-1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 0, 64, 0, -64, 0, 64, 0], #[0, 256, 0, 0, 0, 0, 0, 0], #[-64, 0, 192, 0, 64, 0, -64, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 0, 64, 0, 192, 0, 64, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 0, -64, 0, 64, 0, 192, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified24 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 0, -1, 0, -1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 0, 1, 0, 1, 0, -1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 0, 1, 0, 1, 0, -1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 0, -1, 0, -1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 0, -1, 0, -1, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[-1, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 0, 64, 0, 64, 0, -64, 0], #[0, 256, 0, 0, 0, 0, 0, 0], #[-64, 0, 192, 0, -64, 0, 64, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[-64, 0, -64, 0, 192, 0, 64, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 0, 64, 0, 64, 0, 192, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified25 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 0, -1, 0, -1, 0, -1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 0, 1, 0, 1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 0, 1, 0, 1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 0, 1, 0, 1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 0, -1, 0, -1, 0, -1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 0, 64, 0, 64, 0, 64, 0], #[0, 256, 0, 0, 0, 0, 0, 0], #[-64, 0, 192, 0, -64, 0, -64, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[-64, 0, -64, 0, 192, 0, -64, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 0, -64, 0, -64, 0, 192, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified26 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 1, 0, 0, 0, 0, 1, 1], #[1, 1, 0, 0, 0, 0, 1, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 1, 0, 0, 0, 0, 1, 1], #[1, 1, 0, 0, 0, 0, 1, 1]], + stack := #[#[1, 1, 0, 0, 0, 0, 1, 1], #[-1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[-1, 0, 0, 0, 0, 0, 1, 0], #[-1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, -64, 0, 0, 0, 0, -64, -64], #[64, 192, 0, 0, 0, 0, -64, -64], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, -64, 0, 0, 0, 0, 192, -64], #[64, -64, 0, 0, 0, 0, -64, 192]] }, by decide⟩ + +def certified27 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 1, 0, 0, 0, 0, 1, -1], #[1, 1, 0, 0, 0, 0, 1, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 1, 0, 0, 0, 0, 1, -1], #[-1, -1, 0, 0, 0, 0, -1, 1]], + stack := #[#[1, 1, 0, 0, 0, 0, 1, -1], #[-1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[-1, 0, 0, 0, 0, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, -64, 0, 0, 0, 0, -64, 64], #[64, 192, 0, 0, 0, 0, -64, 64], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, -64, 0, 0, 0, 0, 192, 64], #[-64, 64, 0, 0, 0, 0, 64, 192]] }, by decide⟩ + +def certified28 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 1, 0, 0, 0, 0, -1, 1], #[1, 1, 0, 0, 0, 0, -1, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, -1, 0, 0, 0, 0, 1, -1], #[1, 1, 0, 0, 0, 0, -1, 1]], + stack := #[#[1, 1, 0, 0, 0, 0, -1, 1], #[-1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 1, 0], #[-1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, -64, 0, 0, 0, 0, 64, -64], #[64, 192, 0, 0, 0, 0, 64, -64], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 64, 0, 0, 0, 0, 192, 64], #[64, -64, 0, 0, 0, 0, 64, 192]] }, by decide⟩ + +def certified29 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 1, 0, 0, 0, 0, -1, -1], #[1, 1, 0, 0, 0, 0, -1, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, -1, 0, 0, 0, 0, 1, 1], #[-1, -1, 0, 0, 0, 0, 1, 1]], + stack := #[#[1, 1, 0, 0, 0, 0, -1, -1], #[-1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, -64, 0, 0, 0, 0, 64, 64], #[64, 192, 0, 0, 0, 0, 64, 64], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 64, 0, 0, 0, 0, 192, -64], #[-64, 64, 0, 0, 0, 0, -64, 192]] }, by decide⟩ + +def certified30 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, -1, 0, 0, 0, 0, 1, 1], #[-1, 1, 0, 0, 0, 0, -1, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, -1, 0, 0, 0, 0, 1, 1], #[1, -1, 0, 0, 0, 0, 1, 1]], + stack := #[#[1, -1, 0, 0, 0, 0, 1, 1], #[1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[-1, 0, 0, 0, 0, 0, 1, 0], #[-1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 0, 0, -64, -64], #[-64, 192, 0, 0, 0, 0, 64, 64], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 64, 0, 0, 0, 0, 192, -64], #[64, 64, 0, 0, 0, 0, -64, 192]] }, by decide⟩ + +def certified31 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, -1, 0, 0, 0, 0, 1, -1], #[-1, 1, 0, 0, 0, 0, -1, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, -1, 0, 0, 0, 0, 1, -1], #[-1, 1, 0, 0, 0, 0, -1, 1]], + stack := #[#[1, -1, 0, 0, 0, 0, 1, -1], #[1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[-1, 0, 0, 0, 0, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 0, 0, -64, 64], #[-64, 192, 0, 0, 0, 0, 64, -64], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 64, 0, 0, 0, 0, 192, 64], #[-64, -64, 0, 0, 0, 0, 64, 192]] }, by decide⟩ + +def certified32 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, -1, 0, 0, 0, 0, -1, 1], #[-1, 1, 0, 0, 0, 0, 1, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 1, 0, 0, 0, 0, 1, -1], #[1, -1, 0, 0, 0, 0, -1, 1]], + stack := #[#[1, -1, 0, 0, 0, 0, -1, 1], #[1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 1, 0], #[-1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 0, 0, 64, -64], #[-64, 192, 0, 0, 0, 0, -64, 64], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, -64, 0, 0, 0, 0, 192, 64], #[64, 64, 0, 0, 0, 0, 64, 192]] }, by decide⟩ + +def certified33 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, -1, 0, 0, 0, 0, -1, -1], #[-1, 1, 0, 0, 0, 0, 1, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 1, 0, 0, 0, 0, 1, 1], #[-1, 1, 0, 0, 0, 0, 1, 1]], + stack := #[#[1, -1, 0, 0, 0, 0, -1, -1], #[1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 0, 0, 64, 64], #[-64, 192, 0, 0, 0, 0, -64, -64], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, -64, 0, 0, 0, 0, 192, -64], #[-64, -64, 0, 0, 0, 0, -64, 192]] }, by decide⟩ + +def certified34 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 1, 0, 0, 1, 1, 0, 0], #[1, 1, 0, 0, 1, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 1, 0, 0, 1, 1, 0, 0], #[1, 1, 0, 0, 1, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 1, 0, 0, 1, 1, 0, 0], #[-1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[-1, 0, 0, 0, 1, 0, 0, 0], #[-1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, -64, 0, 0, -64, -64, 0, 0], #[64, 192, 0, 0, -64, -64, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, -64, 0, 0, 192, -64, 0, 0], #[64, -64, 0, 0, -64, 192, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified35 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 1, 0, 0, 1, -1, 0, 0], #[1, 1, 0, 0, 1, -1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 1, 0, 0, 1, -1, 0, 0], #[-1, -1, 0, 0, -1, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 1, 0, 0, 1, -1, 0, 0], #[-1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[-1, 0, 0, 0, 1, 0, 0, 0], #[1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, -64, 0, 0, -64, 64, 0, 0], #[64, 192, 0, 0, -64, 64, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, -64, 0, 0, 192, 64, 0, 0], #[-64, 64, 0, 0, 64, 192, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified36 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 1, 0, 0, -1, 1, 0, 0], #[1, 1, 0, 0, -1, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, -1, 0, 0, 1, -1, 0, 0], #[1, 1, 0, 0, -1, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 1, 0, 0, -1, 1, 0, 0], #[-1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[1, 0, 0, 0, 1, 0, 0, 0], #[-1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, -64, 0, 0, 64, -64, 0, 0], #[64, 192, 0, 0, 64, -64, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[-64, 64, 0, 0, 192, 64, 0, 0], #[64, -64, 0, 0, 64, 192, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified37 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 1, 0, 0, -1, -1, 0, 0], #[1, 1, 0, 0, -1, -1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, -1, 0, 0, 1, 1, 0, 0], #[-1, -1, 0, 0, 1, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 1, 0, 0, -1, -1, 0, 0], #[-1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[1, 0, 0, 0, 1, 0, 0, 0], #[1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, -64, 0, 0, 64, 64, 0, 0], #[64, 192, 0, 0, 64, 64, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[-64, 64, 0, 0, 192, -64, 0, 0], #[-64, 64, 0, 0, -64, 192, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified38 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, -1, 0, 0, 1, 1, 0, 0], #[-1, 1, 0, 0, -1, -1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, -1, 0, 0, 1, 1, 0, 0], #[1, -1, 0, 0, 1, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, -1, 0, 0, 1, 1, 0, 0], #[1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[-1, 0, 0, 0, 1, 0, 0, 0], #[-1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, -64, -64, 0, 0], #[-64, 192, 0, 0, 64, 64, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 64, 0, 0, 192, -64, 0, 0], #[64, 64, 0, 0, -64, 192, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified39 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, -1, 0, 0, 1, -1, 0, 0], #[-1, 1, 0, 0, -1, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, -1, 0, 0, 1, -1, 0, 0], #[-1, 1, 0, 0, -1, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, -1, 0, 0, 1, -1, 0, 0], #[1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[-1, 0, 0, 0, 1, 0, 0, 0], #[1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, -64, 64, 0, 0], #[-64, 192, 0, 0, 64, -64, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 64, 0, 0, 192, 64, 0, 0], #[-64, -64, 0, 0, 64, 192, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified40 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, -1, 0, 0, -1, 1, 0, 0], #[-1, 1, 0, 0, 1, -1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 1, 0, 0, 1, -1, 0, 0], #[1, -1, 0, 0, -1, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, -1, 0, 0, -1, 1, 0, 0], #[1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[1, 0, 0, 0, 1, 0, 0, 0], #[-1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 64, -64, 0, 0], #[-64, 192, 0, 0, -64, 64, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 0, 0, 192, 64, 0, 0], #[64, 64, 0, 0, 64, 192, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified41 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, -1, 0, 0, -1, -1, 0, 0], #[-1, 1, 0, 0, 1, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 1, 0, 0, 1, 1, 0, 0], #[-1, 1, 0, 0, 1, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, -1, 0, 0, -1, -1, 0, 0], #[1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[1, 0, 0, 0, 1, 0, 0, 0], #[1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 64, 64, 0, 0], #[-64, 192, 0, 0, -64, -64, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 0, 0, 192, -64, 0, 0], #[-64, -64, 0, 0, -64, 192, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified42 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 0, 1, 0, 0, 1, 0, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 0, 1, 0, 0, 1, 0, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 0, 1, 0, 0, 1, 0, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 0, 1, 0, 0, 1, 0, 1]], + stack := #[#[1, 0, 1, 0, 0, 1, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[-1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[-1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[-1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 0, -64, 0, 0, -64, 0, -64], #[0, 256, 0, 0, 0, 0, 0, 0], #[64, 0, 192, 0, 0, -64, 0, -64], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, 0, -64, 0, 0, 192, 0, -64], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 0, -64, 0, 0, -64, 0, 192]] }, by decide⟩ + +def certified43 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 0, 1, 0, 0, 1, 0, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 0, 1, 0, 0, 1, 0, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 0, 1, 0, 0, 1, 0, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 0, -1, 0, 0, -1, 0, 1]], + stack := #[#[1, 0, 1, 0, 0, 1, 0, -1], #[0, 1, 0, 0, 0, 0, 0, 0], #[-1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[-1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 0, -64, 0, 0, -64, 0, 64], #[0, 256, 0, 0, 0, 0, 0, 0], #[64, 0, 192, 0, 0, -64, 0, 64], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, 0, -64, 0, 0, 192, 0, 64], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 0, 64, 0, 0, 64, 0, 192]] }, by decide⟩ + +def certified44 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 0, 1, 0, 0, -1, 0, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 0, 1, 0, 0, -1, 0, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 0, -1, 0, 0, 1, 0, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 0, 1, 0, 0, -1, 0, 1]], + stack := #[#[1, 0, 1, 0, 0, -1, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[-1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[-1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 0, -64, 0, 0, 64, 0, -64], #[0, 256, 0, 0, 0, 0, 0, 0], #[64, 0, 192, 0, 0, 64, 0, -64], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, 0, 64, 0, 0, 192, 0, 64], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 0, -64, 0, 0, 64, 0, 192]] }, by decide⟩ + +def certified45 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 0, 1, 0, 0, -1, 0, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 0, 1, 0, 0, -1, 0, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 0, -1, 0, 0, 1, 0, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 0, -1, 0, 0, 1, 0, 1]], + stack := #[#[1, 0, 1, 0, 0, -1, 0, -1], #[0, 1, 0, 0, 0, 0, 0, 0], #[-1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 0, -64, 0, 0, 64, 0, 64], #[0, 256, 0, 0, 0, 0, 0, 0], #[64, 0, 192, 0, 0, 64, 0, 64], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, 0, 64, 0, 0, 192, 0, -64], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 0, 64, 0, 0, -64, 0, 192]] }, by decide⟩ + +def certified46 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 0, -1, 0, 0, 1, 0, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 0, 1, 0, 0, -1, 0, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 0, -1, 0, 0, 1, 0, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 0, -1, 0, 0, 1, 0, 1]], + stack := #[#[1, 0, -1, 0, 0, 1, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[-1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[-1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 0, 64, 0, 0, -64, 0, -64], #[0, 256, 0, 0, 0, 0, 0, 0], #[-64, 0, 192, 0, 0, 64, 0, 64], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, 0, 64, 0, 0, 192, 0, -64], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 0, 64, 0, 0, -64, 0, 192]] }, by decide⟩ + +def certified47 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 0, -1, 0, 0, 1, 0, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 0, 1, 0, 0, -1, 0, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 0, -1, 0, 0, 1, 0, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 0, 1, 0, 0, -1, 0, 1]], + stack := #[#[1, 0, -1, 0, 0, 1, 0, -1], #[0, 1, 0, 0, 0, 0, 0, 0], #[1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[-1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 0, 64, 0, 0, -64, 0, 64], #[0, 256, 0, 0, 0, 0, 0, 0], #[-64, 0, 192, 0, 0, 64, 0, -64], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, 0, 64, 0, 0, 192, 0, 64], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 0, -64, 0, 0, 64, 0, 192]] }, by decide⟩ + +def certified48 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 0, -1, 0, 0, -1, 0, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 0, 1, 0, 0, 1, 0, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 0, 1, 0, 0, 1, 0, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 0, -1, 0, 0, -1, 0, 1]], + stack := #[#[1, 0, -1, 0, 0, -1, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[-1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 0, 64, 0, 0, 64, 0, -64], #[0, 256, 0, 0, 0, 0, 0, 0], #[-64, 0, 192, 0, 0, -64, 0, 64], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, 0, -64, 0, 0, 192, 0, 64], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 0, 64, 0, 0, 64, 0, 192]] }, by decide⟩ + +def certified49 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 0, -1, 0, 0, -1, 0, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 0, 1, 0, 0, 1, 0, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 0, 1, 0, 0, 1, 0, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 0, 1, 0, 0, 1, 0, 1]], + stack := #[#[1, 0, -1, 0, 0, -1, 0, -1], #[0, 1, 0, 0, 0, 0, 0, 0], #[1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 0, 64, 0, 0, 64, 0, 64], #[0, 256, 0, 0, 0, 0, 0, 0], #[-64, 0, 192, 0, 0, -64, 0, -64], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, 0, -64, 0, 0, 192, 0, -64], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 0, -64, 0, 0, -64, 0, 192]] }, by decide⟩ + +def certified50 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 1, 0, 0, 1, 1, 0], #[0, 1, 1, 0, 0, 1, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 1, 0, 0, 1, 1, 0], #[0, 1, 1, 0, 0, 1, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 1, 1, 0, 0, 1, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, -1, 0, 0, 0, 1, 0, 0], #[0, -1, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[64, 0, -64, 0, 0, -64, -64, 0], #[64, 0, 192, 0, 0, -64, -64, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, 0, -64, 0, 0, 192, -64, 0], #[64, 0, -64, 0, 0, -64, 192, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified51 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 1, 0, 0, 1, -1, 0], #[0, 1, 1, 0, 0, 1, -1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 1, 0, 0, 1, -1, 0], #[0, -1, -1, 0, 0, -1, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 1, 1, 0, 0, 1, -1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, -1, 0, 0, 0, 1, 0, 0], #[0, 1, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[64, 0, -64, 0, 0, -64, 64, 0], #[64, 0, 192, 0, 0, -64, 64, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, 0, -64, 0, 0, 192, 64, 0], #[-64, 0, 64, 0, 0, 64, 192, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified52 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 1, 0, 0, -1, 1, 0], #[0, 1, 1, 0, 0, -1, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -1, -1, 0, 0, 1, -1, 0], #[0, 1, 1, 0, 0, -1, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 1, 1, 0, 0, -1, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 1, 0, 0, 0, 1, 0, 0], #[0, -1, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[64, 0, -64, 0, 0, 64, -64, 0], #[64, 0, 192, 0, 0, 64, -64, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, 0, 64, 0, 0, 192, 64, 0], #[64, 0, -64, 0, 0, 64, 192, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified53 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 1, 0, 0, -1, -1, 0], #[0, 1, 1, 0, 0, -1, -1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -1, -1, 0, 0, 1, 1, 0], #[0, -1, -1, 0, 0, 1, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 1, 1, 0, 0, -1, -1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 1, 0, 0, 0, 1, 0, 0], #[0, 1, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[64, 0, -64, 0, 0, 64, 64, 0], #[64, 0, 192, 0, 0, 64, 64, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, 0, 64, 0, 0, 192, -64, 0], #[-64, 0, 64, 0, 0, -64, 192, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified54 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, -1, 0, 0, 1, 1, 0], #[0, -1, 1, 0, 0, -1, -1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, -1, 0, 0, 1, 1, 0], #[0, 1, -1, 0, 0, 1, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 1, -1, 0, 0, 1, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, -1, 0, 0, 0, 1, 0, 0], #[0, -1, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[64, 0, 64, 0, 0, -64, -64, 0], #[-64, 0, 192, 0, 0, 64, 64, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, 0, 64, 0, 0, 192, -64, 0], #[64, 0, 64, 0, 0, -64, 192, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified55 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, -1, 0, 0, 1, -1, 0], #[0, -1, 1, 0, 0, -1, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, -1, 0, 0, 1, -1, 0], #[0, -1, 1, 0, 0, -1, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 1, -1, 0, 0, 1, -1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, -1, 0, 0, 0, 1, 0, 0], #[0, 1, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[64, 0, 64, 0, 0, -64, 64, 0], #[-64, 0, 192, 0, 0, 64, -64, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, 0, 64, 0, 0, 192, 64, 0], #[-64, 0, -64, 0, 0, 64, 192, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified56 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, -1, 0, 0, -1, 1, 0], #[0, -1, 1, 0, 0, 1, -1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 1, 0, 0, 1, -1, 0], #[0, 1, -1, 0, 0, -1, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 1, -1, 0, 0, -1, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 1, 0, 0, 0, 1, 0, 0], #[0, -1, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[64, 0, 64, 0, 0, 64, -64, 0], #[-64, 0, 192, 0, 0, -64, 64, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, 0, -64, 0, 0, 192, 64, 0], #[64, 0, 64, 0, 0, 64, 192, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified57 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, -1, 0, 0, -1, -1, 0], #[0, -1, 1, 0, 0, 1, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 1, 0, 0, 1, 1, 0], #[0, -1, 1, 0, 0, 1, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 1, -1, 0, 0, -1, -1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 1, 0, 0, 0, 1, 0, 0], #[0, 1, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[64, 0, 64, 0, 0, 64, 64, 0], #[-64, 0, 192, 0, 0, -64, -64, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, 0, -64, 0, 0, 192, -64, 0], #[-64, 0, -64, 0, 0, -64, 192, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified58 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 1, 1, 1], #[0, 0, 0, 0, 1, 1, 1, 1], #[0, 0, 0, 0, 1, 1, 1, 1], #[0, 0, 0, 0, 1, 1, 1, 1]], + stack := #[#[0, 0, 0, 0, 1, 1, 1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, -1, 1, 0, 0], #[0, 0, 0, 0, -1, 0, 1, 0], #[0, 0, 0, 0, -1, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, 0, 0, 0, 0, -64, -64, -64], #[64, 0, 0, 0, 0, 192, -64, -64], #[64, 0, 0, 0, 0, -64, 192, -64], #[64, 0, 0, 0, 0, -64, -64, 192]] }, by decide⟩ + +def certified59 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 1, 1, -1], #[0, 0, 0, 0, 1, 1, 1, -1], #[0, 0, 0, 0, 1, 1, 1, -1], #[0, 0, 0, 0, -1, -1, -1, 1]], + stack := #[#[0, 0, 0, 0, 1, 1, 1, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, -1, 1, 0, 0], #[0, 0, 0, 0, -1, 0, 1, 0], #[0, 0, 0, 0, 1, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, 0, 0, 0, 0, -64, -64, 64], #[64, 0, 0, 0, 0, 192, -64, 64], #[64, 0, 0, 0, 0, -64, 192, 64], #[-64, 0, 0, 0, 0, 64, 64, 192]] }, by decide⟩ + +def certified60 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 1, -1, 1], #[0, 0, 0, 0, 1, 1, -1, 1], #[0, 0, 0, 0, -1, -1, 1, -1], #[0, 0, 0, 0, 1, 1, -1, 1]], + stack := #[#[0, 0, 0, 0, 1, 1, -1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, -1, 1, 0, 0], #[0, 0, 0, 0, 1, 0, 1, 0], #[0, 0, 0, 0, -1, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, 0, 0, 0, 0, -64, 64, -64], #[64, 0, 0, 0, 0, 192, 64, -64], #[-64, 0, 0, 0, 0, 64, 192, 64], #[64, 0, 0, 0, 0, -64, 64, 192]] }, by decide⟩ + +def certified61 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 1, -1, -1], #[0, 0, 0, 0, 1, 1, -1, -1], #[0, 0, 0, 0, -1, -1, 1, 1], #[0, 0, 0, 0, -1, -1, 1, 1]], + stack := #[#[0, 0, 0, 0, 1, 1, -1, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, -1, 1, 0, 0], #[0, 0, 0, 0, 1, 0, 1, 0], #[0, 0, 0, 0, 1, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, 0, 0, 0, 0, -64, 64, 64], #[64, 0, 0, 0, 0, 192, 64, 64], #[-64, 0, 0, 0, 0, 64, 192, -64], #[-64, 0, 0, 0, 0, 64, -64, 192]] }, by decide⟩ + +def certified62 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, -1, 1, 1], #[0, 0, 0, 0, -1, 1, -1, -1], #[0, 0, 0, 0, 1, -1, 1, 1], #[0, 0, 0, 0, 1, -1, 1, 1]], + stack := #[#[0, 0, 0, 0, 1, -1, 1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 1, 0, 0], #[0, 0, 0, 0, -1, 0, 1, 0], #[0, 0, 0, 0, -1, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, 0, 0, 0, 0, 64, -64, -64], #[-64, 0, 0, 0, 0, 192, 64, 64], #[64, 0, 0, 0, 0, 64, 192, -64], #[64, 0, 0, 0, 0, 64, -64, 192]] }, by decide⟩ + +def certified63 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, -1, 1, -1], #[0, 0, 0, 0, -1, 1, -1, 1], #[0, 0, 0, 0, 1, -1, 1, -1], #[0, 0, 0, 0, -1, 1, -1, 1]], + stack := #[#[0, 0, 0, 0, 1, -1, 1, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 1, 0, 0], #[0, 0, 0, 0, -1, 0, 1, 0], #[0, 0, 0, 0, 1, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, 0, 0, 0, 0, 64, -64, 64], #[-64, 0, 0, 0, 0, 192, 64, -64], #[64, 0, 0, 0, 0, 64, 192, 64], #[-64, 0, 0, 0, 0, -64, 64, 192]] }, by decide⟩ + +def certified64 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, -1, -1, 1], #[0, 0, 0, 0, -1, 1, 1, -1], #[0, 0, 0, 0, -1, 1, 1, -1], #[0, 0, 0, 0, 1, -1, -1, 1]], + stack := #[#[0, 0, 0, 0, 1, -1, -1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 1, 0, 0], #[0, 0, 0, 0, 1, 0, 1, 0], #[0, 0, 0, 0, -1, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, 0, 0, 0, 0, 64, 64, -64], #[-64, 0, 0, 0, 0, 192, -64, 64], #[-64, 0, 0, 0, 0, -64, 192, 64], #[64, 0, 0, 0, 0, 64, 64, 192]] }, by decide⟩ + +def certified65 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, -1, -1, -1], #[0, 0, 0, 0, -1, 1, 1, 1], #[0, 0, 0, 0, -1, 1, 1, 1], #[0, 0, 0, 0, -1, 1, 1, 1]], + stack := #[#[0, 0, 0, 0, 1, -1, -1, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 1, 0, 0], #[0, 0, 0, 0, 1, 0, 1, 0], #[0, 0, 0, 0, 1, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, 0, 0, 0, 0, 64, 64, 64], #[-64, 0, 0, 0, 0, 192, -64, -64], #[-64, 0, 0, 0, 0, -64, 192, -64], #[-64, 0, 0, 0, 0, -64, -64, 192]] }, by decide⟩ + +def certified66 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 1, 1, 1, 0, 0, 0, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 1, 1, 1, 0, 0, 0, 0], #[-1, 1, 0, 0, 0, 0, 0, 0], #[-1, 0, 1, 0, 0, 0, 0, 0], #[-1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, -64, -64, -64, 0, 0, 0, 0], #[64, 192, -64, -64, 0, 0, 0, 0], #[64, -64, 192, -64, 0, 0, 0, 0], #[64, -64, -64, 192, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified67 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 1, 1, -1, 0, 0, 0, 0], #[1, 1, 1, -1, 0, 0, 0, 0], #[1, 1, 1, -1, 0, 0, 0, 0], #[-1, -1, -1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 1, 1, -1, 0, 0, 0, 0], #[-1, 1, 0, 0, 0, 0, 0, 0], #[-1, 0, 1, 0, 0, 0, 0, 0], #[1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, -64, -64, 64, 0, 0, 0, 0], #[64, 192, -64, 64, 0, 0, 0, 0], #[64, -64, 192, 64, 0, 0, 0, 0], #[-64, 64, 64, 192, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified68 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 1, -1, 1, 0, 0, 0, 0], #[1, 1, -1, 1, 0, 0, 0, 0], #[-1, -1, 1, -1, 0, 0, 0, 0], #[1, 1, -1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 1, -1, 1, 0, 0, 0, 0], #[-1, 1, 0, 0, 0, 0, 0, 0], #[1, 0, 1, 0, 0, 0, 0, 0], #[-1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, -64, 64, -64, 0, 0, 0, 0], #[64, 192, 64, -64, 0, 0, 0, 0], #[-64, 64, 192, 64, 0, 0, 0, 0], #[64, -64, 64, 192, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified69 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 1, -1, -1, 0, 0, 0, 0], #[1, 1, -1, -1, 0, 0, 0, 0], #[-1, -1, 1, 1, 0, 0, 0, 0], #[-1, -1, 1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 1, -1, -1, 0, 0, 0, 0], #[-1, 1, 0, 0, 0, 0, 0, 0], #[1, 0, 1, 0, 0, 0, 0, 0], #[1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, -64, 64, 64, 0, 0, 0, 0], #[64, 192, 64, 64, 0, 0, 0, 0], #[-64, 64, 192, -64, 0, 0, 0, 0], #[-64, 64, -64, 192, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified70 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, -1, 1, 1, 0, 0, 0, 0], #[-1, 1, -1, -1, 0, 0, 0, 0], #[1, -1, 1, 1, 0, 0, 0, 0], #[1, -1, 1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, -1, 1, 1, 0, 0, 0, 0], #[1, 1, 0, 0, 0, 0, 0, 0], #[-1, 0, 1, 0, 0, 0, 0, 0], #[-1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, -64, -64, 0, 0, 0, 0], #[-64, 192, 64, 64, 0, 0, 0, 0], #[64, 64, 192, -64, 0, 0, 0, 0], #[64, 64, -64, 192, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified71 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, -1, 1, -1, 0, 0, 0, 0], #[-1, 1, -1, 1, 0, 0, 0, 0], #[1, -1, 1, -1, 0, 0, 0, 0], #[-1, 1, -1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, -1, 1, -1, 0, 0, 0, 0], #[1, 1, 0, 0, 0, 0, 0, 0], #[-1, 0, 1, 0, 0, 0, 0, 0], #[1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, -64, 64, 0, 0, 0, 0], #[-64, 192, 64, -64, 0, 0, 0, 0], #[64, 64, 192, 64, 0, 0, 0, 0], #[-64, -64, 64, 192, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified72 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, -1, -1, 1, 0, 0, 0, 0], #[-1, 1, 1, -1, 0, 0, 0, 0], #[-1, 1, 1, -1, 0, 0, 0, 0], #[1, -1, -1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, -1, -1, 1, 0, 0, 0, 0], #[1, 1, 0, 0, 0, 0, 0, 0], #[1, 0, 1, 0, 0, 0, 0, 0], #[-1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 64, -64, 0, 0, 0, 0], #[-64, 192, -64, 64, 0, 0, 0, 0], #[-64, -64, 192, 64, 0, 0, 0, 0], #[64, 64, 64, 192, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified73 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, -1, -1, -1, 0, 0, 0, 0], #[-1, 1, 1, 1, 0, 0, 0, 0], #[-1, 1, 1, 1, 0, 0, 0, 0], #[-1, 1, 1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, -1, -1, -1, 0, 0, 0, 0], #[1, 1, 0, 0, 0, 0, 0, 0], #[1, 0, 1, 0, 0, 0, 0, 0], #[1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 64, 64, 0, 0, 0, 0], #[-64, 192, -64, -64, 0, 0, 0, 0], #[-64, -64, 192, -64, 0, 0, 0, 0], #[-64, -64, -64, 192, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified74 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 0, 0, 1, 1, 0, 0, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 0, 0, 1, 1, 0, 0, 1], #[1, 0, 0, 1, 1, 0, 0, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 0, 0, 1, 1, 0, 0, 1]], + stack := #[#[1, 0, 0, 1, 1, 0, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[-1, 0, 0, 1, 0, 0, 0, 0], #[-1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[-1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 0, 0, -64, -64, 0, 0, -64], #[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, 0, 0, 192, -64, 0, 0, -64], #[64, 0, 0, -64, 192, 0, 0, -64], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 0, 0, -64, -64, 0, 0, 192]] }, by decide⟩ + +def certified75 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 0, 0, 1, 1, 0, 0, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 0, 0, 1, 1, 0, 0, -1], #[1, 0, 0, 1, 1, 0, 0, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 0, 0, -1, -1, 0, 0, 1]], + stack := #[#[1, 0, 0, 1, 1, 0, 0, -1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[-1, 0, 0, 1, 0, 0, 0, 0], #[-1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 0, 0, -64, -64, 0, 0, 64], #[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, 0, 0, 192, -64, 0, 0, 64], #[64, 0, 0, -64, 192, 0, 0, 64], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 0, 0, 64, 64, 0, 0, 192]] }, by decide⟩ + +def certified76 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 0, 0, 1, -1, 0, 0, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 0, 0, 1, -1, 0, 0, 1], #[-1, 0, 0, -1, 1, 0, 0, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 0, 0, 1, -1, 0, 0, 1]], + stack := #[#[1, 0, 0, 1, -1, 0, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[-1, 0, 0, 1, 0, 0, 0, 0], #[1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[-1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 0, 0, -64, 64, 0, 0, -64], #[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, 0, 0, 192, 64, 0, 0, -64], #[-64, 0, 0, 64, 192, 0, 0, 64], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 0, 0, -64, 64, 0, 0, 192]] }, by decide⟩ + +def certified77 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 0, 0, 1, -1, 0, 0, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 0, 0, 1, -1, 0, 0, -1], #[-1, 0, 0, -1, 1, 0, 0, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 0, 0, -1, 1, 0, 0, 1]], + stack := #[#[1, 0, 0, 1, -1, 0, 0, -1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[-1, 0, 0, 1, 0, 0, 0, 0], #[1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 0, 0, -64, 64, 0, 0, 64], #[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, 0, 0, 192, 64, 0, 0, 64], #[-64, 0, 0, 64, 192, 0, 0, -64], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 0, 0, 64, -64, 0, 0, 192]] }, by decide⟩ + +def certified78 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 0, 0, -1, 1, 0, 0, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 0, 0, 1, -1, 0, 0, -1], #[1, 0, 0, -1, 1, 0, 0, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 0, 0, -1, 1, 0, 0, 1]], + stack := #[#[1, 0, 0, -1, 1, 0, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[1, 0, 0, 1, 0, 0, 0, 0], #[-1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[-1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 0, 0, 64, -64, 0, 0, -64], #[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[-64, 0, 0, 192, 64, 0, 0, 64], #[64, 0, 0, 64, 192, 0, 0, -64], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 0, 0, 64, -64, 0, 0, 192]] }, by decide⟩ + +def certified79 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 0, 0, -1, 1, 0, 0, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 0, 0, 1, -1, 0, 0, 1], #[1, 0, 0, -1, 1, 0, 0, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 0, 0, 1, -1, 0, 0, 1]], + stack := #[#[1, 0, 0, -1, 1, 0, 0, -1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[1, 0, 0, 1, 0, 0, 0, 0], #[-1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 0, 0, 64, -64, 0, 0, 64], #[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[-64, 0, 0, 192, 64, 0, 0, -64], #[64, 0, 0, 64, 192, 0, 0, 64], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 0, 0, -64, 64, 0, 0, 192]] }, by decide⟩ + +def certified80 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 0, 0, -1, -1, 0, 0, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 0, 0, 1, 1, 0, 0, -1], #[-1, 0, 0, 1, 1, 0, 0, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 0, 0, -1, -1, 0, 0, 1]], + stack := #[#[1, 0, 0, -1, -1, 0, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[1, 0, 0, 1, 0, 0, 0, 0], #[1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[-1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 0, 0, 64, 64, 0, 0, -64], #[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[-64, 0, 0, 192, -64, 0, 0, 64], #[-64, 0, 0, -64, 192, 0, 0, 64], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 0, 0, 64, 64, 0, 0, 192]] }, by decide⟩ + +def certified81 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 0, 0, -1, -1, 0, 0, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 0, 0, 1, 1, 0, 0, 1], #[-1, 0, 0, 1, 1, 0, 0, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 0, 0, 1, 1, 0, 0, 1]], + stack := #[#[1, 0, 0, -1, -1, 0, 0, -1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[1, 0, 0, 1, 0, 0, 0, 0], #[1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 0, 0, 64, 64, 0, 0, 64], #[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[-64, 0, 0, 192, -64, 0, 0, -64], #[-64, 0, 0, -64, 192, 0, 0, -64], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 0, 0, -64, -64, 0, 0, 192]] }, by decide⟩ + +def certified82 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 1, 1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 1, 1, 0, 1, 0], #[0, 1, 0, 1, 1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 1, 1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 1, 0, 1, 1, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, -1, 0, 1, 0, 0, 0, 0], #[0, -1, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, -1, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[64, 0, 0, -64, -64, 0, -64, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, 0, 0, 192, -64, 0, -64, 0], #[64, 0, 0, -64, 192, 0, -64, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 0, 0, -64, -64, 0, 192, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified83 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 1, 1, 0, -1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 1, 1, 0, -1, 0], #[0, 1, 0, 1, 1, 0, -1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 0, -1, -1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 1, 0, 1, 1, 0, -1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, -1, 0, 1, 0, 0, 0, 0], #[0, -1, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 1, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[64, 0, 0, -64, -64, 0, 64, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, 0, 0, 192, -64, 0, 64, 0], #[64, 0, 0, -64, 192, 0, 64, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 0, 0, 64, 64, 0, 192, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified84 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 1, -1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 1, -1, 0, 1, 0], #[0, -1, 0, -1, 1, 0, -1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 1, -1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 1, 0, 1, -1, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, -1, 0, 1, 0, 0, 0, 0], #[0, 1, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, -1, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[64, 0, 0, -64, 64, 0, -64, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, 0, 0, 192, 64, 0, -64, 0], #[-64, 0, 0, 64, 192, 0, 64, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 0, 0, -64, 64, 0, 192, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified85 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 1, -1, 0, -1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 1, -1, 0, -1, 0], #[0, -1, 0, -1, 1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 0, -1, 1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 1, 0, 1, -1, 0, -1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, -1, 0, 1, 0, 0, 0, 0], #[0, 1, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 1, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[64, 0, 0, -64, 64, 0, 64, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, 0, 0, 192, 64, 0, 64, 0], #[-64, 0, 0, 64, 192, 0, -64, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 0, 0, 64, -64, 0, 192, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified86 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, -1, 1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 0, 1, -1, 0, -1, 0], #[0, 1, 0, -1, 1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, -1, 1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 1, 0, -1, 1, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 1, 0, 1, 0, 0, 0, 0], #[0, -1, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, -1, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[64, 0, 0, 64, -64, 0, -64, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[-64, 0, 0, 192, 64, 0, 64, 0], #[64, 0, 0, 64, 192, 0, -64, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 0, 0, 64, -64, 0, 192, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified87 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, -1, 1, 0, -1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 0, 1, -1, 0, 1, 0], #[0, 1, 0, -1, 1, 0, -1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 0, 1, -1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 1, 0, -1, 1, 0, -1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 1, 0, 1, 0, 0, 0, 0], #[0, -1, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 1, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[64, 0, 0, 64, -64, 0, 64, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[-64, 0, 0, 192, 64, 0, -64, 0], #[64, 0, 0, 64, 192, 0, 64, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 0, 0, -64, 64, 0, 192, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified88 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, -1, -1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 0, 1, 1, 0, -1, 0], #[0, -1, 0, 1, 1, 0, -1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, -1, -1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 1, 0, -1, -1, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 1, 0, 1, 0, 0, 0, 0], #[0, 1, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, -1, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[64, 0, 0, 64, 64, 0, -64, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[-64, 0, 0, 192, -64, 0, 64, 0], #[-64, 0, 0, -64, 192, 0, 64, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 0, 0, 64, 64, 0, 192, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified89 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, -1, -1, 0, -1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 0, 1, 1, 0, 1, 0], #[0, -1, 0, 1, 1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 0, 1, 1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 1, 0, -1, -1, 0, -1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 1, 0, 1, 0, 0, 0, 0], #[0, 1, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 1, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[64, 0, 0, 64, 64, 0, 64, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[-64, 0, 0, 192, -64, 0, -64, 0], #[-64, 0, 0, -64, 192, 0, -64, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 0, 0, -64, -64, 0, 192, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified90 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 1, 0, 0, 1, 1], #[0, 0, 1, 1, 0, 0, 1, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 1, 0, 0, 1, 1], #[0, 0, 1, 1, 0, 0, 1, 1]], + stack := #[#[0, 0, 1, 1, 0, 0, 1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, -1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, -1, 0, 0, 0, 1, 0], #[0, 0, -1, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, 0, 0, -64, 0, 0, -64, -64], #[64, 0, 0, 192, 0, 0, -64, -64], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 0, 0, -64, 0, 0, 192, -64], #[64, 0, 0, -64, 0, 0, -64, 192]] }, by decide⟩ + +def certified91 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 1, 0, 0, 1, -1], #[0, 0, 1, 1, 0, 0, 1, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 1, 0, 0, 1, -1], #[0, 0, -1, -1, 0, 0, -1, 1]], + stack := #[#[0, 0, 1, 1, 0, 0, 1, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, -1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, -1, 0, 0, 0, 1, 0], #[0, 0, 1, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, 0, 0, -64, 0, 0, -64, 64], #[64, 0, 0, 192, 0, 0, -64, 64], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 0, 0, -64, 0, 0, 192, 64], #[-64, 0, 0, 64, 0, 0, 64, 192]] }, by decide⟩ + +def certified92 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 1, 0, 0, -1, 1], #[0, 0, 1, 1, 0, 0, -1, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -1, -1, 0, 0, 1, -1], #[0, 0, 1, 1, 0, 0, -1, 1]], + stack := #[#[0, 0, 1, 1, 0, 0, -1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, -1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 1, 0, 0, 0, 1, 0], #[0, 0, -1, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, 0, 0, -64, 0, 0, 64, -64], #[64, 0, 0, 192, 0, 0, 64, -64], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 0, 0, 64, 0, 0, 192, 64], #[64, 0, 0, -64, 0, 0, 64, 192]] }, by decide⟩ + +def certified93 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 1, 0, 0, -1, -1], #[0, 0, 1, 1, 0, 0, -1, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -1, -1, 0, 0, 1, 1], #[0, 0, -1, -1, 0, 0, 1, 1]], + stack := #[#[0, 0, 1, 1, 0, 0, -1, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, -1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 1, 0, 0, 0, 1, 0], #[0, 0, 1, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, 0, 0, -64, 0, 0, 64, 64], #[64, 0, 0, 192, 0, 0, 64, 64], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 0, 0, 64, 0, 0, 192, -64], #[-64, 0, 0, 64, 0, 0, -64, 192]] }, by decide⟩ + +def certified94 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, -1, 0, 0, 1, 1], #[0, 0, -1, 1, 0, 0, -1, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, -1, 0, 0, 1, 1], #[0, 0, 1, -1, 0, 0, 1, 1]], + stack := #[#[0, 0, 1, -1, 0, 0, 1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, -1, 0, 0, 0, 1, 0], #[0, 0, -1, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, 0, 0, 64, 0, 0, -64, -64], #[-64, 0, 0, 192, 0, 0, 64, 64], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 0, 0, 64, 0, 0, 192, -64], #[64, 0, 0, 64, 0, 0, -64, 192]] }, by decide⟩ + +def certified95 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, -1, 0, 0, 1, -1], #[0, 0, -1, 1, 0, 0, -1, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, -1, 0, 0, 1, -1], #[0, 0, -1, 1, 0, 0, -1, 1]], + stack := #[#[0, 0, 1, -1, 0, 0, 1, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, -1, 0, 0, 0, 1, 0], #[0, 0, 1, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, 0, 0, 64, 0, 0, -64, 64], #[-64, 0, 0, 192, 0, 0, 64, -64], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 0, 0, 64, 0, 0, 192, 64], #[-64, 0, 0, -64, 0, 0, 64, 192]] }, by decide⟩ + +def certified96 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, -1, 0, 0, -1, 1], #[0, 0, -1, 1, 0, 0, 1, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -1, 1, 0, 0, 1, -1], #[0, 0, 1, -1, 0, 0, -1, 1]], + stack := #[#[0, 0, 1, -1, 0, 0, -1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 1, 0, 0, 0, 1, 0], #[0, 0, -1, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, 0, 0, 64, 0, 0, 64, -64], #[-64, 0, 0, 192, 0, 0, -64, 64], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 0, 0, -64, 0, 0, 192, 64], #[64, 0, 0, 64, 0, 0, 64, 192]] }, by decide⟩ + +def certified97 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, -1, 0, 0, -1, -1], #[0, 0, -1, 1, 0, 0, 1, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -1, 1, 0, 0, 1, 1], #[0, 0, -1, 1, 0, 0, 1, 1]], + stack := #[#[0, 0, 1, -1, 0, 0, -1, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 1, 0, 0, 0, 1, 0], #[0, 0, 1, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, 0, 0, 64, 0, 0, 64, 64], #[-64, 0, 0, 192, 0, 0, -64, -64], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 0, 0, -64, 0, 0, 192, -64], #[-64, 0, 0, -64, 0, 0, -64, 192]] }, by decide⟩ + +def certified98 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 1, 1, 1, 0, 0], #[0, 0, 1, 1, 1, 1, 0, 0], #[0, 0, 1, 1, 1, 1, 0, 0], #[0, 0, 1, 1, 1, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 1, 1, 1, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, -1, 1, 0, 0, 0, 0], #[0, 0, -1, 0, 1, 0, 0, 0], #[0, 0, -1, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, 0, 0, -64, -64, -64, 0, 0], #[64, 0, 0, 192, -64, -64, 0, 0], #[64, 0, 0, -64, 192, -64, 0, 0], #[64, 0, 0, -64, -64, 192, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified99 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 1, 1, -1, 0, 0], #[0, 0, 1, 1, 1, -1, 0, 0], #[0, 0, 1, 1, 1, -1, 0, 0], #[0, 0, -1, -1, -1, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 1, 1, 1, -1, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, -1, 1, 0, 0, 0, 0], #[0, 0, -1, 0, 1, 0, 0, 0], #[0, 0, 1, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, 0, 0, -64, -64, 64, 0, 0], #[64, 0, 0, 192, -64, 64, 0, 0], #[64, 0, 0, -64, 192, 64, 0, 0], #[-64, 0, 0, 64, 64, 192, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified100 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 1, -1, 1, 0, 0], #[0, 0, 1, 1, -1, 1, 0, 0], #[0, 0, -1, -1, 1, -1, 0, 0], #[0, 0, 1, 1, -1, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 1, 1, -1, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, -1, 1, 0, 0, 0, 0], #[0, 0, 1, 0, 1, 0, 0, 0], #[0, 0, -1, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, 0, 0, -64, 64, -64, 0, 0], #[64, 0, 0, 192, 64, -64, 0, 0], #[-64, 0, 0, 64, 192, 64, 0, 0], #[64, 0, 0, -64, 64, 192, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified101 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 1, -1, -1, 0, 0], #[0, 0, 1, 1, -1, -1, 0, 0], #[0, 0, -1, -1, 1, 1, 0, 0], #[0, 0, -1, -1, 1, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 1, 1, -1, -1, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, -1, 1, 0, 0, 0, 0], #[0, 0, 1, 0, 1, 0, 0, 0], #[0, 0, 1, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, 0, 0, -64, 64, 64, 0, 0], #[64, 0, 0, 192, 64, 64, 0, 0], #[-64, 0, 0, 64, 192, -64, 0, 0], #[-64, 0, 0, 64, -64, 192, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified102 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, -1, 1, 1, 0, 0], #[0, 0, -1, 1, -1, -1, 0, 0], #[0, 0, 1, -1, 1, 1, 0, 0], #[0, 0, 1, -1, 1, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 1, -1, 1, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 1, 0, 0, 0, 0], #[0, 0, -1, 0, 1, 0, 0, 0], #[0, 0, -1, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, 0, 0, 64, -64, -64, 0, 0], #[-64, 0, 0, 192, 64, 64, 0, 0], #[64, 0, 0, 64, 192, -64, 0, 0], #[64, 0, 0, 64, -64, 192, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified103 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, -1, 1, -1, 0, 0], #[0, 0, -1, 1, -1, 1, 0, 0], #[0, 0, 1, -1, 1, -1, 0, 0], #[0, 0, -1, 1, -1, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 1, -1, 1, -1, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 1, 0, 0, 0, 0], #[0, 0, -1, 0, 1, 0, 0, 0], #[0, 0, 1, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, 0, 0, 64, -64, 64, 0, 0], #[-64, 0, 0, 192, 64, -64, 0, 0], #[64, 0, 0, 64, 192, 64, 0, 0], #[-64, 0, 0, -64, 64, 192, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified104 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, -1, -1, 1, 0, 0], #[0, 0, -1, 1, 1, -1, 0, 0], #[0, 0, -1, 1, 1, -1, 0, 0], #[0, 0, 1, -1, -1, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 1, -1, -1, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 1, 0, 0, 0, 0], #[0, 0, 1, 0, 1, 0, 0, 0], #[0, 0, -1, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, 0, 0, 64, 64, -64, 0, 0], #[-64, 0, 0, 192, -64, 64, 0, 0], #[-64, 0, 0, -64, 192, 64, 0, 0], #[64, 0, 0, 64, 64, 192, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified105 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, -1, -1, -1, 0, 0], #[0, 0, -1, 1, 1, 1, 0, 0], #[0, 0, -1, 1, 1, 1, 0, 0], #[0, 0, -1, 1, 1, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 1, -1, -1, -1, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 1, 0, 0, 0, 0], #[0, 0, 1, 0, 1, 0, 0, 0], #[0, 0, 1, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, 0, 0, 64, 64, 64, 0, 0], #[-64, 0, 0, 192, -64, -64, 0, 0], #[-64, 0, 0, -64, 192, -64, 0, 0], #[-64, 0, 0, -64, -64, 192, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified106 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 1, 0, 1, 0, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 1, 0, 1, 0, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 1, 0, 1, 0, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 1, 0, 1, 0, 1]], + stack := #[#[0, 1, 0, 1, 0, 1, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, -1, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, -1, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, -1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[64, 0, 0, -64, 0, -64, 0, -64], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, 0, 0, 192, 0, -64, 0, -64], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, 0, 0, -64, 0, 192, 0, -64], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 0, 0, -64, 0, -64, 0, 192]] }, by decide⟩ + +def certified107 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 1, 0, 1, 0, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 1, 0, 1, 0, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 1, 0, 1, 0, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 0, -1, 0, -1, 0, 1]], + stack := #[#[0, 1, 0, 1, 0, 1, 0, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, -1, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, -1, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[64, 0, 0, -64, 0, -64, 0, 64], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, 0, 0, 192, 0, -64, 0, 64], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, 0, 0, -64, 0, 192, 0, 64], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 0, 0, 64, 0, 64, 0, 192]] }, by decide⟩ + +def certified108 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 1, 0, -1, 0, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 1, 0, -1, 0, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 0, -1, 0, 1, 0, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 1, 0, -1, 0, 1]], + stack := #[#[0, 1, 0, 1, 0, -1, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, -1, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 1, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, -1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[64, 0, 0, -64, 0, 64, 0, -64], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, 0, 0, 192, 0, 64, 0, -64], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, 0, 0, 64, 0, 192, 0, 64], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 0, 0, -64, 0, 64, 0, 192]] }, by decide⟩ + +def certified109 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 1, 0, -1, 0, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 1, 0, -1, 0, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 0, -1, 0, 1, 0, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 0, -1, 0, 1, 0, 1]], + stack := #[#[0, 1, 0, 1, 0, -1, 0, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, -1, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 1, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[64, 0, 0, -64, 0, 64, 0, 64], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, 0, 0, 192, 0, 64, 0, 64], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, 0, 0, 64, 0, 192, 0, -64], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 0, 0, 64, 0, -64, 0, 192]] }, by decide⟩ + +def certified110 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, -1, 0, 1, 0, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 0, 1, 0, -1, 0, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, -1, 0, 1, 0, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, -1, 0, 1, 0, 1]], + stack := #[#[0, 1, 0, -1, 0, 1, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 1, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, -1, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, -1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[64, 0, 0, 64, 0, -64, 0, -64], #[0, 0, 256, 0, 0, 0, 0, 0], #[-64, 0, 0, 192, 0, 64, 0, 64], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, 0, 0, 64, 0, 192, 0, -64], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 0, 0, 64, 0, -64, 0, 192]] }, by decide⟩ + +def certified111 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, -1, 0, 1, 0, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 0, 1, 0, -1, 0, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, -1, 0, 1, 0, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 0, 1, 0, -1, 0, 1]], + stack := #[#[0, 1, 0, -1, 0, 1, 0, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 1, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, -1, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[64, 0, 0, 64, 0, -64, 0, 64], #[0, 0, 256, 0, 0, 0, 0, 0], #[-64, 0, 0, 192, 0, 64, 0, -64], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, 0, 0, 64, 0, 192, 0, 64], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 0, 0, -64, 0, 64, 0, 192]] }, by decide⟩ + +def certified112 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, -1, 0, -1, 0, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 0, 1, 0, 1, 0, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 0, 1, 0, 1, 0, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, -1, 0, -1, 0, 1]], + stack := #[#[0, 1, 0, -1, 0, -1, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 1, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 1, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, -1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[64, 0, 0, 64, 0, 64, 0, -64], #[0, 0, 256, 0, 0, 0, 0, 0], #[-64, 0, 0, 192, 0, -64, 0, 64], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, 0, 0, -64, 0, 192, 0, 64], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 0, 0, 64, 0, 64, 0, 192]] }, by decide⟩ + +def certified113 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, -1, 0, -1, 0, -1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 0, 1, 0, 1, 0, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 0, 1, 0, 1, 0, 1], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 0, 1, 0, 1, 0, 1]], + stack := #[#[0, 1, 0, -1, 0, -1, 0, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 1, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 1, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 256, 0, 0, 0, 0, 0, 0], #[64, 0, 0, 64, 0, 64, 0, 64], #[0, 0, 256, 0, 0, 0, 0, 0], #[-64, 0, 0, 192, 0, -64, 0, -64], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, 0, 0, -64, 0, 192, 0, -64], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 0, 0, -64, 0, -64, 0, 192]] }, by decide⟩ + +def certified114 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 0, 0, 1, 0, 1, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 0, 0, 1, 0, 1, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 0, 0, 1, 0, 1, 1, 0], #[1, 0, 0, 1, 0, 1, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 0, 0, 1, 0, 1, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[-1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[-1, 0, 0, 0, 0, 1, 0, 0], #[-1, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 0, 0, -64, 0, -64, -64, 0], #[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, 0, 0, 192, 0, -64, -64, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, 0, 0, -64, 0, 192, -64, 0], #[64, 0, 0, -64, 0, -64, 192, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified115 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 0, 0, 1, 0, 1, -1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 0, 0, 1, 0, 1, -1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 0, 0, 1, 0, 1, -1, 0], #[-1, 0, 0, -1, 0, -1, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 0, 0, 1, 0, 1, -1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[-1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[-1, 0, 0, 0, 0, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 0, 0, -64, 0, -64, 64, 0], #[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, 0, 0, 192, 0, -64, 64, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, 0, 0, -64, 0, 192, 64, 0], #[-64, 0, 0, 64, 0, 64, 192, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified116 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 0, 0, 1, 0, -1, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 0, 0, 1, 0, -1, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 0, 0, -1, 0, 1, -1, 0], #[1, 0, 0, 1, 0, -1, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 0, 0, 1, 0, -1, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[-1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[1, 0, 0, 0, 0, 1, 0, 0], #[-1, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 0, 0, -64, 0, 64, -64, 0], #[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, 0, 0, 192, 0, 64, -64, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, 0, 0, 64, 0, 192, 64, 0], #[64, 0, 0, -64, 0, 64, 192, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified117 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 0, 0, 1, 0, -1, -1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 0, 0, 1, 0, -1, -1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 0, 0, -1, 0, 1, 1, 0], #[-1, 0, 0, -1, 0, 1, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 0, 0, 1, 0, -1, -1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[-1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[1, 0, 0, 0, 0, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 0, 0, -64, 0, 64, 64, 0], #[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, 0, 0, 192, 0, 64, 64, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, 0, 0, 64, 0, 192, -64, 0], #[-64, 0, 0, 64, 0, -64, 192, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified118 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 0, 0, -1, 0, 1, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 0, 0, 1, 0, -1, -1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 0, 0, -1, 0, 1, 1, 0], #[1, 0, 0, -1, 0, 1, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 0, 0, -1, 0, 1, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[-1, 0, 0, 0, 0, 1, 0, 0], #[-1, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 0, 0, 64, 0, -64, -64, 0], #[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[-64, 0, 0, 192, 0, 64, 64, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, 0, 0, 64, 0, 192, -64, 0], #[64, 0, 0, 64, 0, -64, 192, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified119 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 0, 0, -1, 0, 1, -1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 0, 0, 1, 0, -1, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[1, 0, 0, -1, 0, 1, -1, 0], #[-1, 0, 0, 1, 0, -1, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 0, 0, -1, 0, 1, -1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[-1, 0, 0, 0, 0, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 0, 0, 64, 0, -64, 64, 0], #[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[-64, 0, 0, 192, 0, 64, -64, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, 0, 0, 64, 0, 192, 64, 0], #[-64, 0, 0, -64, 0, 64, 192, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified120 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 0, 0, -1, 0, -1, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 0, 0, 1, 0, 1, -1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 0, 0, 1, 0, 1, -1, 0], #[1, 0, 0, -1, 0, -1, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 0, 0, -1, 0, -1, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[1, 0, 0, 0, 0, 1, 0, 0], #[-1, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 0, 0, 64, 0, 64, -64, 0], #[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[-64, 0, 0, 192, 0, -64, 64, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, 0, 0, -64, 0, 192, 64, 0], #[64, 0, 0, 64, 0, 64, 192, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified121 : CertifiedFrame := + ⟨{ dimension := 1, scaled := #[#[1, 0, 0, -1, 0, -1, -1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 0, 0, 1, 0, 1, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-1, 0, 0, 1, 0, 1, 1, 0], #[-1, 0, 0, 1, 0, 1, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 0, 0, -1, 0, -1, -1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[1, 0, 0, 0, 0, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 0, 0, 64, 0, 64, 64, 0], #[0, 256, 0, 0, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[-64, 0, 0, 192, 0, -64, -64, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, 0, 0, -64, 0, 192, -64, 0], #[-64, 0, 0, -64, 0, -64, 192, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified122 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 2, 0, 0, 0, 0, 0, 0], #[2, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 2, 0, 0, 0, 0], #[0, 0, 2, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 1, 1, 1, 0, 0, 0, 0], #[1, 1, -1, -1, 0, 0, 0, 0], #[-1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, -1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, -128, 0, 0, 0, 0, 0], #[64, 64, 128, 0, 0, 0, 0, 0], #[64, -64, 0, -128, 0, 0, 0, 0], #[64, -64, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified123 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 2, 0, 0, 0, 0, 0, 0], #[2, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, -2, 0, 0, 0, 0], #[0, 0, -2, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 1, 1, -1, 0, 0, 0, 0], #[1, 1, -1, 1, 0, 0, 0, 0], #[-1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, -128, 0, 0, 0, 0, 0], #[64, 64, 128, 0, 0, 0, 0, 0], #[64, -64, 0, 128, 0, 0, 0, 0], #[-64, 64, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified124 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, -2, 0, 0, 0, 0, 0, 0], #[-2, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 2, 0, 0, 0, 0], #[0, 0, 2, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, -1, 1, 1, 0, 0, 0, 0], #[1, -1, -1, -1, 0, 0, 0, 0], #[1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, -1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 128, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, 0], #[64, -64, 0, -128, 0, 0, 0, 0], #[64, -64, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified125 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, -2, 0, 0, 0, 0, 0, 0], #[-2, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, -2, 0, 0, 0, 0], #[0, 0, -2, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, -1, 1, -1, 0, 0, 0, 0], #[1, -1, -1, 1, 0, 0, 0, 0], #[1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 128, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, 0], #[64, -64, 0, 128, 0, 0, 0, 0], #[-64, 64, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified126 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 2, 0, 0, 0, 0, 0], #[0, 2, 0, 2, 0, 0, 0, 0], #[2, 0, 2, 0, 0, 0, 0, 0], #[0, 2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 1, 1, 1, 0, 0, 0, 0], #[1, -1, 1, -1, 0, 0, 0, 0], #[-1, 0, 1, 0, 0, 0, 0, 0], #[0, -1, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, -128, 0, 0, 0, 0, 0], #[64, -64, 0, -128, 0, 0, 0, 0], #[64, 64, 128, 0, 0, 0, 0, 0], #[64, -64, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified127 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 2, 0, 0, 0, 0, 0], #[0, 2, 0, -2, 0, 0, 0, 0], #[2, 0, 2, 0, 0, 0, 0, 0], #[0, -2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 1, 1, -1, 0, 0, 0, 0], #[1, -1, 1, 1, 0, 0, 0, 0], #[-1, 0, 1, 0, 0, 0, 0, 0], #[0, 1, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, -128, 0, 0, 0, 0, 0], #[64, -64, 0, 128, 0, 0, 0, 0], #[64, 64, 128, 0, 0, 0, 0, 0], #[-64, 64, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified128 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, -2, 0, 0, 0, 0, 0], #[0, 2, 0, 2, 0, 0, 0, 0], #[-2, 0, 2, 0, 0, 0, 0, 0], #[0, 2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 1, -1, 1, 0, 0, 0, 0], #[1, -1, -1, -1, 0, 0, 0, 0], #[1, 0, 1, 0, 0, 0, 0, 0], #[0, -1, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 128, 0, 0, 0, 0, 0], #[64, -64, 0, -128, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, 0], #[64, -64, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified129 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, -2, 0, 0, 0, 0, 0], #[0, 2, 0, -2, 0, 0, 0, 0], #[-2, 0, 2, 0, 0, 0, 0, 0], #[0, -2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 1, -1, -1, 0, 0, 0, 0], #[1, -1, -1, 1, 0, 0, 0, 0], #[1, 0, 1, 0, 0, 0, 0, 0], #[0, 1, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 128, 0, 0, 0, 0, 0], #[64, -64, 0, 128, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, 0], #[-64, 64, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified130 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 2, 0, 0, 0, 0], #[0, 2, 2, 0, 0, 0, 0, 0], #[0, 2, 2, 0, 0, 0, 0, 0], #[2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 1, 1, 1, 0, 0, 0, 0], #[1, -1, -1, 1, 0, 0, 0, 0], #[0, -1, 1, 0, 0, 0, 0, 0], #[-1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, -128, 0, 0, 0, 0], #[64, -64, -128, 0, 0, 0, 0, 0], #[64, -64, 128, 0, 0, 0, 0, 0], #[64, 64, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified131 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 2, 0, 0, 0, 0], #[0, 2, -2, 0, 0, 0, 0, 0], #[0, -2, 2, 0, 0, 0, 0, 0], #[2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 1, -1, 1, 0, 0, 0, 0], #[1, -1, 1, 1, 0, 0, 0, 0], #[0, 1, 1, 0, 0, 0, 0, 0], #[-1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, -128, 0, 0, 0, 0], #[64, -64, 128, 0, 0, 0, 0, 0], #[-64, 64, 128, 0, 0, 0, 0, 0], #[64, 64, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified132 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, -2, 0, 0, 0, 0], #[0, 2, 2, 0, 0, 0, 0, 0], #[0, 2, 2, 0, 0, 0, 0, 0], #[-2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 1, 1, -1, 0, 0, 0, 0], #[1, -1, -1, -1, 0, 0, 0, 0], #[0, -1, 1, 0, 0, 0, 0, 0], #[1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 128, 0, 0, 0, 0], #[64, -64, -128, 0, 0, 0, 0, 0], #[64, -64, 128, 0, 0, 0, 0, 0], #[-64, -64, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified133 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, -2, 0, 0, 0, 0], #[0, 2, -2, 0, 0, 0, 0, 0], #[0, -2, 2, 0, 0, 0, 0, 0], #[-2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 1, -1, -1, 0, 0, 0, 0], #[1, -1, 1, -1, 0, 0, 0, 0], #[0, 1, 1, 0, 0, 0, 0, 0], #[1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 128, 0, 0, 0, 0], #[64, -64, 128, 0, 0, 0, 0, 0], #[-64, 64, 128, 0, 0, 0, 0, 0], #[-64, -64, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified134 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 2, 0, 0, 0, 0, 0, 0], #[2, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 2, 0, 0], #[0, 0, 0, 0, 2, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 1, 0, 0, 1, 1, 0, 0], #[1, 1, 0, 0, -1, -1, 0, 0], #[-1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, -1, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, -128, 0, 0, 0, 0, 0], #[64, 64, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, -64, 0, 0, 0, -128, 0, 0], #[64, -64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified135 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 2, 0, 0, 0, 0, 0, 0], #[2, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, -2, 0, 0], #[0, 0, 0, 0, -2, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 1, 0, 0, 1, -1, 0, 0], #[1, 1, 0, 0, -1, 1, 0, 0], #[-1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, -128, 0, 0, 0, 0, 0], #[64, 64, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, -64, 0, 0, 0, 128, 0, 0], #[-64, 64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified136 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, -2, 0, 0, 0, 0, 0, 0], #[-2, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 2, 0, 0], #[0, 0, 0, 0, 2, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, -1, 0, 0, 1, 1, 0, 0], #[1, -1, 0, 0, -1, -1, 0, 0], #[1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, -1, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 128, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, -64, 0, 0, 0, -128, 0, 0], #[64, -64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified137 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, -2, 0, 0, 0, 0, 0, 0], #[-2, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, -2, 0, 0], #[0, 0, 0, 0, -2, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, -1, 0, 0, 1, -1, 0, 0], #[1, -1, 0, 0, -1, 1, 0, 0], #[1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 128, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, -64, 0, 0, 0, 128, 0, 0], #[-64, 64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified138 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, 2, 0, 0, 0], #[0, 2, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[2, 0, 0, 0, 2, 0, 0, 0], #[0, 2, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 1, 0, 0, 1, 1, 0, 0], #[1, -1, 0, 0, 1, -1, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[-1, 0, 0, 0, 1, 0, 0, 0], #[0, -1, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, -128, 0, 0, 0], #[64, -64, 0, 0, 0, -128, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 64, 0, 0, 128, 0, 0, 0], #[64, -64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified139 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, 2, 0, 0, 0], #[0, 2, 0, 0, 0, -2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[2, 0, 0, 0, 2, 0, 0, 0], #[0, -2, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 1, 0, 0, 1, -1, 0, 0], #[1, -1, 0, 0, 1, 1, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[-1, 0, 0, 0, 1, 0, 0, 0], #[0, 1, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, -128, 0, 0, 0], #[64, -64, 0, 0, 0, 128, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 64, 0, 0, 128, 0, 0, 0], #[-64, 64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified140 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, -2, 0, 0, 0], #[0, 2, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-2, 0, 0, 0, 2, 0, 0, 0], #[0, 2, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 1, 0, 0, -1, 1, 0, 0], #[1, -1, 0, 0, -1, -1, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[1, 0, 0, 0, 1, 0, 0, 0], #[0, -1, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 128, 0, 0, 0], #[64, -64, 0, 0, 0, -128, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, 0], #[64, -64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified141 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, -2, 0, 0, 0], #[0, 2, 0, 0, 0, -2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-2, 0, 0, 0, 2, 0, 0, 0], #[0, -2, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 1, 0, 0, -1, -1, 0, 0], #[1, -1, 0, 0, -1, 1, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[1, 0, 0, 0, 1, 0, 0, 0], #[0, 1, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 128, 0, 0, 0], #[64, -64, 0, 0, 0, 128, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, 0], #[-64, 64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified142 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, 0, 2, 0, 0], #[0, 2, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 2, 0, 0, 0], #[2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 1, 0, 0, 1, 1, 0, 0], #[1, -1, 0, 0, -1, 1, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, -1, 0, 0, 1, 0, 0, 0], #[-1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 0, -128, 0, 0], #[64, -64, 0, 0, -128, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, -64, 0, 0, 128, 0, 0, 0], #[64, 64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified143 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, 0, 2, 0, 0], #[0, 2, 0, 0, -2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -2, 0, 0, 2, 0, 0, 0], #[2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 1, 0, 0, -1, 1, 0, 0], #[1, -1, 0, 0, 1, 1, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 1, 0, 0, 1, 0, 0, 0], #[-1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 0, -128, 0, 0], #[64, -64, 0, 0, 128, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[-64, 64, 0, 0, 128, 0, 0, 0], #[64, 64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified144 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, 0, -2, 0, 0], #[0, 2, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 2, 0, 0, 0], #[-2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 1, 0, 0, 1, -1, 0, 0], #[1, -1, 0, 0, -1, -1, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, -1, 0, 0, 1, 0, 0, 0], #[1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 0, 128, 0, 0], #[64, -64, 0, 0, -128, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, -64, 0, 0, 128, 0, 0, 0], #[-64, -64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified145 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, 0, -2, 0, 0], #[0, 2, 0, 0, -2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -2, 0, 0, 2, 0, 0, 0], #[-2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 1, 0, 0, -1, -1, 0, 0], #[1, -1, 0, 0, 1, -1, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 1, 0, 0, 1, 0, 0, 0], #[1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 0, 128, 0, 0], #[64, -64, 0, 0, 128, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[-64, 64, 0, 0, 128, 0, 0, 0], #[-64, -64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified146 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 2, 0, 0, 0, 0, 0, 0], #[2, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 2], #[0, 0, 0, 0, 0, 0, 2, 2]], + stack := #[#[1, 1, 0, 0, 0, 0, 1, 1], #[1, 1, 0, 0, 0, 0, -1, -1], #[-1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, -1, 1]], + inverse256 := #[#[64, 64, -128, 0, 0, 0, 0, 0], #[64, 64, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, -64, 0, 0, 0, 0, 0, -128], #[64, -64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified147 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 2, 0, 0, 0, 0, 0, 0], #[2, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, -2], #[0, 0, 0, 0, 0, 0, -2, 2]], + stack := #[#[1, 1, 0, 0, 0, 0, 1, -1], #[1, 1, 0, 0, 0, 0, -1, 1], #[-1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 1]], + inverse256 := #[#[64, 64, -128, 0, 0, 0, 0, 0], #[64, 64, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, -64, 0, 0, 0, 0, 0, 128], #[-64, 64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified148 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, -2, 0, 0, 0, 0, 0, 0], #[-2, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 2], #[0, 0, 0, 0, 0, 0, 2, 2]], + stack := #[#[1, -1, 0, 0, 0, 0, 1, 1], #[1, -1, 0, 0, 0, 0, -1, -1], #[1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, -1, 1]], + inverse256 := #[#[64, 64, 128, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, -64, 0, 0, 0, 0, 0, -128], #[64, -64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified149 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, -2, 0, 0, 0, 0, 0, 0], #[-2, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, -2], #[0, 0, 0, 0, 0, 0, -2, 2]], + stack := #[#[1, -1, 0, 0, 0, 0, 1, -1], #[1, -1, 0, 0, 0, 0, -1, 1], #[1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 1]], + inverse256 := #[#[64, 64, 128, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, -64, 0, 0, 0, 0, 0, 128], #[-64, 64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified150 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, 0, 0, 2, 0], #[0, 2, 0, 0, 0, 0, 0, 2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[2, 0, 0, 0, 0, 0, 2, 0], #[0, 2, 0, 0, 0, 0, 0, 2]], + stack := #[#[1, 1, 0, 0, 0, 0, 1, 1], #[1, -1, 0, 0, 0, 0, 1, -1], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[-1, 0, 0, 0, 0, 0, 1, 0], #[0, -1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 0, 0, -128, 0], #[64, -64, 0, 0, 0, 0, 0, -128], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 64, 0, 0, 0, 0, 128, 0], #[64, -64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified151 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, 0, 0, 2, 0], #[0, 2, 0, 0, 0, 0, 0, -2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[2, 0, 0, 0, 0, 0, 2, 0], #[0, -2, 0, 0, 0, 0, 0, 2]], + stack := #[#[1, 1, 0, 0, 0, 0, 1, -1], #[1, -1, 0, 0, 0, 0, 1, 1], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[-1, 0, 0, 0, 0, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 0, 0, -128, 0], #[64, -64, 0, 0, 0, 0, 0, 128], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 64, 0, 0, 0, 0, 128, 0], #[-64, 64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified152 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, 0, 0, -2, 0], #[0, 2, 0, 0, 0, 0, 0, 2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-2, 0, 0, 0, 0, 0, 2, 0], #[0, 2, 0, 0, 0, 0, 0, 2]], + stack := #[#[1, 1, 0, 0, 0, 0, -1, 1], #[1, -1, 0, 0, 0, 0, -1, -1], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 1, 0], #[0, -1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 0, 0, 128, 0], #[64, -64, 0, 0, 0, 0, 0, -128], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, -64, 0, 0, 0, 0, 128, 0], #[64, -64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified153 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, 0, 0, -2, 0], #[0, 2, 0, 0, 0, 0, 0, -2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-2, 0, 0, 0, 0, 0, 2, 0], #[0, -2, 0, 0, 0, 0, 0, 2]], + stack := #[#[1, 1, 0, 0, 0, 0, -1, -1], #[1, -1, 0, 0, 0, 0, -1, 1], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 0, 0, 128, 0], #[64, -64, 0, 0, 0, 0, 0, 128], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, -64, 0, 0, 0, 0, 128, 0], #[-64, 64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified154 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, 0, 0, 0, 2], #[0, 2, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 2, 0], #[2, 0, 0, 0, 0, 0, 0, 2]], + stack := #[#[1, 1, 0, 0, 0, 0, 1, 1], #[1, -1, 0, 0, 0, 0, -1, 1], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, -1, 0, 0, 0, 0, 1, 0], #[-1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 0, 0, 0, -128], #[64, -64, 0, 0, 0, 0, -128, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, -64, 0, 0, 0, 0, 128, 0], #[64, 64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified155 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, 0, 0, 0, 2], #[0, 2, 0, 0, 0, 0, -2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -2, 0, 0, 0, 0, 2, 0], #[2, 0, 0, 0, 0, 0, 0, 2]], + stack := #[#[1, 1, 0, 0, 0, 0, -1, 1], #[1, -1, 0, 0, 0, 0, 1, 1], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 1, 0, 0, 0, 0, 1, 0], #[-1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 0, 0, 0, -128], #[64, -64, 0, 0, 0, 0, 128, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 64, 0, 0, 0, 0, 128, 0], #[64, 64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified156 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, 0, 0, 0, -2], #[0, 2, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 2, 0], #[-2, 0, 0, 0, 0, 0, 0, 2]], + stack := #[#[1, 1, 0, 0, 0, 0, 1, -1], #[1, -1, 0, 0, 0, 0, -1, -1], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, -1, 0, 0, 0, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 0, 0, 0, 128], #[64, -64, 0, 0, 0, 0, -128, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, -64, 0, 0, 0, 0, 128, 0], #[-64, -64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified157 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, 0, 0, 0, -2], #[0, 2, 0, 0, 0, 0, -2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -2, 0, 0, 0, 0, 2, 0], #[-2, 0, 0, 0, 0, 0, 0, 2]], + stack := #[#[1, 1, 0, 0, 0, 0, -1, -1], #[1, -1, 0, 0, 0, 0, 1, -1], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 1, 0, 0, 0, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 0, 0, 0, 128], #[64, -64, 0, 0, 0, 0, 128, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 64, 0, 0, 0, 0, 128, 0], #[-64, -64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified158 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[2, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 0, 1, 0, 1, 0, 1, 0], #[1, 0, 1, 0, -1, 0, -1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[-1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, -1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, -128, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, -64, 0, 0, 0, 0, -128, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, -64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified159 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[2, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, -2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, -2, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 0, 1, 0, 1, 0, -1, 0], #[1, 0, 1, 0, -1, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[-1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, -128, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, -64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified160 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, -2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-2, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 0, -1, 0, 1, 0, 1, 0], #[1, 0, -1, 0, -1, 0, -1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, -1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 128, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[-64, -64, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, -64, 0, 0, 0, 0, -128, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, -64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified161 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, -2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-2, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, -2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, -2, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 0, -1, 0, 1, 0, -1, 0], #[1, 0, -1, 0, -1, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 128, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[-64, -64, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, -64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified162 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[2, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 0, 1, 0, 1, 0, 1, 0], #[1, 0, -1, 0, 1, 0, -1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[-1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, -1, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, -128, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, -64, 0, 0, 0, 0, -128, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, -64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified163 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, -2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[2, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -2, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 0, 1, 0, 1, 0, -1, 0], #[1, 0, -1, 0, 1, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[-1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 1, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, -128, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, -64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified164 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, -2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-2, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 0, 1, 0, -1, 0, 1, 0], #[1, 0, -1, 0, -1, 0, -1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, -1, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 128, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, -64, 0, 0, 0, 0, -128, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, -64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified165 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, -2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, -2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-2, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -2, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 0, 1, 0, -1, 0, -1, 0], #[1, 0, -1, 0, -1, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 1, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 128, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, -64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified166 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[2, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 0, 1, 0, 1, 0, 1, 0], #[1, 0, -1, 0, -1, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, -1, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[-1, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 0, 0, -128, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, -64, 0, 0, -128, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, -64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified167 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, -2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -2, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[2, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 0, 1, 0, -1, 0, 1, 0], #[1, 0, -1, 0, 1, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 1, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[-1, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 0, 0, -128, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, -64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[-64, 64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified168 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, 0, 0, -2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-2, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 0, 1, 0, 1, 0, -1, 0], #[1, 0, -1, 0, -1, 0, -1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, -1, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 0, 0, 128, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, -64, 0, 0, -128, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, -64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, -64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified169 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, 0, 0, -2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, -2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -2, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-2, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 0, 1, 0, -1, 0, -1, 0], #[1, 0, -1, 0, 1, 0, -1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 1, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 0, 0, 128, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, -64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[-64, 64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, -64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified170 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[2, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 2]], + stack := #[#[1, 0, 1, 0, 0, 1, 0, 1], #[1, 0, 1, 0, 0, -1, 0, -1], #[0, 1, 0, 0, 0, 0, 0, 0], #[-1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, -1, 0, 1]], + inverse256 := #[#[64, 64, 0, -128, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, -64, 0, 0, 0, 0, 0, -128], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, -64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified171 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[2, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, -2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, -2, 0, 2]], + stack := #[#[1, 0, 1, 0, 0, 1, 0, -1], #[1, 0, 1, 0, 0, -1, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[-1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 1, 0, 1]], + inverse256 := #[#[64, 64, 0, -128, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, -64, 0, 0, 0, 0, 0, 128], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified172 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, -2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-2, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 2]], + stack := #[#[1, 0, -1, 0, 0, 1, 0, 1], #[1, 0, -1, 0, 0, -1, 0, -1], #[0, 1, 0, 0, 0, 0, 0, 0], #[1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, -1, 0, 1]], + inverse256 := #[#[64, 64, 0, 128, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[-64, -64, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, -64, 0, 0, 0, 0, 0, -128], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, -64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified173 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, -2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-2, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, -2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, -2, 0, 2]], + stack := #[#[1, 0, -1, 0, 0, 1, 0, -1], #[1, 0, -1, 0, 0, -1, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 1, 0, 1]], + inverse256 := #[#[64, 64, 0, 128, 0, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[-64, -64, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, -64, 0, 0, 0, 0, 0, 128], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified174 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 2]], + stack := #[#[1, 0, 1, 0, 0, 1, 0, 1], #[1, 0, -1, 0, 0, 1, 0, -1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[-1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, -1, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 0, -128, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, -64, 0, 0, 0, 0, 0, -128], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, 64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, -64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified175 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, -2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -2, 0, 0, 0, 0, 2]], + stack := #[#[1, 0, 1, 0, 0, 1, 0, -1], #[1, 0, -1, 0, 0, 1, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[-1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 1, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 0, -128, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, -64, 0, 0, 0, 0, 0, 128], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, 64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified176 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, 0, -2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 2]], + stack := #[#[1, 0, 1, 0, 0, -1, 0, 1], #[1, 0, -1, 0, 0, -1, 0, -1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, -1, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 0, 128, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, -64, 0, 0, 0, 0, 0, -128], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, -64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified177 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, 0, -2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, -2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -2, 0, 0, 0, 0, 2]], + stack := #[#[1, 0, 1, 0, 0, -1, 0, -1], #[1, 0, -1, 0, 0, -1, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 1, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 0, 128, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, -64, 0, 0, 0, 0, 0, 128], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified178 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, 0, 0, 0, 2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[2, 0, 0, 0, 0, 0, 0, 2]], + stack := #[#[1, 0, 1, 0, 0, 1, 0, 1], #[1, 0, -1, 0, 0, -1, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, -1, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[-1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 0, 0, 0, -128], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, -64, 0, 0, 0, -128, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, -64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified179 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, 0, 0, 0, 2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, -2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -2, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[2, 0, 0, 0, 0, 0, 0, 2]], + stack := #[#[1, 0, 1, 0, 0, -1, 0, 1], #[1, 0, -1, 0, 0, 1, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 1, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[-1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 0, 0, 0, -128], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, -64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, 64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified180 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, 0, 0, 0, -2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-2, 0, 0, 0, 0, 0, 0, 2]], + stack := #[#[1, 0, 1, 0, 0, 1, 0, -1], #[1, 0, -1, 0, 0, -1, 0, -1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, -1, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 0, 0, 0, 128], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, -64, 0, 0, 0, -128, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, -64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, -64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified181 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, 0, 0, 0, -2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, -2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -2, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-2, 0, 0, 0, 0, 0, 0, 2]], + stack := #[#[1, 0, 1, 0, 0, -1, 0, -1], #[1, 0, -1, 0, 0, 1, 0, -1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 1, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 0, 0, 0, 128], #[0, 0, 256, 0, 0, 0, 0, 0], #[64, -64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, 64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, -64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified182 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 2]], + stack := #[#[1, 0, 0, 1, 1, 0, 0, 1], #[1, 0, 0, 1, -1, 0, 0, -1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[-1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, -1, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, -128, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 64, 0, 0, 128, 0, 0, 0], #[64, -64, 0, 0, 0, 0, 0, -128], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, -64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified183 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, -2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, -2, 0, 0, 2]], + stack := #[#[1, 0, 0, 1, 1, 0, 0, -1], #[1, 0, 0, 1, -1, 0, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[-1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 1, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, -128, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 64, 0, 0, 128, 0, 0, 0], #[64, -64, 0, 0, 0, 0, 0, 128], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified184 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, -2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 2]], + stack := #[#[1, 0, 0, -1, 1, 0, 0, 1], #[1, 0, 0, -1, -1, 0, 0, -1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, -1, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 128, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, 0], #[64, -64, 0, 0, 0, 0, 0, -128], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, -64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified185 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, -2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, -2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, -2, 0, 0, 2]], + stack := #[#[1, 0, 0, -1, 1, 0, 0, -1], #[1, 0, 0, -1, -1, 0, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 1, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 128, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, 0], #[64, -64, 0, 0, 0, 0, 0, 128], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified186 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 2], #[2, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 2]], + stack := #[#[1, 0, 0, 1, 1, 0, 0, 1], #[1, 0, 0, -1, 1, 0, 0, -1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[-1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, -1, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, -128, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, -64, 0, 0, 0, 0, 0, -128], #[64, 64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, -64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified187 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, -2], #[2, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, -2, 0, 0, 0, 2]], + stack := #[#[1, 0, 0, 1, 1, 0, 0, -1], #[1, 0, 0, -1, 1, 0, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[-1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 1, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, -128, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, -64, 0, 0, 0, 0, 0, 128], #[64, 64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified188 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, -2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 2], #[-2, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 2]], + stack := #[#[1, 0, 0, 1, -1, 0, 0, 1], #[1, 0, 0, -1, -1, 0, 0, -1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, -1, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 128, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, -64, 0, 0, 0, 0, 0, -128], #[-64, -64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, -64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified189 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, -2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, -2], #[-2, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, -2, 0, 0, 0, 2]], + stack := #[#[1, 0, 0, 1, -1, 0, 0, -1], #[1, 0, 0, -1, -1, 0, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 1, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 128, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, -64, 0, 0, 0, 0, 0, 128], #[-64, -64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified190 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, 0, 0, 0, 2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 2, 0, 0, 0], #[0, 0, 0, 2, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[2, 0, 0, 0, 0, 0, 0, 2]], + stack := #[#[1, 0, 0, 1, 1, 0, 0, 1], #[1, 0, 0, -1, -1, 0, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, -1, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[-1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 0, 0, 0, -128], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, -64, 0, 0, -128, 0, 0, 0], #[64, -64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified191 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, 0, 0, 0, 2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, -2, 0, 0, 0], #[0, 0, 0, -2, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[2, 0, 0, 0, 0, 0, 0, 2]], + stack := #[#[1, 0, 0, 1, -1, 0, 0, 1], #[1, 0, 0, -1, 1, 0, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[-1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 0, 0, 0, -128], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, -64, 0, 0, 128, 0, 0, 0], #[-64, 64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified192 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, 0, 0, 0, -2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 2, 0, 0, 0], #[0, 0, 0, 2, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-2, 0, 0, 0, 0, 0, 0, 2]], + stack := #[#[1, 0, 0, 1, 1, 0, 0, -1], #[1, 0, 0, -1, -1, 0, 0, -1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, -1, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 0, 0, 0, 128], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, -64, 0, 0, -128, 0, 0, 0], #[64, -64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, -64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified193 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, 0, 0, 0, -2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, -2, 0, 0, 0], #[0, 0, 0, -2, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-2, 0, 0, 0, 0, 0, 0, 2]], + stack := #[#[1, 0, 0, 1, -1, 0, 0, -1], #[1, 0, 0, -1, 1, 0, 0, -1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 0, 0, 0, 128], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, -64, 0, 0, 128, 0, 0, 0], #[-64, 64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, -64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified194 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 2, 0], #[0, 0, 0, 0, 0, 2, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 0, 0, 1, 0, 1, 1, 0], #[1, 0, 0, 1, 0, -1, -1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[-1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, -1, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, -128, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, -64, 0, 0, 0, 0, -128, 0], #[64, -64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified195 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, -2, 0], #[0, 0, 0, 0, 0, -2, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 0, 0, 1, 0, 1, -1, 0], #[1, 0, 0, 1, 0, -1, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[-1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, -128, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, -64, 0, 0, 0, 0, 128, 0], #[-64, 64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified196 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, -2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 2, 0], #[0, 0, 0, 0, 0, 2, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 0, 0, -1, 0, 1, 1, 0], #[1, 0, 0, -1, 0, -1, -1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, -1, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 128, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, -64, 0, 0, 0, 0, -128, 0], #[64, -64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified197 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, -2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, -2, 0], #[0, 0, 0, 0, 0, -2, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 0, 0, -1, 0, 1, -1, 0], #[1, 0, 0, -1, 0, -1, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 128, 0, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, -64, 0, 0, 0, 0, 128, 0], #[-64, 64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified198 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 2, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 0, 0, 1, 0, 1, 1, 0], #[1, 0, 0, -1, 0, 1, -1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[-1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, -1, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 0, -128, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, -64, 0, 0, 0, 0, -128, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, 64, 0, 0, 0, 128, 0, 0], #[64, -64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified199 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, -2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, -2, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 0, 0, 1, 0, 1, -1, 0], #[1, 0, 0, -1, 0, 1, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[-1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 1, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 0, -128, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, -64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, 64, 0, 0, 0, 128, 0, 0], #[-64, 64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified200 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, 0, -2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 2, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 0, 0, 1, 0, -1, 1, 0], #[1, 0, 0, -1, 0, -1, -1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, -1, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 0, 128, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, -64, 0, 0, 0, 0, -128, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 0, 0, 0, 128, 0, 0], #[64, -64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified201 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, 0, -2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, -2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, -2, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 0, 0, 1, 0, -1, -1, 0], #[1, 0, 0, -1, 0, -1, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 1, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 0, 128, 0, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, -64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 0, 0, 0, 128, 0, 0], #[-64, 64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified202 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 2, 0, 0], #[2, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 0, 0, 1, 0, 1, 1, 0], #[1, 0, 0, -1, 0, -1, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, -1, 0, 1, 0, 0], #[-1, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 0, 0, -128, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, -64, 0, 0, 0, -128, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, -64, 0, 0, 0, 128, 0, 0], #[64, 64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified203 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, -2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, -2, 0, 2, 0, 0], #[2, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 0, 0, 1, 0, -1, 1, 0], #[1, 0, 0, -1, 0, 1, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 1, 0, 1, 0, 0], #[-1, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 0, 0, -128, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, -64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, 64, 0, 0, 0, 128, 0, 0], #[64, 64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified204 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, 0, 0, -2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 2, 0, 0], #[-2, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 0, 0, 1, 0, 1, -1, 0], #[1, 0, 0, -1, 0, -1, -1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, -1, 0, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 0, 0, 128, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, -64, 0, 0, 0, -128, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, -64, 0, 0, 0, 128, 0, 0], #[-64, -64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified205 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[2, 0, 0, 0, 0, 0, -2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, -2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, -2, 0, 2, 0, 0], #[-2, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[1, 0, 0, 1, 0, -1, -1, 0], #[1, 0, 0, -1, 0, 1, -1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 1, 0, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[64, 64, 0, 0, 0, 0, 128, 0], #[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, -64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, 64, 0, 0, 0, 128, 0, 0], #[-64, -64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified206 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 2, 0, 0, 0, 0, 0], #[0, 2, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 2]], + stack := #[#[0, 1, 1, 0, 1, 0, 0, 1], #[0, 1, 1, 0, -1, 0, 0, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, -1, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, -128, 0, 0, 0, 0], #[64, 64, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, -64, 0, 0, 0, 0, 0, -128], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, -64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified207 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 2, 0, 0, 0, 0, 0], #[0, 2, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, -2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, -2, 0, 0, 2]], + stack := #[#[0, 1, 1, 0, 1, 0, 0, -1], #[0, 1, 1, 0, -1, 0, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 1, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, -128, 0, 0, 0, 0], #[64, 64, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, -64, 0, 0, 0, 0, 0, 128], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified208 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, -2, 0, 0, 0, 0, 0], #[0, -2, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 2]], + stack := #[#[0, 1, -1, 0, 1, 0, 0, 1], #[0, 1, -1, 0, -1, 0, 0, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, -1, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 128, 0, 0, 0, 0], #[-64, -64, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, -64, 0, 0, 0, 0, 0, -128], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, -64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified209 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, -2, 0, 0, 0, 0, 0], #[0, -2, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, -2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, -2, 0, 0, 2]], + stack := #[#[0, 1, -1, 0, 1, 0, 0, -1], #[0, 1, -1, 0, -1, 0, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 1, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 128, 0, 0, 0, 0], #[-64, -64, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, -64, 0, 0, 0, 0, 0, 128], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified210 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 2, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 2]], + stack := #[#[0, 1, 1, 0, 1, 0, 0, 1], #[0, 1, -1, 0, 1, 0, 0, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, -1, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, -1, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 0, -128, 0, 0, 0], #[64, -64, 0, 0, 0, 0, 0, -128], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, -64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified211 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 2, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, -2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -2, 0, 0, 0, 0, 2]], + stack := #[#[0, 1, 1, 0, 1, 0, 0, -1], #[0, 1, -1, 0, 1, 0, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, -1, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 1, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 0, -128, 0, 0, 0], #[64, -64, 0, 0, 0, 0, 0, 128], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified212 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, -2, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -2, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 2]], + stack := #[#[0, 1, 1, 0, -1, 0, 0, 1], #[0, 1, -1, 0, -1, 0, 0, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 1, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, -1, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 0, 128, 0, 0, 0], #[64, -64, 0, 0, 0, 0, 0, -128], #[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, -64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified213 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, -2, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, -2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -2, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -2, 0, 0, 0, 0, 2]], + stack := #[#[0, 1, 1, 0, -1, 0, 0, -1], #[0, 1, -1, 0, -1, 0, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 1, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 1, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 0, 128, 0, 0, 0], #[64, -64, 0, 0, 0, 0, 0, 128], #[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified214 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 2], #[0, 0, 2, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 2]], + stack := #[#[0, 1, 1, 0, 1, 0, 0, 1], #[0, 1, -1, 0, -1, 0, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, -1, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, -1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 0, 0, 0, 0, -128], #[64, -64, 0, 0, -128, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, -64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified215 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 2], #[0, 0, 2, 0, -2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -2, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 2]], + stack := #[#[0, 1, 1, 0, -1, 0, 0, 1], #[0, 1, -1, 0, 1, 0, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 1, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, -1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 0, 0, 0, 0, -128], #[64, -64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[-64, 64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified216 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, -2], #[0, 0, 2, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -2, 0, 0, 0, 0, 0, 2]], + stack := #[#[0, 1, 1, 0, 1, 0, 0, -1], #[0, 1, -1, 0, -1, 0, 0, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, -1, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 0, 0, 0, 0, 128], #[64, -64, 0, 0, -128, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, -64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, -64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified217 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, -2], #[0, 0, 2, 0, -2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -2, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -2, 0, 0, 0, 0, 0, 2]], + stack := #[#[0, 1, 1, 0, -1, 0, 0, -1], #[0, 1, -1, 0, 1, 0, 0, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 1, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 0, 0, 0, 0, 128], #[64, -64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[-64, 64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, -64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified218 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 2, 0, 0, 0, 0, 0], #[0, 2, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 2, 0], #[0, 0, 0, 0, 0, 2, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 1, 1, 0, 0, 1, 1, 0], #[0, 1, 1, 0, 0, -1, -1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, -1, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, -128, 0, 0, 0, 0], #[64, 64, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, -64, 0, 0, 0, 0, -128, 0], #[64, -64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified219 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 2, 0, 0, 0, 0, 0], #[0, 2, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, -2, 0], #[0, 0, 0, 0, 0, -2, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 1, 1, 0, 0, 1, -1, 0], #[0, 1, 1, 0, 0, -1, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, -128, 0, 0, 0, 0], #[64, 64, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, -64, 0, 0, 0, 0, 128, 0], #[-64, 64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified220 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, -2, 0, 0, 0, 0, 0], #[0, -2, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 2, 0], #[0, 0, 0, 0, 0, 2, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 1, -1, 0, 0, 1, 1, 0], #[0, 1, -1, 0, 0, -1, -1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, -1, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 128, 0, 0, 0, 0], #[-64, -64, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, -64, 0, 0, 0, 0, -128, 0], #[64, -64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified221 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, -2, 0, 0, 0, 0, 0], #[0, -2, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, -2, 0], #[0, 0, 0, 0, 0, -2, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 1, -1, 0, 0, 1, -1, 0], #[0, 1, -1, 0, 0, -1, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 128, 0, 0, 0, 0], #[-64, -64, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, -64, 0, 0, 0, 0, 128, 0], #[-64, 64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified222 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 2, 0, 0], #[0, 0, 2, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 2, 0, 0], #[0, 0, 2, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 1, 1, 0, 0, 1, 1, 0], #[0, 1, -1, 0, 0, 1, -1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, -1, 0, 0, 0, 1, 0, 0], #[0, 0, -1, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 0, 0, -128, 0, 0], #[64, -64, 0, 0, 0, 0, -128, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, 64, 0, 0, 0, 128, 0, 0], #[64, -64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified223 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 2, 0, 0], #[0, 0, 2, 0, 0, 0, -2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 2, 0, 0], #[0, 0, -2, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 1, 1, 0, 0, 1, -1, 0], #[0, 1, -1, 0, 0, 1, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, -1, 0, 0, 0, 1, 0, 0], #[0, 0, 1, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 0, 0, -128, 0, 0], #[64, -64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, 64, 0, 0, 0, 128, 0, 0], #[-64, 64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified224 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, -2, 0, 0], #[0, 0, 2, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -2, 0, 0, 0, 2, 0, 0], #[0, 0, 2, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 1, 1, 0, 0, -1, 1, 0], #[0, 1, -1, 0, 0, -1, -1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 1, 0, 0, 0, 1, 0, 0], #[0, 0, -1, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 0, 0, 128, 0, 0], #[64, -64, 0, 0, 0, 0, -128, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 0, 0, 0, 128, 0, 0], #[64, -64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified225 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, -2, 0, 0], #[0, 0, 2, 0, 0, 0, -2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -2, 0, 0, 0, 2, 0, 0], #[0, 0, -2, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 1, 1, 0, 0, -1, -1, 0], #[0, 1, -1, 0, 0, -1, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 1, 0, 0, 0, 1, 0, 0], #[0, 0, 1, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 0, 0, 128, 0, 0], #[64, -64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 0, 0, 0, 128, 0, 0], #[-64, 64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified226 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 2, 0], #[0, 0, 2, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 2, 0, 0], #[0, 2, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 1, 1, 0, 0, 1, 1, 0], #[0, 1, -1, 0, 0, -1, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, -1, 0, 0, 1, 0, 0], #[0, -1, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 0, 0, 0, -128, 0], #[64, -64, 0, 0, 0, -128, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, -64, 0, 0, 0, 128, 0, 0], #[64, 64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified227 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 2, 0], #[0, 0, 2, 0, 0, -2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -2, 0, 0, 2, 0, 0], #[0, 2, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 1, 1, 0, 0, -1, 1, 0], #[0, 1, -1, 0, 0, 1, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 1, 0, 0, 1, 0, 0], #[0, -1, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 0, 0, 0, -128, 0], #[64, -64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, 64, 0, 0, 0, 128, 0, 0], #[64, 64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified228 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, -2, 0], #[0, 0, 2, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 2, 0, 0], #[0, -2, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 1, 1, 0, 0, 1, -1, 0], #[0, 1, -1, 0, 0, -1, -1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, -1, 0, 0, 1, 0, 0], #[0, 1, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 0, 0, 0, 128, 0], #[64, -64, 0, 0, 0, -128, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, -64, 0, 0, 0, 128, 0, 0], #[-64, -64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified229 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, -2, 0], #[0, 0, 2, 0, 0, -2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -2, 0, 0, 2, 0, 0], #[0, -2, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 1, 1, 0, 0, -1, -1, 0], #[0, 1, -1, 0, 0, 1, -1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 1, 0, 0, 1, 0, 0], #[0, 1, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 0, 0, 0, 128, 0], #[64, -64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, 64, 0, 0, 0, 128, 0, 0], #[-64, -64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified230 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 1, 0, 1, 1, 0, 1, 0], #[0, 1, 0, 1, -1, 0, -1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, -1, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, -1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 0, -128, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 64, 0, 0, 128, 0, 0, 0], #[64, -64, 0, 0, 0, 0, -128, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, -64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified231 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, -2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, -2, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 1, 0, 1, 1, 0, -1, 0], #[0, 1, 0, 1, -1, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, -1, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 0, -128, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 64, 0, 0, 128, 0, 0, 0], #[64, -64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified232 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, -2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 1, 0, -1, 1, 0, 1, 0], #[0, 1, 0, -1, -1, 0, -1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 1, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, -1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, 0], #[64, -64, 0, 0, 0, 0, -128, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, -64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified233 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, -2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, -2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, -2, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 1, 0, -1, 1, 0, -1, 0], #[0, 1, 0, -1, -1, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 1, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, 0], #[64, -64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified234 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 2, 0], #[0, 2, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 1, 0, 1, 1, 0, 1, 0], #[0, 1, 0, -1, 1, 0, -1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, -1, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, -1, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 0, -128, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, -64, 0, 0, 0, 0, -128, 0], #[64, 64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, -64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified235 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, -2, 0], #[0, 2, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, -2, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 1, 0, 1, 1, 0, -1, 0], #[0, 1, 0, -1, 1, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, -1, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 1, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 0, -128, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, -64, 0, 0, 0, 0, 128, 0], #[64, 64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified236 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, -2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 2, 0], #[0, -2, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 1, 0, 1, -1, 0, 1, 0], #[0, 1, 0, -1, -1, 0, -1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, -1, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, -64, 0, 0, 0, 0, -128, 0], #[-64, -64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, -64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified237 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, -2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, -2, 0], #[0, -2, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, -2, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 1, 0, 1, -1, 0, -1, 0], #[0, 1, 0, -1, -1, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 1, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, -64, 0, 0, 0, 0, 128, 0], #[-64, -64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified238 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 2, 0, 0, 0], #[0, 0, 0, 2, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 1, 0, 1, 1, 0, 1, 0], #[0, 1, 0, -1, -1, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, -1, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, -1, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 0, 0, 0, -128, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, -64, 0, 0, -128, 0, 0, 0], #[64, -64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified239 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, -2, 0, 0, 0], #[0, 0, 0, -2, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 1, 0, 1, -1, 0, 1, 0], #[0, 1, 0, -1, 1, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, -1, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 0, 0, 0, -128, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, -64, 0, 0, 128, 0, 0, 0], #[-64, 64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified240 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, -2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 2, 0, 0, 0], #[0, 0, 0, 2, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -2, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 1, 0, 1, 1, 0, -1, 0], #[0, 1, 0, -1, -1, 0, -1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, -1, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 1, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, -64, 0, 0, -128, 0, 0, 0], #[64, -64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, -64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified241 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, -2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, -2, 0, 0, 0], #[0, 0, 0, -2, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -2, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 1, 0, 1, -1, 0, -1, 0], #[0, 1, 0, -1, 1, 0, -1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 1, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, -64, 0, 0, 128, 0, 0, 0], #[-64, 64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, -64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified242 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 2]], + stack := #[#[0, 1, 0, 1, 0, 1, 0, 1], #[0, 1, 0, 1, 0, -1, 0, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, -1, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, -1, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 0, -128, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, -64, 0, 0, 0, 0, 0, -128], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, -64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified243 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, -2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, -2, 0, 2]], + stack := #[#[0, 1, 0, 1, 0, 1, 0, -1], #[0, 1, 0, 1, 0, -1, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, -1, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 1, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 0, -128, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, -64, 0, 0, 0, 0, 0, 128], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified244 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, -2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 2]], + stack := #[#[0, 1, 0, -1, 0, 1, 0, 1], #[0, 1, 0, -1, 0, -1, 0, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 1, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, -1, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, -64, 0, 0, 0, 0, 0, -128], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, -64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified245 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, -2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, -2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, -2, 0, 2]], + stack := #[#[0, 1, 0, -1, 0, 1, 0, -1], #[0, 1, 0, -1, 0, -1, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 1, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 1, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, -64, 0, 0, 0, 0, 0, 128], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified246 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 2]], + stack := #[#[0, 1, 0, 1, 0, 1, 0, 1], #[0, 1, 0, -1, 0, 1, 0, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, -1, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, -1, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 0, 0, -128, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, -64, 0, 0, 0, 0, 0, -128], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, 64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, -64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified247 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, -2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, -2, 0, 0, 0, 2]], + stack := #[#[0, 1, 0, 1, 0, 1, 0, -1], #[0, 1, 0, -1, 0, 1, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, -1, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 1, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 0, 0, -128, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, -64, 0, 0, 0, 0, 0, 128], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, 64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified248 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, -2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -2, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 2]], + stack := #[#[0, 1, 0, 1, 0, -1, 0, 1], #[0, 1, 0, -1, 0, -1, 0, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 1, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, -1, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, -64, 0, 0, 0, 0, 0, -128], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, -64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified249 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, -2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, -2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -2, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, -2, 0, 0, 0, 2]], + stack := #[#[0, 1, 0, 1, 0, -1, 0, -1], #[0, 1, 0, -1, 0, -1, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 1, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 1, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, -64, 0, 0, 0, 0, 0, 128], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified250 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 2]], + stack := #[#[0, 1, 0, 1, 0, 1, 0, 1], #[0, 1, 0, -1, 0, -1, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, -1, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, -1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 0, 0, 0, 0, -128], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, -64, 0, 0, 0, -128, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, -64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified251 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, -2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, -2, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 2]], + stack := #[#[0, 1, 0, 1, 0, -1, 0, 1], #[0, 1, 0, -1, 0, 1, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 1, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, -1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 0, 0, 0, 0, -128], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, -64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, 64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified252 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, -2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -2, 0, 0, 0, 0, 0, 2]], + stack := #[#[0, 1, 0, 1, 0, 1, 0, -1], #[0, 1, 0, -1, 0, -1, 0, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, -1, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 0, 0, 0, 0, 128], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, -64, 0, 0, 0, -128, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, -64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, -64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified253 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, -2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, -2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, -2, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -2, 0, 0, 0, 0, 0, 2]], + stack := #[#[0, 1, 0, 1, 0, -1, 0, -1], #[0, 1, 0, -1, 0, 1, 0, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 1, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[64, 64, 0, 0, 0, 0, 0, 128], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, -64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, 64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, -64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified254 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 2, 0, 0, 0, 0], #[0, 0, 2, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 2, 0, 0], #[0, 0, 0, 0, 2, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 1, 1, 1, 1, 0, 0], #[0, 0, 1, 1, -1, -1, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, -1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, -1, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 64, 0, 0, -128, 0, 0, 0], #[64, 64, 0, 0, 128, 0, 0, 0], #[64, -64, 0, 0, 0, -128, 0, 0], #[64, -64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified255 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 2, 0, 0, 0, 0], #[0, 0, 2, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, -2, 0, 0], #[0, 0, 0, 0, -2, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 1, 1, 1, -1, 0, 0], #[0, 0, 1, 1, -1, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, -1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 64, 0, 0, -128, 0, 0, 0], #[64, 64, 0, 0, 128, 0, 0, 0], #[64, -64, 0, 0, 0, 128, 0, 0], #[-64, 64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified256 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, -2, 0, 0, 0, 0], #[0, 0, -2, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 2, 0, 0], #[0, 0, 0, 0, 2, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 1, -1, 1, 1, 0, 0], #[0, 0, 1, -1, -1, -1, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, -1, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 64, 0, 0, 128, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, 0], #[64, -64, 0, 0, 0, -128, 0, 0], #[64, -64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified257 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, -2, 0, 0, 0, 0], #[0, 0, -2, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, -2, 0, 0], #[0, 0, 0, 0, -2, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 1, -1, 1, -1, 0, 0], #[0, 0, 1, -1, -1, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 64, 0, 0, 128, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, 0], #[64, -64, 0, 0, 0, 128, 0, 0], #[-64, 64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified258 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 2, 0, 0, 0], #[0, 0, 0, 2, 0, 2, 0, 0], #[0, 0, 2, 0, 2, 0, 0, 0], #[0, 0, 0, 2, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 1, 1, 1, 1, 0, 0], #[0, 0, 1, -1, 1, -1, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, -1, 0, 1, 0, 0, 0], #[0, 0, 0, -1, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 64, 0, 0, -128, 0, 0, 0], #[64, -64, 0, 0, 0, -128, 0, 0], #[64, 64, 0, 0, 128, 0, 0, 0], #[64, -64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified259 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 2, 0, 0, 0], #[0, 0, 0, 2, 0, -2, 0, 0], #[0, 0, 2, 0, 2, 0, 0, 0], #[0, 0, 0, -2, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 1, 1, 1, -1, 0, 0], #[0, 0, 1, -1, 1, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, -1, 0, 1, 0, 0, 0], #[0, 0, 0, 1, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 64, 0, 0, -128, 0, 0, 0], #[64, -64, 0, 0, 0, 128, 0, 0], #[64, 64, 0, 0, 128, 0, 0, 0], #[-64, 64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified260 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, -2, 0, 0, 0], #[0, 0, 0, 2, 0, 2, 0, 0], #[0, 0, -2, 0, 2, 0, 0, 0], #[0, 0, 0, 2, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 1, 1, -1, 1, 0, 0], #[0, 0, 1, -1, -1, -1, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 1, 0, 0, 0], #[0, 0, 0, -1, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 64, 0, 0, 128, 0, 0, 0], #[64, -64, 0, 0, 0, -128, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, 0], #[64, -64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified261 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, -2, 0, 0, 0], #[0, 0, 0, 2, 0, -2, 0, 0], #[0, 0, -2, 0, 2, 0, 0, 0], #[0, 0, 0, -2, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 1, 1, -1, -1, 0, 0], #[0, 0, 1, -1, -1, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 1, 0, 0, 0], #[0, 0, 0, 1, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 64, 0, 0, 128, 0, 0, 0], #[64, -64, 0, 0, 0, 128, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, 0], #[-64, 64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified262 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 2, 0, 0], #[0, 0, 0, 2, 2, 0, 0, 0], #[0, 0, 0, 2, 2, 0, 0, 0], #[0, 0, 2, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 1, 1, 1, 1, 0, 0], #[0, 0, 1, -1, -1, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, -1, 1, 0, 0, 0], #[0, 0, -1, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 64, 0, 0, 0, -128, 0, 0], #[64, -64, 0, 0, -128, 0, 0, 0], #[64, -64, 0, 0, 128, 0, 0, 0], #[64, 64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified263 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 2, 0, 0], #[0, 0, 0, 2, -2, 0, 0, 0], #[0, 0, 0, -2, 2, 0, 0, 0], #[0, 0, 2, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 1, 1, -1, 1, 0, 0], #[0, 0, 1, -1, 1, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 1, 0, 0, 0], #[0, 0, -1, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 64, 0, 0, 0, -128, 0, 0], #[64, -64, 0, 0, 128, 0, 0, 0], #[-64, 64, 0, 0, 128, 0, 0, 0], #[64, 64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified264 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, -2, 0, 0], #[0, 0, 0, 2, 2, 0, 0, 0], #[0, 0, 0, 2, 2, 0, 0, 0], #[0, 0, -2, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 1, 1, 1, -1, 0, 0], #[0, 0, 1, -1, -1, -1, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, -1, 1, 0, 0, 0], #[0, 0, 1, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 64, 0, 0, 0, 128, 0, 0], #[64, -64, 0, 0, -128, 0, 0, 0], #[64, -64, 0, 0, 128, 0, 0, 0], #[-64, -64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified265 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, -2, 0, 0], #[0, 0, 0, 2, -2, 0, 0, 0], #[0, 0, 0, -2, 2, 0, 0, 0], #[0, 0, -2, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 1, 1, -1, -1, 0, 0], #[0, 0, 1, -1, 1, -1, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 1, 0, 0, 0], #[0, 0, 1, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 64, 0, 0, 0, 128, 0, 0], #[64, -64, 0, 0, 128, 0, 0, 0], #[-64, 64, 0, 0, 128, 0, 0, 0], #[-64, -64, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified266 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 2, 0, 0, 0, 0], #[0, 0, 2, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 2], #[0, 0, 0, 0, 0, 0, 2, 2]], + stack := #[#[0, 0, 1, 1, 0, 0, 1, 1], #[0, 0, 1, 1, 0, 0, -1, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, -1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, -1, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 64, 0, 0, -128, 0, 0, 0], #[64, 64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, -64, 0, 0, 0, 0, 0, -128], #[64, -64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified267 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 2, 0, 0, 0, 0], #[0, 0, 2, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, -2], #[0, 0, 0, 0, 0, 0, -2, 2]], + stack := #[#[0, 0, 1, 1, 0, 0, 1, -1], #[0, 0, 1, 1, 0, 0, -1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, -1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 64, 0, 0, -128, 0, 0, 0], #[64, 64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, -64, 0, 0, 0, 0, 0, 128], #[-64, 64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified268 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, -2, 0, 0, 0, 0], #[0, 0, -2, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 2], #[0, 0, 0, 0, 0, 0, 2, 2]], + stack := #[#[0, 0, 1, -1, 0, 0, 1, 1], #[0, 0, 1, -1, 0, 0, -1, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, -1, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 64, 0, 0, 128, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, -64, 0, 0, 0, 0, 0, -128], #[64, -64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified269 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, -2, 0, 0, 0, 0], #[0, 0, -2, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, -2], #[0, 0, 0, 0, 0, 0, -2, 2]], + stack := #[#[0, 0, 1, -1, 0, 0, 1, -1], #[0, 0, 1, -1, 0, 0, -1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 64, 0, 0, 128, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, -64, 0, 0, 0, 0, 0, 128], #[-64, 64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified270 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 2, 0], #[0, 0, 0, 2, 0, 0, 0, 2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 2, 0], #[0, 0, 0, 2, 0, 0, 0, 2]], + stack := #[#[0, 0, 1, 1, 0, 0, 1, 1], #[0, 0, 1, -1, 0, 0, 1, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, -1, 0, 0, 0, 1, 0], #[0, 0, 0, -1, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 64, 0, 0, 0, 0, -128, 0], #[64, -64, 0, 0, 0, 0, 0, -128], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 64, 0, 0, 0, 0, 128, 0], #[64, -64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified271 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 2, 0], #[0, 0, 0, 2, 0, 0, 0, -2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 2, 0], #[0, 0, 0, -2, 0, 0, 0, 2]], + stack := #[#[0, 0, 1, 1, 0, 0, 1, -1], #[0, 0, 1, -1, 0, 0, 1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, -1, 0, 0, 0, 1, 0], #[0, 0, 0, 1, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 64, 0, 0, 0, 0, -128, 0], #[64, -64, 0, 0, 0, 0, 0, 128], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 64, 0, 0, 0, 0, 128, 0], #[-64, 64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified272 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, -2, 0], #[0, 0, 0, 2, 0, 0, 0, 2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -2, 0, 0, 0, 2, 0], #[0, 0, 0, 2, 0, 0, 0, 2]], + stack := #[#[0, 0, 1, 1, 0, 0, -1, 1], #[0, 0, 1, -1, 0, 0, -1, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 1, 0, 0, 0, 1, 0], #[0, 0, 0, -1, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 64, 0, 0, 0, 0, 128, 0], #[64, -64, 0, 0, 0, 0, 0, -128], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, -64, 0, 0, 0, 0, 128, 0], #[64, -64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified273 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, -2, 0], #[0, 0, 0, 2, 0, 0, 0, -2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -2, 0, 0, 0, 2, 0], #[0, 0, 0, -2, 0, 0, 0, 2]], + stack := #[#[0, 0, 1, 1, 0, 0, -1, -1], #[0, 0, 1, -1, 0, 0, -1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 1, 0, 0, 0, 1, 0], #[0, 0, 0, 1, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 64, 0, 0, 0, 0, 128, 0], #[64, -64, 0, 0, 0, 0, 0, 128], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, -64, 0, 0, 0, 0, 128, 0], #[-64, 64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified274 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 2], #[0, 0, 0, 2, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 2, 0], #[0, 0, 2, 0, 0, 0, 0, 2]], + stack := #[#[0, 0, 1, 1, 0, 0, 1, 1], #[0, 0, 1, -1, 0, 0, -1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, -1, 0, 0, 1, 0], #[0, 0, -1, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 64, 0, 0, 0, 0, 0, -128], #[64, -64, 0, 0, 0, 0, -128, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, -64, 0, 0, 0, 0, 128, 0], #[64, 64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified275 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 2], #[0, 0, 0, 2, 0, 0, -2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, -2, 0, 0, 2, 0], #[0, 0, 2, 0, 0, 0, 0, 2]], + stack := #[#[0, 0, 1, 1, 0, 0, -1, 1], #[0, 0, 1, -1, 0, 0, 1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 1, 0, 0, 1, 0], #[0, 0, -1, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 64, 0, 0, 0, 0, 0, -128], #[64, -64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 64, 0, 0, 0, 0, 128, 0], #[64, 64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified276 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, -2], #[0, 0, 0, 2, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 2, 0], #[0, 0, -2, 0, 0, 0, 0, 2]], + stack := #[#[0, 0, 1, 1, 0, 0, 1, -1], #[0, 0, 1, -1, 0, 0, -1, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, -1, 0, 0, 1, 0], #[0, 0, 1, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 64, 0, 0, 0, 0, 0, 128], #[64, -64, 0, 0, 0, 0, -128, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, -64, 0, 0, 0, 0, 128, 0], #[-64, -64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified277 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, -2], #[0, 0, 0, 2, 0, 0, -2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, -2, 0, 0, 2, 0], #[0, 0, -2, 0, 0, 0, 0, 2]], + stack := #[#[0, 0, 1, 1, 0, 0, -1, -1], #[0, 0, 1, -1, 0, 0, 1, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 1, 0, 0, 1, 0], #[0, 0, 1, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 64, 0, 0, 0, 0, 0, 128], #[64, -64, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 64, 0, 0, 0, 0, 128, 0], #[-64, -64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified278 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 2, 0, 0], #[0, 0, 0, 0, 2, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 2], #[0, 0, 0, 0, 0, 0, 2, 2]], + stack := #[#[0, 0, 0, 0, 1, 1, 1, 1], #[0, 0, 0, 0, 1, 1, -1, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, -1, 1, 0, 0], #[0, 0, 0, 0, 0, 0, -1, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 64, 0, 0, 0, 0, -128, 0], #[64, 64, 0, 0, 0, 0, 128, 0], #[64, -64, 0, 0, 0, 0, 0, -128], #[64, -64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified279 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 2, 0, 0], #[0, 0, 0, 0, 2, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, -2], #[0, 0, 0, 0, 0, 0, -2, 2]], + stack := #[#[0, 0, 0, 0, 1, 1, 1, -1], #[0, 0, 0, 0, 1, 1, -1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, -1, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 64, 0, 0, 0, 0, -128, 0], #[64, 64, 0, 0, 0, 0, 128, 0], #[64, -64, 0, 0, 0, 0, 0, 128], #[-64, 64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified280 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, -2, 0, 0], #[0, 0, 0, 0, -2, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 2], #[0, 0, 0, 0, 0, 0, 2, 2]], + stack := #[#[0, 0, 0, 0, 1, -1, 1, 1], #[0, 0, 0, 0, 1, -1, -1, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 1, 0, 0], #[0, 0, 0, 0, 0, 0, -1, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 64, 0, 0, 0, 0, 128, 0], #[-64, -64, 0, 0, 0, 0, 128, 0], #[64, -64, 0, 0, 0, 0, 0, -128], #[64, -64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified281 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, -2, 0, 0], #[0, 0, 0, 0, -2, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, -2], #[0, 0, 0, 0, 0, 0, -2, 2]], + stack := #[#[0, 0, 0, 0, 1, -1, 1, -1], #[0, 0, 0, 0, 1, -1, -1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 64, 0, 0, 0, 0, 128, 0], #[-64, -64, 0, 0, 0, 0, 128, 0], #[64, -64, 0, 0, 0, 0, 0, 128], #[-64, 64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified282 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 2, 0], #[0, 0, 0, 0, 0, 2, 0, 2], #[0, 0, 0, 0, 2, 0, 2, 0], #[0, 0, 0, 0, 0, 2, 0, 2]], + stack := #[#[0, 0, 0, 0, 1, 1, 1, 1], #[0, 0, 0, 0, 1, -1, 1, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, -1, 0, 1, 0], #[0, 0, 0, 0, 0, -1, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 64, 0, 0, 0, 0, -128, 0], #[64, -64, 0, 0, 0, 0, 0, -128], #[64, 64, 0, 0, 0, 0, 128, 0], #[64, -64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified283 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 2, 0], #[0, 0, 0, 0, 0, 2, 0, -2], #[0, 0, 0, 0, 2, 0, 2, 0], #[0, 0, 0, 0, 0, -2, 0, 2]], + stack := #[#[0, 0, 0, 0, 1, 1, 1, -1], #[0, 0, 0, 0, 1, -1, 1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, -1, 0, 1, 0], #[0, 0, 0, 0, 0, 1, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 64, 0, 0, 0, 0, -128, 0], #[64, -64, 0, 0, 0, 0, 0, 128], #[64, 64, 0, 0, 0, 0, 128, 0], #[-64, 64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified284 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, -2, 0], #[0, 0, 0, 0, 0, 2, 0, 2], #[0, 0, 0, 0, -2, 0, 2, 0], #[0, 0, 0, 0, 0, 2, 0, 2]], + stack := #[#[0, 0, 0, 0, 1, 1, -1, 1], #[0, 0, 0, 0, 1, -1, -1, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 1, 0], #[0, 0, 0, 0, 0, -1, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 64, 0, 0, 0, 0, 128, 0], #[64, -64, 0, 0, 0, 0, 0, -128], #[-64, -64, 0, 0, 0, 0, 128, 0], #[64, -64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified285 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, -2, 0], #[0, 0, 0, 0, 0, 2, 0, -2], #[0, 0, 0, 0, -2, 0, 2, 0], #[0, 0, 0, 0, 0, -2, 0, 2]], + stack := #[#[0, 0, 0, 0, 1, 1, -1, -1], #[0, 0, 0, 0, 1, -1, -1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 1, 0], #[0, 0, 0, 0, 0, 1, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 64, 0, 0, 0, 0, 128, 0], #[64, -64, 0, 0, 0, 0, 0, 128], #[-64, -64, 0, 0, 0, 0, 128, 0], #[-64, 64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified286 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 2], #[0, 0, 0, 0, 0, 2, 2, 0], #[0, 0, 0, 0, 0, 2, 2, 0], #[0, 0, 0, 0, 2, 0, 0, 2]], + stack := #[#[0, 0, 0, 0, 1, 1, 1, 1], #[0, 0, 0, 0, 1, -1, -1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, -1, 1, 0], #[0, 0, 0, 0, -1, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 64, 0, 0, 0, 0, 0, -128], #[64, -64, 0, 0, 0, 0, -128, 0], #[64, -64, 0, 0, 0, 0, 128, 0], #[64, 64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified287 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 2], #[0, 0, 0, 0, 0, 2, -2, 0], #[0, 0, 0, 0, 0, -2, 2, 0], #[0, 0, 0, 0, 2, 0, 0, 2]], + stack := #[#[0, 0, 0, 0, 1, 1, -1, 1], #[0, 0, 0, 0, 1, -1, 1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 1, 0], #[0, 0, 0, 0, -1, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 64, 0, 0, 0, 0, 0, -128], #[64, -64, 0, 0, 0, 0, 128, 0], #[-64, 64, 0, 0, 0, 0, 128, 0], #[64, 64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified288 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, -2], #[0, 0, 0, 0, 0, 2, 2, 0], #[0, 0, 0, 0, 0, 2, 2, 0], #[0, 0, 0, 0, -2, 0, 0, 2]], + stack := #[#[0, 0, 0, 0, 1, 1, 1, -1], #[0, 0, 0, 0, 1, -1, -1, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, -1, 1, 0], #[0, 0, 0, 0, 1, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 64, 0, 0, 0, 0, 0, 128], #[64, -64, 0, 0, 0, 0, -128, 0], #[64, -64, 0, 0, 0, 0, 128, 0], #[-64, -64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified289 : CertifiedFrame := + ⟨{ dimension := 2, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, -2], #[0, 0, 0, 0, 0, 2, -2, 0], #[0, 0, 0, 0, 0, -2, 2, 0], #[0, 0, 0, 0, -2, 0, 0, 2]], + stack := #[#[0, 0, 0, 0, 1, 1, -1, -1], #[0, 0, 0, 0, 1, -1, 1, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 1, 0], #[0, 0, 0, 0, 1, 0, 0, 1]], + inverse256 := #[#[0, 0, 256, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 64, 0, 0, 0, 0, 0, 128], #[64, -64, 0, 0, 0, 0, 128, 0], #[-64, 64, 0, 0, 0, 0, 128, 0], #[-64, -64, 0, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified290 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[2, 2, 0, 0, 0, 0, 0, 0], #[2, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[-1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, -64, 128, -128, 0, 0, 0, 0], #[-64, -64, 128, 128, 0, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified291 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[2, -2, 0, 0, 0, 0, 0, 0], #[-2, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[1, -1, 1, 1, 0, 0, 0, 0], #[1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, -64, 128, 128, 0, 0, 0, 0], #[64, 64, -128, 128, 0, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified292 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[2, 0, 2, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[2, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[-1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, -64, 128, -128, 0, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 128, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified293 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[2, 0, -2, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[-2, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[1, 1, -1, 1, 0, 0, 0, 0], #[1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, -64, 128, 128, 0, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[64, 64, -128, 128, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified294 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[2, 0, 0, 2, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[-1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, -64, 128, -128, 0, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified295 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[2, 0, 0, -2, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[-2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[1, 1, 1, -1, 0, 0, 0, 0], #[1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, -64, 128, 128, 0, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 64, -128, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified296 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 2, 0, 0, 0, 0, 0], #[0, 2, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[0, -1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, -128, 0, 0, 0, 0], #[-64, -64, 128, 128, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified297 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, -2, 0, 0, 0, 0, 0], #[0, -2, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[1, 1, -1, 1, 0, 0, 0, 0], #[0, 1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 128, 0, 0, 0, 0], #[64, 64, -128, 128, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified298 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 2, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[0, -1, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, -128, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified299 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, -2, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, -2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[1, 1, 1, -1, 0, 0, 0, 0], #[0, 1, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 128, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 64, -128, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified300 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 2, 0, 0, 0, 0], #[0, 0, 2, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[0, 0, -1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, -128, 0, 0, 0, 0], #[-64, -64, 128, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified301 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, -2, 0, 0, 0, 0], #[0, 0, -2, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[1, 1, 1, -1, 0, 0, 0, 0], #[0, 0, 1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 128, 0, 0, 0, 0], #[64, 64, -128, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified302 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[2, 2, 0, 0, 0, 0, 0, 0], #[2, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, 1, 0, 0, 1, 1, 0, 0], #[-1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, -64, 128, -128, 0, 0, 0, 0], #[-64, -64, 128, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified303 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[2, -2, 0, 0, 0, 0, 0, 0], #[-2, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, -1, 0, 0, 1, 1, 0, 0], #[1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, -64, 128, 128, 0, 0, 0, 0], #[64, 64, -128, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified304 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[2, 0, 0, 0, 2, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[2, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, 1, 0, 0, 1, 1, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[-1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, -64, 128, 0, 0, -128, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, 128, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified305 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[2, 0, 0, 0, -2, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-2, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, 1, 0, 0, -1, 1, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, -64, 128, 0, 0, 128, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, 64, -128, 0, 0, 128, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified306 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[2, 0, 0, 0, 0, 2, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[1, 1, 0, 0, 1, 1, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[-1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, -64, 128, 0, 0, -128, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified307 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[2, 0, 0, 0, 0, -2, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[-2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[1, 1, 0, 0, 1, -1, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, -64, 128, 0, 0, 128, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 64, -128, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified308 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, 1, 0, 0, 1, 1, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, -1, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, -128, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, 128, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified309 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, -2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -2, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, 1, 0, 0, -1, 1, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 1, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 128, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, 64, -128, 0, 0, 128, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified310 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 2, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[1, 1, 0, 0, 1, 1, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, -1, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, -128, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified311 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, -2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, -2, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[1, 1, 0, 0, 1, -1, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 128, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 64, -128, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified312 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 2, 0, 0], #[0, 0, 0, 0, 2, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[1, 1, 0, 0, 1, 1, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, -1, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, -128, 0, 0], #[-64, -64, 128, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified313 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, -2, 0, 0], #[0, 0, 0, 0, -2, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[1, 1, 0, 0, 1, -1, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, 128, 0, 0], #[64, 64, -128, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified314 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[2, 2, 0, 0, 0, 0, 0, 0], #[2, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 0, 0, 0, 0, 1, 1], #[-1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0]], + inverse256 := #[#[-64, -64, 128, -128, 0, 0, 0, 0], #[-64, -64, 128, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified315 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[2, -2, 0, 0, 0, 0, 0, 0], #[-2, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, -1, 0, 0, 0, 0, 1, 1], #[1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0]], + inverse256 := #[#[-64, -64, 128, 128, 0, 0, 0, 0], #[64, 64, -128, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified316 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[2, 0, 0, 0, 0, 0, 2, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[2, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 0, 0, 0, 0, 1, 1], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[-1, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[-64, -64, 128, 0, 0, 0, 0, -128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, -64, 128, 0, 0, 0, 0, 128], #[0, 128, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified317 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[2, 0, 0, 0, 0, 0, -2, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-2, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 0, 0, 0, 0, -1, 1], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[-64, -64, 128, 0, 0, 0, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 64, -128, 0, 0, 0, 0, 128], #[0, 128, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified318 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[2, 0, 0, 0, 0, 0, 0, 2], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[2, 0, 0, 0, 0, 0, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 1, 0, 0, 0, 0, 1, 1], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[-1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, -64, 128, 0, 0, 0, 0, -128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified319 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[2, 0, 0, 0, 0, 0, 0, -2], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[-2, 0, 0, 0, 0, 0, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 1, 0, 0, 0, 0, 1, -1], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, -64, 128, 0, 0, 0, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 64, -128, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified320 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 2, 0, 0, 0, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 1, 0, 0, 0, 0, 1, 1], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, -1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, -128], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified321 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, -2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, -2, 0, 0, 0, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 1, 0, 0, 0, 0, 1, -1], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, 128], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 64, -128, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified322 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 0, 0, 0, 0, 1, 1], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, -1, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, -128], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, -64, 128, 0, 0, 0, 0, 128], #[0, 128, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified323 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, -2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -2, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 0, 0, 0, 0, -1, 1], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 1, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, 128], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 64, -128, 0, 0, 0, 0, 128], #[0, 128, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified324 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 2], #[0, 0, 0, 0, 0, 0, 2, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[1, 1, 0, 0, 0, 0, 1, 1], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, -1, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, -64, 128, 0, 0, 0, 0, -128], #[-64, -64, 128, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified325 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, -2], #[0, 0, 0, 0, 0, 0, -2, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[1, 1, 0, 0, 0, 0, 1, -1], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, -64, 128, 0, 0, 0, 0, 128], #[64, 64, -128, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified326 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[2, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[2, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 0, 1, 0, 1, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[-1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, -64, 128, 0, -128, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 128, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified327 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[2, 0, -2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-2, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 0, -1, 0, 1, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, -64, 128, 0, 128, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 64, -128, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified328 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[2, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[2, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 0, 1, 0, 1, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[-1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, -64, 128, 0, 0, -128, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified329 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[2, 0, 0, 0, -2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-2, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 0, 1, 0, -1, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, -64, 128, 0, 0, 128, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, 64, -128, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified330 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[2, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[2, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[1, 0, 1, 0, 1, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[-1, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, -64, 128, 0, 0, 0, -128, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, -64, 128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified331 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[2, 0, 0, 0, 0, 0, -2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-2, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[1, 0, 1, 0, 1, 0, -1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, -64, 128, 0, 0, 0, 128, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 64, -128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified332 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 0, 1, 0, 1, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, -1, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, -128, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified333 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, -2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -2, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 0, 1, 0, -1, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 1, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, 64, -128, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified334 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[1, 0, 1, 0, 1, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, -1, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, -128, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, -64, 128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified335 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, -2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -2, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[1, 0, 1, 0, 1, 0, -1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 1, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 64, -128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified336 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[1, 0, 1, 0, 1, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, -1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, -128, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, -64, 128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified337 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, -2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, -2, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[1, 0, 1, 0, 1, 0, -1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 64, -128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified338 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[2, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[2, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 0, 1, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[-1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[-64, -64, 128, 0, -128, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 128, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 128, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified339 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[2, 0, -2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-2, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, -1, 0, 0, 1, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[-64, -64, 128, 0, 128, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[64, 64, -128, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 128, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified340 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 0, 1, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[-1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[-64, -64, 128, 0, 0, 0, -128, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, -64, 128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 128, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified341 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[2, 0, 0, 0, 0, -2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 0, -1, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[-64, -64, 128, 0, 0, 0, 128, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 64, -128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 128, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified342 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[2, 0, 0, 0, 0, 0, 0, 2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[2, 0, 0, 0, 0, 0, 0, 2]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, 0, 1, 0, 0, 1, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[-1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, -64, 128, 0, 0, 0, 0, -128], #[0, 0, 0, 256, 0, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, -64, 128, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified343 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[2, 0, 0, 0, 0, 0, 0, -2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-2, 0, 0, 0, 0, 0, 0, 2]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, 0, 1, 0, 0, 1, 0, -1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, -64, 128, 0, 0, 0, 0, 128], #[0, 0, 0, 256, 0, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 64, -128, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified344 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, 0, 1, 0, 0, 1, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, -1, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, -128], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, -64, 128, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified345 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, -2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -2, 0, 0, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, 0, 1, 0, 0, 1, 0, -1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 1, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, 128], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 64, -128, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified346 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 0, 1, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, -1, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, -128, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, -64, 128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 128, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified347 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, -2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -2, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 0, -1, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 1, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 64, -128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 128, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified348 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[1, 0, 1, 0, 0, 1, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, -1, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, -128], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, -64, 128, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified349 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, -2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, -2, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[1, 0, 1, 0, 0, 1, 0, -1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 1, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, 128], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 64, -128, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified350 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 0, 1, 1, 0, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[-1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[-64, -64, 128, 0, 0, -128, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, 128, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 128, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified351 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[2, 0, 0, -2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 0, -1, 1, 0, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[-64, -64, 128, 0, 0, 128, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, 64, -128, 0, 0, 128, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 128, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified352 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[2, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[2, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 0, 1, 1, 0, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[-1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[-64, -64, 128, 0, 0, -128, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 128, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified353 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[2, 0, 0, 0, -2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[-2, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 0, 1, -1, 0, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[-64, -64, 128, 0, 0, 128, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[64, 64, -128, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 128, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified354 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[2, 0, 0, 0, 0, 0, 0, 2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[2, 0, 0, 0, 0, 0, 0, 2]], + stack := #[#[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[1, 0, 0, 1, 1, 0, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[-1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, -64, 128, 0, 0, 0, 0, -128], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, -64, 128, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified355 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[2, 0, 0, 0, 0, 0, 0, -2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-2, 0, 0, 0, 0, 0, 0, 2]], + stack := #[#[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[1, 0, 0, 1, 1, 0, 0, -1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, -64, 128, 0, 0, 0, 0, 128], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 64, -128, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified356 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[1, 0, 0, 1, 1, 0, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, -1, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, -128], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, -64, 128, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified357 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, -2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, -2, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[1, 0, 0, 1, 1, 0, 0, -1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 1, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, 128], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 64, -128, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified358 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 2, 0, 0, 0], #[0, 0, 0, 2, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 0, 1, 1, 0, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, -1, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, -128, 0, 0], #[-64, -64, 128, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 128, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified359 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, -2, 0, 0, 0], #[0, 0, 0, -2, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 0, 1, -1, 0, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, 128, 0, 0], #[64, 64, -128, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 128, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified360 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 2], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[1, 0, 0, 1, 1, 0, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, -1, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, -128], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, -64, 128, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified361 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, -2], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, -2, 0, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[1, 0, 0, 1, 1, 0, 0, -1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 1, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, 128], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 64, -128, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified362 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 0, 0, 1, 0, 1, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[-1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, -64, 128, 0, 0, -128, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified363 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[2, 0, 0, -2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 0, 0, -1, 0, 1, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, -64, 128, 0, 0, 128, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, 64, -128, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified364 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 0, 0, 1, 0, 1, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[-1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, -64, 128, 0, 0, 0, -128, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, -64, 128, 0, 0, 0, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified365 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[2, 0, 0, 0, 0, -2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 0, 0, 1, 0, -1, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, -64, 128, 0, 0, 0, 128, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 64, -128, 0, 0, 0, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified366 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[2, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[2, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, 0, 0, 1, 0, 1, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[-1, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, -64, 128, 0, 0, 0, -128, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified367 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[2, 0, 0, 0, 0, 0, -2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[-2, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, 0, 0, 1, 0, 1, -1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[1, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, -64, 128, 0, 0, 0, 128, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 64, -128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified368 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 2, 0], #[0, 0, 0, 0, 0, 2, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[1, 0, 0, 1, 0, 1, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, -1, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, -64, 128, 0, 0, 0, -128, 0], #[-64, -64, 128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified369 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, -2, 0], #[0, 0, 0, 0, 0, -2, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[1, 0, 0, 1, 0, 1, -1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, -64, 128, 0, 0, 0, 128, 0], #[64, 64, -128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified370 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 2, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, 0, 0, 1, 0, 1, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, -1, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, -128, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified371 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, -2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, -2, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, 0, 0, 1, 0, 1, -1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 64, -128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified372 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 0, 0, 1, 0, 1, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, -1, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, -128, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, -64, 128, 0, 0, 0, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified373 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, -2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, -2, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 0, 0, 1, 0, -1, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 1, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 64, -128, 0, 0, 0, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified374 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 2, 0, 0, 0, 0, 0], #[0, 2, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 128, 0, -128, 0, 0, 0], #[-64, -64, 128, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 128, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified375 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, -2, 0, 0, 0, 0, 0], #[0, -2, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, -1, 0, 1, 0, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 128, 0, 128, 0, 0, 0], #[64, 64, -128, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 128, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified376 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 2, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, -1, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, -128, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 128, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified377 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, -2, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -2, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, -1, 0, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 1, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 128, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, 64, -128, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 128, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified378 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 2], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 2]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, -1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, -128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, -64, 128, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified379 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, -2], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -2, 0, 0, 0, 0, 0, 2]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 64, -128, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified380 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, -1, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, -128, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 128, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified381 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, -2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -2, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, -1, 0, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 1, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, 64, -128, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 128, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified382 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, -1, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, -128], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, -64, 128, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified383 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, -2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -2, 0, 0, 0, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 1, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, 128], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 64, -128, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified384 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, -1, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, -128], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, -64, 128, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified385 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, -2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, -2, 0, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 1, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, 128], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 64, -128, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified386 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 2, 0, 0, 0, 0, 0], #[0, 2, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 0, 1, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 128, 0, -128, 0, 0, 0], #[-64, -64, 128, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified387 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, -2, 0, 0, 0, 0, 0], #[0, -2, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, -1, 0, 0, 1, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 128, 0, 128, 0, 0, 0], #[64, 64, -128, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified388 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 2, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 0, 1, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, -1, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, -128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, -64, 128, 0, 0, 0, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified389 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, -2, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -2, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 0, -1, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 1, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 64, -128, 0, 0, 0, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified390 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 2, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 2, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 1, 1, 0, 0, 1, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, -1, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, -128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified391 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, -2, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, -2, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 1, 1, 0, 0, 1, -1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 64, -128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified392 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 2, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 1, 1, 0, 0, 1, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, -1, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, -128, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified393 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, -2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, -2, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 1, 1, 0, 0, 1, -1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 64, -128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified394 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 0, 1, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, -1, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, -128, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, -64, 128, 0, 0, 0, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified395 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, -2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -2, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 0, -1, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 1, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 64, -128, 0, 0, 0, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified396 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 2, 0], #[0, 0, 0, 0, 0, 2, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 1, 1, 0, 0, 1, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, -1, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, -64, 128, 0, 0, 0, -128, 0], #[-64, -64, 128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified397 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, -2, 0], #[0, 0, 0, 0, 0, -2, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 1, 1, 0, 0, 1, -1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, -64, 128, 0, 0, 0, 128, 0], #[64, 64, -128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified398 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 0, 1, 1, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, -1, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, -128, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, 128, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified399 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, -2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 0, -1, 1, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 1, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, 64, -128, 0, 0, 128, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified400 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 2, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 0, 1, 1, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, -1, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, -128, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified401 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, -2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, -2, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 0, 1, -1, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[64, 64, -128, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified402 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 1, 0, 1, 1, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, -1, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, -128, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, -64, 128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified403 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, -2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -2, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 1, 0, 1, 1, 0, -1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 1, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 64, -128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified404 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 1, 0, 1, 1, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, -1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, -128, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, -64, 128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified405 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, -2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, -2, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 1, 0, 1, 1, 0, -1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 64, -128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified406 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 2, 0, 0, 0], #[0, 0, 0, 2, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 0, 1, 1, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, -1, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, -128, 0, 0], #[-64, -64, 128, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified407 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, -2, 0, 0, 0], #[0, 0, 0, -2, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 0, 1, -1, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, 128, 0, 0], #[64, 64, -128, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified408 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 2, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 1, 0, 1, 1, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, -1, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, -128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, -64, 128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified409 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, -2, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, -2, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 1, 0, 1, 1, 0, -1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 1, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 64, -128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified410 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 0, 1, 0, 1, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, -1, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, -128, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 128, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified411 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, -2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 0, -1, 0, 1, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 1, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[64, 64, -128, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 128, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified412 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 0, 1, 0, 1, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, -1, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, -128, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, -64, 128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 128, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified413 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, -2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -2, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 0, 1, 0, -1, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 1, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 64, -128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 128, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified414 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 2]], + stack := #[#[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 1, 0, 1, 0, 1, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, -1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, -128], #[0, 0, 0, 0, 256, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, -64, 128, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified415 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, -2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -2, 0, 0, 0, 0, 0, 2]], + stack := #[#[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 1, 0, 1, 0, 1, 0, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, 128], #[0, 0, 0, 0, 256, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 64, -128, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified416 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 1, 0, 1, 0, 1, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, -1, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, -128], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, -64, 128, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified417 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, -2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, -2, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 1, 0, 1, 0, 1, 0, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 1, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, 128], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 64, -128, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified418 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 1, 0, 1, 0, 1, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, -1, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, -128], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, -64, 128, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified419 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, -2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, -2, 0, 0, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 1, 0, 1, 0, 1, 0, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 1, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, 128], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 64, -128, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified420 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 0, 1, 0, 1, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, -1, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, -128, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, -64, 128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 128, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified421 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, -2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, -2, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 0, 1, 0, -1, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 1, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 64, -128, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 128, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified422 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 2, 0, 0, 0, 0], #[0, 0, 2, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 1, 1, 1, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, -1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, -128, 0, 0], #[-64, -64, 128, 0, 0, 128, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified423 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, -2, 0, 0, 0, 0], #[0, 0, -2, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 1, -1, 1, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, 128, 0, 0], #[64, 64, -128, 0, 0, 128, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified424 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 2, 0, 0], #[0, 0, 0, 0, 2, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 1, 1, 1, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, -1, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, -128, 0, 0], #[-64, -64, 128, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified425 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 2, -2, 0, 0], #[0, 0, 0, 0, -2, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 1, 1, 1, -1, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 128, 0, 0], #[64, 64, -128, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified426 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 2, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 2, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 1, 1, 1, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, -1, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, -128, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 128, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified427 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, -2, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, -2, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 1, 1, -1, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, 128, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[64, 64, -128, 0, 0, 128, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified428 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 2, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 2, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 1, 1, 1, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, -1, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, -128, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified429 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, -2, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, -2, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 1, 1, 1, -1, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, 128, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 64, -128, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified430 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 2, 0, 0, 0], #[0, 0, 0, 2, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 1, 1, 1, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, -1, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, -128, 0, 0], #[-64, -64, 128, 0, 0, 128, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified431 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, -2, 0, 0, 0], #[0, 0, 0, -2, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 1, 1, -1, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 128, 0, 0], #[64, 64, -128, 0, 0, 128, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified432 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 2, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 2, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 1, 1, 1, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, -1, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, -128, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified433 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, -2, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, -2, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 1, 1, 1, -1, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 128, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 64, -128, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified434 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 2, 0, 0, 0, 0], #[0, 0, 2, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 0, 1, 1, 0, 0, 1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, -1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, -128, 0, 0], #[-64, -64, 128, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified435 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, -2, 0, 0, 0, 0], #[0, 0, -2, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 0, 1, -1, 0, 0, 1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, 128, 0, 0], #[64, 64, -128, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified436 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 2], #[0, 0, 0, 0, 0, 0, 2, 2]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 1, 1, 0, 0, 1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, -1, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, -64, 128, 0, 0, 0, 0, -128], #[-64, -64, 128, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified437 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, -2], #[0, 0, 0, 0, 0, 0, -2, 2]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 1, 1, 0, 0, 1, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, -64, 128, 0, 0, 0, 0, 128], #[64, 64, -128, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified438 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 2, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 0, 1, 1, 0, 0, 1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, -1, 0, 0, 0, 1, 0]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, -128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, -64, 128, 0, 0, 0, 0, 128], #[0, 128, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified439 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, -2, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -2, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 0, 1, 1, 0, 0, -1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 1, 0, 0, 0, 1, 0]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 64, -128, 0, 0, 0, 0, 128], #[0, 128, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified440 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 2], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 2, 0, 0, 0, 0, 2]], + stack := #[#[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 1, 1, 0, 0, 1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, -1, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, -128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified441 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, -2], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, -2, 0, 0, 0, 0, 2]], + stack := #[#[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 1, 1, 0, 0, 1, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 64, -128, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified442 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 2, 0, 0, 0, 2]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 1, 1, 0, 0, 1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, -1, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, -128], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified443 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, -2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, -2, 0, 0, 0, 2]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 1, 1, 0, 0, 1, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, 128], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 64, -128, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified444 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 0, 1, 1, 0, 0, 1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, -1, 0, 0, 1, 0]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, -128], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, -64, 128, 0, 0, 0, 0, 128], #[0, 128, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified445 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, -2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, -2, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 0, 1, 1, 0, 0, -1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 1, 0, 0, 1, 0]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, 128], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 64, -128, 0, 0, 0, 0, 128], #[0, 128, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified446 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 2, 0, 0], #[0, 0, 0, 0, 2, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 0, 0, 0, 1, 1, 1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, -1, 1, 0, 0]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, -64, 128, 0, 0, 0, 0, -128], #[-64, -64, 128, 0, 0, 0, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified447 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, -2, 0, 0], #[0, 0, 0, 0, -2, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 0, 0, 0, 1, -1, 1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 1, 0, 0]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, -64, 128, 0, 0, 0, 0, 128], #[64, 64, -128, 0, 0, 0, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified448 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 2], #[0, 0, 0, 0, 0, 0, 2, 2]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 1, 1, 1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, -1, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, -128], #[-64, -64, 128, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified449 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 2, -2], #[0, 0, 0, 0, 0, 0, -2, 2]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 1, 1, 1, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, 128], #[64, 64, -128, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified450 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 2, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 2, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 0, 0, 0, 1, 1, 1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, -1, 0, 1, 0]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, -64, 128, 0, 0, 0, 0, -128], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, 128], #[0, 128, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified451 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, -2, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, -2, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 0, 0, 0, 1, 1, -1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 1, 0]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, -64, 128, 0, 0, 0, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[64, 64, -128, 0, 0, 0, 0, 128], #[0, 128, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified452 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 2], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 2, 0, 2]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 1, 1, 1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, -1, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, -128], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified453 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, -2], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, -2, 0, 2]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 1, 1, 1, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, 128], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 64, -128, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified454 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 2], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 2, 0, 0, 2]], + stack := #[#[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 1, 1, 1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, -1, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, -64, 128, 0, 0, 0, 0, -128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified455 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, -2], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, -2, 0, 0, 2]], + stack := #[#[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 1, 1, 1, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, -64, 128, 0, 0, 0, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 64, -128, 0, 0, 0, 0, 128]] }, by decide⟩ + +def certified456 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 2, 0], #[0, 0, 0, 0, 0, 2, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 0, 0, 0, 1, 1, 1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, -1, 1, 0]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, -128], #[-64, -64, 128, 0, 0, 0, 0, 128], #[0, 128, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified457 : CertifiedFrame := + ⟨{ dimension := 3, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 2, -2, 0], #[0, 0, 0, 0, 0, -2, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 0, 0, 0, 1, 1, -1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 1, 0]], + inverse256 := #[#[0, 0, 0, 256, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 128, 0, 0, 0, 0, 128], #[64, 64, -128, 0, 0, 0, 0, 128], #[0, 128, 0, 0, 0, 0, 0, 0]] }, by decide⟩ + +def certified458 : CertifiedFrame := + ⟨{ dimension := 4, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified459 : CertifiedFrame := + ⟨{ dimension := 4, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified460 : CertifiedFrame := + ⟨{ dimension := 4, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified461 : CertifiedFrame := + ⟨{ dimension := 4, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified462 : CertifiedFrame := + ⟨{ dimension := 4, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified463 : CertifiedFrame := + ⟨{ dimension := 4, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified464 : CertifiedFrame := + ⟨{ dimension := 4, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified465 : CertifiedFrame := + ⟨{ dimension := 4, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[0, 0, 0, 0, 256, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified466 : CertifiedFrame := + ⟨{ dimension := 4, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 0, 256, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified467 : CertifiedFrame := + ⟨{ dimension := 4, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 0, 256, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified468 : CertifiedFrame := + ⟨{ dimension := 4, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[0, 0, 0, 0, 256, 0, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified469 : CertifiedFrame := + ⟨{ dimension := 4, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified470 : CertifiedFrame := + ⟨{ dimension := 4, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0]], + inverse256 := #[#[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified471 : CertifiedFrame := + ⟨{ dimension := 4, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0]], + inverse256 := #[#[0, 0, 0, 0, 256, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified472 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[2, 2, 0, 0, 0, 0, 0, 0], #[2, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 0, 0, 0, 0, 1, 1], #[-1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0]], + inverse256 := #[#[0, 0, -64, -64, 128, -128, 0, 0], #[0, 0, -64, -64, 128, 128, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified473 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[2, 2, 0, 0, 0, 0, 0, 0], #[2, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, 1, 0, 0, 1, 1, 0, 0], #[-1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, -64, -64, 128, -128, 0, 0], #[0, 0, -64, -64, 128, 128, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified474 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[2, -2, 0, 0, 0, 0, 0, 0], #[-2, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, -1, 0, 0, 0, 0, 1, 1], #[1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0]], + inverse256 := #[#[0, 0, -64, -64, 128, 128, 0, 0], #[0, 0, 64, 64, -128, 128, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified475 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[2, -2, 0, 0, 0, 0, 0, 0], #[-2, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, -1, 0, 0, 1, 1, 0, 0], #[1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, -64, -64, 128, 128, 0, 0], #[0, 0, 64, 64, -128, 128, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified476 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[2, 0, 2, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[2, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 0, 1, 0, 1], #[-1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[0, 0, -64, -64, 128, -128, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -64, -64, 128, 128, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified477 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[2, 0, 2, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[2, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 0, 1, 0, 1, 0, 1, 0], #[-1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, -64, -64, 128, -128, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -64, -64, 128, 128, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified478 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[2, 0, -2, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[-2, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, -1, 0, 0, 1, 0, 1], #[1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[0, 0, -64, -64, 128, 128, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 64, 64, -128, 128, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified479 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[2, 0, -2, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[-2, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 0, -1, 0, 1, 0, 1, 0], #[1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, -64, -64, 128, 128, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 64, 64, -128, 128, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified480 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[2, 0, 0, 2, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[-1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, -64, 0, 0, 128, -128, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified481 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[2, 0, 0, 2, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 1, 1, 0, 0, 0, 0], #[-1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[-64, -64, 0, 0, 128, -128, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 128, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified482 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[2, 0, 0, -2, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[-2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 1, 1, -1, 0, 0, 0, 0], #[1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, -64, 0, 0, 128, 128, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 64, 0, 0, -128, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified483 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[2, 0, 0, -2, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[-2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 1, -1, 0, 0, 0, 0], #[1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[-64, -64, 0, 0, 128, 128, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 64, 0, 0, -128, 128, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified484 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 2, 0, 0, 0, 0, 0], #[0, 2, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 0, 1, 1, 0], #[0, -1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -64, -64, 128, -128, 0, 0], #[0, 0, -64, -64, 128, 128, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified485 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 2, 0, 0, 0, 0, 0], #[0, 2, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[0, -1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -64, -64, 128, -128, 0, 0], #[0, 0, -64, -64, 128, 128, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified486 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, -2, 0, 0, 0, 0, 0], #[0, -2, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, -1, 0, 0, 1, 1, 0], #[0, 1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -64, -64, 128, 128, 0, 0], #[0, 0, 64, 64, -128, 128, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified487 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, -2, 0, 0, 0, 0, 0], #[0, -2, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, -1, 0, 1, 0, 0, 1], #[0, 1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -64, -64, 128, 128, 0, 0], #[0, 0, 64, 64, -128, 128, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified488 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 2, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 1, 1, 0, 0, 0, 0], #[0, -1, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, -128, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified489 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 2, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[0, -1, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, -128, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 128, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified490 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, -2, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, -2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 1, -1, 0, 0, 0, 0], #[0, 1, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 128, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 64, 0, 0, -128, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified491 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, -2, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, -2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 1, 1, -1, 0, 0, 0, 0], #[0, 1, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 128, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 64, 0, 0, -128, 128, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified492 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 2, 0, 0, 0, 0], #[0, 0, 2, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 1, 1, 0, 0, 0, 0], #[0, 0, -1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, -128, 0, 0], #[-64, -64, 0, 0, 128, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified493 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 2, 0, 0, 0, 0], #[0, 0, 2, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[0, 0, -1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, -128, 0, 0], #[-64, -64, 0, 0, 128, 128, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified494 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, -2, 0, 0, 0, 0], #[0, 0, -2, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 1, -1, 0, 0, 0, 0], #[0, 0, 1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 128, 0, 0], #[64, 64, 0, 0, -128, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified495 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, -2, 0, 0, 0, 0], #[0, 0, -2, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, 1, 1, -1, 0, 0, 0, 0], #[0, 0, 1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 128, 0, 0], #[64, 64, 0, 0, -128, 128, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified496 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[2, 2, 0, 0, 0, 0, 0, 0], #[2, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 0, 0, 0, 0, 1, 1], #[-1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0]], + inverse256 := #[#[0, 0, -64, -64, 128, -128, 0, 0], #[0, 0, -64, -64, 128, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified497 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[2, -2, 0, 0, 0, 0, 0, 0], #[-2, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, -1, 0, 0, 0, 0, 1, 1], #[1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0]], + inverse256 := #[#[0, 0, -64, -64, 128, 128, 0, 0], #[0, 0, 64, 64, -128, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified498 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[2, 0, 0, 0, 2, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[2, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 0, 0, 1, 1, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[-1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[-64, 0, -64, 0, 128, 0, -128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified499 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[2, 0, 0, 0, 2, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[2, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 0, 1, 0, 1, 0, 1, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[-1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, -64, 0, -64, 128, 0, -128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, -64, 0, -64, 128, 0, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified500 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[2, 0, 0, 0, -2, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[-2, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 0, 0, -1, 1, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[-64, 0, -64, 0, 128, 0, 128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 0, 64, 0, -128, 0, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified501 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[2, 0, 0, 0, -2, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-2, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 0, 1, 0, -1, 0, 1, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, -64, 0, -64, 128, 0, 128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 64, 0, 64, -128, 0, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified502 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[2, 0, 0, 0, 0, 2, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 1, 0, 0, 1, 1, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[-1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, 0, -64, 0, 128, 0, -128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 128, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified503 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[2, 0, 0, 0, 0, 2, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 0, 0, 1, 1, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[-1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[-64, 0, -64, 0, 128, 0, -128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified504 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[2, 0, 0, 0, 0, -2, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[-2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 1, 0, 0, 1, -1, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, 0, -64, 0, 128, 0, 128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, 0, 64, 0, -128, 0, 128, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified505 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[2, 0, 0, 0, 0, -2, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[-2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 0, 0, 1, -1, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[-64, 0, -64, 0, 128, 0, 128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, 0, 64, 0, -128, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified506 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 2, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 1, 0, 0, 1, 1, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, -1, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, -128, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified507 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 2, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, -1, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, -64, 0, -64, 128, 0, -128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, -64, 0, -64, 128, 0, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified508 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, -2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, -2, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 1, 0, 0, -1, 1, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 128, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 0, 64, 0, -128, 0, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified509 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, -2, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -2, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, -1, 0, 0, 1], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 1, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, -64, 0, -64, 128, 0, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 64, 0, 64, -128, 0, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified510 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 2, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 0, 0, 1, 1, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, -1, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, -128, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified511 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 2, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 2, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 1, 0, 0, 1, 1, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, -1, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, -128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 128, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified512 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, -2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, -2, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 0, 0, 1, -1, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 128, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, 0, 64, 0, -128, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified513 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, -2, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, -2, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 1, 0, 0, 1, -1, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, 0, 64, 0, -128, 0, 128, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified514 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 2, 0, 0], #[0, 0, 0, 0, 2, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 0, 0, 1, 1, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, -1, 1, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, -64, 0, 0, 128, 0, 0, -128], #[-64, -64, 0, 0, 128, 0, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified515 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 2, 0, 0], #[0, 0, 0, 0, 2, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[1, 1, 0, 0, 1, 1, 0, 0], #[0, 0, 0, 0, -1, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, -128, 0, 0], #[-64, -64, 0, 0, 128, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified516 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, -2, 0, 0], #[0, 0, 0, 0, -2, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 0, 0, 1, -1, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 1, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, -64, 0, 0, 128, 0, 0, 128], #[64, 64, 0, 0, -128, 0, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified517 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 2, -2, 0, 0], #[0, 0, 0, 0, -2, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[1, 1, 0, 0, 1, -1, 0, 0], #[0, 0, 0, 0, 1, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 128, 0, 0], #[64, 64, 0, 0, -128, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified518 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[2, 0, 0, 0, 0, 0, 2, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[2, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 0, 0, 0, 0, 1, 1], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[-1, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[-64, 0, 0, -64, 128, 0, 0, -128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified519 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[2, 0, 0, 0, 0, 0, 2, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[2, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 1, 0, 1, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[-1, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[0, -64, -64, 0, 128, 0, 0, -128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, -64, -64, 0, 128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified520 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[2, 0, 0, 0, 0, 0, -2, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[-2, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 0, 0, 0, 0, -1, 1], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[1, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[-64, 0, 0, -64, 128, 0, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, 0, 0, 64, -128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified521 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[2, 0, 0, 0, 0, 0, -2, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-2, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 1, 0, -1, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[0, -64, -64, 0, 128, 0, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 64, 64, 0, -128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified522 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[2, 0, 0, 0, 0, 0, 0, 2], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[2, 0, 0, 0, 0, 0, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 1, 0, 0, 0, 0, 1, 1], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[-1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, 0, 0, -64, 128, 0, 0, -128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 0, 128]] }, by decide⟩ + +def certified523 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[2, 0, 0, 0, 0, 0, 0, 2], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[2, 0, 0, 0, 0, 0, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 1, 0, 0, 0, 0, 1, 1], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[-1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, 0, 0, -64, 128, 0, 0, -128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 0, 128]] }, by decide⟩ + +def certified524 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[2, 0, 0, 0, 0, 0, 0, -2], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[-2, 0, 0, 0, 0, 0, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 1, 0, 0, 0, 0, 1, -1], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, 0, 0, -64, 128, 0, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, 0, 0, 64, -128, 0, 0, 128]] }, by decide⟩ + +def certified525 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[2, 0, 0, 0, 0, 0, 0, -2], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[-2, 0, 0, 0, 0, 0, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 1, 0, 0, 0, 0, 1, -1], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, 0, 0, -64, 128, 0, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, 0, 0, 64, -128, 0, 0, 128]] }, by decide⟩ + +def certified526 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 2, 0, 0, 0, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 1, 0, 0, 0, 0, 1, 1], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, -1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 0, -128], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 0, 128]] }, by decide⟩ + +def certified527 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 2], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 2, 0, 0, 0, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, -1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, -64, -64, 0, 128, 0, 0, -128], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, -64, -64, 0, 128, 0, 0, 128]] }, by decide⟩ + +def certified528 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, -2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, -2, 0, 0, 0, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 1, 0, 0, 0, 0, 1, -1], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 0, 128], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, 0, 0, 64, -128, 0, 0, 128]] }, by decide⟩ + +def certified529 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, -2], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, -2, 0, 0, 0, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, -64, -64, 0, 128, 0, 0, 128], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 64, 64, 0, -128, 0, 0, 128]] }, by decide⟩ + +def certified530 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 0, 0, 0, 0, 1, 1], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, -1, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 0, -128], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 0, 0, -64, 128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified531 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 2, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 2, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 0, 0, 0, 0, 1, 1], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, -1, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 0, -128], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified532 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, -2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -2, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 0, 0, 0, 0, -1, 1], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 1, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 0, 128], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 0, 0, 64, -128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified533 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, -2, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, -2, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 0, 0, 0, 0, -1, 1], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 0, 128], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, 0, 0, 64, -128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified534 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 2], #[0, 0, 0, 0, 0, 0, 2, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, 1, 0, 0, 0, 0, 1, 1], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, -1, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, -128], #[-64, -64, 0, 0, 128, 0, 0, 128]] }, by decide⟩ + +def certified535 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 2], #[0, 0, 0, 0, 0, 0, 2, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[1, 1, 0, 0, 0, 0, 1, 1], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, -1, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, -64, 0, 0, 128, 0, 0, -128], #[-64, -64, 0, 0, 128, 0, 0, 128]] }, by decide⟩ + +def certified536 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 2, -2], #[0, 0, 0, 0, 0, 0, -2, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, 1, 0, 0, 0, 0, 1, -1], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, 128], #[64, 64, 0, 0, -128, 0, 0, 128]] }, by decide⟩ + +def certified537 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, -2], #[0, 0, 0, 0, 0, 0, -2, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[1, 1, 0, 0, 0, 0, 1, -1], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, -64, 0, 0, 128, 0, 0, 128], #[64, 64, 0, 0, -128, 0, 0, 128]] }, by decide⟩ + +def certified538 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[2, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[2, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 1, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[-1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0]], + inverse256 := #[#[-64, 0, -64, 0, 128, 0, -128, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 0, -64, 0, 128, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified539 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[2, 0, -2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-2, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, -1, 0, 1, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0]], + inverse256 := #[#[-64, 0, -64, 0, 128, 0, 128, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 0, 64, 0, -128, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified540 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[2, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[2, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 1, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[-1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0]], + inverse256 := #[#[-64, 0, -64, 0, 128, 0, -128, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified541 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[2, 0, 0, 0, -2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[-2, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, -1, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0]], + inverse256 := #[#[-64, 0, -64, 0, 128, 0, 128, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 0, 64, 0, -128, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified542 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[2, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[2, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, 0, 1, 0, 1, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[-1, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, 0, -64, 0, 128, 0, -128, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified543 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[2, 0, 0, 0, 0, 0, -2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[-2, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, 0, 1, 0, 1, 0, -1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[1, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, 0, -64, 0, 128, 0, 128, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, 0, 64, 0, -128, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified544 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 2, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 2, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 0, 1, 0, 1, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, -1, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 0, 0, -64, 128, 0, -128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified545 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, -1, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, -64, 0, -64, 128, 0, -128, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, -64, 0, -64, 128, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified546 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, -2, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, -2, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 0, 1, 0, -1, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 0, 0, -64, 128, 0, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 0, 0, 64, -128, 0, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified547 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, -2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -2, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, -1, 0, 0, 1], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 1, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, -64, 0, -64, 128, 0, 128, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 64, 0, 64, -128, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified548 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 2, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 1, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, -1, 0, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 0, -64, 0, 128, 0, 0, -128], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 0, -64, 0, 128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified549 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 2, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, 0, 1, 0, 1, 0, 1, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, -1, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, -128, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified550 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, -2, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -2, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 1, 0, -1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 1, 0, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 0, -64, 0, 128, 0, 0, 128], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 0, 64, 0, -128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified551 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, -2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, -2, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, 0, 1, 0, 1, 0, -1, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 128, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, 0, 64, 0, -128, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified552 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 2, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 2, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 1, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, -1, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, -64, 0, 0, 128, 0, 0, -128], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified553 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[1, 0, 1, 0, 1, 0, 1, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, -1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, -128, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 0, -64, 0, 128, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified554 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, -2, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, -2, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 1, 0, -1, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, -64, 0, 0, 128, 0, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, 64, 0, 0, -128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified555 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, -2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, -2, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[1, 0, 1, 0, 1, 0, -1, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 1, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 128, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[64, 0, 64, 0, -128, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified556 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 0, 1, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[-1, 0, 0, 0, 0, 1, 0, 0]], + inverse256 := #[#[-64, 0, 0, -64, 128, 0, 0, -128], #[0, 0, 0, 0, 0, 256, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 0, 0, -64, 128, 0, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified557 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[2, 0, 0, 0, 0, -2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 0, -1, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[1, 0, 0, 0, 0, 1, 0, 0]], + inverse256 := #[#[-64, 0, 0, -64, 128, 0, 0, 128], #[0, 0, 0, 0, 0, 256, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 0, 0, 64, -128, 0, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified558 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[2, 0, 0, 0, 0, 0, 0, 2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[2, 0, 0, 0, 0, 0, 0, 2]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, 0, 1, 0, 0, 1, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[-1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, 0, 0, -64, 128, 0, 0, -128], #[0, 0, 0, 0, 0, 256, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 0, 0, -64, 128, 0, 0, 128]] }, by decide⟩ + +def certified559 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[2, 0, 0, 0, 0, 0, 0, -2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-2, 0, 0, 0, 0, 0, 0, 2]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, 0, 1, 0, 0, 1, 0, -1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, 0, 0, -64, 128, 0, 0, 128], #[0, 0, 0, 0, 0, 256, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 0, 0, 64, -128, 0, 0, 128]] }, by decide⟩ + +def certified560 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 2], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 2, 0, 0, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 0, 1, 0, 0, 1, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, -1, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 0, -64, 0, 128, 0, 0, -128], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 0, 128]] }, by decide⟩ + +def certified561 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, -1, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, -64, -64, 0, 128, 0, 0, -128], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, -64, -64, 0, 128, 0, 0, 128]] }, by decide⟩ + +def certified562 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, -2], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, -2, 0, 0, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 0, 1, 0, 0, 1, 0, -1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 0, -64, 0, 128, 0, 0, 128], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, 0, 64, 0, -128, 0, 0, 128]] }, by decide⟩ + +def certified563 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, -2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -2, 0, 0, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 1, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, -64, -64, 0, 128, 0, 0, 128], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 64, 64, 0, -128, 0, 0, 128]] }, by decide⟩ + +def certified564 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 2, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 2, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 0, 1, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, -1, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 0, 0, -64, 128, 0, -128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified565 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 0, 1, 0, 1], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, -1, 0, 0, 1, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 0, -128], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 0, 0, -64, 128, 0, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified566 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, -2, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, -2, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 0, -1, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 0, 0, -64, 128, 0, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, 0, 0, 64, -128, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified567 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, -2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -2, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 0, -1, 0, 1], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 1, 0, 0, 1, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 0, 128], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 0, 0, 64, -128, 0, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified568 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 2], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 2, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 0, 1, 0, 0, 1, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, -1, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, -128], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, 128]] }, by decide⟩ + +def certified569 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[1, 0, 1, 0, 0, 1, 0, 1], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, -1, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 0, -64, 0, 128, 0, 0, -128], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 0, -64, 0, 128, 0, 0, 128]] }, by decide⟩ + +def certified570 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, -2], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, -2, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 0, 1, 0, 0, 1, 0, -1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, 64, 0, 0, -128, 0, 0, 128]] }, by decide⟩ + +def certified571 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, -2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, -2, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[1, 0, 1, 0, 0, 1, 0, -1], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 1, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 0, -64, 0, 128, 0, 0, 128], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 0, 64, 0, -128, 0, 0, 128]] }, by decide⟩ + +def certified572 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 0, 1, 1, 0, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[-1, 0, 0, 1, 0, 0, 0, 0]], + inverse256 := #[#[-64, 0, 0, -64, 128, 0, 0, -128], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 0, 0, -64, 128, 0, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified573 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[2, 0, 0, -2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[-2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 0, -1, 1, 0, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[1, 0, 0, 1, 0, 0, 0, 0]], + inverse256 := #[#[-64, 0, 0, -64, 128, 0, 0, 128], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 0, 0, 64, -128, 0, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified574 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 2], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 2, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 1, 1, 1, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, -1, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, -64, -64, 128, 0, 0, -128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, -64, -64, 128, 0, 0, 128]] }, by decide⟩ + +def certified575 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, -1, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, -64, -64, 0, 128, 0, 0, -128], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, -64, -64, 0, 128, 0, 0, 128]] }, by decide⟩ + +def certified576 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, -2], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, -2, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 1, 1, 1, -1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, -64, -64, 128, 0, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 64, 64, -128, 0, 0, 128]] }, by decide⟩ + +def certified577 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, -2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, -2, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 1, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, -64, -64, 0, 128, 0, 0, 128], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 64, 64, 0, -128, 0, 0, 128]] }, by decide⟩ + +def certified578 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 2, 0, 0, 0], #[0, 0, 0, 2, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 0, 1, 1, 0, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, -1, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, -128, 0], #[-64, 0, 0, -64, 128, 0, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified579 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 2, 0, 0, 0], #[0, 0, 0, 2, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 0, 1, 1, 0, 0, 1], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, -1, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 0, 0, -64, 128, 0, -128, 0], #[-64, 0, 0, -64, 128, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified580 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, -2, 0, 0, 0], #[0, 0, 0, -2, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 0, 1, -1, 0, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 128, 0], #[64, 0, 0, 64, -128, 0, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified581 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, -2, 0, 0, 0], #[0, 0, 0, -2, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 0, 1, -1, 0, 0, 1], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 0, 0, -64, 128, 0, 128, 0], #[64, 0, 0, 64, -128, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified582 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 2], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 2, 0, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 0, 0, 1, 1, 0, 0, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, -1, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 0, -128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 0, 128]] }, by decide⟩ + +def certified583 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 2], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, 0, 0, 1, 1, 0, 0, 1], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, -1, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 0, -64, 0, 128, 0, 0, -128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 0, -64, 0, 128, 0, 0, 128]] }, by decide⟩ + +def certified584 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, -2], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, -2, 0, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 0, 0, 1, 1, 0, 0, -1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, 0, 64, 0, -128, 0, 0, 128]] }, by decide⟩ + +def certified585 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, -2], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, -2, 0, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, 0, 0, 1, 1, 0, 0, -1], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 1, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 0, -64, 0, 128, 0, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 0, 64, 0, -128, 0, 0, 128]] }, by decide⟩ + +def certified586 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 2, 0], #[0, 0, 0, 0, 0, 2, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 0, 0, 0, 1, 1, 1, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, -1, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, -64, -64, 128, 0, 0, -128], #[0, 0, -64, -64, 128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified587 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 2, 0], #[0, 0, 0, 0, 0, 2, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 1, 1, 0, 0, 1, 1, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, -1, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, -64, -64, 0, 128, 0, -128, 0], #[0, -64, -64, 0, 128, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified588 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 2, -2, 0], #[0, 0, 0, 0, 0, -2, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 0, 0, 0, 1, 1, -1, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, -64, -64, 128, 0, 0, 128], #[0, 0, 64, 64, -128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified589 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, -2, 0], #[0, 0, 0, 0, 0, -2, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 1, 1, 0, 0, 1, -1, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, -64, -64, 0, 128, 0, 128, 0], #[0, 64, 64, 0, -128, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified590 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 2, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 0, 1, 1, 0, 0, 1, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, -1, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, -64, 0, -64, 128, 0, 0, -128], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, -64, 0, -64, 128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified591 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 2, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 2, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 1, 0, 1, 1, 0, 1, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, -1, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, -64, -64, 0, 128, 0, -128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, -64, -64, 0, 128, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified592 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, -2, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, -2, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 0, 1, 1, 0, 0, -1, 1], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, -64, 0, -64, 128, 0, 0, 128], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 64, 0, 64, -128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified593 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, -2, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, -2, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 1, 0, 1, 1, 0, -1, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, -64, -64, 0, 128, 0, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 64, 64, 0, -128, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified594 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 2, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 2, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 1, 1, 1, 1, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, -1, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, -64, -64, 0, 128, 0, -128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, -64, -64, 0, 128, 0, 128, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified595 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 0, 1, 0, 1, 0, 1], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, -1, 0, 1, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, -64, 0, -64, 128, 0, 0, -128], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, -64, 0, -64, 128, 0, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified596 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, -2, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, -2, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 1, 1, 1, -1, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, -64, -64, 0, 128, 0, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 64, 64, 0, -128, 0, 128, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified597 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, -2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, -2, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 0, 1, 0, -1, 0, 1], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 1, 0, 1, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 256, 0, 0], #[0, -64, 0, -64, 128, 0, 0, 128], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 64, 0, 64, -128, 0, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified598 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 2, 0, 0, 0, 0, 0], #[0, 2, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0]], + inverse256 := #[#[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 0, 0, -64, 128, 0, -128, 0], #[-64, 0, 0, -64, 128, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified599 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, -2, 0, 0, 0, 0, 0], #[0, -2, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, -1, 0, 1, 0, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0]], + inverse256 := #[#[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 0, 0, -64, 128, 0, 128, 0], #[64, 0, 0, 64, -128, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified600 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 2, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 2, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0]], + inverse256 := #[#[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 0, 0, -64, 128, 0, -128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified601 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, -2, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, -2, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, -1, 0, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0]], + inverse256 := #[#[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 0, 0, -64, 128, 0, 128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 0, 0, 64, -128, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified602 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 2], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 2]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, -1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 0, -64, 0, 128, 0, 0, -128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 0, -64, 0, 128, 0, 0, 128]] }, by decide⟩ + +def certified603 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, -2], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -2, 0, 0, 0, 0, 0, 2]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 0, -64, 0, 128, 0, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 0, 64, 0, -128, 0, 0, 128]] }, by decide⟩ + +def certified604 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 2, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 2, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -1, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[0, 0, 0, 0, 0, 256, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, -128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified605 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, -2, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, -2, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, -1, 0, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[0, 0, 0, 0, 0, 256, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 0, 0, 64, -128, 0, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified606 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 2], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 2, 0, 0, 0, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, -1, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 0, 0, 256, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 0, -128], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 0, 128]] }, by decide⟩ + +def certified607 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, -2], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, -2, 0, 0, 0, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 0, 0, 256, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 0, 128], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, 0, 64, 0, -128, 0, 0, 128]] }, by decide⟩ + +def certified608 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 2], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 2, 0, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, -1, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 0, 0, 256, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, -64, 0, 0, 128, 0, 0, -128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, 128]] }, by decide⟩ + +def certified609 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, -2], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, -2, 0, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 0, 0, 256, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, -64, 0, 0, 128, 0, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, 64, 0, 0, -128, 0, 0, 128]] }, by decide⟩ + +def certified610 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 2, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 0, 1, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, -1, 0, 0, 0, 1, 0, 0]], + inverse256 := #[#[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 0, -64, 0, 128, 0, 0, -128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 0, -64, 0, 128, 0, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified611 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, -2, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -2, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 0, -1, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 1, 0, 0, 0, 1, 0, 0]], + inverse256 := #[#[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 0, -64, 0, 128, 0, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 0, 64, 0, -128, 0, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified612 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 2, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 2, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 1, 1, 0, 0, 1, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, -1, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 0, 0, -64, 128, 0, -128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified613 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, -2, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, -2, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 1, 1, 0, 0, 1, -1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 0, 0, -64, 128, 0, 128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, 0, 0, 64, -128, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified614 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 2, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 2, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 0, 1, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, -1, 0, 0, 0, 1, 0]], + inverse256 := #[#[0, 0, 0, 0, 0, 256, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 0, -128], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified615 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, -2, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, -2, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 0, 1, -1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 1, 0]], + inverse256 := #[#[0, 0, 0, 0, 0, 256, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 0, 128], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, 0, 64, 0, -128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified616 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 2, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 2, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 0, 1, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -1, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 0, 0, 256, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, -128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 128, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified617 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, -2, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, -2, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 0, -1, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 0, 0, 256, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, 0, 0, 64, -128, 0, 128, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified618 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 2, 0], #[0, 0, 0, 0, 0, 2, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 0, 1, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, -1, 1, 0]], + inverse256 := #[#[0, 0, 0, 0, 0, 256, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, -128], #[-64, -64, 0, 0, 128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified619 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 2, -2, 0], #[0, 0, 0, 0, 0, -2, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 0, 1, -1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 1, 0]], + inverse256 := #[#[0, 0, 0, 0, 0, 256, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, 128], #[64, 64, 0, 0, -128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified620 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 0, 1, 1, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, -1, 0, 1, 0, 0, 0, 0]], + inverse256 := #[#[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 0, -64, 0, 128, 0, 0, -128], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 0, -64, 0, 128, 0, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified621 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, -2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, -2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 0, -1, 1, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 1, 0, 1, 0, 0, 0, 0]], + inverse256 := #[#[0, 0, 0, 0, 0, 256, 0, 0], #[-64, 0, -64, 0, 128, 0, 0, 128], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 0, 64, 0, -128, 0, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified622 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 2, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 2, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 0, 0, 0, 1, 1, 1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, -1, 0, 1, 0]], + inverse256 := #[#[0, 0, 0, 0, 0, 256, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, -64, -64, 128, 0, 0, -128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, -64, -64, 128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified623 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, -2, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, -2, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 0, 0, 0, 1, 1, -1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 1, 0]], + inverse256 := #[#[0, 0, 0, 0, 0, 256, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, -64, -64, 128, 0, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 64, 64, -128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified624 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 2, 0, 0, 0], #[0, 0, 0, 2, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 0, 1, 1, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, -1, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 0, 0, 256, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, -128, 0], #[-64, 0, 0, -64, 128, 0, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified625 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, -2, 0, 0, 0], #[0, 0, 0, -2, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 0, 1, -1, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 0, 0, 256, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 128, 0], #[64, 0, 0, 64, -128, 0, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified626 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 2, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 0, 1, 1, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, -1, 0, 0, 1, 0]], + inverse256 := #[#[0, 0, 0, 0, 0, 256, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 0, -128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[-64, 0, -64, 0, 128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified627 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, -2, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, -2, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 0, 1, 1, 0, -1, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 1, 0, 0, 1, 0]], + inverse256 := #[#[0, 0, 0, 0, 0, 256, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[64, 0, 64, 0, -128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified628 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 2], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 2, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 1, 1, 1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, -1, 0, 1]], + inverse256 := #[#[0, 0, 0, 0, 0, 256, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, -64, -64, 128, 0, 0, -128], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, -64, -64, 128, 0, 0, 128]] }, by decide⟩ + +def certified629 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, -2], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, -2, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 1, 1, 1, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 1]], + inverse256 := #[#[0, 0, 0, 0, 0, 256, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, -64, -64, 128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 64, 64, -128, 0, 0, 128]] }, by decide⟩ + +def certified630 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 2, 0, 0, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 1, 1, 0, 0, 1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, -1, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 0, 0, 256, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, -64, 0, -64, 128, 0, 0, -128], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, -64, 0, -64, 128, 0, 0, 128]] }, by decide⟩ + +def certified631 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, -2], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, -2, 0, 0, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 1, 1, 0, 0, 1, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 0, 0, 256, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, -64, 0, -64, 128, 0, 0, 128], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 64, 0, 64, -128, 0, 0, 128]] }, by decide⟩ + +def certified632 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 2, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 2, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 0, 1, 1, 1, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, -1, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[0, 0, 0, 0, 0, 256, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, -64, -64, 0, 128, 0, -128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, -64, -64, 0, 128, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified633 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, -2, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, -2, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 0, 1, 1, 1, -1, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[0, 0, 0, 0, 0, 256, 0, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, -64, -64, 0, 128, 0, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 64, 64, 0, -128, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified634 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 2, 0, 0, 0, 0], #[0, 0, 2, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 0, 1, 1, 0, 0, 1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, -1, 1, 0, 0, 0, 0]], + inverse256 := #[#[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, -64, -64, 128, 0, 0, -128], #[0, 0, -64, -64, 128, 0, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified635 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, -2, 0, 0, 0, 0], #[0, 0, -2, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 0, 1, -1, 0, 0, 1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 1, 0, 0, 0, 0]], + inverse256 := #[#[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, -64, -64, 128, 0, 0, 128], #[0, 0, 64, 64, -128, 0, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified636 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 2, 0, 0], #[0, 0, 0, 0, 2, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 0, 0, 0, 1, 1, 1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, -1, 1, 0, 0]], + inverse256 := #[#[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, -64, -64, 128, 0, 0, -128], #[0, 0, -64, -64, 128, 0, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified637 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 2, -2, 0, 0], #[0, 0, 0, 0, -2, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 0, 0, 0, 1, -1, 1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 1, 0, 0]], + inverse256 := #[#[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, -64, -64, 128, 0, 0, 128], #[0, 0, 64, 64, -128, 0, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified638 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 2], #[0, 0, 0, 0, 0, 0, 2, 2]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 1, 1, 1, 1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, -1, 1]], + inverse256 := #[#[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, -64, -64, 128, 0, 0, -128], #[0, 0, -64, -64, 128, 0, 0, 128]] }, by decide⟩ + +def certified639 : CertifiedFrame := + ⟨{ dimension := 5, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 2, -2], #[0, 0, 0, 0, 0, 0, -2, 2]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 1, 1, 1, -1], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 1]], + inverse256 := #[#[0, 0, 0, 0, 0, 256, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, -64, -64, 128, 0, 0, 128], #[0, 0, 64, 64, -128, 0, 0, 128]] }, by decide⟩ + +def certified640 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, -2, 0, 0, 0, 0, 0, 0], #[-2, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, -2, 0, 0, 0, 0], #[0, 0, -2, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, -1, 0, 0, 0, 0, 1, 1], #[1, -1, 1, -1, 0, 0, 0, 0], #[1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 1, 0, 0, 0, 0]], + inverse256 := #[#[0, 0, -64, -64, 128, 0, 128, 0], #[0, 0, 64, 64, -128, 0, 128, 0], #[0, 0, 64, 64, -128, 128, 0, 128], #[0, 0, -64, -64, 128, -128, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified641 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, -2, 0, 0, 0, 0], #[0, 2, -2, 0, 0, 0, 0, 0], #[0, -2, 2, 0, 0, 0, 0, 0], #[-2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, -1, 0, 1, 0, 0, 1], #[1, 1, -1, -1, 0, 0, 0, 0], #[0, 1, 1, 0, 0, 0, 0, 0], #[1, 0, 0, 1, 0, 0, 0, 0]], + inverse256 := #[#[64, 0, 0, 64, -128, 128, 0, 128], #[-64, 0, 0, -64, 128, 0, 128, 0], #[64, 0, 0, 64, -128, 0, 128, 0], #[-64, 0, 0, -64, 128, -128, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified642 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, -2, 0, 0, 0, 0, 0], #[0, 2, 0, -2, 0, 0, 0, 0], #[-2, 0, 2, 0, 0, 0, 0, 0], #[0, -2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, -1, 0, 1, 0, 1, 0], #[1, 1, -1, -1, 0, 0, 0, 0], #[1, 0, 1, 0, 0, 0, 0, 0], #[0, 1, 0, 1, 0, 0, 0, 0]], + inverse256 := #[#[-64, 0, -64, 0, 128, 0, 128, 0], #[64, 0, 64, 0, -128, 128, 0, 128], #[64, 0, 64, 0, -128, 0, 128, 0], #[-64, 0, -64, 0, 128, -128, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified643 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 2, 0, 0, 0, 0, 0], #[0, 2, 0, 2, 0, 0, 0, 0], #[2, 0, 2, 0, 0, 0, 0, 0], #[0, 2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[-1, 0, 1, 0, 0, 0, 0, 0], #[0, -1, 0, 1, 0, 0, 0, 0]], + inverse256 := #[#[-64, 0, -64, 0, 128, 0, -128, 0], #[64, 0, 64, 0, -128, 128, 0, -128], #[-64, 0, -64, 0, 128, 0, 128, 0], #[64, 0, 64, 0, -128, 128, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified644 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 2, 0, 0, 0, 0], #[0, 2, 2, 0, 0, 0, 0, 0], #[0, 2, 2, 0, 0, 0, 0, 0], #[2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 1, 1, 1, 0, 0, 0, 0], #[0, -1, 1, 0, 0, 0, 0, 0], #[-1, 0, 0, 1, 0, 0, 0, 0]], + inverse256 := #[#[64, 0, 0, 64, -128, 128, 0, -128], #[-64, 0, 0, -64, 128, 0, -128, 0], #[-64, 0, 0, -64, 128, 0, 128, 0], #[64, 0, 0, 64, -128, 128, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified645 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 2, 0, 0, 0, 0, 0, 0], #[2, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 2, 0, 0, 0, 0], #[0, 0, 2, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 0, 0, 0, 0, 1, 1], #[1, 1, 1, 1, 0, 0, 0, 0], #[-1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, -1, 1, 0, 0, 0, 0]], + inverse256 := #[#[0, 0, -64, -64, 128, 0, -128, 0], #[0, 0, -64, -64, 128, 0, 128, 0], #[0, 0, 64, 64, -128, 128, 0, -128], #[0, 0, 64, 64, -128, 128, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified646 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, -2, 0, 0, 0, 0, 0, 0], #[-2, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 2, 0, 0, 0, 0], #[0, 0, 2, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, -1, 0, 0, 0, 0, 1, 1], #[1, -1, 1, 1, 0, 0, 0, 0], #[1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, -1, 1, 0, 0, 0, 0]], + inverse256 := #[#[0, 0, -64, -64, 128, 0, 128, 0], #[0, 0, 64, 64, -128, 0, 128, 0], #[0, 0, 64, 64, -128, 128, 0, -128], #[0, 0, 64, 64, -128, 128, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified647 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 2, 0, 0, 0, 0], #[0, 2, -2, 0, 0, 0, 0, 0], #[0, -2, 2, 0, 0, 0, 0, 0], #[2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, -1, 0, 1, 0, 0, 1], #[1, 1, -1, 1, 0, 0, 0, 0], #[0, 1, 1, 0, 0, 0, 0, 0], #[-1, 0, 0, 1, 0, 0, 0, 0]], + inverse256 := #[#[64, 0, 0, 64, -128, 128, 0, -128], #[-64, 0, 0, -64, 128, 0, 128, 0], #[64, 0, 0, 64, -128, 0, 128, 0], #[64, 0, 0, 64, -128, 128, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified648 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, -2, 0, 0, 0, 0, 0], #[0, 2, 0, 2, 0, 0, 0, 0], #[-2, 0, 2, 0, 0, 0, 0, 0], #[0, 2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, -1, 0, 1, 0, 1, 0], #[1, 1, -1, 1, 0, 0, 0, 0], #[1, 0, 1, 0, 0, 0, 0, 0], #[0, -1, 0, 1, 0, 0, 0, 0]], + inverse256 := #[#[-64, 0, -64, 0, 128, 0, 128, 0], #[64, 0, 64, 0, -128, 128, 0, -128], #[64, 0, 64, 0, -128, 0, 128, 0], #[64, 0, 64, 0, -128, 128, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified649 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 2, 0, 0, 0, 0, 0], #[0, 2, 0, -2, 0, 0, 0, 0], #[2, 0, 2, 0, 0, 0, 0, 0], #[0, -2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 1, -1, 0, 0, 0, 0], #[-1, 0, 1, 0, 0, 0, 0, 0], #[0, 1, 0, 1, 0, 0, 0, 0]], + inverse256 := #[#[-64, 0, -64, 0, 128, 0, -128, 0], #[64, 0, 64, 0, -128, 128, 0, 128], #[-64, 0, -64, 0, 128, 0, 128, 0], #[-64, 0, -64, 0, 128, -128, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified650 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, -2, 0, 0, 0, 0], #[0, 2, 2, 0, 0, 0, 0, 0], #[0, 2, 2, 0, 0, 0, 0, 0], #[-2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 1, 1, -1, 0, 0, 0, 0], #[0, -1, 1, 0, 0, 0, 0, 0], #[1, 0, 0, 1, 0, 0, 0, 0]], + inverse256 := #[#[64, 0, 0, 64, -128, 128, 0, 128], #[-64, 0, 0, -64, 128, 0, -128, 0], #[-64, 0, 0, -64, 128, 0, 128, 0], #[-64, 0, 0, -64, 128, -128, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified651 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 2, 0, 0, 0, 0, 0, 0], #[2, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, -2, 0, 0, 0, 0], #[0, 0, -2, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 0, 0, 0, 0, 1, 1], #[1, 1, 1, -1, 0, 0, 0, 0], #[-1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 1, 0, 0, 0, 0]], + inverse256 := #[#[0, 0, -64, -64, 128, 0, -128, 0], #[0, 0, -64, -64, 128, 0, 128, 0], #[0, 0, 64, 64, -128, 128, 0, 128], #[0, 0, -64, -64, 128, -128, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified652 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, -2, 0, 0, 0, 0, 0, 0], #[-2, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 2, -2, 0, 0], #[0, 0, 0, 0, -2, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, -1, 0, 0, 0, 0, 1, 1], #[1, -1, 0, 0, 1, -1, 0, 0], #[1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 1, 0, 0]], + inverse256 := #[#[0, 0, -64, -64, 128, 0, 128, 0], #[0, 0, 64, 64, -128, 0, 128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 64, 64, -128, 128, 0, 128], #[0, 0, -64, -64, 128, -128, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified653 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, 0, -2, 0, 0], #[0, 2, 0, 0, -2, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, -2, 0, 0, 2, 0, 0, 0], #[-2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, -1, 0, 0, 1], #[1, 1, 0, 0, -1, -1, 0, 0], #[0, 1, 0, 0, 1, 0, 0, 0], #[1, 0, 0, 0, 0, 1, 0, 0]], + inverse256 := #[#[64, 0, 0, 64, -128, 128, 0, 128], #[-64, 0, 0, -64, 128, 0, 128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 0, 0, 64, -128, 0, 128, 0], #[-64, 0, 0, -64, 128, -128, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified654 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, -2, 0, 0, 0], #[0, 2, 0, 0, 0, -2, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[-2, 0, 0, 0, 2, 0, 0, 0], #[0, -2, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, -1, 0, 1, 0], #[1, 1, 0, 0, -1, -1, 0, 0], #[1, 0, 0, 0, 1, 0, 0, 0], #[0, 1, 0, 0, 0, 1, 0, 0]], + inverse256 := #[#[-64, 0, -64, 0, 128, 0, 128, 0], #[64, 0, 64, 0, -128, 128, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 0, 64, 0, -128, 0, 128, 0], #[-64, 0, -64, 0, 128, -128, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified655 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, 2, 0, 0, 0], #[0, 2, 0, 0, 0, 2, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[2, 0, 0, 0, 2, 0, 0, 0], #[0, 2, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 0, 0, 1, 1, 0, 0], #[-1, 0, 0, 0, 1, 0, 0, 0], #[0, -1, 0, 0, 0, 1, 0, 0]], + inverse256 := #[#[-64, 0, -64, 0, 128, 0, -128, 0], #[64, 0, 64, 0, -128, 128, 0, -128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 128, 0], #[64, 0, 64, 0, -128, 128, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified656 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, 0, 2, 0, 0], #[0, 2, 0, 0, 2, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 2, 0, 0, 2, 0, 0, 0], #[2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 1, 0, 0, 1, 1, 0, 0], #[0, -1, 0, 0, 1, 0, 0, 0], #[-1, 0, 0, 0, 0, 1, 0, 0]], + inverse256 := #[#[64, 0, 0, 64, -128, 128, 0, -128], #[-64, 0, 0, -64, 128, 0, -128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 128, 0], #[64, 0, 0, 64, -128, 128, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified657 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 2, 0, 0, 0, 0, 0, 0], #[2, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 2, 0, 0], #[0, 0, 0, 0, 2, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 0, 0, 0, 0, 1, 1], #[1, 1, 0, 0, 1, 1, 0, 0], #[-1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, -1, 1, 0, 0]], + inverse256 := #[#[0, 0, -64, -64, 128, 0, -128, 0], #[0, 0, -64, -64, 128, 0, 128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 64, 64, -128, 128, 0, -128], #[0, 0, 64, 64, -128, 128, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified658 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, -2, 0, 0, 0, 0, 0, 0], #[-2, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 2, 0, 0], #[0, 0, 0, 0, 2, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, -1, 0, 0, 0, 0, 1, 1], #[1, -1, 0, 0, 1, 1, 0, 0], #[1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, -1, 1, 0, 0]], + inverse256 := #[#[0, 0, -64, -64, 128, 0, 128, 0], #[0, 0, 64, 64, -128, 0, 128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 64, 64, -128, 128, 0, -128], #[0, 0, 64, 64, -128, 128, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified659 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, 0, 2, 0, 0], #[0, 2, 0, 0, -2, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, -2, 0, 0, 2, 0, 0, 0], #[2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, -1, 0, 0, 1], #[1, 1, 0, 0, -1, 1, 0, 0], #[0, 1, 0, 0, 1, 0, 0, 0], #[-1, 0, 0, 0, 0, 1, 0, 0]], + inverse256 := #[#[64, 0, 0, 64, -128, 128, 0, -128], #[-64, 0, 0, -64, 128, 0, 128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 0, 0, 64, -128, 0, 128, 0], #[64, 0, 0, 64, -128, 128, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified660 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, -2, 0, 0, 0], #[0, 2, 0, 0, 0, 2, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[-2, 0, 0, 0, 2, 0, 0, 0], #[0, 2, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, -1, 0, 1, 0], #[1, 1, 0, 0, -1, 1, 0, 0], #[1, 0, 0, 0, 1, 0, 0, 0], #[0, -1, 0, 0, 0, 1, 0, 0]], + inverse256 := #[#[-64, 0, -64, 0, 128, 0, 128, 0], #[64, 0, 64, 0, -128, 128, 0, -128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 0, 64, 0, -128, 0, 128, 0], #[64, 0, 64, 0, -128, 128, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified661 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, 2, 0, 0, 0], #[0, 2, 0, 0, 0, -2, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[2, 0, 0, 0, 2, 0, 0, 0], #[0, -2, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 0, 0, 1, -1, 0, 0], #[-1, 0, 0, 0, 1, 0, 0, 0], #[0, 1, 0, 0, 0, 1, 0, 0]], + inverse256 := #[#[-64, 0, -64, 0, 128, 0, -128, 0], #[64, 0, 64, 0, -128, 128, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 128, 0], #[-64, 0, -64, 0, 128, -128, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified662 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, 0, -2, 0, 0], #[0, 2, 0, 0, 2, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 2, 0, 0, 2, 0, 0, 0], #[-2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 1, 0, 0, 1, -1, 0, 0], #[0, -1, 0, 0, 1, 0, 0, 0], #[1, 0, 0, 0, 0, 1, 0, 0]], + inverse256 := #[#[64, 0, 0, 64, -128, 128, 0, 128], #[-64, 0, 0, -64, 128, 0, -128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 128, 0], #[-64, 0, 0, -64, 128, -128, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified663 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 2, 0, 0, 0, 0, 0, 0], #[2, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 2, -2, 0, 0], #[0, 0, 0, 0, -2, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 0, 0, 0, 0, 1, 1], #[1, 1, 0, 0, 1, -1, 0, 0], #[-1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 1, 0, 0]], + inverse256 := #[#[0, 0, -64, -64, 128, 0, -128, 0], #[0, 0, -64, -64, 128, 0, 128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 64, 64, -128, 128, 0, 128], #[0, 0, -64, -64, 128, -128, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified664 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, -2, 0, 0, 0, 0, 0, 0], #[-2, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 2, -2], #[0, 0, 0, 0, 0, 0, -2, 2]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, -1, 0, 0, 0, 0, 1, -1], #[1, -1, 0, 0, 0, 0, -1, 1], #[1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 1]], + inverse256 := #[#[0, 0, 0, 0, 64, 64, 128, 0], #[0, 0, 0, 0, -64, -64, 128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 64, -64, 0, 128], #[0, 0, 0, 0, -64, 64, 0, 128]] }, by decide⟩ + +def certified665 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, 0, 0, 0, -2], #[0, 2, 0, 0, 0, 0, -2, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, -2, 0, 0, 0, 0, 2, 0], #[-2, 0, 0, 0, 0, 0, 0, 2]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, 1, 0, 0, 0, 0, -1, -1], #[1, -1, 0, 0, 0, 0, 1, -1], #[0, 1, 0, 0, 0, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 0, 64, 64, 0, 128], #[0, 0, 0, 0, 64, -64, 128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, -64, 64, 128, 0], #[0, 0, 0, 0, -64, -64, 0, 128]] }, by decide⟩ + +def certified666 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, 0, 0, -2, 0], #[0, 2, 0, 0, 0, 0, 0, -2], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[-2, 0, 0, 0, 0, 0, 2, 0], #[0, -2, 0, 0, 0, 0, 0, 2]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[1, 0, 1, 0, 1, 0, -1, 0], #[1, 0, 0, 0, 0, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, 0, -64, 0, 0, 128, 128, 0], #[-64, 0, -64, 0, 128, 0, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, 0, 64, 0, 0, -128, 128, 0], #[64, 0, 64, 0, -128, 0, 0, 128]] }, by decide⟩ + +def certified667 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, 0, 0, 2, 0], #[0, 2, 0, 0, 0, 0, 0, 2], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[2, 0, 0, 0, 0, 0, 2, 0], #[0, 2, 0, 0, 0, 0, 0, 2]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, 1, 0], #[-1, 0, 0, 0, 0, 0, 1, 0], #[0, -1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, 0, -64, 0, 0, 128, -128, 0], #[-64, 0, -64, 0, 128, 0, 0, -128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, 0, -64, 0, 0, 128, 128, 0], #[-64, 0, -64, 0, 128, 0, 0, 128]] }, by decide⟩ + +def certified668 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, 0, 0, 0, 2], #[0, 2, 0, 0, 0, 0, 2, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 2, 0, 0, 0, 0, 2, 0], #[2, 0, 0, 0, 0, 0, 0, 2]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, 1, 0, 0, 0, 0, 1, 1], #[1, -1, 0, 0, 0, 0, -1, 1], #[0, -1, 0, 0, 0, 0, 1, 0], #[-1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 0, 64, 64, 0, -128], #[0, 0, 0, 0, 64, -64, -128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 64, -64, 128, 0], #[0, 0, 0, 0, 64, 64, 0, 128]] }, by decide⟩ + +def certified669 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 2, 0, 0, 0, 0, 0, 0], #[2, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 2], #[0, 0, 0, 0, 0, 0, 2, 2]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, 1, 0, 0, 0, 0, 1, 1], #[1, 1, 0, 0, 0, 0, -1, -1], #[-1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, -1, 1]], + inverse256 := #[#[0, 0, 0, 0, 64, 64, -128, 0], #[0, 0, 0, 0, 64, 64, 128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 64, -64, 0, -128], #[0, 0, 0, 0, 64, -64, 0, 128]] }, by decide⟩ + +def certified670 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, -2, 0, 0, 0, 0, 0, 0], #[-2, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 2], #[0, 0, 0, 0, 0, 0, 2, 2]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, -1, 0, 0, 0, 0, 1, 1], #[1, -1, 0, 0, 0, 0, -1, -1], #[1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, -1, 1]], + inverse256 := #[#[0, 0, 0, 0, 64, 64, 128, 0], #[0, 0, 0, 0, -64, -64, 128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 64, -64, 0, -128], #[0, 0, 0, 0, 64, -64, 0, 128]] }, by decide⟩ + +def certified671 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, 0, 0, 0, 2], #[0, 2, 0, 0, 0, 0, -2, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, -2, 0, 0, 0, 0, 2, 0], #[2, 0, 0, 0, 0, 0, 0, 2]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, 1, 0, 0, 0, 0, -1, 1], #[1, -1, 0, 0, 0, 0, 1, 1], #[0, 1, 0, 0, 0, 0, 1, 0], #[-1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 0, 64, 64, 0, -128], #[0, 0, 0, 0, 64, -64, 128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, -64, 64, 128, 0], #[0, 0, 0, 0, 64, 64, 0, 128]] }, by decide⟩ + +def certified672 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, 0, 0, -2, 0], #[0, 2, 0, 0, 0, 0, 0, 2], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[-2, 0, 0, 0, 0, 0, 2, 0], #[0, 2, 0, 0, 0, 0, 0, 2]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, -1, 0], #[1, 0, 0, 0, 0, 0, 1, 0], #[0, -1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, 0, -64, 0, 0, 128, 128, 0], #[-64, 0, -64, 0, 128, 0, 0, -128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, 0, 64, 0, 0, -128, 128, 0], #[-64, 0, -64, 0, 128, 0, 0, 128]] }, by decide⟩ + +def certified673 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, 0, 0, 2, 0], #[0, 2, 0, 0, 0, 0, 0, -2], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[2, 0, 0, 0, 0, 0, 2, 0], #[0, -2, 0, 0, 0, 0, 0, 2]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[1, 0, 1, 0, 1, 0, 1, 0], #[-1, 0, 0, 0, 0, 0, 1, 0], #[0, 1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, 0, -64, 0, 0, 128, -128, 0], #[-64, 0, -64, 0, 128, 0, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, 0, -64, 0, 0, 128, 128, 0], #[64, 0, 64, 0, -128, 0, 0, 128]] }, by decide⟩ + +def certified674 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, 0, 0, 0, -2], #[0, 2, 0, 0, 0, 0, 2, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 2, 0, 0, 0, 0, 2, 0], #[-2, 0, 0, 0, 0, 0, 0, 2]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, 1, 0, 0, 0, 0, 1, -1], #[1, -1, 0, 0, 0, 0, -1, -1], #[0, -1, 0, 0, 0, 0, 1, 0], #[1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 0, 64, 64, 0, 128], #[0, 0, 0, 0, 64, -64, -128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 64, -64, 128, 0], #[0, 0, 0, 0, -64, -64, 0, 128]] }, by decide⟩ + +def certified675 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 2, 0, 0, 0, 0, 0, 0], #[2, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 2, -2], #[0, 0, 0, 0, 0, 0, -2, 2]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, 1, 0, 0, 0, 0, 1, -1], #[1, 1, 0, 0, 0, 0, -1, 1], #[-1, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 1]], + inverse256 := #[#[0, 0, 0, 0, 64, 64, -128, 0], #[0, 0, 0, 0, 64, 64, 128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 64, -64, 0, 128], #[0, 0, 0, 0, -64, 64, 0, 128]] }, by decide⟩ + +def certified676 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, -2, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[-2, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, -2, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, -2, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, -1, 0, 1, 0, -1, 0], #[1, 0, -1, 0, -1, 0, 1, 0], #[1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 1, 0]], + inverse256 := #[#[0, 0, 0, 0, 64, 64, 128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, -64, -64, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, -64, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, -64, 64, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified677 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, 0, 0, -2, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, -2, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, -2, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[-2, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, -1, 0, 0, 1], #[1, 0, 1, 0, -1, 0, -1, 0], #[0, 0, 1, 0, 1, 0, 0, 0], #[1, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[64, 0, 0, 64, -128, 128, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 0, 0, 64, -128, 0, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, -128, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified678 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, -2, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, -2, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[-2, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, -2, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, -1, 0, -1, 0], #[1, 0, -1, 0, -1, 0, 1, 0], #[1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 1, 0]], + inverse256 := #[#[0, 0, 0, 0, 64, 64, 128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, -64, 0, 128], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, -64, -64, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, -64, 64, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified679 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, 2, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 2, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[2, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 2, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 0, -1, 0, 1, 0, -1, 0], #[-1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, -1, 0, 0, 0, 1, 0]], + inverse256 := #[#[0, 0, 0, 0, 64, 64, -128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, -64, 0, -128], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, 64, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, -64, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified680 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, 0, 0, 2, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 2, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 2, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[2, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, 1, 0], #[0, 0, -1, 0, 1, 0, 0, 0], #[-1, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[64, 0, 0, 64, -128, 128, 0, -128], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, -128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, 0, 0, 64, -128, 128, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified681 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 2, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[2, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 2, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 2, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 0, 1, 0, -1, 0, -1, 0], #[-1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, -1, 0, 1, 0]], + inverse256 := #[#[0, 0, 0, 0, 64, 64, -128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, 64, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, -64, 0, -128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, -64, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified682 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, -2, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[-2, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 2, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 2, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, -1, 0, 1, 0, 1, 0], #[1, 0, -1, 0, -1, 0, -1, 0], #[1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, -1, 0, 1, 0]], + inverse256 := #[#[0, 0, 0, 0, 64, 64, 128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, -64, -64, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, -64, 0, -128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, -64, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified683 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, 0, 0, 2, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, -2, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, -2, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[2, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, -1, 0, 0, 1], #[1, 0, 1, 0, -1, 0, 1, 0], #[0, 0, 1, 0, 1, 0, 0, 0], #[-1, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[64, 0, 0, 64, -128, 128, 0, -128], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 0, 0, 64, -128, 0, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, 0, 0, 64, -128, 128, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified684 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, -2, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 2, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[-2, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 2, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, -1, 0, 1, 0], #[1, 0, -1, 0, -1, 0, -1, 0], #[1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, -1, 0, 0, 0, 1, 0]], + inverse256 := #[#[0, 0, 0, 0, 64, 64, 128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, -64, 0, -128], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, -64, -64, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, -64, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified685 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, 2, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, -2, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[2, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, -2, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 1, 0, -1, 0], #[1, 0, -1, 0, 1, 0, 1, 0], #[-1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 1, 0]], + inverse256 := #[#[0, 0, 0, 0, 64, 64, -128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, -64, 0, 128], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, 64, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, -64, 64, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified686 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, 0, 0, -2, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 2, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 2, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[-2, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, -1, 0], #[0, 0, -1, 0, 1, 0, 0, 0], #[1, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[64, 0, 0, 64, -128, 128, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, -128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, -128, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified687 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 2, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[2, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, -2, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, -2, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 1, 0, -1, 0], #[1, 0, 1, 0, -1, 0, 1, 0], #[-1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 1, 0]], + inverse256 := #[#[0, 0, 0, 0, 64, 64, -128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, 64, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, -64, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, -64, 64, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified688 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, -2, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[-2, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, -2], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, -2, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 0, -1, 0, 1, 0, 1, 0], #[1, 0, -1, 0, 0, 1, 0, -1], #[1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 1]], + inverse256 := #[#[0, 0, -64, -64, 128, 0, 128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 64, 64, -128, 0, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 64, 64, -128, 128, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, -64, -64, 128, -128, 0, 128]] }, by decide⟩ + +def certified689 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, 0, 0, 0, -2], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, -2, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, -2, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[-2, 0, 0, 0, 0, 0, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 1, 0, 0, 0, 0, 1, -1], #[1, 0, 1, 0, 0, -1, 0, -1], #[0, 0, 1, 0, 0, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, 0, 0, -64, 128, 0, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[64, 0, 0, 64, -128, 128, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, -128, 128, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, 0, 0, 64, -128, 0, 0, 128]] }, by decide⟩ + +def certified690 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, 0, -2, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, -2], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[-2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, -2, 0, 0, 0, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[1, 1, 0, 0, 1, -1, 0, 0], #[1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, 0, -64, 0, 0, 128, 128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 0, 128], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, 0, 64, 0, 0, -128, 128, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, 0, 64, 0, -128, 0, 0, 128]] }, by decide⟩ + +def certified691 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, 0, 2, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 2], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 2, 0, 0, 0, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 1, 0, 0, 1, 1, 0, 0], #[-1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, -1, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, 0, -64, 0, 0, 128, -128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 0, -128], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 0, 128, 128, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 0, 128]] }, by decide⟩ + +def certified692 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, 0, 0, 0, 2], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 2, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 2, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[2, 0, 0, 0, 0, 0, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 1, 0, 0, 0, 0, 1, 1], #[1, 0, 1, 0, 0, 1, 0, 1], #[0, 0, -1, 0, 0, 1, 0, 0], #[-1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, 0, 0, -64, 128, 0, 0, -128], #[128, 0, 0, 0, 0, 0, 0, 0], #[64, 0, 0, 64, -128, 128, -128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, 0, 0, 64, -128, 128, 128, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 0, 128]] }, by decide⟩ + +def certified693 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 2, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[2, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 2], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 2, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 0, 1, 0, 0, 1, 0, 1], #[-1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, -1, 0, 1]], + inverse256 := #[#[0, 0, -64, -64, 128, 0, -128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -64, -64, 128, 0, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 64, 64, -128, 128, 0, -128], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 64, 64, -128, 128, 0, 128]] }, by decide⟩ + +def certified694 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, -2, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[-2, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 2], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 2, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 0, -1, 0, 1, 0, 1, 0], #[1, 0, -1, 0, 0, 1, 0, 1], #[1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, -1, 0, 1]], + inverse256 := #[#[0, 0, -64, -64, 128, 0, 128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 64, 64, -128, 0, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 64, 64, -128, 128, 0, -128], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 64, 64, -128, 128, 0, 128]] }, by decide⟩ + +def certified695 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, 0, 0, 0, 2], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, -2, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, -2, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[2, 0, 0, 0, 0, 0, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 1, 0, 0, 0, 0, 1, 1], #[1, 0, 1, 0, 0, -1, 0, 1], #[0, 0, 1, 0, 0, 1, 0, 0], #[-1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, 0, 0, -64, 128, 0, 0, -128], #[128, 0, 0, 0, 0, 0, 0, 0], #[64, 0, 0, 64, -128, 128, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, -128, 128, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 0, 128]] }, by decide⟩ + +def certified696 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, 0, -2, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 2], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[-2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 2, 0, 0, 0, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 1, 0, 0, 1, -1, 0, 0], #[1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, -1, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, 0, -64, 0, 0, 128, 128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 0, -128], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, 0, 64, 0, 0, -128, 128, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 0, 128]] }, by decide⟩ + +def certified697 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, 0, 2, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, -2], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, -2, 0, 0, 0, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[1, 1, 0, 0, 1, 1, 0, 0], #[-1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, 0, -64, 0, 0, 128, -128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 0, 128], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 0, 128, 128, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, 0, 64, 0, -128, 0, 0, 128]] }, by decide⟩ + +def certified698 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, 0, 0, 0, -2], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 2, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 2, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[-2, 0, 0, 0, 0, 0, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 1, 0, 0, 0, 0, 1, -1], #[1, 0, 1, 0, 0, 1, 0, -1], #[0, 0, -1, 0, 0, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, 0, 0, -64, 128, 0, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[64, 0, 0, 64, -128, 128, -128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, 0, 0, 64, -128, 128, 128, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, 0, 0, 64, -128, 0, 0, 128]] }, by decide⟩ + +def certified699 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 2, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[2, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, -2], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, -2, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 0, 1, 0, 0, 1, 0, -1], #[-1, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 1]], + inverse256 := #[#[0, 0, -64, -64, 128, 0, -128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -64, -64, 128, 0, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 64, 64, -128, 128, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, -64, -64, 128, -128, 0, 128]] }, by decide⟩ + +def certified700 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, -2, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[-2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, -2], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, -2, 0, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[1, 1, 1, -1, 0, 0, 0, 0], #[1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 1]], + inverse256 := #[#[-64, -64, 0, 0, 0, 128, 128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 64, 0, 0, 0, -128, 128, 0], #[-64, -64, 0, 0, 128, 0, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, 64, 0, 0, -128, 0, 0, 128]] }, by decide⟩ + +def certified701 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, 0, 0, 0, -2], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, -2, 0, 0, 0], #[0, 0, 0, -2, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[-2, 0, 0, 0, 0, 0, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 1, 0, 0, 0, 0, 1, -1], #[1, 0, 0, 1, -1, 0, 0, -1], #[0, 0, 0, 1, 1, 0, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, 0, 0, -64, 128, 0, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 0, 0, 64, -128, 128, 128, 0], #[-64, 0, 0, -64, 128, -128, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, 0, 0, 64, -128, 0, 0, 128]] }, by decide⟩ + +def certified702 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, -2, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, -2], #[-2, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, -2, 0, 0, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 0, 1, 0, -1, 0, 1, 0], #[1, 0, 0, 1, -1, 0, 0, -1], #[1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 1]], + inverse256 := #[#[0, -64, 0, -64, 128, 0, 128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 64, 0, 64, -128, 128, 0, 128], #[0, 64, 0, 64, -128, 0, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, -64, 0, -64, 128, -128, 0, 128]] }, by decide⟩ + +def certified703 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, 2, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 2], #[2, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 2, 0, 0, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 0, 0, 1, 1, 0, 0, 1], #[-1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, -1, 0, 0, 0, 1]], + inverse256 := #[#[0, -64, 0, -64, 128, 0, -128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 64, 0, 64, -128, 128, 0, -128], #[0, -64, 0, -64, 128, 0, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 64, 0, 64, -128, 128, 0, 128]] }, by decide⟩ + +def certified704 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, 0, 0, 0, 2], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 2, 0, 0, 0], #[0, 0, 0, 2, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[2, 0, 0, 0, 0, 0, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 1, 0, 0, 0, 0, 1, 1], #[1, 0, 0, 1, 1, 0, 0, 1], #[0, 0, 0, -1, 1, 0, 0, 0], #[-1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, 0, 0, -64, 128, 0, 0, -128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 0, 0, 64, -128, 128, -128, 0], #[64, 0, 0, 64, -128, 128, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 0, 128]] }, by decide⟩ + +def certified705 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 2, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 2], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 2, 0, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 1, 1, 1, 0, 0, 0, 0], #[-1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, -1, 0, 0, 1]], + inverse256 := #[#[-64, -64, 0, 0, 0, 128, -128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 0, 128, 128, 0], #[-64, -64, 0, 0, 128, 0, 0, -128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, 128]] }, by decide⟩ + +def certified706 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, -2, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[-2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 2], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 2, 0, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 1, 1, -1, 0, 0, 0, 0], #[1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, -1, 0, 0, 1]], + inverse256 := #[#[-64, -64, 0, 0, 0, 128, 128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 64, 0, 0, 0, -128, 128, 0], #[-64, -64, 0, 0, 128, 0, 0, -128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, 128]] }, by decide⟩ + +def certified707 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, 0, 0, 0, 2], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, -2, 0, 0, 0], #[0, 0, 0, -2, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[2, 0, 0, 0, 0, 0, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 1, 0, 0, 0, 0, 1, 1], #[1, 0, 0, 1, -1, 0, 0, 1], #[0, 0, 0, 1, 1, 0, 0, 0], #[-1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, 0, 0, -64, 128, 0, 0, -128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 0, 0, 64, -128, 128, 128, 0], #[-64, 0, 0, -64, 128, -128, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 0, 128]] }, by decide⟩ + +def certified708 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, -2, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 2], #[-2, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 2, 0, 0, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 0, 1, 0, -1, 0, 1, 0], #[1, 0, 0, 1, -1, 0, 0, 1], #[1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, -1, 0, 0, 0, 1]], + inverse256 := #[#[0, -64, 0, -64, 128, 0, 128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 64, 0, 64, -128, 128, 0, -128], #[0, 64, 0, 64, -128, 0, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 64, 0, 64, -128, 128, 0, 128]] }, by decide⟩ + +def certified709 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, 2, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, -2], #[2, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, -2, 0, 0, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 0, 0, 1, 1, 0, 0, -1], #[-1, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 1]], + inverse256 := #[#[0, -64, 0, -64, 128, 0, -128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 64, 0, 64, -128, 128, 0, 128], #[0, -64, 0, -64, 128, 0, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, -64, 0, -64, 128, -128, 0, 128]] }, by decide⟩ + +def certified710 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, 0, 0, 0, -2], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 2, 0, 0, 0], #[0, 0, 0, 2, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[-2, 0, 0, 0, 0, 0, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 1, 0, 0, 0, 0, 1, -1], #[1, 0, 0, 1, 1, 0, 0, -1], #[0, 0, 0, -1, 1, 0, 0, 0], #[1, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[-64, 0, 0, -64, 128, 0, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 0, 0, 64, -128, 128, -128, 0], #[64, 0, 0, 64, -128, 128, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, 0, 0, 64, -128, 0, 0, 128]] }, by decide⟩ + +def certified711 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 2, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, -2], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, -2, 0, 0, 2]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[1, 1, 1, 1, 0, 0, 0, 0], #[-1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 1]], + inverse256 := #[#[-64, -64, 0, 0, 0, 128, -128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 0, 128, 128, 0], #[-64, -64, 0, 0, 128, 0, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, 64, 0, 0, -128, 0, 0, 128]] }, by decide⟩ + +def certified712 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, -2, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[-2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 2, -2, 0], #[0, 0, 0, 0, 0, -2, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 0, 1, -1, 0], #[1, 1, 1, -1, 0, 0, 0, 0], #[1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 1, 0]], + inverse256 := #[#[-64, -64, 0, 0, 0, 128, 128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 64, 0, 0, 0, -128, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, 128], #[64, 64, 0, 0, -128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified713 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, 0, 0, -2, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, -2, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, -2, 0, 2, 0, 0], #[-2, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 1, 0, -1, 0], #[0, 0, 1, 1, 1, -1, 0, 0], #[0, 0, 0, 1, 0, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[0, -64, -64, 0, 128, 0, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, -64, -64, 0, 0, 128, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 64, 64, 0, 0, -128, 128, 0], #[0, 64, 64, 0, -128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified714 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, 0, -2, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, -2, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[-2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, -2, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 0, 0, 1, -1, 0, 0], #[0, 1, 0, 1, 1, 0, -1, 0], #[1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 1, 0, 0, 1, 0]], + inverse256 := #[#[-64, 0, -64, 0, 128, 0, 128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 0, 128, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, 0, 64, 0, -128, 0, 128, 0], #[64, 0, 64, 0, 0, -128, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified715 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, 0, 2, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 2, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 2, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 0, 0, 1, 1, 0, 0], #[0, 1, 0, 1, 1, 0, 1, 0], #[-1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, -1, 0, 0, 1, 0]], + inverse256 := #[#[-64, 0, -64, 0, 128, 0, -128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 0, 128, 0, -128], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 128, 0], #[-64, 0, -64, 0, 0, 128, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified716 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, 0, 0, 2, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 2, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 2, 0, 2, 0, 0], #[2, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 1, 0, 1, 0], #[0, 0, 1, 1, 1, 1, 0, 0], #[0, 0, 0, -1, 0, 1, 0, 0], #[-1, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[0, -64, -64, 0, 128, 0, 0, -128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, -64, -64, 0, 0, 128, -128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, -64, -64, 0, 0, 128, 128, 0], #[0, -64, -64, 0, 128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified717 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 2, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 2, 0], #[0, 0, 0, 0, 0, 2, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 0, 1, 1, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[-1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, -1, 1, 0]], + inverse256 := #[#[-64, -64, 0, 0, 0, 128, -128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 0, 128, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, -128], #[-64, -64, 0, 0, 128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified718 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, -2, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[-2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 2, 0], #[0, 0, 0, 0, 0, 2, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 0, 1, 1, 0], #[1, 1, 1, -1, 0, 0, 0, 0], #[1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, -1, 1, 0]], + inverse256 := #[#[-64, -64, 0, 0, 0, 128, 128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 64, 0, 0, 0, -128, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, -128], #[-64, -64, 0, 0, 128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified719 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, 0, 0, 2, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, -2, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, -2, 0, 2, 0, 0], #[2, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 1, 0, 1, 0], #[0, 0, 1, 1, 1, -1, 0, 0], #[0, 0, 0, 1, 0, 1, 0, 0], #[-1, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[0, -64, -64, 0, 128, 0, 0, -128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, -64, -64, 0, 0, 128, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 64, 64, 0, 0, -128, 128, 0], #[0, -64, -64, 0, 128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified720 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, 0, -2, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 2, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[-2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 2, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 0, 0, 1, -1, 0, 0], #[0, 1, 0, 1, 1, 0, 1, 0], #[1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, -1, 0, 0, 1, 0]], + inverse256 := #[#[-64, 0, -64, 0, 128, 0, 128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 0, 128, 0, -128], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, 0, 64, 0, -128, 0, 128, 0], #[-64, 0, -64, 0, 0, 128, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified721 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, 0, 2, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, -2, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[2, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, -2, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 0, 0, 1, 1, 0, 0], #[0, 1, 0, 1, 1, 0, -1, 0], #[-1, 0, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 1, 0, 0, 1, 0]], + inverse256 := #[#[-64, 0, -64, 0, 128, 0, -128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 0, 128, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 128, 0], #[64, 0, 64, 0, 0, -128, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified722 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 0, 0, 0, -2, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 2, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 2, 0, 2, 0, 0], #[-2, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 1, 0, -1, 0], #[0, 0, 1, 1, 1, 1, 0, 0], #[0, 0, 0, -1, 0, 1, 0, 0], #[1, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[0, -64, -64, 0, 128, 0, 0, 128], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, -64, -64, 0, 0, 128, -128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, -64, -64, 0, 0, 128, 128, 0], #[0, 64, 64, 0, -128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified723 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[2, 0, 0, 2, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[2, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 2, -2, 0], #[0, 0, 0, 0, 0, -2, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 0, 1, -1, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[-1, 0, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 1, 0]], + inverse256 := #[#[-64, -64, 0, 0, 0, 128, -128, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 0, 128, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, 128], #[64, 64, 0, 0, -128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified724 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, -2, 0, 0, 0, 0, 0], #[0, -2, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, -2], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, -2, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, -1, 0, 1, 0, 0, -1], #[0, 1, -1, 0, -1, 0, 0, 1], #[0, 1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, 64, 128, 0], #[0, 0, 0, 0, -64, -64, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, -64, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, -64, 64, 0, 128]] }, by decide⟩ + +def certified725 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, -2], #[0, 0, 2, 0, -2, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, -2, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, -2, 0, 0, 0, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, -1, 0, 0, -1], #[0, 1, -1, 0, 1, 0, 0, -1], #[0, 0, 1, 0, 1, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, 64, 0, 128], #[0, 0, 0, 0, 64, -64, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, -64, 64, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, -64, -64, 0, 128]] }, by decide⟩ + +def certified726 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, -2, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, -2], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, -2, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, -2, 0, 0, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, -1, 0, 0, -1], #[0, 1, -1, 0, -1, 0, 0, 1], #[0, 1, 0, 0, 1, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, 64, 128, 0], #[0, 0, 0, 0, 64, -64, 0, 128], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, -64, -64, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, -64, 64, 0, 128]] }, by decide⟩ + +def certified727 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 2, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 2], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 2, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 2, 0, 0, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[0, 1, -1, 0, 1, 0, 0, -1], #[0, -1, 0, 0, 1, 0, 0, 0], #[0, 0, -1, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, 64, -128, 0], #[0, 0, 0, 0, 64, -64, 0, -128], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, 64, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 64, -64, 0, 128]] }, by decide⟩ + +def certified728 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 2], #[0, 0, 2, 0, 2, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 2, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 2, 0, 0, 0, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[0, 1, -1, 0, -1, 0, 0, 1], #[0, 0, -1, 0, 1, 0, 0, 0], #[0, -1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, 64, 0, -128], #[0, 0, 0, 0, 64, -64, -128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, -64, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 64, 64, 0, 128]] }, by decide⟩ + +def certified729 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 2, 0, 0, 0, 0, 0], #[0, 2, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 2], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 2, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[0, 1, 1, 0, -1, 0, 0, -1], #[0, -1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, -1, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, 64, -128, 0], #[0, 0, 0, 0, 64, 64, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, -64, 0, -128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 64, -64, 0, 128]] }, by decide⟩ + +def certified730 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, -2, 0, 0, 0, 0, 0], #[0, -2, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 2], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 2, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, -1, 0, 1, 0, 0, 1], #[0, 1, -1, 0, -1, 0, 0, -1], #[0, 1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, -1, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, 64, 128, 0], #[0, 0, 0, 0, -64, -64, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, -64, 0, -128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 64, -64, 0, 128]] }, by decide⟩ + +def certified731 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 2], #[0, 0, 2, 0, -2, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, -2, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 2, 0, 0, 0, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, -1, 0, 0, 1], #[0, 1, -1, 0, 1, 0, 0, 1], #[0, 0, 1, 0, 1, 0, 0, 0], #[0, -1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, 64, 0, -128], #[0, 0, 0, 0, 64, -64, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, -64, 64, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 64, 64, 0, 128]] }, by decide⟩ + +def certified732 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, -2, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 2], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, -2, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 2, 0, 0, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, -1, 0, 0, 1], #[0, 1, -1, 0, -1, 0, 0, -1], #[0, 1, 0, 0, 1, 0, 0, 0], #[0, 0, -1, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, 64, 128, 0], #[0, 0, 0, 0, 64, -64, 0, -128], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, -64, -64, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 64, -64, 0, 128]] }, by decide⟩ + +def certified733 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 2, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, -2], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 2, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, -2, 0, 0, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[0, 1, -1, 0, 1, 0, 0, 1], #[0, -1, 0, 0, 1, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, 64, -128, 0], #[0, 0, 0, 0, 64, -64, 0, 128], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, 64, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, -64, 64, 0, 128]] }, by decide⟩ + +def certified734 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, -2], #[0, 0, 2, 0, 2, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 2, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, -2, 0, 0, 0, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[0, 1, -1, 0, -1, 0, 0, -1], #[0, 0, -1, 0, 1, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, 64, 0, 128], #[0, 0, 0, 0, 64, -64, -128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, -64, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, -64, -64, 0, 128]] }, by decide⟩ + +def certified735 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 2, 0, 0, 0, 0, 0], #[0, 2, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, -2], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, -2, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[0, 1, 1, 0, -1, 0, 0, 1], #[0, -1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, 64, -128, 0], #[0, 0, 0, 0, 64, 64, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, -64, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, -64, 64, 0, 128]] }, by decide⟩ + +def certified736 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, -2, 0, 0, 0, 0, 0], #[0, -2, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 2, -2, 0], #[0, 0, 0, 0, 0, -2, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, -1, 0, 1, 0, 0, 1], #[0, 1, -1, 0, 0, 1, -1, 0], #[0, 1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -64, -64, 128, 0, 128, 0], #[0, 0, 64, 64, -128, 0, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 64, 64, -128, 128, 0, 128], #[0, 0, -64, -64, 128, -128, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified737 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, -2, 0], #[0, 0, 2, 0, 0, -2, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, -2, 0, 0, 2, 0, 0], #[0, -2, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 0, 0, 0, 0, -1, 1], #[1, 0, 1, 0, 0, -1, 0, 1], #[0, 0, 1, 0, 0, 1, 0, 0], #[0, 1, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 0, 128], #[-64, 0, 0, -64, 0, 128, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, 0, 0, 64, 0, -128, 128, 0], #[64, 0, 0, 64, -128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified738 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, -2, 0, 0], #[0, 0, 2, 0, 0, 0, -2, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, -2, 0, 0, 0, 2, 0, 0], #[0, 0, -2, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 1, 0, -1, 0], #[1, 1, 0, 0, 1, -1, 0, 0], #[0, 1, 0, 0, 0, 1, 0, 0], #[0, 0, 1, 0, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 0, 128, 128, 0], #[-64, 0, -64, 0, 128, 0, 0, 128], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, 0, 64, 0, 0, -128, 128, 0], #[64, 0, 64, 0, -128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified739 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 2, 0, 0], #[0, 0, 2, 0, 0, 0, 2, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 2, 0, 0, 0, 2, 0, 0], #[0, 0, 2, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 0, 0, 1, 1, 0, 0], #[0, -1, 0, 0, 0, 1, 0, 0], #[0, 0, -1, 0, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 0, 128, -128, 0], #[-64, 0, -64, 0, 128, 0, 0, -128], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 0, 128, 128, 0], #[-64, 0, -64, 0, 128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified740 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 2, 0], #[0, 0, 2, 0, 0, 2, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 2, 0, 0, 2, 0, 0], #[0, 2, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 0, 0, 0, 0, 1, 1], #[1, 0, 1, 0, 0, 1, 0, 1], #[0, 0, -1, 0, 0, 1, 0, 0], #[0, -1, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 0, -128], #[-64, 0, 0, -64, 0, 128, -128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 0, 128, 128, 0], #[-64, 0, 0, -64, 128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified741 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 2, 0, 0, 0, 0, 0], #[0, 2, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 2, 0], #[0, 0, 0, 0, 0, 2, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[0, 1, 1, 0, 0, 1, 1, 0], #[0, -1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, -1, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -64, -64, 128, 0, -128, 0], #[0, 0, -64, -64, 128, 0, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 64, 64, -128, 128, 0, -128], #[0, 0, 64, 64, -128, 128, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified742 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, -2, 0, 0, 0, 0, 0], #[0, -2, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 2, 0], #[0, 0, 0, 0, 0, 2, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, -1, 0, 1, 0, 0, 1], #[0, 1, -1, 0, 0, 1, 1, 0], #[0, 1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, -1, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -64, -64, 128, 0, 128, 0], #[0, 0, 64, 64, -128, 0, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 64, 64, -128, 128, 0, -128], #[0, 0, 64, 64, -128, 128, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified743 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 2, 0], #[0, 0, 2, 0, 0, -2, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, -2, 0, 0, 2, 0, 0], #[0, 2, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 0, 0, 0, 0, 1, 1], #[1, 0, 1, 0, 0, -1, 0, 1], #[0, 0, 1, 0, 0, 1, 0, 0], #[0, -1, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 0, -128], #[-64, 0, 0, -64, 0, 128, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, 0, 0, 64, 0, -128, 128, 0], #[-64, 0, 0, -64, 128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified744 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, -2, 0, 0], #[0, 0, 2, 0, 0, 0, 2, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, -2, 0, 0, 0, 2, 0, 0], #[0, 0, 2, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 0, 0, 1, -1, 0, 0], #[0, 1, 0, 0, 0, 1, 0, 0], #[0, 0, -1, 0, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 0, 128, 128, 0], #[-64, 0, -64, 0, 128, 0, 0, -128], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, 0, 64, 0, 0, -128, 128, 0], #[-64, 0, -64, 0, 128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified745 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 2, 0, 0], #[0, 0, 2, 0, 0, 0, -2, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 2, 0, 0, 0, 2, 0, 0], #[0, 0, -2, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 1, 0, -1, 0], #[1, 1, 0, 0, 1, 1, 0, 0], #[0, -1, 0, 0, 0, 1, 0, 0], #[0, 0, 1, 0, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 0, 128, -128, 0], #[-64, 0, -64, 0, 128, 0, 0, 128], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 0, 128, 128, 0], #[64, 0, 64, 0, -128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified746 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, -2, 0], #[0, 0, 2, 0, 0, 2, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 2, 0, 0, 2, 0, 0], #[0, -2, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 0, 0, 0, 0, -1, 1], #[1, 0, 1, 0, 0, 1, 0, 1], #[0, 0, -1, 0, 0, 1, 0, 0], #[0, 1, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 0, 128], #[-64, 0, 0, -64, 0, 128, -128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 0, 128, 128, 0], #[64, 0, 0, 64, -128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified747 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 2, 0, 0, 0, 0, 0], #[0, 2, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 2, -2, 0], #[0, 0, 0, 0, 0, -2, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[0, 1, 1, 0, 0, 1, -1, 0], #[0, -1, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -64, -64, 128, 0, -128, 0], #[0, 0, -64, -64, 128, 0, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 64, 64, -128, 128, 0, 128], #[0, 0, -64, -64, 128, -128, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified748 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, -2, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, -2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, -2, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, -2, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 1, 0, -1, 0], #[1, 1, 1, -1, 0, 0, 0, 0], #[0, 1, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 0, 128, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 64, 0, 0, 0, -128, 128, 0], #[-64, -64, 0, 0, 128, 0, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, 64, 0, 0, -128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified749 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, -2, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, -2, 0, 0, 0], #[0, 0, 0, -2, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, -2, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 0, 0, 0, 0, -1, 1], #[1, 0, 0, 1, -1, 0, 0, 1], #[0, 0, 0, 1, 1, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 0, 128], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 0, 128, 128, 0], #[64, 0, 0, 64, 0, -128, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, 0, 0, 64, -128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified750 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, -2, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, -2, 0], #[0, -2, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, -2, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, -1, 0, 0, 1], #[0, 1, 0, 1, -1, 0, -1, 0], #[0, 1, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, -64, 0, -64, 128, 0, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 64, 0, 64, -128, 128, 0, 128], #[0, 64, 0, 64, -128, 0, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, -64, 0, -64, 128, -128, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified751 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 2, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 2, 0], #[0, 2, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 2, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[0, 1, 0, 1, 1, 0, 1, 0], #[0, -1, 0, 0, 1, 0, 0, 0], #[0, 0, 0, -1, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, -64, 0, -64, 128, 0, -128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 64, 0, 64, -128, 128, 0, -128], #[0, -64, 0, -64, 128, 0, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 64, 0, 64, -128, 128, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified752 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 2, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 2, 0, 0, 0], #[0, 0, 0, 2, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 2, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 0, 0, 0, 0, 1, 1], #[1, 0, 0, 1, 1, 0, 0, 1], #[0, 0, 0, -1, 1, 0, 0, 0], #[0, -1, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 0, -128], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 0, 128, -128, 0], #[-64, 0, 0, -64, 0, 128, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified753 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 2, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 2, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 2, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[0, -1, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, -1, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 0, 128, -128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 0, 128, 128, 0], #[-64, -64, 0, 0, 128, 0, 0, -128], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified754 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, -2, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, -2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 2, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 2, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 1, -1, 0, 0, 0, 0], #[0, 1, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, -1, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 0, 128, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 64, 0, 0, 0, -128, 128, 0], #[-64, -64, 0, 0, 128, 0, 0, -128], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified755 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 2, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, -2, 0, 0, 0], #[0, 0, 0, -2, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 2, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 0, 0, 0, 0, 1, 1], #[1, 0, 0, 1, -1, 0, 0, 1], #[0, 0, 0, 1, 1, 0, 0, 0], #[0, -1, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 0, -128], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 0, 128, 128, 0], #[64, 0, 0, 64, 0, -128, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified756 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, -2, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 2, 0], #[0, -2, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 2, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, -1, 0, 0, 1], #[0, 1, 0, 1, -1, 0, 1, 0], #[0, 1, 0, 0, 1, 0, 0, 0], #[0, 0, 0, -1, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, -64, 0, -64, 128, 0, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 64, 0, 64, -128, 128, 0, -128], #[0, 64, 0, 64, -128, 0, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 64, 0, 64, -128, 128, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified757 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 2, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, -2, 0], #[0, 2, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, -2, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[0, 1, 0, 1, 1, 0, -1, 0], #[0, -1, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, -64, 0, -64, 128, 0, -128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 64, 0, 64, -128, 128, 0, 128], #[0, -64, 0, -64, 128, 0, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, -64, 0, -64, 128, -128, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified758 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, -2, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 2, 0, 0, 0], #[0, 0, 0, 2, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, -2, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 0, 0, 0, 0, -1, 1], #[1, 0, 0, 1, 1, 0, 0, 1], #[0, 0, 0, -1, 1, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 0, 128], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 0, 128, -128, 0], #[-64, 0, 0, -64, 0, 128, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, 0, 0, 64, -128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified759 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 2, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, -2, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, -2, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 1, 0, -1, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[0, -1, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 0, 128, -128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 0, 128, 128, 0], #[-64, -64, 0, 0, 128, 0, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, 64, 0, 0, -128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified760 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, -2, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, -2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, -2], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, -2, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 0, 1, 0, 0, 1, 0, -1], #[1, 1, 1, -1, 0, 0, 0, 0], #[0, 1, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 0, 128, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 64, 0, 0, 0, -128, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, 64, 0, 0, -128, 0, 0, 128]] }, by decide⟩ + +def certified761 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, -2], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, -2, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, -2, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, -2, 0, 0, 0, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[0, 0, 1, 1, 1, -1, 0, 0], #[0, 0, 0, 1, 0, 1, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, -64, -64, 0, 128, 0, 0, 128], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, -64, -64, 0, 0, 128, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 64, 64, 0, 0, -128, 128, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 64, 64, 0, -128, 0, 0, 128]] }, by decide⟩ + +def certified762 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, -2, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, -2], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, -2, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, -2, 0, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 1, 0, 0, 1, -1, 0, 0], #[1, 0, 0, 1, 1, 0, 0, -1], #[0, 1, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 0, 128, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, 0, 64, 0, -128, 0, 128, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, 0, 64, 0, 0, -128, 0, 128]] }, by decide⟩ + +def certified763 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 2, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 2], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 2, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 2, 0, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 1, 0, 0, 1, 1, 0, 0], #[1, 0, 0, 1, 1, 0, 0, 1], #[0, -1, 0, 0, 0, 1, 0, 0], #[0, 0, 0, -1, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, -128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 0, 128, 0, -128], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 128, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, 0, -64, 0, 0, 128, 0, 128]] }, by decide⟩ + +def certified764 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 2], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 2, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 2, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 2, 0, 0, 0, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[0, 0, 1, 1, 1, 1, 0, 0], #[0, 0, 0, -1, 0, 1, 0, 0], #[0, -1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, -64, -64, 0, 128, 0, 0, -128], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, -64, -64, 0, 0, 128, -128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, -64, -64, 0, 0, 128, 128, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, -64, -64, 0, 128, 0, 0, 128]] }, by decide⟩ + +def certified765 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 2, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 2], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 2, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 0, 1, 0, 0, 1, 0, 1], #[1, 1, 1, 1, 0, 0, 0, 0], #[0, -1, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, -1, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 0, 128, -128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 0, 128, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, -128], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, 128]] }, by decide⟩ + +def certified766 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, -2, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, -2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 2], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 2, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 0, 1, 0, 0, 1, 0, 1], #[1, 1, 1, -1, 0, 0, 0, 0], #[0, 1, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, -1, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 0, 128, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 64, 0, 0, 0, -128, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, -128], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, 128]] }, by decide⟩ + +def certified767 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 2], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, -2, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, -2, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 2, 0, 0, 0, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[0, 0, 1, 1, 1, -1, 0, 0], #[0, 0, 0, 1, 0, 1, 0, 0], #[0, -1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, -64, -64, 0, 128, 0, 0, -128], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, -64, -64, 0, 0, 128, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 64, 64, 0, 0, -128, 128, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, -64, -64, 0, 128, 0, 0, 128]] }, by decide⟩ + +def certified768 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, -2, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 2], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, -2, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 2, 0, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 1, 0, 0, 1, -1, 0, 0], #[1, 0, 0, 1, 1, 0, 0, 1], #[0, 1, 0, 0, 0, 1, 0, 0], #[0, 0, 0, -1, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 0, 128, 0, -128], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, 0, 64, 0, -128, 0, 128, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, 0, -64, 0, 0, 128, 0, 128]] }, by decide⟩ + +def certified769 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 2, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, -2], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 2, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, -2, 0, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 1, 0, 0, 1, 1, 0, 0], #[1, 0, 0, 1, 1, 0, 0, -1], #[0, -1, 0, 0, 0, 1, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, -128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 0, 128, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 128, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, 0, 64, 0, 0, -128, 0, 128]] }, by decide⟩ + +def certified770 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, -2], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 2, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 2, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, -2, 0, 0, 0, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[0, 0, 1, 1, 1, 1, 0, 0], #[0, 0, 0, -1, 0, 1, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, -64, -64, 0, 128, 0, 0, 128], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, -64, -64, 0, 0, 128, -128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, -64, -64, 0, 0, 128, 128, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 64, 64, 0, -128, 0, 0, 128]] }, by decide⟩ + +def certified771 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 2, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 2, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, -2], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, -2, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 0, 1, 0, 0, 1, 0, -1], #[1, 1, 1, 1, 0, 0, 0, 0], #[0, -1, 0, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 0, 128, -128, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 0, 128, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, 128], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, 64, 0, 0, -128, 0, 0, 128]] }, by decide⟩ + +def certified772 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, -2, 0, 0, 0, 0], #[0, 0, -2, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, -2, 0, 0], #[0, 0, 0, 0, -2, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 0, 0, 1, -1, 0, 0], #[1, 1, 1, -1, 0, 0, 0, 0], #[0, 0, 1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 1, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 0, 128, 128, 0], #[64, 64, 0, 0, 0, -128, 128, 0], #[-64, -64, 0, 0, 128, 0, 0, 128], #[64, 64, 0, 0, -128, 0, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified773 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, -2, 0, 0], #[0, 0, 0, 2, -2, 0, 0, 0], #[0, 0, 0, -2, 2, 0, 0, 0], #[0, 0, -2, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 0, -1, 0, 1], #[1, 0, 0, 1, -1, 0, 0, 1], #[0, 0, 0, 1, 1, 0, 0, 0], #[0, 0, 1, 0, 0, 1, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 0, 128], #[-64, 0, 0, -64, 0, 128, 128, 0], #[64, 0, 0, 64, 0, -128, 128, 0], #[64, 0, 0, 64, -128, 0, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified774 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, -2, 0, 0, 0], #[0, 0, 0, 2, 0, -2, 0, 0], #[0, 0, -2, 0, 2, 0, 0, 0], #[0, 0, 0, -2, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, -1, 0, 0, 1], #[0, 0, 1, 1, -1, -1, 0, 0], #[0, 0, 1, 0, 1, 0, 0, 0], #[0, 0, 0, 1, 0, 1, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, -64, 0, -64, 128, 0, 128, 0], #[0, 64, 0, 64, -128, 128, 0, 128], #[0, 64, 0, 64, -128, 0, 128, 0], #[0, -64, 0, -64, 128, -128, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified775 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 2, 0, 0, 0], #[0, 0, 0, 2, 0, 2, 0, 0], #[0, 0, 2, 0, 2, 0, 0, 0], #[0, 0, 0, 2, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[0, 0, 1, 1, 1, 1, 0, 0], #[0, 0, -1, 0, 1, 0, 0, 0], #[0, 0, 0, -1, 0, 1, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, -64, 0, -64, 128, 0, -128, 0], #[0, 64, 0, 64, -128, 128, 0, -128], #[0, -64, 0, -64, 128, 0, 128, 0], #[0, 64, 0, 64, -128, 128, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified776 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 2, 0, 0], #[0, 0, 0, 2, 2, 0, 0, 0], #[0, 0, 0, 2, 2, 0, 0, 0], #[0, 0, 2, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 0, 1, 0, 1], #[1, 0, 0, 1, 1, 0, 0, 1], #[0, 0, 0, -1, 1, 0, 0, 0], #[0, 0, -1, 0, 0, 1, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 0, -128], #[-64, 0, 0, -64, 0, 128, -128, 0], #[-64, 0, 0, -64, 0, 128, 128, 0], #[-64, 0, 0, -64, 128, 0, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified777 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 2, 0, 0, 0, 0], #[0, 0, 2, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 2, 0, 0], #[0, 0, 0, 0, 2, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 0, 0, 1, 1, 0, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[0, 0, -1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, -1, 1, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 0, 128, -128, 0], #[-64, -64, 0, 0, 0, 128, 128, 0], #[-64, -64, 0, 0, 128, 0, 0, -128], #[-64, -64, 0, 0, 128, 0, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified778 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, -2, 0, 0, 0, 0], #[0, 0, -2, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 2, 0, 0], #[0, 0, 0, 0, 2, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 0, 0, 1, 1, 0, 0], #[1, 1, 1, -1, 0, 0, 0, 0], #[0, 0, 1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, -1, 1, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 0, 128, 128, 0], #[64, 64, 0, 0, 0, -128, 128, 0], #[-64, -64, 0, 0, 128, 0, 0, -128], #[-64, -64, 0, 0, 128, 0, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified779 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 2, 0, 0], #[0, 0, 0, 2, -2, 0, 0, 0], #[0, 0, 0, -2, 2, 0, 0, 0], #[0, 0, 2, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 0, 1, 0, 1], #[1, 0, 0, 1, -1, 0, 0, 1], #[0, 0, 0, 1, 1, 0, 0, 0], #[0, 0, -1, 0, 0, 1, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 0, -128], #[-64, 0, 0, -64, 0, 128, 128, 0], #[64, 0, 0, 64, 0, -128, 128, 0], #[-64, 0, 0, -64, 128, 0, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified780 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, -2, 0, 0, 0], #[0, 0, 0, 2, 0, 2, 0, 0], #[0, 0, -2, 0, 2, 0, 0, 0], #[0, 0, 0, 2, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, -1, 0, 0, 1], #[0, 0, 1, 1, -1, 1, 0, 0], #[0, 0, 1, 0, 1, 0, 0, 0], #[0, 0, 0, -1, 0, 1, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, -64, 0, -64, 128, 0, 128, 0], #[0, 64, 0, 64, -128, 128, 0, -128], #[0, 64, 0, 64, -128, 0, 128, 0], #[0, 64, 0, 64, -128, 128, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified781 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 2, 0, 0, 0], #[0, 0, 0, 2, 0, -2, 0, 0], #[0, 0, 2, 0, 2, 0, 0, 0], #[0, 0, 0, -2, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[0, 0, 1, 1, 1, -1, 0, 0], #[0, 0, -1, 0, 1, 0, 0, 0], #[0, 0, 0, 1, 0, 1, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, -64, 0, -64, 128, 0, -128, 0], #[0, 64, 0, 64, -128, 128, 0, 128], #[0, -64, 0, -64, 128, 0, 128, 0], #[0, -64, 0, -64, 128, -128, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified782 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, -2, 0, 0], #[0, 0, 0, 2, 2, 0, 0, 0], #[0, 0, 0, 2, 2, 0, 0, 0], #[0, 0, -2, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 0, -1, 0, 1], #[1, 0, 0, 1, 1, 0, 0, 1], #[0, 0, 0, -1, 1, 0, 0, 0], #[0, 0, 1, 0, 0, 1, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 0, 128], #[-64, 0, 0, -64, 0, 128, -128, 0], #[-64, 0, 0, -64, 0, 128, 128, 0], #[64, 0, 0, 64, -128, 0, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified783 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 2, 0, 0, 0, 0], #[0, 0, 2, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, -2, 0, 0], #[0, 0, 0, 0, -2, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 1, 0, 0, 1, -1, 0, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[0, 0, -1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 1, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 0, 128, -128, 0], #[-64, -64, 0, 0, 0, 128, 128, 0], #[-64, -64, 0, 0, 128, 0, 0, 128], #[64, 64, 0, 0, -128, 0, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified784 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, -2, 0, 0, 0, 0], #[0, 0, -2, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 2, -2], #[0, 0, 0, 0, 0, 0, -2, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, 1, 0, 0, 0, 0, 1, -1], #[1, 1, 1, -1, 0, 0, 0, 0], #[0, 0, 1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 0, 128, 128, 0], #[64, 64, 0, 0, 0, -128, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, 128], #[64, 64, 0, 0, -128, 0, 0, 128]] }, by decide⟩ + +def certified785 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, -2], #[0, 0, 0, 2, 0, 0, -2, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, -2, 0, 0, 2, 0], #[0, 0, -2, 0, 0, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[0, 1, 0, 1, 1, 0, -1, 0], #[0, 0, 0, 1, 0, 0, 1, 0], #[0, 0, 1, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, -64, -64, 0, 128, 0, 0, 128], #[0, -64, -64, 0, 0, 128, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 64, 64, 0, 0, -128, 128, 0], #[0, 64, 64, 0, -128, 0, 0, 128]] }, by decide⟩ + +def certified786 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, -2, 0], #[0, 0, 0, 2, 0, 0, 0, -2], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, -2, 0, 0, 0, 2, 0], #[0, 0, 0, -2, 0, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, 0, 1, 0, 1, 0, -1, 0], #[1, 0, 0, 1, 1, 0, 0, -1], #[0, 0, 1, 0, 0, 0, 1, 0], #[0, 0, 0, 1, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 128, 0], #[-64, 0, -64, 0, 0, 128, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, 0, 64, 0, -128, 0, 128, 0], #[64, 0, 64, 0, 0, -128, 0, 128]] }, by decide⟩ + +def certified787 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 2, 0], #[0, 0, 0, 2, 0, 0, 0, 2], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 2, 0, 0, 0, 2, 0], #[0, 0, 0, 2, 0, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 0, 0, 1, 1, 0, 0, 1], #[0, 0, -1, 0, 0, 0, 1, 0], #[0, 0, 0, -1, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, -128, 0], #[-64, 0, -64, 0, 0, 128, 0, -128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 128, 0], #[-64, 0, -64, 0, 0, 128, 0, 128]] }, by decide⟩ + +def certified788 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 2], #[0, 0, 0, 2, 0, 0, 2, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 2, 0, 0, 2, 0], #[0, 0, 2, 0, 0, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[0, 1, 0, 1, 1, 0, 1, 0], #[0, 0, 0, -1, 0, 0, 1, 0], #[0, 0, -1, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, -64, -64, 0, 128, 0, 0, -128], #[0, -64, -64, 0, 0, 128, -128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, -64, -64, 0, 0, 128, 128, 0], #[0, -64, -64, 0, 128, 0, 0, 128]] }, by decide⟩ + +def certified789 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 2, 0, 0, 0, 0], #[0, 0, 2, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 2], #[0, 0, 0, 0, 0, 0, 2, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, 1, 0, 0, 0, 0, 1, 1], #[1, 1, 1, 1, 0, 0, 0, 0], #[0, 0, -1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, -1, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 0, 128, -128, 0], #[-64, -64, 0, 0, 0, 128, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, -128], #[-64, -64, 0, 0, 128, 0, 0, 128]] }, by decide⟩ + +def certified790 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, -2, 0, 0, 0, 0], #[0, 0, -2, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 2], #[0, 0, 0, 0, 0, 0, 2, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, 1, 0, 0, 0, 0, 1, 1], #[1, 1, 1, -1, 0, 0, 0, 0], #[0, 0, 1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, -1, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 0, 128, 128, 0], #[64, 64, 0, 0, 0, -128, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, -128], #[-64, -64, 0, 0, 128, 0, 0, 128]] }, by decide⟩ + +def certified791 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 2], #[0, 0, 0, 2, 0, 0, -2, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, -2, 0, 0, 2, 0], #[0, 0, 2, 0, 0, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[0, 1, 0, 1, 1, 0, -1, 0], #[0, 0, 0, 1, 0, 0, 1, 0], #[0, 0, -1, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, -64, -64, 0, 128, 0, 0, -128], #[0, -64, -64, 0, 0, 128, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 64, 64, 0, 0, -128, 128, 0], #[0, -64, -64, 0, 128, 0, 0, 128]] }, by decide⟩ + +def certified792 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, -2, 0], #[0, 0, 0, 2, 0, 0, 0, 2], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, -2, 0, 0, 0, 2, 0], #[0, 0, 0, 2, 0, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, 0, 1, 0, 1, 0, -1, 0], #[1, 0, 0, 1, 1, 0, 0, 1], #[0, 0, 1, 0, 0, 0, 1, 0], #[0, 0, 0, -1, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 128, 0], #[-64, 0, -64, 0, 0, 128, 0, -128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, 0, 64, 0, -128, 0, 128, 0], #[-64, 0, -64, 0, 0, 128, 0, 128]] }, by decide⟩ + +def certified793 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 2, 0], #[0, 0, 0, 2, 0, 0, 0, -2], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 2, 0, 0, 0, 2, 0], #[0, 0, 0, -2, 0, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 0, 0, 1, 1, 0, 0, -1], #[0, 0, -1, 0, 0, 0, 1, 0], #[0, 0, 0, 1, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, -128, 0], #[-64, 0, -64, 0, 0, 128, 0, 128], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 128, 0], #[64, 0, 64, 0, 0, -128, 0, 128]] }, by decide⟩ + +def certified794 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, -2], #[0, 0, 0, 2, 0, 0, 2, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 2, 0, 0, 2, 0], #[0, 0, -2, 0, 0, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[0, 1, 0, 1, 1, 0, 1, 0], #[0, 0, 0, -1, 0, 0, 1, 0], #[0, 0, 1, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, -64, -64, 0, 128, 0, 0, 128], #[0, -64, -64, 0, 0, 128, -128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, -64, -64, 0, 0, 128, 128, 0], #[0, 64, 64, 0, -128, 0, 0, 128]] }, by decide⟩ + +def certified795 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 2, 0, 0, 0, 0], #[0, 0, 2, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 2, -2], #[0, 0, 0, 0, 0, 0, -2, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[1, 1, 0, 0, 0, 0, 1, -1], #[1, 1, 1, 1, 0, 0, 0, 0], #[0, 0, -1, 1, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 0, 0, 0, 128, -128, 0], #[-64, -64, 0, 0, 0, 128, 128, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, -64, 0, 0, 128, 0, 0, 128], #[64, 64, 0, 0, -128, 0, 0, 128]] }, by decide⟩ + +def certified796 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 2, -2, 0, 0], #[0, 0, 0, 0, -2, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, -2], #[0, 0, 0, 0, 0, 0, -2, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[1, 1, 0, 0, 0, 0, 1, -1], #[1, 1, 0, 0, 1, -1, 0, 0], #[0, 0, 0, 0, 1, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, -64, 0, 0, 0, 128, 128, 0], #[64, 64, 0, 0, 0, -128, 128, 0], #[-64, -64, 0, 0, 128, 0, 0, 128], #[64, 64, 0, 0, -128, 0, 0, 128]] }, by decide⟩ + +def certified797 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, -2], #[0, 0, 0, 0, 0, 2, -2, 0], #[0, 0, 0, 0, 0, -2, 2, 0], #[0, 0, 0, 0, -2, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[0, 1, 1, 0, 0, 1, -1, 0], #[0, 0, 0, 0, 0, 1, 1, 0], #[0, 0, 0, 0, 1, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, -64, -64, 0, 128, 0, 0, 128], #[0, -64, -64, 0, 0, 128, 128, 0], #[0, 64, 64, 0, 0, -128, 128, 0], #[0, 64, 64, 0, -128, 0, 0, 128]] }, by decide⟩ + +def certified798 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, -2, 0], #[0, 0, 0, 0, 0, 2, 0, -2], #[0, 0, 0, 0, -2, 0, 2, 0], #[0, 0, 0, 0, 0, -2, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[1, 0, 1, 0, 1, 0, -1, 0], #[1, 0, 1, 0, 0, 1, 0, -1], #[0, 0, 0, 0, 1, 0, 1, 0], #[0, 0, 0, 0, 0, 1, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 128, 0], #[-64, 0, -64, 0, 0, 128, 0, 128], #[64, 0, 64, 0, -128, 0, 128, 0], #[64, 0, 64, 0, 0, -128, 0, 128]] }, by decide⟩ + +def certified799 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 2, 0], #[0, 0, 0, 0, 0, 2, 0, 2], #[0, 0, 0, 0, 2, 0, 2, 0], #[0, 0, 0, 0, 0, 2, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 0, 1, 0, 0, 1, 0, 1], #[0, 0, 0, 0, -1, 0, 1, 0], #[0, 0, 0, 0, 0, -1, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, -128, 0], #[-64, 0, -64, 0, 0, 128, 0, -128], #[-64, 0, -64, 0, 128, 0, 128, 0], #[-64, 0, -64, 0, 0, 128, 0, 128]] }, by decide⟩ + +def certified800 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 2], #[0, 0, 0, 0, 0, 2, 2, 0], #[0, 0, 0, 0, 0, 2, 2, 0], #[0, 0, 0, 0, 2, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[0, 1, 1, 0, 0, 1, 1, 0], #[0, 0, 0, 0, 0, -1, 1, 0], #[0, 0, 0, 0, -1, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, -64, -64, 0, 128, 0, 0, -128], #[0, -64, -64, 0, 0, 128, -128, 0], #[0, -64, -64, 0, 0, 128, 128, 0], #[0, -64, -64, 0, 128, 0, 0, 128]] }, by decide⟩ + +def certified801 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 2, 0, 0], #[0, 0, 0, 0, 2, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 2], #[0, 0, 0, 0, 0, 0, 2, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[1, 1, 0, 0, 0, 0, 1, 1], #[1, 1, 0, 0, 1, 1, 0, 0], #[0, 0, 0, 0, -1, 1, 0, 0], #[0, 0, 0, 0, 0, 0, -1, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, -64, 0, 0, 0, 128, -128, 0], #[-64, -64, 0, 0, 0, 128, 128, 0], #[-64, -64, 0, 0, 128, 0, 0, -128], #[-64, -64, 0, 0, 128, 0, 0, 128]] }, by decide⟩ + +def certified802 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 2, -2, 0, 0], #[0, 0, 0, 0, -2, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 2], #[0, 0, 0, 0, 0, 0, 2, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[1, 1, 0, 0, 0, 0, 1, 1], #[1, 1, 0, 0, 1, -1, 0, 0], #[0, 0, 0, 0, 1, 1, 0, 0], #[0, 0, 0, 0, 0, 0, -1, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, -64, 0, 0, 0, 128, 128, 0], #[64, 64, 0, 0, 0, -128, 128, 0], #[-64, -64, 0, 0, 128, 0, 0, -128], #[-64, -64, 0, 0, 128, 0, 0, 128]] }, by decide⟩ + +def certified803 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 2], #[0, 0, 0, 0, 0, 2, -2, 0], #[0, 0, 0, 0, 0, -2, 2, 0], #[0, 0, 0, 0, 2, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[0, 1, 1, 0, 0, 1, -1, 0], #[0, 0, 0, 0, 0, 1, 1, 0], #[0, 0, 0, 0, -1, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, -64, -64, 0, 128, 0, 0, -128], #[0, -64, -64, 0, 0, 128, 128, 0], #[0, 64, 64, 0, 0, -128, 128, 0], #[0, -64, -64, 0, 128, 0, 0, 128]] }, by decide⟩ + +def certified804 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, -2, 0], #[0, 0, 0, 0, 0, 2, 0, 2], #[0, 0, 0, 0, -2, 0, 2, 0], #[0, 0, 0, 0, 0, 2, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[1, 0, 1, 0, 1, 0, -1, 0], #[1, 0, 1, 0, 0, 1, 0, 1], #[0, 0, 0, 0, 1, 0, 1, 0], #[0, 0, 0, 0, 0, -1, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, 128, 0], #[-64, 0, -64, 0, 0, 128, 0, -128], #[64, 0, 64, 0, -128, 0, 128, 0], #[-64, 0, -64, 0, 0, 128, 0, 128]] }, by decide⟩ + +def certified805 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 2, 0], #[0, 0, 0, 0, 0, 2, 0, -2], #[0, 0, 0, 0, 2, 0, 2, 0], #[0, 0, 0, 0, 0, -2, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 0, 1, 0, 0, 1, 0, -1], #[0, 0, 0, 0, -1, 0, 1, 0], #[0, 0, 0, 0, 0, 1, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, 0, -64, 0, 128, 0, -128, 0], #[-64, 0, -64, 0, 0, 128, 0, 128], #[-64, 0, -64, 0, 128, 0, 128, 0], #[64, 0, 64, 0, 0, -128, 0, 128]] }, by decide⟩ + +def certified806 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, -2], #[0, 0, 0, 0, 0, 2, 2, 0], #[0, 0, 0, 0, 0, 2, 2, 0], #[0, 0, 0, 0, -2, 0, 0, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[0, 1, 1, 0, 0, 1, 1, 0], #[0, 0, 0, 0, 0, -1, 1, 0], #[0, 0, 0, 0, 1, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, -64, -64, 0, 128, 0, 0, 128], #[0, -64, -64, 0, 0, 128, -128, 0], #[0, -64, -64, 0, 0, 128, 128, 0], #[0, 64, 64, 0, -128, 0, 0, 128]] }, by decide⟩ + +def certified807 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 2, 0, 0], #[0, 0, 0, 0, 2, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, -2], #[0, 0, 0, 0, 0, 0, -2, 2]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[1, 1, 0, 0, 0, 0, 1, -1], #[1, 1, 0, 0, 1, 1, 0, 0], #[0, 0, 0, 0, -1, 1, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, -64, 0, 0, 0, 128, -128, 0], #[-64, -64, 0, 0, 0, 128, 128, 0], #[-64, -64, 0, 0, 128, 0, 0, 128], #[64, 64, 0, 0, -128, 0, 0, 128]] }, by decide⟩ + +def certified808 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0]], + inverse256 := #[#[0, 0, 0, 0, 0, 0, 256, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 128, 0, 0]] }, by decide⟩ + +def certified809 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0]], + inverse256 := #[#[0, 0, 0, 0, 0, 0, 256, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 128, 0, 0]] }, by decide⟩ + +def certified810 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 1, 0, 0, 0, 0, 0, 0]], + inverse256 := #[#[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 128, 0, 0]] }, by decide⟩ + +def certified811 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 1, 0, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 128, 0, 0]] }, by decide⟩ + +def certified812 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 128, 0, 0]] }, by decide⟩ + +def certified813 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 0, 1, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 128, 0, 0]] }, by decide⟩ + +def certified814 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 128, 0, 0]] }, by decide⟩ + +def certified815 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 1, 0, 0, 0, 0, 0]], + inverse256 := #[#[0, 0, 0, 0, 0, 0, 256, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 128, 0, 0]] }, by decide⟩ + +def certified816 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 128, 0, 0]] }, by decide⟩ + +def certified817 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 1, 0, 0, 0, 0]], + inverse256 := #[#[0, 0, 0, 0, 0, 0, 256, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 128, 0, 0]] }, by decide⟩ + +def certified818 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 0, 0, 0, 1, 0, 0, 0], #[0, 0, 0, 0, 0, 1, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 128, 0, 0]] }, by decide⟩ + +def certified819 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 0, 0, 0, 128, 0, 0]] }, by decide⟩ + +def certified820 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified821 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[0, 0, 0, 0, 0, 0, 256, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 0, 0, 0, 128, 0, 0]] }, by decide⟩ + +def certified822 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 256, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified823 : CertifiedFrame := + ⟨{ dimension := 6, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[1, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[0, 0, 0, 0, 0, 0, 256, 0], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified824 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[0, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 0, 0, 0, 0, 0, 0]], + inverse256 := #[#[0, 0, 0, 0, 0, 0, 0, 256], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 128, 0]] }, by decide⟩ + +def certified825 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 0, 0, 0, 0, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 128, 0]] }, by decide⟩ + +def certified826 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 0, 1, 0, 0, 0, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 128, 0]] }, by decide⟩ + +def certified827 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 0, 0, 1, 0, 0, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 128, 0]] }, by decide⟩ + +def certified828 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 0, 0, 0, 1, 0, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 128, 0]] }, by decide⟩ + +def certified829 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 0, 0, 0, 0, 1, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 128, 0]] }, by decide⟩ + +def certified830 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 0, 0, 0, 0, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 256], #[0, 0, 0, 0, 0, 0, 128, 0]] }, by decide⟩ + +def certified831 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 0]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 128, 0, 0, 0], #[0, 0, 0, 0, 0, 128, 0, 0], #[0, 0, 0, 0, 0, 0, 128, 0], #[0, 0, 0, 0, 0, 0, 0, 256]] }, by decide⟩ + +def certified832 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 3, -1, 0, -1, 0, 0, -1], #[0, -1, 3, 0, -1, 0, 0, -1], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, -1, -1, 0, 3, 0, 0, -1], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, -1, -1, 0, -1, 0, 0, 3]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, -1, 0, 0, -1], #[0, 1, -1, 0, 1, 0, 0, -1], #[0, 1, -1, 0, -1, 0, 0, 1], #[0, 1, 1, 0, 1, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, 64, 64, 64], #[0, 0, 0, 0, 64, -64, -64, 64], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, -64, 64, -64, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, -64, -64, 64, 64]] }, by decide⟩ + +def certified833 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 3, -1, 0, -1, 0, 0, 1], #[0, -1, 3, 0, -1, 0, 0, 1], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, -1, -1, 0, 3, 0, 0, 1], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 1, 1, 0, 1, 0, 0, 3]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, -1, 0, 0, 1], #[0, 1, -1, 0, 1, 0, 0, 1], #[0, 1, -1, 0, -1, 0, 0, -1], #[0, -1, -1, 0, -1, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, 64, 64, -64], #[0, 0, 0, 0, 64, -64, -64, -64], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, -64, 64, -64, -64], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 64, 64, -64, 64]] }, by decide⟩ + +def certified834 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 3, -1, 0, 1, 0, 0, -1], #[0, -1, 3, 0, 1, 0, 0, -1], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 1, 1, 0, 3, 0, 0, 1], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, -1, -1, 0, 1, 0, 0, 3]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[0, 1, -1, 0, 1, 0, 0, 1], #[0, 1, -1, 0, -1, 0, 0, -1], #[0, 1, 1, 0, -1, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, 64, 64, 64], #[0, 0, 0, 0, 64, -64, -64, 64], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, 64, -64, -64], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, -64, 64, -64, 64]] }, by decide⟩ + +def certified835 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 3, -1, 0, 1, 0, 0, 1], #[0, -1, 3, 0, 1, 0, 0, 1], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 1, 1, 0, 3, 0, 0, -1], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 1, 1, 0, -1, 0, 0, 3]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[0, 1, -1, 0, 1, 0, 0, -1], #[0, 1, -1, 0, -1, 0, 0, 1], #[0, -1, -1, 0, 1, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, 64, 64, -64], #[0, 0, 0, 0, 64, -64, -64, -64], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, 64, -64, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 64, -64, 64, 64]] }, by decide⟩ + +def certified836 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 3, 1, 0, -1, 0, 0, -1], #[0, 1, 3, 0, 1, 0, 0, 1], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, -1, 1, 0, 3, 0, 0, -1], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, -1, 1, 0, -1, 0, 0, 3]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[0, 1, 1, 0, -1, 0, 0, 1], #[0, 1, -1, 0, -1, 0, 0, -1], #[0, 1, -1, 0, 1, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, 64, 64, 64], #[0, 0, 0, 0, 64, 64, -64, -64], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, -64, -64, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, -64, 64, -64, 64]] }, by decide⟩ + +def certified837 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 3, 1, 0, -1, 0, 0, 1], #[0, 1, 3, 0, 1, 0, 0, -1], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, -1, 1, 0, 3, 0, 0, 1], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 1, -1, 0, 1, 0, 0, 3]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[0, 1, 1, 0, -1, 0, 0, -1], #[0, 1, -1, 0, -1, 0, 0, 1], #[0, -1, 1, 0, -1, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, 64, 64, -64], #[0, 0, 0, 0, 64, 64, -64, 64], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, -64, -64, -64], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 64, -64, 64, 64]] }, by decide⟩ + +def certified838 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 3, 1, 0, 1, 0, 0, -1], #[0, 1, 3, 0, -1, 0, 0, 1], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 1, -1, 0, 3, 0, 0, 1], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, -1, 1, 0, 1, 0, 0, 3]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[0, 1, 1, 0, -1, 0, 0, -1], #[0, 1, -1, 0, 1, 0, 0, -1], #[0, 1, -1, 0, -1, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, 64, 64, 64], #[0, 0, 0, 0, 64, 64, -64, -64], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, -64, 64, -64], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, 64, -64, -64, 64]] }, by decide⟩ + +def certified839 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 3, 1, 0, 1, 0, 0, 1], #[0, 1, 3, 0, -1, 0, 0, -1], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 1, -1, 0, 3, 0, 0, -1], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 1, -1, 0, -1, 0, 0, 3]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[0, 1, 1, 0, -1, 0, 0, 1], #[0, 1, -1, 0, 1, 0, 0, 1], #[0, -1, 1, 0, 1, 0, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, 64, 64, -64], #[0, 0, 0, 0, 64, 64, -64, 64], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 64, -64, 64, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[0, 0, 0, 0, -64, 64, 64, 64]] }, by decide⟩ + +def certified840 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 0, -1, 0, -1, 0, -1, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[-1, 0, 3, 0, -1, 0, -1, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[-1, 0, -1, 0, 3, 0, -1, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[-1, 0, -1, 0, -1, 0, 3, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, -1, 0, 0, 1], #[1, 0, 1, 0, -1, 0, -1, 0], #[1, 0, -1, 0, -1, 0, 1, 0], #[1, 0, 1, 0, 1, 0, 1, 0]], + inverse256 := #[#[64, 0, 0, 64, -128, 128, 64, 64], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, -64, 64], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 0, 0, 64, -128, 0, -64, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, -128, 64, 64], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified841 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 0, -1, 0, -1, 0, 1, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[-1, 0, 3, 0, -1, 0, 1, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[-1, 0, -1, 0, 3, 0, 1, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[1, 0, 1, 0, 1, 0, 3, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, -1, 0, 0, 1], #[1, 0, 1, 0, -1, 0, 1, 0], #[1, 0, -1, 0, -1, 0, -1, 0], #[-1, 0, -1, 0, -1, 0, 1, 0]], + inverse256 := #[#[64, 0, 0, 64, -128, 128, 64, -64], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, -64, -64], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 0, 0, 64, -128, 0, -64, -64], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, 0, 0, 64, -128, 128, -64, 64], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified842 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 0, -1, 0, 1, 0, -1, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[-1, 0, 3, 0, 1, 0, -1, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[1, 0, 1, 0, 3, 0, 1, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[-1, 0, -1, 0, 1, 0, 3, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, -1, 0], #[1, 0, -1, 0, 1, 0, 1, 0], #[1, 0, 1, 0, -1, 0, 1, 0]], + inverse256 := #[#[64, 0, 0, 64, -128, 128, 64, 64], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, -64, 64], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 64, -64], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, -128, 64, 64], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified843 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 0, -1, 0, 1, 0, 1, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[-1, 0, 3, 0, 1, 0, 1, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[1, 0, 1, 0, 3, 0, -1, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[1, 0, 1, 0, -1, 0, 3, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 0, -1, 0, 1, 0, -1, 0], #[-1, 0, -1, 0, 1, 0, 1, 0]], + inverse256 := #[#[64, 0, 0, 64, -128, 128, 64, -64], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, -64, -64], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 64, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, 0, 0, 64, -128, 128, -64, 64], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified844 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 0, 1, 0, -1, 0, -1, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[1, 0, 3, 0, 1, 0, 1, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[-1, 0, 1, 0, 3, 0, -1, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[-1, 0, 1, 0, -1, 0, 3, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, -1, 0], #[1, 0, 1, 0, -1, 0, 1, 0], #[1, 0, -1, 0, 1, 0, 1, 0]], + inverse256 := #[#[64, 0, 0, 64, -128, 128, 64, 64], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 64, -64], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, -64, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, -128, 64, 64], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified845 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 0, 1, 0, -1, 0, 1, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[1, 0, 3, 0, 1, 0, -1, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[-1, 0, 1, 0, 3, 0, 1, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[1, 0, -1, 0, 1, 0, 3, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 0, 1, 0, -1, 0, -1, 0], #[-1, 0, 1, 0, -1, 0, 1, 0]], + inverse256 := #[#[64, 0, 0, 64, -128, 128, 64, -64], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, 64, 64], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 0, -64, -64], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, 0, 0, 64, -128, 128, -64, 64], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified846 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 0, 1, 0, 1, 0, -1, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[1, 0, 3, 0, -1, 0, 1, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[1, 0, -1, 0, 3, 0, 1, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[-1, 0, 1, 0, 1, 0, 3, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, -1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 0, 1, 0, -1, 0, -1, 0], #[1, 0, -1, 0, -1, 0, 1, 0]], + inverse256 := #[#[64, 0, 0, 64, -128, 64, 128, 64], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 64, 0, -64], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 0, 0, 64, -128, 64, 0, -64], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 64, -128, 64], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified847 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 0, 1, 0, 1, 0, 1, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[1, 0, 3, 0, -1, 0, -1, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[1, 0, -1, 0, 3, 0, -1, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[1, 0, -1, 0, -1, 0, 3, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, -1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, -1, 0], #[1, 0, 1, 0, -1, 0, 1, 0], #[-1, 0, 1, 0, 1, 0, 1, 0]], + inverse256 := #[#[64, 0, 0, 64, -128, 64, 128, -64], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, -64, 128, 64, 0, 64], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 0, 0, 64, -128, 64, 0, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, 0, 0, 64, -128, -64, 128, 64], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified848 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, -1, 0, 0, 0, 0, -1, -1], #[-1, 3, 0, 0, 0, 0, -1, -1], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[-1, -1, 0, 0, 0, 0, 3, -1], #[-1, -1, 0, 0, 0, 0, -1, 3]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[1, 0, 1, 0, 1, 0, -1, 0], #[1, -1, 0, 0, 0, 0, 1, -1], #[1, 1, 0, 0, 0, 0, 1, 1]], + inverse256 := #[#[-64, 0, -64, 0, 0, 128, 64, 64], #[-64, 0, -64, 0, 128, 0, -64, 64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, 0, 64, 0, 0, -128, 64, 64], #[64, 0, 64, 0, -128, 0, -64, 64]] }, by decide⟩ + +def certified849 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, -1, 0, 0, 0, 0, -1, 1], #[-1, 3, 0, 0, 0, 0, -1, 1], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[-1, -1, 0, 0, 0, 0, 3, 1], #[1, 1, 0, 0, 0, 0, 1, 3]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, -1, 0], #[1, -1, 0, 0, 0, 0, 1, 1], #[-1, -1, 0, 0, 0, 0, -1, 1]], + inverse256 := #[#[-64, 0, -64, 0, 0, 128, 64, -64], #[-64, 0, -64, 0, 128, 0, -64, -64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, 0, 64, 0, 0, -128, 64, -64], #[-64, 0, -64, 0, 128, 0, 64, 64]] }, by decide⟩ + +def certified850 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, -1, 0, 0, 0, 0, 1, -1], #[-1, 3, 0, 0, 0, 0, 1, -1], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[1, 1, 0, 0, 0, 0, 3, 1], #[-1, -1, 0, 0, 0, 0, 1, 3]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, -1, 0, 0, 0, 0, -1, -1], #[1, 1, 0, 0, 0, 0, -1, 1]], + inverse256 := #[#[-64, 0, -64, 0, 0, 128, 64, 64], #[-64, 0, -64, 0, 128, 0, -64, 64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, 0, -64, 0, 0, 128, -64, -64], #[64, 0, 64, 0, -128, 0, -64, 64]] }, by decide⟩ + +def certified851 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, -1, 0, 0, 0, 0, 1, 1], #[-1, 3, 0, 0, 0, 0, 1, 1], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[1, 1, 0, 0, 0, 0, 3, -1], #[1, 1, 0, 0, 0, 0, -1, 3]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, -1, 0, 0, 0, 0, -1, 1], #[-1, -1, 0, 0, 0, 0, 1, 1]], + inverse256 := #[#[-64, 0, -64, 0, 0, 128, 64, -64], #[-64, 0, -64, 0, 128, 0, -64, -64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, 0, -64, 0, 0, 128, -64, 64], #[-64, 0, -64, 0, 128, 0, 64, 64]] }, by decide⟩ + +def certified852 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 1, 0, 0, 0, 0, -1, -1], #[1, 3, 0, 0, 0, 0, 1, 1], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[-1, 1, 0, 0, 0, 0, 3, -1], #[-1, 1, 0, 0, 0, 0, -1, 3]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, -1, 0], #[1, 1, 0, 0, 0, 0, 1, -1], #[1, -1, 0, 0, 0, 0, 1, 1]], + inverse256 := #[#[-64, 0, -64, 0, 0, 128, 64, 64], #[-64, 0, -64, 0, 128, 0, 64, -64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, 0, 64, 0, 0, -128, 64, 64], #[-64, 0, -64, 0, 128, 0, -64, 64]] }, by decide⟩ + +def certified853 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 1, 0, 0, 0, 0, -1, 1], #[1, 3, 0, 0, 0, 0, 1, -1], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[-1, 1, 0, 0, 0, 0, 3, 1], #[1, -1, 0, 0, 0, 0, 1, 3]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[1, 0, 1, 0, 1, 0, -1, 0], #[1, 1, 0, 0, 0, 0, 1, 1], #[-1, 1, 0, 0, 0, 0, -1, 1]], + inverse256 := #[#[-64, 0, -64, 0, 0, 128, 64, -64], #[-64, 0, -64, 0, 128, 0, 64, 64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, 0, 64, 0, 0, -128, 64, -64], #[64, 0, 64, 0, -128, 0, 64, 64]] }, by decide⟩ + +def certified854 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 1, 0, 0, 0, 0, 1, -1], #[1, 3, 0, 0, 0, 0, -1, 1], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[1, -1, 0, 0, 0, 0, 3, 1], #[-1, 1, 0, 0, 0, 0, 1, 3]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 0, 0, 0, 0, -1, -1], #[1, -1, 0, 0, 0, 0, -1, 1]], + inverse256 := #[#[-64, 0, -64, 0, 0, 128, 64, 64], #[-64, 0, -64, 0, 128, 0, 64, -64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, 0, -64, 0, 0, 128, -64, -64], #[-64, 0, -64, 0, 128, 0, -64, 64]] }, by decide⟩ + +def certified855 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 1, 0, 0, 0, 0, 1, 1], #[1, 3, 0, 0, 0, 0, -1, -1], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[1, -1, 0, 0, 0, 0, 3, -1], #[1, -1, 0, 0, 0, 0, -1, 3]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 0, 0, 0, 0, -1, 1], #[-1, 1, 0, 0, 0, 0, 1, 1]], + inverse256 := #[#[-64, 0, -64, 0, 0, 128, 64, -64], #[-64, 0, -64, 0, 128, 0, 64, 64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, 0, -64, 0, 0, 128, -64, 64], #[64, 0, 64, 0, -128, 0, 64, 64]] }, by decide⟩ + +def certified856 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, -1, 0, 0, -1, -1, 0, 0], #[-1, 3, 0, 0, -1, -1, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[-1, -1, 0, 0, 3, -1, 0, 0], #[-1, -1, 0, 0, -1, 3, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, -1, 0, 0, 1], #[1, 0, 1, 0, -1, 0, 1, 0], #[1, 1, 0, 0, -1, -1, 0, 0], #[1, 1, 0, 0, 1, 1, 0, 0]], + inverse256 := #[#[0, 0, -64, 64, -128, 128, 64, 64], #[0, 0, 64, -64, 128, -128, 64, 64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[128, 0, 64, 64, -128, -128, 64, 64], #[-128, 0, -64, -64, 128, 128, -192, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified857 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, -1, 0, 0, -1, 1, 0, 0], #[-1, 3, 0, 0, -1, 1, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[-1, -1, 0, 0, 3, 1, 0, 0], #[1, 1, 0, 0, 1, 3, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, -1, 0, 0, 1], #[1, 0, 1, 0, -1, 0, 1, 0], #[1, 1, 0, 0, -1, 1, 0, 0], #[-1, -1, 0, 0, -1, 1, 0, 0]], + inverse256 := #[#[0, 0, -64, 64, -128, 128, 64, -64], #[0, 0, 64, -64, 128, -128, 64, -64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[128, 0, 64, 64, -128, -128, 64, -64], #[128, 0, 64, 64, -128, -128, 192, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified858 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, -1, 0, 0, 1, -1, 0, 0], #[-1, 3, 0, 0, 1, -1, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[1, 1, 0, 0, 3, 1, 0, 0], #[-1, -1, 0, 0, 1, 3, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 0, 0, 1, -1, 0, 0], #[1, 1, 0, 0, -1, 1, 0, 0]], + inverse256 := #[#[0, 0, -64, 64, -128, 128, 64, 64], #[0, 0, 64, -64, 128, -128, 64, 64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-128, 0, -64, -64, 128, 128, -64, -64], #[-128, 0, -64, -64, 128, 128, -192, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified859 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, -1, 0, 0, 1, 1, 0, 0], #[-1, 3, 0, 0, 1, 1, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[1, 1, 0, 0, 3, -1, 0, 0], #[1, 1, 0, 0, -1, 3, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 0, 0, 1, 1, 0, 0], #[-1, -1, 0, 0, 1, 1, 0, 0]], + inverse256 := #[#[0, 0, -64, 64, -128, 128, 64, -64], #[0, 0, 64, -64, 128, -128, 64, -64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-128, 0, -64, -64, 128, 128, -64, 64], #[128, 0, 64, 64, -128, -128, 192, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified860 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 1, 0, 0, -1, -1, 0, 0], #[1, 3, 0, 0, 1, 1, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[-1, 1, 0, 0, 3, -1, 0, 0], #[-1, 1, 0, 0, -1, 3, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, -1, 0, 1, 0], #[1, 1, 0, 0, 1, -1, 0, 0], #[1, -1, 0, 0, 1, 1, 0, 0]], + inverse256 := #[#[-64, 0, -64, 0, 0, 128, 64, 64], #[-192, 0, -64, -128, 256, 128, -64, -64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 0, 64, 0, 0, -128, 64, 64], #[-192, 0, -64, -128, 256, 128, -192, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified861 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 1, 0, 0, -1, 1, 0, 0], #[1, 3, 0, 0, 1, -1, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[-1, 1, 0, 0, 3, 1, 0, 0], #[1, -1, 0, 0, 1, 3, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, -1, 0, 1, 0], #[1, 1, 0, 0, 1, 1, 0, 0], #[-1, 1, 0, 0, -1, 1, 0, 0]], + inverse256 := #[#[-64, 0, -64, 0, 0, 128, 64, -64], #[-192, 0, -64, -128, 256, 128, -64, 64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 0, 64, 0, 0, -128, 64, -64], #[192, 0, 64, 128, -256, -128, 192, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified862 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 1, 0, 0, 1, -1, 0, 0], #[1, 3, 0, 0, -1, 1, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[1, -1, 0, 0, 3, 1, 0, 0], #[-1, 1, 0, 0, 1, 3, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, -1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 0, 0, 1, 1, 0, 0], #[1, -1, 0, 0, -1, 1, 0, 0]], + inverse256 := #[#[-192, 0, -128, -64, 128, 256, -64, 64], #[-64, 0, 0, -64, 128, 0, 64, -64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 0, 0, 64, -128, 0, 64, -64], #[192, 0, 128, 64, -128, -256, 192, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified863 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 1, 0, 0, 1, 1, 0, 0], #[1, 3, 0, 0, -1, -1, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[1, -1, 0, 0, 3, -1, 0, 0], #[1, -1, 0, 0, -1, 3, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, -1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 0, 0, 1, -1, 0, 0], #[-1, 1, 0, 0, 1, 1, 0, 0]], + inverse256 := #[#[-192, 0, -128, -64, 128, 256, -64, -64], #[-64, 0, 0, -64, 128, 0, 64, 64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 0, 0, 64, -128, 0, 64, 64], #[-192, 0, -128, -64, 128, 256, -192, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified864 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 0, -1, 0, 0, -1, 0, -1], #[0, 4, 0, 0, 0, 0, 0, 0], #[-1, 0, 3, 0, 0, -1, 0, -1], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[-1, 0, -1, 0, 0, 3, 0, -1], #[0, 0, 0, 0, 0, 0, 4, 0], #[-1, 0, -1, 0, 0, -1, 0, 3]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[1, 0, -1, 0, 1, 0, 1, 0], #[1, 1, 0, 0, 1, -1, 0, 0], #[1, 0, 1, 0, 0, 1, 0, 1]], + inverse256 := #[#[-64, 0, -128, -64, 64, 128, 64, 64], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, 64, 64, -128, 64, 64], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, 0, 0, -64, 64, 128, -192, 64], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, 0, 128, 64, -192, -128, 64, 64]] }, by decide⟩ + +def certified865 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 0, -1, 0, 0, -1, 0, 1], #[0, 4, 0, 0, 0, 0, 0, 0], #[-1, 0, 3, 0, 0, -1, 0, 1], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[-1, 0, -1, 0, 0, 3, 0, 1], #[0, 0, 0, 0, 0, 0, 4, 0], #[1, 0, 1, 0, 0, 1, 0, 3]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, -1, 0, 1, 0, 1, 0], #[1, 1, 0, 0, 1, -1, 0, 0], #[-1, 0, -1, 0, 0, -1, 0, 1]], + inverse256 := #[#[-64, 0, -128, -64, 64, 128, 64, -64], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, 64, 64, -128, 64, -64], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, 0, 0, -64, 64, 128, -192, -64], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, 0, -128, -64, 192, 128, -64, 64]] }, by decide⟩ + +def certified866 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 0, -1, 0, 0, 1, 0, -1], #[0, 4, 0, 0, 0, 0, 0, 0], #[-1, 0, 3, 0, 0, 1, 0, -1], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[1, 0, 1, 0, 0, 3, 0, 1], #[0, 0, 0, 0, 0, 0, 4, 0], #[-1, 0, -1, 0, 0, 1, 0, 3]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[1, 0, -1, 0, 1, 0, 1, 0], #[1, 1, 0, 0, 1, 1, 0, 0], #[1, 0, 1, 0, 0, -1, 0, 1]], + inverse256 := #[#[-64, 0, -128, -64, 64, 128, 64, 64], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, 64, 64, -128, 64, 64], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, 0, 0, 64, -64, -128, 192, -64], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, 0, 128, 64, -192, -128, 64, 64]] }, by decide⟩ + +def certified867 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 0, -1, 0, 0, 1, 0, 1], #[0, 4, 0, 0, 0, 0, 0, 0], #[-1, 0, 3, 0, 0, 1, 0, 1], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[1, 0, 1, 0, 0, 3, 0, -1], #[0, 0, 0, 0, 0, 0, 4, 0], #[1, 0, 1, 0, 0, -1, 0, 3]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, -1, 0, 1, 0, 1, 0], #[1, 1, 0, 0, 1, 1, 0, 0], #[-1, 0, -1, 0, 0, 1, 0, 1]], + inverse256 := #[#[-64, 0, -128, -64, 64, 128, 64, -64], #[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, 64, 64, -128, 64, -64], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, 0, 0, 64, -64, -128, 192, 64], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, 0, -128, -64, 192, 128, -64, 64]] }, by decide⟩ + +def certified868 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 0, 1, 0, 0, -1, 0, -1], #[0, 4, 0, 0, 0, 0, 0, 0], #[1, 0, 3, 0, 0, 1, 0, 1], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[-1, 0, 1, 0, 0, 3, 0, -1], #[0, 0, 0, 0, 0, 0, 4, 0], #[-1, 0, 1, 0, 0, -1, 0, 3]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 0, 0, 1, -1, 0, 0], #[1, 0, -1, 0, 0, 1, 0, 1]], + inverse256 := #[#[0, 0, -64, -64, -64, 128, 64, 64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -64, -64, 64, 128, -64, -64], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[128, 0, 64, -64, -64, 128, -192, 64], #[0, 0, 0, 128, 0, 0, 0, 0], #[-128, 0, -64, 64, 192, -128, 64, 64]] }, by decide⟩ + +def certified869 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 0, 1, 0, 0, -1, 0, 1], #[0, 4, 0, 0, 0, 0, 0, 0], #[1, 0, 3, 0, 0, 1, 0, -1], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[-1, 0, 1, 0, 0, 3, 0, 1], #[0, 0, 0, 0, 0, 0, 4, 0], #[1, 0, -1, 0, 0, 1, 0, 3]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 0, 0, 1, -1, 0, 0], #[-1, 0, 1, 0, 0, -1, 0, 1]], + inverse256 := #[#[0, 0, -64, -64, -64, 128, 64, -64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -64, -64, 64, 128, -64, 64], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[128, 0, 64, -64, -64, 128, -192, -64], #[0, 0, 0, 128, 0, 0, 0, 0], #[128, 0, 64, -64, -192, 128, -64, 64]] }, by decide⟩ + +def certified870 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 0, 1, 0, 0, 1, 0, -1], #[0, 4, 0, 0, 0, 0, 0, 0], #[1, 0, 3, 0, 0, -1, 0, 1], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[1, 0, -1, 0, 0, 3, 0, 1], #[0, 0, 0, 0, 0, 0, 4, 0], #[-1, 0, 1, 0, 0, 1, 0, 3]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 0, 0, 1, 1, 0, 0], #[1, 0, -1, 0, 0, -1, 0, 1]], + inverse256 := #[#[0, 0, -64, -64, -64, 128, 64, 64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -64, -64, 64, 128, -64, -64], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[-128, 0, -64, 64, 64, -128, 192, -64], #[0, 0, 0, 128, 0, 0, 0, 0], #[-128, 0, -64, 64, 192, -128, 64, 64]] }, by decide⟩ + +def certified871 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 0, 1, 0, 0, 1, 0, 1], #[0, 4, 0, 0, 0, 0, 0, 0], #[1, 0, 3, 0, 0, -1, 0, -1], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[1, 0, -1, 0, 0, 3, 0, -1], #[0, 0, 0, 0, 0, 0, 4, 0], #[1, 0, -1, 0, 0, -1, 0, 3]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 0, 0, 1, 1, 0, 0], #[-1, 0, 1, 0, 0, 1, 0, 1]], + inverse256 := #[#[0, 0, -64, -64, -64, 128, 64, -64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -64, -64, 64, 128, -64, 64], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[-128, 0, -64, 64, 64, -128, 192, 64], #[0, 0, 0, 128, 0, 0, 0, 0], #[128, 0, 64, -64, -192, 128, -64, 64]] }, by decide⟩ + +def certified872 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 3, -1, 0, 0, -1, -1, 0], #[0, -1, 3, 0, 0, -1, -1, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, -1, -1, 0, 0, 3, -1, 0], #[0, -1, -1, 0, 0, -1, 3, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, -1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, -1, 0], #[1, 1, 0, 0, 1, -1, 0, 0], #[0, 1, 1, 0, 0, 1, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, -128, -64, 128, 64, 64, 64], #[-64, 0, 0, 64, -128, 64, 64, 64], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, 0, 0, -64, 128, 64, -192, 64], #[64, 0, 128, 64, -128, -192, 64, 64], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified873 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 3, -1, 0, 0, -1, 1, 0], #[0, -1, 3, 0, 0, -1, 1, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, -1, -1, 0, 0, 3, 1, 0], #[0, 1, 1, 0, 0, 1, 3, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, -1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 0, 0, 1, -1, 0, 0], #[0, -1, -1, 0, 0, -1, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, -128, -64, 128, 64, 64, -64], #[-64, 0, 0, 64, -128, 64, 64, -64], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, 0, 0, -64, 128, 64, -192, -64], #[-64, 0, -128, -64, 128, 192, -64, 64], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified874 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 3, -1, 0, 0, 1, -1, 0], #[0, -1, 3, 0, 0, 1, -1, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 1, 1, 0, 0, 3, 1, 0], #[0, -1, -1, 0, 0, 1, 3, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, -1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, -1, 0], #[1, 1, 0, 0, 1, 1, 0, 0], #[0, 1, 1, 0, 0, -1, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, -128, -64, 128, 64, 64, 64], #[-64, 0, 0, 64, -128, 64, 64, 64], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, 0, 0, 64, -128, -64, 192, -64], #[64, 0, 128, 64, -128, -192, 64, 64], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified875 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 3, -1, 0, 0, 1, 1, 0], #[0, -1, 3, 0, 0, 1, 1, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 1, 1, 0, 0, 3, -1, 0], #[0, 1, 1, 0, 0, -1, 3, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, -1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 0, 0, 1, 1, 0, 0], #[0, -1, -1, 0, 0, 1, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, 0, -128, -64, 128, 64, 64, -64], #[-64, 0, 0, 64, -128, 64, 64, -64], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, 0, 0, 64, -128, -64, 192, 64], #[-64, 0, -128, -64, 128, 192, -64, 64], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified876 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 3, 1, 0, 0, -1, -1, 0], #[0, 1, 3, 0, 0, 1, 1, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, -1, 1, 0, 0, 3, -1, 0], #[0, -1, 1, 0, 0, -1, 3, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 0, 0, 1, -1, 0, 0], #[0, 1, -1, 0, 0, 1, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -64, -64, 128, -64, 64, 64], #[0, 0, -64, -64, 128, 64, -64, -64], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[128, 0, 64, -64, 128, -64, -192, 64], #[-128, 0, -64, 64, -128, 192, 64, 64], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified877 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 3, 1, 0, 0, -1, 1, 0], #[0, 1, 3, 0, 0, 1, -1, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, -1, 1, 0, 0, 3, 1, 0], #[0, 1, -1, 0, 0, 1, 3, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, -1, 0], #[1, 1, 0, 0, 1, -1, 0, 0], #[0, -1, 1, 0, 0, -1, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -64, -64, 128, -64, 64, -64], #[0, 0, -64, -64, 128, 64, -64, 64], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[128, 0, 64, -64, 128, -64, -192, -64], #[128, 0, 64, -64, 128, -192, -64, 64], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified878 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 3, 1, 0, 0, 1, -1, 0], #[0, 1, 3, 0, 0, -1, 1, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 1, -1, 0, 0, 3, 1, 0], #[0, -1, 1, 0, 0, 1, 3, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 0, 0, 1, 1, 0, 0], #[0, 1, -1, 0, 0, -1, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -64, -64, 128, -64, 64, 64], #[0, 0, -64, -64, 128, 64, -64, -64], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[-128, 0, -64, 64, -128, 64, 192, -64], #[-128, 0, -64, 64, -128, 192, 64, 64], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified879 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 3, 1, 0, 0, 1, 1, 0], #[0, 1, 3, 0, 0, -1, -1, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 1, -1, 0, 0, 3, -1, 0], #[0, 1, -1, 0, 0, -1, 3, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, -1, 0], #[1, 1, 0, 0, 1, 1, 0, 0], #[0, -1, 1, 0, 0, 1, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 0, -64, -64, 128, -64, 64, -64], #[0, 0, -64, -64, 128, 64, -64, 64], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[-128, 0, -64, 64, -128, 64, 192, 64], #[128, 0, 64, -64, 128, -192, -64, 64], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified880 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 3, -1, -1, -1], #[0, 0, 0, 0, -1, 3, -1, -1], #[0, 0, 0, 0, -1, -1, 3, -1], #[0, 0, 0, 0, -1, -1, -1, 3]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[1, 0, 1, 0, 1, 0, -1, 0], #[1, 1, 0, 0, 1, -1, 0, 0], #[0, 0, 0, 0, 1, 1, 1, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, -64, -64, 0, 64, 64, 64, 64], #[64, 64, -64, 0, 64, 64, -192, 64], #[64, -64, 64, 0, 64, -192, 64, 64], #[-64, 64, 64, 0, -192, 64, 64, 64]] }, by decide⟩ + +def certified881 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 3, -1, -1, 1], #[0, 0, 0, 0, -1, 3, -1, 1], #[0, 0, 0, 0, -1, -1, 3, 1], #[0, 0, 0, 0, 1, 1, 1, 3]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, -1, 0], #[1, 1, 0, 0, 1, -1, 0, 0], #[0, 0, 0, 0, -1, -1, -1, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, -64, -64, 0, 64, 64, 64, -64], #[64, 64, -64, 0, 64, 64, -192, -64], #[64, -64, 64, 0, 64, -192, 64, -64], #[64, -64, -64, 0, 192, -64, -64, 64]] }, by decide⟩ + +def certified882 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 3, -1, 1, -1], #[0, 0, 0, 0, -1, 3, 1, -1], #[0, 0, 0, 0, 1, 1, 3, 1], #[0, 0, 0, 0, -1, -1, 1, 3]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 0, 0, 1, -1, 0, 0], #[0, 0, 0, 0, 1, 1, -1, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, -64, -64, 0, 64, 64, 64, 64], #[64, 64, -64, 0, 64, 64, -192, 64], #[-64, 64, -64, 0, -64, 192, -64, -64], #[-64, 64, 64, 0, -192, 64, 64, 64]] }, by decide⟩ + +def certified883 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 3, -1, 1, 1], #[0, 0, 0, 0, -1, 3, 1, 1], #[0, 0, 0, 0, 1, 1, 3, -1], #[0, 0, 0, 0, 1, 1, -1, 3]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 0, 0, 1, -1, 0, 0], #[0, 0, 0, 0, -1, -1, 1, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, -64, -64, 0, 64, 64, 64, -64], #[64, 64, -64, 0, 64, 64, -192, -64], #[-64, 64, -64, 0, -64, 192, -64, 64], #[64, -64, -64, 0, 192, -64, -64, 64]] }, by decide⟩ + +def certified884 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 3, 1, -1, -1], #[0, 0, 0, 0, 1, 3, 1, 1], #[0, 0, 0, 0, -1, 1, 3, -1], #[0, 0, 0, 0, -1, 1, -1, 3]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[1, 0, 1, 0, 1, 0, -1, 0], #[1, 1, 0, 0, 1, 1, 0, 0], #[0, 0, 0, 0, 1, -1, 1, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, -64, -64, 0, 64, 64, 64, 64], #[-64, -64, 64, 0, -64, -64, 192, -64], #[64, -64, 64, 0, 64, -192, 64, 64], #[-64, 64, 64, 0, -192, 64, 64, 64]] }, by decide⟩ + +def certified885 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 3, 1, -1, 1], #[0, 0, 0, 0, 1, 3, 1, -1], #[0, 0, 0, 0, -1, 1, 3, 1], #[0, 0, 0, 0, 1, -1, 1, 3]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, -1, 0], #[1, 1, 0, 0, 1, 1, 0, 0], #[0, 0, 0, 0, -1, 1, -1, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, -64, -64, 0, 64, 64, 64, -64], #[-64, -64, 64, 0, -64, -64, 192, 64], #[64, -64, 64, 0, 64, -192, 64, -64], #[64, -64, -64, 0, 192, -64, -64, 64]] }, by decide⟩ + +def certified886 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 3, 1, 1, -1], #[0, 0, 0, 0, 1, 3, -1, 1], #[0, 0, 0, 0, 1, -1, 3, 1], #[0, 0, 0, 0, -1, 1, 1, 3]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 0, 0, 1, 1, 0, 0], #[0, 0, 0, 0, 1, -1, -1, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, -64, -64, 0, 64, 64, 64, 64], #[-64, -64, 64, 0, -64, -64, 192, -64], #[-64, 64, -64, 0, -64, 192, -64, -64], #[-64, 64, 64, 0, -192, 64, 64, 64]] }, by decide⟩ + +def certified887 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 0, 0, 4, 0, 0, 0, 0], #[0, 0, 0, 0, 3, 1, 1, 1], #[0, 0, 0, 0, 1, 3, -1, -1], #[0, 0, 0, 0, 1, -1, 3, -1], #[0, 0, 0, 0, 1, -1, -1, 3]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 2, 0, 0, 0, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 0, 0, 1, 1, 0, 0], #[0, 0, 0, 0, -1, 1, 1, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, -64, -64, 0, 64, 64, 64, -64], #[-64, -64, 64, 0, -64, -64, 192, 64], #[-64, 64, -64, 0, -64, 192, -64, 64], #[64, -64, -64, 0, 192, -64, -64, 64]] }, by decide⟩ + +def certified888 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, -1, -1, -1, 0, 0, 0, 0], #[-1, 3, -1, -1, 0, 0, 0, 0], #[-1, -1, 3, -1, 0, 0, 0, 0], #[-1, -1, -1, 3, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, -1, 0, 1, 0, 0, 1], #[1, 0, -1, 0, 1, 0, 1, 0], #[1, 1, -1, -1, 0, 0, 0, 0], #[1, 1, 1, 1, 0, 0, 0, 0]], + inverse256 := #[#[0, 0, -64, 64, -128, 128, 64, 64], #[0, 0, 64, -64, 128, -128, 64, 64], #[128, 0, 64, 64, -128, -128, 64, 64], #[-128, 0, -64, -64, 128, 128, -192, 64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified889 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, -1, -1, 1, 0, 0, 0, 0], #[-1, 3, -1, 1, 0, 0, 0, 0], #[-1, -1, 3, 1, 0, 0, 0, 0], #[1, 1, 1, 3, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, -1, 0, 1, 0, 0, 1], #[1, 0, -1, 0, 1, 0, 1, 0], #[1, 1, -1, 1, 0, 0, 0, 0], #[-1, -1, -1, 1, 0, 0, 0, 0]], + inverse256 := #[#[0, 0, -64, 64, -128, 128, 64, -64], #[0, 0, 64, -64, 128, -128, 64, -64], #[128, 0, 64, 64, -128, -128, 64, -64], #[128, 0, 64, 64, -128, -128, 192, 64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified890 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, -1, 1, -1, 0, 0, 0, 0], #[-1, 3, 1, -1, 0, 0, 0, 0], #[1, 1, 3, 1, 0, 0, 0, 0], #[-1, -1, 1, 3, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 1, -1, 0, 0, 0, 0], #[1, 1, -1, 1, 0, 0, 0, 0]], + inverse256 := #[#[0, 0, -64, 64, -128, 128, 64, 64], #[0, 0, 64, -64, 128, -128, 64, 64], #[-128, 0, -64, -64, 128, 128, -64, -64], #[-128, 0, -64, -64, 128, 128, -192, 64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified891 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, -1, 1, 1, 0, 0, 0, 0], #[-1, 3, 1, 1, 0, 0, 0, 0], #[1, 1, 3, -1, 0, 0, 0, 0], #[1, 1, -1, 3, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[-1, -1, 1, 1, 0, 0, 0, 0]], + inverse256 := #[#[0, 0, -64, 64, -128, 128, 64, -64], #[0, 0, 64, -64, 128, -128, 64, -64], #[-128, 0, -64, -64, 128, 128, -64, 64], #[128, 0, 64, 64, -128, -128, 192, 64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified892 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 1, -1, -1, 0, 0, 0, 0], #[1, 3, 1, 1, 0, 0, 0, 0], #[-1, 1, 3, -1, 0, 0, 0, 0], #[-1, 1, -1, 3, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, -1, 0, 1, 0, 1, 0], #[1, 1, 1, -1, 0, 0, 0, 0], #[1, -1, 1, 1, 0, 0, 0, 0]], + inverse256 := #[#[-64, 0, -64, 0, 0, 128, 64, 64], #[-192, 0, -64, -128, 256, 128, -64, -64], #[64, 0, 64, 0, 0, -128, 64, 64], #[-192, 0, -64, -128, 256, 128, -192, 64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified893 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 1, -1, 1, 0, 0, 0, 0], #[1, 3, 1, -1, 0, 0, 0, 0], #[-1, 1, 3, 1, 0, 0, 0, 0], #[1, -1, 1, 3, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, -1, 0, 1, 0, 1, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[-1, 1, -1, 1, 0, 0, 0, 0]], + inverse256 := #[#[-64, 0, -64, 0, 0, 128, 64, -64], #[-192, 0, -64, -128, 256, 128, -64, 64], #[64, 0, 64, 0, 0, -128, 64, -64], #[192, 0, 64, 128, -256, -128, 192, 64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified894 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 1, 1, -1, 0, 0, 0, 0], #[1, 3, -1, 1, 0, 0, 0, 0], #[1, -1, 3, 1, 0, 0, 0, 0], #[-1, 1, 1, 3, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, -1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[1, -1, -1, 1, 0, 0, 0, 0]], + inverse256 := #[#[-192, 0, -128, -64, 128, 256, -64, 64], #[-64, 0, 0, -64, 128, 0, 64, -64], #[64, 0, 0, 64, -128, 0, 64, -64], #[192, 0, 128, 64, -128, -256, 192, 64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified895 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 1, 1, 1, 0, 0, 0, 0], #[1, 3, -1, -1, 0, 0, 0, 0], #[1, -1, 3, -1, 0, 0, 0, 0], #[1, -1, -1, 3, 0, 0, 0, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, -1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 1, -1, 0, 0, 0, 0], #[-1, 1, 1, 1, 0, 0, 0, 0]], + inverse256 := #[#[-192, 0, -128, -64, 128, 256, -64, -64], #[-64, 0, 0, -64, 128, 0, 64, 64], #[64, 0, 0, 64, -128, 0, 64, 64], #[-192, 0, -128, -64, 128, 256, -192, 64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified896 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 0, 0, -1, -1, 0, 0, -1], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[-1, 0, 0, 3, -1, 0, 0, -1], #[-1, 0, 0, -1, 3, 0, 0, -1], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[-1, 0, 0, -1, -1, 0, 0, 3]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[1, 0, 1, 0, -1, 0, 1, 0], #[1, 1, 1, -1, 0, 0, 0, 0], #[1, 0, 0, 1, 1, 0, 0, 1]], + inverse256 := #[#[-64, -128, 0, -64, 64, 128, 64, 64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 0, 0, -64, 64, 128, -192, 64], #[-64, 0, 0, 64, 64, -128, 64, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, 128, 0, 64, -192, -128, 64, 64]] }, by decide⟩ + +def certified897 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 0, 0, -1, -1, 0, 0, 1], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[-1, 0, 0, 3, -1, 0, 0, 1], #[-1, 0, 0, -1, 3, 0, 0, 1], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[1, 0, 0, 1, 1, 0, 0, 3]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, -1, 0, 1, 0], #[1, 1, 1, -1, 0, 0, 0, 0], #[-1, 0, 0, -1, -1, 0, 0, 1]], + inverse256 := #[#[-64, -128, 0, -64, 64, 128, 64, -64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 0, 0, -64, 64, 128, -192, -64], #[-64, 0, 0, 64, 64, -128, 64, -64], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, -128, 0, -64, 192, 128, -64, 64]] }, by decide⟩ + +def certified898 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 0, 0, -1, 1, 0, 0, -1], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[-1, 0, 0, 3, 1, 0, 0, -1], #[1, 0, 0, 1, 3, 0, 0, 1], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[-1, 0, 0, -1, 1, 0, 0, 3]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 1, -1, 0, 0, 0, 0], #[1, 0, 0, 1, -1, 0, 0, 1]], + inverse256 := #[#[0, -64, 0, -64, -64, 128, 64, 64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[128, 64, 0, -64, -64, 128, -192, 64], #[0, -64, 0, -64, 64, 128, -64, -64], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-128, -64, 0, 64, 192, -128, 64, 64]] }, by decide⟩ + +def certified899 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 0, 0, -1, 1, 0, 0, 1], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[-1, 0, 0, 3, 1, 0, 0, 1], #[1, 0, 0, 1, 3, 0, 0, -1], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[1, 0, 0, 1, -1, 0, 0, 3]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 1, -1, 0, 0, 0, 0], #[-1, 0, 0, -1, 1, 0, 0, 1]], + inverse256 := #[#[0, -64, 0, -64, -64, 128, 64, -64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[128, 64, 0, -64, -64, 128, -192, -64], #[0, -64, 0, -64, 64, 128, -64, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[128, 64, 0, -64, -192, 128, -64, 64]] }, by decide⟩ + +def certified900 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 0, 0, 1, -1, 0, 0, -1], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[1, 0, 0, 3, 1, 0, 0, 1], #[-1, 0, 0, 1, 3, 0, 0, -1], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[-1, 0, 0, 1, -1, 0, 0, 3]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[1, 0, 1, 0, -1, 0, 1, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[1, 0, 0, -1, 1, 0, 0, 1]], + inverse256 := #[#[-64, -128, 0, -64, 64, 128, 64, 64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, 64, -64, -128, 192, -64], #[-64, 0, 0, 64, 64, -128, 64, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, 128, 0, 64, -192, -128, 64, 64]] }, by decide⟩ + +def certified901 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 0, 0, 1, -1, 0, 0, 1], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[1, 0, 0, 3, 1, 0, 0, -1], #[-1, 0, 0, 1, 3, 0, 0, 1], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[1, 0, 0, -1, 1, 0, 0, 3]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, -1, 0, 1, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[-1, 0, 0, 1, -1, 0, 0, 1]], + inverse256 := #[#[-64, -128, 0, -64, 64, 128, 64, -64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, 64, -64, -128, 192, 64], #[-64, 0, 0, 64, 64, -128, 64, -64], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, -128, 0, -64, 192, 128, -64, 64]] }, by decide⟩ + +def certified902 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 0, 0, 1, 1, 0, 0, -1], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[1, 0, 0, 3, -1, 0, 0, 1], #[1, 0, 0, -1, 3, 0, 0, 1], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[-1, 0, 0, 1, 1, 0, 0, 3]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[1, 0, 0, -1, -1, 0, 0, 1]], + inverse256 := #[#[0, -64, 0, -64, -64, 128, 64, 64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-128, -64, 0, 64, 64, -128, 192, -64], #[0, -64, 0, -64, 64, 128, -64, -64], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-128, -64, 0, 64, 192, -128, 64, 64]] }, by decide⟩ + +def certified903 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 0, 0, 1, 1, 0, 0, 1], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[1, 0, 0, 3, -1, 0, 0, -1], #[1, 0, 0, -1, 3, 0, 0, -1], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[1, 0, 0, -1, -1, 0, 0, 3]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[-1, 0, 0, 1, 1, 0, 0, 1]], + inverse256 := #[#[0, -64, 0, -64, -64, 128, 64, -64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-128, -64, 0, 64, 64, -128, 192, 64], #[0, -64, 0, -64, 64, 128, -64, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[128, 64, 0, -64, -192, 128, -64, 64]] }, by decide⟩ + +def certified904 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 3, 0, -1, -1, 0, -1, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, -1, 0, 3, -1, 0, -1, 0], #[0, -1, 0, -1, 3, 0, -1, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, -1, 0, -1, -1, 0, 3, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, -1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, -1, 0], #[1, 1, 1, -1, 0, 0, 0, 0], #[0, 1, 0, 1, 1, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -128, 0, -64, 128, 64, 64, 64], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 0, 0, -64, 128, 64, -192, 64], #[-64, 0, 0, 64, -128, 64, 64, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, 128, 0, 64, -128, -192, 64, 64], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified905 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 3, 0, -1, -1, 0, 1, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, -1, 0, 3, -1, 0, 1, 0], #[0, -1, 0, -1, 3, 0, 1, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 1, 0, 1, 1, 0, 3, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, -1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 1, -1, 0, 0, 0, 0], #[0, -1, 0, -1, -1, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -128, 0, -64, 128, 64, 64, -64], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 0, 0, -64, 128, 64, -192, -64], #[-64, 0, 0, 64, -128, 64, 64, -64], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, -128, 0, -64, 128, 192, -64, 64], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified906 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 3, 0, -1, 1, 0, -1, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, -1, 0, 3, 1, 0, -1, 0], #[0, 1, 0, 1, 3, 0, 1, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, -1, 0, -1, 1, 0, 3, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 1, -1, 0, 0, 0, 0], #[0, 1, 0, 1, -1, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, -64, 0, -64, 128, -64, 64, 64], #[0, 128, 0, 0, 0, 0, 0, 0], #[128, 64, 0, -64, 128, -64, -192, 64], #[0, -64, 0, -64, 128, 64, -64, -64], #[0, 0, 128, 0, 0, 0, 0, 0], #[-128, -64, 0, 64, -128, 192, 64, 64], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified907 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 3, 0, -1, 1, 0, 1, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, -1, 0, 3, 1, 0, 1, 0], #[0, 1, 0, 1, 3, 0, -1, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 1, 0, 1, -1, 0, 3, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, -1, 0], #[1, 1, 1, -1, 0, 0, 0, 0], #[0, -1, 0, -1, 1, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, -64, 0, -64, 128, -64, 64, -64], #[0, 128, 0, 0, 0, 0, 0, 0], #[128, 64, 0, -64, 128, -64, -192, -64], #[0, -64, 0, -64, 128, 64, -64, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[128, 64, 0, -64, 128, -192, -64, 64], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified908 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 3, 0, 1, -1, 0, -1, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 1, 0, 3, 1, 0, 1, 0], #[0, -1, 0, 1, 3, 0, -1, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, -1, 0, 1, -1, 0, 3, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, -1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, -1, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[0, 1, 0, -1, 1, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -128, 0, -64, 128, 64, 64, 64], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, 64, -128, -64, 192, -64], #[-64, 0, 0, 64, -128, 64, 64, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, 128, 0, 64, -128, -192, 64, 64], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified909 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 3, 0, 1, -1, 0, 1, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 1, 0, 3, 1, 0, -1, 0], #[0, -1, 0, 1, 3, 0, 1, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 1, 0, -1, 1, 0, 3, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, -1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[0, -1, 0, 1, -1, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -128, 0, -64, 128, 64, 64, -64], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, 0, 0, 64, -128, -64, 192, 64], #[-64, 0, 0, 64, -128, 64, 64, -64], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, -128, 0, -64, 128, 192, -64, 64], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified910 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 3, 0, 1, 1, 0, -1, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 1, 0, 3, -1, 0, 1, 0], #[0, 1, 0, -1, 3, 0, 1, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, -1, 0, 1, 1, 0, 3, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[0, 1, 0, -1, -1, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, -64, 0, -64, 128, -64, 64, 64], #[0, 128, 0, 0, 0, 0, 0, 0], #[-128, -64, 0, 64, -128, 64, 192, -64], #[0, -64, 0, -64, 128, 64, -64, -64], #[0, 0, 128, 0, 0, 0, 0, 0], #[-128, -64, 0, 64, -128, 192, 64, 64], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified911 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 3, 0, 1, 1, 0, 1, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 1, 0, 3, -1, 0, -1, 0], #[0, 1, 0, -1, 3, 0, -1, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 1, 0, -1, -1, 0, 3, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, -1, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[0, -1, 0, 1, 1, 0, 1, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, -64, 0, -64, 128, -64, 64, -64], #[0, 128, 0, 0, 0, 0, 0, 0], #[-128, -64, 0, 64, -128, 64, 192, 64], #[0, -64, 0, -64, 128, 64, -64, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[128, 64, 0, -64, 128, -192, -64, 64], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified912 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 3, -1, 0, 0, -1, -1], #[0, 0, -1, 3, 0, 0, -1, -1], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, -1, -1, 0, 0, 3, -1], #[0, 0, -1, -1, 0, 0, -1, 3]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[1, 0, 1, 0, 1, 0, -1, 0], #[1, 1, 1, -1, 0, 0, 0, 0], #[0, 0, 1, 1, 0, 0, 1, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, -64, 0, 64, 64, 64, 64], #[64, 64, -64, 0, 64, 64, -192, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, -64, 64, 0, 64, -192, 64, 64], #[-64, 64, 64, 0, -192, 64, 64, 64]] }, by decide⟩ + +def certified913 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 3, -1, 0, 0, -1, 1], #[0, 0, -1, 3, 0, 0, -1, 1], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, -1, -1, 0, 0, 3, 1], #[0, 0, 1, 1, 0, 0, 1, 3]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, -1, 0], #[1, 1, 1, -1, 0, 0, 0, 0], #[0, 0, -1, -1, 0, 0, -1, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, -64, 0, 64, 64, 64, -64], #[64, 64, -64, 0, 64, 64, -192, -64], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, -64, 64, 0, 64, -192, 64, -64], #[64, -64, -64, 0, 192, -64, -64, 64]] }, by decide⟩ + +def certified914 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 3, -1, 0, 0, 1, -1], #[0, 0, -1, 3, 0, 0, 1, -1], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 1, 1, 0, 0, 3, 1], #[0, 0, -1, -1, 0, 0, 1, 3]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 1, -1, 0, 0, 0, 0], #[0, 0, 1, 1, 0, 0, -1, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, -64, 0, 64, 64, 64, 64], #[64, 64, -64, 0, 64, 64, -192, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, 64, -64, 0, -64, 192, -64, -64], #[-64, 64, 64, 0, -192, 64, 64, 64]] }, by decide⟩ + +def certified915 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 3, -1, 0, 0, 1, 1], #[0, 0, -1, 3, 0, 0, 1, 1], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 1, 1, 0, 0, 3, -1], #[0, 0, 1, 1, 0, 0, -1, 3]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 1, -1, 0, 0, 0, 0], #[0, 0, -1, -1, 0, 0, 1, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, -64, 0, 64, 64, 64, -64], #[64, 64, -64, 0, 64, 64, -192, -64], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, 64, -64, 0, -64, 192, -64, 64], #[64, -64, -64, 0, 192, -64, -64, 64]] }, by decide⟩ + +def certified916 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 3, 1, 0, 0, -1, -1], #[0, 0, 1, 3, 0, 0, 1, 1], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, -1, 1, 0, 0, 3, -1], #[0, 0, -1, 1, 0, 0, -1, 3]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[1, 0, 1, 0, 1, 0, -1, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[0, 0, 1, -1, 0, 0, 1, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, -64, 0, 64, 64, 64, 64], #[-64, -64, 64, 0, -64, -64, 192, -64], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, -64, 64, 0, 64, -192, 64, 64], #[-64, 64, 64, 0, -192, 64, 64, 64]] }, by decide⟩ + +def certified917 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 3, 1, 0, 0, -1, 1], #[0, 0, 1, 3, 0, 0, 1, -1], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, -1, 1, 0, 0, 3, 1], #[0, 0, 1, -1, 0, 0, 1, 3]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, -1, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[0, 0, -1, 1, 0, 0, -1, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, -64, 0, 64, 64, 64, -64], #[-64, -64, 64, 0, -64, -64, 192, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, -64, 64, 0, 64, -192, 64, -64], #[64, -64, -64, 0, 192, -64, -64, 64]] }, by decide⟩ + +def certified918 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 3, 1, 0, 0, 1, -1], #[0, 0, 1, 3, 0, 0, -1, 1], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 1, -1, 0, 0, 3, 1], #[0, 0, -1, 1, 0, 0, 1, 3]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[0, 0, 1, -1, 0, 0, -1, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, -64, 0, 64, 64, 64, 64], #[-64, -64, 64, 0, -64, -64, 192, -64], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, 64, -64, 0, -64, 192, -64, -64], #[-64, 64, 64, 0, -192, 64, 64, 64]] }, by decide⟩ + +def certified919 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 3, 1, 0, 0, 1, 1], #[0, 0, 1, 3, 0, 0, -1, -1], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 0, 0, 0, 0, 4, 0, 0], #[0, 0, 1, -1, 0, 0, 3, -1], #[0, 0, 1, -1, 0, 0, -1, 3]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 2, 0, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[0, 0, -1, 1, 0, 0, 1, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, -64, 0, 64, 64, 64, -64], #[-64, -64, 64, 0, -64, -64, 192, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, 64, -64, 0, -64, 192, -64, 64], #[64, -64, -64, 0, 192, -64, -64, 64]] }, by decide⟩ + +def certified920 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 3, -1, -1, -1, 0, 0], #[0, 0, -1, 3, -1, -1, 0, 0], #[0, 0, -1, -1, 3, -1, 0, 0], #[0, 0, -1, -1, -1, 3, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, -1, 0, 0, 1], #[1, 1, 0, 0, 1, -1, 0, 0], #[1, 1, 1, -1, 0, 0, 0, 0], #[0, 0, 1, 1, 1, 1, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -128, 0, -64, 128, 64, 64, 64], #[64, 0, 0, -64, 128, 64, -192, 64], #[-64, 0, 0, 64, -128, 64, 64, 64], #[64, 128, 0, 64, -128, -192, 64, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified921 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 3, -1, -1, 1, 0, 0], #[0, 0, -1, 3, -1, 1, 0, 0], #[0, 0, -1, -1, 3, 1, 0, 0], #[0, 0, 1, 1, 1, 3, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, -1, 0, 0, 1], #[1, 1, 0, 0, 1, 1, 0, 0], #[1, 1, 1, -1, 0, 0, 0, 0], #[0, 0, -1, -1, -1, 1, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -128, 0, -64, 128, 64, 64, -64], #[64, 0, 0, -64, 128, 64, -192, -64], #[-64, 0, 0, 64, -128, 64, 64, -64], #[-64, -128, 0, -64, 128, 192, -64, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified922 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 3, -1, 1, -1, 0, 0], #[0, 0, -1, 3, 1, -1, 0, 0], #[0, 0, 1, 1, 3, 1, 0, 0], #[0, 0, -1, -1, 1, 3, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 1, 0, 0, 1, 1, 0, 0], #[1, 1, 1, -1, 0, 0, 0, 0], #[0, 0, 1, 1, -1, 1, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, -64, 0, -64, 128, -64, 64, 64], #[128, 64, 0, -64, 128, -64, -192, 64], #[0, -64, 0, -64, 128, 64, -64, -64], #[-128, -64, 0, 64, -128, 192, 64, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified923 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 3, -1, 1, 1, 0, 0], #[0, 0, -1, 3, 1, 1, 0, 0], #[0, 0, 1, 1, 3, -1, 0, 0], #[0, 0, 1, 1, -1, 3, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 1, 0, 0, 1, -1, 0, 0], #[1, 1, 1, -1, 0, 0, 0, 0], #[0, 0, -1, -1, 1, 1, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, -64, 0, -64, 128, -64, 64, -64], #[128, 64, 0, -64, 128, -64, -192, -64], #[0, -64, 0, -64, 128, 64, -64, 64], #[128, 64, 0, -64, 128, -192, -64, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified924 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 3, 1, -1, -1, 0, 0], #[0, 0, 1, 3, 1, 1, 0, 0], #[0, 0, -1, 1, 3, -1, 0, 0], #[0, 0, -1, 1, -1, 3, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, -1, 0, 0, 1], #[1, 1, 0, 0, 1, -1, 0, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[0, 0, 1, -1, 1, 1, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -128, 0, -64, 128, 64, 64, 64], #[-64, 0, 0, 64, -128, -64, 192, -64], #[-64, 0, 0, 64, -128, 64, 64, 64], #[64, 128, 0, 64, -128, -192, 64, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified925 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 3, 1, -1, 1, 0, 0], #[0, 0, 1, 3, 1, -1, 0, 0], #[0, 0, -1, 1, 3, 1, 0, 0], #[0, 0, 1, -1, 1, 3, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, -1, 0, 0, 1], #[1, 1, 0, 0, 1, 1, 0, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[0, 0, -1, 1, -1, 1, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -128, 0, -64, 128, 64, 64, -64], #[-64, 0, 0, 64, -128, -64, 192, 64], #[-64, 0, 0, 64, -128, 64, 64, -64], #[-64, -128, 0, -64, 128, 192, -64, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified926 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 3, 1, 1, -1, 0, 0], #[0, 0, 1, 3, -1, 1, 0, 0], #[0, 0, 1, -1, 3, 1, 0, 0], #[0, 0, -1, 1, 1, 3, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 1, 0, 0, 1, 1, 0, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[0, 0, 1, -1, -1, 1, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, -64, 0, -64, 128, -64, 64, 64], #[-128, -64, 0, 64, -128, 64, 192, -64], #[0, -64, 0, -64, 128, 64, -64, -64], #[-128, -64, 0, 64, -128, 192, 64, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified927 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 3, 1, 1, 1, 0, 0], #[0, 0, 1, 3, -1, -1, 0, 0], #[0, 0, 1, -1, 3, -1, 0, 0], #[0, 0, 1, -1, -1, 3, 0, 0], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 1, 0, 0, 1, -1, 0, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[0, 0, -1, 1, 1, 1, 0, 0]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[0, -64, 0, -64, 128, -64, 64, -64], #[-128, -64, 0, 64, -128, 64, 192, 64], #[0, -64, 0, -64, 128, 64, -64, 64], #[128, 64, 0, -64, 128, -192, -64, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified928 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 3, 0, -1, 0, -1, 0, -1], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, -1, 0, 3, 0, -1, 0, -1], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, -1, 0, -1, 0, 3, 0, -1], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, -1, 0, -1, 0, -1, 0, 3]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[1, 1, 0, 0, 1, -1, 0, 0], #[1, 1, 1, -1, 0, 0, 0, 0], #[0, 1, 0, 1, 0, 1, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, -64, 0, 64, 64, 64, 64], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 64, -64, 0, 64, 64, -192, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, -64, 64, 0, 64, -192, 64, 64], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, 64, 64, 0, -192, 64, 64, 64]] }, by decide⟩ + +def certified929 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 3, 0, -1, 0, -1, 0, 1], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, -1, 0, 3, 0, -1, 0, 1], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, -1, 0, -1, 0, 3, 0, 1], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 1, 0, 1, 0, 1, 0, 3]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 1, 0, 0, 1, -1, 0, 0], #[1, 1, 1, -1, 0, 0, 0, 0], #[0, -1, 0, -1, 0, -1, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, -64, 0, 64, 64, 64, -64], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 64, -64, 0, 64, 64, -192, -64], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, -64, 64, 0, 64, -192, 64, -64], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, -64, -64, 0, 192, -64, -64, 64]] }, by decide⟩ + +def certified930 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 3, 0, -1, 0, 1, 0, -1], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, -1, 0, 3, 0, 1, 0, -1], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 1, 0, 1, 0, 3, 0, 1], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, -1, 0, -1, 0, 1, 0, 3]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[1, 1, 0, 0, 1, 1, 0, 0], #[1, 1, 1, -1, 0, 0, 0, 0], #[0, 1, 0, 1, 0, -1, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, -64, 0, 64, 64, 64, 64], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 64, -64, 0, 64, 64, -192, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, 64, -64, 0, -64, 192, -64, -64], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, 64, 64, 0, -192, 64, 64, 64]] }, by decide⟩ + +def certified931 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 3, 0, -1, 0, 1, 0, 1], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, -1, 0, 3, 0, 1, 0, 1], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 1, 0, 1, 0, 3, 0, -1], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 1, 0, 1, 0, -1, 0, 3]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 1, 0, 0, 1, 1, 0, 0], #[1, 1, 1, -1, 0, 0, 0, 0], #[0, -1, 0, -1, 0, 1, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, -64, 0, 64, 64, 64, -64], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 64, -64, 0, 64, 64, -192, -64], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, 64, -64, 0, -64, 192, -64, 64], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, -64, -64, 0, 192, -64, -64, 64]] }, by decide⟩ + +def certified932 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 3, 0, 1, 0, -1, 0, -1], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 1, 0, 3, 0, 1, 0, 1], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, -1, 0, 1, 0, 3, 0, -1], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, -1, 0, 1, 0, -1, 0, 3]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[1, 1, 0, 0, 1, -1, 0, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[0, 1, 0, -1, 0, 1, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, -64, 0, 64, 64, 64, 64], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 64, 0, -64, -64, 192, -64], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, -64, 64, 0, 64, -192, 64, 64], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, 64, 64, 0, -192, 64, 64, 64]] }, by decide⟩ + +def certified933 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 3, 0, 1, 0, -1, 0, 1], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 1, 0, 3, 0, 1, 0, -1], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, -1, 0, 1, 0, 3, 0, 1], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 1, 0, -1, 0, 1, 0, 3]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 1, 0, 0, 1, -1, 0, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[0, -1, 0, 1, 0, -1, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, -64, 0, 64, 64, 64, -64], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 64, 0, -64, -64, 192, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, -64, 64, 0, 64, -192, 64, -64], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, -64, -64, 0, 192, -64, -64, 64]] }, by decide⟩ + +def certified934 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 3, 0, 1, 0, 1, 0, -1], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 1, 0, 3, 0, -1, 0, 1], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 1, 0, -1, 0, 3, 0, 1], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, -1, 0, 1, 0, 1, 0, 3]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, -1], #[1, 1, 0, 0, 1, 1, 0, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[0, 1, 0, -1, 0, -1, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, -64, 0, 64, 64, 64, 64], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 64, 0, -64, -64, 192, -64], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, 64, -64, 0, -64, 192, -64, -64], #[0, 0, 0, 128, 0, 0, 0, 0], #[-64, 64, 64, 0, -192, 64, 64, 64]] }, by decide⟩ + +def certified935 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[4, 0, 0, 0, 0, 0, 0, 0], #[0, 3, 0, 1, 0, 1, 0, 1], #[0, 0, 4, 0, 0, 0, 0, 0], #[0, 1, 0, 3, 0, -1, 0, -1], #[0, 0, 0, 0, 4, 0, 0, 0], #[0, 1, 0, -1, 0, 3, 0, -1], #[0, 0, 0, 0, 0, 0, 4, 0], #[0, 1, 0, -1, 0, -1, 0, 3]], + stack := #[#[2, 0, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 2, 0], #[0, 1, 1, 0, 1, 0, 0, 1], #[1, 1, 0, 0, 1, 1, 0, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[0, -1, 0, 1, 0, 1, 0, 1]], + inverse256 := #[#[128, 0, 0, 0, 0, 0, 0, 0], #[-64, -64, -64, 0, 64, 64, 64, -64], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 64, 0, -64, -64, 192, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, 64, -64, 0, -64, 192, -64, 64], #[0, 0, 0, 128, 0, 0, 0, 0], #[64, -64, -64, 0, 192, -64, -64, 64]] }, by decide⟩ + +def certified936 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 0, 0, -1, 0, -1, -1, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[-1, 0, 0, 3, 0, -1, -1, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[-1, 0, 0, -1, 0, 3, -1, 0], #[-1, 0, 0, -1, 0, -1, 3, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 1, 0, -1, 0], #[1, 1, 0, 0, 1, -1, 0, 0], #[1, 1, 1, -1, 0, 0, 0, 0], #[1, 0, 0, 1, 0, 1, 1, 0]], + inverse256 := #[#[-64, -64, -64, 0, 64, 64, 64, 64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 64, -64, 0, 64, 64, -192, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, -64, 64, 0, 64, -192, 64, 64], #[-64, 64, 64, 0, -192, 64, 64, 64], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified937 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 0, 0, -1, 0, -1, 1, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[-1, 0, 0, 3, 0, -1, 1, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[-1, 0, 0, -1, 0, 3, 1, 0], #[1, 0, 0, 1, 0, 1, 3, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 0, 0, 1, -1, 0, 0], #[1, 1, 1, -1, 0, 0, 0, 0], #[-1, 0, 0, -1, 0, -1, 1, 0]], + inverse256 := #[#[-64, -64, -64, 0, 64, 64, 64, -64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 64, -64, 0, 64, 64, -192, -64], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, -64, 64, 0, 64, -192, 64, -64], #[64, -64, -64, 0, 192, -64, -64, 64], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified938 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 0, 0, -1, 0, 1, -1, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[-1, 0, 0, 3, 0, 1, -1, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[1, 0, 0, 1, 0, 3, 1, 0], #[-1, 0, 0, -1, 0, 1, 3, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 1, 0, -1, 0], #[1, 1, 0, 0, 1, 1, 0, 0], #[1, 1, 1, -1, 0, 0, 0, 0], #[1, 0, 0, 1, 0, -1, 1, 0]], + inverse256 := #[#[-64, -64, -64, 0, 64, 64, 64, 64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 64, -64, 0, 64, 64, -192, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, 64, -64, 0, -64, 192, -64, -64], #[-64, 64, 64, 0, -192, 64, 64, 64], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified939 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 0, 0, -1, 0, 1, 1, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[-1, 0, 0, 3, 0, 1, 1, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[1, 0, 0, 1, 0, 3, -1, 0], #[1, 0, 0, 1, 0, -1, 3, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 0, 0, 1, 1, 0, 0], #[1, 1, 1, -1, 0, 0, 0, 0], #[-1, 0, 0, -1, 0, 1, 1, 0]], + inverse256 := #[#[-64, -64, -64, 0, 64, 64, 64, -64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[64, 64, -64, 0, 64, 64, -192, -64], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, 64, -64, 0, -64, 192, -64, 64], #[64, -64, -64, 0, 192, -64, -64, 64], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified940 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 0, 0, 1, 0, -1, -1, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[1, 0, 0, 3, 0, 1, 1, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[-1, 0, 0, 1, 0, 3, -1, 0], #[-1, 0, 0, 1, 0, -1, 3, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 1, 0, -1, 0], #[1, 1, 0, 0, 1, -1, 0, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[1, 0, 0, -1, 0, 1, 1, 0]], + inverse256 := #[#[-64, -64, -64, 0, 64, 64, 64, 64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 64, 0, -64, -64, 192, -64], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, -64, 64, 0, 64, -192, 64, 64], #[-64, 64, 64, 0, -192, 64, 64, 64], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified941 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 0, 0, 1, 0, -1, 1, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[1, 0, 0, 3, 0, 1, -1, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[-1, 0, 0, 1, 0, 3, 1, 0], #[1, 0, 0, -1, 0, 1, 3, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 0, 0, 1, -1, 0, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[-1, 0, 0, 1, 0, -1, 1, 0]], + inverse256 := #[#[-64, -64, -64, 0, 64, 64, 64, -64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 64, 0, -64, -64, 192, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[64, -64, 64, 0, 64, -192, 64, -64], #[64, -64, -64, 0, 192, -64, -64, 64], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified942 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 0, 0, 1, 0, 1, -1, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[1, 0, 0, 3, 0, -1, 1, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[1, 0, 0, -1, 0, 3, 1, 0], #[-1, 0, 0, 1, 0, 1, 3, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 1, 0, -1, 0], #[1, 1, 0, 0, 1, 1, 0, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[1, 0, 0, -1, 0, -1, 1, 0]], + inverse256 := #[#[-64, -64, -64, 0, 64, 64, 64, 64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 64, 0, -64, -64, 192, -64], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, 64, -64, 0, -64, 192, -64, -64], #[-64, 64, 64, 0, -192, 64, 64, 64], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def certified943 : CertifiedFrame := + ⟨{ dimension := 7, scaled := #[#[3, 0, 0, 1, 0, 1, 1, 0], #[0, 4, 0, 0, 0, 0, 0, 0], #[0, 0, 4, 0, 0, 0, 0, 0], #[1, 0, 0, 3, 0, -1, -1, 0], #[0, 0, 0, 0, 4, 0, 0, 0], #[1, 0, 0, -1, 0, 3, -1, 0], #[1, 0, 0, -1, 0, -1, 3, 0], #[0, 0, 0, 0, 0, 0, 0, 4]], + stack := #[#[0, 2, 0, 0, 0, 0, 0, 0], #[0, 0, 2, 0, 0, 0, 0, 0], #[0, 0, 0, 0, 2, 0, 0, 0], #[0, 0, 0, 0, 0, 0, 0, 2], #[1, 0, 1, 0, 1, 0, 1, 0], #[1, 1, 0, 0, 1, 1, 0, 0], #[1, 1, 1, 1, 0, 0, 0, 0], #[-1, 0, 0, 1, 0, 1, 1, 0]], + inverse256 := #[#[-64, -64, -64, 0, 64, 64, 64, -64], #[128, 0, 0, 0, 0, 0, 0, 0], #[0, 128, 0, 0, 0, 0, 0, 0], #[-64, -64, 64, 0, -64, -64, 192, 64], #[0, 0, 128, 0, 0, 0, 0, 0], #[-64, 64, -64, 0, -64, 192, -64, 64], #[64, -64, -64, 0, 192, -64, -64, 64], #[0, 0, 0, 128, 0, 0, 0, 0]] }, by decide⟩ + +def lookup (n : Nat) : CertifiedFrame := + (if n < 472 then (if n < 236 then (if n < 118 then (if n < 59 then (if n < 29 then (if n < 14 then (if n < 7 then (if n < 3 then (if n < 1 then certified0 else (if n < 2 then certified1 else certified2)) else (if n < 5 then (if n < 4 then certified3 else certified4) else (if n < 6 then certified5 else certified6))) else (if n < 10 then (if n < 8 then certified7 else (if n < 9 then certified8 else certified9)) else (if n < 12 then (if n < 11 then certified10 else certified11) else (if n < 13 then certified12 else certified13)))) else (if n < 21 then (if n < 17 then (if n < 15 then certified14 else (if n < 16 then certified15 else certified16)) else (if n < 19 then (if n < 18 then certified17 else certified18) else (if n < 20 then certified19 else certified20))) else (if n < 25 then (if n < 23 then (if n < 22 then certified21 else certified22) else (if n < 24 then certified23 else certified24)) else (if n < 27 then (if n < 26 then certified25 else certified26) else (if n < 28 then certified27 else certified28))))) else (if n < 44 then (if n < 36 then (if n < 32 then (if n < 30 then certified29 else (if n < 31 then certified30 else certified31)) else (if n < 34 then (if n < 33 then certified32 else certified33) else (if n < 35 then certified34 else certified35))) else (if n < 40 then (if n < 38 then (if n < 37 then certified36 else certified37) else (if n < 39 then certified38 else certified39)) else (if n < 42 then (if n < 41 then certified40 else certified41) else (if n < 43 then certified42 else certified43)))) else (if n < 51 then (if n < 47 then (if n < 45 then certified44 else (if n < 46 then certified45 else certified46)) else (if n < 49 then (if n < 48 then certified47 else certified48) else (if n < 50 then certified49 else certified50))) else (if n < 55 then (if n < 53 then (if n < 52 then certified51 else certified52) else (if n < 54 then certified53 else certified54)) else (if n < 57 then (if n < 56 then certified55 else certified56) else (if n < 58 then certified57 else certified58)))))) else (if n < 88 then (if n < 73 then (if n < 66 then (if n < 62 then (if n < 60 then certified59 else (if n < 61 then certified60 else certified61)) else (if n < 64 then (if n < 63 then certified62 else certified63) else (if n < 65 then certified64 else certified65))) else (if n < 69 then (if n < 67 then certified66 else (if n < 68 then certified67 else certified68)) else (if n < 71 then (if n < 70 then certified69 else certified70) else (if n < 72 then certified71 else certified72)))) else (if n < 80 then (if n < 76 then (if n < 74 then certified73 else (if n < 75 then certified74 else certified75)) else (if n < 78 then (if n < 77 then certified76 else certified77) else (if n < 79 then certified78 else certified79))) else (if n < 84 then (if n < 82 then (if n < 81 then certified80 else certified81) else (if n < 83 then certified82 else certified83)) else (if n < 86 then (if n < 85 then certified84 else certified85) else (if n < 87 then certified86 else certified87))))) else (if n < 103 then (if n < 95 then (if n < 91 then (if n < 89 then certified88 else (if n < 90 then certified89 else certified90)) else (if n < 93 then (if n < 92 then certified91 else certified92) else (if n < 94 then certified93 else certified94))) else (if n < 99 then (if n < 97 then (if n < 96 then certified95 else certified96) else (if n < 98 then certified97 else certified98)) else (if n < 101 then (if n < 100 then certified99 else certified100) else (if n < 102 then certified101 else certified102)))) else (if n < 110 then (if n < 106 then (if n < 104 then certified103 else (if n < 105 then certified104 else certified105)) else (if n < 108 then (if n < 107 then certified106 else certified107) else (if n < 109 then certified108 else certified109))) else (if n < 114 then (if n < 112 then (if n < 111 then certified110 else certified111) else (if n < 113 then certified112 else certified113)) else (if n < 116 then (if n < 115 then certified114 else certified115) else (if n < 117 then certified116 else certified117))))))) else (if n < 177 then (if n < 147 then (if n < 132 then (if n < 125 then (if n < 121 then (if n < 119 then certified118 else (if n < 120 then certified119 else certified120)) else (if n < 123 then (if n < 122 then certified121 else certified122) else (if n < 124 then certified123 else certified124))) else (if n < 128 then (if n < 126 then certified125 else (if n < 127 then certified126 else certified127)) else (if n < 130 then (if n < 129 then certified128 else certified129) else (if n < 131 then certified130 else certified131)))) else (if n < 139 then (if n < 135 then (if n < 133 then certified132 else (if n < 134 then certified133 else certified134)) else (if n < 137 then (if n < 136 then certified135 else certified136) else (if n < 138 then certified137 else certified138))) else (if n < 143 then (if n < 141 then (if n < 140 then certified139 else certified140) else (if n < 142 then certified141 else certified142)) else (if n < 145 then (if n < 144 then certified143 else certified144) else (if n < 146 then certified145 else certified146))))) else (if n < 162 then (if n < 154 then (if n < 150 then (if n < 148 then certified147 else (if n < 149 then certified148 else certified149)) else (if n < 152 then (if n < 151 then certified150 else certified151) else (if n < 153 then certified152 else certified153))) else (if n < 158 then (if n < 156 then (if n < 155 then certified154 else certified155) else (if n < 157 then certified156 else certified157)) else (if n < 160 then (if n < 159 then certified158 else certified159) else (if n < 161 then certified160 else certified161)))) else (if n < 169 then (if n < 165 then (if n < 163 then certified162 else (if n < 164 then certified163 else certified164)) else (if n < 167 then (if n < 166 then certified165 else certified166) else (if n < 168 then certified167 else certified168))) else (if n < 173 then (if n < 171 then (if n < 170 then certified169 else certified170) else (if n < 172 then certified171 else certified172)) else (if n < 175 then (if n < 174 then certified173 else certified174) else (if n < 176 then certified175 else certified176)))))) else (if n < 206 then (if n < 191 then (if n < 184 then (if n < 180 then (if n < 178 then certified177 else (if n < 179 then certified178 else certified179)) else (if n < 182 then (if n < 181 then certified180 else certified181) else (if n < 183 then certified182 else certified183))) else (if n < 187 then (if n < 185 then certified184 else (if n < 186 then certified185 else certified186)) else (if n < 189 then (if n < 188 then certified187 else certified188) else (if n < 190 then certified189 else certified190)))) else (if n < 198 then (if n < 194 then (if n < 192 then certified191 else (if n < 193 then certified192 else certified193)) else (if n < 196 then (if n < 195 then certified194 else certified195) else (if n < 197 then certified196 else certified197))) else (if n < 202 then (if n < 200 then (if n < 199 then certified198 else certified199) else (if n < 201 then certified200 else certified201)) else (if n < 204 then (if n < 203 then certified202 else certified203) else (if n < 205 then certified204 else certified205))))) else (if n < 221 then (if n < 213 then (if n < 209 then (if n < 207 then certified206 else (if n < 208 then certified207 else certified208)) else (if n < 211 then (if n < 210 then certified209 else certified210) else (if n < 212 then certified211 else certified212))) else (if n < 217 then (if n < 215 then (if n < 214 then certified213 else certified214) else (if n < 216 then certified215 else certified216)) else (if n < 219 then (if n < 218 then certified217 else certified218) else (if n < 220 then certified219 else certified220)))) else (if n < 228 then (if n < 224 then (if n < 222 then certified221 else (if n < 223 then certified222 else certified223)) else (if n < 226 then (if n < 225 then certified224 else certified225) else (if n < 227 then certified226 else certified227))) else (if n < 232 then (if n < 230 then (if n < 229 then certified228 else certified229) else (if n < 231 then certified230 else certified231)) else (if n < 234 then (if n < 233 then certified232 else certified233) else (if n < 235 then certified234 else certified235)))))))) else (if n < 354 then (if n < 295 then (if n < 265 then (if n < 250 then (if n < 243 then (if n < 239 then (if n < 237 then certified236 else (if n < 238 then certified237 else certified238)) else (if n < 241 then (if n < 240 then certified239 else certified240) else (if n < 242 then certified241 else certified242))) else (if n < 246 then (if n < 244 then certified243 else (if n < 245 then certified244 else certified245)) else (if n < 248 then (if n < 247 then certified246 else certified247) else (if n < 249 then certified248 else certified249)))) else (if n < 257 then (if n < 253 then (if n < 251 then certified250 else (if n < 252 then certified251 else certified252)) else (if n < 255 then (if n < 254 then certified253 else certified254) else (if n < 256 then certified255 else certified256))) else (if n < 261 then (if n < 259 then (if n < 258 then certified257 else certified258) else (if n < 260 then certified259 else certified260)) else (if n < 263 then (if n < 262 then certified261 else certified262) else (if n < 264 then certified263 else certified264))))) else (if n < 280 then (if n < 272 then (if n < 268 then (if n < 266 then certified265 else (if n < 267 then certified266 else certified267)) else (if n < 270 then (if n < 269 then certified268 else certified269) else (if n < 271 then certified270 else certified271))) else (if n < 276 then (if n < 274 then (if n < 273 then certified272 else certified273) else (if n < 275 then certified274 else certified275)) else (if n < 278 then (if n < 277 then certified276 else certified277) else (if n < 279 then certified278 else certified279)))) else (if n < 287 then (if n < 283 then (if n < 281 then certified280 else (if n < 282 then certified281 else certified282)) else (if n < 285 then (if n < 284 then certified283 else certified284) else (if n < 286 then certified285 else certified286))) else (if n < 291 then (if n < 289 then (if n < 288 then certified287 else certified288) else (if n < 290 then certified289 else certified290)) else (if n < 293 then (if n < 292 then certified291 else certified292) else (if n < 294 then certified293 else certified294)))))) else (if n < 324 then (if n < 309 then (if n < 302 then (if n < 298 then (if n < 296 then certified295 else (if n < 297 then certified296 else certified297)) else (if n < 300 then (if n < 299 then certified298 else certified299) else (if n < 301 then certified300 else certified301))) else (if n < 305 then (if n < 303 then certified302 else (if n < 304 then certified303 else certified304)) else (if n < 307 then (if n < 306 then certified305 else certified306) else (if n < 308 then certified307 else certified308)))) else (if n < 316 then (if n < 312 then (if n < 310 then certified309 else (if n < 311 then certified310 else certified311)) else (if n < 314 then (if n < 313 then certified312 else certified313) else (if n < 315 then certified314 else certified315))) else (if n < 320 then (if n < 318 then (if n < 317 then certified316 else certified317) else (if n < 319 then certified318 else certified319)) else (if n < 322 then (if n < 321 then certified320 else certified321) else (if n < 323 then certified322 else certified323))))) else (if n < 339 then (if n < 331 then (if n < 327 then (if n < 325 then certified324 else (if n < 326 then certified325 else certified326)) else (if n < 329 then (if n < 328 then certified327 else certified328) else (if n < 330 then certified329 else certified330))) else (if n < 335 then (if n < 333 then (if n < 332 then certified331 else certified332) else (if n < 334 then certified333 else certified334)) else (if n < 337 then (if n < 336 then certified335 else certified336) else (if n < 338 then certified337 else certified338)))) else (if n < 346 then (if n < 342 then (if n < 340 then certified339 else (if n < 341 then certified340 else certified341)) else (if n < 344 then (if n < 343 then certified342 else certified343) else (if n < 345 then certified344 else certified345))) else (if n < 350 then (if n < 348 then (if n < 347 then certified346 else certified347) else (if n < 349 then certified348 else certified349)) else (if n < 352 then (if n < 351 then certified350 else certified351) else (if n < 353 then certified352 else certified353))))))) else (if n < 413 then (if n < 383 then (if n < 368 then (if n < 361 then (if n < 357 then (if n < 355 then certified354 else (if n < 356 then certified355 else certified356)) else (if n < 359 then (if n < 358 then certified357 else certified358) else (if n < 360 then certified359 else certified360))) else (if n < 364 then (if n < 362 then certified361 else (if n < 363 then certified362 else certified363)) else (if n < 366 then (if n < 365 then certified364 else certified365) else (if n < 367 then certified366 else certified367)))) else (if n < 375 then (if n < 371 then (if n < 369 then certified368 else (if n < 370 then certified369 else certified370)) else (if n < 373 then (if n < 372 then certified371 else certified372) else (if n < 374 then certified373 else certified374))) else (if n < 379 then (if n < 377 then (if n < 376 then certified375 else certified376) else (if n < 378 then certified377 else certified378)) else (if n < 381 then (if n < 380 then certified379 else certified380) else (if n < 382 then certified381 else certified382))))) else (if n < 398 then (if n < 390 then (if n < 386 then (if n < 384 then certified383 else (if n < 385 then certified384 else certified385)) else (if n < 388 then (if n < 387 then certified386 else certified387) else (if n < 389 then certified388 else certified389))) else (if n < 394 then (if n < 392 then (if n < 391 then certified390 else certified391) else (if n < 393 then certified392 else certified393)) else (if n < 396 then (if n < 395 then certified394 else certified395) else (if n < 397 then certified396 else certified397)))) else (if n < 405 then (if n < 401 then (if n < 399 then certified398 else (if n < 400 then certified399 else certified400)) else (if n < 403 then (if n < 402 then certified401 else certified402) else (if n < 404 then certified403 else certified404))) else (if n < 409 then (if n < 407 then (if n < 406 then certified405 else certified406) else (if n < 408 then certified407 else certified408)) else (if n < 411 then (if n < 410 then certified409 else certified410) else (if n < 412 then certified411 else certified412)))))) else (if n < 442 then (if n < 427 then (if n < 420 then (if n < 416 then (if n < 414 then certified413 else (if n < 415 then certified414 else certified415)) else (if n < 418 then (if n < 417 then certified416 else certified417) else (if n < 419 then certified418 else certified419))) else (if n < 423 then (if n < 421 then certified420 else (if n < 422 then certified421 else certified422)) else (if n < 425 then (if n < 424 then certified423 else certified424) else (if n < 426 then certified425 else certified426)))) else (if n < 434 then (if n < 430 then (if n < 428 then certified427 else (if n < 429 then certified428 else certified429)) else (if n < 432 then (if n < 431 then certified430 else certified431) else (if n < 433 then certified432 else certified433))) else (if n < 438 then (if n < 436 then (if n < 435 then certified434 else certified435) else (if n < 437 then certified436 else certified437)) else (if n < 440 then (if n < 439 then certified438 else certified439) else (if n < 441 then certified440 else certified441))))) else (if n < 457 then (if n < 449 then (if n < 445 then (if n < 443 then certified442 else (if n < 444 then certified443 else certified444)) else (if n < 447 then (if n < 446 then certified445 else certified446) else (if n < 448 then certified447 else certified448))) else (if n < 453 then (if n < 451 then (if n < 450 then certified449 else certified450) else (if n < 452 then certified451 else certified452)) else (if n < 455 then (if n < 454 then certified453 else certified454) else (if n < 456 then certified455 else certified456)))) else (if n < 464 then (if n < 460 then (if n < 458 then certified457 else (if n < 459 then certified458 else certified459)) else (if n < 462 then (if n < 461 then certified460 else certified461) else (if n < 463 then certified462 else certified463))) else (if n < 468 then (if n < 466 then (if n < 465 then certified464 else certified465) else (if n < 467 then certified466 else certified467)) else (if n < 470 then (if n < 469 then certified468 else certified469) else (if n < 471 then certified470 else certified471))))))))) else (if n < 708 then (if n < 590 then (if n < 531 then (if n < 501 then (if n < 486 then (if n < 479 then (if n < 475 then (if n < 473 then certified472 else (if n < 474 then certified473 else certified474)) else (if n < 477 then (if n < 476 then certified475 else certified476) else (if n < 478 then certified477 else certified478))) else (if n < 482 then (if n < 480 then certified479 else (if n < 481 then certified480 else certified481)) else (if n < 484 then (if n < 483 then certified482 else certified483) else (if n < 485 then certified484 else certified485)))) else (if n < 493 then (if n < 489 then (if n < 487 then certified486 else (if n < 488 then certified487 else certified488)) else (if n < 491 then (if n < 490 then certified489 else certified490) else (if n < 492 then certified491 else certified492))) else (if n < 497 then (if n < 495 then (if n < 494 then certified493 else certified494) else (if n < 496 then certified495 else certified496)) else (if n < 499 then (if n < 498 then certified497 else certified498) else (if n < 500 then certified499 else certified500))))) else (if n < 516 then (if n < 508 then (if n < 504 then (if n < 502 then certified501 else (if n < 503 then certified502 else certified503)) else (if n < 506 then (if n < 505 then certified504 else certified505) else (if n < 507 then certified506 else certified507))) else (if n < 512 then (if n < 510 then (if n < 509 then certified508 else certified509) else (if n < 511 then certified510 else certified511)) else (if n < 514 then (if n < 513 then certified512 else certified513) else (if n < 515 then certified514 else certified515)))) else (if n < 523 then (if n < 519 then (if n < 517 then certified516 else (if n < 518 then certified517 else certified518)) else (if n < 521 then (if n < 520 then certified519 else certified520) else (if n < 522 then certified521 else certified522))) else (if n < 527 then (if n < 525 then (if n < 524 then certified523 else certified524) else (if n < 526 then certified525 else certified526)) else (if n < 529 then (if n < 528 then certified527 else certified528) else (if n < 530 then certified529 else certified530)))))) else (if n < 560 then (if n < 545 then (if n < 538 then (if n < 534 then (if n < 532 then certified531 else (if n < 533 then certified532 else certified533)) else (if n < 536 then (if n < 535 then certified534 else certified535) else (if n < 537 then certified536 else certified537))) else (if n < 541 then (if n < 539 then certified538 else (if n < 540 then certified539 else certified540)) else (if n < 543 then (if n < 542 then certified541 else certified542) else (if n < 544 then certified543 else certified544)))) else (if n < 552 then (if n < 548 then (if n < 546 then certified545 else (if n < 547 then certified546 else certified547)) else (if n < 550 then (if n < 549 then certified548 else certified549) else (if n < 551 then certified550 else certified551))) else (if n < 556 then (if n < 554 then (if n < 553 then certified552 else certified553) else (if n < 555 then certified554 else certified555)) else (if n < 558 then (if n < 557 then certified556 else certified557) else (if n < 559 then certified558 else certified559))))) else (if n < 575 then (if n < 567 then (if n < 563 then (if n < 561 then certified560 else (if n < 562 then certified561 else certified562)) else (if n < 565 then (if n < 564 then certified563 else certified564) else (if n < 566 then certified565 else certified566))) else (if n < 571 then (if n < 569 then (if n < 568 then certified567 else certified568) else (if n < 570 then certified569 else certified570)) else (if n < 573 then (if n < 572 then certified571 else certified572) else (if n < 574 then certified573 else certified574)))) else (if n < 582 then (if n < 578 then (if n < 576 then certified575 else (if n < 577 then certified576 else certified577)) else (if n < 580 then (if n < 579 then certified578 else certified579) else (if n < 581 then certified580 else certified581))) else (if n < 586 then (if n < 584 then (if n < 583 then certified582 else certified583) else (if n < 585 then certified584 else certified585)) else (if n < 588 then (if n < 587 then certified586 else certified587) else (if n < 589 then certified588 else certified589))))))) else (if n < 649 then (if n < 619 then (if n < 604 then (if n < 597 then (if n < 593 then (if n < 591 then certified590 else (if n < 592 then certified591 else certified592)) else (if n < 595 then (if n < 594 then certified593 else certified594) else (if n < 596 then certified595 else certified596))) else (if n < 600 then (if n < 598 then certified597 else (if n < 599 then certified598 else certified599)) else (if n < 602 then (if n < 601 then certified600 else certified601) else (if n < 603 then certified602 else certified603)))) else (if n < 611 then (if n < 607 then (if n < 605 then certified604 else (if n < 606 then certified605 else certified606)) else (if n < 609 then (if n < 608 then certified607 else certified608) else (if n < 610 then certified609 else certified610))) else (if n < 615 then (if n < 613 then (if n < 612 then certified611 else certified612) else (if n < 614 then certified613 else certified614)) else (if n < 617 then (if n < 616 then certified615 else certified616) else (if n < 618 then certified617 else certified618))))) else (if n < 634 then (if n < 626 then (if n < 622 then (if n < 620 then certified619 else (if n < 621 then certified620 else certified621)) else (if n < 624 then (if n < 623 then certified622 else certified623) else (if n < 625 then certified624 else certified625))) else (if n < 630 then (if n < 628 then (if n < 627 then certified626 else certified627) else (if n < 629 then certified628 else certified629)) else (if n < 632 then (if n < 631 then certified630 else certified631) else (if n < 633 then certified632 else certified633)))) else (if n < 641 then (if n < 637 then (if n < 635 then certified634 else (if n < 636 then certified635 else certified636)) else (if n < 639 then (if n < 638 then certified637 else certified638) else (if n < 640 then certified639 else certified640))) else (if n < 645 then (if n < 643 then (if n < 642 then certified641 else certified642) else (if n < 644 then certified643 else certified644)) else (if n < 647 then (if n < 646 then certified645 else certified646) else (if n < 648 then certified647 else certified648)))))) else (if n < 678 then (if n < 663 then (if n < 656 then (if n < 652 then (if n < 650 then certified649 else (if n < 651 then certified650 else certified651)) else (if n < 654 then (if n < 653 then certified652 else certified653) else (if n < 655 then certified654 else certified655))) else (if n < 659 then (if n < 657 then certified656 else (if n < 658 then certified657 else certified658)) else (if n < 661 then (if n < 660 then certified659 else certified660) else (if n < 662 then certified661 else certified662)))) else (if n < 670 then (if n < 666 then (if n < 664 then certified663 else (if n < 665 then certified664 else certified665)) else (if n < 668 then (if n < 667 then certified666 else certified667) else (if n < 669 then certified668 else certified669))) else (if n < 674 then (if n < 672 then (if n < 671 then certified670 else certified671) else (if n < 673 then certified672 else certified673)) else (if n < 676 then (if n < 675 then certified674 else certified675) else (if n < 677 then certified676 else certified677))))) else (if n < 693 then (if n < 685 then (if n < 681 then (if n < 679 then certified678 else (if n < 680 then certified679 else certified680)) else (if n < 683 then (if n < 682 then certified681 else certified682) else (if n < 684 then certified683 else certified684))) else (if n < 689 then (if n < 687 then (if n < 686 then certified685 else certified686) else (if n < 688 then certified687 else certified688)) else (if n < 691 then (if n < 690 then certified689 else certified690) else (if n < 692 then certified691 else certified692)))) else (if n < 700 then (if n < 696 then (if n < 694 then certified693 else (if n < 695 then certified694 else certified695)) else (if n < 698 then (if n < 697 then certified696 else certified697) else (if n < 699 then certified698 else certified699))) else (if n < 704 then (if n < 702 then (if n < 701 then certified700 else certified701) else (if n < 703 then certified702 else certified703)) else (if n < 706 then (if n < 705 then certified704 else certified705) else (if n < 707 then certified706 else certified707)))))))) else (if n < 826 then (if n < 767 then (if n < 737 then (if n < 722 then (if n < 715 then (if n < 711 then (if n < 709 then certified708 else (if n < 710 then certified709 else certified710)) else (if n < 713 then (if n < 712 then certified711 else certified712) else (if n < 714 then certified713 else certified714))) else (if n < 718 then (if n < 716 then certified715 else (if n < 717 then certified716 else certified717)) else (if n < 720 then (if n < 719 then certified718 else certified719) else (if n < 721 then certified720 else certified721)))) else (if n < 729 then (if n < 725 then (if n < 723 then certified722 else (if n < 724 then certified723 else certified724)) else (if n < 727 then (if n < 726 then certified725 else certified726) else (if n < 728 then certified727 else certified728))) else (if n < 733 then (if n < 731 then (if n < 730 then certified729 else certified730) else (if n < 732 then certified731 else certified732)) else (if n < 735 then (if n < 734 then certified733 else certified734) else (if n < 736 then certified735 else certified736))))) else (if n < 752 then (if n < 744 then (if n < 740 then (if n < 738 then certified737 else (if n < 739 then certified738 else certified739)) else (if n < 742 then (if n < 741 then certified740 else certified741) else (if n < 743 then certified742 else certified743))) else (if n < 748 then (if n < 746 then (if n < 745 then certified744 else certified745) else (if n < 747 then certified746 else certified747)) else (if n < 750 then (if n < 749 then certified748 else certified749) else (if n < 751 then certified750 else certified751)))) else (if n < 759 then (if n < 755 then (if n < 753 then certified752 else (if n < 754 then certified753 else certified754)) else (if n < 757 then (if n < 756 then certified755 else certified756) else (if n < 758 then certified757 else certified758))) else (if n < 763 then (if n < 761 then (if n < 760 then certified759 else certified760) else (if n < 762 then certified761 else certified762)) else (if n < 765 then (if n < 764 then certified763 else certified764) else (if n < 766 then certified765 else certified766)))))) else (if n < 796 then (if n < 781 then (if n < 774 then (if n < 770 then (if n < 768 then certified767 else (if n < 769 then certified768 else certified769)) else (if n < 772 then (if n < 771 then certified770 else certified771) else (if n < 773 then certified772 else certified773))) else (if n < 777 then (if n < 775 then certified774 else (if n < 776 then certified775 else certified776)) else (if n < 779 then (if n < 778 then certified777 else certified778) else (if n < 780 then certified779 else certified780)))) else (if n < 788 then (if n < 784 then (if n < 782 then certified781 else (if n < 783 then certified782 else certified783)) else (if n < 786 then (if n < 785 then certified784 else certified785) else (if n < 787 then certified786 else certified787))) else (if n < 792 then (if n < 790 then (if n < 789 then certified788 else certified789) else (if n < 791 then certified790 else certified791)) else (if n < 794 then (if n < 793 then certified792 else certified793) else (if n < 795 then certified794 else certified795))))) else (if n < 811 then (if n < 803 then (if n < 799 then (if n < 797 then certified796 else (if n < 798 then certified797 else certified798)) else (if n < 801 then (if n < 800 then certified799 else certified800) else (if n < 802 then certified801 else certified802))) else (if n < 807 then (if n < 805 then (if n < 804 then certified803 else certified804) else (if n < 806 then certified805 else certified806)) else (if n < 809 then (if n < 808 then certified807 else certified808) else (if n < 810 then certified809 else certified810)))) else (if n < 818 then (if n < 814 then (if n < 812 then certified811 else (if n < 813 then certified812 else certified813)) else (if n < 816 then (if n < 815 then certified814 else certified815) else (if n < 817 then certified816 else certified817))) else (if n < 822 then (if n < 820 then (if n < 819 then certified818 else certified819) else (if n < 821 then certified820 else certified821)) else (if n < 824 then (if n < 823 then certified822 else certified823) else (if n < 825 then certified824 else certified825))))))) else (if n < 885 then (if n < 855 then (if n < 840 then (if n < 833 then (if n < 829 then (if n < 827 then certified826 else (if n < 828 then certified827 else certified828)) else (if n < 831 then (if n < 830 then certified829 else certified830) else (if n < 832 then certified831 else certified832))) else (if n < 836 then (if n < 834 then certified833 else (if n < 835 then certified834 else certified835)) else (if n < 838 then (if n < 837 then certified836 else certified837) else (if n < 839 then certified838 else certified839)))) else (if n < 847 then (if n < 843 then (if n < 841 then certified840 else (if n < 842 then certified841 else certified842)) else (if n < 845 then (if n < 844 then certified843 else certified844) else (if n < 846 then certified845 else certified846))) else (if n < 851 then (if n < 849 then (if n < 848 then certified847 else certified848) else (if n < 850 then certified849 else certified850)) else (if n < 853 then (if n < 852 then certified851 else certified852) else (if n < 854 then certified853 else certified854))))) else (if n < 870 then (if n < 862 then (if n < 858 then (if n < 856 then certified855 else (if n < 857 then certified856 else certified857)) else (if n < 860 then (if n < 859 then certified858 else certified859) else (if n < 861 then certified860 else certified861))) else (if n < 866 then (if n < 864 then (if n < 863 then certified862 else certified863) else (if n < 865 then certified864 else certified865)) else (if n < 868 then (if n < 867 then certified866 else certified867) else (if n < 869 then certified868 else certified869)))) else (if n < 877 then (if n < 873 then (if n < 871 then certified870 else (if n < 872 then certified871 else certified872)) else (if n < 875 then (if n < 874 then certified873 else certified874) else (if n < 876 then certified875 else certified876))) else (if n < 881 then (if n < 879 then (if n < 878 then certified877 else certified878) else (if n < 880 then certified879 else certified880)) else (if n < 883 then (if n < 882 then certified881 else certified882) else (if n < 884 then certified883 else certified884)))))) else (if n < 914 then (if n < 899 then (if n < 892 then (if n < 888 then (if n < 886 then certified885 else (if n < 887 then certified886 else certified887)) else (if n < 890 then (if n < 889 then certified888 else certified889) else (if n < 891 then certified890 else certified891))) else (if n < 895 then (if n < 893 then certified892 else (if n < 894 then certified893 else certified894)) else (if n < 897 then (if n < 896 then certified895 else certified896) else (if n < 898 then certified897 else certified898)))) else (if n < 906 then (if n < 902 then (if n < 900 then certified899 else (if n < 901 then certified900 else certified901)) else (if n < 904 then (if n < 903 then certified902 else certified903) else (if n < 905 then certified904 else certified905))) else (if n < 910 then (if n < 908 then (if n < 907 then certified906 else certified907) else (if n < 909 then certified908 else certified909)) else (if n < 912 then (if n < 911 then certified910 else certified911) else (if n < 913 then certified912 else certified913))))) else (if n < 929 then (if n < 921 then (if n < 917 then (if n < 915 then certified914 else (if n < 916 then certified915 else certified916)) else (if n < 919 then (if n < 918 then certified917 else certified918) else (if n < 920 then certified919 else certified920))) else (if n < 925 then (if n < 923 then (if n < 922 then certified921 else certified922) else (if n < 924 then certified923 else certified924)) else (if n < 927 then (if n < 926 then certified925 else certified926) else (if n < 928 then certified927 else certified928)))) else (if n < 936 then (if n < 932 then (if n < 930 then certified929 else (if n < 931 then certified930 else certified931)) else (if n < 934 then (if n < 933 then certified932 else certified933) else (if n < 935 then certified934 else certified935))) else (if n < 940 then (if n < 938 then (if n < 937 then certified936 else certified937) else (if n < 939 then certified938 else certified939)) else (if n < 942 then (if n < 941 then certified940 else certified941) else (if n < 943 then certified942 else certified943)))))))))) + +def frame (f : Fin 944) : FrameDatum := (lookup f.val).val +def scaled (f : Fin 944) : IntMatrix8 := entry (frame f).scaled +def stack (f : Fin 944) : IntMatrix8 := entry (frame f).stack +def inverse256 (f : Fin 944) : IntMatrix8 := entry (frame f).inverse256 + +theorem frame_valid (f : Fin 944) : ValidFrame (frame f) := (lookup f.val).property +theorem scaled_idempotent_entries (f : Fin 944) (i j : Fin 8) : + dot8 (scaled f) (scaled f) i j = 4 * scaled f i j := (frame_valid f).2.1 i j +theorem scaled_symmetric_entries (f : Fin 944) (i j : Fin 8) : + scaled f i j = scaled f j i := (frame_valid f).2.2.1 i j +theorem scaled_stack_entries (f : Fin 944) (i j : Fin 8) : + dot8 (scaled f) (fun a b => stack f b a) i j = + if j.val < (frame f).dimension then 4 * stack f j i else 0 := + (frame_valid f).2.2.2.1 i j +theorem stack_inverse_entries (f : Fin 944) (i j : Fin 8) : + dot8 (stack f) (inverse256 f) i j = if i = j then 256 else 0 := + (frame_valid f).2.2.2.2.1 i j +theorem inverse_stack_entries (f : Fin 944) (i j : Fin 8) : + dot8 (inverse256 f) (stack f) i j = if i = j then 256 else 0 := + (frame_valid f).2.2.2.2.2 i j + +def Absorbs (small large : Fin 944) : Prop := + (∀ i j : Fin 8, dot8 (scaled small) (scaled large) i j = 4 * scaled small i j) ∧ + (∀ i j : Fin 8, dot8 (scaled large) (scaled small) i j = 4 * scaled small i j) + +instance (small large : Fin 944) : Decidable (Absorbs small large) := by + unfold Absorbs + infer_instance + +def transition0 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 2), by decide⟩ +def transition1 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 3), by decide⟩ +def transition2 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 4), by decide⟩ +def transition3 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 5), by decide⟩ +def transition4 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 6), by decide⟩ +def transition5 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 7), by decide⟩ +def transition6 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 8), by decide⟩ +def transition7 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 9), by decide⟩ +def transition8 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 10), by decide⟩ +def transition9 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 11), by decide⟩ +def transition10 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 12), by decide⟩ +def transition11 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 13), by decide⟩ +def transition12 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 14), by decide⟩ +def transition13 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 15), by decide⟩ +def transition14 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 16), by decide⟩ +def transition15 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 17), by decide⟩ +def transition16 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 18), by decide⟩ +def transition17 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 19), by decide⟩ +def transition18 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 20), by decide⟩ +def transition19 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 21), by decide⟩ +def transition20 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 22), by decide⟩ +def transition21 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 23), by decide⟩ +def transition22 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 24), by decide⟩ +def transition23 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 25), by decide⟩ +def transition24 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 26), by decide⟩ +def transition25 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 27), by decide⟩ +def transition26 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 28), by decide⟩ +def transition27 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 29), by decide⟩ +def transition28 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 30), by decide⟩ +def transition29 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 31), by decide⟩ +def transition30 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 32), by decide⟩ +def transition31 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 33), by decide⟩ +def transition32 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 34), by decide⟩ +def transition33 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 35), by decide⟩ +def transition34 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 36), by decide⟩ +def transition35 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 37), by decide⟩ +def transition36 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 38), by decide⟩ +def transition37 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 39), by decide⟩ +def transition38 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 40), by decide⟩ +def transition39 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 41), by decide⟩ +def transition40 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 42), by decide⟩ +def transition41 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 43), by decide⟩ +def transition42 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 44), by decide⟩ +def transition43 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 45), by decide⟩ +def transition44 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 46), by decide⟩ +def transition45 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 47), by decide⟩ +def transition46 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 48), by decide⟩ +def transition47 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 49), by decide⟩ +def transition48 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 50), by decide⟩ +def transition49 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 51), by decide⟩ +def transition50 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 52), by decide⟩ +def transition51 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 53), by decide⟩ +def transition52 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 54), by decide⟩ +def transition53 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 55), by decide⟩ +def transition54 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 56), by decide⟩ +def transition55 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 57), by decide⟩ +def transition56 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 58), by decide⟩ +def transition57 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 59), by decide⟩ +def transition58 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 60), by decide⟩ +def transition59 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 61), by decide⟩ +def transition60 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 62), by decide⟩ +def transition61 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 63), by decide⟩ +def transition62 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 64), by decide⟩ +def transition63 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 65), by decide⟩ +def transition64 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 66), by decide⟩ +def transition65 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 67), by decide⟩ +def transition66 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 68), by decide⟩ +def transition67 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 69), by decide⟩ +def transition68 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 70), by decide⟩ +def transition69 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 71), by decide⟩ +def transition70 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 72), by decide⟩ +def transition71 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 73), by decide⟩ +def transition72 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 74), by decide⟩ +def transition73 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 75), by decide⟩ +def transition74 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 76), by decide⟩ +def transition75 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 77), by decide⟩ +def transition76 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 78), by decide⟩ +def transition77 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 79), by decide⟩ +def transition78 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 80), by decide⟩ +def transition79 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 81), by decide⟩ +def transition80 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 82), by decide⟩ +def transition81 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 83), by decide⟩ +def transition82 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 84), by decide⟩ +def transition83 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 85), by decide⟩ +def transition84 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 86), by decide⟩ +def transition85 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 87), by decide⟩ +def transition86 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 88), by decide⟩ +def transition87 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 89), by decide⟩ +def transition88 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 90), by decide⟩ +def transition89 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 91), by decide⟩ +def transition90 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 92), by decide⟩ +def transition91 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 93), by decide⟩ +def transition92 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 94), by decide⟩ +def transition93 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 95), by decide⟩ +def transition94 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 96), by decide⟩ +def transition95 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 97), by decide⟩ +def transition96 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 98), by decide⟩ +def transition97 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 99), by decide⟩ +def transition98 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 100), by decide⟩ +def transition99 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 101), by decide⟩ +def transition100 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 102), by decide⟩ +def transition101 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 103), by decide⟩ +def transition102 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 104), by decide⟩ +def transition103 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 105), by decide⟩ +def transition104 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 106), by decide⟩ +def transition105 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 107), by decide⟩ +def transition106 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 108), by decide⟩ +def transition107 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 109), by decide⟩ +def transition108 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 110), by decide⟩ +def transition109 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 111), by decide⟩ +def transition110 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 112), by decide⟩ +def transition111 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 113), by decide⟩ +def transition112 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 114), by decide⟩ +def transition113 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 115), by decide⟩ +def transition114 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 116), by decide⟩ +def transition115 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 117), by decide⟩ +def transition116 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 118), by decide⟩ +def transition117 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 119), by decide⟩ +def transition118 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 120), by decide⟩ +def transition119 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 121), by decide⟩ +def transition120 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 122), by decide⟩ +def transition121 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 123), by decide⟩ +def transition122 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 124), by decide⟩ +def transition123 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 125), by decide⟩ +def transition124 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 126), by decide⟩ +def transition125 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 127), by decide⟩ +def transition126 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 128), by decide⟩ +def transition127 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 129), by decide⟩ +def transition128 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 130), by decide⟩ +def transition129 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 131), by decide⟩ +def transition130 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 132), by decide⟩ +def transition131 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 133), by decide⟩ +def transition132 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 134), by decide⟩ +def transition133 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 135), by decide⟩ +def transition134 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 136), by decide⟩ +def transition135 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 137), by decide⟩ +def transition136 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 138), by decide⟩ +def transition137 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 139), by decide⟩ +def transition138 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 140), by decide⟩ +def transition139 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 141), by decide⟩ +def transition140 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 142), by decide⟩ +def transition141 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 143), by decide⟩ +def transition142 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 144), by decide⟩ +def transition143 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 145), by decide⟩ +def transition144 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 146), by decide⟩ +def transition145 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 147), by decide⟩ +def transition146 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 148), by decide⟩ +def transition147 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 149), by decide⟩ +def transition148 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 150), by decide⟩ +def transition149 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 151), by decide⟩ +def transition150 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 152), by decide⟩ +def transition151 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 153), by decide⟩ +def transition152 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 154), by decide⟩ +def transition153 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 155), by decide⟩ +def transition154 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 156), by decide⟩ +def transition155 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 157), by decide⟩ +def transition156 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 158), by decide⟩ +def transition157 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 159), by decide⟩ +def transition158 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 160), by decide⟩ +def transition159 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 161), by decide⟩ +def transition160 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 162), by decide⟩ +def transition161 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 163), by decide⟩ +def transition162 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 164), by decide⟩ +def transition163 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 165), by decide⟩ +def transition164 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 166), by decide⟩ +def transition165 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 167), by decide⟩ +def transition166 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 168), by decide⟩ +def transition167 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 169), by decide⟩ +def transition168 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 170), by decide⟩ +def transition169 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 171), by decide⟩ +def transition170 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 172), by decide⟩ +def transition171 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 173), by decide⟩ +def transition172 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 174), by decide⟩ +def transition173 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 175), by decide⟩ +def transition174 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 176), by decide⟩ +def transition175 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 177), by decide⟩ +def transition176 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 178), by decide⟩ +def transition177 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 179), by decide⟩ +def transition178 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 180), by decide⟩ +def transition179 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 181), by decide⟩ +def transition180 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 182), by decide⟩ +def transition181 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 183), by decide⟩ +def transition182 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 184), by decide⟩ +def transition183 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 185), by decide⟩ +def transition184 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 186), by decide⟩ +def transition185 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 187), by decide⟩ +def transition186 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 188), by decide⟩ +def transition187 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 189), by decide⟩ +def transition188 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 190), by decide⟩ +def transition189 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 191), by decide⟩ +def transition190 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 192), by decide⟩ +def transition191 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 193), by decide⟩ +def transition192 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 194), by decide⟩ +def transition193 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 195), by decide⟩ +def transition194 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 196), by decide⟩ +def transition195 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 197), by decide⟩ +def transition196 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 198), by decide⟩ +def transition197 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 199), by decide⟩ +def transition198 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 200), by decide⟩ +def transition199 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 201), by decide⟩ +def transition200 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 202), by decide⟩ +def transition201 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 203), by decide⟩ +def transition202 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 204), by decide⟩ +def transition203 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 205), by decide⟩ +def transition204 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 206), by decide⟩ +def transition205 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 207), by decide⟩ +def transition206 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 208), by decide⟩ +def transition207 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 209), by decide⟩ +def transition208 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 210), by decide⟩ +def transition209 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 211), by decide⟩ +def transition210 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 212), by decide⟩ +def transition211 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 213), by decide⟩ +def transition212 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 214), by decide⟩ +def transition213 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 215), by decide⟩ +def transition214 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 216), by decide⟩ +def transition215 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 217), by decide⟩ +def transition216 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 218), by decide⟩ +def transition217 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 219), by decide⟩ +def transition218 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 220), by decide⟩ +def transition219 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 221), by decide⟩ +def transition220 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 222), by decide⟩ +def transition221 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 223), by decide⟩ +def transition222 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 224), by decide⟩ +def transition223 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 225), by decide⟩ +def transition224 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 226), by decide⟩ +def transition225 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 227), by decide⟩ +def transition226 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 228), by decide⟩ +def transition227 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 229), by decide⟩ +def transition228 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 230), by decide⟩ +def transition229 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 231), by decide⟩ +def transition230 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 232), by decide⟩ +def transition231 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 233), by decide⟩ +def transition232 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 234), by decide⟩ +def transition233 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 235), by decide⟩ +def transition234 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 236), by decide⟩ +def transition235 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 237), by decide⟩ +def transition236 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 238), by decide⟩ +def transition237 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 239), by decide⟩ +def transition238 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 240), by decide⟩ +def transition239 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 241), by decide⟩ +def transition240 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 242), by decide⟩ +def transition241 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 243), by decide⟩ +def transition242 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 244), by decide⟩ +def transition243 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 245), by decide⟩ +def transition244 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 246), by decide⟩ +def transition245 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 247), by decide⟩ +def transition246 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 248), by decide⟩ +def transition247 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 249), by decide⟩ +def transition248 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 250), by decide⟩ +def transition249 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 251), by decide⟩ +def transition250 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 252), by decide⟩ +def transition251 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 253), by decide⟩ +def transition252 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 254), by decide⟩ +def transition253 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 255), by decide⟩ +def transition254 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 256), by decide⟩ +def transition255 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 257), by decide⟩ +def transition256 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 258), by decide⟩ +def transition257 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 259), by decide⟩ +def transition258 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 260), by decide⟩ +def transition259 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 261), by decide⟩ +def transition260 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 262), by decide⟩ +def transition261 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 263), by decide⟩ +def transition262 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 264), by decide⟩ +def transition263 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 265), by decide⟩ +def transition264 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 266), by decide⟩ +def transition265 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 267), by decide⟩ +def transition266 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 268), by decide⟩ +def transition267 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 269), by decide⟩ +def transition268 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 270), by decide⟩ +def transition269 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 271), by decide⟩ +def transition270 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 272), by decide⟩ +def transition271 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 273), by decide⟩ +def transition272 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 274), by decide⟩ +def transition273 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 275), by decide⟩ +def transition274 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 276), by decide⟩ +def transition275 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 277), by decide⟩ +def transition276 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 278), by decide⟩ +def transition277 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 279), by decide⟩ +def transition278 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 280), by decide⟩ +def transition279 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 281), by decide⟩ +def transition280 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 282), by decide⟩ +def transition281 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 283), by decide⟩ +def transition282 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 284), by decide⟩ +def transition283 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 285), by decide⟩ +def transition284 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 286), by decide⟩ +def transition285 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 287), by decide⟩ +def transition286 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 288), by decide⟩ +def transition287 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 289), by decide⟩ +def transition288 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 308), by decide⟩ +def transition289 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 309), by decide⟩ +def transition290 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 322), by decide⟩ +def transition291 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 323), by decide⟩ +def transition292 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 326), by decide⟩ +def transition293 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 327), by decide⟩ +def transition294 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 380), by decide⟩ +def transition295 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 381), by decide⟩ +def transition296 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 386), by decide⟩ +def transition297 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 387), by decide⟩ +def transition298 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 398), by decide⟩ +def transition299 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 399), by decide⟩ +def transition300 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 404), by decide⟩ +def transition301 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 405), by decide⟩ +def transition302 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 410), by decide⟩ +def transition303 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 411), by decide⟩ +def transition304 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 422), by decide⟩ +def transition305 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 423), by decide⟩ +def transition306 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 434), by decide⟩ +def transition307 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 435), by decide⟩ +def transition308 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 438), by decide⟩ +def transition309 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 439), by decide⟩ +def transition310 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 442), by decide⟩ +def transition311 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 443), by decide⟩ +def transition312 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 446), by decide⟩ +def transition313 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 447), by decide⟩ +def transition314 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 452), by decide⟩ +def transition315 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 453), by decide⟩ +def transition316 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 458), by decide⟩ +def transition317 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 459), by decide⟩ +def transition318 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 460), by decide⟩ +def transition319 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 461), by decide⟩ +def transition320 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 462), by decide⟩ +def transition321 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 463), by decide⟩ +def transition322 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 464), by decide⟩ +def transition323 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 465), by decide⟩ +def transition324 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 466), by decide⟩ +def transition325 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 467), by decide⟩ +def transition326 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 468), by decide⟩ +def transition327 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 469), by decide⟩ +def transition328 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 470), by decide⟩ +def transition329 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 471), by decide⟩ +def transition330 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 472), by decide⟩ +def transition331 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 473), by decide⟩ +def transition332 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 476), by decide⟩ +def transition333 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 477), by decide⟩ +def transition334 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 480), by decide⟩ +def transition335 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 481), by decide⟩ +def transition336 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 484), by decide⟩ +def transition337 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 485), by decide⟩ +def transition338 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 488), by decide⟩ +def transition339 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 489), by decide⟩ +def transition340 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 492), by decide⟩ +def transition341 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 493), by decide⟩ +def transition342 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 496), by decide⟩ +def transition343 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 515), by decide⟩ +def transition344 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 548), by decide⟩ +def transition345 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 550), by decide⟩ +def transition346 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 564), by decide⟩ +def transition347 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 566), by decide⟩ +def transition348 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 582), by decide⟩ +def transition349 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 584), by decide⟩ +def transition350 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 585), by decide⟩ +def transition351 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 589), by decide⟩ +def transition352 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 591), by decide⟩ +def transition353 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 593), by decide⟩ +def transition354 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 594), by decide⟩ +def transition355 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 596), by decide⟩ +def transition356 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 601), by decide⟩ +def transition357 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 602), by decide⟩ +def transition358 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 603), by decide⟩ +def transition359 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 604), by decide⟩ +def transition360 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 605), by decide⟩ +def transition361 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 606), by decide⟩ +def transition362 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 607), by decide⟩ +def transition363 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 610), by decide⟩ +def transition364 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 611), by decide⟩ +def transition365 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 612), by decide⟩ +def transition366 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 613), by decide⟩ +def transition367 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 614), by decide⟩ +def transition368 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 615), by decide⟩ +def transition369 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 616), by decide⟩ +def transition370 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 617), by decide⟩ +def transition371 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 624), by decide⟩ +def transition372 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 625), by decide⟩ +def transition373 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 626), by decide⟩ +def transition374 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 627), by decide⟩ +def transition375 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 630), by decide⟩ +def transition376 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 631), by decide⟩ +def transition377 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 632), by decide⟩ +def transition378 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 633), by decide⟩ +def transition379 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 839), by decide⟩ +def transition380 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 847), by decide⟩ +def transition381 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 855), by decide⟩ +def transition382 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 863), by decide⟩ +def transition383 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 871), by decide⟩ +def transition384 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 879), by decide⟩ +def transition385 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 887), by decide⟩ +def transition386 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 895), by decide⟩ +def transition387 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 903), by decide⟩ +def transition388 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 911), by decide⟩ +def transition389 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 919), by decide⟩ +def transition390 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 927), by decide⟩ +def transition391 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 935), by decide⟩ +def transition392 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(0, 943), by decide⟩ +def transition393 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 296), by decide⟩ +def transition394 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 297), by decide⟩ +def transition395 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 298), by decide⟩ +def transition396 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 299), by decide⟩ +def transition397 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 300), by decide⟩ +def transition398 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 301), by decide⟩ +def transition399 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 310), by decide⟩ +def transition400 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 311), by decide⟩ +def transition401 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 312), by decide⟩ +def transition402 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 313), by decide⟩ +def transition403 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 320), by decide⟩ +def transition404 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 321), by decide⟩ +def transition405 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 324), by decide⟩ +def transition406 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 325), by decide⟩ +def transition407 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 332), by decide⟩ +def transition408 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 333), by decide⟩ +def transition409 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 334), by decide⟩ +def transition410 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 335), by decide⟩ +def transition411 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 336), by decide⟩ +def transition412 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 337), by decide⟩ +def transition413 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 344), by decide⟩ +def transition414 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 345), by decide⟩ +def transition415 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 346), by decide⟩ +def transition416 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 347), by decide⟩ +def transition417 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 348), by decide⟩ +def transition418 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 349), by decide⟩ +def transition419 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 356), by decide⟩ +def transition420 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 357), by decide⟩ +def transition421 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 358), by decide⟩ +def transition422 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 359), by decide⟩ +def transition423 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 360), by decide⟩ +def transition424 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 361), by decide⟩ +def transition425 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 368), by decide⟩ +def transition426 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 369), by decide⟩ +def transition427 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 370), by decide⟩ +def transition428 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 371), by decide⟩ +def transition429 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 372), by decide⟩ +def transition430 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 373), by decide⟩ +def transition431 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 458), by decide⟩ +def transition432 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 459), by decide⟩ +def transition433 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 460), by decide⟩ +def transition434 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 461), by decide⟩ +def transition435 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 462), by decide⟩ +def transition436 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 463), by decide⟩ +def transition437 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(2, 464), by decide⟩ +def transition438 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(3, 292), by decide⟩ +def transition439 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(3, 293), by decide⟩ +def transition440 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(3, 294), by decide⟩ +def transition441 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(3, 295), by decide⟩ +def transition442 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(3, 306), by decide⟩ +def transition443 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(3, 307), by decide⟩ +def transition444 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(3, 316), by decide⟩ +def transition445 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(3, 317), by decide⟩ +def transition446 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(3, 318), by decide⟩ +def transition447 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(3, 319), by decide⟩ +def transition448 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(3, 382), by decide⟩ +def transition449 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(3, 383), by decide⟩ +def transition450 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(3, 384), by decide⟩ +def transition451 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(3, 385), by decide⟩ +def transition452 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(3, 394), by decide⟩ +def transition453 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(3, 395), by decide⟩ +def transition454 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(3, 396), by decide⟩ +def transition455 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(3, 397), by decide⟩ +def transition456 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(3, 406), by decide⟩ +def transition457 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(3, 407), by decide⟩ +def transition458 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(3, 408), by decide⟩ +def transition459 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(3, 409), by decide⟩ +def transition460 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(3, 416), by decide⟩ +def transition461 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(3, 417), by decide⟩ +def transition462 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(3, 420), by decide⟩ +def transition463 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(3, 421), by decide⟩ +def transition464 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(3, 458), by decide⟩ +def transition465 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(3, 459), by decide⟩ +def transition466 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(3, 460), by decide⟩ +def transition467 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(3, 465), by decide⟩ +def transition468 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(3, 466), by decide⟩ +def transition469 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(3, 467), by decide⟩ +def transition470 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(3, 468), by decide⟩ +def transition471 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(4, 290), by decide⟩ +def transition472 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(4, 291), by decide⟩ +def transition473 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(4, 328), by decide⟩ +def transition474 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(4, 329), by decide⟩ +def transition475 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(4, 340), by decide⟩ +def transition476 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(4, 341), by decide⟩ +def transition477 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(4, 342), by decide⟩ +def transition478 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(4, 343), by decide⟩ +def transition479 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(4, 376), by decide⟩ +def transition480 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(4, 377), by decide⟩ +def transition481 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(4, 388), by decide⟩ +def transition482 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(4, 389), by decide⟩ +def transition483 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(4, 390), by decide⟩ +def transition484 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(4, 391), by decide⟩ +def transition485 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(4, 424), by decide⟩ +def transition486 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(4, 425), by decide⟩ +def transition487 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(4, 432), by decide⟩ +def transition488 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(4, 433), by decide⟩ +def transition489 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(4, 436), by decide⟩ +def transition490 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(4, 437), by decide⟩ +def transition491 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(4, 444), by decide⟩ +def transition492 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(4, 445), by decide⟩ +def transition493 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(4, 458), by decide⟩ +def transition494 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(4, 461), by decide⟩ +def transition495 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(4, 462), by decide⟩ +def transition496 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(4, 465), by decide⟩ +def transition497 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(4, 466), by decide⟩ +def transition498 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(4, 469), by decide⟩ +def transition499 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(4, 470), by decide⟩ +def transition500 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(5, 364), by decide⟩ +def transition501 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(5, 365), by decide⟩ +def transition502 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(5, 400), by decide⟩ +def transition503 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(5, 401), by decide⟩ +def transition504 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(5, 440), by decide⟩ +def transition505 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(5, 441), by decide⟩ +def transition506 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(5, 458), by decide⟩ +def transition507 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(5, 463), by decide⟩ +def transition508 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(5, 464), by decide⟩ +def transition509 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(5, 467), by decide⟩ +def transition510 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(5, 468), by decide⟩ +def transition511 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(5, 469), by decide⟩ +def transition512 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(5, 470), by decide⟩ +def transition513 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(6, 302), by decide⟩ +def transition514 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(6, 303), by decide⟩ +def transition515 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(6, 326), by decide⟩ +def transition516 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(6, 327), by decide⟩ +def transition517 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(6, 330), by decide⟩ +def transition518 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(6, 331), by decide⟩ +def transition519 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(6, 350), by decide⟩ +def transition520 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(6, 351), by decide⟩ +def transition521 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(6, 354), by decide⟩ +def transition522 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(6, 355), by decide⟩ +def transition523 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(6, 374), by decide⟩ +def transition524 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(6, 375), by decide⟩ +def transition525 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(6, 378), by decide⟩ +def transition526 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(6, 379), by decide⟩ +def transition527 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(6, 398), by decide⟩ +def transition528 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(6, 399), by decide⟩ +def transition529 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(6, 402), by decide⟩ +def transition530 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(6, 403), by decide⟩ +def transition531 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(6, 422), by decide⟩ +def transition532 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(6, 423), by decide⟩ +def transition533 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(6, 428), by decide⟩ +def transition534 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(6, 429), by decide⟩ +def transition535 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(6, 448), by decide⟩ +def transition536 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(6, 449), by decide⟩ +def transition537 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(6, 459), by decide⟩ +def transition538 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(6, 461), by decide⟩ +def transition539 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(6, 463), by decide⟩ +def transition540 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(6, 465), by decide⟩ +def transition541 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(6, 467), by decide⟩ +def transition542 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(6, 469), by decide⟩ +def transition543 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(6, 471), by decide⟩ +def transition544 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(7, 304), by decide⟩ +def transition545 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(7, 305), by decide⟩ +def transition546 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(7, 338), by decide⟩ +def transition547 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(7, 339), by decide⟩ +def transition548 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(7, 362), by decide⟩ +def transition549 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(7, 363), by decide⟩ +def transition550 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(7, 366), by decide⟩ +def transition551 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(7, 367), by decide⟩ +def transition552 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(7, 386), by decide⟩ +def transition553 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(7, 387), by decide⟩ +def transition554 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(7, 392), by decide⟩ +def transition555 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(7, 393), by decide⟩ +def transition556 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(7, 410), by decide⟩ +def transition557 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(7, 411), by decide⟩ +def transition558 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(7, 414), by decide⟩ +def transition559 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(7, 415), by decide⟩ +def transition560 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(7, 418), by decide⟩ +def transition561 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(7, 419), by decide⟩ +def transition562 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(7, 426), by decide⟩ +def transition563 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(7, 427), by decide⟩ +def transition564 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(7, 430), by decide⟩ +def transition565 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(7, 431), by decide⟩ +def transition566 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(7, 450), by decide⟩ +def transition567 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(7, 451), by decide⟩ +def transition568 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(7, 454), by decide⟩ +def transition569 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(7, 455), by decide⟩ +def transition570 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(7, 459), by decide⟩ +def transition571 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(7, 462), by decide⟩ +def transition572 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(7, 464), by decide⟩ +def transition573 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(7, 466), by decide⟩ +def transition574 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(7, 468), by decide⟩ +def transition575 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(7, 469), by decide⟩ +def transition576 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(7, 471), by decide⟩ +def transition577 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(8, 460), by decide⟩ +def transition578 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(8, 461), by decide⟩ +def transition579 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(8, 464), by decide⟩ +def transition580 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(8, 466), by decide⟩ +def transition581 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(8, 467), by decide⟩ +def transition582 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(8, 470), by decide⟩ +def transition583 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(8, 471), by decide⟩ +def transition584 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(9, 314), by decide⟩ +def transition585 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(9, 315), by decide⟩ +def transition586 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(9, 350), by decide⟩ +def transition587 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(9, 351), by decide⟩ +def transition588 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(9, 352), by decide⟩ +def transition589 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(9, 353), by decide⟩ +def transition590 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(9, 374), by decide⟩ +def transition591 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(9, 375), by decide⟩ +def transition592 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(9, 412), by decide⟩ +def transition593 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(9, 413), by decide⟩ +def transition594 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(9, 446), by decide⟩ +def transition595 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(9, 447), by decide⟩ +def transition596 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(9, 456), by decide⟩ +def transition597 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(9, 457), by decide⟩ +def transition598 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(9, 460), by decide⟩ +def transition599 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(9, 462), by decide⟩ +def transition600 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(9, 463), by decide⟩ +def transition601 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(9, 465), by decide⟩ +def transition602 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(9, 468), by decide⟩ +def transition603 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(9, 470), by decide⟩ +def transition604 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(9, 471), by decide⟩ +def transition605 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(10, 206), by decide⟩ +def transition606 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(10, 210), by decide⟩ +def transition607 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(10, 214), by decide⟩ +def transition608 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(10, 729), by decide⟩ +def transition609 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(11, 207), by decide⟩ +def transition610 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(11, 211), by decide⟩ +def transition611 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(11, 216), by decide⟩ +def transition612 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(11, 735), by decide⟩ +def transition613 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(12, 207), by decide⟩ +def transition614 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(12, 212), by decide⟩ +def transition615 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(12, 215), by decide⟩ +def transition616 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(13, 206), by decide⟩ +def transition617 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(13, 213), by decide⟩ +def transition618 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(13, 217), by decide⟩ +def transition619 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(14, 208), by decide⟩ +def transition620 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(14, 211), by decide⟩ +def transition621 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(14, 215), by decide⟩ +def transition622 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(14, 730), by decide⟩ +def transition623 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(15, 209), by decide⟩ +def transition624 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(15, 210), by decide⟩ +def transition625 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(15, 217), by decide⟩ +def transition626 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(15, 724), by decide⟩ +def transition627 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(16, 209), by decide⟩ +def transition628 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(16, 213), by decide⟩ +def transition629 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(16, 214), by decide⟩ +def transition630 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(17, 208), by decide⟩ +def transition631 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(17, 212), by decide⟩ +def transition632 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(17, 216), by decide⟩ +def transition633 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(18, 158), by decide⟩ +def transition634 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(18, 162), by decide⟩ +def transition635 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(18, 166), by decide⟩ +def transition636 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(18, 681), by decide⟩ +def transition637 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(19, 159), by decide⟩ +def transition638 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(19, 163), by decide⟩ +def transition639 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(19, 168), by decide⟩ +def transition640 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(19, 687), by decide⟩ +def transition641 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(20, 159), by decide⟩ +def transition642 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(20, 164), by decide⟩ +def transition643 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(20, 167), by decide⟩ +def transition644 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(21, 158), by decide⟩ +def transition645 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(21, 165), by decide⟩ +def transition646 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(21, 169), by decide⟩ +def transition647 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(22, 160), by decide⟩ +def transition648 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(22, 163), by decide⟩ +def transition649 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(22, 167), by decide⟩ +def transition650 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(22, 682), by decide⟩ +def transition651 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(23, 161), by decide⟩ +def transition652 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(23, 162), by decide⟩ +def transition653 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(23, 169), by decide⟩ +def transition654 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(23, 676), by decide⟩ +def transition655 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(24, 161), by decide⟩ +def transition656 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(24, 165), by decide⟩ +def transition657 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(24, 166), by decide⟩ +def transition658 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(25, 160), by decide⟩ +def transition659 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(25, 164), by decide⟩ +def transition660 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(25, 168), by decide⟩ +def transition661 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(26, 146), by decide⟩ +def transition662 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(26, 150), by decide⟩ +def transition663 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(26, 154), by decide⟩ +def transition664 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(26, 669), by decide⟩ +def transition665 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(27, 147), by decide⟩ +def transition666 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(27, 151), by decide⟩ +def transition667 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(27, 156), by decide⟩ +def transition668 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(27, 675), by decide⟩ +def transition669 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(28, 147), by decide⟩ +def transition670 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(28, 152), by decide⟩ +def transition671 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(28, 155), by decide⟩ +def transition672 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(29, 146), by decide⟩ +def transition673 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(29, 153), by decide⟩ +def transition674 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(29, 157), by decide⟩ +def transition675 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(30, 148), by decide⟩ +def transition676 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(30, 151), by decide⟩ +def transition677 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(30, 155), by decide⟩ +def transition678 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(30, 670), by decide⟩ +def transition679 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(31, 149), by decide⟩ +def transition680 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(31, 150), by decide⟩ +def transition681 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(31, 157), by decide⟩ +def transition682 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(31, 664), by decide⟩ +def transition683 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(32, 149), by decide⟩ +def transition684 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(32, 153), by decide⟩ +def transition685 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(32, 154), by decide⟩ +def transition686 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(33, 148), by decide⟩ +def transition687 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(33, 152), by decide⟩ +def transition688 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(33, 156), by decide⟩ +def transition689 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(34, 134), by decide⟩ +def transition690 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(34, 138), by decide⟩ +def transition691 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(34, 142), by decide⟩ +def transition692 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(34, 657), by decide⟩ +def transition693 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(35, 135), by decide⟩ +def transition694 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(35, 139), by decide⟩ +def transition695 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(35, 144), by decide⟩ +def transition696 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(35, 663), by decide⟩ +def transition697 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(36, 135), by decide⟩ +def transition698 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(36, 140), by decide⟩ +def transition699 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(36, 143), by decide⟩ +def transition700 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(37, 134), by decide⟩ +def transition701 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(37, 141), by decide⟩ +def transition702 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(37, 145), by decide⟩ +def transition703 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(38, 136), by decide⟩ +def transition704 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(38, 139), by decide⟩ +def transition705 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(38, 143), by decide⟩ +def transition706 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(38, 658), by decide⟩ +def transition707 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(39, 137), by decide⟩ +def transition708 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(39, 138), by decide⟩ +def transition709 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(39, 145), by decide⟩ +def transition710 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(39, 652), by decide⟩ +def transition711 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(40, 137), by decide⟩ +def transition712 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(40, 141), by decide⟩ +def transition713 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(40, 142), by decide⟩ +def transition714 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(41, 136), by decide⟩ +def transition715 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(41, 140), by decide⟩ +def transition716 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(41, 144), by decide⟩ +def transition717 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(42, 170), by decide⟩ +def transition718 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(42, 174), by decide⟩ +def transition719 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(42, 178), by decide⟩ +def transition720 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(42, 693), by decide⟩ +def transition721 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(43, 171), by decide⟩ +def transition722 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(43, 175), by decide⟩ +def transition723 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(43, 180), by decide⟩ +def transition724 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(43, 699), by decide⟩ +def transition725 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(44, 171), by decide⟩ +def transition726 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(44, 176), by decide⟩ +def transition727 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(44, 179), by decide⟩ +def transition728 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(45, 170), by decide⟩ +def transition729 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(45, 177), by decide⟩ +def transition730 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(45, 181), by decide⟩ +def transition731 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(46, 172), by decide⟩ +def transition732 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(46, 175), by decide⟩ +def transition733 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(46, 179), by decide⟩ +def transition734 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(46, 694), by decide⟩ +def transition735 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(47, 173), by decide⟩ +def transition736 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(47, 174), by decide⟩ +def transition737 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(47, 181), by decide⟩ +def transition738 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(47, 688), by decide⟩ +def transition739 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(48, 173), by decide⟩ +def transition740 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(48, 177), by decide⟩ +def transition741 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(48, 178), by decide⟩ +def transition742 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(49, 172), by decide⟩ +def transition743 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(49, 176), by decide⟩ +def transition744 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(49, 180), by decide⟩ +def transition745 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(50, 218), by decide⟩ +def transition746 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(50, 222), by decide⟩ +def transition747 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(50, 226), by decide⟩ +def transition748 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(50, 741), by decide⟩ +def transition749 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(51, 219), by decide⟩ +def transition750 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(51, 223), by decide⟩ +def transition751 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(51, 228), by decide⟩ +def transition752 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(51, 747), by decide⟩ +def transition753 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(52, 219), by decide⟩ +def transition754 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(52, 224), by decide⟩ +def transition755 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(52, 227), by decide⟩ +def transition756 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(53, 218), by decide⟩ +def transition757 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(53, 225), by decide⟩ +def transition758 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(53, 229), by decide⟩ +def transition759 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(54, 220), by decide⟩ +def transition760 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(54, 223), by decide⟩ +def transition761 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(54, 227), by decide⟩ +def transition762 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(54, 742), by decide⟩ +def transition763 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(55, 221), by decide⟩ +def transition764 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(55, 222), by decide⟩ +def transition765 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(55, 229), by decide⟩ +def transition766 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(55, 736), by decide⟩ +def transition767 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(56, 221), by decide⟩ +def transition768 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(56, 225), by decide⟩ +def transition769 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(56, 226), by decide⟩ +def transition770 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(57, 220), by decide⟩ +def transition771 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(57, 224), by decide⟩ +def transition772 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(57, 228), by decide⟩ +def transition773 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(58, 278), by decide⟩ +def transition774 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(58, 282), by decide⟩ +def transition775 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(58, 286), by decide⟩ +def transition776 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(58, 801), by decide⟩ +def transition777 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(59, 279), by decide⟩ +def transition778 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(59, 283), by decide⟩ +def transition779 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(59, 288), by decide⟩ +def transition780 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(59, 807), by decide⟩ +def transition781 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(60, 279), by decide⟩ +def transition782 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(60, 284), by decide⟩ +def transition783 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(60, 287), by decide⟩ +def transition784 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(61, 278), by decide⟩ +def transition785 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(61, 285), by decide⟩ +def transition786 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(61, 289), by decide⟩ +def transition787 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(62, 280), by decide⟩ +def transition788 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(62, 283), by decide⟩ +def transition789 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(62, 287), by decide⟩ +def transition790 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(62, 802), by decide⟩ +def transition791 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(63, 281), by decide⟩ +def transition792 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(63, 282), by decide⟩ +def transition793 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(63, 289), by decide⟩ +def transition794 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(63, 796), by decide⟩ +def transition795 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(64, 281), by decide⟩ +def transition796 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(64, 285), by decide⟩ +def transition797 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(64, 286), by decide⟩ +def transition798 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(65, 280), by decide⟩ +def transition799 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(65, 284), by decide⟩ +def transition800 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(65, 288), by decide⟩ +def transition801 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(66, 122), by decide⟩ +def transition802 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(66, 126), by decide⟩ +def transition803 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(66, 130), by decide⟩ +def transition804 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(66, 645), by decide⟩ +def transition805 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(67, 123), by decide⟩ +def transition806 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(67, 127), by decide⟩ +def transition807 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(67, 132), by decide⟩ +def transition808 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(67, 651), by decide⟩ +def transition809 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(68, 123), by decide⟩ +def transition810 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(68, 128), by decide⟩ +def transition811 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(68, 131), by decide⟩ +def transition812 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(69, 122), by decide⟩ +def transition813 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(69, 129), by decide⟩ +def transition814 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(69, 133), by decide⟩ +def transition815 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(70, 124), by decide⟩ +def transition816 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(70, 127), by decide⟩ +def transition817 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(70, 131), by decide⟩ +def transition818 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(70, 646), by decide⟩ +def transition819 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(71, 125), by decide⟩ +def transition820 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(71, 126), by decide⟩ +def transition821 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(71, 133), by decide⟩ +def transition822 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(71, 640), by decide⟩ +def transition823 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(72, 125), by decide⟩ +def transition824 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(72, 129), by decide⟩ +def transition825 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(72, 130), by decide⟩ +def transition826 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(73, 124), by decide⟩ +def transition827 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(73, 128), by decide⟩ +def transition828 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(73, 132), by decide⟩ +def transition829 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(74, 182), by decide⟩ +def transition830 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(74, 186), by decide⟩ +def transition831 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(74, 190), by decide⟩ +def transition832 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(74, 705), by decide⟩ +def transition833 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(75, 183), by decide⟩ +def transition834 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(75, 187), by decide⟩ +def transition835 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(75, 192), by decide⟩ +def transition836 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(75, 711), by decide⟩ +def transition837 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(76, 183), by decide⟩ +def transition838 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(76, 188), by decide⟩ +def transition839 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(76, 191), by decide⟩ +def transition840 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(77, 182), by decide⟩ +def transition841 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(77, 189), by decide⟩ +def transition842 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(77, 193), by decide⟩ +def transition843 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(78, 184), by decide⟩ +def transition844 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(78, 187), by decide⟩ +def transition845 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(78, 191), by decide⟩ +def transition846 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(78, 706), by decide⟩ +def transition847 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(79, 185), by decide⟩ +def transition848 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(79, 186), by decide⟩ +def transition849 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(79, 193), by decide⟩ +def transition850 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(79, 700), by decide⟩ +def transition851 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(80, 185), by decide⟩ +def transition852 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(80, 189), by decide⟩ +def transition853 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(80, 190), by decide⟩ +def transition854 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(81, 184), by decide⟩ +def transition855 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(81, 188), by decide⟩ +def transition856 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(81, 192), by decide⟩ +def transition857 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(82, 230), by decide⟩ +def transition858 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(82, 234), by decide⟩ +def transition859 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(82, 238), by decide⟩ +def transition860 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(82, 753), by decide⟩ +def transition861 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(83, 231), by decide⟩ +def transition862 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(83, 235), by decide⟩ +def transition863 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(83, 240), by decide⟩ +def transition864 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(83, 759), by decide⟩ +def transition865 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(84, 231), by decide⟩ +def transition866 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(84, 236), by decide⟩ +def transition867 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(84, 239), by decide⟩ +def transition868 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(85, 230), by decide⟩ +def transition869 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(85, 237), by decide⟩ +def transition870 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(85, 241), by decide⟩ +def transition871 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(86, 232), by decide⟩ +def transition872 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(86, 235), by decide⟩ +def transition873 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(86, 239), by decide⟩ +def transition874 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(86, 754), by decide⟩ +def transition875 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(87, 233), by decide⟩ +def transition876 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(87, 234), by decide⟩ +def transition877 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(87, 241), by decide⟩ +def transition878 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(87, 748), by decide⟩ +def transition879 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(88, 233), by decide⟩ +def transition880 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(88, 237), by decide⟩ +def transition881 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(88, 238), by decide⟩ +def transition882 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(89, 232), by decide⟩ +def transition883 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(89, 236), by decide⟩ +def transition884 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(89, 240), by decide⟩ +def transition885 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(90, 266), by decide⟩ +def transition886 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(90, 270), by decide⟩ +def transition887 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(90, 274), by decide⟩ +def transition888 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(90, 789), by decide⟩ +def transition889 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(91, 267), by decide⟩ +def transition890 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(91, 271), by decide⟩ +def transition891 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(91, 276), by decide⟩ +def transition892 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(91, 795), by decide⟩ +def transition893 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(92, 267), by decide⟩ +def transition894 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(92, 272), by decide⟩ +def transition895 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(92, 275), by decide⟩ +def transition896 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(93, 266), by decide⟩ +def transition897 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(93, 273), by decide⟩ +def transition898 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(93, 277), by decide⟩ +def transition899 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(94, 268), by decide⟩ +def transition900 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(94, 271), by decide⟩ +def transition901 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(94, 275), by decide⟩ +def transition902 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(94, 790), by decide⟩ +def transition903 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(95, 269), by decide⟩ +def transition904 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(95, 270), by decide⟩ +def transition905 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(95, 277), by decide⟩ +def transition906 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(95, 784), by decide⟩ +def transition907 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(96, 269), by decide⟩ +def transition908 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(96, 273), by decide⟩ +def transition909 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(96, 274), by decide⟩ +def transition910 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(97, 268), by decide⟩ +def transition911 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(97, 272), by decide⟩ +def transition912 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(97, 276), by decide⟩ +def transition913 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(98, 254), by decide⟩ +def transition914 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(98, 258), by decide⟩ +def transition915 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(98, 262), by decide⟩ +def transition916 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(98, 777), by decide⟩ +def transition917 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(99, 255), by decide⟩ +def transition918 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(99, 259), by decide⟩ +def transition919 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(99, 264), by decide⟩ +def transition920 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(99, 783), by decide⟩ +def transition921 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(100, 255), by decide⟩ +def transition922 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(100, 260), by decide⟩ +def transition923 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(100, 263), by decide⟩ +def transition924 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(101, 254), by decide⟩ +def transition925 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(101, 261), by decide⟩ +def transition926 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(101, 265), by decide⟩ +def transition927 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(102, 256), by decide⟩ +def transition928 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(102, 259), by decide⟩ +def transition929 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(102, 263), by decide⟩ +def transition930 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(102, 778), by decide⟩ +def transition931 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(103, 257), by decide⟩ +def transition932 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(103, 258), by decide⟩ +def transition933 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(103, 265), by decide⟩ +def transition934 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(103, 772), by decide⟩ +def transition935 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(104, 257), by decide⟩ +def transition936 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(104, 261), by decide⟩ +def transition937 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(104, 262), by decide⟩ +def transition938 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(105, 256), by decide⟩ +def transition939 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(105, 260), by decide⟩ +def transition940 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(105, 264), by decide⟩ +def transition941 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(106, 242), by decide⟩ +def transition942 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(106, 246), by decide⟩ +def transition943 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(106, 250), by decide⟩ +def transition944 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(106, 765), by decide⟩ +def transition945 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(107, 243), by decide⟩ +def transition946 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(107, 247), by decide⟩ +def transition947 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(107, 252), by decide⟩ +def transition948 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(107, 771), by decide⟩ +def transition949 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(108, 243), by decide⟩ +def transition950 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(108, 248), by decide⟩ +def transition951 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(108, 251), by decide⟩ +def transition952 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(109, 242), by decide⟩ +def transition953 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(109, 249), by decide⟩ +def transition954 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(109, 253), by decide⟩ +def transition955 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(110, 244), by decide⟩ +def transition956 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(110, 247), by decide⟩ +def transition957 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(110, 251), by decide⟩ +def transition958 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(110, 766), by decide⟩ +def transition959 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(111, 245), by decide⟩ +def transition960 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(111, 246), by decide⟩ +def transition961 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(111, 253), by decide⟩ +def transition962 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(111, 760), by decide⟩ +def transition963 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(112, 245), by decide⟩ +def transition964 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(112, 249), by decide⟩ +def transition965 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(112, 250), by decide⟩ +def transition966 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(113, 244), by decide⟩ +def transition967 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(113, 248), by decide⟩ +def transition968 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(113, 252), by decide⟩ +def transition969 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(114, 194), by decide⟩ +def transition970 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(114, 198), by decide⟩ +def transition971 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(114, 202), by decide⟩ +def transition972 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(114, 717), by decide⟩ +def transition973 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(115, 195), by decide⟩ +def transition974 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(115, 199), by decide⟩ +def transition975 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(115, 204), by decide⟩ +def transition976 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(115, 723), by decide⟩ +def transition977 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(116, 195), by decide⟩ +def transition978 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(116, 200), by decide⟩ +def transition979 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(116, 203), by decide⟩ +def transition980 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(117, 194), by decide⟩ +def transition981 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(117, 201), by decide⟩ +def transition982 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(117, 205), by decide⟩ +def transition983 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(118, 196), by decide⟩ +def transition984 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(118, 199), by decide⟩ +def transition985 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(118, 203), by decide⟩ +def transition986 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(118, 718), by decide⟩ +def transition987 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(119, 197), by decide⟩ +def transition988 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(119, 198), by decide⟩ +def transition989 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(119, 205), by decide⟩ +def transition990 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(119, 712), by decide⟩ +def transition991 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(120, 197), by decide⟩ +def transition992 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(120, 201), by decide⟩ +def transition993 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(120, 202), by decide⟩ +def transition994 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(121, 196), by decide⟩ +def transition995 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(121, 200), by decide⟩ +def transition996 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(121, 204), by decide⟩ +def transition997 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(122, 290), by decide⟩ +def transition998 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(122, 300), by decide⟩ +def transition999 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(122, 645), by decide⟩ +def transition1000 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(123, 290), by decide⟩ +def transition1001 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(123, 301), by decide⟩ +def transition1002 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(123, 651), by decide⟩ +def transition1003 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(124, 291), by decide⟩ +def transition1004 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(124, 300), by decide⟩ +def transition1005 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(124, 646), by decide⟩ +def transition1006 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(125, 291), by decide⟩ +def transition1007 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(125, 301), by decide⟩ +def transition1008 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(125, 640), by decide⟩ +def transition1009 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(126, 292), by decide⟩ +def transition1010 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(126, 298), by decide⟩ +def transition1011 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(126, 643), by decide⟩ +def transition1012 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(127, 292), by decide⟩ +def transition1013 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(127, 299), by decide⟩ +def transition1014 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(127, 649), by decide⟩ +def transition1015 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(128, 293), by decide⟩ +def transition1016 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(128, 298), by decide⟩ +def transition1017 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(128, 648), by decide⟩ +def transition1018 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(129, 293), by decide⟩ +def transition1019 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(129, 299), by decide⟩ +def transition1020 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(129, 642), by decide⟩ +def transition1021 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(130, 294), by decide⟩ +def transition1022 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(130, 296), by decide⟩ +def transition1023 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(130, 644), by decide⟩ +def transition1024 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(131, 294), by decide⟩ +def transition1025 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(131, 297), by decide⟩ +def transition1026 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(131, 647), by decide⟩ +def transition1027 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(132, 295), by decide⟩ +def transition1028 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(132, 296), by decide⟩ +def transition1029 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(132, 650), by decide⟩ +def transition1030 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(133, 295), by decide⟩ +def transition1031 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(133, 297), by decide⟩ +def transition1032 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(133, 641), by decide⟩ +def transition1033 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(134, 302), by decide⟩ +def transition1034 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(134, 312), by decide⟩ +def transition1035 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(134, 657), by decide⟩ +def transition1036 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(135, 302), by decide⟩ +def transition1037 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(135, 313), by decide⟩ +def transition1038 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(135, 663), by decide⟩ +def transition1039 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(136, 303), by decide⟩ +def transition1040 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(136, 312), by decide⟩ +def transition1041 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(136, 658), by decide⟩ +def transition1042 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(137, 303), by decide⟩ +def transition1043 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(137, 313), by decide⟩ +def transition1044 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(137, 652), by decide⟩ +def transition1045 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(138, 304), by decide⟩ +def transition1046 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(138, 310), by decide⟩ +def transition1047 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(138, 655), by decide⟩ +def transition1048 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(139, 304), by decide⟩ +def transition1049 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(139, 311), by decide⟩ +def transition1050 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(139, 661), by decide⟩ +def transition1051 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(140, 305), by decide⟩ +def transition1052 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(140, 310), by decide⟩ +def transition1053 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(140, 660), by decide⟩ +def transition1054 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(141, 305), by decide⟩ +def transition1055 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(141, 311), by decide⟩ +def transition1056 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(141, 654), by decide⟩ +def transition1057 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(142, 306), by decide⟩ +def transition1058 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(142, 308), by decide⟩ +def transition1059 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(142, 656), by decide⟩ +def transition1060 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(143, 306), by decide⟩ +def transition1061 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(143, 309), by decide⟩ +def transition1062 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(143, 659), by decide⟩ +def transition1063 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(144, 307), by decide⟩ +def transition1064 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(144, 308), by decide⟩ +def transition1065 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(144, 662), by decide⟩ +def transition1066 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(145, 307), by decide⟩ +def transition1067 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(145, 309), by decide⟩ +def transition1068 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(145, 653), by decide⟩ +def transition1069 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(146, 314), by decide⟩ +def transition1070 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(146, 324), by decide⟩ +def transition1071 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(146, 669), by decide⟩ +def transition1072 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(147, 314), by decide⟩ +def transition1073 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(147, 325), by decide⟩ +def transition1074 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(147, 675), by decide⟩ +def transition1075 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(148, 315), by decide⟩ +def transition1076 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(148, 324), by decide⟩ +def transition1077 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(148, 670), by decide⟩ +def transition1078 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(149, 315), by decide⟩ +def transition1079 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(149, 325), by decide⟩ +def transition1080 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(149, 664), by decide⟩ +def transition1081 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(150, 316), by decide⟩ +def transition1082 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(150, 320), by decide⟩ +def transition1083 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(150, 667), by decide⟩ +def transition1084 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(151, 316), by decide⟩ +def transition1085 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(151, 321), by decide⟩ +def transition1086 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(151, 673), by decide⟩ +def transition1087 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(152, 317), by decide⟩ +def transition1088 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(152, 320), by decide⟩ +def transition1089 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(152, 672), by decide⟩ +def transition1090 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(153, 317), by decide⟩ +def transition1091 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(153, 321), by decide⟩ +def transition1092 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(153, 666), by decide⟩ +def transition1093 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(154, 318), by decide⟩ +def transition1094 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(154, 322), by decide⟩ +def transition1095 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(154, 668), by decide⟩ +def transition1096 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(155, 318), by decide⟩ +def transition1097 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(155, 323), by decide⟩ +def transition1098 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(155, 671), by decide⟩ +def transition1099 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(156, 319), by decide⟩ +def transition1100 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(156, 322), by decide⟩ +def transition1101 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(156, 674), by decide⟩ +def transition1102 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(157, 319), by decide⟩ +def transition1103 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(157, 323), by decide⟩ +def transition1104 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(157, 665), by decide⟩ +def transition1105 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(158, 326), by decide⟩ +def transition1106 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(158, 336), by decide⟩ +def transition1107 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(158, 681), by decide⟩ +def transition1108 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(159, 326), by decide⟩ +def transition1109 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(159, 337), by decide⟩ +def transition1110 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(159, 687), by decide⟩ +def transition1111 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(160, 327), by decide⟩ +def transition1112 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(160, 336), by decide⟩ +def transition1113 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(160, 682), by decide⟩ +def transition1114 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(161, 327), by decide⟩ +def transition1115 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(161, 337), by decide⟩ +def transition1116 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(161, 676), by decide⟩ +def transition1117 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(162, 328), by decide⟩ +def transition1118 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(162, 334), by decide⟩ +def transition1119 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(162, 679), by decide⟩ +def transition1120 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(163, 328), by decide⟩ +def transition1121 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(163, 335), by decide⟩ +def transition1122 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(163, 685), by decide⟩ +def transition1123 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(164, 329), by decide⟩ +def transition1124 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(164, 334), by decide⟩ +def transition1125 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(164, 684), by decide⟩ +def transition1126 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(165, 329), by decide⟩ +def transition1127 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(165, 335), by decide⟩ +def transition1128 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(165, 678), by decide⟩ +def transition1129 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(166, 330), by decide⟩ +def transition1130 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(166, 332), by decide⟩ +def transition1131 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(166, 680), by decide⟩ +def transition1132 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(167, 330), by decide⟩ +def transition1133 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(167, 333), by decide⟩ +def transition1134 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(167, 683), by decide⟩ +def transition1135 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(168, 331), by decide⟩ +def transition1136 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(168, 332), by decide⟩ +def transition1137 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(168, 686), by decide⟩ +def transition1138 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(169, 331), by decide⟩ +def transition1139 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(169, 333), by decide⟩ +def transition1140 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(169, 677), by decide⟩ +def transition1141 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(170, 338), by decide⟩ +def transition1142 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(170, 348), by decide⟩ +def transition1143 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(170, 693), by decide⟩ +def transition1144 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(171, 338), by decide⟩ +def transition1145 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(171, 349), by decide⟩ +def transition1146 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(171, 699), by decide⟩ +def transition1147 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(172, 339), by decide⟩ +def transition1148 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(172, 348), by decide⟩ +def transition1149 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(172, 694), by decide⟩ +def transition1150 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(173, 339), by decide⟩ +def transition1151 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(173, 349), by decide⟩ +def transition1152 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(173, 688), by decide⟩ +def transition1153 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(174, 340), by decide⟩ +def transition1154 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(174, 344), by decide⟩ +def transition1155 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(174, 691), by decide⟩ +def transition1156 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(175, 340), by decide⟩ +def transition1157 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(175, 345), by decide⟩ +def transition1158 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(175, 697), by decide⟩ +def transition1159 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(176, 341), by decide⟩ +def transition1160 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(176, 344), by decide⟩ +def transition1161 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(176, 696), by decide⟩ +def transition1162 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(177, 341), by decide⟩ +def transition1163 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(177, 345), by decide⟩ +def transition1164 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(177, 690), by decide⟩ +def transition1165 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(178, 342), by decide⟩ +def transition1166 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(178, 346), by decide⟩ +def transition1167 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(178, 692), by decide⟩ +def transition1168 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(179, 342), by decide⟩ +def transition1169 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(179, 347), by decide⟩ +def transition1170 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(179, 695), by decide⟩ +def transition1171 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(180, 343), by decide⟩ +def transition1172 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(180, 346), by decide⟩ +def transition1173 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(180, 698), by decide⟩ +def transition1174 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(181, 343), by decide⟩ +def transition1175 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(181, 347), by decide⟩ +def transition1176 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(181, 689), by decide⟩ +def transition1177 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(182, 350), by decide⟩ +def transition1178 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(182, 356), by decide⟩ +def transition1179 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(182, 705), by decide⟩ +def transition1180 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(183, 350), by decide⟩ +def transition1181 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(183, 357), by decide⟩ +def transition1182 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(183, 711), by decide⟩ +def transition1183 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(184, 351), by decide⟩ +def transition1184 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(184, 356), by decide⟩ +def transition1185 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(184, 706), by decide⟩ +def transition1186 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(185, 351), by decide⟩ +def transition1187 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(185, 357), by decide⟩ +def transition1188 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(185, 700), by decide⟩ +def transition1189 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(186, 352), by decide⟩ +def transition1190 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(186, 360), by decide⟩ +def transition1191 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(186, 703), by decide⟩ +def transition1192 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(187, 352), by decide⟩ +def transition1193 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(187, 361), by decide⟩ +def transition1194 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(187, 709), by decide⟩ +def transition1195 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(188, 353), by decide⟩ +def transition1196 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(188, 360), by decide⟩ +def transition1197 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(188, 708), by decide⟩ +def transition1198 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(189, 353), by decide⟩ +def transition1199 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(189, 361), by decide⟩ +def transition1200 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(189, 702), by decide⟩ +def transition1201 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(190, 354), by decide⟩ +def transition1202 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(190, 358), by decide⟩ +def transition1203 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(190, 704), by decide⟩ +def transition1204 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(191, 354), by decide⟩ +def transition1205 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(191, 359), by decide⟩ +def transition1206 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(191, 707), by decide⟩ +def transition1207 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(192, 355), by decide⟩ +def transition1208 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(192, 358), by decide⟩ +def transition1209 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(192, 710), by decide⟩ +def transition1210 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(193, 355), by decide⟩ +def transition1211 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(193, 359), by decide⟩ +def transition1212 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(193, 701), by decide⟩ +def transition1213 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(194, 362), by decide⟩ +def transition1214 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(194, 368), by decide⟩ +def transition1215 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(194, 717), by decide⟩ +def transition1216 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(195, 362), by decide⟩ +def transition1217 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(195, 369), by decide⟩ +def transition1218 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(195, 723), by decide⟩ +def transition1219 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(196, 363), by decide⟩ +def transition1220 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(196, 368), by decide⟩ +def transition1221 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(196, 718), by decide⟩ +def transition1222 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(197, 363), by decide⟩ +def transition1223 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(197, 369), by decide⟩ +def transition1224 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(197, 712), by decide⟩ +def transition1225 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(198, 364), by decide⟩ +def transition1226 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(198, 370), by decide⟩ +def transition1227 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(198, 715), by decide⟩ +def transition1228 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(199, 364), by decide⟩ +def transition1229 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(199, 371), by decide⟩ +def transition1230 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(199, 721), by decide⟩ +def transition1231 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(200, 365), by decide⟩ +def transition1232 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(200, 370), by decide⟩ +def transition1233 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(200, 720), by decide⟩ +def transition1234 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(201, 365), by decide⟩ +def transition1235 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(201, 371), by decide⟩ +def transition1236 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(201, 714), by decide⟩ +def transition1237 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(202, 366), by decide⟩ +def transition1238 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(202, 372), by decide⟩ +def transition1239 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(202, 716), by decide⟩ +def transition1240 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(203, 366), by decide⟩ +def transition1241 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(203, 373), by decide⟩ +def transition1242 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(203, 719), by decide⟩ +def transition1243 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(204, 367), by decide⟩ +def transition1244 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(204, 372), by decide⟩ +def transition1245 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(204, 722), by decide⟩ +def transition1246 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(205, 367), by decide⟩ +def transition1247 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(205, 373), by decide⟩ +def transition1248 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(205, 713), by decide⟩ +def transition1249 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(206, 374), by decide⟩ +def transition1250 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(206, 384), by decide⟩ +def transition1251 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(206, 729), by decide⟩ +def transition1252 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(207, 374), by decide⟩ +def transition1253 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(207, 385), by decide⟩ +def transition1254 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(207, 735), by decide⟩ +def transition1255 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(208, 375), by decide⟩ +def transition1256 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(208, 384), by decide⟩ +def transition1257 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(208, 730), by decide⟩ +def transition1258 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(209, 375), by decide⟩ +def transition1259 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(209, 385), by decide⟩ +def transition1260 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(209, 724), by decide⟩ +def transition1261 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(210, 376), by decide⟩ +def transition1262 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(210, 382), by decide⟩ +def transition1263 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(210, 727), by decide⟩ +def transition1264 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(211, 376), by decide⟩ +def transition1265 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(211, 383), by decide⟩ +def transition1266 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(211, 733), by decide⟩ +def transition1267 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(212, 377), by decide⟩ +def transition1268 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(212, 382), by decide⟩ +def transition1269 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(212, 732), by decide⟩ +def transition1270 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(213, 377), by decide⟩ +def transition1271 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(213, 383), by decide⟩ +def transition1272 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(213, 726), by decide⟩ +def transition1273 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(214, 378), by decide⟩ +def transition1274 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(214, 380), by decide⟩ +def transition1275 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(214, 728), by decide⟩ +def transition1276 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(215, 378), by decide⟩ +def transition1277 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(215, 381), by decide⟩ +def transition1278 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(215, 731), by decide⟩ +def transition1279 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(216, 379), by decide⟩ +def transition1280 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(216, 380), by decide⟩ +def transition1281 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(216, 734), by decide⟩ +def transition1282 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(217, 379), by decide⟩ +def transition1283 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(217, 381), by decide⟩ +def transition1284 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(217, 725), by decide⟩ +def transition1285 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(218, 386), by decide⟩ +def transition1286 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(218, 396), by decide⟩ +def transition1287 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(218, 741), by decide⟩ +def transition1288 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(219, 386), by decide⟩ +def transition1289 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(219, 397), by decide⟩ +def transition1290 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(219, 747), by decide⟩ +def transition1291 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(220, 387), by decide⟩ +def transition1292 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(220, 396), by decide⟩ +def transition1293 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(220, 742), by decide⟩ +def transition1294 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(221, 387), by decide⟩ +def transition1295 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(221, 397), by decide⟩ +def transition1296 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(221, 736), by decide⟩ +def transition1297 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(222, 388), by decide⟩ +def transition1298 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(222, 392), by decide⟩ +def transition1299 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(222, 739), by decide⟩ +def transition1300 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(223, 388), by decide⟩ +def transition1301 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(223, 393), by decide⟩ +def transition1302 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(223, 745), by decide⟩ +def transition1303 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(224, 389), by decide⟩ +def transition1304 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(224, 392), by decide⟩ +def transition1305 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(224, 744), by decide⟩ +def transition1306 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(225, 389), by decide⟩ +def transition1307 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(225, 393), by decide⟩ +def transition1308 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(225, 738), by decide⟩ +def transition1309 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(226, 390), by decide⟩ +def transition1310 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(226, 394), by decide⟩ +def transition1311 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(226, 740), by decide⟩ +def transition1312 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(227, 390), by decide⟩ +def transition1313 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(227, 395), by decide⟩ +def transition1314 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(227, 743), by decide⟩ +def transition1315 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(228, 391), by decide⟩ +def transition1316 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(228, 394), by decide⟩ +def transition1317 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(228, 746), by decide⟩ +def transition1318 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(229, 391), by decide⟩ +def transition1319 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(229, 395), by decide⟩ +def transition1320 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(229, 737), by decide⟩ +def transition1321 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(230, 398), by decide⟩ +def transition1322 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(230, 404), by decide⟩ +def transition1323 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(230, 753), by decide⟩ +def transition1324 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(231, 398), by decide⟩ +def transition1325 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(231, 405), by decide⟩ +def transition1326 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(231, 759), by decide⟩ +def transition1327 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(232, 399), by decide⟩ +def transition1328 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(232, 404), by decide⟩ +def transition1329 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(232, 754), by decide⟩ +def transition1330 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(233, 399), by decide⟩ +def transition1331 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(233, 405), by decide⟩ +def transition1332 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(233, 748), by decide⟩ +def transition1333 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(234, 400), by decide⟩ +def transition1334 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(234, 408), by decide⟩ +def transition1335 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(234, 751), by decide⟩ +def transition1336 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(235, 400), by decide⟩ +def transition1337 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(235, 409), by decide⟩ +def transition1338 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(235, 757), by decide⟩ +def transition1339 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(236, 401), by decide⟩ +def transition1340 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(236, 408), by decide⟩ +def transition1341 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(236, 756), by decide⟩ +def transition1342 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(237, 401), by decide⟩ +def transition1343 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(237, 409), by decide⟩ +def transition1344 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(237, 750), by decide⟩ +def transition1345 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(238, 402), by decide⟩ +def transition1346 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(238, 406), by decide⟩ +def transition1347 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(238, 752), by decide⟩ +def transition1348 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(239, 402), by decide⟩ +def transition1349 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(239, 407), by decide⟩ +def transition1350 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(239, 755), by decide⟩ +def transition1351 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(240, 403), by decide⟩ +def transition1352 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(240, 406), by decide⟩ +def transition1353 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(240, 758), by decide⟩ +def transition1354 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(241, 403), by decide⟩ +def transition1355 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(241, 407), by decide⟩ +def transition1356 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(241, 749), by decide⟩ +def transition1357 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(242, 410), by decide⟩ +def transition1358 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(242, 416), by decide⟩ +def transition1359 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(242, 765), by decide⟩ +def transition1360 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(243, 410), by decide⟩ +def transition1361 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(243, 417), by decide⟩ +def transition1362 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(243, 771), by decide⟩ +def transition1363 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(244, 411), by decide⟩ +def transition1364 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(244, 416), by decide⟩ +def transition1365 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(244, 766), by decide⟩ +def transition1366 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(245, 411), by decide⟩ +def transition1367 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(245, 417), by decide⟩ +def transition1368 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(245, 760), by decide⟩ +def transition1369 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(246, 412), by decide⟩ +def transition1370 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(246, 418), by decide⟩ +def transition1371 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(246, 763), by decide⟩ +def transition1372 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(247, 412), by decide⟩ +def transition1373 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(247, 419), by decide⟩ +def transition1374 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(247, 769), by decide⟩ +def transition1375 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(248, 413), by decide⟩ +def transition1376 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(248, 418), by decide⟩ +def transition1377 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(248, 768), by decide⟩ +def transition1378 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(249, 413), by decide⟩ +def transition1379 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(249, 419), by decide⟩ +def transition1380 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(249, 762), by decide⟩ +def transition1381 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(250, 414), by decide⟩ +def transition1382 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(250, 420), by decide⟩ +def transition1383 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(250, 764), by decide⟩ +def transition1384 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(251, 414), by decide⟩ +def transition1385 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(251, 421), by decide⟩ +def transition1386 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(251, 767), by decide⟩ +def transition1387 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(252, 415), by decide⟩ +def transition1388 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(252, 420), by decide⟩ +def transition1389 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(252, 770), by decide⟩ +def transition1390 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(253, 415), by decide⟩ +def transition1391 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(253, 421), by decide⟩ +def transition1392 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(253, 761), by decide⟩ +def transition1393 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(254, 422), by decide⟩ +def transition1394 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(254, 424), by decide⟩ +def transition1395 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(254, 777), by decide⟩ +def transition1396 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(255, 422), by decide⟩ +def transition1397 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(255, 425), by decide⟩ +def transition1398 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(255, 783), by decide⟩ +def transition1399 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(256, 423), by decide⟩ +def transition1400 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(256, 424), by decide⟩ +def transition1401 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(256, 778), by decide⟩ +def transition1402 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(257, 423), by decide⟩ +def transition1403 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(257, 425), by decide⟩ +def transition1404 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(257, 772), by decide⟩ +def transition1405 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(258, 426), by decide⟩ +def transition1406 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(258, 432), by decide⟩ +def transition1407 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(258, 775), by decide⟩ +def transition1408 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(259, 426), by decide⟩ +def transition1409 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(259, 433), by decide⟩ +def transition1410 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(259, 781), by decide⟩ +def transition1411 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(260, 427), by decide⟩ +def transition1412 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(260, 432), by decide⟩ +def transition1413 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(260, 780), by decide⟩ +def transition1414 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(261, 427), by decide⟩ +def transition1415 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(261, 433), by decide⟩ +def transition1416 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(261, 774), by decide⟩ +def transition1417 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(262, 428), by decide⟩ +def transition1418 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(262, 430), by decide⟩ +def transition1419 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(262, 776), by decide⟩ +def transition1420 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(263, 428), by decide⟩ +def transition1421 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(263, 431), by decide⟩ +def transition1422 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(263, 779), by decide⟩ +def transition1423 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(264, 429), by decide⟩ +def transition1424 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(264, 430), by decide⟩ +def transition1425 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(264, 782), by decide⟩ +def transition1426 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(265, 429), by decide⟩ +def transition1427 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(265, 431), by decide⟩ +def transition1428 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(265, 773), by decide⟩ +def transition1429 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(266, 434), by decide⟩ +def transition1430 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(266, 436), by decide⟩ +def transition1431 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(266, 789), by decide⟩ +def transition1432 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(267, 434), by decide⟩ +def transition1433 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(267, 437), by decide⟩ +def transition1434 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(267, 795), by decide⟩ +def transition1435 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(268, 435), by decide⟩ +def transition1436 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(268, 436), by decide⟩ +def transition1437 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(268, 790), by decide⟩ +def transition1438 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(269, 435), by decide⟩ +def transition1439 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(269, 437), by decide⟩ +def transition1440 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(269, 784), by decide⟩ +def transition1441 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(270, 438), by decide⟩ +def transition1442 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(270, 442), by decide⟩ +def transition1443 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(270, 787), by decide⟩ +def transition1444 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(271, 438), by decide⟩ +def transition1445 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(271, 443), by decide⟩ +def transition1446 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(271, 793), by decide⟩ +def transition1447 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(272, 439), by decide⟩ +def transition1448 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(272, 442), by decide⟩ +def transition1449 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(272, 792), by decide⟩ +def transition1450 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(273, 439), by decide⟩ +def transition1451 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(273, 443), by decide⟩ +def transition1452 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(273, 786), by decide⟩ +def transition1453 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(274, 440), by decide⟩ +def transition1454 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(274, 444), by decide⟩ +def transition1455 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(274, 788), by decide⟩ +def transition1456 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(275, 440), by decide⟩ +def transition1457 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(275, 445), by decide⟩ +def transition1458 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(275, 791), by decide⟩ +def transition1459 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(276, 441), by decide⟩ +def transition1460 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(276, 444), by decide⟩ +def transition1461 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(276, 794), by decide⟩ +def transition1462 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(277, 441), by decide⟩ +def transition1463 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(277, 445), by decide⟩ +def transition1464 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(277, 785), by decide⟩ +def transition1465 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(278, 446), by decide⟩ +def transition1466 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(278, 448), by decide⟩ +def transition1467 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(278, 801), by decide⟩ +def transition1468 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(279, 446), by decide⟩ +def transition1469 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(279, 449), by decide⟩ +def transition1470 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(279, 807), by decide⟩ +def transition1471 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(280, 447), by decide⟩ +def transition1472 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(280, 448), by decide⟩ +def transition1473 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(280, 802), by decide⟩ +def transition1474 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(281, 447), by decide⟩ +def transition1475 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(281, 449), by decide⟩ +def transition1476 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(281, 796), by decide⟩ +def transition1477 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(282, 450), by decide⟩ +def transition1478 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(282, 452), by decide⟩ +def transition1479 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(282, 799), by decide⟩ +def transition1480 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(283, 450), by decide⟩ +def transition1481 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(283, 453), by decide⟩ +def transition1482 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(283, 805), by decide⟩ +def transition1483 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(284, 451), by decide⟩ +def transition1484 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(284, 452), by decide⟩ +def transition1485 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(284, 804), by decide⟩ +def transition1486 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(285, 451), by decide⟩ +def transition1487 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(285, 453), by decide⟩ +def transition1488 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(285, 798), by decide⟩ +def transition1489 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(286, 454), by decide⟩ +def transition1490 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(286, 456), by decide⟩ +def transition1491 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(286, 800), by decide⟩ +def transition1492 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(287, 454), by decide⟩ +def transition1493 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(287, 457), by decide⟩ +def transition1494 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(287, 803), by decide⟩ +def transition1495 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(288, 455), by decide⟩ +def transition1496 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(288, 456), by decide⟩ +def transition1497 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(288, 806), by decide⟩ +def transition1498 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(289, 455), by decide⟩ +def transition1499 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(289, 457), by decide⟩ +def transition1500 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(289, 797), by decide⟩ +def transition1501 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(290, 458), by decide⟩ +def transition1502 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(290, 472), by decide⟩ +def transition1503 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(290, 473), by decide⟩ +def transition1504 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(291, 458), by decide⟩ +def transition1505 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(291, 474), by decide⟩ +def transition1506 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(291, 475), by decide⟩ +def transition1507 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(292, 458), by decide⟩ +def transition1508 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(292, 476), by decide⟩ +def transition1509 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(292, 477), by decide⟩ +def transition1510 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(293, 458), by decide⟩ +def transition1511 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(293, 478), by decide⟩ +def transition1512 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(293, 479), by decide⟩ +def transition1513 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(294, 458), by decide⟩ +def transition1514 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(294, 480), by decide⟩ +def transition1515 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(294, 481), by decide⟩ +def transition1516 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(295, 458), by decide⟩ +def transition1517 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(295, 482), by decide⟩ +def transition1518 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(295, 483), by decide⟩ +def transition1519 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(296, 458), by decide⟩ +def transition1520 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(296, 484), by decide⟩ +def transition1521 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(296, 485), by decide⟩ +def transition1522 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(297, 486), by decide⟩ +def transition1523 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(297, 487), by decide⟩ +def transition1524 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(297, 515), by decide⟩ +def transition1525 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(298, 458), by decide⟩ +def transition1526 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(298, 488), by decide⟩ +def transition1527 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(298, 489), by decide⟩ +def transition1528 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(299, 458), by decide⟩ +def transition1529 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(299, 490), by decide⟩ +def transition1530 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(299, 491), by decide⟩ +def transition1531 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(300, 458), by decide⟩ +def transition1532 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(300, 492), by decide⟩ +def transition1533 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(300, 493), by decide⟩ +def transition1534 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(301, 458), by decide⟩ +def transition1535 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(301, 494), by decide⟩ +def transition1536 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(301, 495), by decide⟩ +def transition1537 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(302, 459), by decide⟩ +def transition1538 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(302, 473), by decide⟩ +def transition1539 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(302, 496), by decide⟩ +def transition1540 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(303, 459), by decide⟩ +def transition1541 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(303, 475), by decide⟩ +def transition1542 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(303, 497), by decide⟩ +def transition1543 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(304, 459), by decide⟩ +def transition1544 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(304, 498), by decide⟩ +def transition1545 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(304, 499), by decide⟩ +def transition1546 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(305, 495), by decide⟩ +def transition1547 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(305, 500), by decide⟩ +def transition1548 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(305, 501), by decide⟩ +def transition1549 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(306, 459), by decide⟩ +def transition1550 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(306, 502), by decide⟩ +def transition1551 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(306, 503), by decide⟩ +def transition1552 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(307, 504), by decide⟩ +def transition1553 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(307, 505), by decide⟩ +def transition1554 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(307, 549), by decide⟩ +def transition1555 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(308, 459), by decide⟩ +def transition1556 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(308, 506), by decide⟩ +def transition1557 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(308, 507), by decide⟩ +def transition1558 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(309, 508), by decide⟩ +def transition1559 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(309, 509), by decide⟩ +def transition1560 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(309, 549), by decide⟩ +def transition1561 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(310, 459), by decide⟩ +def transition1562 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(310, 510), by decide⟩ +def transition1563 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(310, 511), by decide⟩ +def transition1564 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(311, 495), by decide⟩ +def transition1565 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(311, 512), by decide⟩ +def transition1566 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(311, 513), by decide⟩ +def transition1567 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(312, 459), by decide⟩ +def transition1568 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(312, 514), by decide⟩ +def transition1569 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(312, 515), by decide⟩ +def transition1570 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(313, 493), by decide⟩ +def transition1571 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(313, 516), by decide⟩ +def transition1572 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(313, 517), by decide⟩ +def transition1573 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(314, 460), by decide⟩ +def transition1574 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(314, 472), by decide⟩ +def transition1575 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(314, 496), by decide⟩ +def transition1576 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(315, 460), by decide⟩ +def transition1577 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(315, 474), by decide⟩ +def transition1578 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(315, 497), by decide⟩ +def transition1579 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(316, 460), by decide⟩ +def transition1580 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(316, 518), by decide⟩ +def transition1581 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(316, 519), by decide⟩ +def transition1582 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(317, 492), by decide⟩ +def transition1583 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(317, 520), by decide⟩ +def transition1584 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(317, 521), by decide⟩ +def transition1585 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(318, 460), by decide⟩ +def transition1586 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(318, 522), by decide⟩ +def transition1587 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(318, 523), by decide⟩ +def transition1588 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(319, 494), by decide⟩ +def transition1589 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(319, 524), by decide⟩ +def transition1590 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(319, 525), by decide⟩ +def transition1591 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(320, 460), by decide⟩ +def transition1592 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(320, 526), by decide⟩ +def transition1593 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(320, 527), by decide⟩ +def transition1594 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(321, 492), by decide⟩ +def transition1595 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(321, 528), by decide⟩ +def transition1596 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(321, 529), by decide⟩ +def transition1597 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(322, 460), by decide⟩ +def transition1598 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(322, 530), by decide⟩ +def transition1599 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(322, 531), by decide⟩ +def transition1600 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(323, 494), by decide⟩ +def transition1601 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(323, 532), by decide⟩ +def transition1602 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(323, 533), by decide⟩ +def transition1603 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(324, 460), by decide⟩ +def transition1604 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(324, 534), by decide⟩ +def transition1605 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(324, 535), by decide⟩ +def transition1606 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(325, 460), by decide⟩ +def transition1607 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(325, 536), by decide⟩ +def transition1608 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(325, 537), by decide⟩ +def transition1609 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(326, 461), by decide⟩ +def transition1610 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(326, 477), by decide⟩ +def transition1611 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(326, 538), by decide⟩ +def transition1612 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(327, 461), by decide⟩ +def transition1613 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(327, 479), by decide⟩ +def transition1614 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(327, 539), by decide⟩ +def transition1615 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(328, 461), by decide⟩ +def transition1616 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(328, 499), by decide⟩ +def transition1617 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(328, 540), by decide⟩ +def transition1618 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(329, 461), by decide⟩ +def transition1619 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(329, 501), by decide⟩ +def transition1620 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(329, 541), by decide⟩ +def transition1621 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(330, 461), by decide⟩ +def transition1622 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(330, 519), by decide⟩ +def transition1623 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(330, 542), by decide⟩ +def transition1624 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(331, 461), by decide⟩ +def transition1625 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(331, 521), by decide⟩ +def transition1626 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(331, 543), by decide⟩ +def transition1627 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(332, 461), by decide⟩ +def transition1628 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(332, 544), by decide⟩ +def transition1629 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(332, 545), by decide⟩ +def transition1630 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(333, 489), by decide⟩ +def transition1631 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(333, 546), by decide⟩ +def transition1632 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(333, 547), by decide⟩ +def transition1633 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(334, 461), by decide⟩ +def transition1634 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(334, 548), by decide⟩ +def transition1635 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(334, 549), by decide⟩ +def transition1636 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(335, 461), by decide⟩ +def transition1637 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(335, 550), by decide⟩ +def transition1638 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(335, 551), by decide⟩ +def transition1639 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(336, 461), by decide⟩ +def transition1640 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(336, 552), by decide⟩ +def transition1641 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(336, 553), by decide⟩ +def transition1642 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(337, 461), by decide⟩ +def transition1643 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(337, 554), by decide⟩ +def transition1644 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(337, 555), by decide⟩ +def transition1645 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(338, 462), by decide⟩ +def transition1646 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(338, 476), by decide⟩ +def transition1647 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(338, 538), by decide⟩ +def transition1648 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(339, 462), by decide⟩ +def transition1649 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(339, 478), by decide⟩ +def transition1650 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(339, 539), by decide⟩ +def transition1651 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(340, 462), by decide⟩ +def transition1652 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(340, 503), by decide⟩ +def transition1653 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(340, 556), by decide⟩ +def transition1654 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(341, 488), by decide⟩ +def transition1655 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(341, 505), by decide⟩ +def transition1656 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(341, 557), by decide⟩ +def transition1657 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(342, 462), by decide⟩ +def transition1658 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(342, 523), by decide⟩ +def transition1659 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(342, 558), by decide⟩ +def transition1660 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(343, 490), by decide⟩ +def transition1661 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(343, 525), by decide⟩ +def transition1662 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(343, 559), by decide⟩ +def transition1663 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(344, 462), by decide⟩ +def transition1664 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(344, 560), by decide⟩ +def transition1665 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(344, 561), by decide⟩ +def transition1666 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(345, 488), by decide⟩ +def transition1667 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(345, 562), by decide⟩ +def transition1668 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(345, 563), by decide⟩ +def transition1669 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(346, 462), by decide⟩ +def transition1670 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(346, 564), by decide⟩ +def transition1671 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(346, 565), by decide⟩ +def transition1672 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(347, 490), by decide⟩ +def transition1673 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(347, 566), by decide⟩ +def transition1674 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(347, 567), by decide⟩ +def transition1675 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(348, 462), by decide⟩ +def transition1676 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(348, 568), by decide⟩ +def transition1677 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(348, 569), by decide⟩ +def transition1678 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(349, 462), by decide⟩ +def transition1679 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(349, 570), by decide⟩ +def transition1680 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(349, 571), by decide⟩ +def transition1681 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(350, 463), by decide⟩ +def transition1682 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(350, 481), by decide⟩ +def transition1683 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(350, 572), by decide⟩ +def transition1684 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(351, 463), by decide⟩ +def transition1685 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(351, 483), by decide⟩ +def transition1686 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(351, 573), by decide⟩ +def transition1687 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(352, 463), by decide⟩ +def transition1688 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(352, 498), by decide⟩ +def transition1689 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(352, 540), by decide⟩ +def transition1690 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(353, 463), by decide⟩ +def transition1691 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(353, 500), by decide⟩ +def transition1692 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(353, 541), by decide⟩ +def transition1693 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(354, 463), by decide⟩ +def transition1694 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(354, 522), by decide⟩ +def transition1695 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(354, 558), by decide⟩ +def transition1696 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(355, 463), by decide⟩ +def transition1697 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(355, 524), by decide⟩ +def transition1698 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(355, 559), by decide⟩ +def transition1699 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(356, 463), by decide⟩ +def transition1700 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(356, 574), by decide⟩ +def transition1701 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(356, 575), by decide⟩ +def transition1702 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(357, 463), by decide⟩ +def transition1703 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(357, 576), by decide⟩ +def transition1704 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(357, 577), by decide⟩ +def transition1705 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(358, 463), by decide⟩ +def transition1706 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(358, 578), by decide⟩ +def transition1707 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(358, 579), by decide⟩ +def transition1708 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(359, 485), by decide⟩ +def transition1709 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(359, 580), by decide⟩ +def transition1710 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(359, 581), by decide⟩ +def transition1711 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(360, 463), by decide⟩ +def transition1712 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(360, 582), by decide⟩ +def transition1713 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(360, 583), by decide⟩ +def transition1714 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(361, 463), by decide⟩ +def transition1715 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(361, 584), by decide⟩ +def transition1716 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(361, 585), by decide⟩ +def transition1717 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(362, 464), by decide⟩ +def transition1718 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(362, 480), by decide⟩ +def transition1719 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(362, 572), by decide⟩ +def transition1720 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(363, 464), by decide⟩ +def transition1721 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(363, 482), by decide⟩ +def transition1722 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(363, 573), by decide⟩ +def transition1723 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(364, 464), by decide⟩ +def transition1724 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(364, 502), by decide⟩ +def transition1725 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(364, 556), by decide⟩ +def transition1726 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(365, 484), by decide⟩ +def transition1727 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(365, 504), by decide⟩ +def transition1728 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(365, 557), by decide⟩ +def transition1729 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(366, 464), by decide⟩ +def transition1730 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(366, 518), by decide⟩ +def transition1731 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(366, 542), by decide⟩ +def transition1732 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(367, 486), by decide⟩ +def transition1733 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(367, 520), by decide⟩ +def transition1734 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(367, 543), by decide⟩ +def transition1735 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(368, 464), by decide⟩ +def transition1736 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(368, 586), by decide⟩ +def transition1737 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(368, 587), by decide⟩ +def transition1738 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(369, 464), by decide⟩ +def transition1739 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(369, 588), by decide⟩ +def transition1740 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(369, 589), by decide⟩ +def transition1741 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(370, 464), by decide⟩ +def transition1742 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(370, 590), by decide⟩ +def transition1743 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(370, 591), by decide⟩ +def transition1744 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(371, 484), by decide⟩ +def transition1745 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(371, 592), by decide⟩ +def transition1746 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(371, 593), by decide⟩ +def transition1747 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(372, 464), by decide⟩ +def transition1748 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(372, 594), by decide⟩ +def transition1749 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(372, 595), by decide⟩ +def transition1750 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(373, 486), by decide⟩ +def transition1751 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(373, 596), by decide⟩ +def transition1752 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(373, 597), by decide⟩ +def transition1753 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(374, 465), by decide⟩ +def transition1754 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(374, 485), by decide⟩ +def transition1755 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(374, 598), by decide⟩ +def transition1756 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(375, 465), by decide⟩ +def transition1757 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(375, 487), by decide⟩ +def transition1758 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(375, 599), by decide⟩ +def transition1759 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(376, 465), by decide⟩ +def transition1760 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(376, 507), by decide⟩ +def transition1761 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(376, 600), by decide⟩ +def transition1762 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(377, 465), by decide⟩ +def transition1763 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(377, 509), by decide⟩ +def transition1764 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(377, 601), by decide⟩ +def transition1765 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(378, 465), by decide⟩ +def transition1766 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(378, 527), by decide⟩ +def transition1767 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(378, 602), by decide⟩ +def transition1768 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(379, 465), by decide⟩ +def transition1769 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(379, 529), by decide⟩ +def transition1770 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(379, 603), by decide⟩ +def transition1771 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(380, 465), by decide⟩ +def transition1772 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(380, 545), by decide⟩ +def transition1773 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(380, 604), by decide⟩ +def transition1774 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(381, 481), by decide⟩ +def transition1775 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(381, 547), by decide⟩ +def transition1776 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(381, 605), by decide⟩ +def transition1777 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(382, 465), by decide⟩ +def transition1778 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(382, 561), by decide⟩ +def transition1779 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(382, 606), by decide⟩ +def transition1780 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(383, 465), by decide⟩ +def transition1781 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(383, 563), by decide⟩ +def transition1782 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(383, 607), by decide⟩ +def transition1783 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(384, 465), by decide⟩ +def transition1784 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(384, 575), by decide⟩ +def transition1785 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(384, 608), by decide⟩ +def transition1786 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(385, 465), by decide⟩ +def transition1787 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(385, 577), by decide⟩ +def transition1788 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(385, 609), by decide⟩ +def transition1789 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(386, 466), by decide⟩ +def transition1790 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(386, 484), by decide⟩ +def transition1791 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(386, 598), by decide⟩ +def transition1792 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(387, 466), by decide⟩ +def transition1793 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(387, 486), by decide⟩ +def transition1794 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(387, 599), by decide⟩ +def transition1795 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(388, 466), by decide⟩ +def transition1796 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(388, 511), by decide⟩ +def transition1797 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(388, 610), by decide⟩ +def transition1798 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(389, 466), by decide⟩ +def transition1799 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(389, 513), by decide⟩ +def transition1800 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(389, 611), by decide⟩ +def transition1801 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(390, 466), by decide⟩ +def transition1802 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(390, 531), by decide⟩ +def transition1803 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(390, 612), by decide⟩ +def transition1804 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(391, 466), by decide⟩ +def transition1805 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(391, 533), by decide⟩ +def transition1806 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(391, 613), by decide⟩ +def transition1807 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(392, 466), by decide⟩ +def transition1808 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(392, 549), by decide⟩ +def transition1809 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(392, 614), by decide⟩ +def transition1810 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(393, 466), by decide⟩ +def transition1811 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(393, 551), by decide⟩ +def transition1812 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(393, 615), by decide⟩ +def transition1813 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(394, 466), by decide⟩ +def transition1814 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(394, 565), by decide⟩ +def transition1815 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(394, 616), by decide⟩ +def transition1816 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(395, 480), by decide⟩ +def transition1817 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(395, 567), by decide⟩ +def transition1818 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(395, 617), by decide⟩ +def transition1819 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(396, 466), by decide⟩ +def transition1820 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(396, 587), by decide⟩ +def transition1821 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(396, 618), by decide⟩ +def transition1822 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(397, 466), by decide⟩ +def transition1823 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(397, 589), by decide⟩ +def transition1824 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(397, 619), by decide⟩ +def transition1825 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(398, 467), by decide⟩ +def transition1826 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(398, 489), by decide⟩ +def transition1827 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(398, 620), by decide⟩ +def transition1828 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(399, 467), by decide⟩ +def transition1829 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(399, 491), by decide⟩ +def transition1830 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(399, 621), by decide⟩ +def transition1831 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(400, 467), by decide⟩ +def transition1832 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(400, 506), by decide⟩ +def transition1833 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(400, 600), by decide⟩ +def transition1834 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(401, 467), by decide⟩ +def transition1835 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(401, 508), by decide⟩ +def transition1836 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(401, 601), by decide⟩ +def transition1837 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(402, 467), by decide⟩ +def transition1838 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(402, 530), by decide⟩ +def transition1839 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(402, 612), by decide⟩ +def transition1840 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(403, 467), by decide⟩ +def transition1841 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(403, 532), by decide⟩ +def transition1842 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(403, 613), by decide⟩ +def transition1843 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(404, 467), by decide⟩ +def transition1844 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(404, 553), by decide⟩ +def transition1845 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(404, 622), by decide⟩ +def transition1846 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(405, 467), by decide⟩ +def transition1847 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(405, 555), by decide⟩ +def transition1848 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(405, 623), by decide⟩ +def transition1849 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(406, 467), by decide⟩ +def transition1850 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(406, 579), by decide⟩ +def transition1851 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(406, 624), by decide⟩ +def transition1852 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(407, 477), by decide⟩ +def transition1853 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(407, 581), by decide⟩ +def transition1854 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(407, 625), by decide⟩ +def transition1855 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(408, 467), by decide⟩ +def transition1856 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(408, 591), by decide⟩ +def transition1857 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(408, 626), by decide⟩ +def transition1858 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(409, 467), by decide⟩ +def transition1859 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(409, 593), by decide⟩ +def transition1860 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(409, 627), by decide⟩ +def transition1861 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(410, 468), by decide⟩ +def transition1862 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(410, 488), by decide⟩ +def transition1863 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(410, 620), by decide⟩ +def transition1864 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(411, 468), by decide⟩ +def transition1865 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(411, 490), by decide⟩ +def transition1866 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(411, 621), by decide⟩ +def transition1867 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(412, 468), by decide⟩ +def transition1868 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(412, 510), by decide⟩ +def transition1869 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(412, 610), by decide⟩ +def transition1870 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(413, 468), by decide⟩ +def transition1871 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(413, 512), by decide⟩ +def transition1872 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(413, 611), by decide⟩ +def transition1873 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(414, 468), by decide⟩ +def transition1874 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(414, 526), by decide⟩ +def transition1875 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(414, 602), by decide⟩ +def transition1876 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(415, 468), by decide⟩ +def transition1877 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(415, 528), by decide⟩ +def transition1878 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(415, 603), by decide⟩ +def transition1879 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(416, 468), by decide⟩ +def transition1880 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(416, 569), by decide⟩ +def transition1881 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(416, 628), by decide⟩ +def transition1882 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(417, 468), by decide⟩ +def transition1883 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(417, 571), by decide⟩ +def transition1884 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(417, 629), by decide⟩ +def transition1885 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(418, 468), by decide⟩ +def transition1886 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(418, 583), by decide⟩ +def transition1887 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(418, 630), by decide⟩ +def transition1888 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(419, 468), by decide⟩ +def transition1889 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(419, 585), by decide⟩ +def transition1890 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(419, 631), by decide⟩ +def transition1891 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(420, 468), by decide⟩ +def transition1892 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(420, 595), by decide⟩ +def transition1893 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(420, 632), by decide⟩ +def transition1894 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(421, 476), by decide⟩ +def transition1895 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(421, 597), by decide⟩ +def transition1896 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(421, 633), by decide⟩ +def transition1897 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(422, 469), by decide⟩ +def transition1898 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(422, 493), by decide⟩ +def transition1899 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(422, 634), by decide⟩ +def transition1900 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(423, 469), by decide⟩ +def transition1901 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(423, 495), by decide⟩ +def transition1902 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(423, 635), by decide⟩ +def transition1903 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(424, 469), by decide⟩ +def transition1904 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(424, 515), by decide⟩ +def transition1905 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(424, 636), by decide⟩ +def transition1906 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(425, 469), by decide⟩ +def transition1907 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(425, 517), by decide⟩ +def transition1908 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(425, 637), by decide⟩ +def transition1909 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(426, 469), by decide⟩ +def transition1910 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(426, 544), by decide⟩ +def transition1911 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(426, 604), by decide⟩ +def transition1912 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(427, 469), by decide⟩ +def transition1913 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(427, 546), by decide⟩ +def transition1914 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(427, 605), by decide⟩ +def transition1915 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(428, 469), by decide⟩ +def transition1916 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(428, 564), by decide⟩ +def transition1917 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(428, 616), by decide⟩ +def transition1918 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(429, 469), by decide⟩ +def transition1919 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(429, 566), by decide⟩ +def transition1920 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(429, 617), by decide⟩ +def transition1921 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(430, 469), by decide⟩ +def transition1922 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(430, 578), by decide⟩ +def transition1923 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(430, 624), by decide⟩ +def transition1924 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(431, 473), by decide⟩ +def transition1925 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(431, 580), by decide⟩ +def transition1926 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(431, 625), by decide⟩ +def transition1927 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(432, 469), by decide⟩ +def transition1928 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(432, 594), by decide⟩ +def transition1929 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(432, 632), by decide⟩ +def transition1930 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(433, 469), by decide⟩ +def transition1931 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(433, 596), by decide⟩ +def transition1932 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(433, 633), by decide⟩ +def transition1933 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(434, 470), by decide⟩ +def transition1934 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(434, 492), by decide⟩ +def transition1935 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(434, 634), by decide⟩ +def transition1936 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(435, 470), by decide⟩ +def transition1937 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(435, 494), by decide⟩ +def transition1938 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(435, 635), by decide⟩ +def transition1939 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(436, 470), by decide⟩ +def transition1940 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(436, 535), by decide⟩ +def transition1941 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(436, 638), by decide⟩ +def transition1942 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(437, 470), by decide⟩ +def transition1943 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(437, 537), by decide⟩ +def transition1944 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(437, 639), by decide⟩ +def transition1945 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(438, 470), by decide⟩ +def transition1946 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(438, 548), by decide⟩ +def transition1947 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(438, 614), by decide⟩ +def transition1948 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(439, 470), by decide⟩ +def transition1949 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(439, 550), by decide⟩ +def transition1950 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(439, 615), by decide⟩ +def transition1951 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(440, 470), by decide⟩ +def transition1952 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(440, 560), by decide⟩ +def transition1953 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(440, 606), by decide⟩ +def transition1954 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(441, 470), by decide⟩ +def transition1955 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(441, 562), by decide⟩ +def transition1956 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(441, 607), by decide⟩ +def transition1957 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(442, 470), by decide⟩ +def transition1958 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(442, 582), by decide⟩ +def transition1959 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(442, 630), by decide⟩ +def transition1960 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(443, 470), by decide⟩ +def transition1961 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(443, 584), by decide⟩ +def transition1962 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(443, 631), by decide⟩ +def transition1963 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(444, 470), by decide⟩ +def transition1964 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(444, 590), by decide⟩ +def transition1965 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(444, 626), by decide⟩ +def transition1966 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(445, 472), by decide⟩ +def transition1967 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(445, 592), by decide⟩ +def transition1968 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(445, 627), by decide⟩ +def transition1969 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(446, 471), by decide⟩ +def transition1970 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(446, 514), by decide⟩ +def transition1971 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(446, 636), by decide⟩ +def transition1972 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(447, 471), by decide⟩ +def transition1973 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(447, 516), by decide⟩ +def transition1974 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(447, 637), by decide⟩ +def transition1975 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(448, 471), by decide⟩ +def transition1976 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(448, 534), by decide⟩ +def transition1977 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(448, 638), by decide⟩ +def transition1978 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(449, 471), by decide⟩ +def transition1979 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(449, 536), by decide⟩ +def transition1980 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(449, 639), by decide⟩ +def transition1981 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(450, 471), by decide⟩ +def transition1982 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(450, 552), by decide⟩ +def transition1983 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(450, 622), by decide⟩ +def transition1984 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(451, 496), by decide⟩ +def transition1985 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(451, 554), by decide⟩ +def transition1986 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(451, 623), by decide⟩ +def transition1987 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(452, 471), by decide⟩ +def transition1988 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(452, 568), by decide⟩ +def transition1989 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(452, 628), by decide⟩ +def transition1990 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(453, 496), by decide⟩ +def transition1991 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(453, 570), by decide⟩ +def transition1992 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(453, 629), by decide⟩ +def transition1993 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(454, 471), by decide⟩ +def transition1994 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(454, 574), by decide⟩ +def transition1995 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(454, 608), by decide⟩ +def transition1996 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(455, 497), by decide⟩ +def transition1997 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(455, 576), by decide⟩ +def transition1998 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(455, 609), by decide⟩ +def transition1999 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(456, 471), by decide⟩ +def transition2000 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(456, 586), by decide⟩ +def transition2001 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(456, 618), by decide⟩ +def transition2002 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(457, 497), by decide⟩ +def transition2003 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(457, 588), by decide⟩ +def transition2004 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(457, 619), by decide⟩ +def transition2005 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(458, 1), by decide⟩ +def transition2006 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(458, 515), by decide⟩ +def transition2007 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(458, 517), by decide⟩ +def transition2008 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(458, 535), by decide⟩ +def transition2009 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(458, 537), by decide⟩ +def transition2010 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(458, 553), by decide⟩ +def transition2011 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(458, 555), by decide⟩ +def transition2012 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(458, 569), by decide⟩ +def transition2013 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(458, 571), by decide⟩ +def transition2014 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(458, 575), by decide⟩ +def transition2015 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(458, 577), by decide⟩ +def transition2016 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(458, 587), by decide⟩ +def transition2017 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(458, 818), by decide⟩ +def transition2018 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(458, 820), by decide⟩ +def transition2019 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(458, 828), by decide⟩ +def transition2020 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(458, 829), by decide⟩ +def transition2021 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(458, 831), by decide⟩ +def transition2022 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(459, 1), by decide⟩ +def transition2023 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(459, 493), by decide⟩ +def transition2024 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(459, 534), by decide⟩ +def transition2025 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(459, 536), by decide⟩ +def transition2026 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(459, 551), by decide⟩ +def transition2027 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(459, 561), by decide⟩ +def transition2028 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(459, 563), by decide⟩ +def transition2029 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(459, 583), by decide⟩ +def transition2030 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(459, 813), by decide⟩ +def transition2031 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(459, 820), by decide⟩ +def transition2032 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(459, 827), by decide⟩ +def transition2033 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(459, 830), by decide⟩ +def transition2034 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(459, 831), by decide⟩ +def transition2035 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(460, 1), by decide⟩ +def transition2036 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(460, 492), by decide⟩ +def transition2037 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(460, 514), by decide⟩ +def transition2038 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(460, 516), by decide⟩ +def transition2039 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(460, 545), by decide⟩ +def transition2040 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(460, 547), by decide⟩ +def transition2041 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(460, 565), by decide⟩ +def transition2042 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(460, 567), by decide⟩ +def transition2043 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(460, 579), by decide⟩ +def transition2044 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(460, 581), by decide⟩ +def transition2045 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(460, 595), by decide⟩ +def transition2046 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(460, 597), by decide⟩ +def transition2047 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(460, 813), by decide⟩ +def transition2048 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(460, 818), by decide⟩ +def transition2049 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(461, 1), by decide⟩ +def transition2050 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(461, 489), by decide⟩ +def transition2051 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(461, 491), by decide⟩ +def transition2052 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(461, 511), by decide⟩ +def transition2053 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(461, 513), by decide⟩ +def transition2054 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(461, 527), by decide⟩ +def transition2055 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(461, 529), by decide⟩ +def transition2056 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(461, 568), by decide⟩ +def transition2057 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(461, 570), by decide⟩ +def transition2058 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(461, 812), by decide⟩ +def transition2059 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(461, 827), by decide⟩ +def transition2060 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(461, 831), by decide⟩ +def transition2061 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(462, 1), by decide⟩ +def transition2062 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(462, 488), by decide⟩ +def transition2063 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(462, 507), by decide⟩ +def transition2064 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(462, 509), by decide⟩ +def transition2065 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(462, 531), by decide⟩ +def transition2066 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(462, 533), by decide⟩ +def transition2067 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(462, 552), by decide⟩ +def transition2068 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(462, 554), by decide⟩ +def transition2069 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(462, 578), by decide⟩ +def transition2070 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(462, 580), by decide⟩ +def transition2071 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(462, 590), by decide⟩ +def transition2072 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(462, 592), by decide⟩ +def transition2073 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(462, 811), by decide⟩ +def transition2074 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(462, 827), by decide⟩ +def transition2075 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(462, 830), by decide⟩ +def transition2076 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(463, 1), by decide⟩ +def transition2077 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(463, 485), by decide⟩ +def transition2078 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(463, 487), by decide⟩ +def transition2079 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(463, 510), by decide⟩ +def transition2080 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(463, 512), by decide⟩ +def transition2081 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(463, 530), by decide⟩ +def transition2082 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(463, 532), by decide⟩ +def transition2083 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(463, 586), by decide⟩ +def transition2084 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(463, 588), by decide⟩ +def transition2085 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(463, 812), by decide⟩ +def transition2086 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(463, 826), by decide⟩ +def transition2087 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(463, 830), by decide⟩ +def transition2088 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(464, 1), by decide⟩ +def transition2089 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(464, 484), by decide⟩ +def transition2090 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(464, 506), by decide⟩ +def transition2091 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(464, 508), by decide⟩ +def transition2092 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(464, 526), by decide⟩ +def transition2093 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(464, 528), by decide⟩ +def transition2094 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(464, 544), by decide⟩ +def transition2095 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(464, 546), by decide⟩ +def transition2096 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(464, 560), by decide⟩ +def transition2097 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(464, 562), by decide⟩ +def transition2098 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(464, 574), by decide⟩ +def transition2099 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(464, 576), by decide⟩ +def transition2100 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(464, 811), by decide⟩ +def transition2101 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(464, 826), by decide⟩ +def transition2102 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(464, 828), by decide⟩ +def transition2103 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(464, 831), by decide⟩ +def transition2104 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(465, 1), by decide⟩ +def transition2105 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(465, 481), by decide⟩ +def transition2106 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(465, 483), by decide⟩ +def transition2107 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(465, 503), by decide⟩ +def transition2108 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(465, 505), by decide⟩ +def transition2109 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(465, 519), by decide⟩ +def transition2110 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(465, 521), by decide⟩ +def transition2111 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(465, 618), by decide⟩ +def transition2112 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(465, 619), by decide⟩ +def transition2113 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(465, 809), by decide⟩ +def transition2114 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(465, 827), by decide⟩ +def transition2115 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(465, 830), by decide⟩ +def transition2116 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(466, 1), by decide⟩ +def transition2117 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(466, 480), by decide⟩ +def transition2118 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(466, 482), by decide⟩ +def transition2119 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(466, 499), by decide⟩ +def transition2120 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(466, 501), by decide⟩ +def transition2121 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(466, 523), by decide⟩ +def transition2122 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(466, 525), by decide⟩ +def transition2123 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(466, 608), by decide⟩ +def transition2124 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(466, 609), by decide⟩ +def transition2125 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(466, 808), by decide⟩ +def transition2126 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(466, 824), by decide⟩ +def transition2127 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(466, 827), by decide⟩ +def transition2128 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(466, 831), by decide⟩ +def transition2129 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(467, 1), by decide⟩ +def transition2130 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(467, 477), by decide⟩ +def transition2131 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(467, 479), by decide⟩ +def transition2132 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(467, 502), by decide⟩ +def transition2133 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(467, 504), by decide⟩ +def transition2134 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(467, 522), by decide⟩ +def transition2135 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(467, 524), by decide⟩ +def transition2136 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(467, 628), by decide⟩ +def transition2137 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(467, 629), by decide⟩ +def transition2138 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(467, 809), by decide⟩ +def transition2139 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(467, 826), by decide⟩ +def transition2140 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(467, 831), by decide⟩ +def transition2141 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(468, 1), by decide⟩ +def transition2142 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(468, 476), by decide⟩ +def transition2143 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(468, 478), by decide⟩ +def transition2144 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(468, 498), by decide⟩ +def transition2145 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(468, 500), by decide⟩ +def transition2146 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(468, 518), by decide⟩ +def transition2147 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(468, 520), by decide⟩ +def transition2148 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(468, 622), by decide⟩ +def transition2149 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(468, 623), by decide⟩ +def transition2150 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(468, 824), by decide⟩ +def transition2151 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(468, 826), by decide⟩ +def transition2152 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(468, 828), by decide⟩ +def transition2153 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(468, 830), by decide⟩ +def transition2154 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(469, 1), by decide⟩ +def transition2155 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(469, 473), by decide⟩ +def transition2156 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(469, 475), by decide⟩ +def transition2157 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(469, 542), by decide⟩ +def transition2158 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(469, 543), by decide⟩ +def transition2159 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(469, 558), by decide⟩ +def transition2160 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(469, 559), by decide⟩ +def transition2161 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(469, 638), by decide⟩ +def transition2162 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(469, 639), by decide⟩ +def transition2163 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(469, 810), by decide⟩ +def transition2164 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(469, 830), by decide⟩ +def transition2165 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(469, 831), by decide⟩ +def transition2166 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(470, 1), by decide⟩ +def transition2167 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(470, 472), by decide⟩ +def transition2168 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(470, 474), by decide⟩ +def transition2169 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(470, 540), by decide⟩ +def transition2170 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(470, 541), by decide⟩ +def transition2171 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(470, 556), by decide⟩ +def transition2172 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(470, 557), by decide⟩ +def transition2173 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(470, 600), by decide⟩ +def transition2174 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(470, 636), by decide⟩ +def transition2175 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(470, 637), by decide⟩ +def transition2176 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(470, 808), by decide⟩ +def transition2177 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(470, 810), by decide⟩ +def transition2178 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(470, 811), by decide⟩ +def transition2179 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(470, 829), by decide⟩ +def transition2180 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(471, 1), by decide⟩ +def transition2181 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(471, 496), by decide⟩ +def transition2182 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(471, 538), by decide⟩ +def transition2183 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(471, 539), by decide⟩ +def transition2184 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(471, 572), by decide⟩ +def transition2185 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(471, 573), by decide⟩ +def transition2186 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(471, 598), by decide⟩ +def transition2187 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(471, 599), by decide⟩ +def transition2188 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(471, 620), by decide⟩ +def transition2189 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(471, 621), by decide⟩ +def transition2190 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(471, 634), by decide⟩ +def transition2191 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(471, 635), by decide⟩ +def transition2192 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(471, 810), by decide⟩ +def transition2193 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(471, 813), by decide⟩ +def transition2194 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(472, 1), by decide⟩ +def transition2195 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(472, 657), by decide⟩ +def transition2196 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(472, 663), by decide⟩ +def transition2197 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(472, 863), by decide⟩ +def transition2198 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(473, 1), by decide⟩ +def transition2199 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(473, 669), by decide⟩ +def transition2200 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(473, 675), by decide⟩ +def transition2201 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(473, 855), by decide⟩ +def transition2202 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(474, 1), by decide⟩ +def transition2203 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(474, 652), by decide⟩ +def transition2204 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(474, 658), by decide⟩ +def transition2205 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(475, 1), by decide⟩ +def transition2206 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(475, 664), by decide⟩ +def transition2207 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(475, 670), by decide⟩ +def transition2208 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(476, 1), by decide⟩ +def transition2209 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(476, 681), by decide⟩ +def transition2210 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(476, 687), by decide⟩ +def transition2211 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(476, 847), by decide⟩ +def transition2212 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(477, 1), by decide⟩ +def transition2213 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(477, 693), by decide⟩ +def transition2214 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(477, 699), by decide⟩ +def transition2215 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(477, 871), by decide⟩ +def transition2216 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(478, 1), by decide⟩ +def transition2217 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(478, 676), by decide⟩ +def transition2218 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(478, 682), by decide⟩ +def transition2219 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(479, 1), by decide⟩ +def transition2220 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(479, 688), by decide⟩ +def transition2221 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(479, 694), by decide⟩ +def transition2222 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(480, 1), by decide⟩ +def transition2223 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(480, 705), by decide⟩ +def transition2224 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(480, 711), by decide⟩ +def transition2225 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(480, 903), by decide⟩ +def transition2226 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(481, 1), by decide⟩ +def transition2227 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(481, 717), by decide⟩ +def transition2228 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(481, 723), by decide⟩ +def transition2229 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(481, 943), by decide⟩ +def transition2230 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(482, 1), by decide⟩ +def transition2231 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(482, 700), by decide⟩ +def transition2232 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(482, 706), by decide⟩ +def transition2233 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(483, 1), by decide⟩ +def transition2234 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(483, 712), by decide⟩ +def transition2235 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(483, 718), by decide⟩ +def transition2236 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(484, 1), by decide⟩ +def transition2237 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(484, 729), by decide⟩ +def transition2238 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(484, 735), by decide⟩ +def transition2239 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(484, 839), by decide⟩ +def transition2240 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(485, 1), by decide⟩ +def transition2241 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(485, 741), by decide⟩ +def transition2242 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(485, 747), by decide⟩ +def transition2243 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(485, 879), by decide⟩ +def transition2244 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(486, 1), by decide⟩ +def transition2245 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(486, 724), by decide⟩ +def transition2246 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(486, 730), by decide⟩ +def transition2247 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(487, 1), by decide⟩ +def transition2248 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(487, 736), by decide⟩ +def transition2249 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(487, 742), by decide⟩ +def transition2250 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(488, 1), by decide⟩ +def transition2251 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(488, 753), by decide⟩ +def transition2252 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(488, 759), by decide⟩ +def transition2253 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(488, 911), by decide⟩ +def transition2254 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(489, 1), by decide⟩ +def transition2255 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(489, 765), by decide⟩ +def transition2256 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(489, 771), by decide⟩ +def transition2257 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(489, 935), by decide⟩ +def transition2258 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(490, 1), by decide⟩ +def transition2259 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(490, 748), by decide⟩ +def transition2260 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(490, 754), by decide⟩ +def transition2261 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(491, 1), by decide⟩ +def transition2262 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(491, 760), by decide⟩ +def transition2263 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(491, 766), by decide⟩ +def transition2264 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(492, 1), by decide⟩ +def transition2265 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(492, 777), by decide⟩ +def transition2266 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(492, 783), by decide⟩ +def transition2267 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(492, 927), by decide⟩ +def transition2268 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(493, 1), by decide⟩ +def transition2269 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(493, 789), by decide⟩ +def transition2270 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(493, 795), by decide⟩ +def transition2271 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(493, 919), by decide⟩ +def transition2272 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(494, 1), by decide⟩ +def transition2273 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(494, 772), by decide⟩ +def transition2274 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(494, 778), by decide⟩ +def transition2275 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(495, 1), by decide⟩ +def transition2276 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(495, 784), by decide⟩ +def transition2277 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(495, 790), by decide⟩ +def transition2278 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(496, 1), by decide⟩ +def transition2279 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(496, 645), by decide⟩ +def transition2280 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(496, 651), by decide⟩ +def transition2281 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(496, 895), by decide⟩ +def transition2282 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(497, 1), by decide⟩ +def transition2283 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(497, 640), by decide⟩ +def transition2284 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(497, 646), by decide⟩ +def transition2285 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(498, 1), by decide⟩ +def transition2286 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(498, 679), by decide⟩ +def transition2287 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(498, 685), by decide⟩ +def transition2288 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(499, 1), by decide⟩ +def transition2289 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(499, 703), by decide⟩ +def transition2290 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(499, 709), by decide⟩ +def transition2291 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(500, 1), by decide⟩ +def transition2292 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(500, 678), by decide⟩ +def transition2293 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(500, 684), by decide⟩ +def transition2294 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(501, 1), by decide⟩ +def transition2295 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(501, 702), by decide⟩ +def transition2296 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(501, 708), by decide⟩ +def transition2297 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(502, 1), by decide⟩ +def transition2298 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(502, 691), by decide⟩ +def transition2299 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(502, 697), by decide⟩ +def transition2300 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(503, 1), by decide⟩ +def transition2301 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(503, 715), by decide⟩ +def transition2302 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(503, 721), by decide⟩ +def transition2303 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(504, 1), by decide⟩ +def transition2304 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(504, 690), by decide⟩ +def transition2305 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(504, 696), by decide⟩ +def transition2306 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(505, 1), by decide⟩ +def transition2307 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(505, 714), by decide⟩ +def transition2308 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(505, 720), by decide⟩ +def transition2309 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(506, 1), by decide⟩ +def transition2310 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(506, 727), by decide⟩ +def transition2311 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(506, 733), by decide⟩ +def transition2312 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(507, 1), by decide⟩ +def transition2313 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(507, 751), by decide⟩ +def transition2314 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(507, 757), by decide⟩ +def transition2315 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(508, 1), by decide⟩ +def transition2316 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(508, 726), by decide⟩ +def transition2317 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(508, 732), by decide⟩ +def transition2318 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(509, 1), by decide⟩ +def transition2319 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(509, 750), by decide⟩ +def transition2320 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(509, 756), by decide⟩ +def transition2321 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(510, 1), by decide⟩ +def transition2322 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(510, 739), by decide⟩ +def transition2323 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(510, 745), by decide⟩ +def transition2324 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(511, 1), by decide⟩ +def transition2325 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(511, 763), by decide⟩ +def transition2326 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(511, 769), by decide⟩ +def transition2327 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(512, 1), by decide⟩ +def transition2328 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(512, 738), by decide⟩ +def transition2329 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(512, 744), by decide⟩ +def transition2330 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(513, 1), by decide⟩ +def transition2331 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(513, 762), by decide⟩ +def transition2332 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(513, 768), by decide⟩ +def transition2333 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(514, 1), by decide⟩ +def transition2334 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(514, 777), by decide⟩ +def transition2335 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(514, 778), by decide⟩ +def transition2336 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(515, 1), by decide⟩ +def transition2337 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(515, 801), by decide⟩ +def transition2338 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(515, 807), by decide⟩ +def transition2339 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(515, 887), by decide⟩ +def transition2340 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(516, 1), by decide⟩ +def transition2341 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(516, 772), by decide⟩ +def transition2342 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(516, 783), by decide⟩ +def transition2343 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(517, 1), by decide⟩ +def transition2344 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(517, 796), by decide⟩ +def transition2345 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(517, 802), by decide⟩ +def transition2346 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(518, 1), by decide⟩ +def transition2347 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(518, 680), by decide⟩ +def transition2348 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(518, 683), by decide⟩ +def transition2349 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(519, 1), by decide⟩ +def transition2350 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(519, 716), by decide⟩ +def transition2351 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(519, 719), by decide⟩ +def transition2352 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(520, 1), by decide⟩ +def transition2353 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(520, 677), by decide⟩ +def transition2354 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(520, 686), by decide⟩ +def transition2355 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(521, 1), by decide⟩ +def transition2356 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(521, 713), by decide⟩ +def transition2357 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(521, 722), by decide⟩ +def transition2358 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(522, 1), by decide⟩ +def transition2359 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(522, 692), by decide⟩ +def transition2360 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(522, 695), by decide⟩ +def transition2361 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(523, 1), by decide⟩ +def transition2362 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(523, 704), by decide⟩ +def transition2363 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(523, 707), by decide⟩ +def transition2364 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(524, 1), by decide⟩ +def transition2365 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(524, 689), by decide⟩ +def transition2366 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(524, 698), by decide⟩ +def transition2367 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(525, 1), by decide⟩ +def transition2368 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(525, 701), by decide⟩ +def transition2369 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(525, 710), by decide⟩ +def transition2370 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(526, 1), by decide⟩ +def transition2371 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(526, 728), by decide⟩ +def transition2372 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(526, 731), by decide⟩ +def transition2373 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(527, 1), by decide⟩ +def transition2374 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(527, 764), by decide⟩ +def transition2375 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(527, 767), by decide⟩ +def transition2376 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(528, 1), by decide⟩ +def transition2377 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(528, 725), by decide⟩ +def transition2378 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(528, 734), by decide⟩ +def transition2379 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(529, 1), by decide⟩ +def transition2380 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(529, 761), by decide⟩ +def transition2381 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(529, 770), by decide⟩ +def transition2382 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(530, 1), by decide⟩ +def transition2383 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(530, 740), by decide⟩ +def transition2384 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(530, 743), by decide⟩ +def transition2385 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(531, 1), by decide⟩ +def transition2386 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(531, 752), by decide⟩ +def transition2387 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(531, 755), by decide⟩ +def transition2388 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(532, 1), by decide⟩ +def transition2389 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(532, 737), by decide⟩ +def transition2390 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(532, 746), by decide⟩ +def transition2391 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(533, 1), by decide⟩ +def transition2392 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(533, 749), by decide⟩ +def transition2393 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(533, 758), by decide⟩ +def transition2394 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(534, 1), by decide⟩ +def transition2395 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(534, 789), by decide⟩ +def transition2396 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(534, 790), by decide⟩ +def transition2397 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(535, 1), by decide⟩ +def transition2398 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(535, 801), by decide⟩ +def transition2399 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(535, 802), by decide⟩ +def transition2400 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(536, 1), by decide⟩ +def transition2401 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(536, 784), by decide⟩ +def transition2402 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(536, 795), by decide⟩ +def transition2403 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(537, 1), by decide⟩ +def transition2404 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(537, 796), by decide⟩ +def transition2405 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(537, 807), by decide⟩ +def transition2406 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(538, 1), by decide⟩ +def transition2407 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(538, 643), by decide⟩ +def transition2408 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(538, 649), by decide⟩ +def transition2409 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(539, 1), by decide⟩ +def transition2410 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(539, 642), by decide⟩ +def transition2411 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(539, 648), by decide⟩ +def transition2412 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(540, 655), by decide⟩ +def transition2413 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(540, 661), by decide⟩ +def transition2414 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(540, 812), by decide⟩ +def transition2415 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(541, 654), by decide⟩ +def transition2416 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(541, 660), by decide⟩ +def transition2417 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(541, 812), by decide⟩ +def transition2418 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(542, 1), by decide⟩ +def transition2419 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(542, 667), by decide⟩ +def transition2420 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(542, 673), by decide⟩ +def transition2421 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(543, 1), by decide⟩ +def transition2422 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(543, 666), by decide⟩ +def transition2423 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(543, 672), by decide⟩ +def transition2424 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(544, 1), by decide⟩ +def transition2425 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(544, 728), by decide⟩ +def transition2426 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(544, 734), by decide⟩ +def transition2427 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(545, 1), by decide⟩ +def transition2428 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(545, 775), by decide⟩ +def transition2429 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(545, 781), by decide⟩ +def transition2430 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(546, 1), by decide⟩ +def transition2431 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(546, 725), by decide⟩ +def transition2432 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(546, 731), by decide⟩ +def transition2433 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(547, 1), by decide⟩ +def transition2434 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(547, 774), by decide⟩ +def transition2435 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(547, 780), by decide⟩ +def transition2436 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(548, 1), by decide⟩ +def transition2437 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(548, 739), by decide⟩ +def transition2438 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(548, 744), by decide⟩ +def transition2439 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(549, 1), by decide⟩ +def transition2440 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(549, 787), by decide⟩ +def transition2441 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(549, 793), by decide⟩ +def transition2442 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(550, 1), by decide⟩ +def transition2443 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(550, 738), by decide⟩ +def transition2444 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(550, 745), by decide⟩ +def transition2445 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(551, 1), by decide⟩ +def transition2446 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(551, 786), by decide⟩ +def transition2447 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(551, 792), by decide⟩ +def transition2448 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(552, 1), by decide⟩ +def transition2449 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(552, 753), by decide⟩ +def transition2450 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(552, 754), by decide⟩ +def transition2451 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(553, 1), by decide⟩ +def transition2452 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(553, 799), by decide⟩ +def transition2453 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(553, 805), by decide⟩ +def transition2454 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(554, 1), by decide⟩ +def transition2455 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(554, 748), by decide⟩ +def transition2456 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(554, 759), by decide⟩ +def transition2457 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(555, 1), by decide⟩ +def transition2458 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(555, 798), by decide⟩ +def transition2459 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(555, 804), by decide⟩ +def transition2460 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(556, 1), by decide⟩ +def transition2461 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(556, 656), by decide⟩ +def transition2462 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(556, 659), by decide⟩ +def transition2463 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(557, 1), by decide⟩ +def transition2464 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(557, 653), by decide⟩ +def transition2465 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(557, 662), by decide⟩ +def transition2466 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(558, 1), by decide⟩ +def transition2467 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(558, 668), by decide⟩ +def transition2468 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(558, 671), by decide⟩ +def transition2469 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(559, 1), by decide⟩ +def transition2470 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(559, 665), by decide⟩ +def transition2471 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(559, 674), by decide⟩ +def transition2472 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(560, 1), by decide⟩ +def transition2473 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(560, 727), by decide⟩ +def transition2474 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(560, 732), by decide⟩ +def transition2475 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(561, 1), by decide⟩ +def transition2476 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(561, 788), by decide⟩ +def transition2477 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(561, 791), by decide⟩ +def transition2478 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(562, 1), by decide⟩ +def transition2479 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(562, 726), by decide⟩ +def transition2480 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(562, 733), by decide⟩ +def transition2481 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(563, 1), by decide⟩ +def transition2482 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(563, 785), by decide⟩ +def transition2483 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(563, 794), by decide⟩ +def transition2484 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(564, 1), by decide⟩ +def transition2485 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(564, 740), by decide⟩ +def transition2486 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(564, 746), by decide⟩ +def transition2487 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(565, 1), by decide⟩ +def transition2488 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(565, 776), by decide⟩ +def transition2489 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(565, 779), by decide⟩ +def transition2490 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(566, 1), by decide⟩ +def transition2491 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(566, 737), by decide⟩ +def transition2492 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(566, 743), by decide⟩ +def transition2493 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(567, 1), by decide⟩ +def transition2494 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(567, 773), by decide⟩ +def transition2495 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(567, 782), by decide⟩ +def transition2496 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(568, 1), by decide⟩ +def transition2497 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(568, 765), by decide⟩ +def transition2498 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(568, 766), by decide⟩ +def transition2499 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(569, 1), by decide⟩ +def transition2500 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(569, 799), by decide⟩ +def transition2501 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(569, 804), by decide⟩ +def transition2502 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(570, 1), by decide⟩ +def transition2503 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(570, 760), by decide⟩ +def transition2504 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(570, 771), by decide⟩ +def transition2505 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(571, 1), by decide⟩ +def transition2506 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(571, 798), by decide⟩ +def transition2507 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(571, 805), by decide⟩ +def transition2508 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(572, 1), by decide⟩ +def transition2509 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(572, 644), by decide⟩ +def transition2510 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(572, 647), by decide⟩ +def transition2511 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(573, 1), by decide⟩ +def transition2512 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(573, 641), by decide⟩ +def transition2513 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(573, 650), by decide⟩ +def transition2514 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(574, 1), by decide⟩ +def transition2515 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(574, 729), by decide⟩ +def transition2516 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(574, 730), by decide⟩ +def transition2517 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(575, 1), by decide⟩ +def transition2518 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(575, 800), by decide⟩ +def transition2519 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(575, 803), by decide⟩ +def transition2520 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(576, 1), by decide⟩ +def transition2521 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(576, 724), by decide⟩ +def transition2522 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(576, 735), by decide⟩ +def transition2523 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(577, 1), by decide⟩ +def transition2524 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(577, 797), by decide⟩ +def transition2525 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(577, 806), by decide⟩ +def transition2526 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(578, 1), by decide⟩ +def transition2527 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(578, 752), by decide⟩ +def transition2528 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(578, 758), by decide⟩ +def transition2529 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(579, 1), by decide⟩ +def transition2530 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(579, 776), by decide⟩ +def transition2531 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(579, 782), by decide⟩ +def transition2532 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(580, 1), by decide⟩ +def transition2533 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(580, 749), by decide⟩ +def transition2534 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(580, 755), by decide⟩ +def transition2535 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(581, 1), by decide⟩ +def transition2536 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(581, 773), by decide⟩ +def transition2537 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(581, 779), by decide⟩ +def transition2538 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(582, 1), by decide⟩ +def transition2539 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(582, 763), by decide⟩ +def transition2540 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(582, 768), by decide⟩ +def transition2541 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(583, 1), by decide⟩ +def transition2542 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(583, 787), by decide⟩ +def transition2543 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(583, 792), by decide⟩ +def transition2544 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(584, 1), by decide⟩ +def transition2545 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(584, 762), by decide⟩ +def transition2546 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(584, 769), by decide⟩ +def transition2547 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(585, 1), by decide⟩ +def transition2548 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(585, 786), by decide⟩ +def transition2549 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(585, 793), by decide⟩ +def transition2550 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(586, 1), by decide⟩ +def transition2551 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(586, 741), by decide⟩ +def transition2552 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(586, 742), by decide⟩ +def transition2553 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(587, 1), by decide⟩ +def transition2554 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(587, 800), by decide⟩ +def transition2555 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(587, 806), by decide⟩ +def transition2556 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(588, 1), by decide⟩ +def transition2557 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(588, 736), by decide⟩ +def transition2558 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(588, 747), by decide⟩ +def transition2559 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(589, 1), by decide⟩ +def transition2560 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(589, 797), by decide⟩ +def transition2561 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(589, 803), by decide⟩ +def transition2562 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(590, 1), by decide⟩ +def transition2563 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(590, 751), by decide⟩ +def transition2564 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(590, 756), by decide⟩ +def transition2565 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(591, 1), by decide⟩ +def transition2566 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(591, 788), by decide⟩ +def transition2567 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(591, 794), by decide⟩ +def transition2568 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(592, 1), by decide⟩ +def transition2569 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(592, 750), by decide⟩ +def transition2570 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(592, 757), by decide⟩ +def transition2571 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(593, 1), by decide⟩ +def transition2572 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(593, 785), by decide⟩ +def transition2573 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(593, 791), by decide⟩ +def transition2574 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(594, 1), by decide⟩ +def transition2575 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(594, 764), by decide⟩ +def transition2576 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(594, 770), by decide⟩ +def transition2577 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(595, 1), by decide⟩ +def transition2578 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(595, 775), by decide⟩ +def transition2579 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(595, 780), by decide⟩ +def transition2580 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(596, 1), by decide⟩ +def transition2581 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(596, 761), by decide⟩ +def transition2582 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(596, 767), by decide⟩ +def transition2583 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(597, 1), by decide⟩ +def transition2584 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(597, 774), by decide⟩ +def transition2585 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(597, 781), by decide⟩ +def transition2586 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(598, 1), by decide⟩ +def transition2587 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(598, 644), by decide⟩ +def transition2588 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(598, 650), by decide⟩ +def transition2589 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(599, 1), by decide⟩ +def transition2590 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(599, 641), by decide⟩ +def transition2591 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(599, 647), by decide⟩ +def transition2592 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(600, 1), by decide⟩ +def transition2593 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(600, 656), by decide⟩ +def transition2594 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(600, 662), by decide⟩ +def transition2595 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(601, 1), by decide⟩ +def transition2596 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(601, 653), by decide⟩ +def transition2597 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(601, 659), by decide⟩ +def transition2598 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(602, 1), by decide⟩ +def transition2599 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(602, 667), by decide⟩ +def transition2600 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(602, 672), by decide⟩ +def transition2601 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(603, 1), by decide⟩ +def transition2602 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(603, 666), by decide⟩ +def transition2603 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(603, 673), by decide⟩ +def transition2604 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(604, 1), by decide⟩ +def transition2605 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(604, 680), by decide⟩ +def transition2606 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(604, 686), by decide⟩ +def transition2607 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(605, 1), by decide⟩ +def transition2608 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(605, 677), by decide⟩ +def transition2609 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(605, 683), by decide⟩ +def transition2610 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(606, 1), by decide⟩ +def transition2611 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(606, 691), by decide⟩ +def transition2612 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(606, 696), by decide⟩ +def transition2613 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(607, 1), by decide⟩ +def transition2614 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(607, 690), by decide⟩ +def transition2615 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(607, 697), by decide⟩ +def transition2616 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(608, 1), by decide⟩ +def transition2617 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(608, 705), by decide⟩ +def transition2618 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(608, 706), by decide⟩ +def transition2619 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(609, 1), by decide⟩ +def transition2620 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(609, 700), by decide⟩ +def transition2621 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(609, 711), by decide⟩ +def transition2622 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(610, 1), by decide⟩ +def transition2623 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(610, 655), by decide⟩ +def transition2624 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(610, 660), by decide⟩ +def transition2625 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(611, 1), by decide⟩ +def transition2626 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(611, 654), by decide⟩ +def transition2627 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(611, 661), by decide⟩ +def transition2628 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(612, 1), by decide⟩ +def transition2629 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(612, 668), by decide⟩ +def transition2630 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(612, 674), by decide⟩ +def transition2631 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(613, 1), by decide⟩ +def transition2632 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(613, 665), by decide⟩ +def transition2633 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(613, 671), by decide⟩ +def transition2634 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(614, 1), by decide⟩ +def transition2635 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(614, 679), by decide⟩ +def transition2636 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(614, 684), by decide⟩ +def transition2637 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(615, 1), by decide⟩ +def transition2638 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(615, 678), by decide⟩ +def transition2639 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(615, 685), by decide⟩ +def transition2640 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(616, 1), by decide⟩ +def transition2641 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(616, 692), by decide⟩ +def transition2642 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(616, 698), by decide⟩ +def transition2643 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(617, 1), by decide⟩ +def transition2644 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(617, 689), by decide⟩ +def transition2645 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(617, 695), by decide⟩ +def transition2646 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(618, 1), by decide⟩ +def transition2647 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(618, 717), by decide⟩ +def transition2648 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(618, 718), by decide⟩ +def transition2649 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(619, 1), by decide⟩ +def transition2650 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(619, 712), by decide⟩ +def transition2651 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(619, 723), by decide⟩ +def transition2652 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(620, 1), by decide⟩ +def transition2653 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(620, 643), by decide⟩ +def transition2654 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(620, 648), by decide⟩ +def transition2655 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(621, 1), by decide⟩ +def transition2656 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(621, 642), by decide⟩ +def transition2657 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(621, 649), by decide⟩ +def transition2658 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(622, 1), by decide⟩ +def transition2659 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(622, 681), by decide⟩ +def transition2660 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(622, 682), by decide⟩ +def transition2661 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(623, 1), by decide⟩ +def transition2662 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(623, 676), by decide⟩ +def transition2663 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(623, 687), by decide⟩ +def transition2664 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(624, 1), by decide⟩ +def transition2665 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(624, 704), by decide⟩ +def transition2666 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(624, 710), by decide⟩ +def transition2667 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(625, 1), by decide⟩ +def transition2668 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(625, 701), by decide⟩ +def transition2669 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(625, 707), by decide⟩ +def transition2670 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(626, 1), by decide⟩ +def transition2671 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(626, 715), by decide⟩ +def transition2672 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(626, 720), by decide⟩ +def transition2673 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(627, 1), by decide⟩ +def transition2674 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(627, 714), by decide⟩ +def transition2675 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(627, 721), by decide⟩ +def transition2676 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(628, 1), by decide⟩ +def transition2677 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(628, 693), by decide⟩ +def transition2678 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(628, 694), by decide⟩ +def transition2679 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(629, 1), by decide⟩ +def transition2680 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(629, 688), by decide⟩ +def transition2681 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(629, 699), by decide⟩ +def transition2682 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(630, 1), by decide⟩ +def transition2683 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(630, 703), by decide⟩ +def transition2684 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(630, 708), by decide⟩ +def transition2685 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(631, 1), by decide⟩ +def transition2686 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(631, 702), by decide⟩ +def transition2687 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(631, 709), by decide⟩ +def transition2688 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(632, 1), by decide⟩ +def transition2689 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(632, 716), by decide⟩ +def transition2690 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(632, 722), by decide⟩ +def transition2691 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(633, 1), by decide⟩ +def transition2692 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(633, 713), by decide⟩ +def transition2693 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(633, 719), by decide⟩ +def transition2694 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(634, 1), by decide⟩ +def transition2695 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(634, 645), by decide⟩ +def transition2696 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(634, 646), by decide⟩ +def transition2697 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(635, 640), by decide⟩ +def transition2698 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(635, 651), by decide⟩ +def transition2699 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(635, 810), by decide⟩ +def transition2700 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(636, 1), by decide⟩ +def transition2701 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(636, 657), by decide⟩ +def transition2702 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(636, 658), by decide⟩ +def transition2703 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(637, 1), by decide⟩ +def transition2704 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(637, 652), by decide⟩ +def transition2705 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(637, 663), by decide⟩ +def transition2706 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(638, 1), by decide⟩ +def transition2707 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(638, 669), by decide⟩ +def transition2708 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(638, 670), by decide⟩ +def transition2709 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(639, 1), by decide⟩ +def transition2710 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(639, 664), by decide⟩ +def transition2711 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(639, 675), by decide⟩ +def transition2712 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(640, 1), by decide⟩ +def transition2713 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(640, 888), by decide⟩ +def transition2714 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(640, 891), by decide⟩ +def transition2715 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(641, 1), by decide⟩ +def transition2716 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(641, 888), by decide⟩ +def transition2717 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(641, 894), by decide⟩ +def transition2718 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(642, 1), by decide⟩ +def transition2719 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(642, 888), by decide⟩ +def transition2720 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(642, 893), by decide⟩ +def transition2721 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(643, 1), by decide⟩ +def transition2722 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(643, 891), by decide⟩ +def transition2723 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(643, 894), by decide⟩ +def transition2724 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(644, 1), by decide⟩ +def transition2725 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(644, 891), by decide⟩ +def transition2726 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(644, 893), by decide⟩ +def transition2727 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(645, 1), by decide⟩ +def transition2728 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(645, 893), by decide⟩ +def transition2729 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(645, 894), by decide⟩ +def transition2730 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(646, 1), by decide⟩ +def transition2731 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(646, 889), by decide⟩ +def transition2732 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(646, 890), by decide⟩ +def transition2733 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(647, 1), by decide⟩ +def transition2734 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(647, 889), by decide⟩ +def transition2735 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(647, 895), by decide⟩ +def transition2736 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(648, 1), by decide⟩ +def transition2737 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(648, 889), by decide⟩ +def transition2738 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(648, 892), by decide⟩ +def transition2739 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(649, 1), by decide⟩ +def transition2740 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(649, 890), by decide⟩ +def transition2741 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(649, 895), by decide⟩ +def transition2742 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(650, 1), by decide⟩ +def transition2743 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(650, 890), by decide⟩ +def transition2744 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(650, 892), by decide⟩ +def transition2745 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(651, 1), by decide⟩ +def transition2746 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(651, 892), by decide⟩ +def transition2747 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(651, 895), by decide⟩ +def transition2748 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(652, 1), by decide⟩ +def transition2749 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(652, 856), by decide⟩ +def transition2750 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(652, 859), by decide⟩ +def transition2751 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(653, 1), by decide⟩ +def transition2752 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(653, 856), by decide⟩ +def transition2753 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(653, 862), by decide⟩ +def transition2754 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(654, 1), by decide⟩ +def transition2755 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(654, 856), by decide⟩ +def transition2756 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(654, 861), by decide⟩ +def transition2757 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(655, 1), by decide⟩ +def transition2758 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(655, 859), by decide⟩ +def transition2759 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(655, 862), by decide⟩ +def transition2760 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(656, 1), by decide⟩ +def transition2761 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(656, 859), by decide⟩ +def transition2762 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(656, 861), by decide⟩ +def transition2763 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(657, 1), by decide⟩ +def transition2764 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(657, 861), by decide⟩ +def transition2765 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(657, 862), by decide⟩ +def transition2766 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(658, 1), by decide⟩ +def transition2767 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(658, 857), by decide⟩ +def transition2768 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(658, 858), by decide⟩ +def transition2769 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(659, 1), by decide⟩ +def transition2770 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(659, 857), by decide⟩ +def transition2771 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(659, 863), by decide⟩ +def transition2772 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(660, 1), by decide⟩ +def transition2773 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(660, 857), by decide⟩ +def transition2774 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(660, 860), by decide⟩ +def transition2775 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(661, 1), by decide⟩ +def transition2776 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(661, 858), by decide⟩ +def transition2777 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(661, 863), by decide⟩ +def transition2778 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(662, 1), by decide⟩ +def transition2779 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(662, 858), by decide⟩ +def transition2780 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(662, 860), by decide⟩ +def transition2781 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(663, 1), by decide⟩ +def transition2782 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(663, 860), by decide⟩ +def transition2783 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(663, 863), by decide⟩ +def transition2784 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(664, 1), by decide⟩ +def transition2785 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(664, 848), by decide⟩ +def transition2786 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(664, 851), by decide⟩ +def transition2787 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(665, 1), by decide⟩ +def transition2788 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(665, 848), by decide⟩ +def transition2789 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(665, 854), by decide⟩ +def transition2790 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(666, 1), by decide⟩ +def transition2791 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(666, 848), by decide⟩ +def transition2792 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(666, 853), by decide⟩ +def transition2793 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(667, 1), by decide⟩ +def transition2794 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(667, 851), by decide⟩ +def transition2795 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(667, 854), by decide⟩ +def transition2796 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(668, 1), by decide⟩ +def transition2797 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(668, 851), by decide⟩ +def transition2798 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(668, 853), by decide⟩ +def transition2799 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(669, 1), by decide⟩ +def transition2800 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(669, 853), by decide⟩ +def transition2801 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(669, 854), by decide⟩ +def transition2802 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(670, 1), by decide⟩ +def transition2803 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(670, 849), by decide⟩ +def transition2804 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(670, 850), by decide⟩ +def transition2805 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(671, 1), by decide⟩ +def transition2806 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(671, 849), by decide⟩ +def transition2807 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(671, 855), by decide⟩ +def transition2808 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(672, 1), by decide⟩ +def transition2809 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(672, 849), by decide⟩ +def transition2810 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(672, 852), by decide⟩ +def transition2811 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(673, 1), by decide⟩ +def transition2812 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(673, 850), by decide⟩ +def transition2813 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(673, 855), by decide⟩ +def transition2814 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(674, 1), by decide⟩ +def transition2815 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(674, 850), by decide⟩ +def transition2816 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(674, 852), by decide⟩ +def transition2817 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(675, 1), by decide⟩ +def transition2818 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(675, 852), by decide⟩ +def transition2819 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(675, 855), by decide⟩ +def transition2820 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(676, 1), by decide⟩ +def transition2821 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(676, 840), by decide⟩ +def transition2822 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(676, 843), by decide⟩ +def transition2823 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(677, 1), by decide⟩ +def transition2824 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(677, 840), by decide⟩ +def transition2825 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(677, 846), by decide⟩ +def transition2826 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(678, 1), by decide⟩ +def transition2827 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(678, 840), by decide⟩ +def transition2828 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(678, 845), by decide⟩ +def transition2829 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(679, 1), by decide⟩ +def transition2830 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(679, 843), by decide⟩ +def transition2831 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(679, 846), by decide⟩ +def transition2832 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(680, 1), by decide⟩ +def transition2833 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(680, 843), by decide⟩ +def transition2834 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(680, 845), by decide⟩ +def transition2835 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(681, 1), by decide⟩ +def transition2836 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(681, 845), by decide⟩ +def transition2837 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(681, 846), by decide⟩ +def transition2838 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(682, 1), by decide⟩ +def transition2839 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(682, 841), by decide⟩ +def transition2840 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(682, 842), by decide⟩ +def transition2841 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(683, 1), by decide⟩ +def transition2842 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(683, 841), by decide⟩ +def transition2843 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(683, 847), by decide⟩ +def transition2844 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(684, 1), by decide⟩ +def transition2845 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(684, 841), by decide⟩ +def transition2846 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(684, 844), by decide⟩ +def transition2847 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(685, 1), by decide⟩ +def transition2848 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(685, 842), by decide⟩ +def transition2849 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(685, 847), by decide⟩ +def transition2850 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(686, 1), by decide⟩ +def transition2851 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(686, 842), by decide⟩ +def transition2852 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(686, 844), by decide⟩ +def transition2853 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(687, 1), by decide⟩ +def transition2854 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(687, 844), by decide⟩ +def transition2855 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(687, 847), by decide⟩ +def transition2856 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(688, 1), by decide⟩ +def transition2857 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(688, 864), by decide⟩ +def transition2858 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(688, 867), by decide⟩ +def transition2859 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(689, 1), by decide⟩ +def transition2860 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(689, 864), by decide⟩ +def transition2861 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(689, 870), by decide⟩ +def transition2862 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(690, 1), by decide⟩ +def transition2863 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(690, 864), by decide⟩ +def transition2864 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(690, 869), by decide⟩ +def transition2865 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(691, 1), by decide⟩ +def transition2866 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(691, 867), by decide⟩ +def transition2867 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(691, 870), by decide⟩ +def transition2868 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(692, 1), by decide⟩ +def transition2869 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(692, 867), by decide⟩ +def transition2870 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(692, 869), by decide⟩ +def transition2871 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(693, 1), by decide⟩ +def transition2872 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(693, 869), by decide⟩ +def transition2873 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(693, 870), by decide⟩ +def transition2874 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(694, 1), by decide⟩ +def transition2875 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(694, 865), by decide⟩ +def transition2876 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(694, 866), by decide⟩ +def transition2877 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(695, 1), by decide⟩ +def transition2878 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(695, 865), by decide⟩ +def transition2879 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(695, 871), by decide⟩ +def transition2880 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(696, 1), by decide⟩ +def transition2881 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(696, 865), by decide⟩ +def transition2882 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(696, 868), by decide⟩ +def transition2883 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(697, 1), by decide⟩ +def transition2884 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(697, 866), by decide⟩ +def transition2885 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(697, 871), by decide⟩ +def transition2886 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(698, 1), by decide⟩ +def transition2887 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(698, 866), by decide⟩ +def transition2888 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(698, 868), by decide⟩ +def transition2889 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(699, 1), by decide⟩ +def transition2890 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(699, 868), by decide⟩ +def transition2891 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(699, 871), by decide⟩ +def transition2892 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(700, 1), by decide⟩ +def transition2893 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(700, 896), by decide⟩ +def transition2894 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(700, 899), by decide⟩ +def transition2895 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(701, 1), by decide⟩ +def transition2896 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(701, 896), by decide⟩ +def transition2897 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(701, 902), by decide⟩ +def transition2898 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(702, 1), by decide⟩ +def transition2899 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(702, 896), by decide⟩ +def transition2900 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(702, 901), by decide⟩ +def transition2901 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(703, 1), by decide⟩ +def transition2902 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(703, 899), by decide⟩ +def transition2903 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(703, 902), by decide⟩ +def transition2904 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(704, 1), by decide⟩ +def transition2905 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(704, 899), by decide⟩ +def transition2906 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(704, 901), by decide⟩ +def transition2907 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(705, 1), by decide⟩ +def transition2908 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(705, 901), by decide⟩ +def transition2909 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(705, 902), by decide⟩ +def transition2910 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(706, 1), by decide⟩ +def transition2911 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(706, 897), by decide⟩ +def transition2912 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(706, 898), by decide⟩ +def transition2913 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(707, 1), by decide⟩ +def transition2914 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(707, 897), by decide⟩ +def transition2915 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(707, 903), by decide⟩ +def transition2916 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(708, 1), by decide⟩ +def transition2917 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(708, 897), by decide⟩ +def transition2918 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(708, 900), by decide⟩ +def transition2919 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(709, 1), by decide⟩ +def transition2920 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(709, 898), by decide⟩ +def transition2921 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(709, 903), by decide⟩ +def transition2922 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(710, 1), by decide⟩ +def transition2923 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(710, 898), by decide⟩ +def transition2924 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(710, 900), by decide⟩ +def transition2925 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(711, 1), by decide⟩ +def transition2926 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(711, 900), by decide⟩ +def transition2927 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(711, 903), by decide⟩ +def transition2928 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(712, 1), by decide⟩ +def transition2929 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(712, 936), by decide⟩ +def transition2930 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(712, 939), by decide⟩ +def transition2931 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(713, 1), by decide⟩ +def transition2932 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(713, 936), by decide⟩ +def transition2933 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(713, 942), by decide⟩ +def transition2934 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(714, 1), by decide⟩ +def transition2935 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(714, 936), by decide⟩ +def transition2936 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(714, 941), by decide⟩ +def transition2937 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(715, 1), by decide⟩ +def transition2938 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(715, 939), by decide⟩ +def transition2939 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(715, 942), by decide⟩ +def transition2940 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(716, 1), by decide⟩ +def transition2941 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(716, 939), by decide⟩ +def transition2942 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(716, 941), by decide⟩ +def transition2943 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(717, 1), by decide⟩ +def transition2944 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(717, 941), by decide⟩ +def transition2945 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(717, 942), by decide⟩ +def transition2946 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(718, 1), by decide⟩ +def transition2947 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(718, 937), by decide⟩ +def transition2948 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(718, 938), by decide⟩ +def transition2949 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(719, 1), by decide⟩ +def transition2950 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(719, 937), by decide⟩ +def transition2951 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(719, 943), by decide⟩ +def transition2952 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(720, 1), by decide⟩ +def transition2953 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(720, 937), by decide⟩ +def transition2954 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(720, 940), by decide⟩ +def transition2955 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(721, 1), by decide⟩ +def transition2956 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(721, 938), by decide⟩ +def transition2957 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(721, 943), by decide⟩ +def transition2958 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(722, 1), by decide⟩ +def transition2959 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(722, 938), by decide⟩ +def transition2960 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(722, 940), by decide⟩ +def transition2961 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(723, 1), by decide⟩ +def transition2962 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(723, 940), by decide⟩ +def transition2963 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(723, 943), by decide⟩ +def transition2964 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(724, 1), by decide⟩ +def transition2965 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(724, 832), by decide⟩ +def transition2966 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(724, 835), by decide⟩ +def transition2967 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(725, 1), by decide⟩ +def transition2968 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(725, 832), by decide⟩ +def transition2969 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(725, 838), by decide⟩ +def transition2970 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(726, 1), by decide⟩ +def transition2971 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(726, 832), by decide⟩ +def transition2972 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(726, 837), by decide⟩ +def transition2973 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(727, 1), by decide⟩ +def transition2974 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(727, 835), by decide⟩ +def transition2975 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(727, 838), by decide⟩ +def transition2976 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(728, 1), by decide⟩ +def transition2977 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(728, 835), by decide⟩ +def transition2978 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(728, 837), by decide⟩ +def transition2979 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(729, 1), by decide⟩ +def transition2980 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(729, 837), by decide⟩ +def transition2981 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(729, 838), by decide⟩ +def transition2982 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(730, 1), by decide⟩ +def transition2983 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(730, 833), by decide⟩ +def transition2984 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(730, 834), by decide⟩ +def transition2985 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(731, 1), by decide⟩ +def transition2986 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(731, 833), by decide⟩ +def transition2987 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(731, 839), by decide⟩ +def transition2988 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(732, 1), by decide⟩ +def transition2989 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(732, 833), by decide⟩ +def transition2990 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(732, 836), by decide⟩ +def transition2991 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(733, 1), by decide⟩ +def transition2992 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(733, 834), by decide⟩ +def transition2993 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(733, 839), by decide⟩ +def transition2994 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(734, 1), by decide⟩ +def transition2995 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(734, 834), by decide⟩ +def transition2996 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(734, 836), by decide⟩ +def transition2997 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(735, 1), by decide⟩ +def transition2998 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(735, 836), by decide⟩ +def transition2999 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(735, 839), by decide⟩ +def transition3000 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(736, 1), by decide⟩ +def transition3001 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(736, 872), by decide⟩ +def transition3002 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(736, 875), by decide⟩ +def transition3003 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(737, 1), by decide⟩ +def transition3004 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(737, 872), by decide⟩ +def transition3005 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(737, 878), by decide⟩ +def transition3006 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(738, 1), by decide⟩ +def transition3007 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(738, 872), by decide⟩ +def transition3008 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(738, 877), by decide⟩ +def transition3009 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(739, 1), by decide⟩ +def transition3010 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(739, 875), by decide⟩ +def transition3011 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(739, 878), by decide⟩ +def transition3012 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(740, 1), by decide⟩ +def transition3013 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(740, 875), by decide⟩ +def transition3014 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(740, 877), by decide⟩ +def transition3015 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(741, 1), by decide⟩ +def transition3016 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(741, 877), by decide⟩ +def transition3017 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(741, 878), by decide⟩ +def transition3018 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(742, 1), by decide⟩ +def transition3019 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(742, 873), by decide⟩ +def transition3020 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(742, 874), by decide⟩ +def transition3021 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(743, 1), by decide⟩ +def transition3022 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(743, 873), by decide⟩ +def transition3023 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(743, 879), by decide⟩ +def transition3024 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(744, 1), by decide⟩ +def transition3025 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(744, 873), by decide⟩ +def transition3026 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(744, 876), by decide⟩ +def transition3027 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(745, 1), by decide⟩ +def transition3028 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(745, 874), by decide⟩ +def transition3029 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(745, 879), by decide⟩ +def transition3030 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(746, 1), by decide⟩ +def transition3031 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(746, 874), by decide⟩ +def transition3032 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(746, 876), by decide⟩ +def transition3033 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(747, 1), by decide⟩ +def transition3034 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(747, 876), by decide⟩ +def transition3035 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(747, 879), by decide⟩ +def transition3036 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(748, 1), by decide⟩ +def transition3037 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(748, 904), by decide⟩ +def transition3038 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(748, 907), by decide⟩ +def transition3039 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(749, 1), by decide⟩ +def transition3040 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(749, 904), by decide⟩ +def transition3041 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(749, 910), by decide⟩ +def transition3042 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(750, 1), by decide⟩ +def transition3043 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(750, 904), by decide⟩ +def transition3044 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(750, 909), by decide⟩ +def transition3045 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(751, 1), by decide⟩ +def transition3046 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(751, 907), by decide⟩ +def transition3047 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(751, 910), by decide⟩ +def transition3048 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(752, 1), by decide⟩ +def transition3049 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(752, 907), by decide⟩ +def transition3050 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(752, 909), by decide⟩ +def transition3051 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(753, 1), by decide⟩ +def transition3052 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(753, 909), by decide⟩ +def transition3053 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(753, 910), by decide⟩ +def transition3054 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(754, 1), by decide⟩ +def transition3055 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(754, 905), by decide⟩ +def transition3056 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(754, 906), by decide⟩ +def transition3057 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(755, 1), by decide⟩ +def transition3058 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(755, 905), by decide⟩ +def transition3059 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(755, 911), by decide⟩ +def transition3060 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(756, 1), by decide⟩ +def transition3061 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(756, 905), by decide⟩ +def transition3062 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(756, 908), by decide⟩ +def transition3063 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(757, 1), by decide⟩ +def transition3064 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(757, 906), by decide⟩ +def transition3065 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(757, 911), by decide⟩ +def transition3066 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(758, 1), by decide⟩ +def transition3067 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(758, 906), by decide⟩ +def transition3068 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(758, 908), by decide⟩ +def transition3069 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(759, 1), by decide⟩ +def transition3070 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(759, 908), by decide⟩ +def transition3071 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(759, 911), by decide⟩ +def transition3072 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(760, 1), by decide⟩ +def transition3073 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(760, 928), by decide⟩ +def transition3074 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(760, 931), by decide⟩ +def transition3075 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(761, 1), by decide⟩ +def transition3076 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(761, 928), by decide⟩ +def transition3077 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(761, 934), by decide⟩ +def transition3078 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(762, 1), by decide⟩ +def transition3079 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(762, 928), by decide⟩ +def transition3080 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(762, 933), by decide⟩ +def transition3081 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(763, 1), by decide⟩ +def transition3082 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(763, 931), by decide⟩ +def transition3083 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(763, 934), by decide⟩ +def transition3084 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(764, 1), by decide⟩ +def transition3085 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(764, 931), by decide⟩ +def transition3086 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(764, 933), by decide⟩ +def transition3087 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(765, 1), by decide⟩ +def transition3088 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(765, 933), by decide⟩ +def transition3089 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(765, 934), by decide⟩ +def transition3090 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(766, 1), by decide⟩ +def transition3091 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(766, 929), by decide⟩ +def transition3092 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(766, 930), by decide⟩ +def transition3093 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(767, 1), by decide⟩ +def transition3094 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(767, 929), by decide⟩ +def transition3095 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(767, 935), by decide⟩ +def transition3096 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(768, 1), by decide⟩ +def transition3097 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(768, 929), by decide⟩ +def transition3098 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(768, 932), by decide⟩ +def transition3099 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(769, 1), by decide⟩ +def transition3100 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(769, 930), by decide⟩ +def transition3101 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(769, 935), by decide⟩ +def transition3102 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(770, 1), by decide⟩ +def transition3103 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(770, 930), by decide⟩ +def transition3104 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(770, 932), by decide⟩ +def transition3105 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(771, 1), by decide⟩ +def transition3106 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(771, 932), by decide⟩ +def transition3107 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(771, 935), by decide⟩ +def transition3108 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(772, 1), by decide⟩ +def transition3109 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(772, 920), by decide⟩ +def transition3110 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(772, 923), by decide⟩ +def transition3111 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(773, 1), by decide⟩ +def transition3112 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(773, 920), by decide⟩ +def transition3113 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(773, 926), by decide⟩ +def transition3114 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(774, 1), by decide⟩ +def transition3115 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(774, 920), by decide⟩ +def transition3116 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(774, 925), by decide⟩ +def transition3117 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(775, 1), by decide⟩ +def transition3118 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(775, 923), by decide⟩ +def transition3119 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(775, 926), by decide⟩ +def transition3120 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(776, 1), by decide⟩ +def transition3121 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(776, 923), by decide⟩ +def transition3122 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(776, 925), by decide⟩ +def transition3123 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(777, 1), by decide⟩ +def transition3124 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(777, 925), by decide⟩ +def transition3125 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(777, 926), by decide⟩ +def transition3126 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(778, 1), by decide⟩ +def transition3127 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(778, 921), by decide⟩ +def transition3128 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(778, 922), by decide⟩ +def transition3129 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(779, 1), by decide⟩ +def transition3130 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(779, 921), by decide⟩ +def transition3131 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(779, 927), by decide⟩ +def transition3132 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(780, 1), by decide⟩ +def transition3133 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(780, 921), by decide⟩ +def transition3134 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(780, 924), by decide⟩ +def transition3135 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(781, 1), by decide⟩ +def transition3136 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(781, 922), by decide⟩ +def transition3137 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(781, 927), by decide⟩ +def transition3138 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(782, 1), by decide⟩ +def transition3139 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(782, 922), by decide⟩ +def transition3140 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(782, 924), by decide⟩ +def transition3141 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(783, 1), by decide⟩ +def transition3142 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(783, 924), by decide⟩ +def transition3143 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(783, 927), by decide⟩ +def transition3144 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(784, 1), by decide⟩ +def transition3145 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(784, 912), by decide⟩ +def transition3146 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(784, 915), by decide⟩ +def transition3147 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(785, 1), by decide⟩ +def transition3148 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(785, 912), by decide⟩ +def transition3149 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(785, 918), by decide⟩ +def transition3150 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(786, 1), by decide⟩ +def transition3151 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(786, 912), by decide⟩ +def transition3152 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(786, 917), by decide⟩ +def transition3153 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(787, 1), by decide⟩ +def transition3154 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(787, 915), by decide⟩ +def transition3155 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(787, 918), by decide⟩ +def transition3156 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(788, 1), by decide⟩ +def transition3157 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(788, 915), by decide⟩ +def transition3158 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(788, 917), by decide⟩ +def transition3159 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(789, 1), by decide⟩ +def transition3160 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(789, 917), by decide⟩ +def transition3161 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(789, 918), by decide⟩ +def transition3162 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(790, 1), by decide⟩ +def transition3163 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(790, 913), by decide⟩ +def transition3164 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(790, 914), by decide⟩ +def transition3165 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(791, 1), by decide⟩ +def transition3166 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(791, 913), by decide⟩ +def transition3167 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(791, 919), by decide⟩ +def transition3168 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(792, 1), by decide⟩ +def transition3169 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(792, 913), by decide⟩ +def transition3170 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(792, 916), by decide⟩ +def transition3171 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(793, 1), by decide⟩ +def transition3172 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(793, 914), by decide⟩ +def transition3173 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(793, 919), by decide⟩ +def transition3174 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(794, 1), by decide⟩ +def transition3175 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(794, 914), by decide⟩ +def transition3176 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(794, 916), by decide⟩ +def transition3177 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(795, 1), by decide⟩ +def transition3178 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(795, 916), by decide⟩ +def transition3179 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(795, 919), by decide⟩ +def transition3180 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(796, 1), by decide⟩ +def transition3181 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(796, 880), by decide⟩ +def transition3182 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(796, 883), by decide⟩ +def transition3183 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(797, 1), by decide⟩ +def transition3184 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(797, 880), by decide⟩ +def transition3185 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(797, 886), by decide⟩ +def transition3186 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(798, 1), by decide⟩ +def transition3187 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(798, 880), by decide⟩ +def transition3188 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(798, 885), by decide⟩ +def transition3189 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(799, 1), by decide⟩ +def transition3190 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(799, 883), by decide⟩ +def transition3191 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(799, 886), by decide⟩ +def transition3192 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(800, 1), by decide⟩ +def transition3193 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(800, 883), by decide⟩ +def transition3194 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(800, 885), by decide⟩ +def transition3195 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(801, 1), by decide⟩ +def transition3196 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(801, 885), by decide⟩ +def transition3197 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(801, 886), by decide⟩ +def transition3198 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(802, 1), by decide⟩ +def transition3199 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(802, 881), by decide⟩ +def transition3200 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(802, 882), by decide⟩ +def transition3201 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(803, 1), by decide⟩ +def transition3202 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(803, 881), by decide⟩ +def transition3203 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(803, 887), by decide⟩ +def transition3204 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(804, 1), by decide⟩ +def transition3205 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(804, 881), by decide⟩ +def transition3206 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(804, 884), by decide⟩ +def transition3207 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(805, 1), by decide⟩ +def transition3208 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(805, 882), by decide⟩ +def transition3209 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(805, 887), by decide⟩ +def transition3210 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(806, 1), by decide⟩ +def transition3211 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(806, 882), by decide⟩ +def transition3212 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(806, 884), by decide⟩ +def transition3213 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(807, 1), by decide⟩ +def transition3214 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(807, 884), by decide⟩ +def transition3215 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(807, 887), by decide⟩ +def transition3216 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(808, 824), by decide⟩ +def transition3217 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(808, 828), by decide⟩ +def transition3218 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(809, 1), by decide⟩ +def transition3219 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(809, 824), by decide⟩ +def transition3220 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(809, 829), by decide⟩ +def transition3221 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(810, 1), by decide⟩ +def transition3222 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(810, 824), by decide⟩ +def transition3223 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(810, 825), by decide⟩ +def transition3224 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(811, 1), by decide⟩ +def transition3225 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(811, 825), by decide⟩ +def transition3226 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(811, 828), by decide⟩ +def transition3227 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(812, 1), by decide⟩ +def transition3228 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(812, 825), by decide⟩ +def transition3229 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(812, 829), by decide⟩ +def transition3230 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(813, 1), by decide⟩ +def transition3231 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(813, 826), by decide⟩ +def transition3232 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(813, 827), by decide⟩ +def transition3233 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(818, 828), by decide⟩ +def transition3234 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(818, 829), by decide⟩ +def transition3235 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(820, 830), by decide⟩ +def transition3236 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(820, 831), by decide⟩ +def transition3237 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(824, 1), by decide⟩ +def transition3238 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(825, 1), by decide⟩ +def transition3239 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(826, 1), by decide⟩ +def transition3240 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(827, 1), by decide⟩ +def transition3241 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(828, 1), by decide⟩ +def transition3242 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(829, 1), by decide⟩ +def transition3243 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(830, 1), by decide⟩ +def transition3244 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(831, 1), by decide⟩ +def transition3245 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(832, 1), by decide⟩ +def transition3246 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(833, 1), by decide⟩ +def transition3247 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(834, 1), by decide⟩ +def transition3248 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(835, 1), by decide⟩ +def transition3249 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(836, 1), by decide⟩ +def transition3250 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(837, 1), by decide⟩ +def transition3251 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(838, 1), by decide⟩ +def transition3252 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(839, 1), by decide⟩ +def transition3253 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(840, 1), by decide⟩ +def transition3254 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(841, 1), by decide⟩ +def transition3255 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(842, 1), by decide⟩ +def transition3256 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(843, 1), by decide⟩ +def transition3257 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(844, 1), by decide⟩ +def transition3258 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(845, 1), by decide⟩ +def transition3259 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(846, 1), by decide⟩ +def transition3260 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(847, 1), by decide⟩ +def transition3261 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(848, 1), by decide⟩ +def transition3262 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(849, 1), by decide⟩ +def transition3263 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(850, 1), by decide⟩ +def transition3264 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(851, 1), by decide⟩ +def transition3265 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(852, 1), by decide⟩ +def transition3266 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(853, 1), by decide⟩ +def transition3267 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(854, 1), by decide⟩ +def transition3268 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(855, 1), by decide⟩ +def transition3269 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(856, 1), by decide⟩ +def transition3270 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(857, 1), by decide⟩ +def transition3271 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(858, 1), by decide⟩ +def transition3272 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(859, 1), by decide⟩ +def transition3273 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(860, 1), by decide⟩ +def transition3274 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(861, 1), by decide⟩ +def transition3275 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(862, 1), by decide⟩ +def transition3276 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(863, 1), by decide⟩ +def transition3277 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(864, 1), by decide⟩ +def transition3278 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(865, 1), by decide⟩ +def transition3279 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(866, 1), by decide⟩ +def transition3280 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(867, 1), by decide⟩ +def transition3281 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(868, 1), by decide⟩ +def transition3282 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(869, 1), by decide⟩ +def transition3283 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(870, 1), by decide⟩ +def transition3284 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(871, 1), by decide⟩ +def transition3285 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(872, 1), by decide⟩ +def transition3286 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(873, 1), by decide⟩ +def transition3287 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(874, 1), by decide⟩ +def transition3288 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(875, 1), by decide⟩ +def transition3289 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(876, 1), by decide⟩ +def transition3290 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(877, 1), by decide⟩ +def transition3291 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(878, 1), by decide⟩ +def transition3292 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(879, 1), by decide⟩ +def transition3293 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(880, 1), by decide⟩ +def transition3294 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(881, 1), by decide⟩ +def transition3295 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(882, 1), by decide⟩ +def transition3296 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(883, 1), by decide⟩ +def transition3297 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(884, 1), by decide⟩ +def transition3298 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(885, 1), by decide⟩ +def transition3299 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(886, 1), by decide⟩ +def transition3300 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(887, 1), by decide⟩ +def transition3301 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(888, 1), by decide⟩ +def transition3302 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(889, 1), by decide⟩ +def transition3303 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(890, 1), by decide⟩ +def transition3304 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(891, 1), by decide⟩ +def transition3305 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(892, 1), by decide⟩ +def transition3306 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(893, 1), by decide⟩ +def transition3307 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(894, 1), by decide⟩ +def transition3308 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(895, 1), by decide⟩ +def transition3309 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(896, 1), by decide⟩ +def transition3310 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(897, 1), by decide⟩ +def transition3311 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(898, 1), by decide⟩ +def transition3312 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(899, 1), by decide⟩ +def transition3313 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(900, 1), by decide⟩ +def transition3314 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(901, 1), by decide⟩ +def transition3315 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(902, 1), by decide⟩ +def transition3316 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(903, 1), by decide⟩ +def transition3317 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(904, 1), by decide⟩ +def transition3318 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(905, 1), by decide⟩ +def transition3319 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(906, 1), by decide⟩ +def transition3320 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(907, 1), by decide⟩ +def transition3321 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(908, 1), by decide⟩ +def transition3322 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(909, 1), by decide⟩ +def transition3323 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(910, 1), by decide⟩ +def transition3324 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(911, 1), by decide⟩ +def transition3325 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(912, 1), by decide⟩ +def transition3326 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(913, 1), by decide⟩ +def transition3327 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(914, 1), by decide⟩ +def transition3328 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(915, 1), by decide⟩ +def transition3329 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(916, 1), by decide⟩ +def transition3330 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(917, 1), by decide⟩ +def transition3331 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(918, 1), by decide⟩ +def transition3332 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(919, 1), by decide⟩ +def transition3333 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(920, 1), by decide⟩ +def transition3334 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(921, 1), by decide⟩ +def transition3335 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(922, 1), by decide⟩ +def transition3336 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(923, 1), by decide⟩ +def transition3337 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(924, 1), by decide⟩ +def transition3338 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(925, 1), by decide⟩ +def transition3339 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(926, 1), by decide⟩ +def transition3340 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(927, 1), by decide⟩ +def transition3341 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(928, 1), by decide⟩ +def transition3342 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(929, 1), by decide⟩ +def transition3343 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(930, 1), by decide⟩ +def transition3344 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(931, 1), by decide⟩ +def transition3345 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(932, 1), by decide⟩ +def transition3346 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(933, 1), by decide⟩ +def transition3347 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(934, 1), by decide⟩ +def transition3348 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(935, 1), by decide⟩ +def transition3349 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(936, 1), by decide⟩ +def transition3350 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(937, 1), by decide⟩ +def transition3351 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(938, 1), by decide⟩ +def transition3352 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(939, 1), by decide⟩ +def transition3353 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(940, 1), by decide⟩ +def transition3354 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(941, 1), by decide⟩ +def transition3355 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(942, 1), by decide⟩ +def transition3356 : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + ⟨(943, 1), by decide⟩ +def transitionLookup (n : Nat) : { p : Fin 944 × Fin 944 // Absorbs p.1 p.2 } := + (if n < 1678 then (if n < 839 then (if n < 419 then (if n < 209 then (if n < 104 then (if n < 52 then (if n < 26 then (if n < 13 then (if n < 6 then (if n < 3 then (if n < 1 then transition0 else (if n < 2 then transition1 else transition2)) else (if n < 4 then transition3 else (if n < 5 then transition4 else transition5))) else (if n < 9 then (if n < 7 then transition6 else (if n < 8 then transition7 else transition8)) else (if n < 11 then (if n < 10 then transition9 else transition10) else (if n < 12 then transition11 else transition12)))) else (if n < 19 then (if n < 16 then (if n < 14 then transition13 else (if n < 15 then transition14 else transition15)) else (if n < 17 then transition16 else (if n < 18 then transition17 else transition18))) else (if n < 22 then (if n < 20 then transition19 else (if n < 21 then transition20 else transition21)) else (if n < 24 then (if n < 23 then transition22 else transition23) else (if n < 25 then transition24 else transition25))))) else (if n < 39 then (if n < 32 then (if n < 29 then (if n < 27 then transition26 else (if n < 28 then transition27 else transition28)) else (if n < 30 then transition29 else (if n < 31 then transition30 else transition31))) else (if n < 35 then (if n < 33 then transition32 else (if n < 34 then transition33 else transition34)) else (if n < 37 then (if n < 36 then transition35 else transition36) else (if n < 38 then transition37 else transition38)))) else (if n < 45 then (if n < 42 then (if n < 40 then transition39 else (if n < 41 then transition40 else transition41)) else (if n < 43 then transition42 else (if n < 44 then transition43 else transition44))) else (if n < 48 then (if n < 46 then transition45 else (if n < 47 then transition46 else transition47)) else (if n < 50 then (if n < 49 then transition48 else transition49) else (if n < 51 then transition50 else transition51)))))) else (if n < 78 then (if n < 65 then (if n < 58 then (if n < 55 then (if n < 53 then transition52 else (if n < 54 then transition53 else transition54)) else (if n < 56 then transition55 else (if n < 57 then transition56 else transition57))) else (if n < 61 then (if n < 59 then transition58 else (if n < 60 then transition59 else transition60)) else (if n < 63 then (if n < 62 then transition61 else transition62) else (if n < 64 then transition63 else transition64)))) else (if n < 71 then (if n < 68 then (if n < 66 then transition65 else (if n < 67 then transition66 else transition67)) else (if n < 69 then transition68 else (if n < 70 then transition69 else transition70))) else (if n < 74 then (if n < 72 then transition71 else (if n < 73 then transition72 else transition73)) else (if n < 76 then (if n < 75 then transition74 else transition75) else (if n < 77 then transition76 else transition77))))) else (if n < 91 then (if n < 84 then (if n < 81 then (if n < 79 then transition78 else (if n < 80 then transition79 else transition80)) else (if n < 82 then transition81 else (if n < 83 then transition82 else transition83))) else (if n < 87 then (if n < 85 then transition84 else (if n < 86 then transition85 else transition86)) else (if n < 89 then (if n < 88 then transition87 else transition88) else (if n < 90 then transition89 else transition90)))) else (if n < 97 then (if n < 94 then (if n < 92 then transition91 else (if n < 93 then transition92 else transition93)) else (if n < 95 then transition94 else (if n < 96 then transition95 else transition96))) else (if n < 100 then (if n < 98 then transition97 else (if n < 99 then transition98 else transition99)) else (if n < 102 then (if n < 101 then transition100 else transition101) else (if n < 103 then transition102 else transition103))))))) else (if n < 156 then (if n < 130 then (if n < 117 then (if n < 110 then (if n < 107 then (if n < 105 then transition104 else (if n < 106 then transition105 else transition106)) else (if n < 108 then transition107 else (if n < 109 then transition108 else transition109))) else (if n < 113 then (if n < 111 then transition110 else (if n < 112 then transition111 else transition112)) else (if n < 115 then (if n < 114 then transition113 else transition114) else (if n < 116 then transition115 else transition116)))) else (if n < 123 then (if n < 120 then (if n < 118 then transition117 else (if n < 119 then transition118 else transition119)) else (if n < 121 then transition120 else (if n < 122 then transition121 else transition122))) else (if n < 126 then (if n < 124 then transition123 else (if n < 125 then transition124 else transition125)) else (if n < 128 then (if n < 127 then transition126 else transition127) else (if n < 129 then transition128 else transition129))))) else (if n < 143 then (if n < 136 then (if n < 133 then (if n < 131 then transition130 else (if n < 132 then transition131 else transition132)) else (if n < 134 then transition133 else (if n < 135 then transition134 else transition135))) else (if n < 139 then (if n < 137 then transition136 else (if n < 138 then transition137 else transition138)) else (if n < 141 then (if n < 140 then transition139 else transition140) else (if n < 142 then transition141 else transition142)))) else (if n < 149 then (if n < 146 then (if n < 144 then transition143 else (if n < 145 then transition144 else transition145)) else (if n < 147 then transition146 else (if n < 148 then transition147 else transition148))) else (if n < 152 then (if n < 150 then transition149 else (if n < 151 then transition150 else transition151)) else (if n < 154 then (if n < 153 then transition152 else transition153) else (if n < 155 then transition154 else transition155)))))) else (if n < 182 then (if n < 169 then (if n < 162 then (if n < 159 then (if n < 157 then transition156 else (if n < 158 then transition157 else transition158)) else (if n < 160 then transition159 else (if n < 161 then transition160 else transition161))) else (if n < 165 then (if n < 163 then transition162 else (if n < 164 then transition163 else transition164)) else (if n < 167 then (if n < 166 then transition165 else transition166) else (if n < 168 then transition167 else transition168)))) else (if n < 175 then (if n < 172 then (if n < 170 then transition169 else (if n < 171 then transition170 else transition171)) else (if n < 173 then transition172 else (if n < 174 then transition173 else transition174))) else (if n < 178 then (if n < 176 then transition175 else (if n < 177 then transition176 else transition177)) else (if n < 180 then (if n < 179 then transition178 else transition179) else (if n < 181 then transition180 else transition181))))) else (if n < 195 then (if n < 188 then (if n < 185 then (if n < 183 then transition182 else (if n < 184 then transition183 else transition184)) else (if n < 186 then transition185 else (if n < 187 then transition186 else transition187))) else (if n < 191 then (if n < 189 then transition188 else (if n < 190 then transition189 else transition190)) else (if n < 193 then (if n < 192 then transition191 else transition192) else (if n < 194 then transition193 else transition194)))) else (if n < 202 then (if n < 198 then (if n < 196 then transition195 else (if n < 197 then transition196 else transition197)) else (if n < 200 then (if n < 199 then transition198 else transition199) else (if n < 201 then transition200 else transition201))) else (if n < 205 then (if n < 203 then transition202 else (if n < 204 then transition203 else transition204)) else (if n < 207 then (if n < 206 then transition205 else transition206) else (if n < 208 then transition207 else transition208)))))))) else (if n < 314 then (if n < 261 then (if n < 235 then (if n < 222 then (if n < 215 then (if n < 212 then (if n < 210 then transition209 else (if n < 211 then transition210 else transition211)) else (if n < 213 then transition212 else (if n < 214 then transition213 else transition214))) else (if n < 218 then (if n < 216 then transition215 else (if n < 217 then transition216 else transition217)) else (if n < 220 then (if n < 219 then transition218 else transition219) else (if n < 221 then transition220 else transition221)))) else (if n < 228 then (if n < 225 then (if n < 223 then transition222 else (if n < 224 then transition223 else transition224)) else (if n < 226 then transition225 else (if n < 227 then transition226 else transition227))) else (if n < 231 then (if n < 229 then transition228 else (if n < 230 then transition229 else transition230)) else (if n < 233 then (if n < 232 then transition231 else transition232) else (if n < 234 then transition233 else transition234))))) else (if n < 248 then (if n < 241 then (if n < 238 then (if n < 236 then transition235 else (if n < 237 then transition236 else transition237)) else (if n < 239 then transition238 else (if n < 240 then transition239 else transition240))) else (if n < 244 then (if n < 242 then transition241 else (if n < 243 then transition242 else transition243)) else (if n < 246 then (if n < 245 then transition244 else transition245) else (if n < 247 then transition246 else transition247)))) else (if n < 254 then (if n < 251 then (if n < 249 then transition248 else (if n < 250 then transition249 else transition250)) else (if n < 252 then transition251 else (if n < 253 then transition252 else transition253))) else (if n < 257 then (if n < 255 then transition254 else (if n < 256 then transition255 else transition256)) else (if n < 259 then (if n < 258 then transition257 else transition258) else (if n < 260 then transition259 else transition260)))))) else (if n < 287 then (if n < 274 then (if n < 267 then (if n < 264 then (if n < 262 then transition261 else (if n < 263 then transition262 else transition263)) else (if n < 265 then transition264 else (if n < 266 then transition265 else transition266))) else (if n < 270 then (if n < 268 then transition267 else (if n < 269 then transition268 else transition269)) else (if n < 272 then (if n < 271 then transition270 else transition271) else (if n < 273 then transition272 else transition273)))) else (if n < 280 then (if n < 277 then (if n < 275 then transition274 else (if n < 276 then transition275 else transition276)) else (if n < 278 then transition277 else (if n < 279 then transition278 else transition279))) else (if n < 283 then (if n < 281 then transition280 else (if n < 282 then transition281 else transition282)) else (if n < 285 then (if n < 284 then transition283 else transition284) else (if n < 286 then transition285 else transition286))))) else (if n < 300 then (if n < 293 then (if n < 290 then (if n < 288 then transition287 else (if n < 289 then transition288 else transition289)) else (if n < 291 then transition290 else (if n < 292 then transition291 else transition292))) else (if n < 296 then (if n < 294 then transition293 else (if n < 295 then transition294 else transition295)) else (if n < 298 then (if n < 297 then transition296 else transition297) else (if n < 299 then transition298 else transition299)))) else (if n < 307 then (if n < 303 then (if n < 301 then transition300 else (if n < 302 then transition301 else transition302)) else (if n < 305 then (if n < 304 then transition303 else transition304) else (if n < 306 then transition305 else transition306))) else (if n < 310 then (if n < 308 then transition307 else (if n < 309 then transition308 else transition309)) else (if n < 312 then (if n < 311 then transition310 else transition311) else (if n < 313 then transition312 else transition313))))))) else (if n < 366 then (if n < 340 then (if n < 327 then (if n < 320 then (if n < 317 then (if n < 315 then transition314 else (if n < 316 then transition315 else transition316)) else (if n < 318 then transition317 else (if n < 319 then transition318 else transition319))) else (if n < 323 then (if n < 321 then transition320 else (if n < 322 then transition321 else transition322)) else (if n < 325 then (if n < 324 then transition323 else transition324) else (if n < 326 then transition325 else transition326)))) else (if n < 333 then (if n < 330 then (if n < 328 then transition327 else (if n < 329 then transition328 else transition329)) else (if n < 331 then transition330 else (if n < 332 then transition331 else transition332))) else (if n < 336 then (if n < 334 then transition333 else (if n < 335 then transition334 else transition335)) else (if n < 338 then (if n < 337 then transition336 else transition337) else (if n < 339 then transition338 else transition339))))) else (if n < 353 then (if n < 346 then (if n < 343 then (if n < 341 then transition340 else (if n < 342 then transition341 else transition342)) else (if n < 344 then transition343 else (if n < 345 then transition344 else transition345))) else (if n < 349 then (if n < 347 then transition346 else (if n < 348 then transition347 else transition348)) else (if n < 351 then (if n < 350 then transition349 else transition350) else (if n < 352 then transition351 else transition352)))) else (if n < 359 then (if n < 356 then (if n < 354 then transition353 else (if n < 355 then transition354 else transition355)) else (if n < 357 then transition356 else (if n < 358 then transition357 else transition358))) else (if n < 362 then (if n < 360 then transition359 else (if n < 361 then transition360 else transition361)) else (if n < 364 then (if n < 363 then transition362 else transition363) else (if n < 365 then transition364 else transition365)))))) else (if n < 392 then (if n < 379 then (if n < 372 then (if n < 369 then (if n < 367 then transition366 else (if n < 368 then transition367 else transition368)) else (if n < 370 then transition369 else (if n < 371 then transition370 else transition371))) else (if n < 375 then (if n < 373 then transition372 else (if n < 374 then transition373 else transition374)) else (if n < 377 then (if n < 376 then transition375 else transition376) else (if n < 378 then transition377 else transition378)))) else (if n < 385 then (if n < 382 then (if n < 380 then transition379 else (if n < 381 then transition380 else transition381)) else (if n < 383 then transition382 else (if n < 384 then transition383 else transition384))) else (if n < 388 then (if n < 386 then transition385 else (if n < 387 then transition386 else transition387)) else (if n < 390 then (if n < 389 then transition388 else transition389) else (if n < 391 then transition390 else transition391))))) else (if n < 405 then (if n < 398 then (if n < 395 then (if n < 393 then transition392 else (if n < 394 then transition393 else transition394)) else (if n < 396 then transition395 else (if n < 397 then transition396 else transition397))) else (if n < 401 then (if n < 399 then transition398 else (if n < 400 then transition399 else transition400)) else (if n < 403 then (if n < 402 then transition401 else transition402) else (if n < 404 then transition403 else transition404)))) else (if n < 412 then (if n < 408 then (if n < 406 then transition405 else (if n < 407 then transition406 else transition407)) else (if n < 410 then (if n < 409 then transition408 else transition409) else (if n < 411 then transition410 else transition411))) else (if n < 415 then (if n < 413 then transition412 else (if n < 414 then transition413 else transition414)) else (if n < 417 then (if n < 416 then transition415 else transition416) else (if n < 418 then transition417 else transition418))))))))) else (if n < 629 then (if n < 524 then (if n < 471 then (if n < 445 then (if n < 432 then (if n < 425 then (if n < 422 then (if n < 420 then transition419 else (if n < 421 then transition420 else transition421)) else (if n < 423 then transition422 else (if n < 424 then transition423 else transition424))) else (if n < 428 then (if n < 426 then transition425 else (if n < 427 then transition426 else transition427)) else (if n < 430 then (if n < 429 then transition428 else transition429) else (if n < 431 then transition430 else transition431)))) else (if n < 438 then (if n < 435 then (if n < 433 then transition432 else (if n < 434 then transition433 else transition434)) else (if n < 436 then transition435 else (if n < 437 then transition436 else transition437))) else (if n < 441 then (if n < 439 then transition438 else (if n < 440 then transition439 else transition440)) else (if n < 443 then (if n < 442 then transition441 else transition442) else (if n < 444 then transition443 else transition444))))) else (if n < 458 then (if n < 451 then (if n < 448 then (if n < 446 then transition445 else (if n < 447 then transition446 else transition447)) else (if n < 449 then transition448 else (if n < 450 then transition449 else transition450))) else (if n < 454 then (if n < 452 then transition451 else (if n < 453 then transition452 else transition453)) else (if n < 456 then (if n < 455 then transition454 else transition455) else (if n < 457 then transition456 else transition457)))) else (if n < 464 then (if n < 461 then (if n < 459 then transition458 else (if n < 460 then transition459 else transition460)) else (if n < 462 then transition461 else (if n < 463 then transition462 else transition463))) else (if n < 467 then (if n < 465 then transition464 else (if n < 466 then transition465 else transition466)) else (if n < 469 then (if n < 468 then transition467 else transition468) else (if n < 470 then transition469 else transition470)))))) else (if n < 497 then (if n < 484 then (if n < 477 then (if n < 474 then (if n < 472 then transition471 else (if n < 473 then transition472 else transition473)) else (if n < 475 then transition474 else (if n < 476 then transition475 else transition476))) else (if n < 480 then (if n < 478 then transition477 else (if n < 479 then transition478 else transition479)) else (if n < 482 then (if n < 481 then transition480 else transition481) else (if n < 483 then transition482 else transition483)))) else (if n < 490 then (if n < 487 then (if n < 485 then transition484 else (if n < 486 then transition485 else transition486)) else (if n < 488 then transition487 else (if n < 489 then transition488 else transition489))) else (if n < 493 then (if n < 491 then transition490 else (if n < 492 then transition491 else transition492)) else (if n < 495 then (if n < 494 then transition493 else transition494) else (if n < 496 then transition495 else transition496))))) else (if n < 510 then (if n < 503 then (if n < 500 then (if n < 498 then transition497 else (if n < 499 then transition498 else transition499)) else (if n < 501 then transition500 else (if n < 502 then transition501 else transition502))) else (if n < 506 then (if n < 504 then transition503 else (if n < 505 then transition504 else transition505)) else (if n < 508 then (if n < 507 then transition506 else transition507) else (if n < 509 then transition508 else transition509)))) else (if n < 517 then (if n < 513 then (if n < 511 then transition510 else (if n < 512 then transition511 else transition512)) else (if n < 515 then (if n < 514 then transition513 else transition514) else (if n < 516 then transition515 else transition516))) else (if n < 520 then (if n < 518 then transition517 else (if n < 519 then transition518 else transition519)) else (if n < 522 then (if n < 521 then transition520 else transition521) else (if n < 523 then transition522 else transition523))))))) else (if n < 576 then (if n < 550 then (if n < 537 then (if n < 530 then (if n < 527 then (if n < 525 then transition524 else (if n < 526 then transition525 else transition526)) else (if n < 528 then transition527 else (if n < 529 then transition528 else transition529))) else (if n < 533 then (if n < 531 then transition530 else (if n < 532 then transition531 else transition532)) else (if n < 535 then (if n < 534 then transition533 else transition534) else (if n < 536 then transition535 else transition536)))) else (if n < 543 then (if n < 540 then (if n < 538 then transition537 else (if n < 539 then transition538 else transition539)) else (if n < 541 then transition540 else (if n < 542 then transition541 else transition542))) else (if n < 546 then (if n < 544 then transition543 else (if n < 545 then transition544 else transition545)) else (if n < 548 then (if n < 547 then transition546 else transition547) else (if n < 549 then transition548 else transition549))))) else (if n < 563 then (if n < 556 then (if n < 553 then (if n < 551 then transition550 else (if n < 552 then transition551 else transition552)) else (if n < 554 then transition553 else (if n < 555 then transition554 else transition555))) else (if n < 559 then (if n < 557 then transition556 else (if n < 558 then transition557 else transition558)) else (if n < 561 then (if n < 560 then transition559 else transition560) else (if n < 562 then transition561 else transition562)))) else (if n < 569 then (if n < 566 then (if n < 564 then transition563 else (if n < 565 then transition564 else transition565)) else (if n < 567 then transition566 else (if n < 568 then transition567 else transition568))) else (if n < 572 then (if n < 570 then transition569 else (if n < 571 then transition570 else transition571)) else (if n < 574 then (if n < 573 then transition572 else transition573) else (if n < 575 then transition574 else transition575)))))) else (if n < 602 then (if n < 589 then (if n < 582 then (if n < 579 then (if n < 577 then transition576 else (if n < 578 then transition577 else transition578)) else (if n < 580 then transition579 else (if n < 581 then transition580 else transition581))) else (if n < 585 then (if n < 583 then transition582 else (if n < 584 then transition583 else transition584)) else (if n < 587 then (if n < 586 then transition585 else transition586) else (if n < 588 then transition587 else transition588)))) else (if n < 595 then (if n < 592 then (if n < 590 then transition589 else (if n < 591 then transition590 else transition591)) else (if n < 593 then transition592 else (if n < 594 then transition593 else transition594))) else (if n < 598 then (if n < 596 then transition595 else (if n < 597 then transition596 else transition597)) else (if n < 600 then (if n < 599 then transition598 else transition599) else (if n < 601 then transition600 else transition601))))) else (if n < 615 then (if n < 608 then (if n < 605 then (if n < 603 then transition602 else (if n < 604 then transition603 else transition604)) else (if n < 606 then transition605 else (if n < 607 then transition606 else transition607))) else (if n < 611 then (if n < 609 then transition608 else (if n < 610 then transition609 else transition610)) else (if n < 613 then (if n < 612 then transition611 else transition612) else (if n < 614 then transition613 else transition614)))) else (if n < 622 then (if n < 618 then (if n < 616 then transition615 else (if n < 617 then transition616 else transition617)) else (if n < 620 then (if n < 619 then transition618 else transition619) else (if n < 621 then transition620 else transition621))) else (if n < 625 then (if n < 623 then transition622 else (if n < 624 then transition623 else transition624)) else (if n < 627 then (if n < 626 then transition625 else transition626) else (if n < 628 then transition627 else transition628)))))))) else (if n < 734 then (if n < 681 then (if n < 655 then (if n < 642 then (if n < 635 then (if n < 632 then (if n < 630 then transition629 else (if n < 631 then transition630 else transition631)) else (if n < 633 then transition632 else (if n < 634 then transition633 else transition634))) else (if n < 638 then (if n < 636 then transition635 else (if n < 637 then transition636 else transition637)) else (if n < 640 then (if n < 639 then transition638 else transition639) else (if n < 641 then transition640 else transition641)))) else (if n < 648 then (if n < 645 then (if n < 643 then transition642 else (if n < 644 then transition643 else transition644)) else (if n < 646 then transition645 else (if n < 647 then transition646 else transition647))) else (if n < 651 then (if n < 649 then transition648 else (if n < 650 then transition649 else transition650)) else (if n < 653 then (if n < 652 then transition651 else transition652) else (if n < 654 then transition653 else transition654))))) else (if n < 668 then (if n < 661 then (if n < 658 then (if n < 656 then transition655 else (if n < 657 then transition656 else transition657)) else (if n < 659 then transition658 else (if n < 660 then transition659 else transition660))) else (if n < 664 then (if n < 662 then transition661 else (if n < 663 then transition662 else transition663)) else (if n < 666 then (if n < 665 then transition664 else transition665) else (if n < 667 then transition666 else transition667)))) else (if n < 674 then (if n < 671 then (if n < 669 then transition668 else (if n < 670 then transition669 else transition670)) else (if n < 672 then transition671 else (if n < 673 then transition672 else transition673))) else (if n < 677 then (if n < 675 then transition674 else (if n < 676 then transition675 else transition676)) else (if n < 679 then (if n < 678 then transition677 else transition678) else (if n < 680 then transition679 else transition680)))))) else (if n < 707 then (if n < 694 then (if n < 687 then (if n < 684 then (if n < 682 then transition681 else (if n < 683 then transition682 else transition683)) else (if n < 685 then transition684 else (if n < 686 then transition685 else transition686))) else (if n < 690 then (if n < 688 then transition687 else (if n < 689 then transition688 else transition689)) else (if n < 692 then (if n < 691 then transition690 else transition691) else (if n < 693 then transition692 else transition693)))) else (if n < 700 then (if n < 697 then (if n < 695 then transition694 else (if n < 696 then transition695 else transition696)) else (if n < 698 then transition697 else (if n < 699 then transition698 else transition699))) else (if n < 703 then (if n < 701 then transition700 else (if n < 702 then transition701 else transition702)) else (if n < 705 then (if n < 704 then transition703 else transition704) else (if n < 706 then transition705 else transition706))))) else (if n < 720 then (if n < 713 then (if n < 710 then (if n < 708 then transition707 else (if n < 709 then transition708 else transition709)) else (if n < 711 then transition710 else (if n < 712 then transition711 else transition712))) else (if n < 716 then (if n < 714 then transition713 else (if n < 715 then transition714 else transition715)) else (if n < 718 then (if n < 717 then transition716 else transition717) else (if n < 719 then transition718 else transition719)))) else (if n < 727 then (if n < 723 then (if n < 721 then transition720 else (if n < 722 then transition721 else transition722)) else (if n < 725 then (if n < 724 then transition723 else transition724) else (if n < 726 then transition725 else transition726))) else (if n < 730 then (if n < 728 then transition727 else (if n < 729 then transition728 else transition729)) else (if n < 732 then (if n < 731 then transition730 else transition731) else (if n < 733 then transition732 else transition733))))))) else (if n < 786 then (if n < 760 then (if n < 747 then (if n < 740 then (if n < 737 then (if n < 735 then transition734 else (if n < 736 then transition735 else transition736)) else (if n < 738 then transition737 else (if n < 739 then transition738 else transition739))) else (if n < 743 then (if n < 741 then transition740 else (if n < 742 then transition741 else transition742)) else (if n < 745 then (if n < 744 then transition743 else transition744) else (if n < 746 then transition745 else transition746)))) else (if n < 753 then (if n < 750 then (if n < 748 then transition747 else (if n < 749 then transition748 else transition749)) else (if n < 751 then transition750 else (if n < 752 then transition751 else transition752))) else (if n < 756 then (if n < 754 then transition753 else (if n < 755 then transition754 else transition755)) else (if n < 758 then (if n < 757 then transition756 else transition757) else (if n < 759 then transition758 else transition759))))) else (if n < 773 then (if n < 766 then (if n < 763 then (if n < 761 then transition760 else (if n < 762 then transition761 else transition762)) else (if n < 764 then transition763 else (if n < 765 then transition764 else transition765))) else (if n < 769 then (if n < 767 then transition766 else (if n < 768 then transition767 else transition768)) else (if n < 771 then (if n < 770 then transition769 else transition770) else (if n < 772 then transition771 else transition772)))) else (if n < 779 then (if n < 776 then (if n < 774 then transition773 else (if n < 775 then transition774 else transition775)) else (if n < 777 then transition776 else (if n < 778 then transition777 else transition778))) else (if n < 782 then (if n < 780 then transition779 else (if n < 781 then transition780 else transition781)) else (if n < 784 then (if n < 783 then transition782 else transition783) else (if n < 785 then transition784 else transition785)))))) else (if n < 812 then (if n < 799 then (if n < 792 then (if n < 789 then (if n < 787 then transition786 else (if n < 788 then transition787 else transition788)) else (if n < 790 then transition789 else (if n < 791 then transition790 else transition791))) else (if n < 795 then (if n < 793 then transition792 else (if n < 794 then transition793 else transition794)) else (if n < 797 then (if n < 796 then transition795 else transition796) else (if n < 798 then transition797 else transition798)))) else (if n < 805 then (if n < 802 then (if n < 800 then transition799 else (if n < 801 then transition800 else transition801)) else (if n < 803 then transition802 else (if n < 804 then transition803 else transition804))) else (if n < 808 then (if n < 806 then transition805 else (if n < 807 then transition806 else transition807)) else (if n < 810 then (if n < 809 then transition808 else transition809) else (if n < 811 then transition810 else transition811))))) else (if n < 825 then (if n < 818 then (if n < 815 then (if n < 813 then transition812 else (if n < 814 then transition813 else transition814)) else (if n < 816 then transition815 else (if n < 817 then transition816 else transition817))) else (if n < 821 then (if n < 819 then transition818 else (if n < 820 then transition819 else transition820)) else (if n < 823 then (if n < 822 then transition821 else transition822) else (if n < 824 then transition823 else transition824)))) else (if n < 832 then (if n < 828 then (if n < 826 then transition825 else (if n < 827 then transition826 else transition827)) else (if n < 830 then (if n < 829 then transition828 else transition829) else (if n < 831 then transition830 else transition831))) else (if n < 835 then (if n < 833 then transition832 else (if n < 834 then transition833 else transition834)) else (if n < 837 then (if n < 836 then transition835 else transition836) else (if n < 838 then transition837 else transition838)))))))))) else (if n < 1258 then (if n < 1048 then (if n < 943 then (if n < 891 then (if n < 865 then (if n < 852 then (if n < 845 then (if n < 842 then (if n < 840 then transition839 else (if n < 841 then transition840 else transition841)) else (if n < 843 then transition842 else (if n < 844 then transition843 else transition844))) else (if n < 848 then (if n < 846 then transition845 else (if n < 847 then transition846 else transition847)) else (if n < 850 then (if n < 849 then transition848 else transition849) else (if n < 851 then transition850 else transition851)))) else (if n < 858 then (if n < 855 then (if n < 853 then transition852 else (if n < 854 then transition853 else transition854)) else (if n < 856 then transition855 else (if n < 857 then transition856 else transition857))) else (if n < 861 then (if n < 859 then transition858 else (if n < 860 then transition859 else transition860)) else (if n < 863 then (if n < 862 then transition861 else transition862) else (if n < 864 then transition863 else transition864))))) else (if n < 878 then (if n < 871 then (if n < 868 then (if n < 866 then transition865 else (if n < 867 then transition866 else transition867)) else (if n < 869 then transition868 else (if n < 870 then transition869 else transition870))) else (if n < 874 then (if n < 872 then transition871 else (if n < 873 then transition872 else transition873)) else (if n < 876 then (if n < 875 then transition874 else transition875) else (if n < 877 then transition876 else transition877)))) else (if n < 884 then (if n < 881 then (if n < 879 then transition878 else (if n < 880 then transition879 else transition880)) else (if n < 882 then transition881 else (if n < 883 then transition882 else transition883))) else (if n < 887 then (if n < 885 then transition884 else (if n < 886 then transition885 else transition886)) else (if n < 889 then (if n < 888 then transition887 else transition888) else (if n < 890 then transition889 else transition890)))))) else (if n < 917 then (if n < 904 then (if n < 897 then (if n < 894 then (if n < 892 then transition891 else (if n < 893 then transition892 else transition893)) else (if n < 895 then transition894 else (if n < 896 then transition895 else transition896))) else (if n < 900 then (if n < 898 then transition897 else (if n < 899 then transition898 else transition899)) else (if n < 902 then (if n < 901 then transition900 else transition901) else (if n < 903 then transition902 else transition903)))) else (if n < 910 then (if n < 907 then (if n < 905 then transition904 else (if n < 906 then transition905 else transition906)) else (if n < 908 then transition907 else (if n < 909 then transition908 else transition909))) else (if n < 913 then (if n < 911 then transition910 else (if n < 912 then transition911 else transition912)) else (if n < 915 then (if n < 914 then transition913 else transition914) else (if n < 916 then transition915 else transition916))))) else (if n < 930 then (if n < 923 then (if n < 920 then (if n < 918 then transition917 else (if n < 919 then transition918 else transition919)) else (if n < 921 then transition920 else (if n < 922 then transition921 else transition922))) else (if n < 926 then (if n < 924 then transition923 else (if n < 925 then transition924 else transition925)) else (if n < 928 then (if n < 927 then transition926 else transition927) else (if n < 929 then transition928 else transition929)))) else (if n < 936 then (if n < 933 then (if n < 931 then transition930 else (if n < 932 then transition931 else transition932)) else (if n < 934 then transition933 else (if n < 935 then transition934 else transition935))) else (if n < 939 then (if n < 937 then transition936 else (if n < 938 then transition937 else transition938)) else (if n < 941 then (if n < 940 then transition939 else transition940) else (if n < 942 then transition941 else transition942))))))) else (if n < 995 then (if n < 969 then (if n < 956 then (if n < 949 then (if n < 946 then (if n < 944 then transition943 else (if n < 945 then transition944 else transition945)) else (if n < 947 then transition946 else (if n < 948 then transition947 else transition948))) else (if n < 952 then (if n < 950 then transition949 else (if n < 951 then transition950 else transition951)) else (if n < 954 then (if n < 953 then transition952 else transition953) else (if n < 955 then transition954 else transition955)))) else (if n < 962 then (if n < 959 then (if n < 957 then transition956 else (if n < 958 then transition957 else transition958)) else (if n < 960 then transition959 else (if n < 961 then transition960 else transition961))) else (if n < 965 then (if n < 963 then transition962 else (if n < 964 then transition963 else transition964)) else (if n < 967 then (if n < 966 then transition965 else transition966) else (if n < 968 then transition967 else transition968))))) else (if n < 982 then (if n < 975 then (if n < 972 then (if n < 970 then transition969 else (if n < 971 then transition970 else transition971)) else (if n < 973 then transition972 else (if n < 974 then transition973 else transition974))) else (if n < 978 then (if n < 976 then transition975 else (if n < 977 then transition976 else transition977)) else (if n < 980 then (if n < 979 then transition978 else transition979) else (if n < 981 then transition980 else transition981)))) else (if n < 988 then (if n < 985 then (if n < 983 then transition982 else (if n < 984 then transition983 else transition984)) else (if n < 986 then transition985 else (if n < 987 then transition986 else transition987))) else (if n < 991 then (if n < 989 then transition988 else (if n < 990 then transition989 else transition990)) else (if n < 993 then (if n < 992 then transition991 else transition992) else (if n < 994 then transition993 else transition994)))))) else (if n < 1021 then (if n < 1008 then (if n < 1001 then (if n < 998 then (if n < 996 then transition995 else (if n < 997 then transition996 else transition997)) else (if n < 999 then transition998 else (if n < 1000 then transition999 else transition1000))) else (if n < 1004 then (if n < 1002 then transition1001 else (if n < 1003 then transition1002 else transition1003)) else (if n < 1006 then (if n < 1005 then transition1004 else transition1005) else (if n < 1007 then transition1006 else transition1007)))) else (if n < 1014 then (if n < 1011 then (if n < 1009 then transition1008 else (if n < 1010 then transition1009 else transition1010)) else (if n < 1012 then transition1011 else (if n < 1013 then transition1012 else transition1013))) else (if n < 1017 then (if n < 1015 then transition1014 else (if n < 1016 then transition1015 else transition1016)) else (if n < 1019 then (if n < 1018 then transition1017 else transition1018) else (if n < 1020 then transition1019 else transition1020))))) else (if n < 1034 then (if n < 1027 then (if n < 1024 then (if n < 1022 then transition1021 else (if n < 1023 then transition1022 else transition1023)) else (if n < 1025 then transition1024 else (if n < 1026 then transition1025 else transition1026))) else (if n < 1030 then (if n < 1028 then transition1027 else (if n < 1029 then transition1028 else transition1029)) else (if n < 1032 then (if n < 1031 then transition1030 else transition1031) else (if n < 1033 then transition1032 else transition1033)))) else (if n < 1041 then (if n < 1037 then (if n < 1035 then transition1034 else (if n < 1036 then transition1035 else transition1036)) else (if n < 1039 then (if n < 1038 then transition1037 else transition1038) else (if n < 1040 then transition1039 else transition1040))) else (if n < 1044 then (if n < 1042 then transition1041 else (if n < 1043 then transition1042 else transition1043)) else (if n < 1046 then (if n < 1045 then transition1044 else transition1045) else (if n < 1047 then transition1046 else transition1047)))))))) else (if n < 1153 then (if n < 1100 then (if n < 1074 then (if n < 1061 then (if n < 1054 then (if n < 1051 then (if n < 1049 then transition1048 else (if n < 1050 then transition1049 else transition1050)) else (if n < 1052 then transition1051 else (if n < 1053 then transition1052 else transition1053))) else (if n < 1057 then (if n < 1055 then transition1054 else (if n < 1056 then transition1055 else transition1056)) else (if n < 1059 then (if n < 1058 then transition1057 else transition1058) else (if n < 1060 then transition1059 else transition1060)))) else (if n < 1067 then (if n < 1064 then (if n < 1062 then transition1061 else (if n < 1063 then transition1062 else transition1063)) else (if n < 1065 then transition1064 else (if n < 1066 then transition1065 else transition1066))) else (if n < 1070 then (if n < 1068 then transition1067 else (if n < 1069 then transition1068 else transition1069)) else (if n < 1072 then (if n < 1071 then transition1070 else transition1071) else (if n < 1073 then transition1072 else transition1073))))) else (if n < 1087 then (if n < 1080 then (if n < 1077 then (if n < 1075 then transition1074 else (if n < 1076 then transition1075 else transition1076)) else (if n < 1078 then transition1077 else (if n < 1079 then transition1078 else transition1079))) else (if n < 1083 then (if n < 1081 then transition1080 else (if n < 1082 then transition1081 else transition1082)) else (if n < 1085 then (if n < 1084 then transition1083 else transition1084) else (if n < 1086 then transition1085 else transition1086)))) else (if n < 1093 then (if n < 1090 then (if n < 1088 then transition1087 else (if n < 1089 then transition1088 else transition1089)) else (if n < 1091 then transition1090 else (if n < 1092 then transition1091 else transition1092))) else (if n < 1096 then (if n < 1094 then transition1093 else (if n < 1095 then transition1094 else transition1095)) else (if n < 1098 then (if n < 1097 then transition1096 else transition1097) else (if n < 1099 then transition1098 else transition1099)))))) else (if n < 1126 then (if n < 1113 then (if n < 1106 then (if n < 1103 then (if n < 1101 then transition1100 else (if n < 1102 then transition1101 else transition1102)) else (if n < 1104 then transition1103 else (if n < 1105 then transition1104 else transition1105))) else (if n < 1109 then (if n < 1107 then transition1106 else (if n < 1108 then transition1107 else transition1108)) else (if n < 1111 then (if n < 1110 then transition1109 else transition1110) else (if n < 1112 then transition1111 else transition1112)))) else (if n < 1119 then (if n < 1116 then (if n < 1114 then transition1113 else (if n < 1115 then transition1114 else transition1115)) else (if n < 1117 then transition1116 else (if n < 1118 then transition1117 else transition1118))) else (if n < 1122 then (if n < 1120 then transition1119 else (if n < 1121 then transition1120 else transition1121)) else (if n < 1124 then (if n < 1123 then transition1122 else transition1123) else (if n < 1125 then transition1124 else transition1125))))) else (if n < 1139 then (if n < 1132 then (if n < 1129 then (if n < 1127 then transition1126 else (if n < 1128 then transition1127 else transition1128)) else (if n < 1130 then transition1129 else (if n < 1131 then transition1130 else transition1131))) else (if n < 1135 then (if n < 1133 then transition1132 else (if n < 1134 then transition1133 else transition1134)) else (if n < 1137 then (if n < 1136 then transition1135 else transition1136) else (if n < 1138 then transition1137 else transition1138)))) else (if n < 1146 then (if n < 1142 then (if n < 1140 then transition1139 else (if n < 1141 then transition1140 else transition1141)) else (if n < 1144 then (if n < 1143 then transition1142 else transition1143) else (if n < 1145 then transition1144 else transition1145))) else (if n < 1149 then (if n < 1147 then transition1146 else (if n < 1148 then transition1147 else transition1148)) else (if n < 1151 then (if n < 1150 then transition1149 else transition1150) else (if n < 1152 then transition1151 else transition1152))))))) else (if n < 1205 then (if n < 1179 then (if n < 1166 then (if n < 1159 then (if n < 1156 then (if n < 1154 then transition1153 else (if n < 1155 then transition1154 else transition1155)) else (if n < 1157 then transition1156 else (if n < 1158 then transition1157 else transition1158))) else (if n < 1162 then (if n < 1160 then transition1159 else (if n < 1161 then transition1160 else transition1161)) else (if n < 1164 then (if n < 1163 then transition1162 else transition1163) else (if n < 1165 then transition1164 else transition1165)))) else (if n < 1172 then (if n < 1169 then (if n < 1167 then transition1166 else (if n < 1168 then transition1167 else transition1168)) else (if n < 1170 then transition1169 else (if n < 1171 then transition1170 else transition1171))) else (if n < 1175 then (if n < 1173 then transition1172 else (if n < 1174 then transition1173 else transition1174)) else (if n < 1177 then (if n < 1176 then transition1175 else transition1176) else (if n < 1178 then transition1177 else transition1178))))) else (if n < 1192 then (if n < 1185 then (if n < 1182 then (if n < 1180 then transition1179 else (if n < 1181 then transition1180 else transition1181)) else (if n < 1183 then transition1182 else (if n < 1184 then transition1183 else transition1184))) else (if n < 1188 then (if n < 1186 then transition1185 else (if n < 1187 then transition1186 else transition1187)) else (if n < 1190 then (if n < 1189 then transition1188 else transition1189) else (if n < 1191 then transition1190 else transition1191)))) else (if n < 1198 then (if n < 1195 then (if n < 1193 then transition1192 else (if n < 1194 then transition1193 else transition1194)) else (if n < 1196 then transition1195 else (if n < 1197 then transition1196 else transition1197))) else (if n < 1201 then (if n < 1199 then transition1198 else (if n < 1200 then transition1199 else transition1200)) else (if n < 1203 then (if n < 1202 then transition1201 else transition1202) else (if n < 1204 then transition1203 else transition1204)))))) else (if n < 1231 then (if n < 1218 then (if n < 1211 then (if n < 1208 then (if n < 1206 then transition1205 else (if n < 1207 then transition1206 else transition1207)) else (if n < 1209 then transition1208 else (if n < 1210 then transition1209 else transition1210))) else (if n < 1214 then (if n < 1212 then transition1211 else (if n < 1213 then transition1212 else transition1213)) else (if n < 1216 then (if n < 1215 then transition1214 else transition1215) else (if n < 1217 then transition1216 else transition1217)))) else (if n < 1224 then (if n < 1221 then (if n < 1219 then transition1218 else (if n < 1220 then transition1219 else transition1220)) else (if n < 1222 then transition1221 else (if n < 1223 then transition1222 else transition1223))) else (if n < 1227 then (if n < 1225 then transition1224 else (if n < 1226 then transition1225 else transition1226)) else (if n < 1229 then (if n < 1228 then transition1227 else transition1228) else (if n < 1230 then transition1229 else transition1230))))) else (if n < 1244 then (if n < 1237 then (if n < 1234 then (if n < 1232 then transition1231 else (if n < 1233 then transition1232 else transition1233)) else (if n < 1235 then transition1234 else (if n < 1236 then transition1235 else transition1236))) else (if n < 1240 then (if n < 1238 then transition1237 else (if n < 1239 then transition1238 else transition1239)) else (if n < 1242 then (if n < 1241 then transition1240 else transition1241) else (if n < 1243 then transition1242 else transition1243)))) else (if n < 1251 then (if n < 1247 then (if n < 1245 then transition1244 else (if n < 1246 then transition1245 else transition1246)) else (if n < 1249 then (if n < 1248 then transition1247 else transition1248) else (if n < 1250 then transition1249 else transition1250))) else (if n < 1254 then (if n < 1252 then transition1251 else (if n < 1253 then transition1252 else transition1253)) else (if n < 1256 then (if n < 1255 then transition1254 else transition1255) else (if n < 1257 then transition1256 else transition1257))))))))) else (if n < 1468 then (if n < 1363 then (if n < 1310 then (if n < 1284 then (if n < 1271 then (if n < 1264 then (if n < 1261 then (if n < 1259 then transition1258 else (if n < 1260 then transition1259 else transition1260)) else (if n < 1262 then transition1261 else (if n < 1263 then transition1262 else transition1263))) else (if n < 1267 then (if n < 1265 then transition1264 else (if n < 1266 then transition1265 else transition1266)) else (if n < 1269 then (if n < 1268 then transition1267 else transition1268) else (if n < 1270 then transition1269 else transition1270)))) else (if n < 1277 then (if n < 1274 then (if n < 1272 then transition1271 else (if n < 1273 then transition1272 else transition1273)) else (if n < 1275 then transition1274 else (if n < 1276 then transition1275 else transition1276))) else (if n < 1280 then (if n < 1278 then transition1277 else (if n < 1279 then transition1278 else transition1279)) else (if n < 1282 then (if n < 1281 then transition1280 else transition1281) else (if n < 1283 then transition1282 else transition1283))))) else (if n < 1297 then (if n < 1290 then (if n < 1287 then (if n < 1285 then transition1284 else (if n < 1286 then transition1285 else transition1286)) else (if n < 1288 then transition1287 else (if n < 1289 then transition1288 else transition1289))) else (if n < 1293 then (if n < 1291 then transition1290 else (if n < 1292 then transition1291 else transition1292)) else (if n < 1295 then (if n < 1294 then transition1293 else transition1294) else (if n < 1296 then transition1295 else transition1296)))) else (if n < 1303 then (if n < 1300 then (if n < 1298 then transition1297 else (if n < 1299 then transition1298 else transition1299)) else (if n < 1301 then transition1300 else (if n < 1302 then transition1301 else transition1302))) else (if n < 1306 then (if n < 1304 then transition1303 else (if n < 1305 then transition1304 else transition1305)) else (if n < 1308 then (if n < 1307 then transition1306 else transition1307) else (if n < 1309 then transition1308 else transition1309)))))) else (if n < 1336 then (if n < 1323 then (if n < 1316 then (if n < 1313 then (if n < 1311 then transition1310 else (if n < 1312 then transition1311 else transition1312)) else (if n < 1314 then transition1313 else (if n < 1315 then transition1314 else transition1315))) else (if n < 1319 then (if n < 1317 then transition1316 else (if n < 1318 then transition1317 else transition1318)) else (if n < 1321 then (if n < 1320 then transition1319 else transition1320) else (if n < 1322 then transition1321 else transition1322)))) else (if n < 1329 then (if n < 1326 then (if n < 1324 then transition1323 else (if n < 1325 then transition1324 else transition1325)) else (if n < 1327 then transition1326 else (if n < 1328 then transition1327 else transition1328))) else (if n < 1332 then (if n < 1330 then transition1329 else (if n < 1331 then transition1330 else transition1331)) else (if n < 1334 then (if n < 1333 then transition1332 else transition1333) else (if n < 1335 then transition1334 else transition1335))))) else (if n < 1349 then (if n < 1342 then (if n < 1339 then (if n < 1337 then transition1336 else (if n < 1338 then transition1337 else transition1338)) else (if n < 1340 then transition1339 else (if n < 1341 then transition1340 else transition1341))) else (if n < 1345 then (if n < 1343 then transition1342 else (if n < 1344 then transition1343 else transition1344)) else (if n < 1347 then (if n < 1346 then transition1345 else transition1346) else (if n < 1348 then transition1347 else transition1348)))) else (if n < 1356 then (if n < 1352 then (if n < 1350 then transition1349 else (if n < 1351 then transition1350 else transition1351)) else (if n < 1354 then (if n < 1353 then transition1352 else transition1353) else (if n < 1355 then transition1354 else transition1355))) else (if n < 1359 then (if n < 1357 then transition1356 else (if n < 1358 then transition1357 else transition1358)) else (if n < 1361 then (if n < 1360 then transition1359 else transition1360) else (if n < 1362 then transition1361 else transition1362))))))) else (if n < 1415 then (if n < 1389 then (if n < 1376 then (if n < 1369 then (if n < 1366 then (if n < 1364 then transition1363 else (if n < 1365 then transition1364 else transition1365)) else (if n < 1367 then transition1366 else (if n < 1368 then transition1367 else transition1368))) else (if n < 1372 then (if n < 1370 then transition1369 else (if n < 1371 then transition1370 else transition1371)) else (if n < 1374 then (if n < 1373 then transition1372 else transition1373) else (if n < 1375 then transition1374 else transition1375)))) else (if n < 1382 then (if n < 1379 then (if n < 1377 then transition1376 else (if n < 1378 then transition1377 else transition1378)) else (if n < 1380 then transition1379 else (if n < 1381 then transition1380 else transition1381))) else (if n < 1385 then (if n < 1383 then transition1382 else (if n < 1384 then transition1383 else transition1384)) else (if n < 1387 then (if n < 1386 then transition1385 else transition1386) else (if n < 1388 then transition1387 else transition1388))))) else (if n < 1402 then (if n < 1395 then (if n < 1392 then (if n < 1390 then transition1389 else (if n < 1391 then transition1390 else transition1391)) else (if n < 1393 then transition1392 else (if n < 1394 then transition1393 else transition1394))) else (if n < 1398 then (if n < 1396 then transition1395 else (if n < 1397 then transition1396 else transition1397)) else (if n < 1400 then (if n < 1399 then transition1398 else transition1399) else (if n < 1401 then transition1400 else transition1401)))) else (if n < 1408 then (if n < 1405 then (if n < 1403 then transition1402 else (if n < 1404 then transition1403 else transition1404)) else (if n < 1406 then transition1405 else (if n < 1407 then transition1406 else transition1407))) else (if n < 1411 then (if n < 1409 then transition1408 else (if n < 1410 then transition1409 else transition1410)) else (if n < 1413 then (if n < 1412 then transition1411 else transition1412) else (if n < 1414 then transition1413 else transition1414)))))) else (if n < 1441 then (if n < 1428 then (if n < 1421 then (if n < 1418 then (if n < 1416 then transition1415 else (if n < 1417 then transition1416 else transition1417)) else (if n < 1419 then transition1418 else (if n < 1420 then transition1419 else transition1420))) else (if n < 1424 then (if n < 1422 then transition1421 else (if n < 1423 then transition1422 else transition1423)) else (if n < 1426 then (if n < 1425 then transition1424 else transition1425) else (if n < 1427 then transition1426 else transition1427)))) else (if n < 1434 then (if n < 1431 then (if n < 1429 then transition1428 else (if n < 1430 then transition1429 else transition1430)) else (if n < 1432 then transition1431 else (if n < 1433 then transition1432 else transition1433))) else (if n < 1437 then (if n < 1435 then transition1434 else (if n < 1436 then transition1435 else transition1436)) else (if n < 1439 then (if n < 1438 then transition1437 else transition1438) else (if n < 1440 then transition1439 else transition1440))))) else (if n < 1454 then (if n < 1447 then (if n < 1444 then (if n < 1442 then transition1441 else (if n < 1443 then transition1442 else transition1443)) else (if n < 1445 then transition1444 else (if n < 1446 then transition1445 else transition1446))) else (if n < 1450 then (if n < 1448 then transition1447 else (if n < 1449 then transition1448 else transition1449)) else (if n < 1452 then (if n < 1451 then transition1450 else transition1451) else (if n < 1453 then transition1452 else transition1453)))) else (if n < 1461 then (if n < 1457 then (if n < 1455 then transition1454 else (if n < 1456 then transition1455 else transition1456)) else (if n < 1459 then (if n < 1458 then transition1457 else transition1458) else (if n < 1460 then transition1459 else transition1460))) else (if n < 1464 then (if n < 1462 then transition1461 else (if n < 1463 then transition1462 else transition1463)) else (if n < 1466 then (if n < 1465 then transition1464 else transition1465) else (if n < 1467 then transition1466 else transition1467)))))))) else (if n < 1573 then (if n < 1520 then (if n < 1494 then (if n < 1481 then (if n < 1474 then (if n < 1471 then (if n < 1469 then transition1468 else (if n < 1470 then transition1469 else transition1470)) else (if n < 1472 then transition1471 else (if n < 1473 then transition1472 else transition1473))) else (if n < 1477 then (if n < 1475 then transition1474 else (if n < 1476 then transition1475 else transition1476)) else (if n < 1479 then (if n < 1478 then transition1477 else transition1478) else (if n < 1480 then transition1479 else transition1480)))) else (if n < 1487 then (if n < 1484 then (if n < 1482 then transition1481 else (if n < 1483 then transition1482 else transition1483)) else (if n < 1485 then transition1484 else (if n < 1486 then transition1485 else transition1486))) else (if n < 1490 then (if n < 1488 then transition1487 else (if n < 1489 then transition1488 else transition1489)) else (if n < 1492 then (if n < 1491 then transition1490 else transition1491) else (if n < 1493 then transition1492 else transition1493))))) else (if n < 1507 then (if n < 1500 then (if n < 1497 then (if n < 1495 then transition1494 else (if n < 1496 then transition1495 else transition1496)) else (if n < 1498 then transition1497 else (if n < 1499 then transition1498 else transition1499))) else (if n < 1503 then (if n < 1501 then transition1500 else (if n < 1502 then transition1501 else transition1502)) else (if n < 1505 then (if n < 1504 then transition1503 else transition1504) else (if n < 1506 then transition1505 else transition1506)))) else (if n < 1513 then (if n < 1510 then (if n < 1508 then transition1507 else (if n < 1509 then transition1508 else transition1509)) else (if n < 1511 then transition1510 else (if n < 1512 then transition1511 else transition1512))) else (if n < 1516 then (if n < 1514 then transition1513 else (if n < 1515 then transition1514 else transition1515)) else (if n < 1518 then (if n < 1517 then transition1516 else transition1517) else (if n < 1519 then transition1518 else transition1519)))))) else (if n < 1546 then (if n < 1533 then (if n < 1526 then (if n < 1523 then (if n < 1521 then transition1520 else (if n < 1522 then transition1521 else transition1522)) else (if n < 1524 then transition1523 else (if n < 1525 then transition1524 else transition1525))) else (if n < 1529 then (if n < 1527 then transition1526 else (if n < 1528 then transition1527 else transition1528)) else (if n < 1531 then (if n < 1530 then transition1529 else transition1530) else (if n < 1532 then transition1531 else transition1532)))) else (if n < 1539 then (if n < 1536 then (if n < 1534 then transition1533 else (if n < 1535 then transition1534 else transition1535)) else (if n < 1537 then transition1536 else (if n < 1538 then transition1537 else transition1538))) else (if n < 1542 then (if n < 1540 then transition1539 else (if n < 1541 then transition1540 else transition1541)) else (if n < 1544 then (if n < 1543 then transition1542 else transition1543) else (if n < 1545 then transition1544 else transition1545))))) else (if n < 1559 then (if n < 1552 then (if n < 1549 then (if n < 1547 then transition1546 else (if n < 1548 then transition1547 else transition1548)) else (if n < 1550 then transition1549 else (if n < 1551 then transition1550 else transition1551))) else (if n < 1555 then (if n < 1553 then transition1552 else (if n < 1554 then transition1553 else transition1554)) else (if n < 1557 then (if n < 1556 then transition1555 else transition1556) else (if n < 1558 then transition1557 else transition1558)))) else (if n < 1566 then (if n < 1562 then (if n < 1560 then transition1559 else (if n < 1561 then transition1560 else transition1561)) else (if n < 1564 then (if n < 1563 then transition1562 else transition1563) else (if n < 1565 then transition1564 else transition1565))) else (if n < 1569 then (if n < 1567 then transition1566 else (if n < 1568 then transition1567 else transition1568)) else (if n < 1571 then (if n < 1570 then transition1569 else transition1570) else (if n < 1572 then transition1571 else transition1572))))))) else (if n < 1625 then (if n < 1599 then (if n < 1586 then (if n < 1579 then (if n < 1576 then (if n < 1574 then transition1573 else (if n < 1575 then transition1574 else transition1575)) else (if n < 1577 then transition1576 else (if n < 1578 then transition1577 else transition1578))) else (if n < 1582 then (if n < 1580 then transition1579 else (if n < 1581 then transition1580 else transition1581)) else (if n < 1584 then (if n < 1583 then transition1582 else transition1583) else (if n < 1585 then transition1584 else transition1585)))) else (if n < 1592 then (if n < 1589 then (if n < 1587 then transition1586 else (if n < 1588 then transition1587 else transition1588)) else (if n < 1590 then transition1589 else (if n < 1591 then transition1590 else transition1591))) else (if n < 1595 then (if n < 1593 then transition1592 else (if n < 1594 then transition1593 else transition1594)) else (if n < 1597 then (if n < 1596 then transition1595 else transition1596) else (if n < 1598 then transition1597 else transition1598))))) else (if n < 1612 then (if n < 1605 then (if n < 1602 then (if n < 1600 then transition1599 else (if n < 1601 then transition1600 else transition1601)) else (if n < 1603 then transition1602 else (if n < 1604 then transition1603 else transition1604))) else (if n < 1608 then (if n < 1606 then transition1605 else (if n < 1607 then transition1606 else transition1607)) else (if n < 1610 then (if n < 1609 then transition1608 else transition1609) else (if n < 1611 then transition1610 else transition1611)))) else (if n < 1618 then (if n < 1615 then (if n < 1613 then transition1612 else (if n < 1614 then transition1613 else transition1614)) else (if n < 1616 then transition1615 else (if n < 1617 then transition1616 else transition1617))) else (if n < 1621 then (if n < 1619 then transition1618 else (if n < 1620 then transition1619 else transition1620)) else (if n < 1623 then (if n < 1622 then transition1621 else transition1622) else (if n < 1624 then transition1623 else transition1624)))))) else (if n < 1651 then (if n < 1638 then (if n < 1631 then (if n < 1628 then (if n < 1626 then transition1625 else (if n < 1627 then transition1626 else transition1627)) else (if n < 1629 then transition1628 else (if n < 1630 then transition1629 else transition1630))) else (if n < 1634 then (if n < 1632 then transition1631 else (if n < 1633 then transition1632 else transition1633)) else (if n < 1636 then (if n < 1635 then transition1634 else transition1635) else (if n < 1637 then transition1636 else transition1637)))) else (if n < 1644 then (if n < 1641 then (if n < 1639 then transition1638 else (if n < 1640 then transition1639 else transition1640)) else (if n < 1642 then transition1641 else (if n < 1643 then transition1642 else transition1643))) else (if n < 1647 then (if n < 1645 then transition1644 else (if n < 1646 then transition1645 else transition1646)) else (if n < 1649 then (if n < 1648 then transition1647 else transition1648) else (if n < 1650 then transition1649 else transition1650))))) else (if n < 1664 then (if n < 1657 then (if n < 1654 then (if n < 1652 then transition1651 else (if n < 1653 then transition1652 else transition1653)) else (if n < 1655 then transition1654 else (if n < 1656 then transition1655 else transition1656))) else (if n < 1660 then (if n < 1658 then transition1657 else (if n < 1659 then transition1658 else transition1659)) else (if n < 1662 then (if n < 1661 then transition1660 else transition1661) else (if n < 1663 then transition1662 else transition1663)))) else (if n < 1671 then (if n < 1667 then (if n < 1665 then transition1664 else (if n < 1666 then transition1665 else transition1666)) else (if n < 1669 then (if n < 1668 then transition1667 else transition1668) else (if n < 1670 then transition1669 else transition1670))) else (if n < 1674 then (if n < 1672 then transition1671 else (if n < 1673 then transition1672 else transition1673)) else (if n < 1676 then (if n < 1675 then transition1674 else transition1675) else (if n < 1677 then transition1676 else transition1677))))))))))) else (if n < 2517 then (if n < 2097 then (if n < 1887 then (if n < 1782 then (if n < 1730 then (if n < 1704 then (if n < 1691 then (if n < 1684 then (if n < 1681 then (if n < 1679 then transition1678 else (if n < 1680 then transition1679 else transition1680)) else (if n < 1682 then transition1681 else (if n < 1683 then transition1682 else transition1683))) else (if n < 1687 then (if n < 1685 then transition1684 else (if n < 1686 then transition1685 else transition1686)) else (if n < 1689 then (if n < 1688 then transition1687 else transition1688) else (if n < 1690 then transition1689 else transition1690)))) else (if n < 1697 then (if n < 1694 then (if n < 1692 then transition1691 else (if n < 1693 then transition1692 else transition1693)) else (if n < 1695 then transition1694 else (if n < 1696 then transition1695 else transition1696))) else (if n < 1700 then (if n < 1698 then transition1697 else (if n < 1699 then transition1698 else transition1699)) else (if n < 1702 then (if n < 1701 then transition1700 else transition1701) else (if n < 1703 then transition1702 else transition1703))))) else (if n < 1717 then (if n < 1710 then (if n < 1707 then (if n < 1705 then transition1704 else (if n < 1706 then transition1705 else transition1706)) else (if n < 1708 then transition1707 else (if n < 1709 then transition1708 else transition1709))) else (if n < 1713 then (if n < 1711 then transition1710 else (if n < 1712 then transition1711 else transition1712)) else (if n < 1715 then (if n < 1714 then transition1713 else transition1714) else (if n < 1716 then transition1715 else transition1716)))) else (if n < 1723 then (if n < 1720 then (if n < 1718 then transition1717 else (if n < 1719 then transition1718 else transition1719)) else (if n < 1721 then transition1720 else (if n < 1722 then transition1721 else transition1722))) else (if n < 1726 then (if n < 1724 then transition1723 else (if n < 1725 then transition1724 else transition1725)) else (if n < 1728 then (if n < 1727 then transition1726 else transition1727) else (if n < 1729 then transition1728 else transition1729)))))) else (if n < 1756 then (if n < 1743 then (if n < 1736 then (if n < 1733 then (if n < 1731 then transition1730 else (if n < 1732 then transition1731 else transition1732)) else (if n < 1734 then transition1733 else (if n < 1735 then transition1734 else transition1735))) else (if n < 1739 then (if n < 1737 then transition1736 else (if n < 1738 then transition1737 else transition1738)) else (if n < 1741 then (if n < 1740 then transition1739 else transition1740) else (if n < 1742 then transition1741 else transition1742)))) else (if n < 1749 then (if n < 1746 then (if n < 1744 then transition1743 else (if n < 1745 then transition1744 else transition1745)) else (if n < 1747 then transition1746 else (if n < 1748 then transition1747 else transition1748))) else (if n < 1752 then (if n < 1750 then transition1749 else (if n < 1751 then transition1750 else transition1751)) else (if n < 1754 then (if n < 1753 then transition1752 else transition1753) else (if n < 1755 then transition1754 else transition1755))))) else (if n < 1769 then (if n < 1762 then (if n < 1759 then (if n < 1757 then transition1756 else (if n < 1758 then transition1757 else transition1758)) else (if n < 1760 then transition1759 else (if n < 1761 then transition1760 else transition1761))) else (if n < 1765 then (if n < 1763 then transition1762 else (if n < 1764 then transition1763 else transition1764)) else (if n < 1767 then (if n < 1766 then transition1765 else transition1766) else (if n < 1768 then transition1767 else transition1768)))) else (if n < 1775 then (if n < 1772 then (if n < 1770 then transition1769 else (if n < 1771 then transition1770 else transition1771)) else (if n < 1773 then transition1772 else (if n < 1774 then transition1773 else transition1774))) else (if n < 1778 then (if n < 1776 then transition1775 else (if n < 1777 then transition1776 else transition1777)) else (if n < 1780 then (if n < 1779 then transition1778 else transition1779) else (if n < 1781 then transition1780 else transition1781))))))) else (if n < 1834 then (if n < 1808 then (if n < 1795 then (if n < 1788 then (if n < 1785 then (if n < 1783 then transition1782 else (if n < 1784 then transition1783 else transition1784)) else (if n < 1786 then transition1785 else (if n < 1787 then transition1786 else transition1787))) else (if n < 1791 then (if n < 1789 then transition1788 else (if n < 1790 then transition1789 else transition1790)) else (if n < 1793 then (if n < 1792 then transition1791 else transition1792) else (if n < 1794 then transition1793 else transition1794)))) else (if n < 1801 then (if n < 1798 then (if n < 1796 then transition1795 else (if n < 1797 then transition1796 else transition1797)) else (if n < 1799 then transition1798 else (if n < 1800 then transition1799 else transition1800))) else (if n < 1804 then (if n < 1802 then transition1801 else (if n < 1803 then transition1802 else transition1803)) else (if n < 1806 then (if n < 1805 then transition1804 else transition1805) else (if n < 1807 then transition1806 else transition1807))))) else (if n < 1821 then (if n < 1814 then (if n < 1811 then (if n < 1809 then transition1808 else (if n < 1810 then transition1809 else transition1810)) else (if n < 1812 then transition1811 else (if n < 1813 then transition1812 else transition1813))) else (if n < 1817 then (if n < 1815 then transition1814 else (if n < 1816 then transition1815 else transition1816)) else (if n < 1819 then (if n < 1818 then transition1817 else transition1818) else (if n < 1820 then transition1819 else transition1820)))) else (if n < 1827 then (if n < 1824 then (if n < 1822 then transition1821 else (if n < 1823 then transition1822 else transition1823)) else (if n < 1825 then transition1824 else (if n < 1826 then transition1825 else transition1826))) else (if n < 1830 then (if n < 1828 then transition1827 else (if n < 1829 then transition1828 else transition1829)) else (if n < 1832 then (if n < 1831 then transition1830 else transition1831) else (if n < 1833 then transition1832 else transition1833)))))) else (if n < 1860 then (if n < 1847 then (if n < 1840 then (if n < 1837 then (if n < 1835 then transition1834 else (if n < 1836 then transition1835 else transition1836)) else (if n < 1838 then transition1837 else (if n < 1839 then transition1838 else transition1839))) else (if n < 1843 then (if n < 1841 then transition1840 else (if n < 1842 then transition1841 else transition1842)) else (if n < 1845 then (if n < 1844 then transition1843 else transition1844) else (if n < 1846 then transition1845 else transition1846)))) else (if n < 1853 then (if n < 1850 then (if n < 1848 then transition1847 else (if n < 1849 then transition1848 else transition1849)) else (if n < 1851 then transition1850 else (if n < 1852 then transition1851 else transition1852))) else (if n < 1856 then (if n < 1854 then transition1853 else (if n < 1855 then transition1854 else transition1855)) else (if n < 1858 then (if n < 1857 then transition1856 else transition1857) else (if n < 1859 then transition1858 else transition1859))))) else (if n < 1873 then (if n < 1866 then (if n < 1863 then (if n < 1861 then transition1860 else (if n < 1862 then transition1861 else transition1862)) else (if n < 1864 then transition1863 else (if n < 1865 then transition1864 else transition1865))) else (if n < 1869 then (if n < 1867 then transition1866 else (if n < 1868 then transition1867 else transition1868)) else (if n < 1871 then (if n < 1870 then transition1869 else transition1870) else (if n < 1872 then transition1871 else transition1872)))) else (if n < 1880 then (if n < 1876 then (if n < 1874 then transition1873 else (if n < 1875 then transition1874 else transition1875)) else (if n < 1878 then (if n < 1877 then transition1876 else transition1877) else (if n < 1879 then transition1878 else transition1879))) else (if n < 1883 then (if n < 1881 then transition1880 else (if n < 1882 then transition1881 else transition1882)) else (if n < 1885 then (if n < 1884 then transition1883 else transition1884) else (if n < 1886 then transition1885 else transition1886)))))))) else (if n < 1992 then (if n < 1939 then (if n < 1913 then (if n < 1900 then (if n < 1893 then (if n < 1890 then (if n < 1888 then transition1887 else (if n < 1889 then transition1888 else transition1889)) else (if n < 1891 then transition1890 else (if n < 1892 then transition1891 else transition1892))) else (if n < 1896 then (if n < 1894 then transition1893 else (if n < 1895 then transition1894 else transition1895)) else (if n < 1898 then (if n < 1897 then transition1896 else transition1897) else (if n < 1899 then transition1898 else transition1899)))) else (if n < 1906 then (if n < 1903 then (if n < 1901 then transition1900 else (if n < 1902 then transition1901 else transition1902)) else (if n < 1904 then transition1903 else (if n < 1905 then transition1904 else transition1905))) else (if n < 1909 then (if n < 1907 then transition1906 else (if n < 1908 then transition1907 else transition1908)) else (if n < 1911 then (if n < 1910 then transition1909 else transition1910) else (if n < 1912 then transition1911 else transition1912))))) else (if n < 1926 then (if n < 1919 then (if n < 1916 then (if n < 1914 then transition1913 else (if n < 1915 then transition1914 else transition1915)) else (if n < 1917 then transition1916 else (if n < 1918 then transition1917 else transition1918))) else (if n < 1922 then (if n < 1920 then transition1919 else (if n < 1921 then transition1920 else transition1921)) else (if n < 1924 then (if n < 1923 then transition1922 else transition1923) else (if n < 1925 then transition1924 else transition1925)))) else (if n < 1932 then (if n < 1929 then (if n < 1927 then transition1926 else (if n < 1928 then transition1927 else transition1928)) else (if n < 1930 then transition1929 else (if n < 1931 then transition1930 else transition1931))) else (if n < 1935 then (if n < 1933 then transition1932 else (if n < 1934 then transition1933 else transition1934)) else (if n < 1937 then (if n < 1936 then transition1935 else transition1936) else (if n < 1938 then transition1937 else transition1938)))))) else (if n < 1965 then (if n < 1952 then (if n < 1945 then (if n < 1942 then (if n < 1940 then transition1939 else (if n < 1941 then transition1940 else transition1941)) else (if n < 1943 then transition1942 else (if n < 1944 then transition1943 else transition1944))) else (if n < 1948 then (if n < 1946 then transition1945 else (if n < 1947 then transition1946 else transition1947)) else (if n < 1950 then (if n < 1949 then transition1948 else transition1949) else (if n < 1951 then transition1950 else transition1951)))) else (if n < 1958 then (if n < 1955 then (if n < 1953 then transition1952 else (if n < 1954 then transition1953 else transition1954)) else (if n < 1956 then transition1955 else (if n < 1957 then transition1956 else transition1957))) else (if n < 1961 then (if n < 1959 then transition1958 else (if n < 1960 then transition1959 else transition1960)) else (if n < 1963 then (if n < 1962 then transition1961 else transition1962) else (if n < 1964 then transition1963 else transition1964))))) else (if n < 1978 then (if n < 1971 then (if n < 1968 then (if n < 1966 then transition1965 else (if n < 1967 then transition1966 else transition1967)) else (if n < 1969 then transition1968 else (if n < 1970 then transition1969 else transition1970))) else (if n < 1974 then (if n < 1972 then transition1971 else (if n < 1973 then transition1972 else transition1973)) else (if n < 1976 then (if n < 1975 then transition1974 else transition1975) else (if n < 1977 then transition1976 else transition1977)))) else (if n < 1985 then (if n < 1981 then (if n < 1979 then transition1978 else (if n < 1980 then transition1979 else transition1980)) else (if n < 1983 then (if n < 1982 then transition1981 else transition1982) else (if n < 1984 then transition1983 else transition1984))) else (if n < 1988 then (if n < 1986 then transition1985 else (if n < 1987 then transition1986 else transition1987)) else (if n < 1990 then (if n < 1989 then transition1988 else transition1989) else (if n < 1991 then transition1990 else transition1991))))))) else (if n < 2044 then (if n < 2018 then (if n < 2005 then (if n < 1998 then (if n < 1995 then (if n < 1993 then transition1992 else (if n < 1994 then transition1993 else transition1994)) else (if n < 1996 then transition1995 else (if n < 1997 then transition1996 else transition1997))) else (if n < 2001 then (if n < 1999 then transition1998 else (if n < 2000 then transition1999 else transition2000)) else (if n < 2003 then (if n < 2002 then transition2001 else transition2002) else (if n < 2004 then transition2003 else transition2004)))) else (if n < 2011 then (if n < 2008 then (if n < 2006 then transition2005 else (if n < 2007 then transition2006 else transition2007)) else (if n < 2009 then transition2008 else (if n < 2010 then transition2009 else transition2010))) else (if n < 2014 then (if n < 2012 then transition2011 else (if n < 2013 then transition2012 else transition2013)) else (if n < 2016 then (if n < 2015 then transition2014 else transition2015) else (if n < 2017 then transition2016 else transition2017))))) else (if n < 2031 then (if n < 2024 then (if n < 2021 then (if n < 2019 then transition2018 else (if n < 2020 then transition2019 else transition2020)) else (if n < 2022 then transition2021 else (if n < 2023 then transition2022 else transition2023))) else (if n < 2027 then (if n < 2025 then transition2024 else (if n < 2026 then transition2025 else transition2026)) else (if n < 2029 then (if n < 2028 then transition2027 else transition2028) else (if n < 2030 then transition2029 else transition2030)))) else (if n < 2037 then (if n < 2034 then (if n < 2032 then transition2031 else (if n < 2033 then transition2032 else transition2033)) else (if n < 2035 then transition2034 else (if n < 2036 then transition2035 else transition2036))) else (if n < 2040 then (if n < 2038 then transition2037 else (if n < 2039 then transition2038 else transition2039)) else (if n < 2042 then (if n < 2041 then transition2040 else transition2041) else (if n < 2043 then transition2042 else transition2043)))))) else (if n < 2070 then (if n < 2057 then (if n < 2050 then (if n < 2047 then (if n < 2045 then transition2044 else (if n < 2046 then transition2045 else transition2046)) else (if n < 2048 then transition2047 else (if n < 2049 then transition2048 else transition2049))) else (if n < 2053 then (if n < 2051 then transition2050 else (if n < 2052 then transition2051 else transition2052)) else (if n < 2055 then (if n < 2054 then transition2053 else transition2054) else (if n < 2056 then transition2055 else transition2056)))) else (if n < 2063 then (if n < 2060 then (if n < 2058 then transition2057 else (if n < 2059 then transition2058 else transition2059)) else (if n < 2061 then transition2060 else (if n < 2062 then transition2061 else transition2062))) else (if n < 2066 then (if n < 2064 then transition2063 else (if n < 2065 then transition2064 else transition2065)) else (if n < 2068 then (if n < 2067 then transition2066 else transition2067) else (if n < 2069 then transition2068 else transition2069))))) else (if n < 2083 then (if n < 2076 then (if n < 2073 then (if n < 2071 then transition2070 else (if n < 2072 then transition2071 else transition2072)) else (if n < 2074 then transition2073 else (if n < 2075 then transition2074 else transition2075))) else (if n < 2079 then (if n < 2077 then transition2076 else (if n < 2078 then transition2077 else transition2078)) else (if n < 2081 then (if n < 2080 then transition2079 else transition2080) else (if n < 2082 then transition2081 else transition2082)))) else (if n < 2090 then (if n < 2086 then (if n < 2084 then transition2083 else (if n < 2085 then transition2084 else transition2085)) else (if n < 2088 then (if n < 2087 then transition2086 else transition2087) else (if n < 2089 then transition2088 else transition2089))) else (if n < 2093 then (if n < 2091 then transition2090 else (if n < 2092 then transition2091 else transition2092)) else (if n < 2095 then (if n < 2094 then transition2093 else transition2094) else (if n < 2096 then transition2095 else transition2096))))))))) else (if n < 2307 then (if n < 2202 then (if n < 2149 then (if n < 2123 then (if n < 2110 then (if n < 2103 then (if n < 2100 then (if n < 2098 then transition2097 else (if n < 2099 then transition2098 else transition2099)) else (if n < 2101 then transition2100 else (if n < 2102 then transition2101 else transition2102))) else (if n < 2106 then (if n < 2104 then transition2103 else (if n < 2105 then transition2104 else transition2105)) else (if n < 2108 then (if n < 2107 then transition2106 else transition2107) else (if n < 2109 then transition2108 else transition2109)))) else (if n < 2116 then (if n < 2113 then (if n < 2111 then transition2110 else (if n < 2112 then transition2111 else transition2112)) else (if n < 2114 then transition2113 else (if n < 2115 then transition2114 else transition2115))) else (if n < 2119 then (if n < 2117 then transition2116 else (if n < 2118 then transition2117 else transition2118)) else (if n < 2121 then (if n < 2120 then transition2119 else transition2120) else (if n < 2122 then transition2121 else transition2122))))) else (if n < 2136 then (if n < 2129 then (if n < 2126 then (if n < 2124 then transition2123 else (if n < 2125 then transition2124 else transition2125)) else (if n < 2127 then transition2126 else (if n < 2128 then transition2127 else transition2128))) else (if n < 2132 then (if n < 2130 then transition2129 else (if n < 2131 then transition2130 else transition2131)) else (if n < 2134 then (if n < 2133 then transition2132 else transition2133) else (if n < 2135 then transition2134 else transition2135)))) else (if n < 2142 then (if n < 2139 then (if n < 2137 then transition2136 else (if n < 2138 then transition2137 else transition2138)) else (if n < 2140 then transition2139 else (if n < 2141 then transition2140 else transition2141))) else (if n < 2145 then (if n < 2143 then transition2142 else (if n < 2144 then transition2143 else transition2144)) else (if n < 2147 then (if n < 2146 then transition2145 else transition2146) else (if n < 2148 then transition2147 else transition2148)))))) else (if n < 2175 then (if n < 2162 then (if n < 2155 then (if n < 2152 then (if n < 2150 then transition2149 else (if n < 2151 then transition2150 else transition2151)) else (if n < 2153 then transition2152 else (if n < 2154 then transition2153 else transition2154))) else (if n < 2158 then (if n < 2156 then transition2155 else (if n < 2157 then transition2156 else transition2157)) else (if n < 2160 then (if n < 2159 then transition2158 else transition2159) else (if n < 2161 then transition2160 else transition2161)))) else (if n < 2168 then (if n < 2165 then (if n < 2163 then transition2162 else (if n < 2164 then transition2163 else transition2164)) else (if n < 2166 then transition2165 else (if n < 2167 then transition2166 else transition2167))) else (if n < 2171 then (if n < 2169 then transition2168 else (if n < 2170 then transition2169 else transition2170)) else (if n < 2173 then (if n < 2172 then transition2171 else transition2172) else (if n < 2174 then transition2173 else transition2174))))) else (if n < 2188 then (if n < 2181 then (if n < 2178 then (if n < 2176 then transition2175 else (if n < 2177 then transition2176 else transition2177)) else (if n < 2179 then transition2178 else (if n < 2180 then transition2179 else transition2180))) else (if n < 2184 then (if n < 2182 then transition2181 else (if n < 2183 then transition2182 else transition2183)) else (if n < 2186 then (if n < 2185 then transition2184 else transition2185) else (if n < 2187 then transition2186 else transition2187)))) else (if n < 2195 then (if n < 2191 then (if n < 2189 then transition2188 else (if n < 2190 then transition2189 else transition2190)) else (if n < 2193 then (if n < 2192 then transition2191 else transition2192) else (if n < 2194 then transition2193 else transition2194))) else (if n < 2198 then (if n < 2196 then transition2195 else (if n < 2197 then transition2196 else transition2197)) else (if n < 2200 then (if n < 2199 then transition2198 else transition2199) else (if n < 2201 then transition2200 else transition2201))))))) else (if n < 2254 then (if n < 2228 then (if n < 2215 then (if n < 2208 then (if n < 2205 then (if n < 2203 then transition2202 else (if n < 2204 then transition2203 else transition2204)) else (if n < 2206 then transition2205 else (if n < 2207 then transition2206 else transition2207))) else (if n < 2211 then (if n < 2209 then transition2208 else (if n < 2210 then transition2209 else transition2210)) else (if n < 2213 then (if n < 2212 then transition2211 else transition2212) else (if n < 2214 then transition2213 else transition2214)))) else (if n < 2221 then (if n < 2218 then (if n < 2216 then transition2215 else (if n < 2217 then transition2216 else transition2217)) else (if n < 2219 then transition2218 else (if n < 2220 then transition2219 else transition2220))) else (if n < 2224 then (if n < 2222 then transition2221 else (if n < 2223 then transition2222 else transition2223)) else (if n < 2226 then (if n < 2225 then transition2224 else transition2225) else (if n < 2227 then transition2226 else transition2227))))) else (if n < 2241 then (if n < 2234 then (if n < 2231 then (if n < 2229 then transition2228 else (if n < 2230 then transition2229 else transition2230)) else (if n < 2232 then transition2231 else (if n < 2233 then transition2232 else transition2233))) else (if n < 2237 then (if n < 2235 then transition2234 else (if n < 2236 then transition2235 else transition2236)) else (if n < 2239 then (if n < 2238 then transition2237 else transition2238) else (if n < 2240 then transition2239 else transition2240)))) else (if n < 2247 then (if n < 2244 then (if n < 2242 then transition2241 else (if n < 2243 then transition2242 else transition2243)) else (if n < 2245 then transition2244 else (if n < 2246 then transition2245 else transition2246))) else (if n < 2250 then (if n < 2248 then transition2247 else (if n < 2249 then transition2248 else transition2249)) else (if n < 2252 then (if n < 2251 then transition2250 else transition2251) else (if n < 2253 then transition2252 else transition2253)))))) else (if n < 2280 then (if n < 2267 then (if n < 2260 then (if n < 2257 then (if n < 2255 then transition2254 else (if n < 2256 then transition2255 else transition2256)) else (if n < 2258 then transition2257 else (if n < 2259 then transition2258 else transition2259))) else (if n < 2263 then (if n < 2261 then transition2260 else (if n < 2262 then transition2261 else transition2262)) else (if n < 2265 then (if n < 2264 then transition2263 else transition2264) else (if n < 2266 then transition2265 else transition2266)))) else (if n < 2273 then (if n < 2270 then (if n < 2268 then transition2267 else (if n < 2269 then transition2268 else transition2269)) else (if n < 2271 then transition2270 else (if n < 2272 then transition2271 else transition2272))) else (if n < 2276 then (if n < 2274 then transition2273 else (if n < 2275 then transition2274 else transition2275)) else (if n < 2278 then (if n < 2277 then transition2276 else transition2277) else (if n < 2279 then transition2278 else transition2279))))) else (if n < 2293 then (if n < 2286 then (if n < 2283 then (if n < 2281 then transition2280 else (if n < 2282 then transition2281 else transition2282)) else (if n < 2284 then transition2283 else (if n < 2285 then transition2284 else transition2285))) else (if n < 2289 then (if n < 2287 then transition2286 else (if n < 2288 then transition2287 else transition2288)) else (if n < 2291 then (if n < 2290 then transition2289 else transition2290) else (if n < 2292 then transition2291 else transition2292)))) else (if n < 2300 then (if n < 2296 then (if n < 2294 then transition2293 else (if n < 2295 then transition2294 else transition2295)) else (if n < 2298 then (if n < 2297 then transition2296 else transition2297) else (if n < 2299 then transition2298 else transition2299))) else (if n < 2303 then (if n < 2301 then transition2300 else (if n < 2302 then transition2301 else transition2302)) else (if n < 2305 then (if n < 2304 then transition2303 else transition2304) else (if n < 2306 then transition2305 else transition2306)))))))) else (if n < 2412 then (if n < 2359 then (if n < 2333 then (if n < 2320 then (if n < 2313 then (if n < 2310 then (if n < 2308 then transition2307 else (if n < 2309 then transition2308 else transition2309)) else (if n < 2311 then transition2310 else (if n < 2312 then transition2311 else transition2312))) else (if n < 2316 then (if n < 2314 then transition2313 else (if n < 2315 then transition2314 else transition2315)) else (if n < 2318 then (if n < 2317 then transition2316 else transition2317) else (if n < 2319 then transition2318 else transition2319)))) else (if n < 2326 then (if n < 2323 then (if n < 2321 then transition2320 else (if n < 2322 then transition2321 else transition2322)) else (if n < 2324 then transition2323 else (if n < 2325 then transition2324 else transition2325))) else (if n < 2329 then (if n < 2327 then transition2326 else (if n < 2328 then transition2327 else transition2328)) else (if n < 2331 then (if n < 2330 then transition2329 else transition2330) else (if n < 2332 then transition2331 else transition2332))))) else (if n < 2346 then (if n < 2339 then (if n < 2336 then (if n < 2334 then transition2333 else (if n < 2335 then transition2334 else transition2335)) else (if n < 2337 then transition2336 else (if n < 2338 then transition2337 else transition2338))) else (if n < 2342 then (if n < 2340 then transition2339 else (if n < 2341 then transition2340 else transition2341)) else (if n < 2344 then (if n < 2343 then transition2342 else transition2343) else (if n < 2345 then transition2344 else transition2345)))) else (if n < 2352 then (if n < 2349 then (if n < 2347 then transition2346 else (if n < 2348 then transition2347 else transition2348)) else (if n < 2350 then transition2349 else (if n < 2351 then transition2350 else transition2351))) else (if n < 2355 then (if n < 2353 then transition2352 else (if n < 2354 then transition2353 else transition2354)) else (if n < 2357 then (if n < 2356 then transition2355 else transition2356) else (if n < 2358 then transition2357 else transition2358)))))) else (if n < 2385 then (if n < 2372 then (if n < 2365 then (if n < 2362 then (if n < 2360 then transition2359 else (if n < 2361 then transition2360 else transition2361)) else (if n < 2363 then transition2362 else (if n < 2364 then transition2363 else transition2364))) else (if n < 2368 then (if n < 2366 then transition2365 else (if n < 2367 then transition2366 else transition2367)) else (if n < 2370 then (if n < 2369 then transition2368 else transition2369) else (if n < 2371 then transition2370 else transition2371)))) else (if n < 2378 then (if n < 2375 then (if n < 2373 then transition2372 else (if n < 2374 then transition2373 else transition2374)) else (if n < 2376 then transition2375 else (if n < 2377 then transition2376 else transition2377))) else (if n < 2381 then (if n < 2379 then transition2378 else (if n < 2380 then transition2379 else transition2380)) else (if n < 2383 then (if n < 2382 then transition2381 else transition2382) else (if n < 2384 then transition2383 else transition2384))))) else (if n < 2398 then (if n < 2391 then (if n < 2388 then (if n < 2386 then transition2385 else (if n < 2387 then transition2386 else transition2387)) else (if n < 2389 then transition2388 else (if n < 2390 then transition2389 else transition2390))) else (if n < 2394 then (if n < 2392 then transition2391 else (if n < 2393 then transition2392 else transition2393)) else (if n < 2396 then (if n < 2395 then transition2394 else transition2395) else (if n < 2397 then transition2396 else transition2397)))) else (if n < 2405 then (if n < 2401 then (if n < 2399 then transition2398 else (if n < 2400 then transition2399 else transition2400)) else (if n < 2403 then (if n < 2402 then transition2401 else transition2402) else (if n < 2404 then transition2403 else transition2404))) else (if n < 2408 then (if n < 2406 then transition2405 else (if n < 2407 then transition2406 else transition2407)) else (if n < 2410 then (if n < 2409 then transition2408 else transition2409) else (if n < 2411 then transition2410 else transition2411))))))) else (if n < 2464 then (if n < 2438 then (if n < 2425 then (if n < 2418 then (if n < 2415 then (if n < 2413 then transition2412 else (if n < 2414 then transition2413 else transition2414)) else (if n < 2416 then transition2415 else (if n < 2417 then transition2416 else transition2417))) else (if n < 2421 then (if n < 2419 then transition2418 else (if n < 2420 then transition2419 else transition2420)) else (if n < 2423 then (if n < 2422 then transition2421 else transition2422) else (if n < 2424 then transition2423 else transition2424)))) else (if n < 2431 then (if n < 2428 then (if n < 2426 then transition2425 else (if n < 2427 then transition2426 else transition2427)) else (if n < 2429 then transition2428 else (if n < 2430 then transition2429 else transition2430))) else (if n < 2434 then (if n < 2432 then transition2431 else (if n < 2433 then transition2432 else transition2433)) else (if n < 2436 then (if n < 2435 then transition2434 else transition2435) else (if n < 2437 then transition2436 else transition2437))))) else (if n < 2451 then (if n < 2444 then (if n < 2441 then (if n < 2439 then transition2438 else (if n < 2440 then transition2439 else transition2440)) else (if n < 2442 then transition2441 else (if n < 2443 then transition2442 else transition2443))) else (if n < 2447 then (if n < 2445 then transition2444 else (if n < 2446 then transition2445 else transition2446)) else (if n < 2449 then (if n < 2448 then transition2447 else transition2448) else (if n < 2450 then transition2449 else transition2450)))) else (if n < 2457 then (if n < 2454 then (if n < 2452 then transition2451 else (if n < 2453 then transition2452 else transition2453)) else (if n < 2455 then transition2454 else (if n < 2456 then transition2455 else transition2456))) else (if n < 2460 then (if n < 2458 then transition2457 else (if n < 2459 then transition2458 else transition2459)) else (if n < 2462 then (if n < 2461 then transition2460 else transition2461) else (if n < 2463 then transition2462 else transition2463)))))) else (if n < 2490 then (if n < 2477 then (if n < 2470 then (if n < 2467 then (if n < 2465 then transition2464 else (if n < 2466 then transition2465 else transition2466)) else (if n < 2468 then transition2467 else (if n < 2469 then transition2468 else transition2469))) else (if n < 2473 then (if n < 2471 then transition2470 else (if n < 2472 then transition2471 else transition2472)) else (if n < 2475 then (if n < 2474 then transition2473 else transition2474) else (if n < 2476 then transition2475 else transition2476)))) else (if n < 2483 then (if n < 2480 then (if n < 2478 then transition2477 else (if n < 2479 then transition2478 else transition2479)) else (if n < 2481 then transition2480 else (if n < 2482 then transition2481 else transition2482))) else (if n < 2486 then (if n < 2484 then transition2483 else (if n < 2485 then transition2484 else transition2485)) else (if n < 2488 then (if n < 2487 then transition2486 else transition2487) else (if n < 2489 then transition2488 else transition2489))))) else (if n < 2503 then (if n < 2496 then (if n < 2493 then (if n < 2491 then transition2490 else (if n < 2492 then transition2491 else transition2492)) else (if n < 2494 then transition2493 else (if n < 2495 then transition2494 else transition2495))) else (if n < 2499 then (if n < 2497 then transition2496 else (if n < 2498 then transition2497 else transition2498)) else (if n < 2501 then (if n < 2500 then transition2499 else transition2500) else (if n < 2502 then transition2501 else transition2502)))) else (if n < 2510 then (if n < 2506 then (if n < 2504 then transition2503 else (if n < 2505 then transition2504 else transition2505)) else (if n < 2508 then (if n < 2507 then transition2506 else transition2507) else (if n < 2509 then transition2508 else transition2509))) else (if n < 2513 then (if n < 2511 then transition2510 else (if n < 2512 then transition2511 else transition2512)) else (if n < 2515 then (if n < 2514 then transition2513 else transition2514) else (if n < 2516 then transition2515 else transition2516)))))))))) else (if n < 2937 then (if n < 2727 then (if n < 2622 then (if n < 2569 then (if n < 2543 then (if n < 2530 then (if n < 2523 then (if n < 2520 then (if n < 2518 then transition2517 else (if n < 2519 then transition2518 else transition2519)) else (if n < 2521 then transition2520 else (if n < 2522 then transition2521 else transition2522))) else (if n < 2526 then (if n < 2524 then transition2523 else (if n < 2525 then transition2524 else transition2525)) else (if n < 2528 then (if n < 2527 then transition2526 else transition2527) else (if n < 2529 then transition2528 else transition2529)))) else (if n < 2536 then (if n < 2533 then (if n < 2531 then transition2530 else (if n < 2532 then transition2531 else transition2532)) else (if n < 2534 then transition2533 else (if n < 2535 then transition2534 else transition2535))) else (if n < 2539 then (if n < 2537 then transition2536 else (if n < 2538 then transition2537 else transition2538)) else (if n < 2541 then (if n < 2540 then transition2539 else transition2540) else (if n < 2542 then transition2541 else transition2542))))) else (if n < 2556 then (if n < 2549 then (if n < 2546 then (if n < 2544 then transition2543 else (if n < 2545 then transition2544 else transition2545)) else (if n < 2547 then transition2546 else (if n < 2548 then transition2547 else transition2548))) else (if n < 2552 then (if n < 2550 then transition2549 else (if n < 2551 then transition2550 else transition2551)) else (if n < 2554 then (if n < 2553 then transition2552 else transition2553) else (if n < 2555 then transition2554 else transition2555)))) else (if n < 2562 then (if n < 2559 then (if n < 2557 then transition2556 else (if n < 2558 then transition2557 else transition2558)) else (if n < 2560 then transition2559 else (if n < 2561 then transition2560 else transition2561))) else (if n < 2565 then (if n < 2563 then transition2562 else (if n < 2564 then transition2563 else transition2564)) else (if n < 2567 then (if n < 2566 then transition2565 else transition2566) else (if n < 2568 then transition2567 else transition2568)))))) else (if n < 2595 then (if n < 2582 then (if n < 2575 then (if n < 2572 then (if n < 2570 then transition2569 else (if n < 2571 then transition2570 else transition2571)) else (if n < 2573 then transition2572 else (if n < 2574 then transition2573 else transition2574))) else (if n < 2578 then (if n < 2576 then transition2575 else (if n < 2577 then transition2576 else transition2577)) else (if n < 2580 then (if n < 2579 then transition2578 else transition2579) else (if n < 2581 then transition2580 else transition2581)))) else (if n < 2588 then (if n < 2585 then (if n < 2583 then transition2582 else (if n < 2584 then transition2583 else transition2584)) else (if n < 2586 then transition2585 else (if n < 2587 then transition2586 else transition2587))) else (if n < 2591 then (if n < 2589 then transition2588 else (if n < 2590 then transition2589 else transition2590)) else (if n < 2593 then (if n < 2592 then transition2591 else transition2592) else (if n < 2594 then transition2593 else transition2594))))) else (if n < 2608 then (if n < 2601 then (if n < 2598 then (if n < 2596 then transition2595 else (if n < 2597 then transition2596 else transition2597)) else (if n < 2599 then transition2598 else (if n < 2600 then transition2599 else transition2600))) else (if n < 2604 then (if n < 2602 then transition2601 else (if n < 2603 then transition2602 else transition2603)) else (if n < 2606 then (if n < 2605 then transition2604 else transition2605) else (if n < 2607 then transition2606 else transition2607)))) else (if n < 2615 then (if n < 2611 then (if n < 2609 then transition2608 else (if n < 2610 then transition2609 else transition2610)) else (if n < 2613 then (if n < 2612 then transition2611 else transition2612) else (if n < 2614 then transition2613 else transition2614))) else (if n < 2618 then (if n < 2616 then transition2615 else (if n < 2617 then transition2616 else transition2617)) else (if n < 2620 then (if n < 2619 then transition2618 else transition2619) else (if n < 2621 then transition2620 else transition2621))))))) else (if n < 2674 then (if n < 2648 then (if n < 2635 then (if n < 2628 then (if n < 2625 then (if n < 2623 then transition2622 else (if n < 2624 then transition2623 else transition2624)) else (if n < 2626 then transition2625 else (if n < 2627 then transition2626 else transition2627))) else (if n < 2631 then (if n < 2629 then transition2628 else (if n < 2630 then transition2629 else transition2630)) else (if n < 2633 then (if n < 2632 then transition2631 else transition2632) else (if n < 2634 then transition2633 else transition2634)))) else (if n < 2641 then (if n < 2638 then (if n < 2636 then transition2635 else (if n < 2637 then transition2636 else transition2637)) else (if n < 2639 then transition2638 else (if n < 2640 then transition2639 else transition2640))) else (if n < 2644 then (if n < 2642 then transition2641 else (if n < 2643 then transition2642 else transition2643)) else (if n < 2646 then (if n < 2645 then transition2644 else transition2645) else (if n < 2647 then transition2646 else transition2647))))) else (if n < 2661 then (if n < 2654 then (if n < 2651 then (if n < 2649 then transition2648 else (if n < 2650 then transition2649 else transition2650)) else (if n < 2652 then transition2651 else (if n < 2653 then transition2652 else transition2653))) else (if n < 2657 then (if n < 2655 then transition2654 else (if n < 2656 then transition2655 else transition2656)) else (if n < 2659 then (if n < 2658 then transition2657 else transition2658) else (if n < 2660 then transition2659 else transition2660)))) else (if n < 2667 then (if n < 2664 then (if n < 2662 then transition2661 else (if n < 2663 then transition2662 else transition2663)) else (if n < 2665 then transition2664 else (if n < 2666 then transition2665 else transition2666))) else (if n < 2670 then (if n < 2668 then transition2667 else (if n < 2669 then transition2668 else transition2669)) else (if n < 2672 then (if n < 2671 then transition2670 else transition2671) else (if n < 2673 then transition2672 else transition2673)))))) else (if n < 2700 then (if n < 2687 then (if n < 2680 then (if n < 2677 then (if n < 2675 then transition2674 else (if n < 2676 then transition2675 else transition2676)) else (if n < 2678 then transition2677 else (if n < 2679 then transition2678 else transition2679))) else (if n < 2683 then (if n < 2681 then transition2680 else (if n < 2682 then transition2681 else transition2682)) else (if n < 2685 then (if n < 2684 then transition2683 else transition2684) else (if n < 2686 then transition2685 else transition2686)))) else (if n < 2693 then (if n < 2690 then (if n < 2688 then transition2687 else (if n < 2689 then transition2688 else transition2689)) else (if n < 2691 then transition2690 else (if n < 2692 then transition2691 else transition2692))) else (if n < 2696 then (if n < 2694 then transition2693 else (if n < 2695 then transition2694 else transition2695)) else (if n < 2698 then (if n < 2697 then transition2696 else transition2697) else (if n < 2699 then transition2698 else transition2699))))) else (if n < 2713 then (if n < 2706 then (if n < 2703 then (if n < 2701 then transition2700 else (if n < 2702 then transition2701 else transition2702)) else (if n < 2704 then transition2703 else (if n < 2705 then transition2704 else transition2705))) else (if n < 2709 then (if n < 2707 then transition2706 else (if n < 2708 then transition2707 else transition2708)) else (if n < 2711 then (if n < 2710 then transition2709 else transition2710) else (if n < 2712 then transition2711 else transition2712)))) else (if n < 2720 then (if n < 2716 then (if n < 2714 then transition2713 else (if n < 2715 then transition2714 else transition2715)) else (if n < 2718 then (if n < 2717 then transition2716 else transition2717) else (if n < 2719 then transition2718 else transition2719))) else (if n < 2723 then (if n < 2721 then transition2720 else (if n < 2722 then transition2721 else transition2722)) else (if n < 2725 then (if n < 2724 then transition2723 else transition2724) else (if n < 2726 then transition2725 else transition2726)))))))) else (if n < 2832 then (if n < 2779 then (if n < 2753 then (if n < 2740 then (if n < 2733 then (if n < 2730 then (if n < 2728 then transition2727 else (if n < 2729 then transition2728 else transition2729)) else (if n < 2731 then transition2730 else (if n < 2732 then transition2731 else transition2732))) else (if n < 2736 then (if n < 2734 then transition2733 else (if n < 2735 then transition2734 else transition2735)) else (if n < 2738 then (if n < 2737 then transition2736 else transition2737) else (if n < 2739 then transition2738 else transition2739)))) else (if n < 2746 then (if n < 2743 then (if n < 2741 then transition2740 else (if n < 2742 then transition2741 else transition2742)) else (if n < 2744 then transition2743 else (if n < 2745 then transition2744 else transition2745))) else (if n < 2749 then (if n < 2747 then transition2746 else (if n < 2748 then transition2747 else transition2748)) else (if n < 2751 then (if n < 2750 then transition2749 else transition2750) else (if n < 2752 then transition2751 else transition2752))))) else (if n < 2766 then (if n < 2759 then (if n < 2756 then (if n < 2754 then transition2753 else (if n < 2755 then transition2754 else transition2755)) else (if n < 2757 then transition2756 else (if n < 2758 then transition2757 else transition2758))) else (if n < 2762 then (if n < 2760 then transition2759 else (if n < 2761 then transition2760 else transition2761)) else (if n < 2764 then (if n < 2763 then transition2762 else transition2763) else (if n < 2765 then transition2764 else transition2765)))) else (if n < 2772 then (if n < 2769 then (if n < 2767 then transition2766 else (if n < 2768 then transition2767 else transition2768)) else (if n < 2770 then transition2769 else (if n < 2771 then transition2770 else transition2771))) else (if n < 2775 then (if n < 2773 then transition2772 else (if n < 2774 then transition2773 else transition2774)) else (if n < 2777 then (if n < 2776 then transition2775 else transition2776) else (if n < 2778 then transition2777 else transition2778)))))) else (if n < 2805 then (if n < 2792 then (if n < 2785 then (if n < 2782 then (if n < 2780 then transition2779 else (if n < 2781 then transition2780 else transition2781)) else (if n < 2783 then transition2782 else (if n < 2784 then transition2783 else transition2784))) else (if n < 2788 then (if n < 2786 then transition2785 else (if n < 2787 then transition2786 else transition2787)) else (if n < 2790 then (if n < 2789 then transition2788 else transition2789) else (if n < 2791 then transition2790 else transition2791)))) else (if n < 2798 then (if n < 2795 then (if n < 2793 then transition2792 else (if n < 2794 then transition2793 else transition2794)) else (if n < 2796 then transition2795 else (if n < 2797 then transition2796 else transition2797))) else (if n < 2801 then (if n < 2799 then transition2798 else (if n < 2800 then transition2799 else transition2800)) else (if n < 2803 then (if n < 2802 then transition2801 else transition2802) else (if n < 2804 then transition2803 else transition2804))))) else (if n < 2818 then (if n < 2811 then (if n < 2808 then (if n < 2806 then transition2805 else (if n < 2807 then transition2806 else transition2807)) else (if n < 2809 then transition2808 else (if n < 2810 then transition2809 else transition2810))) else (if n < 2814 then (if n < 2812 then transition2811 else (if n < 2813 then transition2812 else transition2813)) else (if n < 2816 then (if n < 2815 then transition2814 else transition2815) else (if n < 2817 then transition2816 else transition2817)))) else (if n < 2825 then (if n < 2821 then (if n < 2819 then transition2818 else (if n < 2820 then transition2819 else transition2820)) else (if n < 2823 then (if n < 2822 then transition2821 else transition2822) else (if n < 2824 then transition2823 else transition2824))) else (if n < 2828 then (if n < 2826 then transition2825 else (if n < 2827 then transition2826 else transition2827)) else (if n < 2830 then (if n < 2829 then transition2828 else transition2829) else (if n < 2831 then transition2830 else transition2831))))))) else (if n < 2884 then (if n < 2858 then (if n < 2845 then (if n < 2838 then (if n < 2835 then (if n < 2833 then transition2832 else (if n < 2834 then transition2833 else transition2834)) else (if n < 2836 then transition2835 else (if n < 2837 then transition2836 else transition2837))) else (if n < 2841 then (if n < 2839 then transition2838 else (if n < 2840 then transition2839 else transition2840)) else (if n < 2843 then (if n < 2842 then transition2841 else transition2842) else (if n < 2844 then transition2843 else transition2844)))) else (if n < 2851 then (if n < 2848 then (if n < 2846 then transition2845 else (if n < 2847 then transition2846 else transition2847)) else (if n < 2849 then transition2848 else (if n < 2850 then transition2849 else transition2850))) else (if n < 2854 then (if n < 2852 then transition2851 else (if n < 2853 then transition2852 else transition2853)) else (if n < 2856 then (if n < 2855 then transition2854 else transition2855) else (if n < 2857 then transition2856 else transition2857))))) else (if n < 2871 then (if n < 2864 then (if n < 2861 then (if n < 2859 then transition2858 else (if n < 2860 then transition2859 else transition2860)) else (if n < 2862 then transition2861 else (if n < 2863 then transition2862 else transition2863))) else (if n < 2867 then (if n < 2865 then transition2864 else (if n < 2866 then transition2865 else transition2866)) else (if n < 2869 then (if n < 2868 then transition2867 else transition2868) else (if n < 2870 then transition2869 else transition2870)))) else (if n < 2877 then (if n < 2874 then (if n < 2872 then transition2871 else (if n < 2873 then transition2872 else transition2873)) else (if n < 2875 then transition2874 else (if n < 2876 then transition2875 else transition2876))) else (if n < 2880 then (if n < 2878 then transition2877 else (if n < 2879 then transition2878 else transition2879)) else (if n < 2882 then (if n < 2881 then transition2880 else transition2881) else (if n < 2883 then transition2882 else transition2883)))))) else (if n < 2910 then (if n < 2897 then (if n < 2890 then (if n < 2887 then (if n < 2885 then transition2884 else (if n < 2886 then transition2885 else transition2886)) else (if n < 2888 then transition2887 else (if n < 2889 then transition2888 else transition2889))) else (if n < 2893 then (if n < 2891 then transition2890 else (if n < 2892 then transition2891 else transition2892)) else (if n < 2895 then (if n < 2894 then transition2893 else transition2894) else (if n < 2896 then transition2895 else transition2896)))) else (if n < 2903 then (if n < 2900 then (if n < 2898 then transition2897 else (if n < 2899 then transition2898 else transition2899)) else (if n < 2901 then transition2900 else (if n < 2902 then transition2901 else transition2902))) else (if n < 2906 then (if n < 2904 then transition2903 else (if n < 2905 then transition2904 else transition2905)) else (if n < 2908 then (if n < 2907 then transition2906 else transition2907) else (if n < 2909 then transition2908 else transition2909))))) else (if n < 2923 then (if n < 2916 then (if n < 2913 then (if n < 2911 then transition2910 else (if n < 2912 then transition2911 else transition2912)) else (if n < 2914 then transition2913 else (if n < 2915 then transition2914 else transition2915))) else (if n < 2919 then (if n < 2917 then transition2916 else (if n < 2918 then transition2917 else transition2918)) else (if n < 2921 then (if n < 2920 then transition2919 else transition2920) else (if n < 2922 then transition2921 else transition2922)))) else (if n < 2930 then (if n < 2926 then (if n < 2924 then transition2923 else (if n < 2925 then transition2924 else transition2925)) else (if n < 2928 then (if n < 2927 then transition2926 else transition2927) else (if n < 2929 then transition2928 else transition2929))) else (if n < 2933 then (if n < 2931 then transition2930 else (if n < 2932 then transition2931 else transition2932)) else (if n < 2935 then (if n < 2934 then transition2933 else transition2934) else (if n < 2936 then transition2935 else transition2936))))))))) else (if n < 3147 then (if n < 3042 then (if n < 2989 then (if n < 2963 then (if n < 2950 then (if n < 2943 then (if n < 2940 then (if n < 2938 then transition2937 else (if n < 2939 then transition2938 else transition2939)) else (if n < 2941 then transition2940 else (if n < 2942 then transition2941 else transition2942))) else (if n < 2946 then (if n < 2944 then transition2943 else (if n < 2945 then transition2944 else transition2945)) else (if n < 2948 then (if n < 2947 then transition2946 else transition2947) else (if n < 2949 then transition2948 else transition2949)))) else (if n < 2956 then (if n < 2953 then (if n < 2951 then transition2950 else (if n < 2952 then transition2951 else transition2952)) else (if n < 2954 then transition2953 else (if n < 2955 then transition2954 else transition2955))) else (if n < 2959 then (if n < 2957 then transition2956 else (if n < 2958 then transition2957 else transition2958)) else (if n < 2961 then (if n < 2960 then transition2959 else transition2960) else (if n < 2962 then transition2961 else transition2962))))) else (if n < 2976 then (if n < 2969 then (if n < 2966 then (if n < 2964 then transition2963 else (if n < 2965 then transition2964 else transition2965)) else (if n < 2967 then transition2966 else (if n < 2968 then transition2967 else transition2968))) else (if n < 2972 then (if n < 2970 then transition2969 else (if n < 2971 then transition2970 else transition2971)) else (if n < 2974 then (if n < 2973 then transition2972 else transition2973) else (if n < 2975 then transition2974 else transition2975)))) else (if n < 2982 then (if n < 2979 then (if n < 2977 then transition2976 else (if n < 2978 then transition2977 else transition2978)) else (if n < 2980 then transition2979 else (if n < 2981 then transition2980 else transition2981))) else (if n < 2985 then (if n < 2983 then transition2982 else (if n < 2984 then transition2983 else transition2984)) else (if n < 2987 then (if n < 2986 then transition2985 else transition2986) else (if n < 2988 then transition2987 else transition2988)))))) else (if n < 3015 then (if n < 3002 then (if n < 2995 then (if n < 2992 then (if n < 2990 then transition2989 else (if n < 2991 then transition2990 else transition2991)) else (if n < 2993 then transition2992 else (if n < 2994 then transition2993 else transition2994))) else (if n < 2998 then (if n < 2996 then transition2995 else (if n < 2997 then transition2996 else transition2997)) else (if n < 3000 then (if n < 2999 then transition2998 else transition2999) else (if n < 3001 then transition3000 else transition3001)))) else (if n < 3008 then (if n < 3005 then (if n < 3003 then transition3002 else (if n < 3004 then transition3003 else transition3004)) else (if n < 3006 then transition3005 else (if n < 3007 then transition3006 else transition3007))) else (if n < 3011 then (if n < 3009 then transition3008 else (if n < 3010 then transition3009 else transition3010)) else (if n < 3013 then (if n < 3012 then transition3011 else transition3012) else (if n < 3014 then transition3013 else transition3014))))) else (if n < 3028 then (if n < 3021 then (if n < 3018 then (if n < 3016 then transition3015 else (if n < 3017 then transition3016 else transition3017)) else (if n < 3019 then transition3018 else (if n < 3020 then transition3019 else transition3020))) else (if n < 3024 then (if n < 3022 then transition3021 else (if n < 3023 then transition3022 else transition3023)) else (if n < 3026 then (if n < 3025 then transition3024 else transition3025) else (if n < 3027 then transition3026 else transition3027)))) else (if n < 3035 then (if n < 3031 then (if n < 3029 then transition3028 else (if n < 3030 then transition3029 else transition3030)) else (if n < 3033 then (if n < 3032 then transition3031 else transition3032) else (if n < 3034 then transition3033 else transition3034))) else (if n < 3038 then (if n < 3036 then transition3035 else (if n < 3037 then transition3036 else transition3037)) else (if n < 3040 then (if n < 3039 then transition3038 else transition3039) else (if n < 3041 then transition3040 else transition3041))))))) else (if n < 3094 then (if n < 3068 then (if n < 3055 then (if n < 3048 then (if n < 3045 then (if n < 3043 then transition3042 else (if n < 3044 then transition3043 else transition3044)) else (if n < 3046 then transition3045 else (if n < 3047 then transition3046 else transition3047))) else (if n < 3051 then (if n < 3049 then transition3048 else (if n < 3050 then transition3049 else transition3050)) else (if n < 3053 then (if n < 3052 then transition3051 else transition3052) else (if n < 3054 then transition3053 else transition3054)))) else (if n < 3061 then (if n < 3058 then (if n < 3056 then transition3055 else (if n < 3057 then transition3056 else transition3057)) else (if n < 3059 then transition3058 else (if n < 3060 then transition3059 else transition3060))) else (if n < 3064 then (if n < 3062 then transition3061 else (if n < 3063 then transition3062 else transition3063)) else (if n < 3066 then (if n < 3065 then transition3064 else transition3065) else (if n < 3067 then transition3066 else transition3067))))) else (if n < 3081 then (if n < 3074 then (if n < 3071 then (if n < 3069 then transition3068 else (if n < 3070 then transition3069 else transition3070)) else (if n < 3072 then transition3071 else (if n < 3073 then transition3072 else transition3073))) else (if n < 3077 then (if n < 3075 then transition3074 else (if n < 3076 then transition3075 else transition3076)) else (if n < 3079 then (if n < 3078 then transition3077 else transition3078) else (if n < 3080 then transition3079 else transition3080)))) else (if n < 3087 then (if n < 3084 then (if n < 3082 then transition3081 else (if n < 3083 then transition3082 else transition3083)) else (if n < 3085 then transition3084 else (if n < 3086 then transition3085 else transition3086))) else (if n < 3090 then (if n < 3088 then transition3087 else (if n < 3089 then transition3088 else transition3089)) else (if n < 3092 then (if n < 3091 then transition3090 else transition3091) else (if n < 3093 then transition3092 else transition3093)))))) else (if n < 3120 then (if n < 3107 then (if n < 3100 then (if n < 3097 then (if n < 3095 then transition3094 else (if n < 3096 then transition3095 else transition3096)) else (if n < 3098 then transition3097 else (if n < 3099 then transition3098 else transition3099))) else (if n < 3103 then (if n < 3101 then transition3100 else (if n < 3102 then transition3101 else transition3102)) else (if n < 3105 then (if n < 3104 then transition3103 else transition3104) else (if n < 3106 then transition3105 else transition3106)))) else (if n < 3113 then (if n < 3110 then (if n < 3108 then transition3107 else (if n < 3109 then transition3108 else transition3109)) else (if n < 3111 then transition3110 else (if n < 3112 then transition3111 else transition3112))) else (if n < 3116 then (if n < 3114 then transition3113 else (if n < 3115 then transition3114 else transition3115)) else (if n < 3118 then (if n < 3117 then transition3116 else transition3117) else (if n < 3119 then transition3118 else transition3119))))) else (if n < 3133 then (if n < 3126 then (if n < 3123 then (if n < 3121 then transition3120 else (if n < 3122 then transition3121 else transition3122)) else (if n < 3124 then transition3123 else (if n < 3125 then transition3124 else transition3125))) else (if n < 3129 then (if n < 3127 then transition3126 else (if n < 3128 then transition3127 else transition3128)) else (if n < 3131 then (if n < 3130 then transition3129 else transition3130) else (if n < 3132 then transition3131 else transition3132)))) else (if n < 3140 then (if n < 3136 then (if n < 3134 then transition3133 else (if n < 3135 then transition3134 else transition3135)) else (if n < 3138 then (if n < 3137 then transition3136 else transition3137) else (if n < 3139 then transition3138 else transition3139))) else (if n < 3143 then (if n < 3141 then transition3140 else (if n < 3142 then transition3141 else transition3142)) else (if n < 3145 then (if n < 3144 then transition3143 else transition3144) else (if n < 3146 then transition3145 else transition3146)))))))) else (if n < 3252 then (if n < 3199 then (if n < 3173 then (if n < 3160 then (if n < 3153 then (if n < 3150 then (if n < 3148 then transition3147 else (if n < 3149 then transition3148 else transition3149)) else (if n < 3151 then transition3150 else (if n < 3152 then transition3151 else transition3152))) else (if n < 3156 then (if n < 3154 then transition3153 else (if n < 3155 then transition3154 else transition3155)) else (if n < 3158 then (if n < 3157 then transition3156 else transition3157) else (if n < 3159 then transition3158 else transition3159)))) else (if n < 3166 then (if n < 3163 then (if n < 3161 then transition3160 else (if n < 3162 then transition3161 else transition3162)) else (if n < 3164 then transition3163 else (if n < 3165 then transition3164 else transition3165))) else (if n < 3169 then (if n < 3167 then transition3166 else (if n < 3168 then transition3167 else transition3168)) else (if n < 3171 then (if n < 3170 then transition3169 else transition3170) else (if n < 3172 then transition3171 else transition3172))))) else (if n < 3186 then (if n < 3179 then (if n < 3176 then (if n < 3174 then transition3173 else (if n < 3175 then transition3174 else transition3175)) else (if n < 3177 then transition3176 else (if n < 3178 then transition3177 else transition3178))) else (if n < 3182 then (if n < 3180 then transition3179 else (if n < 3181 then transition3180 else transition3181)) else (if n < 3184 then (if n < 3183 then transition3182 else transition3183) else (if n < 3185 then transition3184 else transition3185)))) else (if n < 3192 then (if n < 3189 then (if n < 3187 then transition3186 else (if n < 3188 then transition3187 else transition3188)) else (if n < 3190 then transition3189 else (if n < 3191 then transition3190 else transition3191))) else (if n < 3195 then (if n < 3193 then transition3192 else (if n < 3194 then transition3193 else transition3194)) else (if n < 3197 then (if n < 3196 then transition3195 else transition3196) else (if n < 3198 then transition3197 else transition3198)))))) else (if n < 3225 then (if n < 3212 then (if n < 3205 then (if n < 3202 then (if n < 3200 then transition3199 else (if n < 3201 then transition3200 else transition3201)) else (if n < 3203 then transition3202 else (if n < 3204 then transition3203 else transition3204))) else (if n < 3208 then (if n < 3206 then transition3205 else (if n < 3207 then transition3206 else transition3207)) else (if n < 3210 then (if n < 3209 then transition3208 else transition3209) else (if n < 3211 then transition3210 else transition3211)))) else (if n < 3218 then (if n < 3215 then (if n < 3213 then transition3212 else (if n < 3214 then transition3213 else transition3214)) else (if n < 3216 then transition3215 else (if n < 3217 then transition3216 else transition3217))) else (if n < 3221 then (if n < 3219 then transition3218 else (if n < 3220 then transition3219 else transition3220)) else (if n < 3223 then (if n < 3222 then transition3221 else transition3222) else (if n < 3224 then transition3223 else transition3224))))) else (if n < 3238 then (if n < 3231 then (if n < 3228 then (if n < 3226 then transition3225 else (if n < 3227 then transition3226 else transition3227)) else (if n < 3229 then transition3228 else (if n < 3230 then transition3229 else transition3230))) else (if n < 3234 then (if n < 3232 then transition3231 else (if n < 3233 then transition3232 else transition3233)) else (if n < 3236 then (if n < 3235 then transition3234 else transition3235) else (if n < 3237 then transition3236 else transition3237)))) else (if n < 3245 then (if n < 3241 then (if n < 3239 then transition3238 else (if n < 3240 then transition3239 else transition3240)) else (if n < 3243 then (if n < 3242 then transition3241 else transition3242) else (if n < 3244 then transition3243 else transition3244))) else (if n < 3248 then (if n < 3246 then transition3245 else (if n < 3247 then transition3246 else transition3247)) else (if n < 3250 then (if n < 3249 then transition3248 else transition3249) else (if n < 3251 then transition3250 else transition3251))))))) else (if n < 3304 then (if n < 3278 then (if n < 3265 then (if n < 3258 then (if n < 3255 then (if n < 3253 then transition3252 else (if n < 3254 then transition3253 else transition3254)) else (if n < 3256 then transition3255 else (if n < 3257 then transition3256 else transition3257))) else (if n < 3261 then (if n < 3259 then transition3258 else (if n < 3260 then transition3259 else transition3260)) else (if n < 3263 then (if n < 3262 then transition3261 else transition3262) else (if n < 3264 then transition3263 else transition3264)))) else (if n < 3271 then (if n < 3268 then (if n < 3266 then transition3265 else (if n < 3267 then transition3266 else transition3267)) else (if n < 3269 then transition3268 else (if n < 3270 then transition3269 else transition3270))) else (if n < 3274 then (if n < 3272 then transition3271 else (if n < 3273 then transition3272 else transition3273)) else (if n < 3276 then (if n < 3275 then transition3274 else transition3275) else (if n < 3277 then transition3276 else transition3277))))) else (if n < 3291 then (if n < 3284 then (if n < 3281 then (if n < 3279 then transition3278 else (if n < 3280 then transition3279 else transition3280)) else (if n < 3282 then transition3281 else (if n < 3283 then transition3282 else transition3283))) else (if n < 3287 then (if n < 3285 then transition3284 else (if n < 3286 then transition3285 else transition3286)) else (if n < 3289 then (if n < 3288 then transition3287 else transition3288) else (if n < 3290 then transition3289 else transition3290)))) else (if n < 3297 then (if n < 3294 then (if n < 3292 then transition3291 else (if n < 3293 then transition3292 else transition3293)) else (if n < 3295 then transition3294 else (if n < 3296 then transition3295 else transition3296))) else (if n < 3300 then (if n < 3298 then transition3297 else (if n < 3299 then transition3298 else transition3299)) else (if n < 3302 then (if n < 3301 then transition3300 else transition3301) else (if n < 3303 then transition3302 else transition3303)))))) else (if n < 3330 then (if n < 3317 then (if n < 3310 then (if n < 3307 then (if n < 3305 then transition3304 else (if n < 3306 then transition3305 else transition3306)) else (if n < 3308 then transition3307 else (if n < 3309 then transition3308 else transition3309))) else (if n < 3313 then (if n < 3311 then transition3310 else (if n < 3312 then transition3311 else transition3312)) else (if n < 3315 then (if n < 3314 then transition3313 else transition3314) else (if n < 3316 then transition3315 else transition3316)))) else (if n < 3323 then (if n < 3320 then (if n < 3318 then transition3317 else (if n < 3319 then transition3318 else transition3319)) else (if n < 3321 then transition3320 else (if n < 3322 then transition3321 else transition3322))) else (if n < 3326 then (if n < 3324 then transition3323 else (if n < 3325 then transition3324 else transition3325)) else (if n < 3328 then (if n < 3327 then transition3326 else transition3327) else (if n < 3329 then transition3328 else transition3329))))) else (if n < 3343 then (if n < 3336 then (if n < 3333 then (if n < 3331 then transition3330 else (if n < 3332 then transition3331 else transition3332)) else (if n < 3334 then transition3333 else (if n < 3335 then transition3334 else transition3335))) else (if n < 3339 then (if n < 3337 then transition3336 else (if n < 3338 then transition3337 else transition3338)) else (if n < 3341 then (if n < 3340 then transition3339 else transition3340) else (if n < 3342 then transition3341 else transition3342)))) else (if n < 3350 then (if n < 3346 then (if n < 3344 then transition3343 else (if n < 3345 then transition3344 else transition3345)) else (if n < 3348 then (if n < 3347 then transition3346 else transition3347) else (if n < 3349 then transition3348 else transition3349))) else (if n < 3353 then (if n < 3351 then transition3350 else (if n < 3352 then transition3351 else transition3352)) else (if n < 3355 then (if n < 3354 then transition3353 else transition3354) else (if n < 3356 then transition3355 else transition3356)))))))))))) +def transition (n : Fin 3357) : Fin 944 × Fin 944 := (transitionLookup n.val).val +theorem transition_absorbs (n : Fin 3357) : Absorbs (transition n).1 (transition n).2 := + (transitionLookup n.val).property +end FrameGeometry +#print axioms FrameGeometry.frame_valid +#print axioms FrameGeometry.scaled_idempotent_entries +#print axioms FrameGeometry.scaled_symmetric_entries +#print axioms FrameGeometry.scaled_stack_entries +#print axioms FrameGeometry.stack_inverse_entries +#print axioms FrameGeometry.inverse_stack_entries +#print axioms FrameGeometry.transition_absorbs diff --git a/research/lean-multi-host-source/FrameGeometry.lean b/research/lean-multi-host-source/FrameGeometry.lean new file mode 100644 index 0000000000..e0a7a9a25c --- /dev/null +++ b/research/lean-multi-host-source/FrameGeometry.lean @@ -0,0 +1,468 @@ +import FrameData +import FramedReplay +import Mathlib.Data.Matrix.Mul +import Mathlib.Algebra.BigOperators.Fin +import Mathlib.Tactic.FieldSimp +import Mathlib.Tactic.Ring +import Mathlib.Tactic.NormNum + +/-! +Concrete gauges from every literal source frame. Apache-2.0. +Prepared with substantial OpenAI Codex assistance. + +The field has arbitrary characteristic other than two. Integer certificates +are cast directly, then divided by four; no homomorphism from Q is assumed. +The formula and involution argument are the matrix specialization of main's +`AddressGauges.partialSwap` / `matrixPartialSwapGauge`. We use the identical +four-field `FramedReplay.Gauge` interface required by the actual COPY/ERASE +interpreter. This does not import or claim to recheck unrelated FramedXor +fanout proofs from a different Lean build. +-/ +namespace FrameGeometry +open scoped Matrix BigOperators + +/-- The Std data are plain functions; these wrappers select matrix rather +than pointwise multiplication when interpreting their certificates. -/ +abbrev scaledMatrix (f : Fin 944) : Matrix (Fin 8) (Fin 8) Int := Matrix.of (scaled f) +abbrev stackMatrix (f : Fin 944) : Matrix (Fin 8) (Fin 8) Int := Matrix.of (stack f) +abbrev inverseMatrix (f : Fin 944) : Matrix (Fin 8) (Fin 8) Int := Matrix.of (inverse256 f) + +theorem scaled_full_entries : ∀ i j : Fin 8, scaled 1 i j = if i = j then 4 else 0 := by decide +theorem scaled_zero_entries : ∀ i j : Fin 8, scaled 0 i j = 0 := by decide + +theorem scaled_idempotent (f : Fin 944) : + scaledMatrix f * scaledMatrix f = (4 : Int) • scaledMatrix f := by + ext i j + simpa [Matrix.mul_apply, Fin.sum_univ_succ, Matrix.smul_apply, dot8, scaledMatrix, stackMatrix, inverseMatrix] using + scaled_idempotent_entries f i j + +theorem scaled_symmetric (f : Fin 944) : (scaledMatrix f).transpose = scaledMatrix f := by + ext i j + exact (scaled_symmetric_entries f i j).symm + +theorem stack_inverse (f : Fin 944) : + stackMatrix f * inverseMatrix f = (256 : Int) • (1 : Matrix (Fin 8) (Fin 8) Int) := by + ext i j + have h := stack_inverse_entries f i j + by_cases hij : i = j <;> + simpa [Matrix.mul_apply, Fin.sum_univ_succ, Matrix.smul_apply, Matrix.one_apply, dot8, hij, scaledMatrix, stackMatrix, inverseMatrix] using h + +theorem inverse_stack (f : Fin 944) : + inverseMatrix f * stackMatrix f = (256 : Int) • (1 : Matrix (Fin 8) (Fin 8) Int) := by + ext i j + have h := inverse_stack_entries f i j + by_cases hij : i = j <;> + simpa [Matrix.mul_apply, Fin.sum_univ_succ, Matrix.smul_apply, Matrix.one_apply, dot8, hij, scaledMatrix, stackMatrix, inverseMatrix] using h + +def castMatrix (K : Type*) [Field K] (a : Matrix (Fin 8) (Fin 8) Int) : Matrix (Fin 8) (Fin 8) K := + a.map (Int.castRingHom K) + +theorem cast_mul_factor (K : Type*) [Field K] (a b c : Matrix (Fin 8) (Fin 8) Int) (k : Int) + (h : a * b = k • c) : + castMatrix K a * castMatrix K b = (k : K) • castMatrix K c := by + have hc := congrArg (fun m : Matrix (Fin 8) (Fin 8) Int => m.map (Int.castRingHom K)) h + rw [Matrix.map_mul] at hc + change castMatrix K a * castMatrix K b = _ at hc + rw [hc] + ext i j + simp [castMatrix, Matrix.map, Matrix.smul_apply] + +def projector (K : Type*) [Field K] (f : Fin 944) : Matrix (Fin 8) (Fin 8) K := + (4 : K)⁻¹ • castMatrix K (scaledMatrix f) + +theorem four_ne_zero (K : Type*) [Field K] (h2 : (2 : K) ≠ 0) : (4 : K) ≠ 0 := by + have h : (4 : K) = 2 * 2 := by norm_num + rw [h] + exact mul_ne_zero h2 h2 + +theorem two_fifty_six_ne_zero (K : Type*) [Field K] (h2 : (2 : K) ≠ 0) : + (256 : K) ≠ 0 := by + have h : (256 : K) = 2 ^ 8 := by norm_num + rw [h] + exact pow_ne_zero _ h2 + +theorem projector_idempotent (K : Type*) [Field K] (h2 : (2 : K) ≠ 0) (f : Fin 944) : + projector K f * projector K f = projector K f := by + unfold projector + rw [Matrix.smul_mul, Matrix.mul_smul, cast_mul_factor K _ _ _ 4 (scaled_idempotent f)] + have h4 := four_ne_zero K h2 + have hs : ((4 : K)⁻¹ * (4 : K)⁻¹) * 4 = (4 : K)⁻¹ := by + field_simp [h4] + simp only [smul_smul, Int.cast_ofNat, ← mul_assoc, hs] + +theorem projector_symmetric (K : Type*) [Field K] (f : Fin 944) : + (projector K f).transpose = projector K f := by + ext i j + simp only [projector, Matrix.transpose_apply, Matrix.smul_apply, castMatrix, Matrix.map_apply, scaledMatrix, Matrix.of_apply] + rw [scaled_symmetric_entries f j i] + +theorem projector_full (K : Type*) [Field K] (h2 : (2 : K) ≠ 0) : + projector K 1 = 1 := by + ext i j + by_cases hij : i = j <;> + simp [projector, castMatrix, Matrix.smul_apply, Matrix.one_apply, + scaled_full_entries, hij, four_ne_zero K h2] + +theorem projector_zero (K : Type*) [Field K] : projector K 0 = 0 := by + ext i j + simp [projector, castMatrix, Matrix.smul_apply, scaled_zero_entries] + +def basisSelector (K : Type*) [Zero K] [One K] (f : Fin 944) : + Matrix (Fin 8) (Fin 8) K := + Matrix.diagonal fun j => if j.val < (frame f).dimension then 1 else 0 + +theorem scaled_stack (f : Fin 944) : + scaledMatrix f * (stackMatrix f).transpose = (4 : Int) • ((stackMatrix f).transpose * basisSelector Int f) := by + ext i j + simp only [Matrix.smul_apply, smul_eq_mul, Matrix.mul_diagonal, basisSelector] + have h := scaled_stack_entries f i j + by_cases hj : j.val < (frame f).dimension <;> + simpa [Matrix.mul_apply, Fin.sum_univ_succ, Matrix.transpose_apply, dot8, hj, scaledMatrix, stackMatrix, inverseMatrix] using h + +theorem cast_transpose (K : Type*) [Field K] (a : Matrix (Fin 8) (Fin 8) Int) : + castMatrix K a.transpose = (castMatrix K a).transpose := by rfl + +theorem cast_product (K : Type*) [Field K] (a b : Matrix (Fin 8) (Fin 8) Int) : + castMatrix K (a * b) = castMatrix K a * castMatrix K b := by + exact Matrix.map_mul + +theorem cast_selector (K : Type*) [Field K] (f : Fin 944) : + castMatrix K (basisSelector Int f) = basisSelector K f := by + ext i j + by_cases hij : i = j <;> by_cases hj : j.val < (frame f).dimension <;> + simp [castMatrix, Matrix.map, basisSelector, Matrix.diagonal_apply, hij, hj] + +/-- The projector fixes every literal B row and annihilates every literal +A row. Together with the checked inverse of [B;A], this identifies the +projector on a complete basis over every permitted field. -/ +theorem projector_stack (K : Type*) [Field K] (h2 : (2 : K) ≠ 0) (f : Fin 944) : + projector K f * (castMatrix K (stackMatrix f)).transpose = + (castMatrix K (stackMatrix f)).transpose * basisSelector K f := by + have h := cast_mul_factor K _ _ _ 4 (scaled_stack f) + rw [cast_transpose, cast_product, cast_transpose, cast_selector] at h + unfold projector + rw [Matrix.smul_mul, h, smul_smul] + simp [four_ne_zero K h2] + +theorem transition_scaled_left (n : Fin 3357) : + scaledMatrix (transition n).1 * scaledMatrix (transition n).2 = (4 : Int) • scaledMatrix (transition n).1 := by + ext i j + simpa [Matrix.mul_apply, Fin.sum_univ_succ, Matrix.smul_apply, dot8, scaledMatrix, stackMatrix, inverseMatrix] using + (transition_absorbs n).1 i j + +theorem transition_scaled_right (n : Fin 3357) : + scaledMatrix (transition n).2 * scaledMatrix (transition n).1 = (4 : Int) • scaledMatrix (transition n).1 := by + ext i j + simpa [Matrix.mul_apply, Fin.sum_univ_succ, Matrix.smul_apply, dot8, scaledMatrix, stackMatrix, inverseMatrix] using + (transition_absorbs n).2 i j + +theorem normalized_absorption (K : Type*) [Field K] (h2 : (2 : K) ≠ 0) + (a b c : Fin 944) (h : scaledMatrix a * scaledMatrix b = (4 : Int) • scaledMatrix c) : + projector K a * projector K b = projector K c := by + unfold projector + rw [Matrix.smul_mul, Matrix.mul_smul, cast_mul_factor K _ _ _ 4 h] + have h4 := four_ne_zero K h2 + have hs : ((4 : K)⁻¹ * (4 : K)⁻¹) * 4 = (4 : K)⁻¹ := by field_simp [h4] + simp only [smul_smul, Int.cast_ofNat, ← mul_assoc, hs] + +theorem transition_projectors (K : Type*) [Field K] (h2 : (2 : K) ≠ 0) (n : Fin 3357) : + projector K (transition n).1 * projector K (transition n).2 = projector K (transition n).1 ∧ + projector K (transition n).2 * projector K (transition n).1 = projector K (transition n).1 := + ⟨normalized_absorption K h2 _ _ _ (transition_scaled_left n), + normalized_absorption K h2 _ _ _ (transition_scaled_right n)⟩ + +/-- The source's row stack remains invertible after reduction to every odd +field. Hence its B and A rows are a complete basis, not merely eigenvectors. -/ +theorem stack_right_inverse (K : Type*) [Field K] (h2 : (2 : K) ≠ 0) (f : Fin 944) : + castMatrix K (stackMatrix f) * ((256 : K)⁻¹ • castMatrix K (inverseMatrix f)) = 1 := by + rw [Matrix.mul_smul, cast_mul_factor K _ _ _ 256 (stack_inverse f), smul_smul] + simp [two_fifty_six_ne_zero K h2, castMatrix] + +theorem stack_left_inverse (K : Type*) [Field K] (h2 : (2 : K) ≠ 0) (f : Fin 944) : + ((256 : K)⁻¹ • castMatrix K (inverseMatrix f)) * castMatrix K (stackMatrix f) = 1 := by + rw [Matrix.smul_mul, cast_mul_factor K _ _ _ 256 (inverse_stack f), smul_smul] + simp [two_fifty_six_ne_zero K h2, castMatrix] + +def partialSwap {K : Type*} [Field K] (p : Matrix (Fin 8) (Fin 8) K) + (v : (Fin 8 → K) × (Fin 8 → K)) : (Fin 8 → K) × (Fin 8 → K) := + (v.1 + p *ᵥ (v.2 - v.1), v.2 - p *ᵥ (v.2 - v.1)) + +theorem partialSwap_involution {K : Type*} [Field K] (p : Matrix (Fin 8) (Fin 8) K) + (idem : p * p = p) (v : (Fin 8 → K) × (Fin 8 → K)) : + partialSwap p (partialSwap p v) = v := by + apply Prod.ext <;> + simp only [partialSwap, Matrix.mulVec_sub, Matrix.mulVec_add, Matrix.mulVec_mulVec, idem] <;> + ext i <;> simp only [Pi.add_apply, Pi.sub_apply] <;> ring + +theorem partialSwap_nested {K : Type*} [Field K] + (small large : Matrix (Fin 8) (Fin 8) K) (absorb : large * small = small) + (p : (Fin 8 → K) × (Fin 8 → K)) : + partialSwap large (partialSwap small p) = partialSwap (large - small) p := by + apply Prod.ext <;> + simp only [partialSwap, Matrix.mulVec_sub, Matrix.mulVec_add, Matrix.sub_mulVec, + Matrix.mulVec_mulVec, absorb] <;> + ext i <;> simp only [Pi.add_apply, Pi.sub_apply] <;> ring + +theorem partialSwap_nested_reverse {K : Type*} [Field K] + (small large : Matrix (Fin 8) (Fin 8) K) (absorb : small * large = small) + (p : (Fin 8 → K) × (Fin 8 → K)) : + partialSwap small (partialSwap large p) = partialSwap (large - small) p := by + apply Prod.ext <;> + simp only [partialSwap, Matrix.mulVec_sub, Matrix.mulVec_add, Matrix.sub_mulVec, + Matrix.mulVec_mulVec, absorb] <;> + ext i <;> simp only [Pi.add_apply, Pi.sub_apply] <;> ring + +theorem full_after_frame (K : Type*) [Field K] (h2 : (2 : K) ≠ 0) + (f : Fin 944) (p : (Fin 8 → K) × (Fin 8 → K)) : + partialSwap (projector K 1) (partialSwap (projector K f) p) = + partialSwap (projector K 1 - projector K f) p := by + apply partialSwap_nested + rw [projector_full K h2, one_mul] + +theorem frame_after_full (K : Type*) [Field K] (h2 : (2 : K) ≠ 0) + (f : Fin 944) (p : (Fin 8 → K) × (Fin 8 → K)) : + partialSwap (projector K f) (partialSwap (projector K 1) p) = + partialSwap (projector K 1 - projector K f) p := by + apply partialSwap_nested_reverse + rw [projector_full K h2, mul_one] + +def gauge (K : Type) [Field K] (h2 : (2 : K) ≠ 0) (f : Fin 944) : + FramedReplay.Gauge ((Fin 8 → K) × (Fin 8 → K)) where + forward := partialSwap (projector K f) + inverse := partialSwap (projector K f) + inverse_forward := partialSwap_involution _ (projector_idempotent K h2 f) + forward_inverse := partialSwap_involution _ (projector_idempotent K h2 f) + +def firstEight {K : Type*} (v : Fin 64 → K) : Fin 8 → K := + fun i => v ⟨i.val, Nat.lt_trans i.isLt (by decide)⟩ + +def replaceFirst {K : Type*} (v : Fin 64 → K) (w : Fin 8 → K) : Fin 64 → K := + fun i => if hi : i.val < 8 then w ⟨i.val, hi⟩ else v i + +theorem firstEight_replaceFirst {K : Type*} (v : Fin 64 → K) (w : Fin 8 → K) : + firstEight (replaceFirst v w) = w := by + funext i + simp [firstEight, replaceFirst, i.isLt] + +theorem replaceFirst_twice {K : Type*} (v : Fin 64 → K) (w z : Fin 8 → K) : + replaceFirst (replaceFirst v w) z = replaceFirst v z := by + funext i + by_cases hi : i.val < 8 <;> simp [replaceFirst, hi] + +theorem replaceFirst_firstEight {K : Type*} (v : Fin 64 → K) : + replaceFirst v (firstEight v) = v := by + funext i + by_cases hi : i.val < 8 <;> simp [replaceFirst, firstEight, hi] + +def liftPair {K : Type*} + (f : ((Fin 8 → K) × (Fin 8 → K)) → ((Fin 8 → K) × (Fin 8 → K))) + (p : (Fin 64 → K) × (Fin 64 → K)) : (Fin 64 → K) × (Fin 64 → K) := + let q := f (firstEight p.1, firstEight p.2) + (replaceFirst p.1 q.1, replaceFirst p.2 q.2) + +theorem liftPair_comp {K : Type*} + (f g : ((Fin 8 → K) × (Fin 8 → K)) → ((Fin 8 → K) × (Fin 8 → K))) + (p : (Fin 64 → K) × (Fin 64 → K)) : + liftPair f (liftPair g p) = liftPair (f ∘ g) p := by + simp [liftPair, firstEight_replaceFirst, replaceFirst_twice] + +theorem liftPair_id {K : Type*} (p : (Fin 64 → K) × (Fin 64 → K)) : + liftPair id p = p := by + simp [liftPair, replaceFirst_firstEight] + +def liftGauge {K : Type} (g : FramedReplay.Gauge ((Fin 8 → K) × (Fin 8 → K))) : + FramedReplay.Gauge ((Fin 64 → K) × (Fin 64 → K)) where + forward := liftPair g.forward + inverse := liftPair g.inverse + inverse_forward p := by + rw [liftPair_comp] + have h : g.inverse ∘ g.forward = id := by funext x; exact g.inverse_forward x + rw [h, liftPair_id] + forward_inverse p := by + rw [liftPair_comp] + have h : g.forward ∘ g.inverse = id := by funext x; exact g.forward_inverse x + rw [h, liftPair_id] + +def gauge64 (K : Type) [Field K] (h2 : (2 : K) ≠ 0) (f : Fin 944) : + FramedReplay.Gauge ((Fin 64 → K) × (Fin 64 → K)) := + liftGauge (gauge K h2 f) + +def coordinateProjector (K : Type*) [Field K] (mask : Fin 8 → Bool) : + Matrix (Fin 8) (Fin 8) K := Matrix.diagonal fun i => if mask i then 1 else 0 + +theorem partialSwap_coordinate {K : Type*} [Field K] (mask : Fin 8 → Bool) + (p : (Fin 8 → K) × (Fin 8 → K)) : + partialSwap (coordinateProjector K mask) p = + (fun i => if mask i then p.2 i else p.1 i, + fun i => if mask i then p.1 i else p.2 i) := by + apply Prod.ext <;> funext i <;> + simp only [partialSwap, coordinateProjector, Matrix.mulVec_diagonal, Pi.add_apply, Pi.sub_apply] + all_goals cases mask i <;> simp + +/-- A finite integer-table equality is sufficient to identify the source +entrance-to-exit residual with the literal coordinate mask in every odd +field. The hypothesis is intended to be discharged for the selected source +tag table, not assumed from ranks or sampled modular computations. -/ +theorem coordinate_residual (K : Type*) [Field K] (h2 : (2 : K) ≠ 0) + (f : Fin 944) (mask : Fin 8 → Bool) + (hc : ∀ i j : Fin 8, scaledMatrix 1 i j - scaledMatrix f i j = + if i = j ∧ mask i = true then 4 else 0) : + projector K 1 - projector K f = coordinateProjector K mask := by + ext i j + have h := congrArg (fun z : Int => (z : K)) (hc i j) + have h4 := four_ne_zero K h2 + simp only [Int.cast_sub, scaledMatrix, Matrix.of_apply] at h + simp only [Matrix.sub_apply, projector, Matrix.smul_apply, castMatrix, Matrix.map_apply, + coordinateProjector, Matrix.diagonal_apply, scaledMatrix, Matrix.of_apply, smul_eq_mul] + change (4 : K)⁻¹ * (scaled 1 i j : K) - (4 : K)⁻¹ * (scaled f i j : K) = _ + rw [← mul_sub, h] + by_cases hij : i = j <;> cases mask i <;> simp [hij, h4] + +theorem residual_partialSwap (K : Type*) [Field K] (h2 : (2 : K) ≠ 0) + (f : Fin 944) (mask : Fin 8 → Bool) + (hc : ∀ i j : Fin 8, scaledMatrix 1 i j - scaledMatrix f i j = + if i = j ∧ mask i = true then 4 else 0) + (p : (Fin 8 → K) × (Fin 8 → K)) : + partialSwap (projector K 1 - projector K f) p = + (fun i => if mask i then p.2 i else p.1 i, + fun i => if mask i then p.1 i else p.2 i) := by + rw [coordinate_residual K h2 f mask hc] + exact partialSwap_coordinate mask p + +def coordinateSwap64 {K : Type*} (mask : Fin 64 → Bool) + (p : (Fin 64 → K) × (Fin 64 → K)) : (Fin 64 → K) × (Fin 64 → K) := + (fun i => if mask i then p.2 i else p.1 i, + fun i => if mask i then p.1 i else p.2 i) + +/-- Complete source entrance/exit frame transport, on all 64 address +coordinates. The finite certificate refers to the literal projector table; +the outside-support condition prevents an unnoticed change of chart. -/ +theorem full_after_frame64_coordinate (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (f : Fin 944) (mask : Fin 64 → Bool) + (hc : ∀ i j : Fin 8, scaledMatrix 1 i j - scaledMatrix f i j = + if i = j ∧ mask ⟨i.val, Nat.lt_trans i.isLt (by decide)⟩ = true then 4 else 0) + (outside : ∀ i : Fin 64, 8 ≤ i.val → mask i = false) + (p : (Fin 64 → K) × (Fin 64 → K)) : + (gauge64 K h2 1).forward ((gauge64 K h2 f).forward p) = coordinateSwap64 mask p := by + change liftPair (partialSwap (projector K 1)) + (liftPair (partialSwap (projector K f)) p) = _ + rw [liftPair_comp] + have hlocal := full_after_frame K h2 f (firstEight p.1, firstEight p.2) + rw [residual_partialSwap K h2 f + (fun i => mask ⟨i.val, Nat.lt_trans i.isLt (by decide)⟩) hc] at hlocal + change (replaceFirst p.1 ((partialSwap (projector K 1) + (partialSwap (projector K f) (firstEight p.1, firstEight p.2))).1), + replaceFirst p.2 ((partialSwap (projector K 1) + (partialSwap (projector K f) (firstEight p.1, firstEight p.2))).2)) = _ + rw [hlocal] + apply Prod.ext <;> funext i + all_goals + by_cases hi : i.val < 8 + · simp [replaceFirst, firstEight, coordinateSwap64, hi] + · simp [replaceFirst, coordinateSwap64, hi, outside i (Nat.le_of_not_gt hi)] + +theorem frame_after_full64_coordinate (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (f : Fin 944) (mask : Fin 64 → Bool) + (hc : ∀ i j : Fin 8, scaledMatrix 1 i j - scaledMatrix f i j = + if i = j ∧ mask ⟨i.val, Nat.lt_trans i.isLt (by decide)⟩ = true then 4 else 0) + (outside : ∀ i : Fin 64, 8 ≤ i.val → mask i = false) + (p : (Fin 64 → K) × (Fin 64 → K)) : + (gauge64 K h2 f).forward ((gauge64 K h2 1).inverse p) = coordinateSwap64 mask p := by + change liftPair (partialSwap (projector K f)) + (liftPair (partialSwap (projector K 1)) p) = _ + rw [liftPair_comp] + have hlocal := frame_after_full K h2 f (firstEight p.1, firstEight p.2) + rw [residual_partialSwap K h2 f + (fun i => mask ⟨i.val, Nat.lt_trans i.isLt (by decide)⟩) hc] at hlocal + change (replaceFirst p.1 ((partialSwap (projector K f) + (partialSwap (projector K 1) (firstEight p.1, firstEight p.2))).1), + replaceFirst p.2 ((partialSwap (projector K f) + (partialSwap (projector K 1) (firstEight p.1, firstEight p.2))).2)) = _ + rw [hlocal] + apply Prod.ext <;> funext i + all_goals + by_cases hi : i.val < 8 + · simp [replaceFirst, firstEight, coordinateSwap64, hi] + · simp [replaceFirst, coordinateSwap64, hi, outside i (Nat.le_of_not_gt hi)] + +theorem coordinateSwap64_involution {K : Type*} (mask : Fin 64 → Bool) + (p : (Fin 64 → K) × (Fin 64 → K)) : + coordinateSwap64 mask (coordinateSwap64 mask p) = p := by + apply Prod.ext <;> funext i <;> cases hm : mask i <;> simp [coordinateSwap64, hm] + +/-- Literal common stage-2 subspace E₂: coordinates 8 through 21. -/ +def stage2Mask : Fin 64 → Bool := fun i => decide (8 ≤ i.val ∧ i.val < 22) + +/-- The actual stage-2 gauge D_(Pframe ⊕ I14 ⊕ 0). The common E₂ factor is +present on both endpoints and both inverse laws; it is not silently omitted. -/ +def gaugeStage2 (K : Type) [Field K] (h2 : (2 : K) ≠ 0) (f : Fin 944) : + FramedReplay.Gauge ((Fin 64 → K) × (Fin 64 → K)) where + forward p := (gauge64 K h2 f).forward (coordinateSwap64 stage2Mask p) + inverse p := coordinateSwap64 stage2Mask ((gauge64 K h2 f).inverse p) + inverse_forward p := by + rw [(gauge64 K h2 f).inverse_forward, coordinateSwap64_involution] + forward_inverse p := by + rw [coordinateSwap64_involution, (gauge64 K h2 f).forward_inverse] + +theorem stage2_relative_transport (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (initial final : Fin 944) (p : (Fin 64 → K) × (Fin 64 → K)) : + (gaugeStage2 K h2 initial).forward ((gaugeStage2 K h2 final).inverse p) = + (gauge64 K h2 initial).forward ((gauge64 K h2 final).inverse p) := by + simp only [gaugeStage2, coordinateSwap64_involution] + +/-- The raw-payload orientation of the complete stage-2 helper endpoint. +This includes all 64 coordinates and cancels the actual common E₂ factor. -/ +theorem stage2_helper_endpoint (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (f : Fin 944) (mask : Fin 64 → Bool) + (hc : ∀ i j : Fin 8, scaledMatrix 1 i j - scaledMatrix f i j = + if i = j ∧ mask ⟨i.val, Nat.lt_trans i.isLt (by decide)⟩ = true then 4 else 0) + (outside : ∀ i : Fin 64, 8 ≤ i.val → mask i = false) + (p : (Fin 64 → K) × (Fin 64 → K)) : + (gaugeStage2 K h2 f).forward ((gaugeStage2 K h2 1).inverse p) = coordinateSwap64 mask p := by + rw [stage2_relative_transport] + exact frame_after_full64_coordinate K h2 f mask hc outside p + +end FrameGeometry + +#print axioms FrameGeometry.scaled_full_entries +#print axioms FrameGeometry.scaled_zero_entries +#print axioms FrameGeometry.scaled_idempotent +#print axioms FrameGeometry.scaled_symmetric +#print axioms FrameGeometry.stack_inverse +#print axioms FrameGeometry.inverse_stack +#print axioms FrameGeometry.cast_mul_factor +#print axioms FrameGeometry.four_ne_zero +#print axioms FrameGeometry.two_fifty_six_ne_zero +#print axioms FrameGeometry.projector_idempotent +#print axioms FrameGeometry.projector_symmetric +#print axioms FrameGeometry.projector_full +#print axioms FrameGeometry.projector_zero +#print axioms FrameGeometry.scaled_stack +#print axioms FrameGeometry.cast_transpose +#print axioms FrameGeometry.cast_product +#print axioms FrameGeometry.cast_selector +#print axioms FrameGeometry.projector_stack +#print axioms FrameGeometry.transition_scaled_left +#print axioms FrameGeometry.transition_scaled_right +#print axioms FrameGeometry.normalized_absorption +#print axioms FrameGeometry.transition_projectors +#print axioms FrameGeometry.stack_right_inverse +#print axioms FrameGeometry.stack_left_inverse +#print axioms FrameGeometry.partialSwap_involution +#print axioms FrameGeometry.partialSwap_nested +#print axioms FrameGeometry.partialSwap_nested_reverse +#print axioms FrameGeometry.full_after_frame +#print axioms FrameGeometry.frame_after_full +#print axioms FrameGeometry.firstEight_replaceFirst +#print axioms FrameGeometry.replaceFirst_twice +#print axioms FrameGeometry.replaceFirst_firstEight +#print axioms FrameGeometry.liftPair_comp +#print axioms FrameGeometry.liftPair_id +#print axioms FrameGeometry.partialSwap_coordinate +#print axioms FrameGeometry.coordinate_residual +#print axioms FrameGeometry.residual_partialSwap +#print axioms FrameGeometry.full_after_frame64_coordinate +#print axioms FrameGeometry.frame_after_full64_coordinate +#print axioms FrameGeometry.coordinateSwap64_involution +#print axioms FrameGeometry.stage2_relative_transport +#print axioms FrameGeometry.stage2_helper_endpoint diff --git a/research/lean-multi-host-source/FrameLabelData.lean b/research/lean-multi-host-source/FrameLabelData.lean new file mode 100644 index 0000000000..f609619d21 --- /dev/null +++ b/research/lean-multi-host-source/FrameLabelData.lean @@ -0,0 +1,39 @@ +import FrameTraceLiterals + +/-! +Literal label bounds and full-to-zero private COPY/ERASE identification. +The checker reads every event in the actual selected forward word. +Apache-2.0. Prepared with substantial OpenAI Codex assistance. +-/ +namespace SourceFrameLabels +set_option maxRecDepth 100000 +set_option maxHeartbeats 0 + +def labelCheck (e : FrameTrace.Entry) : Bool := + decide (e.oldFrame < 944 ∧ e.newFrame < 944 ∧ + ((e.scalar.op = 2 ∨ e.scalar.op = 3) → e.oldFrame = 1 ∧ e.newFrame = 0)) + +theorem labels_checked : SourceFrameTrace.forward.all labelCheck = true := by decide + +theorem labels_valid (e : FrameTrace.Entry) (he : e ∈ SourceFrameTrace.forward) : + e.oldFrame < 944 ∧ e.newFrame < 944 ∧ + ((e.scalar.op = 2 ∨ e.scalar.op = 3) → e.oldFrame = 1 ∧ e.newFrame = 0) := by + exact of_decide_eq_true (List.all_eq_true.mp labels_checked e he) + +theorem label_range (e : FrameTrace.Entry) (he : e ∈ SourceFrameTrace.forward) : + e.oldFrame < 944 ∧ e.newFrame < 944 := + ⟨(labels_valid e he).1, (labels_valid e he).2.1⟩ + +theorem copy_frames (e : FrameTrace.Entry) (he : e ∈ SourceFrameTrace.forward) + (hop : e.scalar.op = 2) : e.oldFrame = 1 ∧ e.newFrame = 0 := + (labels_valid e he).2.2 (Or.inl hop) + +theorem erase_frames (e : FrameTrace.Entry) (he : e ∈ SourceFrameTrace.forward) + (hop : e.scalar.op = 3) : e.oldFrame = 1 ∧ e.newFrame = 0 := + (labels_valid e he).2.2 (Or.inr hop) + +end SourceFrameLabels +#print axioms SourceFrameLabels.labels_checked +#print axioms SourceFrameLabels.label_range +#print axioms SourceFrameLabels.copy_frames +#print axioms SourceFrameLabels.erase_frames diff --git a/research/lean-multi-host-source/FrameMoveData.lean b/research/lean-multi-host-source/FrameMoveData.lean new file mode 100644 index 0000000000..7a4931db78 --- /dev/null +++ b/research/lean-multi-host-source/FrameMoveData.lean @@ -0,0 +1,68 @@ +import FrameData +import FrameTraceLiterals + +/-! +Each of the actual4291 MOVE events selects one of FrameData's3357 certified +transition pairs. The balanced index is only an untrusted search aid; the +kernel checks the selected pair against the literal old/new frame labels. +Apache-2.0. Prepared with substantial OpenAI Codex assistance. +-/ +namespace SourceFrameMoves +set_option maxRecDepth 100000 +set_option maxHeartbeats 0 + +def pairSearch (n : Nat) : Nat := + (if n < 329918 then (if n < 71935 then (if n < 2244 then (if n < 211 then (if n < 106 then (if n < 54 then (if n < 28 then (if n < 15 then (if n < 8 then (if n < 5 then (if n < 3 then 0 else (if n < 4 then 1 else 2)) else (if n < 6 then 3 else (if n < 7 then 4 else 5))) else (if n < 11 then (if n < 9 then 6 else (if n < 10 then 7 else 8)) else (if n < 13 then (if n < 12 then 9 else 10) else (if n < 14 then 11 else 12)))) else (if n < 21 then (if n < 18 then (if n < 16 then 13 else (if n < 17 then 14 else 15)) else (if n < 19 then 16 else (if n < 20 then 17 else 18))) else (if n < 24 then (if n < 22 then 19 else (if n < 23 then 20 else 21)) else (if n < 26 then (if n < 25 then 22 else 23) else (if n < 27 then 24 else 25))))) else (if n < 41 then (if n < 34 then (if n < 31 then (if n < 29 then 26 else (if n < 30 then 27 else 28)) else (if n < 32 then 29 else (if n < 33 then 30 else 31))) else (if n < 37 then (if n < 35 then 32 else (if n < 36 then 33 else 34)) else (if n < 39 then (if n < 38 then 35 else 36) else (if n < 40 then 37 else 38)))) else (if n < 47 then (if n < 44 then (if n < 42 then 39 else (if n < 43 then 40 else 41)) else (if n < 45 then 42 else (if n < 46 then 43 else 44))) else (if n < 50 then (if n < 48 then 45 else (if n < 49 then 46 else 47)) else (if n < 52 then (if n < 51 then 48 else 49) else (if n < 53 then 50 else 51)))))) else (if n < 80 then (if n < 67 then (if n < 60 then (if n < 57 then (if n < 55 then 52 else (if n < 56 then 53 else 54)) else (if n < 58 then 55 else (if n < 59 then 56 else 57))) else (if n < 63 then (if n < 61 then 58 else (if n < 62 then 59 else 60)) else (if n < 65 then (if n < 64 then 61 else 62) else (if n < 66 then 63 else 64)))) else (if n < 73 then (if n < 70 then (if n < 68 then 65 else (if n < 69 then 66 else 67)) else (if n < 71 then 68 else (if n < 72 then 69 else 70))) else (if n < 76 then (if n < 74 then 71 else (if n < 75 then 72 else 73)) else (if n < 78 then (if n < 77 then 74 else 75) else (if n < 79 then 76 else 77))))) else (if n < 93 then (if n < 86 then (if n < 83 then (if n < 81 then 78 else (if n < 82 then 79 else 80)) else (if n < 84 then 81 else (if n < 85 then 82 else 83))) else (if n < 89 then (if n < 87 then 84 else (if n < 88 then 85 else 86)) else (if n < 91 then (if n < 90 then 87 else 88) else (if n < 92 then 89 else 90)))) else (if n < 99 then (if n < 96 then (if n < 94 then 91 else (if n < 95 then 92 else 93)) else (if n < 97 then 94 else (if n < 98 then 95 else 96))) else (if n < 102 then (if n < 100 then 97 else (if n < 101 then 98 else 99)) else (if n < 104 then (if n < 103 then 100 else 101) else (if n < 105 then 102 else 103))))))) else (if n < 158 then (if n < 132 then (if n < 119 then (if n < 112 then (if n < 109 then (if n < 107 then 104 else (if n < 108 then 105 else 106)) else (if 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2800)) else (if n < 633329 then (if n < 632481 then 2801 else 2802) else (if n < 633330 then 2803 else 2804))))) else (if n < 638052 then (if n < 635313 then (if n < 634369 then (if n < 634273 then 2805 else (if n < 634279 then 2806 else 2807)) else (if n < 635217 then 2808 else (if n < 635220 then 2809 else 2810))) else (if n < 636257 then (if n < 636162 then 2811 else (if n < 636167 then 2812 else 2813)) else (if n < 637108 then (if n < 637106 then 2814 else 2815) else (if n < 637201 then 2816 else 2817)))) else (if n < 639934 then (if n < 638984 then (if n < 638055 then 2818 else (if n < 638145 then 2819 else 2820)) else (if n < 639089 then (if n < 638987 then 2821 else 2822) else (if n < 639928 then 2823 else 2824))) else (if n < 640877 then (if n < 640033 then 2825 else (if n < 640872 then 2826 else 2827)) else (if n < 641819 then (if n < 640977 then 2828 else 2829) else (if n < 641822 then 2830 else 2831))))))) else (if n < 658834 then (if n < 650339 then (if n < 646537 then (if n < 643809 then (if n < 642865 then (if n < 642763 then 2832 else (if n < 642765 then 2833 else 2834)) else (if n < 643709 then 2835 else (if n < 643710 then 2836 else 2837))) else (if n < 644753 then (if n < 644649 then 2838 else (if n < 644650 then 2839 else 2840)) else (if n < 645599 then (if n < 645593 then 2841 else 2842) else (if n < 645697 then 2843 else 2844)))) else (if n < 648426 then (if n < 647482 then (if n < 646540 then 2845 else (if n < 646641 then 2846 else 2847)) else (if n < 647487 then 2848 else (if n < 647585 then 2849 else 2850))) else (if n < 649372 then (if n < 648428 then 2851 else (if n < 648529 then 2852 else 2853)) else (if n < 649473 then (if n < 649375 then 2854 else 2855) else (if n < 650336 then 2856 else 2857))))) else (if n < 654193 then (if n < 652229 then (if n < 651286 then (if n < 650417 then 2858 else (if n < 651280 then 2859 else 2860)) else (if n < 651361 then 2861 else (if n < 652224 then 2862 else 2863))) else (if n < 653174 then (if n < 652305 then 2864 else (if n < 653171 then 2865 else 2866)) else (if n < 654115 then (if n < 653249 then 2867 else 2868) else (if n < 654117 then 2869 else 2870)))) else (if n < 656081 then (if n < 655137 then (if n < 655061 then 2871 else (if n < 655062 then 2872 else 2873)) else (if n < 656001 then 2874 else (if n < 656002 then 2875 else 2876))) else (if n < 657025 then (if n < 656945 then 2877 else (if n < 656951 then 2878 else 2879)) else (if n < 657892 then (if n < 657889 then 2880 else 2881) else (if n < 657969 then 2882 else 2883)))))) else (if n < 666465 then (if n < 662646 then (if n < 660724 then (if n < 659778 then (if n < 658839 then 2884 else (if n < 658913 then 2885 else 2886)) else (if n < 659780 then 2887 else (if n < 659857 then 2888 else 2889))) else (if n < 661696 then (if n < 660727 then 2890 else (if n < 660801 then 2891 else 2892)) else (if n < 661745 then (if n < 661699 then 2893 else 2894) else (if n < 662640 then 2895 else 2896)))) else (if n < 664534 then (if n < 663589 then (if n < 662689 then 2897 else (if n < 663584 then 2898 else 2899)) else (if n < 663633 then 2900 else (if n < 664531 then 2901 else 2902))) else (if n < 665477 then (if n < 664577 then 2903 else (if n < 665475 then 2904 else 2905)) else (if n < 666421 then (if n < 665521 then 2906 else 2907) else (if n < 666422 then 2908 else 2909))))) else (if n < 671138 then (if n < 668353 then (if n < 667409 then (if n < 667361 then 2910 else (if n < 667362 then 2911 else 2912)) else (if n < 668305 then 2913 else (if n < 668311 then 2914 else 2915))) else (if n < 669297 then (if n < 669249 then 2916 else (if n < 669252 then 2917 else 2918)) else (if n < 670199 then (if n < 670194 then 2919 else 2920) else (if n < 670241 then 2921 else 2922)))) else (if n < 673067 then (if n < 672084 then (if n < 671140 then 2923 else (if n < 671185 then 2924 else 2925)) else (if n < 672129 then (if n < 672087 then 2926 else 2927) else (if n < 673064 then 2928 else 2929))) else (if n < 674014 then (if n < 673073 then 2930 else (if n < 674008 then 2931 else 2932)) else (if n < 674952 then (if n < 674017 then 2933 else 2934) else (if n < 674957 then 2935 else 2936))))))))) else (if n < 741041 then (if n < 708001 then (if n < 691841 then (if n < 683455 then (if n < 679673 then (if n < 676849 then (if n < 675905 then (if n < 675899 then 2937 else (if n < 675902 then 2938 else 2939)) else (if n < 676843 then 2940 else (if n < 676845 then 2941 else 2942))) else (if n < 677793 then (if n < 677789 then 2943 else (if n < 677790 then 2944 else 2945)) else (if n < 678730 then (if n < 678729 then 2946 else 2947) else (if n < 678737 then 2948 else 2949)))) else (if n < 681562 then (if n < 680617 then (if n < 679679 then 2950 else (if n < 679681 then 2951 else 2952)) else (if n < 680620 then 2953 else (if n < 680625 then 2954 else 2955))) else (if n < 682506 then (if n < 681567 then 2956 else (if n < 681569 then 2957 else 2958)) else (if n < 682513 then (if n < 682508 then 2959 else 2960) else (if n < 683452 then 2961 else 2962))))) else (if n < 687233 then (if n < 685238 then (if n < 684291 then (if n < 683457 then 2963 else (if n < 684288 then 2964 else 2965)) else (if n < 684401 then 2966 else (if n < 685232 then 2967 else 2968))) else (if n < 686181 then (if n < 685345 then 2969 else (if n < 686176 then 2970 else 2971)) else (if n < 687123 then (if n < 686289 then 2972 else 2973) else (if n < 687126 then 2974 else 2975)))) else (if n < 689121 then (if n < 688177 then (if n < 688067 then 2976 else (if n < 688069 then 2977 else 2978)) else (if n < 689013 then 2979 else (if n < 689014 then 2980 else 2981))) else (if n < 690065 then (if n < 689953 then 2982 else (if n < 689954 then 2983 else 2984)) else (if n < 690903 then (if n < 690897 then 2985 else 2986) else (if n < 691009 then 2987 else 2988)))))) else (if n < 699505 then (if n < 695659 then (if n < 693730 then (if n < 692786 then (if n < 691844 then 2989 else (if n < 691953 then 2990 else 2991)) else (if n < 692791 then 2992 else (if n < 692897 then 2993 else 2994))) else (if n < 694676 then (if n < 693732 then 2995 else (if n < 693841 then 2996 else 2997)) else (if n < 694785 then (if n < 694679 then 2998 else 2999) else (if n < 695656 then 3000 else 3001)))) else (if n < 697549 then (if n < 696606 then (if n < 695729 then 3002 else (if n < 696600 then 3003 else 3004)) else (if n < 696673 then 3005 else (if n < 697544 then 3006 else 3007))) else (if n < 698494 then (if n < 697617 then 3008 else (if n < 698491 then 3009 else 3010)) else (if n < 699435 then (if n < 698561 then 3011 else 3012) else (if n < 699437 then 3013 else 3014))))) else (if n < 704154 then (if n < 701393 then (if n < 700449 then (if n < 700381 then 3015 else (if n < 700382 then 3016 else 3017)) else (if n < 701321 then 3018 else (if n < 701322 then 3019 else 3020))) else (if n < 702337 then (if n < 702265 then 3021 else (if n < 702271 then 3022 else 3023)) else (if n < 703212 then (if n < 703209 then 3024 else 3025) else (if n < 703281 then 3026 else 3027)))) else (if n < 706047 then (if n < 705098 then (if n < 704159 then 3028 else (if n < 704225 then 3029 else 3030)) else (if n < 705169 then (if n < 705100 then 3031 else 3032) else (if n < 706044 then 3033 else 3034))) else (if n < 707019 then (if n < 706113 then 3035 else (if n < 707016 then 3036 else 3037)) else (if n < 707960 then (if n < 707057 then 3038 else 3039) else (if n < 707966 then 3040 else 3041))))))) else (if n < 724977 then (if n < 716460 then (if n < 712681 then (if n < 709889 then (if n < 708945 then (if n < 708904 then 3042 else (if n < 708909 then 3043 else 3044)) else (if n < 709851 then 3045 else (if n < 709854 then 3046 else 3047))) else (if n < 710833 then (if n < 710795 then 3048 else (if n < 710797 then 3049 else 3050)) else (if n < 711742 then (if n < 711741 then 3051 else 3052) else (if n < 711777 then 3053 else 3054)))) else (if n < 714569 then (if n < 713625 then (if n < 712682 then 3055 else (if n < 712721 then 3056 else 3057)) else (if n < 713631 then 3058 else (if n < 713665 then 3059 else 3060))) else (if n < 715514 then (if n < 714572 then 3061 else (if n < 714609 then 3062 else 3063)) else (if n < 715553 then (if n < 715519 then 3064 else 3065) else (if n < 716458 then 3066 else 3067))))) else (if n < 720273 then (if n < 718371 then (if n < 717407 then (if n < 716497 then 3068 else (if n < 717404 then 3069 else 3070)) else (if n < 717441 then 3071 else (if n < 718368 then 3072 else 3073))) else (if n < 719318 then (if n < 718385 then 3074 else (if n < 719312 then 3075 else 3076)) else (if n < 720256 then (if n < 719329 then 3077 else 3078) else (if n < 720261 then 3079 else 3080)))) else (if n < 722161 then (if n < 721217 then (if n < 721203 then 3081 else (if n < 721206 then 3082 else 3083)) else (if n < 722147 then 3084 else (if n < 722149 then 3085 else 3086))) else (if n < 723105 then (if n < 723093 then 3087 else (if n < 723094 then 3088 else 3089)) else (if n < 724034 then (if n < 724033 then 3090 else 3091) else (if n < 724049 then 3092 else 3093)))))) else (if n < 732545 then (if n < 728759 then (if n < 726866 then (if n < 725921 then (if n < 724983 then 3094 else (if n < 724993 then 3095 else 3096)) else (if n < 725924 then 3097 else (if n < 725937 then 3098 else 3099))) else (if n < 727810 then (if n < 726871 then 3100 else (if n < 726881 then 3101 else 3102)) else (if n < 727825 then (if n < 727812 then 3103 else 3104) else (if n < 728756 then 3105 else 3106)))) else (if n < 730638 then (if n < 729691 then (if n < 728769 then 3107 else (if n < 729688 then 3108 else 3109)) else (if n < 729713 then 3110 else (if n < 730632 then 3111 else 3112))) else (if n < 731581 then (if n < 730657 then 3113 else (if n < 731576 then 3114 else 3115)) else (if n < 732523 then (if n < 731601 then 3116 else 3117) else (if n < 732526 then 3118 else 3119))))) else (if n < 737241 then (if n < 734433 then (if n < 733489 then (if n < 733467 then 3120 else (if n < 733469 then 3121 else 3122)) else (if n < 734413 then 3123 else (if n < 734414 then 3124 else 3125))) else (if n < 735377 then (if n < 735353 then 3126 else (if n < 735354 then 3127 else 3128)) else (if n < 736303 then (if n < 736297 then 3129 else 3130) else (if n < 736321 then 3131 else 3132)))) else (if n < 739132 then (if n < 738186 then (if n < 737244 then 3133 else (if n < 737265 then 3134 else 3135)) else (if n < 738209 then (if n < 738191 then 3136 else 3137) else (if n < 739130 then 3138 else 3139))) else (if n < 740079 then (if n < 739153 then 3140 else (if n < 740076 then 3141 else 3142)) else (if n < 741008 then (if n < 740097 then 3143 else 3144) else (if n < 741011 then 3145 else 3146)))))))) else (if n < 792017 then (if n < 757969 then (if n < 749511 then (if n < 745733 then (if n < 742929 then (if n < 741985 then (if n < 741952 then 3147 else (if n < 741958 then 3148 else 3149)) else (if n < 742896 then 3150 else (if n < 742901 then 3151 else 3152))) else (if n < 743873 then (if n < 743843 then 3153 else (if n < 743846 then 3154 else 3155)) else (if n < 744789 then (if n < 744787 then 3156 else 3157) else (if n < 744817 then 3158 else 3159)))) else (if n < 747617 then (if n < 746673 then (if n < 745734 then 3160 else (if n < 745761 then 3161 else 3162)) else (if n < 746674 then 3163 else (if n < 746705 then 3164 else 3165))) else (if n < 748561 then (if n < 747623 then 3166 else (if n < 747649 then 3167 else 3168)) else (if n < 748593 then (if n < 748564 then 3169 else 3170) else (if n < 749506 then 3171 else 3172))))) else (if n < 753313 then (if n < 751399 then (if n < 750452 then (if n < 749537 then 3173 else (if n < 750450 then 3174 else 3175)) else (if n < 750481 then 3176 else (if n < 751396 then 3177 else 3178))) else (if n < 752307 then (if n < 751425 then 3179 else (if n < 752304 then 3180 else 3181)) else (if n < 753248 then (if n < 752369 then 3182 else 3183) else (if n < 753254 then 3184 else 3185)))) else (if n < 755201 then (if n < 754257 then (if n < 754192 then 3186 else (if n < 754197 then 3187 else 3188)) else (if n < 755139 then 3189 else (if n < 755142 then 3190 else 3191))) else (if n < 756145 then (if n < 756083 then 3192 else (if n < 756085 then 3193 else 3194)) else (if n < 757030 then (if n < 757029 then 3195 else 3196) else (if n < 757089 then 3197 else 3198)))))) else (if n < 766409 then (if n < 761748 then (if n < 759857 then (if n < 758913 then (if n < 757970 then 3199 else (if n < 758033 then 3200 else 3201)) else (if n < 758919 then 3202 else (if n < 758977 then 3203 else 3204))) else (if n < 760802 then (if n < 759860 then 3205 else (if n < 759921 then 3206 else 3207)) else (if n < 760865 then (if n < 760807 then 3208 else 3209) else (if n < 761746 then 3210 else 3211)))) else (if n < 763697 then (if n < 762695 then (if n < 761809 then 3212 else (if n < 762692 then 3213 else 3214)) else (if n < 763576 then 3215 else (if n < 763580 then 3216 else 3217))) else (if n < 764641 then (if n < 764520 then 3218 else (if n < 764525 then 3219 else 3220)) else (if n < 765465 then (if n < 765464 then 3221 else 3222) else (if n < 765585 then 3223 else 3224))))) else (if n < 778801 then (if n < 768298 then (if n < 767353 then (if n < 766412 then 3225 else (if n < 766529 then 3226 else 3227)) else (if n < 767357 then 3228 else (if n < 767473 then 3229 else 3230))) else (if n < 773021 then (if n < 768299 then 3231 else (if n < 773020 then 3232 else 3233)) else (if n < 774911 then (if n < 774910 then 3234 else 3235) else (if n < 777857 then 3236 else 3237)))) else (if n < 785409 then (if n < 781633 then (if n < 779745 then 3238 else (if n < 780689 then 3239 else 3240)) else (if n < 783521 then (if n < 782577 then 3241 else 3242) else (if n < 784465 then 3243 else 3244))) else (if n < 788241 then (if n < 786353 then 3245 else (if n < 787297 then 3246 else 3247)) else (if n < 790129 then (if n < 789185 then 3248 else 3249) else (if n < 791073 then 3250 else 3251))))))) else (if n < 841105 then (if n < 816561 then (if n < 804289 then (if n < 797681 then (if n < 794849 then (if n < 792961 then 3252 else (if n < 793905 then 3253 else 3254)) else (if n < 795793 then 3255 else (if n < 796737 then 3256 else 3257))) else (if n < 800513 then (if n < 798625 then 3258 else (if n < 799569 then 3259 else 3260)) else (if n < 802401 then (if n < 801457 then 3261 else 3262) else (if n < 803345 then 3263 else 3264)))) else (if n < 809953 then (if n < 807121 then (if n < 805233 then 3265 else (if n < 806177 then 3266 else 3267)) else (if n < 808065 then 3268 else (if n < 809009 then 3269 else 3270))) else (if n < 812785 then (if n < 810897 then 3271 else (if n < 811841 then 3272 else 3273)) else (if n < 814673 then (if n < 813729 then 3274 else 3275) else (if n < 815617 then 3276 else 3277))))) else (if n < 828833 then (if n < 822225 then (if n < 819393 then (if n < 817505 then 3278 else (if n < 818449 then 3279 else 3280)) else (if n < 820337 then 3281 else (if n < 821281 then 3282 else 3283))) else (if n < 825057 then (if n < 823169 then 3284 else (if n < 824113 then 3285 else 3286)) else (if n < 826945 then (if n < 826001 then 3287 else 3288) else (if n < 827889 then 3289 else 3290)))) else (if n < 834497 then (if n < 831665 then (if n < 829777 then 3291 else (if n < 830721 then 3292 else 3293)) else (if n < 832609 then 3294 else (if n < 833553 then 3295 else 3296))) else (if n < 837329 then (if n < 835441 then 3297 else (if n < 836385 then 3298 else 3299)) else (if n < 839217 then (if n < 838273 then 3300 else 3301) else (if n < 840161 then 3302 else 3303)))))) else (if n < 865649 then (if n < 853377 then (if n < 846769 then (if n < 843937 then (if n < 842049 then 3304 else (if n < 842993 then 3305 else 3306)) else (if n < 844881 then 3307 else (if n < 845825 then 3308 else 3309))) else (if n < 849601 then (if n < 847713 then 3310 else (if n < 848657 then 3311 else 3312)) else (if n < 851489 then (if n < 850545 then 3313 else 3314) else (if n < 852433 then 3315 else 3316)))) else (if n < 859041 then (if n < 856209 then (if n < 854321 then 3317 else (if n < 855265 then 3318 else 3319)) else (if n < 857153 then 3320 else (if n < 858097 then 3321 else 3322))) else (if n < 861873 then (if n < 859985 then 3323 else (if n < 860929 then 3324 else 3325)) else (if n < 863761 then (if n < 862817 then 3326 else 3327) else (if n < 864705 then 3328 else 3329))))) else (if n < 877921 then (if n < 871313 then (if n < 868481 then (if n < 866593 then 3330 else (if n < 867537 then 3331 else 3332)) else (if n < 869425 then 3333 else (if n < 870369 then 3334 else 3335))) else (if n < 874145 then (if n < 872257 then 3336 else (if n < 873201 then 3337 else 3338)) else (if n < 876033 then (if n < 875089 then 3339 else 3340) else (if n < 876977 then 3341 else 3342)))) else (if n < 884529 then (if n < 880753 then (if n < 878865 then 3343 else (if n < 879809 then 3344 else 3345)) else (if n < 882641 then (if n < 881697 then 3346 else 3347) else (if n < 883585 then 3348 else 3349))) else (if n < 887361 then (if n < 885473 then 3350 else (if n < 886417 then 3351 else 3352)) else (if n < 889249 then (if n < 888305 then 3353 else 3354) else (if n < 890193 then 3355 else 3356)))))))))))) + +def moveIndex (e : FrameTrace.Entry) : Fin 3357 := + ⟨pairSearch (944 * e.oldFrame + e.newFrame) % 3357, Nat.mod_lt _ (by decide)⟩ + +def moveCheck (e : FrameTrace.Entry) : Bool := + decide (e.scalar.op = 0 → + (FrameGeometry.transition (moveIndex e)).1.val = e.oldFrame ∧ + (FrameGeometry.transition (moveIndex e)).2.val = e.newFrame) + +theorem moves_checked : SourceFrameTrace.forward.all moveCheck = true := by decide + +theorem move_pair (e : FrameTrace.Entry) (he : e ∈ SourceFrameTrace.forward) + (hop : e.scalar.op = 0) : + (FrameGeometry.transition (moveIndex e)).1.val = e.oldFrame ∧ + (FrameGeometry.transition (moveIndex e)).2.val = e.newFrame := by + have h := List.all_eq_true.mp moves_checked e he + exact of_decide_eq_true h hop + +theorem move_range (e : FrameTrace.Entry) (he : e ∈ SourceFrameTrace.forward) + (hop : e.scalar.op = 0) : e.oldFrame < 944 ∧ e.newFrame < 944 := by + obtain ⟨ha, hb⟩ := move_pair e he hop + exact ⟨ha ▸ (FrameGeometry.transition (moveIndex e)).1.isLt, + hb ▸ (FrameGeometry.transition (moveIndex e)).2.isLt⟩ + +def oldIndex (e : FrameTrace.Entry) : Fin 944 := + ⟨e.oldFrame % 944, Nat.mod_lt _ (by decide)⟩ + +def newIndex (e : FrameTrace.Entry) : Fin 944 := + ⟨e.newFrame % 944, Nat.mod_lt _ (by decide)⟩ + +theorem move_transition (e : FrameTrace.Entry) (he : e ∈ SourceFrameTrace.forward) + (hop : e.scalar.op = 0) : + FrameGeometry.transition (moveIndex e) = (oldIndex e, newIndex e) := by + obtain ⟨ha, hb⟩ := move_pair e he hop + obtain ⟨hra, hrb⟩ := move_range e he hop + apply Prod.ext + · apply Fin.ext + simpa only [oldIndex, Nat.mod_eq_of_lt hra] using ha + · apply Fin.ext + simpa only [newIndex, Nat.mod_eq_of_lt hrb] using hb + +/-- Every actual source MOVE satisfies the checked nested-projector identity. -/ +theorem move_absorbs (e : FrameTrace.Entry) (he : e ∈ SourceFrameTrace.forward) + (hop : e.scalar.op = 0) : FrameGeometry.Absorbs (oldIndex e) (newIndex e) := by + have h := FrameGeometry.transition_absorbs (moveIndex e) + rw [move_transition e he hop] at h + exact h + +end SourceFrameMoves +#print axioms SourceFrameMoves.moves_checked +#print axioms SourceFrameMoves.move_range +#print axioms SourceFrameMoves.move_transition +#print axioms SourceFrameMoves.move_absorbs diff --git a/research/lean-multi-host-source/FrameTraceCheckpoints.lean b/research/lean-multi-host-source/FrameTraceCheckpoints.lean new file mode 100644 index 0000000000..d3880714e6 --- /dev/null +++ b/research/lean-multi-host-source/FrameTraceCheckpoints.lean @@ -0,0 +1,303 @@ +import FrameTraceLiterals +import MatrixData +set_option maxRecDepth 100000 +set_option maxHeartbeats 0 +namespace SourceFrameTrace +open FrameTrace +open TreeReplay (Tree) +theorem initial_tabulate : Tree.tabulate 10 (fun i => state0.frames.get i) = state0.frames := by decide +theorem final_tabulate : Tree.tabulate 10 (fun i => state96.frames.get i) = state96.frames := by decide +theorem project0 : chunk0.map Entry.scalar = SourceMatrix.chunk0 := rfl +theorem checkpoint0 : runChecked chunk0 (state0,true) = (state1,true) := by decide +theorem project1 : chunk1.map Entry.scalar = SourceMatrix.chunk1 := rfl +theorem checkpoint1 : runChecked chunk1 (state1,true) = (state2,true) := by decide +theorem project2 : chunk2.map Entry.scalar = SourceMatrix.chunk2 := rfl +theorem checkpoint2 : runChecked chunk2 (state2,true) = (state3,true) := by decide +theorem project3 : chunk3.map Entry.scalar = SourceMatrix.chunk3 := rfl +theorem checkpoint3 : runChecked chunk3 (state3,true) = (state4,true) := by decide +theorem project4 : chunk4.map Entry.scalar = SourceMatrix.chunk4 := rfl +theorem checkpoint4 : runChecked chunk4 (state4,true) = (state5,true) := by decide +theorem project5 : chunk5.map Entry.scalar = SourceMatrix.chunk5 := rfl +theorem checkpoint5 : runChecked chunk5 (state5,true) = (state6,true) := by decide +theorem project6 : chunk6.map Entry.scalar = SourceMatrix.chunk6 := rfl +theorem checkpoint6 : runChecked chunk6 (state6,true) = (state7,true) := by decide +theorem project7 : chunk7.map Entry.scalar = SourceMatrix.chunk7 := rfl +theorem checkpoint7 : runChecked chunk7 (state7,true) = (state8,true) := by decide +theorem project8 : chunk8.map Entry.scalar = SourceMatrix.chunk8 := rfl +theorem checkpoint8 : runChecked chunk8 (state8,true) = (state9,true) := by decide +theorem project9 : chunk9.map Entry.scalar = SourceMatrix.chunk9 := rfl +theorem checkpoint9 : runChecked chunk9 (state9,true) = (state10,true) := by decide +theorem project10 : chunk10.map Entry.scalar = SourceMatrix.chunk10 := rfl +theorem checkpoint10 : runChecked chunk10 (state10,true) = (state11,true) := by decide +theorem project11 : chunk11.map Entry.scalar = SourceMatrix.chunk11 := rfl +theorem checkpoint11 : runChecked chunk11 (state11,true) = (state12,true) := by decide +theorem project12 : chunk12.map Entry.scalar = SourceMatrix.chunk12 := rfl +theorem checkpoint12 : runChecked chunk12 (state12,true) = (state13,true) := by decide +theorem project13 : chunk13.map Entry.scalar = SourceMatrix.chunk13 := rfl +theorem checkpoint13 : runChecked chunk13 (state13,true) = (state14,true) := by decide +theorem project14 : chunk14.map Entry.scalar = SourceMatrix.chunk14 := rfl +theorem checkpoint14 : runChecked chunk14 (state14,true) = (state15,true) := by decide +theorem project15 : chunk15.map Entry.scalar = SourceMatrix.chunk15 := rfl +theorem checkpoint15 : runChecked chunk15 (state15,true) = (state16,true) := by decide +theorem project16 : chunk16.map Entry.scalar = SourceMatrix.chunk16 := rfl +theorem checkpoint16 : runChecked chunk16 (state16,true) = (state17,true) := by decide +theorem project17 : chunk17.map Entry.scalar = SourceMatrix.chunk17 := rfl +theorem checkpoint17 : runChecked chunk17 (state17,true) = (state18,true) := by decide +theorem project18 : chunk18.map Entry.scalar = SourceMatrix.chunk18 := rfl +theorem checkpoint18 : runChecked chunk18 (state18,true) = (state19,true) := by decide +theorem project19 : chunk19.map Entry.scalar = SourceMatrix.chunk19 := rfl +theorem checkpoint19 : runChecked chunk19 (state19,true) = (state20,true) := by decide +theorem project20 : chunk20.map Entry.scalar = SourceMatrix.chunk20 := rfl +theorem checkpoint20 : runChecked chunk20 (state20,true) = (state21,true) := by decide +theorem project21 : chunk21.map Entry.scalar = SourceMatrix.chunk21 := rfl +theorem checkpoint21 : runChecked chunk21 (state21,true) = (state22,true) := by decide +theorem project22 : chunk22.map Entry.scalar = SourceMatrix.chunk22 := rfl +theorem checkpoint22 : runChecked chunk22 (state22,true) = (state23,true) := by decide +theorem project23 : chunk23.map Entry.scalar = SourceMatrix.chunk23 := rfl +theorem checkpoint23 : runChecked chunk23 (state23,true) = (state24,true) := by decide +theorem project24 : chunk24.map Entry.scalar = SourceMatrix.chunk24 := rfl +theorem checkpoint24 : runChecked chunk24 (state24,true) = (state25,true) := by decide +theorem project25 : chunk25.map Entry.scalar = SourceMatrix.chunk25 := rfl +theorem checkpoint25 : runChecked chunk25 (state25,true) = (state26,true) := by decide +theorem project26 : chunk26.map Entry.scalar = SourceMatrix.chunk26 := rfl +theorem checkpoint26 : runChecked chunk26 (state26,true) = (state27,true) := by decide +theorem project27 : chunk27.map Entry.scalar = SourceMatrix.chunk27 := rfl +theorem checkpoint27 : runChecked chunk27 (state27,true) = (state28,true) := by decide +theorem project28 : chunk28.map Entry.scalar = SourceMatrix.chunk28 := rfl +theorem checkpoint28 : runChecked chunk28 (state28,true) = (state29,true) := by decide +theorem project29 : chunk29.map Entry.scalar = SourceMatrix.chunk29 := rfl +theorem checkpoint29 : runChecked chunk29 (state29,true) = (state30,true) := by decide +theorem project30 : chunk30.map Entry.scalar = SourceMatrix.chunk30 := rfl +theorem checkpoint30 : runChecked chunk30 (state30,true) = (state31,true) := by decide +theorem project31 : chunk31.map Entry.scalar = SourceMatrix.chunk31 := rfl +theorem checkpoint31 : runChecked chunk31 (state31,true) = (state32,true) := by decide +theorem project32 : chunk32.map Entry.scalar = SourceMatrix.chunk32 := rfl +theorem checkpoint32 : runChecked chunk32 (state32,true) = (state33,true) := by decide +theorem project33 : chunk33.map Entry.scalar = SourceMatrix.chunk33 := rfl +theorem checkpoint33 : runChecked chunk33 (state33,true) = (state34,true) := by decide +theorem project34 : chunk34.map Entry.scalar = SourceMatrix.chunk34 := rfl +theorem checkpoint34 : runChecked chunk34 (state34,true) = (state35,true) := by decide +theorem project35 : chunk35.map Entry.scalar = SourceMatrix.chunk35 := rfl +theorem checkpoint35 : runChecked chunk35 (state35,true) = (state36,true) := by decide +theorem project36 : chunk36.map Entry.scalar = SourceMatrix.chunk36 := rfl +theorem checkpoint36 : runChecked chunk36 (state36,true) = (state37,true) := by decide +theorem project37 : chunk37.map Entry.scalar = SourceMatrix.chunk37 := rfl +theorem checkpoint37 : runChecked chunk37 (state37,true) = (state38,true) := by decide +theorem project38 : chunk38.map Entry.scalar = SourceMatrix.chunk38 := rfl +theorem checkpoint38 : runChecked chunk38 (state38,true) = (state39,true) := by decide +theorem project39 : chunk39.map Entry.scalar = SourceMatrix.chunk39 := rfl +theorem checkpoint39 : runChecked chunk39 (state39,true) = (state40,true) := by decide +theorem project40 : chunk40.map Entry.scalar = SourceMatrix.chunk40 := rfl +theorem checkpoint40 : runChecked chunk40 (state40,true) = (state41,true) := by decide +theorem project41 : chunk41.map Entry.scalar = SourceMatrix.chunk41 := rfl +theorem checkpoint41 : runChecked chunk41 (state41,true) = (state42,true) := by decide +theorem project42 : chunk42.map Entry.scalar = SourceMatrix.chunk42 := rfl +theorem checkpoint42 : runChecked chunk42 (state42,true) = (state43,true) := by decide +theorem project43 : chunk43.map Entry.scalar = SourceMatrix.chunk43 := rfl +theorem checkpoint43 : runChecked chunk43 (state43,true) = (state44,true) := by decide +theorem project44 : chunk44.map Entry.scalar = SourceMatrix.chunk44 := rfl +theorem checkpoint44 : runChecked chunk44 (state44,true) = (state45,true) := by decide +theorem project45 : chunk45.map Entry.scalar = SourceMatrix.chunk45 := rfl +theorem checkpoint45 : runChecked chunk45 (state45,true) = (state46,true) := by decide +theorem project46 : chunk46.map Entry.scalar = SourceMatrix.chunk46 := rfl +theorem checkpoint46 : runChecked chunk46 (state46,true) = (state47,true) := by decide +theorem project47 : chunk47.map Entry.scalar = SourceMatrix.chunk47 := rfl +theorem checkpoint47 : runChecked chunk47 (state47,true) = (state48,true) := by decide +theorem project48 : chunk48.map Entry.scalar = SourceMatrix.chunk48 := rfl +theorem checkpoint48 : runChecked chunk48 (state48,true) = (state49,true) := by decide +theorem project49 : chunk49.map Entry.scalar = SourceMatrix.chunk49 := rfl +theorem checkpoint49 : runChecked chunk49 (state49,true) = (state50,true) := by decide +theorem project50 : chunk50.map Entry.scalar = SourceMatrix.chunk50 := rfl +theorem checkpoint50 : runChecked chunk50 (state50,true) = (state51,true) := by decide +theorem project51 : chunk51.map Entry.scalar = SourceMatrix.chunk51 := rfl +theorem checkpoint51 : runChecked chunk51 (state51,true) = (state52,true) := by decide +theorem project52 : chunk52.map Entry.scalar = SourceMatrix.chunk52 := rfl +theorem checkpoint52 : runChecked chunk52 (state52,true) = (state53,true) := by decide +theorem project53 : chunk53.map Entry.scalar = SourceMatrix.chunk53 := rfl +theorem checkpoint53 : runChecked chunk53 (state53,true) = (state54,true) := by decide +theorem project54 : chunk54.map Entry.scalar = SourceMatrix.chunk54 := rfl +theorem checkpoint54 : runChecked chunk54 (state54,true) = (state55,true) := by decide +theorem project55 : chunk55.map Entry.scalar = SourceMatrix.chunk55 := rfl +theorem checkpoint55 : runChecked chunk55 (state55,true) = (state56,true) := by decide +theorem project56 : chunk56.map Entry.scalar = SourceMatrix.chunk56 := rfl +theorem checkpoint56 : runChecked chunk56 (state56,true) = (state57,true) := by decide +theorem project57 : chunk57.map Entry.scalar = SourceMatrix.chunk57 := rfl +theorem checkpoint57 : runChecked chunk57 (state57,true) = (state58,true) := by decide +theorem project58 : chunk58.map Entry.scalar = SourceMatrix.chunk58 := rfl +theorem checkpoint58 : runChecked chunk58 (state58,true) = (state59,true) := by decide +theorem project59 : chunk59.map Entry.scalar = SourceMatrix.chunk59 := rfl +theorem checkpoint59 : runChecked chunk59 (state59,true) = (state60,true) := by decide +theorem project60 : chunk60.map Entry.scalar = SourceMatrix.chunk60 := rfl +theorem checkpoint60 : runChecked chunk60 (state60,true) = (state61,true) := by decide +theorem project61 : chunk61.map Entry.scalar = SourceMatrix.chunk61 := rfl +theorem checkpoint61 : runChecked chunk61 (state61,true) = (state62,true) := by decide +theorem project62 : chunk62.map Entry.scalar = SourceMatrix.chunk62 := rfl +theorem checkpoint62 : runChecked chunk62 (state62,true) = (state63,true) := by decide +theorem project63 : chunk63.map Entry.scalar = SourceMatrix.chunk63 := rfl +theorem checkpoint63 : runChecked chunk63 (state63,true) = (state64,true) := by decide +theorem project64 : chunk64.map Entry.scalar = SourceMatrix.chunk64 := rfl +theorem checkpoint64 : runChecked chunk64 (state64,true) = (state65,true) := by decide +theorem project65 : chunk65.map Entry.scalar = SourceMatrix.chunk65 := rfl +theorem checkpoint65 : runChecked chunk65 (state65,true) = (state66,true) := by decide +theorem project66 : chunk66.map Entry.scalar = SourceMatrix.chunk66 := rfl +theorem checkpoint66 : runChecked chunk66 (state66,true) = (state67,true) := by decide +theorem project67 : chunk67.map Entry.scalar = SourceMatrix.chunk67 := rfl +theorem checkpoint67 : runChecked chunk67 (state67,true) = (state68,true) := by decide +theorem project68 : chunk68.map Entry.scalar = SourceMatrix.chunk68 := rfl +theorem checkpoint68 : runChecked chunk68 (state68,true) = (state69,true) := by decide +theorem project69 : chunk69.map Entry.scalar = SourceMatrix.chunk69 := rfl +theorem checkpoint69 : runChecked chunk69 (state69,true) = (state70,true) := by decide +theorem project70 : chunk70.map Entry.scalar = SourceMatrix.chunk70 := rfl +theorem checkpoint70 : runChecked chunk70 (state70,true) = (state71,true) := by decide +theorem project71 : chunk71.map Entry.scalar = SourceMatrix.chunk71 := rfl +theorem checkpoint71 : runChecked chunk71 (state71,true) = (state72,true) := by decide +theorem project72 : chunk72.map Entry.scalar = SourceMatrix.chunk72 := rfl +theorem checkpoint72 : runChecked chunk72 (state72,true) = (state73,true) := by decide +theorem project73 : chunk73.map Entry.scalar = SourceMatrix.chunk73 := rfl +theorem checkpoint73 : runChecked chunk73 (state73,true) = (state74,true) := by decide +theorem project74 : chunk74.map Entry.scalar = SourceMatrix.chunk74 := rfl +theorem checkpoint74 : runChecked chunk74 (state74,true) = (state75,true) := by decide +theorem project75 : chunk75.map Entry.scalar = SourceMatrix.chunk75 := rfl +theorem checkpoint75 : runChecked chunk75 (state75,true) = (state76,true) := by decide +theorem project76 : chunk76.map Entry.scalar = SourceMatrix.chunk76 := rfl +theorem checkpoint76 : runChecked chunk76 (state76,true) = (state77,true) := by decide +theorem project77 : chunk77.map Entry.scalar = SourceMatrix.chunk77 := rfl +theorem checkpoint77 : runChecked chunk77 (state77,true) = (state78,true) := by decide +theorem project78 : chunk78.map Entry.scalar = SourceMatrix.chunk78 := rfl +theorem checkpoint78 : runChecked chunk78 (state78,true) = (state79,true) := by decide +theorem project79 : chunk79.map Entry.scalar = SourceMatrix.chunk79 := rfl +theorem checkpoint79 : runChecked chunk79 (state79,true) = (state80,true) := by decide +theorem project80 : chunk80.map Entry.scalar = SourceMatrix.chunk80 := rfl +theorem checkpoint80 : runChecked chunk80 (state80,true) = (state81,true) := by decide +theorem project81 : chunk81.map Entry.scalar = SourceMatrix.chunk81 := rfl +theorem checkpoint81 : runChecked chunk81 (state81,true) = (state82,true) := by decide +theorem project82 : chunk82.map Entry.scalar = SourceMatrix.chunk82 := rfl +theorem checkpoint82 : runChecked chunk82 (state82,true) = (state83,true) := by decide +theorem project83 : chunk83.map Entry.scalar = SourceMatrix.chunk83 := rfl +theorem checkpoint83 : runChecked chunk83 (state83,true) = (state84,true) := by decide +theorem project84 : chunk84.map Entry.scalar = SourceMatrix.chunk84 := rfl +theorem checkpoint84 : runChecked chunk84 (state84,true) = (state85,true) := by decide +theorem project85 : chunk85.map Entry.scalar = SourceMatrix.chunk85 := rfl +theorem checkpoint85 : runChecked chunk85 (state85,true) = (state86,true) := by decide +theorem project86 : chunk86.map Entry.scalar = SourceMatrix.chunk86 := rfl +theorem checkpoint86 : runChecked chunk86 (state86,true) = (state87,true) := by decide +theorem project87 : chunk87.map Entry.scalar = SourceMatrix.chunk87 := rfl +theorem checkpoint87 : runChecked chunk87 (state87,true) = (state88,true) := by decide +theorem project88 : chunk88.map Entry.scalar = SourceMatrix.chunk88 := rfl +theorem checkpoint88 : runChecked chunk88 (state88,true) = (state89,true) := by decide +theorem project89 : chunk89.map Entry.scalar = SourceMatrix.chunk89 := rfl +theorem checkpoint89 : runChecked chunk89 (state89,true) = (state90,true) := by decide +theorem project90 : chunk90.map Entry.scalar = SourceMatrix.chunk90 := rfl +theorem checkpoint90 : runChecked chunk90 (state90,true) = (state91,true) := by decide +theorem project91 : chunk91.map Entry.scalar = SourceMatrix.chunk91 := rfl +theorem checkpoint91 : runChecked chunk91 (state91,true) = (state92,true) := by decide +theorem project92 : chunk92.map Entry.scalar = SourceMatrix.chunk92 := rfl +theorem checkpoint92 : runChecked chunk92 (state92,true) = (state93,true) := by decide +theorem project93 : chunk93.map Entry.scalar = SourceMatrix.chunk93 := rfl +theorem checkpoint93 : runChecked chunk93 (state93,true) = (state94,true) := by decide +theorem project94 : chunk94.map Entry.scalar = SourceMatrix.chunk94 := rfl +theorem checkpoint94 : runChecked chunk94 (state94,true) = (state95,true) := by decide +theorem project95 : chunk95.map Entry.scalar = SourceMatrix.chunk95 := rfl +theorem checkpoint95 : runChecked chunk95 (state95,true) = (state96,true) := by decide +theorem combine (p q : List Entry) (s t u : State × Bool) (h : runChecked p s = t) (k : runChecked q t = u) : runChecked (p ++ q) s = u := by + simp only [runChecked, List.foldl_append] + rw [show List.foldl checkedStep s p = t from h] + exact k +theorem finish96 : runChecked suffix96 (state96,true) = (state96,true) := rfl +theorem finish95 : runChecked suffix95 (state95,true) = (state96,true) := combine chunk95 suffix96 (state95,true) (state96,true) (state96,true) checkpoint95 finish96 +theorem finish94 : runChecked suffix94 (state94,true) = (state96,true) := combine chunk94 suffix95 (state94,true) (state95,true) (state96,true) checkpoint94 finish95 +theorem finish93 : runChecked suffix93 (state93,true) = (state96,true) := combine chunk93 suffix94 (state93,true) (state94,true) (state96,true) checkpoint93 finish94 +theorem finish92 : runChecked suffix92 (state92,true) = (state96,true) := combine chunk92 suffix93 (state92,true) (state93,true) (state96,true) checkpoint92 finish93 +theorem finish91 : runChecked suffix91 (state91,true) = (state96,true) := combine chunk91 suffix92 (state91,true) (state92,true) (state96,true) checkpoint91 finish92 +theorem finish90 : runChecked suffix90 (state90,true) = (state96,true) := combine chunk90 suffix91 (state90,true) (state91,true) (state96,true) checkpoint90 finish91 +theorem finish89 : runChecked suffix89 (state89,true) = (state96,true) := combine chunk89 suffix90 (state89,true) (state90,true) (state96,true) checkpoint89 finish90 +theorem finish88 : runChecked suffix88 (state88,true) = (state96,true) := combine chunk88 suffix89 (state88,true) (state89,true) (state96,true) checkpoint88 finish89 +theorem finish87 : runChecked suffix87 (state87,true) = (state96,true) := combine chunk87 suffix88 (state87,true) (state88,true) (state96,true) checkpoint87 finish88 +theorem finish86 : runChecked suffix86 (state86,true) = (state96,true) := combine chunk86 suffix87 (state86,true) (state87,true) (state96,true) checkpoint86 finish87 +theorem finish85 : runChecked suffix85 (state85,true) = (state96,true) := combine chunk85 suffix86 (state85,true) (state86,true) (state96,true) checkpoint85 finish86 +theorem finish84 : runChecked suffix84 (state84,true) = (state96,true) := combine chunk84 suffix85 (state84,true) (state85,true) (state96,true) checkpoint84 finish85 +theorem finish83 : runChecked suffix83 (state83,true) = (state96,true) := combine chunk83 suffix84 (state83,true) (state84,true) (state96,true) checkpoint83 finish84 +theorem finish82 : runChecked suffix82 (state82,true) = (state96,true) := combine chunk82 suffix83 (state82,true) (state83,true) (state96,true) checkpoint82 finish83 +theorem finish81 : runChecked suffix81 (state81,true) = (state96,true) := combine chunk81 suffix82 (state81,true) (state82,true) (state96,true) checkpoint81 finish82 +theorem finish80 : runChecked suffix80 (state80,true) = (state96,true) := combine chunk80 suffix81 (state80,true) (state81,true) (state96,true) checkpoint80 finish81 +theorem finish79 : runChecked suffix79 (state79,true) = (state96,true) := combine chunk79 suffix80 (state79,true) (state80,true) (state96,true) checkpoint79 finish80 +theorem finish78 : runChecked suffix78 (state78,true) = (state96,true) := combine chunk78 suffix79 (state78,true) (state79,true) (state96,true) checkpoint78 finish79 +theorem finish77 : runChecked suffix77 (state77,true) = (state96,true) := combine chunk77 suffix78 (state77,true) (state78,true) (state96,true) checkpoint77 finish78 +theorem finish76 : runChecked suffix76 (state76,true) = (state96,true) := combine chunk76 suffix77 (state76,true) (state77,true) (state96,true) checkpoint76 finish77 +theorem finish75 : runChecked suffix75 (state75,true) = (state96,true) := combine chunk75 suffix76 (state75,true) (state76,true) (state96,true) checkpoint75 finish76 +theorem finish74 : runChecked suffix74 (state74,true) = (state96,true) := combine chunk74 suffix75 (state74,true) (state75,true) (state96,true) checkpoint74 finish75 +theorem finish73 : runChecked suffix73 (state73,true) = (state96,true) := combine chunk73 suffix74 (state73,true) (state74,true) (state96,true) checkpoint73 finish74 +theorem finish72 : runChecked suffix72 (state72,true) = (state96,true) := combine chunk72 suffix73 (state72,true) (state73,true) (state96,true) checkpoint72 finish73 +theorem finish71 : runChecked suffix71 (state71,true) = (state96,true) := combine chunk71 suffix72 (state71,true) (state72,true) (state96,true) checkpoint71 finish72 +theorem finish70 : runChecked suffix70 (state70,true) = (state96,true) := combine chunk70 suffix71 (state70,true) (state71,true) (state96,true) checkpoint70 finish71 +theorem finish69 : runChecked suffix69 (state69,true) = (state96,true) := combine chunk69 suffix70 (state69,true) (state70,true) (state96,true) checkpoint69 finish70 +theorem finish68 : runChecked suffix68 (state68,true) = (state96,true) := combine chunk68 suffix69 (state68,true) (state69,true) (state96,true) checkpoint68 finish69 +theorem finish67 : runChecked suffix67 (state67,true) = (state96,true) := combine chunk67 suffix68 (state67,true) (state68,true) (state96,true) checkpoint67 finish68 +theorem finish66 : runChecked suffix66 (state66,true) = (state96,true) := combine chunk66 suffix67 (state66,true) (state67,true) (state96,true) checkpoint66 finish67 +theorem finish65 : runChecked suffix65 (state65,true) = (state96,true) := combine chunk65 suffix66 (state65,true) (state66,true) (state96,true) checkpoint65 finish66 +theorem finish64 : runChecked suffix64 (state64,true) = (state96,true) := combine chunk64 suffix65 (state64,true) (state65,true) (state96,true) checkpoint64 finish65 +theorem finish63 : runChecked suffix63 (state63,true) = (state96,true) := combine chunk63 suffix64 (state63,true) (state64,true) (state96,true) checkpoint63 finish64 +theorem finish62 : runChecked suffix62 (state62,true) = (state96,true) := combine chunk62 suffix63 (state62,true) (state63,true) (state96,true) checkpoint62 finish63 +theorem finish61 : runChecked suffix61 (state61,true) = (state96,true) := combine chunk61 suffix62 (state61,true) (state62,true) (state96,true) checkpoint61 finish62 +theorem finish60 : runChecked suffix60 (state60,true) = (state96,true) := combine chunk60 suffix61 (state60,true) (state61,true) (state96,true) checkpoint60 finish61 +theorem finish59 : runChecked suffix59 (state59,true) = (state96,true) := combine chunk59 suffix60 (state59,true) (state60,true) (state96,true) checkpoint59 finish60 +theorem finish58 : runChecked suffix58 (state58,true) = (state96,true) := combine chunk58 suffix59 (state58,true) (state59,true) (state96,true) checkpoint58 finish59 +theorem finish57 : runChecked suffix57 (state57,true) = (state96,true) := combine chunk57 suffix58 (state57,true) (state58,true) (state96,true) checkpoint57 finish58 +theorem finish56 : runChecked suffix56 (state56,true) = (state96,true) := combine chunk56 suffix57 (state56,true) (state57,true) (state96,true) checkpoint56 finish57 +theorem finish55 : runChecked suffix55 (state55,true) = (state96,true) := combine chunk55 suffix56 (state55,true) (state56,true) (state96,true) checkpoint55 finish56 +theorem finish54 : runChecked suffix54 (state54,true) = (state96,true) := combine chunk54 suffix55 (state54,true) (state55,true) (state96,true) checkpoint54 finish55 +theorem finish53 : runChecked suffix53 (state53,true) = (state96,true) := combine chunk53 suffix54 (state53,true) (state54,true) (state96,true) checkpoint53 finish54 +theorem finish52 : runChecked suffix52 (state52,true) = (state96,true) := combine chunk52 suffix53 (state52,true) (state53,true) (state96,true) checkpoint52 finish53 +theorem finish51 : runChecked suffix51 (state51,true) = (state96,true) := combine chunk51 suffix52 (state51,true) (state52,true) (state96,true) checkpoint51 finish52 +theorem finish50 : runChecked suffix50 (state50,true) = (state96,true) := combine chunk50 suffix51 (state50,true) (state51,true) (state96,true) checkpoint50 finish51 +theorem finish49 : runChecked suffix49 (state49,true) = (state96,true) := combine chunk49 suffix50 (state49,true) (state50,true) (state96,true) checkpoint49 finish50 +theorem finish48 : runChecked suffix48 (state48,true) = (state96,true) := combine chunk48 suffix49 (state48,true) (state49,true) (state96,true) checkpoint48 finish49 +theorem finish47 : runChecked suffix47 (state47,true) = (state96,true) := combine chunk47 suffix48 (state47,true) (state48,true) (state96,true) checkpoint47 finish48 +theorem finish46 : runChecked suffix46 (state46,true) = (state96,true) := combine chunk46 suffix47 (state46,true) (state47,true) (state96,true) checkpoint46 finish47 +theorem finish45 : runChecked suffix45 (state45,true) = (state96,true) := combine chunk45 suffix46 (state45,true) (state46,true) (state96,true) checkpoint45 finish46 +theorem finish44 : runChecked suffix44 (state44,true) = (state96,true) := combine chunk44 suffix45 (state44,true) (state45,true) (state96,true) checkpoint44 finish45 +theorem finish43 : runChecked suffix43 (state43,true) = (state96,true) := combine chunk43 suffix44 (state43,true) (state44,true) (state96,true) checkpoint43 finish44 +theorem finish42 : runChecked suffix42 (state42,true) = (state96,true) := combine chunk42 suffix43 (state42,true) (state43,true) (state96,true) checkpoint42 finish43 +theorem finish41 : runChecked suffix41 (state41,true) = (state96,true) := combine chunk41 suffix42 (state41,true) (state42,true) (state96,true) checkpoint41 finish42 +theorem finish40 : runChecked suffix40 (state40,true) = (state96,true) := combine chunk40 suffix41 (state40,true) (state41,true) (state96,true) checkpoint40 finish41 +theorem finish39 : runChecked suffix39 (state39,true) = (state96,true) := combine chunk39 suffix40 (state39,true) (state40,true) (state96,true) checkpoint39 finish40 +theorem finish38 : runChecked suffix38 (state38,true) = (state96,true) := combine chunk38 suffix39 (state38,true) (state39,true) (state96,true) checkpoint38 finish39 +theorem finish37 : runChecked suffix37 (state37,true) = (state96,true) := combine chunk37 suffix38 (state37,true) (state38,true) (state96,true) checkpoint37 finish38 +theorem finish36 : runChecked suffix36 (state36,true) = (state96,true) := combine chunk36 suffix37 (state36,true) (state37,true) (state96,true) checkpoint36 finish37 +theorem finish35 : runChecked suffix35 (state35,true) = (state96,true) := combine chunk35 suffix36 (state35,true) (state36,true) (state96,true) checkpoint35 finish36 +theorem finish34 : runChecked suffix34 (state34,true) = (state96,true) := combine chunk34 suffix35 (state34,true) (state35,true) (state96,true) checkpoint34 finish35 +theorem finish33 : runChecked suffix33 (state33,true) = (state96,true) := combine chunk33 suffix34 (state33,true) (state34,true) (state96,true) checkpoint33 finish34 +theorem finish32 : runChecked suffix32 (state32,true) = (state96,true) := combine chunk32 suffix33 (state32,true) (state33,true) (state96,true) checkpoint32 finish33 +theorem finish31 : runChecked suffix31 (state31,true) = (state96,true) := combine chunk31 suffix32 (state31,true) (state32,true) (state96,true) checkpoint31 finish32 +theorem finish30 : runChecked suffix30 (state30,true) = (state96,true) := combine chunk30 suffix31 (state30,true) (state31,true) (state96,true) checkpoint30 finish31 +theorem finish29 : runChecked suffix29 (state29,true) = (state96,true) := combine chunk29 suffix30 (state29,true) (state30,true) (state96,true) checkpoint29 finish30 +theorem finish28 : runChecked suffix28 (state28,true) = (state96,true) := combine chunk28 suffix29 (state28,true) (state29,true) (state96,true) checkpoint28 finish29 +theorem finish27 : runChecked suffix27 (state27,true) = (state96,true) := combine chunk27 suffix28 (state27,true) (state28,true) (state96,true) checkpoint27 finish28 +theorem finish26 : runChecked suffix26 (state26,true) = (state96,true) := combine chunk26 suffix27 (state26,true) (state27,true) (state96,true) checkpoint26 finish27 +theorem finish25 : runChecked suffix25 (state25,true) = (state96,true) := combine chunk25 suffix26 (state25,true) (state26,true) (state96,true) checkpoint25 finish26 +theorem finish24 : runChecked suffix24 (state24,true) = (state96,true) := combine chunk24 suffix25 (state24,true) (state25,true) (state96,true) checkpoint24 finish25 +theorem finish23 : runChecked suffix23 (state23,true) = (state96,true) := combine chunk23 suffix24 (state23,true) (state24,true) (state96,true) checkpoint23 finish24 +theorem finish22 : runChecked suffix22 (state22,true) = (state96,true) := combine chunk22 suffix23 (state22,true) (state23,true) (state96,true) checkpoint22 finish23 +theorem finish21 : runChecked suffix21 (state21,true) = (state96,true) := combine chunk21 suffix22 (state21,true) (state22,true) (state96,true) checkpoint21 finish22 +theorem finish20 : runChecked suffix20 (state20,true) = (state96,true) := combine chunk20 suffix21 (state20,true) (state21,true) (state96,true) checkpoint20 finish21 +theorem finish19 : runChecked suffix19 (state19,true) = (state96,true) := combine chunk19 suffix20 (state19,true) (state20,true) (state96,true) checkpoint19 finish20 +theorem finish18 : runChecked suffix18 (state18,true) = (state96,true) := combine chunk18 suffix19 (state18,true) (state19,true) (state96,true) checkpoint18 finish19 +theorem finish17 : runChecked suffix17 (state17,true) = (state96,true) := combine chunk17 suffix18 (state17,true) (state18,true) (state96,true) checkpoint17 finish18 +theorem finish16 : runChecked suffix16 (state16,true) = (state96,true) := combine chunk16 suffix17 (state16,true) (state17,true) (state96,true) checkpoint16 finish17 +theorem finish15 : runChecked suffix15 (state15,true) = (state96,true) := combine chunk15 suffix16 (state15,true) (state16,true) (state96,true) checkpoint15 finish16 +theorem finish14 : runChecked suffix14 (state14,true) = (state96,true) := combine chunk14 suffix15 (state14,true) (state15,true) (state96,true) checkpoint14 finish15 +theorem finish13 : runChecked suffix13 (state13,true) = (state96,true) := combine chunk13 suffix14 (state13,true) (state14,true) (state96,true) checkpoint13 finish14 +theorem finish12 : runChecked suffix12 (state12,true) = (state96,true) := combine chunk12 suffix13 (state12,true) (state13,true) (state96,true) checkpoint12 finish13 +theorem finish11 : runChecked suffix11 (state11,true) = (state96,true) := combine chunk11 suffix12 (state11,true) (state12,true) (state96,true) checkpoint11 finish12 +theorem finish10 : runChecked suffix10 (state10,true) = (state96,true) := combine chunk10 suffix11 (state10,true) (state11,true) (state96,true) checkpoint10 finish11 +theorem finish9 : runChecked suffix9 (state9,true) = (state96,true) := combine chunk9 suffix10 (state9,true) (state10,true) (state96,true) checkpoint9 finish10 +theorem finish8 : runChecked suffix8 (state8,true) = (state96,true) := combine chunk8 suffix9 (state8,true) (state9,true) (state96,true) checkpoint8 finish9 +theorem finish7 : runChecked suffix7 (state7,true) = (state96,true) := combine chunk7 suffix8 (state7,true) (state8,true) (state96,true) checkpoint7 finish8 +theorem finish6 : runChecked suffix6 (state6,true) = (state96,true) := combine chunk6 suffix7 (state6,true) (state7,true) (state96,true) checkpoint6 finish7 +theorem finish5 : runChecked suffix5 (state5,true) = (state96,true) := combine chunk5 suffix6 (state5,true) (state6,true) (state96,true) checkpoint5 finish6 +theorem finish4 : runChecked suffix4 (state4,true) = (state96,true) := combine chunk4 suffix5 (state4,true) (state5,true) (state96,true) checkpoint4 finish5 +theorem finish3 : runChecked suffix3 (state3,true) = (state96,true) := combine chunk3 suffix4 (state3,true) (state4,true) (state96,true) checkpoint3 finish4 +theorem finish2 : runChecked suffix2 (state2,true) = (state96,true) := combine chunk2 suffix3 (state2,true) (state3,true) (state96,true) checkpoint2 finish3 +theorem finish1 : runChecked suffix1 (state1,true) = (state96,true) := combine chunk1 suffix2 (state1,true) (state2,true) (state96,true) checkpoint1 finish2 +theorem finish0 : runChecked suffix0 (state0,true) = (state96,true) := combine chunk0 suffix1 (state0,true) (state1,true) (state96,true) checkpoint0 finish1 +end SourceFrameTrace diff --git a/research/lean-multi-host-source/FrameTraceCore.lean b/research/lean-multi-host-source/FrameTraceCore.lean new file mode 100644 index 0000000000..6b20ef9667 --- /dev/null +++ b/research/lean-multi-host-source/FrameTraceCore.lean @@ -0,0 +1,85 @@ +import FramedReplay + +/-! +Executable frame-label and retained-center checker for the literal forward +record word. Frame zero represents the unallocated temporary's arbitrary +gauge; the separate `center` field records whether the temporary is live. +No projector equation, owner map, or address isometry follows from labels. +-/ +namespace FrameTrace +open TreeReplay (Tree) + +structure Entry where + scalar : LinearReplay.Event + oldFrame : Nat + newFrame : Nat + rank : Nat + deriving DecidableEq + +structure State where + frames : Tree Nat + center : Option Nat + deriving DecidableEq + +def next (s : State) (e : Entry) : State := + match e.scalar.op with + | 0 => {s with frames := s.frames.put e.scalar.x e.newFrame} + | 1 => s + | 2 => ⟨s.frames.put e.scalar.y e.newFrame, some e.scalar.x⟩ + | _ => ⟨s.frames.put e.scalar.y 0, none⟩ + +def check (s : State) (e : Entry) : Bool := + match e.scalar.op with + | 0 => e.scalar.x < 987 && s.frames.get e.scalar.x == e.oldFrame && + s.center != some e.scalar.x + | 1 => e.scalar.x < 987 && e.scalar.y <= 987 && e.scalar.x != e.scalar.y && + s.frames.get e.scalar.x == e.oldFrame && s.frames.get e.scalar.y == e.oldFrame && + s.center != some e.scalar.x && (e.scalar.y != 987 || s.center.isSome) + | 2 => e.scalar.x < 987 && e.scalar.y == 987 && + s.frames.get e.scalar.x == e.oldFrame && s.center.isNone && e.rank == 8 + | 3 => e.scalar.x < 987 && e.scalar.y == 987 && + s.frames.get e.scalar.x == e.oldFrame && s.frames.get e.scalar.y == e.newFrame && + s.center == some e.scalar.x && e.rank == 0 + | _ => false + +def checkedStep (s : State × Bool) (e : Entry) : State × Bool := + (next s.1 e, s.2 && check s.1 e) + +def runChecked (es : List Entry) (s : State × Bool) : State × Bool := + es.foldl checkedStep s + +def Valid : List Entry → State → Prop + | [], _ => True + | e :: es, s => check s e = true ∧ Valid es (next s e) + +theorem flag_mono (es : List Entry) (s : State × Bool) + (h : (runChecked es s).2 = true) : s.2 = true := by + induction es generalizing s with + | nil => exact h + | cons e es ih => + have h' := ih (checkedStep s e) h + exact (Bool.and_eq_true_iff.mp h').1 + +theorem checked_valid (es : List Entry) (s : State × Bool) + (h : (runChecked es s).2 = true) : Valid es s.1 := by + induction es generalizing s with + | nil => trivial + | cons e es ih => + have h' := flag_mono es (checkedStep s e) h + exact ⟨(Bool.and_eq_true_iff.mp h').2, ih (checkedStep s e) h⟩ + +def toPhysical {X : Type} (gauges : Nat → FramedReplay.Gauge X) (e : Entry) : + FramedReplay.Event X := + ⟨e.scalar, gauges (if e.scalar.op < 3 then e.newFrame else 0)⟩ + +theorem scalar_projection {X : Type} (gauges : Nat → FramedReplay.Gauge X) + (es : List Entry) : + FramedReplay.scalarWord (es.map (toPhysical gauges)) = es.map Entry.scalar := by + simp only [FramedReplay.scalarWord, List.map_map] + rfl + +end FrameTrace + +#print axioms FrameTrace.flag_mono +#print axioms FrameTrace.checked_valid +#print axioms FrameTrace.scalar_projection diff --git a/research/lean-multi-host-source/FrameTraceData.lean b/research/lean-multi-host-source/FrameTraceData.lean new file mode 100644 index 0000000000..5afc76c47d --- /dev/null +++ b/research/lean-multi-host-source/FrameTraceData.lean @@ -0,0 +1,14 @@ +import FrameTraceCheckpoints +set_option maxRecDepth 100000 +set_option maxHeartbeats 0 +namespace SourceFrameTrace +open FrameTrace +open TreeReplay (Tree) +theorem scalar_word : forward.map Entry.scalar = SourceMatrix.forwardWord := by + simp only [forward, chunks, List.flatten_cons, List.flatten_nil, List.map_append, List.map_nil, project0, project1, project2, project3, project4, project5, project6, project7, project8, project9, project10, project11, project12, project13, project14, project15, project16, project17, project18, project19, project20, project21, project22, project23, project24, project25, project26, project27, project28, project29, project30, project31, project32, project33, project34, project35, project36, project37, project38, project39, project40, project41, project42, project43, project44, project45, project46, project47, project48, project49, project50, project51, project52, project53, project54, project55, project56, project57, project58, project59, project60, project61, project62, project63, project64, project65, project66, project67, project68, project69, project70, project71, project72, project73, project74, project75, project76, project77, project78, project79, project80, project81, project82, project83, project84, project85, project86, project87, project88, project89, project90, project91, project92, project93, project94, project95, SourceMatrix.forwardWord, SourceMatrix.forwardChunks] +theorem forward_checked : runChecked forward (state0,true) = (state96,true) := finish0 +theorem forward_valid : Valid forward state0 := checked_valid forward (state0,true) (congrArg Prod.snd forward_checked) +#print axioms scalar_word +#print axioms forward_checked +#print axioms forward_valid +end SourceFrameTrace diff --git a/research/lean-multi-host-source/FrameTraceLiterals.lean b/research/lean-multi-host-source/FrameTraceLiterals.lean new file mode 100644 index 0000000000..27cb1ecce8 --- /dev/null +++ b/research/lean-multi-host-source/FrameTraceLiterals.lean @@ -0,0 +1,35400 @@ +import FrameTraceCore +set_option maxRecDepth 100000 +set_option maxHeartbeats 0 +namespace SourceFrameTrace +open FrameTrace +open TreeReplay (Tree) +def node0 : Tree Nat := .leaf 2 +def node1 : Tree Nat := .leaf 0 +def node2 : Tree Nat := .node node0 node1 +def node3 : Tree Nat := .node node1 node1 +def node4 : Tree Nat := .node node2 node3 +def node5 : Tree Nat := .node node3 node3 +def node6 : Tree Nat := .node node4 node5 +def node7 : Tree Nat := .leaf 66 +def node8 : Tree Nat := .node node7 node1 +def node9 : Tree Nat := .node node1 node0 +def node10 : Tree Nat := .node node8 node9 +def node11 : Tree Nat := .node node10 node5 +def node12 : Tree Nat := .node node6 node11 +def node13 : Tree Nat := .leaf 34 +def node14 : Tree Nat := .node node13 node1 +def node15 : Tree Nat := .node node14 node3 +def node16 : Tree Nat := .node node15 node5 +def node17 : Tree Nat := .leaf 98 +def node18 : Tree Nat := .node node17 node1 +def node19 : Tree Nat := .node node18 node3 +def node20 : Tree Nat := .node node19 node5 +def node21 : Tree Nat := .node node16 node20 +def node22 : Tree Nat := .node node12 node21 +def node23 : Tree Nat := .leaf 18 +def node24 : Tree Nat := .node node23 node1 +def node25 : Tree Nat := .leaf 6 +def node26 : Tree Nat := .node node1 node25 +def node27 : Tree Nat := .node node24 node26 +def node28 : Tree Nat := .node node27 node5 +def node29 : Tree Nat := .leaf 82 +def node30 : Tree Nat := .node node29 node1 +def node31 : Tree Nat := .node node30 node3 +def node32 : Tree Nat := .node node31 node5 +def node33 : Tree Nat := .node node28 node32 +def node34 : Tree Nat := .leaf 50 +def node35 : Tree Nat := .node node34 node1 +def node36 : Tree Nat := .node node35 node3 +def node37 : Tree Nat := .node node36 node5 +def node38 : Tree Nat := .leaf 114 +def node39 : Tree Nat := .node node38 node1 +def node40 : Tree Nat := .node node39 node3 +def node41 : Tree Nat := .node node26 node3 +def node42 : Tree Nat := .node node40 node41 +def node43 : Tree Nat := .node node37 node42 +def node44 : Tree Nat := .node node33 node43 +def node45 : Tree Nat := .node node22 node44 +def node46 : Tree Nat := .leaf 10 +def node47 : Tree Nat := .node node46 node1 +def node48 : Tree Nat := .node node47 node3 +def node49 : Tree Nat := .node node48 node5 +def node50 : Tree Nat := .leaf 74 +def node51 : Tree Nat := .node node50 node1 +def node52 : Tree Nat := .node node51 node26 +def node53 : Tree Nat := .node node52 node5 +def node54 : Tree Nat := .node node49 node53 +def node55 : Tree Nat := .leaf 42 +def node56 : Tree Nat := .node node55 node1 +def node57 : Tree Nat := .leaf 9 +def node58 : Tree Nat := .node node1 node57 +def node59 : Tree Nat := .node node56 node58 +def node60 : Tree Nat := .node node59 node5 +def node61 : Tree Nat := .leaf 106 +def node62 : Tree Nat := .node node61 node1 +def node63 : Tree Nat := .node node62 node3 +def node64 : Tree Nat := .node node63 node5 +def node65 : Tree Nat := .node node60 node64 +def node66 : Tree Nat := .node node54 node65 +def node67 : Tree Nat := .leaf 26 +def node68 : Tree Nat := .node node67 node1 +def node69 : Tree Nat := .node node68 node3 +def node70 : Tree Nat := .node node69 node5 +def node71 : Tree Nat := .leaf 90 +def node72 : Tree Nat := .node node71 node1 +def node73 : Tree Nat := .leaf 7 +def node74 : Tree Nat := .node node1 node73 +def node75 : Tree Nat := .node node72 node74 +def node76 : Tree Nat := .node node75 node5 +def node77 : Tree Nat := .node node70 node76 +def node78 : Tree Nat := .leaf 58 +def node79 : Tree Nat := .node node78 node1 +def node80 : Tree Nat := .node node79 node3 +def node81 : Tree Nat := .node node80 node5 +def node82 : Tree Nat := .leaf 3 +def node83 : Tree Nat := .node node1 node82 +def node84 : Tree Nat := .node node3 node83 +def node85 : Tree Nat := .node node84 node5 +def node86 : Tree Nat := .node node81 node85 +def node87 : Tree Nat := .node node77 node86 +def node88 : Tree Nat := .node node66 node87 +def node89 : Tree Nat := .node node45 node88 +def node90 : Tree Nat := .node node25 node1 +def node91 : Tree Nat := .node node90 node3 +def node92 : Tree Nat := .node node91 node5 +def node93 : Tree Nat := .leaf 70 +def node94 : Tree Nat := .node node93 node1 +def node95 : Tree Nat := .node node94 node58 +def node96 : Tree Nat := .node node95 node5 +def node97 : Tree Nat := .node node92 node96 +def node98 : Tree Nat := .leaf 38 +def node99 : Tree Nat := .node node98 node1 +def node100 : Tree Nat := .node node99 node9 +def node101 : Tree Nat := .node node100 node5 +def node102 : Tree Nat := .leaf 102 +def node103 : Tree Nat := .node node102 node1 +def node104 : Tree Nat := .node node103 node3 +def node105 : Tree Nat := .node node104 node5 +def node106 : Tree Nat := .node node101 node105 +def node107 : Tree Nat := .node node97 node106 +def node108 : Tree Nat := .leaf 22 +def node109 : Tree Nat := .node node108 node1 +def node110 : Tree Nat := .node node109 node3 +def node111 : Tree Nat := .node node110 node5 +def node112 : Tree Nat := .leaf 86 +def node113 : Tree Nat := .node node112 node1 +def node114 : Tree Nat := .leaf 4 +def node115 : Tree Nat := .node node1 node114 +def node116 : Tree Nat := .node node113 node115 +def node117 : Tree Nat := .node node116 node5 +def node118 : Tree Nat := .node node111 node117 +def node119 : Tree Nat := .leaf 54 +def node120 : Tree Nat := .node node119 node1 +def node121 : Tree Nat := .node node120 node3 +def node122 : Tree Nat := .node node121 node5 +def node123 : Tree Nat := .leaf 118 +def node124 : Tree Nat := .node node123 node1 +def node125 : Tree Nat := .node node124 node83 +def node126 : Tree Nat := .node node125 node5 +def node127 : Tree Nat := .node node122 node126 +def node128 : Tree Nat := .node node118 node127 +def node129 : Tree Nat := .node node107 node128 +def node130 : Tree Nat := .leaf 14 +def node131 : Tree Nat := .node node130 node1 +def node132 : Tree Nat := .node node131 node3 +def node133 : Tree Nat := .node node3 node115 +def node134 : Tree Nat := .node node132 node133 +def node135 : Tree Nat := .leaf 78 +def node136 : Tree Nat := .node node135 node1 +def node137 : Tree Nat := .node node136 node3 +def node138 : Tree Nat := .node node137 node5 +def node139 : Tree Nat := .node node134 node138 +def node140 : Tree Nat := .leaf 46 +def node141 : Tree Nat := .node node140 node1 +def node142 : Tree Nat := .node node141 node3 +def node143 : Tree Nat := .node node142 node5 +def node144 : Tree Nat := .leaf 110 +def node145 : Tree Nat := .node node144 node1 +def node146 : Tree Nat := .node node145 node3 +def node147 : Tree Nat := .node node146 node5 +def node148 : Tree Nat := .node node143 node147 +def node149 : Tree Nat := .node node139 node148 +def node150 : Tree Nat := .leaf 30 +def node151 : Tree Nat := .node node150 node1 +def node152 : Tree Nat := .node node151 node3 +def node153 : Tree Nat := .node node152 node5 +def node154 : Tree Nat := .leaf 94 +def node155 : Tree Nat := .node node154 node1 +def node156 : Tree Nat := .node node155 node83 +def node157 : Tree Nat := .node node156 node5 +def node158 : Tree Nat := .node node153 node157 +def node159 : Tree Nat := .leaf 62 +def node160 : Tree Nat := .node node159 node1 +def node161 : Tree Nat := .node node160 node9 +def node162 : Tree Nat := .node node161 node5 +def node163 : Tree Nat := .node node5 node5 +def node164 : Tree Nat := .node node162 node163 +def node165 : Tree Nat := .node node158 node164 +def node166 : Tree Nat := .node node149 node165 +def node167 : Tree Nat := .node node129 node166 +def node168 : Tree Nat := .node node89 node167 +def node169 : Tree Nat := .node node114 node1 +def node170 : Tree Nat := .node node169 node3 +def node171 : Tree Nat := .node node170 node5 +def node172 : Tree Nat := .leaf 68 +def node173 : Tree Nat := .node node172 node1 +def node174 : Tree Nat := .node node173 node3 +def node175 : Tree Nat := .node node174 node5 +def node176 : Tree Nat := .node node171 node175 +def node177 : Tree Nat := .leaf 36 +def node178 : Tree Nat := .node node177 node1 +def node179 : Tree Nat := .node node178 node3 +def node180 : Tree Nat := .node node179 node5 +def node181 : Tree Nat := .leaf 100 +def node182 : Tree Nat := .node node181 node1 +def node183 : Tree Nat := .node node182 node3 +def node184 : Tree Nat := .node node115 node3 +def node185 : Tree Nat := .node node183 node184 +def node186 : Tree Nat := .node node180 node185 +def node187 : Tree Nat := .node node176 node186 +def node188 : Tree Nat := .leaf 20 +def node189 : Tree Nat := .node node188 node1 +def node190 : Tree Nat := .node node189 node3 +def node191 : Tree Nat := .node node190 node5 +def node192 : Tree Nat := .leaf 84 +def node193 : Tree Nat := .node node192 node1 +def node194 : Tree Nat := .node node193 node3 +def node195 : Tree Nat := .leaf 471 +def node196 : Tree Nat := .node node1 node195 +def node197 : Tree Nat := .node node3 node196 +def node198 : Tree Nat := .node node194 node197 +def node199 : Tree Nat := .node node191 node198 +def node200 : Tree Nat := .leaf 52 +def node201 : Tree Nat := .node node200 node1 +def node202 : Tree Nat := .node node201 node9 +def node203 : Tree Nat := .node node202 node5 +def node204 : Tree Nat := .leaf 116 +def node205 : Tree Nat := .node node204 node1 +def node206 : Tree Nat := .node node205 node3 +def node207 : Tree Nat := .node node74 node3 +def node208 : Tree Nat := .node node206 node207 +def node209 : Tree Nat := .node node203 node208 +def node210 : Tree Nat := .node node199 node209 +def node211 : Tree Nat := .node node187 node210 +def node212 : Tree Nat := .leaf 12 +def node213 : Tree Nat := .node node212 node1 +def node214 : Tree Nat := .node node213 node3 +def node215 : Tree Nat := .node node214 node5 +def node216 : Tree Nat := .leaf 76 +def node217 : Tree Nat := .node node216 node1 +def node218 : Tree Nat := .node node217 node3 +def node219 : Tree Nat := .node node218 node5 +def node220 : Tree Nat := .node node215 node219 +def node221 : Tree Nat := .leaf 44 +def node222 : Tree Nat := .node node221 node1 +def node223 : Tree Nat := .node node222 node3 +def node224 : Tree Nat := .leaf 464 +def node225 : Tree Nat := .node node1 node224 +def node226 : Tree Nat := .node node3 node225 +def node227 : Tree Nat := .node node223 node226 +def node228 : Tree Nat := .leaf 108 +def node229 : Tree Nat := .node node228 node1 +def node230 : Tree Nat := .node node229 node83 +def node231 : Tree Nat := .node node230 node5 +def node232 : Tree Nat := .node node227 node231 +def node233 : Tree Nat := .node node220 node232 +def node234 : Tree Nat := .leaf 28 +def node235 : Tree Nat := .node node234 node1 +def node236 : Tree Nat := .node node235 node3 +def node237 : Tree Nat := .node node3 node26 +def node238 : Tree Nat := .node node236 node237 +def node239 : Tree Nat := .leaf 92 +def node240 : Tree Nat := .node node239 node1 +def node241 : Tree Nat := .node node240 node3 +def node242 : Tree Nat := .node node241 node5 +def node243 : Tree Nat := .node node238 node242 +def node244 : Tree Nat := .leaf 60 +def node245 : Tree Nat := .node node244 node1 +def node246 : Tree Nat := .node node245 node3 +def node247 : Tree Nat := .node node246 node5 +def node248 : Tree Nat := .node node247 node163 +def node249 : Tree Nat := .node node243 node248 +def node250 : Tree Nat := .node node233 node249 +def node251 : Tree Nat := .node node211 node250 +def node252 : Tree Nat := .leaf 8 +def node253 : Tree Nat := .node node252 node1 +def node254 : Tree Nat := .node node253 node3 +def node255 : Tree Nat := .node node254 node5 +def node256 : Tree Nat := .leaf 72 +def node257 : Tree Nat := .node node256 node1 +def node258 : Tree Nat := .node node257 node115 +def node259 : Tree Nat := .node node258 node5 +def node260 : Tree Nat := .node node255 node259 +def node261 : Tree Nat := .leaf 40 +def node262 : Tree Nat := .node node261 node1 +def node263 : Tree Nat := .node node262 node3 +def node264 : Tree Nat := .node node263 node5 +def node265 : Tree Nat := .leaf 104 +def node266 : Tree Nat := .node node265 node1 +def node267 : Tree Nat := .node node266 node3 +def node268 : Tree Nat := .node node267 node5 +def node269 : Tree Nat := .node node264 node268 +def node270 : Tree Nat := .node node260 node269 +def node271 : Tree Nat := .leaf 24 +def node272 : Tree Nat := .node node271 node1 +def node273 : Tree Nat := .node node272 node3 +def node274 : Tree Nat := .node node273 node5 +def node275 : Tree Nat := .leaf 88 +def node276 : Tree Nat := .node node275 node1 +def node277 : Tree Nat := .node node276 node3 +def node278 : Tree Nat := .node node277 node5 +def node279 : Tree Nat := .node node274 node278 +def node280 : Tree Nat := .leaf 56 +def node281 : Tree Nat := .node node280 node1 +def node282 : Tree Nat := .node node281 node74 +def node283 : Tree Nat := .node node282 node5 +def node284 : Tree Nat := .leaf 120 +def node285 : Tree Nat := .node node284 node1 +def node286 : Tree Nat := .node node285 node74 +def node287 : Tree Nat := .node node286 node5 +def node288 : Tree Nat := .node node283 node287 +def node289 : Tree Nat := .node node279 node288 +def node290 : Tree Nat := .node node270 node289 +def node291 : Tree Nat := .leaf 16 +def node292 : Tree Nat := .node node291 node1 +def node293 : Tree Nat := .node node292 node3 +def node294 : Tree Nat := .node node293 node5 +def node295 : Tree Nat := .leaf 80 +def node296 : Tree Nat := .node node295 node1 +def node297 : Tree Nat := .node node296 node3 +def node298 : Tree Nat := .node node297 node5 +def node299 : Tree Nat := .node node294 node298 +def node300 : Tree Nat := .leaf 48 +def node301 : Tree Nat := .node node300 node1 +def node302 : Tree Nat := .node node301 node9 +def node303 : Tree Nat := .node node302 node5 +def node304 : Tree Nat := .leaf 112 +def node305 : Tree Nat := .node node304 node1 +def node306 : Tree Nat := .node node305 node3 +def node307 : Tree Nat := .node node306 node5 +def node308 : Tree Nat := .node node303 node307 +def node309 : Tree Nat := .node node299 node308 +def node310 : Tree Nat := .leaf 32 +def node311 : Tree Nat := .node node310 node1 +def node312 : Tree Nat := .node node311 node3 +def node313 : Tree Nat := .node node312 node5 +def node314 : Tree Nat := .leaf 96 +def node315 : Tree Nat := .node node314 node1 +def node316 : Tree Nat := .node node315 node3 +def node317 : Tree Nat := .node node316 node5 +def node318 : Tree Nat := .node node313 node317 +def node319 : Tree Nat := .leaf 64 +def node320 : Tree Nat := .node node319 node1 +def node321 : Tree Nat := .node node320 node9 +def node322 : Tree Nat := .leaf 460 +def node323 : Tree Nat := .node node1 node322 +def node324 : Tree Nat := .node node3 node323 +def node325 : Tree Nat := .node node321 node324 +def node326 : Tree Nat := .node node133 node5 +def node327 : Tree Nat := .node node325 node326 +def node328 : Tree Nat := .node node318 node327 +def node329 : Tree Nat := .node node309 node328 +def node330 : Tree Nat := .node node290 node329 +def node331 : Tree Nat := .node node251 node330 +def node332 : Tree Nat := .node node168 node331 +def node333 : Tree Nat := .node node82 node1 +def node334 : Tree Nat := .node node333 node83 +def node335 : Tree Nat := .node node3 node74 +def node336 : Tree Nat := .node node334 node335 +def node337 : Tree Nat := .leaf 67 +def node338 : Tree Nat := .node node337 node1 +def node339 : Tree Nat := .node node338 node9 +def node340 : Tree Nat := .leaf 470 +def node341 : Tree Nat := .node node1 node340 +def node342 : Tree Nat := .node node3 node341 +def node343 : Tree Nat := .node node339 node342 +def node344 : Tree Nat := .node node336 node343 +def node345 : Tree Nat := .leaf 35 +def node346 : Tree Nat := .node node345 node1 +def node347 : Tree Nat := .node node346 node9 +def node348 : Tree Nat := .node node347 node335 +def node349 : Tree Nat := .leaf 99 +def node350 : Tree Nat := .node node349 node1 +def node351 : Tree Nat := .node node350 node26 +def node352 : Tree Nat := .node node351 node5 +def node353 : Tree Nat := .node node348 node352 +def node354 : Tree Nat := .node node344 node353 +def node355 : Tree Nat := .leaf 19 +def node356 : Tree Nat := .node node355 node1 +def node357 : Tree Nat := .node node356 node26 +def node358 : Tree Nat := .leaf 5 +def node359 : Tree Nat := .node node1 node358 +def node360 : Tree Nat := .node node3 node359 +def node361 : Tree Nat := .node node357 node360 +def node362 : Tree Nat := .leaf 83 +def node363 : Tree Nat := .node node362 node1 +def node364 : Tree Nat := .node node363 node3 +def node365 : Tree Nat := .node node364 node5 +def node366 : Tree Nat := .node node361 node365 +def node367 : Tree Nat := .leaf 51 +def node368 : Tree Nat := .node node367 node1 +def node369 : Tree Nat := .node node368 node9 +def node370 : Tree Nat := .node node369 node5 +def node371 : Tree Nat := .leaf 115 +def node372 : Tree Nat := .node node371 node1 +def node373 : Tree Nat := .node node372 node58 +def node374 : Tree Nat := .node node373 node41 +def node375 : Tree Nat := .node node370 node374 +def node376 : Tree Nat := .node node366 node375 +def node377 : Tree Nat := .node node354 node376 +def node378 : Tree Nat := .leaf 11 +def node379 : Tree Nat := .node node378 node1 +def node380 : Tree Nat := .node node379 node9 +def node381 : Tree Nat := .node node380 node5 +def node382 : Tree Nat := .leaf 75 +def node383 : Tree Nat := .node node382 node1 +def node384 : Tree Nat := .node node383 node26 +def node385 : Tree Nat := .node node384 node5 +def node386 : Tree Nat := .node node381 node385 +def node387 : Tree Nat := .leaf 43 +def node388 : Tree Nat := .node node387 node1 +def node389 : Tree Nat := .node node388 node26 +def node390 : Tree Nat := .node node389 node5 +def node391 : Tree Nat := .leaf 107 +def node392 : Tree Nat := .node node391 node1 +def node393 : Tree Nat := .node node392 node83 +def node394 : Tree Nat := .node node9 node3 +def node395 : Tree Nat := .node node393 node394 +def node396 : Tree Nat := .node node390 node395 +def node397 : Tree Nat := .node node386 node396 +def node398 : Tree Nat := .leaf 27 +def node399 : Tree Nat := .node node398 node1 +def node400 : Tree Nat := .node node399 node3 +def node401 : Tree Nat := .node node3 node58 +def node402 : Tree Nat := .node node400 node401 +def node403 : Tree Nat := .leaf 91 +def node404 : Tree Nat := .node node403 node1 +def node405 : Tree Nat := .node node404 node74 +def node406 : Tree Nat := .node node405 node5 +def node407 : Tree Nat := .node node402 node406 +def node408 : Tree Nat := .leaf 59 +def node409 : Tree Nat := .node node408 node1 +def node410 : Tree Nat := .node node409 node359 +def node411 : Tree Nat := .leaf 462 +def node412 : Tree Nat := .node node1 node411 +def node413 : Tree Nat := .node node3 node412 +def node414 : Tree Nat := .node node410 node413 +def node415 : Tree Nat := .node node84 node394 +def node416 : Tree Nat := .node node414 node415 +def node417 : Tree Nat := .node node407 node416 +def node418 : Tree Nat := .node node397 node417 +def node419 : Tree Nat := .node node377 node418 +def node420 : Tree Nat := .node node73 node1 +def node421 : Tree Nat := .node node420 node9 +def node422 : Tree Nat := .node node421 node335 +def node423 : Tree Nat := .leaf 71 +def node424 : Tree Nat := .node node423 node1 +def node425 : Tree Nat := .node node424 node26 +def node426 : Tree Nat := .node node425 node5 +def node427 : Tree Nat := .node node422 node426 +def node428 : Tree Nat := .leaf 39 +def node429 : Tree Nat := .node node428 node1 +def node430 : Tree Nat := .node node429 node9 +def node431 : Tree Nat := .node node430 node5 +def node432 : Tree Nat := .leaf 103 +def node433 : Tree Nat := .node node432 node1 +def node434 : Tree Nat := .node node433 node26 +def node435 : Tree Nat := .node node83 node3 +def node436 : Tree Nat := .node node434 node435 +def node437 : Tree Nat := .node node431 node436 +def node438 : Tree Nat := .node node427 node437 +def node439 : Tree Nat := .leaf 23 +def node440 : Tree Nat := .node node439 node1 +def node441 : Tree Nat := .node node440 node9 +def node442 : Tree Nat := .node node441 node133 +def node443 : Tree Nat := .leaf 87 +def node444 : Tree Nat := .node node443 node1 +def node445 : Tree Nat := .node node444 node115 +def node446 : Tree Nat := .node node445 node5 +def node447 : Tree Nat := .node node442 node446 +def node448 : Tree Nat := .leaf 55 +def node449 : Tree Nat := .node node448 node1 +def node450 : Tree Nat := .node node449 node3 +def node451 : Tree Nat := .leaf 458 +def node452 : Tree Nat := .node node1 node451 +def node453 : Tree Nat := .node node3 node452 +def node454 : Tree Nat := .node node450 node453 +def node455 : Tree Nat := .leaf 119 +def node456 : Tree Nat := .node node455 node1 +def node457 : Tree Nat := .node node456 node83 +def node458 : Tree Nat := .node node457 node435 +def node459 : Tree Nat := .node node454 node458 +def node460 : Tree Nat := .node node447 node459 +def node461 : Tree Nat := .node node438 node460 +def node462 : Tree Nat := .leaf 15 +def node463 : Tree Nat := .node node462 node1 +def node464 : Tree Nat := .node node463 node26 +def node465 : Tree Nat := .node node464 node133 +def node466 : Tree Nat := .leaf 79 +def node467 : Tree Nat := .node node466 node1 +def node468 : Tree Nat := .node node467 node83 +def node469 : Tree Nat := .node node468 node5 +def node470 : Tree Nat := .node node465 node469 +def node471 : Tree Nat := .leaf 47 +def node472 : Tree Nat := .node node471 node1 +def node473 : Tree Nat := .node node472 node26 +def node474 : Tree Nat := .node node473 node5 +def node475 : Tree Nat := .leaf 111 +def node476 : Tree Nat := .node node475 node1 +def node477 : Tree Nat := .node node476 node74 +def node478 : Tree Nat := .node node477 node5 +def node479 : Tree Nat := .node node474 node478 +def node480 : Tree Nat := .node node470 node479 +def node481 : Tree Nat := .leaf 31 +def node482 : Tree Nat := .node node481 node1 +def node483 : Tree Nat := .node node482 node115 +def node484 : Tree Nat := .node node483 node335 +def node485 : Tree Nat := .leaf 95 +def node486 : Tree Nat := .node node485 node1 +def node487 : Tree Nat := .node node486 node83 +def node488 : Tree Nat := .node node487 node5 +def node489 : Tree Nat := .node node484 node488 +def node490 : Tree Nat := .leaf 63 +def node491 : Tree Nat := .node node490 node1 +def node492 : Tree Nat := .node node491 node9 +def node493 : Tree Nat := .node node492 node5 +def node494 : Tree Nat := .node node237 node5 +def node495 : Tree Nat := .node node493 node494 +def node496 : Tree Nat := .node node489 node495 +def node497 : Tree Nat := .node node480 node496 +def node498 : Tree Nat := .node node461 node497 +def node499 : Tree Nat := .node node419 node498 +def node500 : Tree Nat := .node node358 node1 +def node501 : Tree Nat := .node node500 node83 +def node502 : Tree Nat := .node node501 node237 +def node503 : Tree Nat := .leaf 69 +def node504 : Tree Nat := .node node503 node1 +def node505 : Tree Nat := .node node504 node3 +def node506 : Tree Nat := .node node505 node5 +def node507 : Tree Nat := .node node502 node506 +def node508 : Tree Nat := .leaf 37 +def node509 : Tree Nat := .node node508 node1 +def node510 : Tree Nat := .node node509 node9 +def node511 : Tree Nat := .node node510 node401 +def node512 : Tree Nat := .leaf 101 +def node513 : Tree Nat := .node node512 node1 +def node514 : Tree Nat := .node node513 node359 +def node515 : Tree Nat := .node node514 node184 +def node516 : Tree Nat := .node node511 node515 +def node517 : Tree Nat := .node node507 node516 +def node518 : Tree Nat := .leaf 21 +def node519 : Tree Nat := .node node518 node1 +def node520 : Tree Nat := .node node519 node9 +def node521 : Tree Nat := .node node520 node5 +def node522 : Tree Nat := .leaf 85 +def node523 : Tree Nat := .node node522 node1 +def node524 : Tree Nat := .node node523 node74 +def node525 : Tree Nat := .node node524 node5 +def node526 : Tree Nat := .node node521 node525 +def node527 : Tree Nat := .leaf 53 +def node528 : Tree Nat := .node node527 node1 +def node529 : Tree Nat := .node node528 node9 +def node530 : Tree Nat := .node node529 node5 +def node531 : Tree Nat := .leaf 117 +def node532 : Tree Nat := .node node531 node1 +def node533 : Tree Nat := .node node532 node74 +def node534 : Tree Nat := .node node533 node207 +def node535 : Tree Nat := .node node530 node534 +def node536 : Tree Nat := .node node526 node535 +def node537 : Tree Nat := .node node517 node536 +def node538 : Tree Nat := .leaf 13 +def node539 : Tree Nat := .node node538 node1 +def node540 : Tree Nat := .node node539 node3 +def node541 : Tree Nat := .node node540 node5 +def node542 : Tree Nat := .leaf 77 +def node543 : Tree Nat := .node node542 node1 +def node544 : Tree Nat := .node node543 node3 +def node545 : Tree Nat := .node node544 node5 +def node546 : Tree Nat := .node node541 node545 +def node547 : Tree Nat := .leaf 45 +def node548 : Tree Nat := .node node547 node1 +def node549 : Tree Nat := .node node548 node58 +def node550 : Tree Nat := .node node549 node5 +def node551 : Tree Nat := .leaf 109 +def node552 : Tree Nat := .node node551 node1 +def node553 : Tree Nat := .node node552 node83 +def node554 : Tree Nat := .node node553 node394 +def node555 : Tree Nat := .node node550 node554 +def node556 : Tree Nat := .node node546 node555 +def node557 : Tree Nat := .leaf 29 +def node558 : Tree Nat := .node node557 node1 +def node559 : Tree Nat := .node node558 node74 +def node560 : Tree Nat := .node node559 node237 +def node561 : Tree Nat := .leaf 93 +def node562 : Tree Nat := .node node561 node1 +def node563 : Tree Nat := .node node562 node83 +def node564 : Tree Nat := .node node563 node5 +def node565 : Tree Nat := .node node560 node564 +def node566 : Tree Nat := .leaf 61 +def node567 : Tree Nat := .node node566 node1 +def node568 : Tree Nat := .node node567 node74 +def node569 : Tree Nat := .node node568 node5 +def node570 : Tree Nat := .node node569 node494 +def node571 : Tree Nat := .node node565 node570 +def node572 : Tree Nat := .node node556 node571 +def node573 : Tree Nat := .node node537 node572 +def node574 : Tree Nat := .node node57 node1 +def node575 : Tree Nat := .node node574 node3 +def node576 : Tree Nat := .node node575 node133 +def node577 : Tree Nat := .leaf 73 +def node578 : Tree Nat := .node node577 node1 +def node579 : Tree Nat := .node node578 node115 +def node580 : Tree Nat := .node node579 node5 +def node581 : Tree Nat := .node node576 node580 +def node582 : Tree Nat := .leaf 41 +def node583 : Tree Nat := .node node582 node1 +def node584 : Tree Nat := .node node583 node3 +def node585 : Tree Nat := .node node584 node5 +def node586 : Tree Nat := .leaf 105 +def node587 : Tree Nat := .node node586 node1 +def node588 : Tree Nat := .node node587 node3 +def node589 : Tree Nat := .node node588 node435 +def node590 : Tree Nat := .node node585 node589 +def node591 : Tree Nat := .node node581 node590 +def node592 : Tree Nat := .leaf 25 +def node593 : Tree Nat := .node node592 node1 +def node594 : Tree Nat := .node node593 node9 +def node595 : Tree Nat := .node node594 node401 +def node596 : Tree Nat := .leaf 89 +def node597 : Tree Nat := .node node596 node1 +def node598 : Tree Nat := .node node597 node115 +def node599 : Tree Nat := .node node598 node5 +def node600 : Tree Nat := .node node595 node599 +def node601 : Tree Nat := .leaf 57 +def node602 : Tree Nat := .node node601 node1 +def node603 : Tree Nat := .node node602 node74 +def node604 : Tree Nat := .node node603 node5 +def node605 : Tree Nat := .leaf 121 +def node606 : Tree Nat := .node node605 node1 +def node607 : Tree Nat := .node node606 node74 +def node608 : Tree Nat := .node node607 node5 +def node609 : Tree Nat := .node node604 node608 +def node610 : Tree Nat := .node node600 node609 +def node611 : Tree Nat := .node node591 node610 +def node612 : Tree Nat := .leaf 17 +def node613 : Tree Nat := .node node612 node1 +def node614 : Tree Nat := .node node613 node115 +def node615 : Tree Nat := .node node614 node5 +def node616 : Tree Nat := .leaf 81 +def node617 : Tree Nat := .node node616 node1 +def node618 : Tree Nat := .node node617 node83 +def node619 : Tree Nat := .node node618 node5 +def node620 : Tree Nat := .node node615 node619 +def node621 : Tree Nat := .leaf 49 +def node622 : Tree Nat := .node node621 node1 +def node623 : Tree Nat := .node node622 node9 +def node624 : Tree Nat := .node node623 node5 +def node625 : Tree Nat := .leaf 113 +def node626 : Tree Nat := .node node625 node1 +def node627 : Tree Nat := .node node626 node74 +def node628 : Tree Nat := .node node627 node41 +def node629 : Tree Nat := .node node624 node628 +def node630 : Tree Nat := .node node620 node629 +def node631 : Tree Nat := .leaf 33 +def node632 : Tree Nat := .node node631 node1 +def node633 : Tree Nat := .node node632 node115 +def node634 : Tree Nat := .node node633 node5 +def node635 : Tree Nat := .leaf 97 +def node636 : Tree Nat := .node node635 node1 +def node637 : Tree Nat := .node node636 node26 +def node638 : Tree Nat := .node node637 node5 +def node639 : Tree Nat := .node node634 node638 +def node640 : Tree Nat := .leaf 65 +def node641 : Tree Nat := .node node640 node1 +def node642 : Tree Nat := .node node641 node9 +def node643 : Tree Nat := .node node642 node5 +def node644 : Tree Nat := .node node58 node3 +def node645 : Tree Nat := .node node133 node644 +def node646 : Tree Nat := .node node643 node645 +def node647 : Tree Nat := .node node639 node646 +def node648 : Tree Nat := .node node630 node647 +def node649 : Tree Nat := .node node611 node648 +def node650 : Tree Nat := .node node573 node649 +def node651 : Tree Nat := .node node499 node650 +def node652 : Tree Nat := .node node332 node651 +def node653 : Tree Nat := .node node2 node169 +def node654 : Tree Nat := .node node653 node5 +def node655 : Tree Nat := .node node654 node11 +def node656 : Tree Nat := .node node19 node184 +def node657 : Tree Nat := .node node16 node656 +def node658 : Tree Nat := .node node655 node657 +def node659 : Tree Nat := .node node73 node25 +def node660 : Tree Nat := .node node24 node659 +def node661 : Tree Nat := .node node660 node5 +def node662 : Tree Nat := .node node661 node32 +def node663 : Tree Nat := .node node662 node43 +def node664 : Tree Nat := .node node658 node663 +def node665 : Tree Nat := .node node63 node394 +def node666 : Tree Nat := .node node60 node665 +def node667 : Tree Nat := .node node54 node666 +def node668 : Tree Nat := .node node333 node3 +def node669 : Tree Nat := .node node84 node668 +def node670 : Tree Nat := .node node81 node669 +def node671 : Tree Nat := .node node77 node670 +def node672 : Tree Nat := .node node667 node671 +def node673 : Tree Nat := .node node664 node672 +def node674 : Tree Nat := .node node90 node500 +def node675 : Tree Nat := .node node674 node5 +def node676 : Tree Nat := .node node675 node96 +def node677 : Tree Nat := .node node104 node435 +def node678 : Tree Nat := .node node101 node677 +def node679 : Tree Nat := .node node676 node678 +def node680 : Tree Nat := .node node125 node4 +def node681 : Tree Nat := .node node122 node680 +def node682 : Tree Nat := .node node118 node681 +def node683 : Tree Nat := .node node679 node682 +def node684 : Tree Nat := .node node131 node90 +def node685 : Tree Nat := .node node684 node133 +def node686 : Tree Nat := .node node685 node138 +def node687 : Tree Nat := .node node686 node148 +def node688 : Tree Nat := .node node151 node574 +def node689 : Tree Nat := .node node688 node5 +def node690 : Tree Nat := .node node689 node157 +def node691 : Tree Nat := .node node690 node164 +def node692 : Tree Nat := .node node687 node691 +def node693 : Tree Nat := .node node683 node692 +def node694 : Tree Nat := .node node673 node693 +def node695 : Tree Nat := .node node189 node420 +def node696 : Tree Nat := .node node695 node5 +def node697 : Tree Nat := .node node696 node198 +def node698 : Tree Nat := .node node0 node73 +def node699 : Tree Nat := .node node698 node3 +def node700 : Tree Nat := .node node206 node699 +def node701 : Tree Nat := .node node203 node700 +def node702 : Tree Nat := .node node697 node701 +def node703 : Tree Nat := .node node187 node702 +def node704 : Tree Nat := .node node230 node394 +def node705 : Tree Nat := .node node227 node704 +def node706 : Tree Nat := .node node220 node705 +def node707 : Tree Nat := .node node5 node668 +def node708 : Tree Nat := .node node247 node707 +def node709 : Tree Nat := .node node243 node708 +def node710 : Tree Nat := .node node706 node709 +def node711 : Tree Nat := .node node703 node710 +def node712 : Tree Nat := .node node267 node435 +def node713 : Tree Nat := .node node264 node712 +def node714 : Tree Nat := .node node260 node713 +def node715 : Tree Nat := .node node714 node289 +def node716 : Tree Nat := .node node311 node574 +def node717 : Tree Nat := .node node716 node5 +def node718 : Tree Nat := .node node717 node317 +def node719 : Tree Nat := .node node133 node170 +def node720 : Tree Nat := .node node325 node719 +def node721 : Tree Nat := .node node718 node720 +def node722 : Tree Nat := .node node309 node721 +def node723 : Tree Nat := .node node715 node722 +def node724 : Tree Nat := .node node711 node723 +def node725 : Tree Nat := .node node694 node724 +def node726 : Tree Nat := .node node114 node82 +def node727 : Tree Nat := .node node333 node726 +def node728 : Tree Nat := .node node727 node335 +def node729 : Tree Nat := .node node728 node343 +def node730 : Tree Nat := .node node351 node184 +def node731 : Tree Nat := .node node348 node730 +def node732 : Tree Nat := .node node729 node731 +def node733 : Tree Nat := .node node0 node25 +def node734 : Tree Nat := .node node733 node3 +def node735 : Tree Nat := .node node373 node734 +def node736 : Tree Nat := .node node370 node735 +def node737 : Tree Nat := .node node366 node736 +def node738 : Tree Nat := .node node732 node737 +def node739 : Tree Nat := .node node82 node0 +def node740 : Tree Nat := .node node739 node3 +def node741 : Tree Nat := .node node84 node740 +def node742 : Tree Nat := .node node414 node741 +def node743 : Tree Nat := .node node407 node742 +def node744 : Tree Nat := .node node397 node743 +def node745 : Tree Nat := .node node738 node744 +def node746 : Tree Nat := .node node25 node25 +def node747 : Tree Nat := .node node463 node746 +def node748 : Tree Nat := .node node747 node133 +def node749 : Tree Nat := .node node748 node469 +def node750 : Tree Nat := .node node749 node479 +def node751 : Tree Nat := .node node750 node496 +def node752 : Tree Nat := .node node461 node751 +def node753 : Tree Nat := .node node745 node752 +def node754 : Tree Nat := .node node73 node0 +def node755 : Tree Nat := .node node519 node754 +def node756 : Tree Nat := .node node755 node5 +def node757 : Tree Nat := .node node756 node525 +def node758 : Tree Nat := .node node757 node535 +def node759 : Tree Nat := .node node517 node758 +def node760 : Tree Nat := .node node539 node90 +def node761 : Tree Nat := .node node760 node5 +def node762 : Tree Nat := .node node761 node545 +def node763 : Tree Nat := .node node762 node555 +def node764 : Tree Nat := .node node57 node73 +def node765 : Tree Nat := .node node558 node764 +def node766 : Tree Nat := .node node765 node237 +def node767 : Tree Nat := .node node766 node564 +def node768 : Tree Nat := .node node767 node570 +def node769 : Tree Nat := .node node763 node768 +def node770 : Tree Nat := .node node759 node769 +def node771 : Tree Nat := .node node574 node500 +def node772 : Tree Nat := .node node771 node133 +def node773 : Tree Nat := .node node772 node580 +def node774 : Tree Nat := .node node773 node590 +def node775 : Tree Nat := .node node774 node610 +def node776 : Tree Nat := .node node57 node114 +def node777 : Tree Nat := .node node632 node776 +def node778 : Tree Nat := .node node777 node5 +def node779 : Tree Nat := .node node778 node638 +def node780 : Tree Nat := .node node779 node646 +def node781 : Tree Nat := .node node630 node780 +def node782 : Tree Nat := .node node775 node781 +def node783 : Tree Nat := .node node770 node782 +def node784 : Tree Nat := .node node753 node783 +def node785 : Tree Nat := .node node725 node784 +def node786 : Tree Nat := .node node2 node726 +def node787 : Tree Nat := .node node786 node5 +def node788 : Tree Nat := .node node787 node11 +def node789 : Tree Nat := .node node14 node9 +def node790 : Tree Nat := .node node789 node5 +def node791 : Tree Nat := .node node790 node656 +def node792 : Tree Nat := .node node788 node791 +def node793 : Tree Nat := .node node35 node9 +def node794 : Tree Nat := .node node793 node5 +def node795 : Tree Nat := .node node39 node58 +def node796 : Tree Nat := .node node795 node41 +def node797 : Tree Nat := .node node794 node796 +def node798 : Tree Nat := .node node662 node797 +def node799 : Tree Nat := .node node792 node798 +def node800 : Tree Nat := .node node47 node9 +def node801 : Tree Nat := .node node800 node5 +def node802 : Tree Nat := .node node801 node53 +def node803 : Tree Nat := .node node62 node83 +def node804 : Tree Nat := .node node803 node394 +def node805 : Tree Nat := .node node60 node804 +def node806 : Tree Nat := .node node802 node805 +def node807 : Tree Nat := .node node68 node74 +def node808 : Tree Nat := .node node807 node5 +def node809 : Tree Nat := .node node808 node76 +def node810 : Tree Nat := .node node79 node359 +def node811 : Tree Nat := .node node810 node5 +def node812 : Tree Nat := .node node811 node741 +def node813 : Tree Nat := .node node809 node812 +def node814 : Tree Nat := .node node806 node813 +def node815 : Tree Nat := .node node799 node814 +def node816 : Tree Nat := .node node358 node0 +def node817 : Tree Nat := .node node90 node816 +def node818 : Tree Nat := .node node817 node5 +def node819 : Tree Nat := .node node818 node96 +def node820 : Tree Nat := .node node103 node26 +def node821 : Tree Nat := .node node820 node435 +def node822 : Tree Nat := .node node101 node821 +def node823 : Tree Nat := .node node819 node822 +def node824 : Tree Nat := .node node109 node9 +def node825 : Tree Nat := .node node824 node5 +def node826 : Tree Nat := .node node825 node117 +def node827 : Tree Nat := .node node120 node74 +def node828 : Tree Nat := .node node827 node5 +def node829 : Tree Nat := .node node0 node82 +def node830 : Tree Nat := .node node829 node3 +def node831 : Tree Nat := .node node125 node830 +def node832 : Tree Nat := .node node828 node831 +def node833 : Tree Nat := .node node826 node832 +def node834 : Tree Nat := .node node823 node833 +def node835 : Tree Nat := .node node136 node83 +def node836 : Tree Nat := .node node835 node5 +def node837 : Tree Nat := .node node685 node836 +def node838 : Tree Nat := .node node141 node26 +def node839 : Tree Nat := .node node838 node5 +def node840 : Tree Nat := .node node146 node394 +def node841 : Tree Nat := .node node839 node840 +def node842 : Tree Nat := .node node837 node841 +def node843 : Tree Nat := .node node151 node776 +def node844 : Tree Nat := .node node843 node5 +def node845 : Tree Nat := .node node844 node157 +def node846 : Tree Nat := .node node5 node644 +def node847 : Tree Nat := .node node162 node846 +def node848 : Tree Nat := .node node845 node847 +def node849 : Tree Nat := .node node842 node848 +def node850 : Tree Nat := .node node834 node849 +def node851 : Tree Nat := .node node815 node850 +def node852 : Tree Nat := .node node169 node83 +def node853 : Tree Nat := .node node852 node5 +def node854 : Tree Nat := .node node173 node58 +def node855 : Tree Nat := .node node854 node5 +def node856 : Tree Nat := .node node853 node855 +def node857 : Tree Nat := .node node178 node9 +def node858 : Tree Nat := .node node857 node5 +def node859 : Tree Nat := .node node182 node359 +def node860 : Tree Nat := .node node859 node184 +def node861 : Tree Nat := .node node858 node860 +def node862 : Tree Nat := .node node856 node861 +def node863 : Tree Nat := .node node189 node754 +def node864 : Tree Nat := .node node863 node5 +def node865 : Tree Nat := .node node864 node198 +def node866 : Tree Nat := .node node205 node74 +def node867 : Tree Nat := .node node866 node699 +def node868 : Tree Nat := .node node203 node867 +def node869 : Tree Nat := .node node865 node868 +def node870 : Tree Nat := .node node862 node869 +def node871 : Tree Nat := .node node222 node58 +def node872 : Tree Nat := .node node871 node226 +def node873 : Tree Nat := .node node872 node704 +def node874 : Tree Nat := .node node220 node873 +def node875 : Tree Nat := .node node235 node74 +def node876 : Tree Nat := .node node875 node237 +def node877 : Tree Nat := .node node240 node83 +def node878 : Tree Nat := .node node877 node5 +def node879 : Tree Nat := .node node876 node878 +def node880 : Tree Nat := .node node245 node74 +def node881 : Tree Nat := .node node880 node5 +def node882 : Tree Nat := .node node5 node740 +def node883 : Tree Nat := .node node881 node882 +def node884 : Tree Nat := .node node879 node883 +def node885 : Tree Nat := .node node874 node884 +def node886 : Tree Nat := .node node870 node885 +def node887 : Tree Nat := .node node262 node58 +def node888 : Tree Nat := .node node887 node5 +def node889 : Tree Nat := .node node888 node712 +def node890 : Tree Nat := .node node260 node889 +def node891 : Tree Nat := .node node272 node9 +def node892 : Tree Nat := .node node891 node5 +def node893 : Tree Nat := .node node276 node115 +def node894 : Tree Nat := .node node893 node5 +def node895 : Tree Nat := .node node892 node894 +def node896 : Tree Nat := .node node895 node288 +def node897 : Tree Nat := .node node890 node896 +def node898 : Tree Nat := .node node292 node115 +def node899 : Tree Nat := .node node898 node5 +def node900 : Tree Nat := .node node296 node83 +def node901 : Tree Nat := .node node900 node5 +def node902 : Tree Nat := .node node899 node901 +def node903 : Tree Nat := .node node306 node41 +def node904 : Tree Nat := .node node303 node903 +def node905 : Tree Nat := .node node902 node904 +def node906 : Tree Nat := .node node311 node776 +def node907 : Tree Nat := .node node906 node5 +def node908 : Tree Nat := .node node907 node317 +def node909 : Tree Nat := .node node114 node57 +def node910 : Tree Nat := .node node909 node3 +def node911 : Tree Nat := .node node133 node910 +def node912 : Tree Nat := .node node325 node911 +def node913 : Tree Nat := .node node908 node912 +def node914 : Tree Nat := .node node905 node913 +def node915 : Tree Nat := .node node897 node914 +def node916 : Tree Nat := .node node886 node915 +def node917 : Tree Nat := .node node851 node916 +def node918 : Tree Nat := .node node363 node74 +def node919 : Tree Nat := .node node918 node5 +def node920 : Tree Nat := .node node361 node919 +def node921 : Tree Nat := .node node920 node736 +def node922 : Tree Nat := .node node732 node921 +def node923 : Tree Nat := .node node399 node74 +def node924 : Tree Nat := .node node923 node401 +def node925 : Tree Nat := .node node924 node406 +def node926 : Tree Nat := .node node925 node742 +def node927 : Tree Nat := .node node397 node926 +def node928 : Tree Nat := .node node922 node927 +def node929 : Tree Nat := .node node449 node74 +def node930 : Tree Nat := .node node929 node453 +def node931 : Tree Nat := .node node930 node458 +def node932 : Tree Nat := .node node447 node931 +def node933 : Tree Nat := .node node438 node932 +def node934 : Tree Nat := .node node477 node394 +def node935 : Tree Nat := .node node474 node934 +def node936 : Tree Nat := .node node749 node935 +def node937 : Tree Nat := .node node237 node644 +def node938 : Tree Nat := .node node493 node937 +def node939 : Tree Nat := .node node489 node938 +def node940 : Tree Nat := .node node936 node939 +def node941 : Tree Nat := .node node933 node940 +def node942 : Tree Nat := .node node928 node941 +def node943 : Tree Nat := .node node504 node26 +def node944 : Tree Nat := .node node943 node5 +def node945 : Tree Nat := .node node502 node944 +def node946 : Tree Nat := .node node945 node516 +def node947 : Tree Nat := .node node946 node758 +def node948 : Tree Nat := .node node539 node746 +def node949 : Tree Nat := .node node948 node5 +def node950 : Tree Nat := .node node949 node545 +def node951 : Tree Nat := .node node950 node555 +def node952 : Tree Nat := .node node237 node394 +def node953 : Tree Nat := .node node569 node952 +def node954 : Tree Nat := .node node767 node953 +def node955 : Tree Nat := .node node951 node954 +def node956 : Tree Nat := .node node947 node955 +def node957 : Tree Nat := .node node583 node26 +def node958 : Tree Nat := .node node957 node5 +def node959 : Tree Nat := .node node958 node589 +def node960 : Tree Nat := .node node773 node959 +def node961 : Tree Nat := .node node960 node610 +def node962 : Tree Nat := .node node961 node781 +def node963 : Tree Nat := .node node956 node962 +def node964 : Tree Nat := .node node942 node963 +def node965 : Tree Nat := .node node917 node964 +def node966 : Tree Nat := .node node786 node335 +def node967 : Tree Nat := .node node67 node0 +def node968 : Tree Nat := .node node8 node967 +def node969 : Tree Nat := .node node968 node197 +def node970 : Tree Nat := .node node966 node969 +def node971 : Tree Nat := .node node46 node0 +def node972 : Tree Nat := .node node14 node971 +def node973 : Tree Nat := .node node972 node335 +def node974 : Tree Nat := .node node973 node656 +def node975 : Tree Nat := .node node970 node974 +def node976 : Tree Nat := .node node660 node360 +def node977 : Tree Nat := .node node976 node32 +def node978 : Tree Nat := .node node23 node0 +def node979 : Tree Nat := .node node35 node978 +def node980 : Tree Nat := .node node979 node413 +def node981 : Tree Nat := .node node795 node734 +def node982 : Tree Nat := .node node980 node981 +def node983 : Tree Nat := .node node977 node982 +def node984 : Tree Nat := .node node975 node983 +def node985 : Tree Nat := .node node25 node0 +def node986 : Tree Nat := .node node47 node985 +def node987 : Tree Nat := .node node986 node5 +def node988 : Tree Nat := .node node987 node53 +def node989 : Tree Nat := .node node130 node57 +def node990 : Tree Nat := .node node56 node989 +def node991 : Tree Nat := .node node990 node342 +def node992 : Tree Nat := .node node991 node804 +def node993 : Tree Nat := .node node988 node992 +def node994 : Tree Nat := .node node252 node73 +def node995 : Tree Nat := .node node68 node994 +def node996 : Tree Nat := .node node995 node5 +def node997 : Tree Nat := .node node996 node76 +def node998 : Tree Nat := .node node108 node358 +def node999 : Tree Nat := .node node79 node998 +def node1000 : Tree Nat := .node node999 node5 +def node1001 : Tree Nat := .node node1000 node741 +def node1002 : Tree Nat := .node node997 node1001 +def node1003 : Tree Nat := .node node993 node1002 +def node1004 : Tree Nat := .node node984 node1003 +def node1005 : Tree Nat := .node node817 node335 +def node1006 : Tree Nat := .node node1005 node96 +def node1007 : Tree Nat := .node node212 node0 +def node1008 : Tree Nat := .node node99 node1007 +def node1009 : Tree Nat := .node node1008 node226 +def node1010 : Tree Nat := .node node1009 node821 +def node1011 : Tree Nat := .node node1006 node1010 +def node1012 : Tree Nat := .node node252 node0 +def node1013 : Tree Nat := .node node109 node1012 +def node1014 : Tree Nat := .node node1013 node133 +def node1015 : Tree Nat := .node node1014 node117 +def node1016 : Tree Nat := .node node188 node73 +def node1017 : Tree Nat := .node node120 node1016 +def node1018 : Tree Nat := .node node1017 node5 +def node1019 : Tree Nat := .node node1018 node831 +def node1020 : Tree Nat := .node node1015 node1019 +def node1021 : Tree Nat := .node node1011 node1020 +def node1022 : Tree Nat := .node node291 node25 +def node1023 : Tree Nat := .node node141 node1022 +def node1024 : Tree Nat := .node node1023 node5 +def node1025 : Tree Nat := .node node1024 node840 +def node1026 : Tree Nat := .node node837 node1025 +def node1027 : Tree Nat := .node node843 node335 +def node1028 : Tree Nat := .node node1027 node157 +def node1029 : Tree Nat := .node node271 node0 +def node1030 : Tree Nat := .node node160 node1029 +def node1031 : Tree Nat := .node node1030 node324 +def node1032 : Tree Nat := .node node5 node910 +def node1033 : Tree Nat := .node node1031 node1032 +def node1034 : Tree Nat := .node node1028 node1033 +def node1035 : Tree Nat := .node node1026 node1034 +def node1036 : Tree Nat := .node node1021 node1035 +def node1037 : Tree Nat := .node node1004 node1036 +def node1038 : Tree Nat := .node node358 node82 +def node1039 : Tree Nat := .node node169 node1038 +def node1040 : Tree Nat := .node node1039 node237 +def node1041 : Tree Nat := .node node398 node57 +def node1042 : Tree Nat := .node node173 node1041 +def node1043 : Tree Nat := .node node1042 node5 +def node1044 : Tree Nat := .node node1040 node1043 +def node1045 : Tree Nat := .node node378 node0 +def node1046 : Tree Nat := .node node178 node1045 +def node1047 : Tree Nat := .node node1046 node401 +def node1048 : Tree Nat := .node node1047 node860 +def node1049 : Tree Nat := .node node1044 node1048 +def node1050 : Tree Nat := .node node355 node0 +def node1051 : Tree Nat := .node node201 node1050 +def node1052 : Tree Nat := .node node1051 node5 +def node1053 : Tree Nat := .node node1052 node867 +def node1054 : Tree Nat := .node node865 node1053 +def node1055 : Tree Nat := .node node1049 node1054 +def node1056 : Tree Nat := .node node213 node90 +def node1057 : Tree Nat := .node node1056 node5 +def node1058 : Tree Nat := .node node1057 node219 +def node1059 : Tree Nat := .node node462 node57 +def node1060 : Tree Nat := .node node222 node1059 +def node1061 : Tree Nat := .node node1060 node226 +def node1062 : Tree Nat := .node node1061 node704 +def node1063 : Tree Nat := .node node1058 node1062 +def node1064 : Tree Nat := .node node235 node764 +def node1065 : Tree Nat := .node node1064 node237 +def node1066 : Tree Nat := .node node1065 node878 +def node1067 : Tree Nat := .node node439 node73 +def node1068 : Tree Nat := .node node245 node1067 +def node1069 : Tree Nat := .node node1068 node5 +def node1070 : Tree Nat := .node node1069 node882 +def node1071 : Tree Nat := .node node1066 node1070 +def node1072 : Tree Nat := .node node1063 node1071 +def node1073 : Tree Nat := .node node1055 node1072 +def node1074 : Tree Nat := .node node253 node500 +def node1075 : Tree Nat := .node node1074 node133 +def node1076 : Tree Nat := .node node1075 node259 +def node1077 : Tree Nat := .node node538 node57 +def node1078 : Tree Nat := .node node262 node1077 +def node1079 : Tree Nat := .node node1078 node5 +def node1080 : Tree Nat := .node node1079 node712 +def node1081 : Tree Nat := .node node1076 node1080 +def node1082 : Tree Nat := .node node272 node1012 +def node1083 : Tree Nat := .node node1082 node5 +def node1084 : Tree Nat := .node node1083 node894 +def node1085 : Tree Nat := .node node518 node73 +def node1086 : Tree Nat := .node node281 node1085 +def node1087 : Tree Nat := .node node1086 node5 +def node1088 : Tree Nat := .node node286 node668 +def node1089 : Tree Nat := .node node1087 node1088 +def node1090 : Tree Nat := .node node1084 node1089 +def node1091 : Tree Nat := .node node1081 node1090 +def node1092 : Tree Nat := .node node73 node114 +def node1093 : Tree Nat := .node node292 node1092 +def node1094 : Tree Nat := .node node1093 node5 +def node1095 : Tree Nat := .node node1094 node901 +def node1096 : Tree Nat := .node node612 node0 +def node1097 : Tree Nat := .node node301 node1096 +def node1098 : Tree Nat := .node node1097 node413 +def node1099 : Tree Nat := .node node1098 node903 +def node1100 : Tree Nat := .node node1095 node1099 +def node1101 : Tree Nat := .node node592 node0 +def node1102 : Tree Nat := .node node320 node1101 +def node1103 : Tree Nat := .node node1102 node324 +def node1104 : Tree Nat := .node node1103 node911 +def node1105 : Tree Nat := .node node908 node1104 +def node1106 : Tree Nat := .node node1100 node1105 +def node1107 : Tree Nat := .node node1091 node1106 +def node1108 : Tree Nat := .node node1073 node1107 +def node1109 : Tree Nat := .node node1037 node1108 +def node1110 : Tree Nat := .node node338 node967 +def node1111 : Tree Nat := .node node1110 node342 +def node1112 : Tree Nat := .node node728 node1111 +def node1113 : Tree Nat := .node node346 node971 +def node1114 : Tree Nat := .node node1113 node335 +def node1115 : Tree Nat := .node node1114 node730 +def node1116 : Tree Nat := .node node1112 node1115 +def node1117 : Tree Nat := .node node356 node659 +def node1118 : Tree Nat := .node node1117 node360 +def node1119 : Tree Nat := .node node918 node197 +def node1120 : Tree Nat := .node node1118 node1119 +def node1121 : Tree Nat := .node node368 node978 +def node1122 : Tree Nat := .node node1121 node324 +def node1123 : Tree Nat := .node node1122 node735 +def node1124 : Tree Nat := .node node1120 node1123 +def node1125 : Tree Nat := .node node1116 node1124 +def node1126 : Tree Nat := .node node379 node985 +def node1127 : Tree Nat := .node node1126 node5 +def node1128 : Tree Nat := .node node1127 node385 +def node1129 : Tree Nat := .node node130 node25 +def node1130 : Tree Nat := .node node388 node1129 +def node1131 : Tree Nat := .node node1130 node226 +def node1132 : Tree Nat := .node node1131 node395 +def node1133 : Tree Nat := .node node1128 node1132 +def node1134 : Tree Nat := .node node399 node994 +def node1135 : Tree Nat := .node node1134 node401 +def node1136 : Tree Nat := .node node1135 node406 +def node1137 : Tree Nat := .node node409 node998 +def node1138 : Tree Nat := .node node1137 node413 +def node1139 : Tree Nat := .node node1138 node741 +def node1140 : Tree Nat := .node node1136 node1139 +def node1141 : Tree Nat := .node node1133 node1140 +def node1142 : Tree Nat := .node node1125 node1141 +def node1143 : Tree Nat := .node node420 node816 +def node1144 : Tree Nat := .node node1143 node335 +def node1145 : Tree Nat := .node node1144 node426 +def node1146 : Tree Nat := .node node429 node1007 +def node1147 : Tree Nat := .node node1146 node226 +def node1148 : Tree Nat := .node node1147 node436 +def node1149 : Tree Nat := .node node1145 node1148 +def node1150 : Tree Nat := .node node440 node1012 +def node1151 : Tree Nat := .node node1150 node133 +def node1152 : Tree Nat := .node node1151 node446 +def node1153 : Tree Nat := .node node449 node1016 +def node1154 : Tree Nat := .node node1153 node453 +def node1155 : Tree Nat := .node node457 node830 +def node1156 : Tree Nat := .node node1154 node1155 +def node1157 : Tree Nat := .node node1152 node1156 +def node1158 : Tree Nat := .node node1149 node1157 +def node1159 : Tree Nat := .node node472 node1022 +def node1160 : Tree Nat := .node node1159 node453 +def node1161 : Tree Nat := .node node1160 node934 +def node1162 : Tree Nat := .node node749 node1161 +def node1163 : Tree Nat := .node node482 node776 +def node1164 : Tree Nat := .node node1163 node335 +def node1165 : Tree Nat := .node node1164 node488 +def node1166 : Tree Nat := .node node491 node1029 +def node1167 : Tree Nat := .node node1166 node5 +def node1168 : Tree Nat := .node node237 node910 +def node1169 : Tree Nat := .node node1167 node1168 +def node1170 : Tree Nat := .node node1165 node1169 +def node1171 : Tree Nat := .node node1162 node1170 +def node1172 : Tree Nat := .node node1158 node1171 +def node1173 : Tree Nat := .node node1142 node1172 +def node1174 : Tree Nat := .node node500 node1038 +def node1175 : Tree Nat := .node node1174 node237 +def node1176 : Tree Nat := .node node1175 node944 +def node1177 : Tree Nat := .node node509 node1045 +def node1178 : Tree Nat := .node node1177 node401 +def node1179 : Tree Nat := .node node1178 node515 +def node1180 : Tree Nat := .node node1176 node1179 +def node1181 : Tree Nat := .node node528 node1050 +def node1182 : Tree Nat := .node node1181 node5 +def node1183 : Tree Nat := .node node533 node699 +def node1184 : Tree Nat := .node node1182 node1183 +def node1185 : Tree Nat := .node node757 node1184 +def node1186 : Tree Nat := .node node1180 node1185 +def node1187 : Tree Nat := .node node548 node1059 +def node1188 : Tree Nat := .node node1187 node5 +def node1189 : Tree Nat := .node node1188 node554 +def node1190 : Tree Nat := .node node950 node1189 +def node1191 : Tree Nat := .node node567 node1067 +def node1192 : Tree Nat := .node node1191 node5 +def node1193 : Tree Nat := .node node237 node740 +def node1194 : Tree Nat := .node node1192 node1193 +def node1195 : Tree Nat := .node node767 node1194 +def node1196 : Tree Nat := .node node1190 node1195 +def node1197 : Tree Nat := .node node1186 node1196 +def node1198 : Tree Nat := .node node538 node25 +def node1199 : Tree Nat := .node node583 node1198 +def node1200 : Tree Nat := .node node1199 node5 +def node1201 : Tree Nat := .node node1200 node589 +def node1202 : Tree Nat := .node node773 node1201 +def node1203 : Tree Nat := .node node593 node1012 +def node1204 : Tree Nat := .node node1203 node401 +def node1205 : Tree Nat := .node node1204 node599 +def node1206 : Tree Nat := .node node602 node1085 +def node1207 : Tree Nat := .node node1206 node413 +def node1208 : Tree Nat := .node node607 node668 +def node1209 : Tree Nat := .node node1207 node1208 +def node1210 : Tree Nat := .node node1205 node1209 +def node1211 : Tree Nat := .node node1202 node1210 +def node1212 : Tree Nat := .node node613 node1092 +def node1213 : Tree Nat := .node node1212 node5 +def node1214 : Tree Nat := .node node1213 node619 +def node1215 : Tree Nat := .node node622 node1096 +def node1216 : Tree Nat := .node node1215 node324 +def node1217 : Tree Nat := .node node1216 node628 +def node1218 : Tree Nat := .node node1214 node1217 +def node1219 : Tree Nat := .node node641 node1101 +def node1220 : Tree Nat := .node node1219 node197 +def node1221 : Tree Nat := .node node1220 node911 +def node1222 : Tree Nat := .node node779 node1221 +def node1223 : Tree Nat := .node node1218 node1222 +def node1224 : Tree Nat := .node node1211 node1223 +def node1225 : Tree Nat := .node node1197 node1224 +def node1226 : Tree Nat := .node node1173 node1225 +def node1227 : Tree Nat := .node node1109 node1226 +def node1228 : Tree Nat := .node node78 node73 +def node1229 : Tree Nat := .node node3 node1228 +def node1230 : Tree Nat := .node node786 node1229 +def node1231 : Tree Nat := .node node1230 node969 +def node1232 : Tree Nat := .node node50 node73 +def node1233 : Tree Nat := .node node3 node1232 +def node1234 : Tree Nat := .node node972 node1233 +def node1235 : Tree Nat := .node node18 node56 +def node1236 : Tree Nat := .node node1235 node184 +def node1237 : Tree Nat := .node node1234 node1236 +def node1238 : Tree Nat := .node node1231 node1237 +def node1239 : Tree Nat := .node node7 node358 +def node1240 : Tree Nat := .node node3 node1239 +def node1241 : Tree Nat := .node node660 node1240 +def node1242 : Tree Nat := .node node30 node14 +def node1243 : Tree Nat := .node node1242 node5 +def node1244 : Tree Nat := .node node1241 node1243 +def node1245 : Tree Nat := .node node34 node57 +def node1246 : Tree Nat := .node node39 node1245 +def node1247 : Tree Nat := .node node1246 node734 +def node1248 : Tree Nat := .node node980 node1247 +def node1249 : Tree Nat := .node node1244 node1248 +def node1250 : Tree Nat := .node node1238 node1249 +def node1251 : Tree Nat := .node node3 node160 +def node1252 : Tree Nat := .node node986 node1251 +def node1253 : Tree Nat := .node node150 node25 +def node1254 : Tree Nat := .node node51 node1253 +def node1255 : Tree Nat := .node node1254 node5 +def node1256 : Tree Nat := .node node1252 node1255 +def node1257 : Tree Nat := .node node140 node82 +def node1258 : Tree Nat := .node node62 node1257 +def node1259 : Tree Nat := .node node1258 node394 +def node1260 : Tree Nat := .node node991 node1259 +def node1261 : Tree Nat := .node node1256 node1260 +def node1262 : Tree Nat := .node node3 node94 +def node1263 : Tree Nat := .node node995 node1262 +def node1264 : Tree Nat := .node node98 node73 +def node1265 : Tree Nat := .node node72 node1264 +def node1266 : Tree Nat := .node node1265 node5 +def node1267 : Tree Nat := .node node1263 node1266 +def node1268 : Tree Nat := .node node119 node82 +def node1269 : Tree Nat := .node node3 node1268 +def node1270 : Tree Nat := .node node1269 node740 +def node1271 : Tree Nat := .node node1000 node1270 +def node1272 : Tree Nat := .node node1267 node1271 +def node1273 : Tree Nat := .node node1261 node1272 +def node1274 : Tree Nat := .node node1250 node1273 +def node1275 : Tree Nat := .node node244 node73 +def node1276 : Tree Nat := .node node3 node1275 +def node1277 : Tree Nat := .node node817 node1276 +def node1278 : Tree Nat := .node node234 node57 +def node1279 : Tree Nat := .node node94 node1278 +def node1280 : Tree Nat := .node node1279 node5 +def node1281 : Tree Nat := .node node1277 node1280 +def node1282 : Tree Nat := .node node216 node224 +def node1283 : Tree Nat := .node node3 node1282 +def node1284 : Tree Nat := .node node1008 node1283 +def node1285 : Tree Nat := .node node221 node25 +def node1286 : Tree Nat := .node node103 node1285 +def node1287 : Tree Nat := .node node1286 node435 +def node1288 : Tree Nat := .node node1284 node1287 +def node1289 : Tree Nat := .node node1281 node1288 +def node1290 : Tree Nat := .node node172 node114 +def node1291 : Tree Nat := .node node3 node1290 +def node1292 : Tree Nat := .node node1013 node1291 +def node1293 : Tree Nat := .node node177 node114 +def node1294 : Tree Nat := .node node113 node1293 +def node1295 : Tree Nat := .node node1294 node5 +def node1296 : Tree Nat := .node node1292 node1295 +def node1297 : Tree Nat := .node node200 node82 +def node1298 : Tree Nat := .node node124 node1297 +def node1299 : Tree Nat := .node node1298 node830 +def node1300 : Tree Nat := .node node1018 node1299 +def node1301 : Tree Nat := .node node1296 node1300 +def node1302 : Tree Nat := .node node1289 node1301 +def node1303 : Tree Nat := .node node319 node114 +def node1304 : Tree Nat := .node node3 node1303 +def node1305 : Tree Nat := .node node684 node1304 +def node1306 : Tree Nat := .node node310 node82 +def node1307 : Tree Nat := .node node136 node1306 +def node1308 : Tree Nat := .node node1307 node5 +def node1309 : Tree Nat := .node node1305 node1308 +def node1310 : Tree Nat := .node node145 node301 +def node1311 : Tree Nat := .node node1310 node394 +def node1312 : Tree Nat := .node node1024 node1311 +def node1313 : Tree Nat := .node node1309 node1312 +def node1314 : Tree Nat := .node node256 node73 +def node1315 : Tree Nat := .node node3 node1314 +def node1316 : Tree Nat := .node node843 node1315 +def node1317 : Tree Nat := .node node261 node82 +def node1318 : Tree Nat := .node node155 node1317 +def node1319 : Tree Nat := .node node1318 node5 +def node1320 : Tree Nat := .node node1316 node1319 +def node1321 : Tree Nat := .node node3 node281 +def node1322 : Tree Nat := .node node1321 node910 +def node1323 : Tree Nat := .node node1031 node1322 +def node1324 : Tree Nat := .node node1320 node1323 +def node1325 : Tree Nat := .node node1313 node1324 +def node1326 : Tree Nat := .node node1302 node1325 +def node1327 : Tree Nat := .node node1274 node1326 +def node1328 : Tree Nat := .node node408 node25 +def node1329 : Tree Nat := .node node3 node1328 +def node1330 : Tree Nat := .node node1039 node1329 +def node1331 : Tree Nat := .node node1330 node1043 +def node1332 : Tree Nat := .node node382 node57 +def node1333 : Tree Nat := .node node3 node1332 +def node1334 : Tree Nat := .node node1046 node1333 +def node1335 : Tree Nat := .node node387 node358 +def node1336 : Tree Nat := .node node182 node1335 +def node1337 : Tree Nat := .node node1336 node184 +def node1338 : Tree Nat := .node node1334 node1337 +def node1339 : Tree Nat := .node node1331 node1338 +def node1340 : Tree Nat := .node node3 node338 +def node1341 : Tree Nat := .node node863 node1340 +def node1342 : Tree Nat := .node node193 node346 +def node1343 : Tree Nat := .node node1342 node197 +def node1344 : Tree Nat := .node node1341 node1343 +def node1345 : Tree Nat := .node node367 node73 +def node1346 : Tree Nat := .node node205 node1345 +def node1347 : Tree Nat := .node node1346 node699 +def node1348 : Tree Nat := .node node1052 node1347 +def node1349 : Tree Nat := .node node1344 node1348 +def node1350 : Tree Nat := .node node1339 node1349 +def node1351 : Tree Nat := .node node3 node491 +def node1352 : Tree Nat := .node node1056 node1351 +def node1353 : Tree Nat := .node node217 node482 +def node1354 : Tree Nat := .node node1353 node5 +def node1355 : Tree Nat := .node node1352 node1354 +def node1356 : Tree Nat := .node node471 node82 +def node1357 : Tree Nat := .node node229 node1356 +def node1358 : Tree Nat := .node node1357 node394 +def node1359 : Tree Nat := .node node1061 node1358 +def node1360 : Tree Nat := .node node1355 node1359 +def node1361 : Tree Nat := .node node423 node25 +def node1362 : Tree Nat := .node node3 node1361 +def node1363 : Tree Nat := .node node1064 node1362 +def node1364 : Tree Nat := .node node428 node82 +def node1365 : Tree Nat := .node node240 node1364 +def node1366 : Tree Nat := .node node1365 node5 +def node1367 : Tree Nat := .node node1363 node1366 +def node1368 : Tree Nat := .node node3 node449 +def node1369 : Tree Nat := .node node1368 node740 +def node1370 : Tree Nat := .node node1069 node1369 +def node1371 : Tree Nat := .node node1367 node1370 +def node1372 : Tree Nat := .node node1360 node1371 +def node1373 : Tree Nat := .node node1350 node1372 +def node1374 : Tree Nat := .node node566 node114 +def node1375 : Tree Nat := .node node3 node1374 +def node1376 : Tree Nat := .node node1074 node1375 +def node1377 : Tree Nat := .node node557 node114 +def node1378 : Tree Nat := .node node257 node1377 +def node1379 : Tree Nat := .node node1378 node5 +def node1380 : Tree Nat := .node node1376 node1379 +def node1381 : Tree Nat := .node node3 node543 +def node1382 : Tree Nat := .node node1078 node1381 +def node1383 : Tree Nat := .node node266 node548 +def node1384 : Tree Nat := .node node1383 node435 +def node1385 : Tree Nat := .node node1382 node1384 +def node1386 : Tree Nat := .node node1380 node1385 +def node1387 : Tree Nat := .node node3 node504 +def node1388 : Tree Nat := .node node1082 node1387 +def node1389 : Tree Nat := .node node508 node114 +def node1390 : Tree Nat := .node node276 node1389 +def node1391 : Tree Nat := .node node1390 node5 +def node1392 : Tree Nat := .node node1388 node1391 +def node1393 : Tree Nat := .node node527 node73 +def node1394 : Tree Nat := .node node285 node1393 +def node1395 : Tree Nat := .node node1394 node668 +def node1396 : Tree Nat := .node node1087 node1395 +def node1397 : Tree Nat := .node node1392 node1396 +def node1398 : Tree Nat := .node node1386 node1397 +def node1399 : Tree Nat := .node node3 node641 +def node1400 : Tree Nat := .node node1093 node1399 +def node1401 : Tree Nat := .node node631 node82 +def node1402 : Tree Nat := .node node296 node1401 +def node1403 : Tree Nat := .node node1402 node5 +def node1404 : Tree Nat := .node node1400 node1403 +def node1405 : Tree Nat := .node node305 node622 +def node1406 : Tree Nat := .node node1405 node41 +def node1407 : Tree Nat := .node node1098 node1406 +def node1408 : Tree Nat := .node node1404 node1407 +def node1409 : Tree Nat := .node node3 node578 +def node1410 : Tree Nat := .node node906 node1409 +def node1411 : Tree Nat := .node node315 node583 +def node1412 : Tree Nat := .node node1411 node5 +def node1413 : Tree Nat := .node node1410 node1412 +def node1414 : Tree Nat := .node node601 node114 +def node1415 : Tree Nat := .node node3 node1414 +def node1416 : Tree Nat := .node node1415 node910 +def node1417 : Tree Nat := .node node1103 node1416 +def node1418 : Tree Nat := .node node1413 node1417 +def node1419 : Tree Nat := .node node1408 node1418 +def node1420 : Tree Nat := .node node1398 node1419 +def node1421 : Tree Nat := .node node1373 node1420 +def node1422 : Tree Nat := .node node1327 node1421 +def node1423 : Tree Nat := .node node727 node1229 +def node1424 : Tree Nat := .node node1423 node1111 +def node1425 : Tree Nat := .node node1113 node1233 +def node1426 : Tree Nat := .node node55 node25 +def node1427 : Tree Nat := .node node350 node1426 +def node1428 : Tree Nat := .node node1427 node184 +def node1429 : Tree Nat := .node node1425 node1428 +def node1430 : Tree Nat := .node node1424 node1429 +def node1431 : Tree Nat := .node node1117 node1240 +def node1432 : Tree Nat := .node node13 node73 +def node1433 : Tree Nat := .node node363 node1432 +def node1434 : Tree Nat := .node node1433 node197 +def node1435 : Tree Nat := .node node1431 node1434 +def node1436 : Tree Nat := .node node372 node1245 +def node1437 : Tree Nat := .node node1436 node734 +def node1438 : Tree Nat := .node node1122 node1437 +def node1439 : Tree Nat := .node node1435 node1438 +def node1440 : Tree Nat := .node node1430 node1439 +def node1441 : Tree Nat := .node node1126 node1251 +def node1442 : Tree Nat := .node node383 node1253 +def node1443 : Tree Nat := .node node1442 node5 +def node1444 : Tree Nat := .node node1441 node1443 +def node1445 : Tree Nat := .node node392 node1257 +def node1446 : Tree Nat := .node node1445 node394 +def node1447 : Tree Nat := .node node1131 node1446 +def node1448 : Tree Nat := .node node1444 node1447 +def node1449 : Tree Nat := .node node93 node57 +def node1450 : Tree Nat := .node node3 node1449 +def node1451 : Tree Nat := .node node1134 node1450 +def node1452 : Tree Nat := .node node404 node1264 +def node1453 : Tree Nat := .node node1452 node5 +def node1454 : Tree Nat := .node node1451 node1453 +def node1455 : Tree Nat := .node node1138 node1270 +def node1456 : Tree Nat := .node node1454 node1455 +def node1457 : Tree Nat := .node node1448 node1456 +def node1458 : Tree Nat := .node node1440 node1457 +def node1459 : Tree Nat := .node node1143 node1276 +def node1460 : Tree Nat := .node node234 node25 +def node1461 : Tree Nat := .node node424 node1460 +def node1462 : Tree Nat := .node node1461 node5 +def node1463 : Tree Nat := .node node1459 node1462 +def node1464 : Tree Nat := .node node1146 node1283 +def node1465 : Tree Nat := .node node433 node1285 +def node1466 : Tree Nat := .node node1465 node435 +def node1467 : Tree Nat := .node node1464 node1466 +def node1468 : Tree Nat := .node node1463 node1467 +def node1469 : Tree Nat := .node node1150 node1291 +def node1470 : Tree Nat := .node node444 node1293 +def node1471 : Tree Nat := .node node1470 node5 +def node1472 : Tree Nat := .node node1469 node1471 +def node1473 : Tree Nat := .node node456 node1297 +def node1474 : Tree Nat := .node node1473 node830 +def node1475 : Tree Nat := .node node1154 node1474 +def node1476 : Tree Nat := .node node1472 node1475 +def node1477 : Tree Nat := .node node1468 node1476 +def node1478 : Tree Nat := .node node747 node1304 +def node1479 : Tree Nat := .node node467 node1306 +def node1480 : Tree Nat := .node node1479 node5 +def node1481 : Tree Nat := .node node1478 node1480 +def node1482 : Tree Nat := .node node300 node73 +def node1483 : Tree Nat := .node node476 node1482 +def node1484 : Tree Nat := .node node1483 node394 +def node1485 : Tree Nat := .node node1160 node1484 +def node1486 : Tree Nat := .node node1481 node1485 +def node1487 : Tree Nat := .node node1163 node1315 +def node1488 : Tree Nat := .node node486 node1317 +def node1489 : Tree Nat := .node node1488 node5 +def node1490 : Tree Nat := .node node1487 node1489 +def node1491 : Tree Nat := .node node280 node25 +def node1492 : Tree Nat := .node node3 node1491 +def node1493 : Tree Nat := .node node1492 node910 +def node1494 : Tree Nat := .node node1167 node1493 +def node1495 : Tree Nat := .node node1490 node1494 +def node1496 : Tree Nat := .node node1486 node1495 +def node1497 : Tree Nat := .node node1477 node1496 +def node1498 : Tree Nat := .node node1458 node1497 +def node1499 : Tree Nat := .node node1174 node1329 +def node1500 : Tree Nat := .node node398 node25 +def node1501 : Tree Nat := .node node504 node1500 +def node1502 : Tree Nat := .node node1501 node5 +def node1503 : Tree Nat := .node node1499 node1502 +def node1504 : Tree Nat := .node node1177 node1333 +def node1505 : Tree Nat := .node node513 node1335 +def node1506 : Tree Nat := .node node1505 node184 +def node1507 : Tree Nat := .node node1504 node1506 +def node1508 : Tree Nat := .node node1503 node1507 +def node1509 : Tree Nat := .node node755 node1340 +def node1510 : Tree Nat := .node node345 node73 +def node1511 : Tree Nat := .node node523 node1510 +def node1512 : Tree Nat := .node node1511 node5 +def node1513 : Tree Nat := .node node1509 node1512 +def node1514 : Tree Nat := .node node532 node1345 +def node1515 : Tree Nat := .node node1514 node699 +def node1516 : Tree Nat := .node node1182 node1515 +def node1517 : Tree Nat := .node node1513 node1516 +def node1518 : Tree Nat := .node node1508 node1517 +def node1519 : Tree Nat := .node node948 node1351 +def node1520 : Tree Nat := .node node543 node482 +def node1521 : Tree Nat := .node node1520 node5 +def node1522 : Tree Nat := .node node1519 node1521 +def node1523 : Tree Nat := .node node552 node1356 +def node1524 : Tree Nat := .node node1523 node394 +def node1525 : Tree Nat := .node node1188 node1524 +def node1526 : Tree Nat := .node node1522 node1525 +def node1527 : Tree Nat := .node node765 node1362 +def node1528 : Tree Nat := .node node562 node1364 +def node1529 : Tree Nat := .node node1528 node5 +def node1530 : Tree Nat := .node node1527 node1529 +def node1531 : Tree Nat := .node node448 node25 +def node1532 : Tree Nat := .node node3 node1531 +def node1533 : Tree Nat := .node node1532 node740 +def node1534 : Tree Nat := .node node1192 node1533 +def node1535 : Tree Nat := .node node1530 node1534 +def node1536 : Tree Nat := .node node1526 node1535 +def node1537 : Tree Nat := .node node1518 node1536 +def node1538 : Tree Nat := .node node771 node1375 +def node1539 : Tree Nat := .node node578 node1377 +def node1540 : Tree Nat := .node node1539 node5 +def node1541 : Tree Nat := .node node1538 node1540 +def node1542 : Tree Nat := .node node587 node548 +def node1543 : Tree Nat := .node node1542 node435 +def node1544 : Tree Nat := .node node1200 node1543 +def node1545 : Tree Nat := .node node1541 node1544 +def node1546 : Tree Nat := .node node503 node57 +def node1547 : Tree Nat := .node node3 node1546 +def node1548 : Tree Nat := .node node1203 node1547 +def node1549 : Tree Nat := .node node597 node1389 +def node1550 : Tree Nat := .node node1549 node5 +def node1551 : Tree Nat := .node node1548 node1550 +def node1552 : Tree Nat := .node node606 node1393 +def node1553 : Tree Nat := .node node1552 node668 +def node1554 : Tree Nat := .node node1207 node1553 +def node1555 : Tree Nat := .node node1551 node1554 +def node1556 : Tree Nat := .node node1545 node1555 +def node1557 : Tree Nat := .node node1212 node1399 +def node1558 : Tree Nat := .node node617 node1401 +def node1559 : Tree Nat := .node node1558 node5 +def node1560 : Tree Nat := .node node1557 node1559 +def node1561 : Tree Nat := .node node621 node73 +def node1562 : Tree Nat := .node node626 node1561 +def node1563 : Tree Nat := .node node1562 node41 +def node1564 : Tree Nat := .node node1216 node1563 +def node1565 : Tree Nat := .node node1560 node1564 +def node1566 : Tree Nat := .node node777 node1409 +def node1567 : Tree Nat := .node node582 node25 +def node1568 : Tree Nat := .node node636 node1567 +def node1569 : Tree Nat := .node node1568 node5 +def node1570 : Tree Nat := .node node1566 node1569 +def node1571 : Tree Nat := .node node1220 node1416 +def node1572 : Tree Nat := .node node1570 node1571 +def node1573 : Tree Nat := .node node1565 node1572 +def node1574 : Tree Nat := .node node1556 node1573 +def node1575 : Tree Nat := .node node1537 node1574 +def node1576 : Tree Nat := .node node1498 node1575 +def node1577 : Tree Nat := .node node1422 node1576 +def node1578 : Tree Nat := .leaf 122 +def node1579 : Tree Nat := .node node0 node1578 +def node1580 : Tree Nat := .node node1579 node726 +def node1581 : Tree Nat := .node node1580 node1229 +def node1582 : Tree Nat := .node node71 node195 +def node1583 : Tree Nat := .node node3 node1582 +def node1584 : Tree Nat := .node node968 node1583 +def node1585 : Tree Nat := .node node1581 node1584 +def node1586 : Tree Nat := .node node115 node62 +def node1587 : Tree Nat := .node node1235 node1586 +def node1588 : Tree Nat := .node node1234 node1587 +def node1589 : Tree Nat := .node node1585 node1588 +def node1590 : Tree Nat := .node node3 node18 +def node1591 : Tree Nat := .node node1242 node1590 +def node1592 : Tree Nat := .node node1241 node1591 +def node1593 : Tree Nat := .node node29 node411 +def node1594 : Tree Nat := .node node3 node1593 +def node1595 : Tree Nat := .node node979 node1594 +def node1596 : Tree Nat := .node node733 node39 +def node1597 : Tree Nat := .node node1246 node1596 +def node1598 : Tree Nat := .node node1595 node1597 +def node1599 : Tree Nat := .node node1592 node1598 +def node1600 : Tree Nat := .node node1589 node1599 +def node1601 : Tree Nat := .node node3 node155 +def node1602 : Tree Nat := .node node1254 node1601 +def node1603 : Tree Nat := .node node1252 node1602 +def node1604 : Tree Nat := .node node135 node340 +def node1605 : Tree Nat := .node node3 node1604 +def node1606 : Tree Nat := .node node990 node1605 +def node1607 : Tree Nat := .node node9 node145 +def node1608 : Tree Nat := .node node1258 node1607 +def node1609 : Tree Nat := .node node1606 node1608 +def node1610 : Tree Nat := .node node1603 node1609 +def node1611 : Tree Nat := .node node3 node103 +def node1612 : Tree Nat := .node node1265 node1611 +def node1613 : Tree Nat := .node node1263 node1612 +def node1614 : Tree Nat := .node node3 node113 +def node1615 : Tree Nat := .node node999 node1614 +def node1616 : Tree Nat := .node node739 node124 +def node1617 : Tree Nat := .node node1269 node1616 +def node1618 : Tree Nat := .node node1615 node1617 +def node1619 : Tree Nat := .node node1613 node1618 +def node1620 : Tree Nat := .node node1610 node1619 +def node1621 : Tree Nat := .node node1600 node1620 +def node1622 : Tree Nat := .leaf 124 +def node1623 : Tree Nat := .node node25 node1622 +def node1624 : Tree Nat := .node node1623 node816 +def node1625 : Tree Nat := .node node1624 node1276 +def node1626 : Tree Nat := .node node3 node240 +def node1627 : Tree Nat := .node node1279 node1626 +def node1628 : Tree Nat := .node node1625 node1627 +def node1629 : Tree Nat := .node node83 node229 +def node1630 : Tree Nat := .node node1286 node1629 +def node1631 : Tree Nat := .node node1284 node1630 +def node1632 : Tree Nat := .node node1628 node1631 +def node1633 : Tree Nat := .node node3 node182 +def node1634 : Tree Nat := .node node1294 node1633 +def node1635 : Tree Nat := .node node1292 node1634 +def node1636 : Tree Nat := .node node3 node193 +def node1637 : Tree Nat := .node node1017 node1636 +def node1638 : Tree Nat := .node node829 node205 +def node1639 : Tree Nat := .node node1298 node1638 +def node1640 : Tree Nat := .node node1637 node1639 +def node1641 : Tree Nat := .node node1635 node1640 +def node1642 : Tree Nat := .node node1632 node1641 +def node1643 : Tree Nat := .node node3 node315 +def node1644 : Tree Nat := .node node1307 node1643 +def node1645 : Tree Nat := .node node1305 node1644 +def node1646 : Tree Nat := .node node3 node296 +def node1647 : Tree Nat := .node node1023 node1646 +def node1648 : Tree Nat := .node node9 node305 +def node1649 : Tree Nat := .node node1310 node1648 +def node1650 : Tree Nat := .node node1647 node1649 +def node1651 : Tree Nat := .node node1645 node1650 +def node1652 : Tree Nat := .node node3 node266 +def node1653 : Tree Nat := .node node1318 node1652 +def node1654 : Tree Nat := .node node1316 node1653 +def node1655 : Tree Nat := .node node275 node322 +def node1656 : Tree Nat := .node node3 node1655 +def node1657 : Tree Nat := .node node1030 node1656 +def node1658 : Tree Nat := .node node909 node285 +def node1659 : Tree Nat := .node node1321 node1658 +def node1660 : Tree Nat := .node node1657 node1659 +def node1661 : Tree Nat := .node node1654 node1660 +def node1662 : Tree Nat := .node node1651 node1661 +def node1663 : Tree Nat := .node node1642 node1662 +def node1664 : Tree Nat := .node node1621 node1663 +def node1665 : Tree Nat := .leaf 123 +def node1666 : Tree Nat := .node node114 node1665 +def node1667 : Tree Nat := .node node1666 node1038 +def node1668 : Tree Nat := .node node1667 node1329 +def node1669 : Tree Nat := .node node1665 node1 +def node1670 : Tree Nat := .node node1669 node1041 +def node1671 : Tree Nat := .node node3 node404 +def node1672 : Tree Nat := .node node1670 node1671 +def node1673 : Tree Nat := .node node1668 node1672 +def node1674 : Tree Nat := .node node115 node392 +def node1675 : Tree Nat := .node node1336 node1674 +def node1676 : Tree Nat := .node node1334 node1675 +def node1677 : Tree Nat := .node node1673 node1676 +def node1678 : Tree Nat := .node node349 node195 +def node1679 : Tree Nat := .node node3 node1678 +def node1680 : Tree Nat := .node node1342 node1679 +def node1681 : Tree Nat := .node node1341 node1680 +def node1682 : Tree Nat := .node node3 node363 +def node1683 : Tree Nat := .node node1051 node1682 +def node1684 : Tree Nat := .node node698 node372 +def node1685 : Tree Nat := .node node1346 node1684 +def node1686 : Tree Nat := .node node1683 node1685 +def node1687 : Tree Nat := .node node1681 node1686 +def node1688 : Tree Nat := .node node1677 node1687 +def node1689 : Tree Nat := .node node3 node486 +def node1690 : Tree Nat := .node node1353 node1689 +def node1691 : Tree Nat := .node node1352 node1690 +def node1692 : Tree Nat := .node node466 node224 +def node1693 : Tree Nat := .node node3 node1692 +def node1694 : Tree Nat := .node node1060 node1693 +def node1695 : Tree Nat := .node node9 node476 +def node1696 : Tree Nat := .node node1357 node1695 +def node1697 : Tree Nat := .node node1694 node1696 +def node1698 : Tree Nat := .node node1691 node1697 +def node1699 : Tree Nat := .node node3 node433 +def node1700 : Tree Nat := .node node1365 node1699 +def node1701 : Tree Nat := .node node1363 node1700 +def node1702 : Tree Nat := .node node3 node444 +def node1703 : Tree Nat := .node node1068 node1702 +def node1704 : Tree Nat := .node node739 node456 +def node1705 : Tree Nat := .node node1368 node1704 +def node1706 : Tree Nat := .node node1703 node1705 +def node1707 : Tree Nat := .node node1701 node1706 +def node1708 : Tree Nat := .node node1698 node1707 +def node1709 : Tree Nat := .node node1688 node1708 +def node1710 : Tree Nat := .node node3 node562 +def node1711 : Tree Nat := .node node1378 node1710 +def node1712 : Tree Nat := .node node1376 node1711 +def node1713 : Tree Nat := .node node83 node552 +def node1714 : Tree Nat := .node node1383 node1713 +def node1715 : Tree Nat := .node node1382 node1714 +def node1716 : Tree Nat := .node node1712 node1715 +def node1717 : Tree Nat := .node node3 node513 +def node1718 : Tree Nat := .node node1390 node1717 +def node1719 : Tree Nat := .node node1388 node1718 +def node1720 : Tree Nat := .node node3 node523 +def node1721 : Tree Nat := .node node1086 node1720 +def node1722 : Tree Nat := .node node333 node532 +def node1723 : Tree Nat := .node node1394 node1722 +def node1724 : Tree Nat := .node node1721 node1723 +def node1725 : Tree Nat := .node node1719 node1724 +def node1726 : Tree Nat := .node node1716 node1725 +def node1727 : Tree Nat := .node node3 node636 +def node1728 : Tree Nat := .node node1402 node1727 +def node1729 : Tree Nat := .node node1400 node1728 +def node1730 : Tree Nat := .node node616 node411 +def node1731 : Tree Nat := .node node3 node1730 +def node1732 : Tree Nat := .node node1097 node1731 +def node1733 : Tree Nat := .node node26 node626 +def node1734 : Tree Nat := .node node1405 node1733 +def node1735 : Tree Nat := .node node1732 node1734 +def node1736 : Tree Nat := .node node1729 node1735 +def node1737 : Tree Nat := .node node3 node587 +def node1738 : Tree Nat := .node node1411 node1737 +def node1739 : Tree Nat := .node node1410 node1738 +def node1740 : Tree Nat := .node node596 node322 +def node1741 : Tree Nat := .node node3 node1740 +def node1742 : Tree Nat := .node node1102 node1741 +def node1743 : Tree Nat := .node node909 node606 +def node1744 : Tree Nat := .node node1415 node1743 +def node1745 : Tree Nat := .node node1742 node1744 +def node1746 : Tree Nat := .node node1739 node1745 +def node1747 : Tree Nat := .node node1736 node1746 +def node1748 : Tree Nat := .node node1726 node1747 +def node1749 : Tree Nat := .node node1709 node1748 +def node1750 : Tree Nat := .node node1664 node1749 +def node1751 : Tree Nat := .node node82 node1578 +def node1752 : Tree Nat := .node node1751 node726 +def node1753 : Tree Nat := .node node1752 node1229 +def node1754 : Tree Nat := .node node71 node340 +def node1755 : Tree Nat := .node node3 node1754 +def node1756 : Tree Nat := .node node1110 node1755 +def node1757 : Tree Nat := .node node1753 node1756 +def node1758 : Tree Nat := .node node1427 node1586 +def node1759 : Tree Nat := .node node1425 node1758 +def node1760 : Tree Nat := .node node1757 node1759 +def node1761 : Tree Nat := .node node17 node195 +def node1762 : Tree Nat := .node node3 node1761 +def node1763 : Tree Nat := .node node1433 node1762 +def node1764 : Tree Nat := .node node1431 node1763 +def node1765 : Tree Nat := .node node29 node322 +def node1766 : Tree Nat := .node node3 node1765 +def node1767 : Tree Nat := .node node1121 node1766 +def node1768 : Tree Nat := .node node1436 node1596 +def node1769 : Tree Nat := .node node1767 node1768 +def node1770 : Tree Nat := .node node1764 node1769 +def node1771 : Tree Nat := .node node1760 node1770 +def node1772 : Tree Nat := .node node1442 node1601 +def node1773 : Tree Nat := .node node1441 node1772 +def node1774 : Tree Nat := .node node135 node224 +def node1775 : Tree Nat := .node node3 node1774 +def node1776 : Tree Nat := .node node1130 node1775 +def node1777 : Tree Nat := .node node1445 node1607 +def node1778 : Tree Nat := .node node1776 node1777 +def node1779 : Tree Nat := .node node1773 node1778 +def node1780 : Tree Nat := .node node1452 node1611 +def node1781 : Tree Nat := .node node1451 node1780 +def node1782 : Tree Nat := .node node112 node411 +def node1783 : Tree Nat := .node node3 node1782 +def node1784 : Tree Nat := .node node1137 node1783 +def node1785 : Tree Nat := .node node1784 node1617 +def node1786 : Tree Nat := .node node1781 node1785 +def node1787 : Tree Nat := .node node1779 node1786 +def node1788 : Tree Nat := .node node1771 node1787 +def node1789 : Tree Nat := .node node73 node1622 +def node1790 : Tree Nat := .node node1789 node816 +def node1791 : Tree Nat := .node node1790 node1276 +def node1792 : Tree Nat := .node node1461 node1626 +def node1793 : Tree Nat := .node node1791 node1792 +def node1794 : Tree Nat := .node node1465 node1629 +def node1795 : Tree Nat := .node node1464 node1794 +def node1796 : Tree Nat := .node node1793 node1795 +def node1797 : Tree Nat := .node node1470 node1633 +def node1798 : Tree Nat := .node node1469 node1797 +def node1799 : Tree Nat := .node node192 node451 +def node1800 : Tree Nat := .node node3 node1799 +def node1801 : Tree Nat := .node node1153 node1800 +def node1802 : Tree Nat := .node node1473 node1638 +def node1803 : Tree Nat := .node node1801 node1802 +def node1804 : Tree Nat := .node node1798 node1803 +def node1805 : Tree Nat := .node node1796 node1804 +def node1806 : Tree Nat := .node node1479 node1643 +def node1807 : Tree Nat := .node node1478 node1806 +def node1808 : Tree Nat := .node node295 node451 +def node1809 : Tree Nat := .node node3 node1808 +def node1810 : Tree Nat := .node node1159 node1809 +def node1811 : Tree Nat := .node node1483 node1648 +def node1812 : Tree Nat := .node node1810 node1811 +def node1813 : Tree Nat := .node node1807 node1812 +def node1814 : Tree Nat := .node node1488 node1652 +def node1815 : Tree Nat := .node node1487 node1814 +def node1816 : Tree Nat := .node node3 node276 +def node1817 : Tree Nat := .node node1166 node1816 +def node1818 : Tree Nat := .node node1492 node1658 +def node1819 : Tree Nat := .node node1817 node1818 +def node1820 : Tree Nat := .node node1815 node1819 +def node1821 : Tree Nat := .node node1813 node1820 +def node1822 : Tree Nat := .node node1805 node1821 +def node1823 : Tree Nat := .node node1788 node1822 +def node1824 : Tree Nat := .node node358 node1665 +def node1825 : Tree Nat := .node node1824 node1038 +def node1826 : Tree Nat := .node node1825 node1329 +def node1827 : Tree Nat := .node node1578 node1 +def node1828 : Tree Nat := .node node1827 node1500 +def node1829 : Tree Nat := .node node1828 node1671 +def node1830 : Tree Nat := .node node1826 node1829 +def node1831 : Tree Nat := .node node1505 node1674 +def node1832 : Tree Nat := .node node1504 node1831 +def node1833 : Tree Nat := .node node1830 node1832 +def node1834 : Tree Nat := .node node3 node350 +def node1835 : Tree Nat := .node node1511 node1834 +def node1836 : Tree Nat := .node node1509 node1835 +def node1837 : Tree Nat := .node node1181 node1682 +def node1838 : Tree Nat := .node node1514 node1684 +def node1839 : Tree Nat := .node node1837 node1838 +def node1840 : Tree Nat := .node node1836 node1839 +def node1841 : Tree Nat := .node node1833 node1840 +def node1842 : Tree Nat := .node node1520 node1689 +def node1843 : Tree Nat := .node node1519 node1842 +def node1844 : Tree Nat := .node node3 node467 +def node1845 : Tree Nat := .node node1187 node1844 +def node1846 : Tree Nat := .node node1523 node1695 +def node1847 : Tree Nat := .node node1845 node1846 +def node1848 : Tree Nat := .node node1843 node1847 +def node1849 : Tree Nat := .node node1528 node1699 +def node1850 : Tree Nat := .node node1527 node1849 +def node1851 : Tree Nat := .node node1191 node1702 +def node1852 : Tree Nat := .node node1532 node1704 +def node1853 : Tree Nat := .node node1851 node1852 +def node1854 : Tree Nat := .node node1850 node1853 +def node1855 : Tree Nat := .node node1848 node1854 +def node1856 : Tree Nat := .node node1841 node1855 +def node1857 : Tree Nat := .node node1622 node1 +def node1858 : Tree Nat := .node node1857 node1377 +def node1859 : Tree Nat := .node node1858 node1710 +def node1860 : Tree Nat := .node node1538 node1859 +def node1861 : Tree Nat := .node node1199 node1381 +def node1862 : Tree Nat := .node node1542 node1713 +def node1863 : Tree Nat := .node node1861 node1862 +def node1864 : Tree Nat := .node node1860 node1863 +def node1865 : Tree Nat := .node node1549 node1717 +def node1866 : Tree Nat := .node node1548 node1865 +def node1867 : Tree Nat := .node node522 node411 +def node1868 : Tree Nat := .node node3 node1867 +def node1869 : Tree Nat := .node node1206 node1868 +def node1870 : Tree Nat := .node node1552 node1722 +def node1871 : Tree Nat := .node node1869 node1870 +def node1872 : Tree Nat := .node node1866 node1871 +def node1873 : Tree Nat := .node node1864 node1872 +def node1874 : Tree Nat := .node node1558 node1727 +def node1875 : Tree Nat := .node node1557 node1874 +def node1876 : Tree Nat := .node node616 node322 +def node1877 : Tree Nat := .node node3 node1876 +def node1878 : Tree Nat := .node node1215 node1877 +def node1879 : Tree Nat := .node node1562 node1733 +def node1880 : Tree Nat := .node node1878 node1879 +def node1881 : Tree Nat := .node node1875 node1880 +def node1882 : Tree Nat := .node node1568 node1737 +def node1883 : Tree Nat := .node node1566 node1882 +def node1884 : Tree Nat := .node node596 node195 +def node1885 : Tree Nat := .node node3 node1884 +def node1886 : Tree Nat := .node node1219 node1885 +def node1887 : Tree Nat := .node node1886 node1744 +def node1888 : Tree Nat := .node node1883 node1887 +def node1889 : Tree Nat := .node node1881 node1888 +def node1890 : Tree Nat := .node node1873 node1889 +def node1891 : Tree Nat := .node node1856 node1890 +def node1892 : Tree Nat := .node node1823 node1891 +def node1893 : Tree Nat := .node node1750 node1892 +def node1894 : Tree Nat := .leaf 150 +def node1895 : Tree Nat := .node node1894 node0 +def node1896 : Tree Nat := .node node8 node1895 +def node1897 : Tree Nat := .node node1896 node1583 +def node1898 : Tree Nat := .node node1581 node1897 +def node1899 : Tree Nat := .leaf 146 +def node1900 : Tree Nat := .node node13 node1899 +def node1901 : Tree Nat := .node node1900 node971 +def node1902 : Tree Nat := .node node1901 node1233 +def node1903 : Tree Nat := .node node1902 node1587 +def node1904 : Tree Nat := .node node1898 node1903 +def node1905 : Tree Nat := .leaf 134 +def node1906 : Tree Nat := .node node23 node1905 +def node1907 : Tree Nat := .node node1906 node659 +def node1908 : Tree Nat := .leaf 126 +def node1909 : Tree Nat := .node node1908 node358 +def node1910 : Tree Nat := .node node3 node1909 +def node1911 : Tree Nat := .node node1907 node1910 +def node1912 : Tree Nat := .leaf 138 +def node1913 : Tree Nat := .node node1912 node1 +def node1914 : Tree Nat := .node node30 node1913 +def node1915 : Tree Nat := .node node1914 node1590 +def node1916 : Tree Nat := .node node1911 node1915 +def node1917 : Tree Nat := .leaf 158 +def node1918 : Tree Nat := .node node34 node1917 +def node1919 : Tree Nat := .node node1918 node978 +def node1920 : Tree Nat := .node node1919 node1594 +def node1921 : Tree Nat := .node node1920 node1597 +def node1922 : Tree Nat := .node node1916 node1921 +def node1923 : Tree Nat := .node node1904 node1922 +def node1924 : Tree Nat := .node node46 node1908 +def node1925 : Tree Nat := .node node1924 node985 +def node1926 : Tree Nat := .node node1925 node1251 +def node1927 : Tree Nat := .leaf 151 +def node1928 : Tree Nat := .node node1927 node25 +def node1929 : Tree Nat := .node node51 node1928 +def node1930 : Tree Nat := .node node1929 node1601 +def node1931 : Tree Nat := .node node1926 node1930 +def node1932 : Tree Nat := .node node55 node1894 +def node1933 : Tree Nat := .node node1932 node989 +def node1934 : Tree Nat := .node node1933 node1605 +def node1935 : Tree Nat := .node node1934 node1608 +def node1936 : Tree Nat := .node node1931 node1935 +def node1937 : Tree Nat := .node node67 node1912 +def node1938 : Tree Nat := .node node1937 node994 +def node1939 : Tree Nat := .leaf 127 +def node1940 : Tree Nat := .node node1939 node1 +def node1941 : Tree Nat := .node node3 node1940 +def node1942 : Tree Nat := .node node1938 node1941 +def node1943 : Tree Nat := .leaf 139 +def node1944 : Tree Nat := .node node1943 node73 +def node1945 : Tree Nat := .node node72 node1944 +def node1946 : Tree Nat := .node node1945 node1611 +def node1947 : Tree Nat := .node node1942 node1946 +def node1948 : Tree Nat := .node node1947 node1618 +def node1949 : Tree Nat := .node node1936 node1948 +def node1950 : Tree Nat := .node node1923 node1949 +def node1951 : Tree Nat := .leaf 152 +def node1952 : Tree Nat := .node node1951 node57 +def node1953 : Tree Nat := .node node94 node1952 +def node1954 : Tree Nat := .node node1953 node1626 +def node1955 : Tree Nat := .node node1625 node1954 +def node1956 : Tree Nat := .leaf 148 +def node1957 : Tree Nat := .node node98 node1956 +def node1958 : Tree Nat := .node node1957 node1007 +def node1959 : Tree Nat := .node node1958 node1283 +def node1960 : Tree Nat := .node node1959 node1630 +def node1961 : Tree Nat := .node node1955 node1960 +def node1962 : Tree Nat := .leaf 136 +def node1963 : Tree Nat := .node node108 node1962 +def node1964 : Tree Nat := .node node1963 node1012 +def node1965 : Tree Nat := .leaf 128 +def node1966 : Tree Nat := .node node1965 node114 +def node1967 : Tree Nat := .node node3 node1966 +def node1968 : Tree Nat := .node node1964 node1967 +def node1969 : Tree Nat := .leaf 140 +def node1970 : Tree Nat := .node node1969 node114 +def node1971 : Tree Nat := .node node113 node1970 +def node1972 : Tree Nat := .node node1971 node1633 +def node1973 : Tree Nat := .node node1968 node1972 +def node1974 : Tree Nat := .leaf 160 +def node1975 : Tree Nat := .node node119 node1974 +def node1976 : Tree Nat := .node node1975 node1016 +def node1977 : Tree Nat := .node node1976 node1636 +def node1978 : Tree Nat := .node node1977 node1639 +def node1979 : Tree Nat := .node node1973 node1978 +def node1980 : Tree Nat := .node node1961 node1979 +def node1981 : Tree Nat := .leaf 130 +def node1982 : Tree Nat := .node node130 node1981 +def node1983 : Tree Nat := .node node1982 node90 +def node1984 : Tree Nat := .node node1983 node1304 +def node1985 : Tree Nat := .leaf 153 +def node1986 : Tree Nat := .node node1985 node82 +def node1987 : Tree Nat := .node node136 node1986 +def node1988 : Tree Nat := .node node1987 node1643 +def node1989 : Tree Nat := .node node1984 node1988 +def node1990 : Tree Nat := .leaf 154 +def node1991 : Tree Nat := .node node140 node1990 +def node1992 : Tree Nat := .node node1991 node1022 +def node1993 : Tree Nat := .node node1992 node1646 +def node1994 : Tree Nat := .node node1993 node1649 +def node1995 : Tree Nat := .node node1989 node1994 +def node1996 : Tree Nat := .leaf 142 +def node1997 : Tree Nat := .node node150 node1996 +def node1998 : Tree Nat := .node node1997 node776 +def node1999 : Tree Nat := .leaf 129 +def node2000 : Tree Nat := .node node1999 node73 +def node2001 : Tree Nat := .node node3 node2000 +def node2002 : Tree Nat := .node node1998 node2001 +def node2003 : Tree Nat := .leaf 141 +def node2004 : Tree Nat := .node node2003 node82 +def node2005 : Tree Nat := .node node155 node2004 +def node2006 : Tree Nat := .node node2005 node1652 +def node2007 : Tree Nat := .node node2002 node2006 +def node2008 : Tree Nat := .node node2007 node1660 +def node2009 : Tree Nat := .node node1995 node2008 +def node2010 : Tree Nat := .node node1980 node2009 +def node2011 : Tree Nat := .node node1950 node2010 +def node2012 : Tree Nat := .node node1927 node57 +def node2013 : Tree Nat := .node node1669 node2012 +def node2014 : Tree Nat := .node node2013 node1671 +def node2015 : Tree Nat := .node node1668 node2014 +def node2016 : Tree Nat := .leaf 135 +def node2017 : Tree Nat := .leaf 147 +def node2018 : Tree Nat := .node node2016 node2017 +def node2019 : Tree Nat := .node node2018 node1045 +def node2020 : Tree Nat := .node node2019 node1333 +def node2021 : Tree Nat := .node node2020 node1675 +def node2022 : Tree Nat := .node node2015 node2021 +def node2023 : Tree Nat := .leaf 159 +def node2024 : Tree Nat := .node node2023 node2016 +def node2025 : Tree Nat := .node node2024 node754 +def node2026 : Tree Nat := .node node2025 node1941 +def node2027 : Tree Nat := .node node1943 node1 +def node2028 : Tree Nat := .node node193 node2027 +def node2029 : Tree Nat := .node node2028 node1679 +def node2030 : Tree Nat := .node node2026 node2029 +def node2031 : Tree Nat := .node node200 node2023 +def node2032 : Tree Nat := .node node2031 node1050 +def node2033 : Tree Nat := .node node2032 node1682 +def node2034 : Tree Nat := .node node2033 node1685 +def node2035 : Tree Nat := .node node2030 node2034 +def node2036 : Tree Nat := .node node2022 node2035 +def node2037 : Tree Nat := .node node212 node1965 +def node2038 : Tree Nat := .node node2037 node90 +def node2039 : Tree Nat := .node node2038 node1351 +def node2040 : Tree Nat := .node node1894 node1 +def node2041 : Tree Nat := .node node217 node2040 +def node2042 : Tree Nat := .node node2041 node1689 +def node2043 : Tree Nat := .node node2039 node2042 +def node2044 : Tree Nat := .node node221 node1951 +def node2045 : Tree Nat := .node node2044 node1059 +def node2046 : Tree Nat := .node node2045 node1693 +def node2047 : Tree Nat := .node node2046 node1696 +def node2048 : Tree Nat := .node node2043 node2047 +def node2049 : Tree Nat := .node node2017 node1969 +def node2050 : Tree Nat := .node node2049 node764 +def node2051 : Tree Nat := .node node1908 node25 +def node2052 : Tree Nat := .node node3 node2051 +def node2053 : Tree Nat := .node node2050 node2052 +def node2054 : Tree Nat := .node node1912 node82 +def node2055 : Tree Nat := .node node240 node2054 +def node2056 : Tree Nat := .node node2055 node1699 +def node2057 : Tree Nat := .node node2053 node2056 +def node2058 : Tree Nat := .node node2057 node1706 +def node2059 : Tree Nat := .node node2048 node2058 +def node2060 : Tree Nat := .node node2036 node2059 +def node2061 : Tree Nat := .leaf 125 +def node2062 : Tree Nat := .node node252 node2061 +def node2063 : Tree Nat := .node node2062 node500 +def node2064 : Tree Nat := .node node2063 node1375 +def node2065 : Tree Nat := .node node2061 node1 +def node2066 : Tree Nat := .node node1985 node114 +def node2067 : Tree Nat := .node node2065 node2066 +def node2068 : Tree Nat := .node node2067 node1710 +def node2069 : Tree Nat := .node node2064 node2068 +def node2070 : Tree Nat := .leaf 137 +def node2071 : Tree Nat := .leaf 149 +def node2072 : Tree Nat := .node node2070 node2071 +def node2073 : Tree Nat := .node node2072 node1077 +def node2074 : Tree Nat := .node node2073 node1381 +def node2075 : Tree Nat := .node node2074 node1714 +def node2076 : Tree Nat := .node node2069 node2075 +def node2077 : Tree Nat := .node node271 node2070 +def node2078 : Tree Nat := .node node2077 node1012 +def node2079 : Tree Nat := .node node1999 node1 +def node2080 : Tree Nat := .node node3 node2079 +def node2081 : Tree Nat := .node node2078 node2080 +def node2082 : Tree Nat := .node node2003 node114 +def node2083 : Tree Nat := .node node276 node2082 +def node2084 : Tree Nat := .node node2083 node1717 +def node2085 : Tree Nat := .node node2081 node2084 +def node2086 : Tree Nat := .node node2085 node1724 +def node2087 : Tree Nat := .node node2076 node2086 +def node2088 : Tree Nat := .leaf 132 +def node2089 : Tree Nat := .node node291 node2088 +def node2090 : Tree Nat := .node node2089 node1092 +def node2091 : Tree Nat := .node node2090 node1399 +def node2092 : Tree Nat := .node node1951 node82 +def node2093 : Tree Nat := .node node296 node2092 +def node2094 : Tree Nat := .node node2093 node1727 +def node2095 : Tree Nat := .node node2091 node2094 +def node2096 : Tree Nat := .leaf 156 +def node2097 : Tree Nat := .node node300 node2096 +def node2098 : Tree Nat := .node node2097 node1096 +def node2099 : Tree Nat := .node node2098 node1731 +def node2100 : Tree Nat := .node node2099 node1734 +def node2101 : Tree Nat := .node node2095 node2100 +def node2102 : Tree Nat := .leaf 144 +def node2103 : Tree Nat := .node node2071 node2102 +def node2104 : Tree Nat := .node node2103 node776 +def node2105 : Tree Nat := .node node1965 node1 +def node2106 : Tree Nat := .node node3 node2105 +def node2107 : Tree Nat := .node node2104 node2106 +def node2108 : Tree Nat := .node node1969 node1 +def node2109 : Tree Nat := .node node315 node2108 +def node2110 : Tree Nat := .node node2109 node1737 +def node2111 : Tree Nat := .node node2107 node2110 +def node2112 : Tree Nat := .node node2111 node1745 +def node2113 : Tree Nat := .node node2101 node2112 +def node2114 : Tree Nat := .node node2087 node2113 +def node2115 : Tree Nat := .node node2060 node2114 +def node2116 : Tree Nat := .node node2011 node2115 +def node2117 : Tree Nat := .node node1990 node0 +def node2118 : Tree Nat := .node node338 node2117 +def node2119 : Tree Nat := .node node2118 node1755 +def node2120 : Tree Nat := .node node1753 node2119 +def node2121 : Tree Nat := .node node345 node1899 +def node2122 : Tree Nat := .node node2121 node971 +def node2123 : Tree Nat := .node node2122 node1233 +def node2124 : Tree Nat := .node node2123 node1758 +def node2125 : Tree Nat := .node node2120 node2124 +def node2126 : Tree Nat := .node node355 node1905 +def node2127 : Tree Nat := .node node2126 node659 +def node2128 : Tree Nat := .node node1981 node358 +def node2129 : Tree Nat := .node node3 node2128 +def node2130 : Tree Nat := .node node2127 node2129 +def node2131 : Tree Nat := .node node1996 node73 +def node2132 : Tree Nat := .node node363 node2131 +def node2133 : Tree Nat := .node node2132 node1762 +def node2134 : Tree Nat := .node node2130 node2133 +def node2135 : Tree Nat := .node node367 node1917 +def node2136 : Tree Nat := .node node2135 node978 +def node2137 : Tree Nat := .node node2136 node1766 +def node2138 : Tree Nat := .node node2137 node1768 +def node2139 : Tree Nat := .node node2134 node2138 +def node2140 : Tree Nat := .node node2125 node2139 +def node2141 : Tree Nat := .node node378 node1939 +def node2142 : Tree Nat := .node node2141 node985 +def node2143 : Tree Nat := .node node2142 node1251 +def node2144 : Tree Nat := .leaf 155 +def node2145 : Tree Nat := .node node2144 node25 +def node2146 : Tree Nat := .node node383 node2145 +def node2147 : Tree Nat := .node node2146 node1601 +def node2148 : Tree Nat := .node node2143 node2147 +def node2149 : Tree Nat := .node node387 node1927 +def node2150 : Tree Nat := .node node2149 node1129 +def node2151 : Tree Nat := .node node2150 node1775 +def node2152 : Tree Nat := .node node2151 node1777 +def node2153 : Tree Nat := .node node2148 node2152 +def node2154 : Tree Nat := .node node398 node1943 +def node2155 : Tree Nat := .node node2154 node994 +def node2156 : Tree Nat := .leaf 131 +def node2157 : Tree Nat := .node node2156 node57 +def node2158 : Tree Nat := .node node3 node2157 +def node2159 : Tree Nat := .node node2155 node2158 +def node2160 : Tree Nat := .leaf 143 +def node2161 : Tree Nat := .node node2160 node73 +def node2162 : Tree Nat := .node node404 node2161 +def node2163 : Tree Nat := .node node2162 node1611 +def node2164 : Tree Nat := .node node2159 node2163 +def node2165 : Tree Nat := .node node2164 node1785 +def node2166 : Tree Nat := .node node2153 node2165 +def node2167 : Tree Nat := .node node2140 node2166 +def node2168 : Tree Nat := .node node424 node2145 +def node2169 : Tree Nat := .node node2168 node1626 +def node2170 : Tree Nat := .node node1791 node2169 +def node2171 : Tree Nat := .node node428 node1956 +def node2172 : Tree Nat := .node node2171 node1007 +def node2173 : Tree Nat := .node node2172 node1283 +def node2174 : Tree Nat := .node node2173 node1794 +def node2175 : Tree Nat := .node node2170 node2174 +def node2176 : Tree Nat := .node node439 node1962 +def node2177 : Tree Nat := .node node2176 node1012 +def node2178 : Tree Nat := .node node2156 node114 +def node2179 : Tree Nat := .node node3 node2178 +def node2180 : Tree Nat := .node node2177 node2179 +def node2181 : Tree Nat := .node node2160 node114 +def node2182 : Tree Nat := .node node444 node2181 +def node2183 : Tree Nat := .node node2182 node1633 +def node2184 : Tree Nat := .node node2180 node2183 +def node2185 : Tree Nat := .node node2184 node1803 +def node2186 : Tree Nat := .node node2175 node2185 +def node2187 : Tree Nat := .node node462 node2156 +def node2188 : Tree Nat := .node node2187 node746 +def node2189 : Tree Nat := .node node2188 node1304 +def node2190 : Tree Nat := .node node1990 node82 +def node2191 : Tree Nat := .node node467 node2190 +def node2192 : Tree Nat := .node node2191 node1643 +def node2193 : Tree Nat := .node node2189 node2192 +def node2194 : Tree Nat := .node node471 node2144 +def node2195 : Tree Nat := .node node2194 node1022 +def node2196 : Tree Nat := .node node2195 node1809 +def node2197 : Tree Nat := .node node2196 node1811 +def node2198 : Tree Nat := .node node2193 node2197 +def node2199 : Tree Nat := .node node481 node2160 +def node2200 : Tree Nat := .node node2199 node776 +def node2201 : Tree Nat := .node node1981 node73 +def node2202 : Tree Nat := .node node3 node2201 +def node2203 : Tree Nat := .node node2200 node2202 +def node2204 : Tree Nat := .node node1996 node82 +def node2205 : Tree Nat := .node node486 node2204 +def node2206 : Tree Nat := .node node2205 node1652 +def node2207 : Tree Nat := .node node2203 node2206 +def node2208 : Tree Nat := .node node2207 node1819 +def node2209 : Tree Nat := .node node2198 node2208 +def node2210 : Tree Nat := .node node2186 node2209 +def node2211 : Tree Nat := .node node2167 node2210 +def node2212 : Tree Nat := .node node2096 node25 +def node2213 : Tree Nat := .node node1827 node2212 +def node2214 : Tree Nat := .node node2213 node1671 +def node2215 : Tree Nat := .node node1826 node2214 +def node2216 : Tree Nat := .node node1905 node2017 +def node2217 : Tree Nat := .node node2216 node1045 +def node2218 : Tree Nat := .node node2217 node1333 +def node2219 : Tree Nat := .node node2218 node1831 +def node2220 : Tree Nat := .node node2215 node2219 +def node2221 : Tree Nat := .node node1917 node2016 +def node2222 : Tree Nat := .node node2221 node754 +def node2223 : Tree Nat := .node node2088 node1 +def node2224 : Tree Nat := .node node3 node2223 +def node2225 : Tree Nat := .node node2222 node2224 +def node2226 : Tree Nat := .node node2102 node73 +def node2227 : Tree Nat := .node node523 node2226 +def node2228 : Tree Nat := .node node2227 node1834 +def node2229 : Tree Nat := .node node2225 node2228 +def node2230 : Tree Nat := .node node527 node2023 +def node2231 : Tree Nat := .node node2230 node1050 +def node2232 : Tree Nat := .node node2231 node1682 +def node2233 : Tree Nat := .node node2232 node1838 +def node2234 : Tree Nat := .node node2229 node2233 +def node2235 : Tree Nat := .node node2220 node2234 +def node2236 : Tree Nat := .node node538 node1999 +def node2237 : Tree Nat := .node node2236 node746 +def node2238 : Tree Nat := .node node2237 node1351 +def node2239 : Tree Nat := .leaf 157 +def node2240 : Tree Nat := .node node2239 node1 +def node2241 : Tree Nat := .node node543 node2240 +def node2242 : Tree Nat := .node node2241 node1689 +def node2243 : Tree Nat := .node node2238 node2242 +def node2244 : Tree Nat := .node node547 node1985 +def node2245 : Tree Nat := .node node2244 node1059 +def node2246 : Tree Nat := .node node2245 node1844 +def node2247 : Tree Nat := .node node2246 node1846 +def node2248 : Tree Nat := .node node2243 node2247 +def node2249 : Tree Nat := .node node1899 node2003 +def node2250 : Tree Nat := .node node2249 node764 +def node2251 : Tree Nat := .leaf 133 +def node2252 : Tree Nat := .node node2251 node25 +def node2253 : Tree Nat := .node node3 node2252 +def node2254 : Tree Nat := .node node2250 node2253 +def node2255 : Tree Nat := .leaf 145 +def node2256 : Tree Nat := .node node2255 node82 +def node2257 : Tree Nat := .node node562 node2256 +def node2258 : Tree Nat := .node node2257 node1699 +def node2259 : Tree Nat := .node node2254 node2258 +def node2260 : Tree Nat := .node node2259 node1853 +def node2261 : Tree Nat := .node node2248 node2260 +def node2262 : Tree Nat := .node node2235 node2261 +def node2263 : Tree Nat := .node node57 node2061 +def node2264 : Tree Nat := .node node2263 node500 +def node2265 : Tree Nat := .node node2264 node1375 +def node2266 : Tree Nat := .node node2239 node114 +def node2267 : Tree Nat := .node node1857 node2266 +def node2268 : Tree Nat := .node node2267 node1710 +def node2269 : Tree Nat := .node node2265 node2268 +def node2270 : Tree Nat := .node node1962 node2071 +def node2271 : Tree Nat := .node node2270 node1198 +def node2272 : Tree Nat := .node node2271 node1381 +def node2273 : Tree Nat := .node node2272 node1862 +def node2274 : Tree Nat := .node node2269 node2273 +def node2275 : Tree Nat := .node node592 node2070 +def node2276 : Tree Nat := .node node2275 node1012 +def node2277 : Tree Nat := .node node2251 node57 +def node2278 : Tree Nat := .node node3 node2277 +def node2279 : Tree Nat := .node node2276 node2278 +def node2280 : Tree Nat := .node node2255 node114 +def node2281 : Tree Nat := .node node597 node2280 +def node2282 : Tree Nat := .node node2281 node1717 +def node2283 : Tree Nat := .node node2279 node2282 +def node2284 : Tree Nat := .node node2283 node1871 +def node2285 : Tree Nat := .node node2274 node2284 +def node2286 : Tree Nat := .node node612 node2251 +def node2287 : Tree Nat := .node node2286 node1092 +def node2288 : Tree Nat := .node node2287 node1399 +def node2289 : Tree Nat := .node node2096 node82 +def node2290 : Tree Nat := .node node617 node2289 +def node2291 : Tree Nat := .node node2290 node1727 +def node2292 : Tree Nat := .node node2288 node2291 +def node2293 : Tree Nat := .node node621 node2239 +def node2294 : Tree Nat := .node node2293 node1096 +def node2295 : Tree Nat := .node node2294 node1877 +def node2296 : Tree Nat := .node node2295 node1879 +def node2297 : Tree Nat := .node node2292 node2296 +def node2298 : Tree Nat := .node node1956 node2255 +def node2299 : Tree Nat := .node node2298 node776 +def node2300 : Tree Nat := .node node2299 node2224 +def node2301 : Tree Nat := .node node2102 node25 +def node2302 : Tree Nat := .node node636 node2301 +def node2303 : Tree Nat := .node node2302 node1737 +def node2304 : Tree Nat := .node node2300 node2303 +def node2305 : Tree Nat := .node node2304 node1887 +def node2306 : Tree Nat := .node node2297 node2305 +def node2307 : Tree Nat := .node node2285 node2306 +def node2308 : Tree Nat := .node node2262 node2307 +def node2309 : Tree Nat := .node node2211 node2308 +def node2310 : Tree Nat := .node node2116 node2309 +def node2311 : Tree Nat := .leaf 170 +def node2312 : Tree Nat := .node node7 node2311 +def node2313 : Tree Nat := .node node2312 node1895 +def node2314 : Tree Nat := .node node2313 node1583 +def node2315 : Tree Nat := .node node1581 node2314 +def node2316 : Tree Nat := .leaf 186 +def node2317 : Tree Nat := .node node2316 node73 +def node2318 : Tree Nat := .node node3 node2317 +def node2319 : Tree Nat := .node node1901 node2318 +def node2320 : Tree Nat := .leaf 194 +def node2321 : Tree Nat := .node node17 node2320 +def node2322 : Tree Nat := .leaf 174 +def node2323 : Tree Nat := .node node2322 node1 +def node2324 : Tree Nat := .node node2321 node2323 +def node2325 : Tree Nat := .node node2324 node1586 +def node2326 : Tree Nat := .node node2319 node2325 +def node2327 : Tree Nat := .node node2315 node2326 +def node2328 : Tree Nat := .leaf 182 +def node2329 : Tree Nat := .node node29 node2328 +def node2330 : Tree Nat := .node node2329 node1913 +def node2331 : Tree Nat := .node node2330 node1590 +def node2332 : Tree Nat := .node node1911 node2331 +def node2333 : Tree Nat := .leaf 162 +def node2334 : Tree Nat := .node node2333 node0 +def node2335 : Tree Nat := .node node1918 node2334 +def node2336 : Tree Nat := .node node2335 node1594 +def node2337 : Tree Nat := .node node2336 node1597 +def node2338 : Tree Nat := .node node2332 node2337 +def node2339 : Tree Nat := .node node2327 node2338 +def node2340 : Tree Nat := .node node50 node2322 +def node2341 : Tree Nat := .node node2340 node1928 +def node2342 : Tree Nat := .node node2341 node1601 +def node2343 : Tree Nat := .node node1926 node2342 +def node2344 : Tree Nat := .leaf 187 +def node2345 : Tree Nat := .node node2344 node340 +def node2346 : Tree Nat := .node node3 node2345 +def node2347 : Tree Nat := .node node1933 node2346 +def node2348 : Tree Nat := .leaf 175 +def node2349 : Tree Nat := .node node2348 node82 +def node2350 : Tree Nat := .node node62 node2349 +def node2351 : Tree Nat := .node node2350 node1607 +def node2352 : Tree Nat := .node node2347 node2351 +def node2353 : Tree Nat := .node node2343 node2352 +def node2354 : Tree Nat := .node node71 node2316 +def node2355 : Tree Nat := .node node2354 node1944 +def node2356 : Tree Nat := .node node2355 node1611 +def node2357 : Tree Nat := .node node1942 node2356 +def node2358 : Tree Nat := .node node78 node2333 +def node2359 : Tree Nat := .leaf 163 +def node2360 : Tree Nat := .node node2359 node358 +def node2361 : Tree Nat := .node node2358 node2360 +def node2362 : Tree Nat := .node node2361 node1614 +def node2363 : Tree Nat := .node node2362 node1617 +def node2364 : Tree Nat := .node node2357 node2363 +def node2365 : Tree Nat := .node node2353 node2364 +def node2366 : Tree Nat := .node node2339 node2365 +def node2367 : Tree Nat := .leaf 172 +def node2368 : Tree Nat := .node node93 node2367 +def node2369 : Tree Nat := .node node2368 node1952 +def node2370 : Tree Nat := .node node2369 node1626 +def node2371 : Tree Nat := .node node1625 node2370 +def node2372 : Tree Nat := .leaf 188 +def node2373 : Tree Nat := .node node2372 node224 +def node2374 : Tree Nat := .node node3 node2373 +def node2375 : Tree Nat := .node node1958 node2374 +def node2376 : Tree Nat := .leaf 176 +def node2377 : Tree Nat := .node node2376 node25 +def node2378 : Tree Nat := .node node103 node2377 +def node2379 : Tree Nat := .node node2378 node1629 +def node2380 : Tree Nat := .node node2375 node2379 +def node2381 : Tree Nat := .node node2371 node2380 +def node2382 : Tree Nat := .leaf 184 +def node2383 : Tree Nat := .node node112 node2382 +def node2384 : Tree Nat := .node node2383 node1970 +def node2385 : Tree Nat := .node node2384 node1633 +def node2386 : Tree Nat := .node node1968 node2385 +def node2387 : Tree Nat := .leaf 164 +def node2388 : Tree Nat := .node node2387 node73 +def node2389 : Tree Nat := .node node1975 node2388 +def node2390 : Tree Nat := .node node2389 node1636 +def node2391 : Tree Nat := .node node2390 node1639 +def node2392 : Tree Nat := .node node2386 node2391 +def node2393 : Tree Nat := .node node2381 node2392 +def node2394 : Tree Nat := .leaf 178 +def node2395 : Tree Nat := .node node135 node2394 +def node2396 : Tree Nat := .node node2395 node1986 +def node2397 : Tree Nat := .node node2396 node1643 +def node2398 : Tree Nat := .node node1984 node2397 +def node2399 : Tree Nat := .leaf 189 +def node2400 : Tree Nat := .node node2399 node1 +def node2401 : Tree Nat := .node node3 node2400 +def node2402 : Tree Nat := .node node1992 node2401 +def node2403 : Tree Nat := .leaf 177 +def node2404 : Tree Nat := .node node2403 node1 +def node2405 : Tree Nat := .node node145 node2404 +def node2406 : Tree Nat := .node node2405 node1648 +def node2407 : Tree Nat := .node node2402 node2406 +def node2408 : Tree Nat := .node node2398 node2407 +def node2409 : Tree Nat := .leaf 190 +def node2410 : Tree Nat := .node node154 node2409 +def node2411 : Tree Nat := .node node2410 node2004 +def node2412 : Tree Nat := .node node2411 node1652 +def node2413 : Tree Nat := .node node2002 node2412 +def node2414 : Tree Nat := .leaf 166 +def node2415 : Tree Nat := .node node159 node2414 +def node2416 : Tree Nat := .leaf 165 +def node2417 : Tree Nat := .node node2416 node0 +def node2418 : Tree Nat := .node node2415 node2417 +def node2419 : Tree Nat := .node node2418 node1656 +def node2420 : Tree Nat := .node node2419 node1659 +def node2421 : Tree Nat := .node node2413 node2420 +def node2422 : Tree Nat := .node node2408 node2421 +def node2423 : Tree Nat := .node node2393 node2422 +def node2424 : Tree Nat := .node node2366 node2423 +def node2425 : Tree Nat := .leaf 171 +def node2426 : Tree Nat := .node node1665 node2425 +def node2427 : Tree Nat := .node node2426 node2012 +def node2428 : Tree Nat := .node node2427 node1671 +def node2429 : Tree Nat := .node node1668 node2428 +def node2430 : Tree Nat := .node node2344 node57 +def node2431 : Tree Nat := .node node3 node2430 +def node2432 : Tree Nat := .node node2019 node2431 +def node2433 : Tree Nat := .leaf 195 +def node2434 : Tree Nat := .node node181 node2433 +def node2435 : Tree Nat := .node node2348 node358 +def node2436 : Tree Nat := .node node2434 node2435 +def node2437 : Tree Nat := .node node2436 node1674 +def node2438 : Tree Nat := .node node2432 node2437 +def node2439 : Tree Nat := .node node2429 node2438 +def node2440 : Tree Nat := .leaf 183 +def node2441 : Tree Nat := .node node192 node2440 +def node2442 : Tree Nat := .node node2441 node2027 +def node2443 : Tree Nat := .node node2442 node1679 +def node2444 : Tree Nat := .node node2026 node2443 +def node2445 : Tree Nat := .node node2359 node0 +def node2446 : Tree Nat := .node node2031 node2445 +def node2447 : Tree Nat := .node node2446 node1682 +def node2448 : Tree Nat := .node node2433 node1 +def node2449 : Tree Nat := .node node2448 node1345 +def node2450 : Tree Nat := .node node2449 node1684 +def node2451 : Tree Nat := .node node2447 node2450 +def node2452 : Tree Nat := .node node2444 node2451 +def node2453 : Tree Nat := .node node2439 node2452 +def node2454 : Tree Nat := .node node2440 node2376 +def node2455 : Tree Nat := .node node2454 node2040 +def node2456 : Tree Nat := .node node2455 node1689 +def node2457 : Tree Nat := .node node2039 node2456 +def node2458 : Tree Nat := .node node2425 node1951 +def node2459 : Tree Nat := .node node2458 node1059 +def node2460 : Tree Nat := .node node2316 node224 +def node2461 : Tree Nat := .node node3 node2460 +def node2462 : Tree Nat := .node node2459 node2461 +def node2463 : Tree Nat := .node node2322 node82 +def node2464 : Tree Nat := .node node229 node2463 +def node2465 : Tree Nat := .node node2464 node1695 +def node2466 : Tree Nat := .node node2462 node2465 +def node2467 : Tree Nat := .node node2457 node2466 +def node2468 : Tree Nat := .node node239 node2372 +def node2469 : Tree Nat := .node node2468 node2054 +def node2470 : Tree Nat := .node node2469 node1699 +def node2471 : Tree Nat := .node node2053 node2470 +def node2472 : Tree Nat := .node node244 node2387 +def node2473 : Tree Nat := .node node2333 node73 +def node2474 : Tree Nat := .node node2472 node2473 +def node2475 : Tree Nat := .node node2474 node1702 +def node2476 : Tree Nat := .node node2475 node1705 +def node2477 : Tree Nat := .node node2471 node2476 +def node2478 : Tree Nat := .node node2467 node2477 +def node2479 : Tree Nat := .node node2453 node2478 +def node2480 : Tree Nat := .leaf 173 +def node2481 : Tree Nat := .node node2061 node2480 +def node2482 : Tree Nat := .node node2481 node2066 +def node2483 : Tree Nat := .node node2482 node1710 +def node2484 : Tree Nat := .node node2064 node2483 +def node2485 : Tree Nat := .node node2073 node2401 +def node2486 : Tree Nat := .node node266 node2404 +def node2487 : Tree Nat := .node node2486 node1713 +def node2488 : Tree Nat := .node node2485 node2487 +def node2489 : Tree Nat := .node node2484 node2488 +def node2490 : Tree Nat := .leaf 161 +def node2491 : Tree Nat := .node node2490 node2070 +def node2492 : Tree Nat := .node node2491 node1012 +def node2493 : Tree Nat := .node node2492 node2080 +def node2494 : Tree Nat := .leaf 185 +def node2495 : Tree Nat := .node node275 node2494 +def node2496 : Tree Nat := .node node2495 node2082 +def node2497 : Tree Nat := .node node2496 node1717 +def node2498 : Tree Nat := .node node2493 node2497 +def node2499 : Tree Nat := .node node280 node2490 +def node2500 : Tree Nat := .node node2416 node73 +def node2501 : Tree Nat := .node node2499 node2500 +def node2502 : Tree Nat := .node node2501 node1720 +def node2503 : Tree Nat := .node node2502 node1723 +def node2504 : Tree Nat := .node node2498 node2503 +def node2505 : Tree Nat := .node node2489 node2504 +def node2506 : Tree Nat := .leaf 180 +def node2507 : Tree Nat := .node node2494 node2506 +def node2508 : Tree Nat := .node node2507 node2092 +def node2509 : Tree Nat := .node node2508 node1727 +def node2510 : Tree Nat := .node node2091 node2509 +def node2511 : Tree Nat := .node node2480 node2096 +def node2512 : Tree Nat := .node node2511 node1096 +def node2513 : Tree Nat := .node node2372 node411 +def node2514 : Tree Nat := .node node3 node2513 +def node2515 : Tree Nat := .node node2512 node2514 +def node2516 : Tree Nat := .node node2376 node1 +def node2517 : Tree Nat := .node node305 node2516 +def node2518 : Tree Nat := .node node2517 node1733 +def node2519 : Tree Nat := .node node2515 node2518 +def node2520 : Tree Nat := .node node2510 node2519 +def node2521 : Tree Nat := .leaf 192 +def node2522 : Tree Nat := .node node314 node2521 +def node2523 : Tree Nat := .node node2522 node2108 +def node2524 : Tree Nat := .node node2523 node1737 +def node2525 : Tree Nat := .node node2107 node2524 +def node2526 : Tree Nat := .leaf 168 +def node2527 : Tree Nat := .node node319 node2526 +def node2528 : Tree Nat := .node node2387 node0 +def node2529 : Tree Nat := .node node2527 node2528 +def node2530 : Tree Nat := .node node2529 node1741 +def node2531 : Tree Nat := .node node2530 node1744 +def node2532 : Tree Nat := .node node2525 node2531 +def node2533 : Tree Nat := .node node2520 node2532 +def node2534 : Tree Nat := .node node2505 node2533 +def node2535 : Tree Nat := .node node2479 node2534 +def node2536 : Tree Nat := .node node2424 node2535 +def node2537 : Tree Nat := .node node337 node2311 +def node2538 : Tree Nat := .node node2537 node2117 +def node2539 : Tree Nat := .node node2538 node1755 +def node2540 : Tree Nat := .node node1753 node2539 +def node2541 : Tree Nat := .node node2409 node73 +def node2542 : Tree Nat := .node node3 node2541 +def node2543 : Tree Nat := .node node2122 node2542 +def node2544 : Tree Nat := .node node349 node2320 +def node2545 : Tree Nat := .node node2394 node25 +def node2546 : Tree Nat := .node node2544 node2545 +def node2547 : Tree Nat := .node node2546 node1586 +def node2548 : Tree Nat := .node node2543 node2547 +def node2549 : Tree Nat := .node node2540 node2548 +def node2550 : Tree Nat := .node node362 node2328 +def node2551 : Tree Nat := .node node2550 node2131 +def node2552 : Tree Nat := .node node2551 node1762 +def node2553 : Tree Nat := .node node2130 node2552 +def node2554 : Tree Nat := .node node2414 node0 +def node2555 : Tree Nat := .node node2135 node2554 +def node2556 : Tree Nat := .node node2555 node1766 +def node2557 : Tree Nat := .node node2556 node1768 +def node2558 : Tree Nat := .node node2553 node2557 +def node2559 : Tree Nat := .node node2549 node2558 +def node2560 : Tree Nat := .node node382 node2348 +def node2561 : Tree Nat := .node node2560 node2145 +def node2562 : Tree Nat := .node node2561 node1601 +def node2563 : Tree Nat := .node node2143 node2562 +def node2564 : Tree Nat := .leaf 191 +def node2565 : Tree Nat := .node node2564 node224 +def node2566 : Tree Nat := .node node3 node2565 +def node2567 : Tree Nat := .node node2150 node2566 +def node2568 : Tree Nat := .leaf 179 +def node2569 : Tree Nat := .node node2568 node82 +def node2570 : Tree Nat := .node node392 node2569 +def node2571 : Tree Nat := .node node2570 node1607 +def node2572 : Tree Nat := .node node2567 node2571 +def node2573 : Tree Nat := .node node2563 node2572 +def node2574 : Tree Nat := .node node403 node2344 +def node2575 : Tree Nat := .node node2574 node2161 +def node2576 : Tree Nat := .node node2575 node1611 +def node2577 : Tree Nat := .node node2159 node2576 +def node2578 : Tree Nat := .node node408 node2359 +def node2579 : Tree Nat := .leaf 167 +def node2580 : Tree Nat := .node node2579 node358 +def node2581 : Tree Nat := .node node2578 node2580 +def node2582 : Tree Nat := .node node2581 node1783 +def node2583 : Tree Nat := .node node2582 node1617 +def node2584 : Tree Nat := .node node2577 node2583 +def node2585 : Tree Nat := .node node2573 node2584 +def node2586 : Tree Nat := .node node2559 node2585 +def node2587 : Tree Nat := .node node423 node2367 +def node2588 : Tree Nat := .node node2587 node2145 +def node2589 : Tree Nat := .node node2588 node1626 +def node2590 : Tree Nat := .node node1791 node2589 +def node2591 : Tree Nat := .node node2172 node2566 +def node2592 : Tree Nat := .node node2568 node25 +def node2593 : Tree Nat := .node node433 node2592 +def node2594 : Tree Nat := .node node2593 node1629 +def node2595 : Tree Nat := .node node2591 node2594 +def node2596 : Tree Nat := .node node2590 node2595 +def node2597 : Tree Nat := .node node443 node2382 +def node2598 : Tree Nat := .node node2597 node2181 +def node2599 : Tree Nat := .node node2598 node1633 +def node2600 : Tree Nat := .node node2180 node2599 +def node2601 : Tree Nat := .node node448 node1974 +def node2602 : Tree Nat := .node node2579 node73 +def node2603 : Tree Nat := .node node2601 node2602 +def node2604 : Tree Nat := .node node2603 node1800 +def node2605 : Tree Nat := .node node2604 node1802 +def node2606 : Tree Nat := .node node2600 node2605 +def node2607 : Tree Nat := .node node2596 node2606 +def node2608 : Tree Nat := .node node466 node2568 +def node2609 : Tree Nat := .node node2608 node2190 +def node2610 : Tree Nat := .node node2609 node1643 +def node2611 : Tree Nat := .node node2189 node2610 +def node2612 : Tree Nat := .node node2409 node451 +def node2613 : Tree Nat := .node node3 node2612 +def node2614 : Tree Nat := .node node2195 node2613 +def node2615 : Tree Nat := .node node2394 node73 +def node2616 : Tree Nat := .node node476 node2615 +def node2617 : Tree Nat := .node node2616 node1648 +def node2618 : Tree Nat := .node node2614 node2617 +def node2619 : Tree Nat := .node node2611 node2618 +def node2620 : Tree Nat := .node node485 node2564 +def node2621 : Tree Nat := .node node2620 node2204 +def node2622 : Tree Nat := .node node2621 node1652 +def node2623 : Tree Nat := .node node2203 node2622 +def node2624 : Tree Nat := .node node490 node2579 +def node2625 : Tree Nat := .node node2624 node2554 +def node2626 : Tree Nat := .node node2625 node1816 +def node2627 : Tree Nat := .node node2626 node1818 +def node2628 : Tree Nat := .node node2623 node2627 +def node2629 : Tree Nat := .node node2619 node2628 +def node2630 : Tree Nat := .node node2607 node2629 +def node2631 : Tree Nat := .node node2586 node2630 +def node2632 : Tree Nat := .node node1578 node2425 +def node2633 : Tree Nat := .node node2632 node2212 +def node2634 : Tree Nat := .node node2633 node1671 +def node2635 : Tree Nat := .node node1826 node2634 +def node2636 : Tree Nat := .node node2521 node57 +def node2637 : Tree Nat := .node node3 node2636 +def node2638 : Tree Nat := .node node2217 node2637 +def node2639 : Tree Nat := .node node512 node2433 +def node2640 : Tree Nat := .node node2506 node358 +def node2641 : Tree Nat := .node node2639 node2640 +def node2642 : Tree Nat := .node node2641 node1674 +def node2643 : Tree Nat := .node node2638 node2642 +def node2644 : Tree Nat := .node node2635 node2643 +def node2645 : Tree Nat := .node node522 node2440 +def node2646 : Tree Nat := .node node2645 node2226 +def node2647 : Tree Nat := .node node2646 node1834 +def node2648 : Tree Nat := .node node2225 node2647 +def node2649 : Tree Nat := .node node2526 node0 +def node2650 : Tree Nat := .node node2230 node2649 +def node2651 : Tree Nat := .node node2650 node1682 +def node2652 : Tree Nat := .node node2320 node1 +def node2653 : Tree Nat := .node node2652 node1345 +def node2654 : Tree Nat := .node node2653 node1684 +def node2655 : Tree Nat := .node node2651 node2654 +def node2656 : Tree Nat := .node node2648 node2655 +def node2657 : Tree Nat := .node node2644 node2656 +def node2658 : Tree Nat := .node node2328 node2403 +def node2659 : Tree Nat := .node node2658 node2240 +def node2660 : Tree Nat := .node node2659 node1689 +def node2661 : Tree Nat := .node node2238 node2660 +def node2662 : Tree Nat := .node node2311 node1985 +def node2663 : Tree Nat := .node node2662 node1059 +def node2664 : Tree Nat := .leaf 193 +def node2665 : Tree Nat := .node node2664 node1 +def node2666 : Tree Nat := .node node3 node2665 +def node2667 : Tree Nat := .node node2663 node2666 +def node2668 : Tree Nat := .leaf 181 +def node2669 : Tree Nat := .node node2668 node82 +def node2670 : Tree Nat := .node node552 node2669 +def node2671 : Tree Nat := .node node2670 node1695 +def node2672 : Tree Nat := .node node2667 node2671 +def node2673 : Tree Nat := .node node2661 node2672 +def node2674 : Tree Nat := .node node561 node2399 +def node2675 : Tree Nat := .node node2674 node2256 +def node2676 : Tree Nat := .node node2675 node1699 +def node2677 : Tree Nat := .node node2254 node2676 +def node2678 : Tree Nat := .node node566 node2416 +def node2679 : Tree Nat := .leaf 169 +def node2680 : Tree Nat := .node node2679 node73 +def node2681 : Tree Nat := .node node2678 node2680 +def node2682 : Tree Nat := .node node2681 node1702 +def node2683 : Tree Nat := .node node2682 node1852 +def node2684 : Tree Nat := .node node2677 node2683 +def node2685 : Tree Nat := .node node2673 node2684 +def node2686 : Tree Nat := .node node2657 node2685 +def node2687 : Tree Nat := .node node1622 node2480 +def node2688 : Tree Nat := .node node2687 node2266 +def node2689 : Tree Nat := .node node2688 node1710 +def node2690 : Tree Nat := .node node2265 node2689 +def node2691 : Tree Nat := .node node2271 node2666 +def node2692 : Tree Nat := .node node2668 node1 +def node2693 : Tree Nat := .node node587 node2692 +def node2694 : Tree Nat := .node node2693 node1713 +def node2695 : Tree Nat := .node node2691 node2694 +def node2696 : Tree Nat := .node node2690 node2695 +def node2697 : Tree Nat := .node node1974 node2070 +def node2698 : Tree Nat := .node node2697 node1012 +def node2699 : Tree Nat := .node node2698 node2278 +def node2700 : Tree Nat := .node node596 node2494 +def node2701 : Tree Nat := .node node2700 node2280 +def node2702 : Tree Nat := .node node2701 node1717 +def node2703 : Tree Nat := .node node2699 node2702 +def node2704 : Tree Nat := .node node601 node2490 +def node2705 : Tree Nat := .node node2704 node2680 +def node2706 : Tree Nat := .node node2705 node1868 +def node2707 : Tree Nat := .node node2706 node1870 +def node2708 : Tree Nat := .node node2703 node2707 +def node2709 : Tree Nat := .node node2696 node2708 +def node2710 : Tree Nat := .node node2382 node2668 +def node2711 : Tree Nat := .node node2710 node2289 +def node2712 : Tree Nat := .node node2711 node1727 +def node2713 : Tree Nat := .node node2288 node2712 +def node2714 : Tree Nat := .node node2367 node2239 +def node2715 : Tree Nat := .node node2714 node1096 +def node2716 : Tree Nat := .node node2521 node322 +def node2717 : Tree Nat := .node node3 node2716 +def node2718 : Tree Nat := .node node2715 node2717 +def node2719 : Tree Nat := .node node2506 node73 +def node2720 : Tree Nat := .node node626 node2719 +def node2721 : Tree Nat := .node node2720 node1733 +def node2722 : Tree Nat := .node node2718 node2721 +def node2723 : Tree Nat := .node node2713 node2722 +def node2724 : Tree Nat := .node node635 node2664 +def node2725 : Tree Nat := .node node2724 node2301 +def node2726 : Tree Nat := .node node2725 node1737 +def node2727 : Tree Nat := .node node2300 node2726 +def node2728 : Tree Nat := .node node640 node2679 +def node2729 : Tree Nat := .node node2728 node2649 +def node2730 : Tree Nat := .node node2729 node1885 +def node2731 : Tree Nat := .node node2730 node1744 +def node2732 : Tree Nat := .node node2727 node2731 +def node2733 : Tree Nat := .node node2723 node2732 +def node2734 : Tree Nat := .node node2709 node2733 +def node2735 : Tree Nat := .node node2686 node2734 +def node2736 : Tree Nat := .node node2631 node2735 +def node2737 : Tree Nat := .node node2536 node2736 +def node2738 : Tree Nat := .leaf 218 +def node2739 : Tree Nat := .node node1 node2738 +def node2740 : Tree Nat := .node node2739 node1228 +def node2741 : Tree Nat := .node node1580 node2740 +def node2742 : Tree Nat := .node node2741 node2314 +def node2743 : Tree Nat := .leaf 210 +def node2744 : Tree Nat := .node node2743 node0 +def node2745 : Tree Nat := .node node1900 node2744 +def node2746 : Tree Nat := .node node2745 node2318 +def node2747 : Tree Nat := .node node2746 node2325 +def node2748 : Tree Nat := .node node2742 node2747 +def node2749 : Tree Nat := .leaf 230 +def node2750 : Tree Nat := .node node1 node2749 +def node2751 : Tree Nat := .node node2750 node1909 +def node2752 : Tree Nat := .node node1907 node2751 +def node2753 : Tree Nat := .node node2752 node2331 +def node2754 : Tree Nat := .leaf 206 +def node2755 : Tree Nat := .node node38 node2754 +def node2756 : Tree Nat := .leaf 222 +def node2757 : Tree Nat := .node node2756 node57 +def node2758 : Tree Nat := .node node2755 node2757 +def node2759 : Tree Nat := .leaf 198 +def node2760 : Tree Nat := .node node2759 node1 +def node2761 : Tree Nat := .node node733 node2760 +def node2762 : Tree Nat := .node node2758 node2761 +def node2763 : Tree Nat := .node node2336 node2762 +def node2764 : Tree Nat := .node node2753 node2763 +def node2765 : Tree Nat := .node node2748 node2764 +def node2766 : Tree Nat := .node node1 node2756 +def node2767 : Tree Nat := .node node2766 node160 +def node2768 : Tree Nat := .node node1925 node2767 +def node2769 : Tree Nat := .node node2768 node2342 +def node2770 : Tree Nat := .leaf 211 +def node2771 : Tree Nat := .node node2770 node57 +def node2772 : Tree Nat := .node node1932 node2771 +def node2773 : Tree Nat := .node node2772 node2346 +def node2774 : Tree Nat := .node node61 node2759 +def node2775 : Tree Nat := .node node2774 node2349 +def node2776 : Tree Nat := .node node2775 node1607 +def node2777 : Tree Nat := .node node2773 node2776 +def node2778 : Tree Nat := .node node2769 node2777 +def node2779 : Tree Nat := .node node1 node2743 +def node2780 : Tree Nat := .leaf 223 +def node2781 : Tree Nat := .node node2780 node82 +def node2782 : Tree Nat := .node node2779 node2781 +def node2783 : Tree Nat := .leaf 199 +def node2784 : Tree Nat := .node node2783 node1 +def node2785 : Tree Nat := .node node739 node2784 +def node2786 : Tree Nat := .node node2782 node2785 +def node2787 : Tree Nat := .node node2362 node2786 +def node2788 : Tree Nat := .node node2357 node2787 +def node2789 : Tree Nat := .node node2778 node2788 +def node2790 : Tree Nat := .node node2765 node2789 +def node2791 : Tree Nat := .leaf 220 +def node2792 : Tree Nat := .node node1 node2791 +def node2793 : Tree Nat := .node node2792 node1275 +def node2794 : Tree Nat := .node node1624 node2793 +def node2795 : Tree Nat := .node node2794 node2370 +def node2796 : Tree Nat := .leaf 212 +def node2797 : Tree Nat := .node node2796 node0 +def node2798 : Tree Nat := .node node1957 node2797 +def node2799 : Tree Nat := .node node2798 node2374 +def node2800 : Tree Nat := .leaf 196 +def node2801 : Tree Nat := .node node102 node2800 +def node2802 : Tree Nat := .node node2801 node2377 +def node2803 : Tree Nat := .node node2802 node1629 +def node2804 : Tree Nat := .node node2799 node2803 +def node2805 : Tree Nat := .node node2795 node2804 +def node2806 : Tree Nat := .leaf 208 +def node2807 : Tree Nat := .node node123 node2806 +def node2808 : Tree Nat := .leaf 224 +def node2809 : Tree Nat := .node node2808 node82 +def node2810 : Tree Nat := .node node2807 node2809 +def node2811 : Tree Nat := .leaf 200 +def node2812 : Tree Nat := .node node2811 node1 +def node2813 : Tree Nat := .node node829 node2812 +def node2814 : Tree Nat := .node node2810 node2813 +def node2815 : Tree Nat := .node node2390 node2814 +def node2816 : Tree Nat := .node node2386 node2815 +def node2817 : Tree Nat := .node node2805 node2816 +def node2818 : Tree Nat := .leaf 226 +def node2819 : Tree Nat := .node node1 node2818 +def node2820 : Tree Nat := .node node2819 node1303 +def node2821 : Tree Nat := .node node1983 node2820 +def node2822 : Tree Nat := .node node2821 node2397 +def node2823 : Tree Nat := .leaf 213 +def node2824 : Tree Nat := .node node2823 node25 +def node2825 : Tree Nat := .node node1991 node2824 +def node2826 : Tree Nat := .node node2825 node2401 +def node2827 : Tree Nat := .leaf 202 +def node2828 : Tree Nat := .node node144 node2827 +def node2829 : Tree Nat := .node node2828 node2404 +def node2830 : Tree Nat := .node node2829 node1648 +def node2831 : Tree Nat := .node node2826 node2830 +def node2832 : Tree Nat := .node node2822 node2831 +def node2833 : Tree Nat := .leaf 214 +def node2834 : Tree Nat := .node node1 node2833 +def node2835 : Tree Nat := .leaf 225 +def node2836 : Tree Nat := .node node2835 node1 +def node2837 : Tree Nat := .node node2834 node2836 +def node2838 : Tree Nat := .leaf 201 +def node2839 : Tree Nat := .node node2838 node1 +def node2840 : Tree Nat := .node node909 node2839 +def node2841 : Tree Nat := .node node2837 node2840 +def node2842 : Tree Nat := .node node2419 node2841 +def node2843 : Tree Nat := .node node2413 node2842 +def node2844 : Tree Nat := .node node2832 node2843 +def node2845 : Tree Nat := .node node2817 node2844 +def node2846 : Tree Nat := .node node2790 node2845 +def node2847 : Tree Nat := .leaf 219 +def node2848 : Tree Nat := .node node1 node2847 +def node2849 : Tree Nat := .node node2848 node1328 +def node2850 : Tree Nat := .node node1667 node2849 +def node2851 : Tree Nat := .node node2850 node2428 +def node2852 : Tree Nat := .node node2770 node0 +def node2853 : Tree Nat := .node node2018 node2852 +def node2854 : Tree Nat := .node node2853 node2431 +def node2855 : Tree Nat := .node node2854 node2437 +def node2856 : Tree Nat := .node node2851 node2855 +def node2857 : Tree Nat := .node node1 node362 +def node2858 : Tree Nat := .node node2857 node1940 +def node2859 : Tree Nat := .node node2025 node2858 +def node2860 : Tree Nat := .node node2859 node2443 +def node2861 : Tree Nat := .node node2847 node2023 +def node2862 : Tree Nat := .node node2861 node2445 +def node2863 : Tree Nat := .node node2862 node1682 +def node2864 : Tree Nat := .leaf 207 +def node2865 : Tree Nat := .node node2433 node2864 +def node2866 : Tree Nat := .node node2780 node73 +def node2867 : Tree Nat := .node node2865 node2866 +def node2868 : Tree Nat := .node node698 node2784 +def node2869 : Tree Nat := .node node2867 node2868 +def node2870 : Tree Nat := .node node2863 node2869 +def node2871 : Tree Nat := .node node2860 node2870 +def node2872 : Tree Nat := .node node2856 node2871 +def node2873 : Tree Nat := .node node2864 node1965 +def node2874 : Tree Nat := .node node2873 node90 +def node2875 : Tree Nat := .node node1 node2808 +def node2876 : Tree Nat := .node node2875 node491 +def node2877 : Tree Nat := .node node2874 node2876 +def node2878 : Tree Nat := .node node2877 node2456 +def node2879 : Tree Nat := .node node2743 node57 +def node2880 : Tree Nat := .node node2458 node2879 +def node2881 : Tree Nat := .node node2880 node2461 +def node2882 : Tree Nat := .node node228 node2811 +def node2883 : Tree Nat := .node node2882 node2463 +def node2884 : Tree Nat := .node node2883 node1695 +def node2885 : Tree Nat := .node node2881 node2884 +def node2886 : Tree Nat := .node node2878 node2885 +def node2887 : Tree Nat := .node node1 node2796 +def node2888 : Tree Nat := .node node2756 node1 +def node2889 : Tree Nat := .node node2887 node2888 +def node2890 : Tree Nat := .node node739 node2760 +def node2891 : Tree Nat := .node node2889 node2890 +def node2892 : Tree Nat := .node node2475 node2891 +def node2893 : Tree Nat := .node node2471 node2892 +def node2894 : Tree Nat := .node node2886 node2893 +def node2895 : Tree Nat := .node node2872 node2894 +def node2896 : Tree Nat := .leaf 221 +def node2897 : Tree Nat := .node node1 node2896 +def node2898 : Tree Nat := .node node2897 node1374 +def node2899 : Tree Nat := .node node2063 node2898 +def node2900 : Tree Nat := .node node2899 node2483 +def node2901 : Tree Nat := .node node2823 node57 +def node2902 : Tree Nat := .node node2072 node2901 +def node2903 : Tree Nat := .node node2902 node2401 +def node2904 : Tree Nat := .leaf 197 +def node2905 : Tree Nat := .node node265 node2904 +def node2906 : Tree Nat := .node node2905 node2404 +def node2907 : Tree Nat := .node node2906 node1713 +def node2908 : Tree Nat := .node node2903 node2907 +def node2909 : Tree Nat := .node node2900 node2908 +def node2910 : Tree Nat := .node node2896 node2490 +def node2911 : Tree Nat := .node node2910 node2500 +def node2912 : Tree Nat := .node node2911 node1720 +def node2913 : Tree Nat := .leaf 209 +def node2914 : Tree Nat := .node node2904 node2913 +def node2915 : Tree Nat := .node node2835 node73 +def node2916 : Tree Nat := .node node2914 node2915 +def node2917 : Tree Nat := .node node333 node2839 +def node2918 : Tree Nat := .node node2916 node2917 +def node2919 : Tree Nat := .node node2912 node2918 +def node2920 : Tree Nat := .node node2498 node2919 +def node2921 : Tree Nat := .node node2909 node2920 +def node2922 : Tree Nat := .node node2913 node2088 +def node2923 : Tree Nat := .node node2922 node1092 +def node2924 : Tree Nat := .leaf 228 +def node2925 : Tree Nat := .node node1 node2924 +def node2926 : Tree Nat := .node node2925 node641 +def node2927 : Tree Nat := .node node2923 node2926 +def node2928 : Tree Nat := .node node2927 node2509 +def node2929 : Tree Nat := .node node2511 node2797 +def node2930 : Tree Nat := .node node2929 node2514 +def node2931 : Tree Nat := .leaf 204 +def node2932 : Tree Nat := .node node304 node2931 +def node2933 : Tree Nat := .node node2932 node2516 +def node2934 : Tree Nat := .node node2933 node1733 +def node2935 : Tree Nat := .node node2930 node2934 +def node2936 : Tree Nat := .node node2928 node2935 +def node2937 : Tree Nat := .leaf 216 +def node2938 : Tree Nat := .node node1 node2937 +def node2939 : Tree Nat := .node node2808 node114 +def node2940 : Tree Nat := .node node2938 node2939 +def node2941 : Tree Nat := .node node909 node2812 +def node2942 : Tree Nat := .node node2940 node2941 +def node2943 : Tree Nat := .node node2530 node2942 +def node2944 : Tree Nat := .node node2525 node2943 +def node2945 : Tree Nat := .node node2936 node2944 +def node2946 : Tree Nat := .node node2921 node2945 +def node2947 : Tree Nat := .node node2895 node2946 +def node2948 : Tree Nat := .node node2846 node2947 +def node2949 : Tree Nat := .node node1752 node2740 +def node2950 : Tree Nat := .node node2949 node2539 +def node2951 : Tree Nat := .node node2833 node0 +def node2952 : Tree Nat := .node node2121 node2951 +def node2953 : Tree Nat := .node node2952 node2542 +def node2954 : Tree Nat := .node node2953 node2547 +def node2955 : Tree Nat := .node node2950 node2954 +def node2956 : Tree Nat := .node node2750 node2128 +def node2957 : Tree Nat := .node node2127 node2956 +def node2958 : Tree Nat := .node node2957 node2552 +def node2959 : Tree Nat := .node node371 node2754 +def node2960 : Tree Nat := .node node2818 node57 +def node2961 : Tree Nat := .node node2959 node2960 +def node2962 : Tree Nat := .node node2827 node1 +def node2963 : Tree Nat := .node node733 node2962 +def node2964 : Tree Nat := .node node2961 node2963 +def node2965 : Tree Nat := .node node2556 node2964 +def node2966 : Tree Nat := .node node2958 node2965 +def node2967 : Tree Nat := .node node2955 node2966 +def node2968 : Tree Nat := .node node1 node2780 +def node2969 : Tree Nat := .node node2968 node160 +def node2970 : Tree Nat := .node node2142 node2969 +def node2971 : Tree Nat := .node node2970 node2562 +def node2972 : Tree Nat := .leaf 215 +def node2973 : Tree Nat := .node node2972 node25 +def node2974 : Tree Nat := .node node2149 node2973 +def node2975 : Tree Nat := .node node2974 node2566 +def node2976 : Tree Nat := .node node391 node2783 +def node2977 : Tree Nat := .node node2976 node2569 +def node2978 : Tree Nat := .node node2977 node1607 +def node2979 : Tree Nat := .node node2975 node2978 +def node2980 : Tree Nat := .node node2971 node2979 +def node2981 : Tree Nat := .node node1 node2770 +def node2982 : Tree Nat := .leaf 227 +def node2983 : Tree Nat := .node node2982 node82 +def node2984 : Tree Nat := .node node2981 node2983 +def node2985 : Tree Nat := .leaf 203 +def node2986 : Tree Nat := .node node2985 node1 +def node2987 : Tree Nat := .node node739 node2986 +def node2988 : Tree Nat := .node node2984 node2987 +def node2989 : Tree Nat := .node node2582 node2988 +def node2990 : Tree Nat := .node node2577 node2989 +def node2991 : Tree Nat := .node node2980 node2990 +def node2992 : Tree Nat := .node node2967 node2991 +def node2993 : Tree Nat := .node node1790 node2793 +def node2994 : Tree Nat := .node node2993 node2589 +def node2995 : Tree Nat := .node node2972 node0 +def node2996 : Tree Nat := .node node2171 node2995 +def node2997 : Tree Nat := .node node2996 node2566 +def node2998 : Tree Nat := .node node432 node2800 +def node2999 : Tree Nat := .node node2998 node2592 +def node3000 : Tree Nat := .node node2999 node1629 +def node3001 : Tree Nat := .node node2997 node3000 +def node3002 : Tree Nat := .node node2994 node3001 +def node3003 : Tree Nat := .node node455 node2806 +def node3004 : Tree Nat := .node node3003 node2983 +def node3005 : Tree Nat := .node node829 node2986 +def node3006 : Tree Nat := .node node3004 node3005 +def node3007 : Tree Nat := .node node2604 node3006 +def node3008 : Tree Nat := .node node2600 node3007 +def node3009 : Tree Nat := .node node3002 node3008 +def node3010 : Tree Nat := .node node1 node2982 +def node3011 : Tree Nat := .node node3010 node1303 +def node3012 : Tree Nat := .node node2188 node3011 +def node3013 : Tree Nat := .node node3012 node2610 +def node3014 : Tree Nat := .node node2833 node25 +def node3015 : Tree Nat := .node node2194 node3014 +def node3016 : Tree Nat := .node node3015 node2613 +def node3017 : Tree Nat := .node node475 node2985 +def node3018 : Tree Nat := .node node3017 node2615 +def node3019 : Tree Nat := .node node3018 node1648 +def node3020 : Tree Nat := .node node3016 node3019 +def node3021 : Tree Nat := .node node3013 node3020 +def node3022 : Tree Nat := .node node1 node2972 +def node3023 : Tree Nat := .node node2818 node25 +def node3024 : Tree Nat := .node node3022 node3023 +def node3025 : Tree Nat := .node node909 node2962 +def node3026 : Tree Nat := .node node3024 node3025 +def node3027 : Tree Nat := .node node2626 node3026 +def node3028 : Tree Nat := .node node2623 node3027 +def node3029 : Tree Nat := .node node3021 node3028 +def node3030 : Tree Nat := .node node3009 node3029 +def node3031 : Tree Nat := .node node2992 node3030 +def node3032 : Tree Nat := .node node1825 node2849 +def node3033 : Tree Nat := .node node3032 node2634 +def node3034 : Tree Nat := .node node2937 node0 +def node3035 : Tree Nat := .node node2216 node3034 +def node3036 : Tree Nat := .node node3035 node2637 +def node3037 : Tree Nat := .node node3036 node2642 +def node3038 : Tree Nat := .node node3033 node3037 +def node3039 : Tree Nat := .node node2749 node2440 +def node3040 : Tree Nat := .node node3039 node2226 +def node3041 : Tree Nat := .node node3040 node1834 +def node3042 : Tree Nat := .node node2225 node3041 +def node3043 : Tree Nat := .node node2738 node2023 +def node3044 : Tree Nat := .node node3043 node2649 +def node3045 : Tree Nat := .node node3044 node1682 +def node3046 : Tree Nat := .node node2320 node2864 +def node3047 : Tree Nat := .node node2924 node73 +def node3048 : Tree Nat := .node node3046 node3047 +def node3049 : Tree Nat := .node node2931 node1 +def node3050 : Tree Nat := .node node698 node3049 +def node3051 : Tree Nat := .node node3048 node3050 +def node3052 : Tree Nat := .node node3045 node3051 +def node3053 : Tree Nat := .node node3042 node3052 +def node3054 : Tree Nat := .node node3038 node3053 +def node3055 : Tree Nat := .node node2754 node1999 +def node3056 : Tree Nat := .node node3055 node746 +def node3057 : Tree Nat := .node node1 node2835 +def node3058 : Tree Nat := .node node3057 node491 +def node3059 : Tree Nat := .node node3056 node3058 +def node3060 : Tree Nat := .node node3059 node2660 +def node3061 : Tree Nat := .leaf 217 +def node3062 : Tree Nat := .node node3061 node57 +def node3063 : Tree Nat := .node node2662 node3062 +def node3064 : Tree Nat := .node node3063 node2666 +def node3065 : Tree Nat := .node node551 node2838 +def node3066 : Tree Nat := .node node3065 node2669 +def node3067 : Tree Nat := .node node3066 node1695 +def node3068 : Tree Nat := .node node3064 node3067 +def node3069 : Tree Nat := .node node3060 node3068 +def node3070 : Tree Nat := .node node1 node2823 +def node3071 : Tree Nat := .leaf 229 +def node3072 : Tree Nat := .node node3071 node25 +def node3073 : Tree Nat := .node node3070 node3072 +def node3074 : Tree Nat := .leaf 205 +def node3075 : Tree Nat := .node node3074 node1 +def node3076 : Tree Nat := .node node739 node3075 +def node3077 : Tree Nat := .node node3073 node3076 +def node3078 : Tree Nat := .node node2682 node3077 +def node3079 : Tree Nat := .node node2677 node3078 +def node3080 : Tree Nat := .node node3069 node3079 +def node3081 : Tree Nat := .node node3054 node3080 +def node3082 : Tree Nat := .node node2264 node2898 +def node3083 : Tree Nat := .node node3082 node2689 +def node3084 : Tree Nat := .node node3061 node25 +def node3085 : Tree Nat := .node node2270 node3084 +def node3086 : Tree Nat := .node node3085 node2666 +def node3087 : Tree Nat := .node node586 node2904 +def node3088 : Tree Nat := .node node3087 node2692 +def node3089 : Tree Nat := .node node3088 node1713 +def node3090 : Tree Nat := .node node3086 node3089 +def node3091 : Tree Nat := .node node3083 node3090 +def node3092 : Tree Nat := .node node2791 node2490 +def node3093 : Tree Nat := .node node3092 node2680 +def node3094 : Tree Nat := .node node3093 node1868 +def node3095 : Tree Nat := .node node2800 node2913 +def node3096 : Tree Nat := .node node3071 node73 +def node3097 : Tree Nat := .node node3095 node3096 +def node3098 : Tree Nat := .node node333 node3075 +def node3099 : Tree Nat := .node node3097 node3098 +def node3100 : Tree Nat := .node node3094 node3099 +def node3101 : Tree Nat := .node node2703 node3100 +def node3102 : Tree Nat := .node node3091 node3101 +def node3103 : Tree Nat := .node node2806 node2251 +def node3104 : Tree Nat := .node node3103 node1092 +def node3105 : Tree Nat := .node node1 node3071 +def node3106 : Tree Nat := .node node3105 node641 +def node3107 : Tree Nat := .node node3104 node3106 +def node3108 : Tree Nat := .node node3107 node2712 +def node3109 : Tree Nat := .node node2714 node3034 +def node3110 : Tree Nat := .node node3109 node2717 +def node3111 : Tree Nat := .node node625 node3074 +def node3112 : Tree Nat := .node node3111 node2719 +def node3113 : Tree Nat := .node node3112 node1733 +def node3114 : Tree Nat := .node node3110 node3113 +def node3115 : Tree Nat := .node node3108 node3114 +def node3116 : Tree Nat := .node node1 node3061 +def node3117 : Tree Nat := .node node2924 node114 +def node3118 : Tree Nat := .node node3116 node3117 +def node3119 : Tree Nat := .node node909 node3049 +def node3120 : Tree Nat := .node node3118 node3119 +def node3121 : Tree Nat := .node node2730 node3120 +def node3122 : Tree Nat := .node node2727 node3121 +def node3123 : Tree Nat := .node node3115 node3122 +def node3124 : Tree Nat := .node node3102 node3123 +def node3125 : Tree Nat := .node node3081 node3124 +def node3126 : Tree Nat := .node node3031 node3125 +def node3127 : Tree Nat := .node node2948 node3126 +def node3128 : Tree Nat := .leaf 266 +def node3129 : Tree Nat := .node node1 node3128 +def node3130 : Tree Nat := .node node3129 node1582 +def node3131 : Tree Nat := .node node2313 node3130 +def node3132 : Tree Nat := .node node2741 node3131 +def node3133 : Tree Nat := .leaf 242 +def node3134 : Tree Nat := .node node1 node3133 +def node3135 : Tree Nat := .node node3134 node2317 +def node3136 : Tree Nat := .node node2745 node3135 +def node3137 : Tree Nat := .leaf 246 +def node3138 : Tree Nat := .node node3137 node1 +def node3139 : Tree Nat := .node node115 node3138 +def node3140 : Tree Nat := .node node2324 node3139 +def node3141 : Tree Nat := .node node3136 node3140 +def node3142 : Tree Nat := .node node3132 node3141 +def node3143 : Tree Nat := .leaf 258 +def node3144 : Tree Nat := .node node3143 node1 +def node3145 : Tree Nat := .node node3 node3144 +def node3146 : Tree Nat := .node node2330 node3145 +def node3147 : Tree Nat := .node node2752 node3146 +def node3148 : Tree Nat := .leaf 254 +def node3149 : Tree Nat := .node node1 node3148 +def node3150 : Tree Nat := .leaf 234 +def node3151 : Tree Nat := .node node3150 node411 +def node3152 : Tree Nat := .node node3149 node3151 +def node3153 : Tree Nat := .node node2335 node3152 +def node3154 : Tree Nat := .node node3153 node2762 +def node3155 : Tree Nat := .node node3147 node3154 +def node3156 : Tree Nat := .node node3142 node3155 +def node3157 : Tree Nat := .node node1 node3137 +def node3158 : Tree Nat := .node node3157 node2345 +def node3159 : Tree Nat := .node node2772 node3158 +def node3160 : Tree Nat := .leaf 247 +def node3161 : Tree Nat := .node node3160 node1 +def node3162 : Tree Nat := .node node9 node3161 +def node3163 : Tree Nat := .node node2775 node3162 +def node3164 : Tree Nat := .node node3159 node3163 +def node3165 : Tree Nat := .node node2769 node3164 +def node3166 : Tree Nat := .node node1 node3150 +def node3167 : Tree Nat := .node node3166 node1940 +def node3168 : Tree Nat := .node node1938 node3167 +def node3169 : Tree Nat := .leaf 259 +def node3170 : Tree Nat := .node node3169 node1 +def node3171 : Tree Nat := .node node3 node3170 +def node3172 : Tree Nat := .node node2355 node3171 +def node3173 : Tree Nat := .node node3168 node3172 +def node3174 : Tree Nat := .node node1 node3143 +def node3175 : Tree Nat := .leaf 235 +def node3176 : Tree Nat := .node node3175 node1 +def node3177 : Tree Nat := .node node3174 node3176 +def node3178 : Tree Nat := .node node2361 node3177 +def node3179 : Tree Nat := .node node3178 node2786 +def node3180 : Tree Nat := .node node3173 node3179 +def node3181 : Tree Nat := .node node3165 node3180 +def node3182 : Tree Nat := .node node3156 node3181 +def node3183 : Tree Nat := .leaf 244 +def node3184 : Tree Nat := .node node1 node3183 +def node3185 : Tree Nat := .node node3184 node2373 +def node3186 : Tree Nat := .node node2798 node3185 +def node3187 : Tree Nat := .leaf 248 +def node3188 : Tree Nat := .node node3187 node1 +def node3189 : Tree Nat := .node node83 node3188 +def node3190 : Tree Nat := .node node2802 node3189 +def node3191 : Tree Nat := .node node3186 node3190 +def node3192 : Tree Nat := .node node2795 node3191 +def node3193 : Tree Nat := .leaf 232 +def node3194 : Tree Nat := .node node1 node3193 +def node3195 : Tree Nat := .node node3194 node1966 +def node3196 : Tree Nat := .node node1964 node3195 +def node3197 : Tree Nat := .leaf 260 +def node3198 : Tree Nat := .node node3197 node1 +def node3199 : Tree Nat := .node node3 node3198 +def node3200 : Tree Nat := .node node2384 node3199 +def node3201 : Tree Nat := .node node3196 node3200 +def node3202 : Tree Nat := .leaf 256 +def node3203 : Tree Nat := .node node1 node3202 +def node3204 : Tree Nat := .leaf 236 +def node3205 : Tree Nat := .node node3204 node1 +def node3206 : Tree Nat := .node node3203 node3205 +def node3207 : Tree Nat := .node node2389 node3206 +def node3208 : Tree Nat := .node node3207 node2814 +def node3209 : Tree Nat := .node node3201 node3208 +def node3210 : Tree Nat := .node node3192 node3209 +def node3211 : Tree Nat := .leaf 250 +def node3212 : Tree Nat := .node node1 node3211 +def node3213 : Tree Nat := .node node3212 node2400 +def node3214 : Tree Nat := .node node2825 node3213 +def node3215 : Tree Nat := .leaf 249 +def node3216 : Tree Nat := .node node3215 node1 +def node3217 : Tree Nat := .node node9 node3216 +def node3218 : Tree Nat := .node node2829 node3217 +def node3219 : Tree Nat := .node node3214 node3218 +def node3220 : Tree Nat := .node node2822 node3219 +def node3221 : Tree Nat := .leaf 238 +def node3222 : Tree Nat := .node node1 node3221 +def node3223 : Tree Nat := .node node3222 node2000 +def node3224 : Tree Nat := .node node1998 node3223 +def node3225 : Tree Nat := .leaf 261 +def node3226 : Tree Nat := .node node3225 node1 +def node3227 : Tree Nat := .node node3 node3226 +def node3228 : Tree Nat := .node node2411 node3227 +def node3229 : Tree Nat := .node node3224 node3228 +def node3230 : Tree Nat := .leaf 262 +def node3231 : Tree Nat := .node node1 node3230 +def node3232 : Tree Nat := .leaf 237 +def node3233 : Tree Nat := .node node3232 node322 +def node3234 : Tree Nat := .node node3231 node3233 +def node3235 : Tree Nat := .node node2418 node3234 +def node3236 : Tree Nat := .node node3235 node2841 +def node3237 : Tree Nat := .node node3229 node3236 +def node3238 : Tree Nat := .node node3220 node3237 +def node3239 : Tree Nat := .node node3210 node3238 +def node3240 : Tree Nat := .node node3182 node3239 +def node3241 : Tree Nat := .leaf 243 +def node3242 : Tree Nat := .node node1 node3241 +def node3243 : Tree Nat := .node node3242 node2430 +def node3244 : Tree Nat := .node node2853 node3243 +def node3245 : Tree Nat := .leaf 255 +def node3246 : Tree Nat := .node node3245 node2433 +def node3247 : Tree Nat := .node node3246 node2435 +def node3248 : Tree Nat := .node node115 node3161 +def node3249 : Tree Nat := .node node3247 node3248 +def node3250 : Tree Nat := .node node3244 node3249 +def node3251 : Tree Nat := .node node2851 node3250 +def node3252 : Tree Nat := .leaf 231 +def node3253 : Tree Nat := .node node1 node3252 +def node3254 : Tree Nat := .node node3253 node1940 +def node3255 : Tree Nat := .node node2025 node3254 +def node3256 : Tree Nat := .node node3252 node2440 +def node3257 : Tree Nat := .node node3256 node2027 +def node3258 : Tree Nat := .node node3169 node195 +def node3259 : Tree Nat := .node node3 node3258 +def node3260 : Tree Nat := .node node3257 node3259 +def node3261 : Tree Nat := .node node3255 node3260 +def node3262 : Tree Nat := .node node1 node3245 +def node3263 : Tree Nat := .node node3262 node3176 +def node3264 : Tree Nat := .node node2862 node3263 +def node3265 : Tree Nat := .node node3264 node2869 +def node3266 : Tree Nat := .node node3261 node3265 +def node3267 : Tree Nat := .node node3251 node3266 +def node3268 : Tree Nat := .node node1 node3187 +def node3269 : Tree Nat := .node node3268 node2460 +def node3270 : Tree Nat := .node node2880 node3269 +def node3271 : Tree Nat := .node node3241 node2811 +def node3272 : Tree Nat := .node node3271 node2463 +def node3273 : Tree Nat := .node node9 node3138 +def node3274 : Tree Nat := .node node3272 node3273 +def node3275 : Tree Nat := .node node3270 node3274 +def node3276 : Tree Nat := .node node2878 node3275 +def node3277 : Tree Nat := .node node1 node3204 +def node3278 : Tree Nat := .node node3277 node2051 +def node3279 : Tree Nat := .node node2050 node3278 +def node3280 : Tree Nat := .node node2469 node3145 +def node3281 : Tree Nat := .node node3279 node3280 +def node3282 : Tree Nat := .node node1 node3197 +def node3283 : Tree Nat := .node node3150 node1 +def node3284 : Tree Nat := .node node3282 node3283 +def node3285 : Tree Nat := .node node2474 node3284 +def node3286 : Tree Nat := .node node3285 node2891 +def node3287 : Tree Nat := .node node3281 node3286 +def node3288 : Tree Nat := .node node3276 node3287 +def node3289 : Tree Nat := .node node3267 node3288 +def node3290 : Tree Nat := .leaf 245 +def node3291 : Tree Nat := .node node1 node3290 +def node3292 : Tree Nat := .node node3291 node2400 +def node3293 : Tree Nat := .node node2902 node3292 +def node3294 : Tree Nat := .leaf 257 +def node3295 : Tree Nat := .node node3294 node2904 +def node3296 : Tree Nat := .node node3295 node2404 +def node3297 : Tree Nat := .node node83 node3216 +def node3298 : Tree Nat := .node node3296 node3297 +def node3299 : Tree Nat := .node node3293 node3298 +def node3300 : Tree Nat := .node node2900 node3299 +def node3301 : Tree Nat := .leaf 233 +def node3302 : Tree Nat := .node node1 node3301 +def node3303 : Tree Nat := .node node3302 node2079 +def node3304 : Tree Nat := .node node2492 node3303 +def node3305 : Tree Nat := .node node3301 node2494 +def node3306 : Tree Nat := .node node3305 node2082 +def node3307 : Tree Nat := .node node3306 node3227 +def node3308 : Tree Nat := .node node3304 node3307 +def node3309 : Tree Nat := .node node1 node3294 +def node3310 : Tree Nat := .node node3232 node1 +def node3311 : Tree Nat := .node node3309 node3310 +def node3312 : Tree Nat := .node node2911 node3311 +def node3313 : Tree Nat := .node node3312 node2918 +def node3314 : Tree Nat := .node node3308 node3313 +def node3315 : Tree Nat := .node node3300 node3314 +def node3316 : Tree Nat := .leaf 252 +def node3317 : Tree Nat := .node node1 node3316 +def node3318 : Tree Nat := .node node3317 node2513 +def node3319 : Tree Nat := .node node2929 node3318 +def node3320 : Tree Nat := .node node3290 node2931 +def node3321 : Tree Nat := .node node3320 node2516 +def node3322 : Tree Nat := .node node26 node3188 +def node3323 : Tree Nat := .node node3321 node3322 +def node3324 : Tree Nat := .node node3319 node3323 +def node3325 : Tree Nat := .node node2928 node3324 +def node3326 : Tree Nat := .leaf 240 +def node3327 : Tree Nat := .node node1 node3326 +def node3328 : Tree Nat := .node node3327 node2105 +def node3329 : Tree Nat := .node node2104 node3328 +def node3330 : Tree Nat := .node node2523 node3199 +def node3331 : Tree Nat := .node node3329 node3330 +def node3332 : Tree Nat := .leaf 264 +def node3333 : Tree Nat := .node node1 node3332 +def node3334 : Tree Nat := .node node3204 node322 +def node3335 : Tree Nat := .node node3333 node3334 +def node3336 : Tree Nat := .node node2529 node3335 +def node3337 : Tree Nat := .node node3336 node2942 +def node3338 : Tree Nat := .node node3331 node3337 +def node3339 : Tree Nat := .node node3325 node3338 +def node3340 : Tree Nat := .node node3315 node3339 +def node3341 : Tree Nat := .node node3289 node3340 +def node3342 : Tree Nat := .node node3240 node3341 +def node3343 : Tree Nat := .node node3134 node2541 +def node3344 : Tree Nat := .node node2952 node3343 +def node3345 : Tree Nat := .node node3211 node1 +def node3346 : Tree Nat := .node node115 node3345 +def node3347 : Tree Nat := .node node2546 node3346 +def node3348 : Tree Nat := .node node3344 node3347 +def node3349 : Tree Nat := .node node2950 node3348 +def node3350 : Tree Nat := .node node3230 node195 +def node3351 : Tree Nat := .node node3 node3350 +def node3352 : Tree Nat := .node node2551 node3351 +def node3353 : Tree Nat := .node node2957 node3352 +def node3354 : Tree Nat := .node node3221 node322 +def node3355 : Tree Nat := .node node3149 node3354 +def node3356 : Tree Nat := .node node2555 node3355 +def node3357 : Tree Nat := .node node3356 node2964 +def node3358 : Tree Nat := .node node3353 node3357 +def node3359 : Tree Nat := .node node3349 node3358 +def node3360 : Tree Nat := .node node1 node3160 +def node3361 : Tree Nat := .node node3360 node2565 +def node3362 : Tree Nat := .node node2974 node3361 +def node3363 : Tree Nat := .leaf 251 +def node3364 : Tree Nat := .node node3363 node1 +def node3365 : Tree Nat := .node node9 node3364 +def node3366 : Tree Nat := .node node2977 node3365 +def node3367 : Tree Nat := .node node3362 node3366 +def node3368 : Tree Nat := .node node2971 node3367 +def node3369 : Tree Nat := .node node1 node3175 +def node3370 : Tree Nat := .node node3369 node2157 +def node3371 : Tree Nat := .node node2155 node3370 +def node3372 : Tree Nat := .leaf 263 +def node3373 : Tree Nat := .node node3372 node1 +def node3374 : Tree Nat := .node node3 node3373 +def node3375 : Tree Nat := .node node2575 node3374 +def node3376 : Tree Nat := .node node3371 node3375 +def node3377 : Tree Nat := .node node1 node3169 +def node3378 : Tree Nat := .leaf 239 +def node3379 : Tree Nat := .node node3378 node411 +def node3380 : Tree Nat := .node node3377 node3379 +def node3381 : Tree Nat := .node node2581 node3380 +def node3382 : Tree Nat := .node node3381 node2988 +def node3383 : Tree Nat := .node node3376 node3382 +def node3384 : Tree Nat := .node node3368 node3383 +def node3385 : Tree Nat := .node node3359 node3384 +def node3386 : Tree Nat := .node node3184 node2565 +def node3387 : Tree Nat := .node node2996 node3386 +def node3388 : Tree Nat := .node node83 node3364 +def node3389 : Tree Nat := .node node2999 node3388 +def node3390 : Tree Nat := .node node3387 node3389 +def node3391 : Tree Nat := .node node2994 node3390 +def node3392 : Tree Nat := .node node3194 node2178 +def node3393 : Tree Nat := .node node2177 node3392 +def node3394 : Tree Nat := .node node2598 node3374 +def node3395 : Tree Nat := .node node3393 node3394 +def node3396 : Tree Nat := .node node3378 node451 +def node3397 : Tree Nat := .node node3203 node3396 +def node3398 : Tree Nat := .node node2603 node3397 +def node3399 : Tree Nat := .node node3398 node3006 +def node3400 : Tree Nat := .node node3395 node3399 +def node3401 : Tree Nat := .node node3391 node3400 +def node3402 : Tree Nat := .node node1 node3363 +def node3403 : Tree Nat := .node node3402 node2612 +def node3404 : Tree Nat := .node node3015 node3403 +def node3405 : Tree Nat := .node node9 node3345 +def node3406 : Tree Nat := .node node3018 node3405 +def node3407 : Tree Nat := .node node3404 node3406 +def node3408 : Tree Nat := .node node3013 node3407 +def node3409 : Tree Nat := .node node1 node3378 +def node3410 : Tree Nat := .node node3409 node2201 +def node3411 : Tree Nat := .node node2200 node3410 +def node3412 : Tree Nat := .node node3230 node1 +def node3413 : Tree Nat := .node node3 node3412 +def node3414 : Tree Nat := .node node2621 node3413 +def node3415 : Tree Nat := .node node3411 node3414 +def node3416 : Tree Nat := .node node1 node3372 +def node3417 : Tree Nat := .node node3221 node1 +def node3418 : Tree Nat := .node node3416 node3417 +def node3419 : Tree Nat := .node node2625 node3418 +def node3420 : Tree Nat := .node node3419 node3026 +def node3421 : Tree Nat := .node node3415 node3420 +def node3422 : Tree Nat := .node node3408 node3421 +def node3423 : Tree Nat := .node node3401 node3422 +def node3424 : Tree Nat := .node node3385 node3423 +def node3425 : Tree Nat := .node node3242 node2636 +def node3426 : Tree Nat := .node node3035 node3425 +def node3427 : Tree Nat := .node node3148 node2433 +def node3428 : Tree Nat := .node node3427 node2640 +def node3429 : Tree Nat := .node node3316 node1 +def node3430 : Tree Nat := .node node115 node3429 +def node3431 : Tree Nat := .node node3428 node3430 +def node3432 : Tree Nat := .node node3426 node3431 +def node3433 : Tree Nat := .node node3033 node3432 +def node3434 : Tree Nat := .node node3253 node2223 +def node3435 : Tree Nat := .node node2222 node3434 +def node3436 : Tree Nat := .node node3332 node1 +def node3437 : Tree Nat := .node node3 node3436 +def node3438 : Tree Nat := .node node3040 node3437 +def node3439 : Tree Nat := .node node3435 node3438 +def node3440 : Tree Nat := .node node3326 node1 +def node3441 : Tree Nat := .node node3262 node3440 +def node3442 : Tree Nat := .node node3044 node3441 +def node3443 : Tree Nat := .node node3442 node3051 +def node3444 : Tree Nat := .node node3439 node3443 +def node3445 : Tree Nat := .node node3433 node3444 +def node3446 : Tree Nat := .node node1 node3215 +def node3447 : Tree Nat := .node node3446 node2665 +def node3448 : Tree Nat := .node node3063 node3447 +def node3449 : Tree Nat := .node node3133 node2838 +def node3450 : Tree Nat := .node node3449 node2669 +def node3451 : Tree Nat := .leaf 253 +def node3452 : Tree Nat := .node node3451 node1 +def node3453 : Tree Nat := .node node9 node3452 +def node3454 : Tree Nat := .node node3450 node3453 +def node3455 : Tree Nat := .node node3448 node3454 +def node3456 : Tree Nat := .node node3060 node3455 +def node3457 : Tree Nat := .node node1 node3232 +def node3458 : Tree Nat := .node node3457 node2252 +def node3459 : Tree Nat := .node node2250 node3458 +def node3460 : Tree Nat := .node node3128 node2399 +def node3461 : Tree Nat := .node node3460 node2256 +def node3462 : Tree Nat := .leaf 265 +def node3463 : Tree Nat := .node node3462 node1 +def node3464 : Tree Nat := .node node3 node3463 +def node3465 : Tree Nat := .node node3461 node3464 +def node3466 : Tree Nat := .node node3459 node3465 +def node3467 : Tree Nat := .node node1 node3225 +def node3468 : Tree Nat := .leaf 241 +def node3469 : Tree Nat := .node node3468 node1 +def node3470 : Tree Nat := .node node3467 node3469 +def node3471 : Tree Nat := .node node2681 node3470 +def node3472 : Tree Nat := .node node3471 node3077 +def node3473 : Tree Nat := .node node3466 node3472 +def node3474 : Tree Nat := .node node3456 node3473 +def node3475 : Tree Nat := .node node3445 node3474 +def node3476 : Tree Nat := .node node3291 node2665 +def node3477 : Tree Nat := .node node3085 node3476 +def node3478 : Tree Nat := .node node3202 node2904 +def node3479 : Tree Nat := .node node3478 node2692 +def node3480 : Tree Nat := .node node83 node3452 +def node3481 : Tree Nat := .node node3479 node3480 +def node3482 : Tree Nat := .node node3477 node3481 +def node3483 : Tree Nat := .node node3083 node3482 +def node3484 : Tree Nat := .node node3302 node2277 +def node3485 : Tree Nat := .node node2698 node3484 +def node3486 : Tree Nat := .node node3193 node2494 +def node3487 : Tree Nat := .node node3486 node2280 +def node3488 : Tree Nat := .node node3487 node3464 +def node3489 : Tree Nat := .node node3485 node3488 +def node3490 : Tree Nat := .node node3468 node411 +def node3491 : Tree Nat := .node node3309 node3490 +def node3492 : Tree Nat := .node node3093 node3491 +def node3493 : Tree Nat := .node node3492 node3099 +def node3494 : Tree Nat := .node node3489 node3493 +def node3495 : Tree Nat := .node node3483 node3494 +def node3496 : Tree Nat := .node node1 node3451 +def node3497 : Tree Nat := .node node3496 node2716 +def node3498 : Tree Nat := .node node3109 node3497 +def node3499 : Tree Nat := .node node3183 node3074 +def node3500 : Tree Nat := .node node3499 node2719 +def node3501 : Tree Nat := .node node26 node3429 +def node3502 : Tree Nat := .node node3500 node3501 +def node3503 : Tree Nat := .node node3498 node3502 +def node3504 : Tree Nat := .node node3108 node3503 +def node3505 : Tree Nat := .node node1 node3468 +def node3506 : Tree Nat := .node node3505 node2223 +def node3507 : Tree Nat := .node node2299 node3506 +def node3508 : Tree Nat := .node node2725 node3437 +def node3509 : Tree Nat := .node node3507 node3508 +def node3510 : Tree Nat := .node node1 node3462 +def node3511 : Tree Nat := .node node3326 node195 +def node3512 : Tree Nat := .node node3510 node3511 +def node3513 : Tree Nat := .node node2729 node3512 +def node3514 : Tree Nat := .node node3513 node3120 +def node3515 : Tree Nat := .node node3509 node3514 +def node3516 : Tree Nat := .node node3504 node3515 +def node3517 : Tree Nat := .node node3495 node3516 +def node3518 : Tree Nat := .node node3475 node3517 +def node3519 : Tree Nat := .node node3424 node3518 +def node3520 : Tree Nat := .node node3342 node3519 +def node3521 : Tree Nat := .leaf 290 +def node3522 : Tree Nat := .node node0 node3521 +def node3523 : Tree Nat := .node node3522 node726 +def node3524 : Tree Nat := .leaf 282 +def node3525 : Tree Nat := .node node3524 node73 +def node3526 : Tree Nat := .node node2739 node3525 +def node3527 : Tree Nat := .node node3523 node3526 +def node3528 : Tree Nat := .leaf 270 +def node3529 : Tree Nat := .node node3528 node195 +def node3530 : Tree Nat := .node node3129 node3529 +def node3531 : Tree Nat := .node node2313 node3530 +def node3532 : Tree Nat := .node node3527 node3531 +def node3533 : Tree Nat := .node node1 node3521 +def node3534 : Tree Nat := .node node3533 node3138 +def node3535 : Tree Nat := .node node2324 node3534 +def node3536 : Tree Nat := .node node3136 node3535 +def node3537 : Tree Nat := .node node3532 node3536 +def node3538 : Tree Nat := .leaf 302 +def node3539 : Tree Nat := .node node23 node3538 +def node3540 : Tree Nat := .node node3539 node659 +def node3541 : Tree Nat := .leaf 292 +def node3542 : Tree Nat := .node node3541 node358 +def node3543 : Tree Nat := .node node2750 node3542 +def node3544 : Tree Nat := .node node3540 node3543 +def node3545 : Tree Nat := .leaf 278 +def node3546 : Tree Nat := .node node1 node3545 +def node3547 : Tree Nat := .node node3546 node3144 +def node3548 : Tree Nat := .node node2330 node3547 +def node3549 : Tree Nat := .node node3544 node3548 +def node3550 : Tree Nat := .node node3549 node3154 +def node3551 : Tree Nat := .node node3537 node3550 +def node3552 : Tree Nat := .leaf 298 +def node3553 : Tree Nat := .node node46 node3552 +def node3554 : Tree Nat := .node node3553 node985 +def node3555 : Tree Nat := .leaf 283 +def node3556 : Tree Nat := .node node3555 node1 +def node3557 : Tree Nat := .node node2766 node3556 +def node3558 : Tree Nat := .node node3554 node3557 +def node3559 : Tree Nat := .node node1 node3528 +def node3560 : Tree Nat := .leaf 271 +def node3561 : Tree Nat := .node node3560 node1 +def node3562 : Tree Nat := .node node3559 node3561 +def node3563 : Tree Nat := .node node2341 node3562 +def node3564 : Tree Nat := .node node3558 node3563 +def node3565 : Tree Nat := .leaf 296 +def node3566 : Tree Nat := .node node1 node3565 +def node3567 : Tree Nat := .node node3566 node3161 +def node3568 : Tree Nat := .node node2775 node3567 +def node3569 : Tree Nat := .node node3159 node3568 +def node3570 : Tree Nat := .node node3564 node3569 +def node3571 : Tree Nat := .node node1 node3524 +def node3572 : Tree Nat := .node node3571 node3170 +def node3573 : Tree Nat := .node node2355 node3572 +def node3574 : Tree Nat := .node node3168 node3573 +def node3575 : Tree Nat := .node node3574 node3179 +def node3576 : Tree Nat := .node node3570 node3575 +def node3577 : Tree Nat := .node node3551 node3576 +def node3578 : Tree Nat := .leaf 291 +def node3579 : Tree Nat := .node node25 node3578 +def node3580 : Tree Nat := .node node3579 node816 +def node3581 : Tree Nat := .leaf 284 +def node3582 : Tree Nat := .node node3581 node73 +def node3583 : Tree Nat := .node node2792 node3582 +def node3584 : Tree Nat := .node node3580 node3583 +def node3585 : Tree Nat := .leaf 268 +def node3586 : Tree Nat := .node node1 node3585 +def node3587 : Tree Nat := .leaf 272 +def node3588 : Tree Nat := .node node3587 node1 +def node3589 : Tree Nat := .node node3586 node3588 +def node3590 : Tree Nat := .node node2369 node3589 +def node3591 : Tree Nat := .node node3584 node3590 +def node3592 : Tree Nat := .node node1 node3541 +def node3593 : Tree Nat := .node node3592 node3188 +def node3594 : Tree Nat := .node node2802 node3593 +def node3595 : Tree Nat := .node node3186 node3594 +def node3596 : Tree Nat := .node node3591 node3595 +def node3597 : Tree Nat := .leaf 293 +def node3598 : Tree Nat := .node node3597 node114 +def node3599 : Tree Nat := .node node3194 node3598 +def node3600 : Tree Nat := .node node1964 node3599 +def node3601 : Tree Nat := .leaf 280 +def node3602 : Tree Nat := .node node1 node3601 +def node3603 : Tree Nat := .node node3602 node3198 +def node3604 : Tree Nat := .node node2384 node3603 +def node3605 : Tree Nat := .node node3600 node3604 +def node3606 : Tree Nat := .node node3605 node3208 +def node3607 : Tree Nat := .node node3596 node3606 +def node3608 : Tree Nat := .node node130 node3565 +def node3609 : Tree Nat := .node node3608 node90 +def node3610 : Tree Nat := .leaf 285 +def node3611 : Tree Nat := .node node3610 node114 +def node3612 : Tree Nat := .node node2819 node3611 +def node3613 : Tree Nat := .node node3609 node3612 +def node3614 : Tree Nat := .leaf 274 +def node3615 : Tree Nat := .node node1 node3614 +def node3616 : Tree Nat := .leaf 273 +def node3617 : Tree Nat := .node node3616 node1 +def node3618 : Tree Nat := .node node3615 node3617 +def node3619 : Tree Nat := .node node2396 node3618 +def node3620 : Tree Nat := .node node3613 node3619 +def node3621 : Tree Nat := .leaf 300 +def node3622 : Tree Nat := .node node1 node3621 +def node3623 : Tree Nat := .node node3622 node3216 +def node3624 : Tree Nat := .node node2829 node3623 +def node3625 : Tree Nat := .node node3214 node3624 +def node3626 : Tree Nat := .node node3620 node3625 +def node3627 : Tree Nat := .leaf 286 +def node3628 : Tree Nat := .node node1 node3627 +def node3629 : Tree Nat := .node node3628 node3226 +def node3630 : Tree Nat := .node node2411 node3629 +def node3631 : Tree Nat := .node node3224 node3630 +def node3632 : Tree Nat := .node node3631 node3236 +def node3633 : Tree Nat := .node node3626 node3632 +def node3634 : Tree Nat := .node node3607 node3633 +def node3635 : Tree Nat := .node node3577 node3634 +def node3636 : Tree Nat := .node node114 node3521 +def node3637 : Tree Nat := .node node3636 node1038 +def node3638 : Tree Nat := .node node3555 node25 +def node3639 : Tree Nat := .node node2848 node3638 +def node3640 : Tree Nat := .node node3637 node3639 +def node3641 : Tree Nat := .leaf 267 +def node3642 : Tree Nat := .node node1 node3641 +def node3643 : Tree Nat := .node node3642 node3561 +def node3644 : Tree Nat := .node node2427 node3643 +def node3645 : Tree Nat := .node node3640 node3644 +def node3646 : Tree Nat := .node node1 node3578 +def node3647 : Tree Nat := .node node3646 node3161 +def node3648 : Tree Nat := .node node3247 node3647 +def node3649 : Tree Nat := .node node3244 node3648 +def node3650 : Tree Nat := .node node3645 node3649 +def node3651 : Tree Nat := .node node2023 node3538 +def node3652 : Tree Nat := .node node3651 node754 +def node3653 : Tree Nat := .node node3541 node1 +def node3654 : Tree Nat := .node node3253 node3653 +def node3655 : Tree Nat := .node node3652 node3654 +def node3656 : Tree Nat := .leaf 279 +def node3657 : Tree Nat := .node node1 node3656 +def node3658 : Tree Nat := .node node3657 node3258 +def node3659 : Tree Nat := .node node3257 node3658 +def node3660 : Tree Nat := .node node3655 node3659 +def node3661 : Tree Nat := .node node3660 node3265 +def node3662 : Tree Nat := .node node3650 node3661 +def node3663 : Tree Nat := .node node2864 node3552 +def node3664 : Tree Nat := .node node3663 node90 +def node3665 : Tree Nat := .node node3524 node1 +def node3666 : Tree Nat := .node node2875 node3665 +def node3667 : Tree Nat := .node node3664 node3666 +def node3668 : Tree Nat := .node node1 node3587 +def node3669 : Tree Nat := .node node3528 node1 +def node3670 : Tree Nat := .node node3668 node3669 +def node3671 : Tree Nat := .node node2455 node3670 +def node3672 : Tree Nat := .node node3667 node3671 +def node3673 : Tree Nat := .node node1 node3552 +def node3674 : Tree Nat := .node node3673 node3138 +def node3675 : Tree Nat := .node node3272 node3674 +def node3676 : Tree Nat := .node node3270 node3675 +def node3677 : Tree Nat := .node node3672 node3676 +def node3678 : Tree Nat := .node node3641 node2372 +def node3679 : Tree Nat := .node node3678 node2054 +def node3680 : Tree Nat := .node node1 node3581 +def node3681 : Tree Nat := .node node3680 node3144 +def node3682 : Tree Nat := .node node3679 node3681 +def node3683 : Tree Nat := .node node3279 node3682 +def node3684 : Tree Nat := .node node3656 node2387 +def node3685 : Tree Nat := .node node3684 node2473 +def node3686 : Tree Nat := .node node3685 node3284 +def node3687 : Tree Nat := .node node3686 node2891 +def node3688 : Tree Nat := .node node3683 node3687 +def node3689 : Tree Nat := .node node3677 node3688 +def node3690 : Tree Nat := .node node3662 node3689 +def node3691 : Tree Nat := .node node252 node3578 +def node3692 : Tree Nat := .node node3691 node500 +def node3693 : Tree Nat := .node node2897 node3611 +def node3694 : Tree Nat := .node node3692 node3693 +def node3695 : Tree Nat := .leaf 269 +def node3696 : Tree Nat := .node node1 node3695 +def node3697 : Tree Nat := .node node3696 node3617 +def node3698 : Tree Nat := .node node2482 node3697 +def node3699 : Tree Nat := .node node3694 node3698 +def node3700 : Tree Nat := .leaf 294 +def node3701 : Tree Nat := .node node1 node3700 +def node3702 : Tree Nat := .node node3701 node3216 +def node3703 : Tree Nat := .node node3296 node3702 +def node3704 : Tree Nat := .node node3293 node3703 +def node3705 : Tree Nat := .node node3699 node3704 +def node3706 : Tree Nat := .node node3597 node1 +def node3707 : Tree Nat := .node node3302 node3706 +def node3708 : Tree Nat := .node node2492 node3707 +def node3709 : Tree Nat := .leaf 281 +def node3710 : Tree Nat := .node node1 node3709 +def node3711 : Tree Nat := .node node3710 node3226 +def node3712 : Tree Nat := .node node3306 node3711 +def node3713 : Tree Nat := .node node3708 node3712 +def node3714 : Tree Nat := .node node3713 node3313 +def node3715 : Tree Nat := .node node3705 node3714 +def node3716 : Tree Nat := .node node2913 node3565 +def node3717 : Tree Nat := .node node3716 node1092 +def node3718 : Tree Nat := .node node3581 node1 +def node3719 : Tree Nat := .node node2925 node3718 +def node3720 : Tree Nat := .node node3717 node3719 +def node3721 : Tree Nat := .leaf 276 +def node3722 : Tree Nat := .node node1 node3721 +def node3723 : Tree Nat := .node node3722 node3588 +def node3724 : Tree Nat := .node node2508 node3723 +def node3725 : Tree Nat := .node node3720 node3724 +def node3726 : Tree Nat := .node node1 node3538 +def node3727 : Tree Nat := .node node3726 node3188 +def node3728 : Tree Nat := .node node3321 node3727 +def node3729 : Tree Nat := .node node3319 node3728 +def node3730 : Tree Nat := .node node3725 node3729 +def node3731 : Tree Nat := .node node3695 node2521 +def node3732 : Tree Nat := .node node3731 node2108 +def node3733 : Tree Nat := .leaf 288 +def node3734 : Tree Nat := .node node1 node3733 +def node3735 : Tree Nat := .node node3734 node3198 +def node3736 : Tree Nat := .node node3732 node3735 +def node3737 : Tree Nat := .node node3329 node3736 +def node3738 : Tree Nat := .node node3709 node2526 +def node3739 : Tree Nat := .node node3738 node2528 +def node3740 : Tree Nat := .node node3739 node3335 +def node3741 : Tree Nat := .node node3740 node2942 +def node3742 : Tree Nat := .node node3737 node3741 +def node3743 : Tree Nat := .node node3730 node3742 +def node3744 : Tree Nat := .node node3715 node3743 +def node3745 : Tree Nat := .node node3690 node3744 +def node3746 : Tree Nat := .node node3635 node3745 +def node3747 : Tree Nat := .node node82 node3621 +def node3748 : Tree Nat := .node node3747 node726 +def node3749 : Tree Nat := .node node3627 node73 +def node3750 : Tree Nat := .node node2739 node3749 +def node3751 : Tree Nat := .node node3748 node3750 +def node3752 : Tree Nat := .node node3614 node340 +def node3753 : Tree Nat := .node node3129 node3752 +def node3754 : Tree Nat := .node node2538 node3753 +def node3755 : Tree Nat := .node node3751 node3754 +def node3756 : Tree Nat := .node node3533 node3345 +def node3757 : Tree Nat := .node node2546 node3756 +def node3758 : Tree Nat := .node node3344 node3757 +def node3759 : Tree Nat := .node node3755 node3758 +def node3760 : Tree Nat := .node node3546 node3350 +def node3761 : Tree Nat := .node node2551 node3760 +def node3762 : Tree Nat := .node node2957 node3761 +def node3763 : Tree Nat := .node node3762 node3357 +def node3764 : Tree Nat := .node node3759 node3763 +def node3765 : Tree Nat := .leaf 299 +def node3766 : Tree Nat := .node node378 node3765 +def node3767 : Tree Nat := .node node3766 node985 +def node3768 : Tree Nat := .leaf 287 +def node3769 : Tree Nat := .node node3768 node1 +def node3770 : Tree Nat := .node node2968 node3769 +def node3771 : Tree Nat := .node node3767 node3770 +def node3772 : Tree Nat := .node node1 node3560 +def node3773 : Tree Nat := .leaf 275 +def node3774 : Tree Nat := .node node3773 node1 +def node3775 : Tree Nat := .node node3772 node3774 +def node3776 : Tree Nat := .node node2561 node3775 +def node3777 : Tree Nat := .node node3771 node3776 +def node3778 : Tree Nat := .leaf 297 +def node3779 : Tree Nat := .node node1 node3778 +def node3780 : Tree Nat := .node node3779 node3364 +def node3781 : Tree Nat := .node node2977 node3780 +def node3782 : Tree Nat := .node node3362 node3781 +def node3783 : Tree Nat := .node node3777 node3782 +def node3784 : Tree Nat := .node node3700 node57 +def node3785 : Tree Nat := .node node3369 node3784 +def node3786 : Tree Nat := .node node2155 node3785 +def node3787 : Tree Nat := .node node1 node3555 +def node3788 : Tree Nat := .node node3787 node3373 +def node3789 : Tree Nat := .node node2575 node3788 +def node3790 : Tree Nat := .node node3786 node3789 +def node3791 : Tree Nat := .node node3790 node3382 +def node3792 : Tree Nat := .node node3783 node3791 +def node3793 : Tree Nat := .node node3764 node3792 +def node3794 : Tree Nat := .node node73 node3621 +def node3795 : Tree Nat := .node node3794 node816 +def node3796 : Tree Nat := .node node3768 node73 +def node3797 : Tree Nat := .node node2792 node3796 +def node3798 : Tree Nat := .node node3795 node3797 +def node3799 : Tree Nat := .node node3586 node3774 +def node3800 : Tree Nat := .node node2588 node3799 +def node3801 : Tree Nat := .node node3798 node3800 +def node3802 : Tree Nat := .node node1 node3597 +def node3803 : Tree Nat := .node node3802 node3364 +def node3804 : Tree Nat := .node node2999 node3803 +def node3805 : Tree Nat := .node node3387 node3804 +def node3806 : Tree Nat := .node node3801 node3805 +def node3807 : Tree Nat := .node node3602 node3373 +def node3808 : Tree Nat := .node node2598 node3807 +def node3809 : Tree Nat := .node node3393 node3808 +def node3810 : Tree Nat := .node node3809 node3399 +def node3811 : Tree Nat := .node node3806 node3810 +def node3812 : Tree Nat := .node node462 node3778 +def node3813 : Tree Nat := .node node3812 node746 +def node3814 : Tree Nat := .node node3627 node114 +def node3815 : Tree Nat := .node node3010 node3814 +def node3816 : Tree Nat := .node node3813 node3815 +def node3817 : Tree Nat := .node node1 node3773 +def node3818 : Tree Nat := .node node3614 node1 +def node3819 : Tree Nat := .node node3817 node3818 +def node3820 : Tree Nat := .node node2609 node3819 +def node3821 : Tree Nat := .node node3816 node3820 +def node3822 : Tree Nat := .leaf 301 +def node3823 : Tree Nat := .node node1 node3822 +def node3824 : Tree Nat := .node node3823 node3345 +def node3825 : Tree Nat := .node node3018 node3824 +def node3826 : Tree Nat := .node node3404 node3825 +def node3827 : Tree Nat := .node node3821 node3826 +def node3828 : Tree Nat := .node node3700 node73 +def node3829 : Tree Nat := .node node3409 node3828 +def node3830 : Tree Nat := .node node2200 node3829 +def node3831 : Tree Nat := .node node1 node3768 +def node3832 : Tree Nat := .node node3831 node3412 +def node3833 : Tree Nat := .node node2621 node3832 +def node3834 : Tree Nat := .node node3830 node3833 +def node3835 : Tree Nat := .node node3834 node3420 +def node3836 : Tree Nat := .node node3827 node3835 +def node3837 : Tree Nat := .node node3811 node3836 +def node3838 : Tree Nat := .node node3793 node3837 +def node3839 : Tree Nat := .node node358 node3822 +def node3840 : Tree Nat := .node node3839 node1038 +def node3841 : Tree Nat := .node node3733 node25 +def node3842 : Tree Nat := .node node2848 node3841 +def node3843 : Tree Nat := .node node3840 node3842 +def node3844 : Tree Nat := .node node3721 node1 +def node3845 : Tree Nat := .node node3642 node3844 +def node3846 : Tree Nat := .node node2633 node3845 +def node3847 : Tree Nat := .node node3843 node3846 +def node3848 : Tree Nat := .node node3646 node3429 +def node3849 : Tree Nat := .node node3428 node3848 +def node3850 : Tree Nat := .node node3426 node3849 +def node3851 : Tree Nat := .node node3847 node3850 +def node3852 : Tree Nat := .node node3657 node3436 +def node3853 : Tree Nat := .node node3040 node3852 +def node3854 : Tree Nat := .node node3435 node3853 +def node3855 : Tree Nat := .node node3854 node3443 +def node3856 : Tree Nat := .node node3851 node3855 +def node3857 : Tree Nat := .node node2754 node3765 +def node3858 : Tree Nat := .node node3857 node746 +def node3859 : Tree Nat := .leaf 289 +def node3860 : Tree Nat := .node node3859 node1 +def node3861 : Tree Nat := .node node3057 node3860 +def node3862 : Tree Nat := .node node3858 node3861 +def node3863 : Tree Nat := .node node1 node3616 +def node3864 : Tree Nat := .leaf 277 +def node3865 : Tree Nat := .node node3864 node1 +def node3866 : Tree Nat := .node node3863 node3865 +def node3867 : Tree Nat := .node node2659 node3866 +def node3868 : Tree Nat := .node node3862 node3867 +def node3869 : Tree Nat := .node node1 node3765 +def node3870 : Tree Nat := .node node3869 node3452 +def node3871 : Tree Nat := .node node3450 node3870 +def node3872 : Tree Nat := .node node3448 node3871 +def node3873 : Tree Nat := .node node3868 node3872 +def node3874 : Tree Nat := .leaf 295 +def node3875 : Tree Nat := .node node3874 node25 +def node3876 : Tree Nat := .node node3457 node3875 +def node3877 : Tree Nat := .node node2250 node3876 +def node3878 : Tree Nat := .node node1 node3610 +def node3879 : Tree Nat := .node node3878 node3463 +def node3880 : Tree Nat := .node node3461 node3879 +def node3881 : Tree Nat := .node node3877 node3880 +def node3882 : Tree Nat := .node node3545 node2416 +def node3883 : Tree Nat := .node node3882 node2680 +def node3884 : Tree Nat := .node node3883 node3470 +def node3885 : Tree Nat := .node node3884 node3077 +def node3886 : Tree Nat := .node node3881 node3885 +def node3887 : Tree Nat := .node node3873 node3886 +def node3888 : Tree Nat := .node node3856 node3887 +def node3889 : Tree Nat := .node node57 node3822 +def node3890 : Tree Nat := .node node3889 node500 +def node3891 : Tree Nat := .node node3859 node114 +def node3892 : Tree Nat := .node node2897 node3891 +def node3893 : Tree Nat := .node node3890 node3892 +def node3894 : Tree Nat := .node node3696 node3865 +def node3895 : Tree Nat := .node node2688 node3894 +def node3896 : Tree Nat := .node node3893 node3895 +def node3897 : Tree Nat := .node node1 node3874 +def node3898 : Tree Nat := .node node3897 node3452 +def node3899 : Tree Nat := .node node3479 node3898 +def node3900 : Tree Nat := .node node3477 node3899 +def node3901 : Tree Nat := .node node3896 node3900 +def node3902 : Tree Nat := .node node3710 node3463 +def node3903 : Tree Nat := .node node3487 node3902 +def node3904 : Tree Nat := .node node3485 node3903 +def node3905 : Tree Nat := .node node3904 node3493 +def node3906 : Tree Nat := .node node3901 node3905 +def node3907 : Tree Nat := .node node2806 node3778 +def node3908 : Tree Nat := .node node3907 node1092 +def node3909 : Tree Nat := .node node3733 node1 +def node3910 : Tree Nat := .node node3105 node3909 +def node3911 : Tree Nat := .node node3908 node3910 +def node3912 : Tree Nat := .node node1 node3864 +def node3913 : Tree Nat := .node node3912 node3844 +def node3914 : Tree Nat := .node node2711 node3913 +def node3915 : Tree Nat := .node node3911 node3914 +def node3916 : Tree Nat := .node node3915 node3503 +def node3917 : Tree Nat := .node node3874 node1 +def node3918 : Tree Nat := .node node3505 node3917 +def node3919 : Tree Nat := .node node2299 node3918 +def node3920 : Tree Nat := .node node3585 node2664 +def node3921 : Tree Nat := .node node3920 node2301 +def node3922 : Tree Nat := .node node1 node3859 +def node3923 : Tree Nat := .node node3922 node3436 +def node3924 : Tree Nat := .node node3921 node3923 +def node3925 : Tree Nat := .node node3919 node3924 +def node3926 : Tree Nat := .node node3601 node2679 +def node3927 : Tree Nat := .node node3926 node2649 +def node3928 : Tree Nat := .node node3927 node3512 +def node3929 : Tree Nat := .node node3928 node3120 +def node3930 : Tree Nat := .node node3925 node3929 +def node3931 : Tree Nat := .node node3916 node3930 +def node3932 : Tree Nat := .node node3906 node3931 +def node3933 : Tree Nat := .node node3888 node3932 +def node3934 : Tree Nat := .node node3838 node3933 +def node3935 : Tree Nat := .node node3746 node3934 +def node3936 : Tree Nat := .leaf 316 +def node3937 : Tree Nat := .node node114 node3936 +def node3938 : Tree Nat := .node node3522 node3937 +def node3939 : Tree Nat := .node node3938 node3526 +def node3940 : Tree Nat := .leaf 338 +def node3941 : Tree Nat := .node node7 node3940 +def node3942 : Tree Nat := .node node3936 node0 +def node3943 : Tree Nat := .node node3941 node3942 +def node3944 : Tree Nat := .node node3943 node3530 +def node3945 : Tree Nat := .node node3939 node3944 +def node3946 : Tree Nat := .leaf 314 +def node3947 : Tree Nat := .node node13 node3946 +def node3948 : Tree Nat := .node node3947 node2744 +def node3949 : Tree Nat := .node node3948 node3135 +def node3950 : Tree Nat := .node node3949 node3535 +def node3951 : Tree Nat := .node node3945 node3950 +def node3952 : Tree Nat := .leaf 330 +def node3953 : Tree Nat := .node node73 node3952 +def node3954 : Tree Nat := .node node3539 node3953 +def node3955 : Tree Nat := .node node3954 node3543 +def node3956 : Tree Nat := .node node3955 node3548 +def node3957 : Tree Nat := .leaf 326 +def node3958 : Tree Nat := .node node34 node3957 +def node3959 : Tree Nat := .leaf 328 +def node3960 : Tree Nat := .node node3959 node0 +def node3961 : Tree Nat := .node node3958 node3960 +def node3962 : Tree Nat := .node node3961 node3152 +def node3963 : Tree Nat := .leaf 303 +def node3964 : Tree Nat := .node node0 node3963 +def node3965 : Tree Nat := .node node3964 node2760 +def node3966 : Tree Nat := .node node2758 node3965 +def node3967 : Tree Nat := .node node3962 node3966 +def node3968 : Tree Nat := .node node3956 node3967 +def node3969 : Tree Nat := .node node3951 node3968 +def node3970 : Tree Nat := .leaf 324 +def node3971 : Tree Nat := .node node25 node3970 +def node3972 : Tree Nat := .node node3553 node3971 +def node3973 : Tree Nat := .node node3972 node3557 +def node3974 : Tree Nat := .node node3936 node25 +def node3975 : Tree Nat := .node node2340 node3974 +def node3976 : Tree Nat := .node node3975 node3562 +def node3977 : Tree Nat := .node node3973 node3976 +def node3978 : Tree Nat := .leaf 320 +def node3979 : Tree Nat := .node node55 node3978 +def node3980 : Tree Nat := .node node3979 node2771 +def node3981 : Tree Nat := .node node3980 node3158 +def node3982 : Tree Nat := .node node3981 node3568 +def node3983 : Tree Nat := .node node3977 node3982 +def node3984 : Tree Nat := .leaf 310 +def node3985 : Tree Nat := .node node67 node3984 +def node3986 : Tree Nat := .node node252 node3940 +def node3987 : Tree Nat := .node node3985 node3986 +def node3988 : Tree Nat := .node node3987 node3167 +def node3989 : Tree Nat := .leaf 304 +def node3990 : Tree Nat := .node node3989 node73 +def node3991 : Tree Nat := .node node2354 node3990 +def node3992 : Tree Nat := .node node3991 node3572 +def node3993 : Tree Nat := .node node3988 node3992 +def node3994 : Tree Nat := .leaf 334 +def node3995 : Tree Nat := .node node78 node3994 +def node3996 : Tree Nat := .node node3959 node358 +def node3997 : Tree Nat := .node node3995 node3996 +def node3998 : Tree Nat := .node node3997 node3177 +def node3999 : Tree Nat := .node node82 node3984 +def node4000 : Tree Nat := .node node3999 node2784 +def node4001 : Tree Nat := .node node2782 node4000 +def node4002 : Tree Nat := .node node3998 node4001 +def node4003 : Tree Nat := .node node3993 node4002 +def node4004 : Tree Nat := .node node3983 node4003 +def node4005 : Tree Nat := .node node3969 node4004 +def node4006 : Tree Nat := .node node358 node3978 +def node4007 : Tree Nat := .node node3579 node4006 +def node4008 : Tree Nat := .node node4007 node3583 +def node4009 : Tree Nat := .leaf 339 +def node4010 : Tree Nat := .node node93 node4009 +def node4011 : Tree Nat := .node node4010 node1952 +def node4012 : Tree Nat := .node node4011 node3589 +def node4013 : Tree Nat := .node node4008 node4012 +def node4014 : Tree Nat := .leaf 315 +def node4015 : Tree Nat := .node node98 node4014 +def node4016 : Tree Nat := .node node4015 node2797 +def node4017 : Tree Nat := .node node4016 node3185 +def node4018 : Tree Nat := .node node4017 node3594 +def node4019 : Tree Nat := .node node4013 node4018 +def node4020 : Tree Nat := .node node108 node3963 +def node4021 : Tree Nat := .node node252 node3994 +def node4022 : Tree Nat := .node node4020 node4021 +def node4023 : Tree Nat := .node node4022 node3599 +def node4024 : Tree Nat := .node node4023 node3604 +def node4025 : Tree Nat := .leaf 327 +def node4026 : Tree Nat := .node node119 node4025 +def node4027 : Tree Nat := .node node4026 node2388 +def node4028 : Tree Nat := .node node4027 node3206 +def node4029 : Tree Nat := .leaf 306 +def node4030 : Tree Nat := .node node0 node4029 +def node4031 : Tree Nat := .node node4030 node2812 +def node4032 : Tree Nat := .node node2810 node4031 +def node4033 : Tree Nat := .node node4028 node4032 +def node4034 : Tree Nat := .node node4024 node4033 +def node4035 : Tree Nat := .node node4019 node4034 +def node4036 : Tree Nat := .node node25 node4025 +def node4037 : Tree Nat := .node node3608 node4036 +def node4038 : Tree Nat := .node node4037 node3612 +def node4039 : Tree Nat := .node node4038 node3619 +def node4040 : Tree Nat := .leaf 322 +def node4041 : Tree Nat := .node node140 node4040 +def node4042 : Tree Nat := .node node4041 node2824 +def node4043 : Tree Nat := .node node4042 node3213 +def node4044 : Tree Nat := .node node4043 node3624 +def node4045 : Tree Nat := .node node4039 node4044 +def node4046 : Tree Nat := .leaf 308 +def node4047 : Tree Nat := .node node150 node4046 +def node4048 : Tree Nat := .node node4047 node776 +def node4049 : Tree Nat := .node node4048 node3223 +def node4050 : Tree Nat := .leaf 305 +def node4051 : Tree Nat := .node node4050 node82 +def node4052 : Tree Nat := .node node2410 node4051 +def node4053 : Tree Nat := .node node4052 node3629 +def node4054 : Tree Nat := .node node4049 node4053 +def node4055 : Tree Nat := .leaf 332 +def node4056 : Tree Nat := .node node159 node4055 +def node4057 : Tree Nat := .node node4056 node2417 +def node4058 : Tree Nat := .node node4057 node3234 +def node4059 : Tree Nat := .node node114 node3946 +def node4060 : Tree Nat := .node node4059 node2839 +def node4061 : Tree Nat := .node node2837 node4060 +def node4062 : Tree Nat := .node node4058 node4061 +def node4063 : Tree Nat := .node node4054 node4062 +def node4064 : Tree Nat := .node node4045 node4063 +def node4065 : Tree Nat := .node node4035 node4064 +def node4066 : Tree Nat := .node node4005 node4065 +def node4067 : Tree Nat := .leaf 318 +def node4068 : Tree Nat := .node node358 node4067 +def node4069 : Tree Nat := .node node3636 node4068 +def node4070 : Tree Nat := .node node4069 node3639 +def node4071 : Tree Nat := .node node1665 node3940 +def node4072 : Tree Nat := .node node4071 node2012 +def node4073 : Tree Nat := .node node4072 node3643 +def node4074 : Tree Nat := .node node4070 node4073 +def node4075 : Tree Nat := .node node2016 node3946 +def node4076 : Tree Nat := .node node4075 node2852 +def node4077 : Tree Nat := .node node4076 node3243 +def node4078 : Tree Nat := .node node4077 node3648 +def node4079 : Tree Nat := .node node4074 node4078 +def node4080 : Tree Nat := .node node73 node4055 +def node4081 : Tree Nat := .node node3651 node4080 +def node4082 : Tree Nat := .node node4081 node3654 +def node4083 : Tree Nat := .node node4082 node3659 +def node4084 : Tree Nat := .node node2847 node3957 +def node4085 : Tree Nat := .node node4084 node2445 +def node4086 : Tree Nat := .node node4085 node3263 +def node4087 : Tree Nat := .node node0 node3989 +def node4088 : Tree Nat := .node node4087 node2784 +def node4089 : Tree Nat := .node node2867 node4088 +def node4090 : Tree Nat := .node node4086 node4089 +def node4091 : Tree Nat := .node node4083 node4090 +def node4092 : Tree Nat := .node node4079 node4091 +def node4093 : Tree Nat := .node node25 node3957 +def node4094 : Tree Nat := .node node3663 node4093 +def node4095 : Tree Nat := .node node4094 node3666 +def node4096 : Tree Nat := .node node4095 node3671 +def node4097 : Tree Nat := .node node2425 node3978 +def node4098 : Tree Nat := .node node4097 node2879 +def node4099 : Tree Nat := .node node4098 node3269 +def node4100 : Tree Nat := .node node4099 node3675 +def node4101 : Tree Nat := .node node4096 node4100 +def node4102 : Tree Nat := .node node2017 node3984 +def node4103 : Tree Nat := .node node57 node4009 +def node4104 : Tree Nat := .node node4102 node4103 +def node4105 : Tree Nat := .node node4104 node3278 +def node4106 : Tree Nat := .node node3989 node82 +def node4107 : Tree Nat := .node node3678 node4106 +def node4108 : Tree Nat := .node node4107 node3681 +def node4109 : Tree Nat := .node node4105 node4108 +def node4110 : Tree Nat := .node node3656 node3994 +def node4111 : Tree Nat := .node node4110 node2473 +def node4112 : Tree Nat := .node node4111 node3284 +def node4113 : Tree Nat := .leaf 312 +def node4114 : Tree Nat := .node node82 node4113 +def node4115 : Tree Nat := .node node4114 node2760 +def node4116 : Tree Nat := .node node2889 node4115 +def node4117 : Tree Nat := .node node4112 node4116 +def node4118 : Tree Nat := .node node4109 node4117 +def node4119 : Tree Nat := .node node4101 node4118 +def node4120 : Tree Nat := .node node4092 node4119 +def node4121 : Tree Nat := .node node358 node4040 +def node4122 : Tree Nat := .node node3691 node4121 +def node4123 : Tree Nat := .node node4122 node3693 +def node4124 : Tree Nat := .node node2061 node4009 +def node4125 : Tree Nat := .leaf 317 +def node4126 : Tree Nat := .node node4125 node114 +def node4127 : Tree Nat := .node node4124 node4126 +def node4128 : Tree Nat := .node node4127 node3697 +def node4129 : Tree Nat := .node node4123 node4128 +def node4130 : Tree Nat := .node node2070 node4014 +def node4131 : Tree Nat := .node node4130 node2901 +def node4132 : Tree Nat := .node node4131 node3292 +def node4133 : Tree Nat := .node node4132 node3703 +def node4134 : Tree Nat := .node node4129 node4133 +def node4135 : Tree Nat := .node node2490 node3963 +def node4136 : Tree Nat := .leaf 336 +def node4137 : Tree Nat := .node node252 node4136 +def node4138 : Tree Nat := .node node4135 node4137 +def node4139 : Tree Nat := .node node4138 node3707 +def node4140 : Tree Nat := .node node4139 node3712 +def node4141 : Tree Nat := .node node2896 node4025 +def node4142 : Tree Nat := .leaf 329 +def node4143 : Tree Nat := .node node4142 node73 +def node4144 : Tree Nat := .node node4141 node4143 +def node4145 : Tree Nat := .node node4144 node3311 +def node4146 : Tree Nat := .node node82 node4046 +def node4147 : Tree Nat := .node node4146 node2839 +def node4148 : Tree Nat := .node node2916 node4147 +def node4149 : Tree Nat := .node node4145 node4148 +def node4150 : Tree Nat := .node node4140 node4149 +def node4151 : Tree Nat := .node node4134 node4150 +def node4152 : Tree Nat := .node node73 node3959 +def node4153 : Tree Nat := .node node3716 node4152 +def node4154 : Tree Nat := .node node4153 node3719 +def node4155 : Tree Nat := .node node4125 node82 +def node4156 : Tree Nat := .node node2507 node4155 +def node4157 : Tree Nat := .node node4156 node3723 +def node4158 : Tree Nat := .node node4154 node4157 +def node4159 : Tree Nat := .node node2480 node4040 +def node4160 : Tree Nat := .node node4159 node2797 +def node4161 : Tree Nat := .node node4160 node3318 +def node4162 : Tree Nat := .node node4161 node3728 +def node4163 : Tree Nat := .node node4158 node4162 +def node4164 : Tree Nat := .node node2071 node4046 +def node4165 : Tree Nat := .node node4164 node776 +def node4166 : Tree Nat := .node node4165 node3328 +def node4167 : Tree Nat := .node node4050 node1 +def node4168 : Tree Nat := .node node3731 node4167 +def node4169 : Tree Nat := .node node4168 node3735 +def node4170 : Tree Nat := .node node4166 node4169 +def node4171 : Tree Nat := .node node3709 node4055 +def node4172 : Tree Nat := .node node4142 node0 +def node4173 : Tree Nat := .node node4171 node4172 +def node4174 : Tree Nat := .node node4173 node3335 +def node4175 : Tree Nat := .node node114 node4014 +def node4176 : Tree Nat := .node node4175 node2812 +def node4177 : Tree Nat := .node node2940 node4176 +def node4178 : Tree Nat := .node node4174 node4177 +def node4179 : Tree Nat := .node node4170 node4178 +def node4180 : Tree Nat := .node node4163 node4179 +def node4181 : Tree Nat := .node node4151 node4180 +def node4182 : Tree Nat := .node node4120 node4181 +def node4183 : Tree Nat := .node node4066 node4182 +def node4184 : Tree Nat := .node node114 node4125 +def node4185 : Tree Nat := .node node3747 node4184 +def node4186 : Tree Nat := .node node4185 node3750 +def node4187 : Tree Nat := .node node4186 node3754 +def node4188 : Tree Nat := .node node345 node3970 +def node4189 : Tree Nat := .node node4188 node2951 +def node4190 : Tree Nat := .node node4189 node3343 +def node4191 : Tree Nat := .node node4190 node3757 +def node4192 : Tree Nat := .node node4187 node4191 +def node4193 : Tree Nat := .node node355 node4113 +def node4194 : Tree Nat := .leaf 331 +def node4195 : Tree Nat := .node node73 node4194 +def node4196 : Tree Nat := .node node4193 node4195 +def node4197 : Tree Nat := .node node4196 node2956 +def node4198 : Tree Nat := .node node4029 node73 +def node4199 : Tree Nat := .node node2550 node4198 +def node4200 : Tree Nat := .node node4199 node3760 +def node4201 : Tree Nat := .node node4197 node4200 +def node4202 : Tree Nat := .node node367 node4136 +def node4203 : Tree Nat := .node node4202 node2554 +def node4204 : Tree Nat := .node node4203 node3355 +def node4205 : Tree Nat := .node node3964 node2962 +def node4206 : Tree Nat := .node node2961 node4205 +def node4207 : Tree Nat := .node node4204 node4206 +def node4208 : Tree Nat := .node node4201 node4207 +def node4209 : Tree Nat := .node node4192 node4208 +def node4210 : Tree Nat := .leaf 325 +def node4211 : Tree Nat := .node node25 node4210 +def node4212 : Tree Nat := .node node3766 node4211 +def node4213 : Tree Nat := .node node4212 node3770 +def node4214 : Tree Nat := .node node4213 node3776 +def node4215 : Tree Nat := .leaf 321 +def node4216 : Tree Nat := .node node387 node4215 +def node4217 : Tree Nat := .node node4216 node2973 +def node4218 : Tree Nat := .node node4217 node3361 +def node4219 : Tree Nat := .node node4218 node3781 +def node4220 : Tree Nat := .node node4214 node4219 +def node4221 : Tree Nat := .leaf 311 +def node4222 : Tree Nat := .node node398 node4221 +def node4223 : Tree Nat := .node node4222 node3986 +def node4224 : Tree Nat := .node node4223 node3785 +def node4225 : Tree Nat := .node node4224 node3789 +def node4226 : Tree Nat := .leaf 335 +def node4227 : Tree Nat := .node node408 node4226 +def node4228 : Tree Nat := .node node4227 node2580 +def node4229 : Tree Nat := .node node4228 node3380 +def node4230 : Tree Nat := .node node82 node4221 +def node4231 : Tree Nat := .node node4230 node2986 +def node4232 : Tree Nat := .node node2984 node4231 +def node4233 : Tree Nat := .node node4229 node4232 +def node4234 : Tree Nat := .node node4225 node4233 +def node4235 : Tree Nat := .node node4220 node4234 +def node4236 : Tree Nat := .node node4209 node4235 +def node4237 : Tree Nat := .node node358 node4215 +def node4238 : Tree Nat := .node node3794 node4237 +def node4239 : Tree Nat := .node node4238 node3797 +def node4240 : Tree Nat := .node node4067 node25 +def node4241 : Tree Nat := .node node2587 node4240 +def node4242 : Tree Nat := .node node4241 node3799 +def node4243 : Tree Nat := .node node4239 node4242 +def node4244 : Tree Nat := .node node428 node3970 +def node4245 : Tree Nat := .node node4244 node2995 +def node4246 : Tree Nat := .node node4245 node3386 +def node4247 : Tree Nat := .node node4246 node3804 +def node4248 : Tree Nat := .node node4243 node4247 +def node4249 : Tree Nat := .node node439 node4113 +def node4250 : Tree Nat := .node node252 node4226 +def node4251 : Tree Nat := .node node4249 node4250 +def node4252 : Tree Nat := .node node4251 node3392 +def node4253 : Tree Nat := .node node4029 node114 +def node4254 : Tree Nat := .node node2597 node4253 +def node4255 : Tree Nat := .node node4254 node3807 +def node4256 : Tree Nat := .node node4252 node4255 +def node4257 : Tree Nat := .node node448 node4136 +def node4258 : Tree Nat := .node node3952 node73 +def node4259 : Tree Nat := .node node4257 node4258 +def node4260 : Tree Nat := .node node4259 node3397 +def node4261 : Tree Nat := .leaf 307 +def node4262 : Tree Nat := .node node0 node4261 +def node4263 : Tree Nat := .node node4262 node2986 +def node4264 : Tree Nat := .node node3004 node4263 +def node4265 : Tree Nat := .node node4260 node4264 +def node4266 : Tree Nat := .node node4256 node4265 +def node4267 : Tree Nat := .node node4248 node4266 +def node4268 : Tree Nat := .node node3812 node4036 +def node4269 : Tree Nat := .node node4268 node3815 +def node4270 : Tree Nat := .node node4067 node82 +def node4271 : Tree Nat := .node node2608 node4270 +def node4272 : Tree Nat := .node node4271 node3819 +def node4273 : Tree Nat := .node node4269 node4272 +def node4274 : Tree Nat := .leaf 323 +def node4275 : Tree Nat := .node node471 node4274 +def node4276 : Tree Nat := .node node4275 node3014 +def node4277 : Tree Nat := .node node4276 node3403 +def node4278 : Tree Nat := .node node4277 node3825 +def node4279 : Tree Nat := .node node4273 node4278 +def node4280 : Tree Nat := .leaf 309 +def node4281 : Tree Nat := .node node481 node4280 +def node4282 : Tree Nat := .node node4281 node776 +def node4283 : Tree Nat := .node node4282 node3829 +def node4284 : Tree Nat := .node node4283 node3833 +def node4285 : Tree Nat := .leaf 333 +def node4286 : Tree Nat := .node node490 node4285 +def node4287 : Tree Nat := .node node3952 node0 +def node4288 : Tree Nat := .node node4286 node4287 +def node4289 : Tree Nat := .node node4288 node3418 +def node4290 : Tree Nat := .node node4059 node2962 +def node4291 : Tree Nat := .node node3024 node4290 +def node4292 : Tree Nat := .node node4289 node4291 +def node4293 : Tree Nat := .node node4284 node4292 +def node4294 : Tree Nat := .node node4279 node4293 +def node4295 : Tree Nat := .node node4267 node4294 +def node4296 : Tree Nat := .node node4236 node4295 +def node4297 : Tree Nat := .leaf 319 +def node4298 : Tree Nat := .node node358 node4297 +def node4299 : Tree Nat := .node node3839 node4298 +def node4300 : Tree Nat := .node node4299 node3842 +def node4301 : Tree Nat := .node node4297 node25 +def node4302 : Tree Nat := .node node2632 node4301 +def node4303 : Tree Nat := .node node4302 node3845 +def node4304 : Tree Nat := .node node4300 node4303 +def node4305 : Tree Nat := .node node1905 node4210 +def node4306 : Tree Nat := .node node4305 node3034 +def node4307 : Tree Nat := .node node4306 node3425 +def node4308 : Tree Nat := .node node4307 node3849 +def node4309 : Tree Nat := .node node4304 node4308 +def node4310 : Tree Nat := .leaf 313 +def node4311 : Tree Nat := .node node1917 node4310 +def node4312 : Tree Nat := .node node73 node4285 +def node4313 : Tree Nat := .node node4311 node4312 +def node4314 : Tree Nat := .node node4313 node3434 +def node4315 : Tree Nat := .node node4261 node73 +def node4316 : Tree Nat := .node node3039 node4315 +def node4317 : Tree Nat := .node node4316 node3852 +def node4318 : Tree Nat := .node node4314 node4317 +def node4319 : Tree Nat := .leaf 337 +def node4320 : Tree Nat := .node node2738 node4319 +def node4321 : Tree Nat := .node node4194 node0 +def node4322 : Tree Nat := .node node4320 node4321 +def node4323 : Tree Nat := .node node4322 node3441 +def node4324 : Tree Nat := .node node0 node4050 +def node4325 : Tree Nat := .node node4324 node3049 +def node4326 : Tree Nat := .node node3048 node4325 +def node4327 : Tree Nat := .node node4323 node4326 +def node4328 : Tree Nat := .node node4318 node4327 +def node4329 : Tree Nat := .node node4309 node4328 +def node4330 : Tree Nat := .node node3857 node4093 +def node4331 : Tree Nat := .node node4330 node3861 +def node4332 : Tree Nat := .node node4297 node1 +def node4333 : Tree Nat := .node node2658 node4332 +def node4334 : Tree Nat := .node node4333 node3866 +def node4335 : Tree Nat := .node node4331 node4334 +def node4336 : Tree Nat := .node node2311 node4215 +def node4337 : Tree Nat := .node node4336 node3062 +def node4338 : Tree Nat := .node node4337 node3447 +def node4339 : Tree Nat := .node node4338 node3871 +def node4340 : Tree Nat := .node node4335 node4339 +def node4341 : Tree Nat := .node node1899 node4221 +def node4342 : Tree Nat := .node node4341 node4103 +def node4343 : Tree Nat := .node node4342 node3876 +def node4344 : Tree Nat := .node node4343 node3880 +def node4345 : Tree Nat := .node node3545 node4226 +def node4346 : Tree Nat := .node node4194 node73 +def node4347 : Tree Nat := .node node4345 node4346 +def node4348 : Tree Nat := .node node4347 node3470 +def node4349 : Tree Nat := .node node82 node4310 +def node4350 : Tree Nat := .node node4349 node3075 +def node4351 : Tree Nat := .node node3073 node4350 +def node4352 : Tree Nat := .node node4348 node4351 +def node4353 : Tree Nat := .node node4344 node4352 +def node4354 : Tree Nat := .node node4340 node4353 +def node4355 : Tree Nat := .node node4329 node4354 +def node4356 : Tree Nat := .node node358 node4274 +def node4357 : Tree Nat := .node node3889 node4356 +def node4358 : Tree Nat := .node node4357 node3892 +def node4359 : Tree Nat := .node node4358 node3895 +def node4360 : Tree Nat := .node node1962 node4210 +def node4361 : Tree Nat := .node node4360 node3084 +def node4362 : Tree Nat := .node node4361 node3476 +def node4363 : Tree Nat := .node node4362 node3899 +def node4364 : Tree Nat := .node node4359 node4363 +def node4365 : Tree Nat := .node node1974 node4310 +def node4366 : Tree Nat := .node node252 node4319 +def node4367 : Tree Nat := .node node4365 node4366 +def node4368 : Tree Nat := .node node4367 node3484 +def node4369 : Tree Nat := .node node4261 node114 +def node4370 : Tree Nat := .node node3486 node4369 +def node4371 : Tree Nat := .node node4370 node3902 +def node4372 : Tree Nat := .node node4368 node4371 +def node4373 : Tree Nat := .node node2791 node4319 +def node4374 : Tree Nat := .node node4373 node2680 +def node4375 : Tree Nat := .node node4374 node3491 +def node4376 : Tree Nat := .node node82 node4280 +def node4377 : Tree Nat := .node node4376 node3075 +def node4378 : Tree Nat := .node node3097 node4377 +def node4379 : Tree Nat := .node node4375 node4378 +def node4380 : Tree Nat := .node node4372 node4379 +def node4381 : Tree Nat := .node node4364 node4380 +def node4382 : Tree Nat := .node node73 node4142 +def node4383 : Tree Nat := .node node3907 node4382 +def node4384 : Tree Nat := .node node4383 node3910 +def node4385 : Tree Nat := .node node4384 node3914 +def node4386 : Tree Nat := .node node2367 node4274 +def node4387 : Tree Nat := .node node4386 node3034 +def node4388 : Tree Nat := .node node4387 node3497 +def node4389 : Tree Nat := .node node3726 node3429 +def node4390 : Tree Nat := .node node3500 node4389 +def node4391 : Tree Nat := .node node4388 node4390 +def node4392 : Tree Nat := .node node4385 node4391 +def node4393 : Tree Nat := .node node1956 node4280 +def node4394 : Tree Nat := .node node4393 node776 +def node4395 : Tree Nat := .node node4394 node3918 +def node4396 : Tree Nat := .node node4395 node3924 +def node4397 : Tree Nat := .node node3601 node4285 +def node4398 : Tree Nat := .node node4397 node2649 +def node4399 : Tree Nat := .node node4398 node3512 +def node4400 : Tree Nat := .node node4175 node3049 +def node4401 : Tree Nat := .node node3118 node4400 +def node4402 : Tree Nat := .node node4399 node4401 +def node4403 : Tree Nat := .node node4396 node4402 +def node4404 : Tree Nat := .node node4392 node4403 +def node4405 : Tree Nat := .node node4381 node4404 +def node4406 : Tree Nat := .node node4355 node4405 +def node4407 : Tree Nat := .node node4296 node4406 +def node4408 : Tree Nat := .node node4183 node4407 +def node4409 : Tree Nat := .leaf 372 +def node4410 : Tree Nat := .node node3936 node4409 +def node4411 : Tree Nat := .node node3941 node4410 +def node4412 : Tree Nat := .node node4411 node3530 +def node4413 : Tree Nat := .node node3939 node4412 +def node4414 : Tree Nat := .leaf 376 +def node4415 : Tree Nat := .leaf 344 +def node4416 : Tree Nat := .node node4414 node4415 +def node4417 : Tree Nat := .node node3947 node4416 +def node4418 : Tree Nat := .leaf 352 +def node4419 : Tree Nat := .node node4418 node73 +def node4420 : Tree Nat := .node node3134 node4419 +def node4421 : Tree Nat := .node node4417 node4420 +def node4422 : Tree Nat := .leaf 362 +def node4423 : Tree Nat := .node node17 node4422 +def node4424 : Tree Nat := .leaf 340 +def node4425 : Tree Nat := .node node4424 node1 +def node4426 : Tree Nat := .node node4423 node4425 +def node4427 : Tree Nat := .node node4426 node3534 +def node4428 : Tree Nat := .node node4421 node4427 +def node4429 : Tree Nat := .node node4413 node4428 +def node4430 : Tree Nat := .leaf 350 +def node4431 : Tree Nat := .node node29 node4430 +def node4432 : Tree Nat := .node node4431 node1913 +def node4433 : Tree Nat := .node node4432 node3547 +def node4434 : Tree Nat := .node node3955 node4433 +def node4435 : Tree Nat := .leaf 358 +def node4436 : Tree Nat := .node node3959 node4435 +def node4437 : Tree Nat := .node node3958 node4436 +def node4438 : Tree Nat := .node node4437 node3152 +def node4439 : Tree Nat := .leaf 374 +def node4440 : Tree Nat := .node node38 node4439 +def node4441 : Tree Nat := .node node4440 node2757 +def node4442 : Tree Nat := .node node4441 node3965 +def node4443 : Tree Nat := .node node4438 node4442 +def node4444 : Tree Nat := .node node4434 node4443 +def node4445 : Tree Nat := .node node4429 node4444 +def node4446 : Tree Nat := .node node50 node4415 +def node4447 : Tree Nat := .node node4446 node3974 +def node4448 : Tree Nat := .node node4447 node3562 +def node4449 : Tree Nat := .node node3973 node4448 +def node4450 : Tree Nat := .leaf 351 +def node4451 : Tree Nat := .node node2770 node4450 +def node4452 : Tree Nat := .node node3979 node4451 +def node4453 : Tree Nat := .node node4418 node340 +def node4454 : Tree Nat := .node node3157 node4453 +def node4455 : Tree Nat := .node node4452 node4454 +def node4456 : Tree Nat := .leaf 370 +def node4457 : Tree Nat := .node node61 node4456 +def node4458 : Tree Nat := .node node4457 node2349 +def node4459 : Tree Nat := .node node4458 node3567 +def node4460 : Tree Nat := .node node4455 node4459 +def node4461 : Tree Nat := .node node4449 node4460 +def node4462 : Tree Nat := .leaf 360 +def node4463 : Tree Nat := .node node71 node4462 +def node4464 : Tree Nat := .node node4463 node3990 +def node4465 : Tree Nat := .node node4464 node3572 +def node4466 : Tree Nat := .node node3988 node4465 +def node4467 : Tree Nat := .leaf 364 +def node4468 : Tree Nat := .node node3959 node4467 +def node4469 : Tree Nat := .node node3995 node4468 +def node4470 : Tree Nat := .node node4469 node3177 +def node4471 : Tree Nat := .node node4467 node1 +def node4472 : Tree Nat := .node node3999 node4471 +def node4473 : Tree Nat := .node node2782 node4472 +def node4474 : Tree Nat := .node node4470 node4473 +def node4475 : Tree Nat := .node node4466 node4474 +def node4476 : Tree Nat := .node node4461 node4475 +def node4477 : Tree Nat := .node node4445 node4476 +def node4478 : Tree Nat := .leaf 375 +def node4479 : Tree Nat := .node node1951 node4478 +def node4480 : Tree Nat := .node node4010 node4479 +def node4481 : Tree Nat := .node node4480 node3589 +def node4482 : Tree Nat := .node node4008 node4481 +def node4483 : Tree Nat := .leaf 377 +def node4484 : Tree Nat := .leaf 348 +def node4485 : Tree Nat := .node node4483 node4484 +def node4486 : Tree Nat := .node node4015 node4485 +def node4487 : Tree Nat := .node node4486 node3185 +def node4488 : Tree Nat := .leaf 363 +def node4489 : Tree Nat := .node node102 node4488 +def node4490 : Tree Nat := .leaf 341 +def node4491 : Tree Nat := .node node4490 node25 +def node4492 : Tree Nat := .node node4489 node4491 +def node4493 : Tree Nat := .node node4492 node3593 +def node4494 : Tree Nat := .node node4487 node4493 +def node4495 : Tree Nat := .node node4482 node4494 +def node4496 : Tree Nat := .node node112 node4450 +def node4497 : Tree Nat := .node node4496 node1970 +def node4498 : Tree Nat := .node node4497 node3603 +def node4499 : Tree Nat := .node node4023 node4498 +def node4500 : Tree Nat := .node node2387 node4422 +def node4501 : Tree Nat := .node node4026 node4500 +def node4502 : Tree Nat := .node node4501 node3206 +def node4503 : Tree Nat := .node node123 node4478 +def node4504 : Tree Nat := .node node4503 node2809 +def node4505 : Tree Nat := .node node4504 node4031 +def node4506 : Tree Nat := .node node4502 node4505 +def node4507 : Tree Nat := .node node4499 node4506 +def node4508 : Tree Nat := .node node4495 node4507 +def node4509 : Tree Nat := .leaf 346 +def node4510 : Tree Nat := .node node135 node4509 +def node4511 : Tree Nat := .node node4510 node1986 +def node4512 : Tree Nat := .node node4511 node3618 +def node4513 : Tree Nat := .node node4038 node4512 +def node4514 : Tree Nat := .leaf 354 +def node4515 : Tree Nat := .node node2823 node4514 +def node4516 : Tree Nat := .node node4041 node4515 +def node4517 : Tree Nat := .node node4516 node3213 +def node4518 : Tree Nat := .node node144 node4409 +def node4519 : Tree Nat := .node node4518 node2404 +def node4520 : Tree Nat := .node node4519 node3623 +def node4521 : Tree Nat := .node node4517 node4520 +def node4522 : Tree Nat := .node node4513 node4521 +def node4523 : Tree Nat := .node node57 node4424 +def node4524 : Tree Nat := .node node4047 node4523 +def node4525 : Tree Nat := .node node4524 node3223 +def node4526 : Tree Nat := .node node154 node4435 +def node4527 : Tree Nat := .node node4526 node4051 +def node4528 : Tree Nat := .node node4527 node3629 +def node4529 : Tree Nat := .node node4525 node4528 +def node4530 : Tree Nat := .leaf 368 +def node4531 : Tree Nat := .node node2416 node4530 +def node4532 : Tree Nat := .node node4056 node4531 +def node4533 : Tree Nat := .node node4532 node3234 +def node4534 : Tree Nat := .leaf 365 +def node4535 : Tree Nat := .node node4534 node1 +def node4536 : Tree Nat := .node node4059 node4535 +def node4537 : Tree Nat := .node node2837 node4536 +def node4538 : Tree Nat := .node node4533 node4537 +def node4539 : Tree Nat := .node node4529 node4538 +def node4540 : Tree Nat := .node node4522 node4539 +def node4541 : Tree Nat := .node node4508 node4540 +def node4542 : Tree Nat := .node node4477 node4541 +def node4543 : Tree Nat := .node node1927 node4439 +def node4544 : Tree Nat := .node node4071 node4543 +def node4545 : Tree Nat := .node node4544 node3643 +def node4546 : Tree Nat := .node node4070 node4545 +def node4547 : Tree Nat := .node node4414 node4509 +def node4548 : Tree Nat := .node node4075 node4547 +def node4549 : Tree Nat := .node node4548 node3243 +def node4550 : Tree Nat := .node node3245 node4422 +def node4551 : Tree Nat := .node node4424 node358 +def node4552 : Tree Nat := .node node4550 node4551 +def node4553 : Tree Nat := .node node4552 node3647 +def node4554 : Tree Nat := .node node4549 node4553 +def node4555 : Tree Nat := .node node4546 node4554 +def node4556 : Tree Nat := .node node3252 node4430 +def node4557 : Tree Nat := .node node4556 node2027 +def node4558 : Tree Nat := .node node4557 node3658 +def node4559 : Tree Nat := .node node4082 node4558 +def node4560 : Tree Nat := .node node2359 node4462 +def node4561 : Tree Nat := .node node4084 node4560 +def node4562 : Tree Nat := .node node4561 node3263 +def node4563 : Tree Nat := .node node2433 node4439 +def node4564 : Tree Nat := .node node4563 node2866 +def node4565 : Tree Nat := .node node4564 node4088 +def node4566 : Tree Nat := .node node4562 node4565 +def node4567 : Tree Nat := .node node4559 node4566 +def node4568 : Tree Nat := .node node4555 node4567 +def node4569 : Tree Nat := .node node2440 node4415 +def node4570 : Tree Nat := .node node4569 node2040 +def node4571 : Tree Nat := .node node4570 node3670 +def node4572 : Tree Nat := .node node4095 node4571 +def node4573 : Tree Nat := .node node2743 node4418 +def node4574 : Tree Nat := .node node4097 node4573 +def node4575 : Tree Nat := .node node4574 node3269 +def node4576 : Tree Nat := .node node3241 node4456 +def node4577 : Tree Nat := .node node4576 node2463 +def node4578 : Tree Nat := .node node4577 node3674 +def node4579 : Tree Nat := .node node4575 node4578 +def node4580 : Tree Nat := .node node4572 node4579 +def node4581 : Tree Nat := .node node3641 node4462 +def node4582 : Tree Nat := .node node4581 node4106 +def node4583 : Tree Nat := .node node4582 node3681 +def node4584 : Tree Nat := .node node4105 node4583 +def node4585 : Tree Nat := .leaf 366 +def node4586 : Tree Nat := .node node2333 node4585 +def node4587 : Tree Nat := .node node4110 node4586 +def node4588 : Tree Nat := .node node4587 node3284 +def node4589 : Tree Nat := .node node4114 node4471 +def node4590 : Tree Nat := .node node2889 node4589 +def node4591 : Tree Nat := .node node4588 node4590 +def node4592 : Tree Nat := .node node4584 node4591 +def node4593 : Tree Nat := .node node4580 node4592 +def node4594 : Tree Nat := .node node4568 node4593 +def node4595 : Tree Nat := .node node4125 node4414 +def node4596 : Tree Nat := .node node4124 node4595 +def node4597 : Tree Nat := .node node4596 node3697 +def node4598 : Tree Nat := .node node4123 node4597 +def node4599 : Tree Nat := .node node4483 node4430 +def node4600 : Tree Nat := .node node4130 node4599 +def node4601 : Tree Nat := .leaf 353 +def node4602 : Tree Nat := .node node4601 node1 +def node4603 : Tree Nat := .node node3291 node4602 +def node4604 : Tree Nat := .node node4600 node4603 +def node4605 : Tree Nat := .node node3294 node4488 +def node4606 : Tree Nat := .node node4490 node1 +def node4607 : Tree Nat := .node node4605 node4606 +def node4608 : Tree Nat := .node node4607 node3702 +def node4609 : Tree Nat := .node node4604 node4608 +def node4610 : Tree Nat := .node node4598 node4609 +def node4611 : Tree Nat := .node node3301 node4450 +def node4612 : Tree Nat := .node node4611 node2082 +def node4613 : Tree Nat := .node node4612 node3711 +def node4614 : Tree Nat := .node node4139 node4613 +def node4615 : Tree Nat := .node node4142 node4488 +def node4616 : Tree Nat := .node node4141 node4615 +def node4617 : Tree Nat := .node node4616 node3311 +def node4618 : Tree Nat := .node node2904 node4478 +def node4619 : Tree Nat := .node node4618 node2915 +def node4620 : Tree Nat := .node node4619 node4147 +def node4621 : Tree Nat := .node node4617 node4620 +def node4622 : Tree Nat := .node node4614 node4621 +def node4623 : Tree Nat := .node node4610 node4622 +def node4624 : Tree Nat := .node node2494 node4509 +def node4625 : Tree Nat := .node node4624 node4155 +def node4626 : Tree Nat := .node node4625 node3723 +def node4627 : Tree Nat := .node node4154 node4626 +def node4628 : Tree Nat := .leaf 356 +def node4629 : Tree Nat := .node node2796 node4628 +def node4630 : Tree Nat := .node node4159 node4629 +def node4631 : Tree Nat := .node node4601 node411 +def node4632 : Tree Nat := .node node3317 node4631 +def node4633 : Tree Nat := .node node4630 node4632 +def node4634 : Tree Nat := .node node3290 node4409 +def node4635 : Tree Nat := .node node4634 node2516 +def node4636 : Tree Nat := .node node4635 node3727 +def node4637 : Tree Nat := .node node4633 node4636 +def node4638 : Tree Nat := .node node4627 node4637 +def node4639 : Tree Nat := .leaf 342 +def node4640 : Tree Nat := .node node57 node4639 +def node4641 : Tree Nat := .node node4164 node4640 +def node4642 : Tree Nat := .node node4641 node3328 +def node4643 : Tree Nat := .node node3695 node4435 +def node4644 : Tree Nat := .node node4643 node4167 +def node4645 : Tree Nat := .node node4644 node3735 +def node4646 : Tree Nat := .node node4642 node4645 +def node4647 : Tree Nat := .node node4142 node4456 +def node4648 : Tree Nat := .node node4171 node4647 +def node4649 : Tree Nat := .node node4648 node3335 +def node4650 : Tree Nat := .node node4175 node4535 +def node4651 : Tree Nat := .node node2940 node4650 +def node4652 : Tree Nat := .node node4649 node4651 +def node4653 : Tree Nat := .node node4646 node4652 +def node4654 : Tree Nat := .node node4638 node4653 +def node4655 : Tree Nat := .node node4623 node4654 +def node4656 : Tree Nat := .node node4594 node4655 +def node4657 : Tree Nat := .node node4542 node4656 +def node4658 : Tree Nat := .node node337 node4484 +def node4659 : Tree Nat := .leaf 373 +def node4660 : Tree Nat := .node node1990 node4659 +def node4661 : Tree Nat := .node node4658 node4660 +def node4662 : Tree Nat := .node node4661 node3753 +def node4663 : Tree Nat := .node node4186 node4662 +def node4664 : Tree Nat := .leaf 345 +def node4665 : Tree Nat := .node node2833 node4664 +def node4666 : Tree Nat := .node node4188 node4665 +def node4667 : Tree Nat := .node node4666 node3343 +def node4668 : Tree Nat := .node node349 node4530 +def node4669 : Tree Nat := .node node4668 node2545 +def node4670 : Tree Nat := .node node4669 node3756 +def node4671 : Tree Nat := .node node4667 node4670 +def node4672 : Tree Nat := .node node4663 node4671 +def node4673 : Tree Nat := .node node362 node4628 +def node4674 : Tree Nat := .node node4673 node4198 +def node4675 : Tree Nat := .node node4674 node3760 +def node4676 : Tree Nat := .node node4197 node4675 +def node4677 : Tree Nat := .leaf 359 +def node4678 : Tree Nat := .node node2414 node4677 +def node4679 : Tree Nat := .node node4202 node4678 +def node4680 : Tree Nat := .node node4679 node3355 +def node4681 : Tree Nat := .node node4585 node1 +def node4682 : Tree Nat := .node node3964 node4681 +def node4683 : Tree Nat := .node node2961 node4682 +def node4684 : Tree Nat := .node node4680 node4683 +def node4685 : Tree Nat := .node node4676 node4684 +def node4686 : Tree Nat := .node node4672 node4685 +def node4687 : Tree Nat := .node node382 node4664 +def node4688 : Tree Nat := .node node4687 node2145 +def node4689 : Tree Nat := .node node4688 node3775 +def node4690 : Tree Nat := .node node4213 node4689 +def node4691 : Tree Nat := .node node2972 node4450 +def node4692 : Tree Nat := .node node4216 node4691 +def node4693 : Tree Nat := .node node4692 node3361 +def node4694 : Tree Nat := .leaf 371 +def node4695 : Tree Nat := .node node391 node4694 +def node4696 : Tree Nat := .node node4639 node82 +def node4697 : Tree Nat := .node node4695 node4696 +def node4698 : Tree Nat := .node node4697 node3780 +def node4699 : Tree Nat := .node node4693 node4698 +def node4700 : Tree Nat := .node node4690 node4699 +def node4701 : Tree Nat := .leaf 361 +def node4702 : Tree Nat := .node node403 node4701 +def node4703 : Tree Nat := .node node4702 node2161 +def node4704 : Tree Nat := .node node4703 node3788 +def node4705 : Tree Nat := .node node4224 node4704 +def node4706 : Tree Nat := .node node2579 node4534 +def node4707 : Tree Nat := .node node4227 node4706 +def node4708 : Tree Nat := .node node4707 node3380 +def node4709 : Tree Nat := .node node4708 node4232 +def node4710 : Tree Nat := .node node4705 node4709 +def node4711 : Tree Nat := .node node4700 node4710 +def node4712 : Tree Nat := .node node4686 node4711 +def node4713 : Tree Nat := .node node423 node4484 +def node4714 : Tree Nat := .node node4067 node4478 +def node4715 : Tree Nat := .node node4713 node4714 +def node4716 : Tree Nat := .node node4715 node3799 +def node4717 : Tree Nat := .node node4239 node4716 +def node4718 : Tree Nat := .leaf 349 +def node4719 : Tree Nat := .node node2972 node4718 +def node4720 : Tree Nat := .node node4244 node4719 +def node4721 : Tree Nat := .node node4514 node224 +def node4722 : Tree Nat := .node node3184 node4721 +def node4723 : Tree Nat := .node node4720 node4722 +def node4724 : Tree Nat := .node node432 node4530 +def node4725 : Tree Nat := .node node4724 node2592 +def node4726 : Tree Nat := .node node4725 node3803 +def node4727 : Tree Nat := .node node4723 node4726 +def node4728 : Tree Nat := .node node4717 node4727 +def node4729 : Tree Nat := .node node443 node4628 +def node4730 : Tree Nat := .node node4729 node4253 +def node4731 : Tree Nat := .node node4730 node3807 +def node4732 : Tree Nat := .node node4252 node4731 +def node4733 : Tree Nat := .node node3952 node4422 +def node4734 : Tree Nat := .node node4257 node4733 +def node4735 : Tree Nat := .node node4734 node3397 +def node4736 : Tree Nat := .node node4262 node4681 +def node4737 : Tree Nat := .node node3004 node4736 +def node4738 : Tree Nat := .node node4735 node4737 +def node4739 : Tree Nat := .node node4732 node4738 +def node4740 : Tree Nat := .node node4728 node4739 +def node4741 : Tree Nat := .leaf 347 +def node4742 : Tree Nat := .node node466 node4741 +def node4743 : Tree Nat := .node node4742 node4270 +def node4744 : Tree Nat := .node node4743 node3819 +def node4745 : Tree Nat := .node node4269 node4744 +def node4746 : Tree Nat := .leaf 355 +def node4747 : Tree Nat := .node node2833 node4746 +def node4748 : Tree Nat := .node node4275 node4747 +def node4749 : Tree Nat := .node node4514 node451 +def node4750 : Tree Nat := .node node3402 node4749 +def node4751 : Tree Nat := .node node4748 node4750 +def node4752 : Tree Nat := .node node475 node4659 +def node4753 : Tree Nat := .node node4639 node73 +def node4754 : Tree Nat := .node node4752 node4753 +def node4755 : Tree Nat := .node node4754 node3824 +def node4756 : Tree Nat := .node node4751 node4755 +def node4757 : Tree Nat := .node node4745 node4756 +def node4758 : Tree Nat := .node node57 node4490 +def node4759 : Tree Nat := .node node4281 node4758 +def node4760 : Tree Nat := .node node4759 node3829 +def node4761 : Tree Nat := .node node485 node4677 +def node4762 : Tree Nat := .node node4761 node2204 +def node4763 : Tree Nat := .node node4762 node3832 +def node4764 : Tree Nat := .node node4760 node4763 +def node4765 : Tree Nat := .leaf 369 +def node4766 : Tree Nat := .node node3952 node4765 +def node4767 : Tree Nat := .node node4286 node4766 +def node4768 : Tree Nat := .node node4767 node3418 +def node4769 : Tree Nat := .node node4768 node4291 +def node4770 : Tree Nat := .node node4764 node4769 +def node4771 : Tree Nat := .node node4757 node4770 +def node4772 : Tree Nat := .node node4740 node4771 +def node4773 : Tree Nat := .node node4712 node4772 +def node4774 : Tree Nat := .node node1578 node4718 +def node4775 : Tree Nat := .node node4297 node4439 +def node4776 : Tree Nat := .node node4774 node4775 +def node4777 : Tree Nat := .node node4776 node3845 +def node4778 : Tree Nat := .node node4300 node4777 +def node4779 : Tree Nat := .node node2937 node4741 +def node4780 : Tree Nat := .node node4305 node4779 +def node4781 : Tree Nat := .node node4746 node57 +def node4782 : Tree Nat := .node node3242 node4781 +def node4783 : Tree Nat := .node node4780 node4782 +def node4784 : Tree Nat := .node node3148 node4765 +def node4785 : Tree Nat := .node node4784 node2640 +def node4786 : Tree Nat := .node node4785 node3848 +def node4787 : Tree Nat := .node node4783 node4786 +def node4788 : Tree Nat := .node node4778 node4787 +def node4789 : Tree Nat := .leaf 357 +def node4790 : Tree Nat := .node node2749 node4789 +def node4791 : Tree Nat := .node node4790 node4315 +def node4792 : Tree Nat := .node node4791 node3852 +def node4793 : Tree Nat := .node node4314 node4792 +def node4794 : Tree Nat := .node node4194 node4701 +def node4795 : Tree Nat := .node node4320 node4794 +def node4796 : Tree Nat := .node node4795 node3441 +def node4797 : Tree Nat := .leaf 367 +def node4798 : Tree Nat := .node node4797 node1 +def node4799 : Tree Nat := .node node4324 node4798 +def node4800 : Tree Nat := .node node3048 node4799 +def node4801 : Tree Nat := .node node4796 node4800 +def node4802 : Tree Nat := .node node4793 node4801 +def node4803 : Tree Nat := .node node4788 node4802 +def node4804 : Tree Nat := .node node2328 node4664 +def node4805 : Tree Nat := .node node4804 node4332 +def node4806 : Tree Nat := .node node4805 node3866 +def node4807 : Tree Nat := .node node4331 node4806 +def node4808 : Tree Nat := .node node3061 node4601 +def node4809 : Tree Nat := .node node4336 node4808 +def node4810 : Tree Nat := .node node4746 node1 +def node4811 : Tree Nat := .node node3446 node4810 +def node4812 : Tree Nat := .node node4809 node4811 +def node4813 : Tree Nat := .node node3133 node4694 +def node4814 : Tree Nat := .leaf 343 +def node4815 : Tree Nat := .node node4814 node82 +def node4816 : Tree Nat := .node node4813 node4815 +def node4817 : Tree Nat := .node node4816 node3870 +def node4818 : Tree Nat := .node node4812 node4817 +def node4819 : Tree Nat := .node node4807 node4818 +def node4820 : Tree Nat := .node node3128 node4701 +def node4821 : Tree Nat := .node node4820 node2256 +def node4822 : Tree Nat := .node node4821 node3879 +def node4823 : Tree Nat := .node node4343 node4822 +def node4824 : Tree Nat := .node node4194 node4797 +def node4825 : Tree Nat := .node node4345 node4824 +def node4826 : Tree Nat := .node node4825 node3470 +def node4827 : Tree Nat := .node node4826 node4351 +def node4828 : Tree Nat := .node node4823 node4827 +def node4829 : Tree Nat := .node node4819 node4828 +def node4830 : Tree Nat := .node node4803 node4829 +def node4831 : Tree Nat := .node node1622 node4718 +def node4832 : Tree Nat := .node node4831 node2266 +def node4833 : Tree Nat := .node node4832 node3894 +def node4834 : Tree Nat := .node node4358 node4833 +def node4835 : Tree Nat := .node node3061 node4430 +def node4836 : Tree Nat := .node node4360 node4835 +def node4837 : Tree Nat := .node node4836 node3476 +def node4838 : Tree Nat := .node node3202 node4765 +def node4839 : Tree Nat := .node node4838 node2692 +def node4840 : Tree Nat := .node node4839 node3898 +def node4841 : Tree Nat := .node node4837 node4840 +def node4842 : Tree Nat := .node node4834 node4841 +def node4843 : Tree Nat := .node node3193 node4789 +def node4844 : Tree Nat := .node node4843 node4369 +def node4845 : Tree Nat := .node node4844 node3902 +def node4846 : Tree Nat := .node node4368 node4845 +def node4847 : Tree Nat := .node node2679 node4488 +def node4848 : Tree Nat := .node node4373 node4847 +def node4849 : Tree Nat := .node node4848 node3491 +def node4850 : Tree Nat := .node node4376 node4798 +def node4851 : Tree Nat := .node node3097 node4850 +def node4852 : Tree Nat := .node node4849 node4851 +def node4853 : Tree Nat := .node node4846 node4852 +def node4854 : Tree Nat := .node node4842 node4853 +def node4855 : Tree Nat := .node node2382 node4741 +def node4856 : Tree Nat := .node node4855 node2289 +def node4857 : Tree Nat := .node node4856 node3913 +def node4858 : Tree Nat := .node node4384 node4857 +def node4859 : Tree Nat := .node node2937 node4789 +def node4860 : Tree Nat := .node node4386 node4859 +def node4861 : Tree Nat := .node node4860 node3497 +def node4862 : Tree Nat := .node node3183 node4659 +def node4863 : Tree Nat := .node node4814 node73 +def node4864 : Tree Nat := .node node4862 node4863 +def node4865 : Tree Nat := .node node4864 node4389 +def node4866 : Tree Nat := .node node4861 node4865 +def node4867 : Tree Nat := .node node4858 node4866 +def node4868 : Tree Nat := .node node57 node4814 +def node4869 : Tree Nat := .node node4393 node4868 +def node4870 : Tree Nat := .node node4869 node3918 +def node4871 : Tree Nat := .node node3585 node4677 +def node4872 : Tree Nat := .node node4871 node2301 +def node4873 : Tree Nat := .node node4872 node3923 +def node4874 : Tree Nat := .node node4870 node4873 +def node4875 : Tree Nat := .node node2526 node4694 +def node4876 : Tree Nat := .node node4397 node4875 +def node4877 : Tree Nat := .node node4876 node3512 +def node4878 : Tree Nat := .node node4877 node4401 +def node4879 : Tree Nat := .node node4874 node4878 +def node4880 : Tree Nat := .node node4867 node4879 +def node4881 : Tree Nat := .node node4854 node4880 +def node4882 : Tree Nat := .node node4830 node4881 +def node4883 : Tree Nat := .node node4773 node4882 +def node4884 : Tree Nat := .node node4657 node4883 +def node4885 : Tree Nat := .leaf 386 +def node4886 : Tree Nat := .node node1 node4885 +def node4887 : Tree Nat := .node node4886 node3525 +def node4888 : Tree Nat := .node node3938 node4887 +def node4889 : Tree Nat := .node node4888 node4412 +def node4890 : Tree Nat := .leaf 410 +def node4891 : Tree Nat := .node node1 node4890 +def node4892 : Tree Nat := .node node4891 node4419 +def node4893 : Tree Nat := .node node4417 node4892 +def node4894 : Tree Nat := .leaf 399 +def node4895 : Tree Nat := .node node4424 node4894 +def node4896 : Tree Nat := .node node4423 node4895 +def node4897 : Tree Nat := .node node4896 node3534 +def node4898 : Tree Nat := .node node4893 node4897 +def node4899 : Tree Nat := .node node4889 node4898 +def node4900 : Tree Nat := .leaf 398 +def node4901 : Tree Nat := .node node1 node4900 +def node4902 : Tree Nat := .node node4901 node3542 +def node4903 : Tree Nat := .node node3954 node4902 +def node4904 : Tree Nat := .node node1912 node4885 +def node4905 : Tree Nat := .node node4431 node4904 +def node4906 : Tree Nat := .node node4905 node3547 +def node4907 : Tree Nat := .node node4903 node4906 +def node4908 : Tree Nat := .leaf 388 +def node4909 : Tree Nat := .leaf 412 +def node4910 : Tree Nat := .node node4908 node4909 +def node4911 : Tree Nat := .node node4440 node4910 +def node4912 : Tree Nat := .node node4911 node3965 +def node4913 : Tree Nat := .node node4438 node4912 +def node4914 : Tree Nat := .node node4907 node4913 +def node4915 : Tree Nat := .node node4899 node4914 +def node4916 : Tree Nat := .leaf 392 +def node4917 : Tree Nat := .node node1 node4916 +def node4918 : Tree Nat := .node node4917 node3556 +def node4919 : Tree Nat := .node node3972 node4918 +def node4920 : Tree Nat := .leaf 378 +def node4921 : Tree Nat := .node node3936 node4920 +def node4922 : Tree Nat := .node node4446 node4921 +def node4923 : Tree Nat := .node node4922 node3562 +def node4924 : Tree Nat := .node node4919 node4923 +def node4925 : Tree Nat := .leaf 406 +def node4926 : Tree Nat := .node node2348 node4925 +def node4927 : Tree Nat := .node node4457 node4926 +def node4928 : Tree Nat := .node node4927 node3567 +def node4929 : Tree Nat := .node node4455 node4928 +def node4930 : Tree Nat := .node node4924 node4929 +def node4931 : Tree Nat := .leaf 408 +def node4932 : Tree Nat := .node node1 node4931 +def node4933 : Tree Nat := .node node4932 node1940 +def node4934 : Tree Nat := .node node3987 node4933 +def node4935 : Tree Nat := .node node3989 node4916 +def node4936 : Tree Nat := .node node4463 node4935 +def node4937 : Tree Nat := .node node4936 node3572 +def node4938 : Tree Nat := .node node4934 node4937 +def node4939 : Tree Nat := .leaf 382 +def node4940 : Tree Nat := .node node1 node4939 +def node4941 : Tree Nat := .node node4908 node82 +def node4942 : Tree Nat := .node node4940 node4941 +def node4943 : Tree Nat := .node node4942 node4472 +def node4944 : Tree Nat := .node node4470 node4943 +def node4945 : Tree Nat := .node node4938 node4944 +def node4946 : Tree Nat := .node node4930 node4945 +def node4947 : Tree Nat := .node node4915 node4946 +def node4948 : Tree Nat := .leaf 387 +def node4949 : Tree Nat := .node node1 node4948 +def node4950 : Tree Nat := .node node4949 node3582 +def node4951 : Tree Nat := .node node4007 node4950 +def node4952 : Tree Nat := .node node4951 node4481 +def node4953 : Tree Nat := .leaf 411 +def node4954 : Tree Nat := .node node1 node4953 +def node4955 : Tree Nat := .node node4954 node2373 +def node4956 : Tree Nat := .node node4486 node4955 +def node4957 : Tree Nat := .leaf 402 +def node4958 : Tree Nat := .node node4490 node4957 +def node4959 : Tree Nat := .node node4489 node4958 +def node4960 : Tree Nat := .leaf 413 +def node4961 : Tree Nat := .node node4960 node1 +def node4962 : Tree Nat := .node node3592 node4961 +def node4963 : Tree Nat := .node node4959 node4962 +def node4964 : Tree Nat := .node node4956 node4963 +def node4965 : Tree Nat := .node node4952 node4964 +def node4966 : Tree Nat := .node node1 node4894 +def node4967 : Tree Nat := .node node4966 node3598 +def node4968 : Tree Nat := .node node4022 node4967 +def node4969 : Tree Nat := .node node1969 node4908 +def node4970 : Tree Nat := .node node4496 node4969 +def node4971 : Tree Nat := .node node4970 node3603 +def node4972 : Tree Nat := .node node4968 node4971 +def node4973 : Tree Nat := .leaf 401 +def node4974 : Tree Nat := .node node4973 node1 +def node4975 : Tree Nat := .node node3203 node4974 +def node4976 : Tree Nat := .node node4501 node4975 +def node4977 : Tree Nat := .node node4976 node4505 +def node4978 : Tree Nat := .node node4972 node4977 +def node4979 : Tree Nat := .node node4965 node4978 +def node4980 : Tree Nat := .leaf 394 +def node4981 : Tree Nat := .node node1 node4980 +def node4982 : Tree Nat := .node node4981 node3611 +def node4983 : Tree Nat := .node node4037 node4982 +def node4984 : Tree Nat := .node node1985 node4939 +def node4985 : Tree Nat := .node node4510 node4984 +def node4986 : Tree Nat := .node node4985 node3618 +def node4987 : Tree Nat := .node node4983 node4986 +def node4988 : Tree Nat := .node node2403 node4890 +def node4989 : Tree Nat := .node node4518 node4988 +def node4990 : Tree Nat := .node node3622 node4961 +def node4991 : Tree Nat := .node node4989 node4990 +def node4992 : Tree Nat := .node node4517 node4991 +def node4993 : Tree Nat := .node node4987 node4992 +def node4994 : Tree Nat := .node node1 node4925 +def node4995 : Tree Nat := .node node4994 node2000 +def node4996 : Tree Nat := .node node4524 node4995 +def node4997 : Tree Nat := .leaf 396 +def node4998 : Tree Nat := .node node4050 node4997 +def node4999 : Tree Nat := .node node4526 node4998 +def node5000 : Tree Nat := .node node4999 node3629 +def node5001 : Tree Nat := .node node4996 node5000 +def node5002 : Tree Nat := .node node4973 node322 +def node5003 : Tree Nat := .node node3231 node5002 +def node5004 : Tree Nat := .node node4532 node5003 +def node5005 : Tree Nat := .leaf 380 +def node5006 : Tree Nat := .node node1 node5005 +def node5007 : Tree Nat := .node node5006 node2836 +def node5008 : Tree Nat := .node node5007 node4536 +def node5009 : Tree Nat := .node node5004 node5008 +def node5010 : Tree Nat := .node node5001 node5009 +def node5011 : Tree Nat := .node node4993 node5010 +def node5012 : Tree Nat := .node node4979 node5011 +def node5013 : Tree Nat := .node node4947 node5012 +def node5014 : Tree Nat := .node node4886 node3638 +def node5015 : Tree Nat := .node node4069 node5014 +def node5016 : Tree Nat := .node node5015 node4545 +def node5017 : Tree Nat := .node node4891 node2430 +def node5018 : Tree Nat := .node node4548 node5017 +def node5019 : Tree Nat := .leaf 400 +def node5020 : Tree Nat := .node node4424 node5019 +def node5021 : Tree Nat := .node node4550 node5020 +def node5022 : Tree Nat := .node node4909 node1 +def node5023 : Tree Nat := .node node3646 node5022 +def node5024 : Tree Nat := .node node5021 node5023 +def node5025 : Tree Nat := .node node5018 node5024 +def node5026 : Tree Nat := .node node5016 node5025 +def node5027 : Tree Nat := .node node4901 node3653 +def node5028 : Tree Nat := .node node4081 node5027 +def node5029 : Tree Nat := .node node1943 node4948 +def node5030 : Tree Nat := .node node4556 node5029 +def node5031 : Tree Nat := .node node5030 node3658 +def node5032 : Tree Nat := .node node5028 node5031 +def node5033 : Tree Nat := .node node5019 node1 +def node5034 : Tree Nat := .node node3262 node5033 +def node5035 : Tree Nat := .node node4561 node5034 +def node5036 : Tree Nat := .leaf 414 +def node5037 : Tree Nat := .node node2780 node5036 +def node5038 : Tree Nat := .node node4563 node5037 +def node5039 : Tree Nat := .node node5038 node4088 +def node5040 : Tree Nat := .node node5035 node5039 +def node5041 : Tree Nat := .node node5032 node5040 +def node5042 : Tree Nat := .node node5026 node5041 +def node5043 : Tree Nat := .node node4917 node3665 +def node5044 : Tree Nat := .node node4094 node5043 +def node5045 : Tree Nat := .node node1894 node5005 +def node5046 : Tree Nat := .node node4569 node5045 +def node5047 : Tree Nat := .node node5046 node3670 +def node5048 : Tree Nat := .node node5044 node5047 +def node5049 : Tree Nat := .node node2322 node4931 +def node5050 : Tree Nat := .node node4576 node5049 +def node5051 : Tree Nat := .node node3673 node5022 +def node5052 : Tree Nat := .node node5050 node5051 +def node5053 : Tree Nat := .node node4575 node5052 +def node5054 : Tree Nat := .node node5048 node5053 +def node5055 : Tree Nat := .node node4932 node2051 +def node5056 : Tree Nat := .node node4104 node5055 +def node5057 : Tree Nat := .node node3989 node4980 +def node5058 : Tree Nat := .node node4581 node5057 +def node5059 : Tree Nat := .node node5058 node3681 +def node5060 : Tree Nat := .node node5056 node5059 +def node5061 : Tree Nat := .node node3282 node5033 +def node5062 : Tree Nat := .node node4587 node5061 +def node5063 : Tree Nat := .node node4940 node2888 +def node5064 : Tree Nat := .node node5063 node4589 +def node5065 : Tree Nat := .node node5062 node5064 +def node5066 : Tree Nat := .node node5060 node5065 +def node5067 : Tree Nat := .node node5054 node5066 +def node5068 : Tree Nat := .node node5042 node5067 +def node5069 : Tree Nat := .node node4949 node3611 +def node5070 : Tree Nat := .node node4122 node5069 +def node5071 : Tree Nat := .node node5070 node4597 +def node5072 : Tree Nat := .node node4954 node4602 +def node5073 : Tree Nat := .node node4600 node5072 +def node5074 : Tree Nat := .leaf 404 +def node5075 : Tree Nat := .node node4490 node5074 +def node5076 : Tree Nat := .node node4605 node5075 +def node5077 : Tree Nat := .node node5076 node3702 +def node5078 : Tree Nat := .node node5073 node5077 +def node5079 : Tree Nat := .node node5071 node5078 +def node5080 : Tree Nat := .node node4966 node3706 +def node5081 : Tree Nat := .node node4138 node5080 +def node5082 : Tree Nat := .leaf 390 +def node5083 : Tree Nat := .node node2003 node5082 +def node5084 : Tree Nat := .node node4611 node5083 +def node5085 : Tree Nat := .node node5084 node3711 +def node5086 : Tree Nat := .node node5081 node5085 +def node5087 : Tree Nat := .leaf 389 +def node5088 : Tree Nat := .node node5087 node73 +def node5089 : Tree Nat := .node node4618 node5088 +def node5090 : Tree Nat := .node node5089 node4147 +def node5091 : Tree Nat := .node node4617 node5090 +def node5092 : Tree Nat := .node node5086 node5091 +def node5093 : Tree Nat := .node node5079 node5092 +def node5094 : Tree Nat := .node node4981 node3718 +def node5095 : Tree Nat := .node node4153 node5094 +def node5096 : Tree Nat := .leaf 384 +def node5097 : Tree Nat := .node node4125 node5096 +def node5098 : Tree Nat := .node node4624 node5097 +def node5099 : Tree Nat := .node node5098 node3723 +def node5100 : Tree Nat := .node node5095 node5099 +def node5101 : Tree Nat := .node node2376 node4953 +def node5102 : Tree Nat := .node node4634 node5101 +def node5103 : Tree Nat := .node node5102 node3727 +def node5104 : Tree Nat := .node node4633 node5103 +def node5105 : Tree Nat := .node node5100 node5104 +def node5106 : Tree Nat := .node node4994 node2105 +def node5107 : Tree Nat := .node node4641 node5106 +def node5108 : Tree Nat := .node node4050 node4900 +def node5109 : Tree Nat := .node node4643 node5108 +def node5110 : Tree Nat := .node node5109 node3735 +def node5111 : Tree Nat := .node node5107 node5110 +def node5112 : Tree Nat := .node node5087 node114 +def node5113 : Tree Nat := .node node5006 node5112 +def node5114 : Tree Nat := .node node5113 node4650 +def node5115 : Tree Nat := .node node4649 node5114 +def node5116 : Tree Nat := .node node5111 node5115 +def node5117 : Tree Nat := .node node5105 node5116 +def node5118 : Tree Nat := .node node5093 node5117 +def node5119 : Tree Nat := .node node5068 node5118 +def node5120 : Tree Nat := .node node5013 node5119 +def node5121 : Tree Nat := .node node1 node4997 +def node5122 : Tree Nat := .node node5121 node3749 +def node5123 : Tree Nat := .node node4185 node5122 +def node5124 : Tree Nat := .node node5123 node4662 +def node5125 : Tree Nat := .node node2394 node4894 +def node5126 : Tree Nat := .node node4668 node5125 +def node5127 : Tree Nat := .node node5036 node1 +def node5128 : Tree Nat := .node node3533 node5127 +def node5129 : Tree Nat := .node node5126 node5128 +def node5130 : Tree Nat := .node node4667 node5129 +def node5131 : Tree Nat := .node node5124 node5130 +def node5132 : Tree Nat := .node node1 node5074 +def node5133 : Tree Nat := .node node5132 node2128 +def node5134 : Tree Nat := .node node4196 node5133 +def node5135 : Tree Nat := .node node4029 node4885 +def node5136 : Tree Nat := .node node4673 node5135 +def node5137 : Tree Nat := .node node5136 node3760 +def node5138 : Tree Nat := .node node5134 node5137 +def node5139 : Tree Nat := .node node4957 node322 +def node5140 : Tree Nat := .node node3149 node5139 +def node5141 : Tree Nat := .node node4679 node5140 +def node5142 : Tree Nat := .node node371 node5096 +def node5143 : Tree Nat := .node node2818 node4960 +def node5144 : Tree Nat := .node node5142 node5143 +def node5145 : Tree Nat := .node node5144 node4682 +def node5146 : Tree Nat := .node node5141 node5145 +def node5147 : Tree Nat := .node node5138 node5146 +def node5148 : Tree Nat := .node node5131 node5147 +def node5149 : Tree Nat := .leaf 393 +def node5150 : Tree Nat := .node node1 node5149 +def node5151 : Tree Nat := .node node5150 node3769 +def node5152 : Tree Nat := .node node4212 node5151 +def node5153 : Tree Nat := .leaf 379 +def node5154 : Tree Nat := .node node2144 node5153 +def node5155 : Tree Nat := .node node4687 node5154 +def node5156 : Tree Nat := .node node5155 node3775 +def node5157 : Tree Nat := .node node5152 node5156 +def node5158 : Tree Nat := .node node4920 node4450 +def node5159 : Tree Nat := .node node4216 node5158 +def node5160 : Tree Nat := .node node5159 node3361 +def node5161 : Tree Nat := .leaf 407 +def node5162 : Tree Nat := .node node4639 node5161 +def node5163 : Tree Nat := .node node4695 node5162 +def node5164 : Tree Nat := .node node3779 node5127 +def node5165 : Tree Nat := .node node5163 node5164 +def node5166 : Tree Nat := .node node5160 node5165 +def node5167 : Tree Nat := .node node5157 node5166 +def node5168 : Tree Nat := .leaf 409 +def node5169 : Tree Nat := .node node1 node5168 +def node5170 : Tree Nat := .node node5169 node3784 +def node5171 : Tree Nat := .node node4223 node5170 +def node5172 : Tree Nat := .node node2160 node5149 +def node5173 : Tree Nat := .node node4702 node5172 +def node5174 : Tree Nat := .node node5173 node3788 +def node5175 : Tree Nat := .node node5171 node5174 +def node5176 : Tree Nat := .node node4957 node411 +def node5177 : Tree Nat := .node node3377 node5176 +def node5178 : Tree Nat := .node node4707 node5177 +def node5179 : Tree Nat := .leaf 383 +def node5180 : Tree Nat := .node node1 node5179 +def node5181 : Tree Nat := .node node5180 node2983 +def node5182 : Tree Nat := .node node5181 node4231 +def node5183 : Tree Nat := .node node5178 node5182 +def node5184 : Tree Nat := .node node5175 node5183 +def node5185 : Tree Nat := .node node5167 node5184 +def node5186 : Tree Nat := .node node5148 node5185 +def node5187 : Tree Nat := .node node5121 node3796 +def node5188 : Tree Nat := .node node4238 node5187 +def node5189 : Tree Nat := .node node5188 node4716 +def node5190 : Tree Nat := .leaf 403 +def node5191 : Tree Nat := .node node2568 node5190 +def node5192 : Tree Nat := .node node4724 node5191 +def node5193 : Tree Nat := .node node5192 node3803 +def node5194 : Tree Nat := .node node4723 node5193 +def node5195 : Tree Nat := .node node5189 node5194 +def node5196 : Tree Nat := .node node5132 node2178 +def node5197 : Tree Nat := .node node4251 node5196 +def node5198 : Tree Nat := .node node4029 node5087 +def node5199 : Tree Nat := .node node4729 node5198 +def node5200 : Tree Nat := .node node5199 node3807 +def node5201 : Tree Nat := .node node5197 node5200 +def node5202 : Tree Nat := .node node455 node5096 +def node5203 : Tree Nat := .node node5082 node82 +def node5204 : Tree Nat := .node node5202 node5203 +def node5205 : Tree Nat := .node node5204 node4736 +def node5206 : Tree Nat := .node node4735 node5205 +def node5207 : Tree Nat := .node node5201 node5206 +def node5208 : Tree Nat := .node node5195 node5207 +def node5209 : Tree Nat := .leaf 395 +def node5210 : Tree Nat := .node node1 node5209 +def node5211 : Tree Nat := .node node5210 node3814 +def node5212 : Tree Nat := .node node4268 node5211 +def node5213 : Tree Nat := .node node4067 node5179 +def node5214 : Tree Nat := .node node4742 node5213 +def node5215 : Tree Nat := .node node5214 node3819 +def node5216 : Tree Nat := .node node5212 node5215 +def node5217 : Tree Nat := .node node4920 node4746 +def node5218 : Tree Nat := .node node4275 node5217 +def node5219 : Tree Nat := .node node5218 node4750 +def node5220 : Tree Nat := .node node4639 node4890 +def node5221 : Tree Nat := .node node4752 node5220 +def node5222 : Tree Nat := .node node5221 node3824 +def node5223 : Tree Nat := .node node5219 node5222 +def node5224 : Tree Nat := .node node5216 node5223 +def node5225 : Tree Nat := .node node1 node5161 +def node5226 : Tree Nat := .node node5225 node3828 +def node5227 : Tree Nat := .node node4759 node5226 +def node5228 : Tree Nat := .leaf 397 +def node5229 : Tree Nat := .node node1996 node5228 +def node5230 : Tree Nat := .node node4761 node5229 +def node5231 : Tree Nat := .node node5230 node3832 +def node5232 : Tree Nat := .node node5227 node5231 +def node5233 : Tree Nat := .leaf 381 +def node5234 : Tree Nat := .node node1 node5233 +def node5235 : Tree Nat := .node node5082 node25 +def node5236 : Tree Nat := .node node5234 node5235 +def node5237 : Tree Nat := .node node5236 node4290 +def node5238 : Tree Nat := .node node4768 node5237 +def node5239 : Tree Nat := .node node5232 node5238 +def node5240 : Tree Nat := .node node5224 node5239 +def node5241 : Tree Nat := .node node5208 node5240 +def node5242 : Tree Nat := .node node5186 node5241 +def node5243 : Tree Nat := .node node1 node5228 +def node5244 : Tree Nat := .node node5243 node3841 +def node5245 : Tree Nat := .node node4299 node5244 +def node5246 : Tree Nat := .node node5245 node4777 +def node5247 : Tree Nat := .node node2506 node4973 +def node5248 : Tree Nat := .node node4784 node5247 +def node5249 : Tree Nat := .node node5248 node3848 +def node5250 : Tree Nat := .node node4783 node5249 +def node5251 : Tree Nat := .node node5246 node5250 +def node5252 : Tree Nat := .leaf 405 +def node5253 : Tree Nat := .node node1 node5252 +def node5254 : Tree Nat := .node node5253 node2223 +def node5255 : Tree Nat := .node node4313 node5254 +def node5256 : Tree Nat := .node node4261 node4948 +def node5257 : Tree Nat := .node node4790 node5256 +def node5258 : Tree Nat := .node node5257 node3852 +def node5259 : Tree Nat := .node node5255 node5258 +def node5260 : Tree Nat := .leaf 385 +def node5261 : Tree Nat := .node node2320 node5260 +def node5262 : Tree Nat := .leaf 391 +def node5263 : Tree Nat := .node node5262 node73 +def node5264 : Tree Nat := .node node5261 node5263 +def node5265 : Tree Nat := .node node5264 node4799 +def node5266 : Tree Nat := .node node4796 node5265 +def node5267 : Tree Nat := .node node5259 node5266 +def node5268 : Tree Nat := .node node5251 node5267 +def node5269 : Tree Nat := .node node5150 node3860 +def node5270 : Tree Nat := .node node4330 node5269 +def node5271 : Tree Nat := .node node4297 node5233 +def node5272 : Tree Nat := .node node4804 node5271 +def node5273 : Tree Nat := .node node5272 node3866 +def node5274 : Tree Nat := .node node5270 node5273 +def node5275 : Tree Nat := .node node5153 node4601 +def node5276 : Tree Nat := .node node4336 node5275 +def node5277 : Tree Nat := .node node5276 node4811 +def node5278 : Tree Nat := .node node4814 node5168 +def node5279 : Tree Nat := .node node4813 node5278 +def node5280 : Tree Nat := .node node5279 node3870 +def node5281 : Tree Nat := .node node5277 node5280 +def node5282 : Tree Nat := .node node5274 node5281 +def node5283 : Tree Nat := .node node5169 node3875 +def node5284 : Tree Nat := .node node4342 node5283 +def node5285 : Tree Nat := .node node2255 node5209 +def node5286 : Tree Nat := .node node4820 node5285 +def node5287 : Tree Nat := .node node5286 node3879 +def node5288 : Tree Nat := .node node5284 node5287 +def node5289 : Tree Nat := .node node5262 node25 +def node5290 : Tree Nat := .node node5180 node5289 +def node5291 : Tree Nat := .node node5290 node4350 +def node5292 : Tree Nat := .node node4826 node5291 +def node5293 : Tree Nat := .node node5288 node5292 +def node5294 : Tree Nat := .node node5282 node5293 +def node5295 : Tree Nat := .node node5268 node5294 +def node5296 : Tree Nat := .node node5243 node3891 +def node5297 : Tree Nat := .node node4357 node5296 +def node5298 : Tree Nat := .node node2239 node4483 +def node5299 : Tree Nat := .node node4831 node5298 +def node5300 : Tree Nat := .node node5299 node3894 +def node5301 : Tree Nat := .node node5297 node5300 +def node5302 : Tree Nat := .node node2668 node5252 +def node5303 : Tree Nat := .node node4838 node5302 +def node5304 : Tree Nat := .node node5303 node3898 +def node5305 : Tree Nat := .node node4837 node5304 +def node5306 : Tree Nat := .node node5301 node5305 +def node5307 : Tree Nat := .node node5253 node2277 +def node5308 : Tree Nat := .node node4367 node5307 +def node5309 : Tree Nat := .node node4261 node5262 +def node5310 : Tree Nat := .node node4843 node5309 +def node5311 : Tree Nat := .node node5310 node3902 +def node5312 : Tree Nat := .node node5308 node5311 +def node5313 : Tree Nat := .node node5190 node411 +def node5314 : Tree Nat := .node node3309 node5313 +def node5315 : Tree Nat := .node node4848 node5314 +def node5316 : Tree Nat := .node node2800 node5260 +def node5317 : Tree Nat := .node node5316 node3096 +def node5318 : Tree Nat := .node node5317 node4850 +def node5319 : Tree Nat := .node node5315 node5318 +def node5320 : Tree Nat := .node node5312 node5319 +def node5321 : Tree Nat := .node node5306 node5320 +def node5322 : Tree Nat := .node node5210 node3909 +def node5323 : Tree Nat := .node node4383 node5322 +def node5324 : Tree Nat := .node node2096 node5260 +def node5325 : Tree Nat := .node node4855 node5324 +def node5326 : Tree Nat := .node node5325 node3913 +def node5327 : Tree Nat := .node node5323 node5326 +def node5328 : Tree Nat := .node node5153 node4789 +def node5329 : Tree Nat := .node node4386 node5328 +def node5330 : Tree Nat := .node node5329 node3497 +def node5331 : Tree Nat := .node node4814 node4953 +def node5332 : Tree Nat := .node node4862 node5331 +def node5333 : Tree Nat := .node node5332 node4389 +def node5334 : Tree Nat := .node node5330 node5333 +def node5335 : Tree Nat := .node node5327 node5334 +def node5336 : Tree Nat := .node node5225 node3917 +def node5337 : Tree Nat := .node node4869 node5336 +def node5338 : Tree Nat := .node node2102 node4900 +def node5339 : Tree Nat := .node node4871 node5338 +def node5340 : Tree Nat := .node node5339 node3923 +def node5341 : Tree Nat := .node node5337 node5340 +def node5342 : Tree Nat := .node node5190 node195 +def node5343 : Tree Nat := .node node3510 node5342 +def node5344 : Tree Nat := .node node4876 node5343 +def node5345 : Tree Nat := .node node5234 node3117 +def node5346 : Tree Nat := .node node5345 node4400 +def node5347 : Tree Nat := .node node5344 node5346 +def node5348 : Tree Nat := .node node5341 node5347 +def node5349 : Tree Nat := .node node5335 node5348 +def node5350 : Tree Nat := .node node5321 node5349 +def node5351 : Tree Nat := .node node5295 node5350 +def node5352 : Tree Nat := .node node5242 node5351 +def node5353 : Tree Nat := .node node5120 node5352 +def node5354 : Tree Nat := .leaf 450 +def node5355 : Tree Nat := .leaf 426 +def node5356 : Tree Nat := .node node5354 node5355 +def node5357 : Tree Nat := .node node4886 node5356 +def node5358 : Tree Nat := .node node3938 node5357 +def node5359 : Tree Nat := .leaf 434 +def node5360 : Tree Nat := .node node1 node5359 +def node5361 : Tree Nat := .node node5360 node3529 +def node5362 : Tree Nat := .node node4411 node5361 +def node5363 : Tree Nat := .node node5358 node5362 +def node5364 : Tree Nat := .node node5363 node4898 +def node5365 : Tree Nat := .leaf 440 +def node5366 : Tree Nat := .node node3541 node5365 +def node5367 : Tree Nat := .node node4901 node5366 +def node5368 : Tree Nat := .node node3954 node5367 +def node5369 : Tree Nat := .leaf 446 +def node5370 : Tree Nat := .node node1 node5369 +def node5371 : Tree Nat := .node node5370 node3144 +def node5372 : Tree Nat := .node node4905 node5371 +def node5373 : Tree Nat := .node node5368 node5372 +def node5374 : Tree Nat := .leaf 422 +def node5375 : Tree Nat := .node node1 node5374 +def node5376 : Tree Nat := .node node5375 node3151 +def node5377 : Tree Nat := .node node4437 node5376 +def node5378 : Tree Nat := .node node5377 node4912 +def node5379 : Tree Nat := .node node5373 node5378 +def node5380 : Tree Nat := .node node5364 node5379 +def node5381 : Tree Nat := .node node3555 node5359 +def node5382 : Tree Nat := .node node4917 node5381 +def node5383 : Tree Nat := .node node3972 node5382 +def node5384 : Tree Nat := .leaf 442 +def node5385 : Tree Nat := .node node1 node5384 +def node5386 : Tree Nat := .node node5385 node3561 +def node5387 : Tree Nat := .node node4922 node5386 +def node5388 : Tree Nat := .node node5383 node5387 +def node5389 : Tree Nat := .leaf 418 +def node5390 : Tree Nat := .node node1 node5389 +def node5391 : Tree Nat := .node node5390 node4453 +def node5392 : Tree Nat := .node node4452 node5391 +def node5393 : Tree Nat := .node node5392 node4928 +def node5394 : Tree Nat := .node node5388 node5393 +def node5395 : Tree Nat := .leaf 447 +def node5396 : Tree Nat := .node node1939 node5395 +def node5397 : Tree Nat := .node node4932 node5396 +def node5398 : Tree Nat := .node node3987 node5397 +def node5399 : Tree Nat := .leaf 452 +def node5400 : Tree Nat := .node node1 node5399 +def node5401 : Tree Nat := .node node5400 node3170 +def node5402 : Tree Nat := .node node4936 node5401 +def node5403 : Tree Nat := .node node5398 node5402 +def node5404 : Tree Nat := .leaf 432 +def node5405 : Tree Nat := .node node1 node5404 +def node5406 : Tree Nat := .node node5405 node3176 +def node5407 : Tree Nat := .node node4469 node5406 +def node5408 : Tree Nat := .leaf 420 +def node5409 : Tree Nat := .node node4908 node5408 +def node5410 : Tree Nat := .node node4940 node5409 +def node5411 : Tree Nat := .node node5410 node4472 +def node5412 : Tree Nat := .node node5407 node5411 +def node5413 : Tree Nat := .node node5403 node5412 +def node5414 : Tree Nat := .node node5394 node5413 +def node5415 : Tree Nat := .node node5380 node5414 +def node5416 : Tree Nat := .leaf 451 +def node5417 : Tree Nat := .leaf 430 +def node5418 : Tree Nat := .node node5416 node5417 +def node5419 : Tree Nat := .node node4949 node5418 +def node5420 : Tree Nat := .node node4007 node5419 +def node5421 : Tree Nat := .leaf 435 +def node5422 : Tree Nat := .node node1 node5421 +def node5423 : Tree Nat := .leaf 439 +def node5424 : Tree Nat := .node node5423 node1 +def node5425 : Tree Nat := .node node5422 node5424 +def node5426 : Tree Nat := .node node4480 node5425 +def node5427 : Tree Nat := .node node5420 node5426 +def node5428 : Tree Nat := .node node5427 node4964 +def node5429 : Tree Nat := .leaf 444 +def node5430 : Tree Nat := .node node3597 node5429 +def node5431 : Tree Nat := .node node4966 node5430 +def node5432 : Tree Nat := .node node4022 node5431 +def node5433 : Tree Nat := .node node1 node5395 +def node5434 : Tree Nat := .leaf 427 +def node5435 : Tree Nat := .node node5434 node1 +def node5436 : Tree Nat := .node node5433 node5435 +def node5437 : Tree Nat := .node node4970 node5436 +def node5438 : Tree Nat := .node node5432 node5437 +def node5439 : Tree Nat := .leaf 423 +def node5440 : Tree Nat := .node node1 node5439 +def node5441 : Tree Nat := .node node5440 node4974 +def node5442 : Tree Nat := .node node4501 node5441 +def node5443 : Tree Nat := .leaf 416 +def node5444 : Tree Nat := .node node2808 node5443 +def node5445 : Tree Nat := .node node4503 node5444 +def node5446 : Tree Nat := .node node5445 node4031 +def node5447 : Tree Nat := .node node5442 node5446 +def node5448 : Tree Nat := .node node5438 node5447 +def node5449 : Tree Nat := .node node5428 node5448 +def node5450 : Tree Nat := .leaf 436 +def node5451 : Tree Nat := .node node3610 node5450 +def node5452 : Tree Nat := .node node4981 node5451 +def node5453 : Tree Nat := .node node4037 node5452 +def node5454 : Tree Nat := .node node1 node5429 +def node5455 : Tree Nat := .node node5454 node5424 +def node5456 : Tree Nat := .node node4985 node5455 +def node5457 : Tree Nat := .node node5453 node5456 +def node5458 : Tree Nat := .node node1 node5408 +def node5459 : Tree Nat := .node node5458 node2400 +def node5460 : Tree Nat := .node node4516 node5459 +def node5461 : Tree Nat := .node node5460 node4991 +def node5462 : Tree Nat := .node node5457 node5461 +def node5463 : Tree Nat := .node node1999 node5354 +def node5464 : Tree Nat := .node node4994 node5463 +def node5465 : Tree Nat := .node node4524 node5464 +def node5466 : Tree Nat := .node node3628 node5435 +def node5467 : Tree Nat := .node node4999 node5466 +def node5468 : Tree Nat := .node node5465 node5467 +def node5469 : Tree Nat := .node node1 node5417 +def node5470 : Tree Nat := .node node5469 node5002 +def node5471 : Tree Nat := .node node4532 node5470 +def node5472 : Tree Nat := .node node2835 node5439 +def node5473 : Tree Nat := .node node5006 node5472 +def node5474 : Tree Nat := .node node5473 node4536 +def node5475 : Tree Nat := .node node5471 node5474 +def node5476 : Tree Nat := .node node5468 node5475 +def node5477 : Tree Nat := .node node5462 node5476 +def node5478 : Tree Nat := .node node5449 node5477 +def node5479 : Tree Nat := .node node5415 node5478 +def node5480 : Tree Nat := .leaf 428 +def node5481 : Tree Nat := .node node5354 node5480 +def node5482 : Tree Nat := .node node4886 node5481 +def node5483 : Tree Nat := .node node4069 node5482 +def node5484 : Tree Nat := .leaf 438 +def node5485 : Tree Nat := .node node5484 node1 +def node5486 : Tree Nat := .node node5360 node5485 +def node5487 : Tree Nat := .node node4544 node5486 +def node5488 : Tree Nat := .node node5483 node5487 +def node5489 : Tree Nat := .node node5488 node5025 +def node5490 : Tree Nat := .node node3541 node5384 +def node5491 : Tree Nat := .node node4901 node5490 +def node5492 : Tree Nat := .node node4081 node5491 +def node5493 : Tree Nat := .node node5355 node195 +def node5494 : Tree Nat := .node node5370 node5493 +def node5495 : Tree Nat := .node node5030 node5494 +def node5496 : Tree Nat := .node node5492 node5495 +def node5497 : Tree Nat := .node node5375 node5033 +def node5498 : Tree Nat := .node node4561 node5497 +def node5499 : Tree Nat := .node node5498 node5039 +def node5500 : Tree Nat := .node node5496 node5499 +def node5501 : Tree Nat := .node node5489 node5500 +def node5502 : Tree Nat := .node node3524 node5421 +def node5503 : Tree Nat := .node node4917 node5502 +def node5504 : Tree Nat := .node node4094 node5503 +def node5505 : Tree Nat := .node node5385 node5485 +def node5506 : Tree Nat := .node node5046 node5505 +def node5507 : Tree Nat := .node node5504 node5506 +def node5508 : Tree Nat := .node node5390 node2460 +def node5509 : Tree Nat := .node node4574 node5508 +def node5510 : Tree Nat := .node node5509 node5052 +def node5511 : Tree Nat := .node node5507 node5510 +def node5512 : Tree Nat := .leaf 448 +def node5513 : Tree Nat := .node node1908 node5512 +def node5514 : Tree Nat := .node node4932 node5513 +def node5515 : Tree Nat := .node node4104 node5514 +def node5516 : Tree Nat := .node node5355 node1 +def node5517 : Tree Nat := .node node5400 node5516 +def node5518 : Tree Nat := .node node5058 node5517 +def node5519 : Tree Nat := .node node5515 node5518 +def node5520 : Tree Nat := .node node5405 node5033 +def node5521 : Tree Nat := .node node4587 node5520 +def node5522 : Tree Nat := .node node2756 node5374 +def node5523 : Tree Nat := .node node4940 node5522 +def node5524 : Tree Nat := .node node5523 node4589 +def node5525 : Tree Nat := .node node5521 node5524 +def node5526 : Tree Nat := .node node5519 node5525 +def node5527 : Tree Nat := .node node5511 node5526 +def node5528 : Tree Nat := .node node5501 node5527 +def node5529 : Tree Nat := .node node5416 node5404 +def node5530 : Tree Nat := .node node4949 node5529 +def node5531 : Tree Nat := .node node4122 node5530 +def node5532 : Tree Nat := .node node5422 node3617 +def node5533 : Tree Nat := .node node4596 node5532 +def node5534 : Tree Nat := .node node5531 node5533 +def node5535 : Tree Nat := .node node5534 node5078 +def node5536 : Tree Nat := .node node3597 node5369 +def node5537 : Tree Nat := .node node4966 node5536 +def node5538 : Tree Nat := .node node4138 node5537 +def node5539 : Tree Nat := .node node5433 node3226 +def node5540 : Tree Nat := .node node5084 node5539 +def node5541 : Tree Nat := .node node5538 node5540 +def node5542 : Tree Nat := .node node5440 node3310 +def node5543 : Tree Nat := .node node4616 node5542 +def node5544 : Tree Nat := .node node5087 node5389 +def node5545 : Tree Nat := .node node4618 node5544 +def node5546 : Tree Nat := .node node5545 node4147 +def node5547 : Tree Nat := .node node5543 node5546 +def node5548 : Tree Nat := .node node5541 node5547 +def node5549 : Tree Nat := .node node5535 node5548 +def node5550 : Tree Nat := .node node3581 node5484 +def node5551 : Tree Nat := .node node4981 node5550 +def node5552 : Tree Nat := .node node4153 node5551 +def node5553 : Tree Nat := .node node5454 node3588 +def node5554 : Tree Nat := .node node5098 node5553 +def node5555 : Tree Nat := .node node5552 node5554 +def node5556 : Tree Nat := .node node5458 node4631 +def node5557 : Tree Nat := .node node4630 node5556 +def node5558 : Tree Nat := .node node5557 node5103 +def node5559 : Tree Nat := .node node5555 node5558 +def node5560 : Tree Nat := .node node5469 node3334 +def node5561 : Tree Nat := .node node4648 node5560 +def node5562 : Tree Nat := .leaf 424 +def node5563 : Tree Nat := .node node5087 node5562 +def node5564 : Tree Nat := .node node5006 node5563 +def node5565 : Tree Nat := .node node5564 node4650 +def node5566 : Tree Nat := .node node5561 node5565 +def node5567 : Tree Nat := .node node5111 node5566 +def node5568 : Tree Nat := .node node5559 node5567 +def node5569 : Tree Nat := .node node5549 node5568 +def node5570 : Tree Nat := .node node5528 node5569 +def node5571 : Tree Nat := .node node5479 node5570 +def node5572 : Tree Nat := .node node3627 node5434 +def node5573 : Tree Nat := .node node5121 node5572 +def node5574 : Tree Nat := .node node4185 node5573 +def node5575 : Tree Nat := .node node1 node5450 +def node5576 : Tree Nat := .node node5365 node340 +def node5577 : Tree Nat := .node node5575 node5576 +def node5578 : Tree Nat := .node node4661 node5577 +def node5579 : Tree Nat := .node node5574 node5578 +def node5580 : Tree Nat := .node node1 node5443 +def node5581 : Tree Nat := .node node5580 node2541 +def node5582 : Tree Nat := .node node4666 node5581 +def node5583 : Tree Nat := .node node5582 node5129 +def node5584 : Tree Nat := .node node5579 node5583 +def node5585 : Tree Nat := .leaf 441 +def node5586 : Tree Nat := .node node1981 node5585 +def node5587 : Tree Nat := .node node5132 node5586 +def node5588 : Tree Nat := .node node4196 node5587 +def node5589 : Tree Nat := .node node1 node5512 +def node5590 : Tree Nat := .node node5480 node195 +def node5591 : Tree Nat := .node node5589 node5590 +def node5592 : Tree Nat := .node node5136 node5591 +def node5593 : Tree Nat := .node node5588 node5592 +def node5594 : Tree Nat := .node node1 node5562 +def node5595 : Tree Nat := .node node5594 node5139 +def node5596 : Tree Nat := .node node4679 node5595 +def node5597 : Tree Nat := .node node5596 node5145 +def node5598 : Tree Nat := .node node5593 node5597 +def node5599 : Tree Nat := .node node5584 node5598 +def node5600 : Tree Nat := .node node3768 node5359 +def node5601 : Tree Nat := .node node5150 node5600 +def node5602 : Tree Nat := .node node4212 node5601 +def node5603 : Tree Nat := .leaf 443 +def node5604 : Tree Nat := .node node1 node5603 +def node5605 : Tree Nat := .node node5365 node1 +def node5606 : Tree Nat := .node node5604 node5605 +def node5607 : Tree Nat := .node node5155 node5606 +def node5608 : Tree Nat := .node node5602 node5607 +def node5609 : Tree Nat := .leaf 419 +def node5610 : Tree Nat := .node node1 node5609 +def node5611 : Tree Nat := .node node5610 node2565 +def node5612 : Tree Nat := .node node5159 node5611 +def node5613 : Tree Nat := .node node5612 node5165 +def node5614 : Tree Nat := .node node5608 node5613 +def node5615 : Tree Nat := .node node3700 node5395 +def node5616 : Tree Nat := .node node5169 node5615 +def node5617 : Tree Nat := .node node4223 node5616 +def node5618 : Tree Nat := .node node5480 node1 +def node5619 : Tree Nat := .node node3787 node5618 +def node5620 : Tree Nat := .node node5173 node5619 +def node5621 : Tree Nat := .node node5617 node5620 +def node5622 : Tree Nat := .leaf 433 +def node5623 : Tree Nat := .node node1 node5622 +def node5624 : Tree Nat := .node node5623 node5176 +def node5625 : Tree Nat := .node node4707 node5624 +def node5626 : Tree Nat := .leaf 421 +def node5627 : Tree Nat := .node node2982 node5626 +def node5628 : Tree Nat := .node node5180 node5627 +def node5629 : Tree Nat := .node node5628 node4231 +def node5630 : Tree Nat := .node node5625 node5629 +def node5631 : Tree Nat := .node node5621 node5630 +def node5632 : Tree Nat := .node node5614 node5631 +def node5633 : Tree Nat := .node node5599 node5632 +def node5634 : Tree Nat := .leaf 431 +def node5635 : Tree Nat := .node node3768 node5634 +def node5636 : Tree Nat := .node node5121 node5635 +def node5637 : Tree Nat := .node node4238 node5636 +def node5638 : Tree Nat := .node node5575 node3774 +def node5639 : Tree Nat := .node node4715 node5638 +def node5640 : Tree Nat := .node node5637 node5639 +def node5641 : Tree Nat := .node node5580 node4721 +def node5642 : Tree Nat := .node node4720 node5641 +def node5643 : Tree Nat := .node node5642 node5193 +def node5644 : Tree Nat := .node node5640 node5643 +def node5645 : Tree Nat := .leaf 445 +def node5646 : Tree Nat := .node node2156 node5645 +def node5647 : Tree Nat := .node node5132 node5646 +def node5648 : Tree Nat := .node node4251 node5647 +def node5649 : Tree Nat := .node node5589 node3373 +def node5650 : Tree Nat := .node node5199 node5649 +def node5651 : Tree Nat := .node node5648 node5650 +def node5652 : Tree Nat := .node node5594 node3396 +def node5653 : Tree Nat := .node node4734 node5652 +def node5654 : Tree Nat := .leaf 417 +def node5655 : Tree Nat := .node node5082 node5654 +def node5656 : Tree Nat := .node node5202 node5655 +def node5657 : Tree Nat := .node node5656 node4736 +def node5658 : Tree Nat := .node node5653 node5657 +def node5659 : Tree Nat := .node node5651 node5658 +def node5660 : Tree Nat := .node node5644 node5659 +def node5661 : Tree Nat := .leaf 437 +def node5662 : Tree Nat := .node node3627 node5661 +def node5663 : Tree Nat := .node node5210 node5662 +def node5664 : Tree Nat := .node node4268 node5663 +def node5665 : Tree Nat := .node node1 node5645 +def node5666 : Tree Nat := .node node5665 node3818 +def node5667 : Tree Nat := .node node5214 node5666 +def node5668 : Tree Nat := .node node5664 node5667 +def node5669 : Tree Nat := .node node1 node5626 +def node5670 : Tree Nat := .node node5669 node4749 +def node5671 : Tree Nat := .node node5218 node5670 +def node5672 : Tree Nat := .node node5671 node5222 +def node5673 : Tree Nat := .node node5668 node5672 +def node5674 : Tree Nat := .node node3700 node5416 +def node5675 : Tree Nat := .node node5225 node5674 +def node5676 : Tree Nat := .node node4759 node5675 +def node5677 : Tree Nat := .node node5676 node5231 +def node5678 : Tree Nat := .node node1 node5634 +def node5679 : Tree Nat := .node node5678 node3417 +def node5680 : Tree Nat := .node node4767 node5679 +def node5681 : Tree Nat := .node node5082 node5439 +def node5682 : Tree Nat := .node node5234 node5681 +def node5683 : Tree Nat := .node node5682 node4290 +def node5684 : Tree Nat := .node node5680 node5683 +def node5685 : Tree Nat := .node node5677 node5684 +def node5686 : Tree Nat := .node node5673 node5685 +def node5687 : Tree Nat := .node node5660 node5686 +def node5688 : Tree Nat := .node node5633 node5687 +def node5689 : Tree Nat := .leaf 429 +def node5690 : Tree Nat := .node node3733 node5689 +def node5691 : Tree Nat := .node node5243 node5690 +def node5692 : Tree Nat := .node node4299 node5691 +def node5693 : Tree Nat := .node node1 node5661 +def node5694 : Tree Nat := .node node5693 node3844 +def node5695 : Tree Nat := .node node4776 node5694 +def node5696 : Tree Nat := .node node5692 node5695 +def node5697 : Tree Nat := .node node1 node5654 +def node5698 : Tree Nat := .node node5697 node4781 +def node5699 : Tree Nat := .node node4780 node5698 +def node5700 : Tree Nat := .node node5699 node5249 +def node5701 : Tree Nat := .node node5696 node5700 +def node5702 : Tree Nat := .node node2088 node5603 +def node5703 : Tree Nat := .node node5253 node5702 +def node5704 : Tree Nat := .node node4313 node5703 +def node5705 : Tree Nat := .leaf 449 +def node5706 : Tree Nat := .node node1 node5705 +def node5707 : Tree Nat := .node node5706 node3436 +def node5708 : Tree Nat := .node node5257 node5707 +def node5709 : Tree Nat := .node node5704 node5708 +def node5710 : Tree Nat := .leaf 425 +def node5711 : Tree Nat := .node node1 node5710 +def node5712 : Tree Nat := .node node5711 node3440 +def node5713 : Tree Nat := .node node4795 node5712 +def node5714 : Tree Nat := .leaf 415 +def node5715 : Tree Nat := .node node5262 node5714 +def node5716 : Tree Nat := .node node5261 node5715 +def node5717 : Tree Nat := .node node5716 node4799 +def node5718 : Tree Nat := .node node5713 node5717 +def node5719 : Tree Nat := .node node5709 node5718 +def node5720 : Tree Nat := .node node5701 node5719 +def node5721 : Tree Nat := .node node3859 node5421 +def node5722 : Tree Nat := .node node5150 node5721 +def node5723 : Tree Nat := .node node4330 node5722 +def node5724 : Tree Nat := .node node5604 node3865 +def node5725 : Tree Nat := .node node5272 node5724 +def node5726 : Tree Nat := .node node5723 node5725 +def node5727 : Tree Nat := .node node5610 node4810 +def node5728 : Tree Nat := .node node5276 node5727 +def node5729 : Tree Nat := .node node5728 node5280 +def node5730 : Tree Nat := .node node5726 node5729 +def node5731 : Tree Nat := .node node3874 node5705 +def node5732 : Tree Nat := .node node5169 node5731 +def node5733 : Tree Nat := .node node4342 node5732 +def node5734 : Tree Nat := .node node5733 node5287 +def node5735 : Tree Nat := .node node5623 node3469 +def node5736 : Tree Nat := .node node4825 node5735 +def node5737 : Tree Nat := .node node5262 node5374 +def node5738 : Tree Nat := .node node5180 node5737 +def node5739 : Tree Nat := .node node5738 node4350 +def node5740 : Tree Nat := .node node5736 node5739 +def node5741 : Tree Nat := .node node5734 node5740 +def node5742 : Tree Nat := .node node5730 node5741 +def node5743 : Tree Nat := .node node5720 node5742 +def node5744 : Tree Nat := .node node3859 node5622 +def node5745 : Tree Nat := .node node5243 node5744 +def node5746 : Tree Nat := .node node4357 node5745 +def node5747 : Tree Nat := .node node5585 node1 +def node5748 : Tree Nat := .node node5693 node5747 +def node5749 : Tree Nat := .node node5299 node5748 +def node5750 : Tree Nat := .node node5746 node5749 +def node5751 : Tree Nat := .node node5697 node2665 +def node5752 : Tree Nat := .node node4836 node5751 +def node5753 : Tree Nat := .node node5714 node1 +def node5754 : Tree Nat := .node node3897 node5753 +def node5755 : Tree Nat := .node node5303 node5754 +def node5756 : Tree Nat := .node node5752 node5755 +def node5757 : Tree Nat := .node node5750 node5756 +def node5758 : Tree Nat := .node node2251 node5369 +def node5759 : Tree Nat := .node node5253 node5758 +def node5760 : Tree Nat := .node node4367 node5759 +def node5761 : Tree Nat := .node node5689 node1 +def node5762 : Tree Nat := .node node5706 node5761 +def node5763 : Tree Nat := .node node5310 node5762 +def node5764 : Tree Nat := .node node5760 node5763 +def node5765 : Tree Nat := .node node5711 node5313 +def node5766 : Tree Nat := .node node4848 node5765 +def node5767 : Tree Nat := .node node3071 node5609 +def node5768 : Tree Nat := .node node5316 node5767 +def node5769 : Tree Nat := .node node5768 node4850 +def node5770 : Tree Nat := .node node5766 node5769 +def node5771 : Tree Nat := .node node5764 node5770 +def node5772 : Tree Nat := .node node5757 node5771 +def node5773 : Tree Nat := .node node3733 node5423 +def node5774 : Tree Nat := .node node5210 node5773 +def node5775 : Tree Nat := .node node4383 node5774 +def node5776 : Tree Nat := .node node5665 node5747 +def node5777 : Tree Nat := .node node5325 node5776 +def node5778 : Tree Nat := .node node5775 node5777 +def node5779 : Tree Nat := .node node5669 node2716 +def node5780 : Tree Nat := .node node5329 node5779 +def node5781 : Tree Nat := .node node3726 node5753 +def node5782 : Tree Nat := .node node5332 node5781 +def node5783 : Tree Nat := .node node5780 node5782 +def node5784 : Tree Nat := .node node5778 node5783 +def node5785 : Tree Nat := .node node3922 node5761 +def node5786 : Tree Nat := .node node5339 node5785 +def node5787 : Tree Nat := .node node5337 node5786 +def node5788 : Tree Nat := .node node5678 node5342 +def node5789 : Tree Nat := .node node4876 node5788 +def node5790 : Tree Nat := .node node2924 node5710 +def node5791 : Tree Nat := .node node5234 node5790 +def node5792 : Tree Nat := .node node5791 node4400 +def node5793 : Tree Nat := .node node5789 node5792 +def node5794 : Tree Nat := .node node5787 node5793 +def node5795 : Tree Nat := .node node5784 node5794 +def node5796 : Tree Nat := .node node5772 node5795 +def node5797 : Tree Nat := .node node5743 node5796 +def node5798 : Tree Nat := .node node5688 node5797 +def node5799 : Tree Nat := .node node5571 node5798 +def node5800 : Tree Nat := .node node451 node451 +def node5801 : Tree Nat := .node node5800 node3937 +def node5802 : Tree Nat := .leaf 466 +def node5803 : Tree Nat := .node node1 node5802 +def node5804 : Tree Nat := .node node5803 node5356 +def node5805 : Tree Nat := .node node5801 node5804 +def node5806 : Tree Nat := .node node7 node411 +def node5807 : Tree Nat := .node node5806 node4410 +def node5808 : Tree Nat := .node node5807 node5361 +def node5809 : Tree Nat := .node node5805 node5808 +def node5810 : Tree Nat := .node node13 node322 +def node5811 : Tree Nat := .node node5810 node4416 +def node5812 : Tree Nat := .leaf 454 +def node5813 : Tree Nat := .node node4418 node5812 +def node5814 : Tree Nat := .node node4891 node5813 +def node5815 : Tree Nat := .node node5811 node5814 +def node5816 : Tree Nat := .node node17 node224 +def node5817 : Tree Nat := .node node5816 node4895 +def node5818 : Tree Nat := .node node5817 node3534 +def node5819 : Tree Nat := .node node5815 node5818 +def node5820 : Tree Nat := .node node5809 node5819 +def node5821 : Tree Nat := .leaf 459 +def node5822 : Tree Nat := .node node23 node5821 +def node5823 : Tree Nat := .node node5802 node3952 +def node5824 : Tree Nat := .node node5822 node5823 +def node5825 : Tree Nat := .node node5824 node5367 +def node5826 : Tree Nat := .leaf 463 +def node5827 : Tree Nat := .node node29 node5826 +def node5828 : Tree Nat := .node node5827 node4904 +def node5829 : Tree Nat := .node node5828 node5371 +def node5830 : Tree Nat := .node node5825 node5829 +def node5831 : Tree Nat := .leaf 461 +def node5832 : Tree Nat := .node node34 node5831 +def node5833 : Tree Nat := .node node5832 node4436 +def node5834 : Tree Nat := .node node5833 node5376 +def node5835 : Tree Nat := .leaf 465 +def node5836 : Tree Nat := .node node38 node5835 +def node5837 : Tree Nat := .node node5836 node4910 +def node5838 : Tree Nat := .node node5821 node3963 +def node5839 : Tree Nat := .node node5838 node2760 +def node5840 : Tree Nat := .node node5837 node5839 +def node5841 : Tree Nat := .node node5834 node5840 +def node5842 : Tree Nat := .node node5830 node5841 +def node5843 : Tree Nat := .node node5820 node5842 +def node5844 : Tree Nat := .node node5831 node3970 +def node5845 : Tree Nat := .node node3553 node5844 +def node5846 : Tree Nat := .node node5845 node5382 +def node5847 : Tree Nat := .node node5846 node5387 +def node5848 : Tree Nat := .node node5847 node5393 +def node5849 : Tree Nat := .node node5835 node3984 +def node5850 : Tree Nat := .node node5849 node4471 +def node5851 : Tree Nat := .node node5410 node5850 +def node5852 : Tree Nat := .node node5407 node5851 +def node5853 : Tree Nat := .node node5403 node5852 +def node5854 : Tree Nat := .node node5848 node5853 +def node5855 : Tree Nat := .node node5843 node5854 +def node5856 : Tree Nat := .node node5821 node451 +def node5857 : Tree Nat := .node node5856 node4006 +def node5858 : Tree Nat := .node node5803 node5418 +def node5859 : Tree Nat := .node node5857 node5858 +def node5860 : Tree Nat := .node node93 node411 +def node5861 : Tree Nat := .node node5860 node4479 +def node5862 : Tree Nat := .node node5861 node5425 +def node5863 : Tree Nat := .node node5859 node5862 +def node5864 : Tree Nat := .node node98 node322 +def node5865 : Tree Nat := .node node5864 node4485 +def node5866 : Tree Nat := .node node5865 node4955 +def node5867 : Tree Nat := .node node102 node224 +def node5868 : Tree Nat := .node node5867 node4958 +def node5869 : Tree Nat := .node node5868 node4962 +def node5870 : Tree Nat := .node node5866 node5869 +def node5871 : Tree Nat := .node node5863 node5870 +def node5872 : Tree Nat := .node node108 node5821 +def node5873 : Tree Nat := .node node5831 node3994 +def node5874 : Tree Nat := .node node5872 node5873 +def node5875 : Tree Nat := .node node5874 node5431 +def node5876 : Tree Nat := .node node112 node5826 +def node5877 : Tree Nat := .node node5876 node4969 +def node5878 : Tree Nat := .node node5877 node5436 +def node5879 : Tree Nat := .node node5875 node5878 +def node5880 : Tree Nat := .node node119 node5831 +def node5881 : Tree Nat := .node node5880 node4500 +def node5882 : Tree Nat := .node node5881 node5441 +def node5883 : Tree Nat := .node node123 node5835 +def node5884 : Tree Nat := .node node5883 node5444 +def node5885 : Tree Nat := .node node5826 node4029 +def node5886 : Tree Nat := .node node5885 node2812 +def node5887 : Tree Nat := .node node5884 node5886 +def node5888 : Tree Nat := .node node5882 node5887 +def node5889 : Tree Nat := .node node5879 node5888 +def node5890 : Tree Nat := .node node5871 node5889 +def node5891 : Tree Nat := .node node5835 node4424 +def node5892 : Tree Nat := .node node4047 node5891 +def node5893 : Tree Nat := .node node5892 node5464 +def node5894 : Tree Nat := .leaf 456 +def node5895 : Tree Nat := .node node1 node5894 +def node5896 : Tree Nat := .node node5895 node5435 +def node5897 : Tree Nat := .node node4999 node5896 +def node5898 : Tree Nat := .node node5893 node5897 +def node5899 : Tree Nat := .node node451 node3946 +def node5900 : Tree Nat := .node node5899 node4535 +def node5901 : Tree Nat := .node node5473 node5900 +def node5902 : Tree Nat := .node node5471 node5901 +def node5903 : Tree Nat := .node node5898 node5902 +def node5904 : Tree Nat := .node node5462 node5903 +def node5905 : Tree Nat := .node node5890 node5904 +def node5906 : Tree Nat := .node node5855 node5905 +def node5907 : Tree Nat := .node node5831 node3521 +def node5908 : Tree Nat := .node node451 node4067 +def node5909 : Tree Nat := .node node5907 node5908 +def node5910 : Tree Nat := .node node5909 node5482 +def node5911 : Tree Nat := .node node5910 node5487 +def node5912 : Tree Nat := .node node2344 node5894 +def node5913 : Tree Nat := .node node4891 node5912 +def node5914 : Tree Nat := .node node4548 node5913 +def node5915 : Tree Nat := .node node5914 node5024 +def node5916 : Tree Nat := .node node5911 node5915 +def node5917 : Tree Nat := .node node5831 node3989 +def node5918 : Tree Nat := .node node5917 node2784 +def node5919 : Tree Nat := .node node5038 node5918 +def node5920 : Tree Nat := .node node5498 node5919 +def node5921 : Tree Nat := .node node5496 node5920 +def node5922 : Tree Nat := .node node5916 node5921 +def node5923 : Tree Nat := .node node5835 node3957 +def node5924 : Tree Nat := .node node3663 node5923 +def node5925 : Tree Nat := .node node5924 node5503 +def node5926 : Tree Nat := .node node5925 node5506 +def node5927 : Tree Nat := .node node5926 node5510 +def node5928 : Tree Nat := .node node411 node4009 +def node5929 : Tree Nat := .node node4102 node5928 +def node5930 : Tree Nat := .node node5929 node5514 +def node5931 : Tree Nat := .node node5930 node5518 +def node5932 : Tree Nat := .node node5931 node5525 +def node5933 : Tree Nat := .node node5927 node5932 +def node5934 : Tree Nat := .node node5922 node5933 +def node5935 : Tree Nat := .node node322 node451 +def node5936 : Tree Nat := .node node5935 node4121 +def node5937 : Tree Nat := .node node5803 node5529 +def node5938 : Tree Nat := .node node5936 node5937 +def node5939 : Tree Nat := .node node2061 node411 +def node5940 : Tree Nat := .node node5939 node4595 +def node5941 : Tree Nat := .node node5940 node5532 +def node5942 : Tree Nat := .node node5938 node5941 +def node5943 : Tree Nat := .node node2070 node322 +def node5944 : Tree Nat := .node node5835 node4430 +def node5945 : Tree Nat := .node node5943 node5944 +def node5946 : Tree Nat := .node node5826 node1 +def node5947 : Tree Nat := .node node4954 node5946 +def node5948 : Tree Nat := .node node5945 node5947 +def node5949 : Tree Nat := .node node3294 node224 +def node5950 : Tree Nat := .node node5949 node5075 +def node5951 : Tree Nat := .node node5950 node3702 +def node5952 : Tree Nat := .node node5948 node5951 +def node5953 : Tree Nat := .node node5942 node5952 +def node5954 : Tree Nat := .node node2490 node5821 +def node5955 : Tree Nat := .node node5802 node4136 +def node5956 : Tree Nat := .node node5954 node5955 +def node5957 : Tree Nat := .node node451 node5369 +def node5958 : Tree Nat := .node node4966 node5957 +def node5959 : Tree Nat := .node node5956 node5958 +def node5960 : Tree Nat := .node node3301 node5826 +def node5961 : Tree Nat := .node node5960 node5083 +def node5962 : Tree Nat := .node node5961 node5539 +def node5963 : Tree Nat := .node node5959 node5962 +def node5964 : Tree Nat := .node node2896 node5831 +def node5965 : Tree Nat := .node node5831 node4488 +def node5966 : Tree Nat := .node node5964 node5965 +def node5967 : Tree Nat := .node node5966 node5542 +def node5968 : Tree Nat := .node node2904 node5835 +def node5969 : Tree Nat := .node node5802 node5389 +def node5970 : Tree Nat := .node node5968 node5969 +def node5971 : Tree Nat := .node node5821 node4046 +def node5972 : Tree Nat := .node node5971 node2839 +def node5973 : Tree Nat := .node node5970 node5972 +def node5974 : Tree Nat := .node node5967 node5973 +def node5975 : Tree Nat := .node node5963 node5974 +def node5976 : Tree Nat := .node node5953 node5975 +def node5977 : Tree Nat := .node node411 node3959 +def node5978 : Tree Nat := .node node3716 node5977 +def node5979 : Tree Nat := .node node5978 node5551 +def node5980 : Tree Nat := .node node5979 node5554 +def node5981 : Tree Nat := .node node5980 node5558 +def node5982 : Tree Nat := .node node1965 node5399 +def node5983 : Tree Nat := .node node4994 node5982 +def node5984 : Tree Nat := .node node4641 node5983 +def node5985 : Tree Nat := .node node5895 node3198 +def node5986 : Tree Nat := .node node5109 node5985 +def node5987 : Tree Nat := .node node5984 node5986 +def node5988 : Tree Nat := .node node5835 node4014 +def node5989 : Tree Nat := .node node5988 node4535 +def node5990 : Tree Nat := .node node5564 node5989 +def node5991 : Tree Nat := .node node5561 node5990 +def node5992 : Tree Nat := .node node5987 node5991 +def node5993 : Tree Nat := .node node5981 node5992 +def node5994 : Tree Nat := .node node5976 node5993 +def node5995 : Tree Nat := .node node5934 node5994 +def node5996 : Tree Nat := .node node5906 node5995 +def node5997 : Tree Nat := .node node451 node3621 +def node5998 : Tree Nat := .node node5997 node4184 +def node5999 : Tree Nat := .node node5998 node5573 +def node6000 : Tree Nat := .node node5999 node5578 +def node6001 : Tree Nat := .leaf 455 +def node6002 : Tree Nat := .node node2409 node6001 +def node6003 : Tree Nat := .node node5580 node6002 +def node6004 : Tree Nat := .node node4666 node6003 +def node6005 : Tree Nat := .node node6004 node5129 +def node6006 : Tree Nat := .node node6000 node6005 +def node6007 : Tree Nat := .node node322 node3963 +def node6008 : Tree Nat := .node node6007 node4681 +def node6009 : Tree Nat := .node node5144 node6008 +def node6010 : Tree Nat := .node node5596 node6009 +def node6011 : Tree Nat := .node node5593 node6010 +def node6012 : Tree Nat := .node node6006 node6011 +def node6013 : Tree Nat := .node node5826 node4210 +def node6014 : Tree Nat := .node node3766 node6013 +def node6015 : Tree Nat := .node node5812 node5359 +def node6016 : Tree Nat := .node node5150 node6015 +def node6017 : Tree Nat := .node node6014 node6016 +def node6018 : Tree Nat := .node node6017 node5607 +def node6019 : Tree Nat := .node node6018 node5613 +def node6020 : Tree Nat := .leaf 453 +def node6021 : Tree Nat := .node node1 node6020 +def node6022 : Tree Nat := .node node6021 node5618 +def node6023 : Tree Nat := .node node5173 node6022 +def node6024 : Tree Nat := .node node5617 node6023 +def node6025 : Tree Nat := .node node5802 node4221 +def node6026 : Tree Nat := .node node6025 node2986 +def node6027 : Tree Nat := .node node5628 node6026 +def node6028 : Tree Nat := .node node5625 node6027 +def node6029 : Tree Nat := .node node6024 node6028 +def node6030 : Tree Nat := .node node6019 node6029 +def node6031 : Tree Nat := .node node6012 node6030 +def node6032 : Tree Nat := .node node5821 node3621 +def node6033 : Tree Nat := .node node6032 node4237 +def node6034 : Tree Nat := .node node6033 node5636 +def node6035 : Tree Nat := .node node6034 node5639 +def node6036 : Tree Nat := .node node6035 node5643 +def node6037 : Tree Nat := .node node439 node5821 +def node6038 : Tree Nat := .node node224 node4226 +def node6039 : Tree Nat := .node node6037 node6038 +def node6040 : Tree Nat := .node node6039 node5647 +def node6041 : Tree Nat := .node node6040 node5650 +def node6042 : Tree Nat := .node node224 node4261 +def node6043 : Tree Nat := .node node6042 node4681 +def node6044 : Tree Nat := .node node5656 node6043 +def node6045 : Tree Nat := .node node5653 node6044 +def node6046 : Tree Nat := .node node6041 node6045 +def node6047 : Tree Nat := .node node6036 node6046 +def node6048 : Tree Nat := .node node5812 node5661 +def node6049 : Tree Nat := .node node5210 node6048 +def node6050 : Tree Nat := .node node4268 node6049 +def node6051 : Tree Nat := .node node6050 node5667 +def node6052 : Tree Nat := .node node6051 node5672 +def node6053 : Tree Nat := .leaf 457 +def node6054 : Tree Nat := .node node1 node6053 +def node6055 : Tree Nat := .node node6054 node3412 +def node6056 : Tree Nat := .node node5230 node6055 +def node6057 : Tree Nat := .node node5676 node6056 +def node6058 : Tree Nat := .node node411 node3946 +def node6059 : Tree Nat := .node node6058 node2962 +def node6060 : Tree Nat := .node node5682 node6059 +def node6061 : Tree Nat := .node node5680 node6060 +def node6062 : Tree Nat := .node node6057 node6061 +def node6063 : Tree Nat := .node node6052 node6062 +def node6064 : Tree Nat := .node node6047 node6063 +def node6065 : Tree Nat := .node node6031 node6064 +def node6066 : Tree Nat := .node node5826 node3822 +def node6067 : Tree Nat := .node node224 node4297 +def node6068 : Tree Nat := .node node6066 node6067 +def node6069 : Tree Nat := .node node6068 node5691 +def node6070 : Tree Nat := .node node6069 node5695 +def node6071 : Tree Nat := .node node4746 node6053 +def node6072 : Tree Nat := .node node5697 node6071 +def node6073 : Tree Nat := .node node4780 node6072 +def node6074 : Tree Nat := .node node6073 node5249 +def node6075 : Tree Nat := .node node6070 node6074 +def node6076 : Tree Nat := .node node411 node4050 +def node6077 : Tree Nat := .node node6076 node4798 +def node6078 : Tree Nat := .node node5716 node6077 +def node6079 : Tree Nat := .node node5713 node6078 +def node6080 : Tree Nat := .node node5709 node6079 +def node6081 : Tree Nat := .node node6075 node6080 +def node6082 : Tree Nat := .node node2754 node451 +def node6083 : Tree Nat := .node node6082 node4093 +def node6084 : Tree Nat := .node node6001 node5421 +def node6085 : Tree Nat := .node node5803 node6084 +def node6086 : Tree Nat := .node node6083 node6085 +def node6087 : Tree Nat := .node node6086 node5725 +def node6088 : Tree Nat := .node node5835 node4601 +def node6089 : Tree Nat := .node node4336 node6088 +def node6090 : Tree Nat := .node node5610 node5946 +def node6091 : Tree Nat := .node node6089 node6090 +def node6092 : Tree Nat := .node node6091 node5280 +def node6093 : Tree Nat := .node node6087 node6092 +def node6094 : Tree Nat := .node node5826 node4009 +def node6095 : Tree Nat := .node node4341 node6094 +def node6096 : Tree Nat := .node node451 node5705 +def node6097 : Tree Nat := .node node5169 node6096 +def node6098 : Tree Nat := .node node6095 node6097 +def node6099 : Tree Nat := .node node3128 node5826 +def node6100 : Tree Nat := .node node6099 node5285 +def node6101 : Tree Nat := .node node6021 node3463 +def node6102 : Tree Nat := .node node6100 node6101 +def node6103 : Tree Nat := .node node6098 node6102 +def node6104 : Tree Nat := .node node3545 node5831 +def node6105 : Tree Nat := .node node5831 node4797 +def node6106 : Tree Nat := .node node6104 node6105 +def node6107 : Tree Nat := .node node6106 node5735 +def node6108 : Tree Nat := .node node1 node5835 +def node6109 : Tree Nat := .node node5802 node5374 +def node6110 : Tree Nat := .node node6108 node6109 +def node6111 : Tree Nat := .node node6110 node4350 +def node6112 : Tree Nat := .node node6107 node6111 +def node6113 : Tree Nat := .node node6103 node6112 +def node6114 : Tree Nat := .node node6093 node6113 +def node6115 : Tree Nat := .node node6081 node6114 +def node6116 : Tree Nat := .node node5935 node4356 +def node6117 : Tree Nat := .node node5803 node5744 +def node6118 : Tree Nat := .node node6116 node6117 +def node6119 : Tree Nat := .node node1622 node411 +def node6120 : Tree Nat := .node node6119 node5298 +def node6121 : Tree Nat := .node node6120 node5748 +def node6122 : Tree Nat := .node node6118 node6121 +def node6123 : Tree Nat := .node node1962 node322 +def node6124 : Tree Nat := .node node6123 node4835 +def node6125 : Tree Nat := .node node6124 node5751 +def node6126 : Tree Nat := .node node3202 node224 +def node6127 : Tree Nat := .node node6126 node5302 +def node6128 : Tree Nat := .node node6127 node5754 +def node6129 : Tree Nat := .node node6125 node6128 +def node6130 : Tree Nat := .node node6122 node6129 +def node6131 : Tree Nat := .node node3193 node5826 +def node6132 : Tree Nat := .node node6131 node5309 +def node6133 : Tree Nat := .node node6132 node5762 +def node6134 : Tree Nat := .node node5760 node6133 +def node6135 : Tree Nat := .node node2791 node5831 +def node6136 : Tree Nat := .node node6135 node4847 +def node6137 : Tree Nat := .node node6136 node5765 +def node6138 : Tree Nat := .node node2800 node5835 +def node6139 : Tree Nat := .node node6138 node5767 +def node6140 : Tree Nat := .node node322 node4280 +def node6141 : Tree Nat := .node node6140 node4798 +def node6142 : Tree Nat := .node node6139 node6141 +def node6143 : Tree Nat := .node node6137 node6142 +def node6144 : Tree Nat := .node node6134 node6143 +def node6145 : Tree Nat := .node node6130 node6144 +def node6146 : Tree Nat := .node node224 node4142 +def node6147 : Tree Nat := .node node3907 node6146 +def node6148 : Tree Nat := .node node6001 node5423 +def node6149 : Tree Nat := .node node5210 node6148 +def node6150 : Tree Nat := .node node6147 node6149 +def node6151 : Tree Nat := .node node6150 node5777 +def node6152 : Tree Nat := .node node6151 node5783 +def node6153 : Tree Nat := .node node3874 node6020 +def node6154 : Tree Nat := .node node5225 node6153 +def node6155 : Tree Nat := .node node4869 node6154 +def node6156 : Tree Nat := .node node6054 node5761 +def node6157 : Tree Nat := .node node5339 node6156 +def node6158 : Tree Nat := .node node6155 node6157 +def node6159 : Tree Nat := .node node5802 node4014 +def node6160 : Tree Nat := .node node6159 node3049 +def node6161 : Tree Nat := .node node5791 node6160 +def node6162 : Tree Nat := .node node5789 node6161 +def node6163 : Tree Nat := .node node6158 node6162 +def node6164 : Tree Nat := .node node6152 node6163 +def node6165 : Tree Nat := .node node6145 node6164 +def node6166 : Tree Nat := .node node6115 node6165 +def node6167 : Tree Nat := .node node6065 node6166 +def node6168 : Tree Nat := .node node5996 node6167 +def node6169 : Tree Nat := .leaf 469 +def node6170 : Tree Nat := .node node6169 node3936 +def node6171 : Tree Nat := .node node5800 node6170 +def node6172 : Tree Nat := .node node6171 node5804 +def node6173 : Tree Nat := .node node341 node3529 +def node6174 : Tree Nat := .node node5807 node6173 +def node6175 : Tree Nat := .node node6172 node6174 +def node6176 : Tree Nat := .leaf 468 +def node6177 : Tree Nat := .node node1 node6176 +def node6178 : Tree Nat := .node node6177 node5813 +def node6179 : Tree Nat := .node node5811 node6178 +def node6180 : Tree Nat := .leaf 472 +def node6181 : Tree Nat := .node node1 node6180 +def node6182 : Tree Nat := .node node6181 node3138 +def node6183 : Tree Nat := .node node5817 node6182 +def node6184 : Tree Nat := .node node6179 node6183 +def node6185 : Tree Nat := .node node6175 node6184 +def node6186 : Tree Nat := .leaf 467 +def node6187 : Tree Nat := .node node1 node6186 +def node6188 : Tree Nat := .leaf 476 +def node6189 : Tree Nat := .node node6188 node5365 +def node6190 : Tree Nat := .node node6187 node6189 +def node6191 : Tree Nat := .node node5824 node6190 +def node6192 : Tree Nat := .leaf 484 +def node6193 : Tree Nat := .node node1912 node6192 +def node6194 : Tree Nat := .node node5827 node6193 +def node6195 : Tree Nat := .node node196 node3144 +def node6196 : Tree Nat := .node node6194 node6195 +def node6197 : Tree Nat := .node node6191 node6196 +def node6198 : Tree Nat := .node node1 node6169 +def node6199 : Tree Nat := .node node6198 node3151 +def node6200 : Tree Nat := .node node5833 node6199 +def node6201 : Tree Nat := .leaf 475 +def node6202 : Tree Nat := .node node5821 node6201 +def node6203 : Tree Nat := .node node6202 node2760 +def node6204 : Tree Nat := .node node5837 node6203 +def node6205 : Tree Nat := .node node6200 node6204 +def node6206 : Tree Nat := .node node6197 node6205 +def node6207 : Tree Nat := .node node6185 node6206 +def node6208 : Tree Nat := .leaf 483 +def node6209 : Tree Nat := .node node2770 node6208 +def node6210 : Tree Nat := .node node3979 node6209 +def node6211 : Tree Nat := .node node6210 node5391 +def node6212 : Tree Nat := .node node6211 node4928 +def node6213 : Tree Nat := .node node5847 node6212 +def node6214 : Tree Nat := .node node340 node6188 +def node6215 : Tree Nat := .node node3985 node6214 +def node6216 : Tree Nat := .node node6215 node5397 +def node6217 : Tree Nat := .node node6216 node5402 +def node6218 : Tree Nat := .node node6217 node5852 +def node6219 : Tree Nat := .node node6213 node6218 +def node6220 : Tree Nat := .node node6207 node6219 +def node6221 : Tree Nat := .node node6186 node3978 +def node6222 : Tree Nat := .node node5856 node6221 +def node6223 : Tree Nat := .node node6222 node5858 +def node6224 : Tree Nat := .node node341 node5424 +def node6225 : Tree Nat := .node node5861 node6224 +def node6226 : Tree Nat := .node node6223 node6225 +def node6227 : Tree Nat := .node node6177 node2373 +def node6228 : Tree Nat := .node node5865 node6227 +def node6229 : Tree Nat := .leaf 477 +def node6230 : Tree Nat := .node node1 node6229 +def node6231 : Tree Nat := .node node6230 node4961 +def node6232 : Tree Nat := .node node5868 node6231 +def node6233 : Tree Nat := .node node6228 node6232 +def node6234 : Tree Nat := .node node6226 node6233 +def node6235 : Tree Nat := .leaf 478 +def node6236 : Tree Nat := .node node6235 node5429 +def node6237 : Tree Nat := .node node6187 node6236 +def node6238 : Tree Nat := .node node5874 node6237 +def node6239 : Tree Nat := .node node196 node5435 +def node6240 : Tree Nat := .node node5877 node6239 +def node6241 : Tree Nat := .node node6238 node6240 +def node6242 : Tree Nat := .leaf 480 +def node6243 : Tree Nat := .node node2387 node6242 +def node6244 : Tree Nat := .node node5880 node6243 +def node6245 : Tree Nat := .node node6198 node4974 +def node6246 : Tree Nat := .node node6244 node6245 +def node6247 : Tree Nat := .node node6246 node5887 +def node6248 : Tree Nat := .node node6241 node6247 +def node6249 : Tree Nat := .node node6234 node6248 +def node6250 : Tree Nat := .node node130 node6192 +def node6251 : Tree Nat := .leaf 479 +def node6252 : Tree Nat := .node node6169 node6251 +def node6253 : Tree Nat := .node node6250 node6252 +def node6254 : Tree Nat := .node node6253 node5452 +def node6255 : Tree Nat := .node node340 node1 +def node6256 : Tree Nat := .node node5454 node6255 +def node6257 : Tree Nat := .node node4985 node6256 +def node6258 : Tree Nat := .node node6254 node6257 +def node6259 : Tree Nat := .node node6176 node1 +def node6260 : Tree Nat := .node node3622 node6259 +def node6261 : Tree Nat := .node node4989 node6260 +def node6262 : Tree Nat := .node node5460 node6261 +def node6263 : Tree Nat := .node node6258 node6262 +def node6264 : Tree Nat := .node node6169 node1 +def node6265 : Tree Nat := .node node5895 node6264 +def node6266 : Tree Nat := .node node4999 node6265 +def node6267 : Tree Nat := .node node5893 node6266 +def node6268 : Tree Nat := .node node6186 node322 +def node6269 : Tree Nat := .node node5469 node6268 +def node6270 : Tree Nat := .node node4532 node6269 +def node6271 : Tree Nat := .node node451 node6180 +def node6272 : Tree Nat := .node node6271 node4535 +def node6273 : Tree Nat := .node node5473 node6272 +def node6274 : Tree Nat := .node node6270 node6273 +def node6275 : Tree Nat := .node node6267 node6274 +def node6276 : Tree Nat := .node node6263 node6275 +def node6277 : Tree Nat := .node node6249 node6276 +def node6278 : Tree Nat := .node node6220 node6277 +def node6279 : Tree Nat := .leaf 474 +def node6280 : Tree Nat := .node node6279 node1 +def node6281 : Tree Nat := .node node341 node6280 +def node6282 : Tree Nat := .node node4544 node6281 +def node6283 : Tree Nat := .node node5910 node6282 +def node6284 : Tree Nat := .node node1 node6279 +def node6285 : Tree Nat := .node node6284 node5022 +def node6286 : Tree Nat := .node node5021 node6285 +def node6287 : Tree Nat := .node node5914 node6286 +def node6288 : Tree Nat := .node node6283 node6287 +def node6289 : Tree Nat := .node node6169 node4055 +def node6290 : Tree Nat := .node node3651 node6289 +def node6291 : Tree Nat := .node node6290 node5491 +def node6292 : Tree Nat := .node node6291 node5495 +def node6293 : Tree Nat := .node node6292 node5920 +def node6294 : Tree Nat := .node node6288 node6293 +def node6295 : Tree Nat := .node node5835 node6229 +def node6296 : Tree Nat := .node node3663 node6295 +def node6297 : Tree Nat := .node node6296 node5503 +def node6298 : Tree Nat := .node node6297 node5506 +def node6299 : Tree Nat := .node node6298 node5510 +def node6300 : Tree Nat := .node node411 node6235 +def node6301 : Tree Nat := .node node4102 node6300 +def node6302 : Tree Nat := .node node6301 node5514 +def node6303 : Tree Nat := .node node6302 node5518 +def node6304 : Tree Nat := .node node6186 node4113 +def node6305 : Tree Nat := .node node6304 node4471 +def node6306 : Tree Nat := .node node5523 node6305 +def node6307 : Tree Nat := .node node5521 node6306 +def node6308 : Tree Nat := .node node6303 node6307 +def node6309 : Tree Nat := .node node6299 node6308 +def node6310 : Tree Nat := .node node6294 node6309 +def node6311 : Tree Nat := .node node6169 node4040 +def node6312 : Tree Nat := .node node5935 node6311 +def node6313 : Tree Nat := .leaf 482 +def node6314 : Tree Nat := .node node1 node6313 +def node6315 : Tree Nat := .node node6314 node5529 +def node6316 : Tree Nat := .node node6312 node6315 +def node6317 : Tree Nat := .node node341 node3617 +def node6318 : Tree Nat := .node node5940 node6317 +def node6319 : Tree Nat := .node node6316 node6318 +def node6320 : Tree Nat := .leaf 481 +def node6321 : Tree Nat := .node node5835 node6320 +def node6322 : Tree Nat := .node node5943 node6321 +def node6323 : Tree Nat := .node node1 node6235 +def node6324 : Tree Nat := .node node6323 node5946 +def node6325 : Tree Nat := .node node6322 node6324 +def node6326 : Tree Nat := .node node1 node6320 +def node6327 : Tree Nat := .node node6326 node3216 +def node6328 : Tree Nat := .node node5950 node6327 +def node6329 : Tree Nat := .node node6325 node6328 +def node6330 : Tree Nat := .node node6319 node6329 +def node6331 : Tree Nat := .node node1 node6251 +def node6332 : Tree Nat := .node node6331 node5957 +def node6333 : Tree Nat := .node node5956 node6332 +def node6334 : Tree Nat := .node node196 node3226 +def node6335 : Tree Nat := .node node5961 node6334 +def node6336 : Tree Nat := .node node6333 node6335 +def node6337 : Tree Nat := .node node5831 node6313 +def node6338 : Tree Nat := .node node5964 node6337 +def node6339 : Tree Nat := .node node1 node6201 +def node6340 : Tree Nat := .node node6339 node3310 +def node6341 : Tree Nat := .node node6338 node6340 +def node6342 : Tree Nat := .node node2904 node6208 +def node6343 : Tree Nat := .node node6342 node5969 +def node6344 : Tree Nat := .node node6343 node5972 +def node6345 : Tree Nat := .node node6341 node6344 +def node6346 : Tree Nat := .node node6336 node6345 +def node6347 : Tree Nat := .node node6330 node6346 +def node6348 : Tree Nat := .leaf 473 +def node6349 : Tree Nat := .node node1 node6348 +def node6350 : Tree Nat := .node node6349 node3188 +def node6351 : Tree Nat := .node node5102 node6350 +def node6352 : Tree Nat := .node node5557 node6351 +def node6353 : Tree Nat := .node node5980 node6352 +def node6354 : Tree Nat := .node node340 node4639 +def node6355 : Tree Nat := .node node4164 node6354 +def node6356 : Tree Nat := .node node6355 node5983 +def node6357 : Tree Nat := .node node6356 node5986 +def node6358 : Tree Nat := .node node5835 node6279 +def node6359 : Tree Nat := .node node6358 node4535 +def node6360 : Tree Nat := .node node5564 node6359 +def node6361 : Tree Nat := .node node5561 node6360 +def node6362 : Tree Nat := .node node6357 node6361 +def node6363 : Tree Nat := .node node6353 node6362 +def node6364 : Tree Nat := .node node6347 node6363 +def node6365 : Tree Nat := .node node6310 node6364 +def node6366 : Tree Nat := .node node6278 node6365 +def node6367 : Tree Nat := .node node340 node4125 +def node6368 : Tree Nat := .node node5997 node6367 +def node6369 : Tree Nat := .node node6368 node5573 +def node6370 : Tree Nat := .node node6369 node5578 +def node6371 : Tree Nat := .node node6349 node5127 +def node6372 : Tree Nat := .node node5126 node6371 +def node6373 : Tree Nat := .node node6004 node6372 +def node6374 : Tree Nat := .node node6370 node6373 +def node6375 : Tree Nat := .node node6176 node4194 +def node6376 : Tree Nat := .node node4193 node6375 +def node6377 : Tree Nat := .node node6376 node5587 +def node6378 : Tree Nat := .node node6377 node5592 +def node6379 : Tree Nat := .node node6378 node6010 +def node6380 : Tree Nat := .node node6374 node6379 +def node6381 : Tree Nat := .node node5604 node6255 +def node6382 : Tree Nat := .node node5155 node6381 +def node6383 : Tree Nat := .node node6017 node6382 +def node6384 : Tree Nat := .node node6383 node5613 +def node6385 : Tree Nat := .node node195 node3940 +def node6386 : Tree Nat := .node node4222 node6385 +def node6387 : Tree Nat := .node node6386 node5616 +def node6388 : Tree Nat := .node node6387 node6023 +def node6389 : Tree Nat := .node node6388 node6028 +def node6390 : Tree Nat := .node node6384 node6389 +def node6391 : Tree Nat := .node node6380 node6390 +def node6392 : Tree Nat := .node node6176 node4215 +def node6393 : Tree Nat := .node node6032 node6392 +def node6394 : Tree Nat := .node node5803 node5635 +def node6395 : Tree Nat := .node node6393 node6394 +def node6396 : Tree Nat := .node node6395 node5639 +def node6397 : Tree Nat := .node node6177 node4721 +def node6398 : Tree Nat := .node node4720 node6397 +def node6399 : Tree Nat := .node node6331 node3364 +def node6400 : Tree Nat := .node node5192 node6399 +def node6401 : Tree Nat := .node node6398 node6400 +def node6402 : Tree Nat := .node node6396 node6401 +def node6403 : Tree Nat := .node node6187 node5646 +def node6404 : Tree Nat := .node node6039 node6403 +def node6405 : Tree Nat := .node node6404 node5650 +def node6406 : Tree Nat := .node node6198 node3396 +def node6407 : Tree Nat := .node node4734 node6406 +def node6408 : Tree Nat := .node node455 node5835 +def node6409 : Tree Nat := .node node6408 node5655 +def node6410 : Tree Nat := .node node6409 node6043 +def node6411 : Tree Nat := .node node6407 node6410 +def node6412 : Tree Nat := .node node6405 node6411 +def node6413 : Tree Nat := .node node6402 node6412 +def node6414 : Tree Nat := .node node195 node4025 +def node6415 : Tree Nat := .node node3812 node6414 +def node6416 : Tree Nat := .node node6415 node6049 +def node6417 : Tree Nat := .node node6416 node5667 +def node6418 : Tree Nat := .node node6417 node5672 +def node6419 : Tree Nat := .node node6176 node4490 +def node6420 : Tree Nat := .node node4281 node6419 +def node6421 : Tree Nat := .node node6242 node5416 +def node6422 : Tree Nat := .node node5225 node6421 +def node6423 : Tree Nat := .node node6420 node6422 +def node6424 : Tree Nat := .node node6423 node6056 +def node6425 : Tree Nat := .node node6424 node6061 +def node6426 : Tree Nat := .node node6418 node6425 +def node6427 : Tree Nat := .node node6413 node6426 +def node6428 : Tree Nat := .node node6391 node6427 +def node6429 : Tree Nat := .node node6339 node3429 +def node6430 : Tree Nat := .node node5248 node6429 +def node6431 : Tree Nat := .node node6073 node6430 +def node6432 : Tree Nat := .node node6070 node6431 +def node6433 : Tree Nat := .node node195 node4285 +def node6434 : Tree Nat := .node node4311 node6433 +def node6435 : Tree Nat := .node node6434 node5703 +def node6436 : Tree Nat := .node node6435 node5708 +def node6437 : Tree Nat := .node node6436 node6079 +def node6438 : Tree Nat := .node node6432 node6437 +def node6439 : Tree Nat := .node node6186 node3957 +def node6440 : Tree Nat := .node node6082 node6439 +def node6441 : Tree Nat := .node node6440 node6085 +def node6442 : Tree Nat := .node node341 node3865 +def node6443 : Tree Nat := .node node5272 node6442 +def node6444 : Tree Nat := .node node6441 node6443 +def node6445 : Tree Nat := .node node6320 node4601 +def node6446 : Tree Nat := .node node4336 node6445 +def node6447 : Tree Nat := .node node6177 node5946 +def node6448 : Tree Nat := .node node6446 node6447 +def node6449 : Tree Nat := .node node3133 node6192 +def node6450 : Tree Nat := .node node6449 node5278 +def node6451 : Tree Nat := .node node6450 node3870 +def node6452 : Tree Nat := .node node6448 node6451 +def node6453 : Tree Nat := .node node6444 node6452 +def node6454 : Tree Nat := .node node6187 node6096 +def node6455 : Tree Nat := .node node6095 node6454 +def node6456 : Tree Nat := .node node6455 node6102 +def node6457 : Tree Nat := .node node6198 node3469 +def node6458 : Tree Nat := .node node6106 node6457 +def node6459 : Tree Nat := .node node6242 node5374 +def node6460 : Tree Nat := .node node6108 node6459 +def node6461 : Tree Nat := .node node6176 node4310 +def node6462 : Tree Nat := .node node6461 node3075 +def node6463 : Tree Nat := .node node6460 node6462 +def node6464 : Tree Nat := .node node6458 node6463 +def node6465 : Tree Nat := .node node6456 node6464 +def node6466 : Tree Nat := .node node6453 node6465 +def node6467 : Tree Nat := .node node6438 node6466 +def node6468 : Tree Nat := .node node340 node4274 +def node6469 : Tree Nat := .node node5935 node6468 +def node6470 : Tree Nat := .node node6469 node6117 +def node6471 : Tree Nat := .node node6180 node1 +def node6472 : Tree Nat := .node node341 node6471 +def node6473 : Tree Nat := .node node6120 node6472 +def node6474 : Tree Nat := .node node6470 node6473 +def node6475 : Tree Nat := .node node6177 node2665 +def node6476 : Tree Nat := .node node6124 node6475 +def node6477 : Tree Nat := .node node1 node6208 +def node6478 : Tree Nat := .node node6188 node1 +def node6479 : Tree Nat := .node node6477 node6478 +def node6480 : Tree Nat := .node node6127 node6479 +def node6481 : Tree Nat := .node node6476 node6480 +def node6482 : Tree Nat := .node node6474 node6481 +def node6483 : Tree Nat := .node node6186 node4319 +def node6484 : Tree Nat := .node node4365 node6483 +def node6485 : Tree Nat := .node node6187 node5758 +def node6486 : Tree Nat := .node node6484 node6485 +def node6487 : Tree Nat := .node node6348 node1 +def node6488 : Tree Nat := .node node196 node6487 +def node6489 : Tree Nat := .node node6132 node6488 +def node6490 : Tree Nat := .node node6486 node6489 +def node6491 : Tree Nat := .node node6229 node411 +def node6492 : Tree Nat := .node node6198 node6491 +def node6493 : Tree Nat := .node node6136 node6492 +def node6494 : Tree Nat := .node node6493 node6142 +def node6495 : Tree Nat := .node node6490 node6494 +def node6496 : Tree Nat := .node node6482 node6495 +def node6497 : Tree Nat := .node node1 node6242 +def node6498 : Tree Nat := .node node6497 node6148 +def node6499 : Tree Nat := .node node6147 node6498 +def node6500 : Tree Nat := .node node6181 node5747 +def node6501 : Tree Nat := .node node5325 node6500 +def node6502 : Tree Nat := .node node6499 node6501 +def node6503 : Tree Nat := .node node1 node6188 +def node6504 : Tree Nat := .node node6503 node2716 +def node6505 : Tree Nat := .node node5329 node6504 +def node6506 : Tree Nat := .node node6505 node5782 +def node6507 : Tree Nat := .node node6502 node6506 +def node6508 : Tree Nat := .node node195 node4814 +def node6509 : Tree Nat := .node node4393 node6508 +def node6510 : Tree Nat := .node node6313 node6020 +def node6511 : Tree Nat := .node node6230 node6510 +def node6512 : Tree Nat := .node node6509 node6511 +def node6513 : Tree Nat := .node node6512 node6157 +def node6514 : Tree Nat := .node node6349 node5342 +def node6515 : Tree Nat := .node node4876 node6514 +def node6516 : Tree Nat := .node node6326 node5790 +def node6517 : Tree Nat := .node node6516 node6160 +def node6518 : Tree Nat := .node node6515 node6517 +def node6519 : Tree Nat := .node node6513 node6518 +def node6520 : Tree Nat := .node node6507 node6519 +def node6521 : Tree Nat := .node node6496 node6520 +def node6522 : Tree Nat := .node node6467 node6521 +def node6523 : Tree Nat := .node node6428 node6522 +def node6524 : Tree Nat := .node node6366 node6523 +def node6525 : Tree Nat := .leaf 507 +def node6526 : Tree Nat := .node node6525 node4415 +def node6527 : Tree Nat := .node node5810 node6526 +def node6528 : Tree Nat := .leaf 498 +def node6529 : Tree Nat := .node node6528 node5812 +def node6530 : Tree Nat := .node node6177 node6529 +def node6531 : Tree Nat := .node node6527 node6530 +def node6532 : Tree Nat := .leaf 503 +def node6533 : Tree Nat := .leaf 491 +def node6534 : Tree Nat := .node node6532 node6533 +def node6535 : Tree Nat := .node node5816 node6534 +def node6536 : Tree Nat := .node node6535 node6182 +def node6537 : Tree Nat := .node node6531 node6536 +def node6538 : Tree Nat := .node node6175 node6537 +def node6539 : Tree Nat := .leaf 499 +def node6540 : Tree Nat := .node node6539 node4435 +def node6541 : Tree Nat := .node node5832 node6540 +def node6542 : Tree Nat := .node node6541 node6199 +def node6543 : Tree Nat := .node node6542 node6204 +def node6544 : Tree Nat := .node node6197 node6543 +def node6545 : Tree Nat := .node node6538 node6544 +def node6546 : Tree Nat := .leaf 488 +def node6547 : Tree Nat := .node node46 node6546 +def node6548 : Tree Nat := .node node6547 node5844 +def node6549 : Tree Nat := .leaf 492 +def node6550 : Tree Nat := .node node3555 node6549 +def node6551 : Tree Nat := .node node4917 node6550 +def node6552 : Tree Nat := .node node6548 node6551 +def node6553 : Tree Nat := .node node6552 node5387 +def node6554 : Tree Nat := .leaf 485 +def node6555 : Tree Nat := .node node1 node6554 +def node6556 : Tree Nat := .node node6555 node3161 +def node6557 : Tree Nat := .node node4927 node6556 +def node6558 : Tree Nat := .node node6211 node6557 +def node6559 : Tree Nat := .node node6553 node6558 +def node6560 : Tree Nat := .node node5802 node5408 +def node6561 : Tree Nat := .node node4940 node6560 +def node6562 : Tree Nat := .node node224 node1 +def node6563 : Tree Nat := .node node5849 node6562 +def node6564 : Tree Nat := .node node6561 node6563 +def node6565 : Tree Nat := .node node5407 node6564 +def node6566 : Tree Nat := .node node6217 node6565 +def node6567 : Tree Nat := .node node6559 node6566 +def node6568 : Tree Nat := .node node6545 node6567 +def node6569 : Tree Nat := .leaf 487 +def node6570 : Tree Nat := .node node1951 node6569 +def node6571 : Tree Nat := .node node5860 node6570 +def node6572 : Tree Nat := .node node6571 node6224 +def node6573 : Tree Nat := .node node6223 node6572 +def node6574 : Tree Nat := .leaf 509 +def node6575 : Tree Nat := .node node6574 node4484 +def node6576 : Tree Nat := .node node5864 node6575 +def node6577 : Tree Nat := .node node6576 node6227 +def node6578 : Tree Nat := .leaf 505 +def node6579 : Tree Nat := .node node6578 node4957 +def node6580 : Tree Nat := .node node5867 node6579 +def node6581 : Tree Nat := .node node6580 node6231 +def node6582 : Tree Nat := .node node6577 node6581 +def node6583 : Tree Nat := .node node6573 node6582 +def node6584 : Tree Nat := .leaf 508 +def node6585 : Tree Nat := .node node6584 node1 +def node6586 : Tree Nat := .node node6198 node6585 +def node6587 : Tree Nat := .node node6244 node6586 +def node6588 : Tree Nat := .node node5826 node6532 +def node6589 : Tree Nat := .node node6588 node2812 +def node6590 : Tree Nat := .node node5884 node6589 +def node6591 : Tree Nat := .node node6587 node6590 +def node6592 : Tree Nat := .node node6241 node6591 +def node6593 : Tree Nat := .node node6583 node6592 +def node6594 : Tree Nat := .node node2403 node6546 +def node6595 : Tree Nat := .node node4518 node6594 +def node6596 : Tree Nat := .leaf 493 +def node6597 : Tree Nat := .node node1 node6596 +def node6598 : Tree Nat := .node node6597 node6259 +def node6599 : Tree Nat := .node node6595 node6598 +def node6600 : Tree Nat := .node node5460 node6599 +def node6601 : Tree Nat := .node node6258 node6600 +def node6602 : Tree Nat := .leaf 506 +def node6603 : Tree Nat := .node node150 node6602 +def node6604 : Tree Nat := .node node6603 node5891 +def node6605 : Tree Nat := .node node6604 node5464 +def node6606 : Tree Nat := .leaf 495 +def node6607 : Tree Nat := .node node6606 node4997 +def node6608 : Tree Nat := .node node4526 node6607 +def node6609 : Tree Nat := .node node6608 node6265 +def node6610 : Tree Nat := .node node6605 node6609 +def node6611 : Tree Nat := .node node2835 node6606 +def node6612 : Tree Nat := .node node5006 node6611 +def node6613 : Tree Nat := .node node6192 node1 +def node6614 : Tree Nat := .node node6271 node6613 +def node6615 : Tree Nat := .node node6612 node6614 +def node6616 : Tree Nat := .node node6270 node6615 +def node6617 : Tree Nat := .node node6610 node6616 +def node6618 : Tree Nat := .node node6601 node6617 +def node6619 : Tree Nat := .node node6593 node6618 +def node6620 : Tree Nat := .node node6568 node6619 +def node6621 : Tree Nat := .node node5803 node5481 +def node6622 : Tree Nat := .node node5909 node6621 +def node6623 : Tree Nat := .node node1665 node411 +def node6624 : Tree Nat := .node node1927 node6554 +def node6625 : Tree Nat := .node node6623 node6624 +def node6626 : Tree Nat := .node node6625 node6281 +def node6627 : Tree Nat := .node node6622 node6626 +def node6628 : Tree Nat := .node node6532 node4509 +def node6629 : Tree Nat := .node node4075 node6628 +def node6630 : Tree Nat := .node node6177 node5912 +def node6631 : Tree Nat := .node node6629 node6630 +def node6632 : Tree Nat := .node node3245 node224 +def node6633 : Tree Nat := .node node411 node5019 +def node6634 : Tree Nat := .node node6632 node6633 +def node6635 : Tree Nat := .node node6528 node1 +def node6636 : Tree Nat := .node node6284 node6635 +def node6637 : Tree Nat := .node node6634 node6636 +def node6638 : Tree Nat := .node node6631 node6637 +def node6639 : Tree Nat := .node node6627 node6638 +def node6640 : Tree Nat := .node node6187 node5490 +def node6641 : Tree Nat := .node node6290 node6640 +def node6642 : Tree Nat := .leaf 486 +def node6643 : Tree Nat := .node node1943 node6642 +def node6644 : Tree Nat := .node node4556 node6643 +def node6645 : Tree Nat := .node node6644 node5494 +def node6646 : Tree Nat := .node node6641 node6645 +def node6647 : Tree Nat := .leaf 502 +def node6648 : Tree Nat := .node node6647 node1 +def node6649 : Tree Nat := .node node5375 node6648 +def node6650 : Tree Nat := .node node4561 node6649 +def node6651 : Tree Nat := .node node2433 node5835 +def node6652 : Tree Nat := .node node6651 node5037 +def node6653 : Tree Nat := .node node5831 node6539 +def node6654 : Tree Nat := .node node6653 node2784 +def node6655 : Tree Nat := .node node6652 node6654 +def node6656 : Tree Nat := .node node6650 node6655 +def node6657 : Tree Nat := .node node6646 node6656 +def node6658 : Tree Nat := .node node6639 node6657 +def node6659 : Tree Nat := .leaf 494 +def node6660 : Tree Nat := .node node3524 node6659 +def node6661 : Tree Nat := .node node4917 node6660 +def node6662 : Tree Nat := .node node6296 node6661 +def node6663 : Tree Nat := .node node6662 node5506 +def node6664 : Tree Nat := .leaf 500 +def node6665 : Tree Nat := .node node1 node6664 +def node6666 : Tree Nat := .node node6665 node2460 +def node6667 : Tree Nat := .node node4574 node6666 +def node6668 : Tree Nat := .leaf 489 +def node6669 : Tree Nat := .node node1 node6668 +def node6670 : Tree Nat := .node node6669 node5022 +def node6671 : Tree Nat := .node node5050 node6670 +def node6672 : Tree Nat := .node node6667 node6671 +def node6673 : Tree Nat := .node node6663 node6672 +def node6674 : Tree Nat := .leaf 504 +def node6675 : Tree Nat := .node node1 node6674 +def node6676 : Tree Nat := .node node6675 node5513 +def node6677 : Tree Nat := .node node6301 node6676 +def node6678 : Tree Nat := .node node6528 node4980 +def node6679 : Tree Nat := .node node4581 node6678 +def node6680 : Tree Nat := .node node6679 node5517 +def node6681 : Tree Nat := .node node6677 node6680 +def node6682 : Tree Nat := .node node6602 node1 +def node6683 : Tree Nat := .node node5405 node6682 +def node6684 : Tree Nat := .node node4587 node6683 +def node6685 : Tree Nat := .node node1 node6578 +def node6686 : Tree Nat := .node node2756 node6596 +def node6687 : Tree Nat := .node node6685 node6686 +def node6688 : Tree Nat := .node node6304 node6648 +def node6689 : Tree Nat := .node node6687 node6688 +def node6690 : Tree Nat := .node node6684 node6689 +def node6691 : Tree Nat := .node node6681 node6690 +def node6692 : Tree Nat := .node node6673 node6691 +def node6693 : Tree Nat := .node node6658 node6692 +def node6694 : Tree Nat := .leaf 496 +def node6695 : Tree Nat := .node node6694 node5404 +def node6696 : Tree Nat := .node node6314 node6695 +def node6697 : Tree Nat := .node node6312 node6696 +def node6698 : Tree Nat := .node node2061 node6525 +def node6699 : Tree Nat := .node node6549 node4414 +def node6700 : Tree Nat := .node node6698 node6699 +def node6701 : Tree Nat := .node node6700 node6317 +def node6702 : Tree Nat := .node node6697 node6701 +def node6703 : Tree Nat := .node node3294 node6602 +def node6704 : Tree Nat := .node node6546 node5074 +def node6705 : Tree Nat := .node node6703 node6704 +def node6706 : Tree Nat := .node node6705 node6327 +def node6707 : Tree Nat := .node node6325 node6706 +def node6708 : Tree Nat := .node node6702 node6707 +def node6709 : Tree Nat := .node node2490 node6596 +def node6710 : Tree Nat := .node node6709 node5955 +def node6711 : Tree Nat := .node node6710 node6332 +def node6712 : Tree Nat := .node node3301 node6569 +def node6713 : Tree Nat := .node node6712 node5083 +def node6714 : Tree Nat := .node node6713 node6334 +def node6715 : Tree Nat := .node node6711 node6714 +def node6716 : Tree Nat := .node node2896 node6533 +def node6717 : Tree Nat := .node node6716 node6337 +def node6718 : Tree Nat := .node node6717 node6340 +def node6719 : Tree Nat := .node node5821 node6525 +def node6720 : Tree Nat := .node node6719 node2839 +def node6721 : Tree Nat := .node node6343 node6720 +def node6722 : Tree Nat := .node node6718 node6721 +def node6723 : Tree Nat := .node node6715 node6722 +def node6724 : Tree Nat := .node node6708 node6723 +def node6725 : Tree Nat := .leaf 501 +def node6726 : Tree Nat := .node node1 node6725 +def node6727 : Tree Nat := .node node6726 node5550 +def node6728 : Tree Nat := .node node5978 node6727 +def node6729 : Tree Nat := .node node6728 node5554 +def node6730 : Tree Nat := .node node6664 node411 +def node6731 : Tree Nat := .node node5458 node6730 +def node6732 : Tree Nat := .node node4630 node6731 +def node6733 : Tree Nat := .leaf 490 +def node6734 : Tree Nat := .node node2376 node6733 +def node6735 : Tree Nat := .node node4634 node6734 +def node6736 : Tree Nat := .node node6735 node6350 +def node6737 : Tree Nat := .node node6732 node6736 +def node6738 : Tree Nat := .node node6729 node6737 +def node6739 : Tree Nat := .node node6664 node6668 +def node6740 : Tree Nat := .node node4643 node6739 +def node6741 : Tree Nat := .node node6740 node5985 +def node6742 : Tree Nat := .node node6356 node6741 +def node6743 : Tree Nat := .node node6725 node4456 +def node6744 : Tree Nat := .node node4171 node6743 +def node6745 : Tree Nat := .node node6744 node5560 +def node6746 : Tree Nat := .node node6674 node1 +def node6747 : Tree Nat := .node node6358 node6746 +def node6748 : Tree Nat := .node node5564 node6747 +def node6749 : Tree Nat := .node node6745 node6748 +def node6750 : Tree Nat := .node node6742 node6749 +def node6751 : Tree Nat := .node node6738 node6750 +def node6752 : Tree Nat := .node node6724 node6751 +def node6753 : Tree Nat := .node node6693 node6752 +def node6754 : Tree Nat := .node node6620 node6753 +def node6755 : Tree Nat := .node node451 node6549 +def node6756 : Tree Nat := .node node6755 node6367 +def node6757 : Tree Nat := .node node6756 node5573 +def node6758 : Tree Nat := .node node6757 node5578 +def node6759 : Tree Nat := .node node6758 node6373 +def node6760 : Tree Nat := .node node6647 node4885 +def node6761 : Tree Nat := .node node4673 node6760 +def node6762 : Tree Nat := .node node6761 node5591 +def node6763 : Tree Nat := .node node6377 node6762 +def node6764 : Tree Nat := .leaf 497 +def node6765 : Tree Nat := .node node322 node6764 +def node6766 : Tree Nat := .node node6765 node4681 +def node6767 : Tree Nat := .node node5144 node6766 +def node6768 : Tree Nat := .node node5596 node6767 +def node6769 : Tree Nat := .node node6763 node6768 +def node6770 : Tree Nat := .node node6759 node6769 +def node6771 : Tree Nat := .node node378 node6733 +def node6772 : Tree Nat := .node node6771 node6013 +def node6773 : Tree Nat := .node node6772 node6016 +def node6774 : Tree Nat := .node node6773 node6382 +def node6775 : Tree Nat := .node node5835 node4450 +def node6776 : Tree Nat := .node node4216 node6775 +def node6777 : Tree Nat := .node node6776 node5611 +def node6778 : Tree Nat := .node node411 node5161 +def node6779 : Tree Nat := .node node4695 node6778 +def node6780 : Tree Nat := .node node1 node6569 +def node6781 : Tree Nat := .node node6780 node6259 +def node6782 : Tree Nat := .node node6779 node6781 +def node6783 : Tree Nat := .node node6777 node6782 +def node6784 : Tree Nat := .node node6774 node6783 +def node6785 : Tree Nat := .node node6186 node411 +def node6786 : Tree Nat := .node node5623 node6785 +def node6787 : Tree Nat := .node node4707 node6786 +def node6788 : Tree Nat := .node node6787 node6027 +def node6789 : Tree Nat := .node node6388 node6788 +def node6790 : Tree Nat := .node node6784 node6789 +def node6791 : Tree Nat := .node node6770 node6790 +def node6792 : Tree Nat := .node node423 node411 +def node6793 : Tree Nat := .node node6792 node4714 +def node6794 : Tree Nat := .node node6793 node5638 +def node6795 : Tree Nat := .node node6395 node6794 +def node6796 : Tree Nat := .node node432 node224 +def node6797 : Tree Nat := .node node6796 node5191 +def node6798 : Tree Nat := .node node6797 node6399 +def node6799 : Tree Nat := .node node6398 node6798 +def node6800 : Tree Nat := .node node6795 node6799 +def node6801 : Tree Nat := .node node443 node5826 +def node6802 : Tree Nat := .node node6801 node5198 +def node6803 : Tree Nat := .node node6802 node5649 +def node6804 : Tree Nat := .node node6404 node6803 +def node6805 : Tree Nat := .node node448 node5831 +def node6806 : Tree Nat := .node node6805 node4733 +def node6807 : Tree Nat := .node node6806 node6406 +def node6808 : Tree Nat := .node node6539 node5654 +def node6809 : Tree Nat := .node node6408 node6808 +def node6810 : Tree Nat := .node node224 node6578 +def node6811 : Tree Nat := .node node6810 node6585 +def node6812 : Tree Nat := .node node6809 node6811 +def node6813 : Tree Nat := .node node6807 node6812 +def node6814 : Tree Nat := .node node6804 node6813 +def node6815 : Tree Nat := .node node6800 node6814 +def node6816 : Tree Nat := .node node462 node6642 +def node6817 : Tree Nat := .node node6816 node6414 +def node6818 : Tree Nat := .node node6817 node6049 +def node6819 : Tree Nat := .node node6818 node5667 +def node6820 : Tree Nat := .node node1 node6606 +def node6821 : Tree Nat := .node node6820 node3345 +def node6822 : Tree Nat := .node node5221 node6821 +def node6823 : Tree Nat := .node node5671 node6822 +def node6824 : Tree Nat := .node node6819 node6823 +def node6825 : Tree Nat := .node node481 node6584 +def node6826 : Tree Nat := .node node6825 node6419 +def node6827 : Tree Nat := .node node6826 node6422 +def node6828 : Tree Nat := .node node6827 node6056 +def node6829 : Tree Nat := .node node411 node6694 +def node6830 : Tree Nat := .node node6829 node2962 +def node6831 : Tree Nat := .node node5682 node6830 +def node6832 : Tree Nat := .node node5680 node6831 +def node6833 : Tree Nat := .node node6828 node6832 +def node6834 : Tree Nat := .node node6824 node6833 +def node6835 : Tree Nat := .node node6815 node6834 +def node6836 : Tree Nat := .node node6791 node6835 +def node6837 : Tree Nat := .node node5826 node6659 +def node6838 : Tree Nat := .node node6837 node6067 +def node6839 : Tree Nat := .node node6838 node5691 +def node6840 : Tree Nat := .node node6839 node5695 +def node6841 : Tree Nat := .node node6840 node6431 +def node6842 : Tree Nat := .node node6674 node4948 +def node6843 : Tree Nat := .node node4790 node6842 +def node6844 : Tree Nat := .node node6843 node5707 +def node6845 : Tree Nat := .node node6435 node6844 +def node6846 : Tree Nat := .node node411 node6725 +def node6847 : Tree Nat := .node node6846 node4798 +def node6848 : Tree Nat := .node node5716 node6847 +def node6849 : Tree Nat := .node node5713 node6848 +def node6850 : Tree Nat := .node node6845 node6849 +def node6851 : Tree Nat := .node node6841 node6850 +def node6852 : Tree Nat := .node node6764 node5421 +def node6853 : Tree Nat := .node node5803 node6852 +def node6854 : Tree Nat := .node node6440 node6853 +def node6855 : Tree Nat := .node node2328 node6546 +def node6856 : Tree Nat := .node node6659 node5233 +def node6857 : Tree Nat := .node node6855 node6856 +def node6858 : Tree Nat := .node node6857 node6442 +def node6859 : Tree Nat := .node node6854 node6858 +def node6860 : Tree Nat := .node node2311 node6549 +def node6861 : Tree Nat := .node node6860 node6445 +def node6862 : Tree Nat := .node node6554 node1 +def node6863 : Tree Nat := .node node6177 node6862 +def node6864 : Tree Nat := .node node6861 node6863 +def node6865 : Tree Nat := .node node6733 node5168 +def node6866 : Tree Nat := .node node6449 node6865 +def node6867 : Tree Nat := .node node1 node6533 +def node6868 : Tree Nat := .node node6867 node3452 +def node6869 : Tree Nat := .node node6866 node6868 +def node6870 : Tree Nat := .node node6864 node6869 +def node6871 : Tree Nat := .node node6859 node6870 +def node6872 : Tree Nat := .node node1899 node6606 +def node6873 : Tree Nat := .node node6872 node6094 +def node6874 : Tree Nat := .node node6873 node6454 +def node6875 : Tree Nat := .node node1 node6694 +def node6876 : Tree Nat := .node node6875 node3463 +def node6877 : Tree Nat := .node node6100 node6876 +def node6878 : Tree Nat := .node node6874 node6877 +def node6879 : Tree Nat := .node node6668 node4797 +def node6880 : Tree Nat := .node node6104 node6879 +def node6881 : Tree Nat := .node node6880 node6457 +def node6882 : Tree Nat := .node node6881 node6463 +def node6883 : Tree Nat := .node node6878 node6882 +def node6884 : Tree Nat := .node node6871 node6883 +def node6885 : Tree Nat := .node node6851 node6884 +def node6886 : Tree Nat := .node node1974 node6596 +def node6887 : Tree Nat := .node node6886 node6483 +def node6888 : Tree Nat := .node node6887 node6485 +def node6889 : Tree Nat := .node node6888 node6489 +def node6890 : Tree Nat := .node node322 node6574 +def node6891 : Tree Nat := .node node6642 node1 +def node6892 : Tree Nat := .node node6890 node6891 +def node6893 : Tree Nat := .node node6139 node6892 +def node6894 : Tree Nat := .node node6493 node6893 +def node6895 : Tree Nat := .node node6889 node6894 +def node6896 : Tree Nat := .node node6482 node6895 +def node6897 : Tree Nat := .node node2382 node6733 +def node6898 : Tree Nat := .node node6897 node5324 +def node6899 : Tree Nat := .node node6898 node6500 +def node6900 : Tree Nat := .node node6499 node6899 +def node6901 : Tree Nat := .node node2367 node6659 +def node6902 : Tree Nat := .node node6901 node5328 +def node6903 : Tree Nat := .node node6902 node6504 +def node6904 : Tree Nat := .node node3183 node6642 +def node6905 : Tree Nat := .node node6904 node5331 +def node6906 : Tree Nat := .node node6875 node5753 +def node6907 : Tree Nat := .node node6905 node6906 +def node6908 : Tree Nat := .node node6903 node6907 +def node6909 : Tree Nat := .node node6900 node6908 +def node6910 : Tree Nat := .node node3585 node6554 +def node6911 : Tree Nat := .node node6910 node5338 +def node6912 : Tree Nat := .node node1 node6764 +def node6913 : Tree Nat := .node node6912 node5761 +def node6914 : Tree Nat := .node node6911 node6913 +def node6915 : Tree Nat := .node node6512 node6914 +def node6916 : Tree Nat := .node node3601 node6668 +def node6917 : Tree Nat := .node node6916 node4875 +def node6918 : Tree Nat := .node node6917 node6514 +def node6919 : Tree Nat := .node node5802 node6764 +def node6920 : Tree Nat := .node node6919 node3049 +def node6921 : Tree Nat := .node node6516 node6920 +def node6922 : Tree Nat := .node node6918 node6921 +def node6923 : Tree Nat := .node node6915 node6922 +def node6924 : Tree Nat := .node node6909 node6923 +def node6925 : Tree Nat := .node node6896 node6924 +def node6926 : Tree Nat := .node node6885 node6925 +def node6927 : Tree Nat := .node node6836 node6926 +def node6928 : Tree Nat := .node node6754 node6927 +def node6929 : Tree Nat := .leaf 519 +def node6930 : Tree Nat := .node node6169 node6929 +def node6931 : Tree Nat := .node node5800 node6930 +def node6932 : Tree Nat := .node node6931 node5804 +def node6933 : Tree Nat := .leaf 518 +def node6934 : Tree Nat := .node node6933 node4409 +def node6935 : Tree Nat := .node node5806 node6934 +def node6936 : Tree Nat := .node node6935 node6173 +def node6937 : Tree Nat := .node node6932 node6936 +def node6938 : Tree Nat := .node node6937 node6537 +def node6939 : Tree Nat := .leaf 511 +def node6940 : Tree Nat := .node node6939 node4909 +def node6941 : Tree Nat := .node node5836 node6940 +def node6942 : Tree Nat := .node node6941 node6203 +def node6943 : Tree Nat := .node node6542 node6942 +def node6944 : Tree Nat := .node node6197 node6943 +def node6945 : Tree Nat := .node node6938 node6944 +def node6946 : Tree Nat := .leaf 535 +def node6947 : Tree Nat := .node node5831 node6946 +def node6948 : Tree Nat := .node node6547 node6947 +def node6949 : Tree Nat := .node node6948 node6551 +def node6950 : Tree Nat := .node node6949 node5387 +def node6951 : Tree Nat := .leaf 526 +def node6952 : Tree Nat := .node node55 node6951 +def node6953 : Tree Nat := .node node6952 node6209 +def node6954 : Tree Nat := .node node5826 node340 +def node6955 : Tree Nat := .node node5390 node6954 +def node6956 : Tree Nat := .node node6953 node6955 +def node6957 : Tree Nat := .node node6956 node6557 +def node6958 : Tree Nat := .node node6950 node6957 +def node6959 : Tree Nat := .leaf 510 +def node6960 : Tree Nat := .node node67 node6959 +def node6961 : Tree Nat := .node node6960 node6214 +def node6962 : Tree Nat := .leaf 516 +def node6963 : Tree Nat := .node node1939 node6962 +def node6964 : Tree Nat := .node node4932 node6963 +def node6965 : Tree Nat := .node node6961 node6964 +def node6966 : Tree Nat := .node node6965 node5402 +def node6967 : Tree Nat := .node node5831 node4467 +def node6968 : Tree Nat := .node node3995 node6967 +def node6969 : Tree Nat := .node node6968 node5406 +def node6970 : Tree Nat := .node node5835 node6939 +def node6971 : Tree Nat := .node node6970 node6562 +def node6972 : Tree Nat := .node node6561 node6971 +def node6973 : Tree Nat := .node node6969 node6972 +def node6974 : Tree Nat := .node node6966 node6973 +def node6975 : Tree Nat := .node node6958 node6974 +def node6976 : Tree Nat := .node node6945 node6975 +def node6977 : Tree Nat := .leaf 527 +def node6978 : Tree Nat := .node node6186 node6977 +def node6979 : Tree Nat := .node node5856 node6978 +def node6980 : Tree Nat := .node node6979 node5858 +def node6981 : Tree Nat := .node node6980 node6572 +def node6982 : Tree Nat := .leaf 512 +def node6983 : Tree Nat := .node node6982 node1 +def node6984 : Tree Nat := .node node6230 node6983 +def node6985 : Tree Nat := .node node6580 node6984 +def node6986 : Tree Nat := .node node6577 node6985 +def node6987 : Tree Nat := .node node6981 node6986 +def node6988 : Tree Nat := .node node6987 node6592 +def node6989 : Tree Nat := .leaf 530 +def node6990 : Tree Nat := .node node140 node6989 +def node6991 : Tree Nat := .node node6990 node4515 +def node6992 : Tree Nat := .node node6991 node5459 +def node6993 : Tree Nat := .leaf 520 +def node6994 : Tree Nat := .node node6993 node1 +def node6995 : Tree Nat := .node node6597 node6994 +def node6996 : Tree Nat := .node node6595 node6995 +def node6997 : Tree Nat := .node node6992 node6996 +def node6998 : Tree Nat := .node node6258 node6997 +def node6999 : Tree Nat := .leaf 524 +def node7000 : Tree Nat := .node node6999 node322 +def node7001 : Tree Nat := .node node5469 node7000 +def node7002 : Tree Nat := .node node4532 node7001 +def node7003 : Tree Nat := .node node7002 node6615 +def node7004 : Tree Nat := .node node6610 node7003 +def node7005 : Tree Nat := .node node6998 node7004 +def node7006 : Tree Nat := .node node6988 node7005 +def node7007 : Tree Nat := .node node6976 node7006 +def node7008 : Tree Nat := .leaf 523 +def node7009 : Tree Nat := .node node451 node7008 +def node7010 : Tree Nat := .node node5907 node7009 +def node7011 : Tree Nat := .node node7010 node6621 +def node7012 : Tree Nat := .node node7011 node6626 +def node7013 : Tree Nat := .node node6574 node5019 +def node7014 : Tree Nat := .node node6632 node7013 +def node7015 : Tree Nat := .node node7014 node6636 +def node7016 : Tree Nat := .node node6631 node7015 +def node7017 : Tree Nat := .node node7012 node7016 +def node7018 : Tree Nat := .node node3252 node5826 +def node7019 : Tree Nat := .node node7018 node6643 +def node7020 : Tree Nat := .node node7019 node5494 +def node7021 : Tree Nat := .node node6641 node7020 +def node7022 : Tree Nat := .node node2847 node5831 +def node7023 : Tree Nat := .node node7022 node4560 +def node7024 : Tree Nat := .node node7023 node6649 +def node7025 : Tree Nat := .node node7024 node6655 +def node7026 : Tree Nat := .node node7021 node7025 +def node7027 : Tree Nat := .node node7017 node7026 +def node7028 : Tree Nat := .node node1 node7008 +def node7029 : Tree Nat := .node node7028 node6660 +def node7030 : Tree Nat := .node node6296 node7029 +def node7031 : Tree Nat := .leaf 531 +def node7032 : Tree Nat := .node node2440 node7031 +def node7033 : Tree Nat := .node node7032 node5045 +def node7034 : Tree Nat := .node node7033 node5505 +def node7035 : Tree Nat := .node node7030 node7034 +def node7036 : Tree Nat := .leaf 528 +def node7037 : Tree Nat := .node node3241 node7036 +def node7038 : Tree Nat := .node node7037 node5049 +def node7039 : Tree Nat := .node node6959 node1 +def node7040 : Tree Nat := .node node6669 node7039 +def node7041 : Tree Nat := .node node7038 node7040 +def node7042 : Tree Nat := .node node6667 node7041 +def node7043 : Tree Nat := .node node7035 node7042 +def node7044 : Tree Nat := .node node3641 node6989 +def node7045 : Tree Nat := .node node7044 node6678 +def node7046 : Tree Nat := .node node7045 node5517 +def node7047 : Tree Nat := .node node6677 node7046 +def node7048 : Tree Nat := .node node3656 node6977 +def node7049 : Tree Nat := .node node7048 node4586 +def node7050 : Tree Nat := .node node7049 node6683 +def node7051 : Tree Nat := .leaf 515 +def node7052 : Tree Nat := .node node6186 node7051 +def node7053 : Tree Nat := .node node7052 node6648 +def node7054 : Tree Nat := .node node6687 node7053 +def node7055 : Tree Nat := .node node7050 node7054 +def node7056 : Tree Nat := .node node7047 node7055 +def node7057 : Tree Nat := .node node7043 node7056 +def node7058 : Tree Nat := .node node7027 node7057 +def node7059 : Tree Nat := .leaf 517 +def node7060 : Tree Nat := .node node322 node7059 +def node7061 : Tree Nat := .node node6169 node7031 +def node7062 : Tree Nat := .node node7060 node7061 +def node7063 : Tree Nat := .node node7062 node6696 +def node7064 : Tree Nat := .node node7063 node6701 +def node7065 : Tree Nat := .leaf 521 +def node7066 : Tree Nat := .node node7065 node6320 +def node7067 : Tree Nat := .node node5943 node7066 +def node7068 : Tree Nat := .leaf 532 +def node7069 : Tree Nat := .node node7068 node1 +def node7070 : Tree Nat := .node node6323 node7069 +def node7071 : Tree Nat := .node node7067 node7070 +def node7072 : Tree Nat := .node node7071 node6706 +def node7073 : Tree Nat := .node node7064 node7072 +def node7074 : Tree Nat := .leaf 514 +def node7075 : Tree Nat := .node node451 node7074 +def node7076 : Tree Nat := .node node6331 node7075 +def node7077 : Tree Nat := .node node6710 node7076 +def node7078 : Tree Nat := .leaf 538 +def node7079 : Tree Nat := .node node1 node7078 +def node7080 : Tree Nat := .node node7079 node3226 +def node7081 : Tree Nat := .node node6713 node7080 +def node7082 : Tree Nat := .node node7077 node7081 +def node7083 : Tree Nat := .leaf 529 +def node7084 : Tree Nat := .node node7083 node6313 +def node7085 : Tree Nat := .node node6716 node7084 +def node7086 : Tree Nat := .node node7085 node6340 +def node7087 : Tree Nat := .leaf 525 +def node7088 : Tree Nat := .node node7087 node5389 +def node7089 : Tree Nat := .node node6342 node7088 +def node7090 : Tree Nat := .node node7089 node6720 +def node7091 : Tree Nat := .node node7086 node7090 +def node7092 : Tree Nat := .node node7082 node7091 +def node7093 : Tree Nat := .node node7073 node7092 +def node7094 : Tree Nat := .leaf 533 +def node7095 : Tree Nat := .node node2494 node7094 +def node7096 : Tree Nat := .node node6993 node5096 +def node7097 : Tree Nat := .node node7095 node7096 +def node7098 : Tree Nat := .node node7097 node5553 +def node7099 : Tree Nat := .node node6728 node7098 +def node7100 : Tree Nat := .node node1 node6933 +def node7101 : Tree Nat := .node node7100 node6730 +def node7102 : Tree Nat := .node node4630 node7101 +def node7103 : Tree Nat := .node node3290 node6951 +def node7104 : Tree Nat := .node node7103 node6734 +def node7105 : Tree Nat := .node node7104 node6350 +def node7106 : Tree Nat := .node node7102 node7105 +def node7107 : Tree Nat := .node node7099 node7106 +def node7108 : Tree Nat := .leaf 522 +def node7109 : Tree Nat := .node node1 node7108 +def node7110 : Tree Nat := .node node7109 node5982 +def node7111 : Tree Nat := .node node6355 node7110 +def node7112 : Tree Nat := .node node3695 node6982 +def node7113 : Tree Nat := .node node7112 node6739 +def node7114 : Tree Nat := .node node7113 node5985 +def node7115 : Tree Nat := .node node7111 node7114 +def node7116 : Tree Nat := .leaf 513 +def node7117 : Tree Nat := .node node3709 node7116 +def node7118 : Tree Nat := .node node7117 node6743 +def node7119 : Tree Nat := .node node7118 node5560 +def node7120 : Tree Nat := .node node1 node6929 +def node7121 : Tree Nat := .node node7116 node5562 +def node7122 : Tree Nat := .node node7120 node7121 +def node7123 : Tree Nat := .node node7122 node6747 +def node7124 : Tree Nat := .node node7119 node7123 +def node7125 : Tree Nat := .node node7115 node7124 +def node7126 : Tree Nat := .node node7107 node7125 +def node7127 : Tree Nat := .node node7093 node7126 +def node7128 : Tree Nat := .node node7058 node7127 +def node7129 : Tree Nat := .node node7007 node7128 +def node7130 : Tree Nat := .node node340 node7065 +def node7131 : Tree Nat := .node node6755 node7130 +def node7132 : Tree Nat := .node node7131 node5573 +def node7133 : Tree Nat := .node node1 node6946 +def node7134 : Tree Nat := .node node7133 node5576 +def node7135 : Tree Nat := .node node4661 node7134 +def node7136 : Tree Nat := .node node7132 node7135 +def node7137 : Tree Nat := .leaf 534 +def node7138 : Tree Nat := .node node345 node7137 +def node7139 : Tree Nat := .node node7138 node4665 +def node7140 : Tree Nat := .node node7139 node6003 +def node7141 : Tree Nat := .node node6951 node1 +def node7142 : Tree Nat := .node node6349 node7141 +def node7143 : Tree Nat := .node node5126 node7142 +def node7144 : Tree Nat := .node node7140 node7143 +def node7145 : Tree Nat := .node node7136 node7144 +def node7146 : Tree Nat := .node node355 node7074 +def node7147 : Tree Nat := .node node7146 node6375 +def node7148 : Tree Nat := .node node7147 node5587 +def node7149 : Tree Nat := .node node1 node7137 +def node7150 : Tree Nat := .node node7149 node5590 +def node7151 : Tree Nat := .node node6761 node7150 +def node7152 : Tree Nat := .node node7148 node7151 +def node7153 : Tree Nat := .node node1 node7051 +def node7154 : Tree Nat := .node node6989 node322 +def node7155 : Tree Nat := .node node7153 node7154 +def node7156 : Tree Nat := .node node4679 node7155 +def node7157 : Tree Nat := .node node6933 node1 +def node7158 : Tree Nat := .node node6765 node7157 +def node7159 : Tree Nat := .node node5144 node7158 +def node7160 : Tree Nat := .node node7156 node7159 +def node7161 : Tree Nat := .node node7152 node7160 +def node7162 : Tree Nat := .node node7145 node7161 +def node7163 : Tree Nat := .leaf 537 +def node7164 : Tree Nat := .node node5826 node7163 +def node7165 : Tree Nat := .node node6771 node7164 +def node7166 : Tree Nat := .node node7165 node6016 +def node7167 : Tree Nat := .node node7166 node6382 +def node7168 : Tree Nat := .node node387 node7036 +def node7169 : Tree Nat := .node node7168 node6775 +def node7170 : Tree Nat := .node node7169 node5611 +def node7171 : Tree Nat := .node node7170 node6782 +def node7172 : Tree Nat := .node node7167 node7171 +def node7173 : Tree Nat := .node node398 node6982 +def node7174 : Tree Nat := .node node195 node7078 +def node7175 : Tree Nat := .node node7173 node7174 +def node7176 : Tree Nat := .node node7175 node5616 +def node7177 : Tree Nat := .node node7176 node6023 +def node7178 : Tree Nat := .node node5802 node7116 +def node7179 : Tree Nat := .node node7178 node2986 +def node7180 : Tree Nat := .node node5628 node7179 +def node7181 : Tree Nat := .node node6787 node7180 +def node7182 : Tree Nat := .node node7177 node7181 +def node7183 : Tree Nat := .node node7172 node7182 +def node7184 : Tree Nat := .node node7162 node7183 +def node7185 : Tree Nat := .node node6176 node7083 +def node7186 : Tree Nat := .node node5856 node7185 +def node7187 : Tree Nat := .node node7186 node6394 +def node7188 : Tree Nat := .node node7187 node6794 +def node7189 : Tree Nat := .node node6959 node224 +def node7190 : Tree Nat := .node node6177 node7189 +def node7191 : Tree Nat := .node node4720 node7190 +def node7192 : Tree Nat := .node node7191 node6798 +def node7193 : Tree Nat := .node node7188 node7192 +def node7194 : Tree Nat := .node node196 node3373 +def node7195 : Tree Nat := .node node6802 node7194 +def node7196 : Tree Nat := .node node6404 node7195 +def node7197 : Tree Nat := .node node6939 node4422 +def node7198 : Tree Nat := .node node6805 node7197 +def node7199 : Tree Nat := .node node7198 node6406 +def node7200 : Tree Nat := .node node7199 node6812 +def node7201 : Tree Nat := .node node7196 node7200 +def node7202 : Tree Nat := .node node7193 node7201 +def node7203 : Tree Nat := .leaf 539 +def node7204 : Tree Nat := .node node195 node7203 +def node7205 : Tree Nat := .node node6816 node7204 +def node7206 : Tree Nat := .node node7205 node6049 +def node7207 : Tree Nat := .node node7108 node5179 +def node7208 : Tree Nat := .node node4742 node7207 +def node7209 : Tree Nat := .node node7208 node5666 +def node7210 : Tree Nat := .node node7206 node7209 +def node7211 : Tree Nat := .node node471 node7068 +def node7212 : Tree Nat := .node node6977 node4746 +def node7213 : Tree Nat := .node node7211 node7212 +def node7214 : Tree Nat := .node node7108 node451 +def node7215 : Tree Nat := .node node5669 node7214 +def node7216 : Tree Nat := .node node7213 node7215 +def node7217 : Tree Nat := .node node7008 node4890 +def node7218 : Tree Nat := .node node4752 node7217 +def node7219 : Tree Nat := .node node7218 node6821 +def node7220 : Tree Nat := .node node7216 node7219 +def node7221 : Tree Nat := .node node7210 node7220 +def node7222 : Tree Nat := .node node6929 node4765 +def node7223 : Tree Nat := .node node4286 node7222 +def node7224 : Tree Nat := .node node7223 node5679 +def node7225 : Tree Nat := .node node7031 node5439 +def node7226 : Tree Nat := .node node5234 node7225 +def node7227 : Tree Nat := .node node7226 node6830 +def node7228 : Tree Nat := .node node7224 node7227 +def node7229 : Tree Nat := .node node6828 node7228 +def node7230 : Tree Nat := .node node7221 node7229 +def node7231 : Tree Nat := .node node7202 node7230 +def node7232 : Tree Nat := .node node7184 node7231 +def node7233 : Tree Nat := .node node224 node7087 +def node7234 : Tree Nat := .node node6837 node7233 +def node7235 : Tree Nat := .node node7234 node5691 +def node7236 : Tree Nat := .node node6999 node4439 +def node7237 : Tree Nat := .node node4774 node7236 +def node7238 : Tree Nat := .node node1 node7163 +def node7239 : Tree Nat := .node node7238 node3844 +def node7240 : Tree Nat := .node node7237 node7239 +def node7241 : Tree Nat := .node node7235 node7240 +def node7242 : Tree Nat := .leaf 536 +def node7243 : Tree Nat := .node node1905 node7242 +def node7244 : Tree Nat := .node node7243 node4779 +def node7245 : Tree Nat := .node node6999 node6053 +def node7246 : Tree Nat := .node node5697 node7245 +def node7247 : Tree Nat := .node node7244 node7246 +def node7248 : Tree Nat := .node node7247 node6430 +def node7249 : Tree Nat := .node node7241 node7248 +def node7250 : Tree Nat := .node node1917 node6962 +def node7251 : Tree Nat := .node node7250 node6433 +def node7252 : Tree Nat := .node node7251 node5703 +def node7253 : Tree Nat := .node node1 node7242 +def node7254 : Tree Nat := .node node7253 node3436 +def node7255 : Tree Nat := .node node6843 node7254 +def node7256 : Tree Nat := .node node7252 node7255 +def node7257 : Tree Nat := .node node7065 node4701 +def node7258 : Tree Nat := .node node4320 node7257 +def node7259 : Tree Nat := .node node1 node7059 +def node7260 : Tree Nat := .node node7259 node3440 +def node7261 : Tree Nat := .node node7258 node7260 +def node7262 : Tree Nat := .node node7094 node5714 +def node7263 : Tree Nat := .node node5261 node7262 +def node7264 : Tree Nat := .node node6846 node6994 +def node7265 : Tree Nat := .node node7263 node7264 +def node7266 : Tree Nat := .node node7261 node7265 +def node7267 : Tree Nat := .node node7256 node7266 +def node7268 : Tree Nat := .node node7249 node7267 +def node7269 : Tree Nat := .node node6186 node7078 +def node7270 : Tree Nat := .node node6082 node7269 +def node7271 : Tree Nat := .node node7270 node6853 +def node7272 : Tree Nat := .node node7271 node6858 +def node7273 : Tree Nat := .node node7272 node6870 +def node7274 : Tree Nat := .node node7051 node5705 +def node7275 : Tree Nat := .node node6187 node7274 +def node7276 : Tree Nat := .node node6873 node7275 +def node7277 : Tree Nat := .node node7276 node6877 +def node7278 : Tree Nat := .node node6176 node7059 +def node7279 : Tree Nat := .node node7278 node3075 +def node7280 : Tree Nat := .node node6460 node7279 +def node7281 : Tree Nat := .node node6881 node7280 +def node7282 : Tree Nat := .node node7277 node7281 +def node7283 : Tree Nat := .node node7273 node7282 +def node7284 : Tree Nat := .node node7268 node7283 +def node7285 : Tree Nat := .node node340 node7094 +def node7286 : Tree Nat := .node node5935 node7285 +def node7287 : Tree Nat := .node node7286 node6117 +def node7288 : Tree Nat := .node node7287 node6473 +def node7289 : Tree Nat := .node node7288 node6481 +def node7290 : Tree Nat := .node node7289 node6895 +def node7291 : Tree Nat := .node node2806 node7051 +def node7292 : Tree Nat := .node node7291 node6146 +def node7293 : Tree Nat := .node node7292 node6498 +def node7294 : Tree Nat := .node node7293 node6899 +def node7295 : Tree Nat := .node node7083 node4789 +def node7296 : Tree Nat := .node node6901 node7295 +def node7297 : Tree Nat := .node node7296 node6504 +def node7298 : Tree Nat := .node node7087 node4953 +def node7299 : Tree Nat := .node node6904 node7298 +def node7300 : Tree Nat := .node node7036 node1 +def node7301 : Tree Nat := .node node6875 node7300 +def node7302 : Tree Nat := .node node7299 node7301 +def node7303 : Tree Nat := .node node7297 node7302 +def node7304 : Tree Nat := .node node7294 node7303 +def node7305 : Tree Nat := .node node7068 node195 +def node7306 : Tree Nat := .node node6349 node7305 +def node7307 : Tree Nat := .node node6917 node7306 +def node7308 : Tree Nat := .node node7307 node6921 +def node7309 : Tree Nat := .node node6915 node7308 +def node7310 : Tree Nat := .node node7304 node7309 +def node7311 : Tree Nat := .node node7290 node7310 +def node7312 : Tree Nat := .node node7284 node7311 +def node7313 : Tree Nat := .node node7232 node7312 +def node7314 : Tree Nat := .node node7129 node7313 +def node7315 : Tree Nat := .leaf 552 +def node7316 : Tree Nat := .node node7315 node5355 +def node7317 : Tree Nat := .node node5803 node7316 +def node7318 : Tree Nat := .node node6931 node7317 +def node7319 : Tree Nat := .node node7318 node6936 +def node7320 : Tree Nat := .leaf 561 +def node7321 : Tree Nat := .node node6525 node7320 +def node7322 : Tree Nat := .node node5810 node7321 +def node7323 : Tree Nat := .node node7322 node6530 +def node7324 : Tree Nat := .node node7323 node6536 +def node7325 : Tree Nat := .node node7319 node7324 +def node7326 : Tree Nat := .leaf 542 +def node7327 : Tree Nat := .node node5802 node7326 +def node7328 : Tree Nat := .node node5822 node7327 +def node7329 : Tree Nat := .node node7328 node6190 +def node7330 : Tree Nat := .node node7329 node6196 +def node7331 : Tree Nat := .node node7330 node6943 +def node7332 : Tree Nat := .node node7325 node7331 +def node7333 : Tree Nat := .leaf 549 +def node7334 : Tree Nat := .node node1 node7333 +def node7335 : Tree Nat := .node node7334 node6550 +def node7336 : Tree Nat := .node node6948 node7335 +def node7337 : Tree Nat := .leaf 560 +def node7338 : Tree Nat := .node node50 node7337 +def node7339 : Tree Nat := .node node322 node4920 +def node7340 : Tree Nat := .node node7338 node7339 +def node7341 : Tree Nat := .node node7340 node5386 +def node7342 : Tree Nat := .node node7336 node7341 +def node7343 : Tree Nat := .leaf 557 +def node7344 : Tree Nat := .node node5826 node7343 +def node7345 : Tree Nat := .node node5390 node7344 +def node7346 : Tree Nat := .node node6953 node7345 +def node7347 : Tree Nat := .node node7346 node6557 +def node7348 : Tree Nat := .node node7342 node7347 +def node7349 : Tree Nat := .node node5821 node4916 +def node7350 : Tree Nat := .node node4463 node7349 +def node7351 : Tree Nat := .node node7350 node5401 +def node7352 : Tree Nat := .node node6965 node7351 +def node7353 : Tree Nat := .leaf 548 +def node7354 : Tree Nat := .node node78 node7353 +def node7355 : Tree Nat := .leaf 556 +def node7356 : Tree Nat := .node node5831 node7355 +def node7357 : Tree Nat := .node node7354 node7356 +def node7358 : Tree Nat := .node node7357 node5406 +def node7359 : Tree Nat := .node node1 node7320 +def node7360 : Tree Nat := .node node7359 node6560 +def node7361 : Tree Nat := .node node7360 node6971 +def node7362 : Tree Nat := .node node7358 node7361 +def node7363 : Tree Nat := .node node7352 node7362 +def node7364 : Tree Nat := .node node7348 node7363 +def node7365 : Tree Nat := .node node7332 node7364 +def node7366 : Tree Nat := .leaf 554 +def node7367 : Tree Nat := .node node7366 node5417 +def node7368 : Tree Nat := .node node5803 node7367 +def node7369 : Tree Nat := .node node6979 node7368 +def node7370 : Tree Nat := .leaf 550 +def node7371 : Tree Nat := .node node7370 node1 +def node7372 : Tree Nat := .node node341 node7371 +def node7373 : Tree Nat := .node node6571 node7372 +def node7374 : Tree Nat := .node node7369 node7373 +def node7375 : Tree Nat := .leaf 544 +def node7376 : Tree Nat := .node node2372 node7375 +def node7377 : Tree Nat := .node node6177 node7376 +def node7378 : Tree Nat := .node node6576 node7377 +def node7379 : Tree Nat := .node node7378 node6985 +def node7380 : Tree Nat := .node node7374 node7379 +def node7381 : Tree Nat := .node node5831 node7333 +def node7382 : Tree Nat := .node node5872 node7381 +def node7383 : Tree Nat := .node node7382 node6237 +def node7384 : Tree Nat := .leaf 546 +def node7385 : Tree Nat := .node node7384 node1 +def node7386 : Tree Nat := .node node196 node7385 +def node7387 : Tree Nat := .node node5877 node7386 +def node7388 : Tree Nat := .node node7383 node7387 +def node7389 : Tree Nat := .node node7388 node6591 +def node7390 : Tree Nat := .node node7380 node7389 +def node7391 : Tree Nat := .leaf 565 +def node7392 : Tree Nat := .node node1 node7391 +def node7393 : Tree Nat := .node node7392 node5451 +def node7394 : Tree Nat := .node node6253 node7393 +def node7395 : Tree Nat := .leaf 564 +def node7396 : Tree Nat := .node node135 node7395 +def node7397 : Tree Nat := .node node7396 node4984 +def node7398 : Tree Nat := .node node7397 node6256 +def node7399 : Tree Nat := .node node7394 node7398 +def node7400 : Tree Nat := .leaf 558 +def node7401 : Tree Nat := .node node2823 node7400 +def node7402 : Tree Nat := .node node6990 node7401 +def node7403 : Tree Nat := .leaf 566 +def node7404 : Tree Nat := .node node2399 node7403 +def node7405 : Tree Nat := .node node5458 node7404 +def node7406 : Tree Nat := .node node7402 node7405 +def node7407 : Tree Nat := .node node7406 node6996 +def node7408 : Tree Nat := .node node7399 node7407 +def node7409 : Tree Nat := .node node5835 node7355 +def node7410 : Tree Nat := .node node6603 node7409 +def node7411 : Tree Nat := .node node7410 node5464 +def node7412 : Tree Nat := .leaf 559 +def node7413 : Tree Nat := .node node7412 node1 +def node7414 : Tree Nat := .node node5895 node7413 +def node7415 : Tree Nat := .node node6608 node7414 +def node7416 : Tree Nat := .node node7411 node7415 +def node7417 : Tree Nat := .node node159 node7375 +def node7418 : Tree Nat := .node node7417 node4531 +def node7419 : Tree Nat := .node node7418 node7001 +def node7420 : Tree Nat := .leaf 545 +def node7421 : Tree Nat := .node node1 node7420 +def node7422 : Tree Nat := .node node7421 node6611 +def node7423 : Tree Nat := .node node7422 node6614 +def node7424 : Tree Nat := .node node7419 node7423 +def node7425 : Tree Nat := .node node7416 node7424 +def node7426 : Tree Nat := .node node7408 node7425 +def node7427 : Tree Nat := .node node7390 node7426 +def node7428 : Tree Nat := .node node7365 node7427 +def node7429 : Tree Nat := .node node5831 node451 +def node7430 : Tree Nat := .node node7429 node7009 +def node7431 : Tree Nat := .node node7203 node5480 +def node7432 : Tree Nat := .node node5803 node7431 +def node7433 : Tree Nat := .node node7430 node7432 +def node7434 : Tree Nat := .node node7433 node6626 +def node7435 : Tree Nat := .node node2016 node322 +def node7436 : Tree Nat := .node node6532 node7391 +def node7437 : Tree Nat := .node node7435 node7436 +def node7438 : Tree Nat := .node node7437 node6630 +def node7439 : Tree Nat := .node node7438 node7015 +def node7440 : Tree Nat := .node node7434 node7439 +def node7441 : Tree Nat := .node node2023 node5821 +def node7442 : Tree Nat := .node node6169 node7420 +def node7443 : Tree Nat := .node node7441 node7442 +def node7444 : Tree Nat := .leaf 553 +def node7445 : Tree Nat := .node node7444 node5384 +def node7446 : Tree Nat := .node node6187 node7445 +def node7447 : Tree Nat := .node node7443 node7446 +def node7448 : Tree Nat := .node node7326 node195 +def node7449 : Tree Nat := .node node196 node7448 +def node7450 : Tree Nat := .node node7019 node7449 +def node7451 : Tree Nat := .node node7447 node7450 +def node7452 : Tree Nat := .node node6198 node6648 +def node7453 : Tree Nat := .node node7023 node7452 +def node7454 : Tree Nat := .node node7453 node6655 +def node7455 : Tree Nat := .node node7451 node7454 +def node7456 : Tree Nat := .node node7440 node7455 +def node7457 : Tree Nat := .leaf 555 +def node7458 : Tree Nat := .node node2864 node7457 +def node7459 : Tree Nat := .node node7458 node6295 +def node7460 : Tree Nat := .node node7459 node7029 +def node7461 : Tree Nat := .node node7353 node1 +def node7462 : Tree Nat := .node node341 node7461 +def node7463 : Tree Nat := .node node7033 node7462 +def node7464 : Tree Nat := .node node7460 node7463 +def node7465 : Tree Nat := .leaf 567 +def node7466 : Tree Nat := .node node2425 node7465 +def node7467 : Tree Nat := .leaf 540 +def node7468 : Tree Nat := .node node2743 node7467 +def node7469 : Tree Nat := .node node7466 node7468 +def node7470 : Tree Nat := .leaf 562 +def node7471 : Tree Nat := .node node2316 node7470 +def node7472 : Tree Nat := .node node6665 node7471 +def node7473 : Tree Nat := .node node7469 node7472 +def node7474 : Tree Nat := .node node7473 node7041 +def node7475 : Tree Nat := .node node7464 node7474 +def node7476 : Tree Nat := .leaf 563 +def node7477 : Tree Nat := .node node2017 node7476 +def node7478 : Tree Nat := .node node7477 node6300 +def node7479 : Tree Nat := .node node7478 node6676 +def node7480 : Tree Nat := .node node7375 node1 +def node7481 : Tree Nat := .node node5400 node7480 +def node7482 : Tree Nat := .node node7045 node7481 +def node7483 : Tree Nat := .node node7479 node7482 +def node7484 : Tree Nat := .node node2333 node7326 +def node7485 : Tree Nat := .node node7048 node7484 +def node7486 : Tree Nat := .leaf 543 +def node7487 : Tree Nat := .node node1 node7486 +def node7488 : Tree Nat := .node node7487 node6682 +def node7489 : Tree Nat := .node node7485 node7488 +def node7490 : Tree Nat := .node node7489 node7054 +def node7491 : Tree Nat := .node node7483 node7490 +def node7492 : Tree Nat := .node node7475 node7491 +def node7493 : Tree Nat := .node node7456 node7492 +def node7494 : Tree Nat := .node node1 node7355 +def node7495 : Tree Nat := .node node7494 node3617 +def node7496 : Tree Nat := .node node6700 node7495 +def node7497 : Tree Nat := .node node7063 node7496 +def node7498 : Tree Nat := .node node2070 node7420 +def node7499 : Tree Nat := .node node7498 node7066 +def node7500 : Tree Nat := .node node7068 node7353 +def node7501 : Tree Nat := .node node6323 node7500 +def node7502 : Tree Nat := .node node7499 node7501 +def node7503 : Tree Nat := .node node7502 node6706 +def node7504 : Tree Nat := .node node7497 node7503 +def node7505 : Tree Nat := .node node5802 node7444 +def node7506 : Tree Nat := .node node6709 node7505 +def node7507 : Tree Nat := .node node7506 node7076 +def node7508 : Tree Nat := .node node7507 node7081 +def node7509 : Tree Nat := .node node7508 node7091 +def node7510 : Tree Nat := .node node7504 node7509 +def node7511 : Tree Nat := .node node411 node7467 +def node7512 : Tree Nat := .node node3716 node7511 +def node7513 : Tree Nat := .node node7512 node6727 +def node7514 : Tree Nat := .leaf 541 +def node7515 : Tree Nat := .node node1 node7514 +def node7516 : Tree Nat := .node node7515 node3588 +def node7517 : Tree Nat := .node node7097 node7516 +def node7518 : Tree Nat := .node node7513 node7517 +def node7519 : Tree Nat := .node node2480 node7391 +def node7520 : Tree Nat := .node node7519 node4629 +def node7521 : Tree Nat := .node node7520 node7101 +def node7522 : Tree Nat := .node node7521 node7105 +def node7523 : Tree Nat := .node node7518 node7522 +def node7524 : Tree Nat := .node node2071 node7320 +def node7525 : Tree Nat := .node node340 node7400 +def node7526 : Tree Nat := .node node7524 node7525 +def node7527 : Tree Nat := .node node7526 node7110 +def node7528 : Tree Nat := .node node7527 node7114 +def node7529 : Tree Nat := .node node1 node7400 +def node7530 : Tree Nat := .node node7529 node3334 +def node7531 : Tree Nat := .node node7118 node7530 +def node7532 : Tree Nat := .node node7531 node7123 +def node7533 : Tree Nat := .node node7528 node7532 +def node7534 : Tree Nat := .node node7523 node7533 +def node7535 : Tree Nat := .node node7510 node7534 +def node7536 : Tree Nat := .node node7493 node7535 +def node7537 : Tree Nat := .node node7428 node7536 +def node7538 : Tree Nat := .node node7337 node340 +def node7539 : Tree Nat := .node node7133 node7538 +def node7540 : Tree Nat := .node node4661 node7539 +def node7541 : Tree Nat := .node node7132 node7540 +def node7542 : Tree Nat := .node node2833 node7476 +def node7543 : Tree Nat := .node node7138 node7542 +def node7544 : Tree Nat := .node node7543 node6003 +def node7545 : Tree Nat := .node node7544 node7143 +def node7546 : Tree Nat := .node node7541 node7545 +def node7547 : Tree Nat := .node node6176 node7486 +def node7548 : Tree Nat := .node node7146 node7547 +def node7549 : Tree Nat := .node node1 node7444 +def node7550 : Tree Nat := .node node7549 node5586 +def node7551 : Tree Nat := .node node7548 node7550 +def node7552 : Tree Nat := .node node7395 node195 +def node7553 : Tree Nat := .node node7149 node7552 +def node7554 : Tree Nat := .node node6761 node7553 +def node7555 : Tree Nat := .node node7551 node7554 +def node7556 : Tree Nat := .node node367 node7315 +def node7557 : Tree Nat := .node node7556 node4678 +def node7558 : Tree Nat := .node node7557 node7155 +def node7559 : Tree Nat := .node node7558 node7159 +def node7560 : Tree Nat := .node node7555 node7559 +def node7561 : Tree Nat := .node node7546 node7560 +def node7562 : Tree Nat := .leaf 551 +def node7563 : Tree Nat := .node node1 node7562 +def node7564 : Tree Nat := .node node195 node5359 +def node7565 : Tree Nat := .node node7563 node7564 +def node7566 : Tree Nat := .node node7165 node7565 +def node7567 : Tree Nat := .node node382 node7470 +def node7568 : Tree Nat := .node node7567 node5154 +def node7569 : Tree Nat := .node node7568 node6381 +def node7570 : Tree Nat := .node node7566 node7569 +def node7571 : Tree Nat := .node node2564 node7337 +def node7572 : Tree Nat := .node node5610 node7571 +def node7573 : Tree Nat := .node node7169 node7572 +def node7574 : Tree Nat := .node node7573 node6782 +def node7575 : Tree Nat := .node node7570 node7574 +def node7576 : Tree Nat := .node node451 node5395 +def node7577 : Tree Nat := .node node5169 node7576 +def node7578 : Tree Nat := .node node7175 node7577 +def node7579 : Tree Nat := .node node6021 node6264 +def node7580 : Tree Nat := .node node5173 node7579 +def node7581 : Tree Nat := .node node7578 node7580 +def node7582 : Tree Nat := .node node408 node7370 +def node7583 : Tree Nat := .node node2579 node7343 +def node7584 : Tree Nat := .node node7582 node7583 +def node7585 : Tree Nat := .node node7584 node6786 +def node7586 : Tree Nat := .node node1 node7476 +def node7587 : Tree Nat := .node node7586 node5627 +def node7588 : Tree Nat := .node node7587 node7179 +def node7589 : Tree Nat := .node node7585 node7588 +def node7590 : Tree Nat := .node node7581 node7589 +def node7591 : Tree Nat := .node node7575 node7590 +def node7592 : Tree Nat := .node node7561 node7591 +def node7593 : Tree Nat := .leaf 547 +def node7594 : Tree Nat := .node node7593 node4478 +def node7595 : Tree Nat := .node node6792 node7594 +def node7596 : Tree Nat := .node node1 node7467 +def node7597 : Tree Nat := .node node7596 node3774 +def node7598 : Tree Nat := .node node7595 node7597 +def node7599 : Tree Nat := .node node7187 node7598 +def node7600 : Tree Nat := .node node428 node322 +def node7601 : Tree Nat := .node node7600 node4719 +def node7602 : Tree Nat := .node node6959 node7384 +def node7603 : Tree Nat := .node node6177 node7602 +def node7604 : Tree Nat := .node node7601 node7603 +def node7605 : Tree Nat := .node node7604 node6798 +def node7606 : Tree Nat := .node node7599 node7605 +def node7607 : Tree Nat := .node node224 node7562 +def node7608 : Tree Nat := .node node6037 node7607 +def node7609 : Tree Nat := .node node7608 node6403 +def node7610 : Tree Nat := .node node7562 node5087 +def node7611 : Tree Nat := .node node6801 node7610 +def node7612 : Tree Nat := .node node7611 node7194 +def node7613 : Tree Nat := .node node7609 node7612 +def node7614 : Tree Nat := .node node7613 node7200 +def node7615 : Tree Nat := .node node7606 node7614 +def node7616 : Tree Nat := .node node1 node7465 +def node7617 : Tree Nat := .node node7616 node6048 +def node7618 : Tree Nat := .node node7205 node7617 +def node7619 : Tree Nat := .node node466 node7403 +def node7620 : Tree Nat := .node node7619 node7207 +def node7621 : Tree Nat := .node node7620 node5666 +def node7622 : Tree Nat := .node node7618 node7621 +def node7623 : Tree Nat := .node node6977 node7412 +def node7624 : Tree Nat := .node node7211 node7623 +def node7625 : Tree Nat := .node node7624 node7215 +def node7626 : Tree Nat := .node node7625 node7219 +def node7627 : Tree Nat := .node node7622 node7626 +def node7628 : Tree Nat := .node node6176 node7343 +def node7629 : Tree Nat := .node node6825 node7628 +def node7630 : Tree Nat := .node node7629 node6422 +def node7631 : Tree Nat := .node node7630 node6056 +def node7632 : Tree Nat := .node node490 node7384 +def node7633 : Tree Nat := .node node7632 node7222 +def node7634 : Tree Nat := .node node7633 node5679 +def node7635 : Tree Nat := .node node1 node7593 +def node7636 : Tree Nat := .node node7635 node7225 +def node7637 : Tree Nat := .node node7636 node6830 +def node7638 : Tree Nat := .node node7634 node7637 +def node7639 : Tree Nat := .node node7631 node7638 +def node7640 : Tree Nat := .node node7627 node7639 +def node7641 : Tree Nat := .node node7615 node7640 +def node7642 : Tree Nat := .node node7592 node7641 +def node7643 : Tree Nat := .node node2937 node7465 +def node7644 : Tree Nat := .node node7243 node7643 +def node7645 : Tree Nat := .node node7644 node7246 +def node7646 : Tree Nat := .node node7645 node6430 +def node7647 : Tree Nat := .node node7241 node7646 +def node7648 : Tree Nat := .node node195 node7593 +def node7649 : Tree Nat := .node node7250 node7648 +def node7650 : Tree Nat := .node node1 node7457 +def node7651 : Tree Nat := .node node7650 node5702 +def node7652 : Tree Nat := .node node7649 node7651 +def node7653 : Tree Nat := .node node7652 node7255 +def node7654 : Tree Nat := .node node2738 node7366 +def node7655 : Tree Nat := .node node7654 node7257 +def node7656 : Tree Nat := .node node7655 node7260 +def node7657 : Tree Nat := .node node7656 node7265 +def node7658 : Tree Nat := .node node7653 node7657 +def node7659 : Tree Nat := .node node7647 node7658 +def node7660 : Tree Nat := .node node6320 node7514 +def node7661 : Tree Nat := .node node6860 node7660 +def node7662 : Tree Nat := .node node6554 node7395 +def node7663 : Tree Nat := .node node6177 node7662 +def node7664 : Tree Nat := .node node7661 node7663 +def node7665 : Tree Nat := .node node7664 node6869 +def node7666 : Tree Nat := .node node7272 node7665 +def node7667 : Tree Nat := .node node5826 node7203 +def node7668 : Tree Nat := .node node6872 node7667 +def node7669 : Tree Nat := .node node7668 node7275 +def node7670 : Tree Nat := .node node7669 node6877 +def node7671 : Tree Nat := .node node6668 node7486 +def node7672 : Tree Nat := .node node6104 node7671 +def node7673 : Tree Nat := .node node7672 node6457 +def node7674 : Tree Nat := .node node7673 node7280 +def node7675 : Tree Nat := .node node7670 node7674 +def node7676 : Tree Nat := .node node7666 node7675 +def node7677 : Tree Nat := .node node7659 node7676 +def node7678 : Tree Nat := .node node2664 node7370 +def node7679 : Tree Nat := .node node6177 node7678 +def node7680 : Tree Nat := .node node6124 node7679 +def node7681 : Tree Nat := .node node7680 node6480 +def node7682 : Tree Nat := .node node7288 node7681 +def node7683 : Tree Nat := .node node6186 node7457 +def node7684 : Tree Nat := .node node6886 node7683 +def node7685 : Tree Nat := .node node7684 node6485 +def node7686 : Tree Nat := .node node7333 node5262 +def node7687 : Tree Nat := .node node6131 node7686 +def node7688 : Tree Nat := .node node7687 node6488 +def node7689 : Tree Nat := .node node7685 node7688 +def node7690 : Tree Nat := .node node7689 node6894 +def node7691 : Tree Nat := .node node7682 node7690 +def node7692 : Tree Nat := .node node224 node7514 +def node7693 : Tree Nat := .node node7291 node7692 +def node7694 : Tree Nat := .node node7693 node6498 +def node7695 : Tree Nat := .node node7470 node1 +def node7696 : Tree Nat := .node node6181 node7695 +def node7697 : Tree Nat := .node node6898 node7696 +def node7698 : Tree Nat := .node node7694 node7697 +def node7699 : Tree Nat := .node node7698 node7303 +def node7700 : Tree Nat := .node node1956 node7333 +def node7701 : Tree Nat := .node node195 node7412 +def node7702 : Tree Nat := .node node7700 node7701 +def node7703 : Tree Nat := .node node7702 node6511 +def node7704 : Tree Nat := .node node7403 node1 +def node7705 : Tree Nat := .node node6912 node7704 +def node7706 : Tree Nat := .node node6911 node7705 +def node7707 : Tree Nat := .node node7703 node7706 +def node7708 : Tree Nat := .node node7707 node7308 +def node7709 : Tree Nat := .node node7699 node7708 +def node7710 : Tree Nat := .node node7691 node7709 +def node7711 : Tree Nat := .node node7677 node7710 +def node7712 : Tree Nat := .node node7642 node7711 +def node7713 : Tree Nat := .node node7537 node7712 +def node7714 : Tree Nat := .leaf 604 +def node7715 : Tree Nat := .node node7315 node7714 +def node7716 : Tree Nat := .node node5803 node7715 +def node7717 : Tree Nat := .node node6931 node7716 +def node7718 : Tree Nat := .leaf 595 +def node7719 : Tree Nat := .node node6933 node7718 +def node7720 : Tree Nat := .node node5806 node7719 +def node7721 : Tree Nat := .leaf 599 +def node7722 : Tree Nat := .node node3528 node7721 +def node7723 : Tree Nat := .node node341 node7722 +def node7724 : Tree Nat := .node node7720 node7723 +def node7725 : Tree Nat := .node node7717 node7724 +def node7726 : Tree Nat := .node node7725 node7324 +def node7727 : Tree Nat := .leaf 606 +def node7728 : Tree Nat := .node node6188 node7727 +def node7729 : Tree Nat := .node node6187 node7728 +def node7730 : Tree Nat := .node node7328 node7729 +def node7731 : Tree Nat := .node node7730 node6196 +def node7732 : Tree Nat := .leaf 579 +def node7733 : Tree Nat := .node node6539 node7732 +def node7734 : Tree Nat := .node node5832 node7733 +def node7735 : Tree Nat := .leaf 580 +def node7736 : Tree Nat := .node node3150 node7735 +def node7737 : Tree Nat := .node node6198 node7736 +def node7738 : Tree Nat := .node node7734 node7737 +def node7739 : Tree Nat := .node node7738 node6942 +def node7740 : Tree Nat := .node node7731 node7739 +def node7741 : Tree Nat := .node node7726 node7740 +def node7742 : Tree Nat := .leaf 602 +def node7743 : Tree Nat := .node node322 node7742 +def node7744 : Tree Nat := .node node7338 node7743 +def node7745 : Tree Nat := .leaf 582 +def node7746 : Tree Nat := .node node1 node7745 +def node7747 : Tree Nat := .leaf 607 +def node7748 : Tree Nat := .node node3560 node7747 +def node7749 : Tree Nat := .node node7746 node7748 +def node7750 : Tree Nat := .node node7744 node7749 +def node7751 : Tree Nat := .node node7336 node7750 +def node7752 : Tree Nat := .leaf 583 +def node7753 : Tree Nat := .node node1 node7752 +def node7754 : Tree Nat := .node node7753 node7344 +def node7755 : Tree Nat := .node node6953 node7754 +def node7756 : Tree Nat := .leaf 590 +def node7757 : Tree Nat := .node node61 node7756 +def node7758 : Tree Nat := .node node7757 node4926 +def node7759 : Tree Nat := .node node7758 node6556 +def node7760 : Tree Nat := .node node7755 node7759 +def node7761 : Tree Nat := .node node7751 node7760 +def node7762 : Tree Nat := .leaf 591 +def node7763 : Tree Nat := .node node1 node7762 +def node7764 : Tree Nat := .node node7763 node6963 +def node7765 : Tree Nat := .node node6961 node7764 +def node7766 : Tree Nat := .node node71 node7745 +def node7767 : Tree Nat := .node node7766 node7349 +def node7768 : Tree Nat := .leaf 568 +def node7769 : Tree Nat := .node node1 node7768 +def node7770 : Tree Nat := .node node7769 node3170 +def node7771 : Tree Nat := .node node7767 node7770 +def node7772 : Tree Nat := .node node7765 node7771 +def node7773 : Tree Nat := .leaf 594 +def node7774 : Tree Nat := .node node1 node7773 +def node7775 : Tree Nat := .node node3175 node7762 +def node7776 : Tree Nat := .node node7774 node7775 +def node7777 : Tree Nat := .node node7357 node7776 +def node7778 : Tree Nat := .node node7777 node7361 +def node7779 : Tree Nat := .node node7772 node7778 +def node7780 : Tree Nat := .node node7761 node7779 +def node7781 : Tree Nat := .node node7741 node7780 +def node7782 : Tree Nat := .leaf 603 +def node7783 : Tree Nat := .node node7370 node7782 +def node7784 : Tree Nat := .node node341 node7783 +def node7785 : Tree Nat := .node node6571 node7784 +def node7786 : Tree Nat := .node node7369 node7785 +def node7787 : Tree Nat := .leaf 569 +def node7788 : Tree Nat := .node node6574 node7787 +def node7789 : Tree Nat := .node node5864 node7788 +def node7790 : Tree Nat := .node node7789 node7377 +def node7791 : Tree Nat := .node node7790 node6985 +def node7792 : Tree Nat := .node node7786 node7791 +def node7793 : Tree Nat := .node node108 node7752 +def node7794 : Tree Nat := .node node7793 node7381 +def node7795 : Tree Nat := .node node7794 node6237 +def node7796 : Tree Nat := .node node7795 node7387 +def node7797 : Tree Nat := .leaf 585 +def node7798 : Tree Nat := .node node6584 node7797 +def node7799 : Tree Nat := .node node6198 node7798 +def node7800 : Tree Nat := .node node6244 node7799 +def node7801 : Tree Nat := .node node7800 node6590 +def node7802 : Tree Nat := .node node7796 node7801 +def node7803 : Tree Nat := .node node7792 node7802 +def node7804 : Tree Nat := .node node1985 node7727 +def node7805 : Tree Nat := .node node7396 node7804 +def node7806 : Tree Nat := .node node1 node7756 +def node7807 : Tree Nat := .node node7806 node6255 +def node7808 : Tree Nat := .node node7805 node7807 +def node7809 : Tree Nat := .node node7394 node7808 +def node7810 : Tree Nat := .node node1 node7718 +def node7811 : Tree Nat := .node node7810 node7404 +def node7812 : Tree Nat := .node node7402 node7811 +def node7813 : Tree Nat := .node node144 node7773 +def node7814 : Tree Nat := .node node7813 node6594 +def node7815 : Tree Nat := .node node7814 node6995 +def node7816 : Tree Nat := .node node7812 node7815 +def node7817 : Tree Nat := .node node7809 node7816 +def node7818 : Tree Nat := .node node1 node7732 +def node7819 : Tree Nat := .node node7818 node5463 +def node7820 : Tree Nat := .node node7410 node7819 +def node7821 : Tree Nat := .leaf 578 +def node7822 : Tree Nat := .node node154 node7821 +def node7823 : Tree Nat := .node node7822 node6607 +def node7824 : Tree Nat := .leaf 586 +def node7825 : Tree Nat := .node node1 node7824 +def node7826 : Tree Nat := .node node7825 node7413 +def node7827 : Tree Nat := .node node7823 node7826 +def node7828 : Tree Nat := .node node7820 node7827 +def node7829 : Tree Nat := .leaf 587 +def node7830 : Tree Nat := .node node2416 node7829 +def node7831 : Tree Nat := .node node7417 node7830 +def node7832 : Tree Nat := .node node1 node7821 +def node7833 : Tree Nat := .node node6999 node7718 +def node7834 : Tree Nat := .node node7832 node7833 +def node7835 : Tree Nat := .node node7831 node7834 +def node7836 : Tree Nat := .leaf 575 +def node7837 : Tree Nat := .node node7836 node6180 +def node7838 : Tree Nat := .node node7837 node6613 +def node7839 : Tree Nat := .node node7422 node7838 +def node7840 : Tree Nat := .node node7835 node7839 +def node7841 : Tree Nat := .node node7828 node7840 +def node7842 : Tree Nat := .node node7817 node7841 +def node7843 : Tree Nat := .node node7803 node7842 +def node7844 : Tree Nat := .node node7781 node7843 +def node7845 : Tree Nat := .leaf 601 +def node7846 : Tree Nat := .node node6279 node7845 +def node7847 : Tree Nat := .node node341 node7846 +def node7848 : Tree Nat := .node node6625 node7847 +def node7849 : Tree Nat := .node node7433 node7848 +def node7850 : Tree Nat := .leaf 600 +def node7851 : Tree Nat := .node node6574 node7850 +def node7852 : Tree Nat := .node node6632 node7851 +def node7853 : Tree Nat := .node node7852 node6636 +def node7854 : Tree Nat := .node node7438 node7853 +def node7855 : Tree Nat := .node node7849 node7854 +def node7856 : Tree Nat := .node node2359 node7752 +def node7857 : Tree Nat := .node node7022 node7856 +def node7858 : Tree Nat := .node node6647 node7745 +def node7859 : Tree Nat := .node node6198 node7858 +def node7860 : Tree Nat := .node node7857 node7859 +def node7861 : Tree Nat := .node node2780 node7742 +def node7862 : Tree Nat := .node node6651 node7861 +def node7863 : Tree Nat := .node node7862 node6654 +def node7864 : Tree Nat := .node node7860 node7863 +def node7865 : Tree Nat := .node node7451 node7864 +def node7866 : Tree Nat := .node node7855 node7865 +def node7867 : Tree Nat := .node node1894 node7714 +def node7868 : Tree Nat := .node node7032 node7867 +def node7869 : Tree Nat := .node node7868 node7462 +def node7870 : Tree Nat := .node node7460 node7869 +def node7871 : Tree Nat := .node node7870 node7474 +def node7872 : Tree Nat := .leaf 572 +def node7873 : Tree Nat := .node node1 node7872 +def node7874 : Tree Nat := .node node7873 node7480 +def node7875 : Tree Nat := .node node7045 node7874 +def node7876 : Tree Nat := .node node7479 node7875 +def node7877 : Tree Nat := .leaf 593 +def node7878 : Tree Nat := .node node6602 node7877 +def node7879 : Tree Nat := .node node7487 node7878 +def node7880 : Tree Nat := .node node7485 node7879 +def node7881 : Tree Nat := .node node7880 node7054 +def node7882 : Tree Nat := .node node7876 node7881 +def node7883 : Tree Nat := .node node7871 node7882 +def node7884 : Tree Nat := .node node7866 node7883 +def node7885 : Tree Nat := .node node6549 node7850 +def node7886 : Tree Nat := .node node6698 node7885 +def node7887 : Tree Nat := .leaf 605 +def node7888 : Tree Nat := .node node3616 node7887 +def node7889 : Tree Nat := .node node7494 node7888 +def node7890 : Tree Nat := .node node7886 node7889 +def node7891 : Tree Nat := .node node7063 node7890 +def node7892 : Tree Nat := .node node7891 node7503 +def node7893 : Tree Nat := .leaf 571 +def node7894 : Tree Nat := .node node7893 node7074 +def node7895 : Tree Nat := .node node6331 node7894 +def node7896 : Tree Nat := .node node7506 node7895 +def node7897 : Tree Nat := .node node7896 node7081 +def node7898 : Tree Nat := .leaf 589 +def node7899 : Tree Nat := .node node3232 node7898 +def node7900 : Tree Nat := .node node6339 node7899 +def node7901 : Tree Nat := .node node7085 node7900 +def node7902 : Tree Nat := .node node7901 node7090 +def node7903 : Tree Nat := .node node7897 node7902 +def node7904 : Tree Nat := .node node7892 node7903 +def node7905 : Tree Nat := .node node2913 node7787 +def node7906 : Tree Nat := .node node7905 node7511 +def node7907 : Tree Nat := .node node7906 node6727 +def node7908 : Tree Nat := .node node7907 node7517 +def node7909 : Tree Nat := .node node2796 node7836 +def node7910 : Tree Nat := .node node7519 node7909 +def node7911 : Tree Nat := .node node6664 node7821 +def node7912 : Tree Nat := .node node7100 node7911 +def node7913 : Tree Nat := .node node7910 node7912 +def node7914 : Tree Nat := .node node7913 node7105 +def node7915 : Tree Nat := .node node7908 node7914 +def node7916 : Tree Nat := .leaf 573 +def node7917 : Tree Nat := .node node1 node7916 +def node7918 : Tree Nat := .node node7917 node3198 +def node7919 : Tree Nat := .node node7113 node7918 +def node7920 : Tree Nat := .node node7527 node7919 +def node7921 : Tree Nat := .node node6725 node7762 +def node7922 : Tree Nat := .node node7117 node7921 +def node7923 : Tree Nat := .leaf 597 +def node7924 : Tree Nat := .node node3204 node7923 +def node7925 : Tree Nat := .node node7529 node7924 +def node7926 : Tree Nat := .node node7922 node7925 +def node7927 : Tree Nat := .node node7926 node7123 +def node7928 : Tree Nat := .node node7920 node7927 +def node7929 : Tree Nat := .node node7915 node7928 +def node7930 : Tree Nat := .node node7904 node7929 +def node7931 : Tree Nat := .node node7884 node7930 +def node7932 : Tree Nat := .node node7844 node7931 +def node7933 : Tree Nat := .node node1 node7829 +def node7934 : Tree Nat := .node node3627 node7887 +def node7935 : Tree Nat := .node node7933 node7934 +def node7936 : Tree Nat := .node node7131 node7935 +def node7937 : Tree Nat := .node node337 node7768 +def node7938 : Tree Nat := .node node1990 node7923 +def node7939 : Tree Nat := .node node7937 node7938 +def node7940 : Tree Nat := .node node7337 node7850 +def node7941 : Tree Nat := .node node7133 node7940 +def node7942 : Tree Nat := .node node7939 node7941 +def node7943 : Tree Nat := .node node7936 node7942 +def node7944 : Tree Nat := .node node1 node7787 +def node7945 : Tree Nat := .node node7944 node6002 +def node7946 : Tree Nat := .node node7543 node7945 +def node7947 : Tree Nat := .node node349 node7824 +def node7948 : Tree Nat := .node node7947 node5125 +def node7949 : Tree Nat := .node node7948 node7142 +def node7950 : Tree Nat := .node node7946 node7949 +def node7951 : Tree Nat := .node node7943 node7950 +def node7952 : Tree Nat := .node node1981 node7747 +def node7953 : Tree Nat := .node node7549 node7952 +def node7954 : Tree Nat := .node node7548 node7953 +def node7955 : Tree Nat := .leaf 574 +def node7956 : Tree Nat := .node node362 node7955 +def node7957 : Tree Nat := .leaf 598 +def node7958 : Tree Nat := .node node6647 node7957 +def node7959 : Tree Nat := .node node7956 node7958 +def node7960 : Tree Nat := .node node7959 node7553 +def node7961 : Tree Nat := .node node7954 node7960 +def node7962 : Tree Nat := .leaf 581 +def node7963 : Tree Nat := .node node2414 node7962 +def node7964 : Tree Nat := .node node7556 node7963 +def node7965 : Tree Nat := .node node6989 node7962 +def node7966 : Tree Nat := .node node7153 node7965 +def node7967 : Tree Nat := .node node7964 node7966 +def node7968 : Tree Nat := .node node371 node7836 +def node7969 : Tree Nat := .node node7968 node5143 +def node7970 : Tree Nat := .node node7969 node7158 +def node7971 : Tree Nat := .node node7967 node7970 +def node7972 : Tree Nat := .node node7961 node7971 +def node7973 : Tree Nat := .node node7951 node7972 +def node7974 : Tree Nat := .node node2144 node7782 +def node7975 : Tree Nat := .node node7567 node7974 +def node7976 : Tree Nat := .leaf 584 +def node7977 : Tree Nat := .node node1 node7976 +def node7978 : Tree Nat := .node node7977 node6255 +def node7979 : Tree Nat := .node node7975 node7978 +def node7980 : Tree Nat := .node node7566 node7979 +def node7981 : Tree Nat := .node node5835 node7916 +def node7982 : Tree Nat := .node node7168 node7981 +def node7983 : Tree Nat := .node node1 node7797 +def node7984 : Tree Nat := .node node7983 node7571 +def node7985 : Tree Nat := .node node7982 node7984 +def node7986 : Tree Nat := .leaf 592 +def node7987 : Tree Nat := .node node391 node7986 +def node7988 : Tree Nat := .node node7987 node6778 +def node7989 : Tree Nat := .node node7988 node6781 +def node7990 : Tree Nat := .node node7985 node7989 +def node7991 : Tree Nat := .node node7980 node7990 +def node7992 : Tree Nat := .node node1 node7877 +def node7993 : Tree Nat := .node node7992 node7576 +def node7994 : Tree Nat := .node node7175 node7993 +def node7995 : Tree Nat := .node node403 node7976 +def node7996 : Tree Nat := .node node7995 node5172 +def node7997 : Tree Nat := .leaf 570 +def node7998 : Tree Nat := .node node1 node7997 +def node7999 : Tree Nat := .node node7998 node6264 +def node8000 : Tree Nat := .node node7996 node7999 +def node8001 : Tree Nat := .node node7994 node8000 +def node8002 : Tree Nat := .leaf 596 +def node8003 : Tree Nat := .node node1 node8002 +def node8004 : Tree Nat := .node node6186 node7986 +def node8005 : Tree Nat := .node node8003 node8004 +def node8006 : Tree Nat := .node node7584 node8005 +def node8007 : Tree Nat := .node node8006 node7588 +def node8008 : Tree Nat := .node node8001 node8007 +def node8009 : Tree Nat := .node node7991 node8008 +def node8010 : Tree Nat := .node node7973 node8009 +def node8011 : Tree Nat := .node node7593 node7721 +def node8012 : Tree Nat := .node node6792 node8011 +def node8013 : Tree Nat := .node node3773 node7714 +def node8014 : Tree Nat := .node node7596 node8013 +def node8015 : Tree Nat := .node node8012 node8014 +def node8016 : Tree Nat := .node node7187 node8015 +def node8017 : Tree Nat := .node node2972 node7893 +def node8018 : Tree Nat := .node node7600 node8017 +def node8019 : Tree Nat := .node node8018 node7603 +def node8020 : Tree Nat := .node node8019 node6798 +def node8021 : Tree Nat := .node node8016 node8020 +def node8022 : Tree Nat := .node node6939 node7872 +def node8023 : Tree Nat := .node node6805 node8022 +def node8024 : Tree Nat := .node node3378 node7829 +def node8025 : Tree Nat := .node node6198 node8024 +def node8026 : Tree Nat := .node node8023 node8025 +def node8027 : Tree Nat := .node node8026 node6812 +def node8028 : Tree Nat := .node node7613 node8027 +def node8029 : Tree Nat := .node node8021 node8028 +def node8030 : Tree Nat := .node node7955 node5661 +def node8031 : Tree Nat := .node node7616 node8030 +def node8032 : Tree Nat := .node node7205 node8031 +def node8033 : Tree Nat := .node node7108 node7747 +def node8034 : Tree Nat := .node node7619 node8033 +def node8035 : Tree Nat := .node node1 node7986 +def node8036 : Tree Nat := .node node8035 node3818 +def node8037 : Tree Nat := .node node8034 node8036 +def node8038 : Tree Nat := .node node8032 node8037 +def node8039 : Tree Nat := .node node1 node7923 +def node8040 : Tree Nat := .leaf 577 +def node8041 : Tree Nat := .node node7108 node8040 +def node8042 : Tree Nat := .node node8039 node8041 +def node8043 : Tree Nat := .node node7624 node8042 +def node8044 : Tree Nat := .node node475 node8002 +def node8045 : Tree Nat := .node node8044 node7217 +def node8046 : Tree Nat := .node node8045 node6821 +def node8047 : Tree Nat := .node node8043 node8046 +def node8048 : Tree Nat := .node node8038 node8047 +def node8049 : Tree Nat := .node node1 node7962 +def node8050 : Tree Nat := .node node8049 node6421 +def node8051 : Tree Nat := .node node7629 node8050 +def node8052 : Tree Nat := .node node485 node7735 +def node8053 : Tree Nat := .node node8052 node5229 +def node8054 : Tree Nat := .leaf 588 +def node8055 : Tree Nat := .node node1 node8054 +def node8056 : Tree Nat := .node node8055 node3412 +def node8057 : Tree Nat := .node node8053 node8056 +def node8058 : Tree Nat := .node node8051 node8057 +def node8059 : Tree Nat := .node node6929 node7898 +def node8060 : Tree Nat := .node node7632 node8059 +def node8061 : Tree Nat := .node node1 node7735 +def node8062 : Tree Nat := .node node3221 node8002 +def node8063 : Tree Nat := .node node8061 node8062 +def node8064 : Tree Nat := .node node8060 node8063 +def node8065 : Tree Nat := .node node8064 node7637 +def node8066 : Tree Nat := .node node8058 node8065 +def node8067 : Tree Nat := .node node8048 node8066 +def node8068 : Tree Nat := .node node8029 node8067 +def node8069 : Tree Nat := .node node8010 node8068 +def node8070 : Tree Nat := .node node1 node7898 +def node8071 : Tree Nat := .node node8070 node5690 +def node8072 : Tree Nat := .node node7234 node8071 +def node8073 : Tree Nat := .node node1578 node7997 +def node8074 : Tree Nat := .node node6999 node7957 +def node8075 : Tree Nat := .node node8073 node8074 +def node8076 : Tree Nat := .node node3721 node7742 +def node8077 : Tree Nat := .node node7238 node8076 +def node8078 : Tree Nat := .node node8075 node8077 +def node8079 : Tree Nat := .node node8072 node8078 +def node8080 : Tree Nat := .node node1 node7893 +def node8081 : Tree Nat := .node node8080 node7245 +def node8082 : Tree Nat := .node node7644 node8081 +def node8083 : Tree Nat := .node node3148 node8054 +def node8084 : Tree Nat := .node node2506 node7845 +def node8085 : Tree Nat := .node node8083 node8084 +def node8086 : Tree Nat := .node node8085 node6429 +def node8087 : Tree Nat := .node node8082 node8086 +def node8088 : Tree Nat := .node node8079 node8087 +def node8089 : Tree Nat := .leaf 576 +def node8090 : Tree Nat := .node node2749 node8089 +def node8091 : Tree Nat := .node node6674 node7721 +def node8092 : Tree Nat := .node node8090 node8091 +def node8093 : Tree Nat := .node node8092 node7254 +def node8094 : Tree Nat := .node node7652 node8093 +def node8095 : Tree Nat := .node node7065 node7797 +def node8096 : Tree Nat := .node node7654 node8095 +def node8097 : Tree Nat := .node node3326 node7976 +def node8098 : Tree Nat := .node node7259 node8097 +def node8099 : Tree Nat := .node node8096 node8098 +def node8100 : Tree Nat := .node node2320 node8040 +def node8101 : Tree Nat := .node node7094 node7782 +def node8102 : Tree Nat := .node node8100 node8101 +def node8103 : Tree Nat := .node node8102 node7264 +def node8104 : Tree Nat := .node node8099 node8103 +def node8105 : Tree Nat := .node node8094 node8104 +def node8106 : Tree Nat := .node node8088 node8105 +def node8107 : Tree Nat := .node node6659 node7887 +def node8108 : Tree Nat := .node node6855 node8107 +def node8109 : Tree Nat := .node node8108 node6442 +def node8110 : Tree Nat := .node node7271 node8109 +def node8111 : Tree Nat := .node node8110 node7665 +def node8112 : Tree Nat := .node node3468 node7773 +def node8113 : Tree Nat := .node node6198 node8112 +def node8114 : Tree Nat := .node node7672 node8113 +def node8115 : Tree Nat := .node node8114 node7280 +def node8116 : Tree Nat := .node node7670 node8115 +def node8117 : Tree Nat := .node node8111 node8116 +def node8118 : Tree Nat := .node node8106 node8117 +def node8119 : Tree Nat := .node node2239 node7845 +def node8120 : Tree Nat := .node node6119 node8119 +def node8121 : Tree Nat := .node node6180 node7727 +def node8122 : Tree Nat := .node node341 node8121 +def node8123 : Tree Nat := .node node8120 node8122 +def node8124 : Tree Nat := .node node7287 node8123 +def node8125 : Tree Nat := .node node3061 node7872 +def node8126 : Tree Nat := .node node6123 node8125 +def node8127 : Tree Nat := .node node8126 node7679 +def node8128 : Tree Nat := .node node8127 node6480 +def node8129 : Tree Nat := .node node8124 node8128 +def node8130 : Tree Nat := .node node2679 node7916 +def node8131 : Tree Nat := .node node6135 node8130 +def node8132 : Tree Nat := .node node6229 node7756 +def node8133 : Tree Nat := .node node6198 node8132 +def node8134 : Tree Nat := .node node8131 node8133 +def node8135 : Tree Nat := .node node8134 node6893 +def node8136 : Tree Nat := .node node7689 node8135 +def node8137 : Tree Nat := .node node8129 node8136 +def node8138 : Tree Nat := .node node8089 node5423 +def node8139 : Tree Nat := .node node6497 node8138 +def node8140 : Tree Nat := .node node7693 node8139 +def node8141 : Tree Nat := .node node8140 node7697 +def node8142 : Tree Nat := .node node7083 node8040 +def node8143 : Tree Nat := .node node6901 node8142 +def node8144 : Tree Nat := .node node2521 node7732 +def node8145 : Tree Nat := .node node6503 node8144 +def node8146 : Tree Nat := .node node8143 node8145 +def node8147 : Tree Nat := .node node8146 node7302 +def node8148 : Tree Nat := .node node8141 node8147 +def node8149 : Tree Nat := .node node2526 node7877 +def node8150 : Tree Nat := .node node6916 node8149 +def node8151 : Tree Nat := .node node7068 node7957 +def node8152 : Tree Nat := .node node6349 node8151 +def node8153 : Tree Nat := .node node8150 node8152 +def node8154 : Tree Nat := .node node8153 node6921 +def node8155 : Tree Nat := .node node7707 node8154 +def node8156 : Tree Nat := .node node8148 node8155 +def node8157 : Tree Nat := .node node8137 node8156 +def node8158 : Tree Nat := .node node8118 node8157 +def node8159 : Tree Nat := .node node8069 node8158 +def node8160 : Tree Nat := .node node7932 node8159 +def node8161 : Tree Nat := .leaf 645 +def node8162 : Tree Nat := .node node8161 node411 +def node8163 : Tree Nat := .node node8162 node7719 +def node8164 : Tree Nat := .leaf 647 +def node8165 : Tree Nat := .node node3528 node8164 +def node8166 : Tree Nat := .node node341 node8165 +def node8167 : Tree Nat := .node node8163 node8166 +def node8168 : Tree Nat := .node node7717 node8167 +def node8169 : Tree Nat := .leaf 608 +def node8170 : Tree Nat := .node node6528 node8169 +def node8171 : Tree Nat := .node node6177 node8170 +def node8172 : Tree Nat := .node node7322 node8171 +def node8173 : Tree Nat := .node node8172 node6536 +def node8174 : Tree Nat := .node node8168 node8173 +def node8175 : Tree Nat := .leaf 617 +def node8176 : Tree Nat := .node node3143 node8175 +def node8177 : Tree Nat := .node node196 node8176 +def node8178 : Tree Nat := .node node6194 node8177 +def node8179 : Tree Nat := .node node7730 node8178 +def node8180 : Tree Nat := .leaf 610 +def node8181 : Tree Nat := .node node6939 node8180 +def node8182 : Tree Nat := .node node5836 node8181 +def node8183 : Tree Nat := .node node8182 node6203 +def node8184 : Tree Nat := .node node7738 node8183 +def node8185 : Tree Nat := .node node8179 node8184 +def node8186 : Tree Nat := .node node8174 node8185 +def node8187 : Tree Nat := .leaf 624 +def node8188 : Tree Nat := .node node2348 node8187 +def node8189 : Tree Nat := .node node7757 node8188 +def node8190 : Tree Nat := .node node8189 node6556 +def node8191 : Tree Nat := .node node7755 node8190 +def node8192 : Tree Nat := .node node7751 node8191 +def node8193 : Tree Nat := .leaf 649 +def node8194 : Tree Nat := .node node8193 node6962 +def node8195 : Tree Nat := .node node7763 node8194 +def node8196 : Tree Nat := .node node6961 node8195 +def node8197 : Tree Nat := .leaf 614 +def node8198 : Tree Nat := .node node5821 node8197 +def node8199 : Tree Nat := .node node7766 node8198 +def node8200 : Tree Nat := .leaf 631 +def node8201 : Tree Nat := .node node3169 node8200 +def node8202 : Tree Nat := .node node7769 node8201 +def node8203 : Tree Nat := .node node8199 node8202 +def node8204 : Tree Nat := .node node8196 node8203 +def node8205 : Tree Nat := .leaf 632 +def node8206 : Tree Nat := .node node5802 node8205 +def node8207 : Tree Nat := .node node7359 node8206 +def node8208 : Tree Nat := .node node8207 node6971 +def node8209 : Tree Nat := .node node7777 node8208 +def node8210 : Tree Nat := .node node8204 node8209 +def node8211 : Tree Nat := .node node8192 node8210 +def node8212 : Tree Nat := .node node8186 node8211 +def node8213 : Tree Nat := .node node7366 node8187 +def node8214 : Tree Nat := .node node5803 node8213 +def node8215 : Tree Nat := .node node6979 node8214 +def node8216 : Tree Nat := .leaf 646 +def node8217 : Tree Nat := .node node8216 node411 +def node8218 : Tree Nat := .node node8217 node6570 +def node8219 : Tree Nat := .node node8218 node7784 +def node8220 : Tree Nat := .node node8215 node8219 +def node8221 : Tree Nat := .leaf 612 +def node8222 : Tree Nat := .node node6578 node8221 +def node8223 : Tree Nat := .node node5867 node8222 +def node8224 : Tree Nat := .node node8223 node6984 +def node8225 : Tree Nat := .node node7790 node8224 +def node8226 : Tree Nat := .node node8220 node8225 +def node8227 : Tree Nat := .leaf 626 +def node8228 : Tree Nat := .node node6235 node8227 +def node8229 : Tree Nat := .node node6187 node8228 +def node8230 : Tree Nat := .node node7794 node8229 +def node8231 : Tree Nat := .node node1969 node8180 +def node8232 : Tree Nat := .node node5876 node8231 +def node8233 : Tree Nat := .leaf 625 +def node8234 : Tree Nat := .node node7384 node8233 +def node8235 : Tree Nat := .node node196 node8234 +def node8236 : Tree Nat := .node node8232 node8235 +def node8237 : Tree Nat := .node node8230 node8236 +def node8238 : Tree Nat := .leaf 628 +def node8239 : Tree Nat := .node node2808 node8238 +def node8240 : Tree Nat := .node node5883 node8239 +def node8241 : Tree Nat := .node node8240 node6589 +def node8242 : Tree Nat := .node node7800 node8241 +def node8243 : Tree Nat := .node node8237 node8242 +def node8244 : Tree Nat := .node node8226 node8243 +def node8245 : Tree Nat := .leaf 638 +def node8246 : Tree Nat := .node node3610 node8245 +def node8247 : Tree Nat := .node node7392 node8246 +def node8248 : Tree Nat := .node node6253 node8247 +def node8249 : Tree Nat := .leaf 613 +def node8250 : Tree Nat := .node node340 node8249 +def node8251 : Tree Nat := .node node7806 node8250 +def node8252 : Tree Nat := .node node7805 node8251 +def node8253 : Tree Nat := .node node8248 node8252 +def node8254 : Tree Nat := .node node8253 node7816 +def node8255 : Tree Nat := .leaf 642 +def node8256 : Tree Nat := .leaf 622 +def node8257 : Tree Nat := .node node8255 node8256 +def node8258 : Tree Nat := .node node7818 node8257 +def node8259 : Tree Nat := .node node7410 node8258 +def node8260 : Tree Nat := .leaf 618 +def node8261 : Tree Nat := .node node6606 node8260 +def node8262 : Tree Nat := .node node7822 node8261 +def node8263 : Tree Nat := .node node8262 node7826 +def node8264 : Tree Nat := .node node8259 node8263 +def node8265 : Tree Nat := .node node8264 node7840 +def node8266 : Tree Nat := .node node8254 node8265 +def node8267 : Tree Nat := .node node8244 node8266 +def node8268 : Tree Nat := .node node8212 node8267 +def node8269 : Tree Nat := .leaf 648 +def node8270 : Tree Nat := .leaf 616 +def node8271 : Tree Nat := .node node8269 node8270 +def node8272 : Tree Nat := .node node5803 node8271 +def node8273 : Tree Nat := .node node7430 node8272 +def node8274 : Tree Nat := .leaf 651 +def node8275 : Tree Nat := .node node8274 node411 +def node8276 : Tree Nat := .node node8275 node6624 +def node8277 : Tree Nat := .node node8276 node7847 +def node8278 : Tree Nat := .node node8273 node8277 +def node8279 : Tree Nat := .node node2344 node8260 +def node8280 : Tree Nat := .node node6177 node8279 +def node8281 : Tree Nat := .node node7437 node8280 +def node8282 : Tree Nat := .leaf 652 +def node8283 : Tree Nat := .node node1 node8282 +def node8284 : Tree Nat := .node node8283 node6635 +def node8285 : Tree Nat := .node node7852 node8284 +def node8286 : Tree Nat := .node node8281 node8285 +def node8287 : Tree Nat := .node node8278 node8286 +def node8288 : Tree Nat := .leaf 630 +def node8289 : Tree Nat := .node node7444 node8288 +def node8290 : Tree Nat := .node node6187 node8289 +def node8291 : Tree Nat := .node node7443 node8290 +def node8292 : Tree Nat := .node node7326 node8193 +def node8293 : Tree Nat := .node node196 node8292 +def node8294 : Tree Nat := .node node7019 node8293 +def node8295 : Tree Nat := .node node8291 node8294 +def node8296 : Tree Nat := .node node8295 node7864 +def node8297 : Tree Nat := .node node8287 node8296 +def node8298 : Tree Nat := .leaf 611 +def node8299 : Tree Nat := .node node7353 node8298 +def node8300 : Tree Nat := .node node341 node8299 +def node8301 : Tree Nat := .node node7868 node8300 +def node8302 : Tree Nat := .node node7460 node8301 +def node8303 : Tree Nat := .node node2322 node8227 +def node8304 : Tree Nat := .node node7037 node8303 +def node8305 : Tree Nat := .node node8304 node7040 +def node8306 : Tree Nat := .node node7473 node8305 +def node8307 : Tree Nat := .node node8302 node8306 +def node8308 : Tree Nat := .leaf 643 +def node8309 : Tree Nat := .node node8308 node8245 +def node8310 : Tree Nat := .node node6675 node8309 +def node8311 : Tree Nat := .node node7478 node8310 +def node8312 : Tree Nat := .node node6528 node8270 +def node8313 : Tree Nat := .node node7044 node8312 +def node8314 : Tree Nat := .node node1 node8164 +def node8315 : Tree Nat := .leaf 633 +def node8316 : Tree Nat := .node node7375 node8315 +def node8317 : Tree Nat := .node node8314 node8316 +def node8318 : Tree Nat := .node node8313 node8317 +def node8319 : Tree Nat := .node node8311 node8318 +def node8320 : Tree Nat := .node node8319 node7881 +def node8321 : Tree Nat := .node node8307 node8320 +def node8322 : Tree Nat := .node node8297 node8321 +def node8323 : Tree Nat := .node node6694 node8205 +def node8324 : Tree Nat := .node node6314 node8323 +def node8325 : Tree Nat := .node node7062 node8324 +def node8326 : Tree Nat := .leaf 640 +def node8327 : Tree Nat := .node node8326 node6525 +def node8328 : Tree Nat := .node node8327 node7885 +def node8329 : Tree Nat := .node node8328 node7889 +def node8330 : Tree Nat := .node node8325 node8329 +def node8331 : Tree Nat := .node node8282 node7420 +def node8332 : Tree Nat := .node node8331 node7066 +def node8333 : Tree Nat := .node node8332 node7501 +def node8334 : Tree Nat := .node node6546 node8256 +def node8335 : Tree Nat := .node node6703 node8334 +def node8336 : Tree Nat := .node node8335 node6327 +def node8337 : Tree Nat := .node node8333 node8336 +def node8338 : Tree Nat := .node node8330 node8337 +def node8339 : Tree Nat := .node node2003 node8221 +def node8340 : Tree Nat := .node node6712 node8339 +def node8341 : Tree Nat := .node node1 node8193 +def node8342 : Tree Nat := .leaf 627 +def node8343 : Tree Nat := .node node3225 node8342 +def node8344 : Tree Nat := .node node8341 node8343 +def node8345 : Tree Nat := .node node8340 node8344 +def node8346 : Tree Nat := .node node7896 node8345 +def node8347 : Tree Nat := .node node7087 node8288 +def node8348 : Tree Nat := .node node6342 node8347 +def node8349 : Tree Nat := .node node8348 node6720 +def node8350 : Tree Nat := .node node7901 node8349 +def node8351 : Tree Nat := .node node8346 node8350 +def node8352 : Tree Nat := .node node8338 node8351 +def node8353 : Tree Nat := .node node3581 node8197 +def node8354 : Tree Nat := .node node6726 node8353 +def node8355 : Tree Nat := .node node7906 node8354 +def node8356 : Tree Nat := .node node6993 node8169 +def node8357 : Tree Nat := .node node7095 node8356 +def node8358 : Tree Nat := .leaf 615 +def node8359 : Tree Nat := .node node3587 node8358 +def node8360 : Tree Nat := .node node7515 node8359 +def node8361 : Tree Nat := .node node8357 node8360 +def node8362 : Tree Nat := .node node8355 node8361 +def node8363 : Tree Nat := .node node8362 node7914 +def node8364 : Tree Nat := .node node8269 node8238 +def node8365 : Tree Nat := .node node7109 node8364 +def node8366 : Tree Nat := .node node7526 node8365 +def node8367 : Tree Nat := .leaf 650 +def node8368 : Tree Nat := .node node1 node8367 +def node8369 : Tree Nat := .node node8368 node3198 +def node8370 : Tree Nat := .node node7113 node8369 +def node8371 : Tree Nat := .node node8366 node8370 +def node8372 : Tree Nat := .leaf 636 +def node8373 : Tree Nat := .node node7116 node8372 +def node8374 : Tree Nat := .node node7120 node8373 +def node8375 : Tree Nat := .node node8374 node6747 +def node8376 : Tree Nat := .node node7926 node8375 +def node8377 : Tree Nat := .node node8371 node8376 +def node8378 : Tree Nat := .node node8363 node8377 +def node8379 : Tree Nat := .node node8352 node8378 +def node8380 : Tree Nat := .node node8322 node8379 +def node8381 : Tree Nat := .node node8268 node8380 +def node8382 : Tree Nat := .node node8274 node7768 +def node8383 : Tree Nat := .node node8382 node7938 +def node8384 : Tree Nat := .node node8383 node7941 +def node8385 : Tree Nat := .node node7936 node8384 +def node8386 : Tree Nat := .leaf 609 +def node8387 : Tree Nat := .node node2409 node8386 +def node8388 : Tree Nat := .node node7944 node8387 +def node8389 : Tree Nat := .node node7543 node8388 +def node8390 : Tree Nat := .node node2394 node8255 +def node8391 : Tree Nat := .node node7947 node8390 +def node8392 : Tree Nat := .node node8391 node7142 +def node8393 : Tree Nat := .node node8389 node8392 +def node8394 : Tree Nat := .node node8385 node8393 +def node8395 : Tree Nat := .leaf 644 +def node8396 : Tree Nat := .node node8395 node7747 +def node8397 : Tree Nat := .node node7549 node8396 +def node8398 : Tree Nat := .node node7548 node8397 +def node8399 : Tree Nat := .node node7395 node8269 +def node8400 : Tree Nat := .node node7149 node8399 +def node8401 : Tree Nat := .node node7959 node8400 +def node8402 : Tree Nat := .node node8398 node8401 +def node8403 : Tree Nat := .node node2818 node8298 +def node8404 : Tree Nat := .node node7968 node8403 +def node8405 : Tree Nat := .node node322 node8326 +def node8406 : Tree Nat := .node node8405 node7157 +def node8407 : Tree Nat := .node node8404 node8406 +def node8408 : Tree Nat := .node node7967 node8407 +def node8409 : Tree Nat := .node node8402 node8408 +def node8410 : Tree Nat := .node node8394 node8409 +def node8411 : Tree Nat := .leaf 634 +def node8412 : Tree Nat := .node node195 node8411 +def node8413 : Tree Nat := .node node7563 node8412 +def node8414 : Tree Nat := .node node7165 node8413 +def node8415 : Tree Nat := .node node340 node8180 +def node8416 : Tree Nat := .node node7977 node8415 +def node8417 : Tree Nat := .node node7975 node8416 +def node8418 : Tree Nat := .node node8414 node8417 +def node8419 : Tree Nat := .leaf 641 +def node8420 : Tree Nat := .node node5835 node8419 +def node8421 : Tree Nat := .node node7168 node8420 +def node8422 : Tree Nat := .node node8421 node7984 +def node8423 : Tree Nat := .node node411 node8233 +def node8424 : Tree Nat := .node node7987 node8423 +def node8425 : Tree Nat := .node node8424 node6781 +def node8426 : Tree Nat := .node node8422 node8425 +def node8427 : Tree Nat := .node node8418 node8426 +def node8428 : Tree Nat := .leaf 637 +def node8429 : Tree Nat := .node node451 node8428 +def node8430 : Tree Nat := .node node7992 node8429 +def node8431 : Tree Nat := .node node7175 node8430 +def node8432 : Tree Nat := .node node2160 node8358 +def node8433 : Tree Nat := .node node7995 node8432 +def node8434 : Tree Nat := .node node6169 node8205 +def node8435 : Tree Nat := .node node7998 node8434 +def node8436 : Tree Nat := .node node8433 node8435 +def node8437 : Tree Nat := .node node8431 node8436 +def node8438 : Tree Nat := .node node2982 node8315 +def node8439 : Tree Nat := .node node7586 node8438 +def node8440 : Tree Nat := .node node8439 node7179 +def node8441 : Tree Nat := .node node8006 node8440 +def node8442 : Tree Nat := .node node8437 node8441 +def node8443 : Tree Nat := .node node8427 node8442 +def node8444 : Tree Nat := .node node8410 node8443 +def node8445 : Tree Nat := .node node3768 node8233 +def node8446 : Tree Nat := .node node5803 node8445 +def node8447 : Tree Nat := .node node7186 node8446 +def node8448 : Tree Nat := .node node8326 node411 +def node8449 : Tree Nat := .node node7593 node8419 +def node8450 : Tree Nat := .node node8448 node8449 +def node8451 : Tree Nat := .node node8450 node8014 +def node8452 : Tree Nat := .node node8447 node8451 +def node8453 : Tree Nat := .node node8282 node322 +def node8454 : Tree Nat := .node node8453 node8017 +def node8455 : Tree Nat := .node node8454 node7603 +def node8456 : Tree Nat := .node node2568 node8249 +def node8457 : Tree Nat := .node node6796 node8456 +def node8458 : Tree Nat := .node node8457 node6399 +def node8459 : Tree Nat := .node node8455 node8458 +def node8460 : Tree Nat := .node node8452 node8459 +def node8461 : Tree Nat := .node node8164 node8342 +def node8462 : Tree Nat := .node node6187 node8461 +def node8463 : Tree Nat := .node node7608 node8462 +def node8464 : Tree Nat := .node node7562 node8298 +def node8465 : Tree Nat := .node node6801 node8464 +def node8466 : Tree Nat := .node node3372 node8227 +def node8467 : Tree Nat := .node node196 node8466 +def node8468 : Tree Nat := .node node8465 node8467 +def node8469 : Tree Nat := .node node8463 node8468 +def node8470 : Tree Nat := .leaf 629 +def node8471 : Tree Nat := .node node6539 node8470 +def node8472 : Tree Nat := .node node6408 node8471 +def node8473 : Tree Nat := .node node8472 node6811 +def node8474 : Tree Nat := .node node8026 node8473 +def node8475 : Tree Nat := .node node8469 node8474 +def node8476 : Tree Nat := .node node8460 node8475 +def node8477 : Tree Nat := .node node195 node8255 +def node8478 : Tree Nat := .node node6816 node8477 +def node8479 : Tree Nat := .leaf 639 +def node8480 : Tree Nat := .node node7955 node8479 +def node8481 : Tree Nat := .node node7616 node8480 +def node8482 : Tree Nat := .node node8478 node8481 +def node8483 : Tree Nat := .node node3614 node8197 +def node8484 : Tree Nat := .node node8035 node8483 +def node8485 : Tree Nat := .node node8034 node8484 +def node8486 : Tree Nat := .node node8482 node8485 +def node8487 : Tree Nat := .leaf 620 +def node8488 : Tree Nat := .node node7008 node8487 +def node8489 : Tree Nat := .node node8044 node8488 +def node8490 : Tree Nat := .node node8489 node6821 +def node8491 : Tree Nat := .node node8043 node8490 +def node8492 : Tree Nat := .node node8486 node8491 +def node8493 : Tree Nat := .leaf 653 +def node8494 : Tree Nat := .node node6176 node8493 +def node8495 : Tree Nat := .node node6825 node8494 +def node8496 : Tree Nat := .leaf 623 +def node8497 : Tree Nat := .node node6242 node8496 +def node8498 : Tree Nat := .node node8049 node8497 +def node8499 : Tree Nat := .node node8495 node8498 +def node8500 : Tree Nat := .leaf 619 +def node8501 : Tree Nat := .node node1996 node8500 +def node8502 : Tree Nat := .node node8052 node8501 +def node8503 : Tree Nat := .node node8502 node8056 +def node8504 : Tree Nat := .node node8499 node8503 +def node8505 : Tree Nat := .leaf 635 +def node8506 : Tree Nat := .node node7031 node8505 +def node8507 : Tree Nat := .node node7635 node8506 +def node8508 : Tree Nat := .node node8507 node6830 +def node8509 : Tree Nat := .node node8064 node8508 +def node8510 : Tree Nat := .node node8504 node8509 +def node8511 : Tree Nat := .node node8492 node8510 +def node8512 : Tree Nat := .node node8476 node8511 +def node8513 : Tree Nat := .node node8444 node8512 +def node8514 : Tree Nat := .node node3733 node8175 +def node8515 : Tree Nat := .node node8070 node8514 +def node8516 : Tree Nat := .node node7234 node8515 +def node8517 : Tree Nat := .node node8161 node7997 +def node8518 : Tree Nat := .node node6999 node8395 +def node8519 : Tree Nat := .node node8517 node8518 +def node8520 : Tree Nat := .node node8519 node8077 +def node8521 : Tree Nat := .node node8516 node8520 +def node8522 : Tree Nat := .node node6999 node8500 +def node8523 : Tree Nat := .node node8080 node8522 +def node8524 : Tree Nat := .node node7644 node8523 +def node8525 : Tree Nat := .node node8524 node8086 +def node8526 : Tree Nat := .node node8521 node8525 +def node8527 : Tree Nat := .node node8367 node8200 +def node8528 : Tree Nat := .node node7650 node8527 +def node8529 : Tree Nat := .node node7649 node8528 +def node8530 : Tree Nat := .node node3332 node8187 +def node8531 : Tree Nat := .node node7253 node8530 +def node8532 : Tree Nat := .node node8092 node8531 +def node8533 : Tree Nat := .node node8529 node8532 +def node8534 : Tree Nat := .node node8533 node8104 +def node8535 : Tree Nat := .node node8526 node8534 +def node8536 : Tree Nat := .node node6186 node8308 +def node8537 : Tree Nat := .node node6082 node8536 +def node8538 : Tree Nat := .node node6764 node8505 +def node8539 : Tree Nat := .node node5803 node8538 +def node8540 : Tree Nat := .node node8537 node8539 +def node8541 : Tree Nat := .node node3864 node8221 +def node8542 : Tree Nat := .node node341 node8541 +def node8543 : Tree Nat := .node node8108 node8542 +def node8544 : Tree Nat := .node node8540 node8543 +def node8545 : Tree Nat := .node node6733 node8342 +def node8546 : Tree Nat := .node node6449 node8545 +def node8547 : Tree Nat := .node node8546 node6868 +def node8548 : Tree Nat := .node node7664 node8547 +def node8549 : Tree Nat := .node node8544 node8548 +def node8550 : Tree Nat := .node node7051 node8479 +def node8551 : Tree Nat := .node node6187 node8550 +def node8552 : Tree Nat := .node node7668 node8551 +def node8553 : Tree Nat := .node node2255 node8175 +def node8554 : Tree Nat := .node node6099 node8553 +def node8555 : Tree Nat := .node node1 node8274 +def node8556 : Tree Nat := .node node8555 node3463 +def node8557 : Tree Nat := .node node8554 node8556 +def node8558 : Tree Nat := .node node8552 node8557 +def node8559 : Tree Nat := .node node6242 node8411 +def node8560 : Tree Nat := .node node6108 node8559 +def node8561 : Tree Nat := .node node8560 node7279 +def node8562 : Tree Nat := .node node8114 node8561 +def node8563 : Tree Nat := .node node8558 node8562 +def node8564 : Tree Nat := .node node8549 node8563 +def node8565 : Tree Nat := .node node8535 node8564 +def node8566 : Tree Nat := .node node3859 node8315 +def node8567 : Tree Nat := .node node5803 node8566 +def node8568 : Tree Nat := .node node7286 node8567 +def node8569 : Tree Nat := .node node2239 node8493 +def node8570 : Tree Nat := .node node8217 node8569 +def node8571 : Tree Nat := .node node8570 node8122 +def node8572 : Tree Nat := .node node8568 node8571 +def node8573 : Tree Nat := .node node3061 node8395 +def node8574 : Tree Nat := .node node6123 node8573 +def node8575 : Tree Nat := .node node8574 node7679 +def node8576 : Tree Nat := .node node2668 node8496 +def node8577 : Tree Nat := .node node6126 node8576 +def node8578 : Tree Nat := .node node8577 node6479 +def node8579 : Tree Nat := .node node8575 node8578 +def node8580 : Tree Nat := .node node8572 node8579 +def node8581 : Tree Nat := .node node8419 node8372 +def node8582 : Tree Nat := .node node6187 node8581 +def node8583 : Tree Nat := .node node7684 node8582 +def node8584 : Tree Nat := .node node7333 node8249 +def node8585 : Tree Nat := .node node6131 node8584 +def node8586 : Tree Nat := .node node6348 node8288 +def node8587 : Tree Nat := .node node196 node8586 +def node8588 : Tree Nat := .node node8585 node8587 +def node8589 : Tree Nat := .node node8583 node8588 +def node8590 : Tree Nat := .node node3071 node8200 +def node8591 : Tree Nat := .node node6138 node8590 +def node8592 : Tree Nat := .node node8591 node6892 +def node8593 : Tree Nat := .node node8134 node8592 +def node8594 : Tree Nat := .node node8589 node8593 +def node8595 : Tree Nat := .node node8580 node8594 +def node8596 : Tree Nat := .node node8089 node8358 +def node8597 : Tree Nat := .node node6497 node8596 +def node8598 : Tree Nat := .node node7693 node8597 +def node8599 : Tree Nat := .node node2096 node8386 +def node8600 : Tree Nat := .node node6897 node8599 +def node8601 : Tree Nat := .node node7470 node8270 +def node8602 : Tree Nat := .node node6181 node8601 +def node8603 : Tree Nat := .node node8600 node8602 +def node8604 : Tree Nat := .node node8598 node8603 +def node8605 : Tree Nat := .leaf 621 +def node8606 : Tree Nat := .node node7087 node8605 +def node8607 : Tree Nat := .node node6904 node8606 +def node8608 : Tree Nat := .node node1 node8161 +def node8609 : Tree Nat := .node node8608 node7300 +def node8610 : Tree Nat := .node node8607 node8609 +def node8611 : Tree Nat := .node node8146 node8610 +def node8612 : Tree Nat := .node node8604 node8611 +def node8613 : Tree Nat := .node node6313 node8470 +def node8614 : Tree Nat := .node node6230 node8613 +def node8615 : Tree Nat := .node node7702 node8614 +def node8616 : Tree Nat := .node node2102 node8308 +def node8617 : Tree Nat := .node node6910 node8616 +def node8618 : Tree Nat := .node node1 node8216 +def node8619 : Tree Nat := .node node8618 node7704 +def node8620 : Tree Nat := .node node8617 node8619 +def node8621 : Tree Nat := .node node8615 node8620 +def node8622 : Tree Nat := .node node7068 node8367 +def node8623 : Tree Nat := .node node6349 node8622 +def node8624 : Tree Nat := .node node8150 node8623 +def node8625 : Tree Nat := .node node2924 node8428 +def node8626 : Tree Nat := .node node6326 node8625 +def node8627 : Tree Nat := .node node8626 node6920 +def node8628 : Tree Nat := .node node8624 node8627 +def node8629 : Tree Nat := .node node8621 node8628 +def node8630 : Tree Nat := .node node8612 node8629 +def node8631 : Tree Nat := .node node8595 node8630 +def node8632 : Tree Nat := .node node8565 node8631 +def node8633 : Tree Nat := .node node8513 node8632 +def node8634 : Tree Nat := .node node8381 node8633 +def node8635 : Tree Nat := .leaf 680 +def node8636 : Tree Nat := .node node8635 node7718 +def node8637 : Tree Nat := .node node8162 node8636 +def node8638 : Tree Nat := .node node8637 node8166 +def node8639 : Tree Nat := .node node7717 node8638 +def node8640 : Tree Nat := .leaf 657 +def node8641 : Tree Nat := .node node8640 node322 +def node8642 : Tree Nat := .node node8641 node7321 +def node8643 : Tree Nat := .node node8642 node8171 +def node8644 : Tree Nat := .node node1 node8640 +def node8645 : Tree Nat := .node node8644 node3138 +def node8646 : Tree Nat := .node node6535 node8645 +def node8647 : Tree Nat := .node node8643 node8646 +def node8648 : Tree Nat := .node node8639 node8647 +def node8649 : Tree Nat := .leaf 681 +def node8650 : Tree Nat := .node node8649 node5821 +def node8651 : Tree Nat := .leaf 667 +def node8652 : Tree Nat := .node node5802 node8651 +def node8653 : Tree Nat := .node node8650 node8652 +def node8654 : Tree Nat := .node node8649 node7727 +def node8655 : Tree Nat := .node node6187 node8654 +def node8656 : Tree Nat := .node node8653 node8655 +def node8657 : Tree Nat := .leaf 655 +def node8658 : Tree Nat := .node node8657 node6192 +def node8659 : Tree Nat := .node node5827 node8658 +def node8660 : Tree Nat := .node node8659 node8177 +def node8661 : Tree Nat := .node node8656 node8660 +def node8662 : Tree Nat := .node node8661 node8184 +def node8663 : Tree Nat := .node node8648 node8662 +def node8664 : Tree Nat := .node node322 node8651 +def node8665 : Tree Nat := .node node7338 node8664 +def node8666 : Tree Nat := .node node8665 node7749 +def node8667 : Tree Nat := .node node7336 node8666 +def node8668 : Tree Nat := .leaf 693 +def node8669 : Tree Nat := .node node8668 node6951 +def node8670 : Tree Nat := .node node8669 node6209 +def node8671 : Tree Nat := .leaf 662 +def node8672 : Tree Nat := .node node5826 node8671 +def node8673 : Tree Nat := .node node7753 node8672 +def node8674 : Tree Nat := .node node8670 node8673 +def node8675 : Tree Nat := .node node8674 node8190 +def node8676 : Tree Nat := .node node8667 node8675 +def node8677 : Tree Nat := .leaf 669 +def node8678 : Tree Nat := .node node8677 node6959 +def node8679 : Tree Nat := .node node8678 node6214 +def node8680 : Tree Nat := .node node8679 node8195 +def node8681 : Tree Nat := .leaf 679 +def node8682 : Tree Nat := .node node5821 node8681 +def node8683 : Tree Nat := .node node7766 node8682 +def node8684 : Tree Nat := .node node8683 node8202 +def node8685 : Tree Nat := .node node8680 node8684 +def node8686 : Tree Nat := .node node8685 node8209 +def node8687 : Tree Nat := .node node8676 node8686 +def node8688 : Tree Nat := .node node8663 node8687 +def node8689 : Tree Nat := .leaf 672 +def node8690 : Tree Nat := .node node8689 node6569 +def node8691 : Tree Nat := .node node8217 node8690 +def node8692 : Tree Nat := .leaf 673 +def node8693 : Tree Nat := .node node7370 node8692 +def node8694 : Tree Nat := .node node341 node8693 +def node8695 : Tree Nat := .node node8691 node8694 +def node8696 : Tree Nat := .node node8215 node8695 +def node8697 : Tree Nat := .leaf 658 +def node8698 : Tree Nat := .node node8697 node322 +def node8699 : Tree Nat := .node node8698 node7788 +def node8700 : Tree Nat := .node node8699 node7377 +def node8701 : Tree Nat := .node node1 node8668 +def node8702 : Tree Nat := .node node8701 node6983 +def node8703 : Tree Nat := .node node8223 node8702 +def node8704 : Tree Nat := .node node8700 node8703 +def node8705 : Tree Nat := .node node8696 node8704 +def node8706 : Tree Nat := .leaf 682 +def node8707 : Tree Nat := .node node8706 node7752 +def node8708 : Tree Nat := .node node8707 node7381 +def node8709 : Tree Nat := .leaf 676 +def node8710 : Tree Nat := .node node8709 node8227 +def node8711 : Tree Nat := .node node6187 node8710 +def node8712 : Tree Nat := .node node8708 node8711 +def node8713 : Tree Nat := .leaf 660 +def node8714 : Tree Nat := .node node8713 node8657 +def node8715 : Tree Nat := .node node5876 node8714 +def node8716 : Tree Nat := .node node8715 node8235 +def node8717 : Tree Nat := .node node8712 node8716 +def node8718 : Tree Nat := .leaf 684 +def node8719 : Tree Nat := .node node8718 node6242 +def node8720 : Tree Nat := .node node5880 node8719 +def node8721 : Tree Nat := .node node8720 node7799 +def node8722 : Tree Nat := .node node8721 node8241 +def node8723 : Tree Nat := .node node8717 node8722 +def node8724 : Tree Nat := .node node8705 node8723 +def node8725 : Tree Nat := .leaf 666 +def node8726 : Tree Nat := .leaf 691 +def node8727 : Tree Nat := .node node8725 node8726 +def node8728 : Tree Nat := .node node7396 node8727 +def node8729 : Tree Nat := .leaf 671 +def node8730 : Tree Nat := .node node340 node8729 +def node8731 : Tree Nat := .node node7806 node8730 +def node8732 : Tree Nat := .node node8728 node8731 +def node8733 : Tree Nat := .node node8248 node8732 +def node8734 : Tree Nat := .leaf 690 +def node8735 : Tree Nat := .node node8734 node6546 +def node8736 : Tree Nat := .node node7813 node8735 +def node8737 : Tree Nat := .leaf 686 +def node8738 : Tree Nat := .node node8737 node1 +def node8739 : Tree Nat := .node node6597 node8738 +def node8740 : Tree Nat := .node node8736 node8739 +def node8741 : Tree Nat := .node node7812 node8740 +def node8742 : Tree Nat := .node node8733 node8741 +def node8743 : Tree Nat := .leaf 670 +def node8744 : Tree Nat := .node node8743 node6602 +def node8745 : Tree Nat := .leaf 656 +def node8746 : Tree Nat := .node node5835 node8745 +def node8747 : Tree Nat := .node node8744 node8746 +def node8748 : Tree Nat := .node node8747 node8258 +def node8749 : Tree Nat := .leaf 674 +def node8750 : Tree Nat := .node node8749 node1 +def node8751 : Tree Nat := .node node7825 node8750 +def node8752 : Tree Nat := .node node8262 node8751 +def node8753 : Tree Nat := .node node8748 node8752 +def node8754 : Tree Nat := .leaf 678 +def node8755 : Tree Nat := .node node8754 node7829 +def node8756 : Tree Nat := .node node7417 node8755 +def node8757 : Tree Nat := .node node8756 node7834 +def node8758 : Tree Nat := .node node8757 node7839 +def node8759 : Tree Nat := .node node8753 node8758 +def node8760 : Tree Nat := .node node8742 node8759 +def node8761 : Tree Nat := .node node8724 node8760 +def node8762 : Tree Nat := .node node8688 node8761 +def node8763 : Tree Nat := .node node8692 node6554 +def node8764 : Tree Nat := .node node8275 node8763 +def node8765 : Tree Nat := .leaf 659 +def node8766 : Tree Nat := .node node8697 node8765 +def node8767 : Tree Nat := .node node341 node8766 +def node8768 : Tree Nat := .node node8764 node8767 +def node8769 : Tree Nat := .node node8273 node8768 +def node8770 : Tree Nat := .leaf 663 +def node8771 : Tree Nat := .node node8770 node322 +def node8772 : Tree Nat := .node node8771 node7436 +def node8773 : Tree Nat := .node node8772 node8280 +def node8774 : Tree Nat := .leaf 685 +def node8775 : Tree Nat := .node node8774 node1 +def node8776 : Tree Nat := .node node8283 node8775 +def node8777 : Tree Nat := .node node7852 node8776 +def node8778 : Tree Nat := .node node8773 node8777 +def node8779 : Tree Nat := .node node8769 node8778 +def node8780 : Tree Nat := .leaf 687 +def node8781 : Tree Nat := .node node8780 node5821 +def node8782 : Tree Nat := .node node8781 node7442 +def node8783 : Tree Nat := .node node8782 node8290 +def node8784 : Tree Nat := .leaf 661 +def node8785 : Tree Nat := .node node8784 node6642 +def node8786 : Tree Nat := .node node7018 node8785 +def node8787 : Tree Nat := .node node8692 node8193 +def node8788 : Tree Nat := .node node196 node8787 +def node8789 : Tree Nat := .node node8786 node8788 +def node8790 : Tree Nat := .node node8783 node8789 +def node8791 : Tree Nat := .node node8774 node7752 +def node8792 : Tree Nat := .node node7022 node8791 +def node8793 : Tree Nat := .node node8792 node7859 +def node8794 : Tree Nat := .node node8793 node7863 +def node8795 : Tree Nat := .node node8790 node8794 +def node8796 : Tree Nat := .node node8779 node8795 +def node8797 : Tree Nat := .node node8651 node8635 +def node8798 : Tree Nat := .node node7032 node8797 +def node8799 : Tree Nat := .node node7353 node8784 +def node8800 : Tree Nat := .node node341 node8799 +def node8801 : Tree Nat := .node node8798 node8800 +def node8802 : Tree Nat := .node node7460 node8801 +def node8803 : Tree Nat := .node node1 node8718 +def node8804 : Tree Nat := .node node8803 node7471 +def node8805 : Tree Nat := .node node7469 node8804 +def node8806 : Tree Nat := .node node8805 node8305 +def node8807 : Tree Nat := .node node8802 node8806 +def node8808 : Tree Nat := .leaf 675 +def node8809 : Tree Nat := .node node8808 node7476 +def node8810 : Tree Nat := .node node8809 node6300 +def node8811 : Tree Nat := .node node8810 node8310 +def node8812 : Tree Nat := .leaf 692 +def node8813 : Tree Nat := .node node8681 node8812 +def node8814 : Tree Nat := .node node7044 node8813 +def node8815 : Tree Nat := .node node8814 node8317 +def node8816 : Tree Nat := .node node8811 node8815 +def node8817 : Tree Nat := .node node8681 node7326 +def node8818 : Tree Nat := .node node7048 node8817 +def node8819 : Tree Nat := .node node1 node8689 +def node8820 : Tree Nat := .node node8819 node7878 +def node8821 : Tree Nat := .node node8818 node8820 +def node8822 : Tree Nat := .node node8821 node7054 +def node8823 : Tree Nat := .node node8816 node8822 +def node8824 : Tree Nat := .node node8807 node8823 +def node8825 : Tree Nat := .node node8796 node8824 +def node8826 : Tree Nat := .node node6549 node8745 +def node8827 : Tree Nat := .node node8327 node8826 +def node8828 : Tree Nat := .node node1 node8765 +def node8829 : Tree Nat := .leaf 683 +def node8830 : Tree Nat := .node node3616 node8829 +def node8831 : Tree Nat := .node node8828 node8830 +def node8832 : Tree Nat := .node node8827 node8831 +def node8833 : Tree Nat := .node node8325 node8832 +def node8834 : Tree Nat := .node node1 node8706 +def node8835 : Tree Nat := .node node8834 node7500 +def node8836 : Tree Nat := .node node8332 node8835 +def node8837 : Tree Nat := .node node8836 node8336 +def node8838 : Tree Nat := .node node8833 node8837 +def node8839 : Tree Nat := .node node8709 node6596 +def node8840 : Tree Nat := .node node8839 node7505 +def node8841 : Tree Nat := .node node8840 node7895 +def node8842 : Tree Nat := .leaf 654 +def node8843 : Tree Nat := .leaf 668 +def node8844 : Tree Nat := .node node8842 node8843 +def node8845 : Tree Nat := .node node6712 node8844 +def node8846 : Tree Nat := .node node8845 node8344 +def node8847 : Tree Nat := .node node8841 node8846 +def node8848 : Tree Nat := .node node1 node8743 +def node8849 : Tree Nat := .node node8848 node7899 +def node8850 : Tree Nat := .node node7085 node8849 +def node8851 : Tree Nat := .node node8850 node8349 +def node8852 : Tree Nat := .node node8847 node8851 +def node8853 : Tree Nat := .node node8838 node8852 +def node8854 : Tree Nat := .node node411 node8657 +def node8855 : Tree Nat := .node node7905 node8854 +def node8856 : Tree Nat := .node node8855 node8354 +def node8857 : Tree Nat := .leaf 677 +def node8858 : Tree Nat := .node node8857 node8169 +def node8859 : Tree Nat := .node node7095 node8858 +def node8860 : Tree Nat := .node node1 node8713 +def node8861 : Tree Nat := .node node3587 node8774 +def node8862 : Tree Nat := .node node8860 node8861 +def node8863 : Tree Nat := .node node8859 node8862 +def node8864 : Tree Nat := .node node8856 node8863 +def node8865 : Tree Nat := .leaf 688 +def node8866 : Tree Nat := .node node8865 node7391 +def node8867 : Tree Nat := .node node8866 node7909 +def node8868 : Tree Nat := .node node1 node8829 +def node8869 : Tree Nat := .node node8868 node7911 +def node8870 : Tree Nat := .node node8867 node8869 +def node8871 : Tree Nat := .node node8870 node7105 +def node8872 : Tree Nat := .node node8864 node8871 +def node8873 : Tree Nat := .leaf 664 +def node8874 : Tree Nat := .node node8873 node7320 +def node8875 : Tree Nat := .node node340 node8843 +def node8876 : Tree Nat := .node node8874 node8875 +def node8877 : Tree Nat := .node node8876 node8365 +def node8878 : Tree Nat := .node node8754 node6668 +def node8879 : Tree Nat := .node node7112 node8878 +def node8880 : Tree Nat := .node node8879 node8369 +def node8881 : Tree Nat := .node node8877 node8880 +def node8882 : Tree Nat := .node node1 node8729 +def node8883 : Tree Nat := .node node8882 node7924 +def node8884 : Tree Nat := .node node7922 node8883 +def node8885 : Tree Nat := .node node8884 node8375 +def node8886 : Tree Nat := .node node8881 node8885 +def node8887 : Tree Nat := .node node8872 node8886 +def node8888 : Tree Nat := .node node8853 node8887 +def node8889 : Tree Nat := .node node8825 node8888 +def node8890 : Tree Nat := .node node8762 node8889 +def node8891 : Tree Nat := .node node8843 node7923 +def node8892 : Tree Nat := .node node8382 node8891 +def node8893 : Tree Nat := .node node7337 node8671 +def node8894 : Tree Nat := .node node7133 node8893 +def node8895 : Tree Nat := .node node8892 node8894 +def node8896 : Tree Nat := .node node7936 node8895 +def node8897 : Tree Nat := .node node8770 node7137 +def node8898 : Tree Nat := .node node8897 node7542 +def node8899 : Tree Nat := .node node8898 node8388 +def node8900 : Tree Nat := .node node8812 node8255 +def node8901 : Tree Nat := .node node7947 node8900 +def node8902 : Tree Nat := .node node1 node8677 +def node8903 : Tree Nat := .node node8902 node7141 +def node8904 : Tree Nat := .node node8901 node8903 +def node8905 : Tree Nat := .node node8899 node8904 +def node8906 : Tree Nat := .node node8896 node8905 +def node8907 : Tree Nat := .node node8780 node7074 +def node8908 : Tree Nat := .node node6176 node8725 +def node8909 : Tree Nat := .node node8907 node8908 +def node8910 : Tree Nat := .node node8909 node8397 +def node8911 : Tree Nat := .node node8726 node7957 +def node8912 : Tree Nat := .node node7956 node8911 +def node8913 : Tree Nat := .node node8912 node8400 +def node8914 : Tree Nat := .node node8910 node8913 +def node8915 : Tree Nat := .node node8635 node7962 +def node8916 : Tree Nat := .node node7556 node8915 +def node8917 : Tree Nat := .node node8916 node7966 +def node8918 : Tree Nat := .node node8917 node8407 +def node8919 : Tree Nat := .node node8914 node8918 +def node8920 : Tree Nat := .node node8906 node8919 +def node8921 : Tree Nat := .node node8729 node8725 +def node8922 : Tree Nat := .node node7567 node8921 +def node8923 : Tree Nat := .node node340 node8713 +def node8924 : Tree Nat := .node node7977 node8923 +def node8925 : Tree Nat := .node node8922 node8924 +def node8926 : Tree Nat := .node node8414 node8925 +def node8927 : Tree Nat := .node node8926 node8426 +def node8928 : Tree Nat := .node node8808 node6982 +def node8929 : Tree Nat := .node node8928 node7174 +def node8930 : Tree Nat := .node node8929 node8430 +def node8931 : Tree Nat := .node node8765 node8754 +def node8932 : Tree Nat := .node node7995 node8931 +def node8933 : Tree Nat := .node node8932 node8435 +def node8934 : Tree Nat := .node node8930 node8933 +def node8935 : Tree Nat := .node node8829 node7343 +def node8936 : Tree Nat := .node node7582 node8935 +def node8937 : Tree Nat := .node node8936 node8005 +def node8938 : Tree Nat := .node node8937 node8440 +def node8939 : Tree Nat := .node node8934 node8938 +def node8940 : Tree Nat := .node node8927 node8939 +def node8941 : Tree Nat := .node node8920 node8940 +def node8942 : Tree Nat := .node node1 node8784 +def node8943 : Tree Nat := .node node3773 node8737 +def node8944 : Tree Nat := .node node8942 node8943 +def node8945 : Tree Nat := .node node8450 node8944 +def node8946 : Tree Nat := .node node8447 node8945 +def node8947 : Tree Nat := .node node1 node8865 +def node8948 : Tree Nat := .node node8947 node3364 +def node8949 : Tree Nat := .node node8457 node8948 +def node8950 : Tree Nat := .node node8455 node8949 +def node8951 : Tree Nat := .node node8946 node8950 +def node8952 : Tree Nat := .node node8709 node5821 +def node8953 : Tree Nat := .node node8952 node7607 +def node8954 : Tree Nat := .node node8953 node8462 +def node8955 : Tree Nat := .node node7562 node8842 +def node8956 : Tree Nat := .node node6801 node8955 +def node8957 : Tree Nat := .node node8956 node8467 +def node8958 : Tree Nat := .node node8954 node8957 +def node8959 : Tree Nat := .node node8958 node8474 +def node8960 : Tree Nat := .node node8951 node8959 +def node8961 : Tree Nat := .node node8812 node8734 +def node8962 : Tree Nat := .node node7619 node8961 +def node8963 : Tree Nat := .node node3614 node8718 +def node8964 : Tree Nat := .node node8035 node8963 +def node8965 : Tree Nat := .node node8962 node8964 +def node8966 : Tree Nat := .node node8482 node8965 +def node8967 : Tree Nat := .node node8865 node7068 +def node8968 : Tree Nat := .node node8967 node7623 +def node8969 : Tree Nat := .node node8968 node8042 +def node8970 : Tree Nat := .node node8969 node8490 +def node8971 : Tree Nat := .node node8966 node8970 +def node8972 : Tree Nat := .node node8873 node6584 +def node8973 : Tree Nat := .node node8972 node8494 +def node8974 : Tree Nat := .node node8973 node8498 +def node8975 : Tree Nat := .node node8745 node8500 +def node8976 : Tree Nat := .node node8052 node8975 +def node8977 : Tree Nat := .node node8976 node8056 +def node8978 : Tree Nat := .node node8974 node8977 +def node8979 : Tree Nat := .node node8978 node8509 +def node8980 : Tree Nat := .node node8971 node8979 +def node8981 : Tree Nat := .node node8960 node8980 +def node8982 : Tree Nat := .node node8941 node8981 +def node8983 : Tree Nat := .leaf 689 +def node8984 : Tree Nat := .node node8983 node8395 +def node8985 : Tree Nat := .node node8517 node8984 +def node8986 : Tree Nat := .node node3721 node8689 +def node8987 : Tree Nat := .node node7238 node8986 +def node8988 : Tree Nat := .node node8985 node8987 +def node8989 : Tree Nat := .node node8516 node8988 +def node8990 : Tree Nat := .node node8640 node7242 +def node8991 : Tree Nat := .node node8990 node7643 +def node8992 : Tree Nat := .node node8991 node8523 +def node8993 : Tree Nat := .node node1 node8873 +def node8994 : Tree Nat := .node node8993 node3429 +def node8995 : Tree Nat := .node node8085 node8994 +def node8996 : Tree Nat := .node node8992 node8995 +def node8997 : Tree Nat := .node node8989 node8996 +def node8998 : Tree Nat := .node node8649 node6962 +def node8999 : Tree Nat := .node node8998 node7648 +def node9000 : Tree Nat := .node node8999 node8528 +def node9001 : Tree Nat := .node node8734 node7721 +def node9002 : Tree Nat := .node node8090 node9001 +def node9003 : Tree Nat := .node node9002 node8531 +def node9004 : Tree Nat := .node node9000 node9003 +def node9005 : Tree Nat := .node node9004 node8104 +def node9006 : Tree Nat := .node node8997 node9005 +def node9007 : Tree Nat := .node node6659 node8857 +def node9008 : Tree Nat := .node node6855 node9007 +def node9009 : Tree Nat := .node node3864 node8749 +def node9010 : Tree Nat := .node node341 node9009 +def node9011 : Tree Nat := .node node9008 node9010 +def node9012 : Tree Nat := .node node8540 node9011 +def node9013 : Tree Nat := .node node8668 node6549 +def node9014 : Tree Nat := .node node9013 node7660 +def node9015 : Tree Nat := .node node9014 node7663 +def node9016 : Tree Nat := .node node9015 node8547 +def node9017 : Tree Nat := .node node9012 node9016 +def node9018 : Tree Nat := .node node8677 node6606 +def node9019 : Tree Nat := .node node9018 node7667 +def node9020 : Tree Nat := .node node9019 node8551 +def node9021 : Tree Nat := .node node8493 node8983 +def node9022 : Tree Nat := .node node6099 node9021 +def node9023 : Tree Nat := .node node9022 node8556 +def node9024 : Tree Nat := .node node9020 node9023 +def node9025 : Tree Nat := .node node9024 node8562 +def node9026 : Tree Nat := .node node9017 node9025 +def node9027 : Tree Nat := .node node9006 node9026 +def node9028 : Tree Nat := .leaf 665 +def node9029 : Tree Nat := .node node9028 node8493 +def node9030 : Tree Nat := .node node8217 node9029 +def node9031 : Tree Nat := .node node9030 node8122 +def node9032 : Tree Nat := .node node8568 node9031 +def node9033 : Tree Nat := .node node8698 node8573 +def node9034 : Tree Nat := .node node9033 node7679 +def node9035 : Tree Nat := .node node8983 node8496 +def node9036 : Tree Nat := .node node6126 node9035 +def node9037 : Tree Nat := .node node9036 node6479 +def node9038 : Tree Nat := .node node9034 node9037 +def node9039 : Tree Nat := .node node9032 node9038 +def node9040 : Tree Nat := .node node8706 node6596 +def node9041 : Tree Nat := .node node9040 node7683 +def node9042 : Tree Nat := .node node9041 node8582 +def node9043 : Tree Nat := .node node7333 node9028 +def node9044 : Tree Nat := .node node6131 node9043 +def node9045 : Tree Nat := .node node9044 node8587 +def node9046 : Tree Nat := .node node9042 node9045 +def node9047 : Tree Nat := .node node8857 node7916 +def node9048 : Tree Nat := .node node6135 node9047 +def node9049 : Tree Nat := .node node9048 node8133 +def node9050 : Tree Nat := .node node9049 node8592 +def node9051 : Tree Nat := .node node9046 node9050 +def node9052 : Tree Nat := .node node9039 node9051 +def node9053 : Tree Nat := .node node224 node8842 +def node9054 : Tree Nat := .node node7291 node9053 +def node9055 : Tree Nat := .node node9054 node8597 +def node9056 : Tree Nat := .node node8749 node8386 +def node9057 : Tree Nat := .node node6897 node9056 +def node9058 : Tree Nat := .node node1 node8770 +def node9059 : Tree Nat := .node node9058 node8601 +def node9060 : Tree Nat := .node node9057 node9059 +def node9061 : Tree Nat := .node node9055 node9060 +def node9062 : Tree Nat := .node node1 node8780 +def node9063 : Tree Nat := .node node9062 node8144 +def node9064 : Tree Nat := .node node8143 node9063 +def node9065 : Tree Nat := .node node9064 node8610 +def node9066 : Tree Nat := .node node9061 node9065 +def node9067 : Tree Nat := .node node8743 node7333 +def node9068 : Tree Nat := .node node195 node9028 +def node9069 : Tree Nat := .node node9067 node9068 +def node9070 : Tree Nat := .node node9069 node8614 +def node9071 : Tree Nat := .node node8671 node8308 +def node9072 : Tree Nat := .node node6910 node9071 +def node9073 : Tree Nat := .node node9072 node8619 +def node9074 : Tree Nat := .node node9070 node9073 +def node9075 : Tree Nat := .node node8737 node7877 +def node9076 : Tree Nat := .node node6916 node9075 +def node9077 : Tree Nat := .node node1 node8808 +def node9078 : Tree Nat := .node node9077 node8622 +def node9079 : Tree Nat := .node node9076 node9078 +def node9080 : Tree Nat := .node node9079 node8627 +def node9081 : Tree Nat := .node node9074 node9080 +def node9082 : Tree Nat := .node node9066 node9081 +def node9083 : Tree Nat := .node node9052 node9082 +def node9084 : Tree Nat := .node node9027 node9083 +def node9085 : Tree Nat := .node node8982 node9084 +def node9086 : Tree Nat := .node node8890 node9085 +def node9087 : Tree Nat := .leaf 716 +def node9088 : Tree Nat := .node node6169 node9087 +def node9089 : Tree Nat := .node node5800 node9088 +def node9090 : Tree Nat := .node node9089 node7716 +def node9091 : Tree Nat := .node node9090 node8638 +def node9092 : Tree Nat := .node node9091 node8647 +def node9093 : Tree Nat := .leaf 695 +def node9094 : Tree Nat := .node node3143 node9093 +def node9095 : Tree Nat := .node node196 node9094 +def node9096 : Tree Nat := .node node8659 node9095 +def node9097 : Tree Nat := .node node8656 node9096 +def node9098 : Tree Nat := .leaf 717 +def node9099 : Tree Nat := .node node9098 node5835 +def node9100 : Tree Nat := .node node9099 node8181 +def node9101 : Tree Nat := .leaf 715 +def node9102 : Tree Nat := .node node9101 node1 +def node9103 : Tree Nat := .node node6202 node9102 +def node9104 : Tree Nat := .node node9100 node9103 +def node9105 : Tree Nat := .node node7738 node9104 +def node9106 : Tree Nat := .node node9097 node9105 +def node9107 : Tree Nat := .node node9092 node9106 +def node9108 : Tree Nat := .leaf 729 +def node9109 : Tree Nat := .node node9108 node6546 +def node9110 : Tree Nat := .node node9109 node6947 +def node9111 : Tree Nat := .node node9110 node7335 +def node9112 : Tree Nat := .leaf 705 +def node9113 : Tree Nat := .leaf 727 +def node9114 : Tree Nat := .node node9112 node9113 +def node9115 : Tree Nat := .node node9114 node8664 +def node9116 : Tree Nat := .leaf 697 +def node9117 : Tree Nat := .node node3560 node9116 +def node9118 : Tree Nat := .node node7746 node9117 +def node9119 : Tree Nat := .node node9115 node9118 +def node9120 : Tree Nat := .node node9111 node9119 +def node9121 : Tree Nat := .leaf 728 +def node9122 : Tree Nat := .node node8668 node9121 +def node9123 : Tree Nat := .node node9122 node6209 +def node9124 : Tree Nat := .node node9123 node8673 +def node9125 : Tree Nat := .leaf 704 +def node9126 : Tree Nat := .node node9116 node9125 +def node9127 : Tree Nat := .node node7757 node9126 +def node9128 : Tree Nat := .node node9127 node6556 +def node9129 : Tree Nat := .node node9124 node9128 +def node9130 : Tree Nat := .node node9120 node9129 +def node9131 : Tree Nat := .leaf 709 +def node9132 : Tree Nat := .node node3169 node9131 +def node9133 : Tree Nat := .node node7769 node9132 +def node9134 : Tree Nat := .node node8683 node9133 +def node9135 : Tree Nat := .node node8680 node9134 +def node9136 : Tree Nat := .node node5802 node9087 +def node9137 : Tree Nat := .node node7359 node9136 +def node9138 : Tree Nat := .node node9137 node6971 +def node9139 : Tree Nat := .node node7777 node9138 +def node9140 : Tree Nat := .node node9135 node9139 +def node9141 : Tree Nat := .node node9130 node9140 +def node9142 : Tree Nat := .node node9107 node9141 +def node9143 : Tree Nat := .leaf 708 +def node9144 : Tree Nat := .leaf 734 +def node9145 : Tree Nat := .node node9143 node9144 +def node9146 : Tree Nat := .node node6177 node9145 +def node9147 : Tree Nat := .node node8699 node9146 +def node9148 : Tree Nat := .node node9147 node8703 +def node9149 : Tree Nat := .node node8696 node9148 +def node9150 : Tree Nat := .leaf 707 +def node9151 : Tree Nat := .node node7384 node9150 +def node9152 : Tree Nat := .node node196 node9151 +def node9153 : Tree Nat := .node node8715 node9152 +def node9154 : Tree Nat := .node node8712 node9153 +def node9155 : Tree Nat := .leaf 718 +def node9156 : Tree Nat := .node node9155 node5835 +def node9157 : Tree Nat := .node node9156 node8239 +def node9158 : Tree Nat := .node node5826 node9101 +def node9159 : Tree Nat := .leaf 720 +def node9160 : Tree Nat := .node node9159 node1 +def node9161 : Tree Nat := .node node9158 node9160 +def node9162 : Tree Nat := .node node9157 node9161 +def node9163 : Tree Nat := .node node8721 node9162 +def node9164 : Tree Nat := .node node9154 node9163 +def node9165 : Tree Nat := .node node9149 node9164 +def node9166 : Tree Nat := .leaf 730 +def node9167 : Tree Nat := .node node9166 node9108 +def node9168 : Tree Nat := .node node9167 node6252 +def node9169 : Tree Nat := .node node9168 node8247 +def node9170 : Tree Nat := .leaf 706 +def node9171 : Tree Nat := .node node9170 node7395 +def node9172 : Tree Nat := .node node9171 node8727 +def node9173 : Tree Nat := .node node9172 node8731 +def node9174 : Tree Nat := .node node9169 node9173 +def node9175 : Tree Nat := .leaf 694 +def node9176 : Tree Nat := .node node9175 node6989 +def node9177 : Tree Nat := .leaf 726 +def node9178 : Tree Nat := .node node9177 node7400 +def node9179 : Tree Nat := .node node9176 node9178 +def node9180 : Tree Nat := .leaf 702 +def node9181 : Tree Nat := .node node9180 node7403 +def node9182 : Tree Nat := .node node7810 node9181 +def node9183 : Tree Nat := .node node9179 node9182 +def node9184 : Tree Nat := .node node9183 node8740 +def node9185 : Tree Nat := .node node9174 node9184 +def node9186 : Tree Nat := .node node8743 node9113 +def node9187 : Tree Nat := .node node9186 node8746 +def node9188 : Tree Nat := .node node9187 node8258 +def node9189 : Tree Nat := .node node9188 node8752 +def node9190 : Tree Nat := .node node159 node9121 +def node9191 : Tree Nat := .node node9190 node8755 +def node9192 : Tree Nat := .leaf 698 +def node9193 : Tree Nat := .node node9192 node7718 +def node9194 : Tree Nat := .node node7832 node9193 +def node9195 : Tree Nat := .node node9191 node9194 +def node9196 : Tree Nat := .node node9195 node7839 +def node9197 : Tree Nat := .node node9189 node9196 +def node9198 : Tree Nat := .node node9185 node9197 +def node9199 : Tree Nat := .node node9165 node9198 +def node9200 : Tree Nat := .node node9142 node9199 +def node9201 : Tree Nat := .node node451 node9125 +def node9202 : Tree Nat := .node node7429 node9201 +def node9203 : Tree Nat := .node node9202 node8272 +def node9204 : Tree Nat := .node node9203 node8768 +def node9205 : Tree Nat := .leaf 721 +def node9206 : Tree Nat := .node node9205 node7391 +def node9207 : Tree Nat := .node node8771 node9206 +def node9208 : Tree Nat := .node node9131 node8260 +def node9209 : Tree Nat := .node node6177 node9208 +def node9210 : Tree Nat := .node node9207 node9209 +def node9211 : Tree Nat := .node node9210 node8777 +def node9212 : Tree Nat := .node node9204 node9211 +def node9213 : Tree Nat := .node node9116 node7745 +def node9214 : Tree Nat := .node node6198 node9213 +def node9215 : Tree Nat := .node node8792 node9214 +def node9216 : Tree Nat := .leaf 723 +def node9217 : Tree Nat := .node node9216 node5835 +def node9218 : Tree Nat := .node node9217 node7861 +def node9219 : Tree Nat := .leaf 703 +def node9220 : Tree Nat := .node node5831 node9219 +def node9221 : Tree Nat := .node node9205 node1 +def node9222 : Tree Nat := .node node9220 node9221 +def node9223 : Tree Nat := .node node9218 node9222 +def node9224 : Tree Nat := .node node9215 node9223 +def node9225 : Tree Nat := .node node8790 node9224 +def node9226 : Tree Nat := .node node9212 node9225 +def node9227 : Tree Nat := .node node1 node9150 +def node9228 : Tree Nat := .node node9227 node6660 +def node9229 : Tree Nat := .node node7459 node9228 +def node9230 : Tree Nat := .leaf 711 +def node9231 : Tree Nat := .node node9230 node7031 +def node9232 : Tree Nat := .node node9231 node8797 +def node9233 : Tree Nat := .node node9232 node8800 +def node9234 : Tree Nat := .node node9229 node9233 +def node9235 : Tree Nat := .leaf 699 +def node9236 : Tree Nat := .node node9235 node7465 +def node9237 : Tree Nat := .node node9113 node7467 +def node9238 : Tree Nat := .node node9236 node9237 +def node9239 : Tree Nat := .leaf 733 +def node9240 : Tree Nat := .node node9219 node9239 +def node9241 : Tree Nat := .node node8803 node9240 +def node9242 : Tree Nat := .node node9238 node9241 +def node9243 : Tree Nat := .node node3241 node9144 +def node9244 : Tree Nat := .node node8726 node9101 +def node9245 : Tree Nat := .node node9243 node9244 +def node9246 : Tree Nat := .node node9245 node7040 +def node9247 : Tree Nat := .node node9242 node9246 +def node9248 : Tree Nat := .node node9234 node9247 +def node9249 : Tree Nat := .leaf 696 +def node9250 : Tree Nat := .node node1 node9249 +def node9251 : Tree Nat := .node node9250 node8309 +def node9252 : Tree Nat := .node node8810 node9251 +def node9253 : Tree Nat := .leaf 719 +def node9254 : Tree Nat := .node node7375 node9253 +def node9255 : Tree Nat := .node node8314 node9254 +def node9256 : Tree Nat := .node node8814 node9255 +def node9257 : Tree Nat := .node node9252 node9256 +def node9258 : Tree Nat := .node node1 node9159 +def node9259 : Tree Nat := .node node9258 node6686 +def node9260 : Tree Nat := .node node9259 node7053 +def node9261 : Tree Nat := .node node8821 node9260 +def node9262 : Tree Nat := .node node9257 node9261 +def node9263 : Tree Nat := .node node9248 node9262 +def node9264 : Tree Nat := .node node9226 node9263 +def node9265 : Tree Nat := .node node1 node9170 +def node9266 : Tree Nat := .node node9265 node8323 +def node9267 : Tree Nat := .node node7062 node9266 +def node9268 : Tree Nat := .node node9267 node8832 +def node9269 : Tree Nat := .leaf 722 +def node9270 : Tree Nat := .node node9269 node6320 +def node9271 : Tree Nat := .node node8331 node9270 +def node9272 : Tree Nat := .node node9271 node8835 +def node9273 : Tree Nat := .node node3294 node9239 +def node9274 : Tree Nat := .node node9273 node8334 +def node9275 : Tree Nat := .node node1 node9098 +def node9276 : Tree Nat := .node node9275 node3216 +def node9277 : Tree Nat := .node node9274 node9276 +def node9278 : Tree Nat := .node node9272 node9277 +def node9279 : Tree Nat := .node node9268 node9278 +def node9280 : Tree Nat := .node node1 node9175 +def node9281 : Tree Nat := .node node9280 node7894 +def node9282 : Tree Nat := .node node8840 node9281 +def node9283 : Tree Nat := .node node3225 node9205 +def node9284 : Tree Nat := .node node8341 node9283 +def node9285 : Tree Nat := .node node8845 node9284 +def node9286 : Tree Nat := .node node9282 node9285 +def node9287 : Tree Nat := .leaf 712 +def node9288 : Tree Nat := .node node9287 node9155 +def node9289 : Tree Nat := .leaf 710 +def node9290 : Tree Nat := .node node9289 node9219 +def node9291 : Tree Nat := .node node9288 node9290 +def node9292 : Tree Nat := .leaf 714 +def node9293 : Tree Nat := .node node9292 node1 +def node9294 : Tree Nat := .node node6719 node9293 +def node9295 : Tree Nat := .node node9291 node9294 +def node9296 : Tree Nat := .node node8850 node9295 +def node9297 : Tree Nat := .node node9286 node9296 +def node9298 : Tree Nat := .node node9279 node9297 +def node9299 : Tree Nat := .leaf 724 +def node9300 : Tree Nat := .node node9299 node7787 +def node9301 : Tree Nat := .node node9300 node8854 +def node9302 : Tree Nat := .node node1 node9143 +def node9303 : Tree Nat := .node node9302 node8353 +def node9304 : Tree Nat := .node node9301 node9303 +def node9305 : Tree Nat := .leaf 700 +def node9306 : Tree Nat := .node node9305 node7094 +def node9307 : Tree Nat := .node node9306 node8858 +def node9308 : Tree Nat := .node node9307 node8862 +def node9309 : Tree Nat := .node node9304 node9308 +def node9310 : Tree Nat := .leaf 731 +def node9311 : Tree Nat := .node node3290 node9310 +def node9312 : Tree Nat := .node node9249 node6733 +def node9313 : Tree Nat := .node node9311 node9312 +def node9314 : Tree Nat := .node node9313 node6350 +def node9315 : Tree Nat := .node node8870 node9314 +def node9316 : Tree Nat := .node node9309 node9315 +def node9317 : Tree Nat := .node node1 node9093 +def node9318 : Tree Nat := .node node9317 node8364 +def node9319 : Tree Nat := .node node8876 node9318 +def node9320 : Tree Nat := .node node9319 node8880 +def node9321 : Tree Nat := .node node1 node9253 +def node9322 : Tree Nat := .node node9321 node8373 +def node9323 : Tree Nat := .node node9322 node6747 +def node9324 : Tree Nat := .node node8884 node9323 +def node9325 : Tree Nat := .node node9320 node9324 +def node9326 : Tree Nat := .node node9316 node9325 +def node9327 : Tree Nat := .node node9298 node9326 +def node9328 : Tree Nat := .node node9264 node9327 +def node9329 : Tree Nat := .node node9200 node9328 +def node9330 : Tree Nat := .leaf 713 +def node9331 : Tree Nat := .node node340 node9330 +def node9332 : Tree Nat := .node node6755 node9331 +def node9333 : Tree Nat := .node node9332 node7935 +def node9334 : Tree Nat := .node node9333 node8895 +def node9335 : Tree Nat := .node node9121 node7476 +def node9336 : Tree Nat := .node node8897 node9335 +def node9337 : Tree Nat := .node node9125 node8386 +def node9338 : Tree Nat := .node node7944 node9337 +def node9339 : Tree Nat := .node node9336 node9338 +def node9340 : Tree Nat := .node node9339 node8904 +def node9341 : Tree Nat := .node node9334 node9340 +def node9342 : Tree Nat := .node node9216 node7836 +def node9343 : Tree Nat := .node node9342 node8403 +def node9344 : Tree Nat := .node node9343 node8406 +def node9345 : Tree Nat := .node node8917 node9344 +def node9346 : Tree Nat := .node node8914 node9345 +def node9347 : Tree Nat := .node node9341 node9346 +def node9348 : Tree Nat := .node node9230 node9177 +def node9349 : Tree Nat := .node node9348 node8921 +def node9350 : Tree Nat := .node node9349 node8924 +def node9351 : Tree Nat := .node node8414 node9350 +def node9352 : Tree Nat := .leaf 725 +def node9353 : Tree Nat := .node node9235 node9352 +def node9354 : Tree Nat := .node node9353 node8420 +def node9355 : Tree Nat := .leaf 732 +def node9356 : Tree Nat := .node node9150 node9355 +def node9357 : Tree Nat := .node node7983 node9356 +def node9358 : Tree Nat := .node node9354 node9357 +def node9359 : Tree Nat := .leaf 701 +def node9360 : Tree Nat := .node node411 node9359 +def node9361 : Tree Nat := .node node7987 node9360 +def node9362 : Tree Nat := .node node9361 node6781 +def node9363 : Tree Nat := .node node9358 node9362 +def node9364 : Tree Nat := .node node9351 node9363 +def node9365 : Tree Nat := .node node6169 node9269 +def node9366 : Tree Nat := .node node7998 node9365 +def node9367 : Tree Nat := .node node8932 node9366 +def node9368 : Tree Nat := .node node8930 node9367 +def node9369 : Tree Nat := .node node2982 node9330 +def node9370 : Tree Nat := .node node7586 node9369 +def node9371 : Tree Nat := .node node9253 node1 +def node9372 : Tree Nat := .node node7178 node9371 +def node9373 : Tree Nat := .node node9370 node9372 +def node9374 : Tree Nat := .node node8937 node9373 +def node9375 : Tree Nat := .node node9368 node9374 +def node9376 : Tree Nat := .node node9364 node9375 +def node9377 : Tree Nat := .node node9347 node9376 +def node9378 : Tree Nat := .node node9310 node7893 +def node9379 : Tree Nat := .node node8453 node9378 +def node9380 : Tree Nat := .node node6959 node9310 +def node9381 : Tree Nat := .node node6177 node9380 +def node9382 : Tree Nat := .node node9379 node9381 +def node9383 : Tree Nat := .node node9093 node8249 +def node9384 : Tree Nat := .node node6796 node9383 +def node9385 : Tree Nat := .node node9384 node8948 +def node9386 : Tree Nat := .node node9382 node9385 +def node9387 : Tree Nat := .node node8946 node9386 +def node9388 : Tree Nat := .node node3372 node9159 +def node9389 : Tree Nat := .node node196 node9388 +def node9390 : Tree Nat := .node node8956 node9389 +def node9391 : Tree Nat := .node node8954 node9390 +def node9392 : Tree Nat := .node node9287 node5835 +def node9393 : Tree Nat := .node node9131 node8470 +def node9394 : Tree Nat := .node node9392 node9393 +def node9395 : Tree Nat := .node node224 node9292 +def node9396 : Tree Nat := .node node9355 node1 +def node9397 : Tree Nat := .node node9395 node9396 +def node9398 : Tree Nat := .node node9394 node9397 +def node9399 : Tree Nat := .node node8026 node9398 +def node9400 : Tree Nat := .node node9391 node9399 +def node9401 : Tree Nat := .node node9387 node9400 +def node9402 : Tree Nat := .node node9299 node9299 +def node9403 : Tree Nat := .node node9402 node8477 +def node9404 : Tree Nat := .node node9403 node8481 +def node9405 : Tree Nat := .node node9305 node7403 +def node9406 : Tree Nat := .node node9405 node8961 +def node9407 : Tree Nat := .node node9406 node8964 +def node9408 : Tree Nat := .node node9404 node9407 +def node9409 : Tree Nat := .node node9408 node8970 +def node9410 : Tree Nat := .node node8873 node9177 +def node9411 : Tree Nat := .node node9410 node8494 +def node9412 : Tree Nat := .node node9112 node8496 +def node9413 : Tree Nat := .node node8049 node9412 +def node9414 : Tree Nat := .node node9411 node9413 +def node9415 : Tree Nat := .node node9414 node8977 +def node9416 : Tree Nat := .node node490 node9352 +def node9417 : Tree Nat := .node node9416 node8059 +def node9418 : Tree Nat := .node node9417 node8063 +def node9419 : Tree Nat := .node node9087 node1 +def node9420 : Tree Nat := .node node6829 node9419 +def node9421 : Tree Nat := .node node8507 node9420 +def node9422 : Tree Nat := .node node9418 node9421 +def node9423 : Tree Nat := .node node9415 node9422 +def node9424 : Tree Nat := .node node9409 node9423 +def node9425 : Tree Nat := .node node9401 node9424 +def node9426 : Tree Nat := .node node9377 node9425 +def node9427 : Tree Nat := .node node224 node9359 +def node9428 : Tree Nat := .node node6837 node9427 +def node9429 : Tree Nat := .node node9428 node8515 +def node9430 : Tree Nat := .node node9429 node8988 +def node9431 : Tree Nat := .node node9192 node7845 +def node9432 : Tree Nat := .node node8083 node9431 +def node9433 : Tree Nat := .node node9432 node8994 +def node9434 : Tree Nat := .node node8992 node9433 +def node9435 : Tree Nat := .node node9430 node9434 +def node9436 : Tree Nat := .node node3332 node9289 +def node9437 : Tree Nat := .node node7253 node9436 +def node9438 : Tree Nat := .node node9002 node9437 +def node9439 : Tree Nat := .node node9000 node9438 +def node9440 : Tree Nat := .node node9098 node8040 +def node9441 : Tree Nat := .node node9440 node8101 +def node9442 : Tree Nat := .node node411 node9180 +def node9443 : Tree Nat := .node node9442 node6994 +def node9444 : Tree Nat := .node node9441 node9443 +def node9445 : Tree Nat := .node node8099 node9444 +def node9446 : Tree Nat := .node node9439 node9445 +def node9447 : Tree Nat := .node node9435 node9446 +def node9448 : Tree Nat := .node node9108 node451 +def node9449 : Tree Nat := .node node9448 node8536 +def node9450 : Tree Nat := .node node9449 node8539 +def node9451 : Tree Nat := .node node9112 node6546 +def node9452 : Tree Nat := .node node9451 node9007 +def node9453 : Tree Nat := .node node9452 node9010 +def node9454 : Tree Nat := .node node9450 node9453 +def node9455 : Tree Nat := .node node6733 node9292 +def node9456 : Tree Nat := .node node6449 node9455 +def node9457 : Tree Nat := .node node9456 node6868 +def node9458 : Tree Nat := .node node9015 node9457 +def node9459 : Tree Nat := .node node9454 node9458 +def node9460 : Tree Nat := .node node9330 node1 +def node9461 : Tree Nat := .node node7278 node9460 +def node9462 : Tree Nat := .node node8560 node9461 +def node9463 : Tree Nat := .node node8114 node9462 +def node9464 : Tree Nat := .node node9024 node9463 +def node9465 : Tree Nat := .node node9459 node9464 +def node9466 : Tree Nat := .node node9447 node9465 +def node9467 : Tree Nat := .node node6180 node9249 +def node9468 : Tree Nat := .node node341 node9467 +def node9469 : Tree Nat := .node node9030 node9468 +def node9470 : Tree Nat := .node node8568 node9469 +def node9471 : Tree Nat := .node node9352 node8395 +def node9472 : Tree Nat := .node node8698 node9471 +def node9473 : Tree Nat := .node node9359 node7370 +def node9474 : Tree Nat := .node node6177 node9473 +def node9475 : Tree Nat := .node node9472 node9474 +def node9476 : Tree Nat := .node node1 node9287 +def node9477 : Tree Nat := .node node9476 node6478 +def node9478 : Tree Nat := .node node9036 node9477 +def node9479 : Tree Nat := .node node9475 node9478 +def node9480 : Tree Nat := .node node9470 node9479 +def node9481 : Tree Nat := .node node6348 node9143 +def node9482 : Tree Nat := .node node196 node9481 +def node9483 : Tree Nat := .node node9044 node9482 +def node9484 : Tree Nat := .node node9042 node9483 +def node9485 : Tree Nat := .node node3071 node9180 +def node9486 : Tree Nat := .node node9156 node9485 +def node9487 : Tree Nat := .node node9486 node6892 +def node9488 : Tree Nat := .node node9049 node9487 +def node9489 : Tree Nat := .node node9484 node9488 +def node9490 : Tree Nat := .node node9480 node9489 +def node9491 : Tree Nat := .node node9166 node7051 +def node9492 : Tree Nat := .node node9491 node9053 +def node9493 : Tree Nat := .node node1 node9230 +def node9494 : Tree Nat := .node node9493 node8596 +def node9495 : Tree Nat := .node node9492 node9494 +def node9496 : Tree Nat := .node node9170 node6733 +def node9497 : Tree Nat := .node node9496 node9056 +def node9498 : Tree Nat := .node node7470 node9192 +def node9499 : Tree Nat := .node node9058 node9498 +def node9500 : Tree Nat := .node node9497 node9499 +def node9501 : Tree Nat := .node node9495 node9500 +def node9502 : Tree Nat := .node node9175 node6659 +def node9503 : Tree Nat := .node node9502 node8142 +def node9504 : Tree Nat := .node node9289 node7732 +def node9505 : Tree Nat := .node node9062 node9504 +def node9506 : Tree Nat := .node node9503 node9505 +def node9507 : Tree Nat := .node node3183 node9166 +def node9508 : Tree Nat := .node node9507 node8606 +def node9509 : Tree Nat := .node node9508 node8609 +def node9510 : Tree Nat := .node node9506 node9509 +def node9511 : Tree Nat := .node node9501 node9510 +def node9512 : Tree Nat := .node node1 node9235 +def node9513 : Tree Nat := .node node9305 node8470 +def node9514 : Tree Nat := .node node9512 node9513 +def node9515 : Tree Nat := .node node9069 node9514 +def node9516 : Tree Nat := .node node9515 node9073 +def node9517 : Tree Nat := .node node1 node9216 +def node9518 : Tree Nat := .node node9517 node8625 +def node9519 : Tree Nat := .node node9269 node1 +def node9520 : Tree Nat := .node node6919 node9519 +def node9521 : Tree Nat := .node node9518 node9520 +def node9522 : Tree Nat := .node node9079 node9521 +def node9523 : Tree Nat := .node node9516 node9522 +def node9524 : Tree Nat := .node node9511 node9523 +def node9525 : Tree Nat := .node node9490 node9524 +def node9526 : Tree Nat := .node node9466 node9525 +def node9527 : Tree Nat := .node node9426 node9526 +def node9528 : Tree Nat := .node node9329 node9527 +def node9529 : Tree Nat := .leaf 763 +def node9530 : Tree Nat := .node node9529 node1 +def node9531 : Tree Nat := .node node8644 node9530 +def node9532 : Tree Nat := .node node6535 node9531 +def node9533 : Tree Nat := .node node8643 node9532 +def node9534 : Tree Nat := .node node9091 node9533 +def node9535 : Tree Nat := .leaf 753 +def node9536 : Tree Nat := .node node9535 node5826 +def node9537 : Tree Nat := .node node9536 node8658 +def node9538 : Tree Nat := .node node9537 node9095 +def node9539 : Tree Nat := .node node8656 node9538 +def node9540 : Tree Nat := .leaf 741 +def node9541 : Tree Nat := .node node9540 node5831 +def node9542 : Tree Nat := .node node9541 node7733 +def node9543 : Tree Nat := .leaf 751 +def node9544 : Tree Nat := .leaf 755 +def node9545 : Tree Nat := .node node9543 node9544 +def node9546 : Tree Nat := .node node6198 node9545 +def node9547 : Tree Nat := .node node9542 node9546 +def node9548 : Tree Nat := .node node9547 node9104 +def node9549 : Tree Nat := .node node9539 node9548 +def node9550 : Tree Nat := .node node9534 node9549 +def node9551 : Tree Nat := .node node9108 node9535 +def node9552 : Tree Nat := .node node9551 node6947 +def node9553 : Tree Nat := .node node9552 node7335 +def node9554 : Tree Nat := .node node9553 node9119 +def node9555 : Tree Nat := .node node9239 node6208 +def node9556 : Tree Nat := .node node9122 node9555 +def node9557 : Tree Nat := .node node9556 node8673 +def node9558 : Tree Nat := .leaf 765 +def node9559 : Tree Nat := .node node9558 node9543 +def node9560 : Tree Nat := .node node9559 node9126 +def node9561 : Tree Nat := .node node1 node9540 +def node9562 : Tree Nat := .leaf 769 +def node9563 : Tree Nat := .node node9562 node1 +def node9564 : Tree Nat := .node node9561 node9563 +def node9565 : Tree Nat := .node node9560 node9564 +def node9566 : Tree Nat := .node node9557 node9565 +def node9567 : Tree Nat := .node node9554 node9566 +def node9568 : Tree Nat := .leaf 739 +def node9569 : Tree Nat := .node node8677 node9568 +def node9570 : Tree Nat := .node node9569 node6214 +def node9571 : Tree Nat := .node node9570 node8195 +def node9572 : Tree Nat := .node node71 node9529 +def node9573 : Tree Nat := .node node9572 node8682 +def node9574 : Tree Nat := .node node9573 node9133 +def node9575 : Tree Nat := .node node9571 node9574 +def node9576 : Tree Nat := .node node78 node9568 +def node9577 : Tree Nat := .node node9576 node7356 +def node9578 : Tree Nat := .leaf 757 +def node9579 : Tree Nat := .node node9578 node7762 +def node9580 : Tree Nat := .node node7774 node9579 +def node9581 : Tree Nat := .node node9577 node9580 +def node9582 : Tree Nat := .node node5835 node9529 +def node9583 : Tree Nat := .node node9582 node6562 +def node9584 : Tree Nat := .node node9137 node9583 +def node9585 : Tree Nat := .node node9581 node9584 +def node9586 : Tree Nat := .node node9575 node9585 +def node9587 : Tree Nat := .node node9567 node9586 +def node9588 : Tree Nat := .node node9550 node9587 +def node9589 : Tree Nat := .leaf 764 +def node9590 : Tree Nat := .node node6186 node9589 +def node9591 : Tree Nat := .node node5856 node9590 +def node9592 : Tree Nat := .node node9591 node8214 +def node9593 : Tree Nat := .node node9592 node8695 +def node9594 : Tree Nat := .node node9593 node9148 +def node9595 : Tree Nat := .leaf 754 +def node9596 : Tree Nat := .node node9595 node5826 +def node9597 : Tree Nat := .node node9596 node8714 +def node9598 : Tree Nat := .node node9597 node9152 +def node9599 : Tree Nat := .node node8712 node9598 +def node9600 : Tree Nat := .leaf 742 +def node9601 : Tree Nat := .node node9600 node5831 +def node9602 : Tree Nat := .node node9601 node8719 +def node9603 : Tree Nat := .node node9602 node7799 +def node9604 : Tree Nat := .leaf 744 +def node9605 : Tree Nat := .node node9604 node8238 +def node9606 : Tree Nat := .node node9156 node9605 +def node9607 : Tree Nat := .node node9606 node9161 +def node9608 : Tree Nat := .node node9603 node9607 +def node9609 : Tree Nat := .node node9599 node9608 +def node9610 : Tree Nat := .node node9594 node9609 +def node9611 : Tree Nat := .leaf 740 +def node9612 : Tree Nat := .node node9170 node9611 +def node9613 : Tree Nat := .node node9612 node8727 +def node9614 : Tree Nat := .node node9613 node8731 +def node9615 : Tree Nat := .node node9169 node9614 +def node9616 : Tree Nat := .node node9175 node9611 +def node9617 : Tree Nat := .node node9616 node9178 +def node9618 : Tree Nat := .leaf 743 +def node9619 : Tree Nat := .node node9180 node9618 +def node9620 : Tree Nat := .node node7810 node9619 +def node9621 : Tree Nat := .node node9617 node9620 +def node9622 : Tree Nat := .leaf 766 +def node9623 : Tree Nat := .node node9622 node9589 +def node9624 : Tree Nat := .node node9623 node8735 +def node9625 : Tree Nat := .node node9624 node8739 +def node9626 : Tree Nat := .node node9621 node9625 +def node9627 : Tree Nat := .node node9615 node9626 +def node9628 : Tree Nat := .leaf 752 +def node9629 : Tree Nat := .node node154 node9628 +def node9630 : Tree Nat := .node node9629 node8261 +def node9631 : Tree Nat := .node node9630 node8751 +def node9632 : Tree Nat := .node node9188 node9631 +def node9633 : Tree Nat := .leaf 738 +def node9634 : Tree Nat := .node node9633 node6606 +def node9635 : Tree Nat := .node node7421 node9634 +def node9636 : Tree Nat := .node node9635 node7838 +def node9637 : Tree Nat := .node node9195 node9636 +def node9638 : Tree Nat := .node node9632 node9637 +def node9639 : Tree Nat := .node node9627 node9638 +def node9640 : Tree Nat := .node node9610 node9639 +def node9641 : Tree Nat := .node node9588 node9640 +def node9642 : Tree Nat := .leaf 756 +def node9643 : Tree Nat := .node node9642 node7850 +def node9644 : Tree Nat := .node node6632 node9643 +def node9645 : Tree Nat := .node node9644 node8776 +def node9646 : Tree Nat := .node node9210 node9645 +def node9647 : Tree Nat := .node node9204 node9646 +def node9648 : Tree Nat := .leaf 759 +def node9649 : Tree Nat := .node node9648 node5826 +def node9650 : Tree Nat := .node node9649 node8785 +def node9651 : Tree Nat := .node node9650 node8788 +def node9652 : Tree Nat := .node node8783 node9651 +def node9653 : Tree Nat := .leaf 747 +def node9654 : Tree Nat := .node node9653 node5831 +def node9655 : Tree Nat := .node node9654 node8791 +def node9656 : Tree Nat := .leaf 768 +def node9657 : Tree Nat := .node node9116 node9656 +def node9658 : Tree Nat := .node node6198 node9657 +def node9659 : Tree Nat := .node node9655 node9658 +def node9660 : Tree Nat := .leaf 745 +def node9661 : Tree Nat := .node node9660 node7742 +def node9662 : Tree Nat := .node node9217 node9661 +def node9663 : Tree Nat := .node node9662 node9222 +def node9664 : Tree Nat := .node node9659 node9663 +def node9665 : Tree Nat := .node node9652 node9664 +def node9666 : Tree Nat := .node node9647 node9665 +def node9667 : Tree Nat := .leaf 735 +def node9668 : Tree Nat := .node node9667 node7457 +def node9669 : Tree Nat := .node node9668 node6295 +def node9670 : Tree Nat := .node node9669 node9228 +def node9671 : Tree Nat := .node node9230 node9544 +def node9672 : Tree Nat := .node node9671 node8797 +def node9673 : Tree Nat := .node node9672 node8800 +def node9674 : Tree Nat := .node node9670 node9673 +def node9675 : Tree Nat := .leaf 771 +def node9676 : Tree Nat := .node node9675 node9144 +def node9677 : Tree Nat := .node node9676 node9244 +def node9678 : Tree Nat := .node node1 node9558 +def node9679 : Tree Nat := .node node9678 node7039 +def node9680 : Tree Nat := .node node9677 node9679 +def node9681 : Tree Nat := .node node9242 node9680 +def node9682 : Tree Nat := .node node9674 node9681 +def node9683 : Tree Nat := .node node3641 node9618 +def node9684 : Tree Nat := .node node9683 node8813 +def node9685 : Tree Nat := .node node9684 node9255 +def node9686 : Tree Nat := .node node9252 node9685 +def node9687 : Tree Nat := .leaf 767 +def node9688 : Tree Nat := .node node3656 node9687 +def node9689 : Tree Nat := .node node9688 node8817 +def node9690 : Tree Nat := .node node9689 node8820 +def node9691 : Tree Nat := .node node9568 node6596 +def node9692 : Tree Nat := .node node9258 node9691 +def node9693 : Tree Nat := .node node9692 node7053 +def node9694 : Tree Nat := .node node9690 node9693 +def node9695 : Tree Nat := .node node9686 node9694 +def node9696 : Tree Nat := .node node9682 node9695 +def node9697 : Tree Nat := .node node9666 node9696 +def node9698 : Tree Nat := .node node6169 node9628 +def node9699 : Tree Nat := .node node7060 node9698 +def node9700 : Tree Nat := .node node9699 node9266 +def node9701 : Tree Nat := .node node8326 node9578 +def node9702 : Tree Nat := .node node9701 node8826 +def node9703 : Tree Nat := .node node9702 node8831 +def node9704 : Tree Nat := .node node9700 node9703 +def node9705 : Tree Nat := .leaf 746 +def node9706 : Tree Nat := .node node9705 node9604 +def node9707 : Tree Nat := .node node8834 node9706 +def node9708 : Tree Nat := .node node9271 node9707 +def node9709 : Tree Nat := .leaf 772 +def node9710 : Tree Nat := .node node9709 node9239 +def node9711 : Tree Nat := .node node9710 node8334 +def node9712 : Tree Nat := .leaf 762 +def node9713 : Tree Nat := .node node9712 node1 +def node9714 : Tree Nat := .node node9275 node9713 +def node9715 : Tree Nat := .node node9711 node9714 +def node9716 : Tree Nat := .node node9708 node9715 +def node9717 : Tree Nat := .node node9704 node9716 +def node9718 : Tree Nat := .leaf 748 +def node9719 : Tree Nat := .node node9718 node9600 +def node9720 : Tree Nat := .node node9719 node8844 +def node9721 : Tree Nat := .node node9720 node9284 +def node9722 : Tree Nat := .node node9282 node9721 +def node9723 : Tree Nat := .leaf 736 +def node9724 : Tree Nat := .node node9723 node9622 +def node9725 : Tree Nat := .leaf 770 +def node9726 : Tree Nat := .node node9725 node6313 +def node9727 : Tree Nat := .node node9724 node9726 +def node9728 : Tree Nat := .leaf 750 +def node9729 : Tree Nat := .node node9728 node7898 +def node9730 : Tree Nat := .node node8848 node9729 +def node9731 : Tree Nat := .node node9727 node9730 +def node9732 : Tree Nat := .node node5821 node9543 +def node9733 : Tree Nat := .node node9732 node9293 +def node9734 : Tree Nat := .node node9291 node9733 +def node9735 : Tree Nat := .node node9731 node9734 +def node9736 : Tree Nat := .node node9722 node9735 +def node9737 : Tree Nat := .node node9717 node9736 +def node9738 : Tree Nat := .leaf 758 +def node9739 : Tree Nat := .node node9305 node9738 +def node9740 : Tree Nat := .node node9739 node8858 +def node9741 : Tree Nat := .node node9740 node8862 +def node9742 : Tree Nat := .node node9304 node9741 +def node9743 : Tree Nat := .node node9355 node7836 +def node9744 : Tree Nat := .node node8866 node9743 +def node9745 : Tree Nat := .node node6664 node9738 +def node9746 : Tree Nat := .node node8868 node9745 +def node9747 : Tree Nat := .node node9744 node9746 +def node9748 : Tree Nat := .leaf 760 +def node9749 : Tree Nat := .node node9748 node9310 +def node9750 : Tree Nat := .node node9749 node9312 +def node9751 : Tree Nat := .node node9656 node1 +def node9752 : Tree Nat := .node node6349 node9751 +def node9753 : Tree Nat := .node node9750 node9752 +def node9754 : Tree Nat := .node node9747 node9753 +def node9755 : Tree Nat := .node node9742 node9754 +def node9756 : Tree Nat := .node node3695 node9604 +def node9757 : Tree Nat := .node node9756 node8878 +def node9758 : Tree Nat := .node node9757 node8369 +def node9759 : Tree Nat := .node node9319 node9758 +def node9760 : Tree Nat := .node node3709 node9656 +def node9761 : Tree Nat := .node node9760 node7921 +def node9762 : Tree Nat := .node node9642 node7923 +def node9763 : Tree Nat := .node node8882 node9762 +def node9764 : Tree Nat := .node node9761 node9763 +def node9765 : Tree Nat := .node node9764 node9323 +def node9766 : Tree Nat := .node node9759 node9765 +def node9767 : Tree Nat := .node node9755 node9766 +def node9768 : Tree Nat := .node node9737 node9767 +def node9769 : Tree Nat := .node node9697 node9768 +def node9770 : Tree Nat := .node node9641 node9769 +def node9771 : Tree Nat := .node node9648 node7955 +def node9772 : Tree Nat := .node node9771 node8911 +def node9773 : Tree Nat := .node node9772 node8400 +def node9774 : Tree Nat := .node node8910 node9773 +def node9775 : Tree Nat := .node node9653 node7315 +def node9776 : Tree Nat := .leaf 773 +def node9777 : Tree Nat := .node node8635 node9776 +def node9778 : Tree Nat := .node node9775 node9777 +def node9779 : Tree Nat := .node node9778 node7966 +def node9780 : Tree Nat := .node node9611 node8298 +def node9781 : Tree Nat := .node node9342 node9780 +def node9782 : Tree Nat := .node node9781 node8406 +def node9783 : Tree Nat := .node node9779 node9782 +def node9784 : Tree Nat := .node node9774 node9783 +def node9785 : Tree Nat := .node node9341 node9784 +def node9786 : Tree Nat := .node node9667 node9718 +def node9787 : Tree Nat := .node node9786 node7164 +def node9788 : Tree Nat := .node node9787 node8413 +def node9789 : Tree Nat := .node node9788 node9350 +def node9790 : Tree Nat := .node node9675 node9728 +def node9791 : Tree Nat := .node node9790 node9360 +def node9792 : Tree Nat := .node node1 node9723 +def node9793 : Tree Nat := .node node9792 node6259 +def node9794 : Tree Nat := .node node9791 node9793 +def node9795 : Tree Nat := .node node9358 node9794 +def node9796 : Tree Nat := .node node9789 node9795 +def node9797 : Tree Nat := .node node8808 node9633 +def node9798 : Tree Nat := .node node9797 node7174 +def node9799 : Tree Nat := .node node9798 node8430 +def node9800 : Tree Nat := .node node403 node9712 +def node9801 : Tree Nat := .node node9800 node8931 +def node9802 : Tree Nat := .node node9801 node9366 +def node9803 : Tree Nat := .node node9799 node9802 +def node9804 : Tree Nat := .node node408 node9633 +def node9805 : Tree Nat := .node node9804 node8935 +def node9806 : Tree Nat := .node node6186 node9578 +def node9807 : Tree Nat := .node node8003 node9806 +def node9808 : Tree Nat := .node node9805 node9807 +def node9809 : Tree Nat := .node node9618 node9330 +def node9810 : Tree Nat := .node node7586 node9809 +def node9811 : Tree Nat := .node node5802 node9712 +def node9812 : Tree Nat := .node node9811 node9371 +def node9813 : Tree Nat := .node node9810 node9812 +def node9814 : Tree Nat := .node node9808 node9813 +def node9815 : Tree Nat := .node node9803 node9814 +def node9816 : Tree Nat := .node node9796 node9815 +def node9817 : Tree Nat := .node node9785 node9816 +def node9818 : Tree Nat := .leaf 761 +def node9819 : Tree Nat := .node node6176 node9818 +def node9820 : Tree Nat := .node node5856 node9819 +def node9821 : Tree Nat := .node node9820 node8446 +def node9822 : Tree Nat := .node node9821 node8945 +def node9823 : Tree Nat := .node node9660 node9310 +def node9824 : Tree Nat := .node node6177 node9823 +def node9825 : Tree Nat := .node node9379 node9824 +def node9826 : Tree Nat := .node node9709 node224 +def node9827 : Tree Nat := .node node9826 node9383 +def node9828 : Tree Nat := .node node9687 node1 +def node9829 : Tree Nat := .node node8947 node9828 +def node9830 : Tree Nat := .node node9827 node9829 +def node9831 : Tree Nat := .node node9825 node9830 +def node9832 : Tree Nat := .node node9822 node9831 +def node9833 : Tree Nat := .node node9718 node5826 +def node9834 : Tree Nat := .node node9833 node8955 +def node9835 : Tree Nat := .node node9834 node9389 +def node9836 : Tree Nat := .node node8954 node9835 +def node9837 : Tree Nat := .node node9723 node5831 +def node9838 : Tree Nat := .node node9562 node7872 +def node9839 : Tree Nat := .node node9837 node9838 +def node9840 : Tree Nat := .node node9544 node7829 +def node9841 : Tree Nat := .node node6198 node9840 +def node9842 : Tree Nat := .node node9839 node9841 +def node9843 : Tree Nat := .node node9842 node9398 +def node9844 : Tree Nat := .node node9836 node9843 +def node9845 : Tree Nat := .node node9832 node9844 +def node9846 : Tree Nat := .leaf 737 +def node9847 : Tree Nat := .node node9305 node9846 +def node9848 : Tree Nat := .node node9847 node8961 +def node9849 : Tree Nat := .node node9848 node8964 +def node9850 : Tree Nat := .node node9404 node9849 +def node9851 : Tree Nat := .node node8865 node9846 +def node9852 : Tree Nat := .node node9851 node7623 +def node9853 : Tree Nat := .node node9852 node8042 +def node9854 : Tree Nat := .node node9748 node9818 +def node9855 : Tree Nat := .node node9854 node8488 +def node9856 : Tree Nat := .node node9589 node1 +def node9857 : Tree Nat := .node node6820 node9856 +def node9858 : Tree Nat := .node node9855 node9857 +def node9859 : Tree Nat := .node node9853 node9858 +def node9860 : Tree Nat := .node node9850 node9859 +def node9861 : Tree Nat := .leaf 749 +def node9862 : Tree Nat := .node node485 node9861 +def node9863 : Tree Nat := .node node9862 node8975 +def node9864 : Tree Nat := .node node9863 node8056 +def node9865 : Tree Nat := .node node9414 node9864 +def node9866 : Tree Nat := .node node9628 node9687 +def node9867 : Tree Nat := .node node8061 node9866 +def node9868 : Tree Nat := .node node9417 node9867 +def node9869 : Tree Nat := .node node9868 node9421 +def node9870 : Tree Nat := .node node9865 node9869 +def node9871 : Tree Nat := .node node9860 node9870 +def node9872 : Tree Nat := .node node9845 node9871 +def node9873 : Tree Nat := .node node9817 node9872 +def node9874 : Tree Nat := .node node5826 node9709 +def node9875 : Tree Nat := .node node9874 node9427 +def node9876 : Tree Nat := .node node9875 node8515 +def node9877 : Tree Nat := .node node9876 node8988 +def node9878 : Tree Nat := .node node9144 node9776 +def node9879 : Tree Nat := .node node8990 node9878 +def node9880 : Tree Nat := .node node9879 node8523 +def node9881 : Tree Nat := .node node9725 node1 +def node9882 : Tree Nat := .node node8993 node9881 +def node9883 : Tree Nat := .node node9432 node9882 +def node9884 : Tree Nat := .node node9880 node9883 +def node9885 : Tree Nat := .node node9877 node9884 +def node9886 : Tree Nat := .node node9535 node8089 +def node9887 : Tree Nat := .node node9886 node9001 +def node9888 : Tree Nat := .node node9887 node9437 +def node9889 : Tree Nat := .node node9000 node9888 +def node9890 : Tree Nat := .node node9540 node7366 +def node9891 : Tree Nat := .node node9890 node8095 +def node9892 : Tree Nat := .node node9738 node9562 +def node9893 : Tree Nat := .node node7259 node9892 +def node9894 : Tree Nat := .node node9891 node9893 +def node9895 : Tree Nat := .node node9894 node9444 +def node9896 : Tree Nat := .node node9889 node9895 +def node9897 : Tree Nat := .node node9885 node9896 +def node9898 : Tree Nat := .node node9112 node9648 +def node9899 : Tree Nat := .node node9898 node9007 +def node9900 : Tree Nat := .node node9899 node9010 +def node9901 : Tree Nat := .node node9450 node9900 +def node9902 : Tree Nat := .node node6554 node9705 +def node9903 : Tree Nat := .node node6177 node9902 +def node9904 : Tree Nat := .node node9014 node9903 +def node9905 : Tree Nat := .node node9558 node9667 +def node9906 : Tree Nat := .node node9905 node9455 +def node9907 : Tree Nat := .node node1 node9748 +def node9908 : Tree Nat := .node node9818 node1 +def node9909 : Tree Nat := .node node9907 node9908 +def node9910 : Tree Nat := .node node9906 node9909 +def node9911 : Tree Nat := .node node9904 node9910 +def node9912 : Tree Nat := .node node9901 node9911 +def node9913 : Tree Nat := .node node9861 node9725 +def node9914 : Tree Nat := .node node6198 node9913 +def node9915 : Tree Nat := .node node7672 node9914 +def node9916 : Tree Nat := .node node9915 node9462 +def node9917 : Tree Nat := .node node9024 node9916 +def node9918 : Tree Nat := .node node9912 node9917 +def node9919 : Tree Nat := .node node9897 node9918 +def node9920 : Tree Nat := .node node340 node9861 +def node9921 : Tree Nat := .node node5935 node9920 +def node9922 : Tree Nat := .node node9921 node8567 +def node9923 : Tree Nat := .node node9922 node9469 +def node9924 : Tree Nat := .node node9359 node9660 +def node9925 : Tree Nat := .node node6177 node9924 +def node9926 : Tree Nat := .node node9472 node9925 +def node9927 : Tree Nat := .node node9926 node9478 +def node9928 : Tree Nat := .node node9923 node9927 +def node9929 : Tree Nat := .node node9596 node9043 +def node9930 : Tree Nat := .node node9929 node9482 +def node9931 : Tree Nat := .node node9042 node9930 +def node9932 : Tree Nat := .node node9601 node9047 +def node9933 : Tree Nat := .node node6229 node9642 +def node9934 : Tree Nat := .node node6198 node9933 +def node9935 : Tree Nat := .node node9932 node9934 +def node9936 : Tree Nat := .node node9846 node9180 +def node9937 : Tree Nat := .node node9156 node9936 +def node9938 : Tree Nat := .node node322 node9728 +def node9939 : Tree Nat := .node node9938 node6891 +def node9940 : Tree Nat := .node node9937 node9939 +def node9941 : Tree Nat := .node node9935 node9940 +def node9942 : Tree Nat := .node node9931 node9941 +def node9943 : Tree Nat := .node node9928 node9942 +def node9944 : Tree Nat := .node node9170 node9595 +def node9945 : Tree Nat := .node node9944 node9056 +def node9946 : Tree Nat := .node node9945 node9499 +def node9947 : Tree Nat := .node node9495 node9946 +def node9948 : Tree Nat := .node node9622 node9166 +def node9949 : Tree Nat := .node node9948 node8606 +def node9950 : Tree Nat := .node node9949 node8609 +def node9951 : Tree Nat := .node node9506 node9950 +def node9952 : Tree Nat := .node node9947 node9951 +def node9953 : Tree Nat := .node node3585 node9653 +def node9954 : Tree Nat := .node node9953 node9071 +def node9955 : Tree Nat := .node node9954 node8619 +def node9956 : Tree Nat := .node node9515 node9955 +def node9957 : Tree Nat := .node node3601 node9675 +def node9958 : Tree Nat := .node node9957 node9075 +def node9959 : Tree Nat := .node node9958 node9078 +def node9960 : Tree Nat := .node node9705 node8428 +def node9961 : Tree Nat := .node node9517 node9960 +def node9962 : Tree Nat := .node node9961 node9520 +def node9963 : Tree Nat := .node node9959 node9962 +def node9964 : Tree Nat := .node node9956 node9963 +def node9965 : Tree Nat := .node node9952 node9964 +def node9966 : Tree Nat := .node node9943 node9965 +def node9967 : Tree Nat := .node node9919 node9966 +def node9968 : Tree Nat := .node node9873 node9967 +def node9969 : Tree Nat := .node node9770 node9968 +def node9970 : Tree Nat := .leaf 808 +def node9971 : Tree Nat := .node node1 node9970 +def node9972 : Tree Nat := .node node9971 node7715 +def node9973 : Tree Nat := .node node9089 node9972 +def node9974 : Tree Nat := .leaf 811 +def node9975 : Tree Nat := .node node8161 node9974 +def node9976 : Tree Nat := .leaf 775 +def node9977 : Tree Nat := .node node8635 node9976 +def node9978 : Tree Nat := .node node9975 node9977 +def node9979 : Tree Nat := .leaf 824 +def node9980 : Tree Nat := .node node1 node9979 +def node9981 : Tree Nat := .leaf 787 +def node9982 : Tree Nat := .node node9981 node8164 +def node9983 : Tree Nat := .node node9980 node9982 +def node9984 : Tree Nat := .node node9978 node9983 +def node9985 : Tree Nat := .node node9973 node9984 +def node9986 : Tree Nat := .leaf 788 +def node9987 : Tree Nat := .node node6525 node9986 +def node9988 : Tree Nat := .node node8641 node9987 +def node9989 : Tree Nat := .node node9988 node8171 +def node9990 : Tree Nat := .leaf 777 +def node9991 : Tree Nat := .node node9990 node224 +def node9992 : Tree Nat := .node node9991 node6534 +def node9993 : Tree Nat := .node node9992 node9531 +def node9994 : Tree Nat := .node node9989 node9993 +def node9995 : Tree Nat := .node node9985 node9994 +def node9996 : Tree Nat := .leaf 809 +def node9997 : Tree Nat := .node node1 node9996 +def node9998 : Tree Nat := .node node9997 node8654 +def node9999 : Tree Nat := .node node8653 node9998 +def node10000 : Tree Nat := .leaf 810 +def node10001 : Tree Nat := .node node1 node10000 +def node10002 : Tree Nat := .node node9976 node9093 +def node10003 : Tree Nat := .node node10001 node10002 +def node10004 : Tree Nat := .node node9537 node10003 +def node10005 : Tree Nat := .node node9999 node10004 +def node10006 : Tree Nat := .leaf 812 +def node10007 : Tree Nat := .node node9540 node10006 +def node10008 : Tree Nat := .leaf 776 +def node10009 : Tree Nat := .node node6539 node10008 +def node10010 : Tree Nat := .node node10007 node10009 +def node10011 : Tree Nat := .node node10001 node9545 +def node10012 : Tree Nat := .node node10010 node10011 +def node10013 : Tree Nat := .node node9098 node9996 +def node10014 : Tree Nat := .node node10013 node8181 +def node10015 : Tree Nat := .node node10014 node9103 +def node10016 : Tree Nat := .node node10012 node10015 +def node10017 : Tree Nat := .node node10005 node10016 +def node10018 : Tree Nat := .node node9995 node10017 +def node10019 : Tree Nat := .leaf 805 +def node10020 : Tree Nat := .node node10019 node6549 +def node10021 : Tree Nat := .node node7334 node10020 +def node10022 : Tree Nat := .node node9552 node10021 +def node10023 : Tree Nat := .leaf 793 +def node10024 : Tree Nat := .node node10023 node9116 +def node10025 : Tree Nat := .node node7746 node10024 +def node10026 : Tree Nat := .node node9115 node10025 +def node10027 : Tree Nat := .node node10022 node10026 +def node10028 : Tree Nat := .node node10027 node9566 +def node10029 : Tree Nat := .leaf 789 +def node10030 : Tree Nat := .node node10029 node9529 +def node10031 : Tree Nat := .node node10030 node8682 +def node10032 : Tree Nat := .leaf 781 +def node10033 : Tree Nat := .node node10032 node9131 +def node10034 : Tree Nat := .node node7769 node10033 +def node10035 : Tree Nat := .node node10031 node10034 +def node10036 : Tree Nat := .node node9571 node10035 +def node10037 : Tree Nat := .leaf 801 +def node10038 : Tree Nat := .node node10037 node9568 +def node10039 : Tree Nat := .node node10038 node7356 +def node10040 : Tree Nat := .leaf 794 +def node10041 : Tree Nat := .node node9578 node10040 +def node10042 : Tree Nat := .node node7774 node10041 +def node10043 : Tree Nat := .node node10039 node10042 +def node10044 : Tree Nat := .node node10043 node9584 +def node10045 : Tree Nat := .node node10036 node10044 +def node10046 : Tree Nat := .node node10028 node10045 +def node10047 : Tree Nat := .node node10018 node10046 +def node10048 : Tree Nat := .node node10001 node8693 +def node10049 : Tree Nat := .node node8691 node10048 +def node10050 : Tree Nat := .node node9592 node10049 +def node10051 : Tree Nat := .leaf 799 +def node10052 : Tree Nat := .node node6574 node10051 +def node10053 : Tree Nat := .node node8698 node10052 +def node10054 : Tree Nat := .node node10053 node9146 +def node10055 : Tree Nat := .leaf 778 +def node10056 : Tree Nat := .node node10055 node224 +def node10057 : Tree Nat := .node node10056 node8222 +def node10058 : Tree Nat := .node node10057 node8702 +def node10059 : Tree Nat := .node node10054 node10058 +def node10060 : Tree Nat := .node node10050 node10059 +def node10061 : Tree Nat := .leaf 792 +def node10062 : Tree Nat := .node node8706 node10061 +def node10063 : Tree Nat := .node node5831 node9981 +def node10064 : Tree Nat := .node node10062 node10063 +def node10065 : Tree Nat := .node node10064 node8711 +def node10066 : Tree Nat := .node node10065 node9598 +def node10067 : Tree Nat := .node node6584 node10023 +def node10068 : Tree Nat := .node node6198 node10067 +def node10069 : Tree Nat := .node node9602 node10068 +def node10070 : Tree Nat := .node node10069 node9607 +def node10071 : Tree Nat := .node node10066 node10070 +def node10072 : Tree Nat := .node node10060 node10071 +def node10073 : Tree Nat := .leaf 798 +def node10074 : Tree Nat := .node node10073 node8245 +def node10075 : Tree Nat := .node node7392 node10074 +def node10076 : Tree Nat := .node node9168 node10075 +def node10077 : Tree Nat := .node node10076 node9614 +def node10078 : Tree Nat := .node node1 node10029 +def node10079 : Tree Nat := .node node10078 node8738 +def node10080 : Tree Nat := .node node9624 node10079 +def node10081 : Tree Nat := .node node9621 node10080 +def node10082 : Tree Nat := .node node10077 node10081 +def node10083 : Tree Nat := .leaf 790 +def node10084 : Tree Nat := .node node10083 node9628 +def node10085 : Tree Nat := .node node10084 node8261 +def node10086 : Tree Nat := .node node10085 node8751 +def node10087 : Tree Nat := .node node9188 node10086 +def node10088 : Tree Nat := .leaf 802 +def node10089 : Tree Nat := .node node10088 node9121 +def node10090 : Tree Nat := .leaf 800 +def node10091 : Tree Nat := .node node8754 node10090 +def node10092 : Tree Nat := .node node10089 node10091 +def node10093 : Tree Nat := .leaf 780 +def node10094 : Tree Nat := .node node9192 node10093 +def node10095 : Tree Nat := .node node7832 node10094 +def node10096 : Tree Nat := .node node10092 node10095 +def node10097 : Tree Nat := .leaf 803 +def node10098 : Tree Nat := .node node10097 node6180 +def node10099 : Tree Nat := .node node10098 node6613 +def node10100 : Tree Nat := .node node9635 node10099 +def node10101 : Tree Nat := .node node10096 node10100 +def node10102 : Tree Nat := .node node10087 node10101 +def node10103 : Tree Nat := .node node10082 node10102 +def node10104 : Tree Nat := .node node10072 node10103 +def node10105 : Tree Nat := .node node10047 node10104 +def node10106 : Tree Nat := .node node9205 node10008 +def node10107 : Tree Nat := .node node8771 node10106 +def node10108 : Tree Nat := .node node10107 node9209 +def node10109 : Tree Nat := .leaf 783 +def node10110 : Tree Nat := .node node10109 node224 +def node10111 : Tree Nat := .node node10110 node9643 +def node10112 : Tree Nat := .node node10111 node8776 +def node10113 : Tree Nat := .node node10108 node10112 +def node10114 : Tree Nat := .node node9204 node10113 +def node10115 : Tree Nat := .node node6169 node9976 +def node10116 : Tree Nat := .node node8781 node10115 +def node10117 : Tree Nat := .node node10019 node8288 +def node10118 : Tree Nat := .node node6187 node10117 +def node10119 : Tree Nat := .node node10116 node10118 +def node10120 : Tree Nat := .node node10119 node9651 +def node10121 : Tree Nat := .node node8774 node9981 +def node10122 : Tree Nat := .node node9654 node10121 +def node10123 : Tree Nat := .node node10122 node9658 +def node10124 : Tree Nat := .node node10123 node9663 +def node10125 : Tree Nat := .node node10120 node10124 +def node10126 : Tree Nat := .node node10114 node10125 +def node10127 : Tree Nat := .leaf 804 +def node10128 : Tree Nat := .node node9667 node10127 +def node10129 : Tree Nat := .node node9996 node6229 +def node10130 : Tree Nat := .node node10128 node10129 +def node10131 : Tree Nat := .node node10051 node6659 +def node10132 : Tree Nat := .node node9227 node10131 +def node10133 : Tree Nat := .node node10130 node10132 +def node10134 : Tree Nat := .node node10133 node9673 +def node10135 : Tree Nat := .leaf 782 +def node10136 : Tree Nat := .node node9235 node10135 +def node10137 : Tree Nat := .node node10136 node9237 +def node10138 : Tree Nat := .node node10137 node9241 +def node10139 : Tree Nat := .node node10138 node9680 +def node10140 : Tree Nat := .node node10134 node10139 +def node10141 : Tree Nat := .node node8808 node10040 +def node10142 : Tree Nat := .node node9974 node6235 +def node10143 : Tree Nat := .node node10141 node10142 +def node10144 : Tree Nat := .node node10143 node9251 +def node10145 : Tree Nat := .leaf 795 +def node10146 : Tree Nat := .node node10145 node9618 +def node10147 : Tree Nat := .node node10146 node8813 +def node10148 : Tree Nat := .node node10147 node9255 +def node10149 : Tree Nat := .node node10144 node10148 +def node10150 : Tree Nat := .leaf 807 +def node10151 : Tree Nat := .node node10150 node9687 +def node10152 : Tree Nat := .node node10151 node8817 +def node10153 : Tree Nat := .leaf 791 +def node10154 : Tree Nat := .node node6602 node10153 +def node10155 : Tree Nat := .node node8819 node10154 +def node10156 : Tree Nat := .node node10152 node10155 +def node10157 : Tree Nat := .node node6186 node10037 +def node10158 : Tree Nat := .node node10157 node6648 +def node10159 : Tree Nat := .node node9692 node10158 +def node10160 : Tree Nat := .node node10156 node10159 +def node10161 : Tree Nat := .node node10149 node10160 +def node10162 : Tree Nat := .node node10140 node10161 +def node10163 : Tree Nat := .node node10126 node10162 +def node10164 : Tree Nat := .node node322 node10088 +def node10165 : Tree Nat := .node node10164 node9698 +def node10166 : Tree Nat := .node node10165 node9266 +def node10167 : Tree Nat := .leaf 786 +def node10168 : Tree Nat := .node node10167 node8829 +def node10169 : Tree Nat := .node node8828 node10168 +def node10170 : Tree Nat := .node node9702 node10169 +def node10171 : Tree Nat := .node node10166 node10170 +def node10172 : Tree Nat := .node node8282 node10032 +def node10173 : Tree Nat := .node node10172 node9270 +def node10174 : Tree Nat := .node node10173 node9707 +def node10175 : Tree Nat := .node node10174 node9715 +def node10176 : Tree Nat := .node node10171 node10175 +def node10177 : Tree Nat := .node node9979 node10051 +def node10178 : Tree Nat := .node node8839 node10177 +def node10179 : Tree Nat := .node node10019 node7074 +def node10180 : Tree Nat := .node node9280 node10179 +def node10181 : Tree Nat := .node node10178 node10180 +def node10182 : Tree Nat := .leaf 774 +def node10183 : Tree Nat := .node node10182 node9205 +def node10184 : Tree Nat := .node node8341 node10183 +def node10185 : Tree Nat := .node node9720 node10184 +def node10186 : Tree Nat := .node node10181 node10185 +def node10187 : Tree Nat := .node node9728 node10097 +def node10188 : Tree Nat := .node node8848 node10187 +def node10189 : Tree Nat := .node node9727 node10188 +def node10190 : Tree Nat := .node node10189 node9734 +def node10191 : Tree Nat := .node node10186 node10190 +def node10192 : Tree Nat := .node node10176 node10191 +def node10193 : Tree Nat := .node node9299 node10127 +def node10194 : Tree Nat := .node node10193 node8854 +def node10195 : Tree Nat := .node node10127 node8197 +def node10196 : Tree Nat := .node node9302 node10195 +def node10197 : Tree Nat := .node node10194 node10196 +def node10198 : Tree Nat := .node node10061 node8774 +def node10199 : Tree Nat := .node node8860 node10198 +def node10200 : Tree Nat := .node node9740 node10199 +def node10201 : Tree Nat := .node node10197 node10200 +def node10202 : Tree Nat := .leaf 779 +def node10203 : Tree Nat := .node node8865 node10202 +def node10204 : Tree Nat := .node node9355 node10090 +def node10205 : Tree Nat := .node node10203 node10204 +def node10206 : Tree Nat := .node node10205 node9746 +def node10207 : Tree Nat := .node node10206 node9753 +def node10208 : Tree Nat := .node node10201 node10207 +def node10209 : Tree Nat := .node node8873 node10153 +def node10210 : Tree Nat := .node node10209 node8875 +def node10211 : Tree Nat := .node node10210 node9318 +def node10212 : Tree Nat := .leaf 784 +def node10213 : Tree Nat := .node node10212 node9604 +def node10214 : Tree Nat := .node node10213 node8878 +def node10215 : Tree Nat := .node node10093 node1 +def node10216 : Tree Nat := .node node8368 node10215 +def node10217 : Tree Nat := .node node10214 node10216 +def node10218 : Tree Nat := .node node10211 node10217 +def node10219 : Tree Nat := .leaf 796 +def node10220 : Tree Nat := .node node10219 node9656 +def node10221 : Tree Nat := .node node6725 node9986 +def node10222 : Tree Nat := .node node10220 node10221 +def node10223 : Tree Nat := .node node9642 node10032 +def node10224 : Tree Nat := .node node8882 node10223 +def node10225 : Tree Nat := .node node10222 node10224 +def node10226 : Tree Nat := .node node10225 node9323 +def node10227 : Tree Nat := .node node10218 node10226 +def node10228 : Tree Nat := .node node10208 node10227 +def node10229 : Tree Nat := .node node10192 node10228 +def node10230 : Tree Nat := .node node10163 node10229 +def node10231 : Tree Nat := .node node10105 node10230 +def node10232 : Tree Nat := .node node451 node9990 +def node10233 : Tree Nat := .node node10232 node9331 +def node10234 : Tree Nat := .node node10090 node7887 +def node10235 : Tree Nat := .node node7933 node10234 +def node10236 : Tree Nat := .node node10233 node10235 +def node10237 : Tree Nat := .node node8843 node10182 +def node10238 : Tree Nat := .node node8382 node10237 +def node10239 : Tree Nat := .node node10238 node8894 +def node10240 : Tree Nat := .node node10236 node10239 +def node10241 : Tree Nat := .leaf 785 +def node10242 : Tree Nat := .node node9121 node10241 +def node10243 : Tree Nat := .node node8897 node10242 +def node10244 : Tree Nat := .node node10243 node9338 +def node10245 : Tree Nat := .node node10109 node7824 +def node10246 : Tree Nat := .node node10245 node8900 +def node10247 : Tree Nat := .node node10246 node8903 +def node10248 : Tree Nat := .node node10244 node10247 +def node10249 : Tree Nat := .node node10240 node10248 +def node10250 : Tree Nat := .node node6989 node10202 +def node10251 : Tree Nat := .node node7153 node10250 +def node10252 : Tree Nat := .node node9778 node10251 +def node10253 : Tree Nat := .node node10252 node9782 +def node10254 : Tree Nat := .node node9774 node10253 +def node10255 : Tree Nat := .node node10249 node10254 +def node10256 : Tree Nat := .node node10145 node9712 +def node10257 : Tree Nat := .node node10256 node8931 +def node10258 : Tree Nat := .node node10257 node9366 +def node10259 : Tree Nat := .node node9799 node10258 +def node10260 : Tree Nat := .node node10150 node9633 +def node10261 : Tree Nat := .node node10260 node8935 +def node10262 : Tree Nat := .node node10261 node9807 +def node10263 : Tree Nat := .node node10262 node9813 +def node10264 : Tree Nat := .node node10259 node10263 +def node10265 : Tree Nat := .node node9796 node10264 +def node10266 : Tree Nat := .node node10255 node10265 +def node10267 : Tree Nat := .node node10097 node8233 +def node10268 : Tree Nat := .node node5803 node10267 +def node10269 : Tree Nat := .node node9820 node10268 +def node10270 : Tree Nat := .node node10093 node8419 +def node10271 : Tree Nat := .node node8448 node10270 +def node10272 : Tree Nat := .node node10153 node8737 +def node10273 : Tree Nat := .node node8942 node10272 +def node10274 : Tree Nat := .node node10271 node10273 +def node10275 : Tree Nat := .node node10269 node10274 +def node10276 : Tree Nat := .node node9310 node10073 +def node10277 : Tree Nat := .node node8453 node10276 +def node10278 : Tree Nat := .node node10277 node9824 +def node10279 : Tree Nat := .node node10278 node9830 +def node10280 : Tree Nat := .node node10275 node10279 +def node10281 : Tree Nat := .node node224 node10167 +def node10282 : Tree Nat := .node node8952 node10281 +def node10283 : Tree Nat := .node node10282 node8462 +def node10284 : Tree Nat := .node node10061 node8842 +def node10285 : Tree Nat := .node node9833 node10284 +def node10286 : Tree Nat := .node node10202 node9159 +def node10287 : Tree Nat := .node node196 node10286 +def node10288 : Tree Nat := .node node10285 node10287 +def node10289 : Tree Nat := .node node10283 node10288 +def node10290 : Tree Nat := .leaf 806 +def node10291 : Tree Nat := .node node9544 node10290 +def node10292 : Tree Nat := .node node6198 node10291 +def node10293 : Tree Nat := .node node9839 node10292 +def node10294 : Tree Nat := .node node10293 node9398 +def node10295 : Tree Nat := .node node10289 node10294 +def node10296 : Tree Nat := .node node10280 node10295 +def node10297 : Tree Nat := .node node9986 node8718 +def node10298 : Tree Nat := .node node8035 node10297 +def node10299 : Tree Nat := .node node9848 node10298 +def node10300 : Tree Nat := .node node9404 node10299 +def node10301 : Tree Nat := .node node7108 node10290 +def node10302 : Tree Nat := .node node8039 node10301 +def node10303 : Tree Nat := .node node9852 node10302 +def node10304 : Tree Nat := .node node1 node10212 +def node10305 : Tree Nat := .node node10304 node9856 +def node10306 : Tree Nat := .node node9855 node10305 +def node10307 : Tree Nat := .node node10303 node10306 +def node10308 : Tree Nat := .node node10300 node10307 +def node10309 : Tree Nat := .node node10212 node9861 +def node10310 : Tree Nat := .node node10309 node8975 +def node10311 : Tree Nat := .node node10008 node1 +def node10312 : Tree Nat := .node node8055 node10311 +def node10313 : Tree Nat := .node node10310 node10312 +def node10314 : Tree Nat := .node node9414 node10313 +def node10315 : Tree Nat := .node node10219 node9352 +def node10316 : Tree Nat := .leaf 797 +def node10317 : Tree Nat := .node node6929 node10316 +def node10318 : Tree Nat := .node node10315 node10317 +def node10319 : Tree Nat := .node node10318 node9867 +def node10320 : Tree Nat := .node node9974 node6694 +def node10321 : Tree Nat := .node node10320 node9419 +def node10322 : Tree Nat := .node node8507 node10321 +def node10323 : Tree Nat := .node node10319 node10322 +def node10324 : Tree Nat := .node node10314 node10323 +def node10325 : Tree Nat := .node node10308 node10324 +def node10326 : Tree Nat := .node node10296 node10325 +def node10327 : Tree Nat := .node node10266 node10326 +def node10328 : Tree Nat := .node node10290 node8175 +def node10329 : Tree Nat := .node node8070 node10328 +def node10330 : Tree Nat := .node node9875 node10329 +def node10331 : Tree Nat := .node node10040 node8689 +def node10332 : Tree Nat := .node node7238 node10331 +def node10333 : Tree Nat := .node node8985 node10332 +def node10334 : Tree Nat := .node node10330 node10333 +def node10335 : Tree Nat := .node node9990 node8054 +def node10336 : Tree Nat := .node node10335 node9431 +def node10337 : Tree Nat := .node node10336 node9882 +def node10338 : Tree Nat := .node node9880 node10337 +def node10339 : Tree Nat := .node node10334 node10338 +def node10340 : Tree Nat := .node node195 node10182 +def node10341 : Tree Nat := .node node8998 node10340 +def node10342 : Tree Nat := .node node10341 node8528 +def node10343 : Tree Nat := .node node10135 node9289 +def node10344 : Tree Nat := .node node7253 node10343 +def node10345 : Tree Nat := .node node9887 node10344 +def node10346 : Tree Nat := .node node10342 node10345 +def node10347 : Tree Nat := .node node7065 node10167 +def node10348 : Tree Nat := .node node9890 node10347 +def node10349 : Tree Nat := .node node10348 node9893 +def node10350 : Tree Nat := .node node10349 node9444 +def node10351 : Tree Nat := .node node10346 node10350 +def node10352 : Tree Nat := .node node10339 node10351 +def node10353 : Tree Nat := .node node6764 node10000 +def node10354 : Tree Nat := .node node5803 node10353 +def node10355 : Tree Nat := .node node9449 node10354 +def node10356 : Tree Nat := .node node10241 node8749 +def node10357 : Tree Nat := .node node341 node10356 +def node10358 : Tree Nat := .node node9899 node10357 +def node10359 : Tree Nat := .node node10355 node10358 +def node10360 : Tree Nat := .node node8668 node10109 +def node10361 : Tree Nat := .node node10360 node7660 +def node10362 : Tree Nat := .node node10361 node9903 +def node10363 : Tree Nat := .node node10362 node9910 +def node10364 : Tree Nat := .node node10359 node10363 +def node10365 : Tree Nat := .node node8677 node10083 +def node10366 : Tree Nat := .node node10365 node7667 +def node10367 : Tree Nat := .node node10366 node8551 +def node10368 : Tree Nat := .node node10029 node5826 +def node10369 : Tree Nat := .node node10368 node9021 +def node10370 : Tree Nat := .node node9776 node1 +def node10371 : Tree Nat := .node node8555 node10370 +def node10372 : Tree Nat := .node node10369 node10371 +def node10373 : Tree Nat := .node node10367 node10372 +def node10374 : Tree Nat := .node node10037 node5831 +def node10375 : Tree Nat := .node node10374 node7671 +def node10376 : Tree Nat := .node node10375 node9914 +def node10377 : Tree Nat := .node node6176 node10219 +def node10378 : Tree Nat := .node node10377 node9460 +def node10379 : Tree Nat := .node node8560 node10378 +def node10380 : Tree Nat := .node node10376 node10379 +def node10381 : Tree Nat := .node node10373 node10380 +def node10382 : Tree Nat := .node node10364 node10381 +def node10383 : Tree Nat := .node node10352 node10382 +def node10384 : Tree Nat := .node node10316 node8315 +def node10385 : Tree Nat := .node node5803 node10384 +def node10386 : Tree Nat := .node node9921 node10385 +def node10387 : Tree Nat := .node node1 node9974 +def node10388 : Tree Nat := .node node10387 node9467 +def node10389 : Tree Nat := .node node9030 node10388 +def node10390 : Tree Nat := .node node10386 node10389 +def node10391 : Tree Nat := .node node10056 node9035 +def node10392 : Tree Nat := .node node10391 node9477 +def node10393 : Tree Nat := .node node9926 node10392 +def node10394 : Tree Nat := .node node10390 node10393 +def node10395 : Tree Nat := .node node8706 node10145 +def node10396 : Tree Nat := .node node6186 node10073 +def node10397 : Tree Nat := .node node10395 node10396 +def node10398 : Tree Nat := .node node10397 node8582 +def node10399 : Tree Nat := .node node10398 node9930 +def node10400 : Tree Nat := .node node10399 node9941 +def node10401 : Tree Nat := .node node10394 node10400 +def node10402 : Tree Nat := .node node9166 node10150 +def node10403 : Tree Nat := .node node10402 node9053 +def node10404 : Tree Nat := .node node10403 node9494 +def node10405 : Tree Nat := .node node10404 node9946 +def node10406 : Tree Nat := .node node9175 node10055 +def node10407 : Tree Nat := .node node7083 node10316 +def node10408 : Tree Nat := .node node10406 node10407 +def node10409 : Tree Nat := .node node9289 node10135 +def node10410 : Tree Nat := .node node9062 node10409 +def node10411 : Tree Nat := .node node10408 node10410 +def node10412 : Tree Nat := .node node10411 node9950 +def node10413 : Tree Nat := .node node10405 node10412 +def node10414 : Tree Nat := .node node8743 node10023 +def node10415 : Tree Nat := .node node10414 node9068 +def node10416 : Tree Nat := .node node10415 node9514 +def node10417 : Tree Nat := .node node10083 node9653 +def node10418 : Tree Nat := .node node10417 node9071 +def node10419 : Tree Nat := .node node10418 node8619 +def node10420 : Tree Nat := .node node10416 node10419 +def node10421 : Tree Nat := .node node10088 node9675 +def node10422 : Tree Nat := .node node8737 node10241 +def node10423 : Tree Nat := .node node10421 node10422 +def node10424 : Tree Nat := .node node10423 node9078 +def node10425 : Tree Nat := .node node9979 node6764 +def node10426 : Tree Nat := .node node10425 node9519 +def node10427 : Tree Nat := .node node9961 node10426 +def node10428 : Tree Nat := .node node10424 node10427 +def node10429 : Tree Nat := .node node10420 node10428 +def node10430 : Tree Nat := .node node10413 node10429 +def node10431 : Tree Nat := .node node10401 node10430 +def node10432 : Tree Nat := .node node10383 node10431 +def node10433 : Tree Nat := .node node10327 node10432 +def node10434 : Tree Nat := .node node10231 node10433 +def node10435 : Tree Nat := .leaf 1 +def node10436 : Tree Nat := .leaf 828 +def node10437 : Tree Nat := .node node10435 node10436 +def node10438 : Tree Nat := .node node10437 node9088 +def node10439 : Tree Nat := .node node1 node10436 +def node10440 : Tree Nat := .node node10439 node7715 +def node10441 : Tree Nat := .node node10438 node10440 +def node10442 : Tree Nat := .node node10435 node9974 +def node10443 : Tree Nat := .node node10442 node9977 +def node10444 : Tree Nat := .node node10443 node9983 +def node10445 : Tree Nat := .node node10441 node10444 +def node10446 : Tree Nat := .leaf 813 +def node10447 : Tree Nat := .node node10435 node10446 +def node10448 : Tree Nat := .node node10447 node9987 +def node10449 : Tree Nat := .leaf 826 +def node10450 : Tree Nat := .node node1 node10449 +def node10451 : Tree Nat := .node node10450 node8170 +def node10452 : Tree Nat := .node node10448 node10451 +def node10453 : Tree Nat := .node node9990 node10449 +def node10454 : Tree Nat := .node node10453 node6534 +def node10455 : Tree Nat := .node node10454 node9531 +def node10456 : Tree Nat := .node node10452 node10455 +def node10457 : Tree Nat := .node node10445 node10456 +def node10458 : Tree Nat := .leaf 831 +def node10459 : Tree Nat := .node node10435 node10458 +def node10460 : Tree Nat := .node node10459 node8652 +def node10461 : Tree Nat := .node node10460 node9998 +def node10462 : Tree Nat := .node node9535 node10006 +def node10463 : Tree Nat := .node node10462 node8658 +def node10464 : Tree Nat := .node node10463 node10003 +def node10465 : Tree Nat := .node node10461 node10464 +def node10466 : Tree Nat := .node node10435 node9996 +def node10467 : Tree Nat := .node node10466 node8181 +def node10468 : Tree Nat := .node node10467 node9103 +def node10469 : Tree Nat := .node node10012 node10468 +def node10470 : Tree Nat := .node node10465 node10469 +def node10471 : Tree Nat := .node node10457 node10470 +def node10472 : Tree Nat := .node node10435 node9535 +def node10473 : Tree Nat := .node node10006 node6946 +def node10474 : Tree Nat := .node node10472 node10473 +def node10475 : Tree Nat := .node node10474 node10021 +def node10476 : Tree Nat := .node node10475 node10026 +def node10477 : Tree Nat := .node node10435 node9543 +def node10478 : Tree Nat := .node node10477 node9126 +def node10479 : Tree Nat := .node node10478 node9564 +def node10480 : Tree Nat := .node node9557 node10479 +def node10481 : Tree Nat := .node node10476 node10480 +def node10482 : Tree Nat := .leaf 829 +def node10483 : Tree Nat := .node node10482 node6188 +def node10484 : Tree Nat := .node node9569 node10483 +def node10485 : Tree Nat := .node node10484 node8195 +def node10486 : Tree Nat := .node node10485 node10035 +def node10487 : Tree Nat := .node node10486 node10044 +def node10488 : Tree Nat := .node node10481 node10487 +def node10489 : Tree Nat := .node node10471 node10488 +def node10490 : Tree Nat := .node node10435 node451 +def node10491 : Tree Nat := .node node10490 node9590 +def node10492 : Tree Nat := .node node10491 node8214 +def node10493 : Tree Nat := .node node10492 node10049 +def node10494 : Tree Nat := .node node10493 node10059 +def node10495 : Tree Nat := .node node10458 node9981 +def node10496 : Tree Nat := .node node10062 node10495 +def node10497 : Tree Nat := .node node10496 node8711 +def node10498 : Tree Nat := .node node10497 node9598 +def node10499 : Tree Nat := .node node10435 node5835 +def node10500 : Tree Nat := .node node10499 node9605 +def node10501 : Tree Nat := .node node10500 node9161 +def node10502 : Tree Nat := .node node10069 node10501 +def node10503 : Tree Nat := .node node10498 node10502 +def node10504 : Tree Nat := .node node10494 node10503 +def node10505 : Tree Nat := .node node10435 node9589 +def node10506 : Tree Nat := .node node10505 node8735 +def node10507 : Tree Nat := .node node10506 node10079 +def node10508 : Tree Nat := .node node9621 node10507 +def node10509 : Tree Nat := .node node10077 node10508 +def node10510 : Tree Nat := .node node10509 node10102 +def node10511 : Tree Nat := .node node10504 node10510 +def node10512 : Tree Nat := .node node10489 node10511 +def node10513 : Tree Nat := .node node10490 node9201 +def node10514 : Tree Nat := .node node10513 node8272 +def node10515 : Tree Nat := .node node10514 node8768 +def node10516 : Tree Nat := .node node10515 node10113 +def node10517 : Tree Nat := .node node10499 node9661 +def node10518 : Tree Nat := .node node10517 node9222 +def node10519 : Tree Nat := .node node10123 node10518 +def node10520 : Tree Nat := .node node10120 node10519 +def node10521 : Tree Nat := .node node10516 node10520 +def node10522 : Tree Nat := .node node9113 node10006 +def node10523 : Tree Nat := .node node10136 node10522 +def node10524 : Tree Nat := .node node10523 node9241 +def node10525 : Tree Nat := .node node10435 node9144 +def node10526 : Tree Nat := .node node10525 node9244 +def node10527 : Tree Nat := .node node10526 node9679 +def node10528 : Tree Nat := .node node10524 node10527 +def node10529 : Tree Nat := .node node10134 node10528 +def node10530 : Tree Nat := .node node10529 node10161 +def node10531 : Tree Nat := .node node10521 node10530 +def node10532 : Tree Nat := .node node10446 node10088 +def node10533 : Tree Nat := .leaf 830 +def node10534 : Tree Nat := .node node10533 node9628 +def node10535 : Tree Nat := .node node10532 node10534 +def node10536 : Tree Nat := .node node10535 node9266 +def node10537 : Tree Nat := .node node10536 node10170 +def node10538 : Tree Nat := .node node10537 node10175 +def node10539 : Tree Nat := .node node10435 node9155 +def node10540 : Tree Nat := .node node10539 node9290 +def node10541 : Tree Nat := .node node10533 node9543 +def node10542 : Tree Nat := .node node10541 node9293 +def node10543 : Tree Nat := .node node10540 node10542 +def node10544 : Tree Nat := .node node10189 node10543 +def node10545 : Tree Nat := .node node10186 node10544 +def node10546 : Tree Nat := .node node10538 node10545 +def node10547 : Tree Nat := .node node10435 node9310 +def node10548 : Tree Nat := .node node10547 node9312 +def node10549 : Tree Nat := .node node10548 node9752 +def node10550 : Tree Nat := .node node10206 node10549 +def node10551 : Tree Nat := .node node10201 node10550 +def node10552 : Tree Nat := .node node10482 node8843 +def node10553 : Tree Nat := .node node10209 node10552 +def node10554 : Tree Nat := .node node10553 node9318 +def node10555 : Tree Nat := .node node10554 node10217 +def node10556 : Tree Nat := .node node10555 node10226 +def node10557 : Tree Nat := .node node10551 node10556 +def node10558 : Tree Nat := .node node10546 node10557 +def node10559 : Tree Nat := .node node10531 node10558 +def node10560 : Tree Nat := .node node10512 node10559 +def node10561 : Tree Nat := .node node10435 node9990 +def node10562 : Tree Nat := .node node10561 node9331 +def node10563 : Tree Nat := .node node10562 node10235 +def node10564 : Tree Nat := .node node10563 node10239 +def node10565 : Tree Nat := .node node10564 node10248 +def node10566 : Tree Nat := .node node10435 node7836 +def node10567 : Tree Nat := .node node10566 node9780 +def node10568 : Tree Nat := .node node10567 node8406 +def node10569 : Tree Nat := .node node10252 node10568 +def node10570 : Tree Nat := .node node9774 node10569 +def node10571 : Tree Nat := .node node10565 node10570 +def node10572 : Tree Nat := .node node10435 node9718 +def node10573 : Tree Nat := .node node10533 node7163 +def node10574 : Tree Nat := .node node10572 node10573 +def node10575 : Tree Nat := .node node10574 node8413 +def node10576 : Tree Nat := .node node10575 node9350 +def node10577 : Tree Nat := .node node10435 node9728 +def node10578 : Tree Nat := .node node10577 node9360 +def node10579 : Tree Nat := .node node10578 node9793 +def node10580 : Tree Nat := .node node9358 node10579 +def node10581 : Tree Nat := .node node10576 node10580 +def node10582 : Tree Nat := .node node10581 node10264 +def node10583 : Tree Nat := .node node10571 node10582 +def node10584 : Tree Nat := .node node10458 node451 +def node10585 : Tree Nat := .node node10584 node9819 +def node10586 : Tree Nat := .node node10585 node10268 +def node10587 : Tree Nat := .node node10586 node10274 +def node10588 : Tree Nat := .node node10587 node10279 +def node10589 : Tree Nat := .node node10499 node9393 +def node10590 : Tree Nat := .node node10589 node9397 +def node10591 : Tree Nat := .node node10293 node10590 +def node10592 : Tree Nat := .node node10289 node10591 +def node10593 : Tree Nat := .node node10588 node10592 +def node10594 : Tree Nat := .node node10435 node9818 +def node10595 : Tree Nat := .node node10594 node8488 +def node10596 : Tree Nat := .node node10595 node10305 +def node10597 : Tree Nat := .node node10303 node10596 +def node10598 : Tree Nat := .node node10300 node10597 +def node10599 : Tree Nat := .node node10598 node10324 +def node10600 : Tree Nat := .node node10593 node10599 +def node10601 : Tree Nat := .node node10583 node10600 +def node10602 : Tree Nat := .node node10449 node9709 +def node10603 : Tree Nat := .node node10602 node9427 +def node10604 : Tree Nat := .node node10603 node10329 +def node10605 : Tree Nat := .node node10604 node10333 +def node10606 : Tree Nat := .node node10605 node10338 +def node10607 : Tree Nat := .node node10435 node8040 +def node10608 : Tree Nat := .node node10607 node8101 +def node10609 : Tree Nat := .node node10608 node9443 +def node10610 : Tree Nat := .node node10349 node10609 +def node10611 : Tree Nat := .node node10346 node10610 +def node10612 : Tree Nat := .node node10606 node10611 +def node10613 : Tree Nat := .node node1 node10458 +def node10614 : Tree Nat := .node node10613 node10353 +def node10615 : Tree Nat := .node node9449 node10614 +def node10616 : Tree Nat := .node node1 node10482 +def node10617 : Tree Nat := .node node10616 node10356 +def node10618 : Tree Nat := .node node9899 node10617 +def node10619 : Tree Nat := .node node10615 node10618 +def node10620 : Tree Nat := .node node6320 node10006 +def node10621 : Tree Nat := .node node10360 node10620 +def node10622 : Tree Nat := .node node1 node10533 +def node10623 : Tree Nat := .node node10622 node9902 +def node10624 : Tree Nat := .node node10621 node10623 +def node10625 : Tree Nat := .node node10435 node9667 +def node10626 : Tree Nat := .node node10625 node9455 +def node10627 : Tree Nat := .node node10626 node9909 +def node10628 : Tree Nat := .node node10624 node10627 +def node10629 : Tree Nat := .node node10619 node10628 +def node10630 : Tree Nat := .node node10613 node8550 +def node10631 : Tree Nat := .node node10366 node10630 +def node10632 : Tree Nat := .node node10029 node10533 +def node10633 : Tree Nat := .node node10632 node9021 +def node10634 : Tree Nat := .node node10633 node10371 +def node10635 : Tree Nat := .node node10631 node10634 +def node10636 : Tree Nat := .node node10037 node10458 +def node10637 : Tree Nat := .node node10636 node7671 +def node10638 : Tree Nat := .node node10613 node9913 +def node10639 : Tree Nat := .node node10637 node10638 +def node10640 : Tree Nat := .node node10622 node8559 +def node10641 : Tree Nat := .node node10640 node10378 +def node10642 : Tree Nat := .node node10639 node10641 +def node10643 : Tree Nat := .node node10635 node10642 +def node10644 : Tree Nat := .node node10629 node10643 +def node10645 : Tree Nat := .node node10612 node10644 +def node10646 : Tree Nat := .node node10446 node10533 +def node10647 : Tree Nat := .node node10646 node9920 +def node10648 : Tree Nat := .leaf 827 +def node10649 : Tree Nat := .node node1 node10648 +def node10650 : Tree Nat := .node node10649 node10384 +def node10651 : Tree Nat := .node node10647 node10650 +def node10652 : Tree Nat := .node node8216 node10648 +def node10653 : Tree Nat := .node node10652 node9029 +def node10654 : Tree Nat := .node node10653 node10388 +def node10655 : Tree Nat := .node node10651 node10654 +def node10656 : Tree Nat := .node node8697 node10482 +def node10657 : Tree Nat := .node node10656 node9471 +def node10658 : Tree Nat := .node node10439 node9924 +def node10659 : Tree Nat := .node node10657 node10658 +def node10660 : Tree Nat := .node node10459 node9035 +def node10661 : Tree Nat := .node node10660 node9477 +def node10662 : Tree Nat := .node node10659 node10661 +def node10663 : Tree Nat := .node node10655 node10662 +def node10664 : Tree Nat := .node node10450 node8581 +def node10665 : Tree Nat := .node node10397 node10664 +def node10666 : Tree Nat := .node node9595 node10449 +def node10667 : Tree Nat := .node node10666 node9043 +def node10668 : Tree Nat := .node node1 node10446 +def node10669 : Tree Nat := .node node10668 node9481 +def node10670 : Tree Nat := .node node10667 node10669 +def node10671 : Tree Nat := .node node10665 node10670 +def node10672 : Tree Nat := .node node9600 node10648 +def node10673 : Tree Nat := .node node10672 node9047 +def node10674 : Tree Nat := .node node10622 node9933 +def node10675 : Tree Nat := .node node10673 node10674 +def node10676 : Tree Nat := .node node10435 node10648 +def node10677 : Tree Nat := .node node10676 node9936 +def node10678 : Tree Nat := .node node10677 node9939 +def node10679 : Tree Nat := .node node10675 node10678 +def node10680 : Tree Nat := .node node10671 node10679 +def node10681 : Tree Nat := .node node10663 node10680 +def node10682 : Tree Nat := .node node10435 node9166 +def node10683 : Tree Nat := .node node10682 node8606 +def node10684 : Tree Nat := .node node10683 node8609 +def node10685 : Tree Nat := .node node10411 node10684 +def node10686 : Tree Nat := .node node10405 node10685 +def node10687 : Tree Nat := .node node10686 node10429 +def node10688 : Tree Nat := .node node10681 node10687 +def node10689 : Tree Nat := .node node10645 node10688 +def node10690 : Tree Nat := .node node10601 node10689 +def node10691 : Tree Nat := .node node10560 node10690 +def node10692 : Tree Nat := .node node10435 node10449 +def node10693 : Tree Nat := .node node10692 node6534 +def node10694 : Tree Nat := .node node10693 node9531 +def node10695 : Tree Nat := .node node10452 node10694 +def node10696 : Tree Nat := .node node10445 node10695 +def node10697 : Tree Nat := .node node10435 node10006 +def node10698 : Tree Nat := .node node10697 node8658 +def node10699 : Tree Nat := .node node10698 node10003 +def node10700 : Tree Nat := .node node10461 node10699 +def node10701 : Tree Nat := .node node10700 node10469 +def node10702 : Tree Nat := .node node10696 node10701 +def node10703 : Tree Nat := .node node10435 node9113 +def node10704 : Tree Nat := .node node10703 node8664 +def node10705 : Tree Nat := .node node10704 node10025 +def node10706 : Tree Nat := .node node10475 node10705 +def node10707 : Tree Nat := .node node10706 node10480 +def node10708 : Tree Nat := .node node10435 node9529 +def node10709 : Tree Nat := .node node10708 node8682 +def node10710 : Tree Nat := .node node10709 node10034 +def node10711 : Tree Nat := .node node10485 node10710 +def node10712 : Tree Nat := .node node10711 node10044 +def node10713 : Tree Nat := .node node10707 node10712 +def node10714 : Tree Nat := .node node10702 node10713 +def node10715 : Tree Nat := .node node10435 node224 +def node10716 : Tree Nat := .node node10715 node8222 +def node10717 : Tree Nat := .node node10716 node8702 +def node10718 : Tree Nat := .node node10054 node10717 +def node10719 : Tree Nat := .node node10493 node10718 +def node10720 : Tree Nat := .node node10435 node5826 +def node10721 : Tree Nat := .node node10720 node8714 +def node10722 : Tree Nat := .node node10721 node9152 +def node10723 : Tree Nat := .node node10497 node10722 +def node10724 : Tree Nat := .node node10723 node10502 +def node10725 : Tree Nat := .node node10719 node10724 +def node10726 : Tree Nat := .node node10435 node9611 +def node10727 : Tree Nat := .node node10726 node8727 +def node10728 : Tree Nat := .node node10727 node8731 +def node10729 : Tree Nat := .node node10076 node10728 +def node10730 : Tree Nat := .node node10729 node10508 +def node10731 : Tree Nat := .node node10435 node9628 +def node10732 : Tree Nat := .node node10731 node8261 +def node10733 : Tree Nat := .node node10732 node8751 +def node10734 : Tree Nat := .node node9188 node10733 +def node10735 : Tree Nat := .node node10734 node10101 +def node10736 : Tree Nat := .node node10730 node10735 +def node10737 : Tree Nat := .node node10725 node10736 +def node10738 : Tree Nat := .node node10714 node10737 +def node10739 : Tree Nat := .node node10715 node9643 +def node10740 : Tree Nat := .node node10739 node8776 +def node10741 : Tree Nat := .node node10108 node10740 +def node10742 : Tree Nat := .node node10515 node10741 +def node10743 : Tree Nat := .node node10720 node8785 +def node10744 : Tree Nat := .node node10743 node8788 +def node10745 : Tree Nat := .node node10119 node10744 +def node10746 : Tree Nat := .node node10745 node10519 +def node10747 : Tree Nat := .node node10742 node10746 +def node10748 : Tree Nat := .node node10435 node9544 +def node10749 : Tree Nat := .node node10748 node8797 +def node10750 : Tree Nat := .node node10749 node8800 +def node10751 : Tree Nat := .node node10133 node10750 +def node10752 : Tree Nat := .node node10751 node10528 +def node10753 : Tree Nat := .node node10435 node9618 +def node10754 : Tree Nat := .node node10753 node8813 +def node10755 : Tree Nat := .node node10754 node9255 +def node10756 : Tree Nat := .node node10144 node10755 +def node10757 : Tree Nat := .node node10756 node10160 +def node10758 : Tree Nat := .node node10752 node10757 +def node10759 : Tree Nat := .node node10747 node10758 +def node10760 : Tree Nat := .node node10435 node9578 +def node10761 : Tree Nat := .node node10760 node8826 +def node10762 : Tree Nat := .node node10761 node10169 +def node10763 : Tree Nat := .node node10536 node10762 +def node10764 : Tree Nat := .node node10435 node9239 +def node10765 : Tree Nat := .node node10764 node8334 +def node10766 : Tree Nat := .node node10765 node9714 +def node10767 : Tree Nat := .node node10174 node10766 +def node10768 : Tree Nat := .node node10763 node10767 +def node10769 : Tree Nat := .node node10435 node9600 +def node10770 : Tree Nat := .node node10769 node8844 +def node10771 : Tree Nat := .node node10770 node10184 +def node10772 : Tree Nat := .node node10181 node10771 +def node10773 : Tree Nat := .node node10772 node10544 +def node10774 : Tree Nat := .node node10768 node10773 +def node10775 : Tree Nat := .node node10435 node9738 +def node10776 : Tree Nat := .node node10775 node8858 +def node10777 : Tree Nat := .node node10776 node10199 +def node10778 : Tree Nat := .node node10197 node10777 +def node10779 : Tree Nat := .node node10778 node10550 +def node10780 : Tree Nat := .node node10435 node9604 +def node10781 : Tree Nat := .node node10780 node8878 +def node10782 : Tree Nat := .node node10781 node10216 +def node10783 : Tree Nat := .node node10554 node10782 +def node10784 : Tree Nat := .node node10783 node10226 +def node10785 : Tree Nat := .node node10779 node10784 +def node10786 : Tree Nat := .node node10774 node10785 +def node10787 : Tree Nat := .node node10759 node10786 +def node10788 : Tree Nat := .node node10738 node10787 +def node10789 : Tree Nat := .node node10435 node7824 +def node10790 : Tree Nat := .node node10789 node8900 +def node10791 : Tree Nat := .node node10790 node8903 +def node10792 : Tree Nat := .node node10244 node10791 +def node10793 : Tree Nat := .node node10564 node10792 +def node10794 : Tree Nat := .node node10435 node7955 +def node10795 : Tree Nat := .node node10794 node8911 +def node10796 : Tree Nat := .node node10795 node8400 +def node10797 : Tree Nat := .node node8910 node10796 +def node10798 : Tree Nat := .node node10797 node10569 +def node10799 : Tree Nat := .node node10793 node10798 +def node10800 : Tree Nat := .node node10435 node9177 +def node10801 : Tree Nat := .node node10800 node8921 +def node10802 : Tree Nat := .node node10801 node8924 +def node10803 : Tree Nat := .node node10575 node10802 +def node10804 : Tree Nat := .node node10803 node10580 +def node10805 : Tree Nat := .node node10435 node9712 +def node10806 : Tree Nat := .node node10805 node8931 +def node10807 : Tree Nat := .node node10806 node9366 +def node10808 : Tree Nat := .node node9799 node10807 +def node10809 : Tree Nat := .node node10808 node10263 +def node10810 : Tree Nat := .node node10804 node10809 +def node10811 : Tree Nat := .node node10799 node10810 +def node10812 : Tree Nat := .node node10435 node411 +def node10813 : Tree Nat := .node node10812 node10270 +def node10814 : Tree Nat := .node node10813 node10273 +def node10815 : Tree Nat := .node node10586 node10814 +def node10816 : Tree Nat := .node node10715 node9383 +def node10817 : Tree Nat := .node node10816 node9829 +def node10818 : Tree Nat := .node node10278 node10817 +def node10819 : Tree Nat := .node node10815 node10818 +def node10820 : Tree Nat := .node node10720 node10284 +def node10821 : Tree Nat := .node node10820 node10287 +def node10822 : Tree Nat := .node node10283 node10821 +def node10823 : Tree Nat := .node node10822 node10591 +def node10824 : Tree Nat := .node node10819 node10823 +def node10825 : Tree Nat := .node node10435 node9846 +def node10826 : Tree Nat := .node node10825 node8961 +def node10827 : Tree Nat := .node node10826 node10298 +def node10828 : Tree Nat := .node node9404 node10827 +def node10829 : Tree Nat := .node node10828 node10597 +def node10830 : Tree Nat := .node node10435 node9861 +def node10831 : Tree Nat := .node node10830 node8975 +def node10832 : Tree Nat := .node node10831 node10312 +def node10833 : Tree Nat := .node node9414 node10832 +def node10834 : Tree Nat := .node node10833 node10323 +def node10835 : Tree Nat := .node node10829 node10834 +def node10836 : Tree Nat := .node node10824 node10835 +def node10837 : Tree Nat := .node node10811 node10836 +def node10838 : Tree Nat := .node node10435 node8054 +def node10839 : Tree Nat := .node node10838 node9431 +def node10840 : Tree Nat := .node node10839 node9882 +def node10841 : Tree Nat := .node node9880 node10840 +def node10842 : Tree Nat := .node node10605 node10841 +def node10843 : Tree Nat := .node node10435 node8089 +def node10844 : Tree Nat := .node node10843 node9001 +def node10845 : Tree Nat := .node node10844 node10344 +def node10846 : Tree Nat := .node node10342 node10845 +def node10847 : Tree Nat := .node node10846 node10610 +def node10848 : Tree Nat := .node node10842 node10847 +def node10849 : Tree Nat := .node node10435 node9648 +def node10850 : Tree Nat := .node node10849 node9007 +def node10851 : Tree Nat := .node node10850 node10617 +def node10852 : Tree Nat := .node node10615 node10851 +def node10853 : Tree Nat := .node node10852 node10628 +def node10854 : Tree Nat := .node node10435 node10533 +def node10855 : Tree Nat := .node node10854 node9021 +def node10856 : Tree Nat := .node node10855 node10371 +def node10857 : Tree Nat := .node node10631 node10856 +def node10858 : Tree Nat := .node node10857 node10642 +def node10859 : Tree Nat := .node node10853 node10858 +def node10860 : Tree Nat := .node node10848 node10859 +def node10861 : Tree Nat := .node node10676 node9029 +def node10862 : Tree Nat := .node node10861 node10388 +def node10863 : Tree Nat := .node node10651 node10862 +def node10864 : Tree Nat := .node node10863 node10662 +def node10865 : Tree Nat := .node node10692 node9043 +def node10866 : Tree Nat := .node node10865 node10669 +def node10867 : Tree Nat := .node node10665 node10866 +def node10868 : Tree Nat := .node node10867 node10679 +def node10869 : Tree Nat := .node node10864 node10868 +def node10870 : Tree Nat := .node node10435 node9595 +def node10871 : Tree Nat := .node node10870 node9056 +def node10872 : Tree Nat := .node node10871 node9499 +def node10873 : Tree Nat := .node node10404 node10872 +def node10874 : Tree Nat := .node node10873 node10685 +def node10875 : Tree Nat := .node node10435 node9653 +def node10876 : Tree Nat := .node node10875 node9071 +def node10877 : Tree Nat := .node node10876 node8619 +def node10878 : Tree Nat := .node node10416 node10877 +def node10879 : Tree Nat := .node node10878 node10428 +def node10880 : Tree Nat := .node node10874 node10879 +def node10881 : Tree Nat := .node node10869 node10880 +def node10882 : Tree Nat := .node node10860 node10881 +def node10883 : Tree Nat := .node node10837 node10882 +def node10884 : Tree Nat := .node node10788 node10883 +def node10885 : Tree Nat := .node node10697 node10009 +def node10886 : Tree Nat := .node node10885 node10011 +def node10887 : Tree Nat := .node node10886 node10468 +def node10888 : Tree Nat := .node node10700 node10887 +def node10889 : Tree Nat := .node node10696 node10888 +def node10890 : Tree Nat := .node node10435 node9121 +def node10891 : Tree Nat := .node node10890 node9555 +def node10892 : Tree Nat := .node node10891 node8673 +def node10893 : Tree Nat := .node node10892 node10479 +def node10894 : Tree Nat := .node node10706 node10893 +def node10895 : Tree Nat := .node node10435 node9568 +def node10896 : Tree Nat := .node node10895 node7356 +def node10897 : Tree Nat := .node node10896 node10042 +def node10898 : Tree Nat := .node node10897 node9584 +def node10899 : Tree Nat := .node node10711 node10898 +def node10900 : Tree Nat := .node node10894 node10899 +def node10901 : Tree Nat := .node node10889 node10900 +def node10902 : Tree Nat := .node node10812 node8690 +def node10903 : Tree Nat := .node node10902 node10048 +def node10904 : Tree Nat := .node node10492 node10903 +def node10905 : Tree Nat := .node node10435 node322 +def node10906 : Tree Nat := .node node10905 node10052 +def node10907 : Tree Nat := .node node10906 node9146 +def node10908 : Tree Nat := .node node10907 node10717 +def node10909 : Tree Nat := .node node10904 node10908 +def node10910 : Tree Nat := .node node10435 node5831 +def node10911 : Tree Nat := .node node10910 node8719 +def node10912 : Tree Nat := .node node10911 node10068 +def node10913 : Tree Nat := .node node10912 node10501 +def node10914 : Tree Nat := .node node10723 node10913 +def node10915 : Tree Nat := .node node10909 node10914 +def node10916 : Tree Nat := .node node10726 node9178 +def node10917 : Tree Nat := .node node10916 node9620 +def node10918 : Tree Nat := .node node10917 node10507 +def node10919 : Tree Nat := .node node10729 node10918 +def node10920 : Tree Nat := .node node10890 node10091 +def node10921 : Tree Nat := .node node10920 node10095 +def node10922 : Tree Nat := .node node10921 node10100 +def node10923 : Tree Nat := .node node10734 node10922 +def node10924 : Tree Nat := .node node10919 node10923 +def node10925 : Tree Nat := .node node10915 node10924 +def node10926 : Tree Nat := .node node10901 node10925 +def node10927 : Tree Nat := .node node10812 node8763 +def node10928 : Tree Nat := .node node10927 node8767 +def node10929 : Tree Nat := .node node10514 node10928 +def node10930 : Tree Nat := .node node10905 node10106 +def node10931 : Tree Nat := .node node10930 node9209 +def node10932 : Tree Nat := .node node10931 node10740 +def node10933 : Tree Nat := .node node10929 node10932 +def node10934 : Tree Nat := .node node10910 node10121 +def node10935 : Tree Nat := .node node10934 node9658 +def node10936 : Tree Nat := .node node10935 node10518 +def node10937 : Tree Nat := .node node10745 node10936 +def node10938 : Tree Nat := .node node10933 node10937 +def node10939 : Tree Nat := .node node10435 node10135 +def node10940 : Tree Nat := .node node10939 node10522 +def node10941 : Tree Nat := .node node10940 node9241 +def node10942 : Tree Nat := .node node10941 node10527 +def node10943 : Tree Nat := .node node10751 node10942 +def node10944 : Tree Nat := .node node10435 node9687 +def node10945 : Tree Nat := .node node10944 node8817 +def node10946 : Tree Nat := .node node10945 node10155 +def node10947 : Tree Nat := .node node10946 node10159 +def node10948 : Tree Nat := .node node10756 node10947 +def node10949 : Tree Nat := .node node10943 node10948 +def node10950 : Tree Nat := .node node10938 node10949 +def node10951 : Tree Nat := .node node10435 node10032 +def node10952 : Tree Nat := .node node10951 node9270 +def node10953 : Tree Nat := .node node10952 node9707 +def node10954 : Tree Nat := .node node10953 node10766 +def node10955 : Tree Nat := .node node10763 node10954 +def node10956 : Tree Nat := .node node10435 node9622 +def node10957 : Tree Nat := .node node10956 node9726 +def node10958 : Tree Nat := .node node10957 node10188 +def node10959 : Tree Nat := .node node10958 node10543 +def node10960 : Tree Nat := .node node10772 node10959 +def node10961 : Tree Nat := .node node10955 node10960 +def node10962 : Tree Nat := .node node10435 node10202 +def node10963 : Tree Nat := .node node10962 node10204 +def node10964 : Tree Nat := .node node10963 node9746 +def node10965 : Tree Nat := .node node10964 node10549 +def node10966 : Tree Nat := .node node10778 node10965 +def node10967 : Tree Nat := .node node10435 node9656 +def node10968 : Tree Nat := .node node10967 node10221 +def node10969 : Tree Nat := .node node10968 node10224 +def node10970 : Tree Nat := .node node10969 node9323 +def node10971 : Tree Nat := .node node10783 node10970 +def node10972 : Tree Nat := .node node10966 node10971 +def node10973 : Tree Nat := .node node10961 node10972 +def node10974 : Tree Nat := .node node10950 node10973 +def node10975 : Tree Nat := .node node10926 node10974 +def node10976 : Tree Nat := .node node10435 node7768 +def node10977 : Tree Nat := .node node10976 node10237 +def node10978 : Tree Nat := .node node10977 node8894 +def node10979 : Tree Nat := .node node10563 node10978 +def node10980 : Tree Nat := .node node10435 node7137 +def node10981 : Tree Nat := .node node10980 node10242 +def node10982 : Tree Nat := .node node10981 node9338 +def node10983 : Tree Nat := .node node10982 node10791 +def node10984 : Tree Nat := .node node10979 node10983 +def node10985 : Tree Nat := .node node10435 node7315 +def node10986 : Tree Nat := .node node10985 node9777 +def node10987 : Tree Nat := .node node10986 node10251 +def node10988 : Tree Nat := .node node10987 node10568 +def node10989 : Tree Nat := .node node10797 node10988 +def node10990 : Tree Nat := .node node10984 node10989 +def node10991 : Tree Nat := .node node10435 node9352 +def node10992 : Tree Nat := .node node10991 node8420 +def node10993 : Tree Nat := .node node10992 node9357 +def node10994 : Tree Nat := .node node10993 node10579 +def node10995 : Tree Nat := .node node10803 node10994 +def node10996 : Tree Nat := .node node10435 node9633 +def node10997 : Tree Nat := .node node10996 node8935 +def node10998 : Tree Nat := .node node10997 node9807 +def node10999 : Tree Nat := .node node10998 node9813 +def node11000 : Tree Nat := .node node10808 node10999 +def node11001 : Tree Nat := .node node10995 node11000 +def node11002 : Tree Nat := .node node10990 node11001 +def node11003 : Tree Nat := .node node10905 node10276 +def node11004 : Tree Nat := .node node11003 node9824 +def node11005 : Tree Nat := .node node11004 node10817 +def node11006 : Tree Nat := .node node10815 node11005 +def node11007 : Tree Nat := .node node10910 node9838 +def node11008 : Tree Nat := .node node11007 node10292 +def node11009 : Tree Nat := .node node11008 node10590 +def node11010 : Tree Nat := .node node10822 node11009 +def node11011 : Tree Nat := .node node11006 node11010 +def node11012 : Tree Nat := .node node10825 node7623 +def node11013 : Tree Nat := .node node11012 node10302 +def node11014 : Tree Nat := .node node11013 node10596 +def node11015 : Tree Nat := .node node10828 node11014 +def node11016 : Tree Nat := .node node10991 node10317 +def node11017 : Tree Nat := .node node11016 node9867 +def node11018 : Tree Nat := .node node11017 node10322 +def node11019 : Tree Nat := .node node10833 node11018 +def node11020 : Tree Nat := .node node11015 node11019 +def node11021 : Tree Nat := .node node11011 node11020 +def node11022 : Tree Nat := .node node11002 node11021 +def node11023 : Tree Nat := .node node10435 node7997 +def node11024 : Tree Nat := .node node11023 node8984 +def node11025 : Tree Nat := .node node11024 node10332 +def node11026 : Tree Nat := .node node10604 node11025 +def node11027 : Tree Nat := .node node10435 node7242 +def node11028 : Tree Nat := .node node11027 node9878 +def node11029 : Tree Nat := .node node11028 node8523 +def node11030 : Tree Nat := .node node11029 node10840 +def node11031 : Tree Nat := .node node11026 node11030 +def node11032 : Tree Nat := .node node10435 node7366 +def node11033 : Tree Nat := .node node11032 node10347 +def node11034 : Tree Nat := .node node11033 node9893 +def node11035 : Tree Nat := .node node11034 node10609 +def node11036 : Tree Nat := .node node10846 node11035 +def node11037 : Tree Nat := .node node11031 node11036 +def node11038 : Tree Nat := .node node10435 node10109 +def node11039 : Tree Nat := .node node11038 node10620 +def node11040 : Tree Nat := .node node11039 node10623 +def node11041 : Tree Nat := .node node11040 node10627 +def node11042 : Tree Nat := .node node10852 node11041 +def node11043 : Tree Nat := .node node10459 node7671 +def node11044 : Tree Nat := .node node11043 node10638 +def node11045 : Tree Nat := .node node11044 node10641 +def node11046 : Tree Nat := .node node10857 node11045 +def node11047 : Tree Nat := .node node11042 node11046 +def node11048 : Tree Nat := .node node11037 node11047 +def node11049 : Tree Nat := .node node10435 node10482 +def node11050 : Tree Nat := .node node11049 node9471 +def node11051 : Tree Nat := .node node11050 node10658 +def node11052 : Tree Nat := .node node11051 node10661 +def node11053 : Tree Nat := .node node10863 node11052 +def node11054 : Tree Nat := .node node10676 node9047 +def node11055 : Tree Nat := .node node11054 node10674 +def node11056 : Tree Nat := .node node11055 node10678 +def node11057 : Tree Nat := .node node10867 node11056 +def node11058 : Tree Nat := .node node11053 node11057 +def node11059 : Tree Nat := .node node10435 node10055 +def node11060 : Tree Nat := .node node11059 node10407 +def node11061 : Tree Nat := .node node11060 node10410 +def node11062 : Tree Nat := .node node11061 node10684 +def node11063 : Tree Nat := .node node10873 node11062 +def node11064 : Tree Nat := .node node10435 node9675 +def node11065 : Tree Nat := .node node11064 node10422 +def node11066 : Tree Nat := .node node11065 node9078 +def node11067 : Tree Nat := .node node11066 node10427 +def node11068 : Tree Nat := .node node10878 node11067 +def node11069 : Tree Nat := .node node11063 node11068 +def node11070 : Tree Nat := .node node11058 node11069 +def node11071 : Tree Nat := .node node11048 node11070 +def node11072 : Tree Nat := .node node11022 node11071 +def node11073 : Tree Nat := .node node10975 node11072 +def node11074 : Tree Nat := .node node10895 node10483 +def node11075 : Tree Nat := .node node11074 node8195 +def node11076 : Tree Nat := .node node11075 node10710 +def node11077 : Tree Nat := .node node11076 node10898 +def node11078 : Tree Nat := .node node10894 node11077 +def node11079 : Tree Nat := .node node10889 node11078 +def node11080 : Tree Nat := .node node10435 node10061 +def node11081 : Tree Nat := .node node11080 node10495 +def node11082 : Tree Nat := .node node11081 node8711 +def node11083 : Tree Nat := .node node11082 node10722 +def node11084 : Tree Nat := .node node11083 node10913 +def node11085 : Tree Nat := .node node10909 node11084 +def node11086 : Tree Nat := .node node10435 node9108 +def node11087 : Tree Nat := .node node11086 node6252 +def node11088 : Tree Nat := .node node11087 node10075 +def node11089 : Tree Nat := .node node11088 node10728 +def node11090 : Tree Nat := .node node11089 node10918 +def node11091 : Tree Nat := .node node10703 node8746 +def node11092 : Tree Nat := .node node11091 node8258 +def node11093 : Tree Nat := .node node11092 node10733 +def node11094 : Tree Nat := .node node11093 node10922 +def node11095 : Tree Nat := .node node11090 node11094 +def node11096 : Tree Nat := .node node11085 node11095 +def node11097 : Tree Nat := .node node11079 node11096 +def node11098 : Tree Nat := .node node10435 node5821 +def node11099 : Tree Nat := .node node11098 node10115 +def node11100 : Tree Nat := .node node11099 node10118 +def node11101 : Tree Nat := .node node11100 node10744 +def node11102 : Tree Nat := .node node11101 node10936 +def node11103 : Tree Nat := .node node10933 node11102 +def node11104 : Tree Nat := .node node10435 node10127 +def node11105 : Tree Nat := .node node11104 node10129 +def node11106 : Tree Nat := .node node11105 node10132 +def node11107 : Tree Nat := .node node11106 node10750 +def node11108 : Tree Nat := .node node11107 node10942 +def node11109 : Tree Nat := .node node10435 node10040 +def node11110 : Tree Nat := .node node11109 node10142 +def node11111 : Tree Nat := .node node11110 node9251 +def node11112 : Tree Nat := .node node11111 node10755 +def node11113 : Tree Nat := .node node11112 node10947 +def node11114 : Tree Nat := .node node11108 node11113 +def node11115 : Tree Nat := .node node11103 node11114 +def node11116 : Tree Nat := .node node10435 node10088 +def node11117 : Tree Nat := .node node11116 node10534 +def node11118 : Tree Nat := .node node11117 node9266 +def node11119 : Tree Nat := .node node11118 node10762 +def node11120 : Tree Nat := .node node11119 node10954 +def node11121 : Tree Nat := .node node10435 node6596 +def node11122 : Tree Nat := .node node11121 node10177 +def node11123 : Tree Nat := .node node11122 node10180 +def node11124 : Tree Nat := .node node11123 node10771 +def node11125 : Tree Nat := .node node11124 node10959 +def node11126 : Tree Nat := .node node11120 node11125 +def node11127 : Tree Nat := .node node11104 node8854 +def node11128 : Tree Nat := .node node11127 node10196 +def node11129 : Tree Nat := .node node11128 node10777 +def node11130 : Tree Nat := .node node11129 node10965 +def node11131 : Tree Nat := .node node10435 node10153 +def node11132 : Tree Nat := .node node11131 node10552 +def node11133 : Tree Nat := .node node11132 node9318 +def node11134 : Tree Nat := .node node11133 node10782 +def node11135 : Tree Nat := .node node11134 node10970 +def node11136 : Tree Nat := .node node11130 node11135 +def node11137 : Tree Nat := .node node11126 node11136 +def node11138 : Tree Nat := .node node11115 node11137 +def node11139 : Tree Nat := .node node11097 node11138 +def node11140 : Tree Nat := .node node10435 node7074 +def node11141 : Tree Nat := .node node11140 node8908 +def node11142 : Tree Nat := .node node11141 node8397 +def node11143 : Tree Nat := .node node11142 node10796 +def node11144 : Tree Nat := .node node11143 node10988 +def node11145 : Tree Nat := .node node10984 node11144 +def node11146 : Tree Nat := .node node10996 node7174 +def node11147 : Tree Nat := .node node11146 node8430 +def node11148 : Tree Nat := .node node11147 node10807 +def node11149 : Tree Nat := .node node11148 node10999 +def node11150 : Tree Nat := .node node10995 node11149 +def node11151 : Tree Nat := .node node11145 node11150 +def node11152 : Tree Nat := .node node10490 node9819 +def node11153 : Tree Nat := .node node11152 node10268 +def node11154 : Tree Nat := .node node11153 node10814 +def node11155 : Tree Nat := .node node11154 node11005 +def node11156 : Tree Nat := .node node11098 node10281 +def node11157 : Tree Nat := .node node11156 node8462 +def node11158 : Tree Nat := .node node11157 node10821 +def node11159 : Tree Nat := .node node11158 node11009 +def node11160 : Tree Nat := .node node11155 node11159 +def node11161 : Tree Nat := .node node10435 node9299 +def node11162 : Tree Nat := .node node11161 node8477 +def node11163 : Tree Nat := .node node11162 node8481 +def node11164 : Tree Nat := .node node11163 node10827 +def node11165 : Tree Nat := .node node11164 node11014 +def node11166 : Tree Nat := .node node10800 node8494 +def node11167 : Tree Nat := .node node11166 node9413 +def node11168 : Tree Nat := .node node11167 node10832 +def node11169 : Tree Nat := .node node11168 node11018 +def node11170 : Tree Nat := .node node11165 node11169 +def node11171 : Tree Nat := .node node11160 node11170 +def node11172 : Tree Nat := .node node11151 node11171 +def node11173 : Tree Nat := .node node10435 node9709 +def node11174 : Tree Nat := .node node11173 node9427 +def node11175 : Tree Nat := .node node11174 node10329 +def node11176 : Tree Nat := .node node11175 node11025 +def node11177 : Tree Nat := .node node11176 node11030 +def node11178 : Tree Nat := .node node10435 node6962 +def node11179 : Tree Nat := .node node11178 node10340 +def node11180 : Tree Nat := .node node11179 node8528 +def node11181 : Tree Nat := .node node11180 node10845 +def node11182 : Tree Nat := .node node11181 node11035 +def node11183 : Tree Nat := .node node11177 node11182 +def node11184 : Tree Nat := .node node10490 node8536 +def node11185 : Tree Nat := .node node11184 node10614 +def node11186 : Tree Nat := .node node11185 node10851 +def node11187 : Tree Nat := .node node11186 node11041 +def node11188 : Tree Nat := .node node10435 node10083 +def node11189 : Tree Nat := .node node11188 node7667 +def node11190 : Tree Nat := .node node11189 node10630 +def node11191 : Tree Nat := .node node11190 node10856 +def node11192 : Tree Nat := .node node11191 node11045 +def node11193 : Tree Nat := .node node11187 node11192 +def node11194 : Tree Nat := .node node11183 node11193 +def node11195 : Tree Nat := .node node10854 node9920 +def node11196 : Tree Nat := .node node11195 node10650 +def node11197 : Tree Nat := .node node11196 node10862 +def node11198 : Tree Nat := .node node11197 node11052 +def node11199 : Tree Nat := .node node10435 node10145 +def node11200 : Tree Nat := .node node11199 node10396 +def node11201 : Tree Nat := .node node11200 node10664 +def node11202 : Tree Nat := .node node11201 node10866 +def node11203 : Tree Nat := .node node11202 node11056 +def node11204 : Tree Nat := .node node11198 node11203 +def node11205 : Tree Nat := .node node10435 node10150 +def node11206 : Tree Nat := .node node11205 node9053 +def node11207 : Tree Nat := .node node11206 node9494 +def node11208 : Tree Nat := .node node11207 node10872 +def node11209 : Tree Nat := .node node11208 node11062 +def node11210 : Tree Nat := .node node10435 node10023 +def node11211 : Tree Nat := .node node11210 node9068 +def node11212 : Tree Nat := .node node11211 node9514 +def node11213 : Tree Nat := .node node11212 node10877 +def node11214 : Tree Nat := .node node11213 node11067 +def node11215 : Tree Nat := .node node11209 node11214 +def node11216 : Tree Nat := .node node11204 node11215 +def node11217 : Tree Nat := .node node11194 node11216 +def node11218 : Tree Nat := .node node11172 node11217 +def node11219 : Tree Nat := .node node11139 node11218 +def node11220 : Tree Nat := .node node5831 node8640 +def node11221 : Tree Nat := .node node11220 node9530 +def node11222 : Tree Nat := .node node10693 node11221 +def node11223 : Tree Nat := .node node10452 node11222 +def node11224 : Tree Nat := .node node10445 node11223 +def node11225 : Tree Nat := .node node5821 node10000 +def node11226 : Tree Nat := .node node11225 node10002 +def node11227 : Tree Nat := .node node10698 node11226 +def node11228 : Tree Nat := .node node10461 node11227 +def node11229 : Tree Nat := .node node451 node10000 +def node11230 : Tree Nat := .node node11229 node9545 +def node11231 : Tree Nat := .node node10885 node11230 +def node11232 : Tree Nat := .leaf 919 +def node11233 : Tree Nat := .node node11232 node6201 +def node11234 : Tree Nat := .node node11233 node9102 +def node11235 : Tree Nat := .node node10467 node11234 +def node11236 : Tree Nat := .node node11231 node11235 +def node11237 : Tree Nat := .node node11228 node11236 +def node11238 : Tree Nat := .node node11224 node11237 +def node11239 : Tree Nat := .node node411 node7745 +def node11240 : Tree Nat := .node node11239 node10024 +def node11241 : Tree Nat := .node node10704 node11240 +def node11242 : Tree Nat := .node node10475 node11241 +def node11243 : Tree Nat := .node node11242 node10893 +def node11244 : Tree Nat := .node node322 node7768 +def node11245 : Tree Nat := .node node11244 node10033 +def node11246 : Tree Nat := .node node10709 node11245 +def node11247 : Tree Nat := .node node11075 node11246 +def node11248 : Tree Nat := .node node11247 node10898 +def node11249 : Tree Nat := .node node11243 node11248 +def node11250 : Tree Nat := .node node11238 node11249 +def node11251 : Tree Nat := .node node6668 node8668 +def node11252 : Tree Nat := .node node11251 node6983 +def node11253 : Tree Nat := .node node10716 node11252 +def node11254 : Tree Nat := .node node10907 node11253 +def node11255 : Tree Nat := .node node10904 node11254 +def node11256 : Tree Nat := .node node6596 node195 +def node11257 : Tree Nat := .node node11256 node9151 +def node11258 : Tree Nat := .node node10721 node11257 +def node11259 : Tree Nat := .node node11082 node11258 +def node11260 : Tree Nat := .node node7051 node6169 +def node11261 : Tree Nat := .node node11260 node10067 +def node11262 : Tree Nat := .node node10911 node11261 +def node11263 : Tree Nat := .node node11262 node10501 +def node11264 : Tree Nat := .node node11259 node11263 +def node11265 : Tree Nat := .node node11255 node11264 +def node11266 : Tree Nat := .node node6546 node7756 +def node11267 : Tree Nat := .node node11266 node8730 +def node11268 : Tree Nat := .node node10727 node11267 +def node11269 : Tree Nat := .node node11088 node11268 +def node11270 : Tree Nat := .node node11269 node10918 +def node11271 : Tree Nat := .node node6549 node7824 +def node11272 : Tree Nat := .node node11271 node8750 +def node11273 : Tree Nat := .node node10732 node11272 +def node11274 : Tree Nat := .node node11092 node11273 +def node11275 : Tree Nat := .node node11274 node10922 +def node11276 : Tree Nat := .node node11270 node11275 +def node11277 : Tree Nat := .node node11265 node11276 +def node11278 : Tree Nat := .node node11250 node11277 +def node11279 : Tree Nat := .node node5831 node8282 +def node11280 : Tree Nat := .node node11279 node8775 +def node11281 : Tree Nat := .node node10739 node11280 +def node11282 : Tree Nat := .node node10931 node11281 +def node11283 : Tree Nat := .node node10929 node11282 +def node11284 : Tree Nat := .node node5821 node195 +def node11285 : Tree Nat := .node node11284 node8787 +def node11286 : Tree Nat := .node node10743 node11285 +def node11287 : Tree Nat := .node node11100 node11286 +def node11288 : Tree Nat := .node node451 node6169 +def node11289 : Tree Nat := .node node11288 node9657 +def node11290 : Tree Nat := .node node10934 node11289 +def node11291 : Tree Nat := .leaf 935 +def node11292 : Tree Nat := .node node11291 node9219 +def node11293 : Tree Nat := .node node11292 node9221 +def node11294 : Tree Nat := .node node10517 node11293 +def node11295 : Tree Nat := .node node11290 node11294 +def node11296 : Tree Nat := .node node11287 node11295 +def node11297 : Tree Nat := .node node11283 node11296 +def node11298 : Tree Nat := .node node411 node340 +def node11299 : Tree Nat := .node node11298 node8799 +def node11300 : Tree Nat := .node node10749 node11299 +def node11301 : Tree Nat := .node node11106 node11300 +def node11302 : Tree Nat := .node node11301 node10942 +def node11303 : Tree Nat := .node node322 node8164 +def node11304 : Tree Nat := .node node11303 node9254 +def node11305 : Tree Nat := .node node10754 node11304 +def node11306 : Tree Nat := .node node11111 node11305 +def node11307 : Tree Nat := .node node5821 node9159 +def node11308 : Tree Nat := .node node11307 node9691 +def node11309 : Tree Nat := .node node11308 node10158 +def node11310 : Tree Nat := .node node10946 node11309 +def node11311 : Tree Nat := .node node11306 node11310 +def node11312 : Tree Nat := .node node11302 node11311 +def node11313 : Tree Nat := .node node11297 node11312 +def node11314 : Tree Nat := .node node6668 node9098 +def node11315 : Tree Nat := .node node11314 node9713 +def node11316 : Tree Nat := .node node10765 node11315 +def node11317 : Tree Nat := .node node10953 node11316 +def node11318 : Tree Nat := .node node11119 node11317 +def node11319 : Tree Nat := .node node6596 node8193 +def node11320 : Tree Nat := .node node11319 node10183 +def node11321 : Tree Nat := .node node10770 node11320 +def node11322 : Tree Nat := .node node11123 node11321 +def node11323 : Tree Nat := .node node7051 node8743 +def node11324 : Tree Nat := .node node11323 node10187 +def node11325 : Tree Nat := .node node10957 node11324 +def node11326 : Tree Nat := .node node11325 node10543 +def node11327 : Tree Nat := .node node11322 node11326 +def node11328 : Tree Nat := .node node11318 node11327 +def node11329 : Tree Nat := .node node6546 node8713 +def node11330 : Tree Nat := .node node11329 node10198 +def node11331 : Tree Nat := .node node10776 node11330 +def node11332 : Tree Nat := .node node11128 node11331 +def node11333 : Tree Nat := .node node11332 node10965 +def node11334 : Tree Nat := .node node6549 node8367 +def node11335 : Tree Nat := .node node11334 node10215 +def node11336 : Tree Nat := .node node10781 node11335 +def node11337 : Tree Nat := .node node11133 node11336 +def node11338 : Tree Nat := .node node411 node9253 +def node11339 : Tree Nat := .node node11338 node8373 +def node11340 : Tree Nat := .node node11339 node6747 +def node11341 : Tree Nat := .node node10969 node11340 +def node11342 : Tree Nat := .node node11337 node11341 +def node11343 : Tree Nat := .node node11333 node11342 +def node11344 : Tree Nat := .node node11328 node11343 +def node11345 : Tree Nat := .node node11313 node11344 +def node11346 : Tree Nat := .node node11278 node11345 +def node11347 : Tree Nat := .node node5831 node8677 +def node11348 : Tree Nat := .node node11347 node7141 +def node11349 : Tree Nat := .node node10790 node11348 +def node11350 : Tree Nat := .node node10982 node11349 +def node11351 : Tree Nat := .node node10979 node11350 +def node11352 : Tree Nat := .node node5821 node7137 +def node11353 : Tree Nat := .node node11352 node8399 +def node11354 : Tree Nat := .node node10795 node11353 +def node11355 : Tree Nat := .node node11142 node11354 +def node11356 : Tree Nat := .node node451 node7051 +def node11357 : Tree Nat := .node node11356 node10250 +def node11358 : Tree Nat := .node node10986 node11357 +def node11359 : Tree Nat := .leaf 927 +def node11360 : Tree Nat := .node node11359 node8326 +def node11361 : Tree Nat := .node node11360 node7157 +def node11362 : Tree Nat := .node node10567 node11361 +def node11363 : Tree Nat := .node node11358 node11362 +def node11364 : Tree Nat := .node node11355 node11363 +def node11365 : Tree Nat := .node node11351 node11364 +def node11366 : Tree Nat := .node node411 node7976 +def node11367 : Tree Nat := .node node11366 node8923 +def node11368 : Tree Nat := .node node10801 node11367 +def node11369 : Tree Nat := .node node10575 node11368 +def node11370 : Tree Nat := .node node11369 node10994 +def node11371 : Tree Nat := .node node322 node7997 +def node11372 : Tree Nat := .node node11371 node9365 +def node11373 : Tree Nat := .node node10806 node11372 +def node11374 : Tree Nat := .node node11147 node11373 +def node11375 : Tree Nat := .node node11374 node10999 +def node11376 : Tree Nat := .node node11370 node11375 +def node11377 : Tree Nat := .node node11365 node11376 +def node11378 : Tree Nat := .node node6668 node8865 +def node11379 : Tree Nat := .node node11378 node9828 +def node11380 : Tree Nat := .node node10816 node11379 +def node11381 : Tree Nat := .node node11004 node11380 +def node11382 : Tree Nat := .node node11154 node11381 +def node11383 : Tree Nat := .node node11256 node10286 +def node11384 : Tree Nat := .node node10820 node11383 +def node11385 : Tree Nat := .node node11157 node11384 +def node11386 : Tree Nat := .node node11260 node10291 +def node11387 : Tree Nat := .node node11007 node11386 +def node11388 : Tree Nat := .node node11387 node10590 +def node11389 : Tree Nat := .node node11385 node11388 +def node11390 : Tree Nat := .node node11382 node11389 +def node11391 : Tree Nat := .node node6546 node7986 +def node11392 : Tree Nat := .node node11391 node10297 +def node11393 : Tree Nat := .node node10826 node11392 +def node11394 : Tree Nat := .node node11163 node11393 +def node11395 : Tree Nat := .node node11394 node11014 +def node11396 : Tree Nat := .node node6549 node8054 +def node11397 : Tree Nat := .node node11396 node10311 +def node11398 : Tree Nat := .node node10831 node11397 +def node11399 : Tree Nat := .node node11167 node11398 +def node11400 : Tree Nat := .node node451 node7593 +def node11401 : Tree Nat := .node node11400 node8506 +def node11402 : Tree Nat := .node node11401 node10321 +def node11403 : Tree Nat := .node node11017 node11402 +def node11404 : Tree Nat := .node node11399 node11403 +def node11405 : Tree Nat := .node node11395 node11404 +def node11406 : Tree Nat := .node node11390 node11405 +def node11407 : Tree Nat := .node node11377 node11406 +def node11408 : Tree Nat := .node node5831 node8873 +def node11409 : Tree Nat := .node node11408 node9881 +def node11410 : Tree Nat := .node node10839 node11409 +def node11411 : Tree Nat := .node node11029 node11410 +def node11412 : Tree Nat := .node node11176 node11411 +def node11413 : Tree Nat := .node node5821 node7242 +def node11414 : Tree Nat := .node node11413 node10343 +def node11415 : Tree Nat := .node node10844 node11414 +def node11416 : Tree Nat := .node node11180 node11415 +def node11417 : Tree Nat := .node node451 node7059 +def node11418 : Tree Nat := .node node11417 node9892 +def node11419 : Tree Nat := .node node11033 node11418 +def node11420 : Tree Nat := .node node6546 node9180 +def node11421 : Tree Nat := .node node11420 node6994 +def node11422 : Tree Nat := .node node10608 node11421 +def node11423 : Tree Nat := .node node11419 node11422 +def node11424 : Tree Nat := .node node11416 node11423 +def node11425 : Tree Nat := .node node11412 node11424 +def node11426 : Tree Nat := .leaf 887 +def node11427 : Tree Nat := .node node10435 node11426 +def node11428 : Tree Nat := .node node11427 node8536 +def node11429 : Tree Nat := .node node11428 node10614 +def node11430 : Tree Nat := .node node411 node10482 +def node11431 : Tree Nat := .node node11430 node10356 +def node11432 : Tree Nat := .node node10850 node11431 +def node11433 : Tree Nat := .node node11429 node11432 +def node11434 : Tree Nat := .node node11433 node11041 +def node11435 : Tree Nat := .node node322 node8274 +def node11436 : Tree Nat := .node node11435 node10370 +def node11437 : Tree Nat := .node node10855 node11436 +def node11438 : Tree Nat := .node node11190 node11437 +def node11439 : Tree Nat := .node node5821 node10533 +def node11440 : Tree Nat := .node node11439 node8559 +def node11441 : Tree Nat := .node node11440 node10378 +def node11442 : Tree Nat := .node node11044 node11441 +def node11443 : Tree Nat := .node node11438 node11442 +def node11444 : Tree Nat := .node node11434 node11443 +def node11445 : Tree Nat := .node node11425 node11444 +def node11446 : Tree Nat := .node node11291 node9287 +def node11447 : Tree Nat := .node node11446 node6478 +def node11448 : Tree Nat := .node node10660 node11447 +def node11449 : Tree Nat := .node node11051 node11448 +def node11450 : Tree Nat := .node node11197 node11449 +def node11451 : Tree Nat := .node node11232 node10446 +def node11452 : Tree Nat := .node node11451 node9481 +def node11453 : Tree Nat := .node node10865 node11452 +def node11454 : Tree Nat := .node node11201 node11453 +def node11455 : Tree Nat := .node node11426 node10533 +def node11456 : Tree Nat := .node node11455 node9933 +def node11457 : Tree Nat := .node node11054 node11456 +def node11458 : Tree Nat := .node node11457 node10678 +def node11459 : Tree Nat := .node node11454 node11458 +def node11460 : Tree Nat := .node node11450 node11459 +def node11461 : Tree Nat := .node node11359 node8216 +def node11462 : Tree Nat := .node node11461 node7704 +def node11463 : Tree Nat := .node node10876 node11462 +def node11464 : Tree Nat := .node node11212 node11463 +def node11465 : Tree Nat := .node node451 node9216 +def node11466 : Tree Nat := .node node11465 node9960 +def node11467 : Tree Nat := .node node11466 node10426 +def node11468 : Tree Nat := .node node11066 node11467 +def node11469 : Tree Nat := .node node11464 node11468 +def node11470 : Tree Nat := .node node11209 node11469 +def node11471 : Tree Nat := .node node11460 node11470 +def node11472 : Tree Nat := .node node11445 node11471 +def node11473 : Tree Nat := .node node11407 node11472 +def node11474 : Tree Nat := .node node11346 node11473 +def node11475 : Tree Nat := .leaf 855 +def node11476 : Tree Nat := .node node11475 node9087 +def node11477 : Tree Nat := .node node10437 node11476 +def node11478 : Tree Nat := .node node224 node10436 +def node11479 : Tree Nat := .node node11478 node7715 +def node11480 : Tree Nat := .node node11477 node11479 +def node11481 : Tree Nat := .node node5802 node9979 +def node11482 : Tree Nat := .node node11481 node9982 +def node11483 : Tree Nat := .node node10443 node11482 +def node11484 : Tree Nat := .node node11480 node11483 +def node11485 : Tree Nat := .node node6186 node10449 +def node11486 : Tree Nat := .node node11485 node8170 +def node11487 : Tree Nat := .node node10448 node11486 +def node11488 : Tree Nat := .node node11487 node11222 +def node11489 : Tree Nat := .node node11484 node11488 +def node11490 : Tree Nat := .node node6169 node9996 +def node11491 : Tree Nat := .node node11490 node8654 +def node11492 : Tree Nat := .node node10460 node11491 +def node11493 : Tree Nat := .node node11492 node11227 +def node11494 : Tree Nat := .node node11493 node11236 +def node11495 : Tree Nat := .node node11489 node11494 +def node11496 : Tree Nat := .node node6176 node7333 +def node11497 : Tree Nat := .node node11496 node10020 +def node11498 : Tree Nat := .node node10474 node11497 +def node11499 : Tree Nat := .node node11498 node11241 +def node11500 : Tree Nat := .node node5826 node7752 +def node11501 : Tree Nat := .node node11500 node8672 +def node11502 : Tree Nat := .node node10891 node11501 +def node11503 : Tree Nat := .node node5835 node9540 +def node11504 : Tree Nat := .node node11503 node9563 +def node11505 : Tree Nat := .node node10478 node11504 +def node11506 : Tree Nat := .node node11502 node11505 +def node11507 : Tree Nat := .node node11499 node11506 +def node11508 : Tree Nat := .node node340 node7762 +def node11509 : Tree Nat := .node node11508 node8194 +def node11510 : Tree Nat := .node node11074 node11509 +def node11511 : Tree Nat := .node node6962 node7768 +def node11512 : Tree Nat := .node node11511 node10033 +def node11513 : Tree Nat := .node node10709 node11512 +def node11514 : Tree Nat := .node node11510 node11513 +def node11515 : Tree Nat := .node node195 node7773 +def node11516 : Tree Nat := .node node11515 node10041 +def node11517 : Tree Nat := .node node10896 node11516 +def node11518 : Tree Nat := .node node6176 node7320 +def node11519 : Tree Nat := .node node11518 node9136 +def node11520 : Tree Nat := .leaf 943 +def node11521 : Tree Nat := .node node11520 node9529 +def node11522 : Tree Nat := .node node11521 node6562 +def node11523 : Tree Nat := .node node11519 node11522 +def node11524 : Tree Nat := .node node11517 node11523 +def node11525 : Tree Nat := .node node11514 node11524 +def node11526 : Tree Nat := .node node11507 node11525 +def node11527 : Tree Nat := .node node11495 node11526 +def node11528 : Tree Nat := .node node6192 node5802 +def node11529 : Tree Nat := .node node11528 node8213 +def node11530 : Tree Nat := .node node10491 node11529 +def node11531 : Tree Nat := .node node6242 node10000 +def node11532 : Tree Nat := .node node11531 node8693 +def node11533 : Tree Nat := .node node10902 node11532 +def node11534 : Tree Nat := .node node11530 node11533 +def node11535 : Tree Nat := .node node6229 node6176 +def node11536 : Tree Nat := .node node11535 node9145 +def node11537 : Tree Nat := .node node10906 node11536 +def node11538 : Tree Nat := .node node11537 node11253 +def node11539 : Tree Nat := .node node11534 node11538 +def node11540 : Tree Nat := .node node6348 node6186 +def node11541 : Tree Nat := .node node11540 node8710 +def node11542 : Tree Nat := .node node11081 node11541 +def node11543 : Tree Nat := .node node11542 node11258 +def node11544 : Tree Nat := .leaf 879 +def node11545 : Tree Nat := .node node11544 node9101 +def node11546 : Tree Nat := .node node11545 node9160 +def node11547 : Tree Nat := .node node10500 node11546 +def node11548 : Tree Nat := .node node11262 node11547 +def node11549 : Tree Nat := .node node11543 node11548 +def node11550 : Tree Nat := .node node11539 node11549 +def node11551 : Tree Nat := .node node6188 node7391 +def node11552 : Tree Nat := .node node11551 node10074 +def node11553 : Tree Nat := .node node11087 node11552 +def node11554 : Tree Nat := .node node11553 node11268 +def node11555 : Tree Nat := .node node6554 node7718 +def node11556 : Tree Nat := .node node11555 node9619 +def node11557 : Tree Nat := .node node10916 node11556 +def node11558 : Tree Nat := .node node6320 node10029 +def node11559 : Tree Nat := .node node11558 node8738 +def node11560 : Tree Nat := .node node10506 node11559 +def node11561 : Tree Nat := .node node11557 node11560 +def node11562 : Tree Nat := .node node11554 node11561 +def node11563 : Tree Nat := .node node6180 node7732 +def node11564 : Tree Nat := .node node11563 node8257 +def node11565 : Tree Nat := .node node11091 node11564 +def node11566 : Tree Nat := .node node10245 node8750 +def node11567 : Tree Nat := .node node10732 node11566 +def node11568 : Tree Nat := .node node11565 node11567 +def node11569 : Tree Nat := .node node6694 node7821 +def node11570 : Tree Nat := .node node11569 node10094 +def node11571 : Tree Nat := .node node10920 node11570 +def node11572 : Tree Nat := .node node224 node7420 +def node11573 : Tree Nat := .node node11572 node9634 +def node11574 : Tree Nat := .node node11573 node10099 +def node11575 : Tree Nat := .node node11571 node11574 +def node11576 : Tree Nat := .node node11568 node11575 +def node11577 : Tree Nat := .node node11562 node11576 +def node11578 : Tree Nat := .node node11550 node11577 +def node11579 : Tree Nat := .node node11527 node11578 +def node11580 : Tree Nat := .node node224 node5802 +def node11581 : Tree Nat := .node node11580 node8271 +def node11582 : Tree Nat := .node node10513 node11581 +def node11583 : Tree Nat := .node node5802 node340 +def node11584 : Tree Nat := .node node11583 node8766 +def node11585 : Tree Nat := .node node10927 node11584 +def node11586 : Tree Nat := .node node11582 node11585 +def node11587 : Tree Nat := .node node6186 node6176 +def node11588 : Tree Nat := .node node11587 node9208 +def node11589 : Tree Nat := .node node10930 node11588 +def node11590 : Tree Nat := .node node11589 node11281 +def node11591 : Tree Nat := .node node11586 node11590 +def node11592 : Tree Nat := .node node6169 node6186 +def node11593 : Tree Nat := .node node11592 node10117 +def node11594 : Tree Nat := .node node11099 node11593 +def node11595 : Tree Nat := .node node7137 node195 +def node11596 : Tree Nat := .node node11595 node8787 +def node11597 : Tree Nat := .node node10743 node11596 +def node11598 : Tree Nat := .node node11594 node11597 +def node11599 : Tree Nat := .node node11598 node11295 +def node11600 : Tree Nat := .node node11591 node11599 +def node11601 : Tree Nat := .node node6176 node9150 +def node11602 : Tree Nat := .node node11601 node10131 +def node11603 : Tree Nat := .node node11105 node11602 +def node11604 : Tree Nat := .node node11603 node11300 +def node11605 : Tree Nat := .node node5826 node8718 +def node11606 : Tree Nat := .node node11605 node9240 +def node11607 : Tree Nat := .node node10940 node11606 +def node11608 : Tree Nat := .node node5835 node9558 +def node11609 : Tree Nat := .node node11608 node7039 +def node11610 : Tree Nat := .node node10526 node11609 +def node11611 : Tree Nat := .node node11607 node11610 +def node11612 : Tree Nat := .node node11604 node11611 +def node11613 : Tree Nat := .node node340 node9249 +def node11614 : Tree Nat := .node node11613 node8309 +def node11615 : Tree Nat := .node node11110 node11614 +def node11616 : Tree Nat := .node node7074 node8164 +def node11617 : Tree Nat := .node node11616 node9254 +def node11618 : Tree Nat := .node node10754 node11617 +def node11619 : Tree Nat := .node node11615 node11618 +def node11620 : Tree Nat := .node node195 node8689 +def node11621 : Tree Nat := .node node11620 node10154 +def node11622 : Tree Nat := .node node10945 node11621 +def node11623 : Tree Nat := .leaf 871 +def node11624 : Tree Nat := .node node11623 node10037 +def node11625 : Tree Nat := .node node11624 node6648 +def node11626 : Tree Nat := .node node11308 node11625 +def node11627 : Tree Nat := .node node11622 node11626 +def node11628 : Tree Nat := .node node11619 node11627 +def node11629 : Tree Nat := .node node11612 node11628 +def node11630 : Tree Nat := .node node11600 node11629 +def node11631 : Tree Nat := .node node6192 node9170 +def node11632 : Tree Nat := .node node11631 node8323 +def node11633 : Tree Nat := .node node11117 node11632 +def node11634 : Tree Nat := .node node6242 node8765 +def node11635 : Tree Nat := .node node11634 node10168 +def node11636 : Tree Nat := .node node10761 node11635 +def node11637 : Tree Nat := .node node11633 node11636 +def node11638 : Tree Nat := .node node6229 node8706 +def node11639 : Tree Nat := .node node11638 node9706 +def node11640 : Tree Nat := .node node10952 node11639 +def node11641 : Tree Nat := .node node11640 node11316 +def node11642 : Tree Nat := .node node11637 node11641 +def node11643 : Tree Nat := .node node6348 node9175 +def node11644 : Tree Nat := .node node11643 node10179 +def node11645 : Tree Nat := .node node11122 node11644 +def node11646 : Tree Nat := .node node10029 node8193 +def node11647 : Tree Nat := .node node11646 node10183 +def node11648 : Tree Nat := .node node10770 node11647 +def node11649 : Tree Nat := .node node11645 node11648 +def node11650 : Tree Nat := .node node11649 node11326 +def node11651 : Tree Nat := .node node11642 node11650 +def node11652 : Tree Nat := .node node6188 node9143 +def node11653 : Tree Nat := .node node11652 node10195 +def node11654 : Tree Nat := .node node11127 node11653 +def node11655 : Tree Nat := .node node11654 node11331 +def node11656 : Tree Nat := .node node6554 node8829 +def node11657 : Tree Nat := .node node11656 node9745 +def node11658 : Tree Nat := .node node10963 node11657 +def node11659 : Tree Nat := .node node6320 node6348 +def node11660 : Tree Nat := .node node11659 node9751 +def node11661 : Tree Nat := .node node10548 node11660 +def node11662 : Tree Nat := .node node11658 node11661 +def node11663 : Tree Nat := .node node11655 node11662 +def node11664 : Tree Nat := .node node6180 node9093 +def node11665 : Tree Nat := .node node11664 node8364 +def node11666 : Tree Nat := .node node11132 node11665 +def node11667 : Tree Nat := .node node9990 node8367 +def node11668 : Tree Nat := .node node11667 node10215 +def node11669 : Tree Nat := .node node10781 node11668 +def node11670 : Tree Nat := .node node11666 node11669 +def node11671 : Tree Nat := .node node6694 node8729 +def node11672 : Tree Nat := .node node11671 node10223 +def node11673 : Tree Nat := .node node10968 node11672 +def node11674 : Tree Nat := .node node11673 node11340 +def node11675 : Tree Nat := .node node11670 node11674 +def node11676 : Tree Nat := .node node11663 node11675 +def node11677 : Tree Nat := .node node11651 node11676 +def node11678 : Tree Nat := .node node11630 node11677 +def node11679 : Tree Nat := .node node11579 node11678 +def node11680 : Tree Nat := .leaf 863 +def node11681 : Tree Nat := .node node11680 node9330 +def node11682 : Tree Nat := .node node10561 node11681 +def node11683 : Tree Nat := .node node224 node7829 +def node11684 : Tree Nat := .node node11683 node10234 +def node11685 : Tree Nat := .node node11682 node11684 +def node11686 : Tree Nat := .node node5802 node6946 +def node11687 : Tree Nat := .node node11686 node8893 +def node11688 : Tree Nat := .node node10977 node11687 +def node11689 : Tree Nat := .node node11685 node11688 +def node11690 : Tree Nat := .node node10435 node10029 +def node11691 : Tree Nat := .node node11690 node10242 +def node11692 : Tree Nat := .node node6186 node7787 +def node11693 : Tree Nat := .node node11692 node9337 +def node11694 : Tree Nat := .node node11691 node11693 +def node11695 : Tree Nat := .node node11694 node11349 +def node11696 : Tree Nat := .node node11689 node11695 +def node11697 : Tree Nat := .node node10561 node8908 +def node11698 : Tree Nat := .node node6169 node7444 +def node11699 : Tree Nat := .node node11698 node8396 +def node11700 : Tree Nat := .node node11697 node11699 +def node11701 : Tree Nat := .node node7137 node7137 +def node11702 : Tree Nat := .node node11701 node8399 +def node11703 : Tree Nat := .node node10795 node11702 +def node11704 : Tree Nat := .node node11700 node11703 +def node11705 : Tree Nat := .node node6946 node7051 +def node11706 : Tree Nat := .node node11705 node10250 +def node11707 : Tree Nat := .node node10986 node11706 +def node11708 : Tree Nat := .node node11707 node11362 +def node11709 : Tree Nat := .node node11704 node11708 +def node11710 : Tree Nat := .node node11696 node11709 +def node11711 : Tree Nat := .node node6176 node7562 +def node11712 : Tree Nat := .node node11711 node8412 +def node11713 : Tree Nat := .node node10574 node11712 +def node11714 : Tree Nat := .node node11713 node11368 +def node11715 : Tree Nat := .node node5826 node7797 +def node11716 : Tree Nat := .node node11715 node9356 +def node11717 : Tree Nat := .node node10992 node11716 +def node11718 : Tree Nat := .node node5835 node9723 +def node11719 : Tree Nat := .node node11718 node6259 +def node11720 : Tree Nat := .node node10578 node11719 +def node11721 : Tree Nat := .node node11717 node11720 +def node11722 : Tree Nat := .node node11714 node11721 +def node11723 : Tree Nat := .node node340 node7877 +def node11724 : Tree Nat := .node node11723 node8429 +def node11725 : Tree Nat := .node node11146 node11724 +def node11726 : Tree Nat := .node node7074 node7997 +def node11727 : Tree Nat := .node node11726 node9365 +def node11728 : Tree Nat := .node node10806 node11727 +def node11729 : Tree Nat := .node node11725 node11728 +def node11730 : Tree Nat := .node node195 node8002 +def node11731 : Tree Nat := .node node11730 node9806 +def node11732 : Tree Nat := .node node10997 node11731 +def node11733 : Tree Nat := .node node224 node7476 +def node11734 : Tree Nat := .node node11733 node9809 +def node11735 : Tree Nat := .leaf 903 +def node11736 : Tree Nat := .node node11735 node9712 +def node11737 : Tree Nat := .node node11736 node9371 +def node11738 : Tree Nat := .node node11734 node11737 +def node11739 : Tree Nat := .node node11732 node11738 +def node11740 : Tree Nat := .node node11729 node11739 +def node11741 : Tree Nat := .node node11722 node11740 +def node11742 : Tree Nat := .node node11710 node11741 +def node11743 : Tree Nat := .node node11528 node10267 +def node11744 : Tree Nat := .node node11152 node11743 +def node11745 : Tree Nat := .node node6242 node8784 +def node11746 : Tree Nat := .node node11745 node10272 +def node11747 : Tree Nat := .node node10813 node11746 +def node11748 : Tree Nat := .node node11744 node11747 +def node11749 : Tree Nat := .node node11535 node9823 +def node11750 : Tree Nat := .node node11003 node11749 +def node11751 : Tree Nat := .node node11750 node11380 +def node11752 : Tree Nat := .node node11748 node11751 +def node11753 : Tree Nat := .node node11540 node8461 +def node11754 : Tree Nat := .node node11156 node11753 +def node11755 : Tree Nat := .node node10029 node195 +def node11756 : Tree Nat := .node node11755 node10286 +def node11757 : Tree Nat := .node node10820 node11756 +def node11758 : Tree Nat := .node node11754 node11757 +def node11759 : Tree Nat := .leaf 839 +def node11760 : Tree Nat := .node node11759 node9292 +def node11761 : Tree Nat := .node node11760 node9396 +def node11762 : Tree Nat := .node node10589 node11761 +def node11763 : Tree Nat := .node node11387 node11762 +def node11764 : Tree Nat := .node node11758 node11763 +def node11765 : Tree Nat := .node node11752 node11764 +def node11766 : Tree Nat := .leaf 895 +def node11767 : Tree Nat := .node node11766 node8255 +def node11768 : Tree Nat := .node node11161 node11767 +def node11769 : Tree Nat := .node node6188 node7465 +def node11770 : Tree Nat := .node node11769 node8480 +def node11771 : Tree Nat := .node node11768 node11770 +def node11772 : Tree Nat := .node node11771 node11393 +def node11773 : Tree Nat := .node node6554 node7923 +def node11774 : Tree Nat := .node node11773 node10301 +def node11775 : Tree Nat := .node node11012 node11774 +def node11776 : Tree Nat := .node node6320 node10212 +def node11777 : Tree Nat := .node node11776 node9856 +def node11778 : Tree Nat := .node node10595 node11777 +def node11779 : Tree Nat := .node node11775 node11778 +def node11780 : Tree Nat := .node node11772 node11779 +def node11781 : Tree Nat := .node node6180 node7962 +def node11782 : Tree Nat := .node node11781 node9412 +def node11783 : Tree Nat := .node node11166 node11782 +def node11784 : Tree Nat := .node node10335 node10311 +def node11785 : Tree Nat := .node node10831 node11784 +def node11786 : Tree Nat := .node node11783 node11785 +def node11787 : Tree Nat := .node node6694 node7735 +def node11788 : Tree Nat := .node node11787 node9866 +def node11789 : Tree Nat := .node node11016 node11788 +def node11790 : Tree Nat := .node node11789 node11402 +def node11791 : Tree Nat := .node node11786 node11790 +def node11792 : Tree Nat := .node node11780 node11791 +def node11793 : Tree Nat := .node node11765 node11792 +def node11794 : Tree Nat := .node node11742 node11793 +def node11795 : Tree Nat := .node node224 node7898 +def node11796 : Tree Nat := .node node11795 node10328 +def node11797 : Tree Nat := .node node11174 node11796 +def node11798 : Tree Nat := .node node5802 node7163 +def node11799 : Tree Nat := .node node11798 node10331 +def node11800 : Tree Nat := .node node11024 node11799 +def node11801 : Tree Nat := .node node11797 node11800 +def node11802 : Tree Nat := .node node6186 node7893 +def node11803 : Tree Nat := .node node11802 node8522 +def node11804 : Tree Nat := .node node11028 node11803 +def node11805 : Tree Nat := .node node11804 node11410 +def node11806 : Tree Nat := .node node11801 node11805 +def node11807 : Tree Nat := .node node10435 node11359 +def node11808 : Tree Nat := .node node11807 node10340 +def node11809 : Tree Nat := .node node6169 node7457 +def node11810 : Tree Nat := .node node11809 node8527 +def node11811 : Tree Nat := .node node11808 node11810 +def node11812 : Tree Nat := .node node11811 node11415 +def node11813 : Tree Nat := .leaf 911 +def node11814 : Tree Nat := .node node11813 node9180 +def node11815 : Tree Nat := .node node11814 node6994 +def node11816 : Tree Nat := .node node10608 node11815 +def node11817 : Tree Nat := .node node11419 node11816 +def node11818 : Tree Nat := .node node11812 node11817 +def node11819 : Tree Nat := .node node11806 node11818 +def node11820 : Tree Nat := .node node6176 node10458 +def node11821 : Tree Nat := .node node11820 node10353 +def node11822 : Tree Nat := .node node11428 node11821 +def node11823 : Tree Nat := .node node11822 node11432 +def node11824 : Tree Nat := .node node5826 node10533 +def node11825 : Tree Nat := .node node11824 node9902 +def node11826 : Tree Nat := .node node11039 node11825 +def node11827 : Tree Nat := .node node5835 node9748 +def node11828 : Tree Nat := .node node11827 node9908 +def node11829 : Tree Nat := .node node10626 node11828 +def node11830 : Tree Nat := .node node11826 node11829 +def node11831 : Tree Nat := .node node11823 node11830 +def node11832 : Tree Nat := .node node340 node10458 +def node11833 : Tree Nat := .node node11832 node8550 +def node11834 : Tree Nat := .node node11189 node11833 +def node11835 : Tree Nat := .node node6962 node8274 +def node11836 : Tree Nat := .node node11835 node10370 +def node11837 : Tree Nat := .node node10855 node11836 +def node11838 : Tree Nat := .node node11834 node11837 +def node11839 : Tree Nat := .node node195 node10458 +def node11840 : Tree Nat := .node node11839 node9913 +def node11841 : Tree Nat := .node node11043 node11840 +def node11842 : Tree Nat := .leaf 847 +def node11843 : Tree Nat := .node node11842 node10219 +def node11844 : Tree Nat := .node node11843 node9460 +def node11845 : Tree Nat := .node node11440 node11844 +def node11846 : Tree Nat := .node node11841 node11845 +def node11847 : Tree Nat := .node node11838 node11846 +def node11848 : Tree Nat := .node node11831 node11847 +def node11849 : Tree Nat := .node node11819 node11848 +def node11850 : Tree Nat := .node node11759 node10648 +def node11851 : Tree Nat := .node node11850 node10384 +def node11852 : Tree Nat := .node node11195 node11851 +def node11853 : Tree Nat := .node node11735 node9974 +def node11854 : Tree Nat := .node node11853 node9467 +def node11855 : Tree Nat := .node node10861 node11854 +def node11856 : Tree Nat := .node node11852 node11855 +def node11857 : Tree Nat := .node node11623 node10436 +def node11858 : Tree Nat := .node node11857 node9924 +def node11859 : Tree Nat := .node node11050 node11858 +def node11860 : Tree Nat := .node node11859 node11448 +def node11861 : Tree Nat := .node node11856 node11860 +def node11862 : Tree Nat := .node node11475 node10449 +def node11863 : Tree Nat := .node node11862 node8581 +def node11864 : Tree Nat := .node node11200 node11863 +def node11865 : Tree Nat := .node node11864 node11453 +def node11866 : Tree Nat := .node node11865 node11458 +def node11867 : Tree Nat := .node node11861 node11866 +def node11868 : Tree Nat := .node node11842 node9230 +def node11869 : Tree Nat := .node node11868 node8596 +def node11870 : Tree Nat := .node node11206 node11869 +def node11871 : Tree Nat := .node node11813 node8770 +def node11872 : Tree Nat := .node node11871 node9498 +def node11873 : Tree Nat := .node node10871 node11872 +def node11874 : Tree Nat := .node node11870 node11873 +def node11875 : Tree Nat := .node node11544 node8780 +def node11876 : Tree Nat := .node node11875 node10409 +def node11877 : Tree Nat := .node node11060 node11876 +def node11878 : Tree Nat := .node node11520 node8161 +def node11879 : Tree Nat := .node node11878 node7300 +def node11880 : Tree Nat := .node node10683 node11879 +def node11881 : Tree Nat := .node node11877 node11880 +def node11882 : Tree Nat := .node node11874 node11881 +def node11883 : Tree Nat := .node node11680 node9235 +def node11884 : Tree Nat := .node node11883 node9513 +def node11885 : Tree Nat := .node node11211 node11884 +def node11886 : Tree Nat := .node node11885 node11463 +def node11887 : Tree Nat := .node node11766 node8808 +def node11888 : Tree Nat := .node node11887 node8622 +def node11889 : Tree Nat := .node node11065 node11888 +def node11890 : Tree Nat := .node node11889 node11467 +def node11891 : Tree Nat := .node node11886 node11890 +def node11892 : Tree Nat := .node node11882 node11891 +def node11893 : Tree Nat := .node node11867 node11892 +def node11894 : Tree Nat := .node node11849 node11893 +def node11895 : Tree Nat := .node node11794 node11894 +def node11896 : Tree Nat := .node node11679 node11895 +def node11897 : Tree Nat := .node node8089 node10436 +def node11898 : Tree Nat := .node node11897 node7715 +def node11899 : Tree Nat := .node node11477 node11898 +def node11900 : Tree Nat := .node node8386 node9979 +def node11901 : Tree Nat := .node node11900 node9982 +def node11902 : Tree Nat := .node node10443 node11901 +def node11903 : Tree Nat := .node node11899 node11902 +def node11904 : Tree Nat := .node node8470 node10449 +def node11905 : Tree Nat := .node node11904 node8170 +def node11906 : Tree Nat := .node node10448 node11905 +def node11907 : Tree Nat := .node node7997 node8640 +def node11908 : Tree Nat := .node node11907 node9530 +def node11909 : Tree Nat := .node node10693 node11908 +def node11910 : Tree Nat := .node node11906 node11909 +def node11911 : Tree Nat := .node node11903 node11910 +def node11912 : Tree Nat := .node node7242 node10000 +def node11913 : Tree Nat := .node node11912 node10002 +def node11914 : Tree Nat := .node node10698 node11913 +def node11915 : Tree Nat := .node node11492 node11914 +def node11916 : Tree Nat := .node node7163 node10000 +def node11917 : Tree Nat := .node node11916 node9545 +def node11918 : Tree Nat := .node node10885 node11917 +def node11919 : Tree Nat := .node node11918 node11235 +def node11920 : Tree Nat := .node node11915 node11919 +def node11921 : Tree Nat := .node node11911 node11920 +def node11922 : Tree Nat := .node node10006 node10037 +def node11923 : Tree Nat := .node node10472 node11922 +def node11924 : Tree Nat := .node node8496 node7333 +def node11925 : Tree Nat := .node node11924 node10020 +def node11926 : Tree Nat := .node node11923 node11925 +def node11927 : Tree Nat := .node node7366 node7745 +def node11928 : Tree Nat := .node node11927 node10024 +def node11929 : Tree Nat := .node node10704 node11928 +def node11930 : Tree Nat := .node node11926 node11929 +def node11931 : Tree Nat := .node node8054 node7752 +def node11932 : Tree Nat := .node node11931 node8672 +def node11933 : Tree Nat := .node node10891 node11932 +def node11934 : Tree Nat := .node node8500 node9540 +def node11935 : Tree Nat := .node node11934 node9563 +def node11936 : Tree Nat := .node node10478 node11935 +def node11937 : Tree Nat := .node node11933 node11936 +def node11938 : Tree Nat := .node node11930 node11937 +def node11939 : Tree Nat := .node node8428 node7762 +def node11940 : Tree Nat := .node node11939 node8194 +def node11941 : Tree Nat := .node node11074 node11940 +def node11942 : Tree Nat := .node node11941 node11513 +def node11943 : Tree Nat := .node node8505 node7773 +def node11944 : Tree Nat := .node node11943 node10041 +def node11945 : Tree Nat := .node node10896 node11944 +def node11946 : Tree Nat := .node node11945 node11523 +def node11947 : Tree Nat := .node node11942 node11946 +def node11948 : Tree Nat := .node node11938 node11947 +def node11949 : Tree Nat := .node node11921 node11948 +def node11950 : Tree Nat := .node node9667 node5802 +def node11951 : Tree Nat := .node node11950 node8213 +def node11952 : Tree Nat := .node node10491 node11951 +def node11953 : Tree Nat := .node node9230 node10000 +def node11954 : Tree Nat := .node node11953 node8693 +def node11955 : Tree Nat := .node node10902 node11954 +def node11956 : Tree Nat := .node node11952 node11955 +def node11957 : Tree Nat := .node node9235 node6176 +def node11958 : Tree Nat := .node node11957 node9145 +def node11959 : Tree Nat := .node node10906 node11958 +def node11960 : Tree Nat := .node node9675 node8668 +def node11961 : Tree Nat := .node node11960 node6983 +def node11962 : Tree Nat := .node node10716 node11961 +def node11963 : Tree Nat := .node node11959 node11962 +def node11964 : Tree Nat := .node node11956 node11963 +def node11965 : Tree Nat := .node node10145 node195 +def node11966 : Tree Nat := .node node11965 node9151 +def node11967 : Tree Nat := .node node10721 node11966 +def node11968 : Tree Nat := .node node11542 node11967 +def node11969 : Tree Nat := .node node10150 node6169 +def node11970 : Tree Nat := .node node11969 node10067 +def node11971 : Tree Nat := .node node10911 node11970 +def node11972 : Tree Nat := .node node9604 node8668 +def node11973 : Tree Nat := .node node10499 node11972 +def node11974 : Tree Nat := .node node11973 node11546 +def node11975 : Tree Nat := .node node11971 node11974 +def node11976 : Tree Nat := .node node11968 node11975 +def node11977 : Tree Nat := .node node11964 node11976 +def node11978 : Tree Nat := .node node8780 node7391 +def node11979 : Tree Nat := .node node11978 node10074 +def node11980 : Tree Nat := .node node11087 node11979 +def node11981 : Tree Nat := .node node9648 node7756 +def node11982 : Tree Nat := .node node11981 node8730 +def node11983 : Tree Nat := .node node10727 node11982 +def node11984 : Tree Nat := .node node11980 node11983 +def node11985 : Tree Nat := .node node9653 node7718 +def node11986 : Tree Nat := .node node11985 node9619 +def node11987 : Tree Nat := .node node10916 node11986 +def node11988 : Tree Nat := .node node9216 node10029 +def node11989 : Tree Nat := .node node11988 node8738 +def node11990 : Tree Nat := .node node10506 node11989 +def node11991 : Tree Nat := .node node11987 node11990 +def node11992 : Tree Nat := .node node11984 node11991 +def node11993 : Tree Nat := .node node6606 node9098 +def node11994 : Tree Nat := .node node10731 node11993 +def node11995 : Tree Nat := .node node11994 node11566 +def node11996 : Tree Nat := .node node11565 node11995 +def node11997 : Tree Nat := .node node8274 node7821 +def node11998 : Tree Nat := .node node11997 node10094 +def node11999 : Tree Nat := .node node10920 node11998 +def node12000 : Tree Nat := .node node11999 node11574 +def node12001 : Tree Nat := .node node11996 node12000 +def node12002 : Tree Nat := .node node11992 node12001 +def node12003 : Tree Nat := .node node11977 node12002 +def node12004 : Tree Nat := .node node11949 node12003 +def node12005 : Tree Nat := .node node7955 node5802 +def node12006 : Tree Nat := .node node12005 node8271 +def node12007 : Tree Nat := .node node10513 node12006 +def node12008 : Tree Nat := .node node8169 node340 +def node12009 : Tree Nat := .node node12008 node8766 +def node12010 : Tree Nat := .node node10927 node12009 +def node12011 : Tree Nat := .node node12007 node12010 +def node12012 : Tree Nat := .node node8238 node6176 +def node12013 : Tree Nat := .node node12012 node9208 +def node12014 : Tree Nat := .node node10930 node12013 +def node12015 : Tree Nat := .node node7768 node8282 +def node12016 : Tree Nat := .node node12015 node8775 +def node12017 : Tree Nat := .node node10739 node12016 +def node12018 : Tree Nat := .node node12014 node12017 +def node12019 : Tree Nat := .node node12011 node12018 +def node12020 : Tree Nat := .node node6946 node6169 +def node12021 : Tree Nat := .node node12020 node9657 +def node12022 : Tree Nat := .node node10934 node12021 +def node12023 : Tree Nat := .node node12022 node11294 +def node12024 : Tree Nat := .node node11598 node12023 +def node12025 : Tree Nat := .node node12019 node12024 +def node12026 : Tree Nat := .node node8256 node9150 +def node12027 : Tree Nat := .node node12026 node10131 +def node12028 : Tree Nat := .node node11105 node12027 +def node12029 : Tree Nat := .node node7315 node340 +def node12030 : Tree Nat := .node node12029 node8799 +def node12031 : Tree Nat := .node node10749 node12030 +def node12032 : Tree Nat := .node node12028 node12031 +def node12033 : Tree Nat := .node node7824 node8718 +def node12034 : Tree Nat := .node node12033 node9240 +def node12035 : Tree Nat := .node node10940 node12034 +def node12036 : Tree Nat := .node node8260 node9558 +def node12037 : Tree Nat := .node node12036 node7039 +def node12038 : Tree Nat := .node node10526 node12037 +def node12039 : Tree Nat := .node node12035 node12038 +def node12040 : Tree Nat := .node node12032 node12039 +def node12041 : Tree Nat := .node node8372 node9249 +def node12042 : Tree Nat := .node node12041 node8309 +def node12043 : Tree Nat := .node node11110 node12042 +def node12044 : Tree Nat := .node node12043 node11618 +def node12045 : Tree Nat := .node node8411 node8689 +def node12046 : Tree Nat := .node node12045 node10154 +def node12047 : Tree Nat := .node node10945 node12046 +def node12048 : Tree Nat := .node node12047 node11626 +def node12049 : Tree Nat := .node node12044 node12048 +def node12050 : Tree Nat := .node node12040 node12049 +def node12051 : Tree Nat := .node node12025 node12050 +def node12052 : Tree Nat := .node node9108 node9170 +def node12053 : Tree Nat := .node node12052 node8323 +def node12054 : Tree Nat := .node node11117 node12053 +def node12055 : Tree Nat := .node node9112 node8765 +def node12056 : Tree Nat := .node node12055 node10168 +def node12057 : Tree Nat := .node node10761 node12056 +def node12058 : Tree Nat := .node node12054 node12057 +def node12059 : Tree Nat := .node node8668 node8706 +def node12060 : Tree Nat := .node node12059 node9706 +def node12061 : Tree Nat := .node node10952 node12060 +def node12062 : Tree Nat := .node node6546 node8649 +def node12063 : Tree Nat := .node node10764 node12062 +def node12064 : Tree Nat := .node node9558 node9098 +def node12065 : Tree Nat := .node node12064 node9713 +def node12066 : Tree Nat := .node node12063 node12065 +def node12067 : Tree Nat := .node node12061 node12066 +def node12068 : Tree Nat := .node node12058 node12067 +def node12069 : Tree Nat := .node node10037 node8743 +def node12070 : Tree Nat := .node node12069 node10187 +def node12071 : Tree Nat := .node node10957 node12070 +def node12072 : Tree Nat := .node node12071 node10543 +def node12073 : Tree Nat := .node node11649 node12072 +def node12074 : Tree Nat := .node node12068 node12073 +def node12075 : Tree Nat := .node node8649 node9143 +def node12076 : Tree Nat := .node node12075 node10195 +def node12077 : Tree Nat := .node node11127 node12076 +def node12078 : Tree Nat := .node node8857 node9112 +def node12079 : Tree Nat := .node node10775 node12078 +def node12080 : Tree Nat := .node node9535 node8713 +def node12081 : Tree Nat := .node node12080 node10198 +def node12082 : Tree Nat := .node node12079 node12081 +def node12083 : Tree Nat := .node node12077 node12082 +def node12084 : Tree Nat := .node node9540 node8829 +def node12085 : Tree Nat := .node node12084 node9745 +def node12086 : Tree Nat := .node node10963 node12085 +def node12087 : Tree Nat := .node node9098 node6348 +def node12088 : Tree Nat := .node node12087 node9751 +def node12089 : Tree Nat := .node node10548 node12088 +def node12090 : Tree Nat := .node node12086 node12089 +def node12091 : Tree Nat := .node node12083 node12090 +def node12092 : Tree Nat := .node node8640 node9093 +def node12093 : Tree Nat := .node node12092 node8364 +def node12094 : Tree Nat := .node node11132 node12093 +def node12095 : Tree Nat := .node node12094 node11669 +def node12096 : Tree Nat := .node node8161 node8729 +def node12097 : Tree Nat := .node node12096 node10223 +def node12098 : Tree Nat := .node node10968 node12097 +def node12099 : Tree Nat := .node node7116 node8640 +def node12100 : Tree Nat := .node node11338 node12099 +def node12101 : Tree Nat := .node node12100 node6747 +def node12102 : Tree Nat := .node node12098 node12101 +def node12103 : Tree Nat := .node node12095 node12102 +def node12104 : Tree Nat := .node node12091 node12103 +def node12105 : Tree Nat := .node node12074 node12104 +def node12106 : Tree Nat := .node node12051 node12105 +def node12107 : Tree Nat := .node node12004 node12106 +def node12108 : Tree Nat := .node node7955 node7829 +def node12109 : Tree Nat := .node node12108 node10234 +def node12110 : Tree Nat := .node node11682 node12109 +def node12111 : Tree Nat := .node node10435 node9558 +def node12112 : Tree Nat := .node node12111 node10237 +def node12113 : Tree Nat := .node node8169 node6946 +def node12114 : Tree Nat := .node node12113 node8893 +def node12115 : Tree Nat := .node node12112 node12114 +def node12116 : Tree Nat := .node node12110 node12115 +def node12117 : Tree Nat := .node node8238 node7787 +def node12118 : Tree Nat := .node node12117 node9337 +def node12119 : Tree Nat := .node node11691 node12118 +def node12120 : Tree Nat := .node node10435 node9540 +def node12121 : Tree Nat := .node node12120 node8900 +def node12122 : Tree Nat := .node node7768 node8677 +def node12123 : Tree Nat := .node node12122 node7141 +def node12124 : Tree Nat := .node node12121 node12123 +def node12125 : Tree Nat := .node node12119 node12124 +def node12126 : Tree Nat := .node node12116 node12125 +def node12127 : Tree Nat := .node node11086 node8911 +def node12128 : Tree Nat := .node node12127 node11702 +def node12129 : Tree Nat := .node node11700 node12128 +def node12130 : Tree Nat := .node node10472 node9777 +def node12131 : Tree Nat := .node node12130 node11706 +def node12132 : Tree Nat := .node node12131 node11362 +def node12133 : Tree Nat := .node node12129 node12132 +def node12134 : Tree Nat := .node node12126 node12133 +def node12135 : Tree Nat := .node node10533 node11426 +def node12136 : Tree Nat := .node node10572 node12135 +def node12137 : Tree Nat := .node node8256 node7562 +def node12138 : Tree Nat := .node node12137 node8412 +def node12139 : Tree Nat := .node node12136 node12138 +def node12140 : Tree Nat := .node node7315 node7976 +def node12141 : Tree Nat := .node node12140 node8923 +def node12142 : Tree Nat := .node node10801 node12141 +def node12143 : Tree Nat := .node node12139 node12142 +def node12144 : Tree Nat := .node node7824 node7797 +def node12145 : Tree Nat := .node node12144 node9356 +def node12146 : Tree Nat := .node node10992 node12145 +def node12147 : Tree Nat := .node node8260 node9723 +def node12148 : Tree Nat := .node node12147 node6259 +def node12149 : Tree Nat := .node node10578 node12148 +def node12150 : Tree Nat := .node node12146 node12149 +def node12151 : Tree Nat := .node node12143 node12150 +def node12152 : Tree Nat := .node node8372 node7877 +def node12153 : Tree Nat := .node node12152 node8429 +def node12154 : Tree Nat := .node node11146 node12153 +def node12155 : Tree Nat := .node node12154 node11728 +def node12156 : Tree Nat := .node node8411 node8002 +def node12157 : Tree Nat := .node node12156 node9806 +def node12158 : Tree Nat := .node node10997 node12157 +def node12159 : Tree Nat := .node node12158 node11738 +def node12160 : Tree Nat := .node node12155 node12159 +def node12161 : Tree Nat := .node node12151 node12160 +def node12162 : Tree Nat := .node node12134 node12161 +def node12163 : Tree Nat := .node node9108 node5802 +def node12164 : Tree Nat := .node node12163 node10267 +def node12165 : Tree Nat := .node node11152 node12164 +def node12166 : Tree Nat := .node node9112 node8784 +def node12167 : Tree Nat := .node node12166 node10272 +def node12168 : Tree Nat := .node node10813 node12167 +def node12169 : Tree Nat := .node node12165 node12168 +def node12170 : Tree Nat := .node node8668 node6176 +def node12171 : Tree Nat := .node node12170 node9823 +def node12172 : Tree Nat := .node node11003 node12171 +def node12173 : Tree Nat := .node node9558 node8865 +def node12174 : Tree Nat := .node node12173 node9828 +def node12175 : Tree Nat := .node node10816 node12174 +def node12176 : Tree Nat := .node node12172 node12175 +def node12177 : Tree Nat := .node node12169 node12176 +def node12178 : Tree Nat := .node node10037 node6169 +def node12179 : Tree Nat := .node node12178 node10291 +def node12180 : Tree Nat := .node node11007 node12179 +def node12181 : Tree Nat := .node node9131 node11623 +def node12182 : Tree Nat := .node node10499 node12181 +def node12183 : Tree Nat := .node node12182 node11761 +def node12184 : Tree Nat := .node node12180 node12183 +def node12185 : Tree Nat := .node node11758 node12184 +def node12186 : Tree Nat := .node node12177 node12185 +def node12187 : Tree Nat := .node node8649 node7465 +def node12188 : Tree Nat := .node node12187 node8480 +def node12189 : Tree Nat := .node node11768 node12188 +def node12190 : Tree Nat := .node node9535 node7986 +def node12191 : Tree Nat := .node node12190 node10297 +def node12192 : Tree Nat := .node node10826 node12191 +def node12193 : Tree Nat := .node node12189 node12192 +def node12194 : Tree Nat := .node node9540 node7923 +def node12195 : Tree Nat := .node node12194 node10301 +def node12196 : Tree Nat := .node node11012 node12195 +def node12197 : Tree Nat := .node node9098 node10212 +def node12198 : Tree Nat := .node node12197 node9856 +def node12199 : Tree Nat := .node node10595 node12198 +def node12200 : Tree Nat := .node node12196 node12199 +def node12201 : Tree Nat := .node node12193 node12200 +def node12202 : Tree Nat := .node node8640 node7962 +def node12203 : Tree Nat := .node node12202 node9412 +def node12204 : Tree Nat := .node node11166 node12203 +def node12205 : Tree Nat := .node node8745 node11520 +def node12206 : Tree Nat := .node node10830 node12205 +def node12207 : Tree Nat := .node node12206 node11784 +def node12208 : Tree Nat := .node node12204 node12207 +def node12209 : Tree Nat := .node node8161 node7735 +def node12210 : Tree Nat := .node node12209 node9866 +def node12211 : Tree Nat := .node node11016 node12210 +def node12212 : Tree Nat := .node node7031 node11766 +def node12213 : Tree Nat := .node node11400 node12212 +def node12214 : Tree Nat := .node node12213 node10321 +def node12215 : Tree Nat := .node node12211 node12214 +def node12216 : Tree Nat := .node node12208 node12215 +def node12217 : Tree Nat := .node node12201 node12216 +def node12218 : Tree Nat := .node node12186 node12217 +def node12219 : Tree Nat := .node node12162 node12218 +def node12220 : Tree Nat := .node node8089 node7898 +def node12221 : Tree Nat := .node node12220 node10328 +def node12222 : Tree Nat := .node node11174 node12221 +def node12223 : Tree Nat := .node node10435 node11291 +def node12224 : Tree Nat := .node node12223 node8984 +def node12225 : Tree Nat := .node node8386 node7163 +def node12226 : Tree Nat := .node node12225 node10331 +def node12227 : Tree Nat := .node node12224 node12226 +def node12228 : Tree Nat := .node node12222 node12227 +def node12229 : Tree Nat := .node node10435 node11232 +def node12230 : Tree Nat := .node node12229 node9878 +def node12231 : Tree Nat := .node node8470 node7893 +def node12232 : Tree Nat := .node node12231 node8522 +def node12233 : Tree Nat := .node node12230 node12232 +def node12234 : Tree Nat := .node node10435 node11544 +def node12235 : Tree Nat := .node node12234 node9431 +def node12236 : Tree Nat := .node node7997 node8873 +def node12237 : Tree Nat := .node node12236 node9881 +def node12238 : Tree Nat := .node node12235 node12237 +def node12239 : Tree Nat := .node node12233 node12238 +def node12240 : Tree Nat := .node node12228 node12239 +def node12241 : Tree Nat := .node node10435 node11759 +def node12242 : Tree Nat := .node node12241 node9001 +def node12243 : Tree Nat := .node node7242 node7242 +def node12244 : Tree Nat := .node node12243 node10343 +def node12245 : Tree Nat := .node node12242 node12244 +def node12246 : Tree Nat := .node node11811 node12245 +def node12247 : Tree Nat := .node node10435 node11813 +def node12248 : Tree Nat := .node node12247 node10347 +def node12249 : Tree Nat := .node node7163 node7059 +def node12250 : Tree Nat := .node node12249 node9892 +def node12251 : Tree Nat := .node node12248 node12250 +def node12252 : Tree Nat := .node node12251 node11816 +def node12253 : Tree Nat := .node node12246 node12252 +def node12254 : Tree Nat := .node node12240 node12253 +def node12255 : Tree Nat := .node node8496 node10458 +def node12256 : Tree Nat := .node node12255 node10353 +def node12257 : Tree Nat := .node node11428 node12256 +def node12258 : Tree Nat := .node node7366 node10482 +def node12259 : Tree Nat := .node node12258 node10356 +def node12260 : Tree Nat := .node node10850 node12259 +def node12261 : Tree Nat := .node node12257 node12260 +def node12262 : Tree Nat := .node node8054 node10533 +def node12263 : Tree Nat := .node node12262 node9902 +def node12264 : Tree Nat := .node node11039 node12263 +def node12265 : Tree Nat := .node node8500 node9748 +def node12266 : Tree Nat := .node node12265 node9908 +def node12267 : Tree Nat := .node node10626 node12266 +def node12268 : Tree Nat := .node node12264 node12267 +def node12269 : Tree Nat := .node node12261 node12268 +def node12270 : Tree Nat := .node node8428 node10458 +def node12271 : Tree Nat := .node node12270 node8550 +def node12272 : Tree Nat := .node node11189 node12271 +def node12273 : Tree Nat := .node node12272 node11837 +def node12274 : Tree Nat := .node node8505 node10458 +def node12275 : Tree Nat := .node node12274 node9913 +def node12276 : Tree Nat := .node node11043 node12275 +def node12277 : Tree Nat := .node node6242 node8161 +def node12278 : Tree Nat := .node node11439 node12277 +def node12279 : Tree Nat := .node node12278 node11844 +def node12280 : Tree Nat := .node node12276 node12279 +def node12281 : Tree Nat := .node node12273 node12280 +def node12282 : Tree Nat := .node node12269 node12281 +def node12283 : Tree Nat := .node node12254 node12282 +def node12284 : Tree Nat := .node node8983 node11842 +def node12285 : Tree Nat := .node node10459 node12284 +def node12286 : Tree Nat := .node node12285 node11447 +def node12287 : Tree Nat := .node node11859 node12286 +def node12288 : Tree Nat := .node node11856 node12287 +def node12289 : Tree Nat := .node node12288 node11866 +def node12290 : Tree Nat := .node node8749 node11735 +def node12291 : Tree Nat := .node node10870 node12290 +def node12292 : Tree Nat := .node node12291 node11872 +def node12293 : Tree Nat := .node node11870 node12292 +def node12294 : Tree Nat := .node node12293 node11881 +def node12295 : Tree Nat := .node node12294 node11891 +def node12296 : Tree Nat := .node node12289 node12295 +def node12297 : Tree Nat := .node node12283 node12296 +def node12298 : Tree Nat := .node node12219 node12297 +def node12299 : Tree Nat := .node node12107 node12298 +def node12300 : Tree Nat := .node node9299 node10436 +def node12301 : Tree Nat := .node node12300 node7715 +def node12302 : Tree Nat := .node node11477 node12301 +def node12303 : Tree Nat := .node node9305 node9979 +def node12304 : Tree Nat := .node node12303 node9982 +def node12305 : Tree Nat := .node node10443 node12304 +def node12306 : Tree Nat := .node node12302 node12305 +def node12307 : Tree Nat := .node node8865 node10449 +def node12308 : Tree Nat := .node node12307 node8170 +def node12309 : Tree Nat := .node node10448 node12308 +def node12310 : Tree Nat := .node node9748 node8640 +def node12311 : Tree Nat := .node node12310 node9530 +def node12312 : Tree Nat := .node node10693 node12311 +def node12313 : Tree Nat := .node node12309 node12312 +def node12314 : Tree Nat := .node node12306 node12313 +def node12315 : Tree Nat := .node node8873 node9996 +def node12316 : Tree Nat := .node node12315 node8654 +def node12317 : Tree Nat := .node node10460 node12316 +def node12318 : Tree Nat := .node node10212 node10000 +def node12319 : Tree Nat := .node node12318 node10002 +def node12320 : Tree Nat := .node node10698 node12319 +def node12321 : Tree Nat := .node node12317 node12320 +def node12322 : Tree Nat := .node node10219 node10000 +def node12323 : Tree Nat := .node node12322 node9545 +def node12324 : Tree Nat := .node node10885 node12323 +def node12325 : Tree Nat := .node node12324 node11235 +def node12326 : Tree Nat := .node node12321 node12325 +def node12327 : Tree Nat := .node node12314 node12326 +def node12328 : Tree Nat := .node node8709 node7333 +def node12329 : Tree Nat := .node node12328 node10020 +def node12330 : Tree Nat := .node node11923 node12329 +def node12331 : Tree Nat := .node node9718 node7745 +def node12332 : Tree Nat := .node node12331 node10024 +def node12333 : Tree Nat := .node node10704 node12332 +def node12334 : Tree Nat := .node node12330 node12333 +def node12335 : Tree Nat := .node node9723 node7752 +def node12336 : Tree Nat := .node node12335 node8672 +def node12337 : Tree Nat := .node node10891 node12336 +def node12338 : Tree Nat := .node node9287 node9540 +def node12339 : Tree Nat := .node node12338 node9563 +def node12340 : Tree Nat := .node node10478 node12339 +def node12341 : Tree Nat := .node node12337 node12340 +def node12342 : Tree Nat := .node node12334 node12341 +def node12343 : Tree Nat := .node node8282 node7762 +def node12344 : Tree Nat := .node node12343 node8194 +def node12345 : Tree Nat := .node node11074 node12344 +def node12346 : Tree Nat := .node node9709 node7768 +def node12347 : Tree Nat := .node node12346 node10033 +def node12348 : Tree Nat := .node node10709 node12347 +def node12349 : Tree Nat := .node node12345 node12348 +def node12350 : Tree Nat := .node node8326 node7773 +def node12351 : Tree Nat := .node node12350 node10041 +def node12352 : Tree Nat := .node node10896 node12351 +def node12353 : Tree Nat := .node node12352 node11523 +def node12354 : Tree Nat := .node node12349 node12353 +def node12355 : Tree Nat := .node node12342 node12354 +def node12356 : Tree Nat := .node node12327 node12355 +def node12357 : Tree Nat := .node node8808 node6186 +def node12358 : Tree Nat := .node node12357 node8710 +def node12359 : Tree Nat := .node node11081 node12358 +def node12360 : Tree Nat := .node node12359 node11967 +def node12361 : Tree Nat := .node node12360 node11975 +def node12362 : Tree Nat := .node node11964 node12361 +def node12363 : Tree Nat := .node node10073 node8677 +def node12364 : Tree Nat := .node node11978 node12363 +def node12365 : Tree Nat := .node node11087 node12364 +def node12366 : Tree Nat := .node node12365 node11983 +def node12367 : Tree Nat := .node node12366 node11991 +def node12368 : Tree Nat := .node node8770 node7732 +def node12369 : Tree Nat := .node node12368 node8257 +def node12370 : Tree Nat := .node node11091 node12369 +def node12371 : Tree Nat := .node node12370 node11995 +def node12372 : Tree Nat := .node node12371 node12000 +def node12373 : Tree Nat := .node node12367 node12372 +def node12374 : Tree Nat := .node node12362 node12373 +def node12375 : Tree Nat := .node node12356 node12374 +def node12376 : Tree Nat := .node node9166 node5802 +def node12377 : Tree Nat := .node node12376 node8271 +def node12378 : Tree Nat := .node node10513 node12377 +def node12379 : Tree Nat := .node node9170 node340 +def node12380 : Tree Nat := .node node12379 node8766 +def node12381 : Tree Nat := .node node10927 node12380 +def node12382 : Tree Nat := .node node12378 node12381 +def node12383 : Tree Nat := .node node9175 node6176 +def node12384 : Tree Nat := .node node12383 node9208 +def node12385 : Tree Nat := .node node10930 node12384 +def node12386 : Tree Nat := .node node9622 node8282 +def node12387 : Tree Nat := .node node12386 node8775 +def node12388 : Tree Nat := .node node10739 node12387 +def node12389 : Tree Nat := .node node12385 node12388 +def node12390 : Tree Nat := .node node12382 node12389 +def node12391 : Tree Nat := .node node8743 node6186 +def node12392 : Tree Nat := .node node12391 node10117 +def node12393 : Tree Nat := .node node11099 node12392 +def node12394 : Tree Nat := .node node10083 node195 +def node12395 : Tree Nat := .node node12394 node8787 +def node12396 : Tree Nat := .node node10743 node12395 +def node12397 : Tree Nat := .node node12393 node12396 +def node12398 : Tree Nat := .node node12397 node12023 +def node12399 : Tree Nat := .node node12390 node12398 +def node12400 : Tree Nat := .node node8706 node9150 +def node12401 : Tree Nat := .node node12400 node10131 +def node12402 : Tree Nat := .node node11105 node12401 +def node12403 : Tree Nat := .node node9595 node340 +def node12404 : Tree Nat := .node node12403 node8799 +def node12405 : Tree Nat := .node node10749 node12404 +def node12406 : Tree Nat := .node node12402 node12405 +def node12407 : Tree Nat := .node node9600 node8718 +def node12408 : Tree Nat := .node node12407 node9240 +def node12409 : Tree Nat := .node node10940 node12408 +def node12410 : Tree Nat := .node node9155 node9558 +def node12411 : Tree Nat := .node node12410 node7039 +def node12412 : Tree Nat := .node node10526 node12411 +def node12413 : Tree Nat := .node node12409 node12412 +def node12414 : Tree Nat := .node node12406 node12413 +def node12415 : Tree Nat := .node node8697 node9249 +def node12416 : Tree Nat := .node node12415 node8309 +def node12417 : Tree Nat := .node node11110 node12416 +def node12418 : Tree Nat := .node node10055 node8164 +def node12419 : Tree Nat := .node node12418 node9254 +def node12420 : Tree Nat := .node node10754 node12419 +def node12421 : Tree Nat := .node node12417 node12420 +def node12422 : Tree Nat := .node node8216 node8689 +def node12423 : Tree Nat := .node node12422 node10154 +def node12424 : Tree Nat := .node node10945 node12423 +def node12425 : Tree Nat := .node node12424 node11626 +def node12426 : Tree Nat := .node node12421 node12425 +def node12427 : Tree Nat := .node node12414 node12426 +def node12428 : Tree Nat := .node node12399 node12427 +def node12429 : Tree Nat := .node node8677 node9175 +def node12430 : Tree Nat := .node node12429 node10179 +def node12431 : Tree Nat := .node node11122 node12430 +def node12432 : Tree Nat := .node node12431 node11648 +def node12433 : Tree Nat := .node node12432 node12072 +def node12434 : Tree Nat := .node node12068 node12433 +def node12435 : Tree Nat := .node node12434 node12104 +def node12436 : Tree Nat := .node node12428 node12435 +def node12437 : Tree Nat := .node node12375 node12436 +def node12438 : Tree Nat := .node node9166 node7829 +def node12439 : Tree Nat := .node node12438 node10234 +def node12440 : Tree Nat := .node node11682 node12439 +def node12441 : Tree Nat := .node node9170 node6946 +def node12442 : Tree Nat := .node node12441 node8893 +def node12443 : Tree Nat := .node node12112 node12442 +def node12444 : Tree Nat := .node node12440 node12443 +def node12445 : Tree Nat := .node node9175 node7787 +def node12446 : Tree Nat := .node node12445 node9337 +def node12447 : Tree Nat := .node node11691 node12446 +def node12448 : Tree Nat := .node node9622 node8677 +def node12449 : Tree Nat := .node node12448 node7141 +def node12450 : Tree Nat := .node node12121 node12449 +def node12451 : Tree Nat := .node node12447 node12450 +def node12452 : Tree Nat := .node node12444 node12451 +def node12453 : Tree Nat := .node node8743 node7444 +def node12454 : Tree Nat := .node node12453 node8396 +def node12455 : Tree Nat := .node node11697 node12454 +def node12456 : Tree Nat := .node node10083 node7137 +def node12457 : Tree Nat := .node node12456 node8399 +def node12458 : Tree Nat := .node node12127 node12457 +def node12459 : Tree Nat := .node node12455 node12458 +def node12460 : Tree Nat := .node node10088 node7051 +def node12461 : Tree Nat := .node node12460 node10250 +def node12462 : Tree Nat := .node node12130 node12461 +def node12463 : Tree Nat := .node node12462 node11362 +def node12464 : Tree Nat := .node node12459 node12463 +def node12465 : Tree Nat := .node node12452 node12464 +def node12466 : Tree Nat := .node node8706 node7562 +def node12467 : Tree Nat := .node node12466 node8412 +def node12468 : Tree Nat := .node node12136 node12467 +def node12469 : Tree Nat := .node node9595 node7976 +def node12470 : Tree Nat := .node node12469 node8923 +def node12471 : Tree Nat := .node node10801 node12470 +def node12472 : Tree Nat := .node node12468 node12471 +def node12473 : Tree Nat := .node node9600 node7797 +def node12474 : Tree Nat := .node node12473 node9356 +def node12475 : Tree Nat := .node node10992 node12474 +def node12476 : Tree Nat := .node node9155 node9723 +def node12477 : Tree Nat := .node node12476 node6259 +def node12478 : Tree Nat := .node node10578 node12477 +def node12479 : Tree Nat := .node node12475 node12478 +def node12480 : Tree Nat := .node node12472 node12479 +def node12481 : Tree Nat := .node node8697 node7877 +def node12482 : Tree Nat := .node node12481 node8429 +def node12483 : Tree Nat := .node node11146 node12482 +def node12484 : Tree Nat := .node node10055 node7997 +def node12485 : Tree Nat := .node node12484 node9365 +def node12486 : Tree Nat := .node node10806 node12485 +def node12487 : Tree Nat := .node node12483 node12486 +def node12488 : Tree Nat := .node node8216 node8002 +def node12489 : Tree Nat := .node node12488 node9806 +def node12490 : Tree Nat := .node node10997 node12489 +def node12491 : Tree Nat := .node node12490 node11738 +def node12492 : Tree Nat := .node node12487 node12491 +def node12493 : Tree Nat := .node node12480 node12492 +def node12494 : Tree Nat := .node node12465 node12493 +def node12495 : Tree Nat := .node node8677 node6186 +def node12496 : Tree Nat := .node node12495 node8461 +def node12497 : Tree Nat := .node node11156 node12496 +def node12498 : Tree Nat := .node node12497 node11757 +def node12499 : Tree Nat := .node node12498 node12184 +def node12500 : Tree Nat := .node node12177 node12499 +def node12501 : Tree Nat := .node node7955 node11475 +def node12502 : Tree Nat := .node node12187 node12501 +def node12503 : Tree Nat := .node node11768 node12502 +def node12504 : Tree Nat := .node node12503 node12192 +def node12505 : Tree Nat := .node node12504 node12200 +def node12506 : Tree Nat := .node node12505 node12216 +def node12507 : Tree Nat := .node node12500 node12506 +def node12508 : Tree Nat := .node node12494 node12507 +def node12509 : Tree Nat := .node node9299 node7898 +def node12510 : Tree Nat := .node node12509 node10328 +def node12511 : Tree Nat := .node node11174 node12510 +def node12512 : Tree Nat := .node node9305 node7163 +def node12513 : Tree Nat := .node node12512 node10331 +def node12514 : Tree Nat := .node node12224 node12513 +def node12515 : Tree Nat := .node node12511 node12514 +def node12516 : Tree Nat := .node node8865 node7893 +def node12517 : Tree Nat := .node node12516 node8522 +def node12518 : Tree Nat := .node node12230 node12517 +def node12519 : Tree Nat := .node node9748 node8873 +def node12520 : Tree Nat := .node node12519 node9881 +def node12521 : Tree Nat := .node node12235 node12520 +def node12522 : Tree Nat := .node node12518 node12521 +def node12523 : Tree Nat := .node node12515 node12522 +def node12524 : Tree Nat := .node node8873 node7457 +def node12525 : Tree Nat := .node node12524 node8527 +def node12526 : Tree Nat := .node node11808 node12525 +def node12527 : Tree Nat := .node node10212 node7242 +def node12528 : Tree Nat := .node node12527 node10343 +def node12529 : Tree Nat := .node node12242 node12528 +def node12530 : Tree Nat := .node node12526 node12529 +def node12531 : Tree Nat := .node node10219 node7059 +def node12532 : Tree Nat := .node node12531 node9892 +def node12533 : Tree Nat := .node node12248 node12532 +def node12534 : Tree Nat := .node node12533 node11816 +def node12535 : Tree Nat := .node node12530 node12534 +def node12536 : Tree Nat := .node node12523 node12535 +def node12537 : Tree Nat := .node node8709 node10458 +def node12538 : Tree Nat := .node node12537 node10353 +def node12539 : Tree Nat := .node node11428 node12538 +def node12540 : Tree Nat := .node node12247 node9007 +def node12541 : Tree Nat := .node node9718 node10482 +def node12542 : Tree Nat := .node node12541 node10356 +def node12543 : Tree Nat := .node node12540 node12542 +def node12544 : Tree Nat := .node node12539 node12543 +def node12545 : Tree Nat := .node node11807 node10620 +def node12546 : Tree Nat := .node node9723 node10533 +def node12547 : Tree Nat := .node node12546 node9902 +def node12548 : Tree Nat := .node node12545 node12547 +def node12549 : Tree Nat := .node node12241 node9455 +def node12550 : Tree Nat := .node node9287 node9748 +def node12551 : Tree Nat := .node node12550 node9908 +def node12552 : Tree Nat := .node node12549 node12551 +def node12553 : Tree Nat := .node node12548 node12552 +def node12554 : Tree Nat := .node node12544 node12553 +def node12555 : Tree Nat := .node node8282 node10458 +def node12556 : Tree Nat := .node node12555 node8550 +def node12557 : Tree Nat := .node node11189 node12556 +def node12558 : Tree Nat := .node node9709 node11766 +def node12559 : Tree Nat := .node node12558 node10370 +def node12560 : Tree Nat := .node node10855 node12559 +def node12561 : Tree Nat := .node node12557 node12560 +def node12562 : Tree Nat := .node node8326 node10458 +def node12563 : Tree Nat := .node node12562 node9913 +def node12564 : Tree Nat := .node node11043 node12563 +def node12565 : Tree Nat := .node node12564 node12279 +def node12566 : Tree Nat := .node node12561 node12565 +def node12567 : Tree Nat := .node node12554 node12566 +def node12568 : Tree Nat := .node node12536 node12567 +def node12569 : Tree Nat := .node node12229 node10396 +def node12570 : Tree Nat := .node node12569 node11863 +def node12571 : Tree Nat := .node node12570 node11453 +def node12572 : Tree Nat := .node node12571 node11458 +def node12573 : Tree Nat := .node node12288 node12572 +def node12574 : Tree Nat := .node node11842 node11735 +def node12575 : Tree Nat := .node node12574 node8596 +def node12576 : Tree Nat := .node node11206 node12575 +def node12577 : Tree Nat := .node node11813 node11680 +def node12578 : Tree Nat := .node node12577 node9498 +def node12579 : Tree Nat := .node node12291 node12578 +def node12580 : Tree Nat := .node node12576 node12579 +def node12581 : Tree Nat := .node node11544 node11842 +def node12582 : Tree Nat := .node node12581 node10409 +def node12583 : Tree Nat := .node node11060 node12582 +def node12584 : Tree Nat := .node node12583 node11880 +def node12585 : Tree Nat := .node node12580 node12584 +def node12586 : Tree Nat := .node node11680 node11623 +def node12587 : Tree Nat := .node node12586 node9513 +def node12588 : Tree Nat := .node node11211 node12587 +def node12589 : Tree Nat := .node node12234 node9071 +def node12590 : Tree Nat := .node node12589 node11462 +def node12591 : Tree Nat := .node node12588 node12590 +def node12592 : Tree Nat := .node node12223 node10422 +def node12593 : Tree Nat := .node node11766 node11475 +def node12594 : Tree Nat := .node node12593 node8622 +def node12595 : Tree Nat := .node node12592 node12594 +def node12596 : Tree Nat := .node node451 node11520 +def node12597 : Tree Nat := .node node9705 node11680 +def node12598 : Tree Nat := .node node12596 node12597 +def node12599 : Tree Nat := .node node12598 node10426 +def node12600 : Tree Nat := .node node12595 node12599 +def node12601 : Tree Nat := .node node12591 node12600 +def node12602 : Tree Nat := .node node12585 node12601 +def node12603 : Tree Nat := .node node12573 node12602 +def node12604 : Tree Nat := .node node12568 node12603 +def node12605 : Tree Nat := .node node12508 node12604 +def node12606 : Tree Nat := .node node12437 node12605 +def node12607 : Tree Nat := .leaf 832 +def node12608 : Tree Nat := .node node12607 node10436 +def node12609 : Tree Nat := .node node12608 node7715 +def node12610 : Tree Nat := .node node11477 node12609 +def node12611 : Tree Nat := .node node10437 node9977 +def node12612 : Tree Nat := .node node12611 node12304 +def node12613 : Tree Nat := .node node12610 node12612 +def node12614 : Tree Nat := .node node10676 node9987 +def node12615 : Tree Nat := .node node12614 node12308 +def node12616 : Tree Nat := .node node12615 node12312 +def node12617 : Tree Nat := .node node12613 node12616 +def node12618 : Tree Nat := .leaf 848 +def node12619 : Tree Nat := .node node12618 node9996 +def node12620 : Tree Nat := .node node12619 node8654 +def node12621 : Tree Nat := .node node10460 node12620 +def node12622 : Tree Nat := .leaf 859 +def node12623 : Tree Nat := .node node12622 node6192 +def node12624 : Tree Nat := .node node11049 node12623 +def node12625 : Tree Nat := .node node12624 node12319 +def node12626 : Tree Nat := .node node12621 node12625 +def node12627 : Tree Nat := .leaf 825 +def node12628 : Tree Nat := .node node10435 node12627 +def node12629 : Tree Nat := .node node12628 node10009 +def node12630 : Tree Nat := .node node10219 node9979 +def node12631 : Tree Nat := .node node12630 node9545 +def node12632 : Tree Nat := .node node12629 node12631 +def node12633 : Tree Nat := .node node11049 node8181 +def node12634 : Tree Nat := .node node12633 node11234 +def node12635 : Tree Nat := .node node12632 node12634 +def node12636 : Tree Nat := .node node12626 node12635 +def node12637 : Tree Nat := .node node12617 node12636 +def node12638 : Tree Nat := .leaf 840 +def node12639 : Tree Nat := .node node12638 node7333 +def node12640 : Tree Nat := .node node12639 node10020 +def node12641 : Tree Nat := .node node11923 node12640 +def node12642 : Tree Nat := .leaf 835 +def node12643 : Tree Nat := .node node10435 node12642 +def node12644 : Tree Nat := .leaf 851 +def node12645 : Tree Nat := .node node322 node12644 +def node12646 : Tree Nat := .node node12643 node12645 +def node12647 : Tree Nat := .node node12646 node12332 +def node12648 : Tree Nat := .node node12641 node12647 +def node12649 : Tree Nat := .node node11759 node6208 +def node12650 : Tree Nat := .node node10890 node12649 +def node12651 : Tree Nat := .node node12650 node12336 +def node12652 : Tree Nat := .node node12651 node12340 +def node12653 : Tree Nat := .node node12648 node12652 +def node12654 : Tree Nat := .leaf 856 +def node12655 : Tree Nat := .node node12654 node7762 +def node12656 : Tree Nat := .node node12655 node8194 +def node12657 : Tree Nat := .node node11074 node12656 +def node12658 : Tree Nat := .leaf 843 +def node12659 : Tree Nat := .node node5821 node12658 +def node12660 : Tree Nat := .node node10708 node12659 +def node12661 : Tree Nat := .node node12660 node12347 +def node12662 : Tree Nat := .node node12657 node12661 +def node12663 : Tree Nat := .node node9979 node7320 +def node12664 : Tree Nat := .node node12663 node9136 +def node12665 : Tree Nat := .node node12664 node11522 +def node12666 : Tree Nat := .node node12352 node12665 +def node12667 : Tree Nat := .node node12662 node12666 +def node12668 : Tree Nat := .node node12653 node12667 +def node12669 : Tree Nat := .node node12637 node12668 +def node12670 : Tree Nat := .leaf 836 +def node12671 : Tree Nat := .node node12670 node5802 +def node12672 : Tree Nat := .node node12671 node8213 +def node12673 : Tree Nat := .node node10491 node12672 +def node12674 : Tree Nat := .leaf 849 +def node12675 : Tree Nat := .node node12674 node6569 +def node12676 : Tree Nat := .node node10812 node12675 +def node12677 : Tree Nat := .node node7370 node11475 +def node12678 : Tree Nat := .node node11953 node12677 +def node12679 : Tree Nat := .node node12676 node12678 +def node12680 : Tree Nat := .node node12673 node12679 +def node12681 : Tree Nat := .node node9143 node12670 +def node12682 : Tree Nat := .node node11957 node12681 +def node12683 : Tree Nat := .node node10906 node12682 +def node12684 : Tree Nat := .node node12683 node11962 +def node12685 : Tree Nat := .node node12680 node12684 +def node12686 : Tree Nat := .leaf 852 +def node12687 : Tree Nat := .node node12686 node6186 +def node12688 : Tree Nat := .node node12687 node8710 +def node12689 : Tree Nat := .node node11081 node12688 +def node12690 : Tree Nat := .leaf 857 +def node12691 : Tree Nat := .leaf 862 +def node12692 : Tree Nat := .node node12690 node12691 +def node12693 : Tree Nat := .node node10720 node12692 +def node12694 : Tree Nat := .node node12693 node11966 +def node12695 : Tree Nat := .node node12689 node12694 +def node12696 : Tree Nat := .leaf 841 +def node12697 : Tree Nat := .node node12696 node6242 +def node12698 : Tree Nat := .node node10910 node12697 +def node12699 : Tree Nat := .node node12698 node11970 +def node12700 : Tree Nat := .node node12699 node11974 +def node12701 : Tree Nat := .node node12695 node12700 +def node12702 : Tree Nat := .node node12685 node12701 +def node12703 : Tree Nat := .leaf 844 +def node12704 : Tree Nat := .node node12703 node7391 +def node12705 : Tree Nat := .node node12704 node12363 +def node12706 : Tree Nat := .node node11087 node12705 +def node12707 : Tree Nat := .leaf 853 +def node12708 : Tree Nat := .node node12707 node8726 +def node12709 : Tree Nat := .node node10726 node12708 +def node12710 : Tree Nat := .node node340 node12674 +def node12711 : Tree Nat := .node node11981 node12710 +def node12712 : Tree Nat := .node node12709 node12711 +def node12713 : Tree Nat := .node node12706 node12712 +def node12714 : Tree Nat := .leaf 837 +def node12715 : Tree Nat := .node node12714 node7400 +def node12716 : Tree Nat := .node node10726 node12715 +def node12717 : Tree Nat := .node node12716 node11986 +def node12718 : Tree Nat := .node node12717 node11990 +def node12719 : Tree Nat := .node node12713 node12718 +def node12720 : Tree Nat := .leaf 860 +def node12721 : Tree Nat := .node node12720 node7732 +def node12722 : Tree Nat := .node node12721 node8257 +def node12723 : Tree Nat := .node node11091 node12722 +def node12724 : Tree Nat := .node node12723 node11995 +def node12725 : Tree Nat := .node node10435 node12714 +def node12726 : Tree Nat := .leaf 845 +def node12727 : Tree Nat := .node node12726 node10090 +def node12728 : Tree Nat := .node node12725 node12727 +def node12729 : Tree Nat := .node node12728 node11998 +def node12730 : Tree Nat := .node node10436 node7420 +def node12731 : Tree Nat := .node node12730 node9634 +def node12732 : Tree Nat := .node node12731 node10099 +def node12733 : Tree Nat := .node node12729 node12732 +def node12734 : Tree Nat := .node node12724 node12733 +def node12735 : Tree Nat := .node node12719 node12734 +def node12736 : Tree Nat := .node node12702 node12735 +def node12737 : Tree Nat := .node node12669 node12736 +def node12738 : Tree Nat := .leaf 834 +def node12739 : Tree Nat := .node node12738 node5802 +def node12740 : Tree Nat := .node node12739 node8271 +def node12741 : Tree Nat := .node node10513 node12740 +def node12742 : Tree Nat := .leaf 850 +def node12743 : Tree Nat := .node node12742 node6554 +def node12744 : Tree Nat := .node node10812 node12743 +def node12745 : Tree Nat := .node node8697 node12690 +def node12746 : Tree Nat := .node node12379 node12745 +def node12747 : Tree Nat := .node node12744 node12746 +def node12748 : Tree Nat := .node node12741 node12747 +def node12749 : Tree Nat := .node node12748 node12389 +def node12750 : Tree Nat := .node node12742 node6186 +def node12751 : Tree Nat := .node node12750 node10117 +def node12752 : Tree Nat := .node node11099 node12751 +def node12753 : Tree Nat := .leaf 858 +def node12754 : Tree Nat := .node node12753 node6642 +def node12755 : Tree Nat := .node node10720 node12754 +def node12756 : Tree Nat := .node node12755 node12395 +def node12757 : Tree Nat := .node node12752 node12756 +def node12758 : Tree Nat := .leaf 842 +def node12759 : Tree Nat := .node node12758 node9981 +def node12760 : Tree Nat := .node node10910 node12759 +def node12761 : Tree Nat := .node node10088 node6169 +def node12762 : Tree Nat := .node node12761 node9657 +def node12763 : Tree Nat := .node node12760 node12762 +def node12764 : Tree Nat := .node node12763 node11294 +def node12765 : Tree Nat := .node node12757 node12764 +def node12766 : Tree Nat := .node node12749 node12765 +def node12767 : Tree Nat := .node node9979 node6229 +def node12768 : Tree Nat := .node node11104 node12767 +def node12769 : Tree Nat := .node node12758 node9150 +def node12770 : Tree Nat := .node node12769 node10131 +def node12771 : Tree Nat := .node node12768 node12770 +def node12772 : Tree Nat := .leaf 854 +def node12773 : Tree Nat := .node node12772 node12726 +def node12774 : Tree Nat := .node node10748 node12773 +def node12775 : Tree Nat := .node node7353 node11680 +def node12776 : Tree Nat := .node node12403 node12775 +def node12777 : Tree Nat := .node node12774 node12776 +def node12778 : Tree Nat := .node node12771 node12777 +def node12779 : Tree Nat := .leaf 838 +def node12780 : Tree Nat := .node node12779 node10006 +def node12781 : Tree Nat := .node node10939 node12780 +def node12782 : Tree Nat := .node node9219 node12738 +def node12783 : Tree Nat := .node node12407 node12782 +def node12784 : Tree Nat := .node node12781 node12783 +def node12785 : Tree Nat := .node node12784 node12412 +def node12786 : Tree Nat := .node node12778 node12785 +def node12787 : Tree Nat := .node node12753 node9249 +def node12788 : Tree Nat := .node node12787 node8309 +def node12789 : Tree Nat := .node node11110 node12788 +def node12790 : Tree Nat := .node node12789 node12420 +def node12791 : Tree Nat := .leaf 846 +def node12792 : Tree Nat := .node node12791 node7326 +def node12793 : Tree Nat := .node node10944 node12792 +def node12794 : Tree Nat := .node node12793 node12423 +def node12795 : Tree Nat := .node node10449 node9159 +def node12796 : Tree Nat := .node node12795 node9691 +def node12797 : Tree Nat := .node node12796 node11625 +def node12798 : Tree Nat := .node node12794 node12797 +def node12799 : Tree Nat := .node node12790 node12798 +def node12800 : Tree Nat := .node node12786 node12799 +def node12801 : Tree Nat := .node node12766 node12800 +def node12802 : Tree Nat := .node node12779 node9170 +def node12803 : Tree Nat := .node node12802 node8323 +def node12804 : Tree Nat := .node node11117 node12803 +def node12805 : Tree Nat := .node node6549 node12622 +def node12806 : Tree Nat := .node node10760 node12805 +def node12807 : Tree Nat := .node node10167 node12696 +def node12808 : Tree Nat := .node node12055 node12807 +def node12809 : Tree Nat := .node node12806 node12808 +def node12810 : Tree Nat := .node node12804 node12809 +def node12811 : Tree Nat := .node node12810 node12067 +def node12812 : Tree Nat := .node node12772 node9175 +def node12813 : Tree Nat := .node node12812 node10179 +def node12814 : Tree Nat := .node node11122 node12813 +def node12815 : Tree Nat := .node node12654 node12707 +def node12816 : Tree Nat := .node node10769 node12815 +def node12817 : Tree Nat := .node node12816 node11647 +def node12818 : Tree Nat := .node node12814 node12817 +def node12819 : Tree Nat := .node node12818 node12072 +def node12820 : Tree Nat := .node node12811 node12819 +def node12821 : Tree Nat := .node node12791 node9143 +def node12822 : Tree Nat := .node node12821 node10195 +def node12823 : Tree Nat := .node node11127 node12822 +def node12824 : Tree Nat := .node node10061 node11842 +def node12825 : Tree Nat := .node node12080 node12824 +def node12826 : Tree Nat := .node node12079 node12825 +def node12827 : Tree Nat := .node node12823 node12826 +def node12828 : Tree Nat := .node node12670 node10090 +def node12829 : Tree Nat := .node node10962 node12828 +def node12830 : Tree Nat := .node node12829 node12085 +def node12831 : Tree Nat := .node node12830 node12089 +def node12832 : Tree Nat := .node node12827 node12831 +def node12833 : Tree Nat := .node node12691 node9093 +def node12834 : Tree Nat := .node node12833 node8364 +def node12835 : Tree Nat := .node node11132 node12834 +def node12836 : Tree Nat := .node node12835 node11669 +def node12837 : Tree Nat := .node node10533 node9253 +def node12838 : Tree Nat := .node node12837 node12099 +def node12839 : Tree Nat := .node node12838 node6747 +def node12840 : Tree Nat := .node node12098 node12839 +def node12841 : Tree Nat := .node node12836 node12840 +def node12842 : Tree Nat := .node node12832 node12841 +def node12843 : Tree Nat := .node node12820 node12842 +def node12844 : Tree Nat := .node node12801 node12843 +def node12845 : Tree Nat := .node node12737 node12844 +def node12846 : Tree Nat := .leaf 833 +def node12847 : Tree Nat := .node node12846 node7829 +def node12848 : Tree Nat := .node node12847 node10234 +def node12849 : Tree Nat := .node node11682 node12848 +def node12850 : Tree Nat := .node node12644 node10182 +def node12851 : Tree Nat := .node node12111 node12850 +def node12852 : Tree Nat := .node node7337 node12753 +def node12853 : Tree Nat := .node node12441 node12852 +def node12854 : Tree Nat := .node node12851 node12853 +def node12855 : Tree Nat := .node node12849 node12854 +def node12856 : Tree Nat := .node node12642 node10241 +def node12857 : Tree Nat := .node node11690 node12856 +def node12858 : Tree Nat := .node node12857 node12446 +def node12859 : Tree Nat := .node node12858 node12450 +def node12860 : Tree Nat := .node node12855 node12859 +def node12861 : Tree Nat := .node node12674 node7444 +def node12862 : Tree Nat := .node node12861 node8396 +def node12863 : Tree Nat := .node node11697 node12862 +def node12864 : Tree Nat := .node node12863 node12458 +def node12865 : Tree Nat := .node node12658 node9776 +def node12866 : Tree Nat := .node node10472 node12865 +def node12867 : Tree Nat := .node node12866 node12461 +def node12868 : Tree Nat := .node node12867 node11362 +def node12869 : Tree Nat := .node node12864 node12868 +def node12870 : Tree Nat := .node node12860 node12869 +def node12871 : Tree Nat := .node node12696 node7562 +def node12872 : Tree Nat := .node node12871 node8412 +def node12873 : Tree Nat := .node node12136 node12872 +def node12874 : Tree Nat := .node node10435 node12607 +def node12875 : Tree Nat := .node node11475 node12618 +def node12876 : Tree Nat := .node node12874 node12875 +def node12877 : Tree Nat := .node node340 node12720 +def node12878 : Tree Nat := .node node12469 node12877 +def node12879 : Tree Nat := .node node12876 node12878 +def node12880 : Tree Nat := .node node12873 node12879 +def node12881 : Tree Nat := .node node9150 node12846 +def node12882 : Tree Nat := .node node12473 node12881 +def node12883 : Tree Nat := .node node10992 node12882 +def node12884 : Tree Nat := .node node12883 node12478 +def node12885 : Tree Nat := .node node12880 node12884 +def node12886 : Tree Nat := .node node12690 node7877 +def node12887 : Tree Nat := .node node12886 node8429 +def node12888 : Tree Nat := .node node11146 node12887 +def node12889 : Tree Nat := .node node8765 node12638 +def node12890 : Tree Nat := .node node10805 node12889 +def node12891 : Tree Nat := .node node12890 node12485 +def node12892 : Tree Nat := .node node12888 node12891 +def node12893 : Tree Nat := .node node11842 node7343 +def node12894 : Tree Nat := .node node10996 node12893 +def node12895 : Tree Nat := .node node12894 node12489 +def node12896 : Tree Nat := .node node12627 node7476 +def node12897 : Tree Nat := .node node12896 node9809 +def node12898 : Tree Nat := .node node12897 node11737 +def node12899 : Tree Nat := .node node12895 node12898 +def node12900 : Tree Nat := .node node12892 node12899 +def node12901 : Tree Nat := .node node12885 node12900 +def node12902 : Tree Nat := .node node12870 node12901 +def node12903 : Tree Nat := .node node12714 node5802 +def node12904 : Tree Nat := .node node12903 node10267 +def node12905 : Tree Nat := .node node11152 node12904 +def node12906 : Tree Nat := .node node10153 node12758 +def node12907 : Tree Nat := .node node12166 node12906 +def node12908 : Tree Nat := .node node10813 node12907 +def node12909 : Tree Nat := .node node12905 node12908 +def node12910 : Tree Nat := .node node12846 node10073 +def node12911 : Tree Nat := .node node10905 node12910 +def node12912 : Tree Nat := .node node9660 node11759 +def node12913 : Tree Nat := .node node12170 node12912 +def node12914 : Tree Nat := .node node12911 node12913 +def node12915 : Tree Nat := .node node12914 node12175 +def node12916 : Tree Nat := .node node12909 node12915 +def node12917 : Tree Nat := .node node12707 node6186 +def node12918 : Tree Nat := .node node12917 node8461 +def node12919 : Tree Nat := .node node11156 node12918 +def node12920 : Tree Nat := .leaf 861 +def node12921 : Tree Nat := .node node10061 node12920 +def node12922 : Tree Nat := .node node10720 node12921 +def node12923 : Tree Nat := .node node12922 node11756 +def node12924 : Tree Nat := .node node12919 node12923 +def node12925 : Tree Nat := .node node12924 node12184 +def node12926 : Tree Nat := .node node12916 node12925 +def node12927 : Tree Nat := .node node12726 node7465 +def node12928 : Tree Nat := .node node12927 node12501 +def node12929 : Tree Nat := .node node11768 node12928 +def node12930 : Tree Nat := .node node9986 node12703 +def node12931 : Tree Nat := .node node12190 node12930 +def node12932 : Tree Nat := .node node10826 node12931 +def node12933 : Tree Nat := .node node12929 node12932 +def node12934 : Tree Nat := .node node12933 node12200 +def node12935 : Tree Nat := .node node12920 node7962 +def node12936 : Tree Nat := .node node12935 node9412 +def node12937 : Tree Nat := .node node11166 node12936 +def node12938 : Tree Nat := .node node12920 node11520 +def node12939 : Tree Nat := .node node10830 node12938 +def node12940 : Tree Nat := .node node12939 node11784 +def node12941 : Tree Nat := .node node12937 node12940 +def node12942 : Tree Nat := .node node10435 node12779 +def node12943 : Tree Nat := .node node12942 node10317 +def node12944 : Tree Nat := .node node12943 node12210 +def node12945 : Tree Nat := .node node10482 node7593 +def node12946 : Tree Nat := .node node12945 node12212 +def node12947 : Tree Nat := .node node12946 node10321 +def node12948 : Tree Nat := .node node12944 node12947 +def node12949 : Tree Nat := .node node12941 node12948 +def node12950 : Tree Nat := .node node12934 node12949 +def node12951 : Tree Nat := .node node12926 node12950 +def node12952 : Tree Nat := .node node12902 node12951 +def node12953 : Tree Nat := .node node12642 node7898 +def node12954 : Tree Nat := .node node12953 node10328 +def node12955 : Tree Nat := .node node11174 node12954 +def node12956 : Tree Nat := .node node10040 node12686 +def node12957 : Tree Nat := .node node12512 node12956 +def node12958 : Tree Nat := .node node12224 node12957 +def node12959 : Tree Nat := .node node12955 node12958 +def node12960 : Tree Nat := .node node12738 node9776 +def node12961 : Tree Nat := .node node12229 node12960 +def node12962 : Tree Nat := .node node12961 node12517 +def node12963 : Tree Nat := .node node12962 node12521 +def node12964 : Tree Nat := .node node12959 node12963 +def node12965 : Tree Nat := .node node12644 node7457 +def node12966 : Tree Nat := .node node12965 node8527 +def node12967 : Tree Nat := .node node11808 node12966 +def node12968 : Tree Nat := .node node12967 node12529 +def node12969 : Tree Nat := .node node12968 node12534 +def node12970 : Tree Nat := .node node12964 node12969 +def node12971 : Tree Nat := .node node12658 node10458 +def node12972 : Tree Nat := .node node6764 node12627 +def node12973 : Tree Nat := .node node12971 node12972 +def node12974 : Tree Nat := .node node11428 node12973 +def node12975 : Tree Nat := .node node6659 node12791 +def node12976 : Tree Nat := .node node12247 node12975 +def node12977 : Tree Nat := .node node10241 node12742 +def node12978 : Tree Nat := .node node12541 node12977 +def node12979 : Tree Nat := .node node12976 node12978 +def node12980 : Tree Nat := .node node12974 node12979 +def node12981 : Tree Nat := .node node12980 node12553 +def node12982 : Tree Nat := .node node12622 node10458 +def node12983 : Tree Nat := .node node12982 node8550 +def node12984 : Tree Nat := .node node11189 node12983 +def node12985 : Tree Nat := .node node12691 node8983 +def node12986 : Tree Nat := .node node10854 node12985 +def node12987 : Tree Nat := .node node12986 node12559 +def node12988 : Tree Nat := .node node12984 node12987 +def node12989 : Tree Nat := .node node10648 node10533 +def node12990 : Tree Nat := .node node12989 node12277 +def node12991 : Tree Nat := .node node12990 node11844 +def node12992 : Tree Nat := .node node12564 node12991 +def node12993 : Tree Nat := .node node12988 node12992 +def node12994 : Tree Nat := .node node12981 node12993 +def node12995 : Tree Nat := .node node12970 node12994 +def node12996 : Tree Nat := .node node12618 node12654 +def node12997 : Tree Nat := .node node10676 node12996 +def node12998 : Tree Nat := .node node12997 node11854 +def node12999 : Tree Nat := .node node11852 node12998 +def node13000 : Tree Nat := .node node12607 node8395 +def node13001 : Tree Nat := .node node11049 node13000 +def node13002 : Tree Nat := .node node13001 node11858 +def node13003 : Tree Nat := .node node13002 node12286 +def node13004 : Tree Nat := .node node12999 node13003 +def node13005 : Tree Nat := .node node7333 node12772 +def node13006 : Tree Nat := .node node10692 node13005 +def node13007 : Tree Nat := .node node13006 node11452 +def node13008 : Tree Nat := .node node12570 node13007 +def node13009 : Tree Nat := .node node12638 node7916 +def node13010 : Tree Nat := .node node10676 node13009 +def node13011 : Tree Nat := .node node13010 node11456 +def node13012 : Tree Nat := .node node13011 node10678 +def node13013 : Tree Nat := .node node13008 node13012 +def node13014 : Tree Nat := .node node13004 node13013 +def node13015 : Tree Nat := .node node11427 node9053 +def node13016 : Tree Nat := .node node13015 node12575 +def node13017 : Tree Nat := .node node12686 node11735 +def node13018 : Tree Nat := .node node10870 node13017 +def node13019 : Tree Nat := .node node13018 node12578 +def node13020 : Tree Nat := .node node13016 node13019 +def node13021 : Tree Nat := .node node13020 node12584 +def node13022 : Tree Nat := .node node12720 node8308 +def node13023 : Tree Nat := .node node12234 node13022 +def node13024 : Tree Nat := .node node13023 node11462 +def node13025 : Tree Nat := .node node12588 node13024 +def node13026 : Tree Nat := .node node12703 node10241 +def node13027 : Tree Nat := .node node12223 node13026 +def node13028 : Tree Nat := .node node13027 node12594 +def node13029 : Tree Nat := .node node10458 node11520 +def node13030 : Tree Nat := .node node13029 node12597 +def node13031 : Tree Nat := .node node13030 node10426 +def node13032 : Tree Nat := .node node13028 node13031 +def node13033 : Tree Nat := .node node13025 node13032 +def node13034 : Tree Nat := .node node13021 node13033 +def node13035 : Tree Nat := .node node13014 node13034 +def node13036 : Tree Nat := .node node12995 node13035 +def node13037 : Tree Nat := .node node12952 node13036 +def node13038 : Tree Nat := .node node12845 node13037 +def node13039 : Tree Nat := .leaf 896 +def node13040 : Tree Nat := .node node13039 node9979 +def node13041 : Tree Nat := .node node9981 node11766 +def node13042 : Tree Nat := .node node13040 node13041 +def node13043 : Tree Nat := .node node12611 node13042 +def node13044 : Tree Nat := .node node12610 node13043 +def node13045 : Tree Nat := .leaf 864 +def node13046 : Tree Nat := .node node13045 node10449 +def node13047 : Tree Nat := .node node13046 node8170 +def node13048 : Tree Nat := .node node12614 node13047 +def node13049 : Tree Nat := .node node13048 node12312 +def node13050 : Tree Nat := .node node13044 node13049 +def node13051 : Tree Nat := .node node9976 node11623 +def node13052 : Tree Nat := .node node12318 node13051 +def node13053 : Tree Nat := .node node12624 node13052 +def node13054 : Tree Nat := .node node12621 node13053 +def node13055 : Tree Nat := .leaf 880 +def node13056 : Tree Nat := .node node13055 node9979 +def node13057 : Tree Nat := .node node13056 node9545 +def node13058 : Tree Nat := .node node12629 node13057 +def node13059 : Tree Nat := .node node13058 node12634 +def node13060 : Tree Nat := .node node13054 node13059 +def node13061 : Tree Nat := .node node13050 node13060 +def node13062 : Tree Nat := .node node11426 node6549 +def node13063 : Tree Nat := .node node12639 node13062 +def node13064 : Tree Nat := .node node11923 node13063 +def node13065 : Tree Nat := .leaf 904 +def node13066 : Tree Nat := .node node13065 node7745 +def node13067 : Tree Nat := .leaf 866 +def node13068 : Tree Nat := .node node10023 node13067 +def node13069 : Tree Nat := .node node13066 node13068 +def node13070 : Tree Nat := .node node12646 node13069 +def node13071 : Tree Nat := .node node13064 node13070 +def node13072 : Tree Nat := .leaf 872 +def node13073 : Tree Nat := .node node13072 node7752 +def node13074 : Tree Nat := .node node13073 node8672 +def node13075 : Tree Nat := .node node12650 node13074 +def node13076 : Tree Nat := .leaf 901 +def node13077 : Tree Nat := .node node11623 node13076 +def node13078 : Tree Nat := .node node10477 node13077 +def node13079 : Tree Nat := .node node13078 node12339 +def node13080 : Tree Nat := .node node13075 node13079 +def node13081 : Tree Nat := .node node13071 node13080 +def node13082 : Tree Nat := .node node11766 node6962 +def node13083 : Tree Nat := .node node12655 node13082 +def node13084 : Tree Nat := .node node11074 node13083 +def node13085 : Tree Nat := .node node10032 node11735 +def node13086 : Tree Nat := .node node12346 node13085 +def node13087 : Tree Nat := .node node12660 node13086 +def node13088 : Tree Nat := .node node13084 node13087 +def node13089 : Tree Nat := .leaf 875 +def node13090 : Tree Nat := .node node10435 node13089 +def node13091 : Tree Nat := .node node13090 node7356 +def node13092 : Tree Nat := .leaf 888 +def node13093 : Tree Nat := .node node13092 node7773 +def node13094 : Tree Nat := .node node13093 node10041 +def node13095 : Tree Nat := .node node13091 node13094 +def node13096 : Tree Nat := .node node13095 node12665 +def node13097 : Tree Nat := .node node13088 node13096 +def node13098 : Tree Nat := .node node13081 node13097 +def node13099 : Tree Nat := .node node13061 node13098 +def node13100 : Tree Nat := .leaf 900 +def node13101 : Tree Nat := .node node13100 node10000 +def node13102 : Tree Nat := .node node13101 node12677 +def node13103 : Tree Nat := .node node12676 node13102 +def node13104 : Tree Nat := .node node12673 node13103 +def node13105 : Tree Nat := .leaf 883 +def node13106 : Tree Nat := .node node6574 node13105 +def node13107 : Tree Nat := .node node10905 node13106 +def node13108 : Tree Nat := .leaf 868 +def node13109 : Tree Nat := .node node13108 node6176 +def node13110 : Tree Nat := .leaf 897 +def node13111 : Tree Nat := .node node13110 node12670 +def node13112 : Tree Nat := .node node13109 node13111 +def node13113 : Tree Nat := .node node13107 node13112 +def node13114 : Tree Nat := .node node13113 node11962 +def node13115 : Tree Nat := .node node13104 node13114 +def node13116 : Tree Nat := .node node7384 node13110 +def node13117 : Tree Nat := .node node11965 node13116 +def node13118 : Tree Nat := .node node12693 node13117 +def node13119 : Tree Nat := .node node12689 node13118 +def node13120 : Tree Nat := .leaf 884 +def node13121 : Tree Nat := .node node13120 node6169 +def node13122 : Tree Nat := .node node13121 node10067 +def node13123 : Tree Nat := .node node12698 node13122 +def node13124 : Tree Nat := .leaf 873 +def node13125 : Tree Nat := .node node13124 node8668 +def node13126 : Tree Nat := .node node10499 node13125 +def node13127 : Tree Nat := .node node13126 node11546 +def node13128 : Tree Nat := .node node13123 node13127 +def node13129 : Tree Nat := .node node13119 node13128 +def node13130 : Tree Nat := .node node13115 node13129 +def node13131 : Tree Nat := .leaf 885 +def node13132 : Tree Nat := .node node13131 node8677 +def node13133 : Tree Nat := .node node12704 node13132 +def node13134 : Tree Nat := .node node11087 node13133 +def node13135 : Tree Nat := .leaf 877 +def node13136 : Tree Nat := .node node10435 node13135 +def node13137 : Tree Nat := .leaf 867 +def node13138 : Tree Nat := .node node12707 node13137 +def node13139 : Tree Nat := .node node13136 node13138 +def node13140 : Tree Nat := .node node13139 node12711 +def node13141 : Tree Nat := .node node13134 node13140 +def node13142 : Tree Nat := .leaf 876 +def node13143 : Tree Nat := .node node13142 node7718 +def node13144 : Tree Nat := .node node13076 node13124 +def node13145 : Tree Nat := .node node13143 node13144 +def node13146 : Tree Nat := .node node12716 node13145 +def node13147 : Tree Nat := .leaf 869 +def node13148 : Tree Nat := .node node13147 node6546 +def node13149 : Tree Nat := .node node10505 node13148 +def node13150 : Tree Nat := .node node13149 node11989 +def node13151 : Tree Nat := .node node13146 node13150 +def node13152 : Tree Nat := .node node13141 node13151 +def node13153 : Tree Nat := .leaf 893 +def node13154 : Tree Nat := .node node13153 node8256 +def node13155 : Tree Nat := .node node12721 node13154 +def node13156 : Tree Nat := .node node11091 node13155 +def node13157 : Tree Nat := .node node13156 node11995 +def node13158 : Tree Nat := .node node12726 node13131 +def node13159 : Tree Nat := .node node12725 node13158 +def node13160 : Tree Nat := .leaf 892 +def node13161 : Tree Nat := .node node13160 node7821 +def node13162 : Tree Nat := .node node13161 node10094 +def node13163 : Tree Nat := .node node13159 node13162 +def node13164 : Tree Nat := .node node13135 node6606 +def node13165 : Tree Nat := .node node12730 node13164 +def node13166 : Tree Nat := .node node13165 node10099 +def node13167 : Tree Nat := .node node13163 node13166 +def node13168 : Tree Nat := .node node13157 node13167 +def node13169 : Tree Nat := .node node13152 node13168 +def node13170 : Tree Nat := .node node13130 node13169 +def node13171 : Tree Nat := .node node13099 node13170 +def node13172 : Tree Nat := .leaf 898 +def node13173 : Tree Nat := .node node13172 node340 +def node13174 : Tree Nat := .node node13173 node12745 +def node13175 : Tree Nat := .node node12744 node13174 +def node13176 : Tree Nat := .node node12741 node13175 +def node13177 : Tree Nat := .node node13067 node6176 +def node13178 : Tree Nat := .node node13172 node8260 +def node13179 : Tree Nat := .node node13177 node13178 +def node13180 : Tree Nat := .node node10930 node13179 +def node13181 : Tree Nat := .node node13180 node12388 +def node13182 : Tree Nat := .node node13176 node13181 +def node13183 : Tree Nat := .leaf 890 +def node13184 : Tree Nat := .node node8692 node13183 +def node13185 : Tree Nat := .node node12394 node13184 +def node13186 : Tree Nat := .node node12755 node13185 +def node13187 : Tree Nat := .node node12752 node13186 +def node13188 : Tree Nat := .leaf 882 +def node13189 : Tree Nat := .node node13188 node6169 +def node13190 : Tree Nat := .node node13189 node9657 +def node13191 : Tree Nat := .node node12760 node13190 +def node13192 : Tree Nat := .leaf 874 +def node13193 : Tree Nat := .node node13192 node7742 +def node13194 : Tree Nat := .node node10499 node13193 +def node13195 : Tree Nat := .node node13194 node11293 +def node13196 : Tree Nat := .node node13191 node13195 +def node13197 : Tree Nat := .node node13187 node13196 +def node13198 : Tree Nat := .node node13182 node13197 +def node13199 : Tree Nat := .leaf 886 +def node13200 : Tree Nat := .node node13199 node6659 +def node13201 : Tree Nat := .node node12769 node13200 +def node13202 : Tree Nat := .node node12768 node13201 +def node13203 : Tree Nat := .node node13202 node12777 +def node13204 : Tree Nat := .node node13192 node8718 +def node13205 : Tree Nat := .leaf 902 +def node13206 : Tree Nat := .node node13205 node12738 +def node13207 : Tree Nat := .node node13204 node13206 +def node13208 : Tree Nat := .node node12781 node13207 +def node13209 : Tree Nat := .leaf 870 +def node13210 : Tree Nat := .node node13209 node9101 +def node13211 : Tree Nat := .node node10525 node13210 +def node13212 : Tree Nat := .node node13211 node12411 +def node13213 : Tree Nat := .node node13208 node13212 +def node13214 : Tree Nat := .node node13203 node13213 +def node13215 : Tree Nat := .leaf 894 +def node13216 : Tree Nat := .node node13215 node8245 +def node13217 : Tree Nat := .node node12787 node13216 +def node13218 : Tree Nat := .node node11110 node13217 +def node13219 : Tree Nat := .node node8681 node13147 +def node13220 : Tree Nat := .node node10753 node13219 +def node13221 : Tree Nat := .node node13220 node12419 +def node13222 : Tree Nat := .node node13218 node13221 +def node13223 : Tree Nat := .node node13183 node8689 +def node13224 : Tree Nat := .node node13223 node10154 +def node13225 : Tree Nat := .node node12793 node13224 +def node13226 : Tree Nat := .leaf 878 +def node13227 : Tree Nat := .node node13226 node6596 +def node13228 : Tree Nat := .node node12795 node13227 +def node13229 : Tree Nat := .node node13228 node11625 +def node13230 : Tree Nat := .node node13225 node13229 +def node13231 : Tree Nat := .node node13222 node13230 +def node13232 : Tree Nat := .node node13214 node13231 +def node13233 : Tree Nat := .node node13198 node13232 +def node13234 : Tree Nat := .node node13205 node8765 +def node13235 : Tree Nat := .node node13234 node12807 +def node13236 : Tree Nat := .node node12806 node13235 +def node13237 : Tree Nat := .node node12804 node13236 +def node13238 : Tree Nat := .node node13209 node8706 +def node13239 : Tree Nat := .node node9705 node13142 +def node13240 : Tree Nat := .node node13238 node13239 +def node13241 : Tree Nat := .node node10952 node13240 +def node13242 : Tree Nat := .node node13241 node12066 +def node13243 : Tree Nat := .node node13237 node13242 +def node13244 : Tree Nat := .node node13188 node7074 +def node13245 : Tree Nat := .node node12812 node13244 +def node13246 : Tree Nat := .node node11122 node13245 +def node13247 : Tree Nat := .node node13246 node12817 +def node13248 : Tree Nat := .node node13199 node8743 +def node13249 : Tree Nat := .node node9728 node11426 +def node13250 : Tree Nat := .node node13248 node13249 +def node13251 : Tree Nat := .node node10957 node13250 +def node13252 : Tree Nat := .leaf 899 +def node13253 : Tree Nat := .node node9289 node13252 +def node13254 : Tree Nat := .node node10539 node13253 +def node13255 : Tree Nat := .node node13254 node10542 +def node13256 : Tree Nat := .node node13251 node13255 +def node13257 : Tree Nat := .node node13247 node13256 +def node13258 : Tree Nat := .node node13243 node13257 +def node13259 : Tree Nat := .leaf 881 +def node13260 : Tree Nat := .node node10435 node13259 +def node13261 : Tree Nat := .node node13260 node8854 +def node13262 : Tree Nat := .node node13120 node8197 +def node13263 : Tree Nat := .node node12821 node13262 +def node13264 : Tree Nat := .node node13261 node13263 +def node13265 : Tree Nat := .node node13264 node12826 +def node13266 : Tree Nat := .node node13226 node8829 +def node13267 : Tree Nat := .node node13266 node9745 +def node13268 : Tree Nat := .node node12829 node13267 +def node13269 : Tree Nat := .node node13108 node6733 +def node13270 : Tree Nat := .node node10547 node13269 +def node13271 : Tree Nat := .node node13270 node12088 +def node13272 : Tree Nat := .node node13268 node13271 +def node13273 : Tree Nat := .node node13265 node13272 +def node13274 : Tree Nat := .node node13160 node8238 +def node13275 : Tree Nat := .node node12833 node13274 +def node13276 : Tree Nat := .node node11132 node13275 +def node13277 : Tree Nat := .node node13276 node11669 +def node13278 : Tree Nat := .node node13215 node8729 +def node13279 : Tree Nat := .node node13278 node10223 +def node13280 : Tree Nat := .node node10968 node13279 +def node13281 : Tree Nat := .node node13280 node12839 +def node13282 : Tree Nat := .node node13277 node13281 +def node13283 : Tree Nat := .node node13273 node13282 +def node13284 : Tree Nat := .node node13258 node13283 +def node13285 : Tree Nat := .node node13233 node13284 +def node13286 : Tree Nat := .node node13171 node13285 +def node13287 : Tree Nat := .node node13105 node7887 +def node13288 : Tree Nat := .node node12847 node13287 +def node13289 : Tree Nat := .node node11682 node13288 +def node13290 : Tree Nat := .node node13110 node6946 +def node13291 : Tree Nat := .node node13290 node12852 +def node13292 : Tree Nat := .node node12851 node13291 +def node13293 : Tree Nat := .node node13289 node13292 +def node13294 : Tree Nat := .leaf 865 +def node13295 : Tree Nat := .node node13294 node7787 +def node13296 : Tree Nat := .node node13252 node8386 +def node13297 : Tree Nat := .node node13295 node13296 +def node13298 : Tree Nat := .node node12857 node13297 +def node13299 : Tree Nat := .node node13137 node13092 +def node13300 : Tree Nat := .node node12120 node13299 +def node13301 : Tree Nat := .node node13300 node12449 +def node13302 : Tree Nat := .node node13298 node13301 +def node13303 : Tree Nat := .node node13293 node13302 +def node13304 : Tree Nat := .leaf 891 +def node13305 : Tree Nat := .node node13304 node7747 +def node13306 : Tree Nat := .node node12861 node13305 +def node13307 : Tree Nat := .node node11697 node13306 +def node13308 : Tree Nat := .leaf 889 +def node13309 : Tree Nat := .node node7395 node13308 +def node13310 : Tree Nat := .node node12456 node13309 +def node13311 : Tree Nat := .node node12127 node13310 +def node13312 : Tree Nat := .node node13307 node13311 +def node13313 : Tree Nat := .node node13259 node7051 +def node13314 : Tree Nat := .node node13313 node10250 +def node13315 : Tree Nat := .node node12866 node13314 +def node13316 : Tree Nat := .node node13089 node8298 +def node13317 : Tree Nat := .node node10566 node13316 +def node13318 : Tree Nat := .node node13317 node11361 +def node13319 : Tree Nat := .node node13315 node13318 +def node13320 : Tree Nat := .node node13312 node13319 +def node13321 : Tree Nat := .node node13303 node13320 +def node13322 : Tree Nat := .node node13124 node7797 +def node13323 : Tree Nat := .node node11735 node12846 +def node13324 : Tree Nat := .node node13322 node13323 +def node13325 : Tree Nat := .node node10992 node13324 +def node13326 : Tree Nat := .node node411 node13205 +def node13327 : Tree Nat := .node node10577 node13326 +def node13328 : Tree Nat := .node node13327 node12477 +def node13329 : Tree Nat := .node node13325 node13328 +def node13330 : Tree Nat := .node node12880 node13329 +def node13331 : Tree Nat := .node node11680 node12638 +def node13332 : Tree Nat := .node node10805 node13331 +def node13333 : Tree Nat := .node node13332 node12485 +def node13334 : Tree Nat := .node node12888 node13333 +def node13335 : Tree Nat := .node node10435 node13072 +def node13336 : Tree Nat := .node node13335 node12893 +def node13337 : Tree Nat := .node node13308 node8002 +def node13338 : Tree Nat := .node node13337 node9806 +def node13339 : Tree Nat := .node node13336 node13338 +def node13340 : Tree Nat := .node node11544 node9330 +def node13341 : Tree Nat := .node node12896 node13340 +def node13342 : Tree Nat := .node node13341 node11737 +def node13343 : Tree Nat := .node node13339 node13342 +def node13344 : Tree Nat := .node node13334 node13343 +def node13345 : Tree Nat := .node node13330 node13344 +def node13346 : Tree Nat := .node node13321 node13345 +def node13347 : Tree Nat := .node node13259 node8233 +def node13348 : Tree Nat := .node node12903 node13347 +def node13349 : Tree Nat := .node node11152 node13348 +def node13350 : Tree Nat := .node node10093 node13215 +def node13351 : Tree Nat := .node node10812 node13350 +def node13352 : Tree Nat := .node node13076 node8784 +def node13353 : Tree Nat := .node node13352 node12906 +def node13354 : Tree Nat := .node node13351 node13353 +def node13355 : Tree Nat := .node node13349 node13354 +def node13356 : Tree Nat := .node node12846 node13055 +def node13357 : Tree Nat := .node node10905 node13356 +def node13358 : Tree Nat := .node node13147 node6176 +def node13359 : Tree Nat := .node node13358 node12912 +def node13360 : Tree Nat := .node node13357 node13359 +def node13361 : Tree Nat := .node node13294 node8249 +def node13362 : Tree Nat := .node node10715 node13361 +def node13363 : Tree Nat := .node node13362 node12174 +def node13364 : Tree Nat := .node node13360 node13363 +def node13365 : Tree Nat := .node node13355 node13364 +def node13366 : Tree Nat := .node node13308 node8342 +def node13367 : Tree Nat := .node node12917 node13366 +def node13368 : Tree Nat := .node node11156 node13367 +def node13369 : Tree Nat := .node node13368 node12923 +def node13370 : Tree Nat := .node node13131 node6169 +def node13371 : Tree Nat := .node node9544 node13120 +def node13372 : Tree Nat := .node node13370 node13371 +def node13373 : Tree Nat := .node node11007 node13372 +def node13374 : Tree Nat := .node node13373 node12183 +def node13375 : Tree Nat := .node node13369 node13374 +def node13376 : Tree Nat := .node node13365 node13375 +def node13377 : Tree Nat := .node node10435 node13226 +def node13378 : Tree Nat := .node node8812 node13045 +def node13379 : Tree Nat := .node node13377 node13378 +def node13380 : Tree Nat := .node node13379 node12931 +def node13381 : Tree Nat := .node node12929 node13380 +def node13382 : Tree Nat := .node node13135 node7923 +def node13383 : Tree Nat := .node node13382 node10301 +def node13384 : Tree Nat := .node node11012 node13383 +def node13385 : Tree Nat := .node node13384 node12199 +def node13386 : Tree Nat := .node node13381 node13385 +def node13387 : Tree Nat := .node node10435 node13065 +def node13388 : Tree Nat := .node node13387 node12938 +def node13389 : Tree Nat := .node node13388 node11784 +def node13390 : Tree Nat := .node node12937 node13389 +def node13391 : Tree Nat := .node node6929 node13199 +def node13392 : Tree Nat := .node node12942 node13391 +def node13393 : Tree Nat := .node node13153 node7735 +def node13394 : Tree Nat := .node node13393 node9866 +def node13395 : Tree Nat := .node node13392 node13394 +def node13396 : Tree Nat := .node node13395 node12947 +def node13397 : Tree Nat := .node node13390 node13396 +def node13398 : Tree Nat := .node node13386 node13397 +def node13399 : Tree Nat := .node node13376 node13398 +def node13400 : Tree Nat := .node node13346 node13399 +def node13401 : Tree Nat := .node node13188 node8175 +def node13402 : Tree Nat := .node node12953 node13401 +def node13403 : Tree Nat := .node node11174 node13402 +def node13404 : Tree Nat := .node node8983 node13153 +def node13405 : Tree Nat := .node node12223 node13404 +def node13406 : Tree Nat := .node node13252 node7163 +def node13407 : Tree Nat := .node node13406 node12956 +def node13408 : Tree Nat := .node node13405 node13407 +def node13409 : Tree Nat := .node node13403 node13408 +def node13410 : Tree Nat := .node node13137 node7893 +def node13411 : Tree Nat := .node node13410 node8522 +def node13412 : Tree Nat := .node node12961 node13411 +def node13413 : Tree Nat := .node node13067 node7845 +def node13414 : Tree Nat := .node node12234 node13413 +def node13415 : Tree Nat := .node node13414 node12520 +def node13416 : Tree Nat := .node node13412 node13415 +def node13417 : Tree Nat := .node node13409 node13416 +def node13418 : Tree Nat := .node node13183 node8200 +def node13419 : Tree Nat := .node node12965 node13418 +def node13420 : Tree Nat := .node node11808 node13419 +def node13421 : Tree Nat := .node node10135 node13172 +def node13422 : Tree Nat := .node node12527 node13421 +def node13423 : Tree Nat := .node node12242 node13422 +def node13424 : Tree Nat := .node node13420 node13423 +def node13425 : Tree Nat := .node node13105 node7059 +def node13426 : Tree Nat := .node node13425 node9892 +def node13427 : Tree Nat := .node node12248 node13426 +def node13428 : Tree Nat := .node node13427 node11816 +def node13429 : Tree Nat := .node node13424 node13428 +def node13430 : Tree Nat := .node node13417 node13429 +def node13431 : Tree Nat := .node node13089 node10533 +def node13432 : Tree Nat := .node node6554 node13192 +def node13433 : Tree Nat := .node node13431 node13432 +def node13434 : Tree Nat := .node node12545 node13433 +def node13435 : Tree Nat := .node node13434 node12552 +def node13436 : Tree Nat := .node node12980 node13435 +def node13437 : Tree Nat := .node node12691 node13209 +def node13438 : Tree Nat := .node node10854 node13437 +def node13439 : Tree Nat := .node node13438 node12559 +def node13440 : Tree Nat := .node node12984 node13439 +def node13441 : Tree Nat := .node node13304 node10458 +def node13442 : Tree Nat := .node node13441 node9913 +def node13443 : Tree Nat := .node node11043 node13442 +def node13444 : Tree Nat := .node node13443 node12991 +def node13445 : Tree Nat := .node node13440 node13444 +def node13446 : Tree Nat := .node node13436 node13445 +def node13447 : Tree Nat := .node node13430 node13446 +def node13448 : Tree Nat := .node node13055 node8315 +def node13449 : Tree Nat := .node node11850 node13448 +def node13450 : Tree Nat := .node node11195 node13449 +def node13451 : Tree Nat := .node node6180 node13294 +def node13452 : Tree Nat := .node node11853 node13451 +def node13453 : Tree Nat := .node node12997 node13452 +def node13454 : Tree Nat := .node node13450 node13453 +def node13455 : Tree Nat := .node node13039 node11544 +def node13456 : Tree Nat := .node node11857 node13455 +def node13457 : Tree Nat := .node node13001 node13456 +def node13458 : Tree Nat := .node node13045 node11842 +def node13459 : Tree Nat := .node node10459 node13458 +def node13460 : Tree Nat := .node node13459 node11447 +def node13461 : Tree Nat := .node node13457 node13460 +def node13462 : Tree Nat := .node node13454 node13461 +def node13463 : Tree Nat := .node node13092 node8372 +def node13464 : Tree Nat := .node node11862 node13463 +def node13465 : Tree Nat := .node node12569 node13464 +def node13466 : Tree Nat := .node node6348 node13100 +def node13467 : Tree Nat := .node node11451 node13466 +def node13468 : Tree Nat := .node node13006 node13467 +def node13469 : Tree Nat := .node node13465 node13468 +def node13470 : Tree Nat := .node node13072 node13039 +def node13471 : Tree Nat := .node node10676 node13470 +def node13472 : Tree Nat := .node node13471 node9939 +def node13473 : Tree Nat := .node node13011 node13472 +def node13474 : Tree Nat := .node node13469 node13473 +def node13475 : Tree Nat := .node node13462 node13474 +def node13476 : Tree Nat := .node node7470 node13108 +def node13477 : Tree Nat := .node node12577 node13476 +def node13478 : Tree Nat := .node node13018 node13477 +def node13479 : Tree Nat := .node node13016 node13478 +def node13480 : Tree Nat := .node node13100 node10135 +def node13481 : Tree Nat := .node node12581 node13480 +def node13482 : Tree Nat := .node node11060 node13481 +def node13483 : Tree Nat := .node node13482 node11880 +def node13484 : Tree Nat := .node node13479 node13483 +def node13485 : Tree Nat := .node node12720 node13304 +def node13486 : Tree Nat := .node node12234 node13485 +def node13487 : Tree Nat := .node node13486 node11462 +def node13488 : Tree Nat := .node node12588 node13487 +def node13489 : Tree Nat := .node node7068 node13160 +def node13490 : Tree Nat := .node node12593 node13489 +def node13491 : Tree Nat := .node node13027 node13490 +def node13492 : Tree Nat := .node node13142 node11680 +def node13493 : Tree Nat := .node node13029 node13492 +def node13494 : Tree Nat := .node node13493 node10426 +def node13495 : Tree Nat := .node node13491 node13494 +def node13496 : Tree Nat := .node node13488 node13495 +def node13497 : Tree Nat := .node node13484 node13496 +def node13498 : Tree Nat := .node node13475 node13497 +def node13499 : Tree Nat := .node node13447 node13498 +def node13500 : Tree Nat := .node node13400 node13499 +def node13501 : Tree Nat := .node node13286 node13500 +def node13502 : Tree Nat := .leaf 926 +def node13503 : Tree Nat := .node node8635 node13502 +def node13504 : Tree Nat := .node node10437 node13503 +def node13505 : Tree Nat := .leaf 915 +def node13506 : Tree Nat := .node node13505 node11766 +def node13507 : Tree Nat := .node node13040 node13506 +def node13508 : Tree Nat := .node node13504 node13507 +def node13509 : Tree Nat := .node node12610 node13508 +def node13510 : Tree Nat := .leaf 928 +def node13511 : Tree Nat := .node node13510 node8640 +def node13512 : Tree Nat := .leaf 931 +def node13513 : Tree Nat := .node node13512 node1 +def node13514 : Tree Nat := .node node13511 node13513 +def node13515 : Tree Nat := .node node10693 node13514 +def node13516 : Tree Nat := .node node13048 node13515 +def node13517 : Tree Nat := .node node13509 node13516 +def node13518 : Tree Nat := .leaf 912 +def node13519 : Tree Nat := .node node13518 node10000 +def node13520 : Tree Nat := .leaf 923 +def node13521 : Tree Nat := .node node13520 node11623 +def node13522 : Tree Nat := .node node13519 node13521 +def node13523 : Tree Nat := .node node12624 node13522 +def node13524 : Tree Nat := .node node12621 node13523 +def node13525 : Tree Nat := .node node6539 node13520 +def node13526 : Tree Nat := .node node12628 node13525 +def node13527 : Tree Nat := .leaf 907 +def node13528 : Tree Nat := .node node13527 node11813 +def node13529 : Tree Nat := .node node13056 node13528 +def node13530 : Tree Nat := .node node13526 node13529 +def node13531 : Tree Nat := .leaf 939 +def node13532 : Tree Nat := .node node13531 node1 +def node13533 : Tree Nat := .node node11233 node13532 +def node13534 : Tree Nat := .node node12633 node13533 +def node13535 : Tree Nat := .node node13530 node13534 +def node13536 : Tree Nat := .node node13524 node13535 +def node13537 : Tree Nat := .node node13517 node13536 +def node13538 : Tree Nat := .node node11232 node13067 +def node13539 : Tree Nat := .node node13066 node13538 +def node13540 : Tree Nat := .node node12646 node13539 +def node13541 : Tree Nat := .node node13064 node13540 +def node13542 : Tree Nat := .leaf 910 +def node13543 : Tree Nat := .node node10435 node13542 +def node13544 : Tree Nat := .node node13543 node13077 +def node13545 : Tree Nat := .leaf 936 +def node13546 : Tree Nat := .node node13545 node9540 +def node13547 : Tree Nat := .node node11291 node1 +def node13548 : Tree Nat := .node node13546 node13547 +def node13549 : Tree Nat := .node node13544 node13548 +def node13550 : Tree Nat := .node node13075 node13549 +def node13551 : Tree Nat := .node node13541 node13550 +def node13552 : Tree Nat := .leaf 934 +def node13553 : Tree Nat := .node node10435 node13552 +def node13554 : Tree Nat := .node node13553 node12659 +def node13555 : Tree Nat := .leaf 920 +def node13556 : Tree Nat := .node node13555 node7768 +def node13557 : Tree Nat := .node node11359 node11735 +def node13558 : Tree Nat := .node node13556 node13557 +def node13559 : Tree Nat := .node node13554 node13558 +def node13560 : Tree Nat := .node node13084 node13559 +def node13561 : Tree Nat := .leaf 916 +def node13562 : Tree Nat := .node node11813 node13561 +def node13563 : Tree Nat := .node node13093 node13562 +def node13564 : Tree Nat := .node node13091 node13563 +def node13565 : Tree Nat := .node node5802 node13531 +def node13566 : Tree Nat := .node node12663 node13565 +def node13567 : Tree Nat := .node node13566 node11522 +def node13568 : Tree Nat := .node node13564 node13567 +def node13569 : Tree Nat := .node node13560 node13568 +def node13570 : Tree Nat := .node node13551 node13569 +def node13571 : Tree Nat := .node node13537 node13570 +def node13572 : Tree Nat := .leaf 932 +def node13573 : Tree Nat := .node node13572 node8668 +def node13574 : Tree Nat := .node node13573 node6983 +def node13575 : Tree Nat := .node node10716 node13574 +def node13576 : Tree Nat := .node node13113 node13575 +def node13577 : Tree Nat := .node node13104 node13576 +def node13578 : Tree Nat := .leaf 913 +def node13579 : Tree Nat := .node node10435 node13578 +def node13580 : Tree Nat := .node node10435 node9981 +def node13581 : Tree Nat := .node node13579 node13580 +def node13582 : Tree Nat := .node node13581 node12688 +def node13583 : Tree Nat := .node node13561 node195 +def node13584 : Tree Nat := .node node13583 node13116 +def node13585 : Tree Nat := .node node12693 node13584 +def node13586 : Tree Nat := .node node13582 node13585 +def node13587 : Tree Nat := .leaf 914 +def node13588 : Tree Nat := .node node6584 node13587 +def node13589 : Tree Nat := .node node13121 node13588 +def node13590 : Tree Nat := .node node12698 node13589 +def node13591 : Tree Nat := .leaf 937 +def node13592 : Tree Nat := .node node13591 node1 +def node13593 : Tree Nat := .node node11545 node13592 +def node13594 : Tree Nat := .node node13126 node13593 +def node13595 : Tree Nat := .node node13590 node13594 +def node13596 : Tree Nat := .node node13586 node13595 +def node13597 : Tree Nat := .node node13577 node13596 +def node13598 : Tree Nat := .leaf 908 +def node13599 : Tree Nat := .node node13598 node7756 +def node13600 : Tree Nat := .node node13599 node12710 +def node13601 : Tree Nat := .node node13139 node13600 +def node13602 : Tree Nat := .node node13134 node13601 +def node13603 : Tree Nat := .node node10435 node13512 +def node13604 : Tree Nat := .node node13603 node13148 +def node13605 : Tree Nat := .leaf 940 +def node13606 : Tree Nat := .node node13605 node10029 +def node13607 : Tree Nat := .node node13606 node8738 +def node13608 : Tree Nat := .node node13604 node13607 +def node13609 : Tree Nat := .node node13146 node13608 +def node13610 : Tree Nat := .node node13602 node13609 +def node13611 : Tree Nat := .node node10435 node13527 +def node13612 : Tree Nat := .node node13611 node11993 +def node13613 : Tree Nat := .leaf 924 +def node13614 : Tree Nat := .node node13613 node7824 +def node13615 : Tree Nat := .node node13614 node8750 +def node13616 : Tree Nat := .node node13612 node13615 +def node13617 : Tree Nat := .node node13156 node13616 +def node13618 : Tree Nat := .leaf 921 +def node13619 : Tree Nat := .node node9192 node13618 +def node13620 : Tree Nat := .node node13161 node13619 +def node13621 : Tree Nat := .node node13159 node13620 +def node13622 : Tree Nat := .node node13621 node13166 +def node13623 : Tree Nat := .node node13617 node13622 +def node13624 : Tree Nat := .node node13610 node13623 +def node13625 : Tree Nat := .node node13597 node13624 +def node13626 : Tree Nat := .node node13571 node13625 +def node13627 : Tree Nat := .leaf 930 +def node13628 : Tree Nat := .node node13627 node8282 +def node13629 : Tree Nat := .node node13628 node8775 +def node13630 : Tree Nat := .node node10739 node13629 +def node13631 : Tree Nat := .node node13180 node13630 +def node13632 : Tree Nat := .node node13176 node13631 +def node13633 : Tree Nat := .node node13587 node195 +def node13634 : Tree Nat := .node node13633 node13184 +def node13635 : Tree Nat := .node node12755 node13634 +def node13636 : Tree Nat := .node node12752 node13635 +def node13637 : Tree Nat := .leaf 918 +def node13638 : Tree Nat := .node node12758 node13637 +def node13639 : Tree Nat := .node node10910 node13638 +def node13640 : Tree Nat := .leaf 929 +def node13641 : Tree Nat := .node node9116 node13640 +def node13642 : Tree Nat := .node node13189 node13641 +def node13643 : Tree Nat := .node node13639 node13642 +def node13644 : Tree Nat := .leaf 938 +def node13645 : Tree Nat := .node node13644 node1 +def node13646 : Tree Nat := .node node11292 node13645 +def node13647 : Tree Nat := .node node13194 node13646 +def node13648 : Tree Nat := .node node13643 node13647 +def node13649 : Tree Nat := .node node13636 node13648 +def node13650 : Tree Nat := .node node13632 node13649 +def node13651 : Tree Nat := .leaf 906 +def node13652 : Tree Nat := .node node13651 node340 +def node13653 : Tree Nat := .node node13652 node12775 +def node13654 : Tree Nat := .node node12774 node13653 +def node13655 : Tree Nat := .node node13202 node13654 +def node13656 : Tree Nat := .leaf 942 +def node13657 : Tree Nat := .node node13209 node13656 +def node13658 : Tree Nat := .node node10525 node13657 +def node13659 : Tree Nat := .node node13644 node9558 +def node13660 : Tree Nat := .node node13659 node7039 +def node13661 : Tree Nat := .node node13658 node13660 +def node13662 : Tree Nat := .node node13208 node13661 +def node13663 : Tree Nat := .node node13655 node13662 +def node13664 : Tree Nat := .leaf 922 +def node13665 : Tree Nat := .node node13664 node8164 +def node13666 : Tree Nat := .node node7375 node13591 +def node13667 : Tree Nat := .node node13665 node13666 +def node13668 : Tree Nat := .node node13220 node13667 +def node13669 : Tree Nat := .node node13218 node13668 +def node13670 : Tree Nat := .node node6602 node11232 +def node13671 : Tree Nat := .node node13223 node13670 +def node13672 : Tree Nat := .node node12793 node13671 +def node13673 : Tree Nat := .node node13672 node13229 +def node13674 : Tree Nat := .node node13669 node13673 +def node13675 : Tree Nat := .node node13663 node13674 +def node13676 : Tree Nat := .node node13650 node13675 +def node13677 : Tree Nat := .node node13518 node12696 +def node13678 : Tree Nat := .node node13234 node13677 +def node13679 : Tree Nat := .node node12806 node13678 +def node13680 : Tree Nat := .node node12804 node13679 +def node13681 : Tree Nat := .node node13552 node9098 +def node13682 : Tree Nat := .node node13510 node1 +def node13683 : Tree Nat := .node node13681 node13682 +def node13684 : Tree Nat := .node node12063 node13683 +def node13685 : Tree Nat := .node node13241 node13684 +def node13686 : Tree Nat := .node node13680 node13685 +def node13687 : Tree Nat := .node node13637 node8193 +def node13688 : Tree Nat := .node node13555 node11520 +def node13689 : Tree Nat := .node node13687 node13688 +def node13690 : Tree Nat := .node node12816 node13689 +def node13691 : Tree Nat := .node node13246 node13690 +def node13692 : Tree Nat := .node node13065 node11426 +def node13693 : Tree Nat := .node node13248 node13692 +def node13694 : Tree Nat := .node node10957 node13693 +def node13695 : Tree Nat := .node node13545 node1 +def node13696 : Tree Nat := .node node10541 node13695 +def node13697 : Tree Nat := .node node13254 node13696 +def node13698 : Tree Nat := .node node13694 node13697 +def node13699 : Tree Nat := .node node13691 node13698 +def node13700 : Tree Nat := .node node13686 node13699 +def node13701 : Tree Nat := .node node13542 node8713 +def node13702 : Tree Nat := .node node13561 node11842 +def node13703 : Tree Nat := .node node13701 node13702 +def node13704 : Tree Nat := .node node12079 node13703 +def node13705 : Tree Nat := .node node13264 node13704 +def node13706 : Tree Nat := .node node6664 node13598 +def node13707 : Tree Nat := .node node13266 node13706 +def node13708 : Tree Nat := .node node12829 node13707 +def node13709 : Tree Nat := .node node13656 node6348 +def node13710 : Tree Nat := .node node13572 node1 +def node13711 : Tree Nat := .node node13709 node13710 +def node13712 : Tree Nat := .node node13270 node13711 +def node13713 : Tree Nat := .node node13708 node13712 +def node13714 : Tree Nat := .node node13705 node13713 +def node13715 : Tree Nat := .node node13502 node8367 +def node13716 : Tree Nat := .node node13613 node1 +def node13717 : Tree Nat := .node node13715 node13716 +def node13718 : Tree Nat := .node node10781 node13717 +def node13719 : Tree Nat := .node node13276 node13718 +def node13720 : Tree Nat := .node node6725 node13505 +def node13721 : Tree Nat := .node node10967 node13720 +def node13722 : Tree Nat := .node node13598 node13664 +def node13723 : Tree Nat := .node node13278 node13722 +def node13724 : Tree Nat := .node node13721 node13723 +def node13725 : Tree Nat := .node node13724 node12839 +def node13726 : Tree Nat := .node node13719 node13725 +def node13727 : Tree Nat := .node node13714 node13726 +def node13728 : Tree Nat := .node node13700 node13727 +def node13729 : Tree Nat := .node node13676 node13728 +def node13730 : Tree Nat := .node node13626 node13729 +def node13731 : Tree Nat := .leaf 925 +def node13732 : Tree Nat := .node node12644 node13731 +def node13733 : Tree Nat := .node node12111 node13732 +def node13734 : Tree Nat := .node node13733 node13291 +def node13735 : Tree Nat := .node node13289 node13734 +def node13736 : Tree Nat := .node node13640 node8677 +def node13737 : Tree Nat := .node node13736 node7141 +def node13738 : Tree Nat := .node node13300 node13737 +def node13739 : Tree Nat := .node node13298 node13738 +def node13740 : Tree Nat := .node node13735 node13739 +def node13741 : Tree Nat := .node node13578 node7137 +def node13742 : Tree Nat := .node node13741 node13309 +def node13743 : Tree Nat := .node node12127 node13742 +def node13744 : Tree Nat := .node node13307 node13743 +def node13745 : Tree Nat := .node node12658 node13555 +def node13746 : Tree Nat := .node node10472 node13745 +def node13747 : Tree Nat := .node node6989 node11359 +def node13748 : Tree Nat := .node node13313 node13747 +def node13749 : Tree Nat := .node node13746 node13748 +def node13750 : Tree Nat := .node node13749 node13318 +def node13751 : Tree Nat := .node node13744 node13750 +def node13752 : Tree Nat := .node node13740 node13751 +def node13753 : Tree Nat := .leaf 905 +def node13754 : Tree Nat := .node node13753 node7976 +def node13755 : Tree Nat := .node node13754 node12877 +def node13756 : Tree Nat := .node node12876 node13755 +def node13757 : Tree Nat := .node node12873 node13756 +def node13758 : Tree Nat := .leaf 909 +def node13759 : Tree Nat := .node node10435 node13758 +def node13760 : Tree Nat := .node node13759 node13326 +def node13761 : Tree Nat := .node node13591 node9723 +def node13762 : Tree Nat := .node node13761 node6259 +def node13763 : Tree Nat := .node node13760 node13762 +def node13764 : Tree Nat := .node node13325 node13763 +def node13765 : Tree Nat := .node node13757 node13764 +def node13766 : Tree Nat := .leaf 933 +def node13767 : Tree Nat := .node node10435 node13766 +def node13768 : Tree Nat := .node node13767 node13331 +def node13769 : Tree Nat := .node node13618 node7997 +def node13770 : Tree Nat := .node node6169 node13644 +def node13771 : Tree Nat := .node node13769 node13770 +def node13772 : Tree Nat := .node node13768 node13771 +def node13773 : Tree Nat := .node node12888 node13772 +def node13774 : Tree Nat := .node node6186 node13651 +def node13775 : Tree Nat := .node node13337 node13774 +def node13776 : Tree Nat := .node node13336 node13775 +def node13777 : Tree Nat := .node node11544 node13545 +def node13778 : Tree Nat := .node node12896 node13777 +def node13779 : Tree Nat := .node node11520 node1 +def node13780 : Tree Nat := .node node11736 node13779 +def node13781 : Tree Nat := .node node13778 node13780 +def node13782 : Tree Nat := .node node13776 node13781 +def node13783 : Tree Nat := .node node13773 node13782 +def node13784 : Tree Nat := .node node13765 node13783 +def node13785 : Tree Nat := .node node13752 node13784 +def node13786 : Tree Nat := .node node13578 node12758 +def node13787 : Tree Nat := .node node13352 node13786 +def node13788 : Tree Nat := .node node13351 node13787 +def node13789 : Tree Nat := .node node13349 node13788 +def node13790 : Tree Nat := .node node13766 node8865 +def node13791 : Tree Nat := .node node13640 node1 +def node13792 : Tree Nat := .node node13790 node13791 +def node13793 : Tree Nat := .node node13362 node13792 +def node13794 : Tree Nat := .node node13360 node13793 +def node13795 : Tree Nat := .node node13789 node13794 +def node13796 : Tree Nat := .leaf 917 +def node13797 : Tree Nat := .node node13796 node195 +def node13798 : Tree Nat := .node node13618 node13605 +def node13799 : Tree Nat := .node node13797 node13798 +def node13800 : Tree Nat := .node node12922 node13799 +def node13801 : Tree Nat := .node node13368 node13800 +def node13802 : Tree Nat := .node node13753 node13120 +def node13803 : Tree Nat := .node node13370 node13802 +def node13804 : Tree Nat := .node node11007 node13803 +def node13805 : Tree Nat := .node node13804 node12183 +def node13806 : Tree Nat := .node node13801 node13805 +def node13807 : Tree Nat := .node node13795 node13806 +def node13808 : Tree Nat := .node node13758 node7986 +def node13809 : Tree Nat := .node node13796 node12703 +def node13810 : Tree Nat := .node node13808 node13809 +def node13811 : Tree Nat := .node node13379 node13810 +def node13812 : Tree Nat := .node node12929 node13811 +def node13813 : Tree Nat := .node node10435 node13510 +def node13814 : Tree Nat := .node node13813 node8488 +def node13815 : Tree Nat := .leaf 941 +def node13816 : Tree Nat := .node node13815 node10212 +def node13817 : Tree Nat := .node node13766 node1 +def node13818 : Tree Nat := .node node13816 node13817 +def node13819 : Tree Nat := .node node13814 node13818 +def node13820 : Tree Nat := .node node13384 node13819 +def node13821 : Tree Nat := .node node13812 node13820 +def node13822 : Tree Nat := .node node13731 node8054 +def node13823 : Tree Nat := .node node13731 node1 +def node13824 : Tree Nat := .node node13822 node13823 +def node13825 : Tree Nat := .node node13388 node13824 +def node13826 : Tree Nat := .node node12937 node13825 +def node13827 : Tree Nat := .node node13758 node11291 +def node13828 : Tree Nat := .node node13393 node13827 +def node13829 : Tree Nat := .node node13392 node13828 +def node13830 : Tree Nat := .node node13815 node1 +def node13831 : Tree Nat := .node node10320 node13830 +def node13832 : Tree Nat := .node node12946 node13831 +def node13833 : Tree Nat := .node node13829 node13832 +def node13834 : Tree Nat := .node node13826 node13833 +def node13835 : Tree Nat := .node node13821 node13834 +def node13836 : Tree Nat := .node node13807 node13835 +def node13837 : Tree Nat := .node node13785 node13836 +def node13838 : Tree Nat := .node node13587 node12686 +def node13839 : Tree Nat := .node node13406 node13838 +def node13840 : Tree Nat := .node node13405 node13839 +def node13841 : Tree Nat := .node node13403 node13840 +def node13842 : Tree Nat := .node node13512 node8873 +def node13843 : Tree Nat := .node node13627 node1 +def node13844 : Tree Nat := .node node13842 node13843 +def node13845 : Tree Nat := .node node13414 node13844 +def node13846 : Tree Nat := .node node13412 node13845 +def node13847 : Tree Nat := .node node13841 node13846 +def node13848 : Tree Nat := .node node13505 node7242 +def node13849 : Tree Nat := .node node13664 node13172 +def node13850 : Tree Nat := .node node13848 node13849 +def node13851 : Tree Nat := .node node12242 node13850 +def node13852 : Tree Nat := .node node13420 node13851 +def node13853 : Tree Nat := .node node7065 node13796 +def node13854 : Tree Nat := .node node12247 node13853 +def node13855 : Tree Nat := .node node13651 node13627 +def node13856 : Tree Nat := .node node13425 node13855 +def node13857 : Tree Nat := .node node13854 node13856 +def node13858 : Tree Nat := .node node13857 node11816 +def node13859 : Tree Nat := .node node13852 node13858 +def node13860 : Tree Nat := .node node13847 node13859 +def node13861 : Tree Nat := .node node12658 node10435 +def node13862 : Tree Nat := .node node13861 node12972 +def node13863 : Tree Nat := .node node11428 node13862 +def node13864 : Tree Nat := .node node13527 node10482 +def node13865 : Tree Nat := .node node13637 node12742 +def node13866 : Tree Nat := .node node13864 node13865 +def node13867 : Tree Nat := .node node12976 node13866 +def node13868 : Tree Nat := .node node13863 node13867 +def node13869 : Tree Nat := .node node6733 node13815 +def node13870 : Tree Nat := .node node12241 node13869 +def node13871 : Tree Nat := .node node13531 node9748 +def node13872 : Tree Nat := .node node13552 node1 +def node13873 : Tree Nat := .node node13871 node13872 +def node13874 : Tree Nat := .node node13870 node13873 +def node13875 : Tree Nat := .node node13434 node13874 +def node13876 : Tree Nat := .node node13868 node13875 +def node13877 : Tree Nat := .node node12622 node10435 +def node13878 : Tree Nat := .node node13877 node8550 +def node13879 : Tree Nat := .node node11189 node13878 +def node13880 : Tree Nat := .node node13520 node11766 +def node13881 : Tree Nat := .node node13502 node1 +def node13882 : Tree Nat := .node node13880 node13881 +def node13883 : Tree Nat := .node node13438 node13882 +def node13884 : Tree Nat := .node node13879 node13883 +def node13885 : Tree Nat := .node node10435 node10435 +def node13886 : Tree Nat := .node node13885 node7671 +def node13887 : Tree Nat := .node node13542 node13572 +def node13888 : Tree Nat := .node node13441 node13887 +def node13889 : Tree Nat := .node node13886 node13888 +def node13890 : Tree Nat := .node node13656 node1 +def node13891 : Tree Nat := .node node11843 node13890 +def node13892 : Tree Nat := .node node12990 node13891 +def node13893 : Tree Nat := .node node13889 node13892 +def node13894 : Tree Nat := .node node13884 node13893 +def node13895 : Tree Nat := .node node13876 node13894 +def node13896 : Tree Nat := .node node13860 node13895 +def node13897 : Tree Nat := .node node13885 node13458 +def node13898 : Tree Nat := .node node13897 node11447 +def node13899 : Tree Nat := .node node13457 node13898 +def node13900 : Tree Nat := .node node13454 node13899 +def node13901 : Tree Nat := .node node6229 node13753 +def node13902 : Tree Nat := .node node11455 node13901 +def node13903 : Tree Nat := .node node13010 node13902 +def node13904 : Tree Nat := .node node13903 node13472 +def node13905 : Tree Nat := .node node13469 node13904 +def node13906 : Tree Nat := .node node13900 node13905 +def node13907 : Tree Nat := .node node13100 node13613 +def node13908 : Tree Nat := .node node12581 node13907 +def node13909 : Tree Nat := .node node11060 node13908 +def node13910 : Tree Nat := .node node13909 node11880 +def node13911 : Tree Nat := .node node13479 node13910 +def node13912 : Tree Nat := .node node12703 node13518 +def node13913 : Tree Nat := .node node12223 node13912 +def node13914 : Tree Nat := .node node13913 node13490 +def node13915 : Tree Nat := .node node13605 node1 +def node13916 : Tree Nat := .node node10425 node13915 +def node13917 : Tree Nat := .node node13493 node13916 +def node13918 : Tree Nat := .node node13914 node13917 +def node13919 : Tree Nat := .node node13488 node13918 +def node13920 : Tree Nat := .node node13911 node13919 +def node13921 : Tree Nat := .node node13906 node13920 +def node13922 : Tree Nat := .node node13896 node13921 +def node13923 : Tree Nat := .node node13837 node13922 +def node13924 : Tree Nat := .node node13730 node13923 +def node13925 : Tree Nat := .node node13885 node11476 +def node13926 : Tree Nat := .node node12607 node10435 +def node13927 : Tree Nat := .node node13926 node7715 +def node13928 : Tree Nat := .node node13925 node13927 +def node13929 : Tree Nat := .node node13885 node13503 +def node13930 : Tree Nat := .node node13039 node10435 +def node13931 : Tree Nat := .node node10435 node11766 +def node13932 : Tree Nat := .node node13930 node13931 +def node13933 : Tree Nat := .node node13929 node13932 +def node13934 : Tree Nat := .node node13928 node13933 +def node13935 : Tree Nat := .node node6525 node10435 +def node13936 : Tree Nat := .node node13885 node13935 +def node13937 : Tree Nat := .node node13045 node10435 +def node13938 : Tree Nat := .node node13937 node8170 +def node13939 : Tree Nat := .node node13936 node13938 +def node13940 : Tree Nat := .node node13885 node6534 +def node13941 : Tree Nat := .node node13940 node13514 +def node13942 : Tree Nat := .node node13939 node13941 +def node13943 : Tree Nat := .node node13934 node13942 +def node13944 : Tree Nat := .node node13885 node8652 +def node13945 : Tree Nat := .node node12618 node10435 +def node13946 : Tree Nat := .node node13945 node8654 +def node13947 : Tree Nat := .node node13944 node13946 +def node13948 : Tree Nat := .node node13885 node12623 +def node13949 : Tree Nat := .node node13518 node10435 +def node13950 : Tree Nat := .node node13949 node13521 +def node13951 : Tree Nat := .node node13948 node13950 +def node13952 : Tree Nat := .node node13947 node13951 +def node13953 : Tree Nat := .node node13885 node13525 +def node13954 : Tree Nat := .node node13055 node10435 +def node13955 : Tree Nat := .node node13954 node13528 +def node13956 : Tree Nat := .node node13953 node13955 +def node13957 : Tree Nat := .node node13885 node8181 +def node13958 : Tree Nat := .node node13957 node13533 +def node13959 : Tree Nat := .node node13956 node13958 +def node13960 : Tree Nat := .node node13952 node13959 +def node13961 : Tree Nat := .node node13943 node13960 +def node13962 : Tree Nat := .node node10435 node10037 +def node13963 : Tree Nat := .node node10472 node13962 +def node13964 : Tree Nat := .node node10435 node6549 +def node13965 : Tree Nat := .node node12639 node13964 +def node13966 : Tree Nat := .node node13963 node13965 +def node13967 : Tree Nat := .node node10435 node13067 +def node13968 : Tree Nat := .node node13066 node13967 +def node13969 : Tree Nat := .node node12646 node13968 +def node13970 : Tree Nat := .node node13966 node13969 +def node13971 : Tree Nat := .node node13970 node13550 +def node13972 : Tree Nat := .node node10435 node6188 +def node13973 : Tree Nat := .node node10895 node13972 +def node13974 : Tree Nat := .node node13973 node13083 +def node13975 : Tree Nat := .node node10435 node11735 +def node13976 : Tree Nat := .node node13556 node13975 +def node13977 : Tree Nat := .node node13554 node13976 +def node13978 : Tree Nat := .node node13974 node13977 +def node13979 : Tree Nat := .node node11813 node10435 +def node13980 : Tree Nat := .node node13093 node13979 +def node13981 : Tree Nat := .node node13091 node13980 +def node13982 : Tree Nat := .node node13981 node13567 +def node13983 : Tree Nat := .node node13978 node13982 +def node13984 : Tree Nat := .node node13971 node13983 +def node13985 : Tree Nat := .node node13961 node13984 +def node13986 : Tree Nat := .node node13100 node10435 +def node13987 : Tree Nat := .node node13986 node12677 +def node13988 : Tree Nat := .node node12676 node13987 +def node13989 : Tree Nat := .node node12673 node13988 +def node13990 : Tree Nat := .node node6574 node10435 +def node13991 : Tree Nat := .node node10905 node13990 +def node13992 : Tree Nat := .node node13991 node13112 +def node13993 : Tree Nat := .node node13992 node13575 +def node13994 : Tree Nat := .node node13989 node13993 +def node13995 : Tree Nat := .node node13885 node13885 +def node13996 : Tree Nat := .node node13995 node12688 +def node13997 : Tree Nat := .node node13996 node13585 +def node13998 : Tree Nat := .node node6584 node10435 +def node13999 : Tree Nat := .node node13121 node13998 +def node14000 : Tree Nat := .node node12698 node13999 +def node14001 : Tree Nat := .node node14000 node13594 +def node14002 : Tree Nat := .node node13997 node14001 +def node14003 : Tree Nat := .node node13994 node14002 +def node14004 : Tree Nat := .node node10435 node8677 +def node14005 : Tree Nat := .node node12704 node14004 +def node14006 : Tree Nat := .node node11087 node14005 +def node14007 : Tree Nat := .node node14006 node13601 +def node14008 : Tree Nat := .node node13605 node10435 +def node14009 : Tree Nat := .node node14008 node8738 +def node14010 : Tree Nat := .node node13604 node14009 +def node14011 : Tree Nat := .node node13146 node14010 +def node14012 : Tree Nat := .node node14007 node14011 +def node14013 : Tree Nat := .node node12726 node10435 +def node14014 : Tree Nat := .node node12725 node14013 +def node14015 : Tree Nat := .node node9192 node10435 +def node14016 : Tree Nat := .node node13161 node14015 +def node14017 : Tree Nat := .node node14014 node14016 +def node14018 : Tree Nat := .node node10435 node6180 +def node14019 : Tree Nat := .node node14018 node6613 +def node14020 : Tree Nat := .node node13165 node14019 +def node14021 : Tree Nat := .node node14017 node14020 +def node14022 : Tree Nat := .node node13617 node14021 +def node14023 : Tree Nat := .node node14012 node14022 +def node14024 : Tree Nat := .node node14003 node14023 +def node14025 : Tree Nat := .node node13985 node14024 +def node14026 : Tree Nat := .node node10435 node8288 +def node14027 : Tree Nat := .node node12750 node14026 +def node14028 : Tree Nat := .node node11099 node14027 +def node14029 : Tree Nat := .node node14028 node13635 +def node14030 : Tree Nat := .node node12758 node10435 +def node14031 : Tree Nat := .node node10910 node14030 +def node14032 : Tree Nat := .node node14031 node13642 +def node14033 : Tree Nat := .node node14032 node13647 +def node14034 : Tree Nat := .node node14029 node14033 +def node14035 : Tree Nat := .node node13632 node14034 +def node14036 : Tree Nat := .node node10435 node6229 +def node14037 : Tree Nat := .node node13885 node14036 +def node14038 : Tree Nat := .node node10435 node6659 +def node14039 : Tree Nat := .node node12769 node14038 +def node14040 : Tree Nat := .node node14037 node14039 +def node14041 : Tree Nat := .node node14040 node13654 +def node14042 : Tree Nat := .node node12779 node10435 +def node14043 : Tree Nat := .node node10939 node14042 +def node14044 : Tree Nat := .node node14043 node13207 +def node14045 : Tree Nat := .node node14044 node13661 +def node14046 : Tree Nat := .node node14041 node14045 +def node14047 : Tree Nat := .node node10435 node6235 +def node14048 : Tree Nat := .node node13885 node14047 +def node14049 : Tree Nat := .node node14048 node13217 +def node14050 : Tree Nat := .node node14049 node13668 +def node14051 : Tree Nat := .node node6602 node10435 +def node14052 : Tree Nat := .node node13223 node14051 +def node14053 : Tree Nat := .node node12793 node14052 +def node14054 : Tree Nat := .node node11623 node10435 +def node14055 : Tree Nat := .node node14054 node6648 +def node14056 : Tree Nat := .node node13228 node14055 +def node14057 : Tree Nat := .node node14053 node14056 +def node14058 : Tree Nat := .node node14050 node14057 +def node14059 : Tree Nat := .node node14046 node14058 +def node14060 : Tree Nat := .node node14035 node14059 +def node14061 : Tree Nat := .node node13885 node10731 +def node14062 : Tree Nat := .node node14061 node12803 +def node14063 : Tree Nat := .node node10435 node12696 +def node14064 : Tree Nat := .node node13234 node14063 +def node14065 : Tree Nat := .node node12806 node14064 +def node14066 : Tree Nat := .node node14062 node14065 +def node14067 : Tree Nat := .node node14066 node13685 +def node14068 : Tree Nat := .node node11121 node13885 +def node14069 : Tree Nat := .node node12812 node11140 +def node14070 : Tree Nat := .node node14068 node14069 +def node14071 : Tree Nat := .node node14070 node13690 +def node14072 : Tree Nat := .node node13065 node10435 +def node14073 : Tree Nat := .node node13248 node14072 +def node14074 : Tree Nat := .node node10957 node14073 +def node14075 : Tree Nat := .node node10477 node13695 +def node14076 : Tree Nat := .node node13254 node14075 +def node14077 : Tree Nat := .node node14074 node14076 +def node14078 : Tree Nat := .node node14071 node14077 +def node14079 : Tree Nat := .node node14067 node14078 +def node14080 : Tree Nat := .node node13885 node8854 +def node14081 : Tree Nat := .node node10435 node8197 +def node14082 : Tree Nat := .node node12821 node14081 +def node14083 : Tree Nat := .node node14080 node14082 +def node14084 : Tree Nat := .node node10435 node11842 +def node14085 : Tree Nat := .node node13701 node14084 +def node14086 : Tree Nat := .node node12079 node14085 +def node14087 : Tree Nat := .node node14083 node14086 +def node14088 : Tree Nat := .node node12670 node10435 +def node14089 : Tree Nat := .node node10962 node14088 +def node14090 : Tree Nat := .node node14089 node13707 +def node14091 : Tree Nat := .node node14090 node13712 +def node14092 : Tree Nat := .node node14087 node14091 +def node14093 : Tree Nat := .node node10435 node8843 +def node14094 : Tree Nat := .node node13885 node14093 +def node14095 : Tree Nat := .node node14094 node13275 +def node14096 : Tree Nat := .node node10435 node1 +def node14097 : Tree Nat := .node node13715 node14096 +def node14098 : Tree Nat := .node node10781 node14097 +def node14099 : Tree Nat := .node node14095 node14098 +def node14100 : Tree Nat := .node node6725 node10435 +def node14101 : Tree Nat := .node node10967 node14100 +def node14102 : Tree Nat := .node node13598 node10435 +def node14103 : Tree Nat := .node node13278 node14102 +def node14104 : Tree Nat := .node node14101 node14103 +def node14105 : Tree Nat := .node node14104 node12839 +def node14106 : Tree Nat := .node node14099 node14105 +def node14107 : Tree Nat := .node node14092 node14106 +def node14108 : Tree Nat := .node node14079 node14107 +def node14109 : Tree Nat := .node node14060 node14108 +def node14110 : Tree Nat := .node node14025 node14109 +def node14111 : Tree Nat := .node node10435 node7887 +def node14112 : Tree Nat := .node node12847 node14111 +def node14113 : Tree Nat := .node node11682 node14112 +def node14114 : Tree Nat := .node node14113 node13734 +def node14115 : Tree Nat := .node node12642 node10435 +def node14116 : Tree Nat := .node node11690 node14115 +def node14117 : Tree Nat := .node node14116 node13297 +def node14118 : Tree Nat := .node node14117 node13738 +def node14119 : Tree Nat := .node node14114 node14118 +def node14120 : Tree Nat := .node node14119 node13751 +def node14121 : Tree Nat := .node node10572 node11427 +def node14122 : Tree Nat := .node node14121 node12872 +def node14123 : Tree Nat := .node node14122 node13756 +def node14124 : Tree Nat := .node node14123 node13764 +def node14125 : Tree Nat := .node node14124 node13783 +def node14126 : Tree Nat := .node node14120 node14125 +def node14127 : Tree Nat := .node node10435 node8233 +def node14128 : Tree Nat := .node node12903 node14127 +def node14129 : Tree Nat := .node node11152 node14128 +def node14130 : Tree Nat := .node node10435 node12758 +def node14131 : Tree Nat := .node node13352 node14130 +def node14132 : Tree Nat := .node node13351 node14131 +def node14133 : Tree Nat := .node node14129 node14132 +def node14134 : Tree Nat := .node node12846 node10435 +def node14135 : Tree Nat := .node node10905 node14134 +def node14136 : Tree Nat := .node node14135 node13359 +def node14137 : Tree Nat := .node node14136 node13793 +def node14138 : Tree Nat := .node node14133 node14137 +def node14139 : Tree Nat := .node node224 node10435 +def node14140 : Tree Nat := .node node11098 node14139 +def node14141 : Tree Nat := .node node14140 node13367 +def node14142 : Tree Nat := .node node10435 node12920 +def node14143 : Tree Nat := .node node10720 node14142 +def node14144 : Tree Nat := .node node14143 node13799 +def node14145 : Tree Nat := .node node14141 node14144 +def node14146 : Tree Nat := .node node13753 node10435 +def node14147 : Tree Nat := .node node13370 node14146 +def node14148 : Tree Nat := .node node11007 node14147 +def node14149 : Tree Nat := .node node14148 node12183 +def node14150 : Tree Nat := .node node14145 node14149 +def node14151 : Tree Nat := .node node14138 node14150 +def node14152 : Tree Nat := .node node10435 node12703 +def node14153 : Tree Nat := .node node13808 node14152 +def node14154 : Tree Nat := .node node13379 node14153 +def node14155 : Tree Nat := .node node12929 node14154 +def node14156 : Tree Nat := .node node7108 node10435 +def node14157 : Tree Nat := .node node13382 node14156 +def node14158 : Tree Nat := .node node11012 node14157 +def node14159 : Tree Nat := .node node13815 node10435 +def node14160 : Tree Nat := .node node14159 node13817 +def node14161 : Tree Nat := .node node13814 node14160 +def node14162 : Tree Nat := .node node14158 node14161 +def node14163 : Tree Nat := .node node14155 node14162 +def node14164 : Tree Nat := .node node6929 node10435 +def node14165 : Tree Nat := .node node12942 node14164 +def node14166 : Tree Nat := .node node14165 node13828 +def node14167 : Tree Nat := .node node10435 node6694 +def node14168 : Tree Nat := .node node14167 node13830 +def node14169 : Tree Nat := .node node12946 node14168 +def node14170 : Tree Nat := .node node14166 node14169 +def node14171 : Tree Nat := .node node13826 node14170 +def node14172 : Tree Nat := .node node14163 node14171 +def node14173 : Tree Nat := .node node14151 node14172 +def node14174 : Tree Nat := .node node14126 node14173 +def node14175 : Tree Nat := .node node10435 node8175 +def node14176 : Tree Nat := .node node12953 node14175 +def node14177 : Tree Nat := .node node11174 node14176 +def node14178 : Tree Nat := .node node10435 node12686 +def node14179 : Tree Nat := .node node13406 node14178 +def node14180 : Tree Nat := .node node13405 node14179 +def node14181 : Tree Nat := .node node14177 node14180 +def node14182 : Tree Nat := .node node14181 node13846 +def node14183 : Tree Nat := .node node7065 node10435 +def node14184 : Tree Nat := .node node12247 node14183 +def node14185 : Tree Nat := .node node14184 node13856 +def node14186 : Tree Nat := .node node14185 node11816 +def node14187 : Tree Nat := .node node13852 node14186 +def node14188 : Tree Nat := .node node14182 node14187 +def node14189 : Tree Nat := .node node6764 node10435 +def node14190 : Tree Nat := .node node13861 node14189 +def node14191 : Tree Nat := .node node11428 node14190 +def node14192 : Tree Nat := .node node13527 node10435 +def node14193 : Tree Nat := .node node10435 node12742 +def node14194 : Tree Nat := .node node14192 node14193 +def node14195 : Tree Nat := .node node12976 node14194 +def node14196 : Tree Nat := .node node14191 node14195 +def node14197 : Tree Nat := .node node6320 node10435 +def node14198 : Tree Nat := .node node13885 node14197 +def node14199 : Tree Nat := .node node13089 node10435 +def node14200 : Tree Nat := .node node14199 node13432 +def node14201 : Tree Nat := .node node14198 node14200 +def node14202 : Tree Nat := .node node14201 node13874 +def node14203 : Tree Nat := .node node14196 node14202 +def node14204 : Tree Nat := .node node13885 node7667 +def node14205 : Tree Nat := .node node14204 node13878 +def node14206 : Tree Nat := .node node13885 node13437 +def node14207 : Tree Nat := .node node14206 node13882 +def node14208 : Tree Nat := .node node14205 node14207 +def node14209 : Tree Nat := .node node13304 node10435 +def node14210 : Tree Nat := .node node14209 node13887 +def node14211 : Tree Nat := .node node13886 node14210 +def node14212 : Tree Nat := .node node10648 node10435 +def node14213 : Tree Nat := .node node14212 node12277 +def node14214 : Tree Nat := .node node11842 node10435 +def node14215 : Tree Nat := .node node14214 node13890 +def node14216 : Tree Nat := .node node14213 node14215 +def node14217 : Tree Nat := .node node14211 node14216 +def node14218 : Tree Nat := .node node14208 node14217 +def node14219 : Tree Nat := .node node14203 node14218 +def node14220 : Tree Nat := .node node14188 node14219 +def node14221 : Tree Nat := .node node13885 node9920 +def node14222 : Tree Nat := .node node11759 node10435 +def node14223 : Tree Nat := .node node10435 node8315 +def node14224 : Tree Nat := .node node14222 node14223 +def node14225 : Tree Nat := .node node14221 node14224 +def node14226 : Tree Nat := .node node13885 node12996 +def node14227 : Tree Nat := .node node11735 node10435 +def node14228 : Tree Nat := .node node14227 node13451 +def node14229 : Tree Nat := .node node14226 node14228 +def node14230 : Tree Nat := .node node14225 node14229 +def node14231 : Tree Nat := .node node13885 node13000 +def node14232 : Tree Nat := .node node14054 node13455 +def node14233 : Tree Nat := .node node14231 node14232 +def node14234 : Tree Nat := .node node14233 node13898 +def node14235 : Tree Nat := .node node14230 node14234 +def node14236 : Tree Nat := .node node6186 node10435 +def node14237 : Tree Nat := .node node13885 node14236 +def node14238 : Tree Nat := .node node11475 node10435 +def node14239 : Tree Nat := .node node14238 node13463 +def node14240 : Tree Nat := .node node14237 node14239 +def node14241 : Tree Nat := .node node13885 node13005 +def node14242 : Tree Nat := .node node11232 node10435 +def node14243 : Tree Nat := .node node14242 node13466 +def node14244 : Tree Nat := .node node14241 node14243 +def node14245 : Tree Nat := .node node14240 node14244 +def node14246 : Tree Nat := .node node13885 node13009 +def node14247 : Tree Nat := .node node11426 node10435 +def node14248 : Tree Nat := .node node14247 node13901 +def node14249 : Tree Nat := .node node14246 node14248 +def node14250 : Tree Nat := .node node13885 node13470 +def node14251 : Tree Nat := .node node14250 node9939 +def node14252 : Tree Nat := .node node14249 node14251 +def node14253 : Tree Nat := .node node14245 node14252 +def node14254 : Tree Nat := .node node14235 node14253 +def node14255 : Tree Nat := .node node13885 node9053 +def node14256 : Tree Nat := .node node14255 node12575 +def node14257 : Tree Nat := .node node14256 node13478 +def node14258 : Tree Nat := .node node7083 node10435 +def node14259 : Tree Nat := .node node11059 node14258 +def node14260 : Tree Nat := .node node14259 node13908 +def node14261 : Tree Nat := .node node14260 node11880 +def node14262 : Tree Nat := .node node14257 node14261 +def node14263 : Tree Nat := .node node13885 node9068 +def node14264 : Tree Nat := .node node14263 node12587 +def node14265 : Tree Nat := .node node14264 node13487 +def node14266 : Tree Nat := .node node12703 node10435 +def node14267 : Tree Nat := .node node12223 node14266 +def node14268 : Tree Nat := .node node14267 node13490 +def node14269 : Tree Nat := .node node10435 node6764 +def node14270 : Tree Nat := .node node14269 node13915 +def node14271 : Tree Nat := .node node13493 node14270 +def node14272 : Tree Nat := .node node14268 node14271 +def node14273 : Tree Nat := .node node14265 node14272 +def node14274 : Tree Nat := .node node14262 node14273 +def node14275 : Tree Nat := .node node14254 node14274 +def node14276 : Tree Nat := .node node14220 node14275 +def node14277 : Tree Nat := .node node14174 node14276 +def node14278 : Tree Nat := .node node14110 node14277 +def node14279 : Tree Nat := .node node8635 node10435 +def node14280 : Tree Nat := .node node13885 node14279 +def node14281 : Tree Nat := .node node14280 node13932 +def node14282 : Tree Nat := .node node13928 node14281 +def node14283 : Tree Nat := .node node13511 node14096 +def node14284 : Tree Nat := .node node13940 node14283 +def node14285 : Tree Nat := .node node13939 node14284 +def node14286 : Tree Nat := .node node14282 node14285 +def node14287 : Tree Nat := .node node10435 node11623 +def node14288 : Tree Nat := .node node13949 node14287 +def node14289 : Tree Nat := .node node13948 node14288 +def node14290 : Tree Nat := .node node13947 node14289 +def node14291 : Tree Nat := .node node6539 node10435 +def node14292 : Tree Nat := .node node13885 node14291 +def node14293 : Tree Nat := .node node13954 node13885 +def node14294 : Tree Nat := .node node14292 node14293 +def node14295 : Tree Nat := .node node14294 node13958 +def node14296 : Tree Nat := .node node14290 node14295 +def node14297 : Tree Nat := .node node14286 node14296 +def node14298 : Tree Nat := .node node13885 node13962 +def node14299 : Tree Nat := .node node14298 node13965 +def node14300 : Tree Nat := .node node14299 node13969 +def node14301 : Tree Nat := .node node10435 node6208 +def node14302 : Tree Nat := .node node10890 node14301 +def node14303 : Tree Nat := .node node14302 node13074 +def node14304 : Tree Nat := .node node13885 node13077 +def node14305 : Tree Nat := .node node13545 node10435 +def node14306 : Tree Nat := .node node14305 node14096 +def node14307 : Tree Nat := .node node14304 node14306 +def node14308 : Tree Nat := .node node14303 node14307 +def node14309 : Tree Nat := .node node14300 node14308 +def node14310 : Tree Nat := .node node13885 node13972 +def node14311 : Tree Nat := .node node14310 node13083 +def node14312 : Tree Nat := .node node13885 node12659 +def node14313 : Tree Nat := .node node14312 node13976 +def node14314 : Tree Nat := .node node14311 node14313 +def node14315 : Tree Nat := .node node13885 node7356 +def node14316 : Tree Nat := .node node13093 node13885 +def node14317 : Tree Nat := .node node14315 node14316 +def node14318 : Tree Nat := .node node11520 node10435 +def node14319 : Tree Nat := .node node14318 node6562 +def node14320 : Tree Nat := .node node13566 node14319 +def node14321 : Tree Nat := .node node14317 node14320 +def node14322 : Tree Nat := .node node14314 node14321 +def node14323 : Tree Nat := .node node14309 node14322 +def node14324 : Tree Nat := .node node14297 node14323 +def node14325 : Tree Nat := .node node10490 node14236 +def node14326 : Tree Nat := .node node14325 node12672 +def node14327 : Tree Nat := .node node14326 node13988 +def node14328 : Tree Nat := .node node14327 node13993 +def node14329 : Tree Nat := .node node10435 node8668 +def node14330 : Tree Nat := .node node10499 node14329 +def node14331 : Tree Nat := .node node14330 node13593 +def node14332 : Tree Nat := .node node14000 node14331 +def node14333 : Tree Nat := .node node13997 node14332 +def node14334 : Tree Nat := .node node14328 node14333 +def node14335 : Tree Nat := .node node13885 node13138 +def node14336 : Tree Nat := .node node14335 node13600 +def node14337 : Tree Nat := .node node14006 node14336 +def node14338 : Tree Nat := .node node13885 node12715 +def node14339 : Tree Nat := .node node13076 node10435 +def node14340 : Tree Nat := .node node13143 node14339 +def node14341 : Tree Nat := .node node14338 node14340 +def node14342 : Tree Nat := .node node13885 node13148 +def node14343 : Tree Nat := .node node14342 node14009 +def node14344 : Tree Nat := .node node14341 node14343 +def node14345 : Tree Nat := .node node14337 node14344 +def node14346 : Tree Nat := .node node13885 node11993 +def node14347 : Tree Nat := .node node14346 node13615 +def node14348 : Tree Nat := .node node13156 node14347 +def node14349 : Tree Nat := .node node10435 node6606 +def node14350 : Tree Nat := .node node12730 node14349 +def node14351 : Tree Nat := .node node14350 node14019 +def node14352 : Tree Nat := .node node14017 node14351 +def node14353 : Tree Nat := .node node14348 node14352 +def node14354 : Tree Nat := .node node14345 node14353 +def node14355 : Tree Nat := .node node14334 node14354 +def node14356 : Tree Nat := .node node14324 node14355 +def node14357 : Tree Nat := .node node9205 node10435 +def node14358 : Tree Nat := .node node10905 node14357 +def node14359 : Tree Nat := .node node14358 node13179 +def node14360 : Tree Nat := .node node10435 node7850 +def node14361 : Tree Nat := .node node10715 node14360 +def node14362 : Tree Nat := .node node14361 node13629 +def node14363 : Tree Nat := .node node14359 node14362 +def node14364 : Tree Nat := .node node13176 node14363 +def node14365 : Tree Nat := .node node6169 node10435 +def node14366 : Tree Nat := .node node11098 node14365 +def node14367 : Tree Nat := .node node14366 node14027 +def node14368 : Tree Nat := .node node14367 node13635 +def node14369 : Tree Nat := .node node9116 node10435 +def node14370 : Tree Nat := .node node13189 node14369 +def node14371 : Tree Nat := .node node14031 node14370 +def node14372 : Tree Nat := .node node10435 node7742 +def node14373 : Tree Nat := .node node10499 node14372 +def node14374 : Tree Nat := .node node14373 node13646 +def node14375 : Tree Nat := .node node14371 node14374 +def node14376 : Tree Nat := .node node14368 node14375 +def node14377 : Tree Nat := .node node14364 node14376 +def node14378 : Tree Nat := .node node13885 node12773 +def node14379 : Tree Nat := .node node14378 node13653 +def node14380 : Tree Nat := .node node14040 node14379 +def node14381 : Tree Nat := .node node13885 node14042 +def node14382 : Tree Nat := .node node14381 node13207 +def node14383 : Tree Nat := .node node13644 node10435 +def node14384 : Tree Nat := .node node14383 node7039 +def node14385 : Tree Nat := .node node13658 node14384 +def node14386 : Tree Nat := .node node14382 node14385 +def node14387 : Tree Nat := .node node14380 node14386 +def node14388 : Tree Nat := .node node13885 node13219 +def node14389 : Tree Nat := .node node14388 node13667 +def node14390 : Tree Nat := .node node14049 node14389 +def node14391 : Tree Nat := .node node13885 node12792 +def node14392 : Tree Nat := .node node14391 node14052 +def node14393 : Tree Nat := .node node12795 node11121 +def node14394 : Tree Nat := .node node14393 node14055 +def node14395 : Tree Nat := .node node14392 node14394 +def node14396 : Tree Nat := .node node14390 node14395 +def node14397 : Tree Nat := .node node14387 node14396 +def node14398 : Tree Nat := .node node14377 node14397 +def node14399 : Tree Nat := .node node13995 node12803 +def node14400 : Tree Nat := .node node13885 node12805 +def node14401 : Tree Nat := .node node14400 node14064 +def node14402 : Tree Nat := .node node14399 node14401 +def node14403 : Tree Nat := .node node13885 node9270 +def node14404 : Tree Nat := .node node13238 node13885 +def node14405 : Tree Nat := .node node14403 node14404 +def node14406 : Tree Nat := .node node13681 node14096 +def node14407 : Tree Nat := .node node12063 node14406 +def node14408 : Tree Nat := .node node14405 node14407 +def node14409 : Tree Nat := .node node14402 node14408 +def node14410 : Tree Nat := .node node13885 node12815 +def node14411 : Tree Nat := .node node10435 node11520 +def node14412 : Tree Nat := .node node13687 node14411 +def node14413 : Tree Nat := .node node14410 node14412 +def node14414 : Tree Nat := .node node14070 node14413 +def node14415 : Tree Nat := .node node10435 node6313 +def node14416 : Tree Nat := .node node13885 node14415 +def node14417 : Tree Nat := .node node13248 node13885 +def node14418 : Tree Nat := .node node14416 node14417 +def node14419 : Tree Nat := .node node13885 node13695 +def node14420 : Tree Nat := .node node13254 node14419 +def node14421 : Tree Nat := .node node14418 node14420 +def node14422 : Tree Nat := .node node14414 node14421 +def node14423 : Tree Nat := .node node14409 node14422 +def node14424 : Tree Nat := .node node13885 node12078 +def node14425 : Tree Nat := .node node14424 node14085 +def node14426 : Tree Nat := .node node14083 node14425 +def node14427 : Tree Nat := .node node13885 node14088 +def node14428 : Tree Nat := .node node6664 node10435 +def node14429 : Tree Nat := .node node13266 node14428 +def node14430 : Tree Nat := .node node14427 node14429 +def node14431 : Tree Nat := .node node13709 node14096 +def node14432 : Tree Nat := .node node13270 node14431 +def node14433 : Tree Nat := .node node14430 node14432 +def node14434 : Tree Nat := .node node14426 node14433 +def node14435 : Tree Nat := .node node13885 node8878 +def node14436 : Tree Nat := .node node14435 node14097 +def node14437 : Tree Nat := .node node14095 node14436 +def node14438 : Tree Nat := .node node13885 node14100 +def node14439 : Tree Nat := .node node13278 node13885 +def node14440 : Tree Nat := .node node14438 node14439 +def node14441 : Tree Nat := .node node14440 node12839 +def node14442 : Tree Nat := .node node14437 node14441 +def node14443 : Tree Nat := .node node14434 node14442 +def node14444 : Tree Nat := .node node14423 node14443 +def node14445 : Tree Nat := .node node14398 node14444 +def node14446 : Tree Nat := .node node14356 node14445 +def node14447 : Tree Nat := .node node13885 node11681 +def node14448 : Tree Nat := .node node14447 node14112 +def node14449 : Tree Nat := .node node12644 node10435 +def node14450 : Tree Nat := .node node12111 node14449 +def node14451 : Tree Nat := .node node14450 node13291 +def node14452 : Tree Nat := .node node14448 node14451 +def node14453 : Tree Nat := .node node14452 node14118 +def node14454 : Tree Nat := .node node10472 node13861 +def node14455 : Tree Nat := .node node6989 node10435 +def node14456 : Tree Nat := .node node13313 node14455 +def node14457 : Tree Nat := .node node14454 node14456 +def node14458 : Tree Nat := .node node10435 node8298 +def node14459 : Tree Nat := .node node10566 node14458 +def node14460 : Tree Nat := .node node14459 node11361 +def node14461 : Tree Nat := .node node14457 node14460 +def node14462 : Tree Nat := .node node13744 node14461 +def node14463 : Tree Nat := .node node14453 node14462 +def node14464 : Tree Nat := .node node13885 node11427 +def node14465 : Tree Nat := .node node14464 node12872 +def node14466 : Tree Nat := .node node14465 node13756 +def node14467 : Tree Nat := .node node13885 node13326 +def node14468 : Tree Nat := .node node13591 node10435 +def node14469 : Tree Nat := .node node14468 node6259 +def node14470 : Tree Nat := .node node14467 node14469 +def node14471 : Tree Nat := .node node13325 node14470 +def node14472 : Tree Nat := .node node14466 node14471 +def node14473 : Tree Nat := .node node13885 node7174 +def node14474 : Tree Nat := .node node14473 node12887 +def node14475 : Tree Nat := .node node13885 node13331 +def node14476 : Tree Nat := .node node14475 node13771 +def node14477 : Tree Nat := .node node14474 node14476 +def node14478 : Tree Nat := .node node13885 node12893 +def node14479 : Tree Nat := .node node13337 node14236 +def node14480 : Tree Nat := .node node14478 node14479 +def node14481 : Tree Nat := .node node10435 node13545 +def node14482 : Tree Nat := .node node12896 node14481 +def node14483 : Tree Nat := .node node14227 node13779 +def node14484 : Tree Nat := .node node14482 node14483 +def node14485 : Tree Nat := .node node14480 node14484 +def node14486 : Tree Nat := .node node14477 node14485 +def node14487 : Tree Nat := .node node14472 node14486 +def node14488 : Tree Nat := .node node14463 node14487 +def node14489 : Tree Nat := .node node6176 node10435 +def node14490 : Tree Nat := .node node10490 node14489 +def node14491 : Tree Nat := .node node14490 node14128 +def node14492 : Tree Nat := .node node10435 node13215 +def node14493 : Tree Nat := .node node10812 node14492 +def node14494 : Tree Nat := .node node14493 node14131 +def node14495 : Tree Nat := .node node14491 node14494 +def node14496 : Tree Nat := .node node13358 node12241 +def node14497 : Tree Nat := .node node14135 node14496 +def node14498 : Tree Nat := .node node13790 node14096 +def node14499 : Tree Nat := .node node13362 node14498 +def node14500 : Tree Nat := .node node14497 node14499 +def node14501 : Tree Nat := .node node14495 node14500 +def node14502 : Tree Nat := .node node10435 node13605 +def node14503 : Tree Nat := .node node13797 node14502 +def node14504 : Tree Nat := .node node14143 node14503 +def node14505 : Tree Nat := .node node14141 node14504 +def node14506 : Tree Nat := .node node10435 node7872 +def node14507 : Tree Nat := .node node10910 node14506 +def node14508 : Tree Nat := .node node13370 node13885 +def node14509 : Tree Nat := .node node14507 node14508 +def node14510 : Tree Nat := .node node14509 node12183 +def node14511 : Tree Nat := .node node14505 node14510 +def node14512 : Tree Nat := .node node14501 node14511 +def node14513 : Tree Nat := .node node13885 node13378 +def node14514 : Tree Nat := .node node14513 node14153 +def node14515 : Tree Nat := .node node12929 node14514 +def node14516 : Tree Nat := .node node13885 node7623 +def node14517 : Tree Nat := .node node14516 node14157 +def node14518 : Tree Nat := .node node13885 node8488 +def node14519 : Tree Nat := .node node14159 node14096 +def node14520 : Tree Nat := .node node14518 node14519 +def node14521 : Tree Nat := .node node14517 node14520 +def node14522 : Tree Nat := .node node14515 node14521 +def node14523 : Tree Nat := .node node13885 node12938 +def node14524 : Tree Nat := .node node13822 node14096 +def node14525 : Tree Nat := .node node14523 node14524 +def node14526 : Tree Nat := .node node12937 node14525 +def node14527 : Tree Nat := .node node13393 node13885 +def node14528 : Tree Nat := .node node14165 node14527 +def node14529 : Tree Nat := .node node14528 node14169 +def node14530 : Tree Nat := .node node14526 node14529 +def node14531 : Tree Nat := .node node14522 node14530 +def node14532 : Tree Nat := .node node14512 node14531 +def node14533 : Tree Nat := .node node14488 node14532 +def node14534 : Tree Nat := .node node13885 node9427 +def node14535 : Tree Nat := .node node14534 node14176 +def node14536 : Tree Nat := .node node14535 node14180 +def node14537 : Tree Nat := .node node12738 node10435 +def node14538 : Tree Nat := .node node12229 node14537 +def node14539 : Tree Nat := .node node14538 node13411 +def node14540 : Tree Nat := .node node13842 node14096 +def node14541 : Tree Nat := .node node13414 node14540 +def node14542 : Tree Nat := .node node14539 node14541 +def node14543 : Tree Nat := .node node14536 node14542 +def node14544 : Tree Nat := .node node195 node10435 +def node14545 : Tree Nat := .node node11807 node14544 +def node14546 : Tree Nat := .node node14545 node13419 +def node14547 : Tree Nat := .node node10435 node13172 +def node14548 : Tree Nat := .node node13848 node14547 +def node14549 : Tree Nat := .node node12242 node14548 +def node14550 : Tree Nat := .node node14546 node14549 +def node14551 : Tree Nat := .node node13425 node13885 +def node14552 : Tree Nat := .node node14184 node14551 +def node14553 : Tree Nat := .node node14552 node11816 +def node14554 : Tree Nat := .node node14550 node14553 +def node14555 : Tree Nat := .node node14543 node14554 +def node14556 : Tree Nat := .node node13885 node12975 +def node14557 : Tree Nat := .node node14556 node14194 +def node14558 : Tree Nat := .node node14191 node14557 +def node14559 : Tree Nat := .node node6554 node10435 +def node14560 : Tree Nat := .node node14199 node14559 +def node14561 : Tree Nat := .node node14198 node14560 +def node14562 : Tree Nat := .node node13531 node10435 +def node14563 : Tree Nat := .node node14562 node14096 +def node14564 : Tree Nat := .node node13870 node14563 +def node14565 : Tree Nat := .node node14561 node14564 +def node14566 : Tree Nat := .node node14558 node14565 +def node14567 : Tree Nat := .node node13880 node14096 +def node14568 : Tree Nat := .node node14206 node14567 +def node14569 : Tree Nat := .node node14205 node14568 +def node14570 : Tree Nat := .node node14209 node13885 +def node14571 : Tree Nat := .node node13886 node14570 +def node14572 : Tree Nat := .node node14571 node14216 +def node14573 : Tree Nat := .node node14569 node14572 +def node14574 : Tree Nat := .node node14566 node14573 +def node14575 : Tree Nat := .node node14555 node14574 +def node14576 : Tree Nat := .node node340 node10435 +def node14577 : Tree Nat := .node node13885 node14576 +def node14578 : Tree Nat := .node node14577 node14224 +def node14579 : Tree Nat := .node node14578 node14229 +def node14580 : Tree Nat := .node node14054 node13930 +def node14581 : Tree Nat := .node node14231 node14580 +def node14582 : Tree Nat := .node node14581 node13898 +def node14583 : Tree Nat := .node node14579 node14582 +def node14584 : Tree Nat := .node node6229 node10435 +def node14585 : Tree Nat := .node node14247 node14584 +def node14586 : Tree Nat := .node node14246 node14585 +def node14587 : Tree Nat := .node node10435 node13039 +def node14588 : Tree Nat := .node node13885 node14587 +def node14589 : Tree Nat := .node node322 node10435 +def node14590 : Tree Nat := .node node14589 node6891 +def node14591 : Tree Nat := .node node14588 node14590 +def node14592 : Tree Nat := .node node14586 node14591 +def node14593 : Tree Nat := .node node14245 node14592 +def node14594 : Tree Nat := .node node14583 node14593 +def node14595 : Tree Nat := .node node13885 node13017 +def node14596 : Tree Nat := .node node14595 node13477 +def node14597 : Tree Nat := .node node14256 node14596 +def node14598 : Tree Nat := .node node13885 node14258 +def node14599 : Tree Nat := .node node12581 node13986 +def node14600 : Tree Nat := .node node14598 node14599 +def node14601 : Tree Nat := .node node14600 node11880 +def node14602 : Tree Nat := .node node14597 node14601 +def node14603 : Tree Nat := .node node13885 node13485 +def node14604 : Tree Nat := .node node14603 node11462 +def node14605 : Tree Nat := .node node14264 node14604 +def node14606 : Tree Nat := .node node13885 node14266 +def node14607 : Tree Nat := .node node14606 node13490 +def node14608 : Tree Nat := .node node10435 node11680 +def node14609 : Tree Nat := .node node13029 node14608 +def node14610 : Tree Nat := .node node14609 node14270 +def node14611 : Tree Nat := .node node14607 node14610 +def node14612 : Tree Nat := .node node14605 node14611 +def node14613 : Tree Nat := .node node14602 node14612 +def node14614 : Tree Nat := .node node14594 node14613 +def node14615 : Tree Nat := .node node14575 node14614 +def node14616 : Tree Nat := .node node14533 node14615 +def node14617 : Tree Nat := .node node14446 node14616 +def node14618 : Tree Nat := .node node13885 node14238 +def node14619 : Tree Nat := .node node14618 node13927 +def node14620 : Tree Nat := .node node14619 node14281 +def node14621 : Tree Nat := .node node14620 node14285 +def node14622 : Tree Nat := .node node13949 node13885 +def node14623 : Tree Nat := .node node13948 node14622 +def node14624 : Tree Nat := .node node13947 node14623 +def node14625 : Tree Nat := .node node11233 node14096 +def node14626 : Tree Nat := .node node13957 node14625 +def node14627 : Tree Nat := .node node14294 node14626 +def node14628 : Tree Nat := .node node14624 node14627 +def node14629 : Tree Nat := .node node14621 node14628 +def node14630 : Tree Nat := .node node13885 node12645 +def node14631 : Tree Nat := .node node13066 node13885 +def node14632 : Tree Nat := .node node14630 node14631 +def node14633 : Tree Nat := .node node14299 node14632 +def node14634 : Tree Nat := .node node13885 node14301 +def node14635 : Tree Nat := .node node14634 node13074 +def node14636 : Tree Nat := .node node13995 node14306 +def node14637 : Tree Nat := .node node14635 node14636 +def node14638 : Tree Nat := .node node14633 node14637 +def node14639 : Tree Nat := .node node13556 node13885 +def node14640 : Tree Nat := .node node14312 node14639 +def node14641 : Tree Nat := .node node14311 node14640 +def node14642 : Tree Nat := .node node5802 node10435 +def node14643 : Tree Nat := .node node12663 node14642 +def node14644 : Tree Nat := .node node14643 node14319 +def node14645 : Tree Nat := .node node14317 node14644 +def node14646 : Tree Nat := .node node14641 node14645 +def node14647 : Tree Nat := .node node14638 node14646 +def node14648 : Tree Nat := .node node14629 node14647 +def node14649 : Tree Nat := .node node13109 node13885 +def node14650 : Tree Nat := .node node13991 node14649 +def node14651 : Tree Nat := .node node13572 node10435 +def node14652 : Tree Nat := .node node14651 node6983 +def node14653 : Tree Nat := .node node10716 node14652 +def node14654 : Tree Nat := .node node14650 node14653 +def node14655 : Tree Nat := .node node14327 node14654 +def node14656 : Tree Nat := .node node7384 node10435 +def node14657 : Tree Nat := .node node13583 node14656 +def node14658 : Tree Nat := .node node12693 node14657 +def node14659 : Tree Nat := .node node13996 node14658 +def node14660 : Tree Nat := .node node11544 node10435 +def node14661 : Tree Nat := .node node14660 node14096 +def node14662 : Tree Nat := .node node14330 node14661 +def node14663 : Tree Nat := .node node14000 node14662 +def node14664 : Tree Nat := .node node14659 node14663 +def node14665 : Tree Nat := .node node14655 node14664 +def node14666 : Tree Nat := .node node13885 node6252 +def node14667 : Tree Nat := .node node14666 node14005 +def node14668 : Tree Nat := .node node12707 node10435 +def node14669 : Tree Nat := .node node13885 node14668 +def node14670 : Tree Nat := .node node14669 node13600 +def node14671 : Tree Nat := .node node14667 node14670 +def node14672 : Tree Nat := .node node10435 node7400 +def node14673 : Tree Nat := .node node13885 node14672 +def node14674 : Tree Nat := .node node13143 node13885 +def node14675 : Tree Nat := .node node14673 node14674 +def node14676 : Tree Nat := .node node10435 node6546 +def node14677 : Tree Nat := .node node13885 node14676 +def node14678 : Tree Nat := .node node14677 node14009 +def node14679 : Tree Nat := .node node14675 node14678 +def node14680 : Tree Nat := .node node14671 node14679 +def node14681 : Tree Nat := .node node13885 node8746 +def node14682 : Tree Nat := .node node14681 node13155 +def node14683 : Tree Nat := .node node14682 node14347 +def node14684 : Tree Nat := .node node13885 node14013 +def node14685 : Tree Nat := .node node13161 node13885 +def node14686 : Tree Nat := .node node14684 node14685 +def node14687 : Tree Nat := .node node14686 node14351 +def node14688 : Tree Nat := .node node14683 node14687 +def node14689 : Tree Nat := .node node14680 node14688 +def node14690 : Tree Nat := .node node14665 node14689 +def node14691 : Tree Nat := .node node14648 node14690 +def node14692 : Tree Nat := .node node451 node10435 +def node14693 : Tree Nat := .node node10490 node14692 +def node14694 : Tree Nat := .node node14693 node12740 +def node14695 : Tree Nat := .node node14694 node13175 +def node14696 : Tree Nat := .node node10905 node13885 +def node14697 : Tree Nat := .node node10435 node8260 +def node14698 : Tree Nat := .node node13177 node14697 +def node14699 : Tree Nat := .node node14696 node14698 +def node14700 : Tree Nat := .node node14699 node14362 +def node14701 : Tree Nat := .node node14695 node14700 +def node14702 : Tree Nat := .node node13189 node13885 +def node14703 : Tree Nat := .node node14031 node14702 +def node14704 : Tree Nat := .node node11291 node10435 +def node14705 : Tree Nat := .node node14704 node14096 +def node14706 : Tree Nat := .node node14373 node14705 +def node14707 : Tree Nat := .node node14703 node14706 +def node14708 : Tree Nat := .node node14368 node14707 +def node14709 : Tree Nat := .node node14701 node14708 +def node14710 : Tree Nat := .node node14030 node14038 +def node14711 : Tree Nat := .node node14037 node14710 +def node14712 : Tree Nat := .node node14711 node14379 +def node14713 : Tree Nat := .node node13204 node13885 +def node14714 : Tree Nat := .node node13995 node14713 +def node14715 : Tree Nat := .node node13995 node14384 +def node14716 : Tree Nat := .node node14714 node14715 +def node14717 : Tree Nat := .node node14712 node14716 +def node14718 : Tree Nat := .node node12753 node10435 +def node14719 : Tree Nat := .node node14718 node13216 +def node14720 : Tree Nat := .node node14048 node14719 +def node14721 : Tree Nat := .node node8681 node10435 +def node14722 : Tree Nat := .node node13885 node14721 +def node14723 : Tree Nat := .node node7375 node10435 +def node14724 : Tree Nat := .node node13665 node14723 +def node14725 : Tree Nat := .node node14722 node14724 +def node14726 : Tree Nat := .node node14720 node14725 +def node14727 : Tree Nat := .node node10449 node10435 +def node14728 : Tree Nat := .node node14727 node11121 +def node14729 : Tree Nat := .node node14728 node14055 +def node14730 : Tree Nat := .node node14392 node14729 +def node14731 : Tree Nat := .node node14726 node14730 +def node14732 : Tree Nat := .node node14717 node14731 +def node14733 : Tree Nat := .node node14709 node14732 +def node14734 : Tree Nat := .node node14042 node8323 +def node14735 : Tree Nat := .node node13995 node14734 +def node14736 : Tree Nat := .node node14735 node14401 +def node14737 : Tree Nat := .node node10435 node6320 +def node14738 : Tree Nat := .node node13885 node14737 +def node14739 : Tree Nat := .node node14738 node14404 +def node14740 : Tree Nat := .node node13885 node12062 +def node14741 : Tree Nat := .node node13552 node10435 +def node14742 : Tree Nat := .node node14741 node14096 +def node14743 : Tree Nat := .node node14740 node14742 +def node14744 : Tree Nat := .node node14739 node14743 +def node14745 : Tree Nat := .node node14736 node14744 +def node14746 : Tree Nat := .node node12772 node10435 +def node14747 : Tree Nat := .node node14746 node11140 +def node14748 : Tree Nat := .node node14068 node14747 +def node14749 : Tree Nat := .node node13687 node13885 +def node14750 : Tree Nat := .node node14410 node14749 +def node14751 : Tree Nat := .node node14748 node14750 +def node14752 : Tree Nat := .node node13885 node14096 +def node14753 : Tree Nat := .node node13995 node14752 +def node14754 : Tree Nat := .node node14418 node14753 +def node14755 : Tree Nat := .node node14751 node14754 +def node14756 : Tree Nat := .node node14745 node14755 +def node14757 : Tree Nat := .node node12791 node10435 +def node14758 : Tree Nat := .node node14757 node14081 +def node14759 : Tree Nat := .node node14080 node14758 +def node14760 : Tree Nat := .node node14759 node14425 +def node14761 : Tree Nat := .node node13995 node14429 +def node14762 : Tree Nat := .node node10435 node6733 +def node14763 : Tree Nat := .node node13885 node14762 +def node14764 : Tree Nat := .node node14763 node14431 +def node14765 : Tree Nat := .node node14761 node14764 +def node14766 : Tree Nat := .node node14760 node14765 +def node14767 : Tree Nat := .node node12691 node10435 +def node14768 : Tree Nat := .node node14767 node13274 +def node14769 : Tree Nat := .node node14094 node14768 +def node14770 : Tree Nat := .node node14769 node14436 +def node14771 : Tree Nat := .node node10533 node10435 +def node14772 : Tree Nat := .node node14771 node12099 +def node14773 : Tree Nat := .node node14772 node6747 +def node14774 : Tree Nat := .node node14440 node14773 +def node14775 : Tree Nat := .node node14770 node14774 +def node14776 : Tree Nat := .node node14766 node14775 +def node14777 : Tree Nat := .node node14756 node14776 +def node14778 : Tree Nat := .node node14733 node14777 +def node14779 : Tree Nat := .node node14691 node14778 +def node14780 : Tree Nat := .node node11680 node10435 +def node14781 : Tree Nat := .node node13885 node14780 +def node14782 : Tree Nat := .node node14781 node14112 +def node14783 : Tree Nat := .node node14782 node14451 +def node14784 : Tree Nat := .node node11690 node13885 +def node14785 : Tree Nat := .node node10435 node8386 +def node14786 : Tree Nat := .node node13295 node14785 +def node14787 : Tree Nat := .node node14784 node14786 +def node14788 : Tree Nat := .node node10435 node13092 +def node14789 : Tree Nat := .node node12120 node14788 +def node14790 : Tree Nat := .node node14789 node13737 +def node14791 : Tree Nat := .node node14787 node14790 +def node14792 : Tree Nat := .node node14783 node14791 +def node14793 : Tree Nat := .node node10435 node7957 +def node14794 : Tree Nat := .node node11086 node14793 +def node14795 : Tree Nat := .node node14794 node13742 +def node14796 : Tree Nat := .node node13307 node14795 +def node14797 : Tree Nat := .node node14796 node14461 +def node14798 : Tree Nat := .node node14792 node14797 +def node14799 : Tree Nat := .node node13885 node12875 +def node14800 : Tree Nat := .node node14799 node13755 +def node14801 : Tree Nat := .node node14465 node14800 +def node14802 : Tree Nat := .node node13885 node8420 +def node14803 : Tree Nat := .node node13322 node13885 +def node14804 : Tree Nat := .node node14802 node14803 +def node14805 : Tree Nat := .node node411 node10435 +def node14806 : Tree Nat := .node node13885 node14805 +def node14807 : Tree Nat := .node node14806 node14469 +def node14808 : Tree Nat := .node node14804 node14807 +def node14809 : Tree Nat := .node node14801 node14808 +def node14810 : Tree Nat := .node node13769 node14365 +def node14811 : Tree Nat := .node node14475 node14810 +def node14812 : Tree Nat := .node node14474 node14811 +def node14813 : Tree Nat := .node node12896 node13885 +def node14814 : Tree Nat := .node node14227 node14096 +def node14815 : Tree Nat := .node node14813 node14814 +def node14816 : Tree Nat := .node node14480 node14815 +def node14817 : Tree Nat := .node node14812 node14816 +def node14818 : Tree Nat := .node node14809 node14817 +def node14819 : Tree Nat := .node node14798 node14818 +def node14820 : Tree Nat := .node node13358 node13885 +def node14821 : Tree Nat := .node node14696 node14820 +def node14822 : Tree Nat := .node node10435 node8249 +def node14823 : Tree Nat := .node node10715 node14822 +def node14824 : Tree Nat := .node node14823 node14498 +def node14825 : Tree Nat := .node node14821 node14824 +def node14826 : Tree Nat := .node node14495 node14825 +def node14827 : Tree Nat := .node node13797 node13885 +def node14828 : Tree Nat := .node node14143 node14827 +def node14829 : Tree Nat := .node node14141 node14828 +def node14830 : Tree Nat := .node node10499 node14287 +def node14831 : Tree Nat := .node node14222 node14096 +def node14832 : Tree Nat := .node node14830 node14831 +def node14833 : Tree Nat := .node node14509 node14832 +def node14834 : Tree Nat := .node node14829 node14833 +def node14835 : Tree Nat := .node node14826 node14834 +def node14836 : Tree Nat := .node node13885 node11767 +def node14837 : Tree Nat := .node node14836 node12928 +def node14838 : Tree Nat := .node node13995 node14153 +def node14839 : Tree Nat := .node node14837 node14838 +def node14840 : Tree Nat := .node node14839 node14521 +def node14841 : Tree Nat := .node node13885 node8494 +def node14842 : Tree Nat := .node node10435 node8496 +def node14843 : Tree Nat := .node node12935 node14842 +def node14844 : Tree Nat := .node node14841 node14843 +def node14845 : Tree Nat := .node node14844 node14525 +def node14846 : Tree Nat := .node node13885 node14164 +def node14847 : Tree Nat := .node node14846 node14527 +def node14848 : Tree Nat := .node node14167 node14096 +def node14849 : Tree Nat := .node node12946 node14848 +def node14850 : Tree Nat := .node node14847 node14849 +def node14851 : Tree Nat := .node node14845 node14850 +def node14852 : Tree Nat := .node node14840 node14851 +def node14853 : Tree Nat := .node node14835 node14852 +def node14854 : Tree Nat := .node node14819 node14853 +def node14855 : Tree Nat := .node node13885 node14139 +def node14856 : Tree Nat := .node node14855 node14176 +def node14857 : Tree Nat := .node node14856 node14180 +def node14858 : Tree Nat := .node node12229 node13885 +def node14859 : Tree Nat := .node node14858 node13411 +def node14860 : Tree Nat := .node node10435 node7845 +def node14861 : Tree Nat := .node node12234 node14860 +def node14862 : Tree Nat := .node node14861 node14540 +def node14863 : Tree Nat := .node node14859 node14862 +def node14864 : Tree Nat := .node node14857 node14863 +def node14865 : Tree Nat := .node node10435 node7721 +def node14866 : Tree Nat := .node node12241 node14865 +def node14867 : Tree Nat := .node node13848 node13885 +def node14868 : Tree Nat := .node node14866 node14867 +def node14869 : Tree Nat := .node node14546 node14868 +def node14870 : Tree Nat := .node node13979 node6994 +def node14871 : Tree Nat := .node node10608 node14870 +def node14872 : Tree Nat := .node node14552 node14871 +def node14873 : Tree Nat := .node node14869 node14872 +def node14874 : Tree Nat := .node node14864 node14873 +def node14875 : Tree Nat := .node node6733 node10435 +def node14876 : Tree Nat := .node node13885 node14875 +def node14877 : Tree Nat := .node node14876 node14563 +def node14878 : Tree Nat := .node node14561 node14877 +def node14879 : Tree Nat := .node node14558 node14878 +def node14880 : Tree Nat := .node node14214 node14096 +def node14881 : Tree Nat := .node node14213 node14880 +def node14882 : Tree Nat := .node node14571 node14881 +def node14883 : Tree Nat := .node node14569 node14882 +def node14884 : Tree Nat := .node node14879 node14883 +def node14885 : Tree Nat := .node node14874 node14884 +def node14886 : Tree Nat := .node node6180 node10435 +def node14887 : Tree Nat := .node node14227 node14886 +def node14888 : Tree Nat := .node node14226 node14887 +def node14889 : Tree Nat := .node node14578 node14888 +def node14890 : Tree Nat := .node node10435 node8395 +def node14891 : Tree Nat := .node node13885 node14890 +def node14892 : Tree Nat := .node node14054 node13885 +def node14893 : Tree Nat := .node node14891 node14892 +def node14894 : Tree Nat := .node node13885 node14084 +def node14895 : Tree Nat := .node node14704 node6478 +def node14896 : Tree Nat := .node node14894 node14895 +def node14897 : Tree Nat := .node node14893 node14896 +def node14898 : Tree Nat := .node node14889 node14897 +def node14899 : Tree Nat := .node node6348 node10435 +def node14900 : Tree Nat := .node node14242 node14899 +def node14901 : Tree Nat := .node node14241 node14900 +def node14902 : Tree Nat := .node node14240 node14901 +def node14903 : Tree Nat := .node node13995 node14590 +def node14904 : Tree Nat := .node node14586 node14903 +def node14905 : Tree Nat := .node node14902 node14904 +def node14906 : Tree Nat := .node node14898 node14905 +def node14907 : Tree Nat := .node node14214 node8596 +def node14908 : Tree Nat := .node node14255 node14907 +def node14909 : Tree Nat := .node node7470 node10435 +def node14910 : Tree Nat := .node node12577 node14909 +def node14911 : Tree Nat := .node node14595 node14910 +def node14912 : Tree Nat := .node node14908 node14911 +def node14913 : Tree Nat := .node node12581 node13885 +def node14914 : Tree Nat := .node node14598 node14913 +def node14915 : Tree Nat := .node node13885 node8606 +def node14916 : Tree Nat := .node node14915 node11879 +def node14917 : Tree Nat := .node node14914 node14916 +def node14918 : Tree Nat := .node node14912 node14917 +def node14919 : Tree Nat := .node node10435 node8470 +def node14920 : Tree Nat := .node node14780 node14919 +def node14921 : Tree Nat := .node node14263 node14920 +def node14922 : Tree Nat := .node node14921 node14604 +def node14923 : Tree Nat := .node node10458 node10435 +def node14924 : Tree Nat := .node node14923 node14608 +def node14925 : Tree Nat := .node node14269 node14096 +def node14926 : Tree Nat := .node node14924 node14925 +def node14927 : Tree Nat := .node node14607 node14926 +def node14928 : Tree Nat := .node node14922 node14927 +def node14929 : Tree Nat := .node node14918 node14928 +def node14930 : Tree Nat := .node node14906 node14929 +def node14931 : Tree Nat := .node node14885 node14930 +def node14932 : Tree Nat := .node node14854 node14931 +def node14933 : Tree Nat := .node node14779 node14932 +def node14934 : Tree Nat := .node node13930 node13885 +def node14935 : Tree Nat := .node node13995 node14934 +def node14936 : Tree Nat := .node node14619 node14935 +def node14937 : Tree Nat := .node node13510 node10435 +def node14938 : Tree Nat := .node node14937 node14096 +def node14939 : Tree Nat := .node node13940 node14938 +def node14940 : Tree Nat := .node node13939 node14939 +def node14941 : Tree Nat := .node node14936 node14940 +def node14942 : Tree Nat := .node node13885 node14642 +def node14943 : Tree Nat := .node node10435 node7727 +def node14944 : Tree Nat := .node node13945 node14943 +def node14945 : Tree Nat := .node node14942 node14944 +def node14946 : Tree Nat := .node node10435 node6192 +def node14947 : Tree Nat := .node node13885 node14946 +def node14948 : Tree Nat := .node node14947 node14622 +def node14949 : Tree Nat := .node node14945 node14948 +def node14950 : Tree Nat := .node node14949 node14627 +def node14951 : Tree Nat := .node node14941 node14950 +def node14952 : Tree Nat := .node node13885 node14589 +def node14953 : Tree Nat := .node node14952 node14631 +def node14954 : Tree Nat := .node node14299 node14953 +def node14955 : Tree Nat := .node node5826 node10435 +def node14956 : Tree Nat := .node node13073 node14955 +def node14957 : Tree Nat := .node node14634 node14956 +def node14958 : Tree Nat := .node node14957 node14636 +def node14959 : Tree Nat := .node node14954 node14958 +def node14960 : Tree Nat := .node node12655 node11178 +def node14961 : Tree Nat := .node node14310 node14960 +def node14962 : Tree Nat := .node node5821 node10435 +def node14963 : Tree Nat := .node node13885 node14962 +def node14964 : Tree Nat := .node node14963 node14639 +def node14965 : Tree Nat := .node node14961 node14964 +def node14966 : Tree Nat := .node node14965 node14645 +def node14967 : Tree Nat := .node node14959 node14966 +def node14968 : Tree Nat := .node node14951 node14967 +def node14969 : Tree Nat := .node node10435 node6569 +def node14970 : Tree Nat := .node node10812 node14969 +def node14971 : Tree Nat := .node node7370 node10435 +def node14972 : Tree Nat := .node node13986 node14971 +def node14973 : Tree Nat := .node node14970 node14972 +def node14974 : Tree Nat := .node node14326 node14973 +def node14975 : Tree Nat := .node node14974 node14654 +def node14976 : Tree Nat := .node node10435 node8227 +def node14977 : Tree Nat := .node node12687 node14976 +def node14978 : Tree Nat := .node node13995 node14977 +def node14979 : Tree Nat := .node node10720 node13885 +def node14980 : Tree Nat := .node node14979 node14657 +def node14981 : Tree Nat := .node node14978 node14980 +def node14982 : Tree Nat := .node node10435 node6242 +def node14983 : Tree Nat := .node node10910 node14982 +def node14984 : Tree Nat := .node node14983 node13999 +def node14985 : Tree Nat := .node node14984 node14662 +def node14986 : Tree Nat := .node node14981 node14985 +def node14987 : Tree Nat := .node node14975 node14986 +def node14988 : Tree Nat := .node node13599 node14576 +def node14989 : Tree Nat := .node node13995 node14988 +def node14990 : Tree Nat := .node node14667 node14989 +def node14991 : Tree Nat := .node node14008 node14096 +def node14992 : Tree Nat := .node node14677 node14991 +def node14993 : Tree Nat := .node node14675 node14992 +def node14994 : Tree Nat := .node node14990 node14993 +def node14995 : Tree Nat := .node node5835 node10435 +def node14996 : Tree Nat := .node node13885 node14995 +def node14997 : Tree Nat := .node node10435 node8256 +def node14998 : Tree Nat := .node node12721 node14997 +def node14999 : Tree Nat := .node node14996 node14998 +def node15000 : Tree Nat := .node node13614 node14096 +def node15001 : Tree Nat := .node node14346 node15000 +def node15002 : Tree Nat := .node node14999 node15001 +def node15003 : Tree Nat := .node node13995 node14685 +def node15004 : Tree Nat := .node node15003 node14351 +def node15005 : Tree Nat := .node node15002 node15004 +def node15006 : Tree Nat := .node node14994 node15005 +def node15007 : Tree Nat := .node node14987 node15006 +def node15008 : Tree Nat := .node node14968 node15007 +def node15009 : Tree Nat := .node node10435 node8270 +def node15010 : Tree Nat := .node node12739 node15009 +def node15011 : Tree Nat := .node node14693 node15010 +def node15012 : Tree Nat := .node node10435 node6554 +def node15013 : Tree Nat := .node node10812 node15012 +def node15014 : Tree Nat := .node node13173 node13885 +def node15015 : Tree Nat := .node node15013 node15014 +def node15016 : Tree Nat := .node node15011 node15015 +def node15017 : Tree Nat := .node node13627 node10435 +def node15018 : Tree Nat := .node node15017 node14096 +def node15019 : Tree Nat := .node node14361 node15018 +def node15020 : Tree Nat := .node node14699 node15019 +def node15021 : Tree Nat := .node node15016 node15020 +def node15022 : Tree Nat := .node node10435 node6642 +def node15023 : Tree Nat := .node node10720 node15022 +def node15024 : Tree Nat := .node node13633 node13885 +def node15025 : Tree Nat := .node node15023 node15024 +def node15026 : Tree Nat := .node node14367 node15025 +def node15027 : Tree Nat := .node node10910 node13885 +def node15028 : Tree Nat := .node node15027 node14702 +def node15029 : Tree Nat := .node node15028 node14706 +def node15030 : Tree Nat := .node node15026 node15029 +def node15031 : Tree Nat := .node node15021 node15030 +def node15032 : Tree Nat := .node node7353 node10435 +def node15033 : Tree Nat := .node node13652 node15032 +def node15034 : Tree Nat := .node node13995 node15033 +def node15035 : Tree Nat := .node node14711 node15034 +def node15036 : Tree Nat := .node node13192 node10435 +def node15037 : Tree Nat := .node node15036 node13885 +def node15038 : Tree Nat := .node node13995 node15037 +def node15039 : Tree Nat := .node node15038 node14715 +def node15040 : Tree Nat := .node node15035 node15039 +def node15041 : Tree Nat := .node node10435 node8245 +def node15042 : Tree Nat := .node node14718 node15041 +def node15043 : Tree Nat := .node node14048 node15042 +def node15044 : Tree Nat := .node node13664 node10435 +def node15045 : Tree Nat := .node node15044 node14723 +def node15046 : Tree Nat := .node node13995 node15045 +def node15047 : Tree Nat := .node node15043 node15046 +def node15048 : Tree Nat := .node node10435 node7326 +def node15049 : Tree Nat := .node node13885 node15048 +def node15050 : Tree Nat := .node node13183 node10435 +def node15051 : Tree Nat := .node node15050 node14051 +def node15052 : Tree Nat := .node node15049 node15051 +def node15053 : Tree Nat := .node node15052 node14729 +def node15054 : Tree Nat := .node node15047 node15053 +def node15055 : Tree Nat := .node node15040 node15054 +def node15056 : Tree Nat := .node node15031 node15055 +def node15057 : Tree Nat := .node node6549 node10435 +def node15058 : Tree Nat := .node node13885 node15057 +def node15059 : Tree Nat := .node node13205 node10435 +def node15060 : Tree Nat := .node node15059 node13885 +def node15061 : Tree Nat := .node node15058 node15060 +def node15062 : Tree Nat := .node node14735 node15061 +def node15063 : Tree Nat := .node node13209 node10435 +def node15064 : Tree Nat := .node node15063 node13885 +def node15065 : Tree Nat := .node node14738 node15064 +def node15066 : Tree Nat := .node node15065 node14743 +def node15067 : Tree Nat := .node node15062 node15066 +def node15068 : Tree Nat := .node node13637 node10435 +def node15069 : Tree Nat := .node node15068 node13885 +def node15070 : Tree Nat := .node node13995 node15069 +def node15071 : Tree Nat := .node node14748 node15070 +def node15072 : Tree Nat := .node node13199 node10435 +def node15073 : Tree Nat := .node node15072 node13885 +def node15074 : Tree Nat := .node node14416 node15073 +def node15075 : Tree Nat := .node node15074 node14753 +def node15076 : Tree Nat := .node node15071 node15075 +def node15077 : Tree Nat := .node node15067 node15076 +def node15078 : Tree Nat := .node node14806 node14758 +def node15079 : Tree Nat := .node node10435 node9112 +def node15080 : Tree Nat := .node node13885 node15079 +def node15081 : Tree Nat := .node node13542 node10435 +def node15082 : Tree Nat := .node node15081 node13885 +def node15083 : Tree Nat := .node node15080 node15082 +def node15084 : Tree Nat := .node node15078 node15083 +def node15085 : Tree Nat := .node node13226 node10435 +def node15086 : Tree Nat := .node node15085 node14428 +def node15087 : Tree Nat := .node node13995 node15086 +def node15088 : Tree Nat := .node node15087 node14764 +def node15089 : Tree Nat := .node node15084 node15088 +def node15090 : Tree Nat := .node node10435 node8238 +def node15091 : Tree Nat := .node node14767 node15090 +def node15092 : Tree Nat := .node node13995 node15091 +def node15093 : Tree Nat := .node node10435 node6668 +def node15094 : Tree Nat := .node node13885 node15093 +def node15095 : Tree Nat := .node node13502 node10435 +def node15096 : Tree Nat := .node node15095 node14096 +def node15097 : Tree Nat := .node node15094 node15096 +def node15098 : Tree Nat := .node node15092 node15097 +def node15099 : Tree Nat := .node node13215 node10435 +def node15100 : Tree Nat := .node node15099 node13885 +def node15101 : Tree Nat := .node node14438 node15100 +def node15102 : Tree Nat := .node node15101 node14773 +def node15103 : Tree Nat := .node node15098 node15102 +def node15104 : Tree Nat := .node node15089 node15103 +def node15105 : Tree Nat := .node node15077 node15104 +def node15106 : Tree Nat := .node node15056 node15105 +def node15107 : Tree Nat := .node node15008 node15106 +def node15108 : Tree Nat := .node node12111 node13885 +def node15109 : Tree Nat := .node node7337 node10435 +def node15110 : Tree Nat := .node node13290 node15109 +def node15111 : Tree Nat := .node node15108 node15110 +def node15112 : Tree Nat := .node node14782 node15111 +def node15113 : Tree Nat := .node node12120 node13885 +def node15114 : Tree Nat := .node node13640 node10435 +def node15115 : Tree Nat := .node node15114 node7141 +def node15116 : Tree Nat := .node node15113 node15115 +def node15117 : Tree Nat := .node node14787 node15116 +def node15118 : Tree Nat := .node node15112 node15117 +def node15119 : Tree Nat := .node node10561 node14489 +def node15120 : Tree Nat := .node node10435 node7747 +def node15121 : Tree Nat := .node node12861 node15120 +def node15122 : Tree Nat := .node node15119 node15121 +def node15123 : Tree Nat := .node node7395 node10435 +def node15124 : Tree Nat := .node node13741 node15123 +def node15125 : Tree Nat := .node node14794 node15124 +def node15126 : Tree Nat := .node node15122 node15125 +def node15127 : Tree Nat := .node node10472 node13885 +def node15128 : Tree Nat := .node node15127 node14456 +def node15129 : Tree Nat := .node node15128 node14460 +def node15130 : Tree Nat := .node node15126 node15129 +def node15131 : Tree Nat := .node node15118 node15130 +def node15132 : Tree Nat := .node node13754 node14576 +def node15133 : Tree Nat := .node node13995 node15132 +def node15134 : Tree Nat := .node node14465 node15133 +def node15135 : Tree Nat := .node node15134 node14808 +def node15136 : Tree Nat := .node node13995 node14810 +def node15137 : Tree Nat := .node node14474 node15136 +def node15138 : Tree Nat := .node node10435 node7343 +def node15139 : Tree Nat := .node node13885 node15138 +def node15140 : Tree Nat := .node node15139 node14479 +def node15141 : Tree Nat := .node node15140 node14815 +def node15142 : Tree Nat := .node node15137 node15141 +def node15143 : Tree Nat := .node node15135 node15142 +def node15144 : Tree Nat := .node node15131 node15143 +def node15145 : Tree Nat := .node node14339 node13885 +def node15146 : Tree Nat := .node node14493 node15145 +def node15147 : Tree Nat := .node node14491 node15146 +def node15148 : Tree Nat := .node node13766 node10435 +def node15149 : Tree Nat := .node node15148 node14096 +def node15150 : Tree Nat := .node node14823 node15149 +def node15151 : Tree Nat := .node node14821 node15150 +def node15152 : Tree Nat := .node node15147 node15151 +def node15153 : Tree Nat := .node node10435 node8342 +def node15154 : Tree Nat := .node node12917 node15153 +def node15155 : Tree Nat := .node node14140 node15154 +def node15156 : Tree Nat := .node node14979 node14827 +def node15157 : Tree Nat := .node node15155 node15156 +def node15158 : Tree Nat := .node node15157 node14833 +def node15159 : Tree Nat := .node node15152 node15158 +def node15160 : Tree Nat := .node node13808 node13885 +def node15161 : Tree Nat := .node node13995 node15160 +def node15162 : Tree Nat := .node node14837 node15161 +def node15163 : Tree Nat := .node node15162 node14521 +def node15164 : Tree Nat := .node node13885 node14489 +def node15165 : Tree Nat := .node node15164 node14843 +def node15166 : Tree Nat := .node node13885 node14411 +def node15167 : Tree Nat := .node node15166 node14524 +def node15168 : Tree Nat := .node node15165 node15167 +def node15169 : Tree Nat := .node node15168 node14850 +def node15170 : Tree Nat := .node node15163 node15169 +def node15171 : Tree Nat := .node node15159 node15170 +def node15172 : Tree Nat := .node node15144 node15171 +def node15173 : Tree Nat := .node node12223 node13885 +def node15174 : Tree Nat := .node node13406 node13885 +def node15175 : Tree Nat := .node node15173 node15174 +def node15176 : Tree Nat := .node node14856 node15175 +def node15177 : Tree Nat := .node node13512 node10435 +def node15178 : Tree Nat := .node node15177 node14096 +def node15179 : Tree Nat := .node node14861 node15178 +def node15180 : Tree Nat := .node node14859 node15179 +def node15181 : Tree Nat := .node node15176 node15180 +def node15182 : Tree Nat := .node node10435 node8200 +def node15183 : Tree Nat := .node node12965 node15182 +def node15184 : Tree Nat := .node node14545 node15183 +def node15185 : Tree Nat := .node node15184 node14868 +def node15186 : Tree Nat := .node node15185 node14872 +def node15187 : Tree Nat := .node node15181 node15186 +def node15188 : Tree Nat := .node node6659 node10435 +def node15189 : Tree Nat := .node node13885 node15188 +def node15190 : Tree Nat := .node node14192 node13885 +def node15191 : Tree Nat := .node node15189 node15190 +def node15192 : Tree Nat := .node node14191 node15191 +def node15193 : Tree Nat := .node node15192 node14878 +def node15194 : Tree Nat := .node node13520 node10435 +def node15195 : Tree Nat := .node node15194 node14096 +def node15196 : Tree Nat := .node node13995 node15195 +def node15197 : Tree Nat := .node node14205 node15196 +def node15198 : Tree Nat := .node node15197 node14882 +def node15199 : Tree Nat := .node node15193 node15198 +def node15200 : Tree Nat := .node node15187 node15199 +def node15201 : Tree Nat := .node node13995 node14887 +def node15202 : Tree Nat := .node node14578 node15201 +def node15203 : Tree Nat := .node node15202 node14897 +def node15204 : Tree Nat := .node node7333 node10435 +def node15205 : Tree Nat := .node node13885 node15204 +def node15206 : Tree Nat := .node node15205 node14900 +def node15207 : Tree Nat := .node node14240 node15206 +def node15208 : Tree Nat := .node node10435 node7916 +def node15209 : Tree Nat := .node node13885 node15208 +def node15210 : Tree Nat := .node node15209 node14585 +def node15211 : Tree Nat := .node node15210 node14903 +def node15212 : Tree Nat := .node node15207 node15211 +def node15213 : Tree Nat := .node node15203 node15212 +def node15214 : Tree Nat := .node node14855 node14907 +def node15215 : Tree Nat := .node node13885 node13975 +def node15216 : Tree Nat := .node node13979 node14909 +def node15217 : Tree Nat := .node node15215 node15216 +def node15218 : Tree Nat := .node node15214 node15217 +def node15219 : Tree Nat := .node node14660 node13885 +def node15220 : Tree Nat := .node node14598 node15219 +def node15221 : Tree Nat := .node node14318 node7300 +def node15222 : Tree Nat := .node node14915 node15221 +def node15223 : Tree Nat := .node node15220 node15222 +def node15224 : Tree Nat := .node node15218 node15223 +def node15225 : Tree Nat := .node node13885 node14544 +def node15226 : Tree Nat := .node node15225 node14920 +def node15227 : Tree Nat := .node node11359 node10435 +def node15228 : Tree Nat := .node node15227 node7704 +def node15229 : Tree Nat := .node node13995 node15228 +def node15230 : Tree Nat := .node node15226 node15229 +def node15231 : Tree Nat := .node node11766 node10435 +def node15232 : Tree Nat := .node node7068 node10435 +def node15233 : Tree Nat := .node node15231 node15232 +def node15234 : Tree Nat := .node node13995 node15233 +def node15235 : Tree Nat := .node node15234 node14926 +def node15236 : Tree Nat := .node node15230 node15235 +def node15237 : Tree Nat := .node node15224 node15236 +def node15238 : Tree Nat := .node node15213 node15237 +def node15239 : Tree Nat := .node node15200 node15238 +def node15240 : Tree Nat := .node node15172 node15239 +def node15241 : Tree Nat := .node node15107 node15240 +def node15242 : Tree Nat := .node node7315 node10435 +def node15243 : Tree Nat := .node node13926 node15242 +def node15244 : Tree Nat := .node node14618 node15243 +def node15245 : Tree Nat := .node node15244 node14935 +def node15246 : Tree Nat := .node node6528 node10435 +def node15247 : Tree Nat := .node node13937 node15246 +def node15248 : Tree Nat := .node node13936 node15247 +def node15249 : Tree Nat := .node node15248 node14939 +def node15250 : Tree Nat := .node node15245 node15249 +def node15251 : Tree Nat := .node node13945 node13885 +def node15252 : Tree Nat := .node node14942 node15251 +def node15253 : Tree Nat := .node node15252 node14948 +def node15254 : Tree Nat := .node node6939 node10435 +def node15255 : Tree Nat := .node node13885 node15254 +def node15256 : Tree Nat := .node node15255 node14625 +def node15257 : Tree Nat := .node node14294 node15256 +def node15258 : Tree Nat := .node node15253 node15257 +def node15259 : Tree Nat := .node node15250 node15258 +def node15260 : Tree Nat := .node node14072 node13885 +def node15261 : Tree Nat := .node node14952 node15260 +def node15262 : Tree Nat := .node node14299 node15261 +def node15263 : Tree Nat := .node node13072 node10435 +def node15264 : Tree Nat := .node node15263 node14955 +def node15265 : Tree Nat := .node node14634 node15264 +def node15266 : Tree Nat := .node node15265 node14636 +def node15267 : Tree Nat := .node node15262 node15266 +def node15268 : Tree Nat := .node node12654 node10435 +def node15269 : Tree Nat := .node node15268 node11178 +def node15270 : Tree Nat := .node node14310 node15269 +def node15271 : Tree Nat := .node node15270 node14964 +def node15272 : Tree Nat := .node node13092 node10435 +def node15273 : Tree Nat := .node node15272 node13885 +def node15274 : Tree Nat := .node node14315 node15273 +def node15275 : Tree Nat := .node node15274 node14644 +def node15276 : Tree Nat := .node node15271 node15275 +def node15277 : Tree Nat := .node node15267 node15276 +def node15278 : Tree Nat := .node node15259 node15277 +def node15279 : Tree Nat := .node node7366 node10435 +def node15280 : Tree Nat := .node node12671 node15279 +def node15281 : Tree Nat := .node node14325 node15280 +def node15282 : Tree Nat := .node node15281 node14973 +def node15283 : Tree Nat := .node node6578 node10435 +def node15284 : Tree Nat := .node node10715 node15283 +def node15285 : Tree Nat := .node node15284 node14652 +def node15286 : Tree Nat := .node node14650 node15285 +def node15287 : Tree Nat := .node node15282 node15286 +def node15288 : Tree Nat := .node node12687 node13885 +def node15289 : Tree Nat := .node node13995 node15288 +def node15290 : Tree Nat := .node node15289 node14980 +def node15291 : Tree Nat := .node node10499 node13885 +def node15292 : Tree Nat := .node node15291 node14661 +def node15293 : Tree Nat := .node node14984 node15292 +def node15294 : Tree Nat := .node node15290 node15293 +def node15295 : Tree Nat := .node node15287 node15294 +def node15296 : Tree Nat := .node node12704 node13885 +def node15297 : Tree Nat := .node node14666 node15296 +def node15298 : Tree Nat := .node node14102 node14576 +def node15299 : Tree Nat := .node node13995 node15298 +def node15300 : Tree Nat := .node node15297 node15299 +def node15301 : Tree Nat := .node node13142 node10435 +def node15302 : Tree Nat := .node node15301 node13885 +def node15303 : Tree Nat := .node node14673 node15302 +def node15304 : Tree Nat := .node node15303 node14992 +def node15305 : Tree Nat := .node node15300 node15304 +def node15306 : Tree Nat := .node node12720 node10435 +def node15307 : Tree Nat := .node node15306 node13885 +def node15308 : Tree Nat := .node node14996 node15307 +def node15309 : Tree Nat := .node node6606 node10435 +def node15310 : Tree Nat := .node node13885 node15309 +def node15311 : Tree Nat := .node node13613 node10435 +def node15312 : Tree Nat := .node node15311 node14096 +def node15313 : Tree Nat := .node node15310 node15312 +def node15314 : Tree Nat := .node node15308 node15313 +def node15315 : Tree Nat := .node node13160 node10435 +def node15316 : Tree Nat := .node node15315 node13885 +def node15317 : Tree Nat := .node node13995 node15316 +def node15318 : Tree Nat := .node node15317 node14351 +def node15319 : Tree Nat := .node node15314 node15318 +def node15320 : Tree Nat := .node node15305 node15319 +def node15321 : Tree Nat := .node node15295 node15320 +def node15322 : Tree Nat := .node node15278 node15321 +def node15323 : Tree Nat := .node node12739 node13885 +def node15324 : Tree Nat := .node node14693 node15323 +def node15325 : Tree Nat := .node node15324 node15015 +def node15326 : Tree Nat := .node node13177 node13885 +def node15327 : Tree Nat := .node node14696 node15326 +def node15328 : Tree Nat := .node node10715 node13885 +def node15329 : Tree Nat := .node node15328 node15018 +def node15330 : Tree Nat := .node node15327 node15329 +def node15331 : Tree Nat := .node node15325 node15330 +def node15332 : Tree Nat := .node node12750 node13885 +def node15333 : Tree Nat := .node node14366 node15332 +def node15334 : Tree Nat := .node node15333 node15025 +def node15335 : Tree Nat := .node node15291 node14705 +def node15336 : Tree Nat := .node node15028 node15335 +def node15337 : Tree Nat := .node node15334 node15336 +def node15338 : Tree Nat := .node node15331 node15337 +def node15339 : Tree Nat := .node node14718 node13885 +def node15340 : Tree Nat := .node node14048 node15339 +def node15341 : Tree Nat := .node node15340 node15046 +def node15342 : Tree Nat := .node node15341 node15053 +def node15343 : Tree Nat := .node node15040 node15342 +def node15344 : Tree Nat := .node node15338 node15343 +def node15345 : Tree Nat := .node node6694 node10435 +def node15346 : Tree Nat := .node node14042 node15345 +def node15347 : Tree Nat := .node node13995 node15346 +def node15348 : Tree Nat := .node node15347 node15061 +def node15349 : Tree Nat := .node node6546 node10435 +def node15350 : Tree Nat := .node node13885 node15349 +def node15351 : Tree Nat := .node node15350 node14742 +def node15352 : Tree Nat := .node node15065 node15351 +def node15353 : Tree Nat := .node node15348 node15352 +def node15354 : Tree Nat := .node node15353 node15076 +def node15355 : Tree Nat := .node node14757 node13885 +def node15356 : Tree Nat := .node node14806 node15355 +def node15357 : Tree Nat := .node node13995 node15082 +def node15358 : Tree Nat := .node node15356 node15357 +def node15359 : Tree Nat := .node node15358 node15088 +def node15360 : Tree Nat := .node node14767 node13885 +def node15361 : Tree Nat := .node node13995 node15360 +def node15362 : Tree Nat := .node node15361 node15097 +def node15363 : Tree Nat := .node node7116 node10435 +def node15364 : Tree Nat := .node node14771 node15363 +def node15365 : Tree Nat := .node node15364 node6747 +def node15366 : Tree Nat := .node node15101 node15365 +def node15367 : Tree Nat := .node node15362 node15366 +def node15368 : Tree Nat := .node node15359 node15367 +def node15369 : Tree Nat := .node node15354 node15368 +def node15370 : Tree Nat := .node node15344 node15369 +def node15371 : Tree Nat := .node node15322 node15370 +def node15372 : Tree Nat := .node node14134 node13885 +def node15373 : Tree Nat := .node node14781 node15372 +def node15374 : Tree Nat := .node node15373 node15111 +def node15375 : Tree Nat := .node node13295 node13885 +def node15376 : Tree Nat := .node node14784 node15375 +def node15377 : Tree Nat := .node node13995 node15115 +def node15378 : Tree Nat := .node node15376 node15377 +def node15379 : Tree Nat := .node node15374 node15378 +def node15380 : Tree Nat := .node node12861 node13885 +def node15381 : Tree Nat := .node node15119 node15380 +def node15382 : Tree Nat := .node node11086 node13885 +def node15383 : Tree Nat := .node node15382 node15124 +def node15384 : Tree Nat := .node node15381 node15383 +def node15385 : Tree Nat := .node node10566 node13885 +def node15386 : Tree Nat := .node node15227 node7157 +def node15387 : Tree Nat := .node node15385 node15386 +def node15388 : Tree Nat := .node node15128 node15387 +def node15389 : Tree Nat := .node node15384 node15388 +def node15390 : Tree Nat := .node node15379 node15389 +def node15391 : Tree Nat := .node node12871 node14544 +def node15392 : Tree Nat := .node node14464 node15391 +def node15393 : Tree Nat := .node node14146 node14576 +def node15394 : Tree Nat := .node node13995 node15393 +def node15395 : Tree Nat := .node node15392 node15394 +def node15396 : Tree Nat := .node node13124 node10435 +def node15397 : Tree Nat := .node node15396 node13885 +def node15398 : Tree Nat := .node node14996 node15397 +def node15399 : Tree Nat := .node node15398 node14807 +def node15400 : Tree Nat := .node node15395 node15399 +def node15401 : Tree Nat := .node node12690 node10435 +def node15402 : Tree Nat := .node node15401 node14692 +def node15403 : Tree Nat := .node node14473 node15402 +def node15404 : Tree Nat := .node node15403 node15136 +def node15405 : Tree Nat := .node node13308 node10435 +def node15406 : Tree Nat := .node node15405 node14236 +def node15407 : Tree Nat := .node node15139 node15406 +def node15408 : Tree Nat := .node node15407 node14815 +def node15409 : Tree Nat := .node node15404 node15408 +def node15410 : Tree Nat := .node node15400 node15409 +def node15411 : Tree Nat := .node node15390 node15410 +def node15412 : Tree Nat := .node node12903 node13885 +def node15413 : Tree Nat := .node node14490 node15412 +def node15414 : Tree Nat := .node node10812 node13885 +def node15415 : Tree Nat := .node node15414 node15145 +def node15416 : Tree Nat := .node node15413 node15415 +def node15417 : Tree Nat := .node node15328 node15149 +def node15418 : Tree Nat := .node node14821 node15417 +def node15419 : Tree Nat := .node node15416 node15418 +def node15420 : Tree Nat := .node node12917 node13885 +def node15421 : Tree Nat := .node node14140 node15420 +def node15422 : Tree Nat := .node node15421 node15156 +def node15423 : Tree Nat := .node node15291 node14831 +def node15424 : Tree Nat := .node node14509 node15423 +def node15425 : Tree Nat := .node node15422 node15424 +def node15426 : Tree Nat := .node node15419 node15425 +def node15427 : Tree Nat := .node node13885 node15231 +def node15428 : Tree Nat := .node node7955 node10435 +def node15429 : Tree Nat := .node node12927 node15428 +def node15430 : Tree Nat := .node node15427 node15429 +def node15431 : Tree Nat := .node node13758 node10435 +def node15432 : Tree Nat := .node node15431 node13885 +def node15433 : Tree Nat := .node node13995 node15432 +def node15434 : Tree Nat := .node node15430 node15433 +def node15435 : Tree Nat := .node node13135 node10435 +def node15436 : Tree Nat := .node node15435 node14156 +def node15437 : Tree Nat := .node node14516 node15436 +def node15438 : Tree Nat := .node node7008 node10435 +def node15439 : Tree Nat := .node node13885 node15438 +def node15440 : Tree Nat := .node node15439 node14519 +def node15441 : Tree Nat := .node node15437 node15440 +def node15442 : Tree Nat := .node node15434 node15441 +def node15443 : Tree Nat := .node node12920 node10435 +def node15444 : Tree Nat := .node node15443 node13885 +def node15445 : Tree Nat := .node node15164 node15444 +def node15446 : Tree Nat := .node node13731 node10435 +def node15447 : Tree Nat := .node node15446 node14096 +def node15448 : Tree Nat := .node node13995 node15447 +def node15449 : Tree Nat := .node node15445 node15448 +def node15450 : Tree Nat := .node node13153 node10435 +def node15451 : Tree Nat := .node node15450 node13885 +def node15452 : Tree Nat := .node node14846 node15451 +def node15453 : Tree Nat := .node node7031 node10435 +def node15454 : Tree Nat := .node node12945 node15453 +def node15455 : Tree Nat := .node node15454 node14848 +def node15456 : Tree Nat := .node node15452 node15455 +def node15457 : Tree Nat := .node node15449 node15456 +def node15458 : Tree Nat := .node node15442 node15457 +def node15459 : Tree Nat := .node node15426 node15458 +def node15460 : Tree Nat := .node node15411 node15459 +def node15461 : Tree Nat := .node node14115 node13885 +def node15462 : Tree Nat := .node node14855 node15461 +def node15463 : Tree Nat := .node node15462 node15175 +def node15464 : Tree Nat := .node node6999 node10435 +def node15465 : Tree Nat := .node node13410 node15464 +def node15466 : Tree Nat := .node node14858 node15465 +def node15467 : Tree Nat := .node node13995 node15178 +def node15468 : Tree Nat := .node node15466 node15467 +def node15469 : Tree Nat := .node node15463 node15468 +def node15470 : Tree Nat := .node node12965 node13885 +def node15471 : Tree Nat := .node node14545 node15470 +def node15472 : Tree Nat := .node node12241 node13885 +def node15473 : Tree Nat := .node node15472 node14867 +def node15474 : Tree Nat := .node node15471 node15473 +def node15475 : Tree Nat := .node node7094 node10435 +def node15476 : Tree Nat := .node node10607 node15475 +def node15477 : Tree Nat := .node node15476 node14870 +def node15478 : Tree Nat := .node node14552 node15477 +def node15479 : Tree Nat := .node node15474 node15478 +def node15480 : Tree Nat := .node node15469 node15479 +def node15481 : Tree Nat := .node node11427 node14236 +def node15482 : Tree Nat := .node node15481 node14190 +def node15483 : Tree Nat := .node node15482 node15191 +def node15484 : Tree Nat := .node node15483 node14878 +def node15485 : Tree Nat := .node node7051 node10435 +def node15486 : Tree Nat := .node node13877 node15485 +def node15487 : Tree Nat := .node node14204 node15486 +def node15488 : Tree Nat := .node node15487 node15196 +def node15489 : Tree Nat := .node node6242 node10435 +def node15490 : Tree Nat := .node node14212 node15489 +def node15491 : Tree Nat := .node node15490 node14880 +def node15492 : Tree Nat := .node node14571 node15491 +def node15493 : Tree Nat := .node node15488 node15492 +def node15494 : Tree Nat := .node node15484 node15493 +def node15495 : Tree Nat := .node node15480 node15494 +def node15496 : Tree Nat := .node node14222 node13885 +def node15497 : Tree Nat := .node node14577 node15496 +def node15498 : Tree Nat := .node node15497 node15201 +def node15499 : Tree Nat := .node node13995 node14892 +def node15500 : Tree Nat := .node node13995 node14895 +def node15501 : Tree Nat := .node node15499 node15500 +def node15502 : Tree Nat := .node node15498 node15501 +def node15503 : Tree Nat := .node node14238 node13885 +def node15504 : Tree Nat := .node node14237 node15503 +def node15505 : Tree Nat := .node node15504 node15206 +def node15506 : Tree Nat := .node node15505 node15211 +def node15507 : Tree Nat := .node node15502 node15506 +def node15508 : Tree Nat := .node node8089 node10435 +def node15509 : Tree Nat := .node node14214 node15508 +def node15510 : Tree Nat := .node node14855 node15509 +def node15511 : Tree Nat := .node node13995 node15216 +def node15512 : Tree Nat := .node node15510 node15511 +def node15513 : Tree Nat := .node node7087 node10435 +def node15514 : Tree Nat := .node node13885 node15513 +def node15515 : Tree Nat := .node node15514 node15221 +def node15516 : Tree Nat := .node node15220 node15515 +def node15517 : Tree Nat := .node node15512 node15516 +def node15518 : Tree Nat := .node node14780 node13885 +def node15519 : Tree Nat := .node node15225 node15518 +def node15520 : Tree Nat := .node node15519 node15229 +def node15521 : Tree Nat := .node node14923 node13885 +def node15522 : Tree Nat := .node node15521 node14925 +def node15523 : Tree Nat := .node node15234 node15522 +def node15524 : Tree Nat := .node node15520 node15523 +def node15525 : Tree Nat := .node node15517 node15524 +def node15526 : Tree Nat := .node node15507 node15525 +def node15527 : Tree Nat := .node node15495 node15526 +def node15528 : Tree Nat := .node node15460 node15527 +def node15529 : Tree Nat := .node node15371 node15528 +def node15530 : Tree Nat := .node node13926 node13885 +def node15531 : Tree Nat := .node node14618 node15530 +def node15532 : Tree Nat := .node node15531 node14935 +def node15533 : Tree Nat := .node node15532 node15249 +def node15534 : Tree Nat := .node node15533 node15258 +def node15535 : Tree Nat := .node node12638 node10435 +def node15536 : Tree Nat := .node node15535 node13964 +def node15537 : Tree Nat := .node node13995 node15536 +def node15538 : Tree Nat := .node node13995 node15260 +def node15539 : Tree Nat := .node node15537 node15538 +def node15540 : Tree Nat := .node node15539 node15266 +def node15541 : Tree Nat := .node node13555 node10435 +def node15542 : Tree Nat := .node node15541 node13885 +def node15543 : Tree Nat := .node node13995 node15542 +def node15544 : Tree Nat := .node node15270 node15543 +def node15545 : Tree Nat := .node node5831 node10435 +def node15546 : Tree Nat := .node node13885 node15545 +def node15547 : Tree Nat := .node node15546 node15273 +def node15548 : Tree Nat := .node node9979 node10435 +def node15549 : Tree Nat := .node node15548 node14642 +def node15550 : Tree Nat := .node node15549 node14319 +def node15551 : Tree Nat := .node node15547 node15550 +def node15552 : Tree Nat := .node node15544 node15551 +def node15553 : Tree Nat := .node node15540 node15552 +def node15554 : Tree Nat := .node node15534 node15553 +def node15555 : Tree Nat := .node node12671 node13885 +def node15556 : Tree Nat := .node node14325 node15555 +def node15557 : Tree Nat := .node node13986 node13885 +def node15558 : Tree Nat := .node node14970 node15557 +def node15559 : Tree Nat := .node node15556 node15558 +def node15560 : Tree Nat := .node node13885 node13990 +def node15561 : Tree Nat := .node node15560 node14649 +def node15562 : Tree Nat := .node node15561 node15285 +def node15563 : Tree Nat := .node node15559 node15562 +def node15564 : Tree Nat := .node node13561 node10435 +def node15565 : Tree Nat := .node node15564 node13885 +def node15566 : Tree Nat := .node node14979 node15565 +def node15567 : Tree Nat := .node node15289 node15566 +def node15568 : Tree Nat := .node node15567 node15293 +def node15569 : Tree Nat := .node node15563 node15568 +def node15570 : Tree Nat := .node node14266 node13885 +def node15571 : Tree Nat := .node node14666 node15570 +def node15572 : Tree Nat := .node node15571 node15299 +def node15573 : Tree Nat := .node node13995 node15302 +def node15574 : Tree Nat := .node node15573 node14992 +def node15575 : Tree Nat := .node node15572 node15574 +def node15576 : Tree Nat := .node node10436 node10435 +def node15577 : Tree Nat := .node node15576 node14349 +def node15578 : Tree Nat := .node node15577 node14019 +def node15579 : Tree Nat := .node node15317 node15578 +def node15580 : Tree Nat := .node node15314 node15579 +def node15581 : Tree Nat := .node node15575 node15580 +def node15582 : Tree Nat := .node node15569 node15581 +def node15583 : Tree Nat := .node node15554 node15582 +def node15584 : Tree Nat := .node node13885 node14692 +def node15585 : Tree Nat := .node node15584 node15323 +def node15586 : Tree Nat := .node node13885 node15012 +def node15587 : Tree Nat := .node node13172 node10435 +def node15588 : Tree Nat := .node node15587 node13885 +def node15589 : Tree Nat := .node node15586 node15588 +def node15590 : Tree Nat := .node node15585 node15589 +def node15591 : Tree Nat := .node node13995 node15326 +def node15592 : Tree Nat := .node node15591 node15329 +def node15593 : Tree Nat := .node node15590 node15592 +def node15594 : Tree Nat := .node node13885 node14365 +def node15595 : Tree Nat := .node node15594 node15332 +def node15596 : Tree Nat := .node node13587 node10435 +def node15597 : Tree Nat := .node node15596 node13885 +def node15598 : Tree Nat := .node node15023 node15597 +def node15599 : Tree Nat := .node node15595 node15598 +def node15600 : Tree Nat := .node node13188 node10435 +def node15601 : Tree Nat := .node node15600 node13885 +def node15602 : Tree Nat := .node node15027 node15601 +def node15603 : Tree Nat := .node node15602 node15335 +def node15604 : Tree Nat := .node node15599 node15603 +def node15605 : Tree Nat := .node node15593 node15604 +def node15606 : Tree Nat := .node node13651 node10435 +def node15607 : Tree Nat := .node node15606 node13885 +def node15608 : Tree Nat := .node node13995 node15607 +def node15609 : Tree Nat := .node node14711 node15608 +def node15610 : Tree Nat := .node node15609 node15039 +def node15611 : Tree Nat := .node node15044 node13885 +def node15612 : Tree Nat := .node node13995 node15611 +def node15613 : Tree Nat := .node node15340 node15612 +def node15614 : Tree Nat := .node node13995 node15051 +def node15615 : Tree Nat := .node node15614 node14729 +def node15616 : Tree Nat := .node node15613 node15615 +def node15617 : Tree Nat := .node node15610 node15616 +def node15618 : Tree Nat := .node node15605 node15617 +def node15619 : Tree Nat := .node node15618 node15369 +def node15620 : Tree Nat := .node node15583 node15619 +def node15621 : Tree Nat := .node node13110 node10435 +def node15622 : Tree Nat := .node node15621 node13885 +def node15623 : Tree Nat := .node node13995 node15622 +def node15624 : Tree Nat := .node node15373 node15623 +def node15625 : Tree Nat := .node node13294 node10435 +def node15626 : Tree Nat := .node node15625 node13885 +def node15627 : Tree Nat := .node node13995 node15626 +def node15628 : Tree Nat := .node node15627 node15377 +def node15629 : Tree Nat := .node node15624 node15628 +def node15630 : Tree Nat := .node node12674 node10435 +def node15631 : Tree Nat := .node node15630 node13885 +def node15632 : Tree Nat := .node node15119 node15631 +def node15633 : Tree Nat := .node node13578 node10435 +def node15634 : Tree Nat := .node node15633 node13885 +def node15635 : Tree Nat := .node node13995 node15634 +def node15636 : Tree Nat := .node node15632 node15635 +def node15637 : Tree Nat := .node node13995 node14456 +def node15638 : Tree Nat := .node node13995 node15386 +def node15639 : Tree Nat := .node node15637 node15638 +def node15640 : Tree Nat := .node node15636 node15639 +def node15641 : Tree Nat := .node node15629 node15640 +def node15642 : Tree Nat := .node node12696 node10435 +def node15643 : Tree Nat := .node node15642 node13885 +def node15644 : Tree Nat := .node node13995 node15643 +def node15645 : Tree Nat := .node node14146 node13885 +def node15646 : Tree Nat := .node node13995 node15645 +def node15647 : Tree Nat := .node node15644 node15646 +def node15648 : Tree Nat := .node node13995 node14469 +def node15649 : Tree Nat := .node node15398 node15648 +def node15650 : Tree Nat := .node node15647 node15649 +def node15651 : Tree Nat := .node node15401 node13885 +def node15652 : Tree Nat := .node node15225 node15651 +def node15653 : Tree Nat := .node node13618 node10435 +def node15654 : Tree Nat := .node node15653 node13885 +def node15655 : Tree Nat := .node node13995 node15654 +def node15656 : Tree Nat := .node node15652 node15655 +def node15657 : Tree Nat := .node node13995 node15406 +def node15658 : Tree Nat := .node node12627 node10435 +def node15659 : Tree Nat := .node node15658 node13885 +def node15660 : Tree Nat := .node node15659 node14814 +def node15661 : Tree Nat := .node node15657 node15660 +def node15662 : Tree Nat := .node node15656 node15661 +def node15663 : Tree Nat := .node node15650 node15662 +def node15664 : Tree Nat := .node node15641 node15663 +def node15665 : Tree Nat := .node node15164 node15412 +def node15666 : Tree Nat := .node node13995 node15145 +def node15667 : Tree Nat := .node node15665 node15666 +def node15668 : Tree Nat := .node node13995 node14820 +def node15669 : Tree Nat := .node node15668 node15417 +def node15670 : Tree Nat := .node node15667 node15669 +def node15671 : Tree Nat := .node node14855 node15420 +def node15672 : Tree Nat := .node node13796 node10435 +def node15673 : Tree Nat := .node node15672 node13885 +def node15674 : Tree Nat := .node node14979 node15673 +def node15675 : Tree Nat := .node node15671 node15674 +def node15676 : Tree Nat := .node node13131 node10435 +def node15677 : Tree Nat := .node node15676 node13885 +def node15678 : Tree Nat := .node node15027 node15677 +def node15679 : Tree Nat := .node node15678 node15423 +def node15680 : Tree Nat := .node node15675 node15679 +def node15681 : Tree Nat := .node node15670 node15680 +def node15682 : Tree Nat := .node node14013 node13885 +def node15683 : Tree Nat := .node node15427 node15682 +def node15684 : Tree Nat := .node node15683 node15433 +def node15685 : Tree Nat := .node node6977 node10435 +def node15686 : Tree Nat := .node node13885 node15685 +def node15687 : Tree Nat := .node node15686 node15436 +def node15688 : Tree Nat := .node node15687 node15440 +def node15689 : Tree Nat := .node node15684 node15688 +def node15690 : Tree Nat := .node node10482 node10435 +def node15691 : Tree Nat := .node node15690 node15453 +def node15692 : Tree Nat := .node node15691 node14848 +def node15693 : Tree Nat := .node node15452 node15692 +def node15694 : Tree Nat := .node node15449 node15693 +def node15695 : Tree Nat := .node node15689 node15694 +def node15696 : Tree Nat := .node node15681 node15695 +def node15697 : Tree Nat := .node node15664 node15696 +def node15698 : Tree Nat := .node node13252 node10435 +def node15699 : Tree Nat := .node node15698 node13885 +def node15700 : Tree Nat := .node node13995 node15699 +def node15701 : Tree Nat := .node node15462 node15700 +def node15702 : Tree Nat := .node node13137 node10435 +def node15703 : Tree Nat := .node node15702 node15464 +def node15704 : Tree Nat := .node node13995 node15703 +def node15705 : Tree Nat := .node node15704 node15467 +def node15706 : Tree Nat := .node node15701 node15705 +def node15707 : Tree Nat := .node node14449 node13885 +def node15708 : Tree Nat := .node node14545 node15707 +def node15709 : Tree Nat := .node node13505 node10435 +def node15710 : Tree Nat := .node node15709 node13885 +def node15711 : Tree Nat := .node node13995 node15710 +def node15712 : Tree Nat := .node node15708 node15711 +def node15713 : Tree Nat := .node node13885 node14183 +def node15714 : Tree Nat := .node node15713 node14551 +def node15715 : Tree Nat := .node node13885 node15475 +def node15716 : Tree Nat := .node node15715 node14870 +def node15717 : Tree Nat := .node node15714 node15716 +def node15718 : Tree Nat := .node node15712 node15717 +def node15719 : Tree Nat := .node node15706 node15718 +def node15720 : Tree Nat := .node node13885 node14955 +def node15721 : Tree Nat := .node node15720 node15486 +def node15722 : Tree Nat := .node node15721 node15196 +def node15723 : Tree Nat := .node node6668 node10435 +def node15724 : Tree Nat := .node node13885 node15723 +def node15725 : Tree Nat := .node node15724 node14570 +def node15726 : Tree Nat := .node node15725 node15491 +def node15727 : Tree Nat := .node node15722 node15726 +def node15728 : Tree Nat := .node node15484 node15727 +def node15729 : Tree Nat := .node node15719 node15728 +def node15730 : Tree Nat := .node node13995 node14900 +def node15731 : Tree Nat := .node node15504 node15730 +def node15732 : Tree Nat := .node node13995 node14585 +def node15733 : Tree Nat := .node node15732 node14903 +def node15734 : Tree Nat := .node node15731 node15733 +def node15735 : Tree Nat := .node node15502 node15734 +def node15736 : Tree Nat := .node node14214 node13885 +def node15737 : Tree Nat := .node node14855 node15736 +def node15738 : Tree Nat := .node node13979 node13885 +def node15739 : Tree Nat := .node node13995 node15738 +def node15740 : Tree Nat := .node node15737 node15739 +def node15741 : Tree Nat := .node node15740 node15516 +def node15742 : Tree Nat := .node node15227 node14096 +def node15743 : Tree Nat := .node node13995 node15742 +def node15744 : Tree Nat := .node node15519 node15743 +def node15745 : Tree Nat := .node node15744 node15523 +def node15746 : Tree Nat := .node node15741 node15745 +def node15747 : Tree Nat := .node node15735 node15746 +def node15748 : Tree Nat := .node node15729 node15747 +def node15749 : Tree Nat := .node node15697 node15748 +def node15750 : Tree Nat := .node node15620 node15749 +def node15751 : Tree Nat := .node node13937 node13885 +def node15752 : Tree Nat := .node node13995 node15751 +def node15753 : Tree Nat := .node node10435 node6533 +def node15754 : Tree Nat := .node node13885 node15753 +def node15755 : Tree Nat := .node node15754 node14938 +def node15756 : Tree Nat := .node node15752 node15755 +def node15757 : Tree Nat := .node node15532 node15756 +def node15758 : Tree Nat := .node node13995 node14293 +def node15759 : Tree Nat := .node node13995 node14625 +def node15760 : Tree Nat := .node node15758 node15759 +def node15761 : Tree Nat := .node node15253 node15760 +def node15762 : Tree Nat := .node node15757 node15761 +def node15763 : Tree Nat := .node node15263 node13885 +def node15764 : Tree Nat := .node node14634 node15763 +def node15765 : Tree Nat := .node node15764 node14636 +def node15766 : Tree Nat := .node node15539 node15765 +def node15767 : Tree Nat := .node node15268 node13885 +def node15768 : Tree Nat := .node node14310 node15767 +def node15769 : Tree Nat := .node node15768 node15543 +def node15770 : Tree Nat := .node node13995 node15273 +def node15771 : Tree Nat := .node node15548 node13885 +def node15772 : Tree Nat := .node node14318 node14096 +def node15773 : Tree Nat := .node node15771 node15772 +def node15774 : Tree Nat := .node node15770 node15773 +def node15775 : Tree Nat := .node node15769 node15774 +def node15776 : Tree Nat := .node node15766 node15775 +def node15777 : Tree Nat := .node node15762 node15776 +def node15778 : Tree Nat := .node node14237 node15555 +def node15779 : Tree Nat := .node node13885 node14969 +def node15780 : Tree Nat := .node node15779 node15557 +def node15781 : Tree Nat := .node node15778 node15780 +def node15782 : Tree Nat := .node node13995 node14649 +def node15783 : Tree Nat := .node node14651 node14096 +def node15784 : Tree Nat := .node node13995 node15783 +def node15785 : Tree Nat := .node node15782 node15784 +def node15786 : Tree Nat := .node node15781 node15785 +def node15787 : Tree Nat := .node node13121 node13885 +def node15788 : Tree Nat := .node node14983 node15787 +def node15789 : Tree Nat := .node node15788 node15292 +def node15790 : Tree Nat := .node node15567 node15789 +def node15791 : Tree Nat := .node node15786 node15790 +def node15792 : Tree Nat := .node node15791 node15581 +def node15793 : Tree Nat := .node node15777 node15792 +def node15794 : Tree Nat := .node node14537 node13885 +def node15795 : Tree Nat := .node node15584 node15794 +def node15796 : Tree Nat := .node node15795 node15589 +def node15797 : Tree Nat := .node node13067 node10435 +def node15798 : Tree Nat := .node node15797 node13885 +def node15799 : Tree Nat := .node node13995 node15798 +def node15800 : Tree Nat := .node node13995 node15018 +def node15801 : Tree Nat := .node node15799 node15800 +def node15802 : Tree Nat := .node node15796 node15801 +def node15803 : Tree Nat := .node node12742 node10435 +def node15804 : Tree Nat := .node node15803 node13885 +def node15805 : Tree Nat := .node node15594 node15804 +def node15806 : Tree Nat := .node node13885 node15022 +def node15807 : Tree Nat := .node node15806 node15597 +def node15808 : Tree Nat := .node node15805 node15807 +def node15809 : Tree Nat := .node node13995 node15601 +def node15810 : Tree Nat := .node node13995 node14705 +def node15811 : Tree Nat := .node node15809 node15810 +def node15812 : Tree Nat := .node node15808 node15811 +def node15813 : Tree Nat := .node node15802 node15812 +def node15814 : Tree Nat := .node node14383 node14096 +def node15815 : Tree Nat := .node node13995 node15814 +def node15816 : Tree Nat := .node node15038 node15815 +def node15817 : Tree Nat := .node node15609 node15816 +def node15818 : Tree Nat := .node node15050 node13885 +def node15819 : Tree Nat := .node node13995 node15818 +def node15820 : Tree Nat := .node node14054 node14096 +def node15821 : Tree Nat := .node node14728 node15820 +def node15822 : Tree Nat := .node node15819 node15821 +def node15823 : Tree Nat := .node node15613 node15822 +def node15824 : Tree Nat := .node node15817 node15823 +def node15825 : Tree Nat := .node node15813 node15824 +def node15826 : Tree Nat := .node node14746 node13885 +def node15827 : Tree Nat := .node node14068 node15826 +def node15828 : Tree Nat := .node node15827 node15070 +def node15829 : Tree Nat := .node node15828 node15075 +def node15830 : Tree Nat := .node node15353 node15829 +def node15831 : Tree Nat := .node node15085 node13885 +def node15832 : Tree Nat := .node node13995 node15831 +def node15833 : Tree Nat := .node node15832 node14764 +def node15834 : Tree Nat := .node node15358 node15833 +def node15835 : Tree Nat := .node node13995 node15100 +def node15836 : Tree Nat := .node node14771 node13885 +def node15837 : Tree Nat := .node node6358 node14096 +def node15838 : Tree Nat := .node node15836 node15837 +def node15839 : Tree Nat := .node node15835 node15838 +def node15840 : Tree Nat := .node node15362 node15839 +def node15841 : Tree Nat := .node node15834 node15840 +def node15842 : Tree Nat := .node node15830 node15841 +def node15843 : Tree Nat := .node node15825 node15842 +def node15844 : Tree Nat := .node node15793 node15843 +def node15845 : Tree Nat := .node node15114 node14096 +def node15846 : Tree Nat := .node node13995 node15845 +def node15847 : Tree Nat := .node node15627 node15846 +def node15848 : Tree Nat := .node node15624 node15847 +def node15849 : Tree Nat := .node node15164 node15631 +def node15850 : Tree Nat := .node node15849 node15635 +def node15851 : Tree Nat := .node node13259 node10435 +def node15852 : Tree Nat := .node node15851 node13885 +def node15853 : Tree Nat := .node node13995 node15852 +def node15854 : Tree Nat := .node node15853 node15743 +def node15855 : Tree Nat := .node node15850 node15854 +def node15856 : Tree Nat := .node node15848 node15855 +def node15857 : Tree Nat := .node node13995 node15397 +def node15858 : Tree Nat := .node node14468 node14096 +def node15859 : Tree Nat := .node node13995 node15858 +def node15860 : Tree Nat := .node node15857 node15859 +def node15861 : Tree Nat := .node node15647 node15860 +def node15862 : Tree Nat := .node node15405 node13885 +def node15863 : Tree Nat := .node node13995 node15862 +def node15864 : Tree Nat := .node node15863 node15660 +def node15865 : Tree Nat := .node node15656 node15864 +def node15866 : Tree Nat := .node node15861 node15865 +def node15867 : Tree Nat := .node node15856 node15866 +def node15868 : Tree Nat := .node node12714 node10435 +def node15869 : Tree Nat := .node node15868 node13885 +def node15870 : Tree Nat := .node node15164 node15869 +def node15871 : Tree Nat := .node node15870 node15666 +def node15872 : Tree Nat := .node node13147 node10435 +def node15873 : Tree Nat := .node node15872 node13885 +def node15874 : Tree Nat := .node node13995 node15873 +def node15875 : Tree Nat := .node node13995 node15149 +def node15876 : Tree Nat := .node node15874 node15875 +def node15877 : Tree Nat := .node node15871 node15876 +def node15878 : Tree Nat := .node node14668 node13885 +def node15879 : Tree Nat := .node node14855 node15878 +def node15880 : Tree Nat := .node node13995 node15673 +def node15881 : Tree Nat := .node node15879 node15880 +def node15882 : Tree Nat := .node node13995 node15677 +def node15883 : Tree Nat := .node node13995 node14831 +def node15884 : Tree Nat := .node node15882 node15883 +def node15885 : Tree Nat := .node node15881 node15884 +def node15886 : Tree Nat := .node node15877 node15885 +def node15887 : Tree Nat := .node node15435 node13885 +def node15888 : Tree Nat := .node node13995 node15887 +def node15889 : Tree Nat := .node node13995 node14519 +def node15890 : Tree Nat := .node node15888 node15889 +def node15891 : Tree Nat := .node node15684 node15890 +def node15892 : Tree Nat := .node node13995 node15451 +def node15893 : Tree Nat := .node node15690 node13885 +def node15894 : Tree Nat := .node node15893 node14848 +def node15895 : Tree Nat := .node node15892 node15894 +def node15896 : Tree Nat := .node node15449 node15895 +def node15897 : Tree Nat := .node node15891 node15896 +def node15898 : Tree Nat := .node node15886 node15897 +def node15899 : Tree Nat := .node node15867 node15898 +def node15900 : Tree Nat := .node node15702 node13885 +def node15901 : Tree Nat := .node node13995 node15900 +def node15902 : Tree Nat := .node node15901 node15467 +def node15903 : Tree Nat := .node node15701 node15902 +def node15904 : Tree Nat := .node node15225 node15707 +def node15905 : Tree Nat := .node node15904 node15711 +def node15906 : Tree Nat := .node node13105 node10435 +def node15907 : Tree Nat := .node node15906 node13885 +def node15908 : Tree Nat := .node node13995 node15907 +def node15909 : Tree Nat := .node node13979 node14096 +def node15910 : Tree Nat := .node node13995 node15909 +def node15911 : Tree Nat := .node node15908 node15910 +def node15912 : Tree Nat := .node node15905 node15911 +def node15913 : Tree Nat := .node node15903 node15912 +def node15914 : Tree Nat := .node node13861 node13885 +def node15915 : Tree Nat := .node node15481 node15914 +def node15916 : Tree Nat := .node node15915 node15191 +def node15917 : Tree Nat := .node node15916 node14878 +def node15918 : Tree Nat := .node node13877 node13885 +def node15919 : Tree Nat := .node node15720 node15918 +def node15920 : Tree Nat := .node node15919 node15196 +def node15921 : Tree Nat := .node node15920 node15726 +def node15922 : Tree Nat := .node node15917 node15921 +def node15923 : Tree Nat := .node node15913 node15922 +def node15924 : Tree Nat := .node node13995 node15219 +def node15925 : Tree Nat := .node node13995 node15772 +def node15926 : Tree Nat := .node node15924 node15925 +def node15927 : Tree Nat := .node node15740 node15926 +def node15928 : Tree Nat := .node node15231 node13885 +def node15929 : Tree Nat := .node node13995 node15928 +def node15930 : Tree Nat := .node node15521 node14752 +def node15931 : Tree Nat := .node node15929 node15930 +def node15932 : Tree Nat := .node node15744 node15931 +def node15933 : Tree Nat := .node node15927 node15932 +def node15934 : Tree Nat := .node node15735 node15933 +def node15935 : Tree Nat := .node node15923 node15934 +def node15936 : Tree Nat := .node node15899 node15935 +def node15937 : Tree Nat := .node node15844 node15936 +def node15938 : Tree Nat := .node node13995 node15530 +def node15939 : Tree Nat := .node node15938 node14935 +def node15940 : Tree Nat := .node node13995 node14938 +def node15941 : Tree Nat := .node node15752 node15940 +def node15942 : Tree Nat := .node node15939 node15941 +def node15943 : Tree Nat := .node node13995 node14622 +def node15944 : Tree Nat := .node node15252 node15943 +def node15945 : Tree Nat := .node node14242 node14096 +def node15946 : Tree Nat := .node node13995 node15945 +def node15947 : Tree Nat := .node node15758 node15946 +def node15948 : Tree Nat := .node node15944 node15947 +def node15949 : Tree Nat := .node node15942 node15948 +def node15950 : Tree Nat := .node node15535 node13885 +def node15951 : Tree Nat := .node node13995 node15950 +def node15952 : Tree Nat := .node node15951 node15538 +def node15953 : Tree Nat := .node node13995 node15763 +def node15954 : Tree Nat := .node node15953 node14636 +def node15955 : Tree Nat := .node node15952 node15954 +def node15956 : Tree Nat := .node node13995 node15767 +def node15957 : Tree Nat := .node node15956 node15543 +def node15958 : Tree Nat := .node node15957 node15774 +def node15959 : Tree Nat := .node node15955 node15958 +def node15960 : Tree Nat := .node node15949 node15959 +def node15961 : Tree Nat := .node node14088 node13885 +def node15962 : Tree Nat := .node node13995 node15961 +def node15963 : Tree Nat := .node node13995 node15557 +def node15964 : Tree Nat := .node node15962 node15963 +def node15965 : Tree Nat := .node node13108 node10435 +def node15966 : Tree Nat := .node node15965 node13885 +def node15967 : Tree Nat := .node node13995 node15966 +def node15968 : Tree Nat := .node node15967 node15784 +def node15969 : Tree Nat := .node node15964 node15968 +def node15970 : Tree Nat := .node node12686 node10435 +def node15971 : Tree Nat := .node node15970 node13885 +def node15972 : Tree Nat := .node node13995 node15971 +def node15973 : Tree Nat := .node node13995 node15565 +def node15974 : Tree Nat := .node node15972 node15973 +def node15975 : Tree Nat := .node node13120 node10435 +def node15976 : Tree Nat := .node node15975 node13885 +def node15977 : Tree Nat := .node node13995 node15976 +def node15978 : Tree Nat := .node node13995 node14661 +def node15979 : Tree Nat := .node node15977 node15978 +def node15980 : Tree Nat := .node node15974 node15979 +def node15981 : Tree Nat := .node node15969 node15980 +def node15982 : Tree Nat := .node node13995 node15570 +def node15983 : Tree Nat := .node node14102 node13885 +def node15984 : Tree Nat := .node node13995 node15983 +def node15985 : Tree Nat := .node node15982 node15984 +def node15986 : Tree Nat := .node node13995 node14991 +def node15987 : Tree Nat := .node node15573 node15986 +def node15988 : Tree Nat := .node node15985 node15987 +def node15989 : Tree Nat := .node node13995 node15312 +def node15990 : Tree Nat := .node node15308 node15989 +def node15991 : Tree Nat := .node node15576 node13885 +def node15992 : Tree Nat := .node node15991 node14752 +def node15993 : Tree Nat := .node node15317 node15992 +def node15994 : Tree Nat := .node node15990 node15993 +def node15995 : Tree Nat := .node node15988 node15994 +def node15996 : Tree Nat := .node node15981 node15995 +def node15997 : Tree Nat := .node node15960 node15996 +def node15998 : Tree Nat := .node node13995 node15588 +def node15999 : Tree Nat := .node node15795 node15998 +def node16000 : Tree Nat := .node node15999 node15801 +def node16001 : Tree Nat := .node node13995 node15804 +def node16002 : Tree Nat := .node node13995 node15597 +def node16003 : Tree Nat := .node node16001 node16002 +def node16004 : Tree Nat := .node node16003 node15811 +def node16005 : Tree Nat := .node node16000 node16004 +def node16006 : Tree Nat := .node node14030 node13885 +def node16007 : Tree Nat := .node node13995 node16006 +def node16008 : Tree Nat := .node node16007 node15608 +def node16009 : Tree Nat := .node node16008 node15816 +def node16010 : Tree Nat := .node node13995 node15339 +def node16011 : Tree Nat := .node node16010 node15612 +def node16012 : Tree Nat := .node node14727 node13885 +def node16013 : Tree Nat := .node node16012 node14752 +def node16014 : Tree Nat := .node node15819 node16013 +def node16015 : Tree Nat := .node node16011 node16014 +def node16016 : Tree Nat := .node node16009 node16015 +def node16017 : Tree Nat := .node node16005 node16016 +def node16018 : Tree Nat := .node node14042 node13885 +def node16019 : Tree Nat := .node node13995 node16018 +def node16020 : Tree Nat := .node node13995 node15060 +def node16021 : Tree Nat := .node node16019 node16020 +def node16022 : Tree Nat := .node node13995 node15064 +def node16023 : Tree Nat := .node node13995 node14742 +def node16024 : Tree Nat := .node node16022 node16023 +def node16025 : Tree Nat := .node node16021 node16024 +def node16026 : Tree Nat := .node node13995 node15826 +def node16027 : Tree Nat := .node node16026 node15070 +def node16028 : Tree Nat := .node node13995 node15073 +def node16029 : Tree Nat := .node node16028 node14753 +def node16030 : Tree Nat := .node node16027 node16029 +def node16031 : Tree Nat := .node node16025 node16030 +def node16032 : Tree Nat := .node node13656 node10435 +def node16033 : Tree Nat := .node node16032 node14096 +def node16034 : Tree Nat := .node node13995 node16033 +def node16035 : Tree Nat := .node node15832 node16034 +def node16036 : Tree Nat := .node node15358 node16035 +def node16037 : Tree Nat := .node node13995 node15096 +def node16038 : Tree Nat := .node node15361 node16037 +def node16039 : Tree Nat := .node node14995 node14096 +def node16040 : Tree Nat := .node node15836 node16039 +def node16041 : Tree Nat := .node node15835 node16040 +def node16042 : Tree Nat := .node node16038 node16041 +def node16043 : Tree Nat := .node node16036 node16042 +def node16044 : Tree Nat := .node node16031 node16043 +def node16045 : Tree Nat := .node node16017 node16044 +def node16046 : Tree Nat := .node node15997 node16045 +def node16047 : Tree Nat := .node node13995 node15372 +def node16048 : Tree Nat := .node node16047 node15623 +def node16049 : Tree Nat := .node node16048 node15847 +def node16050 : Tree Nat := .node node13995 node15631 +def node16051 : Tree Nat := .node node16050 node15635 +def node16052 : Tree Nat := .node node16051 node15854 +def node16053 : Tree Nat := .node node16049 node16052 +def node16054 : Tree Nat := .node node13995 node15651 +def node16055 : Tree Nat := .node node16054 node15655 +def node16056 : Tree Nat := .node node16055 node15864 +def node16057 : Tree Nat := .node node15861 node16056 +def node16058 : Tree Nat := .node node16053 node16057 +def node16059 : Tree Nat := .node node13995 node15869 +def node16060 : Tree Nat := .node node16059 node15666 +def node16061 : Tree Nat := .node node16060 node15876 +def node16062 : Tree Nat := .node node16061 node15885 +def node16063 : Tree Nat := .node node13995 node15682 +def node16064 : Tree Nat := .node node16063 node15433 +def node16065 : Tree Nat := .node node16064 node15890 +def node16066 : Tree Nat := .node node13995 node15444 +def node16067 : Tree Nat := .node node16066 node15448 +def node16068 : Tree Nat := .node node15893 node14752 +def node16069 : Tree Nat := .node node15892 node16068 +def node16070 : Tree Nat := .node node16067 node16069 +def node16071 : Tree Nat := .node node16065 node16070 +def node16072 : Tree Nat := .node node16062 node16071 +def node16073 : Tree Nat := .node node16058 node16072 +def node16074 : Tree Nat := .node node13995 node15707 +def node16075 : Tree Nat := .node node16074 node15711 +def node16076 : Tree Nat := .node node16075 node15911 +def node16077 : Tree Nat := .node node15903 node16076 +def node16078 : Tree Nat := .node node11427 node13885 +def node16079 : Tree Nat := .node node16078 node15914 +def node16080 : Tree Nat := .node node13995 node15190 +def node16081 : Tree Nat := .node node16079 node16080 +def node16082 : Tree Nat := .node node14199 node13885 +def node16083 : Tree Nat := .node node13995 node16082 +def node16084 : Tree Nat := .node node13995 node14563 +def node16085 : Tree Nat := .node node16083 node16084 +def node16086 : Tree Nat := .node node16081 node16085 +def node16087 : Tree Nat := .node node13995 node14570 +def node16088 : Tree Nat := .node node14212 node13885 +def node16089 : Tree Nat := .node node16088 node14752 +def node16090 : Tree Nat := .node node16087 node16089 +def node16091 : Tree Nat := .node node15920 node16090 +def node16092 : Tree Nat := .node node16086 node16091 +def node16093 : Tree Nat := .node node16077 node16092 +def node16094 : Tree Nat := .node node13995 node15496 +def node16095 : Tree Nat := .node node14227 node13885 +def node16096 : Tree Nat := .node node13995 node16095 +def node16097 : Tree Nat := .node node16094 node16096 +def node16098 : Tree Nat := .node node15499 node15810 +def node16099 : Tree Nat := .node node16097 node16098 +def node16100 : Tree Nat := .node node13995 node15503 +def node16101 : Tree Nat := .node node14242 node13885 +def node16102 : Tree Nat := .node node13995 node16101 +def node16103 : Tree Nat := .node node16100 node16102 +def node16104 : Tree Nat := .node node14247 node13885 +def node16105 : Tree Nat := .node node13995 node16104 +def node16106 : Tree Nat := .node node14589 node14096 +def node16107 : Tree Nat := .node node13995 node16106 +def node16108 : Tree Nat := .node node16105 node16107 +def node16109 : Tree Nat := .node node16103 node16108 +def node16110 : Tree Nat := .node node16099 node16109 +def node16111 : Tree Nat := .node node13995 node15518 +def node16112 : Tree Nat := .node node16111 node15743 +def node16113 : Tree Nat := .node node16112 node15931 +def node16114 : Tree Nat := .node node15927 node16113 +def node16115 : Tree Nat := .node node16110 node16114 +def node16116 : Tree Nat := .node node16093 node16115 +def node16117 : Tree Nat := .node node16073 node16116 +def node16118 : Tree Nat := .node node16046 node16117 +def node16119 : Tree Nat := .node node13995 node15251 +def node16120 : Tree Nat := .node node16119 node15943 +def node16121 : Tree Nat := .node node15758 node14753 +def node16122 : Tree Nat := .node node16120 node16121 +def node16123 : Tree Nat := .node node15942 node16122 +def node16124 : Tree Nat := .node node15771 node14752 +def node16125 : Tree Nat := .node node15770 node16124 +def node16126 : Tree Nat := .node node15957 node16125 +def node16127 : Tree Nat := .node node15955 node16126 +def node16128 : Tree Nat := .node node16123 node16127 +def node16129 : Tree Nat := .node node15977 node14753 +def node16130 : Tree Nat := .node node15974 node16129 +def node16131 : Tree Nat := .node node15969 node16130 +def node16132 : Tree Nat := .node node13995 node15307 +def node16133 : Tree Nat := .node node16132 node15989 +def node16134 : Tree Nat := .node node16133 node15993 +def node16135 : Tree Nat := .node node15988 node16134 +def node16136 : Tree Nat := .node node16131 node16135 +def node16137 : Tree Nat := .node node16128 node16136 +def node16138 : Tree Nat := .node node13995 node15794 +def node16139 : Tree Nat := .node node16138 node15998 +def node16140 : Tree Nat := .node node16139 node15801 +def node16141 : Tree Nat := .node node15809 node14753 +def node16142 : Tree Nat := .node node16003 node16141 +def node16143 : Tree Nat := .node node16140 node16142 +def node16144 : Tree Nat := .node node16143 node16016 +def node16145 : Tree Nat := .node node13995 node15355 +def node16146 : Tree Nat := .node node16145 node15357 +def node16147 : Tree Nat := .node node16146 node16035 +def node16148 : Tree Nat := .node node15836 node14752 +def node16149 : Tree Nat := .node node15835 node16148 +def node16150 : Tree Nat := .node node16038 node16149 +def node16151 : Tree Nat := .node node16147 node16150 +def node16152 : Tree Nat := .node node16031 node16151 +def node16153 : Tree Nat := .node node16144 node16152 +def node16154 : Tree Nat := .node node16137 node16153 +def node16155 : Tree Nat := .node node15853 node14753 +def node16156 : Tree Nat := .node node16051 node16155 +def node16157 : Tree Nat := .node node16049 node16156 +def node16158 : Tree Nat := .node node15659 node14752 +def node16159 : Tree Nat := .node node15863 node16158 +def node16160 : Tree Nat := .node node16055 node16159 +def node16161 : Tree Nat := .node node15861 node16160 +def node16162 : Tree Nat := .node node16157 node16161 +def node16163 : Tree Nat := .node node13995 node15878 +def node16164 : Tree Nat := .node node16163 node15880 +def node16165 : Tree Nat := .node node15882 node14753 +def node16166 : Tree Nat := .node node16164 node16165 +def node16167 : Tree Nat := .node node16061 node16166 +def node16168 : Tree Nat := .node node16167 node16071 +def node16169 : Tree Nat := .node node16162 node16168 +def node16170 : Tree Nat := .node node13995 node15461 +def node16171 : Tree Nat := .node node16170 node15700 +def node16172 : Tree Nat := .node node16171 node15902 +def node16173 : Tree Nat := .node node15908 node14753 +def node16174 : Tree Nat := .node node16075 node16173 +def node16175 : Tree Nat := .node node16172 node16174 +def node16176 : Tree Nat := .node node13995 node15914 +def node16177 : Tree Nat := .node node16176 node16080 +def node16178 : Tree Nat := .node node16177 node16085 +def node16179 : Tree Nat := .node node13995 node15918 +def node16180 : Tree Nat := .node node16179 node15196 +def node16181 : Tree Nat := .node node16180 node16090 +def node16182 : Tree Nat := .node node16178 node16181 +def node16183 : Tree Nat := .node node16175 node16182 +def node16184 : Tree Nat := .node node16105 node14753 +def node16185 : Tree Nat := .node node16103 node16184 +def node16186 : Tree Nat := .node node16099 node16185 +def node16187 : Tree Nat := .node node13995 node15736 +def node16188 : Tree Nat := .node node16187 node15739 +def node16189 : Tree Nat := .node node16188 node15926 +def node16190 : Tree Nat := .node node16189 node16113 +def node16191 : Tree Nat := .node node16186 node16190 +def node16192 : Tree Nat := .node node16183 node16191 +def node16193 : Tree Nat := .node node16169 node16192 +def node16194 : Tree Nat := .node node16154 node16193 +def state0 : State := ⟨node652, none⟩ +def state1 : State := ⟨node652, none⟩ +def state2 : State := ⟨node652, none⟩ +def state3 : State := ⟨node652, none⟩ +def state4 : State := ⟨node652, none⟩ +def state5 : State := ⟨node652, none⟩ +def state6 : State := ⟨node652, none⟩ +def state7 : State := ⟨node652, none⟩ +def state8 : State := ⟨node652, none⟩ +def state9 : State := ⟨node652, none⟩ +def state10 : State := ⟨node652, none⟩ +def state11 : State := ⟨node652, none⟩ +def state12 : State := ⟨node652, none⟩ +def state13 : State := ⟨node652, none⟩ +def state14 : State := ⟨node652, none⟩ +def state15 : State := ⟨node652, none⟩ +def state16 : State := ⟨node652, none⟩ +def state17 : State := ⟨node652, none⟩ +def state18 : State := ⟨node652, none⟩ +def state19 : State := ⟨node652, none⟩ +def state20 : State := ⟨node652, none⟩ +def state21 : State := ⟨node652, none⟩ +def state22 : State := ⟨node652, none⟩ +def state23 : State := ⟨node652, none⟩ +def state24 : State := ⟨node652, none⟩ +def state25 : State := ⟨node652, none⟩ +def state26 : State := ⟨node652, none⟩ +def state27 : State := ⟨node652, none⟩ +def state28 : State := ⟨node652, none⟩ +def state29 : State := ⟨node652, none⟩ +def state30 : State := ⟨node652, none⟩ +def state31 : State := ⟨node652, none⟩ +def state32 : State := ⟨node652, none⟩ +def state33 : State := ⟨node652, none⟩ +def state34 : State := ⟨node652, none⟩ +def state35 : State := ⟨node652, none⟩ +def state36 : State := ⟨node652, none⟩ +def state37 : State := ⟨node652, none⟩ +def state38 : State := ⟨node652, none⟩ +def state39 : State := ⟨node652, none⟩ +def state40 : State := ⟨node785, none⟩ +def state41 : State := ⟨node965, none⟩ +def state42 : State := ⟨node1227, none⟩ +def state43 : State := ⟨node1577, none⟩ +def state44 : State := ⟨node1893, none⟩ +def state45 : State := ⟨node2310, none⟩ +def state46 : State := ⟨node2737, none⟩ +def state47 : State := ⟨node3127, none⟩ +def state48 : State := ⟨node3520, none⟩ +def state49 : State := ⟨node3935, none⟩ +def state50 : State := ⟨node4408, none⟩ +def state51 : State := ⟨node4884, none⟩ +def state52 : State := ⟨node5353, none⟩ +def state53 : State := ⟨node5799, none⟩ +def state54 : State := ⟨node6168, none⟩ +def state55 : State := ⟨node6524, none⟩ +def state56 : State := ⟨node6928, none⟩ +def state57 : State := ⟨node7314, none⟩ +def state58 : State := ⟨node7713, none⟩ +def state59 : State := ⟨node8160, none⟩ +def state60 : State := ⟨node8634, none⟩ +def state61 : State := ⟨node9086, none⟩ +def state62 : State := ⟨node9528, none⟩ +def state63 : State := ⟨node9969, none⟩ +def state64 : State := ⟨node10434, none⟩ +def state65 : State := ⟨node10691, none⟩ +def state66 : State := ⟨node10884, none⟩ +def state67 : State := ⟨node11073, none⟩ +def state68 : State := ⟨node11219, some 0⟩ +def state69 : State := ⟨node11219, some 4⟩ +def state70 : State := ⟨node11219, some 16⟩ +def state71 : State := ⟨node11219, none⟩ +def state72 : State := ⟨node11219, none⟩ +def state73 : State := ⟨node11219, none⟩ +def state74 : State := ⟨node11474, none⟩ +def state75 : State := ⟨node11896, none⟩ +def state76 : State := ⟨node12299, none⟩ +def state77 : State := ⟨node12606, none⟩ +def state78 : State := ⟨node13038, none⟩ +def state79 : State := ⟨node13501, none⟩ +def state80 : State := ⟨node13924, none⟩ +def state81 : State := ⟨node14278, none⟩ +def state82 : State := ⟨node14617, none⟩ +def state83 : State := ⟨node14933, none⟩ +def state84 : State := ⟨node15241, none⟩ +def state85 : State := ⟨node15529, none⟩ +def state86 : State := ⟨node15750, none⟩ +def state87 : State := ⟨node15937, none⟩ +def state88 : State := ⟨node16118, none⟩ +def state89 : State := ⟨node16194, none⟩ +def state90 : State := ⟨node16194, none⟩ +def state91 : State := ⟨node16194, none⟩ +def state92 : State := ⟨node16194, none⟩ +def state93 : State := ⟨node16194, none⟩ +def state94 : State := ⟨node16194, none⟩ +def state95 : State := ⟨node16194, none⟩ +def state96 : State := ⟨node16194, none⟩ +def chunk0 : List Entry := [⟨⟨1,120,251,true⟩,0,0,0⟩, +⟨⟨1,120,255,true⟩,0,0,0⟩, +⟨⟨1,120,261,true⟩,0,0,0⟩, +⟨⟨1,120,266,true⟩,0,0,0⟩, +⟨⟨1,120,273,true⟩,0,0,0⟩, +⟨⟨1,120,278,true⟩,0,0,0⟩, +⟨⟨1,120,285,true⟩,0,0,0⟩, +⟨⟨1,120,624,true⟩,0,0,0⟩, +⟨⟨1,120,626,true⟩,0,0,0⟩, +⟨⟨1,120,628,true⟩,0,0,0⟩, +⟨⟨1,120,630,true⟩,0,0,0⟩, +⟨⟨1,120,640,true⟩,0,0,0⟩, +⟨⟨1,120,642,true⟩,0,0,0⟩, +⟨⟨1,120,644,true⟩,0,0,0⟩, +⟨⟨1,120,646,true⟩,0,0,0⟩, +⟨⟨1,120,656,true⟩,0,0,0⟩, +⟨⟨1,120,658,true⟩,0,0,0⟩, +⟨⟨1,120,660,true⟩,0,0,0⟩, +⟨⟨1,120,662,true⟩,0,0,0⟩, +⟨⟨1,120,672,true⟩,0,0,0⟩, +⟨⟨1,120,674,true⟩,0,0,0⟩, +⟨⟨1,120,676,true⟩,0,0,0⟩, +⟨⟨1,120,678,true⟩,0,0,0⟩, +⟨⟨1,120,688,true⟩,0,0,0⟩, +⟨⟨1,120,690,true⟩,0,0,0⟩, +⟨⟨1,120,692,true⟩,0,0,0⟩, +⟨⟨1,120,694,true⟩,0,0,0⟩, +⟨⟨1,120,704,true⟩,0,0,0⟩, +⟨⟨1,120,706,true⟩,0,0,0⟩, +⟨⟨1,120,708,true⟩,0,0,0⟩, +⟨⟨1,120,710,true⟩,0,0,0⟩, +⟨⟨1,120,720,true⟩,0,0,0⟩, +⟨⟨1,120,722,true⟩,0,0,0⟩, +⟨⟨1,120,724,true⟩,0,0,0⟩, +⟨⟨1,120,726,true⟩,0,0,0⟩, +⟨⟨1,121,245,true⟩,0,0,0⟩, +⟨⟨1,121,253,true⟩,0,0,0⟩, +⟨⟨1,121,259,true⟩,0,0,0⟩, +⟨⟨1,121,264,true⟩,0,0,0⟩, +⟨⟨1,121,271,true⟩,0,0,0⟩, +⟨⟨1,121,277,true⟩,0,0,0⟩, +⟨⟨1,121,282,true⟩,0,0,0⟩, +⟨⟨1,121,560,true⟩,0,0,0⟩, +⟨⟨1,121,562,true⟩,0,0,0⟩, +⟨⟨1,121,564,true⟩,0,0,0⟩, +⟨⟨1,121,566,true⟩,0,0,0⟩, +⟨⟨1,121,576,true⟩,0,0,0⟩, +⟨⟨1,121,578,true⟩,0,0,0⟩, +⟨⟨1,121,580,true⟩,0,0,0⟩, +⟨⟨1,121,582,true⟩,0,0,0⟩, +⟨⟨1,121,592,true⟩,0,0,0⟩, +⟨⟨1,121,594,true⟩,0,0,0⟩, +⟨⟨1,121,596,true⟩,0,0,0⟩, +⟨⟨1,121,598,true⟩,0,0,0⟩, +⟨⟨1,121,608,true⟩,0,0,0⟩, +⟨⟨1,121,610,true⟩,0,0,0⟩, +⟨⟨1,121,612,true⟩,0,0,0⟩, +⟨⟨1,121,614,true⟩,0,0,0⟩, +⟨⟨1,121,688,true⟩,0,0,0⟩, +⟨⟨1,121,690,true⟩,0,0,0⟩, +⟨⟨1,121,692,true⟩,0,0,0⟩, +⟨⟨1,121,694,true⟩,0,0,0⟩, +⟨⟨1,121,704,true⟩,0,0,0⟩, +⟨⟨1,121,706,true⟩,0,0,0⟩, +⟨⟨1,121,708,true⟩,0,0,0⟩, +⟨⟨1,121,710,true⟩,0,0,0⟩, +⟨⟨1,121,711,true⟩,0,0,0⟩, +⟨⟨1,121,720,true⟩,0,0,0⟩, +⟨⟨1,121,722,true⟩,0,0,0⟩, +⟨⟨1,121,724,true⟩,0,0,0⟩, +⟨⟨1,121,726,true⟩,0,0,0⟩, +⟨⟨1,121,907,true⟩,0,0,0⟩, +⟨⟨1,122,240,true⟩,0,0,0⟩, +⟨⟨1,122,246,true⟩,0,0,0⟩, +⟨⟨1,122,528,true⟩,0,0,0⟩, +⟨⟨1,122,530,true⟩,0,0,0⟩, +⟨⟨1,122,532,true⟩,0,0,0⟩, +⟨⟨1,122,534,true⟩,0,0,0⟩, +⟨⟨1,122,544,true⟩,0,0,0⟩, +⟨⟨1,122,546,true⟩,0,0,0⟩, +⟨⟨1,122,548,true⟩,0,0,0⟩, +⟨⟨1,122,550,true⟩,0,0,0⟩, +⟨⟨1,122,592,true⟩,0,0,0⟩, +⟨⟨1,122,594,true⟩,0,0,0⟩, +⟨⟨1,122,596,true⟩,0,0,0⟩, +⟨⟨1,122,598,true⟩,0,0,0⟩, +⟨⟨1,122,599,true⟩,0,0,0⟩, +⟨⟨1,122,608,true⟩,0,0,0⟩, +⟨⟨1,122,610,true⟩,0,0,0⟩, +⟨⟨1,122,612,true⟩,0,0,0⟩, +⟨⟨1,122,614,true⟩,0,0,0⟩, +⟨⟨1,122,656,true⟩,0,0,0⟩, +⟨⟨1,122,658,true⟩,0,0,0⟩, +⟨⟨1,122,660,true⟩,0,0,0⟩, +⟨⟨1,122,662,true⟩,0,0,0⟩, +⟨⟨1,122,663,true⟩,0,0,0⟩, +⟨⟨1,122,672,true⟩,0,0,0⟩, +⟨⟨1,122,674,true⟩,0,0,0⟩, +⟨⟨1,122,676,true⟩,0,0,0⟩, +⟨⟨1,122,678,true⟩,0,0,0⟩, +⟨⟨1,122,720,true⟩,0,0,0⟩, +⟨⟨1,122,722,true⟩,0,0,0⟩, +⟨⟨1,122,724,true⟩,0,0,0⟩, +⟨⟨1,122,726,true⟩,0,0,0⟩, +⟨⟨1,122,727,true⟩,0,0,0⟩, +⟨⟨1,123,240,true⟩,0,0,0⟩, +⟨⟨1,123,246,true⟩,0,0,0⟩, +⟨⟨1,123,528,true⟩,0,0,0⟩, +⟨⟨1,123,530,true⟩,0,0,0⟩, +⟨⟨1,123,532,true⟩,0,0,0⟩, +⟨⟨1,123,534,true⟩,0,0,0⟩, +⟨⟨1,123,544,true⟩,0,0,0⟩, +⟨⟨1,123,546,true⟩,0,0,0⟩, +⟨⟨1,123,548,true⟩,0,0,0⟩, +⟨⟨1,123,550,true⟩,0,0,0⟩, +⟨⟨1,123,560,true⟩,0,0,0⟩, +⟨⟨1,123,562,true⟩,0,0,0⟩, +⟨⟨1,123,564,true⟩,0,0,0⟩, +⟨⟨1,123,566,true⟩,0,0,0⟩, +⟨⟨1,123,567,true⟩,0,0,0⟩, +⟨⟨1,123,576,true⟩,0,0,0⟩, +⟨⟨1,123,578,true⟩,0,0,0⟩, +⟨⟨1,123,580,true⟩,0,0,0⟩, +⟨⟨1,123,582,true⟩,0,0,0⟩, +⟨⟨1,123,583,true⟩,0,0,0⟩, +⟨⟨1,123,624,true⟩,0,0,0⟩, +⟨⟨1,123,626,true⟩,0,0,0⟩, +⟨⟨1,123,628,true⟩,0,0,0⟩, +⟨⟨1,123,630,true⟩,0,0,0⟩, +⟨⟨1,123,631,true⟩,0,0,0⟩, +⟨⟨1,123,640,true⟩,0,0,0⟩, +⟨⟨1,123,642,true⟩,0,0,0⟩, +⟨⟨1,123,644,true⟩,0,0,0⟩, +⟨⟨1,123,646,true⟩,0,0,0⟩, +⟨⟨1,123,647,true⟩,0,0,0⟩, +⟨⟨1,123,720,true⟩,0,0,0⟩, +⟨⟨1,123,722,true⟩,0,0,0⟩, +⟨⟨1,123,724,true⟩,0,0,0⟩, +⟨⟨1,123,726,true⟩,0,0,0⟩, +⟨⟨1,123,727,true⟩,0,0,0⟩, +⟨⟨1,124,245,true⟩,0,0,0⟩, +⟨⟨1,124,253,true⟩,0,0,0⟩, +⟨⟨1,124,259,true⟩,0,0,0⟩, +⟨⟨1,124,271,true⟩,0,0,0⟩, +⟨⟨1,124,277,true⟩,0,0,0⟩, +⟨⟨1,124,282,true⟩,0,0,0⟩, +⟨⟨1,124,512,true⟩,0,0,0⟩, +⟨⟨1,124,514,true⟩,0,0,0⟩, +⟨⟨1,124,516,true⟩,0,0,0⟩, +⟨⟨1,124,518,true⟩,0,0,0⟩, +⟨⟨1,124,544,true⟩,0,0,0⟩, +⟨⟨1,124,546,true⟩,0,0,0⟩, +⟨⟨1,124,548,true⟩,0,0,0⟩, +⟨⟨1,124,550,true⟩,0,0,0⟩, +⟨⟨1,124,551,true⟩,0,0,0⟩, +⟨⟨1,124,576,true⟩,0,0,0⟩, +⟨⟨1,124,578,true⟩,0,0,0⟩, +⟨⟨1,124,580,true⟩,0,0,0⟩, +⟨⟨1,124,582,true⟩,0,0,0⟩, +⟨⟨1,124,608,true⟩,0,0,0⟩, +⟨⟨1,124,610,true⟩,0,0,0⟩, +⟨⟨1,124,612,true⟩,0,0,0⟩, +⟨⟨1,124,614,true⟩,0,0,0⟩, +⟨⟨1,124,640,true⟩,0,0,0⟩, +⟨⟨1,124,642,true⟩,0,0,0⟩, +⟨⟨1,124,644,true⟩,0,0,0⟩, +⟨⟨1,124,646,true⟩,0,0,0⟩, +⟨⟨1,124,672,true⟩,0,0,0⟩, +⟨⟨1,124,674,true⟩,0,0,0⟩, +⟨⟨1,124,676,true⟩,0,0,0⟩, +⟨⟨1,124,678,true⟩,0,0,0⟩, +⟨⟨1,124,679,true⟩,0,0,0⟩, +⟨⟨1,124,704,true⟩,0,0,0⟩, +⟨⟨1,124,706,true⟩,0,0,0⟩, +⟨⟨1,124,708,true⟩,0,0,0⟩, +⟨⟨1,124,710,true⟩,0,0,0⟩, +⟨⟨1,124,711,true⟩,0,0,0⟩, +⟨⟨1,125,252,true⟩,0,0,0⟩, +⟨⟨1,125,258,true⟩,0,0,0⟩, +⟨⟨1,125,264,true⟩,0,0,0⟩, +⟨⟨1,125,280,true⟩,0,0,0⟩, +⟨⟨1,125,286,true⟩,0,0,0⟩, +⟨⟨1,125,416,true⟩,0,0,0⟩, +⟨⟨1,125,418,true⟩,0,0,0⟩, +⟨⟨1,125,420,true⟩,0,0,0⟩, +⟨⟨1,125,422,true⟩,0,0,0⟩, +⟨⟨1,125,424,true⟩,0,0,0⟩, +⟨⟨1,125,426,true⟩,0,0,0⟩, +⟨⟨1,125,428,true⟩,0,0,0⟩, +⟨⟨1,125,430,true⟩,0,0,0⟩, +⟨⟨1,125,512,true⟩,0,0,0⟩, +⟨⟨1,125,514,true⟩,0,0,0⟩, +⟨⟨1,125,516,true⟩,0,0,0⟩, +⟨⟨1,125,518,true⟩,0,0,0⟩, +⟨⟨1,125,523,true⟩,0,0,0⟩, +⟨⟨1,125,544,true⟩,0,0,0⟩, +⟨⟨1,125,546,true⟩,0,0,0⟩, +⟨⟨1,125,548,true⟩,0,0,0⟩, +⟨⟨1,125,550,true⟩,0,0,0⟩, +⟨⟨1,125,551,true⟩,0,0,0⟩] +def chunk1 : List Entry := [⟨⟨1,125,560,true⟩,0,0,0⟩, +⟨⟨1,125,562,true⟩,0,0,0⟩, +⟨⟨1,125,564,true⟩,0,0,0⟩, +⟨⟨1,125,566,true⟩,0,0,0⟩, +⟨⟨1,125,624,true⟩,0,0,0⟩, +⟨⟨1,125,626,true⟩,0,0,0⟩, +⟨⟨1,125,628,true⟩,0,0,0⟩, +⟨⟨1,125,630,true⟩,0,0,0⟩, +⟨⟨1,125,656,true⟩,0,0,0⟩, +⟨⟨1,125,658,true⟩,0,0,0⟩, +⟨⟨1,125,660,true⟩,0,0,0⟩, +⟨⟨1,125,662,true⟩,0,0,0⟩, +⟨⟨1,125,704,true⟩,0,0,0⟩, +⟨⟨1,125,706,true⟩,0,0,0⟩, +⟨⟨1,125,708,true⟩,0,0,0⟩, +⟨⟨1,125,710,true⟩,0,0,0⟩, +⟨⟨1,125,715,true⟩,0,0,0⟩, +⟨⟨1,125,810,true⟩,0,0,0⟩, +⟨⟨1,126,243,true⟩,0,0,0⟩, +⟨⟨1,126,246,true⟩,0,0,0⟩, +⟨⟨1,126,253,true⟩,0,0,0⟩, +⟨⟨1,126,262,true⟩,0,0,0⟩, +⟨⟨1,126,265,true⟩,0,0,0⟩, +⟨⟨1,126,270,true⟩,0,0,0⟩, +⟨⟨1,126,282,true⟩,0,0,0⟩, +⟨⟨1,126,512,true⟩,0,0,0⟩, +⟨⟨1,126,514,true⟩,0,0,0⟩, +⟨⟨1,126,516,true⟩,0,0,0⟩, +⟨⟨1,126,518,true⟩,0,0,0⟩, +⟨⟨1,126,519,true⟩,0,0,0⟩, +⟨⟨1,126,528,true⟩,0,0,0⟩, +⟨⟨1,126,530,true⟩,0,0,0⟩, +⟨⟨1,126,532,true⟩,0,0,0⟩, +⟨⟨1,126,534,true⟩,0,0,0⟩, +⟨⟨1,126,576,true⟩,0,0,0⟩, +⟨⟨1,126,578,true⟩,0,0,0⟩, +⟨⟨1,126,580,true⟩,0,0,0⟩, +⟨⟨1,126,582,true⟩,0,0,0⟩, +⟨⟨1,126,592,true⟩,0,0,0⟩, +⟨⟨1,126,594,true⟩,0,0,0⟩, +⟨⟨1,126,596,true⟩,0,0,0⟩, +⟨⟨1,126,598,true⟩,0,0,0⟩, +⟨⟨1,126,603,true⟩,0,0,0⟩, +⟨⟨1,126,624,true⟩,0,0,0⟩, +⟨⟨1,126,626,true⟩,0,0,0⟩, +⟨⟨1,126,628,true⟩,0,0,0⟩, +⟨⟨1,126,630,true⟩,0,0,0⟩, +⟨⟨1,126,635,true⟩,0,0,0⟩, +⟨⟨1,126,672,true⟩,0,0,0⟩, +⟨⟨1,126,674,true⟩,0,0,0⟩, +⟨⟨1,126,676,true⟩,0,0,0⟩, +⟨⟨1,126,678,true⟩,0,0,0⟩, +⟨⟨1,126,683,true⟩,0,0,0⟩, +⟨⟨1,126,688,true⟩,0,0,0⟩, +⟨⟨1,126,690,true⟩,0,0,0⟩, +⟨⟨1,126,692,true⟩,0,0,0⟩, +⟨⟨1,126,694,true⟩,0,0,0⟩, +⟨⟨1,126,695,true⟩,0,0,0⟩, +⟨⟨1,127,252,true⟩,0,0,0⟩, +⟨⟨1,127,258,true⟩,0,0,0⟩, +⟨⟨1,127,276,true⟩,0,0,0⟩, +⟨⟨1,127,512,true⟩,0,0,0⟩, +⟨⟨1,127,514,true⟩,0,0,0⟩, +⟨⟨1,127,516,true⟩,0,0,0⟩, +⟨⟨1,127,518,true⟩,0,0,0⟩, +⟨⟨1,127,523,true⟩,0,0,0⟩, +⟨⟨1,127,528,true⟩,0,0,0⟩, +⟨⟨1,127,530,true⟩,0,0,0⟩, +⟨⟨1,127,532,true⟩,0,0,0⟩, +⟨⟨1,127,534,true⟩,0,0,0⟩, +⟨⟨1,127,560,true⟩,0,0,0⟩, +⟨⟨1,127,562,true⟩,0,0,0⟩, +⟨⟨1,127,564,true⟩,0,0,0⟩, +⟨⟨1,127,566,true⟩,0,0,0⟩, +⟨⟨1,127,571,true⟩,0,0,0⟩, +⟨⟨1,127,608,true⟩,0,0,0⟩, +⟨⟨1,127,610,true⟩,0,0,0⟩, +⟨⟨1,127,612,true⟩,0,0,0⟩, +⟨⟨1,127,614,true⟩,0,0,0⟩, +⟨⟨1,127,615,true⟩,0,0,0⟩, +⟨⟨1,127,640,true⟩,0,0,0⟩, +⟨⟨1,127,642,true⟩,0,0,0⟩, +⟨⟨1,127,644,true⟩,0,0,0⟩, +⟨⟨1,127,646,true⟩,0,0,0⟩, +⟨⟨1,127,651,true⟩,0,0,0⟩, +⟨⟨1,127,656,true⟩,0,0,0⟩, +⟨⟨1,127,658,true⟩,0,0,0⟩, +⟨⟨1,127,660,true⟩,0,0,0⟩, +⟨⟨1,127,662,true⟩,0,0,0⟩, +⟨⟨1,127,667,true⟩,0,0,0⟩, +⟨⟨1,127,688,true⟩,0,0,0⟩, +⟨⟨1,127,690,true⟩,0,0,0⟩, +⟨⟨1,127,692,true⟩,0,0,0⟩, +⟨⟨1,127,694,true⟩,0,0,0⟩, +⟨⟨1,127,699,true⟩,0,0,0⟩, +⟨⟨1,128,245,true⟩,0,0,0⟩, +⟨⟨1,128,259,true⟩,0,0,0⟩, +⟨⟨1,128,271,true⟩,0,0,0⟩, +⟨⟨1,128,277,true⟩,0,0,0⟩, +⟨⟨1,128,295,true⟩,0,0,0⟩, +⟨⟨1,128,309,true⟩,0,0,0⟩, +⟨⟨1,128,311,true⟩,0,0,0⟩, +⟨⟨1,128,313,true⟩,0,0,0⟩, +⟨⟨1,128,315,true⟩,0,0,0⟩, +⟨⟨1,128,322,true⟩,0,0,0⟩, +⟨⟨1,128,326,true⟩,0,0,0⟩, +⟨⟨1,128,328,true⟩,0,0,0⟩, +⟨⟨1,128,332,true⟩,0,0,0⟩, +⟨⟨1,128,341,true⟩,0,0,0⟩, +⟨⟨1,128,343,true⟩,0,0,0⟩, +⟨⟨1,128,345,true⟩,0,0,0⟩, +⟨⟨1,128,347,true⟩,0,0,0⟩, +⟨⟨1,128,354,true⟩,0,0,0⟩, +⟨⟨1,128,358,true⟩,0,0,0⟩, +⟨⟨1,128,360,true⟩,0,0,0⟩, +⟨⟨1,128,364,true⟩,0,0,0⟩, +⟨⟨1,128,387,true⟩,0,0,0⟩, +⟨⟨1,128,391,true⟩,0,0,0⟩, +⟨⟨1,128,395,true⟩,0,0,0⟩, +⟨⟨1,128,399,true⟩,0,0,0⟩, +⟨⟨1,128,405,true⟩,0,0,0⟩, +⟨⟨1,128,407,true⟩,0,0,0⟩, +⟨⟨1,128,409,true⟩,0,0,0⟩, +⟨⟨1,128,411,true⟩,0,0,0⟩, +⟨⟨1,128,436,true⟩,0,0,0⟩, +⟨⟨1,128,438,true⟩,0,0,0⟩, +⟨⟨1,128,444,true⟩,0,0,0⟩, +⟨⟨1,128,446,true⟩,0,0,0⟩, +⟨⟨1,128,451,true⟩,0,0,0⟩, +⟨⟨1,128,455,true⟩,0,0,0⟩, +⟨⟨1,128,459,true⟩,0,0,0⟩, +⟨⟨1,128,463,true⟩,0,0,0⟩, +⟨⟨1,128,468,true⟩,0,0,0⟩, +⟨⟨1,128,470,true⟩,0,0,0⟩, +⟨⟨1,128,476,true⟩,0,0,0⟩, +⟨⟨1,128,478,true⟩,0,0,0⟩, +⟨⟨1,128,483,true⟩,0,0,0⟩, +⟨⟨1,128,487,true⟩,0,0,0⟩, +⟨⟨1,128,491,true⟩,0,0,0⟩, +⟨⟨1,128,495,true⟩,0,0,0⟩, +⟨⟨1,128,525,true⟩,0,0,0⟩, +⟨⟨1,128,527,true⟩,0,0,0⟩, +⟨⟨1,128,541,true⟩,0,0,0⟩, +⟨⟨1,128,543,true⟩,0,0,0⟩, +⟨⟨1,128,553,true⟩,0,0,0⟩, +⟨⟨1,128,555,true⟩,0,0,0⟩, +⟨⟨1,128,573,true⟩,0,0,0⟩, +⟨⟨1,128,575,true⟩,0,0,0⟩, +⟨⟨1,128,585,true⟩,0,0,0⟩, +⟨⟨1,128,587,true⟩,0,0,0⟩, +⟨⟨1,128,594,true⟩,0,0,0⟩, +⟨⟨1,128,595,true⟩,0,0,0⟩, +⟨⟨1,128,598,true⟩,0,0,0⟩, +⟨⟨1,128,599,true⟩,0,0,0⟩, +⟨⟨1,128,608,true⟩,0,0,0⟩, +⟨⟨1,128,610,true⟩,0,0,0⟩, +⟨⟨1,128,612,true⟩,0,0,0⟩, +⟨⟨1,128,614,true⟩,0,0,0⟩, +⟨⟨1,128,644,true⟩,0,0,0⟩, +⟨⟨1,128,646,true⟩,0,0,0⟩, +⟨⟨1,128,850,true⟩,0,0,0⟩, +⟨⟨1,129,245,true⟩,0,0,0⟩, +⟨⟨1,129,259,true⟩,0,0,0⟩, +⟨⟨1,129,271,true⟩,0,0,0⟩, +⟨⟨1,129,277,true⟩,0,0,0⟩, +⟨⟨1,129,293,true⟩,0,0,0⟩, +⟨⟨1,129,309,true⟩,0,0,0⟩, +⟨⟨1,129,311,true⟩,0,0,0⟩, +⟨⟨1,129,313,true⟩,0,0,0⟩, +⟨⟨1,129,315,true⟩,0,0,0⟩, +⟨⟨1,129,320,true⟩,0,0,0⟩, +⟨⟨1,129,324,true⟩,0,0,0⟩, +⟨⟨1,129,330,true⟩,0,0,0⟩, +⟨⟨1,129,334,true⟩,0,0,0⟩, +⟨⟨1,129,341,true⟩,0,0,0⟩, +⟨⟨1,129,343,true⟩,0,0,0⟩, +⟨⟨1,129,345,true⟩,0,0,0⟩, +⟨⟨1,129,347,true⟩,0,0,0⟩, +⟨⟨1,129,352,true⟩,0,0,0⟩, +⟨⟨1,129,356,true⟩,0,0,0⟩, +⟨⟨1,129,362,true⟩,0,0,0⟩, +⟨⟨1,129,366,true⟩,0,0,0⟩, +⟨⟨1,129,385,true⟩,0,0,0⟩, +⟨⟨1,129,389,true⟩,0,0,0⟩, +⟨⟨1,129,393,true⟩,0,0,0⟩, +⟨⟨1,129,397,true⟩,0,0,0⟩, +⟨⟨1,129,405,true⟩,0,0,0⟩, +⟨⟨1,129,407,true⟩,0,0,0⟩, +⟨⟨1,129,409,true⟩,0,0,0⟩, +⟨⟨1,129,411,true⟩,0,0,0⟩, +⟨⟨1,129,436,true⟩,0,0,0⟩, +⟨⟨1,129,438,true⟩,0,0,0⟩, +⟨⟨1,129,444,true⟩,0,0,0⟩, +⟨⟨1,129,446,true⟩,0,0,0⟩, +⟨⟨1,129,449,true⟩,0,0,0⟩, +⟨⟨1,129,453,true⟩,0,0,0⟩, +⟨⟨1,129,457,true⟩,0,0,0⟩, +⟨⟨1,129,461,true⟩,0,0,0⟩, +⟨⟨1,129,468,true⟩,0,0,0⟩, +⟨⟨1,129,470,true⟩,0,0,0⟩] +def chunk2 : List Entry := [⟨⟨1,129,476,true⟩,0,0,0⟩, +⟨⟨1,129,478,true⟩,0,0,0⟩, +⟨⟨1,129,481,true⟩,0,0,0⟩, +⟨⟨1,129,485,true⟩,0,0,0⟩, +⟨⟨1,129,489,true⟩,0,0,0⟩, +⟨⟨1,129,493,true⟩,0,0,0⟩, +⟨⟨1,129,499,true⟩,0,0,0⟩, +⟨⟨1,129,501,true⟩,0,0,0⟩, +⟨⟨1,129,505,true⟩,0,0,0⟩, +⟨⟨1,129,511,true⟩,0,0,0⟩, +⟨⟨1,129,525,true⟩,0,0,0⟩, +⟨⟨1,129,527,true⟩,0,0,0⟩, +⟨⟨1,129,541,true⟩,0,0,0⟩, +⟨⟨1,129,543,true⟩,0,0,0⟩, +⟨⟨1,129,552,true⟩,0,0,0⟩, +⟨⟨1,129,554,true⟩,0,0,0⟩, +⟨⟨1,129,573,true⟩,0,0,0⟩, +⟨⟨1,129,575,true⟩,0,0,0⟩, +⟨⟨1,129,584,true⟩,0,0,0⟩, +⟨⟨1,129,586,true⟩,0,0,0⟩, +⟨⟨1,129,592,true⟩,0,0,0⟩, +⟨⟨1,129,593,true⟩,0,0,0⟩, +⟨⟨1,129,596,true⟩,0,0,0⟩, +⟨⟨1,129,597,true⟩,0,0,0⟩, +⟨⟨1,129,608,true⟩,0,0,0⟩, +⟨⟨1,129,613,true⟩,0,0,0⟩, +⟨⟨1,129,614,true⟩,0,0,0⟩, +⟨⟨1,129,622,true⟩,0,0,0⟩, +⟨⟨1,129,623,true⟩,0,0,0⟩, +⟨⟨1,129,644,true⟩,0,0,0⟩, +⟨⟨1,129,646,true⟩,0,0,0⟩, +⟨⟨1,129,850,true⟩,0,0,0⟩, +⟨⟨1,129,933,true⟩,0,0,0⟩, +⟨⟨1,129,937,true⟩,0,0,0⟩, +⟨⟨1,130,245,true⟩,0,0,0⟩, +⟨⟨1,130,259,true⟩,0,0,0⟩, +⟨⟨1,130,271,true⟩,0,0,0⟩, +⟨⟨1,130,277,true⟩,0,0,0⟩, +⟨⟨1,130,291,true⟩,0,0,0⟩, +⟨⟨1,130,305,true⟩,0,0,0⟩, +⟨⟨1,130,307,true⟩,0,0,0⟩, +⟨⟨1,130,317,true⟩,0,0,0⟩, +⟨⟨1,130,319,true⟩,0,0,0⟩, +⟨⟨1,130,322,true⟩,0,0,0⟩, +⟨⟨1,130,326,true⟩,0,0,0⟩, +⟨⟨1,130,328,true⟩,0,0,0⟩, +⟨⟨1,130,332,true⟩,0,0,0⟩, +⟨⟨1,130,337,true⟩,0,0,0⟩, +⟨⟨1,130,339,true⟩,0,0,0⟩, +⟨⟨1,130,349,true⟩,0,0,0⟩, +⟨⟨1,130,351,true⟩,0,0,0⟩, +⟨⟨1,130,354,true⟩,0,0,0⟩, +⟨⟨1,130,358,true⟩,0,0,0⟩, +⟨⟨1,130,360,true⟩,0,0,0⟩, +⟨⟨1,130,364,true⟩,0,0,0⟩, +⟨⟨1,130,385,true⟩,0,0,0⟩, +⟨⟨1,130,389,true⟩,0,0,0⟩, +⟨⟨1,130,393,true⟩,0,0,0⟩, +⟨⟨1,130,397,true⟩,0,0,0⟩, +⟨⟨1,130,405,true⟩,0,0,0⟩, +⟨⟨1,130,407,true⟩,0,0,0⟩, +⟨⟨1,130,409,true⟩,0,0,0⟩, +⟨⟨1,130,411,true⟩,0,0,0⟩, +⟨⟨1,130,432,true⟩,0,0,0⟩, +⟨⟨1,130,434,true⟩,0,0,0⟩, +⟨⟨1,130,440,true⟩,0,0,0⟩, +⟨⟨1,130,442,true⟩,0,0,0⟩, +⟨⟨1,130,451,true⟩,0,0,0⟩, +⟨⟨1,130,455,true⟩,0,0,0⟩, +⟨⟨1,130,459,true⟩,0,0,0⟩, +⟨⟨1,130,463,true⟩,0,0,0⟩, +⟨⟨1,130,464,true⟩,0,0,0⟩, +⟨⟨1,130,466,true⟩,0,0,0⟩, +⟨⟨1,130,472,true⟩,0,0,0⟩, +⟨⟨1,130,474,true⟩,0,0,0⟩, +⟨⟨1,130,483,true⟩,0,0,0⟩, +⟨⟨1,130,487,true⟩,0,0,0⟩, +⟨⟨1,130,491,true⟩,0,0,0⟩, +⟨⟨1,130,495,true⟩,0,0,0⟩, +⟨⟨1,130,498,true⟩,0,0,0⟩, +⟨⟨1,130,500,true⟩,0,0,0⟩, +⟨⟨1,130,504,true⟩,0,0,0⟩, +⟨⟨1,130,510,true⟩,0,0,0⟩, +⟨⟨1,130,525,true⟩,0,0,0⟩, +⟨⟨1,130,527,true⟩,0,0,0⟩, +⟨⟨1,130,540,true⟩,0,0,0⟩, +⟨⟨1,130,542,true⟩,0,0,0⟩, +⟨⟨1,130,553,true⟩,0,0,0⟩, +⟨⟨1,130,555,true⟩,0,0,0⟩, +⟨⟨1,130,572,true⟩,0,0,0⟩, +⟨⟨1,130,574,true⟩,0,0,0⟩, +⟨⟨1,130,585,true⟩,0,0,0⟩, +⟨⟨1,130,587,true⟩,0,0,0⟩, +⟨⟨1,130,592,true⟩,0,0,0⟩, +⟨⟨1,130,593,true⟩,0,0,0⟩, +⟨⟨1,130,596,true⟩,0,0,0⟩, +⟨⟨1,130,597,true⟩,0,0,0⟩, +⟨⟨1,130,608,true⟩,0,0,0⟩, +⟨⟨1,130,614,true⟩,0,0,0⟩, +⟨⟨1,130,618,true⟩,0,0,0⟩, +⟨⟨1,130,623,true⟩,0,0,0⟩, +⟨⟨1,130,644,true⟩,0,0,0⟩, +⟨⟨1,130,646,true⟩,0,0,0⟩, +⟨⟨1,130,850,true⟩,0,0,0⟩, +⟨⟨1,130,932,true⟩,0,0,0⟩, +⟨⟨1,131,245,true⟩,0,0,0⟩, +⟨⟨1,131,259,true⟩,0,0,0⟩, +⟨⟨1,131,271,true⟩,0,0,0⟩, +⟨⟨1,131,277,true⟩,0,0,0⟩, +⟨⟨1,131,289,true⟩,0,0,0⟩, +⟨⟨1,131,305,true⟩,0,0,0⟩, +⟨⟨1,131,307,true⟩,0,0,0⟩, +⟨⟨1,131,317,true⟩,0,0,0⟩, +⟨⟨1,131,319,true⟩,0,0,0⟩, +⟨⟨1,131,320,true⟩,0,0,0⟩, +⟨⟨1,131,324,true⟩,0,0,0⟩, +⟨⟨1,131,330,true⟩,0,0,0⟩, +⟨⟨1,131,334,true⟩,0,0,0⟩, +⟨⟨1,131,337,true⟩,0,0,0⟩, +⟨⟨1,131,339,true⟩,0,0,0⟩, +⟨⟨1,131,349,true⟩,0,0,0⟩, +⟨⟨1,131,351,true⟩,0,0,0⟩, +⟨⟨1,131,352,true⟩,0,0,0⟩, +⟨⟨1,131,356,true⟩,0,0,0⟩, +⟨⟨1,131,362,true⟩,0,0,0⟩, +⟨⟨1,131,366,true⟩,0,0,0⟩, +⟨⟨1,131,387,true⟩,0,0,0⟩, +⟨⟨1,131,391,true⟩,0,0,0⟩, +⟨⟨1,131,395,true⟩,0,0,0⟩, +⟨⟨1,131,399,true⟩,0,0,0⟩, +⟨⟨1,131,405,true⟩,0,0,0⟩, +⟨⟨1,131,407,true⟩,0,0,0⟩, +⟨⟨1,131,409,true⟩,0,0,0⟩, +⟨⟨1,131,411,true⟩,0,0,0⟩, +⟨⟨1,131,432,true⟩,0,0,0⟩, +⟨⟨1,131,434,true⟩,0,0,0⟩, +⟨⟨1,131,440,true⟩,0,0,0⟩, +⟨⟨1,131,442,true⟩,0,0,0⟩, +⟨⟨1,131,449,true⟩,0,0,0⟩, +⟨⟨1,131,453,true⟩,0,0,0⟩, +⟨⟨1,131,457,true⟩,0,0,0⟩, +⟨⟨1,131,461,true⟩,0,0,0⟩, +⟨⟨1,131,464,true⟩,0,0,0⟩, +⟨⟨1,131,466,true⟩,0,0,0⟩, +⟨⟨1,131,472,true⟩,0,0,0⟩, +⟨⟨1,131,474,true⟩,0,0,0⟩, +⟨⟨1,131,481,true⟩,0,0,0⟩, +⟨⟨1,131,485,true⟩,0,0,0⟩, +⟨⟨1,131,489,true⟩,0,0,0⟩, +⟨⟨1,131,493,true⟩,0,0,0⟩, +⟨⟨1,131,525,true⟩,0,0,0⟩, +⟨⟨1,131,527,true⟩,0,0,0⟩, +⟨⟨1,131,540,true⟩,0,0,0⟩, +⟨⟨1,131,542,true⟩,0,0,0⟩, +⟨⟨1,131,552,true⟩,0,0,0⟩, +⟨⟨1,131,554,true⟩,0,0,0⟩, +⟨⟨1,131,572,true⟩,0,0,0⟩, +⟨⟨1,131,574,true⟩,0,0,0⟩, +⟨⟨1,131,584,true⟩,0,0,0⟩, +⟨⟨1,131,586,true⟩,0,0,0⟩, +⟨⟨1,131,594,true⟩,0,0,0⟩, +⟨⟨1,131,595,true⟩,0,0,0⟩, +⟨⟨1,131,598,true⟩,0,0,0⟩, +⟨⟨1,131,599,true⟩,0,0,0⟩, +⟨⟨1,131,608,true⟩,0,0,0⟩, +⟨⟨1,131,610,true⟩,0,0,0⟩, +⟨⟨1,131,612,true⟩,0,0,0⟩, +⟨⟨1,131,614,true⟩,0,0,0⟩, +⟨⟨1,131,644,true⟩,0,0,0⟩, +⟨⟨1,131,646,true⟩,0,0,0⟩, +⟨⟨1,131,850,true⟩,0,0,0⟩, +⟨⟨1,132,245,true⟩,0,0,0⟩, +⟨⟨1,132,259,true⟩,0,0,0⟩, +⟨⟨1,132,271,true⟩,0,0,0⟩, +⟨⟨1,132,277,true⟩,0,0,0⟩, +⟨⟨1,132,302,true⟩,0,0,0⟩, +⟨⟨1,132,305,true⟩,0,0,0⟩, +⟨⟨1,132,307,true⟩,0,0,0⟩, +⟨⟨1,132,317,true⟩,0,0,0⟩, +⟨⟨1,132,319,true⟩,0,0,0⟩, +⟨⟨1,132,322,true⟩,0,0,0⟩, +⟨⟨1,132,326,true⟩,0,0,0⟩, +⟨⟨1,132,328,true⟩,0,0,0⟩, +⟨⟨1,132,332,true⟩,0,0,0⟩, +⟨⟨1,132,341,true⟩,0,0,0⟩, +⟨⟨1,132,343,true⟩,0,0,0⟩, +⟨⟨1,132,345,true⟩,0,0,0⟩, +⟨⟨1,132,347,true⟩,0,0,0⟩, +⟨⟨1,132,352,true⟩,0,0,0⟩, +⟨⟨1,132,356,true⟩,0,0,0⟩, +⟨⟨1,132,362,true⟩,0,0,0⟩, +⟨⟨1,132,366,true⟩,0,0,0⟩, +⟨⟨1,132,387,true⟩,0,0,0⟩, +⟨⟨1,132,391,true⟩,0,0,0⟩, +⟨⟨1,132,395,true⟩,0,0,0⟩, +⟨⟨1,132,399,true⟩,0,0,0⟩, +⟨⟨1,132,401,true⟩,0,0,0⟩, +⟨⟨1,132,403,true⟩,0,0,0⟩, +⟨⟨1,132,413,true⟩,0,0,0⟩, +⟨⟨1,132,415,true⟩,0,0,0⟩] +def chunk3 : List Entry := [⟨⟨1,132,436,true⟩,0,0,0⟩, +⟨⟨1,132,438,true⟩,0,0,0⟩, +⟨⟨1,132,444,true⟩,0,0,0⟩, +⟨⟨1,132,446,true⟩,0,0,0⟩, +⟨⟨1,132,449,true⟩,0,0,0⟩, +⟨⟨1,132,453,true⟩,0,0,0⟩, +⟨⟨1,132,457,true⟩,0,0,0⟩, +⟨⟨1,132,461,true⟩,0,0,0⟩, +⟨⟨1,132,464,true⟩,0,0,0⟩, +⟨⟨1,132,466,true⟩,0,0,0⟩, +⟨⟨1,132,472,true⟩,0,0,0⟩, +⟨⟨1,132,474,true⟩,0,0,0⟩, +⟨⟨1,132,483,true⟩,0,0,0⟩, +⟨⟨1,132,487,true⟩,0,0,0⟩, +⟨⟨1,132,491,true⟩,0,0,0⟩, +⟨⟨1,132,495,true⟩,0,0,0⟩, +⟨⟨1,132,500,true⟩,0,0,0⟩, +⟨⟨1,132,501,true⟩,0,0,0⟩, +⟨⟨1,132,505,true⟩,0,0,0⟩, +⟨⟨1,132,510,true⟩,0,0,0⟩, +⟨⟨1,132,524,true⟩,0,0,0⟩, +⟨⟨1,132,526,true⟩,0,0,0⟩, +⟨⟨1,132,541,true⟩,0,0,0⟩, +⟨⟨1,132,543,true⟩,0,0,0⟩, +⟨⟨1,132,553,true⟩,0,0,0⟩, +⟨⟨1,132,555,true⟩,0,0,0⟩, +⟨⟨1,132,572,true⟩,0,0,0⟩, +⟨⟨1,132,574,true⟩,0,0,0⟩, +⟨⟨1,132,584,true⟩,0,0,0⟩, +⟨⟨1,132,586,true⟩,0,0,0⟩, +⟨⟨1,132,594,true⟩,0,0,0⟩, +⟨⟨1,132,595,true⟩,0,0,0⟩, +⟨⟨1,132,598,true⟩,0,0,0⟩, +⟨⟨1,132,599,true⟩,0,0,0⟩, +⟨⟨1,132,608,true⟩,0,0,0⟩, +⟨⟨1,132,610,true⟩,0,0,0⟩, +⟨⟨1,132,613,true⟩,0,0,0⟩, +⟨⟨1,132,614,true⟩,0,0,0⟩, +⟨⟨1,132,618,true⟩,0,0,0⟩, +⟨⟨1,132,619,true⟩,0,0,0⟩, +⟨⟨1,132,640,true⟩,0,0,0⟩, +⟨⟨1,132,642,true⟩,0,0,0⟩, +⟨⟨1,132,848,true⟩,0,0,0⟩, +⟨⟨1,132,932,true⟩,0,0,0⟩, +⟨⟨1,132,937,true⟩,0,0,0⟩, +⟨⟨1,133,245,true⟩,0,0,0⟩, +⟨⟨1,133,259,true⟩,0,0,0⟩, +⟨⟨1,133,271,true⟩,0,0,0⟩, +⟨⟨1,133,277,true⟩,0,0,0⟩, +⟨⟨1,133,300,true⟩,0,0,0⟩, +⟨⟨1,133,305,true⟩,0,0,0⟩, +⟨⟨1,133,307,true⟩,0,0,0⟩, +⟨⟨1,133,317,true⟩,0,0,0⟩, +⟨⟨1,133,319,true⟩,0,0,0⟩, +⟨⟨1,133,320,true⟩,0,0,0⟩, +⟨⟨1,133,324,true⟩,0,0,0⟩, +⟨⟨1,133,330,true⟩,0,0,0⟩, +⟨⟨1,133,334,true⟩,0,0,0⟩, +⟨⟨1,133,341,true⟩,0,0,0⟩, +⟨⟨1,133,343,true⟩,0,0,0⟩, +⟨⟨1,133,345,true⟩,0,0,0⟩, +⟨⟨1,133,347,true⟩,0,0,0⟩, +⟨⟨1,133,354,true⟩,0,0,0⟩, +⟨⟨1,133,358,true⟩,0,0,0⟩, +⟨⟨1,133,360,true⟩,0,0,0⟩, +⟨⟨1,133,364,true⟩,0,0,0⟩, +⟨⟨1,133,385,true⟩,0,0,0⟩, +⟨⟨1,133,389,true⟩,0,0,0⟩, +⟨⟨1,133,393,true⟩,0,0,0⟩, +⟨⟨1,133,397,true⟩,0,0,0⟩, +⟨⟨1,133,401,true⟩,0,0,0⟩, +⟨⟨1,133,403,true⟩,0,0,0⟩, +⟨⟨1,133,413,true⟩,0,0,0⟩, +⟨⟨1,133,415,true⟩,0,0,0⟩, +⟨⟨1,133,436,true⟩,0,0,0⟩, +⟨⟨1,133,438,true⟩,0,0,0⟩, +⟨⟨1,133,444,true⟩,0,0,0⟩, +⟨⟨1,133,446,true⟩,0,0,0⟩, +⟨⟨1,133,451,true⟩,0,0,0⟩, +⟨⟨1,133,455,true⟩,0,0,0⟩, +⟨⟨1,133,459,true⟩,0,0,0⟩, +⟨⟨1,133,463,true⟩,0,0,0⟩, +⟨⟨1,133,464,true⟩,0,0,0⟩, +⟨⟨1,133,466,true⟩,0,0,0⟩, +⟨⟨1,133,472,true⟩,0,0,0⟩, +⟨⟨1,133,474,true⟩,0,0,0⟩, +⟨⟨1,133,481,true⟩,0,0,0⟩, +⟨⟨1,133,485,true⟩,0,0,0⟩, +⟨⟨1,133,489,true⟩,0,0,0⟩, +⟨⟨1,133,493,true⟩,0,0,0⟩, +⟨⟨1,133,524,true⟩,0,0,0⟩, +⟨⟨1,133,526,true⟩,0,0,0⟩, +⟨⟨1,133,541,true⟩,0,0,0⟩, +⟨⟨1,133,543,true⟩,0,0,0⟩, +⟨⟨1,133,552,true⟩,0,0,0⟩, +⟨⟨1,133,554,true⟩,0,0,0⟩, +⟨⟨1,133,572,true⟩,0,0,0⟩, +⟨⟨1,133,574,true⟩,0,0,0⟩, +⟨⟨1,133,585,true⟩,0,0,0⟩, +⟨⟨1,133,587,true⟩,0,0,0⟩, +⟨⟨1,133,592,true⟩,0,0,0⟩, +⟨⟨1,133,593,true⟩,0,0,0⟩, +⟨⟨1,133,596,true⟩,0,0,0⟩, +⟨⟨1,133,597,true⟩,0,0,0⟩, +⟨⟨1,133,608,true⟩,0,0,0⟩, +⟨⟨1,133,610,true⟩,0,0,0⟩, +⟨⟨1,133,612,true⟩,0,0,0⟩, +⟨⟨1,133,614,true⟩,0,0,0⟩, +⟨⟨1,133,640,true⟩,0,0,0⟩, +⟨⟨1,133,642,true⟩,0,0,0⟩, +⟨⟨1,133,848,true⟩,0,0,0⟩, +⟨⟨1,134,245,true⟩,0,0,0⟩, +⟨⟨1,134,259,true⟩,0,0,0⟩, +⟨⟨1,134,271,true⟩,0,0,0⟩, +⟨⟨1,134,277,true⟩,0,0,0⟩, +⟨⟨1,134,298,true⟩,0,0,0⟩, +⟨⟨1,134,309,true⟩,0,0,0⟩, +⟨⟨1,134,311,true⟩,0,0,0⟩, +⟨⟨1,134,313,true⟩,0,0,0⟩, +⟨⟨1,134,315,true⟩,0,0,0⟩, +⟨⟨1,134,322,true⟩,0,0,0⟩, +⟨⟨1,134,326,true⟩,0,0,0⟩, +⟨⟨1,134,328,true⟩,0,0,0⟩, +⟨⟨1,134,332,true⟩,0,0,0⟩, +⟨⟨1,134,337,true⟩,0,0,0⟩, +⟨⟨1,134,339,true⟩,0,0,0⟩, +⟨⟨1,134,349,true⟩,0,0,0⟩, +⟨⟨1,134,351,true⟩,0,0,0⟩, +⟨⟨1,134,352,true⟩,0,0,0⟩, +⟨⟨1,134,356,true⟩,0,0,0⟩, +⟨⟨1,134,362,true⟩,0,0,0⟩, +⟨⟨1,134,366,true⟩,0,0,0⟩, +⟨⟨1,134,385,true⟩,0,0,0⟩, +⟨⟨1,134,389,true⟩,0,0,0⟩, +⟨⟨1,134,393,true⟩,0,0,0⟩, +⟨⟨1,134,397,true⟩,0,0,0⟩, +⟨⟨1,134,401,true⟩,0,0,0⟩, +⟨⟨1,134,403,true⟩,0,0,0⟩, +⟨⟨1,134,413,true⟩,0,0,0⟩, +⟨⟨1,134,415,true⟩,0,0,0⟩, +⟨⟨1,134,432,true⟩,0,0,0⟩, +⟨⟨1,134,434,true⟩,0,0,0⟩, +⟨⟨1,134,440,true⟩,0,0,0⟩, +⟨⟨1,134,442,true⟩,0,0,0⟩, +⟨⟨1,134,449,true⟩,0,0,0⟩, +⟨⟨1,134,453,true⟩,0,0,0⟩, +⟨⟨1,134,457,true⟩,0,0,0⟩, +⟨⟨1,134,461,true⟩,0,0,0⟩, +⟨⟨1,134,468,true⟩,0,0,0⟩, +⟨⟨1,134,470,true⟩,0,0,0⟩, +⟨⟨1,134,476,true⟩,0,0,0⟩, +⟨⟨1,134,478,true⟩,0,0,0⟩, +⟨⟨1,134,483,true⟩,0,0,0⟩, +⟨⟨1,134,487,true⟩,0,0,0⟩, +⟨⟨1,134,491,true⟩,0,0,0⟩, +⟨⟨1,134,495,true⟩,0,0,0⟩, +⟨⟨1,134,524,true⟩,0,0,0⟩, +⟨⟨1,134,526,true⟩,0,0,0⟩, +⟨⟨1,134,540,true⟩,0,0,0⟩, +⟨⟨1,134,542,true⟩,0,0,0⟩, +⟨⟨1,134,553,true⟩,0,0,0⟩, +⟨⟨1,134,555,true⟩,0,0,0⟩, +⟨⟨1,134,573,true⟩,0,0,0⟩, +⟨⟨1,134,575,true⟩,0,0,0⟩, +⟨⟨1,134,584,true⟩,0,0,0⟩, +⟨⟨1,134,586,true⟩,0,0,0⟩, +⟨⟨1,134,592,true⟩,0,0,0⟩, +⟨⟨1,134,593,true⟩,0,0,0⟩, +⟨⟨1,134,596,true⟩,0,0,0⟩, +⟨⟨1,134,597,true⟩,0,0,0⟩, +⟨⟨1,134,608,true⟩,0,0,0⟩, +⟨⟨1,134,610,true⟩,0,0,0⟩, +⟨⟨1,134,612,true⟩,0,0,0⟩, +⟨⟨1,134,614,true⟩,0,0,0⟩, +⟨⟨1,134,640,true⟩,0,0,0⟩, +⟨⟨1,134,642,true⟩,0,0,0⟩, +⟨⟨1,134,848,true⟩,0,0,0⟩, +⟨⟨1,135,245,true⟩,0,0,0⟩, +⟨⟨1,135,259,true⟩,0,0,0⟩, +⟨⟨1,135,271,true⟩,0,0,0⟩, +⟨⟨1,135,277,true⟩,0,0,0⟩, +⟨⟨1,135,296,true⟩,0,0,0⟩, +⟨⟨1,135,309,true⟩,0,0,0⟩, +⟨⟨1,135,311,true⟩,0,0,0⟩, +⟨⟨1,135,313,true⟩,0,0,0⟩, +⟨⟨1,135,315,true⟩,0,0,0⟩, +⟨⟨1,135,320,true⟩,0,0,0⟩, +⟨⟨1,135,324,true⟩,0,0,0⟩, +⟨⟨1,135,330,true⟩,0,0,0⟩, +⟨⟨1,135,334,true⟩,0,0,0⟩, +⟨⟨1,135,337,true⟩,0,0,0⟩, +⟨⟨1,135,339,true⟩,0,0,0⟩, +⟨⟨1,135,349,true⟩,0,0,0⟩, +⟨⟨1,135,351,true⟩,0,0,0⟩, +⟨⟨1,135,354,true⟩,0,0,0⟩, +⟨⟨1,135,358,true⟩,0,0,0⟩, +⟨⟨1,135,360,true⟩,0,0,0⟩, +⟨⟨1,135,364,true⟩,0,0,0⟩, +⟨⟨1,135,387,true⟩,0,0,0⟩, +⟨⟨1,135,391,true⟩,0,0,0⟩] +def chunk4 : List Entry := [⟨⟨1,135,395,true⟩,0,0,0⟩, +⟨⟨1,135,399,true⟩,0,0,0⟩, +⟨⟨1,135,401,true⟩,0,0,0⟩, +⟨⟨1,135,403,true⟩,0,0,0⟩, +⟨⟨1,135,413,true⟩,0,0,0⟩, +⟨⟨1,135,415,true⟩,0,0,0⟩, +⟨⟨1,135,432,true⟩,0,0,0⟩, +⟨⟨1,135,434,true⟩,0,0,0⟩, +⟨⟨1,135,440,true⟩,0,0,0⟩, +⟨⟨1,135,442,true⟩,0,0,0⟩, +⟨⟨1,135,451,true⟩,0,0,0⟩, +⟨⟨1,135,455,true⟩,0,0,0⟩, +⟨⟨1,135,459,true⟩,0,0,0⟩, +⟨⟨1,135,463,true⟩,0,0,0⟩, +⟨⟨1,135,468,true⟩,0,0,0⟩, +⟨⟨1,135,470,true⟩,0,0,0⟩, +⟨⟨1,135,476,true⟩,0,0,0⟩, +⟨⟨1,135,478,true⟩,0,0,0⟩, +⟨⟨1,135,481,true⟩,0,0,0⟩, +⟨⟨1,135,485,true⟩,0,0,0⟩, +⟨⟨1,135,489,true⟩,0,0,0⟩, +⟨⟨1,135,493,true⟩,0,0,0⟩, +⟨⟨1,135,498,true⟩,0,0,0⟩, +⟨⟨1,135,499,true⟩,0,0,0⟩, +⟨⟨1,135,504,true⟩,0,0,0⟩, +⟨⟨1,135,511,true⟩,0,0,0⟩, +⟨⟨1,135,524,true⟩,0,0,0⟩, +⟨⟨1,135,526,true⟩,0,0,0⟩, +⟨⟨1,135,540,true⟩,0,0,0⟩, +⟨⟨1,135,542,true⟩,0,0,0⟩, +⟨⟨1,135,552,true⟩,0,0,0⟩, +⟨⟨1,135,554,true⟩,0,0,0⟩, +⟨⟨1,135,573,true⟩,0,0,0⟩, +⟨⟨1,135,575,true⟩,0,0,0⟩, +⟨⟨1,135,585,true⟩,0,0,0⟩, +⟨⟨1,135,587,true⟩,0,0,0⟩, +⟨⟨1,135,594,true⟩,0,0,0⟩, +⟨⟨1,135,595,true⟩,0,0,0⟩, +⟨⟨1,135,598,true⟩,0,0,0⟩, +⟨⟨1,135,599,true⟩,0,0,0⟩, +⟨⟨1,135,608,true⟩,0,0,0⟩, +⟨⟨1,135,610,true⟩,0,0,0⟩, +⟨⟨1,135,614,true⟩,0,0,0⟩, +⟨⟨1,135,619,true⟩,0,0,0⟩, +⟨⟨1,135,622,true⟩,0,0,0⟩, +⟨⟨1,135,640,true⟩,0,0,0⟩, +⟨⟨1,135,642,true⟩,0,0,0⟩, +⟨⟨1,135,848,true⟩,0,0,0⟩, +⟨⟨1,135,933,true⟩,0,0,0⟩, +⟨⟨1,136,251,true⟩,0,0,0⟩, +⟨⟨1,136,261,true⟩,0,0,0⟩, +⟨⟨1,136,273,true⟩,0,0,0⟩, +⟨⟨1,136,285,true⟩,0,0,0⟩, +⟨⟨1,136,293,true⟩,0,0,0⟩, +⟨⟨1,136,295,true⟩,0,0,0⟩, +⟨⟨1,136,297,true⟩,0,0,0⟩, +⟨⟨1,136,299,true⟩,0,0,0⟩, +⟨⟨1,136,311,true⟩,0,0,0⟩, +⟨⟨1,136,324,true⟩,0,0,0⟩, +⟨⟨1,136,326,true⟩,0,0,0⟩, +⟨⟨1,136,332,true⟩,0,0,0⟩, +⟨⟨1,136,334,true⟩,0,0,0⟩, +⟨⟨1,136,340,true⟩,0,0,0⟩, +⟨⟨1,136,342,true⟩,0,0,0⟩, +⟨⟨1,136,348,true⟩,0,0,0⟩, +⟨⟨1,136,350,true⟩,0,0,0⟩, +⟨⟨1,136,370,true⟩,0,0,0⟩, +⟨⟨1,136,374,true⟩,0,0,0⟩, +⟨⟨1,136,376,true⟩,0,0,0⟩, +⟨⟨1,136,380,true⟩,0,0,0⟩, +⟨⟨1,136,388,true⟩,0,0,0⟩, +⟨⟨1,136,390,true⟩,0,0,0⟩, +⟨⟨1,136,396,true⟩,0,0,0⟩, +⟨⟨1,136,398,true⟩,0,0,0⟩, +⟨⟨1,136,404,true⟩,0,0,0⟩, +⟨⟨1,136,406,true⟩,0,0,0⟩, +⟨⟨1,136,412,true⟩,0,0,0⟩, +⟨⟨1,136,414,true⟩,0,0,0⟩, +⟨⟨1,136,420,true⟩,0,0,0⟩, +⟨⟨1,136,422,true⟩,0,0,0⟩, +⟨⟨1,136,428,true⟩,0,0,0⟩, +⟨⟨1,136,430,true⟩,0,0,0⟩, +⟨⟨1,136,452,true⟩,0,0,0⟩, +⟨⟨1,136,454,true⟩,0,0,0⟩, +⟨⟨1,136,460,true⟩,0,0,0⟩, +⟨⟨1,136,462,true⟩,0,0,0⟩, +⟨⟨1,136,468,true⟩,0,0,0⟩, +⟨⟨1,136,470,true⟩,0,0,0⟩, +⟨⟨1,136,476,true⟩,0,0,0⟩, +⟨⟨1,136,478,true⟩,0,0,0⟩, +⟨⟨1,136,499,true⟩,0,0,0⟩, +⟨⟨1,136,503,true⟩,0,0,0⟩, +⟨⟨1,136,507,true⟩,0,0,0⟩, +⟨⟨1,136,511,true⟩,0,0,0⟩, +⟨⟨1,136,580,true⟩,0,0,0⟩, +⟨⟨1,136,582,true⟩,0,0,0⟩, +⟨⟨1,136,637,true⟩,0,0,0⟩, +⟨⟨1,136,639,true⟩,0,0,0⟩, +⟨⟨1,136,649,true⟩,0,0,0⟩, +⟨⟨1,136,651,true⟩,0,0,0⟩, +⟨⟨1,136,658,true⟩,0,0,0⟩, +⟨⟨1,136,659,true⟩,0,0,0⟩, +⟨⟨1,136,662,true⟩,0,0,0⟩, +⟨⟨1,136,663,true⟩,0,0,0⟩, +⟨⟨1,136,672,true⟩,0,0,0⟩, +⟨⟨1,136,674,true⟩,0,0,0⟩, +⟨⟨1,136,676,true⟩,0,0,0⟩, +⟨⟨1,136,678,true⟩,0,0,0⟩, +⟨⟨1,136,794,true⟩,0,0,0⟩, +⟨⟨1,136,843,true⟩,0,0,0⟩, +⟨⟨1,136,871,true⟩,0,0,0⟩, +⟨⟨1,136,911,true⟩,0,0,0⟩, +⟨⟨1,137,251,true⟩,0,0,0⟩, +⟨⟨1,137,261,true⟩,0,0,0⟩, +⟨⟨1,137,273,true⟩,0,0,0⟩, +⟨⟨1,137,285,true⟩,0,0,0⟩, +⟨⟨1,137,293,true⟩,0,0,0⟩, +⟨⟨1,137,295,true⟩,0,0,0⟩, +⟨⟨1,137,297,true⟩,0,0,0⟩, +⟨⟨1,137,299,true⟩,0,0,0⟩, +⟨⟨1,137,308,true⟩,0,0,0⟩, +⟨⟨1,137,320,true⟩,0,0,0⟩, +⟨⟨1,137,322,true⟩,0,0,0⟩, +⟨⟨1,137,328,true⟩,0,0,0⟩, +⟨⟨1,137,330,true⟩,0,0,0⟩, +⟨⟨1,137,340,true⟩,0,0,0⟩, +⟨⟨1,137,342,true⟩,0,0,0⟩, +⟨⟨1,137,348,true⟩,0,0,0⟩, +⟨⟨1,137,350,true⟩,0,0,0⟩, +⟨⟨1,137,368,true⟩,0,0,0⟩, +⟨⟨1,137,372,true⟩,0,0,0⟩, +⟨⟨1,137,378,true⟩,0,0,0⟩, +⟨⟨1,137,382,true⟩,0,0,0⟩, +⟨⟨1,137,384,true⟩,0,0,0⟩, +⟨⟨1,137,386,true⟩,0,0,0⟩, +⟨⟨1,137,392,true⟩,0,0,0⟩, +⟨⟨1,137,394,true⟩,0,0,0⟩, +⟨⟨1,137,404,true⟩,0,0,0⟩, +⟨⟨1,137,406,true⟩,0,0,0⟩, +⟨⟨1,137,412,true⟩,0,0,0⟩, +⟨⟨1,137,414,true⟩,0,0,0⟩, +⟨⟨1,137,420,true⟩,0,0,0⟩, +⟨⟨1,137,422,true⟩,0,0,0⟩, +⟨⟨1,137,428,true⟩,0,0,0⟩, +⟨⟨1,137,430,true⟩,0,0,0⟩, +⟨⟨1,137,448,true⟩,0,0,0⟩, +⟨⟨1,137,450,true⟩,0,0,0⟩, +⟨⟨1,137,456,true⟩,0,0,0⟩, +⟨⟨1,137,458,true⟩,0,0,0⟩, +⟨⟨1,137,468,true⟩,0,0,0⟩, +⟨⟨1,137,470,true⟩,0,0,0⟩, +⟨⟨1,137,476,true⟩,0,0,0⟩, +⟨⟨1,137,478,true⟩,0,0,0⟩, +⟨⟨1,137,483,true⟩,0,0,0⟩, +⟨⟨1,137,484,true⟩,0,0,0⟩, +⟨⟨1,137,494,true⟩,0,0,0⟩, +⟨⟨1,137,495,true⟩,0,0,0⟩, +⟨⟨1,137,497,true⟩,0,0,0⟩, +⟨⟨1,137,501,true⟩,0,0,0⟩, +⟨⟨1,137,505,true⟩,0,0,0⟩, +⟨⟨1,137,509,true⟩,0,0,0⟩, +⟨⟨1,137,580,true⟩,0,0,0⟩, +⟨⟨1,137,582,true⟩,0,0,0⟩, +⟨⟨1,137,637,true⟩,0,0,0⟩, +⟨⟨1,137,639,true⟩,0,0,0⟩, +⟨⟨1,137,648,true⟩,0,0,0⟩, +⟨⟨1,137,650,true⟩,0,0,0⟩, +⟨⟨1,137,656,true⟩,0,0,0⟩, +⟨⟨1,137,657,true⟩,0,0,0⟩, +⟨⟨1,137,660,true⟩,0,0,0⟩, +⟨⟨1,137,661,true⟩,0,0,0⟩, +⟨⟨1,137,672,true⟩,0,0,0⟩, +⟨⟨1,137,676,true⟩,0,0,0⟩, +⟨⟨1,137,677,true⟩,0,0,0⟩, +⟨⟨1,137,678,true⟩,0,0,0⟩, +⟨⟨1,137,682,true⟩,0,0,0⟩, +⟨⟨1,137,686,true⟩,0,0,0⟩, +⟨⟨1,137,794,true⟩,0,0,0⟩, +⟨⟨1,137,843,true⟩,0,0,0⟩, +⟨⟨1,137,870,true⟩,0,0,0⟩, +⟨⟨1,137,910,true⟩,0,0,0⟩, +⟨⟨1,137,924,true⟩,0,0,0⟩, +⟨⟨1,137,966,true⟩,0,0,0⟩, +⟨⟨1,137,973,true⟩,0,0,0⟩, +⟨⟨1,138,251,true⟩,0,0,0⟩, +⟨⟨1,138,261,true⟩,0,0,0⟩, +⟨⟨1,138,273,true⟩,0,0,0⟩, +⟨⟨1,138,285,true⟩,0,0,0⟩, +⟨⟨1,138,289,true⟩,0,0,0⟩, +⟨⟨1,138,291,true⟩,0,0,0⟩, +⟨⟨1,138,301,true⟩,0,0,0⟩, +⟨⟨1,138,303,true⟩,0,0,0⟩, +⟨⟨1,138,306,true⟩,0,0,0⟩, +⟨⟨1,138,324,true⟩,0,0,0⟩, +⟨⟨1,138,326,true⟩,0,0,0⟩, +⟨⟨1,138,332,true⟩,0,0,0⟩, +⟨⟨1,138,334,true⟩,0,0,0⟩, +⟨⟨1,138,336,true⟩,0,0,0⟩, +⟨⟨1,138,338,true⟩,0,0,0⟩, +⟨⟨1,138,344,true⟩,0,0,0⟩] +def chunk5 : List Entry := [⟨⟨1,138,346,true⟩,0,0,0⟩, +⟨⟨1,138,370,true⟩,0,0,0⟩, +⟨⟨1,138,374,true⟩,0,0,0⟩, +⟨⟨1,138,376,true⟩,0,0,0⟩, +⟨⟨1,138,380,true⟩,0,0,0⟩, +⟨⟨1,138,384,true⟩,0,0,0⟩, +⟨⟨1,138,386,true⟩,0,0,0⟩, +⟨⟨1,138,392,true⟩,0,0,0⟩, +⟨⟨1,138,394,true⟩,0,0,0⟩, +⟨⟨1,138,404,true⟩,0,0,0⟩, +⟨⟨1,138,406,true⟩,0,0,0⟩, +⟨⟨1,138,412,true⟩,0,0,0⟩, +⟨⟨1,138,414,true⟩,0,0,0⟩, +⟨⟨1,138,416,true⟩,0,0,0⟩, +⟨⟨1,138,418,true⟩,0,0,0⟩, +⟨⟨1,138,424,true⟩,0,0,0⟩, +⟨⟨1,138,426,true⟩,0,0,0⟩, +⟨⟨1,138,452,true⟩,0,0,0⟩, +⟨⟨1,138,454,true⟩,0,0,0⟩, +⟨⟨1,138,460,true⟩,0,0,0⟩, +⟨⟨1,138,462,true⟩,0,0,0⟩, +⟨⟨1,138,464,true⟩,0,0,0⟩, +⟨⟨1,138,466,true⟩,0,0,0⟩, +⟨⟨1,138,472,true⟩,0,0,0⟩, +⟨⟨1,138,474,true⟩,0,0,0⟩, +⟨⟨1,138,482,true⟩,0,0,0⟩, +⟨⟨1,138,485,true⟩,0,0,0⟩, +⟨⟨1,138,486,true⟩,0,0,0⟩, +⟨⟨1,138,487,true⟩,0,0,0⟩, +⟨⟨1,138,488,true⟩,0,0,0⟩, +⟨⟨1,138,489,true⟩,0,0,0⟩, +⟨⟨1,138,491,true⟩,0,0,0⟩, +⟨⟨1,138,492,true⟩,0,0,0⟩, +⟨⟨1,138,499,true⟩,0,0,0⟩, +⟨⟨1,138,503,true⟩,0,0,0⟩, +⟨⟨1,138,507,true⟩,0,0,0⟩, +⟨⟨1,138,511,true⟩,0,0,0⟩, +⟨⟨1,138,580,true⟩,0,0,0⟩, +⟨⟨1,138,582,true⟩,0,0,0⟩, +⟨⟨1,138,636,true⟩,0,0,0⟩, +⟨⟨1,138,638,true⟩,0,0,0⟩, +⟨⟨1,138,649,true⟩,0,0,0⟩, +⟨⟨1,138,651,true⟩,0,0,0⟩, +⟨⟨1,138,656,true⟩,0,0,0⟩, +⟨⟨1,138,657,true⟩,0,0,0⟩, +⟨⟨1,138,660,true⟩,0,0,0⟩, +⟨⟨1,138,661,true⟩,0,0,0⟩, +⟨⟨1,138,672,true⟩,0,0,0⟩, +⟨⟨1,138,676,true⟩,0,0,0⟩, +⟨⟨1,138,677,true⟩,0,0,0⟩, +⟨⟨1,138,794,true⟩,0,0,0⟩, +⟨⟨1,138,842,true⟩,0,0,0⟩, +⟨⟨1,138,870,true⟩,0,0,0⟩, +⟨⟨1,138,896,true⟩,0,0,0⟩, +⟨⟨1,138,911,true⟩,0,0,0⟩, +⟨⟨1,138,924,true⟩,0,0,0⟩, +⟨⟨1,138,965,true⟩,0,0,0⟩, +⟨⟨1,138,974,true⟩,0,0,0⟩, +⟨⟨1,139,251,true⟩,0,0,0⟩, +⟨⟨1,139,261,true⟩,0,0,0⟩, +⟨⟨1,139,273,true⟩,0,0,0⟩, +⟨⟨1,139,285,true⟩,0,0,0⟩, +⟨⟨1,139,289,true⟩,0,0,0⟩, +⟨⟨1,139,291,true⟩,0,0,0⟩, +⟨⟨1,139,301,true⟩,0,0,0⟩, +⟨⟨1,139,303,true⟩,0,0,0⟩, +⟨⟨1,139,305,true⟩,0,0,0⟩, +⟨⟨1,139,320,true⟩,0,0,0⟩, +⟨⟨1,139,322,true⟩,0,0,0⟩, +⟨⟨1,139,328,true⟩,0,0,0⟩, +⟨⟨1,139,330,true⟩,0,0,0⟩, +⟨⟨1,139,336,true⟩,0,0,0⟩, +⟨⟨1,139,338,true⟩,0,0,0⟩, +⟨⟨1,139,344,true⟩,0,0,0⟩, +⟨⟨1,139,346,true⟩,0,0,0⟩, +⟨⟨1,139,368,true⟩,0,0,0⟩, +⟨⟨1,139,372,true⟩,0,0,0⟩, +⟨⟨1,139,378,true⟩,0,0,0⟩, +⟨⟨1,139,382,true⟩,0,0,0⟩, +⟨⟨1,139,388,true⟩,0,0,0⟩, +⟨⟨1,139,390,true⟩,0,0,0⟩, +⟨⟨1,139,396,true⟩,0,0,0⟩, +⟨⟨1,139,398,true⟩,0,0,0⟩, +⟨⟨1,139,404,true⟩,0,0,0⟩, +⟨⟨1,139,406,true⟩,0,0,0⟩, +⟨⟨1,139,412,true⟩,0,0,0⟩, +⟨⟨1,139,414,true⟩,0,0,0⟩, +⟨⟨1,139,416,true⟩,0,0,0⟩, +⟨⟨1,139,418,true⟩,0,0,0⟩, +⟨⟨1,139,424,true⟩,0,0,0⟩, +⟨⟨1,139,426,true⟩,0,0,0⟩, +⟨⟨1,139,448,true⟩,0,0,0⟩, +⟨⟨1,139,450,true⟩,0,0,0⟩, +⟨⟨1,139,456,true⟩,0,0,0⟩, +⟨⟨1,139,458,true⟩,0,0,0⟩, +⟨⟨1,139,464,true⟩,0,0,0⟩, +⟨⟨1,139,466,true⟩,0,0,0⟩, +⟨⟨1,139,472,true⟩,0,0,0⟩, +⟨⟨1,139,474,true⟩,0,0,0⟩, +⟨⟨1,139,497,true⟩,0,0,0⟩, +⟨⟨1,139,501,true⟩,0,0,0⟩, +⟨⟨1,139,505,true⟩,0,0,0⟩, +⟨⟨1,139,509,true⟩,0,0,0⟩, +⟨⟨1,139,580,true⟩,0,0,0⟩, +⟨⟨1,139,582,true⟩,0,0,0⟩, +⟨⟨1,139,636,true⟩,0,0,0⟩, +⟨⟨1,139,638,true⟩,0,0,0⟩, +⟨⟨1,139,648,true⟩,0,0,0⟩, +⟨⟨1,139,650,true⟩,0,0,0⟩, +⟨⟨1,139,658,true⟩,0,0,0⟩, +⟨⟨1,139,659,true⟩,0,0,0⟩, +⟨⟨1,139,662,true⟩,0,0,0⟩, +⟨⟨1,139,663,true⟩,0,0,0⟩, +⟨⟨1,139,672,true⟩,0,0,0⟩, +⟨⟨1,139,674,true⟩,0,0,0⟩, +⟨⟨1,139,676,true⟩,0,0,0⟩, +⟨⟨1,139,678,true⟩,0,0,0⟩, +⟨⟨1,139,794,true⟩,0,0,0⟩, +⟨⟨1,139,842,true⟩,0,0,0⟩, +⟨⟨1,139,871,true⟩,0,0,0⟩, +⟨⟨1,139,896,true⟩,0,0,0⟩, +⟨⟨1,139,910,true⟩,0,0,0⟩, +⟨⟨1,140,251,true⟩,0,0,0⟩, +⟨⟨1,140,261,true⟩,0,0,0⟩, +⟨⟨1,140,273,true⟩,0,0,0⟩, +⟨⟨1,140,285,true⟩,0,0,0⟩, +⟨⟨1,140,289,true⟩,0,0,0⟩, +⟨⟨1,140,291,true⟩,0,0,0⟩, +⟨⟨1,140,301,true⟩,0,0,0⟩, +⟨⟨1,140,303,true⟩,0,0,0⟩, +⟨⟨1,140,319,true⟩,0,0,0⟩, +⟨⟨1,140,324,true⟩,0,0,0⟩, +⟨⟨1,140,326,true⟩,0,0,0⟩, +⟨⟨1,140,332,true⟩,0,0,0⟩, +⟨⟨1,140,334,true⟩,0,0,0⟩, +⟨⟨1,140,340,true⟩,0,0,0⟩, +⟨⟨1,140,342,true⟩,0,0,0⟩, +⟨⟨1,140,348,true⟩,0,0,0⟩, +⟨⟨1,140,350,true⟩,0,0,0⟩, +⟨⟨1,140,368,true⟩,0,0,0⟩, +⟨⟨1,140,372,true⟩,0,0,0⟩, +⟨⟨1,140,378,true⟩,0,0,0⟩, +⟨⟨1,140,382,true⟩,0,0,0⟩, +⟨⟨1,140,388,true⟩,0,0,0⟩, +⟨⟨1,140,390,true⟩,0,0,0⟩, +⟨⟨1,140,396,true⟩,0,0,0⟩, +⟨⟨1,140,398,true⟩,0,0,0⟩, +⟨⟨1,140,400,true⟩,0,0,0⟩, +⟨⟨1,140,402,true⟩,0,0,0⟩, +⟨⟨1,140,408,true⟩,0,0,0⟩, +⟨⟨1,140,410,true⟩,0,0,0⟩, +⟨⟨1,140,420,true⟩,0,0,0⟩, +⟨⟨1,140,422,true⟩,0,0,0⟩, +⟨⟨1,140,428,true⟩,0,0,0⟩, +⟨⟨1,140,430,true⟩,0,0,0⟩, +⟨⟨1,140,448,true⟩,0,0,0⟩, +⟨⟨1,140,450,true⟩,0,0,0⟩, +⟨⟨1,140,456,true⟩,0,0,0⟩, +⟨⟨1,140,458,true⟩,0,0,0⟩, +⟨⟨1,140,464,true⟩,0,0,0⟩, +⟨⟨1,140,466,true⟩,0,0,0⟩, +⟨⟨1,140,472,true⟩,0,0,0⟩, +⟨⟨1,140,474,true⟩,0,0,0⟩, +⟨⟨1,140,484,true⟩,0,0,0⟩, +⟨⟨1,140,485,true⟩,0,0,0⟩, +⟨⟨1,140,486,true⟩,0,0,0⟩, +⟨⟨1,140,487,true⟩,0,0,0⟩, +⟨⟨1,140,489,true⟩,0,0,0⟩, +⟨⟨1,140,491,true⟩,0,0,0⟩, +⟨⟨1,140,492,true⟩,0,0,0⟩, +⟨⟨1,140,494,true⟩,0,0,0⟩, +⟨⟨1,140,499,true⟩,0,0,0⟩, +⟨⟨1,140,503,true⟩,0,0,0⟩, +⟨⟨1,140,507,true⟩,0,0,0⟩, +⟨⟨1,140,511,true⟩,0,0,0⟩, +⟨⟨1,140,576,true⟩,0,0,0⟩, +⟨⟨1,140,578,true⟩,0,0,0⟩, +⟨⟨1,140,636,true⟩,0,0,0⟩, +⟨⟨1,140,638,true⟩,0,0,0⟩, +⟨⟨1,140,648,true⟩,0,0,0⟩, +⟨⟨1,140,650,true⟩,0,0,0⟩, +⟨⟨1,140,658,true⟩,0,0,0⟩, +⟨⟨1,140,659,true⟩,0,0,0⟩, +⟨⟨1,140,662,true⟩,0,0,0⟩, +⟨⟨1,140,663,true⟩,0,0,0⟩, +⟨⟨1,140,672,true⟩,0,0,0⟩, +⟨⟨1,140,674,true⟩,0,0,0⟩, +⟨⟨1,140,677,true⟩,0,0,0⟩, +⟨⟨1,140,682,true⟩,0,0,0⟩, +⟨⟨1,140,687,true⟩,0,0,0⟩, +⟨⟨1,140,792,true⟩,0,0,0⟩, +⟨⟨1,140,842,true⟩,0,0,0⟩, +⟨⟨1,140,871,true⟩,0,0,0⟩, +⟨⟨1,140,896,true⟩,0,0,0⟩, +⟨⟨1,140,910,true⟩,0,0,0⟩, +⟨⟨1,140,965,true⟩,0,0,0⟩, +⟨⟨1,140,973,true⟩,0,0,0⟩, +⟨⟨1,141,251,true⟩,0,0,0⟩, +⟨⟨1,141,261,true⟩,0,0,0⟩, +⟨⟨1,141,273,true⟩,0,0,0⟩] +def chunk6 : List Entry := [⟨⟨1,141,285,true⟩,0,0,0⟩, +⟨⟨1,141,289,true⟩,0,0,0⟩, +⟨⟨1,141,291,true⟩,0,0,0⟩, +⟨⟨1,141,301,true⟩,0,0,0⟩, +⟨⟨1,141,303,true⟩,0,0,0⟩, +⟨⟨1,141,316,true⟩,0,0,0⟩, +⟨⟨1,141,320,true⟩,0,0,0⟩, +⟨⟨1,141,322,true⟩,0,0,0⟩, +⟨⟨1,141,328,true⟩,0,0,0⟩, +⟨⟨1,141,330,true⟩,0,0,0⟩, +⟨⟨1,141,340,true⟩,0,0,0⟩, +⟨⟨1,141,342,true⟩,0,0,0⟩, +⟨⟨1,141,348,true⟩,0,0,0⟩, +⟨⟨1,141,350,true⟩,0,0,0⟩, +⟨⟨1,141,370,true⟩,0,0,0⟩, +⟨⟨1,141,374,true⟩,0,0,0⟩, +⟨⟨1,141,376,true⟩,0,0,0⟩, +⟨⟨1,141,380,true⟩,0,0,0⟩, +⟨⟨1,141,384,true⟩,0,0,0⟩, +⟨⟨1,141,386,true⟩,0,0,0⟩, +⟨⟨1,141,392,true⟩,0,0,0⟩, +⟨⟨1,141,394,true⟩,0,0,0⟩, +⟨⟨1,141,400,true⟩,0,0,0⟩, +⟨⟨1,141,402,true⟩,0,0,0⟩, +⟨⟨1,141,408,true⟩,0,0,0⟩, +⟨⟨1,141,410,true⟩,0,0,0⟩, +⟨⟨1,141,420,true⟩,0,0,0⟩, +⟨⟨1,141,422,true⟩,0,0,0⟩, +⟨⟨1,141,428,true⟩,0,0,0⟩, +⟨⟨1,141,430,true⟩,0,0,0⟩, +⟨⟨1,141,452,true⟩,0,0,0⟩, +⟨⟨1,141,454,true⟩,0,0,0⟩, +⟨⟨1,141,460,true⟩,0,0,0⟩, +⟨⟨1,141,462,true⟩,0,0,0⟩, +⟨⟨1,141,464,true⟩,0,0,0⟩, +⟨⟨1,141,466,true⟩,0,0,0⟩, +⟨⟨1,141,472,true⟩,0,0,0⟩, +⟨⟨1,141,474,true⟩,0,0,0⟩, +⟨⟨1,141,497,true⟩,0,0,0⟩, +⟨⟨1,141,501,true⟩,0,0,0⟩, +⟨⟨1,141,505,true⟩,0,0,0⟩, +⟨⟨1,141,509,true⟩,0,0,0⟩, +⟨⟨1,141,576,true⟩,0,0,0⟩, +⟨⟨1,141,578,true⟩,0,0,0⟩, +⟨⟨1,141,636,true⟩,0,0,0⟩, +⟨⟨1,141,638,true⟩,0,0,0⟩, +⟨⟨1,141,649,true⟩,0,0,0⟩, +⟨⟨1,141,651,true⟩,0,0,0⟩, +⟨⟨1,141,656,true⟩,0,0,0⟩, +⟨⟨1,141,657,true⟩,0,0,0⟩, +⟨⟨1,141,660,true⟩,0,0,0⟩, +⟨⟨1,141,661,true⟩,0,0,0⟩, +⟨⟨1,141,672,true⟩,0,0,0⟩, +⟨⟨1,141,674,true⟩,0,0,0⟩, +⟨⟨1,141,676,true⟩,0,0,0⟩, +⟨⟨1,141,678,true⟩,0,0,0⟩, +⟨⟨1,141,792,true⟩,0,0,0⟩, +⟨⟨1,141,842,true⟩,0,0,0⟩, +⟨⟨1,141,870,true⟩,0,0,0⟩, +⟨⟨1,141,896,true⟩,0,0,0⟩, +⟨⟨1,141,911,true⟩,0,0,0⟩, +⟨⟨1,141,924,true⟩,0,0,0⟩, +⟨⟨1,142,251,true⟩,0,0,0⟩, +⟨⟨1,142,261,true⟩,0,0,0⟩, +⟨⟨1,142,273,true⟩,0,0,0⟩, +⟨⟨1,142,285,true⟩,0,0,0⟩, +⟨⟨1,142,293,true⟩,0,0,0⟩, +⟨⟨1,142,295,true⟩,0,0,0⟩, +⟨⟨1,142,297,true⟩,0,0,0⟩, +⟨⟨1,142,299,true⟩,0,0,0⟩, +⟨⟨1,142,314,true⟩,0,0,0⟩, +⟨⟨1,142,324,true⟩,0,0,0⟩, +⟨⟨1,142,326,true⟩,0,0,0⟩, +⟨⟨1,142,332,true⟩,0,0,0⟩, +⟨⟨1,142,334,true⟩,0,0,0⟩, +⟨⟨1,142,336,true⟩,0,0,0⟩, +⟨⟨1,142,338,true⟩,0,0,0⟩, +⟨⟨1,142,344,true⟩,0,0,0⟩, +⟨⟨1,142,346,true⟩,0,0,0⟩, +⟨⟨1,142,368,true⟩,0,0,0⟩, +⟨⟨1,142,372,true⟩,0,0,0⟩, +⟨⟨1,142,378,true⟩,0,0,0⟩, +⟨⟨1,142,382,true⟩,0,0,0⟩, +⟨⟨1,142,384,true⟩,0,0,0⟩, +⟨⟨1,142,386,true⟩,0,0,0⟩, +⟨⟨1,142,392,true⟩,0,0,0⟩, +⟨⟨1,142,394,true⟩,0,0,0⟩, +⟨⟨1,142,400,true⟩,0,0,0⟩, +⟨⟨1,142,402,true⟩,0,0,0⟩, +⟨⟨1,142,408,true⟩,0,0,0⟩, +⟨⟨1,142,410,true⟩,0,0,0⟩, +⟨⟨1,142,416,true⟩,0,0,0⟩, +⟨⟨1,142,418,true⟩,0,0,0⟩, +⟨⟨1,142,424,true⟩,0,0,0⟩, +⟨⟨1,142,426,true⟩,0,0,0⟩, +⟨⟨1,142,448,true⟩,0,0,0⟩, +⟨⟨1,142,450,true⟩,0,0,0⟩, +⟨⟨1,142,456,true⟩,0,0,0⟩, +⟨⟨1,142,458,true⟩,0,0,0⟩, +⟨⟨1,142,468,true⟩,0,0,0⟩, +⟨⟨1,142,470,true⟩,0,0,0⟩, +⟨⟨1,142,476,true⟩,0,0,0⟩, +⟨⟨1,142,478,true⟩,0,0,0⟩, +⟨⟨1,142,499,true⟩,0,0,0⟩, +⟨⟨1,142,503,true⟩,0,0,0⟩, +⟨⟨1,142,507,true⟩,0,0,0⟩, +⟨⟨1,142,511,true⟩,0,0,0⟩, +⟨⟨1,142,576,true⟩,0,0,0⟩, +⟨⟨1,142,578,true⟩,0,0,0⟩, +⟨⟨1,142,637,true⟩,0,0,0⟩, +⟨⟨1,142,639,true⟩,0,0,0⟩, +⟨⟨1,142,648,true⟩,0,0,0⟩, +⟨⟨1,142,650,true⟩,0,0,0⟩, +⟨⟨1,142,656,true⟩,0,0,0⟩, +⟨⟨1,142,657,true⟩,0,0,0⟩, +⟨⟨1,142,660,true⟩,0,0,0⟩, +⟨⟨1,142,661,true⟩,0,0,0⟩, +⟨⟨1,142,672,true⟩,0,0,0⟩, +⟨⟨1,142,674,true⟩,0,0,0⟩, +⟨⟨1,142,676,true⟩,0,0,0⟩, +⟨⟨1,142,678,true⟩,0,0,0⟩, +⟨⟨1,142,792,true⟩,0,0,0⟩, +⟨⟨1,142,843,true⟩,0,0,0⟩, +⟨⟨1,142,870,true⟩,0,0,0⟩, +⟨⟨1,142,910,true⟩,0,0,0⟩, +⟨⟨1,142,924,true⟩,0,0,0⟩, +⟨⟨1,143,251,true⟩,0,0,0⟩, +⟨⟨1,143,261,true⟩,0,0,0⟩, +⟨⟨1,143,273,true⟩,0,0,0⟩, +⟨⟨1,143,285,true⟩,0,0,0⟩, +⟨⟨1,143,293,true⟩,0,0,0⟩, +⟨⟨1,143,295,true⟩,0,0,0⟩, +⟨⟨1,143,297,true⟩,0,0,0⟩, +⟨⟨1,143,299,true⟩,0,0,0⟩, +⟨⟨1,143,313,true⟩,0,0,0⟩, +⟨⟨1,143,320,true⟩,0,0,0⟩, +⟨⟨1,143,322,true⟩,0,0,0⟩, +⟨⟨1,143,328,true⟩,0,0,0⟩, +⟨⟨1,143,330,true⟩,0,0,0⟩, +⟨⟨1,143,336,true⟩,0,0,0⟩, +⟨⟨1,143,338,true⟩,0,0,0⟩, +⟨⟨1,143,344,true⟩,0,0,0⟩, +⟨⟨1,143,346,true⟩,0,0,0⟩, +⟨⟨1,143,370,true⟩,0,0,0⟩, +⟨⟨1,143,374,true⟩,0,0,0⟩, +⟨⟨1,143,376,true⟩,0,0,0⟩, +⟨⟨1,143,380,true⟩,0,0,0⟩, +⟨⟨1,143,388,true⟩,0,0,0⟩, +⟨⟨1,143,390,true⟩,0,0,0⟩, +⟨⟨1,143,396,true⟩,0,0,0⟩, +⟨⟨1,143,398,true⟩,0,0,0⟩, +⟨⟨1,143,400,true⟩,0,0,0⟩, +⟨⟨1,143,402,true⟩,0,0,0⟩, +⟨⟨1,143,408,true⟩,0,0,0⟩, +⟨⟨1,143,410,true⟩,0,0,0⟩, +⟨⟨1,143,416,true⟩,0,0,0⟩, +⟨⟨1,143,418,true⟩,0,0,0⟩, +⟨⟨1,143,424,true⟩,0,0,0⟩, +⟨⟨1,143,426,true⟩,0,0,0⟩, +⟨⟨1,143,452,true⟩,0,0,0⟩, +⟨⟨1,143,454,true⟩,0,0,0⟩, +⟨⟨1,143,460,true⟩,0,0,0⟩, +⟨⟨1,143,462,true⟩,0,0,0⟩, +⟨⟨1,143,468,true⟩,0,0,0⟩, +⟨⟨1,143,470,true⟩,0,0,0⟩, +⟨⟨1,143,476,true⟩,0,0,0⟩, +⟨⟨1,143,478,true⟩,0,0,0⟩, +⟨⟨1,143,482,true⟩,0,0,0⟩, +⟨⟨1,143,483,true⟩,0,0,0⟩, +⟨⟨1,143,488,true⟩,0,0,0⟩, +⟨⟨1,143,495,true⟩,0,0,0⟩, +⟨⟨1,143,497,true⟩,0,0,0⟩, +⟨⟨1,143,501,true⟩,0,0,0⟩, +⟨⟨1,143,505,true⟩,0,0,0⟩, +⟨⟨1,143,509,true⟩,0,0,0⟩, +⟨⟨1,143,576,true⟩,0,0,0⟩, +⟨⟨1,143,578,true⟩,0,0,0⟩, +⟨⟨1,143,637,true⟩,0,0,0⟩, +⟨⟨1,143,639,true⟩,0,0,0⟩, +⟨⟨1,143,649,true⟩,0,0,0⟩, +⟨⟨1,143,651,true⟩,0,0,0⟩, +⟨⟨1,143,658,true⟩,0,0,0⟩, +⟨⟨1,143,659,true⟩,0,0,0⟩, +⟨⟨1,143,662,true⟩,0,0,0⟩, +⟨⟨1,143,663,true⟩,0,0,0⟩, +⟨⟨1,143,672,true⟩,0,0,0⟩, +⟨⟨1,143,674,true⟩,0,0,0⟩, +⟨⟨1,143,677,true⟩,0,0,0⟩, +⟨⟨1,143,678,true⟩,0,0,0⟩, +⟨⟨1,143,686,true⟩,0,0,0⟩, +⟨⟨1,143,687,true⟩,0,0,0⟩, +⟨⟨1,143,792,true⟩,0,0,0⟩, +⟨⟨1,143,843,true⟩,0,0,0⟩, +⟨⟨1,143,871,true⟩,0,0,0⟩, +⟨⟨1,143,911,true⟩,0,0,0⟩, +⟨⟨1,143,966,true⟩,0,0,0⟩, +⟨⟨1,143,974,true⟩,0,0,0⟩, +⟨⟨1,144,256,true⟩,0,0,0⟩, +⟨⟨1,144,262,true⟩,0,0,0⟩, +⟨⟨1,144,268,true⟩,0,0,0⟩] +def chunk7 : List Entry := [⟨⟨1,144,274,true⟩,0,0,0⟩, +⟨⟨1,144,291,true⟩,0,0,0⟩, +⟨⟨1,144,295,true⟩,0,0,0⟩, +⟨⟨1,144,299,true⟩,0,0,0⟩, +⟨⟨1,144,303,true⟩,0,0,0⟩, +⟨⟨1,144,307,true⟩,0,0,0⟩, +⟨⟨1,144,311,true⟩,0,0,0⟩, +⟨⟨1,144,315,true⟩,0,0,0⟩, +⟨⟨1,144,319,true⟩,0,0,0⟩, +⟨⟨1,144,327,true⟩,0,0,0⟩, +⟨⟨1,144,355,true⟩,0,0,0⟩, +⟨⟨1,144,359,true⟩,0,0,0⟩, +⟨⟨1,144,363,true⟩,0,0,0⟩, +⟨⟨1,144,367,true⟩,0,0,0⟩, +⟨⟨1,144,371,true⟩,0,0,0⟩, +⟨⟨1,144,375,true⟩,0,0,0⟩, +⟨⟨1,144,379,true⟩,0,0,0⟩, +⟨⟨1,144,383,true⟩,0,0,0⟩, +⟨⟨1,144,419,true⟩,0,0,0⟩, +⟨⟨1,144,423,true⟩,0,0,0⟩, +⟨⟨1,144,427,true⟩,0,0,0⟩, +⟨⟨1,144,431,true⟩,0,0,0⟩, +⟨⟨1,144,435,true⟩,0,0,0⟩, +⟨⟨1,144,439,true⟩,0,0,0⟩, +⟨⟨1,144,443,true⟩,0,0,0⟩, +⟨⟨1,144,447,true⟩,0,0,0⟩, +⟨⟨1,144,483,true⟩,0,0,0⟩, +⟨⟨1,144,487,true⟩,0,0,0⟩, +⟨⟨1,144,491,true⟩,0,0,0⟩, +⟨⟨1,144,495,true⟩,0,0,0⟩, +⟨⟨1,144,499,true⟩,0,0,0⟩, +⟨⟨1,144,503,true⟩,0,0,0⟩, +⟨⟨1,144,507,true⟩,0,0,0⟩, +⟨⟨1,144,511,true⟩,0,0,0⟩, +⟨⟨1,144,516,true⟩,0,0,0⟩, +⟨⟨1,144,518,true⟩,0,0,0⟩, +⟨⟨1,144,532,true⟩,0,0,0⟩, +⟨⟨1,144,534,true⟩,0,0,0⟩, +⟨⟨1,144,688,true⟩,0,0,0⟩, +⟨⟨1,144,690,true⟩,0,0,0⟩, +⟨⟨1,144,692,true⟩,0,0,0⟩, +⟨⟨1,144,694,true⟩,0,0,0⟩, +⟨⟨1,144,706,true⟩,0,0,0⟩, +⟨⟨1,144,707,true⟩,0,0,0⟩, +⟨⟨1,144,710,true⟩,0,0,0⟩, +⟨⟨1,144,711,true⟩,0,0,0⟩, +⟨⟨1,144,722,true⟩,0,0,0⟩, +⟨⟨1,144,723,true⟩,0,0,0⟩, +⟨⟨1,144,726,true⟩,0,0,0⟩, +⟨⟨1,144,727,true⟩,0,0,0⟩, +⟨⟨1,145,256,true⟩,0,0,0⟩, +⟨⟨1,145,262,true⟩,0,0,0⟩, +⟨⟨1,145,268,true⟩,0,0,0⟩, +⟨⟨1,145,274,true⟩,0,0,0⟩, +⟨⟨1,145,289,true⟩,0,0,0⟩, +⟨⟨1,145,293,true⟩,0,0,0⟩, +⟨⟨1,145,297,true⟩,0,0,0⟩, +⟨⟨1,145,301,true⟩,0,0,0⟩, +⟨⟨1,145,307,true⟩,0,0,0⟩, +⟨⟨1,145,311,true⟩,0,0,0⟩, +⟨⟨1,145,315,true⟩,0,0,0⟩, +⟨⟨1,145,319,true⟩,0,0,0⟩, +⟨⟨1,145,324,true⟩,0,0,0⟩, +⟨⟨1,145,353,true⟩,0,0,0⟩, +⟨⟨1,145,357,true⟩,0,0,0⟩, +⟨⟨1,145,361,true⟩,0,0,0⟩, +⟨⟨1,145,365,true⟩,0,0,0⟩, +⟨⟨1,145,371,true⟩,0,0,0⟩, +⟨⟨1,145,375,true⟩,0,0,0⟩, +⟨⟨1,145,379,true⟩,0,0,0⟩, +⟨⟨1,145,383,true⟩,0,0,0⟩, +⟨⟨1,145,417,true⟩,0,0,0⟩, +⟨⟨1,145,421,true⟩,0,0,0⟩, +⟨⟨1,145,425,true⟩,0,0,0⟩, +⟨⟨1,145,429,true⟩,0,0,0⟩, +⟨⟨1,145,435,true⟩,0,0,0⟩, +⟨⟨1,145,439,true⟩,0,0,0⟩, +⟨⟨1,145,443,true⟩,0,0,0⟩, +⟨⟨1,145,447,true⟩,0,0,0⟩, +⟨⟨1,145,467,true⟩,0,0,0⟩, +⟨⟨1,145,468,true⟩,0,0,0⟩, +⟨⟨1,145,478,true⟩,0,0,0⟩, +⟨⟨1,145,479,true⟩,0,0,0⟩, +⟨⟨1,145,481,true⟩,0,0,0⟩, +⟨⟨1,145,485,true⟩,0,0,0⟩, +⟨⟨1,145,489,true⟩,0,0,0⟩, +⟨⟨1,145,493,true⟩,0,0,0⟩, +⟨⟨1,145,499,true⟩,0,0,0⟩, +⟨⟨1,145,503,true⟩,0,0,0⟩, +⟨⟨1,145,507,true⟩,0,0,0⟩, +⟨⟨1,145,511,true⟩,0,0,0⟩, +⟨⟨1,145,516,true⟩,0,0,0⟩, +⟨⟨1,145,518,true⟩,0,0,0⟩, +⟨⟨1,145,532,true⟩,0,0,0⟩, +⟨⟨1,145,534,true⟩,0,0,0⟩, +⟨⟨1,145,688,true⟩,0,0,0⟩, +⟨⟨1,145,692,true⟩,0,0,0⟩, +⟨⟨1,145,693,true⟩,0,0,0⟩, +⟨⟨1,145,694,true⟩,0,0,0⟩, +⟨⟨1,145,698,true⟩,0,0,0⟩, +⟨⟨1,145,702,true⟩,0,0,0⟩, +⟨⟨1,145,704,true⟩,0,0,0⟩, +⟨⟨1,145,705,true⟩,0,0,0⟩, +⟨⟨1,145,708,true⟩,0,0,0⟩, +⟨⟨1,145,709,true⟩,0,0,0⟩, +⟨⟨1,145,720,true⟩,0,0,0⟩, +⟨⟨1,145,721,true⟩,0,0,0⟩, +⟨⟨1,145,724,true⟩,0,0,0⟩, +⟨⟨1,145,725,true⟩,0,0,0⟩, +⟨⟨1,145,798,true⟩,0,0,0⟩, +⟨⟨1,145,812,true⟩,0,0,0⟩, +⟨⟨1,145,882,true⟩,0,0,0⟩, +⟨⟨1,145,963,true⟩,0,0,0⟩, +⟨⟨1,145,972,true⟩,0,0,0⟩, +⟨⟨1,146,256,true⟩,0,0,0⟩, +⟨⟨1,146,262,true⟩,0,0,0⟩, +⟨⟨1,146,268,true⟩,0,0,0⟩, +⟨⟨1,146,274,true⟩,0,0,0⟩, +⟨⟨1,146,291,true⟩,0,0,0⟩, +⟨⟨1,146,295,true⟩,0,0,0⟩, +⟨⟨1,146,299,true⟩,0,0,0⟩, +⟨⟨1,146,303,true⟩,0,0,0⟩, +⟨⟨1,146,305,true⟩,0,0,0⟩, +⟨⟨1,146,309,true⟩,0,0,0⟩, +⟨⟨1,146,313,true⟩,0,0,0⟩, +⟨⟨1,146,317,true⟩,0,0,0⟩, +⟨⟨1,146,322,true⟩,0,0,0⟩, +⟨⟨1,146,355,true⟩,0,0,0⟩, +⟨⟨1,146,359,true⟩,0,0,0⟩, +⟨⟨1,146,363,true⟩,0,0,0⟩, +⟨⟨1,146,367,true⟩,0,0,0⟩, +⟨⟨1,146,369,true⟩,0,0,0⟩, +⟨⟨1,146,373,true⟩,0,0,0⟩, +⟨⟨1,146,377,true⟩,0,0,0⟩, +⟨⟨1,146,381,true⟩,0,0,0⟩, +⟨⟨1,146,419,true⟩,0,0,0⟩, +⟨⟨1,146,423,true⟩,0,0,0⟩, +⟨⟨1,146,427,true⟩,0,0,0⟩, +⟨⟨1,146,431,true⟩,0,0,0⟩, +⟨⟨1,146,433,true⟩,0,0,0⟩, +⟨⟨1,146,437,true⟩,0,0,0⟩, +⟨⟨1,146,441,true⟩,0,0,0⟩, +⟨⟨1,146,445,true⟩,0,0,0⟩, +⟨⟨1,146,466,true⟩,0,0,0⟩, +⟨⟨1,146,469,true⟩,0,0,0⟩, +⟨⟨1,146,470,true⟩,0,0,0⟩, +⟨⟨1,146,471,true⟩,0,0,0⟩, +⟨⟨1,146,472,true⟩,0,0,0⟩, +⟨⟨1,146,473,true⟩,0,0,0⟩, +⟨⟨1,146,475,true⟩,0,0,0⟩, +⟨⟨1,146,476,true⟩,0,0,0⟩, +⟨⟨1,146,483,true⟩,0,0,0⟩, +⟨⟨1,146,487,true⟩,0,0,0⟩, +⟨⟨1,146,491,true⟩,0,0,0⟩, +⟨⟨1,146,495,true⟩,0,0,0⟩, +⟨⟨1,146,497,true⟩,0,0,0⟩, +⟨⟨1,146,501,true⟩,0,0,0⟩, +⟨⟨1,146,505,true⟩,0,0,0⟩, +⟨⟨1,146,509,true⟩,0,0,0⟩, +⟨⟨1,146,516,true⟩,0,0,0⟩, +⟨⟨1,146,518,true⟩,0,0,0⟩, +⟨⟨1,146,532,true⟩,0,0,0⟩, +⟨⟨1,146,534,true⟩,0,0,0⟩, +⟨⟨1,146,688,true⟩,0,0,0⟩, +⟨⟨1,146,692,true⟩,0,0,0⟩, +⟨⟨1,146,693,true⟩,0,0,0⟩, +⟨⟨1,146,704,true⟩,0,0,0⟩, +⟨⟨1,146,705,true⟩,0,0,0⟩, +⟨⟨1,146,708,true⟩,0,0,0⟩, +⟨⟨1,146,709,true⟩,0,0,0⟩, +⟨⟨1,146,720,true⟩,0,0,0⟩, +⟨⟨1,146,721,true⟩,0,0,0⟩, +⟨⟨1,146,724,true⟩,0,0,0⟩, +⟨⟨1,146,725,true⟩,0,0,0⟩, +⟨⟨1,146,826,true⟩,0,0,0⟩, +⟨⟨1,146,854,true⟩,0,0,0⟩, +⟨⟨1,146,868,true⟩,0,0,0⟩, +⟨⟨1,146,964,true⟩,0,0,0⟩, +⟨⟨1,146,971,true⟩,0,0,0⟩, +⟨⟨1,147,256,true⟩,0,0,0⟩, +⟨⟨1,147,262,true⟩,0,0,0⟩, +⟨⟨1,147,268,true⟩,0,0,0⟩, +⟨⟨1,147,274,true⟩,0,0,0⟩, +⟨⟨1,147,289,true⟩,0,0,0⟩, +⟨⟨1,147,293,true⟩,0,0,0⟩, +⟨⟨1,147,297,true⟩,0,0,0⟩, +⟨⟨1,147,301,true⟩,0,0,0⟩, +⟨⟨1,147,305,true⟩,0,0,0⟩, +⟨⟨1,147,309,true⟩,0,0,0⟩, +⟨⟨1,147,313,true⟩,0,0,0⟩, +⟨⟨1,147,317,true⟩,0,0,0⟩, +⟨⟨1,147,321,true⟩,0,0,0⟩, +⟨⟨1,147,353,true⟩,0,0,0⟩, +⟨⟨1,147,357,true⟩,0,0,0⟩, +⟨⟨1,147,361,true⟩,0,0,0⟩, +⟨⟨1,147,365,true⟩,0,0,0⟩, +⟨⟨1,147,369,true⟩,0,0,0⟩, +⟨⟨1,147,373,true⟩,0,0,0⟩, +⟨⟨1,147,377,true⟩,0,0,0⟩, +⟨⟨1,147,381,true⟩,0,0,0⟩] +def chunk8 : List Entry := [⟨⟨1,147,417,true⟩,0,0,0⟩, +⟨⟨1,147,421,true⟩,0,0,0⟩, +⟨⟨1,147,425,true⟩,0,0,0⟩, +⟨⟨1,147,429,true⟩,0,0,0⟩, +⟨⟨1,147,433,true⟩,0,0,0⟩, +⟨⟨1,147,437,true⟩,0,0,0⟩, +⟨⟨1,147,441,true⟩,0,0,0⟩, +⟨⟨1,147,445,true⟩,0,0,0⟩, +⟨⟨1,147,481,true⟩,0,0,0⟩, +⟨⟨1,147,485,true⟩,0,0,0⟩, +⟨⟨1,147,489,true⟩,0,0,0⟩, +⟨⟨1,147,493,true⟩,0,0,0⟩, +⟨⟨1,147,497,true⟩,0,0,0⟩, +⟨⟨1,147,501,true⟩,0,0,0⟩, +⟨⟨1,147,505,true⟩,0,0,0⟩, +⟨⟨1,147,509,true⟩,0,0,0⟩, +⟨⟨1,147,516,true⟩,0,0,0⟩, +⟨⟨1,147,518,true⟩,0,0,0⟩, +⟨⟨1,147,532,true⟩,0,0,0⟩, +⟨⟨1,147,534,true⟩,0,0,0⟩, +⟨⟨1,147,688,true⟩,0,0,0⟩, +⟨⟨1,147,690,true⟩,0,0,0⟩, +⟨⟨1,147,692,true⟩,0,0,0⟩, +⟨⟨1,147,694,true⟩,0,0,0⟩, +⟨⟨1,147,706,true⟩,0,0,0⟩, +⟨⟨1,147,707,true⟩,0,0,0⟩, +⟨⟨1,147,710,true⟩,0,0,0⟩, +⟨⟨1,147,711,true⟩,0,0,0⟩, +⟨⟨1,147,722,true⟩,0,0,0⟩, +⟨⟨1,147,723,true⟩,0,0,0⟩, +⟨⟨1,147,726,true⟩,0,0,0⟩, +⟨⟨1,147,727,true⟩,0,0,0⟩, +⟨⟨1,147,798,true⟩,0,0,0⟩, +⟨⟨1,147,812,true⟩,0,0,0⟩, +⟨⟨1,147,826,true⟩,0,0,0⟩, +⟨⟨1,147,854,true⟩,0,0,0⟩, +⟨⟨1,147,868,true⟩,0,0,0⟩, +⟨⟨1,147,882,true⟩,0,0,0⟩, +⟨⟨1,148,256,true⟩,0,0,0⟩, +⟨⟨1,148,262,true⟩,0,0,0⟩, +⟨⟨1,148,268,true⟩,0,0,0⟩, +⟨⟨1,148,274,true⟩,0,0,0⟩, +⟨⟨1,148,289,true⟩,0,0,0⟩, +⟨⟨1,148,293,true⟩,0,0,0⟩, +⟨⟨1,148,297,true⟩,0,0,0⟩, +⟨⟨1,148,301,true⟩,0,0,0⟩, +⟨⟨1,148,307,true⟩,0,0,0⟩, +⟨⟨1,148,311,true⟩,0,0,0⟩, +⟨⟨1,148,315,true⟩,0,0,0⟩, +⟨⟨1,148,319,true⟩,0,0,0⟩, +⟨⟨1,148,335,true⟩,0,0,0⟩, +⟨⟨1,148,355,true⟩,0,0,0⟩, +⟨⟨1,148,359,true⟩,0,0,0⟩, +⟨⟨1,148,363,true⟩,0,0,0⟩, +⟨⟨1,148,367,true⟩,0,0,0⟩, +⟨⟨1,148,369,true⟩,0,0,0⟩, +⟨⟨1,148,373,true⟩,0,0,0⟩, +⟨⟨1,148,377,true⟩,0,0,0⟩, +⟨⟨1,148,381,true⟩,0,0,0⟩, +⟨⟨1,148,419,true⟩,0,0,0⟩, +⟨⟨1,148,423,true⟩,0,0,0⟩, +⟨⟨1,148,427,true⟩,0,0,0⟩, +⟨⟨1,148,431,true⟩,0,0,0⟩, +⟨⟨1,148,433,true⟩,0,0,0⟩, +⟨⟨1,148,437,true⟩,0,0,0⟩, +⟨⟨1,148,441,true⟩,0,0,0⟩, +⟨⟨1,148,445,true⟩,0,0,0⟩, +⟨⟨1,148,468,true⟩,0,0,0⟩, +⟨⟨1,148,469,true⟩,0,0,0⟩, +⟨⟨1,148,470,true⟩,0,0,0⟩, +⟨⟨1,148,471,true⟩,0,0,0⟩, +⟨⟨1,148,473,true⟩,0,0,0⟩, +⟨⟨1,148,475,true⟩,0,0,0⟩, +⟨⟨1,148,476,true⟩,0,0,0⟩, +⟨⟨1,148,478,true⟩,0,0,0⟩, +⟨⟨1,148,481,true⟩,0,0,0⟩, +⟨⟨1,148,485,true⟩,0,0,0⟩, +⟨⟨1,148,489,true⟩,0,0,0⟩, +⟨⟨1,148,493,true⟩,0,0,0⟩, +⟨⟨1,148,499,true⟩,0,0,0⟩, +⟨⟨1,148,503,true⟩,0,0,0⟩, +⟨⟨1,148,507,true⟩,0,0,0⟩, +⟨⟨1,148,511,true⟩,0,0,0⟩, +⟨⟨1,148,512,true⟩,0,0,0⟩, +⟨⟨1,148,514,true⟩,0,0,0⟩, +⟨⟨1,148,528,true⟩,0,0,0⟩, +⟨⟨1,148,530,true⟩,0,0,0⟩, +⟨⟨1,148,688,true⟩,0,0,0⟩, +⟨⟨1,148,690,true⟩,0,0,0⟩, +⟨⟨1,148,693,true⟩,0,0,0⟩, +⟨⟨1,148,698,true⟩,0,0,0⟩, +⟨⟨1,148,703,true⟩,0,0,0⟩, +⟨⟨1,148,706,true⟩,0,0,0⟩, +⟨⟨1,148,707,true⟩,0,0,0⟩, +⟨⟨1,148,710,true⟩,0,0,0⟩, +⟨⟨1,148,711,true⟩,0,0,0⟩, +⟨⟨1,148,722,true⟩,0,0,0⟩, +⟨⟨1,148,723,true⟩,0,0,0⟩, +⟨⟨1,148,726,true⟩,0,0,0⟩, +⟨⟨1,148,727,true⟩,0,0,0⟩, +⟨⟨1,148,737,true⟩,0,0,0⟩, +⟨⟨1,148,750,true⟩,0,0,0⟩, +⟨⟨1,148,854,true⟩,0,0,0⟩, +⟨⟨1,148,868,true⟩,0,0,0⟩, +⟨⟨1,148,882,true⟩,0,0,0⟩, +⟨⟨1,148,963,true⟩,0,0,0⟩, +⟨⟨1,148,971,true⟩,0,0,0⟩, +⟨⟨1,149,256,true⟩,0,0,0⟩, +⟨⟨1,149,262,true⟩,0,0,0⟩, +⟨⟨1,149,268,true⟩,0,0,0⟩, +⟨⟨1,149,274,true⟩,0,0,0⟩, +⟨⟨1,149,291,true⟩,0,0,0⟩, +⟨⟨1,149,295,true⟩,0,0,0⟩, +⟨⟨1,149,299,true⟩,0,0,0⟩, +⟨⟨1,149,303,true⟩,0,0,0⟩, +⟨⟨1,149,307,true⟩,0,0,0⟩, +⟨⟨1,149,311,true⟩,0,0,0⟩, +⟨⟨1,149,315,true⟩,0,0,0⟩, +⟨⟨1,149,319,true⟩,0,0,0⟩, +⟨⟨1,149,332,true⟩,0,0,0⟩, +⟨⟨1,149,353,true⟩,0,0,0⟩, +⟨⟨1,149,357,true⟩,0,0,0⟩, +⟨⟨1,149,361,true⟩,0,0,0⟩, +⟨⟨1,149,365,true⟩,0,0,0⟩, +⟨⟨1,149,369,true⟩,0,0,0⟩, +⟨⟨1,149,373,true⟩,0,0,0⟩, +⟨⟨1,149,377,true⟩,0,0,0⟩, +⟨⟨1,149,381,true⟩,0,0,0⟩, +⟨⟨1,149,417,true⟩,0,0,0⟩, +⟨⟨1,149,421,true⟩,0,0,0⟩, +⟨⟨1,149,425,true⟩,0,0,0⟩, +⟨⟨1,149,429,true⟩,0,0,0⟩, +⟨⟨1,149,433,true⟩,0,0,0⟩, +⟨⟨1,149,437,true⟩,0,0,0⟩, +⟨⟨1,149,441,true⟩,0,0,0⟩, +⟨⟨1,149,445,true⟩,0,0,0⟩, +⟨⟨1,149,483,true⟩,0,0,0⟩, +⟨⟨1,149,487,true⟩,0,0,0⟩, +⟨⟨1,149,491,true⟩,0,0,0⟩, +⟨⟨1,149,495,true⟩,0,0,0⟩, +⟨⟨1,149,499,true⟩,0,0,0⟩, +⟨⟨1,149,503,true⟩,0,0,0⟩, +⟨⟨1,149,507,true⟩,0,0,0⟩, +⟨⟨1,149,511,true⟩,0,0,0⟩, +⟨⟨1,149,512,true⟩,0,0,0⟩, +⟨⟨1,149,514,true⟩,0,0,0⟩, +⟨⟨1,149,528,true⟩,0,0,0⟩, +⟨⟨1,149,530,true⟩,0,0,0⟩, +⟨⟨1,149,688,true⟩,0,0,0⟩, +⟨⟨1,149,690,true⟩,0,0,0⟩, +⟨⟨1,149,692,true⟩,0,0,0⟩, +⟨⟨1,149,694,true⟩,0,0,0⟩, +⟨⟨1,149,704,true⟩,0,0,0⟩, +⟨⟨1,149,705,true⟩,0,0,0⟩, +⟨⟨1,149,708,true⟩,0,0,0⟩, +⟨⟨1,149,709,true⟩,0,0,0⟩, +⟨⟨1,149,720,true⟩,0,0,0⟩, +⟨⟨1,149,721,true⟩,0,0,0⟩, +⟨⟨1,149,724,true⟩,0,0,0⟩, +⟨⟨1,149,725,true⟩,0,0,0⟩, +⟨⟨1,149,737,true⟩,0,0,0⟩, +⟨⟨1,149,750,true⟩,0,0,0⟩, +⟨⟨1,149,798,true⟩,0,0,0⟩, +⟨⟨1,149,812,true⟩,0,0,0⟩, +⟨⟨1,149,854,true⟩,0,0,0⟩, +⟨⟨1,149,868,true⟩,0,0,0⟩, +⟨⟨1,150,256,true⟩,0,0,0⟩, +⟨⟨1,150,262,true⟩,0,0,0⟩, +⟨⟨1,150,268,true⟩,0,0,0⟩, +⟨⟨1,150,274,true⟩,0,0,0⟩, +⟨⟨1,150,289,true⟩,0,0,0⟩, +⟨⟨1,150,293,true⟩,0,0,0⟩, +⟨⟨1,150,297,true⟩,0,0,0⟩, +⟨⟨1,150,301,true⟩,0,0,0⟩, +⟨⟨1,150,305,true⟩,0,0,0⟩, +⟨⟨1,150,309,true⟩,0,0,0⟩, +⟨⟨1,150,313,true⟩,0,0,0⟩, +⟨⟨1,150,317,true⟩,0,0,0⟩, +⟨⟨1,150,330,true⟩,0,0,0⟩, +⟨⟨1,150,355,true⟩,0,0,0⟩, +⟨⟨1,150,359,true⟩,0,0,0⟩, +⟨⟨1,150,363,true⟩,0,0,0⟩, +⟨⟨1,150,367,true⟩,0,0,0⟩, +⟨⟨1,150,371,true⟩,0,0,0⟩, +⟨⟨1,150,375,true⟩,0,0,0⟩, +⟨⟨1,150,379,true⟩,0,0,0⟩, +⟨⟨1,150,383,true⟩,0,0,0⟩, +⟨⟨1,150,419,true⟩,0,0,0⟩, +⟨⟨1,150,423,true⟩,0,0,0⟩, +⟨⟨1,150,427,true⟩,0,0,0⟩, +⟨⟨1,150,431,true⟩,0,0,0⟩, +⟨⟨1,150,435,true⟩,0,0,0⟩, +⟨⟨1,150,439,true⟩,0,0,0⟩, +⟨⟨1,150,443,true⟩,0,0,0⟩, +⟨⟨1,150,447,true⟩,0,0,0⟩, +⟨⟨1,150,481,true⟩,0,0,0⟩, +⟨⟨1,150,485,true⟩,0,0,0⟩, +⟨⟨1,150,489,true⟩,0,0,0⟩, +⟨⟨1,150,493,true⟩,0,0,0⟩, +⟨⟨1,150,497,true⟩,0,0,0⟩] +def chunk9 : List Entry := [⟨⟨1,150,501,true⟩,0,0,0⟩, +⟨⟨1,150,505,true⟩,0,0,0⟩, +⟨⟨1,150,509,true⟩,0,0,0⟩, +⟨⟨1,150,512,true⟩,0,0,0⟩, +⟨⟨1,150,514,true⟩,0,0,0⟩, +⟨⟨1,150,528,true⟩,0,0,0⟩, +⟨⟨1,150,530,true⟩,0,0,0⟩, +⟨⟨1,150,688,true⟩,0,0,0⟩, +⟨⟨1,150,690,true⟩,0,0,0⟩, +⟨⟨1,150,692,true⟩,0,0,0⟩, +⟨⟨1,150,694,true⟩,0,0,0⟩, +⟨⟨1,150,704,true⟩,0,0,0⟩, +⟨⟨1,150,705,true⟩,0,0,0⟩, +⟨⟨1,150,708,true⟩,0,0,0⟩, +⟨⟨1,150,709,true⟩,0,0,0⟩, +⟨⟨1,150,720,true⟩,0,0,0⟩, +⟨⟨1,150,721,true⟩,0,0,0⟩, +⟨⟨1,150,724,true⟩,0,0,0⟩, +⟨⟨1,150,725,true⟩,0,0,0⟩, +⟨⟨1,150,737,true⟩,0,0,0⟩, +⟨⟨1,150,750,true⟩,0,0,0⟩, +⟨⟨1,150,826,true⟩,0,0,0⟩, +⟨⟨1,150,882,true⟩,0,0,0⟩, +⟨⟨1,151,256,true⟩,0,0,0⟩, +⟨⟨1,151,262,true⟩,0,0,0⟩, +⟨⟨1,151,268,true⟩,0,0,0⟩, +⟨⟨1,151,274,true⟩,0,0,0⟩, +⟨⟨1,151,291,true⟩,0,0,0⟩, +⟨⟨1,151,295,true⟩,0,0,0⟩, +⟨⟨1,151,299,true⟩,0,0,0⟩, +⟨⟨1,151,303,true⟩,0,0,0⟩, +⟨⟨1,151,305,true⟩,0,0,0⟩, +⟨⟨1,151,309,true⟩,0,0,0⟩, +⟨⟨1,151,313,true⟩,0,0,0⟩, +⟨⟨1,151,317,true⟩,0,0,0⟩, +⟨⟨1,151,329,true⟩,0,0,0⟩, +⟨⟨1,151,353,true⟩,0,0,0⟩, +⟨⟨1,151,357,true⟩,0,0,0⟩, +⟨⟨1,151,361,true⟩,0,0,0⟩, +⟨⟨1,151,365,true⟩,0,0,0⟩, +⟨⟨1,151,371,true⟩,0,0,0⟩, +⟨⟨1,151,375,true⟩,0,0,0⟩, +⟨⟨1,151,379,true⟩,0,0,0⟩, +⟨⟨1,151,383,true⟩,0,0,0⟩, +⟨⟨1,151,417,true⟩,0,0,0⟩, +⟨⟨1,151,421,true⟩,0,0,0⟩, +⟨⟨1,151,425,true⟩,0,0,0⟩, +⟨⟨1,151,429,true⟩,0,0,0⟩, +⟨⟨1,151,435,true⟩,0,0,0⟩, +⟨⟨1,151,439,true⟩,0,0,0⟩, +⟨⟨1,151,443,true⟩,0,0,0⟩, +⟨⟨1,151,447,true⟩,0,0,0⟩, +⟨⟨1,151,466,true⟩,0,0,0⟩, +⟨⟨1,151,467,true⟩,0,0,0⟩, +⟨⟨1,151,472,true⟩,0,0,0⟩, +⟨⟨1,151,479,true⟩,0,0,0⟩, +⟨⟨1,151,483,true⟩,0,0,0⟩, +⟨⟨1,151,487,true⟩,0,0,0⟩, +⟨⟨1,151,491,true⟩,0,0,0⟩, +⟨⟨1,151,495,true⟩,0,0,0⟩, +⟨⟨1,151,497,true⟩,0,0,0⟩, +⟨⟨1,151,501,true⟩,0,0,0⟩, +⟨⟨1,151,505,true⟩,0,0,0⟩, +⟨⟨1,151,509,true⟩,0,0,0⟩, +⟨⟨1,151,512,true⟩,0,0,0⟩, +⟨⟨1,151,514,true⟩,0,0,0⟩, +⟨⟨1,151,528,true⟩,0,0,0⟩, +⟨⟨1,151,530,true⟩,0,0,0⟩, +⟨⟨1,151,688,true⟩,0,0,0⟩, +⟨⟨1,151,690,true⟩,0,0,0⟩, +⟨⟨1,151,693,true⟩,0,0,0⟩, +⟨⟨1,151,694,true⟩,0,0,0⟩, +⟨⟨1,151,702,true⟩,0,0,0⟩, +⟨⟨1,151,703,true⟩,0,0,0⟩, +⟨⟨1,151,706,true⟩,0,0,0⟩, +⟨⟨1,151,707,true⟩,0,0,0⟩, +⟨⟨1,151,710,true⟩,0,0,0⟩, +⟨⟨1,151,711,true⟩,0,0,0⟩, +⟨⟨1,151,722,true⟩,0,0,0⟩, +⟨⟨1,151,723,true⟩,0,0,0⟩, +⟨⟨1,151,726,true⟩,0,0,0⟩, +⟨⟨1,151,727,true⟩,0,0,0⟩, +⟨⟨1,151,737,true⟩,0,0,0⟩, +⟨⟨1,151,750,true⟩,0,0,0⟩, +⟨⟨1,151,798,true⟩,0,0,0⟩, +⟨⟨1,151,812,true⟩,0,0,0⟩, +⟨⟨1,151,826,true⟩,0,0,0⟩, +⟨⟨1,151,964,true⟩,0,0,0⟩, +⟨⟨1,151,972,true⟩,0,0,0⟩, +⟨⟨1,152,257,true⟩,0,0,0⟩, +⟨⟨1,152,263,true⟩,0,0,0⟩, +⟨⟨1,152,280,true⟩,0,0,0⟩, +⟨⟨1,152,286,true⟩,0,0,0⟩, +⟨⟨1,152,292,true⟩,0,0,0⟩, +⟨⟨1,152,294,true⟩,0,0,0⟩, +⟨⟨1,152,300,true⟩,0,0,0⟩, +⟨⟨1,152,302,true⟩,0,0,0⟩, +⟨⟨1,152,308,true⟩,0,0,0⟩, +⟨⟨1,152,310,true⟩,0,0,0⟩, +⟨⟨1,152,316,true⟩,0,0,0⟩, +⟨⟨1,152,318,true⟩,0,0,0⟩, +⟨⟨1,152,342,true⟩,0,0,0⟩, +⟨⟨1,152,356,true⟩,0,0,0⟩, +⟨⟨1,152,358,true⟩,0,0,0⟩, +⟨⟨1,152,364,true⟩,0,0,0⟩, +⟨⟨1,152,366,true⟩,0,0,0⟩, +⟨⟨1,152,372,true⟩,0,0,0⟩, +⟨⟨1,152,374,true⟩,0,0,0⟩, +⟨⟨1,152,380,true⟩,0,0,0⟩, +⟨⟨1,152,382,true⟩,0,0,0⟩, +⟨⟨1,152,420,true⟩,0,0,0⟩, +⟨⟨1,152,422,true⟩,0,0,0⟩, +⟨⟨1,152,428,true⟩,0,0,0⟩, +⟨⟨1,152,430,true⟩,0,0,0⟩, +⟨⟨1,152,436,true⟩,0,0,0⟩, +⟨⟨1,152,438,true⟩,0,0,0⟩, +⟨⟨1,152,444,true⟩,0,0,0⟩, +⟨⟨1,152,446,true⟩,0,0,0⟩, +⟨⟨1,152,484,true⟩,0,0,0⟩, +⟨⟨1,152,486,true⟩,0,0,0⟩, +⟨⟨1,152,492,true⟩,0,0,0⟩, +⟨⟨1,152,494,true⟩,0,0,0⟩, +⟨⟨1,152,500,true⟩,0,0,0⟩, +⟨⟨1,152,502,true⟩,0,0,0⟩, +⟨⟨1,152,508,true⟩,0,0,0⟩, +⟨⟨1,152,510,true⟩,0,0,0⟩, +⟨⟨1,152,516,true⟩,0,0,0⟩, +⟨⟨1,152,518,true⟩,0,0,0⟩, +⟨⟨1,152,548,true⟩,0,0,0⟩, +⟨⟨1,152,550,true⟩,0,0,0⟩, +⟨⟨1,152,690,true⟩,0,0,0⟩, +⟨⟨1,152,691,true⟩,0,0,0⟩, +⟨⟨1,152,694,true⟩,0,0,0⟩, +⟨⟨1,152,695,true⟩,0,0,0⟩, +⟨⟨1,152,704,true⟩,0,0,0⟩, +⟨⟨1,152,706,true⟩,0,0,0⟩, +⟨⟨1,152,708,true⟩,0,0,0⟩, +⟨⟨1,152,710,true⟩,0,0,0⟩, +⟨⟨1,152,724,true⟩,0,0,0⟩, +⟨⟨1,152,726,true⟩,0,0,0⟩, +⟨⟨1,152,766,true⟩,0,0,0⟩, +⟨⟨1,153,257,true⟩,0,0,0⟩, +⟨⟨1,153,263,true⟩,0,0,0⟩, +⟨⟨1,153,280,true⟩,0,0,0⟩, +⟨⟨1,153,286,true⟩,0,0,0⟩, +⟨⟨1,153,292,true⟩,0,0,0⟩, +⟨⟨1,153,294,true⟩,0,0,0⟩, +⟨⟨1,153,300,true⟩,0,0,0⟩, +⟨⟨1,153,302,true⟩,0,0,0⟩, +⟨⟨1,153,308,true⟩,0,0,0⟩, +⟨⟨1,153,310,true⟩,0,0,0⟩, +⟨⟨1,153,316,true⟩,0,0,0⟩, +⟨⟨1,153,318,true⟩,0,0,0⟩, +⟨⟨1,153,340,true⟩,0,0,0⟩, +⟨⟨1,153,352,true⟩,0,0,0⟩, +⟨⟨1,153,354,true⟩,0,0,0⟩, +⟨⟨1,153,360,true⟩,0,0,0⟩, +⟨⟨1,153,362,true⟩,0,0,0⟩, +⟨⟨1,153,368,true⟩,0,0,0⟩, +⟨⟨1,153,370,true⟩,0,0,0⟩, +⟨⟨1,153,376,true⟩,0,0,0⟩, +⟨⟨1,153,378,true⟩,0,0,0⟩, +⟨⟨1,153,420,true⟩,0,0,0⟩, +⟨⟨1,153,422,true⟩,0,0,0⟩, +⟨⟨1,153,428,true⟩,0,0,0⟩, +⟨⟨1,153,430,true⟩,0,0,0⟩, +⟨⟨1,153,436,true⟩,0,0,0⟩, +⟨⟨1,153,438,true⟩,0,0,0⟩, +⟨⟨1,153,444,true⟩,0,0,0⟩, +⟨⟨1,153,446,true⟩,0,0,0⟩, +⟨⟨1,153,450,true⟩,0,0,0⟩, +⟨⟨1,153,451,true⟩,0,0,0⟩, +⟨⟨1,153,452,true⟩,0,0,0⟩, +⟨⟨1,153,453,true⟩,0,0,0⟩, +⟨⟨1,153,454,true⟩,0,0,0⟩, +⟨⟨1,153,455,true⟩,0,0,0⟩, +⟨⟨1,153,456,true⟩,0,0,0⟩, +⟨⟨1,153,457,true⟩,0,0,0⟩, +⟨⟨1,153,459,true⟩,0,0,0⟩, +⟨⟨1,153,460,true⟩,0,0,0⟩, +⟨⟨1,153,462,true⟩,0,0,0⟩, +⟨⟨1,153,463,true⟩,0,0,0⟩, +⟨⟨1,153,480,true⟩,0,0,0⟩, +⟨⟨1,153,482,true⟩,0,0,0⟩, +⟨⟨1,153,488,true⟩,0,0,0⟩, +⟨⟨1,153,490,true⟩,0,0,0⟩, +⟨⟨1,153,496,true⟩,0,0,0⟩, +⟨⟨1,153,498,true⟩,0,0,0⟩, +⟨⟨1,153,504,true⟩,0,0,0⟩, +⟨⟨1,153,506,true⟩,0,0,0⟩, +⟨⟨1,153,516,true⟩,0,0,0⟩, +⟨⟨1,153,518,true⟩,0,0,0⟩, +⟨⟨1,153,548,true⟩,0,0,0⟩, +⟨⟨1,153,550,true⟩,0,0,0⟩, +⟨⟨1,153,688,true⟩,0,0,0⟩, +⟨⟨1,153,689,true⟩,0,0,0⟩, +⟨⟨1,153,692,true⟩,0,0,0⟩, +⟨⟨1,153,693,true⟩,0,0,0⟩, +⟨⟨1,153,704,true⟩,0,0,0⟩, +⟨⟨1,153,706,true⟩,0,0,0⟩] +def chunk10 : List Entry := [⟨⟨1,153,708,true⟩,0,0,0⟩, +⟨⟨1,153,714,true⟩,0,0,0⟩, +⟨⟨1,153,718,true⟩,0,0,0⟩, +⟨⟨1,153,720,true⟩,0,0,0⟩, +⟨⟨1,153,722,true⟩,0,0,0⟩, +⟨⟨1,153,766,true⟩,0,0,0⟩, +⟨⟨1,153,796,true⟩,0,0,0⟩, +⟨⟨1,153,824,true⟩,0,0,0⟩, +⟨⟨1,153,880,true⟩,0,0,0⟩, +⟨⟨1,153,962,true⟩,0,0,0⟩, +⟨⟨1,153,969,true⟩,0,0,0⟩, +⟨⟨1,154,257,true⟩,0,0,0⟩, +⟨⟨1,154,263,true⟩,0,0,0⟩, +⟨⟨1,154,280,true⟩,0,0,0⟩, +⟨⟨1,154,286,true⟩,0,0,0⟩, +⟨⟨1,154,288,true⟩,0,0,0⟩, +⟨⟨1,154,290,true⟩,0,0,0⟩, +⟨⟨1,154,296,true⟩,0,0,0⟩, +⟨⟨1,154,298,true⟩,0,0,0⟩, +⟨⟨1,154,304,true⟩,0,0,0⟩, +⟨⟨1,154,306,true⟩,0,0,0⟩, +⟨⟨1,154,312,true⟩,0,0,0⟩, +⟨⟨1,154,314,true⟩,0,0,0⟩, +⟨⟨1,154,338,true⟩,0,0,0⟩, +⟨⟨1,154,356,true⟩,0,0,0⟩, +⟨⟨1,154,358,true⟩,0,0,0⟩, +⟨⟨1,154,364,true⟩,0,0,0⟩, +⟨⟨1,154,366,true⟩,0,0,0⟩, +⟨⟨1,154,372,true⟩,0,0,0⟩, +⟨⟨1,154,374,true⟩,0,0,0⟩, +⟨⟨1,154,380,true⟩,0,0,0⟩, +⟨⟨1,154,382,true⟩,0,0,0⟩, +⟨⟨1,154,416,true⟩,0,0,0⟩, +⟨⟨1,154,418,true⟩,0,0,0⟩, +⟨⟨1,154,424,true⟩,0,0,0⟩, +⟨⟨1,154,426,true⟩,0,0,0⟩, +⟨⟨1,154,432,true⟩,0,0,0⟩, +⟨⟨1,154,434,true⟩,0,0,0⟩, +⟨⟨1,154,440,true⟩,0,0,0⟩, +⟨⟨1,154,442,true⟩,0,0,0⟩, +⟨⟨1,154,450,true⟩,0,0,0⟩, +⟨⟨1,154,452,true⟩,0,0,0⟩, +⟨⟨1,154,456,true⟩,0,0,0⟩, +⟨⟨1,154,462,true⟩,0,0,0⟩, +⟨⟨1,154,484,true⟩,0,0,0⟩, +⟨⟨1,154,486,true⟩,0,0,0⟩, +⟨⟨1,154,492,true⟩,0,0,0⟩, +⟨⟨1,154,494,true⟩,0,0,0⟩, +⟨⟨1,154,500,true⟩,0,0,0⟩, +⟨⟨1,154,502,true⟩,0,0,0⟩, +⟨⟨1,154,508,true⟩,0,0,0⟩, +⟨⟨1,154,510,true⟩,0,0,0⟩, +⟨⟨1,154,516,true⟩,0,0,0⟩, +⟨⟨1,154,518,true⟩,0,0,0⟩, +⟨⟨1,154,548,true⟩,0,0,0⟩, +⟨⟨1,154,550,true⟩,0,0,0⟩, +⟨⟨1,154,688,true⟩,0,0,0⟩, +⟨⟨1,154,689,true⟩,0,0,0⟩, +⟨⟨1,154,692,true⟩,0,0,0⟩, +⟨⟨1,154,693,true⟩,0,0,0⟩, +⟨⟨1,154,704,true⟩,0,0,0⟩, +⟨⟨1,154,709,true⟩,0,0,0⟩, +⟨⟨1,154,710,true⟩,0,0,0⟩, +⟨⟨1,154,714,true⟩,0,0,0⟩, +⟨⟨1,154,720,true⟩,0,0,0⟩, +⟨⟨1,154,722,true⟩,0,0,0⟩, +⟨⟨1,154,766,true⟩,0,0,0⟩, +⟨⟨1,154,782,true⟩,0,0,0⟩, +⟨⟨1,154,810,true⟩,0,0,0⟩, +⟨⟨1,154,866,true⟩,0,0,0⟩, +⟨⟨1,154,936,true⟩,0,0,0⟩, +⟨⟨1,154,970,true⟩,0,0,0⟩, +⟨⟨1,155,257,true⟩,0,0,0⟩, +⟨⟨1,155,263,true⟩,0,0,0⟩, +⟨⟨1,155,280,true⟩,0,0,0⟩, +⟨⟨1,155,286,true⟩,0,0,0⟩, +⟨⟨1,155,288,true⟩,0,0,0⟩, +⟨⟨1,155,290,true⟩,0,0,0⟩, +⟨⟨1,155,296,true⟩,0,0,0⟩, +⟨⟨1,155,298,true⟩,0,0,0⟩, +⟨⟨1,155,304,true⟩,0,0,0⟩, +⟨⟨1,155,306,true⟩,0,0,0⟩, +⟨⟨1,155,312,true⟩,0,0,0⟩, +⟨⟨1,155,314,true⟩,0,0,0⟩, +⟨⟨1,155,336,true⟩,0,0,0⟩, +⟨⟨1,155,352,true⟩,0,0,0⟩, +⟨⟨1,155,354,true⟩,0,0,0⟩, +⟨⟨1,155,360,true⟩,0,0,0⟩, +⟨⟨1,155,362,true⟩,0,0,0⟩, 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+⟨⟨1,155,810,true⟩,0,0,0⟩, +⟨⟨1,155,824,true⟩,0,0,0⟩, +⟨⟨1,155,866,true⟩,0,0,0⟩, +⟨⟨1,155,880,true⟩,0,0,0⟩, +⟨⟨1,156,257,true⟩,0,0,0⟩, +⟨⟨1,156,263,true⟩,0,0,0⟩, +⟨⟨1,156,280,true⟩,0,0,0⟩, +⟨⟨1,156,286,true⟩,0,0,0⟩, +⟨⟨1,156,288,true⟩,0,0,0⟩, +⟨⟨1,156,290,true⟩,0,0,0⟩, +⟨⟨1,156,296,true⟩,0,0,0⟩, +⟨⟨1,156,298,true⟩,0,0,0⟩, +⟨⟨1,156,308,true⟩,0,0,0⟩, +⟨⟨1,156,310,true⟩,0,0,0⟩, +⟨⟨1,156,316,true⟩,0,0,0⟩, +⟨⟨1,156,318,true⟩,0,0,0⟩, +⟨⟨1,156,351,true⟩,0,0,0⟩, +⟨⟨1,156,356,true⟩,0,0,0⟩, +⟨⟨1,156,358,true⟩,0,0,0⟩, +⟨⟨1,156,364,true⟩,0,0,0⟩, +⟨⟨1,156,366,true⟩,0,0,0⟩, +⟨⟨1,156,368,true⟩,0,0,0⟩, +⟨⟨1,156,370,true⟩,0,0,0⟩, +⟨⟨1,156,376,true⟩,0,0,0⟩, +⟨⟨1,156,378,true⟩,0,0,0⟩, +⟨⟨1,156,420,true⟩,0,0,0⟩, +⟨⟨1,156,422,true⟩,0,0,0⟩, +⟨⟨1,156,428,true⟩,0,0,0⟩, +⟨⟨1,156,430,true⟩,0,0,0⟩, +⟨⟨1,156,432,true⟩,0,0,0⟩, +⟨⟨1,156,434,true⟩,0,0,0⟩, +⟨⟨1,156,440,true⟩,0,0,0⟩, +⟨⟨1,156,442,true⟩,0,0,0⟩, +⟨⟨1,156,451,true⟩,0,0,0⟩, +⟨⟨1,156,452,true⟩,0,0,0⟩, +⟨⟨1,156,462,true⟩,0,0,0⟩, +⟨⟨1,156,463,true⟩,0,0,0⟩, +⟨⟨1,156,480,true⟩,0,0,0⟩, +⟨⟨1,156,482,true⟩,0,0,0⟩, +⟨⟨1,156,488,true⟩,0,0,0⟩, +⟨⟨1,156,490,true⟩,0,0,0⟩, +⟨⟨1,156,500,true⟩,0,0,0⟩, +⟨⟨1,156,502,true⟩,0,0,0⟩, +⟨⟨1,156,508,true⟩,0,0,0⟩, +⟨⟨1,156,510,true⟩,0,0,0⟩, +⟨⟨1,156,512,true⟩,0,0,0⟩, +⟨⟨1,156,514,true⟩,0,0,0⟩, +⟨⟨1,156,544,true⟩,0,0,0⟩, +⟨⟨1,156,546,true⟩,0,0,0⟩, +⟨⟨1,156,690,true⟩,0,0,0⟩, +⟨⟨1,156,691,true⟩,0,0,0⟩, +⟨⟨1,156,694,true⟩,0,0,0⟩, +⟨⟨1,156,695,true⟩,0,0,0⟩, +⟨⟨1,156,704,true⟩,0,0,0⟩, +⟨⟨1,156,708,true⟩,0,0,0⟩, +⟨⟨1,156,710,true⟩,0,0,0⟩, +⟨⟨1,156,714,true⟩,0,0,0⟩, +⟨⟨1,156,718,true⟩,0,0,0⟩, +⟨⟨1,156,719,true⟩,0,0,0⟩, +⟨⟨1,156,724,true⟩,0,0,0⟩, +⟨⟨1,156,726,true⟩,0,0,0⟩, +⟨⟨1,156,736,true⟩,0,0,0⟩, +⟨⟨1,156,764,true⟩,0,0,0⟩, +⟨⟨1,156,866,true⟩,0,0,0⟩, +⟨⟨1,156,880,true⟩,0,0,0⟩, +⟨⟨1,156,936,true⟩,0,0,0⟩, +⟨⟨1,156,969,true⟩,0,0,0⟩, +⟨⟨1,157,257,true⟩,0,0,0⟩, +⟨⟨1,157,263,true⟩,0,0,0⟩, +⟨⟨1,157,280,true⟩,0,0,0⟩, +⟨⟨1,157,286,true⟩,0,0,0⟩, +⟨⟨1,157,288,true⟩,0,0,0⟩, +⟨⟨1,157,290,true⟩,0,0,0⟩, +⟨⟨1,157,296,true⟩,0,0,0⟩] +def chunk11 : List Entry := [⟨⟨1,157,298,true⟩,0,0,0⟩, +⟨⟨1,157,308,true⟩,0,0,0⟩, +⟨⟨1,157,310,true⟩,0,0,0⟩, +⟨⟨1,157,316,true⟩,0,0,0⟩, +⟨⟨1,157,318,true⟩,0,0,0⟩, +⟨⟨1,157,349,true⟩,0,0,0⟩, +⟨⟨1,157,352,true⟩,0,0,0⟩, +⟨⟨1,157,354,true⟩,0,0,0⟩, +⟨⟨1,157,360,true⟩,0,0,0⟩, +⟨⟨1,157,362,true⟩,0,0,0⟩, +⟨⟨1,157,372,true⟩,0,0,0⟩, +⟨⟨1,157,374,true⟩,0,0,0⟩, +⟨⟨1,157,380,true⟩,0,0,0⟩, +⟨⟨1,157,382,true⟩,0,0,0⟩, +⟨⟨1,157,420,true⟩,0,0,0⟩, +⟨⟨1,157,422,true⟩,0,0,0⟩, +⟨⟨1,157,428,true⟩,0,0,0⟩, +⟨⟨1,157,430,true⟩,0,0,0⟩, +⟨⟨1,157,432,true⟩,0,0,0⟩, +⟨⟨1,157,434,true⟩,0,0,0⟩, +⟨⟨1,157,440,true⟩,0,0,0⟩, +⟨⟨1,157,442,true⟩,0,0,0⟩, +⟨⟨1,157,484,true⟩,0,0,0⟩, +⟨⟨1,157,486,true⟩,0,0,0⟩, +⟨⟨1,157,492,true⟩,0,0,0⟩, +⟨⟨1,157,494,true⟩,0,0,0⟩, +⟨⟨1,157,496,true⟩,0,0,0⟩, +⟨⟨1,157,498,true⟩,0,0,0⟩, +⟨⟨1,157,504,true⟩,0,0,0⟩, +⟨⟨1,157,506,true⟩,0,0,0⟩, +⟨⟨1,157,512,true⟩,0,0,0⟩, +⟨⟨1,157,514,true⟩,0,0,0⟩, +⟨⟨1,157,544,true⟩,0,0,0⟩, +⟨⟨1,157,546,true⟩,0,0,0⟩, +⟨⟨1,157,688,true⟩,0,0,0⟩, +⟨⟨1,157,689,true⟩,0,0,0⟩, +⟨⟨1,157,692,true⟩,0,0,0⟩, +⟨⟨1,157,693,true⟩,0,0,0⟩, +⟨⟨1,157,704,true⟩,0,0,0⟩, +⟨⟨1,157,706,true⟩,0,0,0⟩, +⟨⟨1,157,708,true⟩,0,0,0⟩, +⟨⟨1,157,710,true⟩,0,0,0⟩, +⟨⟨1,157,720,true⟩,0,0,0⟩, +⟨⟨1,157,722,true⟩,0,0,0⟩, +⟨⟨1,157,736,true⟩,0,0,0⟩, +⟨⟨1,157,764,true⟩,0,0,0⟩, +⟨⟨1,157,796,true⟩,0,0,0⟩, +⟨⟨1,157,824,true⟩,0,0,0⟩, +⟨⟨1,157,866,true⟩,0,0,0⟩, +⟨⟨1,158,257,true⟩,0,0,0⟩, +⟨⟨1,158,263,true⟩,0,0,0⟩, +⟨⟨1,158,280,true⟩,0,0,0⟩, +⟨⟨1,158,286,true⟩,0,0,0⟩, +⟨⟨1,158,292,true⟩,0,0,0⟩, +⟨⟨1,158,294,true⟩,0,0,0⟩, +⟨⟨1,158,300,true⟩,0,0,0⟩, +⟨⟨1,158,302,true⟩,0,0,0⟩, +⟨⟨1,158,304,true⟩,0,0,0⟩, +⟨⟨1,158,306,true⟩,0,0,0⟩, +⟨⟨1,158,312,true⟩,0,0,0⟩, +⟨⟨1,158,314,true⟩,0,0,0⟩, +⟨⟨1,158,347,true⟩,0,0,0⟩, +⟨⟨1,158,356,true⟩,0,0,0⟩, +⟨⟨1,158,358,true⟩,0,0,0⟩, +⟨⟨1,158,364,true⟩,0,0,0⟩, +⟨⟨1,158,366,true⟩,0,0,0⟩, +⟨⟨1,158,368,true⟩,0,0,0⟩, +⟨⟨1,158,370,true⟩,0,0,0⟩, +⟨⟨1,158,376,true⟩,0,0,0⟩, +⟨⟨1,158,378,true⟩,0,0,0⟩, +⟨⟨1,158,416,true⟩,0,0,0⟩, +⟨⟨1,158,418,true⟩,0,0,0⟩, +⟨⟨1,158,424,true⟩,0,0,0⟩, 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+⟨⟨1,159,498,true⟩,0,0,0⟩, +⟨⟨1,159,504,true⟩,0,0,0⟩, +⟨⟨1,159,506,true⟩,0,0,0⟩, +⟨⟨1,159,512,true⟩,0,0,0⟩, +⟨⟨1,159,514,true⟩,0,0,0⟩, +⟨⟨1,159,544,true⟩,0,0,0⟩, +⟨⟨1,159,546,true⟩,0,0,0⟩, +⟨⟨1,159,690,true⟩,0,0,0⟩, +⟨⟨1,159,691,true⟩,0,0,0⟩, +⟨⟨1,159,694,true⟩,0,0,0⟩, +⟨⟨1,159,695,true⟩,0,0,0⟩, +⟨⟨1,159,704,true⟩,0,0,0⟩, +⟨⟨1,159,706,true⟩,0,0,0⟩, +⟨⟨1,159,709,true⟩,0,0,0⟩, +⟨⟨1,159,714,true⟩,0,0,0⟩, +⟨⟨1,159,719,true⟩,0,0,0⟩, +⟨⟨1,159,724,true⟩,0,0,0⟩, +⟨⟨1,159,726,true⟩,0,0,0⟩, +⟨⟨1,159,736,true⟩,0,0,0⟩, +⟨⟨1,159,764,true⟩,0,0,0⟩, +⟨⟨1,159,782,true⟩,0,0,0⟩, +⟨⟨1,159,796,true⟩,0,0,0⟩, +⟨⟨1,159,810,true⟩,0,0,0⟩, +⟨⟨1,159,824,true⟩,0,0,0⟩, +⟨⟨1,159,962,true⟩,0,0,0⟩, +⟨⟨1,159,970,true⟩,0,0,0⟩, +⟨⟨1,160,250,true⟩,0,0,0⟩, +⟨⟨1,160,260,true⟩,0,0,0⟩, +⟨⟨1,160,267,true⟩,0,0,0⟩, +⟨⟨1,160,279,true⟩,0,0,0⟩, +⟨⟨1,160,290,true⟩,0,0,0⟩, +⟨⟨1,160,294,true⟩,0,0,0⟩, +⟨⟨1,160,296,true⟩,0,0,0⟩, +⟨⟨1,160,300,true⟩,0,0,0⟩, +⟨⟨1,160,323,true⟩,0,0,0⟩, +⟨⟨1,160,327,true⟩,0,0,0⟩, +⟨⟨1,160,331,true⟩,0,0,0⟩, +⟨⟨1,160,335,true⟩,0,0,0⟩, +⟨⟨1,160,339,true⟩,0,0,0⟩, +⟨⟨1,160,343,true⟩,0,0,0⟩, +⟨⟨1,160,347,true⟩,0,0,0⟩, +⟨⟨1,160,351,true⟩,0,0,0⟩, +⟨⟨1,160,359,true⟩,0,0,0⟩, +⟨⟨1,160,373,true⟩,0,0,0⟩, +⟨⟨1,160,375,true⟩,0,0,0⟩, +⟨⟨1,160,377,true⟩,0,0,0⟩, +⟨⟨1,160,379,true⟩,0,0,0⟩, +⟨⟨1,160,386,true⟩,0,0,0⟩, +⟨⟨1,160,390,true⟩,0,0,0⟩, +⟨⟨1,160,392,true⟩,0,0,0⟩, +⟨⟨1,160,396,true⟩,0,0,0⟩, +⟨⟨1,160,404,true⟩,0,0,0⟩, +⟨⟨1,160,406,true⟩,0,0,0⟩] +def chunk12 : List Entry := [⟨⟨1,160,412,true⟩,0,0,0⟩, +⟨⟨1,160,414,true⟩,0,0,0⟩, +⟨⟨1,160,419,true⟩,0,0,0⟩, +⟨⟨1,160,423,true⟩,0,0,0⟩, +⟨⟨1,160,427,true⟩,0,0,0⟩, +⟨⟨1,160,431,true⟩,0,0,0⟩, +⟨⟨1,160,451,true⟩,0,0,0⟩, +⟨⟨1,160,455,true⟩,0,0,0⟩, +⟨⟨1,160,459,true⟩,0,0,0⟩, +⟨⟨1,160,463,true⟩,0,0,0⟩, +⟨⟨1,160,467,true⟩,0,0,0⟩, +⟨⟨1,160,471,true⟩,0,0,0⟩, +⟨⟨1,160,475,true⟩,0,0,0⟩, +⟨⟨1,160,479,true⟩,0,0,0⟩, +⟨⟨1,160,500,true⟩,0,0,0⟩, +⟨⟨1,160,502,true⟩,0,0,0⟩, +⟨⟨1,160,508,true⟩,0,0,0⟩, +⟨⟨1,160,510,true⟩,0,0,0⟩, +⟨⟨1,160,564,true⟩,0,0,0⟩, +⟨⟨1,160,566,true⟩,0,0,0⟩, 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+⟨⟨1,162,388,true⟩,0,0,0⟩, +⟨⟨1,162,394,true⟩,0,0,0⟩, +⟨⟨1,162,398,true⟩,0,0,0⟩, +⟨⟨1,162,404,true⟩,0,0,0⟩, +⟨⟨1,162,406,true⟩,0,0,0⟩, +⟨⟨1,162,412,true⟩,0,0,0⟩, +⟨⟨1,162,414,true⟩,0,0,0⟩, +⟨⟨1,162,419,true⟩,0,0,0⟩, +⟨⟨1,162,423,true⟩,0,0,0⟩, +⟨⟨1,162,427,true⟩,0,0,0⟩, +⟨⟨1,162,431,true⟩,0,0,0⟩, +⟨⟨1,162,434,true⟩,0,0,0⟩, +⟨⟨1,162,437,true⟩,0,0,0⟩, +⟨⟨1,162,438,true⟩,0,0,0⟩, +⟨⟨1,162,439,true⟩,0,0,0⟩, +⟨⟨1,162,440,true⟩,0,0,0⟩, +⟨⟨1,162,441,true⟩,0,0,0⟩, +⟨⟨1,162,443,true⟩,0,0,0⟩, +⟨⟨1,162,444,true⟩,0,0,0⟩, +⟨⟨1,162,451,true⟩,0,0,0⟩, +⟨⟨1,162,455,true⟩,0,0,0⟩, +⟨⟨1,162,459,true⟩,0,0,0⟩, +⟨⟨1,162,463,true⟩,0,0,0⟩, +⟨⟨1,162,465,true⟩,0,0,0⟩, +⟨⟨1,162,469,true⟩,0,0,0⟩, +⟨⟨1,162,473,true⟩,0,0,0⟩, +⟨⟨1,162,477,true⟩,0,0,0⟩, +⟨⟨1,162,496,true⟩,0,0,0⟩, +⟨⟨1,162,498,true⟩,0,0,0⟩, +⟨⟨1,162,504,true⟩,0,0,0⟩, +⟨⟨1,162,506,true⟩,0,0,0⟩, +⟨⟨1,162,564,true⟩,0,0,0⟩, +⟨⟨1,162,566,true⟩,0,0,0⟩, +⟨⟨1,162,633,true⟩,0,0,0⟩, +⟨⟨1,162,635,true⟩,0,0,0⟩, +⟨⟨1,162,652,true⟩,0,0,0⟩, +⟨⟨1,162,654,true⟩,0,0,0⟩, +⟨⟨1,162,656,true⟩,0,0,0⟩, +⟨⟨1,162,660,true⟩,0,0,0⟩, +⟨⟨1,162,661,true⟩,0,0,0⟩, +⟨⟨1,162,672,true⟩,0,0,0⟩, +⟨⟨1,162,673,true⟩,0,0,0⟩, +⟨⟨1,162,676,true⟩,0,0,0⟩, +⟨⟨1,162,677,true⟩,0,0,0⟩, +⟨⟨1,162,728,true⟩,0,0,0⟩, +⟨⟨1,162,730,true⟩,0,0,0⟩, +⟨⟨1,162,780,true⟩,0,0,0⟩, +⟨⟨1,162,858,true⟩,0,0,0⟩, +⟨⟨1,162,898,true⟩,0,0,0⟩, +⟨⟨1,162,926,true⟩,0,0,0⟩, +⟨⟨1,162,968,true⟩,0,0,0⟩, +⟨⟨1,162,975,true⟩,0,0,0⟩, +⟨⟨1,163,250,true⟩,0,0,0⟩, +⟨⟨1,163,260,true⟩,0,0,0⟩, +⟨⟨1,163,267,true⟩,0,0,0⟩, +⟨⟨1,163,279,true⟩,0,0,0⟩, +⟨⟨1,163,288,true⟩,0,0,0⟩, +⟨⟨1,163,292,true⟩,0,0,0⟩, +⟨⟨1,163,298,true⟩,0,0,0⟩, +⟨⟨1,163,302,true⟩,0,0,0⟩, +⟨⟨1,163,321,true⟩,0,0,0⟩, +⟨⟨1,163,325,true⟩,0,0,0⟩, +⟨⟨1,163,329,true⟩,0,0,0⟩, +⟨⟨1,163,333,true⟩,0,0,0⟩, +⟨⟨1,163,337,true⟩,0,0,0⟩, +⟨⟨1,163,341,true⟩,0,0,0⟩, +⟨⟨1,163,345,true⟩,0,0,0⟩, +⟨⟨1,163,349,true⟩,0,0,0⟩, +⟨⟨1,163,353,true⟩,0,0,0⟩] +def chunk13 : List Entry := [⟨⟨1,163,369,true⟩,0,0,0⟩, +⟨⟨1,163,371,true⟩,0,0,0⟩, +⟨⟨1,163,381,true⟩,0,0,0⟩, +⟨⟨1,163,383,true⟩,0,0,0⟩, +⟨⟨1,163,386,true⟩,0,0,0⟩, +⟨⟨1,163,390,true⟩,0,0,0⟩, +⟨⟨1,163,392,true⟩,0,0,0⟩, +⟨⟨1,163,396,true⟩,0,0,0⟩, +⟨⟨1,163,404,true⟩,0,0,0⟩, +⟨⟨1,163,406,true⟩,0,0,0⟩, +⟨⟨1,163,412,true⟩,0,0,0⟩, +⟨⟨1,163,414,true⟩,0,0,0⟩, +⟨⟨1,163,417,true⟩,0,0,0⟩, +⟨⟨1,163,421,true⟩,0,0,0⟩, +⟨⟨1,163,425,true⟩,0,0,0⟩, +⟨⟨1,163,429,true⟩,0,0,0⟩, +⟨⟨1,163,449,true⟩,0,0,0⟩, +⟨⟨1,163,453,true⟩,0,0,0⟩, +⟨⟨1,163,457,true⟩,0,0,0⟩, +⟨⟨1,163,461,true⟩,0,0,0⟩, +⟨⟨1,163,465,true⟩,0,0,0⟩, +⟨⟨1,163,469,true⟩,0,0,0⟩, +⟨⟨1,163,473,true⟩,0,0,0⟩, +⟨⟨1,163,477,true⟩,0,0,0⟩, +⟨⟨1,163,496,true⟩,0,0,0⟩, +⟨⟨1,163,498,true⟩,0,0,0⟩, +⟨⟨1,163,504,true⟩,0,0,0⟩, +⟨⟨1,163,506,true⟩,0,0,0⟩, +⟨⟨1,163,564,true⟩,0,0,0⟩, +⟨⟨1,163,566,true⟩,0,0,0⟩, +⟨⟨1,163,632,true⟩,0,0,0⟩, +⟨⟨1,163,634,true⟩,0,0,0⟩, +⟨⟨1,163,652,true⟩,0,0,0⟩, +⟨⟨1,163,654,true⟩,0,0,0⟩, +⟨⟨1,163,656,true⟩,0,0,0⟩, +⟨⟨1,163,658,true⟩,0,0,0⟩, +⟨⟨1,163,660,true⟩,0,0,0⟩, +⟨⟨1,163,662,true⟩,0,0,0⟩, +⟨⟨1,163,674,true⟩,0,0,0⟩, +⟨⟨1,163,675,true⟩,0,0,0⟩, +⟨⟨1,163,678,true⟩,0,0,0⟩, +⟨⟨1,163,679,true⟩,0,0,0⟩, +⟨⟨1,163,729,true⟩,0,0,0⟩, +⟨⟨1,163,731,true⟩,0,0,0⟩, +⟨⟨1,163,780,true⟩,0,0,0⟩, +⟨⟨1,163,844,true⟩,0,0,0⟩, +⟨⟨1,163,858,true⟩,0,0,0⟩, +⟨⟨1,163,898,true⟩,0,0,0⟩, +⟨⟨1,163,912,true⟩,0,0,0⟩, +⟨⟨1,163,927,true⟩,0,0,0⟩, +⟨⟨1,164,250,true⟩,0,0,0⟩, +⟨⟨1,164,260,true⟩,0,0,0⟩, +⟨⟨1,164,267,true⟩,0,0,0⟩, +⟨⟨1,164,279,true⟩,0,0,0⟩, +⟨⟨1,164,288,true⟩,0,0,0⟩, +⟨⟨1,164,292,true⟩,0,0,0⟩, +⟨⟨1,164,298,true⟩,0,0,0⟩, +⟨⟨1,164,302,true⟩,0,0,0⟩, +⟨⟨1,164,323,true⟩,0,0,0⟩, +⟨⟨1,164,327,true⟩,0,0,0⟩, +⟨⟨1,164,331,true⟩,0,0,0⟩, +⟨⟨1,164,335,true⟩,0,0,0⟩, +⟨⟨1,164,339,true⟩,0,0,0⟩, +⟨⟨1,164,343,true⟩,0,0,0⟩, +⟨⟨1,164,347,true⟩,0,0,0⟩, +⟨⟨1,164,351,true⟩,0,0,0⟩, +⟨⟨1,164,366,true⟩,0,0,0⟩, +⟨⟨1,164,369,true⟩,0,0,0⟩, +⟨⟨1,164,371,true⟩,0,0,0⟩, +⟨⟨1,164,381,true⟩,0,0,0⟩, +⟨⟨1,164,383,true⟩,0,0,0⟩, +⟨⟨1,164,386,true⟩,0,0,0⟩, +⟨⟨1,164,390,true⟩,0,0,0⟩, +⟨⟨1,164,392,true⟩,0,0,0⟩, +⟨⟨1,164,396,true⟩,0,0,0⟩, +⟨⟨1,164,400,true⟩,0,0,0⟩, +⟨⟨1,164,402,true⟩,0,0,0⟩, +⟨⟨1,164,408,true⟩,0,0,0⟩, 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+⟨⟨1,165,394,true⟩,0,0,0⟩, +⟨⟨1,165,398,true⟩,0,0,0⟩, +⟨⟨1,165,400,true⟩,0,0,0⟩, +⟨⟨1,165,402,true⟩,0,0,0⟩, +⟨⟨1,165,408,true⟩,0,0,0⟩, +⟨⟨1,165,410,true⟩,0,0,0⟩, +⟨⟨1,165,417,true⟩,0,0,0⟩, +⟨⟨1,165,421,true⟩,0,0,0⟩, +⟨⟨1,165,425,true⟩,0,0,0⟩, +⟨⟨1,165,429,true⟩,0,0,0⟩, +⟨⟨1,165,451,true⟩,0,0,0⟩, +⟨⟨1,165,455,true⟩,0,0,0⟩, +⟨⟨1,165,459,true⟩,0,0,0⟩, +⟨⟨1,165,463,true⟩,0,0,0⟩, +⟨⟨1,165,465,true⟩,0,0,0⟩, +⟨⟨1,165,469,true⟩,0,0,0⟩, +⟨⟨1,165,473,true⟩,0,0,0⟩, +⟨⟨1,165,477,true⟩,0,0,0⟩, +⟨⟨1,165,500,true⟩,0,0,0⟩, +⟨⟨1,165,502,true⟩,0,0,0⟩, +⟨⟨1,165,508,true⟩,0,0,0⟩, +⟨⟨1,165,510,true⟩,0,0,0⟩, +⟨⟨1,165,560,true⟩,0,0,0⟩, +⟨⟨1,165,562,true⟩,0,0,0⟩, +⟨⟨1,165,633,true⟩,0,0,0⟩, +⟨⟨1,165,635,true⟩,0,0,0⟩, +⟨⟨1,165,652,true⟩,0,0,0⟩, +⟨⟨1,165,654,true⟩,0,0,0⟩, +⟨⟨1,165,656,true⟩,0,0,0⟩, +⟨⟨1,165,658,true⟩,0,0,0⟩, +⟨⟨1,165,660,true⟩,0,0,0⟩, +⟨⟨1,165,662,true⟩,0,0,0⟩, +⟨⟨1,165,672,true⟩,0,0,0⟩, +⟨⟨1,165,673,true⟩,0,0,0⟩, +⟨⟨1,165,676,true⟩,0,0,0⟩, +⟨⟨1,165,677,true⟩,0,0,0⟩, +⟨⟨1,165,728,true⟩,0,0,0⟩, +⟨⟨1,165,730,true⟩,0,0,0⟩, +⟨⟨1,165,740,true⟩,0,0,0⟩, +⟨⟨1,165,778,true⟩,0,0,0⟩, +⟨⟨1,165,858,true⟩,0,0,0⟩, +⟨⟨1,165,898,true⟩,0,0,0⟩, +⟨⟨1,165,926,true⟩,0,0,0⟩, +⟨⟨1,166,250,true⟩,0,0,0⟩, +⟨⟨1,166,260,true⟩,0,0,0⟩, +⟨⟨1,166,267,true⟩,0,0,0⟩, +⟨⟨1,166,279,true⟩,0,0,0⟩, +⟨⟨1,166,288,true⟩,0,0,0⟩] +def chunk14 : List Entry := [⟨⟨1,166,292,true⟩,0,0,0⟩, +⟨⟨1,166,298,true⟩,0,0,0⟩, +⟨⟨1,166,302,true⟩,0,0,0⟩, +⟨⟨1,166,323,true⟩,0,0,0⟩, +⟨⟨1,166,327,true⟩,0,0,0⟩, +⟨⟨1,166,331,true⟩,0,0,0⟩, +⟨⟨1,166,335,true⟩,0,0,0⟩, +⟨⟨1,166,337,true⟩,0,0,0⟩, +⟨⟨1,166,341,true⟩,0,0,0⟩, +⟨⟨1,166,345,true⟩,0,0,0⟩, +⟨⟨1,166,349,true⟩,0,0,0⟩, +⟨⟨1,166,362,true⟩,0,0,0⟩, +⟨⟨1,166,373,true⟩,0,0,0⟩, +⟨⟨1,166,375,true⟩,0,0,0⟩, +⟨⟨1,166,377,true⟩,0,0,0⟩, +⟨⟨1,166,379,true⟩,0,0,0⟩, +⟨⟨1,166,384,true⟩,0,0,0⟩, +⟨⟨1,166,388,true⟩,0,0,0⟩, +⟨⟨1,166,394,true⟩,0,0,0⟩, +⟨⟨1,166,398,true⟩,0,0,0⟩, +⟨⟨1,166,400,true⟩,0,0,0⟩, +⟨⟨1,166,402,true⟩,0,0,0⟩, +⟨⟨1,166,408,true⟩,0,0,0⟩, +⟨⟨1,166,410,true⟩,0,0,0⟩, +⟨⟨1,166,419,true⟩,0,0,0⟩, 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+⟨⟨1,168,484,true⟩,0,0,0⟩, +⟨⟨1,168,486,true⟩,0,0,0⟩, +⟨⟨1,168,492,true⟩,0,0,0⟩, +⟨⟨1,168,494,true⟩,0,0,0⟩, +⟨⟨1,168,525,true⟩,0,0,0⟩, +⟨⟨1,168,527,true⟩,0,0,0⟩, +⟨⟨1,168,537,true⟩,0,0,0⟩, +⟨⟨1,168,539,true⟩,0,0,0⟩, +⟨⟨1,168,557,true⟩,0,0,0⟩, +⟨⟨1,168,559,true⟩,0,0,0⟩, +⟨⟨1,168,569,true⟩,0,0,0⟩, +⟨⟨1,168,571,true⟩,0,0,0⟩, +⟨⟨1,168,589,true⟩,0,0,0⟩, +⟨⟨1,168,591,true⟩,0,0,0⟩, +⟨⟨1,168,592,true⟩,0,0,0⟩, +⟨⟨1,168,594,true⟩,0,0,0⟩, +⟨⟨1,168,596,true⟩,0,0,0⟩, +⟨⟨1,168,598,true⟩,0,0,0⟩, +⟨⟨1,168,610,true⟩,0,0,0⟩, +⟨⟨1,168,611,true⟩,0,0,0⟩, +⟨⟨1,168,614,true⟩,0,0,0⟩, +⟨⟨1,168,615,true⟩,0,0,0⟩, +⟨⟨1,168,628,true⟩,0,0,0⟩, +⟨⟨1,168,630,true⟩,0,0,0⟩, +⟨⟨1,168,733,true⟩,0,0,0⟩, +⟨⟨1,168,735,true⟩,0,0,0⟩, +⟨⟨1,169,244,true⟩,0,0,0⟩] +def chunk15 : List Entry := [⟨⟨1,169,265,true⟩,0,0,0⟩, +⟨⟨1,169,283,true⟩,0,0,0⟩, +⟨⟨1,169,304,true⟩,0,0,0⟩, +⟨⟨1,169,308,true⟩,0,0,0⟩, +⟨⟨1,169,314,true⟩,0,0,0⟩, +⟨⟨1,169,318,true⟩,0,0,0⟩, +⟨⟨1,169,321,true⟩,0,0,0⟩, +⟨⟨1,169,323,true⟩,0,0,0⟩, +⟨⟨1,169,333,true⟩,0,0,0⟩, 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+⟨⟨1,169,494,true⟩,0,0,0⟩, +⟨⟨1,169,525,true⟩,0,0,0⟩, +⟨⟨1,169,527,true⟩,0,0,0⟩, +⟨⟨1,169,537,true⟩,0,0,0⟩, +⟨⟨1,169,539,true⟩,0,0,0⟩, +⟨⟨1,169,556,true⟩,0,0,0⟩, +⟨⟨1,169,558,true⟩,0,0,0⟩, +⟨⟨1,169,568,true⟩,0,0,0⟩, +⟨⟨1,169,570,true⟩,0,0,0⟩, +⟨⟨1,169,589,true⟩,0,0,0⟩, +⟨⟨1,169,591,true⟩,0,0,0⟩, +⟨⟨1,169,592,true⟩,0,0,0⟩, +⟨⟨1,169,596,true⟩,0,0,0⟩, +⟨⟨1,169,597,true⟩,0,0,0⟩, +⟨⟨1,169,598,true⟩,0,0,0⟩, +⟨⟨1,169,602,true⟩,0,0,0⟩, +⟨⟨1,169,606,true⟩,0,0,0⟩, +⟨⟨1,169,608,true⟩,0,0,0⟩, +⟨⟨1,169,609,true⟩,0,0,0⟩, +⟨⟨1,169,612,true⟩,0,0,0⟩, +⟨⟨1,169,613,true⟩,0,0,0⟩, +⟨⟨1,169,628,true⟩,0,0,0⟩, +⟨⟨1,169,630,true⟩,0,0,0⟩, +⟨⟨1,169,732,true⟩,0,0,0⟩, +⟨⟨1,169,734,true⟩,0,0,0⟩, +⟨⟨1,169,934,true⟩,0,0,0⟩, +⟨⟨1,169,940,true⟩,0,0,0⟩, +⟨⟨1,170,244,true⟩,0,0,0⟩, +⟨⟨1,170,265,true⟩,0,0,0⟩, +⟨⟨1,170,283,true⟩,0,0,0⟩, +⟨⟨1,170,306,true⟩,0,0,0⟩, +⟨⟨1,170,310,true⟩,0,0,0⟩, +⟨⟨1,170,312,true⟩,0,0,0⟩, +⟨⟨1,170,316,true⟩,0,0,0⟩, +⟨⟨1,170,325,true⟩,0,0,0⟩, +⟨⟨1,170,327,true⟩,0,0,0⟩, +⟨⟨1,170,329,true⟩,0,0,0⟩, 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+⟨⟨1,170,477,true⟩,0,0,0⟩, +⟨⟨1,170,480,true⟩,0,0,0⟩, +⟨⟨1,170,482,true⟩,0,0,0⟩, +⟨⟨1,170,488,true⟩,0,0,0⟩, +⟨⟨1,170,490,true⟩,0,0,0⟩, +⟨⟨1,170,525,true⟩,0,0,0⟩, +⟨⟨1,170,527,true⟩,0,0,0⟩, +⟨⟨1,170,536,true⟩,0,0,0⟩, +⟨⟨1,170,538,true⟩,0,0,0⟩, +⟨⟨1,170,557,true⟩,0,0,0⟩, +⟨⟨1,170,559,true⟩,0,0,0⟩, +⟨⟨1,170,569,true⟩,0,0,0⟩, +⟨⟨1,170,571,true⟩,0,0,0⟩, +⟨⟨1,170,588,true⟩,0,0,0⟩, +⟨⟨1,170,590,true⟩,0,0,0⟩, +⟨⟨1,170,592,true⟩,0,0,0⟩, +⟨⟨1,170,596,true⟩,0,0,0⟩, +⟨⟨1,170,597,true⟩,0,0,0⟩, +⟨⟨1,170,608,true⟩,0,0,0⟩, +⟨⟨1,170,609,true⟩,0,0,0⟩, +⟨⟨1,170,612,true⟩,0,0,0⟩, +⟨⟨1,170,613,true⟩,0,0,0⟩, +⟨⟨1,170,628,true⟩,0,0,0⟩, +⟨⟨1,170,630,true⟩,0,0,0⟩, +⟨⟨1,170,732,true⟩,0,0,0⟩, +⟨⟨1,170,734,true⟩,0,0,0⟩, +⟨⟨1,170,935,true⟩,0,0,0⟩, +⟨⟨1,170,939,true⟩,0,0,0⟩, +⟨⟨1,171,244,true⟩,0,0,0⟩, +⟨⟨1,171,265,true⟩,0,0,0⟩, +⟨⟨1,171,283,true⟩,0,0,0⟩, +⟨⟨1,171,304,true⟩,0,0,0⟩, +⟨⟨1,171,308,true⟩,0,0,0⟩, +⟨⟨1,171,314,true⟩,0,0,0⟩, +⟨⟨1,171,318,true⟩,0,0,0⟩, +⟨⟨1,171,321,true⟩,0,0,0⟩, +⟨⟨1,171,323,true⟩,0,0,0⟩, +⟨⟨1,171,333,true⟩,0,0,0⟩, +⟨⟨1,171,335,true⟩,0,0,0⟩, +⟨⟨1,171,336,true⟩,0,0,0⟩, +⟨⟨1,171,340,true⟩,0,0,0⟩, +⟨⟨1,171,346,true⟩,0,0,0⟩, +⟨⟨1,171,350,true⟩,0,0,0⟩, +⟨⟨1,171,353,true⟩,0,0,0⟩, +⟨⟨1,171,355,true⟩,0,0,0⟩, +⟨⟨1,171,365,true⟩,0,0,0⟩, +⟨⟨1,171,367,true⟩,0,0,0⟩, +⟨⟨1,171,369,true⟩,0,0,0⟩, +⟨⟨1,171,389,true⟩,0,0,0⟩, +⟨⟨1,171,391,true⟩,0,0,0⟩, +⟨⟨1,171,393,true⟩,0,0,0⟩, +⟨⟨1,171,395,true⟩,0,0,0⟩, +⟨⟨1,171,405,true⟩,0,0,0⟩, +⟨⟨1,171,407,true⟩,0,0,0⟩, +⟨⟨1,171,409,true⟩,0,0,0⟩, +⟨⟨1,171,411,true⟩,0,0,0⟩, +⟨⟨1,171,433,true⟩,0,0,0⟩, +⟨⟨1,171,437,true⟩,0,0,0⟩, +⟨⟨1,171,441,true⟩,0,0,0⟩, +⟨⟨1,171,445,true⟩,0,0,0⟩, +⟨⟨1,171,448,true⟩,0,0,0⟩, +⟨⟨1,171,450,true⟩,0,0,0⟩, +⟨⟨1,171,456,true⟩,0,0,0⟩, +⟨⟨1,171,458,true⟩,0,0,0⟩, +⟨⟨1,171,465,true⟩,0,0,0⟩, +⟨⟨1,171,469,true⟩,0,0,0⟩, +⟨⟨1,171,473,true⟩,0,0,0⟩, +⟨⟨1,171,477,true⟩,0,0,0⟩, +⟨⟨1,171,480,true⟩,0,0,0⟩, +⟨⟨1,171,482,true⟩,0,0,0⟩, +⟨⟨1,171,488,true⟩,0,0,0⟩, +⟨⟨1,171,490,true⟩,0,0,0⟩, +⟨⟨1,171,525,true⟩,0,0,0⟩, +⟨⟨1,171,527,true⟩,0,0,0⟩, +⟨⟨1,171,536,true⟩,0,0,0⟩, +⟨⟨1,171,538,true⟩,0,0,0⟩, +⟨⟨1,171,556,true⟩,0,0,0⟩, +⟨⟨1,171,558,true⟩,0,0,0⟩, +⟨⟨1,171,568,true⟩,0,0,0⟩, +⟨⟨1,171,570,true⟩,0,0,0⟩] +def chunk16 : List Entry := [⟨⟨1,171,588,true⟩,0,0,0⟩, +⟨⟨1,171,590,true⟩,0,0,0⟩, +⟨⟨1,171,592,true⟩,0,0,0⟩, +⟨⟨1,171,594,true⟩,0,0,0⟩, +⟨⟨1,171,596,true⟩,0,0,0⟩, +⟨⟨1,171,598,true⟩,0,0,0⟩, +⟨⟨1,171,610,true⟩,0,0,0⟩, +⟨⟨1,171,611,true⟩,0,0,0⟩, +⟨⟨1,171,614,true⟩,0,0,0⟩, +⟨⟨1,171,615,true⟩,0,0,0⟩, +⟨⟨1,171,628,true⟩,0,0,0⟩, +⟨⟨1,171,630,true⟩,0,0,0⟩, +⟨⟨1,171,733,true⟩,0,0,0⟩, +⟨⟨1,171,735,true⟩,0,0,0⟩, +⟨⟨1,172,244,true⟩,0,0,0⟩, +⟨⟨1,172,265,true⟩,0,0,0⟩, +⟨⟨1,172,283,true⟩,0,0,0⟩, +⟨⟨1,172,304,true⟩,0,0,0⟩, +⟨⟨1,172,308,true⟩,0,0,0⟩, +⟨⟨1,172,314,true⟩,0,0,0⟩, +⟨⟨1,172,318,true⟩,0,0,0⟩, +⟨⟨1,172,325,true⟩,0,0,0⟩, +⟨⟨1,172,327,true⟩,0,0,0⟩, +⟨⟨1,172,329,true⟩,0,0,0⟩, +⟨⟨1,172,331,true⟩,0,0,0⟩, +⟨⟨1,172,338,true⟩,0,0,0⟩, +⟨⟨1,172,342,true⟩,0,0,0⟩, +⟨⟨1,172,344,true⟩,0,0,0⟩, +⟨⟨1,172,348,true⟩,0,0,0⟩, +⟨⟨1,172,353,true⟩,0,0,0⟩, +⟨⟨1,172,355,true⟩,0,0,0⟩, +⟨⟨1,172,365,true⟩,0,0,0⟩, +⟨⟨1,172,367,true⟩,0,0,0⟩, +⟨⟨1,172,383,true⟩,0,0,0⟩, +⟨⟨1,172,389,true⟩,0,0,0⟩, +⟨⟨1,172,391,true⟩,0,0,0⟩, +⟨⟨1,172,393,true⟩,0,0,0⟩, +⟨⟨1,172,395,true⟩,0,0,0⟩, +⟨⟨1,172,401,true⟩,0,0,0⟩, +⟨⟨1,172,403,true⟩,0,0,0⟩, +⟨⟨1,172,413,true⟩,0,0,0⟩, +⟨⟨1,172,415,true⟩,0,0,0⟩, +⟨⟨1,172,418,true⟩,0,0,0⟩, +⟨⟨1,172,419,true⟩,0,0,0⟩, +⟨⟨1,172,422,true⟩,0,0,0⟩, +⟨⟨1,172,423,true⟩,0,0,0⟩, +⟨⟨1,172,424,true⟩,0,0,0⟩, +⟨⟨1,172,427,true⟩,0,0,0⟩, +⟨⟨1,172,428,true⟩,0,0,0⟩, +⟨⟨1,172,431,true⟩,0,0,0⟩, +⟨⟨1,172,435,true⟩,0,0,0⟩, +⟨⟨1,172,439,true⟩,0,0,0⟩, +⟨⟨1,172,443,true⟩,0,0,0⟩, +⟨⟨1,172,447,true⟩,0,0,0⟩, +⟨⟨1,172,448,true⟩,0,0,0⟩, +⟨⟨1,172,450,true⟩,0,0,0⟩, +⟨⟨1,172,456,true⟩,0,0,0⟩, +⟨⟨1,172,458,true⟩,0,0,0⟩, +⟨⟨1,172,465,true⟩,0,0,0⟩, +⟨⟨1,172,469,true⟩,0,0,0⟩, +⟨⟨1,172,473,true⟩,0,0,0⟩, +⟨⟨1,172,477,true⟩,0,0,0⟩, +⟨⟨1,172,484,true⟩,0,0,0⟩, +⟨⟨1,172,486,true⟩,0,0,0⟩, +⟨⟨1,172,492,true⟩,0,0,0⟩, +⟨⟨1,172,494,true⟩,0,0,0⟩, +⟨⟨1,172,524,true⟩,0,0,0⟩, +⟨⟨1,172,526,true⟩,0,0,0⟩, +⟨⟨1,172,537,true⟩,0,0,0⟩, +⟨⟨1,172,539,true⟩,0,0,0⟩, +⟨⟨1,172,557,true⟩,0,0,0⟩, +⟨⟨1,172,559,true⟩,0,0,0⟩, +⟨⟨1,172,568,true⟩,0,0,0⟩, +⟨⟨1,172,570,true⟩,0,0,0⟩, +⟨⟨1,172,588,true⟩,0,0,0⟩, +⟨⟨1,172,590,true⟩,0,0,0⟩, +⟨⟨1,172,592,true⟩,0,0,0⟩, +⟨⟨1,172,594,true⟩,0,0,0⟩, +⟨⟨1,172,597,true⟩,0,0,0⟩, +⟨⟨1,172,606,true⟩,0,0,0⟩, +⟨⟨1,172,607,true⟩,0,0,0⟩, +⟨⟨1,172,610,true⟩,0,0,0⟩, +⟨⟨1,172,611,true⟩,0,0,0⟩, +⟨⟨1,172,614,true⟩,0,0,0⟩, +⟨⟨1,172,615,true⟩,0,0,0⟩, +⟨⟨1,172,624,true⟩,0,0,0⟩, +⟨⟨1,172,626,true⟩,0,0,0⟩, +⟨⟨1,172,733,true⟩,0,0,0⟩, +⟨⟨1,172,735,true⟩,0,0,0⟩, +⟨⟨1,172,744,true⟩,0,0,0⟩, +⟨⟨1,172,834,true⟩,0,0,0⟩, +⟨⟨1,172,934,true⟩,0,0,0⟩, +⟨⟨1,172,939,true⟩,0,0,0⟩, +⟨⟨1,173,244,true⟩,0,0,0⟩, +⟨⟨1,173,265,true⟩,0,0,0⟩, +⟨⟨1,173,283,true⟩,0,0,0⟩, +⟨⟨1,173,306,true⟩,0,0,0⟩, +⟨⟨1,173,310,true⟩,0,0,0⟩, +⟨⟨1,173,312,true⟩,0,0,0⟩, +⟨⟨1,173,316,true⟩,0,0,0⟩, +⟨⟨1,173,321,true⟩,0,0,0⟩, +⟨⟨1,173,323,true⟩,0,0,0⟩, +⟨⟨1,173,333,true⟩,0,0,0⟩, +⟨⟨1,173,335,true⟩,0,0,0⟩, +⟨⟨1,173,338,true⟩,0,0,0⟩, +⟨⟨1,173,342,true⟩,0,0,0⟩, +⟨⟨1,173,344,true⟩,0,0,0⟩, +⟨⟨1,173,348,true⟩,0,0,0⟩, +⟨⟨1,173,353,true⟩,0,0,0⟩, +⟨⟨1,173,355,true⟩,0,0,0⟩, +⟨⟨1,173,365,true⟩,0,0,0⟩, +⟨⟨1,173,367,true⟩,0,0,0⟩, +⟨⟨1,173,380,true⟩,0,0,0⟩, +⟨⟨1,173,385,true⟩,0,0,0⟩, +⟨⟨1,173,387,true⟩,0,0,0⟩, +⟨⟨1,173,397,true⟩,0,0,0⟩, +⟨⟨1,173,399,true⟩,0,0,0⟩, +⟨⟨1,173,401,true⟩,0,0,0⟩, +⟨⟨1,173,403,true⟩,0,0,0⟩, +⟨⟨1,173,413,true⟩,0,0,0⟩, +⟨⟨1,173,415,true⟩,0,0,0⟩, +⟨⟨1,173,433,true⟩,0,0,0⟩, +⟨⟨1,173,437,true⟩,0,0,0⟩, +⟨⟨1,173,441,true⟩,0,0,0⟩, +⟨⟨1,173,445,true⟩,0,0,0⟩, +⟨⟨1,173,452,true⟩,0,0,0⟩, +⟨⟨1,173,454,true⟩,0,0,0⟩, +⟨⟨1,173,460,true⟩,0,0,0⟩, +⟨⟨1,173,462,true⟩,0,0,0⟩, +⟨⟨1,173,465,true⟩,0,0,0⟩, +⟨⟨1,173,469,true⟩,0,0,0⟩, +⟨⟨1,173,473,true⟩,0,0,0⟩, +⟨⟨1,173,477,true⟩,0,0,0⟩, +⟨⟨1,173,484,true⟩,0,0,0⟩, +⟨⟨1,173,486,true⟩,0,0,0⟩, +⟨⟨1,173,492,true⟩,0,0,0⟩, +⟨⟨1,173,494,true⟩,0,0,0⟩, +⟨⟨1,173,524,true⟩,0,0,0⟩, +⟨⟨1,173,526,true⟩,0,0,0⟩, +⟨⟨1,173,537,true⟩,0,0,0⟩, +⟨⟨1,173,539,true⟩,0,0,0⟩, +⟨⟨1,173,556,true⟩,0,0,0⟩, +⟨⟨1,173,558,true⟩,0,0,0⟩, +⟨⟨1,173,569,true⟩,0,0,0⟩, +⟨⟨1,173,571,true⟩,0,0,0⟩, +⟨⟨1,173,588,true⟩,0,0,0⟩, +⟨⟨1,173,590,true⟩,0,0,0⟩, +⟨⟨1,173,592,true⟩,0,0,0⟩, +⟨⟨1,173,594,true⟩,0,0,0⟩, +⟨⟨1,173,596,true⟩,0,0,0⟩, +⟨⟨1,173,598,true⟩,0,0,0⟩, +⟨⟨1,173,608,true⟩,0,0,0⟩, +⟨⟨1,173,609,true⟩,0,0,0⟩, +⟨⟨1,173,612,true⟩,0,0,0⟩, +⟨⟨1,173,613,true⟩,0,0,0⟩, +⟨⟨1,173,624,true⟩,0,0,0⟩, +⟨⟨1,173,626,true⟩,0,0,0⟩, +⟨⟨1,173,732,true⟩,0,0,0⟩, +⟨⟨1,173,734,true⟩,0,0,0⟩, +⟨⟨1,173,744,true⟩,0,0,0⟩, +⟨⟨1,173,834,true⟩,0,0,0⟩, +⟨⟨1,174,244,true⟩,0,0,0⟩, +⟨⟨1,174,265,true⟩,0,0,0⟩, +⟨⟨1,174,283,true⟩,0,0,0⟩, +⟨⟨1,174,304,true⟩,0,0,0⟩, +⟨⟨1,174,308,true⟩,0,0,0⟩, +⟨⟨1,174,314,true⟩,0,0,0⟩, +⟨⟨1,174,318,true⟩,0,0,0⟩, +⟨⟨1,174,325,true⟩,0,0,0⟩, +⟨⟨1,174,327,true⟩,0,0,0⟩, +⟨⟨1,174,329,true⟩,0,0,0⟩, +⟨⟨1,174,331,true⟩,0,0,0⟩, +⟨⟨1,174,336,true⟩,0,0,0⟩, +⟨⟨1,174,340,true⟩,0,0,0⟩, +⟨⟨1,174,346,true⟩,0,0,0⟩, +⟨⟨1,174,350,true⟩,0,0,0⟩, +⟨⟨1,174,357,true⟩,0,0,0⟩, +⟨⟨1,174,359,true⟩,0,0,0⟩, +⟨⟨1,174,361,true⟩,0,0,0⟩, +⟨⟨1,174,363,true⟩,0,0,0⟩, +⟨⟨1,174,378,true⟩,0,0,0⟩, +⟨⟨1,174,385,true⟩,0,0,0⟩, +⟨⟨1,174,387,true⟩,0,0,0⟩, +⟨⟨1,174,397,true⟩,0,0,0⟩, +⟨⟨1,174,399,true⟩,0,0,0⟩, +⟨⟨1,174,401,true⟩,0,0,0⟩, +⟨⟨1,174,403,true⟩,0,0,0⟩, +⟨⟨1,174,413,true⟩,0,0,0⟩, +⟨⟨1,174,415,true⟩,0,0,0⟩, +⟨⟨1,174,435,true⟩,0,0,0⟩, +⟨⟨1,174,439,true⟩,0,0,0⟩, +⟨⟨1,174,443,true⟩,0,0,0⟩, +⟨⟨1,174,447,true⟩,0,0,0⟩, +⟨⟨1,174,448,true⟩,0,0,0⟩, +⟨⟨1,174,450,true⟩,0,0,0⟩, +⟨⟨1,174,456,true⟩,0,0,0⟩, +⟨⟨1,174,458,true⟩,0,0,0⟩, +⟨⟨1,174,467,true⟩,0,0,0⟩, +⟨⟨1,174,471,true⟩,0,0,0⟩, +⟨⟨1,174,475,true⟩,0,0,0⟩] +def chunk17 : List Entry := [⟨⟨1,174,479,true⟩,0,0,0⟩, +⟨⟨1,174,480,true⟩,0,0,0⟩, +⟨⟨1,174,482,true⟩,0,0,0⟩, +⟨⟨1,174,488,true⟩,0,0,0⟩, +⟨⟨1,174,490,true⟩,0,0,0⟩, +⟨⟨1,174,524,true⟩,0,0,0⟩, +⟨⟨1,174,526,true⟩,0,0,0⟩, +⟨⟨1,174,536,true⟩,0,0,0⟩, +⟨⟨1,174,538,true⟩,0,0,0⟩, +⟨⟨1,174,557,true⟩,0,0,0⟩, +⟨⟨1,174,559,true⟩,0,0,0⟩, +⟨⟨1,174,568,true⟩,0,0,0⟩, +⟨⟨1,174,570,true⟩,0,0,0⟩, +⟨⟨1,174,589,true⟩,0,0,0⟩, +⟨⟨1,174,591,true⟩,0,0,0⟩, +⟨⟨1,174,592,true⟩,0,0,0⟩, +⟨⟨1,174,594,true⟩,0,0,0⟩, +⟨⟨1,174,596,true⟩,0,0,0⟩, +⟨⟨1,174,598,true⟩,0,0,0⟩, +⟨⟨1,174,608,true⟩,0,0,0⟩, +⟨⟨1,174,609,true⟩,0,0,0⟩, +⟨⟨1,174,612,true⟩,0,0,0⟩, +⟨⟨1,174,613,true⟩,0,0,0⟩, +⟨⟨1,174,624,true⟩,0,0,0⟩, +⟨⟨1,174,626,true⟩,0,0,0⟩, +⟨⟨1,174,732,true⟩,0,0,0⟩, +⟨⟨1,174,734,true⟩,0,0,0⟩, +⟨⟨1,174,744,true⟩,0,0,0⟩, +⟨⟨1,174,834,true⟩,0,0,0⟩, +⟨⟨1,175,244,true⟩,0,0,0⟩, +⟨⟨1,175,265,true⟩,0,0,0⟩, +⟨⟨1,175,283,true⟩,0,0,0⟩, +⟨⟨1,175,306,true⟩,0,0,0⟩, +⟨⟨1,175,310,true⟩,0,0,0⟩, +⟨⟨1,175,312,true⟩,0,0,0⟩, +⟨⟨1,175,316,true⟩,0,0,0⟩, +⟨⟨1,175,321,true⟩,0,0,0⟩, +⟨⟨1,175,323,true⟩,0,0,0⟩, +⟨⟨1,175,333,true⟩,0,0,0⟩, +⟨⟨1,175,335,true⟩,0,0,0⟩, +⟨⟨1,175,336,true⟩,0,0,0⟩, +⟨⟨1,175,340,true⟩,0,0,0⟩, +⟨⟨1,175,346,true⟩,0,0,0⟩, +⟨⟨1,175,350,true⟩,0,0,0⟩, +⟨⟨1,175,357,true⟩,0,0,0⟩, +⟨⟨1,175,359,true⟩,0,0,0⟩, +⟨⟨1,175,361,true⟩,0,0,0⟩, +⟨⟨1,175,363,true⟩,0,0,0⟩, +⟨⟨1,175,377,true⟩,0,0,0⟩, +⟨⟨1,175,389,true⟩,0,0,0⟩, +⟨⟨1,175,391,true⟩,0,0,0⟩, +⟨⟨1,175,393,true⟩,0,0,0⟩, +⟨⟨1,175,395,true⟩,0,0,0⟩, +⟨⟨1,175,401,true⟩,0,0,0⟩, +⟨⟨1,175,403,true⟩,0,0,0⟩, +⟨⟨1,175,413,true⟩,0,0,0⟩, +⟨⟨1,175,415,true⟩,0,0,0⟩, +⟨⟨1,175,420,true⟩,0,0,0⟩, +⟨⟨1,175,421,true⟩,0,0,0⟩, +⟨⟨1,175,425,true⟩,0,0,0⟩, +⟨⟨1,175,430,true⟩,0,0,0⟩, +⟨⟨1,175,433,true⟩,0,0,0⟩, +⟨⟨1,175,437,true⟩,0,0,0⟩, +⟨⟨1,175,441,true⟩,0,0,0⟩, +⟨⟨1,175,445,true⟩,0,0,0⟩, +⟨⟨1,175,452,true⟩,0,0,0⟩, +⟨⟨1,175,454,true⟩,0,0,0⟩, +⟨⟨1,175,460,true⟩,0,0,0⟩, +⟨⟨1,175,462,true⟩,0,0,0⟩, +⟨⟨1,175,467,true⟩,0,0,0⟩, +⟨⟨1,175,471,true⟩,0,0,0⟩, +⟨⟨1,175,475,true⟩,0,0,0⟩, +⟨⟨1,175,479,true⟩,0,0,0⟩, +⟨⟨1,175,480,true⟩,0,0,0⟩, +⟨⟨1,175,482,true⟩,0,0,0⟩, +⟨⟨1,175,488,true⟩,0,0,0⟩, +⟨⟨1,175,490,true⟩,0,0,0⟩, +⟨⟨1,175,524,true⟩,0,0,0⟩, +⟨⟨1,175,526,true⟩,0,0,0⟩, +⟨⟨1,175,536,true⟩,0,0,0⟩, +⟨⟨1,175,538,true⟩,0,0,0⟩, +⟨⟨1,175,556,true⟩,0,0,0⟩, +⟨⟨1,175,558,true⟩,0,0,0⟩, +⟨⟨1,175,569,true⟩,0,0,0⟩, +⟨⟨1,175,571,true⟩,0,0,0⟩, +⟨⟨1,175,589,true⟩,0,0,0⟩, +⟨⟨1,175,591,true⟩,0,0,0⟩, +⟨⟨1,175,592,true⟩,0,0,0⟩, +⟨⟨1,175,594,true⟩,0,0,0⟩, +⟨⟨1,175,597,true⟩,0,0,0⟩, +⟨⟨1,175,598,true⟩,0,0,0⟩, +⟨⟨1,175,602,true⟩,0,0,0⟩, +⟨⟨1,175,607,true⟩,0,0,0⟩, +⟨⟨1,175,610,true⟩,0,0,0⟩, +⟨⟨1,175,611,true⟩,0,0,0⟩, +⟨⟨1,175,614,true⟩,0,0,0⟩, +⟨⟨1,175,615,true⟩,0,0,0⟩, +⟨⟨1,175,624,true⟩,0,0,0⟩, +⟨⟨1,175,626,true⟩,0,0,0⟩, +⟨⟨1,175,733,true⟩,0,0,0⟩, +⟨⟨1,175,735,true⟩,0,0,0⟩, +⟨⟨1,175,744,true⟩,0,0,0⟩, +⟨⟨1,175,834,true⟩,0,0,0⟩, +⟨⟨1,175,935,true⟩,0,0,0⟩, +⟨⟨1,175,940,true⟩,0,0,0⟩, +⟨⟨1,176,252,true⟩,0,0,0⟩, +⟨⟨1,176,258,true⟩,0,0,0⟩, +⟨⟨1,176,391,true⟩,0,0,0⟩, +⟨⟨1,176,512,true⟩,0,0,0⟩, +⟨⟨1,176,514,true⟩,0,0,0⟩, +⟨⟨1,176,516,true⟩,0,0,0⟩, +⟨⟨1,176,518,true⟩,0,0,0⟩, +⟨⟨1,176,523,true⟩,0,0,0⟩, +⟨⟨1,176,530,true⟩,0,0,0⟩, +⟨⟨1,176,531,true⟩,0,0,0⟩, +⟨⟨1,176,534,true⟩,0,0,0⟩, +⟨⟨1,176,535,true⟩,0,0,0⟩, +⟨⟨1,176,546,true⟩,0,0,0⟩, +⟨⟨1,176,547,true⟩,0,0,0⟩, +⟨⟨1,176,550,true⟩,0,0,0⟩, +⟨⟨1,176,551,true⟩,0,0,0⟩, +⟨⟨1,176,562,true⟩,0,0,0⟩, +⟨⟨1,176,563,true⟩,0,0,0⟩, +⟨⟨1,176,566,true⟩,0,0,0⟩, +⟨⟨1,176,567,true⟩,0,0,0⟩, +⟨⟨1,176,578,true⟩,0,0,0⟩, +⟨⟨1,176,579,true⟩,0,0,0⟩, +⟨⟨1,176,582,true⟩,0,0,0⟩, +⟨⟨1,176,583,true⟩,0,0,0⟩, +⟨⟨1,176,594,true⟩,0,0,0⟩, +⟨⟨1,176,595,true⟩,0,0,0⟩, +⟨⟨1,176,598,true⟩,0,0,0⟩, +⟨⟨1,176,599,true⟩,0,0,0⟩, +⟨⟨1,176,610,true⟩,0,0,0⟩, +⟨⟨1,176,611,true⟩,0,0,0⟩, +⟨⟨1,176,614,true⟩,0,0,0⟩, +⟨⟨1,176,615,true⟩,0,0,0⟩, +⟨⟨1,176,626,true⟩,0,0,0⟩, +⟨⟨1,176,627,true⟩,0,0,0⟩, +⟨⟨1,176,630,true⟩,0,0,0⟩, +⟨⟨1,176,631,true⟩,0,0,0⟩, +⟨⟨1,176,642,true⟩,0,0,0⟩, +⟨⟨1,176,643,true⟩,0,0,0⟩, +⟨⟨1,176,646,true⟩,0,0,0⟩, +⟨⟨1,176,647,true⟩,0,0,0⟩, +⟨⟨1,176,658,true⟩,0,0,0⟩, +⟨⟨1,176,659,true⟩,0,0,0⟩, +⟨⟨1,176,662,true⟩,0,0,0⟩, +⟨⟨1,176,663,true⟩,0,0,0⟩, +⟨⟨1,176,674,true⟩,0,0,0⟩, +⟨⟨1,176,675,true⟩,0,0,0⟩, +⟨⟨1,176,678,true⟩,0,0,0⟩, +⟨⟨1,176,679,true⟩,0,0,0⟩, +⟨⟨1,176,690,true⟩,0,0,0⟩, +⟨⟨1,176,691,true⟩,0,0,0⟩, +⟨⟨1,176,694,true⟩,0,0,0⟩, +⟨⟨1,176,695,true⟩,0,0,0⟩, +⟨⟨1,176,706,true⟩,0,0,0⟩, +⟨⟨1,176,707,true⟩,0,0,0⟩, +⟨⟨1,176,710,true⟩,0,0,0⟩, +⟨⟨1,176,711,true⟩,0,0,0⟩, +⟨⟨1,176,763,true⟩,0,0,0⟩, +⟨⟨1,177,252,true⟩,0,0,0⟩, +⟨⟨1,177,258,true⟩,0,0,0⟩, +⟨⟨1,177,389,true⟩,0,0,0⟩, +⟨⟨1,177,403,true⟩,0,0,0⟩, +⟨⟨1,177,404,true⟩,0,0,0⟩, +⟨⟨1,177,414,true⟩,0,0,0⟩, +⟨⟨1,177,415,true⟩,0,0,0⟩, +⟨⟨1,177,512,true⟩,0,0,0⟩, +⟨⟨1,177,516,true⟩,0,0,0⟩, +⟨⟨1,177,517,true⟩,0,0,0⟩, +⟨⟨1,177,518,true⟩,0,0,0⟩, +⟨⟨1,177,522,true⟩,0,0,0⟩, +⟨⟨1,177,526,true⟩,0,0,0⟩, +⟨⟨1,177,530,true⟩,0,0,0⟩, +⟨⟨1,177,531,true⟩,0,0,0⟩, +⟨⟨1,177,534,true⟩,0,0,0⟩, +⟨⟨1,177,535,true⟩,0,0,0⟩, +⟨⟨1,177,544,true⟩,0,0,0⟩, +⟨⟨1,177,545,true⟩,0,0,0⟩, +⟨⟨1,177,548,true⟩,0,0,0⟩, +⟨⟨1,177,549,true⟩,0,0,0⟩, +⟨⟨1,177,562,true⟩,0,0,0⟩, +⟨⟨1,177,563,true⟩,0,0,0⟩, +⟨⟨1,177,566,true⟩,0,0,0⟩, +⟨⟨1,177,567,true⟩,0,0,0⟩, +⟨⟨1,177,576,true⟩,0,0,0⟩, +⟨⟨1,177,577,true⟩,0,0,0⟩, +⟨⟨1,177,580,true⟩,0,0,0⟩, +⟨⟨1,177,581,true⟩,0,0,0⟩, +⟨⟨1,177,592,true⟩,0,0,0⟩, +⟨⟨1,177,593,true⟩,0,0,0⟩, +⟨⟨1,177,596,true⟩,0,0,0⟩, +⟨⟨1,177,597,true⟩,0,0,0⟩, +⟨⟨1,177,610,true⟩,0,0,0⟩, +⟨⟨1,177,611,true⟩,0,0,0⟩, +⟨⟨1,177,614,true⟩,0,0,0⟩, +⟨⟨1,177,615,true⟩,0,0,0⟩, +⟨⟨1,177,624,true⟩,0,0,0⟩] +def chunk18 : List Entry := [⟨⟨1,177,625,true⟩,0,0,0⟩, +⟨⟨1,177,628,true⟩,0,0,0⟩, +⟨⟨1,177,629,true⟩,0,0,0⟩, +⟨⟨1,177,642,true⟩,0,0,0⟩, +⟨⟨1,177,643,true⟩,0,0,0⟩, +⟨⟨1,177,646,true⟩,0,0,0⟩, +⟨⟨1,177,647,true⟩,0,0,0⟩, +⟨⟨1,177,658,true⟩,0,0,0⟩, +⟨⟨1,177,659,true⟩,0,0,0⟩, +⟨⟨1,177,662,true⟩,0,0,0⟩, +⟨⟨1,177,663,true⟩,0,0,0⟩, +⟨⟨1,177,672,true⟩,0,0,0⟩, +⟨⟨1,177,673,true⟩,0,0,0⟩, +⟨⟨1,177,676,true⟩,0,0,0⟩, +⟨⟨1,177,677,true⟩,0,0,0⟩, +⟨⟨1,177,690,true⟩,0,0,0⟩, +⟨⟨1,177,691,true⟩,0,0,0⟩, +⟨⟨1,177,694,true⟩,0,0,0⟩, +⟨⟨1,177,695,true⟩,0,0,0⟩, +⟨⟨1,177,704,true⟩,0,0,0⟩, +⟨⟨1,177,705,true⟩,0,0,0⟩, +⟨⟨1,177,708,true⟩,0,0,0⟩, +⟨⟨1,177,709,true⟩,0,0,0⟩, +⟨⟨1,177,763,true⟩,0,0,0⟩, +⟨⟨1,177,776,true⟩,0,0,0⟩, +⟨⟨1,177,950,true⟩,0,0,0⟩, +⟨⟨1,178,252,true⟩,0,0,0⟩, +⟨⟨1,178,258,true⟩,0,0,0⟩, +⟨⟨1,178,387,true⟩,0,0,0⟩, +⟨⟨1,178,402,true⟩,0,0,0⟩, +⟨⟨1,178,405,true⟩,0,0,0⟩, +⟨⟨1,178,406,true⟩,0,0,0⟩, +⟨⟨1,178,407,true⟩,0,0,0⟩, +⟨⟨1,178,408,true⟩,0,0,0⟩, +⟨⟨1,178,409,true⟩,0,0,0⟩, +⟨⟨1,178,411,true⟩,0,0,0⟩, +⟨⟨1,178,412,true⟩,0,0,0⟩, +⟨⟨1,178,512,true⟩,0,0,0⟩, +⟨⟨1,178,516,true⟩,0,0,0⟩, +⟨⟨1,178,517,true⟩,0,0,0⟩, +⟨⟨1,178,523,true⟩,0,0,0⟩, +⟨⟨1,178,530,true⟩,0,0,0⟩, +⟨⟨1,178,531,true⟩,0,0,0⟩, +⟨⟨1,178,534,true⟩,0,0,0⟩, +⟨⟨1,178,535,true⟩,0,0,0⟩, +⟨⟨1,178,544,true⟩,0,0,0⟩, +⟨⟨1,178,545,true⟩,0,0,0⟩, +⟨⟨1,178,548,true⟩,0,0,0⟩, +⟨⟨1,178,549,true⟩,0,0,0⟩, +⟨⟨1,178,560,true⟩,0,0,0⟩, +⟨⟨1,178,561,true⟩,0,0,0⟩, +⟨⟨1,178,564,true⟩,0,0,0⟩, +⟨⟨1,178,565,true⟩,0,0,0⟩, +⟨⟨1,178,578,true⟩,0,0,0⟩, +⟨⟨1,178,579,true⟩,0,0,0⟩, +⟨⟨1,178,582,true⟩,0,0,0⟩, +⟨⟨1,178,583,true⟩,0,0,0⟩, +⟨⟨1,178,594,true⟩,0,0,0⟩, +⟨⟨1,178,595,true⟩,0,0,0⟩, +⟨⟨1,178,598,true⟩,0,0,0⟩, +⟨⟨1,178,599,true⟩,0,0,0⟩, +⟨⟨1,178,608,true⟩,0,0,0⟩, +⟨⟨1,178,609,true⟩,0,0,0⟩, +⟨⟨1,178,612,true⟩,0,0,0⟩, +⟨⟨1,178,613,true⟩,0,0,0⟩, +⟨⟨1,178,626,true⟩,0,0,0⟩, +⟨⟨1,178,627,true⟩,0,0,0⟩, +⟨⟨1,178,630,true⟩,0,0,0⟩, +⟨⟨1,178,631,true⟩,0,0,0⟩, +⟨⟨1,178,640,true⟩,0,0,0⟩, +⟨⟨1,178,641,true⟩,0,0,0⟩, +⟨⟨1,178,644,true⟩,0,0,0⟩, +⟨⟨1,178,645,true⟩,0,0,0⟩, +⟨⟨1,178,656,true⟩,0,0,0⟩, +⟨⟨1,178,657,true⟩,0,0,0⟩, +⟨⟨1,178,660,true⟩,0,0,0⟩, +⟨⟨1,178,661,true⟩,0,0,0⟩, +⟨⟨1,178,674,true⟩,0,0,0⟩, +⟨⟨1,178,675,true⟩,0,0,0⟩, +⟨⟨1,178,678,true⟩,0,0,0⟩, +⟨⟨1,178,679,true⟩,0,0,0⟩, +⟨⟨1,178,690,true⟩,0,0,0⟩, +⟨⟨1,178,691,true⟩,0,0,0⟩, +⟨⟨1,178,694,true⟩,0,0,0⟩, +⟨⟨1,178,695,true⟩,0,0,0⟩, +⟨⟨1,178,704,true⟩,0,0,0⟩, +⟨⟨1,178,705,true⟩,0,0,0⟩, +⟨⟨1,178,708,true⟩,0,0,0⟩, +⟨⟨1,178,709,true⟩,0,0,0⟩, +⟨⟨1,178,763,true⟩,0,0,0⟩, +⟨⟨1,178,776,true⟩,0,0,0⟩, +⟨⟨1,178,790,true⟩,0,0,0⟩, +⟨⟨1,178,941,true⟩,0,0,0⟩, +⟨⟨1,179,252,true⟩,0,0,0⟩, +⟨⟨1,179,258,true⟩,0,0,0⟩, +⟨⟨1,179,385,true⟩,0,0,0⟩, +⟨⟨1,179,512,true⟩,0,0,0⟩, +⟨⟨1,179,514,true⟩,0,0,0⟩, +⟨⟨1,179,516,true⟩,0,0,0⟩, +⟨⟨1,179,518,true⟩,0,0,0⟩, +⟨⟨1,179,523,true⟩,0,0,0⟩, +⟨⟨1,179,530,true⟩,0,0,0⟩, +⟨⟨1,179,531,true⟩,0,0,0⟩, +⟨⟨1,179,534,true⟩,0,0,0⟩, +⟨⟨1,179,535,true⟩,0,0,0⟩, +⟨⟨1,179,546,true⟩,0,0,0⟩, +⟨⟨1,179,547,true⟩,0,0,0⟩, +⟨⟨1,179,550,true⟩,0,0,0⟩, +⟨⟨1,179,551,true⟩,0,0,0⟩, +⟨⟨1,179,560,true⟩,0,0,0⟩, +⟨⟨1,179,561,true⟩,0,0,0⟩, +⟨⟨1,179,564,true⟩,0,0,0⟩, +⟨⟨1,179,565,true⟩,0,0,0⟩, +⟨⟨1,179,576,true⟩,0,0,0⟩, +⟨⟨1,179,577,true⟩,0,0,0⟩, +⟨⟨1,179,580,true⟩,0,0,0⟩, +⟨⟨1,179,581,true⟩,0,0,0⟩, +⟨⟨1,179,592,true⟩,0,0,0⟩, +⟨⟨1,179,593,true⟩,0,0,0⟩, +⟨⟨1,179,596,true⟩,0,0,0⟩, +⟨⟨1,179,597,true⟩,0,0,0⟩, +⟨⟨1,179,608,true⟩,0,0,0⟩, +⟨⟨1,179,609,true⟩,0,0,0⟩, +⟨⟨1,179,612,true⟩,0,0,0⟩, +⟨⟨1,179,613,true⟩,0,0,0⟩, +⟨⟨1,179,624,true⟩,0,0,0⟩, +⟨⟨1,179,625,true⟩,0,0,0⟩, +⟨⟨1,179,628,true⟩,0,0,0⟩, +⟨⟨1,179,629,true⟩,0,0,0⟩, +⟨⟨1,179,640,true⟩,0,0,0⟩, +⟨⟨1,179,641,true⟩,0,0,0⟩, +⟨⟨1,179,644,true⟩,0,0,0⟩, +⟨⟨1,179,645,true⟩,0,0,0⟩, +⟨⟨1,179,656,true⟩,0,0,0⟩, +⟨⟨1,179,657,true⟩,0,0,0⟩, +⟨⟨1,179,660,true⟩,0,0,0⟩, +⟨⟨1,179,661,true⟩,0,0,0⟩, +⟨⟨1,179,672,true⟩,0,0,0⟩, +⟨⟨1,179,673,true⟩,0,0,0⟩, +⟨⟨1,179,676,true⟩,0,0,0⟩, +⟨⟨1,179,677,true⟩,0,0,0⟩, +⟨⟨1,179,690,true⟩,0,0,0⟩, +⟨⟨1,179,691,true⟩,0,0,0⟩, +⟨⟨1,179,694,true⟩,0,0,0⟩, +⟨⟨1,179,695,true⟩,0,0,0⟩, +⟨⟨1,179,706,true⟩,0,0,0⟩, +⟨⟨1,179,707,true⟩,0,0,0⟩, +⟨⟨1,179,710,true⟩,0,0,0⟩, +⟨⟨1,179,711,true⟩,0,0,0⟩, +⟨⟨1,179,763,true⟩,0,0,0⟩, +⟨⟨1,179,790,true⟩,0,0,0⟩, +⟨⟨1,180,252,true⟩,0,0,0⟩, +⟨⟨1,180,258,true⟩,0,0,0⟩, +⟨⟨1,180,398,true⟩,0,0,0⟩, +⟨⟨1,180,403,true⟩,0,0,0⟩, +⟨⟨1,180,404,true⟩,0,0,0⟩, +⟨⟨1,180,414,true⟩,0,0,0⟩, +⟨⟨1,180,415,true⟩,0,0,0⟩, +⟨⟨1,180,512,true⟩,0,0,0⟩, +⟨⟨1,180,516,true⟩,0,0,0⟩, +⟨⟨1,180,518,true⟩,0,0,0⟩, +⟨⟨1,180,522,true⟩,0,0,0⟩, +⟨⟨1,180,523,true⟩,0,0,0⟩, +⟨⟨1,180,526,true⟩,0,0,0⟩, +⟨⟨1,180,527,true⟩,0,0,0⟩, +⟨⟨1,180,528,true⟩,0,0,0⟩, +⟨⟨1,180,529,true⟩,0,0,0⟩, +⟨⟨1,180,532,true⟩,0,0,0⟩, +⟨⟨1,180,533,true⟩,0,0,0⟩, +⟨⟨1,180,546,true⟩,0,0,0⟩, +⟨⟨1,180,547,true⟩,0,0,0⟩, +⟨⟨1,180,550,true⟩,0,0,0⟩, +⟨⟨1,180,551,true⟩,0,0,0⟩, +⟨⟨1,180,562,true⟩,0,0,0⟩, +⟨⟨1,180,563,true⟩,0,0,0⟩, +⟨⟨1,180,566,true⟩,0,0,0⟩, +⟨⟨1,180,567,true⟩,0,0,0⟩, +⟨⟨1,180,576,true⟩,0,0,0⟩, +⟨⟨1,180,577,true⟩,0,0,0⟩, +⟨⟨1,180,580,true⟩,0,0,0⟩, +⟨⟨1,180,581,true⟩,0,0,0⟩, +⟨⟨1,180,594,true⟩,0,0,0⟩, +⟨⟨1,180,595,true⟩,0,0,0⟩, +⟨⟨1,180,598,true⟩,0,0,0⟩, +⟨⟨1,180,599,true⟩,0,0,0⟩, +⟨⟨1,180,608,true⟩,0,0,0⟩, +⟨⟨1,180,609,true⟩,0,0,0⟩, +⟨⟨1,180,612,true⟩,0,0,0⟩, +⟨⟨1,180,613,true⟩,0,0,0⟩, +⟨⟨1,180,626,true⟩,0,0,0⟩, +⟨⟨1,180,627,true⟩,0,0,0⟩, +⟨⟨1,180,630,true⟩,0,0,0⟩, +⟨⟨1,180,631,true⟩,0,0,0⟩, +⟨⟨1,180,640,true⟩,0,0,0⟩, +⟨⟨1,180,641,true⟩,0,0,0⟩, +⟨⟨1,180,644,true⟩,0,0,0⟩, +⟨⟨1,180,645,true⟩,0,0,0⟩, +⟨⟨1,180,658,true⟩,0,0,0⟩, +⟨⟨1,180,659,true⟩,0,0,0⟩, +⟨⟨1,180,662,true⟩,0,0,0⟩] +def chunk19 : List Entry := [⟨⟨1,180,663,true⟩,0,0,0⟩, +⟨⟨1,180,672,true⟩,0,0,0⟩, +⟨⟨1,180,673,true⟩,0,0,0⟩, +⟨⟨1,180,676,true⟩,0,0,0⟩, +⟨⟨1,180,677,true⟩,0,0,0⟩, +⟨⟨1,180,688,true⟩,0,0,0⟩, +⟨⟨1,180,689,true⟩,0,0,0⟩, +⟨⟨1,180,692,true⟩,0,0,0⟩, +⟨⟨1,180,693,true⟩,0,0,0⟩, +⟨⟨1,180,706,true⟩,0,0,0⟩, +⟨⟨1,180,707,true⟩,0,0,0⟩, +⟨⟨1,180,710,true⟩,0,0,0⟩, +⟨⟨1,180,711,true⟩,0,0,0⟩, +⟨⟨1,180,762,true⟩,0,0,0⟩, +⟨⟨1,180,941,true⟩,0,0,0⟩, +⟨⟨1,181,252,true⟩,0,0,0⟩, +⟨⟨1,181,258,true⟩,0,0,0⟩, +⟨⟨1,181,396,true⟩,0,0,0⟩, +⟨⟨1,181,512,true⟩,0,0,0⟩, +⟨⟨1,181,514,true⟩,0,0,0⟩, +⟨⟨1,181,516,true⟩,0,0,0⟩, +⟨⟨1,181,518,true⟩,0,0,0⟩, +⟨⟨1,181,523,true⟩,0,0,0⟩, +⟨⟨1,181,528,true⟩,0,0,0⟩, +⟨⟨1,181,529,true⟩,0,0,0⟩, +⟨⟨1,181,532,true⟩,0,0,0⟩, +⟨⟨1,181,533,true⟩,0,0,0⟩, +⟨⟨1,181,544,true⟩,0,0,0⟩, +⟨⟨1,181,545,true⟩,0,0,0⟩, +⟨⟨1,181,548,true⟩,0,0,0⟩, +⟨⟨1,181,549,true⟩,0,0,0⟩, +⟨⟨1,181,562,true⟩,0,0,0⟩, +⟨⟨1,181,563,true⟩,0,0,0⟩, +⟨⟨1,181,566,true⟩,0,0,0⟩, +⟨⟨1,181,567,true⟩,0,0,0⟩, +⟨⟨1,181,578,true⟩,0,0,0⟩, +⟨⟨1,181,579,true⟩,0,0,0⟩, +⟨⟨1,181,582,true⟩,0,0,0⟩, +⟨⟨1,181,583,true⟩,0,0,0⟩, +⟨⟨1,181,592,true⟩,0,0,0⟩, +⟨⟨1,181,593,true⟩,0,0,0⟩, +⟨⟨1,181,596,true⟩,0,0,0⟩, +⟨⟨1,181,597,true⟩,0,0,0⟩, +⟨⟨1,181,608,true⟩,0,0,0⟩, +⟨⟨1,181,609,true⟩,0,0,0⟩, +⟨⟨1,181,612,true⟩,0,0,0⟩, +⟨⟨1,181,613,true⟩,0,0,0⟩, +⟨⟨1,181,624,true⟩,0,0,0⟩, +⟨⟨1,181,625,true⟩,0,0,0⟩, +⟨⟨1,181,628,true⟩,0,0,0⟩, +⟨⟨1,181,629,true⟩,0,0,0⟩, +⟨⟨1,181,640,true⟩,0,0,0⟩, +⟨⟨1,181,641,true⟩,0,0,0⟩, +⟨⟨1,181,644,true⟩,0,0,0⟩, +⟨⟨1,181,645,true⟩,0,0,0⟩, +⟨⟨1,181,658,true⟩,0,0,0⟩, +⟨⟨1,181,659,true⟩,0,0,0⟩, +⟨⟨1,181,662,true⟩,0,0,0⟩, +⟨⟨1,181,663,true⟩,0,0,0⟩, +⟨⟨1,181,674,true⟩,0,0,0⟩, +⟨⟨1,181,675,true⟩,0,0,0⟩, +⟨⟨1,181,678,true⟩,0,0,0⟩, +⟨⟨1,181,679,true⟩,0,0,0⟩, +⟨⟨1,181,688,true⟩,0,0,0⟩, +⟨⟨1,181,689,true⟩,0,0,0⟩, +⟨⟨1,181,692,true⟩,0,0,0⟩, +⟨⟨1,181,693,true⟩,0,0,0⟩, +⟨⟨1,181,704,true⟩,0,0,0⟩, +⟨⟨1,181,705,true⟩,0,0,0⟩, +⟨⟨1,181,708,true⟩,0,0,0⟩, +⟨⟨1,181,709,true⟩,0,0,0⟩, +⟨⟨1,181,762,true⟩,0,0,0⟩, +⟨⟨1,181,776,true⟩,0,0,0⟩, +⟨⟨1,182,252,true⟩,0,0,0⟩, +⟨⟨1,182,258,true⟩,0,0,0⟩, +⟨⟨1,182,394,true⟩,0,0,0⟩, +⟨⟨1,182,512,true⟩,0,0,0⟩, +⟨⟨1,182,514,true⟩,0,0,0⟩, +⟨⟨1,182,516,true⟩,0,0,0⟩, +⟨⟨1,182,518,true⟩,0,0,0⟩, +⟨⟨1,182,523,true⟩,0,0,0⟩, +⟨⟨1,182,528,true⟩,0,0,0⟩, +⟨⟨1,182,529,true⟩,0,0,0⟩, +⟨⟨1,182,532,true⟩,0,0,0⟩, +⟨⟨1,182,533,true⟩,0,0,0⟩, +⟨⟨1,182,544,true⟩,0,0,0⟩, +⟨⟨1,182,545,true⟩,0,0,0⟩, +⟨⟨1,182,548,true⟩,0,0,0⟩, +⟨⟨1,182,549,true⟩,0,0,0⟩, +⟨⟨1,182,560,true⟩,0,0,0⟩, +⟨⟨1,182,561,true⟩,0,0,0⟩, +⟨⟨1,182,564,true⟩,0,0,0⟩, +⟨⟨1,182,565,true⟩,0,0,0⟩, +⟨⟨1,182,576,true⟩,0,0,0⟩, +⟨⟨1,182,577,true⟩,0,0,0⟩, +⟨⟨1,182,580,true⟩,0,0,0⟩, +⟨⟨1,182,581,true⟩,0,0,0⟩, +⟨⟨1,182,594,true⟩,0,0,0⟩, +⟨⟨1,182,595,true⟩,0,0,0⟩, +⟨⟨1,182,598,true⟩,0,0,0⟩, +⟨⟨1,182,599,true⟩,0,0,0⟩, +⟨⟨1,182,610,true⟩,0,0,0⟩, +⟨⟨1,182,611,true⟩,0,0,0⟩, +⟨⟨1,182,614,true⟩,0,0,0⟩, +⟨⟨1,182,615,true⟩,0,0,0⟩, +⟨⟨1,182,626,true⟩,0,0,0⟩, +⟨⟨1,182,627,true⟩,0,0,0⟩, +⟨⟨1,182,630,true⟩,0,0,0⟩, +⟨⟨1,182,631,true⟩,0,0,0⟩, +⟨⟨1,182,642,true⟩,0,0,0⟩, +⟨⟨1,182,643,true⟩,0,0,0⟩, +⟨⟨1,182,646,true⟩,0,0,0⟩, +⟨⟨1,182,647,true⟩,0,0,0⟩, +⟨⟨1,182,656,true⟩,0,0,0⟩, +⟨⟨1,182,657,true⟩,0,0,0⟩, +⟨⟨1,182,660,true⟩,0,0,0⟩, +⟨⟨1,182,661,true⟩,0,0,0⟩, +⟨⟨1,182,672,true⟩,0,0,0⟩, +⟨⟨1,182,673,true⟩,0,0,0⟩, +⟨⟨1,182,676,true⟩,0,0,0⟩, +⟨⟨1,182,677,true⟩,0,0,0⟩, +⟨⟨1,182,688,true⟩,0,0,0⟩, +⟨⟨1,182,689,true⟩,0,0,0⟩, +⟨⟨1,182,692,true⟩,0,0,0⟩, +⟨⟨1,182,693,true⟩,0,0,0⟩, +⟨⟨1,182,704,true⟩,0,0,0⟩, +⟨⟨1,182,705,true⟩,0,0,0⟩, +⟨⟨1,182,708,true⟩,0,0,0⟩, +⟨⟨1,182,709,true⟩,0,0,0⟩, +⟨⟨1,182,762,true⟩,0,0,0⟩, +⟨⟨1,182,776,true⟩,0,0,0⟩, +⟨⟨1,182,790,true⟩,0,0,0⟩, +⟨⟨1,183,252,true⟩,0,0,0⟩, +⟨⟨1,183,258,true⟩,0,0,0⟩, +⟨⟨1,183,392,true⟩,0,0,0⟩, +⟨⟨1,183,402,true⟩,0,0,0⟩, +⟨⟨1,183,405,true⟩,0,0,0⟩, +⟨⟨1,183,406,true⟩,0,0,0⟩, +⟨⟨1,183,407,true⟩,0,0,0⟩, +⟨⟨1,183,408,true⟩,0,0,0⟩, +⟨⟨1,183,409,true⟩,0,0,0⟩, +⟨⟨1,183,411,true⟩,0,0,0⟩, +⟨⟨1,183,412,true⟩,0,0,0⟩, +⟨⟨1,183,512,true⟩,0,0,0⟩, +⟨⟨1,183,516,true⟩,0,0,0⟩, +⟨⟨1,183,527,true⟩,0,0,0⟩, +⟨⟨1,183,528,true⟩,0,0,0⟩, +⟨⟨1,183,529,true⟩,0,0,0⟩, +⟨⟨1,183,532,true⟩,0,0,0⟩, +⟨⟨1,183,533,true⟩,0,0,0⟩, +⟨⟨1,183,546,true⟩,0,0,0⟩, +⟨⟨1,183,547,true⟩,0,0,0⟩, +⟨⟨1,183,550,true⟩,0,0,0⟩, +⟨⟨1,183,551,true⟩,0,0,0⟩, +⟨⟨1,183,560,true⟩,0,0,0⟩, +⟨⟨1,183,561,true⟩,0,0,0⟩, +⟨⟨1,183,564,true⟩,0,0,0⟩, +⟨⟨1,183,565,true⟩,0,0,0⟩, +⟨⟨1,183,578,true⟩,0,0,0⟩, +⟨⟨1,183,579,true⟩,0,0,0⟩, +⟨⟨1,183,582,true⟩,0,0,0⟩, +⟨⟨1,183,583,true⟩,0,0,0⟩, +⟨⟨1,183,592,true⟩,0,0,0⟩, +⟨⟨1,183,593,true⟩,0,0,0⟩, +⟨⟨1,183,596,true⟩,0,0,0⟩, +⟨⟨1,183,597,true⟩,0,0,0⟩, +⟨⟨1,183,610,true⟩,0,0,0⟩, +⟨⟨1,183,611,true⟩,0,0,0⟩, +⟨⟨1,183,614,true⟩,0,0,0⟩, +⟨⟨1,183,615,true⟩,0,0,0⟩, +⟨⟨1,183,624,true⟩,0,0,0⟩, +⟨⟨1,183,625,true⟩,0,0,0⟩, +⟨⟨1,183,628,true⟩,0,0,0⟩, +⟨⟨1,183,629,true⟩,0,0,0⟩, +⟨⟨1,183,642,true⟩,0,0,0⟩, +⟨⟨1,183,643,true⟩,0,0,0⟩, +⟨⟨1,183,646,true⟩,0,0,0⟩, +⟨⟨1,183,647,true⟩,0,0,0⟩, +⟨⟨1,183,656,true⟩,0,0,0⟩, +⟨⟨1,183,657,true⟩,0,0,0⟩, +⟨⟨1,183,660,true⟩,0,0,0⟩, +⟨⟨1,183,661,true⟩,0,0,0⟩, +⟨⟨1,183,674,true⟩,0,0,0⟩, +⟨⟨1,183,675,true⟩,0,0,0⟩, +⟨⟨1,183,678,true⟩,0,0,0⟩, +⟨⟨1,183,679,true⟩,0,0,0⟩, +⟨⟨1,183,688,true⟩,0,0,0⟩, +⟨⟨1,183,689,true⟩,0,0,0⟩, +⟨⟨1,183,692,true⟩,0,0,0⟩, +⟨⟨1,183,693,true⟩,0,0,0⟩, +⟨⟨1,183,706,true⟩,0,0,0⟩, +⟨⟨1,183,707,true⟩,0,0,0⟩, +⟨⟨1,183,710,true⟩,0,0,0⟩, +⟨⟨1,183,711,true⟩,0,0,0⟩, +⟨⟨1,183,762,true⟩,0,0,0⟩, +⟨⟨1,183,790,true⟩,0,0,0⟩, +⟨⟨1,183,950,true⟩,0,0,0⟩, +⟨⟨1,184,269,true⟩,0,0,0⟩, +⟨⟨1,184,275,true⟩,0,0,0⟩, +⟨⟨1,184,281,true⟩,0,0,0⟩] +def chunk20 : List Entry := [⟨⟨1,184,287,true⟩,0,0,0⟩, +⟨⟨1,184,407,true⟩,0,0,0⟩, +⟨⟨1,184,532,true⟩,0,0,0⟩, +⟨⟨1,184,534,true⟩,0,0,0⟩, +⟨⟨1,184,548,true⟩,0,0,0⟩, +⟨⟨1,184,550,true⟩,0,0,0⟩, +⟨⟨1,184,564,true⟩,0,0,0⟩, +⟨⟨1,184,566,true⟩,0,0,0⟩, +⟨⟨1,184,580,true⟩,0,0,0⟩, +⟨⟨1,184,582,true⟩,0,0,0⟩, +⟨⟨1,184,596,true⟩,0,0,0⟩, +⟨⟨1,184,598,true⟩,0,0,0⟩, +⟨⟨1,184,612,true⟩,0,0,0⟩, +⟨⟨1,184,614,true⟩,0,0,0⟩, +⟨⟨1,184,628,true⟩,0,0,0⟩, +⟨⟨1,184,630,true⟩,0,0,0⟩, +⟨⟨1,184,644,true⟩,0,0,0⟩, +⟨⟨1,184,646,true⟩,0,0,0⟩, +⟨⟨1,184,660,true⟩,0,0,0⟩, +⟨⟨1,184,662,true⟩,0,0,0⟩, +⟨⟨1,184,676,true⟩,0,0,0⟩, +⟨⟨1,184,678,true⟩,0,0,0⟩, +⟨⟨1,184,692,true⟩,0,0,0⟩, +⟨⟨1,184,694,true⟩,0,0,0⟩, +⟨⟨1,184,708,true⟩,0,0,0⟩, +⟨⟨1,184,710,true⟩,0,0,0⟩, +⟨⟨1,184,720,true⟩,0,0,0⟩, +⟨⟨1,184,722,true⟩,0,0,0⟩, +⟨⟨1,184,724,true⟩,0,0,0⟩, +⟨⟨1,184,726,true⟩,0,0,0⟩, +⟨⟨1,184,907,true⟩,0,0,0⟩, +⟨⟨1,185,269,true⟩,0,0,0⟩, +⟨⟨1,185,275,true⟩,0,0,0⟩, +⟨⟨1,185,281,true⟩,0,0,0⟩, +⟨⟨1,185,287,true⟩,0,0,0⟩, +⟨⟨1,185,386,true⟩,0,0,0⟩, +⟨⟨1,185,388,true⟩,0,0,0⟩, +⟨⟨1,185,392,true⟩,0,0,0⟩, +⟨⟨1,185,398,true⟩,0,0,0⟩, +⟨⟨1,185,405,true⟩,0,0,0⟩, +⟨⟨1,185,532,true⟩,0,0,0⟩, +⟨⟨1,185,534,true⟩,0,0,0⟩, +⟨⟨1,185,548,true⟩,0,0,0⟩, +⟨⟨1,185,550,true⟩,0,0,0⟩, +⟨⟨1,185,564,true⟩,0,0,0⟩, +⟨⟨1,185,566,true⟩,0,0,0⟩, +⟨⟨1,185,580,true⟩,0,0,0⟩, +⟨⟨1,185,582,true⟩,0,0,0⟩, +⟨⟨1,185,592,true⟩,0,0,0⟩, +⟨⟨1,185,594,true⟩,0,0,0⟩, +⟨⟨1,185,608,true⟩,0,0,0⟩, +⟨⟨1,185,610,true⟩,0,0,0⟩, +⟨⟨1,185,628,true⟩,0,0,0⟩, +⟨⟨1,185,630,true⟩,0,0,0⟩, +⟨⟨1,185,644,true⟩,0,0,0⟩, +⟨⟨1,185,646,true⟩,0,0,0⟩, +⟨⟨1,185,656,true⟩,0,0,0⟩, +⟨⟨1,185,658,true⟩,0,0,0⟩, +⟨⟨1,185,672,true⟩,0,0,0⟩, +⟨⟨1,185,674,true⟩,0,0,0⟩, +⟨⟨1,185,688,true⟩,0,0,0⟩, +⟨⟨1,185,690,true⟩,0,0,0⟩, +⟨⟨1,185,704,true⟩,0,0,0⟩, +⟨⟨1,185,706,true⟩,0,0,0⟩, +⟨⟨1,185,720,true⟩,0,0,0⟩, +⟨⟨1,185,725,true⟩,0,0,0⟩, +⟨⟨1,185,726,true⟩,0,0,0⟩, +⟨⟨1,185,730,true⟩,0,0,0⟩, +⟨⟨1,185,735,true⟩,0,0,0⟩, +⟨⟨1,185,807,true⟩,0,0,0⟩, +⟨⟨1,185,821,true⟩,0,0,0⟩, +⟨⟨1,185,905,true⟩,0,0,0⟩, +⟨⟨1,185,960,true⟩,0,0,0⟩, +⟨⟨1,185,977,true⟩,0,0,0⟩, +⟨⟨1,186,269,true⟩,0,0,0⟩, +⟨⟨1,186,275,true⟩,0,0,0⟩, +⟨⟨1,186,281,true⟩,0,0,0⟩, 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+⟨⟨1,186,849,true⟩,0,0,0⟩, +⟨⟨1,186,905,true⟩,0,0,0⟩, +⟨⟨1,186,959,true⟩,0,0,0⟩, +⟨⟨1,187,269,true⟩,0,0,0⟩, +⟨⟨1,187,275,true⟩,0,0,0⟩, +⟨⟨1,187,281,true⟩,0,0,0⟩, +⟨⟨1,187,287,true⟩,0,0,0⟩, +⟨⟨1,187,401,true⟩,0,0,0⟩, +⟨⟨1,187,532,true⟩,0,0,0⟩, +⟨⟨1,187,534,true⟩,0,0,0⟩, +⟨⟨1,187,548,true⟩,0,0,0⟩, +⟨⟨1,187,550,true⟩,0,0,0⟩, +⟨⟨1,187,560,true⟩,0,0,0⟩, +⟨⟨1,187,562,true⟩,0,0,0⟩, +⟨⟨1,187,576,true⟩,0,0,0⟩, +⟨⟨1,187,578,true⟩,0,0,0⟩, +⟨⟨1,187,592,true⟩,0,0,0⟩, +⟨⟨1,187,594,true⟩,0,0,0⟩, +⟨⟨1,187,608,true⟩,0,0,0⟩, +⟨⟨1,187,610,true⟩,0,0,0⟩, +⟨⟨1,187,624,true⟩,0,0,0⟩, +⟨⟨1,187,626,true⟩,0,0,0⟩, +⟨⟨1,187,640,true⟩,0,0,0⟩, +⟨⟨1,187,642,true⟩,0,0,0⟩, +⟨⟨1,187,656,true⟩,0,0,0⟩, +⟨⟨1,187,658,true⟩,0,0,0⟩, +⟨⟨1,187,672,true⟩,0,0,0⟩, +⟨⟨1,187,674,true⟩,0,0,0⟩, +⟨⟨1,187,692,true⟩,0,0,0⟩, +⟨⟨1,187,694,true⟩,0,0,0⟩, +⟨⟨1,187,708,true⟩,0,0,0⟩, +⟨⟨1,187,710,true⟩,0,0,0⟩, +⟨⟨1,187,720,true⟩,0,0,0⟩, +⟨⟨1,187,722,true⟩,0,0,0⟩, +⟨⟨1,187,724,true⟩,0,0,0⟩, +⟨⟨1,187,726,true⟩,0,0,0⟩, +⟨⟨1,187,779,true⟩,0,0,0⟩, +⟨⟨1,187,793,true⟩,0,0,0⟩, +⟨⟨1,187,807,true⟩,0,0,0⟩, +⟨⟨1,187,821,true⟩,0,0,0⟩, +⟨⟨1,187,835,true⟩,0,0,0⟩, +⟨⟨1,187,849,true⟩,0,0,0⟩, +⟨⟨1,187,907,true⟩,0,0,0⟩, +⟨⟨1,188,269,true⟩,0,0,0⟩, +⟨⟨1,188,275,true⟩,0,0,0⟩, +⟨⟨1,188,281,true⟩,0,0,0⟩, +⟨⟨1,188,287,true⟩,0,0,0⟩, +⟨⟨1,188,386,true⟩,0,0,0⟩, +⟨⟨1,188,387,true⟩,0,0,0⟩, +⟨⟨1,188,392,true⟩,0,0,0⟩, +⟨⟨1,188,399,true⟩,0,0,0⟩, +⟨⟨1,188,414,true⟩,0,0,0⟩, +⟨⟨1,188,528,true⟩,0,0,0⟩, +⟨⟨1,188,530,true⟩,0,0,0⟩, +⟨⟨1,188,544,true⟩,0,0,0⟩, +⟨⟨1,188,546,true⟩,0,0,0⟩, +⟨⟨1,188,564,true⟩,0,0,0⟩, +⟨⟨1,188,566,true⟩,0,0,0⟩, +⟨⟨1,188,580,true⟩,0,0,0⟩, +⟨⟨1,188,582,true⟩,0,0,0⟩, +⟨⟨1,188,596,true⟩,0,0,0⟩, +⟨⟨1,188,598,true⟩,0,0,0⟩, +⟨⟨1,188,612,true⟩,0,0,0⟩, +⟨⟨1,188,614,true⟩,0,0,0⟩, +⟨⟨1,188,624,true⟩,0,0,0⟩, +⟨⟨1,188,626,true⟩,0,0,0⟩, +⟨⟨1,188,640,true⟩,0,0,0⟩, +⟨⟨1,188,642,true⟩,0,0,0⟩, +⟨⟨1,188,656,true⟩,0,0,0⟩, +⟨⟨1,188,658,true⟩,0,0,0⟩, +⟨⟨1,188,672,true⟩,0,0,0⟩, +⟨⟨1,188,674,true⟩,0,0,0⟩, +⟨⟨1,188,692,true⟩,0,0,0⟩, +⟨⟨1,188,694,true⟩,0,0,0⟩, +⟨⟨1,188,708,true⟩,0,0,0⟩, +⟨⟨1,188,710,true⟩,0,0,0⟩, +⟨⟨1,188,720,true⟩,0,0,0⟩, +⟨⟨1,188,722,true⟩,0,0,0⟩, +⟨⟨1,188,725,true⟩,0,0,0⟩, +⟨⟨1,188,726,true⟩,0,0,0⟩, +⟨⟨1,188,731,true⟩,0,0,0⟩, +⟨⟨1,188,734,true⟩,0,0,0⟩, +⟨⟨1,188,765,true⟩,0,0,0⟩, +⟨⟨1,188,835,true⟩,0,0,0⟩, +⟨⟨1,188,849,true⟩,0,0,0⟩, +⟨⟨1,188,907,true⟩,0,0,0⟩] +def chunk21 : List Entry := [⟨⟨1,188,959,true⟩,0,0,0⟩, +⟨⟨1,188,977,true⟩,0,0,0⟩, +⟨⟨1,189,269,true⟩,0,0,0⟩, +⟨⟨1,189,275,true⟩,0,0,0⟩, +⟨⟨1,189,281,true⟩,0,0,0⟩, +⟨⟨1,189,287,true⟩,0,0,0⟩, +⟨⟨1,189,412,true⟩,0,0,0⟩, +⟨⟨1,189,528,true⟩,0,0,0⟩, +⟨⟨1,189,530,true⟩,0,0,0⟩, +⟨⟨1,189,544,true⟩,0,0,0⟩, +⟨⟨1,189,546,true⟩,0,0,0⟩, +⟨⟨1,189,564,true⟩,0,0,0⟩, +⟨⟨1,189,566,true⟩,0,0,0⟩, +⟨⟨1,189,580,true⟩,0,0,0⟩, +⟨⟨1,189,582,true⟩,0,0,0⟩, +⟨⟨1,189,592,true⟩,0,0,0⟩, +⟨⟨1,189,594,true⟩,0,0,0⟩, +⟨⟨1,189,608,true⟩,0,0,0⟩, +⟨⟨1,189,610,true⟩,0,0,0⟩, +⟨⟨1,189,624,true⟩,0,0,0⟩, +⟨⟨1,189,626,true⟩,0,0,0⟩, +⟨⟨1,189,640,true⟩,0,0,0⟩, +⟨⟨1,189,642,true⟩,0,0,0⟩, +⟨⟨1,189,660,true⟩,0,0,0⟩, 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+⟨⟨1,192,630,true⟩,0,0,0⟩, +⟨⟨1,192,631,true⟩,0,0,0⟩, +⟨⟨1,192,640,true⟩,0,0,0⟩, +⟨⟨1,192,642,true⟩,0,0,0⟩, +⟨⟨1,192,644,true⟩,0,0,0⟩, +⟨⟨1,192,646,true⟩,0,0,0⟩, +⟨⟨1,192,669,true⟩,0,0,0⟩, +⟨⟨1,192,671,true⟩,0,0,0⟩, +⟨⟨1,192,681,true⟩,0,0,0⟩, +⟨⟨1,192,683,true⟩,0,0,0⟩, +⟨⟨1,192,701,true⟩,0,0,0⟩, +⟨⟨1,192,703,true⟩,0,0,0⟩, +⟨⟨1,192,713,true⟩,0,0,0⟩, +⟨⟨1,192,715,true⟩,0,0,0⟩, +⟨⟨1,192,915,true⟩,0,0,0⟩, +⟨⟨1,193,249,true⟩,0,0,0⟩, +⟨⟨1,193,255,true⟩,0,0,0⟩, +⟨⟨1,193,272,true⟩,0,0,0⟩, +⟨⟨1,193,278,true⟩,0,0,0⟩, +⟨⟨1,193,308,true⟩,0,0,0⟩, +⟨⟨1,193,310,true⟩,0,0,0⟩, +⟨⟨1,193,316,true⟩,0,0,0⟩, +⟨⟨1,193,318,true⟩,0,0,0⟩, +⟨⟨1,193,321,true⟩,0,0,0⟩, +⟨⟨1,193,325,true⟩,0,0,0⟩, +⟨⟨1,193,329,true⟩,0,0,0⟩, +⟨⟨1,193,333,true⟩,0,0,0⟩, +⟨⟨1,193,340,true⟩,0,0,0⟩] +def chunk22 : List Entry := [⟨⟨1,193,342,true⟩,0,0,0⟩, +⟨⟨1,193,348,true⟩,0,0,0⟩, +⟨⟨1,193,350,true⟩,0,0,0⟩, +⟨⟨1,193,353,true⟩,0,0,0⟩, +⟨⟨1,193,357,true⟩,0,0,0⟩, +⟨⟨1,193,361,true⟩,0,0,0⟩, +⟨⟨1,193,365,true⟩,0,0,0⟩, +⟨⟨1,193,371,true⟩,0,0,0⟩, 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+⟨⟨1,195,357,true⟩,0,0,0⟩, +⟨⟨1,195,361,true⟩,0,0,0⟩, +⟨⟨1,195,365,true⟩,0,0,0⟩, +⟨⟨1,195,387,true⟩,0,0,0⟩, +⟨⟨1,195,391,true⟩,0,0,0⟩, +⟨⟨1,195,395,true⟩,0,0,0⟩, +⟨⟨1,195,399,true⟩,0,0,0⟩, +⟨⟨1,195,403,true⟩,0,0,0⟩, +⟨⟨1,195,407,true⟩,0,0,0⟩, +⟨⟨1,195,411,true⟩,0,0,0⟩, +⟨⟨1,195,415,true⟩,0,0,0⟩, +⟨⟨1,195,417,true⟩,0,0,0⟩, +⟨⟨1,195,433,true⟩,0,0,0⟩, +⟨⟨1,195,435,true⟩,0,0,0⟩, +⟨⟨1,195,445,true⟩,0,0,0⟩, +⟨⟨1,195,447,true⟩,0,0,0⟩, +⟨⟨1,195,448,true⟩,0,0,0⟩, +⟨⟨1,195,452,true⟩,0,0,0⟩, +⟨⟨1,195,458,true⟩,0,0,0⟩, +⟨⟨1,195,462,true⟩,0,0,0⟩, +⟨⟨1,195,465,true⟩,0,0,0⟩, +⟨⟨1,195,467,true⟩,0,0,0⟩, +⟨⟨1,195,477,true⟩,0,0,0⟩, +⟨⟨1,195,479,true⟩,0,0,0⟩, +⟨⟨1,195,480,true⟩,0,0,0⟩, +⟨⟨1,195,484,true⟩,0,0,0⟩, +⟨⟨1,195,490,true⟩,0,0,0⟩, +⟨⟨1,195,494,true⟩,0,0,0⟩, +⟨⟨1,195,612,true⟩,0,0,0⟩, +⟨⟨1,195,614,true⟩,0,0,0⟩, +⟨⟨1,195,626,true⟩,0,0,0⟩, +⟨⟨1,195,627,true⟩,0,0,0⟩, +⟨⟨1,195,630,true⟩,0,0,0⟩, +⟨⟨1,195,631,true⟩,0,0,0⟩, +⟨⟨1,195,640,true⟩,0,0,0⟩, +⟨⟨1,195,642,true⟩,0,0,0⟩, +⟨⟨1,195,644,true⟩,0,0,0⟩, +⟨⟨1,195,646,true⟩,0,0,0⟩, +⟨⟨1,195,668,true⟩,0,0,0⟩, +⟨⟨1,195,670,true⟩,0,0,0⟩, +⟨⟨1,195,680,true⟩,0,0,0⟩, +⟨⟨1,195,682,true⟩,0,0,0⟩, +⟨⟨1,195,700,true⟩,0,0,0⟩, +⟨⟨1,195,702,true⟩,0,0,0⟩] +def chunk23 : List Entry := [⟨⟨1,195,712,true⟩,0,0,0⟩, +⟨⟨1,195,714,true⟩,0,0,0⟩, +⟨⟨1,195,770,true⟩,0,0,0⟩, +⟨⟨1,195,872,true⟩,0,0,0⟩, +⟨⟨1,195,900,true⟩,0,0,0⟩, +⟨⟨1,195,914,true⟩,0,0,0⟩, +⟨⟨1,196,249,true⟩,0,0,0⟩, +⟨⟨1,196,255,true⟩,0,0,0⟩, +⟨⟨1,196,272,true⟩,0,0,0⟩, +⟨⟨1,196,278,true⟩,0,0,0⟩, +⟨⟨1,196,308,true⟩,0,0,0⟩, +⟨⟨1,196,310,true⟩,0,0,0⟩, +⟨⟨1,196,316,true⟩,0,0,0⟩, +⟨⟨1,196,318,true⟩,0,0,0⟩, +⟨⟨1,196,323,true⟩,0,0,0⟩, +⟨⟨1,196,327,true⟩,0,0,0⟩, +⟨⟨1,196,331,true⟩,0,0,0⟩, +⟨⟨1,196,335,true⟩,0,0,0⟩, +⟨⟨1,196,340,true⟩,0,0,0⟩, +⟨⟨1,196,342,true⟩,0,0,0⟩, +⟨⟨1,196,348,true⟩,0,0,0⟩, +⟨⟨1,196,350,true⟩,0,0,0⟩, +⟨⟨1,196,355,true⟩,0,0,0⟩, +⟨⟨1,196,359,true⟩,0,0,0⟩, +⟨⟨1,196,363,true⟩,0,0,0⟩, +⟨⟨1,196,367,true⟩,0,0,0⟩, +⟨⟨1,196,370,true⟩,0,0,0⟩, +⟨⟨1,196,371,true⟩,0,0,0⟩, +⟨⟨1,196,374,true⟩,0,0,0⟩, +⟨⟨1,196,375,true⟩,0,0,0⟩, +⟨⟨1,196,376,true⟩,0,0,0⟩, +⟨⟨1,196,379,true⟩,0,0,0⟩, +⟨⟨1,196,380,true⟩,0,0,0⟩, +⟨⟨1,196,383,true⟩,0,0,0⟩, +⟨⟨1,196,387,true⟩,0,0,0⟩, +⟨⟨1,196,391,true⟩,0,0,0⟩, +⟨⟨1,196,395,true⟩,0,0,0⟩, +⟨⟨1,196,399,true⟩,0,0,0⟩, +⟨⟨1,196,401,true⟩,0,0,0⟩, +⟨⟨1,196,405,true⟩,0,0,0⟩, +⟨⟨1,196,409,true⟩,0,0,0⟩, +⟨⟨1,196,413,true⟩,0,0,0⟩, +⟨⟨1,196,431,true⟩,0,0,0⟩, +⟨⟨1,196,433,true⟩,0,0,0⟩, +⟨⟨1,196,435,true⟩,0,0,0⟩, +⟨⟨1,196,445,true⟩,0,0,0⟩, +⟨⟨1,196,447,true⟩,0,0,0⟩, +⟨⟨1,196,448,true⟩,0,0,0⟩, +⟨⟨1,196,452,true⟩,0,0,0⟩, +⟨⟨1,196,458,true⟩,0,0,0⟩, +⟨⟨1,196,462,true⟩,0,0,0⟩, +⟨⟨1,196,465,true⟩,0,0,0⟩, +⟨⟨1,196,467,true⟩,0,0,0⟩, +⟨⟨1,196,477,true⟩,0,0,0⟩, +⟨⟨1,196,479,true⟩,0,0,0⟩, +⟨⟨1,196,480,true⟩,0,0,0⟩, +⟨⟨1,196,484,true⟩,0,0,0⟩, +⟨⟨1,196,490,true⟩,0,0,0⟩, +⟨⟨1,196,494,true⟩,0,0,0⟩, +⟨⟨1,196,608,true⟩,0,0,0⟩, +⟨⟨1,196,610,true⟩,0,0,0⟩, +⟨⟨1,196,626,true⟩,0,0,0⟩, +⟨⟨1,196,627,true⟩,0,0,0⟩, +⟨⟨1,196,630,true⟩,0,0,0⟩, +⟨⟨1,196,631,true⟩,0,0,0⟩, +⟨⟨1,196,640,true⟩,0,0,0⟩, +⟨⟨1,196,642,true⟩,0,0,0⟩, +⟨⟨1,196,645,true⟩,0,0,0⟩, +⟨⟨1,196,654,true⟩,0,0,0⟩, +⟨⟨1,196,655,true⟩,0,0,0⟩, +⟨⟨1,196,668,true⟩,0,0,0⟩, +⟨⟨1,196,670,true⟩,0,0,0⟩, +⟨⟨1,196,680,true⟩,0,0,0⟩, +⟨⟨1,196,682,true⟩,0,0,0⟩, +⟨⟨1,196,700,true⟩,0,0,0⟩, +⟨⟨1,196,702,true⟩,0,0,0⟩, +⟨⟨1,196,712,true⟩,0,0,0⟩, +⟨⟨1,196,714,true⟩,0,0,0⟩, +⟨⟨1,196,820,true⟩,0,0,0⟩, +⟨⟨1,196,872,true⟩,0,0,0⟩, +⟨⟨1,196,900,true⟩,0,0,0⟩, +⟨⟨1,196,914,true⟩,0,0,0⟩, +⟨⟨1,196,979,true⟩,0,0,0⟩, +⟨⟨1,196,983,true⟩,0,0,0⟩, +⟨⟨1,197,249,true⟩,0,0,0⟩, +⟨⟨1,197,255,true⟩,0,0,0⟩, +⟨⟨1,197,272,true⟩,0,0,0⟩, +⟨⟨1,197,278,true⟩,0,0,0⟩, +⟨⟨1,197,308,true⟩,0,0,0⟩, +⟨⟨1,197,310,true⟩,0,0,0⟩, +⟨⟨1,197,316,true⟩,0,0,0⟩, +⟨⟨1,197,318,true⟩,0,0,0⟩, +⟨⟨1,197,321,true⟩,0,0,0⟩, +⟨⟨1,197,325,true⟩,0,0,0⟩, +⟨⟨1,197,329,true⟩,0,0,0⟩, +⟨⟨1,197,333,true⟩,0,0,0⟩, +⟨⟨1,197,340,true⟩,0,0,0⟩, +⟨⟨1,197,342,true⟩,0,0,0⟩, +⟨⟨1,197,348,true⟩,0,0,0⟩, +⟨⟨1,197,350,true⟩,0,0,0⟩, +⟨⟨1,197,353,true⟩,0,0,0⟩, +⟨⟨1,197,357,true⟩,0,0,0⟩, +⟨⟨1,197,361,true⟩,0,0,0⟩, +⟨⟨1,197,365,true⟩,0,0,0⟩, +⟨⟨1,197,385,true⟩,0,0,0⟩, +⟨⟨1,197,389,true⟩,0,0,0⟩, +⟨⟨1,197,393,true⟩,0,0,0⟩, +⟨⟨1,197,397,true⟩,0,0,0⟩, +⟨⟨1,197,401,true⟩,0,0,0⟩, +⟨⟨1,197,405,true⟩,0,0,0⟩, +⟨⟨1,197,409,true⟩,0,0,0⟩, +⟨⟨1,197,413,true⟩,0,0,0⟩, +⟨⟨1,197,428,true⟩,0,0,0⟩, +⟨⟨1,197,433,true⟩,0,0,0⟩, +⟨⟨1,197,435,true⟩,0,0,0⟩, +⟨⟨1,197,445,true⟩,0,0,0⟩, +⟨⟨1,197,447,true⟩,0,0,0⟩, +⟨⟨1,197,450,true⟩,0,0,0⟩, +⟨⟨1,197,454,true⟩,0,0,0⟩, +⟨⟨1,197,456,true⟩,0,0,0⟩, +⟨⟨1,197,460,true⟩,0,0,0⟩, +⟨⟨1,197,465,true⟩,0,0,0⟩, +⟨⟨1,197,467,true⟩,0,0,0⟩, +⟨⟨1,197,477,true⟩,0,0,0⟩, +⟨⟨1,197,479,true⟩,0,0,0⟩, +⟨⟨1,197,482,true⟩,0,0,0⟩, +⟨⟨1,197,486,true⟩,0,0,0⟩, +⟨⟨1,197,488,true⟩,0,0,0⟩, +⟨⟨1,197,492,true⟩,0,0,0⟩, +⟨⟨1,197,608,true⟩,0,0,0⟩, +⟨⟨1,197,610,true⟩,0,0,0⟩, +⟨⟨1,197,624,true⟩,0,0,0⟩, +⟨⟨1,197,625,true⟩,0,0,0⟩, +⟨⟨1,197,628,true⟩,0,0,0⟩, +⟨⟨1,197,629,true⟩,0,0,0⟩, +⟨⟨1,197,640,true⟩,0,0,0⟩, +⟨⟨1,197,642,true⟩,0,0,0⟩, +⟨⟨1,197,644,true⟩,0,0,0⟩, +⟨⟨1,197,646,true⟩,0,0,0⟩, +⟨⟨1,197,668,true⟩,0,0,0⟩, +⟨⟨1,197,670,true⟩,0,0,0⟩, +⟨⟨1,197,681,true⟩,0,0,0⟩, +⟨⟨1,197,683,true⟩,0,0,0⟩, +⟨⟨1,197,700,true⟩,0,0,0⟩, +⟨⟨1,197,702,true⟩,0,0,0⟩, +⟨⟨1,197,713,true⟩,0,0,0⟩, +⟨⟨1,197,715,true⟩,0,0,0⟩, +⟨⟨1,197,770,true⟩,0,0,0⟩, +⟨⟨1,197,820,true⟩,0,0,0⟩, +⟨⟨1,197,846,true⟩,0,0,0⟩, +⟨⟨1,197,872,true⟩,0,0,0⟩, +⟨⟨1,197,900,true⟩,0,0,0⟩, +⟨⟨1,197,915,true⟩,0,0,0⟩, +⟨⟨1,197,928,true⟩,0,0,0⟩, +⟨⟨1,198,249,true⟩,0,0,0⟩, +⟨⟨1,198,255,true⟩,0,0,0⟩, +⟨⟨1,198,272,true⟩,0,0,0⟩, +⟨⟨1,198,278,true⟩,0,0,0⟩, +⟨⟨1,198,304,true⟩,0,0,0⟩, +⟨⟨1,198,306,true⟩,0,0,0⟩, +⟨⟨1,198,312,true⟩,0,0,0⟩, +⟨⟨1,198,314,true⟩,0,0,0⟩, +⟨⟨1,198,323,true⟩,0,0,0⟩, +⟨⟨1,198,327,true⟩,0,0,0⟩, +⟨⟨1,198,331,true⟩,0,0,0⟩, +⟨⟨1,198,335,true⟩,0,0,0⟩, +⟨⟨1,198,336,true⟩,0,0,0⟩, +⟨⟨1,198,338,true⟩,0,0,0⟩, +⟨⟨1,198,344,true⟩,0,0,0⟩, +⟨⟨1,198,346,true⟩,0,0,0⟩, +⟨⟨1,198,355,true⟩,0,0,0⟩, +⟨⟨1,198,359,true⟩,0,0,0⟩, +⟨⟨1,198,363,true⟩,0,0,0⟩, +⟨⟨1,198,367,true⟩,0,0,0⟩, +⟨⟨1,198,385,true⟩,0,0,0⟩, +⟨⟨1,198,389,true⟩,0,0,0⟩, +⟨⟨1,198,393,true⟩,0,0,0⟩, +⟨⟨1,198,397,true⟩,0,0,0⟩, +⟨⟨1,198,401,true⟩,0,0,0⟩, +⟨⟨1,198,405,true⟩,0,0,0⟩, +⟨⟨1,198,409,true⟩,0,0,0⟩, +⟨⟨1,198,413,true⟩,0,0,0⟩, +⟨⟨1,198,426,true⟩,0,0,0⟩, +⟨⟨1,198,437,true⟩,0,0,0⟩, +⟨⟨1,198,439,true⟩,0,0,0⟩, +⟨⟨1,198,441,true⟩,0,0,0⟩, +⟨⟨1,198,443,true⟩,0,0,0⟩, +⟨⟨1,198,448,true⟩,0,0,0⟩, +⟨⟨1,198,452,true⟩,0,0,0⟩, +⟨⟨1,198,458,true⟩,0,0,0⟩, +⟨⟨1,198,462,true⟩,0,0,0⟩, +⟨⟨1,198,469,true⟩,0,0,0⟩, +⟨⟨1,198,471,true⟩,0,0,0⟩, +⟨⟨1,198,473,true⟩,0,0,0⟩, +⟨⟨1,198,475,true⟩,0,0,0⟩, +⟨⟨1,198,480,true⟩,0,0,0⟩, +⟨⟨1,198,484,true⟩,0,0,0⟩, +⟨⟨1,198,490,true⟩,0,0,0⟩, +⟨⟨1,198,494,true⟩,0,0,0⟩, +⟨⟨1,198,608,true⟩,0,0,0⟩] +def chunk24 : List Entry := [⟨⟨1,198,610,true⟩,0,0,0⟩, +⟨⟨1,198,624,true⟩,0,0,0⟩, +⟨⟨1,198,625,true⟩,0,0,0⟩, +⟨⟨1,198,628,true⟩,0,0,0⟩, +⟨⟨1,198,629,true⟩,0,0,0⟩, +⟨⟨1,198,640,true⟩,0,0,0⟩, +⟨⟨1,198,642,true⟩,0,0,0⟩, +⟨⟨1,198,644,true⟩,0,0,0⟩, +⟨⟨1,198,646,true⟩,0,0,0⟩, +⟨⟨1,198,669,true⟩,0,0,0⟩, +⟨⟨1,198,671,true⟩,0,0,0⟩, +⟨⟨1,198,680,true⟩,0,0,0⟩, +⟨⟨1,198,682,true⟩,0,0,0⟩, +⟨⟨1,198,701,true⟩,0,0,0⟩, +⟨⟨1,198,703,true⟩,0,0,0⟩, +⟨⟨1,198,712,true⟩,0,0,0⟩, +⟨⟨1,198,714,true⟩,0,0,0⟩, +⟨⟨1,198,820,true⟩,0,0,0⟩, +⟨⟨1,198,846,true⟩,0,0,0⟩, +⟨⟨1,198,914,true⟩,0,0,0⟩, +⟨⟨1,198,928,true⟩,0,0,0⟩, +⟨⟨1,199,249,true⟩,0,0,0⟩, +⟨⟨1,199,255,true⟩,0,0,0⟩, +⟨⟨1,199,272,true⟩,0,0,0⟩, +⟨⟨1,199,278,true⟩,0,0,0⟩, +⟨⟨1,199,304,true⟩,0,0,0⟩, +⟨⟨1,199,306,true⟩,0,0,0⟩, +⟨⟨1,199,312,true⟩,0,0,0⟩, +⟨⟨1,199,314,true⟩,0,0,0⟩, +⟨⟨1,199,321,true⟩,0,0,0⟩, +⟨⟨1,199,325,true⟩,0,0,0⟩, +⟨⟨1,199,329,true⟩,0,0,0⟩, +⟨⟨1,199,333,true⟩,0,0,0⟩, +⟨⟨1,199,336,true⟩,0,0,0⟩, +⟨⟨1,199,338,true⟩,0,0,0⟩, +⟨⟨1,199,344,true⟩,0,0,0⟩, +⟨⟨1,199,346,true⟩,0,0,0⟩, +⟨⟨1,199,353,true⟩,0,0,0⟩, +⟨⟨1,199,357,true⟩,0,0,0⟩, +⟨⟨1,199,361,true⟩,0,0,0⟩, +⟨⟨1,199,365,true⟩,0,0,0⟩, +⟨⟨1,199,372,true⟩,0,0,0⟩, +⟨⟨1,199,373,true⟩,0,0,0⟩, +⟨⟨1,199,377,true⟩,0,0,0⟩, +⟨⟨1,199,382,true⟩,0,0,0⟩, +⟨⟨1,199,387,true⟩,0,0,0⟩, +⟨⟨1,199,391,true⟩,0,0,0⟩, +⟨⟨1,199,395,true⟩,0,0,0⟩, +⟨⟨1,199,399,true⟩,0,0,0⟩, +⟨⟨1,199,401,true⟩,0,0,0⟩, +⟨⟨1,199,405,true⟩,0,0,0⟩, +⟨⟨1,199,409,true⟩,0,0,0⟩, +⟨⟨1,199,413,true⟩,0,0,0⟩, +⟨⟨1,199,425,true⟩,0,0,0⟩, +⟨⟨1,199,437,true⟩,0,0,0⟩, +⟨⟨1,199,439,true⟩,0,0,0⟩, +⟨⟨1,199,441,true⟩,0,0,0⟩, +⟨⟨1,199,443,true⟩,0,0,0⟩, +⟨⟨1,199,450,true⟩,0,0,0⟩, +⟨⟨1,199,454,true⟩,0,0,0⟩, +⟨⟨1,199,456,true⟩,0,0,0⟩, +⟨⟨1,199,460,true⟩,0,0,0⟩, +⟨⟨1,199,469,true⟩,0,0,0⟩, +⟨⟨1,199,471,true⟩,0,0,0⟩, +⟨⟨1,199,473,true⟩,0,0,0⟩, +⟨⟨1,199,475,true⟩,0,0,0⟩, +⟨⟨1,199,482,true⟩,0,0,0⟩, +⟨⟨1,199,486,true⟩,0,0,0⟩, +⟨⟨1,199,488,true⟩,0,0,0⟩, +⟨⟨1,199,492,true⟩,0,0,0⟩, +⟨⟨1,199,608,true⟩,0,0,0⟩, +⟨⟨1,199,610,true⟩,0,0,0⟩, +⟨⟨1,199,626,true⟩,0,0,0⟩, +⟨⟨1,199,627,true⟩,0,0,0⟩, +⟨⟨1,199,630,true⟩,0,0,0⟩, +⟨⟨1,199,631,true⟩,0,0,0⟩, +⟨⟨1,199,640,true⟩,0,0,0⟩, +⟨⟨1,199,642,true⟩,0,0,0⟩, +⟨⟨1,199,645,true⟩,0,0,0⟩, +⟨⟨1,199,646,true⟩,0,0,0⟩, +⟨⟨1,199,650,true⟩,0,0,0⟩, +⟨⟨1,199,655,true⟩,0,0,0⟩, +⟨⟨1,199,669,true⟩,0,0,0⟩, +⟨⟨1,199,671,true⟩,0,0,0⟩, +⟨⟨1,199,681,true⟩,0,0,0⟩, +⟨⟨1,199,683,true⟩,0,0,0⟩, +⟨⟨1,199,701,true⟩,0,0,0⟩, +⟨⟨1,199,703,true⟩,0,0,0⟩, +⟨⟨1,199,713,true⟩,0,0,0⟩, +⟨⟨1,199,715,true⟩,0,0,0⟩, +⟨⟨1,199,770,true⟩,0,0,0⟩, +⟨⟨1,199,820,true⟩,0,0,0⟩, +⟨⟨1,199,915,true⟩,0,0,0⟩, +⟨⟨1,199,980,true⟩,0,0,0⟩, +⟨⟨1,199,984,true⟩,0,0,0⟩, +⟨⟨1,200,243,true⟩,0,0,0⟩, +⟨⟨1,200,253,true⟩,0,0,0⟩, +⟨⟨1,200,270,true⟩,0,0,0⟩, +⟨⟨1,200,282,true⟩,0,0,0⟩, +⟨⟨1,200,292,true⟩,0,0,0⟩, +⟨⟨1,200,294,true⟩,0,0,0⟩, +⟨⟨1,200,300,true⟩,0,0,0⟩, +⟨⟨1,200,302,true⟩,0,0,0⟩, +⟨⟨1,200,325,true⟩,0,0,0⟩, +⟨⟨1,200,327,true⟩,0,0,0⟩, +⟨⟨1,200,329,true⟩,0,0,0⟩, +⟨⟨1,200,331,true⟩,0,0,0⟩, +⟨⟨1,200,341,true⟩,0,0,0⟩, +⟨⟨1,200,343,true⟩,0,0,0⟩, +⟨⟨1,200,345,true⟩,0,0,0⟩, +⟨⟨1,200,347,true⟩,0,0,0⟩, +⟨⟨1,200,371,true⟩,0,0,0⟩, +⟨⟨1,200,375,true⟩,0,0,0⟩, +⟨⟨1,200,379,true⟩,0,0,0⟩, +⟨⟨1,200,383,true⟩,0,0,0⟩, +⟨⟨1,200,388,true⟩,0,0,0⟩, +⟨⟨1,200,390,true⟩,0,0,0⟩, +⟨⟨1,200,396,true⟩,0,0,0⟩, +⟨⟨1,200,398,true⟩,0,0,0⟩, +⟨⟨1,200,402,true⟩,0,0,0⟩, +⟨⟨1,200,406,true⟩,0,0,0⟩, +⟨⟨1,200,408,true⟩,0,0,0⟩, +⟨⟨1,200,412,true⟩,0,0,0⟩, +⟨⟨1,200,421,true⟩,0,0,0⟩, +⟨⟨1,200,423,true⟩,0,0,0⟩, +⟨⟨1,200,425,true⟩,0,0,0⟩, +⟨⟨1,200,427,true⟩,0,0,0⟩, +⟨⟨1,200,438,true⟩,0,0,0⟩, +⟨⟨1,200,453,true⟩,0,0,0⟩, +⟨⟨1,200,455,true⟩,0,0,0⟩, +⟨⟨1,200,457,true⟩,0,0,0⟩, +⟨⟨1,200,459,true⟩,0,0,0⟩, +⟨⟨1,200,469,true⟩,0,0,0⟩, +⟨⟨1,200,471,true⟩,0,0,0⟩, +⟨⟨1,200,473,true⟩,0,0,0⟩, +⟨⟨1,200,475,true⟩,0,0,0⟩, +⟨⟨1,200,498,true⟩,0,0,0⟩, +⟨⟨1,200,502,true⟩,0,0,0⟩, +⟨⟨1,200,504,true⟩,0,0,0⟩, +⟨⟨1,200,508,true⟩,0,0,0⟩, +⟨⟨1,200,521,true⟩,0,0,0⟩, +⟨⟨1,200,523,true⟩,0,0,0⟩, +⟨⟨1,200,541,true⟩,0,0,0⟩, +⟨⟨1,200,543,true⟩,0,0,0⟩, +⟨⟨1,200,557,true⟩,0,0,0⟩, +⟨⟨1,200,559,true⟩,0,0,0⟩, +⟨⟨1,200,562,true⟩,0,0,0⟩, +⟨⟨1,200,563,true⟩,0,0,0⟩, +⟨⟨1,200,566,true⟩,0,0,0⟩, +⟨⟨1,200,567,true⟩,0,0,0⟩, +⟨⟨1,200,576,true⟩,0,0,0⟩, +⟨⟨1,200,578,true⟩,0,0,0⟩, +⟨⟨1,200,580,true⟩,0,0,0⟩, +⟨⟨1,200,582,true⟩,0,0,0⟩, +⟨⟨1,200,605,true⟩,0,0,0⟩, +⟨⟨1,200,607,true⟩,0,0,0⟩, +⟨⟨1,200,617,true⟩,0,0,0⟩, +⟨⟨1,200,619,true⟩,0,0,0⟩, +⟨⟨1,200,676,true⟩,0,0,0⟩, +⟨⟨1,200,678,true⟩,0,0,0⟩, +⟨⟨1,200,701,true⟩,0,0,0⟩, +⟨⟨1,200,703,true⟩,0,0,0⟩, +⟨⟨1,200,717,true⟩,0,0,0⟩, +⟨⟨1,200,719,true⟩,0,0,0⟩, +⟨⟨1,200,759,true⟩,0,0,0⟩, +⟨⟨1,200,775,true⟩,0,0,0⟩, +⟨⟨1,200,878,true⟩,0,0,0⟩, +⟨⟨1,201,243,true⟩,0,0,0⟩, +⟨⟨1,201,253,true⟩,0,0,0⟩, +⟨⟨1,201,270,true⟩,0,0,0⟩, +⟨⟨1,201,282,true⟩,0,0,0⟩, +⟨⟨1,201,292,true⟩,0,0,0⟩, +⟨⟨1,201,294,true⟩,0,0,0⟩, +⟨⟨1,201,300,true⟩,0,0,0⟩, +⟨⟨1,201,302,true⟩,0,0,0⟩, +⟨⟨1,201,321,true⟩,0,0,0⟩, +⟨⟨1,201,323,true⟩,0,0,0⟩, +⟨⟨1,201,333,true⟩,0,0,0⟩, +⟨⟨1,201,335,true⟩,0,0,0⟩, +⟨⟨1,201,341,true⟩,0,0,0⟩, +⟨⟨1,201,343,true⟩,0,0,0⟩, +⟨⟨1,201,345,true⟩,0,0,0⟩, +⟨⟨1,201,347,true⟩,0,0,0⟩, +⟨⟨1,201,354,true⟩,0,0,0⟩, +⟨⟨1,201,356,true⟩,0,0,0⟩, +⟨⟨1,201,360,true⟩,0,0,0⟩, +⟨⟨1,201,366,true⟩,0,0,0⟩, +⟨⟨1,201,369,true⟩,0,0,0⟩, +⟨⟨1,201,373,true⟩,0,0,0⟩, +⟨⟨1,201,377,true⟩,0,0,0⟩, +⟨⟨1,201,381,true⟩,0,0,0⟩, +⟨⟨1,201,384,true⟩,0,0,0⟩, +⟨⟨1,201,386,true⟩,0,0,0⟩, +⟨⟨1,201,392,true⟩,0,0,0⟩, +⟨⟨1,201,394,true⟩,0,0,0⟩, +⟨⟨1,201,402,true⟩,0,0,0⟩, +⟨⟨1,201,406,true⟩,0,0,0⟩, +⟨⟨1,201,408,true⟩,0,0,0⟩, +⟨⟨1,201,412,true⟩,0,0,0⟩, +⟨⟨1,201,421,true⟩,0,0,0⟩] +def chunk25 : List Entry := [⟨⟨1,201,423,true⟩,0,0,0⟩, +⟨⟨1,201,425,true⟩,0,0,0⟩, +⟨⟨1,201,427,true⟩,0,0,0⟩, +⟨⟨1,201,437,true⟩,0,0,0⟩, +⟨⟨1,201,449,true⟩,0,0,0⟩, +⟨⟨1,201,451,true⟩,0,0,0⟩, +⟨⟨1,201,461,true⟩,0,0,0⟩, +⟨⟨1,201,463,true⟩,0,0,0⟩, +⟨⟨1,201,469,true⟩,0,0,0⟩, +⟨⟨1,201,471,true⟩,0,0,0⟩, +⟨⟨1,201,473,true⟩,0,0,0⟩, +⟨⟨1,201,475,true⟩,0,0,0⟩, +⟨⟨1,201,496,true⟩,0,0,0⟩, +⟨⟨1,201,500,true⟩,0,0,0⟩, +⟨⟨1,201,506,true⟩,0,0,0⟩, +⟨⟨1,201,510,true⟩,0,0,0⟩, +⟨⟨1,201,521,true⟩,0,0,0⟩, +⟨⟨1,201,523,true⟩,0,0,0⟩, +⟨⟨1,201,541,true⟩,0,0,0⟩, +⟨⟨1,201,543,true⟩,0,0,0⟩, +⟨⟨1,201,556,true⟩,0,0,0⟩, +⟨⟨1,201,558,true⟩,0,0,0⟩, +⟨⟨1,201,560,true⟩,0,0,0⟩, +⟨⟨1,201,561,true⟩,0,0,0⟩, +⟨⟨1,201,564,true⟩,0,0,0⟩, +⟨⟨1,201,565,true⟩,0,0,0⟩, +⟨⟨1,201,576,true⟩,0,0,0⟩, +⟨⟨1,201,581,true⟩,0,0,0⟩, +⟨⟨1,201,582,true⟩,0,0,0⟩, +⟨⟨1,201,586,true⟩,0,0,0⟩, +⟨⟨1,201,591,true⟩,0,0,0⟩, +⟨⟨1,201,605,true⟩,0,0,0⟩, +⟨⟨1,201,607,true⟩,0,0,0⟩, +⟨⟨1,201,616,true⟩,0,0,0⟩, +⟨⟨1,201,618,true⟩,0,0,0⟩, +⟨⟨1,201,676,true⟩,0,0,0⟩, +⟨⟨1,201,678,true⟩,0,0,0⟩, +⟨⟨1,201,701,true⟩,0,0,0⟩, +⟨⟨1,201,703,true⟩,0,0,0⟩, +⟨⟨1,201,716,true⟩,0,0,0⟩, +⟨⟨1,201,718,true⟩,0,0,0⟩, +⟨⟨1,201,759,true⟩,0,0,0⟩, +⟨⟨1,201,774,true⟩,0,0,0⟩, +⟨⟨1,201,878,true⟩,0,0,0⟩, +⟨⟨1,201,944,true⟩,0,0,0⟩, +⟨⟨1,201,951,true⟩,0,0,0⟩, +⟨⟨1,202,243,true⟩,0,0,0⟩, +⟨⟨1,202,253,true⟩,0,0,0⟩, +⟨⟨1,202,270,true⟩,0,0,0⟩, +⟨⟨1,202,282,true⟩,0,0,0⟩, +⟨⟨1,202,288,true⟩,0,0,0⟩, +⟨⟨1,202,290,true⟩,0,0,0⟩, +⟨⟨1,202,296,true⟩,0,0,0⟩, +⟨⟨1,202,298,true⟩,0,0,0⟩, +⟨⟨1,202,325,true⟩,0,0,0⟩, +⟨⟨1,202,327,true⟩,0,0,0⟩, +⟨⟨1,202,329,true⟩,0,0,0⟩, +⟨⟨1,202,331,true⟩,0,0,0⟩, +⟨⟨1,202,337,true⟩,0,0,0⟩, +⟨⟨1,202,339,true⟩,0,0,0⟩, +⟨⟨1,202,349,true⟩,0,0,0⟩, +⟨⟨1,202,351,true⟩,0,0,0⟩, +⟨⟨1,202,355,true⟩,0,0,0⟩, +⟨⟨1,202,357,true⟩,0,0,0⟩, +⟨⟨1,202,361,true⟩,0,0,0⟩, +⟨⟨1,202,367,true⟩,0,0,0⟩, +⟨⟨1,202,371,true⟩,0,0,0⟩, +⟨⟨1,202,375,true⟩,0,0,0⟩, +⟨⟨1,202,379,true⟩,0,0,0⟩, +⟨⟨1,202,383,true⟩,0,0,0⟩, +⟨⟨1,202,384,true⟩,0,0,0⟩, +⟨⟨1,202,386,true⟩,0,0,0⟩, +⟨⟨1,202,392,true⟩,0,0,0⟩, +⟨⟨1,202,394,true⟩,0,0,0⟩, +⟨⟨1,202,402,true⟩,0,0,0⟩, +⟨⟨1,202,406,true⟩,0,0,0⟩, +⟨⟨1,202,408,true⟩,0,0,0⟩, +⟨⟨1,202,412,true⟩,0,0,0⟩, +⟨⟨1,202,417,true⟩,0,0,0⟩, +⟨⟨1,202,419,true⟩,0,0,0⟩, +⟨⟨1,202,429,true⟩,0,0,0⟩, +⟨⟨1,202,431,true⟩,0,0,0⟩, +⟨⟨1,202,435,true⟩,0,0,0⟩, +⟨⟨1,202,453,true⟩,0,0,0⟩, +⟨⟨1,202,455,true⟩,0,0,0⟩, +⟨⟨1,202,457,true⟩,0,0,0⟩, +⟨⟨1,202,459,true⟩,0,0,0⟩, +⟨⟨1,202,465,true⟩,0,0,0⟩, +⟨⟨1,202,467,true⟩,0,0,0⟩, +⟨⟨1,202,477,true⟩,0,0,0⟩, +⟨⟨1,202,479,true⟩,0,0,0⟩, +⟨⟨1,202,498,true⟩,0,0,0⟩, +⟨⟨1,202,502,true⟩,0,0,0⟩, +⟨⟨1,202,504,true⟩,0,0,0⟩, +⟨⟨1,202,508,true⟩,0,0,0⟩, +⟨⟨1,202,521,true⟩,0,0,0⟩, +⟨⟨1,202,523,true⟩,0,0,0⟩, +⟨⟨1,202,540,true⟩,0,0,0⟩, +⟨⟨1,202,542,true⟩,0,0,0⟩, +⟨⟨1,202,557,true⟩,0,0,0⟩, +⟨⟨1,202,559,true⟩,0,0,0⟩, +⟨⟨1,202,560,true⟩,0,0,0⟩, +⟨⟨1,202,561,true⟩,0,0,0⟩, +⟨⟨1,202,564,true⟩,0,0,0⟩, +⟨⟨1,202,565,true⟩,0,0,0⟩, +⟨⟨1,202,576,true⟩,0,0,0⟩, +⟨⟨1,202,582,true⟩,0,0,0⟩, +⟨⟨1,202,590,true⟩,0,0,0⟩, +⟨⟨1,202,591,true⟩,0,0,0⟩, +⟨⟨1,202,604,true⟩,0,0,0⟩, +⟨⟨1,202,606,true⟩,0,0,0⟩, +⟨⟨1,202,617,true⟩,0,0,0⟩, +⟨⟨1,202,619,true⟩,0,0,0⟩, +⟨⟨1,202,676,true⟩,0,0,0⟩, +⟨⟨1,202,678,true⟩,0,0,0⟩, +⟨⟨1,202,700,true⟩,0,0,0⟩, +⟨⟨1,202,702,true⟩,0,0,0⟩, +⟨⟨1,202,717,true⟩,0,0,0⟩, +⟨⟨1,202,719,true⟩,0,0,0⟩, +⟨⟨1,202,758,true⟩,0,0,0⟩, +⟨⟨1,202,775,true⟩,0,0,0⟩, +⟨⟨1,202,878,true⟩,0,0,0⟩, +⟨⟨1,202,942,true⟩,0,0,0⟩, +⟨⟨1,203,243,true⟩,0,0,0⟩, +⟨⟨1,203,253,true⟩,0,0,0⟩, +⟨⟨1,203,270,true⟩,0,0,0⟩, +⟨⟨1,203,282,true⟩,0,0,0⟩, +⟨⟨1,203,288,true⟩,0,0,0⟩, +⟨⟨1,203,290,true⟩,0,0,0⟩, +⟨⟨1,203,296,true⟩,0,0,0⟩, +⟨⟨1,203,298,true⟩,0,0,0⟩, +⟨⟨1,203,321,true⟩,0,0,0⟩, +⟨⟨1,203,323,true⟩,0,0,0⟩, +⟨⟨1,203,333,true⟩,0,0,0⟩, +⟨⟨1,203,335,true⟩,0,0,0⟩, +⟨⟨1,203,337,true⟩,0,0,0⟩, +⟨⟨1,203,339,true⟩,0,0,0⟩, +⟨⟨1,203,349,true⟩,0,0,0⟩, +⟨⟨1,203,351,true⟩,0,0,0⟩, +⟨⟨1,203,369,true⟩,0,0,0⟩, +⟨⟨1,203,373,true⟩,0,0,0⟩, +⟨⟨1,203,377,true⟩,0,0,0⟩, +⟨⟨1,203,381,true⟩,0,0,0⟩, +⟨⟨1,203,388,true⟩,0,0,0⟩, +⟨⟨1,203,390,true⟩,0,0,0⟩, +⟨⟨1,203,396,true⟩,0,0,0⟩, +⟨⟨1,203,398,true⟩,0,0,0⟩, +⟨⟨1,203,402,true⟩,0,0,0⟩, +⟨⟨1,203,406,true⟩,0,0,0⟩, +⟨⟨1,203,408,true⟩,0,0,0⟩, +⟨⟨1,203,412,true⟩,0,0,0⟩, +⟨⟨1,203,417,true⟩,0,0,0⟩, +⟨⟨1,203,419,true⟩,0,0,0⟩, +⟨⟨1,203,429,true⟩,0,0,0⟩, +⟨⟨1,203,431,true⟩,0,0,0⟩, +⟨⟨1,203,432,true⟩,0,0,0⟩, +⟨⟨1,203,449,true⟩,0,0,0⟩, +⟨⟨1,203,451,true⟩,0,0,0⟩, +⟨⟨1,203,461,true⟩,0,0,0⟩, +⟨⟨1,203,463,true⟩,0,0,0⟩, +⟨⟨1,203,465,true⟩,0,0,0⟩, +⟨⟨1,203,467,true⟩,0,0,0⟩, +⟨⟨1,203,477,true⟩,0,0,0⟩, +⟨⟨1,203,479,true⟩,0,0,0⟩, +⟨⟨1,203,496,true⟩,0,0,0⟩, +⟨⟨1,203,500,true⟩,0,0,0⟩, +⟨⟨1,203,506,true⟩,0,0,0⟩, +⟨⟨1,203,510,true⟩,0,0,0⟩, +⟨⟨1,203,521,true⟩,0,0,0⟩, +⟨⟨1,203,523,true⟩,0,0,0⟩, +⟨⟨1,203,540,true⟩,0,0,0⟩, +⟨⟨1,203,542,true⟩,0,0,0⟩, +⟨⟨1,203,556,true⟩,0,0,0⟩, +⟨⟨1,203,558,true⟩,0,0,0⟩, +⟨⟨1,203,562,true⟩,0,0,0⟩, +⟨⟨1,203,563,true⟩,0,0,0⟩, +⟨⟨1,203,566,true⟩,0,0,0⟩, +⟨⟨1,203,567,true⟩,0,0,0⟩, +⟨⟨1,203,576,true⟩,0,0,0⟩, +⟨⟨1,203,578,true⟩,0,0,0⟩, +⟨⟨1,203,580,true⟩,0,0,0⟩, +⟨⟨1,203,582,true⟩,0,0,0⟩, +⟨⟨1,203,604,true⟩,0,0,0⟩, +⟨⟨1,203,606,true⟩,0,0,0⟩, +⟨⟨1,203,616,true⟩,0,0,0⟩, +⟨⟨1,203,618,true⟩,0,0,0⟩, +⟨⟨1,203,676,true⟩,0,0,0⟩, +⟨⟨1,203,678,true⟩,0,0,0⟩, +⟨⟨1,203,700,true⟩,0,0,0⟩, +⟨⟨1,203,702,true⟩,0,0,0⟩, +⟨⟨1,203,716,true⟩,0,0,0⟩, +⟨⟨1,203,718,true⟩,0,0,0⟩, +⟨⟨1,203,758,true⟩,0,0,0⟩, +⟨⟨1,203,774,true⟩,0,0,0⟩, +⟨⟨1,203,878,true⟩,0,0,0⟩, +⟨⟨1,204,243,true⟩,0,0,0⟩, +⟨⟨1,204,253,true⟩,0,0,0⟩, +⟨⟨1,204,270,true⟩,0,0,0⟩, +⟨⟨1,204,282,true⟩,0,0,0⟩, +⟨⟨1,204,292,true⟩,0,0,0⟩] +def chunk26 : List Entry := [⟨⟨1,204,294,true⟩,0,0,0⟩, +⟨⟨1,204,300,true⟩,0,0,0⟩, +⟨⟨1,204,302,true⟩,0,0,0⟩, +⟨⟨1,204,325,true⟩,0,0,0⟩, +⟨⟨1,204,327,true⟩,0,0,0⟩, +⟨⟨1,204,329,true⟩,0,0,0⟩, +⟨⟨1,204,331,true⟩,0,0,0⟩, +⟨⟨1,204,341,true⟩,0,0,0⟩, +⟨⟨1,204,343,true⟩,0,0,0⟩, +⟨⟨1,204,345,true⟩,0,0,0⟩, +⟨⟨1,204,347,true⟩,0,0,0⟩, +⟨⟨1,204,354,true⟩,0,0,0⟩, +⟨⟨1,204,355,true⟩,0,0,0⟩, +⟨⟨1,204,360,true⟩,0,0,0⟩, +⟨⟨1,204,367,true⟩,0,0,0⟩, +⟨⟨1,204,371,true⟩,0,0,0⟩, +⟨⟨1,204,375,true⟩,0,0,0⟩, +⟨⟨1,204,379,true⟩,0,0,0⟩, +⟨⟨1,204,383,true⟩,0,0,0⟩, +⟨⟨1,204,388,true⟩,0,0,0⟩, +⟨⟨1,204,390,true⟩,0,0,0⟩, +⟨⟨1,204,396,true⟩,0,0,0⟩, +⟨⟨1,204,398,true⟩,0,0,0⟩, +⟨⟨1,204,400,true⟩,0,0,0⟩, +⟨⟨1,204,404,true⟩,0,0,0⟩, +⟨⟨1,204,410,true⟩,0,0,0⟩, +⟨⟨1,204,414,true⟩,0,0,0⟩, +⟨⟨1,204,417,true⟩,0,0,0⟩, +⟨⟨1,204,419,true⟩,0,0,0⟩, +⟨⟨1,204,429,true⟩,0,0,0⟩, +⟨⟨1,204,431,true⟩,0,0,0⟩, +⟨⟨1,204,446,true⟩,0,0,0⟩, +⟨⟨1,204,449,true⟩,0,0,0⟩, +⟨⟨1,204,451,true⟩,0,0,0⟩, +⟨⟨1,204,461,true⟩,0,0,0⟩, +⟨⟨1,204,463,true⟩,0,0,0⟩, +⟨⟨1,204,465,true⟩,0,0,0⟩, +⟨⟨1,204,467,true⟩,0,0,0⟩, +⟨⟨1,204,477,true⟩,0,0,0⟩, +⟨⟨1,204,479,true⟩,0,0,0⟩, +⟨⟨1,204,496,true⟩,0,0,0⟩, +⟨⟨1,204,500,true⟩,0,0,0⟩, +⟨⟨1,204,506,true⟩,0,0,0⟩, +⟨⟨1,204,510,true⟩,0,0,0⟩, +⟨⟨1,204,520,true⟩,0,0,0⟩, +⟨⟨1,204,522,true⟩,0,0,0⟩, +⟨⟨1,204,541,true⟩,0,0,0⟩, +⟨⟨1,204,543,true⟩,0,0,0⟩, +⟨⟨1,204,557,true⟩,0,0,0⟩, +⟨⟨1,204,559,true⟩,0,0,0⟩, +⟨⟨1,204,562,true⟩,0,0,0⟩, +⟨⟨1,204,563,true⟩,0,0,0⟩, +⟨⟨1,204,566,true⟩,0,0,0⟩, +⟨⟨1,204,567,true⟩,0,0,0⟩, +⟨⟨1,204,576,true⟩,0,0,0⟩, +⟨⟨1,204,578,true⟩,0,0,0⟩, +⟨⟨1,204,581,true⟩,0,0,0⟩, +⟨⟨1,204,582,true⟩,0,0,0⟩, +⟨⟨1,204,587,true⟩,0,0,0⟩, +⟨⟨1,204,590,true⟩,0,0,0⟩, +⟨⟨1,204,604,true⟩,0,0,0⟩, +⟨⟨1,204,606,true⟩,0,0,0⟩, +⟨⟨1,204,616,true⟩,0,0,0⟩, +⟨⟨1,204,618,true⟩,0,0,0⟩, +⟨⟨1,204,672,true⟩,0,0,0⟩, +⟨⟨1,204,674,true⟩,0,0,0⟩, +⟨⟨1,204,700,true⟩,0,0,0⟩, +⟨⟨1,204,702,true⟩,0,0,0⟩, +⟨⟨1,204,716,true⟩,0,0,0⟩, +⟨⟨1,204,718,true⟩,0,0,0⟩, +⟨⟨1,204,759,true⟩,0,0,0⟩, +⟨⟨1,204,775,true⟩,0,0,0⟩, +⟨⟨1,204,876,true⟩,0,0,0⟩, +⟨⟨1,204,942,true⟩,0,0,0⟩, +⟨⟨1,204,951,true⟩,0,0,0⟩, +⟨⟨1,205,243,true⟩,0,0,0⟩, +⟨⟨1,205,253,true⟩,0,0,0⟩, +⟨⟨1,205,270,true⟩,0,0,0⟩, +⟨⟨1,205,282,true⟩,0,0,0⟩, +⟨⟨1,205,292,true⟩,0,0,0⟩, +⟨⟨1,205,294,true⟩,0,0,0⟩, +⟨⟨1,205,300,true⟩,0,0,0⟩, +⟨⟨1,205,302,true⟩,0,0,0⟩, +⟨⟨1,205,321,true⟩,0,0,0⟩, +⟨⟨1,205,323,true⟩,0,0,0⟩, +⟨⟨1,205,333,true⟩,0,0,0⟩, +⟨⟨1,205,335,true⟩,0,0,0⟩, +⟨⟨1,205,341,true⟩,0,0,0⟩, +⟨⟨1,205,343,true⟩,0,0,0⟩, +⟨⟨1,205,345,true⟩,0,0,0⟩, +⟨⟨1,205,347,true⟩,0,0,0⟩, +⟨⟨1,205,369,true⟩,0,0,0⟩, +⟨⟨1,205,373,true⟩,0,0,0⟩, +⟨⟨1,205,377,true⟩,0,0,0⟩, +⟨⟨1,205,381,true⟩,0,0,0⟩, +⟨⟨1,205,384,true⟩,0,0,0⟩, +⟨⟨1,205,386,true⟩,0,0,0⟩, +⟨⟨1,205,392,true⟩,0,0,0⟩, +⟨⟨1,205,394,true⟩,0,0,0⟩, +⟨⟨1,205,400,true⟩,0,0,0⟩, +⟨⟨1,205,404,true⟩,0,0,0⟩, +⟨⟨1,205,410,true⟩,0,0,0⟩, +⟨⟨1,205,414,true⟩,0,0,0⟩, +⟨⟨1,205,417,true⟩,0,0,0⟩, +⟨⟨1,205,419,true⟩,0,0,0⟩, +⟨⟨1,205,429,true⟩,0,0,0⟩, +⟨⟨1,205,431,true⟩,0,0,0⟩, +⟨⟨1,205,445,true⟩,0,0,0⟩, +⟨⟨1,205,453,true⟩,0,0,0⟩, +⟨⟨1,205,455,true⟩,0,0,0⟩, +⟨⟨1,205,457,true⟩,0,0,0⟩, +⟨⟨1,205,459,true⟩,0,0,0⟩, +⟨⟨1,205,465,true⟩,0,0,0⟩, +⟨⟨1,205,467,true⟩,0,0,0⟩, +⟨⟨1,205,477,true⟩,0,0,0⟩, +⟨⟨1,205,479,true⟩,0,0,0⟩, +⟨⟨1,205,498,true⟩,0,0,0⟩, +⟨⟨1,205,502,true⟩,0,0,0⟩, +⟨⟨1,205,504,true⟩,0,0,0⟩, +⟨⟨1,205,508,true⟩,0,0,0⟩, +⟨⟨1,205,520,true⟩,0,0,0⟩, +⟨⟨1,205,522,true⟩,0,0,0⟩, +⟨⟨1,205,541,true⟩,0,0,0⟩, +⟨⟨1,205,543,true⟩,0,0,0⟩, +⟨⟨1,205,556,true⟩,0,0,0⟩, +⟨⟨1,205,558,true⟩,0,0,0⟩, +⟨⟨1,205,560,true⟩,0,0,0⟩, +⟨⟨1,205,561,true⟩,0,0,0⟩, +⟨⟨1,205,564,true⟩,0,0,0⟩, +⟨⟨1,205,565,true⟩,0,0,0⟩, +⟨⟨1,205,576,true⟩,0,0,0⟩, +⟨⟨1,205,578,true⟩,0,0,0⟩, +⟨⟨1,205,580,true⟩,0,0,0⟩, +⟨⟨1,205,582,true⟩,0,0,0⟩, +⟨⟨1,205,604,true⟩,0,0,0⟩, +⟨⟨1,205,606,true⟩,0,0,0⟩, +⟨⟨1,205,617,true⟩,0,0,0⟩, +⟨⟨1,205,619,true⟩,0,0,0⟩, +⟨⟨1,205,672,true⟩,0,0,0⟩, +⟨⟨1,205,674,true⟩,0,0,0⟩, +⟨⟨1,205,700,true⟩,0,0,0⟩, +⟨⟨1,205,702,true⟩,0,0,0⟩, +⟨⟨1,205,717,true⟩,0,0,0⟩, +⟨⟨1,205,719,true⟩,0,0,0⟩, +⟨⟨1,205,759,true⟩,0,0,0⟩, +⟨⟨1,205,774,true⟩,0,0,0⟩, +⟨⟨1,205,876,true⟩,0,0,0⟩, +⟨⟨1,206,243,true⟩,0,0,0⟩, +⟨⟨1,206,253,true⟩,0,0,0⟩, +⟨⟨1,206,270,true⟩,0,0,0⟩, +⟨⟨1,206,282,true⟩,0,0,0⟩, +⟨⟨1,206,288,true⟩,0,0,0⟩, +⟨⟨1,206,290,true⟩,0,0,0⟩, +⟨⟨1,206,296,true⟩,0,0,0⟩, +⟨⟨1,206,298,true⟩,0,0,0⟩, +⟨⟨1,206,325,true⟩,0,0,0⟩, +⟨⟨1,206,327,true⟩,0,0,0⟩, +⟨⟨1,206,329,true⟩,0,0,0⟩, +⟨⟨1,206,331,true⟩,0,0,0⟩, +⟨⟨1,206,337,true⟩,0,0,0⟩, +⟨⟨1,206,339,true⟩,0,0,0⟩, +⟨⟨1,206,349,true⟩,0,0,0⟩, +⟨⟨1,206,351,true⟩,0,0,0⟩, +⟨⟨1,206,371,true⟩,0,0,0⟩, +⟨⟨1,206,375,true⟩,0,0,0⟩, +⟨⟨1,206,379,true⟩,0,0,0⟩, +⟨⟨1,206,383,true⟩,0,0,0⟩, +⟨⟨1,206,384,true⟩,0,0,0⟩, +⟨⟨1,206,386,true⟩,0,0,0⟩, +⟨⟨1,206,392,true⟩,0,0,0⟩, +⟨⟨1,206,394,true⟩,0,0,0⟩, +⟨⟨1,206,400,true⟩,0,0,0⟩, +⟨⟨1,206,404,true⟩,0,0,0⟩, +⟨⟨1,206,410,true⟩,0,0,0⟩, +⟨⟨1,206,414,true⟩,0,0,0⟩, +⟨⟨1,206,421,true⟩,0,0,0⟩, +⟨⟨1,206,423,true⟩,0,0,0⟩, +⟨⟨1,206,425,true⟩,0,0,0⟩, +⟨⟨1,206,427,true⟩,0,0,0⟩, +⟨⟨1,206,443,true⟩,0,0,0⟩, +⟨⟨1,206,449,true⟩,0,0,0⟩, +⟨⟨1,206,451,true⟩,0,0,0⟩, +⟨⟨1,206,461,true⟩,0,0,0⟩, +⟨⟨1,206,463,true⟩,0,0,0⟩, +⟨⟨1,206,469,true⟩,0,0,0⟩, +⟨⟨1,206,471,true⟩,0,0,0⟩, +⟨⟨1,206,473,true⟩,0,0,0⟩, +⟨⟨1,206,475,true⟩,0,0,0⟩, +⟨⟨1,206,496,true⟩,0,0,0⟩, +⟨⟨1,206,500,true⟩,0,0,0⟩, +⟨⟨1,206,506,true⟩,0,0,0⟩, +⟨⟨1,206,510,true⟩,0,0,0⟩, +⟨⟨1,206,520,true⟩,0,0,0⟩, +⟨⟨1,206,522,true⟩,0,0,0⟩, +⟨⟨1,206,540,true⟩,0,0,0⟩, +⟨⟨1,206,542,true⟩,0,0,0⟩, +⟨⟨1,206,557,true⟩,0,0,0⟩, +⟨⟨1,206,559,true⟩,0,0,0⟩, +⟨⟨1,206,560,true⟩,0,0,0⟩, +⟨⟨1,206,561,true⟩,0,0,0⟩] +def chunk27 : List Entry := [⟨⟨1,206,564,true⟩,0,0,0⟩, +⟨⟨1,206,565,true⟩,0,0,0⟩, +⟨⟨1,206,576,true⟩,0,0,0⟩, +⟨⟨1,206,578,true⟩,0,0,0⟩, +⟨⟨1,206,580,true⟩,0,0,0⟩, +⟨⟨1,206,582,true⟩,0,0,0⟩, +⟨⟨1,206,605,true⟩,0,0,0⟩, +⟨⟨1,206,607,true⟩,0,0,0⟩, +⟨⟨1,206,616,true⟩,0,0,0⟩, +⟨⟨1,206,618,true⟩,0,0,0⟩, +⟨⟨1,206,672,true⟩,0,0,0⟩, +⟨⟨1,206,674,true⟩,0,0,0⟩, +⟨⟨1,206,701,true⟩,0,0,0⟩, +⟨⟨1,206,703,true⟩,0,0,0⟩, +⟨⟨1,206,716,true⟩,0,0,0⟩, +⟨⟨1,206,718,true⟩,0,0,0⟩, +⟨⟨1,206,758,true⟩,0,0,0⟩, +⟨⟨1,206,775,true⟩,0,0,0⟩, +⟨⟨1,206,876,true⟩,0,0,0⟩, +⟨⟨1,207,243,true⟩,0,0,0⟩, +⟨⟨1,207,253,true⟩,0,0,0⟩, +⟨⟨1,207,270,true⟩,0,0,0⟩, +⟨⟨1,207,282,true⟩,0,0,0⟩, +⟨⟨1,207,288,true⟩,0,0,0⟩, +⟨⟨1,207,290,true⟩,0,0,0⟩, +⟨⟨1,207,296,true⟩,0,0,0⟩, +⟨⟨1,207,298,true⟩,0,0,0⟩, +⟨⟨1,207,321,true⟩,0,0,0⟩, +⟨⟨1,207,323,true⟩,0,0,0⟩, +⟨⟨1,207,333,true⟩,0,0,0⟩, +⟨⟨1,207,335,true⟩,0,0,0⟩, +⟨⟨1,207,337,true⟩,0,0,0⟩, +⟨⟨1,207,339,true⟩,0,0,0⟩, +⟨⟨1,207,349,true⟩,0,0,0⟩, +⟨⟨1,207,351,true⟩,0,0,0⟩, +⟨⟨1,207,356,true⟩,0,0,0⟩, +⟨⟨1,207,357,true⟩,0,0,0⟩, +⟨⟨1,207,361,true⟩,0,0,0⟩, +⟨⟨1,207,366,true⟩,0,0,0⟩, +⟨⟨1,207,369,true⟩,0,0,0⟩, +⟨⟨1,207,373,true⟩,0,0,0⟩, +⟨⟨1,207,377,true⟩,0,0,0⟩, +⟨⟨1,207,381,true⟩,0,0,0⟩, +⟨⟨1,207,388,true⟩,0,0,0⟩, +⟨⟨1,207,390,true⟩,0,0,0⟩, +⟨⟨1,207,396,true⟩,0,0,0⟩, +⟨⟨1,207,398,true⟩,0,0,0⟩, +⟨⟨1,207,400,true⟩,0,0,0⟩, +⟨⟨1,207,404,true⟩,0,0,0⟩, +⟨⟨1,207,410,true⟩,0,0,0⟩, +⟨⟨1,207,414,true⟩,0,0,0⟩, +⟨⟨1,207,421,true⟩,0,0,0⟩, +⟨⟨1,207,423,true⟩,0,0,0⟩, +⟨⟨1,207,425,true⟩,0,0,0⟩, +⟨⟨1,207,427,true⟩,0,0,0⟩, +⟨⟨1,207,440,true⟩,0,0,0⟩, +⟨⟨1,207,453,true⟩,0,0,0⟩, +⟨⟨1,207,455,true⟩,0,0,0⟩, +⟨⟨1,207,457,true⟩,0,0,0⟩, +⟨⟨1,207,459,true⟩,0,0,0⟩, +⟨⟨1,207,469,true⟩,0,0,0⟩, +⟨⟨1,207,471,true⟩,0,0,0⟩, +⟨⟨1,207,473,true⟩,0,0,0⟩, +⟨⟨1,207,475,true⟩,0,0,0⟩, +⟨⟨1,207,498,true⟩,0,0,0⟩, +⟨⟨1,207,502,true⟩,0,0,0⟩, +⟨⟨1,207,504,true⟩,0,0,0⟩, +⟨⟨1,207,508,true⟩,0,0,0⟩, +⟨⟨1,207,520,true⟩,0,0,0⟩, +⟨⟨1,207,522,true⟩,0,0,0⟩, +⟨⟨1,207,540,true⟩,0,0,0⟩, +⟨⟨1,207,542,true⟩,0,0,0⟩, +⟨⟨1,207,556,true⟩,0,0,0⟩, +⟨⟨1,207,558,true⟩,0,0,0⟩, +⟨⟨1,207,562,true⟩,0,0,0⟩, +⟨⟨1,207,563,true⟩,0,0,0⟩, +⟨⟨1,207,566,true⟩,0,0,0⟩, +⟨⟨1,207,567,true⟩,0,0,0⟩, +⟨⟨1,207,576,true⟩,0,0,0⟩, +⟨⟨1,207,578,true⟩,0,0,0⟩, +⟨⟨1,207,582,true⟩,0,0,0⟩, +⟨⟨1,207,586,true⟩,0,0,0⟩, +⟨⟨1,207,587,true⟩,0,0,0⟩, +⟨⟨1,207,605,true⟩,0,0,0⟩, +⟨⟨1,207,607,true⟩,0,0,0⟩, +⟨⟨1,207,617,true⟩,0,0,0⟩, +⟨⟨1,207,619,true⟩,0,0,0⟩, +⟨⟨1,207,672,true⟩,0,0,0⟩, +⟨⟨1,207,674,true⟩,0,0,0⟩, +⟨⟨1,207,701,true⟩,0,0,0⟩, +⟨⟨1,207,703,true⟩,0,0,0⟩, +⟨⟨1,207,717,true⟩,0,0,0⟩, +⟨⟨1,207,719,true⟩,0,0,0⟩, +⟨⟨1,207,758,true⟩,0,0,0⟩, +⟨⟨1,207,774,true⟩,0,0,0⟩, +⟨⟨1,207,876,true⟩,0,0,0⟩, +⟨⟨1,207,944,true⟩,0,0,0⟩, +⟨⟨1,208,240,true⟩,0,0,0⟩, +⟨⟨1,208,246,true⟩,0,0,0⟩, +⟨⟨1,208,290,true⟩,0,0,0⟩, +⟨⟨1,208,294,true⟩,0,0,0⟩, +⟨⟨1,208,296,true⟩,0,0,0⟩, +⟨⟨1,208,300,true⟩,0,0,0⟩, +⟨⟨1,208,306,true⟩,0,0,0⟩, +⟨⟨1,208,310,true⟩,0,0,0⟩, +⟨⟨1,208,312,true⟩,0,0,0⟩, +⟨⟨1,208,316,true⟩,0,0,0⟩, +⟨⟨1,208,354,true⟩,0,0,0⟩, +⟨⟨1,208,358,true⟩,0,0,0⟩, +⟨⟨1,208,360,true⟩,0,0,0⟩, +⟨⟨1,208,364,true⟩,0,0,0⟩, +⟨⟨1,208,370,true⟩,0,0,0⟩, +⟨⟨1,208,374,true⟩,0,0,0⟩, +⟨⟨1,208,376,true⟩,0,0,0⟩, +⟨⟨1,208,380,true⟩,0,0,0⟩, +⟨⟨1,208,418,true⟩,0,0,0⟩, +⟨⟨1,208,422,true⟩,0,0,0⟩, +⟨⟨1,208,424,true⟩,0,0,0⟩, +⟨⟨1,208,428,true⟩,0,0,0⟩, +⟨⟨1,208,434,true⟩,0,0,0⟩, +⟨⟨1,208,438,true⟩,0,0,0⟩, +⟨⟨1,208,440,true⟩,0,0,0⟩, +⟨⟨1,208,444,true⟩,0,0,0⟩, +⟨⟨1,208,454,true⟩,0,0,0⟩, +⟨⟨1,208,482,true⟩,0,0,0⟩, +⟨⟨1,208,486,true⟩,0,0,0⟩, +⟨⟨1,208,488,true⟩,0,0,0⟩, +⟨⟨1,208,492,true⟩,0,0,0⟩, +⟨⟨1,208,498,true⟩,0,0,0⟩, +⟨⟨1,208,502,true⟩,0,0,0⟩, +⟨⟨1,208,504,true⟩,0,0,0⟩, +⟨⟨1,208,508,true⟩,0,0,0⟩, +⟨⟨1,208,514,true⟩,0,0,0⟩, +⟨⟨1,208,515,true⟩,0,0,0⟩, +⟨⟨1,208,518,true⟩,0,0,0⟩, +⟨⟨1,208,519,true⟩,0,0,0⟩, +⟨⟨1,208,528,true⟩,0,0,0⟩, +⟨⟨1,208,530,true⟩,0,0,0⟩, +⟨⟨1,208,532,true⟩,0,0,0⟩, +⟨⟨1,208,534,true⟩,0,0,0⟩, +⟨⟨1,208,546,true⟩,0,0,0⟩, +⟨⟨1,208,547,true⟩,0,0,0⟩, +⟨⟨1,208,550,true⟩,0,0,0⟩, +⟨⟨1,208,551,true⟩,0,0,0⟩, +⟨⟨1,208,569,true⟩,0,0,0⟩, +⟨⟨1,208,571,true⟩,0,0,0⟩, +⟨⟨1,208,585,true⟩,0,0,0⟩, +⟨⟨1,208,587,true⟩,0,0,0⟩, +⟨⟨1,208,601,true⟩,0,0,0⟩, +⟨⟨1,208,603,true⟩,0,0,0⟩, +⟨⟨1,208,617,true⟩,0,0,0⟩, +⟨⟨1,208,619,true⟩,0,0,0⟩, +⟨⟨1,208,633,true⟩,0,0,0⟩, +⟨⟨1,208,635,true⟩,0,0,0⟩, +⟨⟨1,208,649,true⟩,0,0,0⟩, +⟨⟨1,208,651,true⟩,0,0,0⟩, +⟨⟨1,208,665,true⟩,0,0,0⟩, +⟨⟨1,208,667,true⟩,0,0,0⟩, +⟨⟨1,208,681,true⟩,0,0,0⟩, +⟨⟨1,208,683,true⟩,0,0,0⟩, +⟨⟨1,208,692,true⟩,0,0,0⟩, +⟨⟨1,208,694,true⟩,0,0,0⟩, +⟨⟨1,208,722,true⟩,0,0,0⟩, +⟨⟨1,208,723,true⟩,0,0,0⟩, +⟨⟨1,208,726,true⟩,0,0,0⟩, +⟨⟨1,208,727,true⟩,0,0,0⟩, +⟨⟨1,208,749,true⟩,0,0,0⟩, +⟨⟨1,208,892,true⟩,0,0,0⟩, +⟨⟨1,209,240,true⟩,0,0,0⟩, +⟨⟨1,209,246,true⟩,0,0,0⟩, +⟨⟨1,209,288,true⟩,0,0,0⟩, +⟨⟨1,209,292,true⟩,0,0,0⟩, +⟨⟨1,209,298,true⟩,0,0,0⟩, +⟨⟨1,209,302,true⟩,0,0,0⟩, +⟨⟨1,209,306,true⟩,0,0,0⟩, +⟨⟨1,209,310,true⟩,0,0,0⟩, +⟨⟨1,209,312,true⟩,0,0,0⟩, +⟨⟨1,209,316,true⟩,0,0,0⟩, +⟨⟨1,209,339,true⟩,0,0,0⟩, +⟨⟨1,209,341,true⟩,0,0,0⟩, +⟨⟨1,209,345,true⟩,0,0,0⟩, +⟨⟨1,209,351,true⟩,0,0,0⟩, +⟨⟨1,209,352,true⟩,0,0,0⟩, +⟨⟨1,209,356,true⟩,0,0,0⟩, +⟨⟨1,209,362,true⟩,0,0,0⟩, +⟨⟨1,209,366,true⟩,0,0,0⟩, +⟨⟨1,209,370,true⟩,0,0,0⟩, +⟨⟨1,209,374,true⟩,0,0,0⟩, +⟨⟨1,209,376,true⟩,0,0,0⟩, +⟨⟨1,209,380,true⟩,0,0,0⟩, +⟨⟨1,209,416,true⟩,0,0,0⟩, +⟨⟨1,209,420,true⟩,0,0,0⟩, +⟨⟨1,209,426,true⟩,0,0,0⟩, +⟨⟨1,209,430,true⟩,0,0,0⟩, +⟨⟨1,209,434,true⟩,0,0,0⟩, +⟨⟨1,209,438,true⟩,0,0,0⟩, +⟨⟨1,209,440,true⟩,0,0,0⟩, +⟨⟨1,209,444,true⟩,0,0,0⟩, +⟨⟨1,209,453,true⟩,0,0,0⟩, +⟨⟨1,209,480,true⟩,0,0,0⟩] +def chunk28 : List Entry := [⟨⟨1,209,484,true⟩,0,0,0⟩, +⟨⟨1,209,490,true⟩,0,0,0⟩, +⟨⟨1,209,494,true⟩,0,0,0⟩, +⟨⟨1,209,498,true⟩,0,0,0⟩, +⟨⟨1,209,502,true⟩,0,0,0⟩, +⟨⟨1,209,504,true⟩,0,0,0⟩, +⟨⟨1,209,508,true⟩,0,0,0⟩, +⟨⟨1,209,514,true⟩,0,0,0⟩, +⟨⟨1,209,515,true⟩,0,0,0⟩, +⟨⟨1,209,518,true⟩,0,0,0⟩, +⟨⟨1,209,519,true⟩,0,0,0⟩, +⟨⟨1,209,528,true⟩,0,0,0⟩, +⟨⟨1,209,534,true⟩,0,0,0⟩, +⟨⟨1,209,539,true⟩,0,0,0⟩, +⟨⟨1,209,542,true⟩,0,0,0⟩, +⟨⟨1,209,544,true⟩,0,0,0⟩, +⟨⟨1,209,545,true⟩,0,0,0⟩, +⟨⟨1,209,548,true⟩,0,0,0⟩, +⟨⟨1,209,549,true⟩,0,0,0⟩, +⟨⟨1,209,569,true⟩,0,0,0⟩, +⟨⟨1,209,571,true⟩,0,0,0⟩, +⟨⟨1,209,584,true⟩,0,0,0⟩, +⟨⟨1,209,586,true⟩,0,0,0⟩, +⟨⟨1,209,600,true⟩,0,0,0⟩, +⟨⟨1,209,602,true⟩,0,0,0⟩, +⟨⟨1,209,617,true⟩,0,0,0⟩, +⟨⟨1,209,619,true⟩,0,0,0⟩, +⟨⟨1,209,632,true⟩,0,0,0⟩, +⟨⟨1,209,634,true⟩,0,0,0⟩, +⟨⟨1,209,649,true⟩,0,0,0⟩, +⟨⟨1,209,651,true⟩,0,0,0⟩, +⟨⟨1,209,665,true⟩,0,0,0⟩, +⟨⟨1,209,667,true⟩,0,0,0⟩, +⟨⟨1,209,680,true⟩,0,0,0⟩, +⟨⟨1,209,682,true⟩,0,0,0⟩, +⟨⟨1,209,692,true⟩,0,0,0⟩, +⟨⟨1,209,694,true⟩,0,0,0⟩, +⟨⟨1,209,720,true⟩,0,0,0⟩, +⟨⟨1,209,721,true⟩,0,0,0⟩, +⟨⟨1,209,724,true⟩,0,0,0⟩, +⟨⟨1,209,725,true⟩,0,0,0⟩, +⟨⟨1,209,749,true⟩,0,0,0⟩, +⟨⟨1,209,800,true⟩,0,0,0⟩, +⟨⟨1,209,892,true⟩,0,0,0⟩, +⟨⟨1,209,954,true⟩,0,0,0⟩, +⟨⟨1,210,240,true⟩,0,0,0⟩, +⟨⟨1,210,246,true⟩,0,0,0⟩, +⟨⟨1,210,290,true⟩,0,0,0⟩, +⟨⟨1,210,294,true⟩,0,0,0⟩, +⟨⟨1,210,296,true⟩,0,0,0⟩, +⟨⟨1,210,300,true⟩,0,0,0⟩, +⟨⟨1,210,304,true⟩,0,0,0⟩, +⟨⟨1,210,308,true⟩,0,0,0⟩, +⟨⟨1,210,314,true⟩,0,0,0⟩, +⟨⟨1,210,318,true⟩,0,0,0⟩, +⟨⟨1,210,338,true⟩,0,0,0⟩, +⟨⟨1,210,340,true⟩,0,0,0⟩, +⟨⟨1,210,344,true⟩,0,0,0⟩, +⟨⟨1,210,350,true⟩,0,0,0⟩, +⟨⟨1,210,354,true⟩,0,0,0⟩, +⟨⟨1,210,358,true⟩,0,0,0⟩, +⟨⟨1,210,360,true⟩,0,0,0⟩, +⟨⟨1,210,364,true⟩,0,0,0⟩, +⟨⟨1,210,368,true⟩,0,0,0⟩, +⟨⟨1,210,372,true⟩,0,0,0⟩, +⟨⟨1,210,378,true⟩,0,0,0⟩, +⟨⟨1,210,382,true⟩,0,0,0⟩, +⟨⟨1,210,418,true⟩,0,0,0⟩, +⟨⟨1,210,422,true⟩,0,0,0⟩, +⟨⟨1,210,424,true⟩,0,0,0⟩, +⟨⟨1,210,428,true⟩,0,0,0⟩, +⟨⟨1,210,432,true⟩,0,0,0⟩, +⟨⟨1,210,436,true⟩,0,0,0⟩, +⟨⟨1,210,442,true⟩,0,0,0⟩, +⟨⟨1,210,446,true⟩,0,0,0⟩, +⟨⟨1,210,451,true⟩,0,0,0⟩, +⟨⟨1,210,482,true⟩,0,0,0⟩, +⟨⟨1,210,486,true⟩,0,0,0⟩, +⟨⟨1,210,488,true⟩,0,0,0⟩, +⟨⟨1,210,492,true⟩,0,0,0⟩, +⟨⟨1,210,496,true⟩,0,0,0⟩, +⟨⟨1,210,500,true⟩,0,0,0⟩, +⟨⟨1,210,506,true⟩,0,0,0⟩, +⟨⟨1,210,510,true⟩,0,0,0⟩, +⟨⟨1,210,514,true⟩,0,0,0⟩, +⟨⟨1,210,515,true⟩,0,0,0⟩, +⟨⟨1,210,518,true⟩,0,0,0⟩, +⟨⟨1,210,519,true⟩,0,0,0⟩, +⟨⟨1,210,528,true⟩,0,0,0⟩, +⟨⟨1,210,533,true⟩,0,0,0⟩, +⟨⟨1,210,534,true⟩,0,0,0⟩, +⟨⟨1,210,538,true⟩,0,0,0⟩, +⟨⟨1,210,539,true⟩,0,0,0⟩, +⟨⟨1,210,543,true⟩,0,0,0⟩, +⟨⟨1,210,544,true⟩,0,0,0⟩, +⟨⟨1,210,545,true⟩,0,0,0⟩, +⟨⟨1,210,548,true⟩,0,0,0⟩, +⟨⟨1,210,549,true⟩,0,0,0⟩, +⟨⟨1,210,568,true⟩,0,0,0⟩, +⟨⟨1,210,570,true⟩,0,0,0⟩, +⟨⟨1,210,585,true⟩,0,0,0⟩, +⟨⟨1,210,587,true⟩,0,0,0⟩, +⟨⟨1,210,601,true⟩,0,0,0⟩, +⟨⟨1,210,603,true⟩,0,0,0⟩, +⟨⟨1,210,616,true⟩,0,0,0⟩, +⟨⟨1,210,618,true⟩,0,0,0⟩, +⟨⟨1,210,633,true⟩,0,0,0⟩, +⟨⟨1,210,635,true⟩,0,0,0⟩, +⟨⟨1,210,648,true⟩,0,0,0⟩, +⟨⟨1,210,650,true⟩,0,0,0⟩, +⟨⟨1,210,664,true⟩,0,0,0⟩, +⟨⟨1,210,666,true⟩,0,0,0⟩, +⟨⟨1,210,681,true⟩,0,0,0⟩, +⟨⟨1,210,683,true⟩,0,0,0⟩, +⟨⟨1,210,692,true⟩,0,0,0⟩, +⟨⟨1,210,694,true⟩,0,0,0⟩, +⟨⟨1,210,720,true⟩,0,0,0⟩, +⟨⟨1,210,721,true⟩,0,0,0⟩, +⟨⟨1,210,724,true⟩,0,0,0⟩, +⟨⟨1,210,725,true⟩,0,0,0⟩, +⟨⟨1,210,749,true⟩,0,0,0⟩, +⟨⟨1,210,788,true⟩,0,0,0⟩, +⟨⟨1,210,892,true⟩,0,0,0⟩, +⟨⟨1,210,948,true⟩,0,0,0⟩, +⟨⟨1,210,952,true⟩,0,0,0⟩, +⟨⟨1,211,240,true⟩,0,0,0⟩, +⟨⟨1,211,246,true⟩,0,0,0⟩, +⟨⟨1,211,288,true⟩,0,0,0⟩, +⟨⟨1,211,292,true⟩,0,0,0⟩, +⟨⟨1,211,298,true⟩,0,0,0⟩, +⟨⟨1,211,302,true⟩,0,0,0⟩, +⟨⟨1,211,304,true⟩,0,0,0⟩, +⟨⟨1,211,308,true⟩,0,0,0⟩, +⟨⟨1,211,314,true⟩,0,0,0⟩, +⟨⟨1,211,318,true⟩,0,0,0⟩, +⟨⟨1,211,352,true⟩,0,0,0⟩, +⟨⟨1,211,356,true⟩,0,0,0⟩, +⟨⟨1,211,362,true⟩,0,0,0⟩, +⟨⟨1,211,366,true⟩,0,0,0⟩, +⟨⟨1,211,368,true⟩,0,0,0⟩, +⟨⟨1,211,372,true⟩,0,0,0⟩, +⟨⟨1,211,378,true⟩,0,0,0⟩, +⟨⟨1,211,382,true⟩,0,0,0⟩, +⟨⟨1,211,416,true⟩,0,0,0⟩, +⟨⟨1,211,420,true⟩,0,0,0⟩, +⟨⟨1,211,426,true⟩,0,0,0⟩, +⟨⟨1,211,430,true⟩,0,0,0⟩, +⟨⟨1,211,432,true⟩,0,0,0⟩, +⟨⟨1,211,436,true⟩,0,0,0⟩, +⟨⟨1,211,442,true⟩,0,0,0⟩, +⟨⟨1,211,446,true⟩,0,0,0⟩, +⟨⟨1,211,448,true⟩,0,0,0⟩, +⟨⟨1,211,480,true⟩,0,0,0⟩, +⟨⟨1,211,484,true⟩,0,0,0⟩, +⟨⟨1,211,490,true⟩,0,0,0⟩, +⟨⟨1,211,494,true⟩,0,0,0⟩, +⟨⟨1,211,496,true⟩,0,0,0⟩, +⟨⟨1,211,500,true⟩,0,0,0⟩, +⟨⟨1,211,506,true⟩,0,0,0⟩, +⟨⟨1,211,510,true⟩,0,0,0⟩, +⟨⟨1,211,514,true⟩,0,0,0⟩, +⟨⟨1,211,515,true⟩,0,0,0⟩, +⟨⟨1,211,518,true⟩,0,0,0⟩, +⟨⟨1,211,519,true⟩,0,0,0⟩, +⟨⟨1,211,528,true⟩,0,0,0⟩, +⟨⟨1,211,530,true⟩,0,0,0⟩, +⟨⟨1,211,532,true⟩,0,0,0⟩, +⟨⟨1,211,534,true⟩,0,0,0⟩, +⟨⟨1,211,546,true⟩,0,0,0⟩, +⟨⟨1,211,547,true⟩,0,0,0⟩, +⟨⟨1,211,550,true⟩,0,0,0⟩, +⟨⟨1,211,551,true⟩,0,0,0⟩, +⟨⟨1,211,568,true⟩,0,0,0⟩, +⟨⟨1,211,570,true⟩,0,0,0⟩, +⟨⟨1,211,584,true⟩,0,0,0⟩, +⟨⟨1,211,586,true⟩,0,0,0⟩, +⟨⟨1,211,600,true⟩,0,0,0⟩, +⟨⟨1,211,602,true⟩,0,0,0⟩, +⟨⟨1,211,616,true⟩,0,0,0⟩, +⟨⟨1,211,618,true⟩,0,0,0⟩, +⟨⟨1,211,632,true⟩,0,0,0⟩, +⟨⟨1,211,634,true⟩,0,0,0⟩, +⟨⟨1,211,648,true⟩,0,0,0⟩, +⟨⟨1,211,650,true⟩,0,0,0⟩, +⟨⟨1,211,664,true⟩,0,0,0⟩, +⟨⟨1,211,666,true⟩,0,0,0⟩, +⟨⟨1,211,680,true⟩,0,0,0⟩, +⟨⟨1,211,682,true⟩,0,0,0⟩, +⟨⟨1,211,692,true⟩,0,0,0⟩, +⟨⟨1,211,694,true⟩,0,0,0⟩, +⟨⟨1,211,722,true⟩,0,0,0⟩, +⟨⟨1,211,723,true⟩,0,0,0⟩, +⟨⟨1,211,726,true⟩,0,0,0⟩, +⟨⟨1,211,727,true⟩,0,0,0⟩, +⟨⟨1,211,749,true⟩,0,0,0⟩, +⟨⟨1,211,788,true⟩,0,0,0⟩, +⟨⟨1,211,800,true⟩,0,0,0⟩, +⟨⟨1,211,892,true⟩,0,0,0⟩, +⟨⟨1,212,240,true⟩,0,0,0⟩, +⟨⟨1,212,246,true⟩,0,0,0⟩] +def chunk29 : List Entry := [⟨⟨1,212,290,true⟩,0,0,0⟩, +⟨⟨1,212,294,true⟩,0,0,0⟩, +⟨⟨1,212,296,true⟩,0,0,0⟩, +⟨⟨1,212,300,true⟩,0,0,0⟩, +⟨⟨1,212,306,true⟩,0,0,0⟩, +⟨⟨1,212,310,true⟩,0,0,0⟩, +⟨⟨1,212,312,true⟩,0,0,0⟩, +⟨⟨1,212,316,true⟩,0,0,0⟩, +⟨⟨1,212,340,true⟩,0,0,0⟩, +⟨⟨1,212,341,true⟩,0,0,0⟩, +⟨⟨1,212,345,true⟩,0,0,0⟩, +⟨⟨1,212,350,true⟩,0,0,0⟩, +⟨⟨1,212,354,true⟩,0,0,0⟩, +⟨⟨1,212,358,true⟩,0,0,0⟩, +⟨⟨1,212,360,true⟩,0,0,0⟩, +⟨⟨1,212,364,true⟩,0,0,0⟩, +⟨⟨1,212,370,true⟩,0,0,0⟩, +⟨⟨1,212,374,true⟩,0,0,0⟩, +⟨⟨1,212,376,true⟩,0,0,0⟩, +⟨⟨1,212,380,true⟩,0,0,0⟩, +⟨⟨1,212,416,true⟩,0,0,0⟩, +⟨⟨1,212,420,true⟩,0,0,0⟩, +⟨⟨1,212,426,true⟩,0,0,0⟩, +⟨⟨1,212,430,true⟩,0,0,0⟩, +⟨⟨1,212,432,true⟩,0,0,0⟩, +⟨⟨1,212,436,true⟩,0,0,0⟩, +⟨⟨1,212,442,true⟩,0,0,0⟩, +⟨⟨1,212,446,true⟩,0,0,0⟩, +⟨⟨1,212,462,true⟩,0,0,0⟩, +⟨⟨1,212,480,true⟩,0,0,0⟩, +⟨⟨1,212,484,true⟩,0,0,0⟩, +⟨⟨1,212,490,true⟩,0,0,0⟩, +⟨⟨1,212,494,true⟩,0,0,0⟩, +⟨⟨1,212,496,true⟩,0,0,0⟩, +⟨⟨1,212,500,true⟩,0,0,0⟩, +⟨⟨1,212,506,true⟩,0,0,0⟩, +⟨⟨1,212,510,true⟩,0,0,0⟩, +⟨⟨1,212,512,true⟩,0,0,0⟩, +⟨⟨1,212,513,true⟩,0,0,0⟩, +⟨⟨1,212,516,true⟩,0,0,0⟩, +⟨⟨1,212,517,true⟩,0,0,0⟩, +⟨⟨1,212,528,true⟩,0,0,0⟩, +⟨⟨1,212,530,true⟩,0,0,0⟩, +⟨⟨1,212,534,true⟩,0,0,0⟩, +⟨⟨1,212,535,true⟩,0,0,0⟩, +⟨⟨1,212,538,true⟩,0,0,0⟩, +⟨⟨1,212,546,true⟩,0,0,0⟩, +⟨⟨1,212,547,true⟩,0,0,0⟩, +⟨⟨1,212,550,true⟩,0,0,0⟩, +⟨⟨1,212,551,true⟩,0,0,0⟩, +⟨⟨1,212,569,true⟩,0,0,0⟩, +⟨⟨1,212,571,true⟩,0,0,0⟩, +⟨⟨1,212,585,true⟩,0,0,0⟩, +⟨⟨1,212,587,true⟩,0,0,0⟩, +⟨⟨1,212,600,true⟩,0,0,0⟩, +⟨⟨1,212,602,true⟩,0,0,0⟩, +⟨⟨1,212,616,true⟩,0,0,0⟩, +⟨⟨1,212,618,true⟩,0,0,0⟩, +⟨⟨1,212,633,true⟩,0,0,0⟩, +⟨⟨1,212,635,true⟩,0,0,0⟩, +⟨⟨1,212,649,true⟩,0,0,0⟩, +⟨⟨1,212,651,true⟩,0,0,0⟩, +⟨⟨1,212,664,true⟩,0,0,0⟩, +⟨⟨1,212,666,true⟩,0,0,0⟩, +⟨⟨1,212,680,true⟩,0,0,0⟩, +⟨⟨1,212,682,true⟩,0,0,0⟩, +⟨⟨1,212,688,true⟩,0,0,0⟩, +⟨⟨1,212,690,true⟩,0,0,0⟩, +⟨⟨1,212,722,true⟩,0,0,0⟩, +⟨⟨1,212,723,true⟩,0,0,0⟩, +⟨⟨1,212,726,true⟩,0,0,0⟩, +⟨⟨1,212,727,true⟩,0,0,0⟩, +⟨⟨1,212,748,true⟩,0,0,0⟩, +⟨⟨1,212,890,true⟩,0,0,0⟩, +⟨⟨1,212,952,true⟩,0,0,0⟩, +⟨⟨1,213,240,true⟩,0,0,0⟩, +⟨⟨1,213,246,true⟩,0,0,0⟩, +⟨⟨1,213,288,true⟩,0,0,0⟩, +⟨⟨1,213,292,true⟩,0,0,0⟩, +⟨⟨1,213,298,true⟩,0,0,0⟩, +⟨⟨1,213,302,true⟩,0,0,0⟩, +⟨⟨1,213,306,true⟩,0,0,0⟩, +⟨⟨1,213,310,true⟩,0,0,0⟩, +⟨⟨1,213,312,true⟩,0,0,0⟩, +⟨⟨1,213,316,true⟩,0,0,0⟩, +⟨⟨1,213,352,true⟩,0,0,0⟩, +⟨⟨1,213,356,true⟩,0,0,0⟩, +⟨⟨1,213,362,true⟩,0,0,0⟩, +⟨⟨1,213,366,true⟩,0,0,0⟩, +⟨⟨1,213,370,true⟩,0,0,0⟩, +⟨⟨1,213,374,true⟩,0,0,0⟩, +⟨⟨1,213,376,true⟩,0,0,0⟩, +⟨⟨1,213,380,true⟩,0,0,0⟩, +⟨⟨1,213,418,true⟩,0,0,0⟩, +⟨⟨1,213,422,true⟩,0,0,0⟩, +⟨⟨1,213,424,true⟩,0,0,0⟩, +⟨⟨1,213,428,true⟩,0,0,0⟩, +⟨⟨1,213,432,true⟩,0,0,0⟩, +⟨⟨1,213,436,true⟩,0,0,0⟩, +⟨⟨1,213,442,true⟩,0,0,0⟩, +⟨⟨1,213,446,true⟩,0,0,0⟩, +⟨⟨1,213,461,true⟩,0,0,0⟩, +⟨⟨1,213,482,true⟩,0,0,0⟩, +⟨⟨1,213,486,true⟩,0,0,0⟩, +⟨⟨1,213,488,true⟩,0,0,0⟩, +⟨⟨1,213,492,true⟩,0,0,0⟩, +⟨⟨1,213,496,true⟩,0,0,0⟩, +⟨⟨1,213,500,true⟩,0,0,0⟩, +⟨⟨1,213,506,true⟩,0,0,0⟩, +⟨⟨1,213,510,true⟩,0,0,0⟩, +⟨⟨1,213,512,true⟩,0,0,0⟩, +⟨⟨1,213,513,true⟩,0,0,0⟩, +⟨⟨1,213,516,true⟩,0,0,0⟩, +⟨⟨1,213,517,true⟩,0,0,0⟩, +⟨⟨1,213,528,true⟩,0,0,0⟩, +⟨⟨1,213,530,true⟩,0,0,0⟩, +⟨⟨1,213,532,true⟩,0,0,0⟩, +⟨⟨1,213,534,true⟩,0,0,0⟩, +⟨⟨1,213,544,true⟩,0,0,0⟩, +⟨⟨1,213,545,true⟩,0,0,0⟩, +⟨⟨1,213,548,true⟩,0,0,0⟩, +⟨⟨1,213,549,true⟩,0,0,0⟩, +⟨⟨1,213,569,true⟩,0,0,0⟩, +⟨⟨1,213,571,true⟩,0,0,0⟩, +⟨⟨1,213,584,true⟩,0,0,0⟩, +⟨⟨1,213,586,true⟩,0,0,0⟩, +⟨⟨1,213,601,true⟩,0,0,0⟩, +⟨⟨1,213,603,true⟩,0,0,0⟩, +⟨⟨1,213,616,true⟩,0,0,0⟩, +⟨⟨1,213,618,true⟩,0,0,0⟩, +⟨⟨1,213,632,true⟩,0,0,0⟩, +⟨⟨1,213,634,true⟩,0,0,0⟩, +⟨⟨1,213,649,true⟩,0,0,0⟩, +⟨⟨1,213,651,true⟩,0,0,0⟩, +⟨⟨1,213,664,true⟩,0,0,0⟩, +⟨⟨1,213,666,true⟩,0,0,0⟩, +⟨⟨1,213,681,true⟩,0,0,0⟩, +⟨⟨1,213,683,true⟩,0,0,0⟩, +⟨⟨1,213,688,true⟩,0,0,0⟩, +⟨⟨1,213,690,true⟩,0,0,0⟩, +⟨⟨1,213,720,true⟩,0,0,0⟩, +⟨⟨1,213,721,true⟩,0,0,0⟩, +⟨⟨1,213,724,true⟩,0,0,0⟩, +⟨⟨1,213,725,true⟩,0,0,0⟩, +⟨⟨1,213,748,true⟩,0,0,0⟩, +⟨⟨1,213,800,true⟩,0,0,0⟩, +⟨⟨1,213,890,true⟩,0,0,0⟩, +⟨⟨1,214,240,true⟩,0,0,0⟩, +⟨⟨1,214,246,true⟩,0,0,0⟩, +⟨⟨1,214,290,true⟩,0,0,0⟩, +⟨⟨1,214,294,true⟩,0,0,0⟩, +⟨⟨1,214,296,true⟩,0,0,0⟩, +⟨⟨1,214,300,true⟩,0,0,0⟩, +⟨⟨1,214,304,true⟩,0,0,0⟩, +⟨⟨1,214,308,true⟩,0,0,0⟩, +⟨⟨1,214,314,true⟩,0,0,0⟩, +⟨⟨1,214,318,true⟩,0,0,0⟩, +⟨⟨1,214,354,true⟩,0,0,0⟩, +⟨⟨1,214,358,true⟩,0,0,0⟩, +⟨⟨1,214,360,true⟩,0,0,0⟩, +⟨⟨1,214,364,true⟩,0,0,0⟩, +⟨⟨1,214,368,true⟩,0,0,0⟩, +⟨⟨1,214,372,true⟩,0,0,0⟩, +⟨⟨1,214,378,true⟩,0,0,0⟩, +⟨⟨1,214,382,true⟩,0,0,0⟩, +⟨⟨1,214,416,true⟩,0,0,0⟩, +⟨⟨1,214,420,true⟩,0,0,0⟩, +⟨⟨1,214,426,true⟩,0,0,0⟩, +⟨⟨1,214,430,true⟩,0,0,0⟩, +⟨⟨1,214,434,true⟩,0,0,0⟩, +⟨⟨1,214,438,true⟩,0,0,0⟩, +⟨⟨1,214,440,true⟩,0,0,0⟩, +⟨⟨1,214,444,true⟩,0,0,0⟩, +⟨⟨1,214,459,true⟩,0,0,0⟩, +⟨⟨1,214,480,true⟩,0,0,0⟩, +⟨⟨1,214,484,true⟩,0,0,0⟩, +⟨⟨1,214,490,true⟩,0,0,0⟩, +⟨⟨1,214,494,true⟩,0,0,0⟩, +⟨⟨1,214,498,true⟩,0,0,0⟩, +⟨⟨1,214,502,true⟩,0,0,0⟩, +⟨⟨1,214,504,true⟩,0,0,0⟩, +⟨⟨1,214,508,true⟩,0,0,0⟩, +⟨⟨1,214,512,true⟩,0,0,0⟩, +⟨⟨1,214,513,true⟩,0,0,0⟩, +⟨⟨1,214,516,true⟩,0,0,0⟩, +⟨⟨1,214,517,true⟩,0,0,0⟩, +⟨⟨1,214,528,true⟩,0,0,0⟩, +⟨⟨1,214,530,true⟩,0,0,0⟩, +⟨⟨1,214,532,true⟩,0,0,0⟩, +⟨⟨1,214,534,true⟩,0,0,0⟩, +⟨⟨1,214,544,true⟩,0,0,0⟩, +⟨⟨1,214,545,true⟩,0,0,0⟩, +⟨⟨1,214,548,true⟩,0,0,0⟩, +⟨⟨1,214,549,true⟩,0,0,0⟩, +⟨⟨1,214,568,true⟩,0,0,0⟩, +⟨⟨1,214,570,true⟩,0,0,0⟩, +⟨⟨1,214,585,true⟩,0,0,0⟩, +⟨⟨1,214,587,true⟩,0,0,0⟩, +⟨⟨1,214,600,true⟩,0,0,0⟩, +⟨⟨1,214,602,true⟩,0,0,0⟩] +def chunk30 : List Entry := [⟨⟨1,214,617,true⟩,0,0,0⟩, +⟨⟨1,214,619,true⟩,0,0,0⟩, +⟨⟨1,214,633,true⟩,0,0,0⟩, +⟨⟨1,214,635,true⟩,0,0,0⟩, +⟨⟨1,214,648,true⟩,0,0,0⟩, +⟨⟨1,214,650,true⟩,0,0,0⟩, +⟨⟨1,214,665,true⟩,0,0,0⟩, +⟨⟨1,214,667,true⟩,0,0,0⟩, +⟨⟨1,214,680,true⟩,0,0,0⟩, +⟨⟨1,214,682,true⟩,0,0,0⟩, +⟨⟨1,214,688,true⟩,0,0,0⟩, +⟨⟨1,214,690,true⟩,0,0,0⟩, +⟨⟨1,214,720,true⟩,0,0,0⟩, +⟨⟨1,214,721,true⟩,0,0,0⟩, +⟨⟨1,214,724,true⟩,0,0,0⟩, +⟨⟨1,214,725,true⟩,0,0,0⟩, +⟨⟨1,214,748,true⟩,0,0,0⟩, +⟨⟨1,214,788,true⟩,0,0,0⟩, +⟨⟨1,214,890,true⟩,0,0,0⟩, +⟨⟨1,215,240,true⟩,0,0,0⟩, +⟨⟨1,215,246,true⟩,0,0,0⟩, +⟨⟨1,215,288,true⟩,0,0,0⟩, +⟨⟨1,215,292,true⟩,0,0,0⟩, +⟨⟨1,215,298,true⟩,0,0,0⟩, +⟨⟨1,215,302,true⟩,0,0,0⟩, +⟨⟨1,215,304,true⟩,0,0,0⟩, +⟨⟨1,215,308,true⟩,0,0,0⟩, +⟨⟨1,215,314,true⟩,0,0,0⟩, +⟨⟨1,215,318,true⟩,0,0,0⟩, +⟨⟨1,215,338,true⟩,0,0,0⟩, +⟨⟨1,215,339,true⟩,0,0,0⟩, +⟨⟨1,215,344,true⟩,0,0,0⟩, +⟨⟨1,215,351,true⟩,0,0,0⟩, +⟨⟨1,215,352,true⟩,0,0,0⟩, +⟨⟨1,215,356,true⟩,0,0,0⟩, +⟨⟨1,215,362,true⟩,0,0,0⟩, +⟨⟨1,215,366,true⟩,0,0,0⟩, +⟨⟨1,215,368,true⟩,0,0,0⟩, +⟨⟨1,215,372,true⟩,0,0,0⟩, +⟨⟨1,215,378,true⟩,0,0,0⟩, +⟨⟨1,215,382,true⟩,0,0,0⟩, +⟨⟨1,215,418,true⟩,0,0,0⟩, +⟨⟨1,215,422,true⟩,0,0,0⟩, +⟨⟨1,215,424,true⟩,0,0,0⟩, +⟨⟨1,215,428,true⟩,0,0,0⟩, +⟨⟨1,215,434,true⟩,0,0,0⟩, +⟨⟨1,215,438,true⟩,0,0,0⟩, +⟨⟨1,215,440,true⟩,0,0,0⟩, +⟨⟨1,215,444,true⟩,0,0,0⟩, +⟨⟨1,215,456,true⟩,0,0,0⟩, +⟨⟨1,215,482,true⟩,0,0,0⟩, +⟨⟨1,215,486,true⟩,0,0,0⟩, +⟨⟨1,215,488,true⟩,0,0,0⟩, +⟨⟨1,215,492,true⟩,0,0,0⟩, +⟨⟨1,215,498,true⟩,0,0,0⟩, +⟨⟨1,215,502,true⟩,0,0,0⟩, +⟨⟨1,215,504,true⟩,0,0,0⟩, +⟨⟨1,215,508,true⟩,0,0,0⟩, +⟨⟨1,215,512,true⟩,0,0,0⟩, +⟨⟨1,215,513,true⟩,0,0,0⟩, +⟨⟨1,215,516,true⟩,0,0,0⟩, +⟨⟨1,215,517,true⟩,0,0,0⟩, +⟨⟨1,215,528,true⟩,0,0,0⟩, +⟨⟨1,215,530,true⟩,0,0,0⟩, +⟨⟨1,215,533,true⟩,0,0,0⟩, +⟨⟨1,215,534,true⟩,0,0,0⟩, +⟨⟨1,215,535,true⟩,0,0,0⟩, +⟨⟨1,215,542,true⟩,0,0,0⟩, +⟨⟨1,215,543,true⟩,0,0,0⟩, +⟨⟨1,215,546,true⟩,0,0,0⟩, +⟨⟨1,215,547,true⟩,0,0,0⟩, +⟨⟨1,215,550,true⟩,0,0,0⟩, +⟨⟨1,215,551,true⟩,0,0,0⟩, +⟨⟨1,215,568,true⟩,0,0,0⟩, +⟨⟨1,215,570,true⟩,0,0,0⟩, +⟨⟨1,215,584,true⟩,0,0,0⟩, +⟨⟨1,215,586,true⟩,0,0,0⟩, +⟨⟨1,215,601,true⟩,0,0,0⟩, +⟨⟨1,215,603,true⟩,0,0,0⟩, +⟨⟨1,215,617,true⟩,0,0,0⟩, +⟨⟨1,215,619,true⟩,0,0,0⟩, +⟨⟨1,215,632,true⟩,0,0,0⟩, +⟨⟨1,215,634,true⟩,0,0,0⟩, +⟨⟨1,215,648,true⟩,0,0,0⟩, +⟨⟨1,215,650,true⟩,0,0,0⟩, +⟨⟨1,215,665,true⟩,0,0,0⟩, +⟨⟨1,215,667,true⟩,0,0,0⟩, +⟨⟨1,215,681,true⟩,0,0,0⟩, +⟨⟨1,215,683,true⟩,0,0,0⟩, +⟨⟨1,215,688,true⟩,0,0,0⟩, +⟨⟨1,215,690,true⟩,0,0,0⟩, +⟨⟨1,215,722,true⟩,0,0,0⟩, +⟨⟨1,215,723,true⟩,0,0,0⟩, +⟨⟨1,215,726,true⟩,0,0,0⟩, +⟨⟨1,215,727,true⟩,0,0,0⟩, +⟨⟨1,215,748,true⟩,0,0,0⟩, +⟨⟨1,215,788,true⟩,0,0,0⟩, +⟨⟨1,215,800,true⟩,0,0,0⟩, +⟨⟨1,215,890,true⟩,0,0,0⟩, +⟨⟨1,215,948,true⟩,0,0,0⟩, +⟨⟨1,215,954,true⟩,0,0,0⟩, +⟨⟨1,216,241,true⟩,0,0,0⟩, +⟨⟨1,216,247,true⟩,0,0,0⟩, +⟨⟨1,216,293,true⟩,0,0,0⟩, +⟨⟨1,216,295,true⟩,0,0,0⟩, +⟨⟨1,216,297,true⟩,0,0,0⟩, +⟨⟨1,216,299,true⟩,0,0,0⟩, +⟨⟨1,216,309,true⟩,0,0,0⟩, +⟨⟨1,216,311,true⟩,0,0,0⟩, +⟨⟨1,216,313,true⟩,0,0,0⟩, +⟨⟨1,216,315,true⟩,0,0,0⟩, +⟨⟨1,216,357,true⟩,0,0,0⟩, +⟨⟨1,216,359,true⟩,0,0,0⟩, +⟨⟨1,216,361,true⟩,0,0,0⟩, +⟨⟨1,216,363,true⟩,0,0,0⟩, +⟨⟨1,216,373,true⟩,0,0,0⟩, +⟨⟨1,216,375,true⟩,0,0,0⟩, +⟨⟨1,216,377,true⟩,0,0,0⟩, +⟨⟨1,216,379,true⟩,0,0,0⟩, +⟨⟨1,216,421,true⟩,0,0,0⟩, +⟨⟨1,216,423,true⟩,0,0,0⟩, +⟨⟨1,216,425,true⟩,0,0,0⟩, +⟨⟨1,216,427,true⟩,0,0,0⟩, +⟨⟨1,216,437,true⟩,0,0,0⟩, +⟨⟨1,216,439,true⟩,0,0,0⟩, +⟨⟨1,216,441,true⟩,0,0,0⟩, +⟨⟨1,216,443,true⟩,0,0,0⟩, +⟨⟨1,216,470,true⟩,0,0,0⟩, +⟨⟨1,216,485,true⟩,0,0,0⟩, +⟨⟨1,216,487,true⟩,0,0,0⟩, +⟨⟨1,216,489,true⟩,0,0,0⟩, +⟨⟨1,216,491,true⟩,0,0,0⟩, +⟨⟨1,216,501,true⟩,0,0,0⟩, +⟨⟨1,216,503,true⟩,0,0,0⟩, +⟨⟨1,216,505,true⟩,0,0,0⟩, +⟨⟨1,216,507,true⟩,0,0,0⟩, +⟨⟨1,216,514,true⟩,0,0,0⟩, +⟨⟨1,216,515,true⟩,0,0,0⟩, +⟨⟨1,216,518,true⟩,0,0,0⟩, +⟨⟨1,216,519,true⟩,0,0,0⟩, +⟨⟨1,216,530,true⟩,0,0,0⟩, +⟨⟨1,216,531,true⟩,0,0,0⟩, +⟨⟨1,216,534,true⟩,0,0,0⟩, +⟨⟨1,216,535,true⟩,0,0,0⟩, +⟨⟨1,216,544,true⟩,0,0,0⟩, +⟨⟨1,216,546,true⟩,0,0,0⟩, +⟨⟨1,216,548,true⟩,0,0,0⟩, +⟨⟨1,216,550,true⟩,0,0,0⟩, +⟨⟨1,216,573,true⟩,0,0,0⟩, +⟨⟨1,216,575,true⟩,0,0,0⟩, +⟨⟨1,216,589,true⟩,0,0,0⟩, +⟨⟨1,216,591,true⟩,0,0,0⟩, +⟨⟨1,216,605,true⟩,0,0,0⟩, +⟨⟨1,216,607,true⟩,0,0,0⟩, +⟨⟨1,216,621,true⟩,0,0,0⟩, +⟨⟨1,216,623,true⟩,0,0,0⟩, +⟨⟨1,216,637,true⟩,0,0,0⟩, +⟨⟨1,216,639,true⟩,0,0,0⟩, +⟨⟨1,216,653,true⟩,0,0,0⟩, +⟨⟨1,216,655,true⟩,0,0,0⟩, +⟨⟨1,216,669,true⟩,0,0,0⟩, +⟨⟨1,216,671,true⟩,0,0,0⟩, +⟨⟨1,216,685,true⟩,0,0,0⟩, +⟨⟨1,216,687,true⟩,0,0,0⟩, +⟨⟨1,216,708,true⟩,0,0,0⟩, +⟨⟨1,216,710,true⟩,0,0,0⟩, +⟨⟨1,216,724,true⟩,0,0,0⟩, +⟨⟨1,216,726,true⟩,0,0,0⟩, +⟨⟨1,216,906,true⟩,0,0,0⟩, +⟨⟨1,216,920,true⟩,0,0,0⟩, +⟨⟨1,217,241,true⟩,0,0,0⟩, +⟨⟨1,217,247,true⟩,0,0,0⟩, +⟨⟨1,217,293,true⟩,0,0,0⟩, +⟨⟨1,217,295,true⟩,0,0,0⟩, +⟨⟨1,217,297,true⟩,0,0,0⟩, +⟨⟨1,217,299,true⟩,0,0,0⟩, +⟨⟨1,217,309,true⟩,0,0,0⟩, +⟨⟨1,217,311,true⟩,0,0,0⟩, +⟨⟨1,217,313,true⟩,0,0,0⟩, +⟨⟨1,217,315,true⟩,0,0,0⟩, +⟨⟨1,217,323,true⟩,0,0,0⟩, +⟨⟨1,217,325,true⟩,0,0,0⟩, +⟨⟨1,217,329,true⟩,0,0,0⟩, +⟨⟨1,217,335,true⟩,0,0,0⟩, +⟨⟨1,217,353,true⟩,0,0,0⟩, +⟨⟨1,217,355,true⟩,0,0,0⟩, +⟨⟨1,217,365,true⟩,0,0,0⟩, +⟨⟨1,217,367,true⟩,0,0,0⟩, +⟨⟨1,217,369,true⟩,0,0,0⟩, +⟨⟨1,217,371,true⟩,0,0,0⟩, +⟨⟨1,217,381,true⟩,0,0,0⟩, +⟨⟨1,217,383,true⟩,0,0,0⟩, +⟨⟨1,217,421,true⟩,0,0,0⟩, +⟨⟨1,217,423,true⟩,0,0,0⟩, +⟨⟨1,217,425,true⟩,0,0,0⟩, +⟨⟨1,217,427,true⟩,0,0,0⟩, +⟨⟨1,217,437,true⟩,0,0,0⟩, +⟨⟨1,217,439,true⟩,0,0,0⟩, +⟨⟨1,217,441,true⟩,0,0,0⟩, +⟨⟨1,217,443,true⟩,0,0,0⟩] +def chunk31 : List Entry := [⟨⟨1,217,469,true⟩,0,0,0⟩, +⟨⟨1,217,481,true⟩,0,0,0⟩, +⟨⟨1,217,483,true⟩,0,0,0⟩, +⟨⟨1,217,493,true⟩,0,0,0⟩, +⟨⟨1,217,495,true⟩,0,0,0⟩, +⟨⟨1,217,497,true⟩,0,0,0⟩, +⟨⟨1,217,499,true⟩,0,0,0⟩, +⟨⟨1,217,509,true⟩,0,0,0⟩, +⟨⟨1,217,511,true⟩,0,0,0⟩, +⟨⟨1,217,514,true⟩,0,0,0⟩, +⟨⟨1,217,515,true⟩,0,0,0⟩, +⟨⟨1,217,518,true⟩,0,0,0⟩, +⟨⟨1,217,519,true⟩,0,0,0⟩, +⟨⟨1,217,528,true⟩,0,0,0⟩, +⟨⟨1,217,529,true⟩,0,0,0⟩, +⟨⟨1,217,532,true⟩,0,0,0⟩, +⟨⟨1,217,533,true⟩,0,0,0⟩, +⟨⟨1,217,544,true⟩,0,0,0⟩, +⟨⟨1,217,549,true⟩,0,0,0⟩, +⟨⟨1,217,550,true⟩,0,0,0⟩, +⟨⟨1,217,558,true⟩,0,0,0⟩, +⟨⟨1,217,559,true⟩,0,0,0⟩, +⟨⟨1,217,573,true⟩,0,0,0⟩, +⟨⟨1,217,575,true⟩,0,0,0⟩, +⟨⟨1,217,588,true⟩,0,0,0⟩, +⟨⟨1,217,590,true⟩,0,0,0⟩, +⟨⟨1,217,605,true⟩,0,0,0⟩, +⟨⟨1,217,607,true⟩,0,0,0⟩, +⟨⟨1,217,620,true⟩,0,0,0⟩, +⟨⟨1,217,622,true⟩,0,0,0⟩, +⟨⟨1,217,637,true⟩,0,0,0⟩, +⟨⟨1,217,639,true⟩,0,0,0⟩, +⟨⟨1,217,652,true⟩,0,0,0⟩, +⟨⟨1,217,654,true⟩,0,0,0⟩, +⟨⟨1,217,669,true⟩,0,0,0⟩, +⟨⟨1,217,671,true⟩,0,0,0⟩, +⟨⟨1,217,684,true⟩,0,0,0⟩, +⟨⟨1,217,686,true⟩,0,0,0⟩, +⟨⟨1,217,708,true⟩,0,0,0⟩, +⟨⟨1,217,710,true⟩,0,0,0⟩, +⟨⟨1,217,720,true⟩,0,0,0⟩, +⟨⟨1,217,722,true⟩,0,0,0⟩, +⟨⟨1,217,802,true⟩,0,0,0⟩, +⟨⟨1,217,906,true⟩,0,0,0⟩, +⟨⟨1,217,918,true⟩,0,0,0⟩, +⟨⟨1,217,945,true⟩,0,0,0⟩, +⟨⟨1,217,956,true⟩,0,0,0⟩, +⟨⟨1,218,241,true⟩,0,0,0⟩, +⟨⟨1,218,247,true⟩,0,0,0⟩, +⟨⟨1,218,289,true⟩,0,0,0⟩, +⟨⟨1,218,291,true⟩,0,0,0⟩, +⟨⟨1,218,301,true⟩,0,0,0⟩, +⟨⟨1,218,303,true⟩,0,0,0⟩, +⟨⟨1,218,305,true⟩,0,0,0⟩, +⟨⟨1,218,307,true⟩,0,0,0⟩, +⟨⟨1,218,317,true⟩,0,0,0⟩, +⟨⟨1,218,319,true⟩,0,0,0⟩, +⟨⟨1,218,322,true⟩,0,0,0⟩, +⟨⟨1,218,324,true⟩,0,0,0⟩, +⟨⟨1,218,328,true⟩,0,0,0⟩, +⟨⟨1,218,334,true⟩,0,0,0⟩, +⟨⟨1,218,357,true⟩,0,0,0⟩, +⟨⟨1,218,359,true⟩,0,0,0⟩, +⟨⟨1,218,361,true⟩,0,0,0⟩, +⟨⟨1,218,363,true⟩,0,0,0⟩, +⟨⟨1,218,373,true⟩,0,0,0⟩, +⟨⟨1,218,375,true⟩,0,0,0⟩, +⟨⟨1,218,377,true⟩,0,0,0⟩, +⟨⟨1,218,379,true⟩,0,0,0⟩, +⟨⟨1,218,417,true⟩,0,0,0⟩, +⟨⟨1,218,419,true⟩,0,0,0⟩, +⟨⟨1,218,429,true⟩,0,0,0⟩, +⟨⟨1,218,431,true⟩,0,0,0⟩, +⟨⟨1,218,433,true⟩,0,0,0⟩, +⟨⟨1,218,435,true⟩,0,0,0⟩, +⟨⟨1,218,445,true⟩,0,0,0⟩, +⟨⟨1,218,447,true⟩,0,0,0⟩, +⟨⟨1,218,467,true⟩,0,0,0⟩, +⟨⟨1,218,485,true⟩,0,0,0⟩, +⟨⟨1,218,487,true⟩,0,0,0⟩, +⟨⟨1,218,489,true⟩,0,0,0⟩, +⟨⟨1,218,491,true⟩,0,0,0⟩, +⟨⟨1,218,501,true⟩,0,0,0⟩, +⟨⟨1,218,503,true⟩,0,0,0⟩, +⟨⟨1,218,505,true⟩,0,0,0⟩, +⟨⟨1,218,507,true⟩,0,0,0⟩, +⟨⟨1,218,514,true⟩,0,0,0⟩, +⟨⟨1,218,515,true⟩,0,0,0⟩, +⟨⟨1,218,518,true⟩,0,0,0⟩, +⟨⟨1,218,519,true⟩,0,0,0⟩, +⟨⟨1,218,528,true⟩,0,0,0⟩, +⟨⟨1,218,529,true⟩,0,0,0⟩, +⟨⟨1,218,532,true⟩,0,0,0⟩, +⟨⟨1,218,533,true⟩,0,0,0⟩, +⟨⟨1,218,544,true⟩,0,0,0⟩, +⟨⟨1,218,550,true⟩,0,0,0⟩, +⟨⟨1,218,554,true⟩,0,0,0⟩, +⟨⟨1,218,559,true⟩,0,0,0⟩, +⟨⟨1,218,572,true⟩,0,0,0⟩, +⟨⟨1,218,574,true⟩,0,0,0⟩, +⟨⟨1,218,589,true⟩,0,0,0⟩, +⟨⟨1,218,591,true⟩,0,0,0⟩, +⟨⟨1,218,604,true⟩,0,0,0⟩, +⟨⟨1,218,606,true⟩,0,0,0⟩, +⟨⟨1,218,621,true⟩,0,0,0⟩, +⟨⟨1,218,623,true⟩,0,0,0⟩, +⟨⟨1,218,636,true⟩,0,0,0⟩, +⟨⟨1,218,638,true⟩,0,0,0⟩, +⟨⟨1,218,653,true⟩,0,0,0⟩, +⟨⟨1,218,655,true⟩,0,0,0⟩, +⟨⟨1,218,668,true⟩,0,0,0⟩, +⟨⟨1,218,670,true⟩,0,0,0⟩, +⟨⟨1,218,685,true⟩,0,0,0⟩, +⟨⟨1,218,687,true⟩,0,0,0⟩, +⟨⟨1,218,708,true⟩,0,0,0⟩, +⟨⟨1,218,710,true⟩,0,0,0⟩, +⟨⟨1,218,720,true⟩,0,0,0⟩, +⟨⟨1,218,722,true⟩,0,0,0⟩, +⟨⟨1,218,786,true⟩,0,0,0⟩, +⟨⟨1,218,816,true⟩,0,0,0⟩, +⟨⟨1,218,906,true⟩,0,0,0⟩, +⟨⟨1,218,918,true⟩,0,0,0⟩, +⟨⟨1,218,943,true⟩,0,0,0⟩, +⟨⟨1,219,241,true⟩,0,0,0⟩, +⟨⟨1,219,247,true⟩,0,0,0⟩, +⟨⟨1,219,289,true⟩,0,0,0⟩, +⟨⟨1,219,291,true⟩,0,0,0⟩, +⟨⟨1,219,301,true⟩,0,0,0⟩, +⟨⟨1,219,303,true⟩,0,0,0⟩, +⟨⟨1,219,305,true⟩,0,0,0⟩, +⟨⟨1,219,307,true⟩,0,0,0⟩, +⟨⟨1,219,317,true⟩,0,0,0⟩, +⟨⟨1,219,319,true⟩,0,0,0⟩, +⟨⟨1,219,353,true⟩,0,0,0⟩, +⟨⟨1,219,355,true⟩,0,0,0⟩, +⟨⟨1,219,365,true⟩,0,0,0⟩, +⟨⟨1,219,367,true⟩,0,0,0⟩, +⟨⟨1,219,369,true⟩,0,0,0⟩, +⟨⟨1,219,371,true⟩,0,0,0⟩, +⟨⟨1,219,381,true⟩,0,0,0⟩, +⟨⟨1,219,383,true⟩,0,0,0⟩, +⟨⟨1,219,417,true⟩,0,0,0⟩, +⟨⟨1,219,419,true⟩,0,0,0⟩, +⟨⟨1,219,429,true⟩,0,0,0⟩, +⟨⟨1,219,431,true⟩,0,0,0⟩, +⟨⟨1,219,433,true⟩,0,0,0⟩, +⟨⟨1,219,435,true⟩,0,0,0⟩, +⟨⟨1,219,445,true⟩,0,0,0⟩, +⟨⟨1,219,447,true⟩,0,0,0⟩, +⟨⟨1,219,464,true⟩,0,0,0⟩, +⟨⟨1,219,481,true⟩,0,0,0⟩, +⟨⟨1,219,483,true⟩,0,0,0⟩, +⟨⟨1,219,493,true⟩,0,0,0⟩, +⟨⟨1,219,495,true⟩,0,0,0⟩, +⟨⟨1,219,497,true⟩,0,0,0⟩, +⟨⟨1,219,499,true⟩,0,0,0⟩, +⟨⟨1,219,509,true⟩,0,0,0⟩, +⟨⟨1,219,511,true⟩,0,0,0⟩, +⟨⟨1,219,514,true⟩,0,0,0⟩, +⟨⟨1,219,515,true⟩,0,0,0⟩, +⟨⟨1,219,518,true⟩,0,0,0⟩, +⟨⟨1,219,519,true⟩,0,0,0⟩, +⟨⟨1,219,530,true⟩,0,0,0⟩, +⟨⟨1,219,531,true⟩,0,0,0⟩, +⟨⟨1,219,534,true⟩,0,0,0⟩, +⟨⟨1,219,535,true⟩,0,0,0⟩, +⟨⟨1,219,544,true⟩,0,0,0⟩, +⟨⟨1,219,546,true⟩,0,0,0⟩, +⟨⟨1,219,548,true⟩,0,0,0⟩, +⟨⟨1,219,550,true⟩,0,0,0⟩, +⟨⟨1,219,572,true⟩,0,0,0⟩, +⟨⟨1,219,574,true⟩,0,0,0⟩, +⟨⟨1,219,588,true⟩,0,0,0⟩, +⟨⟨1,219,590,true⟩,0,0,0⟩, +⟨⟨1,219,604,true⟩,0,0,0⟩, +⟨⟨1,219,606,true⟩,0,0,0⟩, +⟨⟨1,219,620,true⟩,0,0,0⟩, +⟨⟨1,219,622,true⟩,0,0,0⟩, +⟨⟨1,219,636,true⟩,0,0,0⟩, +⟨⟨1,219,638,true⟩,0,0,0⟩, +⟨⟨1,219,652,true⟩,0,0,0⟩, +⟨⟨1,219,654,true⟩,0,0,0⟩, +⟨⟨1,219,668,true⟩,0,0,0⟩, +⟨⟨1,219,670,true⟩,0,0,0⟩, +⟨⟨1,219,684,true⟩,0,0,0⟩, +⟨⟨1,219,686,true⟩,0,0,0⟩, +⟨⟨1,219,708,true⟩,0,0,0⟩, +⟨⟨1,219,710,true⟩,0,0,0⟩, +⟨⟨1,219,724,true⟩,0,0,0⟩, +⟨⟨1,219,726,true⟩,0,0,0⟩, +⟨⟨1,219,786,true⟩,0,0,0⟩, +⟨⟨1,219,802,true⟩,0,0,0⟩, +⟨⟨1,219,816,true⟩,0,0,0⟩, +⟨⟨1,219,906,true⟩,0,0,0⟩, +⟨⟨1,219,920,true⟩,0,0,0⟩, +⟨⟨1,220,241,true⟩,0,0,0⟩, +⟨⟨1,220,247,true⟩,0,0,0⟩, +⟨⟨1,220,293,true⟩,0,0,0⟩, +⟨⟨1,220,295,true⟩,0,0,0⟩, +⟨⟨1,220,297,true⟩,0,0,0⟩] +def chunk32 : List Entry := [⟨⟨1,220,299,true⟩,0,0,0⟩, +⟨⟨1,220,309,true⟩,0,0,0⟩, +⟨⟨1,220,311,true⟩,0,0,0⟩, +⟨⟨1,220,313,true⟩,0,0,0⟩, +⟨⟨1,220,315,true⟩,0,0,0⟩, +⟨⟨1,220,324,true⟩,0,0,0⟩, +⟨⟨1,220,325,true⟩,0,0,0⟩, +⟨⟨1,220,329,true⟩,0,0,0⟩, +⟨⟨1,220,334,true⟩,0,0,0⟩, +⟨⟨1,220,357,true⟩,0,0,0⟩, +⟨⟨1,220,359,true⟩,0,0,0⟩, +⟨⟨1,220,361,true⟩,0,0,0⟩, +⟨⟨1,220,363,true⟩,0,0,0⟩, +⟨⟨1,220,373,true⟩,0,0,0⟩, +⟨⟨1,220,375,true⟩,0,0,0⟩, +⟨⟨1,220,377,true⟩,0,0,0⟩, +⟨⟨1,220,379,true⟩,0,0,0⟩, +⟨⟨1,220,417,true⟩,0,0,0⟩, +⟨⟨1,220,419,true⟩,0,0,0⟩, +⟨⟨1,220,429,true⟩,0,0,0⟩, +⟨⟨1,220,431,true⟩,0,0,0⟩, +⟨⟨1,220,433,true⟩,0,0,0⟩, +⟨⟨1,220,435,true⟩,0,0,0⟩, +⟨⟨1,220,445,true⟩,0,0,0⟩, +⟨⟨1,220,447,true⟩,0,0,0⟩, +⟨⟨1,220,478,true⟩,0,0,0⟩, +⟨⟨1,220,481,true⟩,0,0,0⟩, +⟨⟨1,220,483,true⟩,0,0,0⟩, +⟨⟨1,220,493,true⟩,0,0,0⟩, +⟨⟨1,220,495,true⟩,0,0,0⟩, +⟨⟨1,220,497,true⟩,0,0,0⟩, +⟨⟨1,220,499,true⟩,0,0,0⟩, +⟨⟨1,220,509,true⟩,0,0,0⟩, +⟨⟨1,220,511,true⟩,0,0,0⟩, +⟨⟨1,220,512,true⟩,0,0,0⟩, +⟨⟨1,220,513,true⟩,0,0,0⟩, +⟨⟨1,220,516,true⟩,0,0,0⟩, +⟨⟨1,220,517,true⟩,0,0,0⟩, +⟨⟨1,220,530,true⟩,0,0,0⟩, +⟨⟨1,220,531,true⟩,0,0,0⟩, +⟨⟨1,220,534,true⟩,0,0,0⟩, +⟨⟨1,220,535,true⟩,0,0,0⟩, +⟨⟨1,220,544,true⟩,0,0,0⟩, +⟨⟨1,220,546,true⟩,0,0,0⟩, +⟨⟨1,220,549,true⟩,0,0,0⟩, +⟨⟨1,220,550,true⟩,0,0,0⟩, +⟨⟨1,220,554,true⟩,0,0,0⟩, +⟨⟨1,220,555,true⟩,0,0,0⟩, +⟨⟨1,220,573,true⟩,0,0,0⟩, +⟨⟨1,220,575,true⟩,0,0,0⟩, +⟨⟨1,220,589,true⟩,0,0,0⟩, +⟨⟨1,220,591,true⟩,0,0,0⟩, +⟨⟨1,220,604,true⟩,0,0,0⟩, +⟨⟨1,220,606,true⟩,0,0,0⟩, +⟨⟨1,220,620,true⟩,0,0,0⟩, +⟨⟨1,220,622,true⟩,0,0,0⟩, +⟨⟨1,220,637,true⟩,0,0,0⟩, +⟨⟨1,220,639,true⟩,0,0,0⟩, +⟨⟨1,220,653,true⟩,0,0,0⟩, +⟨⟨1,220,655,true⟩,0,0,0⟩, +⟨⟨1,220,668,true⟩,0,0,0⟩, +⟨⟨1,220,670,true⟩,0,0,0⟩, +⟨⟨1,220,684,true⟩,0,0,0⟩, +⟨⟨1,220,686,true⟩,0,0,0⟩, +⟨⟨1,220,704,true⟩,0,0,0⟩, +⟨⟨1,220,706,true⟩,0,0,0⟩, +⟨⟨1,220,724,true⟩,0,0,0⟩, +⟨⟨1,220,726,true⟩,0,0,0⟩, +⟨⟨1,220,816,true⟩,0,0,0⟩, +⟨⟨1,220,904,true⟩,0,0,0⟩, +⟨⟨1,220,920,true⟩,0,0,0⟩, +⟨⟨1,220,943,true⟩,0,0,0⟩, +⟨⟨1,220,956,true⟩,0,0,0⟩, +⟨⟨1,221,241,true⟩,0,0,0⟩, +⟨⟨1,221,247,true⟩,0,0,0⟩, +⟨⟨1,221,293,true⟩,0,0,0⟩, +⟨⟨1,221,295,true⟩,0,0,0⟩, +⟨⟨1,221,297,true⟩,0,0,0⟩, +⟨⟨1,221,299,true⟩,0,0,0⟩, +⟨⟨1,221,309,true⟩,0,0,0⟩, +⟨⟨1,221,311,true⟩,0,0,0⟩, +⟨⟨1,221,313,true⟩,0,0,0⟩, +⟨⟨1,221,315,true⟩,0,0,0⟩, +⟨⟨1,221,353,true⟩,0,0,0⟩, +⟨⟨1,221,355,true⟩,0,0,0⟩, +⟨⟨1,221,365,true⟩,0,0,0⟩, +⟨⟨1,221,367,true⟩,0,0,0⟩, +⟨⟨1,221,369,true⟩,0,0,0⟩, +⟨⟨1,221,371,true⟩,0,0,0⟩, +⟨⟨1,221,381,true⟩,0,0,0⟩, +⟨⟨1,221,383,true⟩,0,0,0⟩, +⟨⟨1,221,417,true⟩,0,0,0⟩, +⟨⟨1,221,419,true⟩,0,0,0⟩, +⟨⟨1,221,429,true⟩,0,0,0⟩, +⟨⟨1,221,431,true⟩,0,0,0⟩, +⟨⟨1,221,433,true⟩,0,0,0⟩, +⟨⟨1,221,435,true⟩,0,0,0⟩, +⟨⟨1,221,445,true⟩,0,0,0⟩, +⟨⟨1,221,447,true⟩,0,0,0⟩, +⟨⟨1,221,477,true⟩,0,0,0⟩, +⟨⟨1,221,485,true⟩,0,0,0⟩, +⟨⟨1,221,487,true⟩,0,0,0⟩, +⟨⟨1,221,489,true⟩,0,0,0⟩, +⟨⟨1,221,491,true⟩,0,0,0⟩, +⟨⟨1,221,501,true⟩,0,0,0⟩, +⟨⟨1,221,503,true⟩,0,0,0⟩, +⟨⟨1,221,505,true⟩,0,0,0⟩, +⟨⟨1,221,507,true⟩,0,0,0⟩, +⟨⟨1,221,512,true⟩,0,0,0⟩, +⟨⟨1,221,513,true⟩,0,0,0⟩, +⟨⟨1,221,516,true⟩,0,0,0⟩, +⟨⟨1,221,517,true⟩,0,0,0⟩, +⟨⟨1,221,528,true⟩,0,0,0⟩, +⟨⟨1,221,529,true⟩,0,0,0⟩, +⟨⟨1,221,532,true⟩,0,0,0⟩, +⟨⟨1,221,533,true⟩,0,0,0⟩, +⟨⟨1,221,544,true⟩,0,0,0⟩, +⟨⟨1,221,546,true⟩,0,0,0⟩, +⟨⟨1,221,548,true⟩,0,0,0⟩, +⟨⟨1,221,550,true⟩,0,0,0⟩, +⟨⟨1,221,573,true⟩,0,0,0⟩, +⟨⟨1,221,575,true⟩,0,0,0⟩, +⟨⟨1,221,588,true⟩,0,0,0⟩, +⟨⟨1,221,590,true⟩,0,0,0⟩, +⟨⟨1,221,604,true⟩,0,0,0⟩, +⟨⟨1,221,606,true⟩,0,0,0⟩, +⟨⟨1,221,621,true⟩,0,0,0⟩, +⟨⟨1,221,623,true⟩,0,0,0⟩, +⟨⟨1,221,637,true⟩,0,0,0⟩, +⟨⟨1,221,639,true⟩,0,0,0⟩, +⟨⟨1,221,652,true⟩,0,0,0⟩, +⟨⟨1,221,654,true⟩,0,0,0⟩, +⟨⟨1,221,668,true⟩,0,0,0⟩, +⟨⟨1,221,670,true⟩,0,0,0⟩, +⟨⟨1,221,685,true⟩,0,0,0⟩, +⟨⟨1,221,687,true⟩,0,0,0⟩, +⟨⟨1,221,704,true⟩,0,0,0⟩, +⟨⟨1,221,706,true⟩,0,0,0⟩, +⟨⟨1,221,720,true⟩,0,0,0⟩, +⟨⟨1,221,722,true⟩,0,0,0⟩, +⟨⟨1,221,802,true⟩,0,0,0⟩, +⟨⟨1,221,816,true⟩,0,0,0⟩, +⟨⟨1,221,904,true⟩,0,0,0⟩, +⟨⟨1,221,918,true⟩,0,0,0⟩, +⟨⟨1,222,241,true⟩,0,0,0⟩, +⟨⟨1,222,247,true⟩,0,0,0⟩, +⟨⟨1,222,289,true⟩,0,0,0⟩, +⟨⟨1,222,291,true⟩,0,0,0⟩, +⟨⟨1,222,301,true⟩,0,0,0⟩, +⟨⟨1,222,303,true⟩,0,0,0⟩, +⟨⟨1,222,305,true⟩,0,0,0⟩, +⟨⟨1,222,307,true⟩,0,0,0⟩, +⟨⟨1,222,317,true⟩,0,0,0⟩, +⟨⟨1,222,319,true⟩,0,0,0⟩, +⟨⟨1,222,357,true⟩,0,0,0⟩, +⟨⟨1,222,359,true⟩,0,0,0⟩, +⟨⟨1,222,361,true⟩,0,0,0⟩, +⟨⟨1,222,363,true⟩,0,0,0⟩, +⟨⟨1,222,373,true⟩,0,0,0⟩, +⟨⟨1,222,375,true⟩,0,0,0⟩, +⟨⟨1,222,377,true⟩,0,0,0⟩, +⟨⟨1,222,379,true⟩,0,0,0⟩, +⟨⟨1,222,421,true⟩,0,0,0⟩, +⟨⟨1,222,423,true⟩,0,0,0⟩, +⟨⟨1,222,425,true⟩,0,0,0⟩, +⟨⟨1,222,427,true⟩,0,0,0⟩, +⟨⟨1,222,437,true⟩,0,0,0⟩, +⟨⟨1,222,439,true⟩,0,0,0⟩, +⟨⟨1,222,441,true⟩,0,0,0⟩, +⟨⟨1,222,443,true⟩,0,0,0⟩, +⟨⟨1,222,475,true⟩,0,0,0⟩, +⟨⟨1,222,481,true⟩,0,0,0⟩, +⟨⟨1,222,483,true⟩,0,0,0⟩, +⟨⟨1,222,493,true⟩,0,0,0⟩, +⟨⟨1,222,495,true⟩,0,0,0⟩, +⟨⟨1,222,497,true⟩,0,0,0⟩, +⟨⟨1,222,499,true⟩,0,0,0⟩, +⟨⟨1,222,509,true⟩,0,0,0⟩, +⟨⟨1,222,511,true⟩,0,0,0⟩, +⟨⟨1,222,512,true⟩,0,0,0⟩, +⟨⟨1,222,513,true⟩,0,0,0⟩, +⟨⟨1,222,516,true⟩,0,0,0⟩, +⟨⟨1,222,517,true⟩,0,0,0⟩, +⟨⟨1,222,528,true⟩,0,0,0⟩, +⟨⟨1,222,529,true⟩,0,0,0⟩, +⟨⟨1,222,532,true⟩,0,0,0⟩, +⟨⟨1,222,533,true⟩,0,0,0⟩, +⟨⟨1,222,544,true⟩,0,0,0⟩, +⟨⟨1,222,546,true⟩,0,0,0⟩, +⟨⟨1,222,548,true⟩,0,0,0⟩, +⟨⟨1,222,550,true⟩,0,0,0⟩, +⟨⟨1,222,572,true⟩,0,0,0⟩, +⟨⟨1,222,574,true⟩,0,0,0⟩, +⟨⟨1,222,589,true⟩,0,0,0⟩, +⟨⟨1,222,591,true⟩,0,0,0⟩, +⟨⟨1,222,605,true⟩,0,0,0⟩, +⟨⟨1,222,607,true⟩,0,0,0⟩, +⟨⟨1,222,620,true⟩,0,0,0⟩, +⟨⟨1,222,622,true⟩,0,0,0⟩, +⟨⟨1,222,636,true⟩,0,0,0⟩] +def chunk33 : List Entry := [⟨⟨1,222,638,true⟩,0,0,0⟩, +⟨⟨1,222,653,true⟩,0,0,0⟩, +⟨⟨1,222,655,true⟩,0,0,0⟩, +⟨⟨1,222,669,true⟩,0,0,0⟩, +⟨⟨1,222,671,true⟩,0,0,0⟩, +⟨⟨1,222,684,true⟩,0,0,0⟩, +⟨⟨1,222,686,true⟩,0,0,0⟩, +⟨⟨1,222,704,true⟩,0,0,0⟩, +⟨⟨1,222,706,true⟩,0,0,0⟩, +⟨⟨1,222,720,true⟩,0,0,0⟩, +⟨⟨1,222,722,true⟩,0,0,0⟩, +⟨⟨1,222,786,true⟩,0,0,0⟩, +⟨⟨1,222,904,true⟩,0,0,0⟩, +⟨⟨1,222,918,true⟩,0,0,0⟩, +⟨⟨1,223,241,true⟩,0,0,0⟩, +⟨⟨1,223,247,true⟩,0,0,0⟩, +⟨⟨1,223,289,true⟩,0,0,0⟩, +⟨⟨1,223,291,true⟩,0,0,0⟩, +⟨⟨1,223,301,true⟩,0,0,0⟩, +⟨⟨1,223,303,true⟩,0,0,0⟩, +⟨⟨1,223,305,true⟩,0,0,0⟩, +⟨⟨1,223,307,true⟩,0,0,0⟩, +⟨⟨1,223,317,true⟩,0,0,0⟩, +⟨⟨1,223,319,true⟩,0,0,0⟩, +⟨⟨1,223,322,true⟩,0,0,0⟩, +⟨⟨1,223,323,true⟩,0,0,0⟩, +⟨⟨1,223,328,true⟩,0,0,0⟩, +⟨⟨1,223,335,true⟩,0,0,0⟩, +⟨⟨1,223,353,true⟩,0,0,0⟩, +⟨⟨1,223,355,true⟩,0,0,0⟩, +⟨⟨1,223,365,true⟩,0,0,0⟩, +⟨⟨1,223,367,true⟩,0,0,0⟩, +⟨⟨1,223,369,true⟩,0,0,0⟩, +⟨⟨1,223,371,true⟩,0,0,0⟩, +⟨⟨1,223,381,true⟩,0,0,0⟩, +⟨⟨1,223,383,true⟩,0,0,0⟩, +⟨⟨1,223,421,true⟩,0,0,0⟩, +⟨⟨1,223,423,true⟩,0,0,0⟩, +⟨⟨1,223,425,true⟩,0,0,0⟩, +⟨⟨1,223,427,true⟩,0,0,0⟩, +⟨⟨1,223,437,true⟩,0,0,0⟩, +⟨⟨1,223,439,true⟩,0,0,0⟩, +⟨⟨1,223,441,true⟩,0,0,0⟩, +⟨⟨1,223,443,true⟩,0,0,0⟩, +⟨⟨1,223,472,true⟩,0,0,0⟩, +⟨⟨1,223,485,true⟩,0,0,0⟩, +⟨⟨1,223,487,true⟩,0,0,0⟩, +⟨⟨1,223,489,true⟩,0,0,0⟩, +⟨⟨1,223,491,true⟩,0,0,0⟩, +⟨⟨1,223,501,true⟩,0,0,0⟩, +⟨⟨1,223,503,true⟩,0,0,0⟩, +⟨⟨1,223,505,true⟩,0,0,0⟩, +⟨⟨1,223,507,true⟩,0,0,0⟩, +⟨⟨1,223,512,true⟩,0,0,0⟩, +⟨⟨1,223,513,true⟩,0,0,0⟩, +⟨⟨1,223,516,true⟩,0,0,0⟩, +⟨⟨1,223,517,true⟩,0,0,0⟩, +⟨⟨1,223,530,true⟩,0,0,0⟩, +⟨⟨1,223,531,true⟩,0,0,0⟩, +⟨⟨1,223,534,true⟩,0,0,0⟩, +⟨⟨1,223,535,true⟩,0,0,0⟩, +⟨⟨1,223,544,true⟩,0,0,0⟩, +⟨⟨1,223,546,true⟩,0,0,0⟩, +⟨⟨1,223,550,true⟩,0,0,0⟩, +⟨⟨1,223,555,true⟩,0,0,0⟩, +⟨⟨1,223,558,true⟩,0,0,0⟩, +⟨⟨1,223,572,true⟩,0,0,0⟩, +⟨⟨1,223,574,true⟩,0,0,0⟩, +⟨⟨1,223,588,true⟩,0,0,0⟩, +⟨⟨1,223,590,true⟩,0,0,0⟩, +⟨⟨1,223,605,true⟩,0,0,0⟩, +⟨⟨1,223,607,true⟩,0,0,0⟩, +⟨⟨1,223,621,true⟩,0,0,0⟩, +⟨⟨1,223,623,true⟩,0,0,0⟩, +⟨⟨1,223,636,true⟩,0,0,0⟩, +⟨⟨1,223,638,true⟩,0,0,0⟩, +⟨⟨1,223,652,true⟩,0,0,0⟩, +⟨⟨1,223,654,true⟩,0,0,0⟩, +⟨⟨1,223,669,true⟩,0,0,0⟩, +⟨⟨1,223,671,true⟩,0,0,0⟩, +⟨⟨1,223,685,true⟩,0,0,0⟩, +⟨⟨1,223,687,true⟩,0,0,0⟩, +⟨⟨1,223,704,true⟩,0,0,0⟩, +⟨⟨1,223,706,true⟩,0,0,0⟩, +⟨⟨1,223,724,true⟩,0,0,0⟩, +⟨⟨1,223,726,true⟩,0,0,0⟩, +⟨⟨1,223,786,true⟩,0,0,0⟩, +⟨⟨1,223,802,true⟩,0,0,0⟩, +⟨⟨1,223,904,true⟩,0,0,0⟩, +⟨⟨1,223,920,true⟩,0,0,0⟩, +⟨⟨1,223,945,true⟩,0,0,0⟩, +⟨⟨1,224,242,true⟩,0,0,0⟩, +⟨⟨1,224,264,true⟩,0,0,0⟩, +⟨⟨1,224,276,true⟩,0,0,0⟩, +⟨⟨1,224,291,true⟩,0,0,0⟩, +⟨⟨1,224,295,true⟩,0,0,0⟩, +⟨⟨1,224,299,true⟩,0,0,0⟩, +⟨⟨1,224,303,true⟩,0,0,0⟩, +⟨⟨1,224,322,true⟩,0,0,0⟩, +⟨⟨1,224,326,true⟩,0,0,0⟩, +⟨⟨1,224,328,true⟩,0,0,0⟩, +⟨⟨1,224,332,true⟩,0,0,0⟩, +⟨⟨1,224,338,true⟩,0,0,0⟩, +⟨⟨1,224,342,true⟩,0,0,0⟩, +⟨⟨1,224,344,true⟩,0,0,0⟩, +⟨⟨1,224,348,true⟩,0,0,0⟩, +⟨⟨1,224,372,true⟩,0,0,0⟩, +⟨⟨1,224,374,true⟩,0,0,0⟩, +⟨⟨1,224,380,true⟩,0,0,0⟩, +⟨⟨1,224,382,true⟩,0,0,0⟩, +⟨⟨1,224,386,true⟩,0,0,0⟩, +⟨⟨1,224,390,true⟩,0,0,0⟩, +⟨⟨1,224,392,true⟩,0,0,0⟩, +⟨⟨1,224,396,true⟩,0,0,0⟩, +⟨⟨1,224,402,true⟩,0,0,0⟩, +⟨⟨1,224,406,true⟩,0,0,0⟩, +⟨⟨1,224,408,true⟩,0,0,0⟩, +⟨⟨1,224,412,true⟩,0,0,0⟩, +⟨⟨1,224,418,true⟩,0,0,0⟩, +⟨⟨1,224,422,true⟩,0,0,0⟩, +⟨⟨1,224,424,true⟩,0,0,0⟩, +⟨⟨1,224,428,true⟩,0,0,0⟩, +⟨⟨1,224,450,true⟩,0,0,0⟩, +⟨⟨1,224,454,true⟩,0,0,0⟩, +⟨⟨1,224,456,true⟩,0,0,0⟩, +⟨⟨1,224,460,true⟩,0,0,0⟩, +⟨⟨1,224,466,true⟩,0,0,0⟩, +⟨⟨1,224,470,true⟩,0,0,0⟩, +⟨⟨1,224,472,true⟩,0,0,0⟩, +⟨⟨1,224,476,true⟩,0,0,0⟩, +⟨⟨1,224,486,true⟩,0,0,0⟩, +⟨⟨1,224,501,true⟩,0,0,0⟩, +⟨⟨1,224,503,true⟩,0,0,0⟩, +⟨⟨1,224,505,true⟩,0,0,0⟩, +⟨⟨1,224,507,true⟩,0,0,0⟩, +⟨⟨1,224,521,true⟩,0,0,0⟩, +⟨⟨1,224,523,true⟩,0,0,0⟩, +⟨⟨1,224,537,true⟩,0,0,0⟩, +⟨⟨1,224,539,true⟩,0,0,0⟩, +⟨⟨1,224,553,true⟩,0,0,0⟩, +⟨⟨1,224,555,true⟩,0,0,0⟩, +⟨⟨1,224,560,true⟩,0,0,0⟩, +⟨⟨1,224,562,true⟩,0,0,0⟩, +⟨⟨1,224,564,true⟩,0,0,0⟩, +⟨⟨1,224,566,true⟩,0,0,0⟩, +⟨⟨1,224,578,true⟩,0,0,0⟩, +⟨⟨1,224,579,true⟩,0,0,0⟩, +⟨⟨1,224,582,true⟩,0,0,0⟩, +⟨⟨1,224,583,true⟩,0,0,0⟩, +⟨⟨1,224,601,true⟩,0,0,0⟩, +⟨⟨1,224,603,true⟩,0,0,0⟩, +⟨⟨1,224,621,true⟩,0,0,0⟩, +⟨⟨1,224,623,true⟩,0,0,0⟩, +⟨⟨1,224,660,true⟩,0,0,0⟩, +⟨⟨1,224,662,true⟩,0,0,0⟩, +⟨⟨1,224,697,true⟩,0,0,0⟩, +⟨⟨1,224,699,true⟩,0,0,0⟩, +⟨⟨1,224,713,true⟩,0,0,0⟩, +⟨⟨1,224,715,true⟩,0,0,0⟩, +⟨⟨1,224,729,true⟩,0,0,0⟩, +⟨⟨1,224,731,true⟩,0,0,0⟩, +⟨⟨1,224,864,true⟩,0,0,0⟩, +⟨⟨1,225,242,true⟩,0,0,0⟩, +⟨⟨1,225,264,true⟩,0,0,0⟩, +⟨⟨1,225,276,true⟩,0,0,0⟩, +⟨⟨1,225,289,true⟩,0,0,0⟩, +⟨⟨1,225,293,true⟩,0,0,0⟩, +⟨⟨1,225,297,true⟩,0,0,0⟩, +⟨⟨1,225,301,true⟩,0,0,0⟩, +⟨⟨1,225,307,true⟩,0,0,0⟩, +⟨⟨1,225,308,true⟩,0,0,0⟩, +⟨⟨1,225,318,true⟩,0,0,0⟩, +⟨⟨1,225,319,true⟩,0,0,0⟩, +⟨⟨1,225,320,true⟩,0,0,0⟩, +⟨⟨1,225,324,true⟩,0,0,0⟩, +⟨⟨1,225,330,true⟩,0,0,0⟩, +⟨⟨1,225,334,true⟩,0,0,0⟩, +⟨⟨1,225,338,true⟩,0,0,0⟩, +⟨⟨1,225,342,true⟩,0,0,0⟩, +⟨⟨1,225,344,true⟩,0,0,0⟩, +⟨⟨1,225,348,true⟩,0,0,0⟩, +⟨⟨1,225,372,true⟩,0,0,0⟩, +⟨⟨1,225,374,true⟩,0,0,0⟩, +⟨⟨1,225,380,true⟩,0,0,0⟩, +⟨⟨1,225,382,true⟩,0,0,0⟩, +⟨⟨1,225,384,true⟩,0,0,0⟩, +⟨⟨1,225,388,true⟩,0,0,0⟩, +⟨⟨1,225,394,true⟩,0,0,0⟩, +⟨⟨1,225,398,true⟩,0,0,0⟩, +⟨⟨1,225,402,true⟩,0,0,0⟩, +⟨⟨1,225,406,true⟩,0,0,0⟩, +⟨⟨1,225,408,true⟩,0,0,0⟩, +⟨⟨1,225,412,true⟩,0,0,0⟩, +⟨⟨1,225,416,true⟩,0,0,0⟩, +⟨⟨1,225,420,true⟩,0,0,0⟩, +⟨⟨1,225,426,true⟩,0,0,0⟩, +⟨⟨1,225,430,true⟩,0,0,0⟩, +⟨⟨1,225,448,true⟩,0,0,0⟩, +⟨⟨1,225,452,true⟩,0,0,0⟩, +⟨⟨1,225,458,true⟩,0,0,0⟩] +def chunk34 : List Entry := [⟨⟨1,225,462,true⟩,0,0,0⟩, +⟨⟨1,225,466,true⟩,0,0,0⟩, +⟨⟨1,225,470,true⟩,0,0,0⟩, +⟨⟨1,225,472,true⟩,0,0,0⟩, +⟨⟨1,225,476,true⟩,0,0,0⟩, +⟨⟨1,225,485,true⟩,0,0,0⟩, +⟨⟨1,225,501,true⟩,0,0,0⟩, +⟨⟨1,225,503,true⟩,0,0,0⟩, +⟨⟨1,225,505,true⟩,0,0,0⟩, +⟨⟨1,225,507,true⟩,0,0,0⟩, +⟨⟨1,225,521,true⟩,0,0,0⟩, +⟨⟨1,225,523,true⟩,0,0,0⟩, +⟨⟨1,225,537,true⟩,0,0,0⟩, +⟨⟨1,225,539,true⟩,0,0,0⟩, +⟨⟨1,225,552,true⟩,0,0,0⟩, +⟨⟨1,225,554,true⟩,0,0,0⟩, +⟨⟨1,225,560,true⟩,0,0,0⟩, +⟨⟨1,225,564,true⟩,0,0,0⟩, +⟨⟨1,225,565,true⟩,0,0,0⟩, +⟨⟨1,225,566,true⟩,0,0,0⟩, +⟨⟨1,225,570,true⟩,0,0,0⟩, +⟨⟨1,225,574,true⟩,0,0,0⟩, +⟨⟨1,225,576,true⟩,0,0,0⟩, +⟨⟨1,225,577,true⟩,0,0,0⟩, +⟨⟨1,225,580,true⟩,0,0,0⟩, +⟨⟨1,225,581,true⟩,0,0,0⟩, +⟨⟨1,225,600,true⟩,0,0,0⟩, +⟨⟨1,225,602,true⟩,0,0,0⟩, +⟨⟨1,225,621,true⟩,0,0,0⟩, +⟨⟨1,225,623,true⟩,0,0,0⟩, +⟨⟨1,225,660,true⟩,0,0,0⟩, +⟨⟨1,225,662,true⟩,0,0,0⟩, +⟨⟨1,225,697,true⟩,0,0,0⟩, +⟨⟨1,225,699,true⟩,0,0,0⟩, +⟨⟨1,225,712,true⟩,0,0,0⟩, +⟨⟨1,225,714,true⟩,0,0,0⟩, +⟨⟨1,225,728,true⟩,0,0,0⟩, +⟨⟨1,225,730,true⟩,0,0,0⟩, +⟨⟨1,225,772,true⟩,0,0,0⟩, +⟨⟨1,225,864,true⟩,0,0,0⟩, +⟨⟨1,225,946,true⟩,0,0,0⟩, +⟨⟨1,225,957,true⟩,0,0,0⟩, +⟨⟨1,226,242,true⟩,0,0,0⟩, +⟨⟨1,226,264,true⟩,0,0,0⟩, +⟨⟨1,226,276,true⟩,0,0,0⟩, +⟨⟨1,226,291,true⟩,0,0,0⟩, +⟨⟨1,226,295,true⟩,0,0,0⟩, +⟨⟨1,226,299,true⟩,0,0,0⟩, +⟨⟨1,226,303,true⟩,0,0,0⟩, +⟨⟨1,226,306,true⟩,0,0,0⟩, +⟨⟨1,226,309,true⟩,0,0,0⟩, +⟨⟨1,226,310,true⟩,0,0,0⟩, +⟨⟨1,226,311,true⟩,0,0,0⟩, +⟨⟨1,226,312,true⟩,0,0,0⟩, +⟨⟨1,226,313,true⟩,0,0,0⟩, +⟨⟨1,226,315,true⟩,0,0,0⟩, +⟨⟨1,226,316,true⟩,0,0,0⟩, +⟨⟨1,226,322,true⟩,0,0,0⟩, +⟨⟨1,226,326,true⟩,0,0,0⟩, +⟨⟨1,226,328,true⟩,0,0,0⟩, +⟨⟨1,226,332,true⟩,0,0,0⟩, +⟨⟨1,226,336,true⟩,0,0,0⟩, +⟨⟨1,226,340,true⟩,0,0,0⟩, +⟨⟨1,226,346,true⟩,0,0,0⟩, +⟨⟨1,226,350,true⟩,0,0,0⟩, +⟨⟨1,226,368,true⟩,0,0,0⟩, +⟨⟨1,226,370,true⟩,0,0,0⟩, +⟨⟨1,226,376,true⟩,0,0,0⟩, +⟨⟨1,226,378,true⟩,0,0,0⟩, +⟨⟨1,226,384,true⟩,0,0,0⟩, +⟨⟨1,226,388,true⟩,0,0,0⟩, +⟨⟨1,226,394,true⟩,0,0,0⟩, +⟨⟨1,226,398,true⟩,0,0,0⟩, +⟨⟨1,226,402,true⟩,0,0,0⟩, +⟨⟨1,226,406,true⟩,0,0,0⟩, +⟨⟨1,226,408,true⟩,0,0,0⟩, +⟨⟨1,226,412,true⟩,0,0,0⟩, +⟨⟨1,226,418,true⟩,0,0,0⟩, +⟨⟨1,226,422,true⟩,0,0,0⟩, +⟨⟨1,226,424,true⟩,0,0,0⟩, +⟨⟨1,226,428,true⟩,0,0,0⟩, +⟨⟨1,226,450,true⟩,0,0,0⟩, +⟨⟨1,226,454,true⟩,0,0,0⟩, +⟨⟨1,226,456,true⟩,0,0,0⟩, +⟨⟨1,226,460,true⟩,0,0,0⟩, +⟨⟨1,226,464,true⟩,0,0,0⟩, +⟨⟨1,226,468,true⟩,0,0,0⟩, +⟨⟨1,226,474,true⟩,0,0,0⟩, +⟨⟨1,226,478,true⟩,0,0,0⟩, +⟨⟨1,226,483,true⟩,0,0,0⟩, +⟨⟨1,226,497,true⟩,0,0,0⟩, +⟨⟨1,226,499,true⟩,0,0,0⟩, +⟨⟨1,226,509,true⟩,0,0,0⟩, +⟨⟨1,226,511,true⟩,0,0,0⟩, +⟨⟨1,226,521,true⟩,0,0,0⟩, +⟨⟨1,226,523,true⟩,0,0,0⟩, +⟨⟨1,226,536,true⟩,0,0,0⟩, +⟨⟨1,226,538,true⟩,0,0,0⟩, +⟨⟨1,226,553,true⟩,0,0,0⟩, +⟨⟨1,226,555,true⟩,0,0,0⟩, +⟨⟨1,226,560,true⟩,0,0,0⟩, +⟨⟨1,226,564,true⟩,0,0,0⟩, +⟨⟨1,226,565,true⟩,0,0,0⟩, +⟨⟨1,226,576,true⟩,0,0,0⟩, +⟨⟨1,226,577,true⟩,0,0,0⟩, +⟨⟨1,226,580,true⟩,0,0,0⟩, +⟨⟨1,226,581,true⟩,0,0,0⟩, +⟨⟨1,226,601,true⟩,0,0,0⟩, +⟨⟨1,226,603,true⟩,0,0,0⟩, +⟨⟨1,226,620,true⟩,0,0,0⟩, +⟨⟨1,226,622,true⟩,0,0,0⟩, +⟨⟨1,226,660,true⟩,0,0,0⟩, +⟨⟨1,226,662,true⟩,0,0,0⟩, +⟨⟨1,226,696,true⟩,0,0,0⟩, +⟨⟨1,226,698,true⟩,0,0,0⟩, +⟨⟨1,226,713,true⟩,0,0,0⟩, +⟨⟨1,226,715,true⟩,0,0,0⟩, +⟨⟨1,226,728,true⟩,0,0,0⟩, +⟨⟨1,226,730,true⟩,0,0,0⟩, +⟨⟨1,226,760,true⟩,0,0,0⟩, +⟨⟨1,226,864,true⟩,0,0,0⟩, +⟨⟨1,226,947,true⟩,0,0,0⟩, +⟨⟨1,226,955,true⟩,0,0,0⟩, +⟨⟨1,227,242,true⟩,0,0,0⟩, +⟨⟨1,227,264,true⟩,0,0,0⟩, +⟨⟨1,227,276,true⟩,0,0,0⟩, +⟨⟨1,227,289,true⟩,0,0,0⟩, +⟨⟨1,227,293,true⟩,0,0,0⟩, +⟨⟨1,227,297,true⟩,0,0,0⟩, +⟨⟨1,227,301,true⟩,0,0,0⟩, +⟨⟨1,227,320,true⟩,0,0,0⟩, +⟨⟨1,227,324,true⟩,0,0,0⟩, +⟨⟨1,227,330,true⟩,0,0,0⟩, +⟨⟨1,227,334,true⟩,0,0,0⟩, +⟨⟨1,227,336,true⟩,0,0,0⟩, +⟨⟨1,227,340,true⟩,0,0,0⟩, +⟨⟨1,227,346,true⟩,0,0,0⟩, +⟨⟨1,227,350,true⟩,0,0,0⟩, +⟨⟨1,227,368,true⟩,0,0,0⟩, +⟨⟨1,227,370,true⟩,0,0,0⟩, +⟨⟨1,227,376,true⟩,0,0,0⟩, +⟨⟨1,227,378,true⟩,0,0,0⟩, +⟨⟨1,227,386,true⟩,0,0,0⟩, +⟨⟨1,227,390,true⟩,0,0,0⟩, +⟨⟨1,227,392,true⟩,0,0,0⟩, +⟨⟨1,227,396,true⟩,0,0,0⟩, +⟨⟨1,227,402,true⟩,0,0,0⟩, +⟨⟨1,227,406,true⟩,0,0,0⟩, +⟨⟨1,227,408,true⟩,0,0,0⟩, +⟨⟨1,227,412,true⟩,0,0,0⟩, +⟨⟨1,227,416,true⟩,0,0,0⟩, +⟨⟨1,227,420,true⟩,0,0,0⟩, +⟨⟨1,227,426,true⟩,0,0,0⟩, +⟨⟨1,227,430,true⟩,0,0,0⟩, +⟨⟨1,227,448,true⟩,0,0,0⟩, +⟨⟨1,227,452,true⟩,0,0,0⟩, +⟨⟨1,227,458,true⟩,0,0,0⟩, +⟨⟨1,227,462,true⟩,0,0,0⟩, +⟨⟨1,227,464,true⟩,0,0,0⟩, +⟨⟨1,227,468,true⟩,0,0,0⟩, +⟨⟨1,227,474,true⟩,0,0,0⟩, +⟨⟨1,227,478,true⟩,0,0,0⟩, +⟨⟨1,227,480,true⟩,0,0,0⟩, +⟨⟨1,227,497,true⟩,0,0,0⟩, +⟨⟨1,227,499,true⟩,0,0,0⟩, +⟨⟨1,227,509,true⟩,0,0,0⟩, +⟨⟨1,227,511,true⟩,0,0,0⟩, +⟨⟨1,227,521,true⟩,0,0,0⟩, +⟨⟨1,227,523,true⟩,0,0,0⟩, +⟨⟨1,227,536,true⟩,0,0,0⟩, +⟨⟨1,227,538,true⟩,0,0,0⟩, +⟨⟨1,227,552,true⟩,0,0,0⟩, +⟨⟨1,227,554,true⟩,0,0,0⟩, +⟨⟨1,227,560,true⟩,0,0,0⟩, +⟨⟨1,227,562,true⟩,0,0,0⟩, +⟨⟨1,227,564,true⟩,0,0,0⟩, +⟨⟨1,227,566,true⟩,0,0,0⟩, +⟨⟨1,227,578,true⟩,0,0,0⟩, +⟨⟨1,227,579,true⟩,0,0,0⟩, +⟨⟨1,227,582,true⟩,0,0,0⟩, +⟨⟨1,227,583,true⟩,0,0,0⟩, +⟨⟨1,227,600,true⟩,0,0,0⟩, +⟨⟨1,227,602,true⟩,0,0,0⟩, +⟨⟨1,227,620,true⟩,0,0,0⟩, +⟨⟨1,227,622,true⟩,0,0,0⟩, +⟨⟨1,227,660,true⟩,0,0,0⟩, +⟨⟨1,227,662,true⟩,0,0,0⟩, +⟨⟨1,227,696,true⟩,0,0,0⟩, +⟨⟨1,227,698,true⟩,0,0,0⟩, +⟨⟨1,227,712,true⟩,0,0,0⟩, +⟨⟨1,227,714,true⟩,0,0,0⟩, +⟨⟨1,227,729,true⟩,0,0,0⟩, +⟨⟨1,227,731,true⟩,0,0,0⟩, +⟨⟨1,227,760,true⟩,0,0,0⟩, +⟨⟨1,227,772,true⟩,0,0,0⟩, +⟨⟨1,227,864,true⟩,0,0,0⟩, +⟨⟨1,228,242,true⟩,0,0,0⟩, +⟨⟨1,228,264,true⟩,0,0,0⟩, +⟨⟨1,228,276,true⟩,0,0,0⟩, +⟨⟨1,228,291,true⟩,0,0,0⟩] +def chunk35 : List Entry := [⟨⟨1,228,295,true⟩,0,0,0⟩, +⟨⟨1,228,299,true⟩,0,0,0⟩, +⟨⟨1,228,303,true⟩,0,0,0⟩, +⟨⟨1,228,306,true⟩,0,0,0⟩, +⟨⟨1,228,307,true⟩,0,0,0⟩, +⟨⟨1,228,310,true⟩,0,0,0⟩, +⟨⟨1,228,311,true⟩,0,0,0⟩, +⟨⟨1,228,312,true⟩,0,0,0⟩, +⟨⟨1,228,315,true⟩,0,0,0⟩, +⟨⟨1,228,316,true⟩,0,0,0⟩, +⟨⟨1,228,319,true⟩,0,0,0⟩, +⟨⟨1,228,322,true⟩,0,0,0⟩, +⟨⟨1,228,326,true⟩,0,0,0⟩, +⟨⟨1,228,328,true⟩,0,0,0⟩, +⟨⟨1,228,332,true⟩,0,0,0⟩, +⟨⟨1,228,338,true⟩,0,0,0⟩, +⟨⟨1,228,342,true⟩,0,0,0⟩, +⟨⟨1,228,344,true⟩,0,0,0⟩, +⟨⟨1,228,348,true⟩,0,0,0⟩, +⟨⟨1,228,372,true⟩,0,0,0⟩, +⟨⟨1,228,374,true⟩,0,0,0⟩, +⟨⟨1,228,380,true⟩,0,0,0⟩, +⟨⟨1,228,382,true⟩,0,0,0⟩, +⟨⟨1,228,386,true⟩,0,0,0⟩, +⟨⟨1,228,390,true⟩,0,0,0⟩, +⟨⟨1,228,392,true⟩,0,0,0⟩, +⟨⟨1,228,396,true⟩,0,0,0⟩, +⟨⟨1,228,400,true⟩,0,0,0⟩, +⟨⟨1,228,404,true⟩,0,0,0⟩, +⟨⟨1,228,410,true⟩,0,0,0⟩, +⟨⟨1,228,414,true⟩,0,0,0⟩, +⟨⟨1,228,416,true⟩,0,0,0⟩, +⟨⟨1,228,420,true⟩,0,0,0⟩, +⟨⟨1,228,426,true⟩,0,0,0⟩, +⟨⟨1,228,430,true⟩,0,0,0⟩, +⟨⟨1,228,448,true⟩,0,0,0⟩, +⟨⟨1,228,452,true⟩,0,0,0⟩, +⟨⟨1,228,458,true⟩,0,0,0⟩, +⟨⟨1,228,462,true⟩,0,0,0⟩, +⟨⟨1,228,464,true⟩,0,0,0⟩, +⟨⟨1,228,468,true⟩,0,0,0⟩, +⟨⟨1,228,474,true⟩,0,0,0⟩, +⟨⟨1,228,478,true⟩,0,0,0⟩, +⟨⟨1,228,494,true⟩,0,0,0⟩, +⟨⟨1,228,497,true⟩,0,0,0⟩, +⟨⟨1,228,499,true⟩,0,0,0⟩, +⟨⟨1,228,509,true⟩,0,0,0⟩, +⟨⟨1,228,511,true⟩,0,0,0⟩, +⟨⟨1,228,520,true⟩,0,0,0⟩, +⟨⟨1,228,522,true⟩,0,0,0⟩, +⟨⟨1,228,537,true⟩,0,0,0⟩, +⟨⟨1,228,539,true⟩,0,0,0⟩, +⟨⟨1,228,553,true⟩,0,0,0⟩, +⟨⟨1,228,555,true⟩,0,0,0⟩, +⟨⟨1,228,560,true⟩,0,0,0⟩, +⟨⟨1,228,562,true⟩,0,0,0⟩, +⟨⟨1,228,565,true⟩,0,0,0⟩, +⟨⟨1,228,574,true⟩,0,0,0⟩, +⟨⟨1,228,575,true⟩,0,0,0⟩, +⟨⟨1,228,578,true⟩,0,0,0⟩, +⟨⟨1,228,579,true⟩,0,0,0⟩, +⟨⟨1,228,582,true⟩,0,0,0⟩, +⟨⟨1,228,583,true⟩,0,0,0⟩, +⟨⟨1,228,600,true⟩,0,0,0⟩, +⟨⟨1,228,602,true⟩,0,0,0⟩, +⟨⟨1,228,620,true⟩,0,0,0⟩, +⟨⟨1,228,622,true⟩,0,0,0⟩, +⟨⟨1,228,656,true⟩,0,0,0⟩, +⟨⟨1,228,658,true⟩,0,0,0⟩, +⟨⟨1,228,696,true⟩,0,0,0⟩, +⟨⟨1,228,698,true⟩,0,0,0⟩, +⟨⟨1,228,712,true⟩,0,0,0⟩, +⟨⟨1,228,714,true⟩,0,0,0⟩, +⟨⟨1,228,729,true⟩,0,0,0⟩, +⟨⟨1,228,731,true⟩,0,0,0⟩, +⟨⟨1,228,746,true⟩,0,0,0⟩, +⟨⟨1,228,862,true⟩,0,0,0⟩, +⟨⟨1,228,946,true⟩,0,0,0⟩, +⟨⟨1,228,955,true⟩,0,0,0⟩, +⟨⟨1,229,242,true⟩,0,0,0⟩, +⟨⟨1,229,264,true⟩,0,0,0⟩, +⟨⟨1,229,276,true⟩,0,0,0⟩, +⟨⟨1,229,289,true⟩,0,0,0⟩, +⟨⟨1,229,293,true⟩,0,0,0⟩, +⟨⟨1,229,297,true⟩,0,0,0⟩, +⟨⟨1,229,301,true⟩,0,0,0⟩, +⟨⟨1,229,320,true⟩,0,0,0⟩, +⟨⟨1,229,324,true⟩,0,0,0⟩, +⟨⟨1,229,330,true⟩,0,0,0⟩, +⟨⟨1,229,334,true⟩,0,0,0⟩, +⟨⟨1,229,338,true⟩,0,0,0⟩, +⟨⟨1,229,342,true⟩,0,0,0⟩, +⟨⟨1,229,344,true⟩,0,0,0⟩, +⟨⟨1,229,348,true⟩,0,0,0⟩, +⟨⟨1,229,372,true⟩,0,0,0⟩, +⟨⟨1,229,374,true⟩,0,0,0⟩, +⟨⟨1,229,380,true⟩,0,0,0⟩, +⟨⟨1,229,382,true⟩,0,0,0⟩, +⟨⟨1,229,384,true⟩,0,0,0⟩, +⟨⟨1,229,388,true⟩,0,0,0⟩, +⟨⟨1,229,394,true⟩,0,0,0⟩, +⟨⟨1,229,398,true⟩,0,0,0⟩, +⟨⟨1,229,400,true⟩,0,0,0⟩, +⟨⟨1,229,404,true⟩,0,0,0⟩, +⟨⟨1,229,410,true⟩,0,0,0⟩, +⟨⟨1,229,414,true⟩,0,0,0⟩, +⟨⟨1,229,418,true⟩,0,0,0⟩, +⟨⟨1,229,422,true⟩,0,0,0⟩, +⟨⟨1,229,424,true⟩,0,0,0⟩, +⟨⟨1,229,428,true⟩,0,0,0⟩, +⟨⟨1,229,450,true⟩,0,0,0⟩, +⟨⟨1,229,454,true⟩,0,0,0⟩, +⟨⟨1,229,456,true⟩,0,0,0⟩, +⟨⟨1,229,460,true⟩,0,0,0⟩, +⟨⟨1,229,464,true⟩,0,0,0⟩, +⟨⟨1,229,468,true⟩,0,0,0⟩, +⟨⟨1,229,474,true⟩,0,0,0⟩, +⟨⟨1,229,478,true⟩,0,0,0⟩, +⟨⟨1,229,493,true⟩,0,0,0⟩, +⟨⟨1,229,497,true⟩,0,0,0⟩, +⟨⟨1,229,499,true⟩,0,0,0⟩, +⟨⟨1,229,509,true⟩,0,0,0⟩, +⟨⟨1,229,511,true⟩,0,0,0⟩, +⟨⟨1,229,520,true⟩,0,0,0⟩, +⟨⟨1,229,522,true⟩,0,0,0⟩, +⟨⟨1,229,537,true⟩,0,0,0⟩, +⟨⟨1,229,539,true⟩,0,0,0⟩, +⟨⟨1,229,552,true⟩,0,0,0⟩, +⟨⟨1,229,554,true⟩,0,0,0⟩, +⟨⟨1,229,560,true⟩,0,0,0⟩, +⟨⟨1,229,562,true⟩,0,0,0⟩, +⟨⟨1,229,564,true⟩,0,0,0⟩, +⟨⟨1,229,566,true⟩,0,0,0⟩, +⟨⟨1,229,576,true⟩,0,0,0⟩, +⟨⟨1,229,577,true⟩,0,0,0⟩, +⟨⟨1,229,580,true⟩,0,0,0⟩, +⟨⟨1,229,581,true⟩,0,0,0⟩, +⟨⟨1,229,601,true⟩,0,0,0⟩, +⟨⟨1,229,603,true⟩,0,0,0⟩, +⟨⟨1,229,620,true⟩,0,0,0⟩, +⟨⟨1,229,622,true⟩,0,0,0⟩, +⟨⟨1,229,656,true⟩,0,0,0⟩, +⟨⟨1,229,658,true⟩,0,0,0⟩, +⟨⟨1,229,696,true⟩,0,0,0⟩, +⟨⟨1,229,698,true⟩,0,0,0⟩, +⟨⟨1,229,713,true⟩,0,0,0⟩, +⟨⟨1,229,715,true⟩,0,0,0⟩, +⟨⟨1,229,728,true⟩,0,0,0⟩, +⟨⟨1,229,730,true⟩,0,0,0⟩, +⟨⟨1,229,746,true⟩,0,0,0⟩, +⟨⟨1,229,772,true⟩,0,0,0⟩, +⟨⟨1,229,862,true⟩,0,0,0⟩, +⟨⟨1,230,242,true⟩,0,0,0⟩, +⟨⟨1,230,264,true⟩,0,0,0⟩, +⟨⟨1,230,276,true⟩,0,0,0⟩, +⟨⟨1,230,291,true⟩,0,0,0⟩, +⟨⟨1,230,295,true⟩,0,0,0⟩, +⟨⟨1,230,299,true⟩,0,0,0⟩, +⟨⟨1,230,303,true⟩,0,0,0⟩, +⟨⟨1,230,322,true⟩,0,0,0⟩, +⟨⟨1,230,326,true⟩,0,0,0⟩, +⟨⟨1,230,328,true⟩,0,0,0⟩, +⟨⟨1,230,332,true⟩,0,0,0⟩, +⟨⟨1,230,336,true⟩,0,0,0⟩, +⟨⟨1,230,340,true⟩,0,0,0⟩, +⟨⟨1,230,346,true⟩,0,0,0⟩, +⟨⟨1,230,350,true⟩,0,0,0⟩, +⟨⟨1,230,368,true⟩,0,0,0⟩, +⟨⟨1,230,370,true⟩,0,0,0⟩, +⟨⟨1,230,376,true⟩,0,0,0⟩, +⟨⟨1,230,378,true⟩,0,0,0⟩, +⟨⟨1,230,384,true⟩,0,0,0⟩, +⟨⟨1,230,388,true⟩,0,0,0⟩, +⟨⟨1,230,394,true⟩,0,0,0⟩, +⟨⟨1,230,398,true⟩,0,0,0⟩, +⟨⟨1,230,400,true⟩,0,0,0⟩, +⟨⟨1,230,404,true⟩,0,0,0⟩, +⟨⟨1,230,410,true⟩,0,0,0⟩, +⟨⟨1,230,414,true⟩,0,0,0⟩, +⟨⟨1,230,416,true⟩,0,0,0⟩, +⟨⟨1,230,420,true⟩,0,0,0⟩, +⟨⟨1,230,426,true⟩,0,0,0⟩, +⟨⟨1,230,430,true⟩,0,0,0⟩, +⟨⟨1,230,448,true⟩,0,0,0⟩, +⟨⟨1,230,452,true⟩,0,0,0⟩, +⟨⟨1,230,458,true⟩,0,0,0⟩, +⟨⟨1,230,462,true⟩,0,0,0⟩, +⟨⟨1,230,466,true⟩,0,0,0⟩, +⟨⟨1,230,470,true⟩,0,0,0⟩, +⟨⟨1,230,472,true⟩,0,0,0⟩, +⟨⟨1,230,476,true⟩,0,0,0⟩, +⟨⟨1,230,491,true⟩,0,0,0⟩, +⟨⟨1,230,501,true⟩,0,0,0⟩, +⟨⟨1,230,503,true⟩,0,0,0⟩, +⟨⟨1,230,505,true⟩,0,0,0⟩, +⟨⟨1,230,507,true⟩,0,0,0⟩, +⟨⟨1,230,520,true⟩,0,0,0⟩, +⟨⟨1,230,522,true⟩,0,0,0⟩, +⟨⟨1,230,536,true⟩,0,0,0⟩, +⟨⟨1,230,538,true⟩,0,0,0⟩] +def chunk36 : List Entry := [⟨⟨1,230,553,true⟩,0,0,0⟩, +⟨⟨1,230,555,true⟩,0,0,0⟩, +⟨⟨1,230,560,true⟩,0,0,0⟩, +⟨⟨1,230,562,true⟩,0,0,0⟩, +⟨⟨1,230,564,true⟩,0,0,0⟩, +⟨⟨1,230,566,true⟩,0,0,0⟩, 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+⟨⟨1,232,332,true⟩,0,0,0⟩, +⟨⟨1,232,334,true⟩,0,0,0⟩, +⟨⟨1,232,339,true⟩,0,0,0⟩, +⟨⟨1,232,343,true⟩,0,0,0⟩, +⟨⟨1,232,347,true⟩,0,0,0⟩, +⟨⟨1,232,351,true⟩,0,0,0⟩, +⟨⟨1,232,356,true⟩,0,0,0⟩, +⟨⟨1,232,358,true⟩,0,0,0⟩, +⟨⟨1,232,364,true⟩,0,0,0⟩, +⟨⟨1,232,366,true⟩,0,0,0⟩, +⟨⟨1,232,389,true⟩,0,0,0⟩, +⟨⟨1,232,391,true⟩,0,0,0⟩, +⟨⟨1,232,393,true⟩,0,0,0⟩, +⟨⟨1,232,395,true⟩,0,0,0⟩, +⟨⟨1,232,403,true⟩,0,0,0⟩, +⟨⟨1,232,407,true⟩,0,0,0⟩, +⟨⟨1,232,411,true⟩,0,0,0⟩, +⟨⟨1,232,415,true⟩,0,0,0⟩, +⟨⟨1,232,434,true⟩,0,0,0⟩, +⟨⟨1,232,438,true⟩,0,0,0⟩, +⟨⟨1,232,440,true⟩,0,0,0⟩, +⟨⟨1,232,444,true⟩,0,0,0⟩, +⟨⟨1,232,453,true⟩,0,0,0⟩, +⟨⟨1,232,455,true⟩,0,0,0⟩, +⟨⟨1,232,457,true⟩,0,0,0⟩, +⟨⟨1,232,459,true⟩,0,0,0⟩, +⟨⟨1,232,466,true⟩,0,0,0⟩, +⟨⟨1,232,470,true⟩,0,0,0⟩, +⟨⟨1,232,472,true⟩,0,0,0⟩, +⟨⟨1,232,476,true⟩,0,0,0⟩, +⟨⟨1,232,485,true⟩,0,0,0⟩, +⟨⟨1,232,487,true⟩,0,0,0⟩, +⟨⟨1,232,489,true⟩,0,0,0⟩, +⟨⟨1,232,491,true⟩,0,0,0⟩, +⟨⟨1,232,502,true⟩,0,0,0⟩, +⟨⟨1,232,596,true⟩,0,0,0⟩, +⟨⟨1,232,598,true⟩,0,0,0⟩, +⟨⟨1,232,624,true⟩,0,0,0⟩, +⟨⟨1,232,626,true⟩,0,0,0⟩, +⟨⟨1,232,628,true⟩,0,0,0⟩, +⟨⟨1,232,630,true⟩,0,0,0⟩, +⟨⟨1,232,642,true⟩,0,0,0⟩, +⟨⟨1,232,643,true⟩,0,0,0⟩, +⟨⟨1,232,646,true⟩,0,0,0⟩, +⟨⟨1,232,647,true⟩,0,0,0⟩, +⟨⟨1,232,665,true⟩,0,0,0⟩, +⟨⟨1,232,667,true⟩,0,0,0⟩, +⟨⟨1,232,685,true⟩,0,0,0⟩, +⟨⟨1,232,687,true⟩,0,0,0⟩, +⟨⟨1,232,697,true⟩,0,0,0⟩, +⟨⟨1,232,699,true⟩,0,0,0⟩, +⟨⟨1,232,717,true⟩,0,0,0⟩, +⟨⟨1,232,719,true⟩,0,0,0⟩, +⟨⟨1,232,733,true⟩,0,0,0⟩, +⟨⟨1,232,735,true⟩,0,0,0⟩, +⟨⟨1,233,248,true⟩,0,0,0⟩, +⟨⟨1,233,254,true⟩,0,0,0⟩, +⟨⟨1,233,266,true⟩,0,0,0⟩, +⟨⟨1,233,284,true⟩,0,0,0⟩, +⟨⟨1,233,291,true⟩,0,0,0⟩, +⟨⟨1,233,292,true⟩,0,0,0⟩, +⟨⟨1,233,302,true⟩,0,0,0⟩, +⟨⟨1,233,303,true⟩,0,0,0⟩, +⟨⟨1,233,305,true⟩,0,0,0⟩, +⟨⟨1,233,309,true⟩,0,0,0⟩, +⟨⟨1,233,313,true⟩,0,0,0⟩, +⟨⟨1,233,317,true⟩,0,0,0⟩, +⟨⟨1,233,320,true⟩,0,0,0⟩, +⟨⟨1,233,322,true⟩,0,0,0⟩, +⟨⟨1,233,328,true⟩,0,0,0⟩, +⟨⟨1,233,330,true⟩,0,0,0⟩, +⟨⟨1,233,339,true⟩,0,0,0⟩, +⟨⟨1,233,343,true⟩,0,0,0⟩, +⟨⟨1,233,347,true⟩,0,0,0⟩, +⟨⟨1,233,351,true⟩,0,0,0⟩, +⟨⟨1,233,356,true⟩,0,0,0⟩, +⟨⟨1,233,358,true⟩,0,0,0⟩, +⟨⟨1,233,364,true⟩,0,0,0⟩, +⟨⟨1,233,366,true⟩,0,0,0⟩, +⟨⟨1,233,385,true⟩,0,0,0⟩, +⟨⟨1,233,387,true⟩,0,0,0⟩, +⟨⟨1,233,397,true⟩,0,0,0⟩, +⟨⟨1,233,399,true⟩,0,0,0⟩] +def chunk37 : List Entry := [⟨⟨1,233,403,true⟩,0,0,0⟩, +⟨⟨1,233,407,true⟩,0,0,0⟩, +⟨⟨1,233,411,true⟩,0,0,0⟩, +⟨⟨1,233,415,true⟩,0,0,0⟩, +⟨⟨1,233,432,true⟩,0,0,0⟩, +⟨⟨1,233,436,true⟩,0,0,0⟩, +⟨⟨1,233,442,true⟩,0,0,0⟩, +⟨⟨1,233,446,true⟩,0,0,0⟩, +⟨⟨1,233,449,true⟩,0,0,0⟩, +⟨⟨1,233,451,true⟩,0,0,0⟩, +⟨⟨1,233,461,true⟩,0,0,0⟩, +⟨⟨1,233,463,true⟩,0,0,0⟩, +⟨⟨1,233,466,true⟩,0,0,0⟩, +⟨⟨1,233,470,true⟩,0,0,0⟩, +⟨⟨1,233,472,true⟩,0,0,0⟩, +⟨⟨1,233,476,true⟩,0,0,0⟩, +⟨⟨1,233,485,true⟩,0,0,0⟩, +⟨⟨1,233,487,true⟩,0,0,0⟩, +⟨⟨1,233,489,true⟩,0,0,0⟩, +⟨⟨1,233,491,true⟩,0,0,0⟩, +⟨⟨1,233,500,true⟩,0,0,0⟩, +⟨⟨1,233,596,true⟩,0,0,0⟩, +⟨⟨1,233,598,true⟩,0,0,0⟩, +⟨⟨1,233,624,true⟩,0,0,0⟩, +⟨⟨1,233,628,true⟩,0,0,0⟩, +⟨⟨1,233,629,true⟩,0,0,0⟩, +⟨⟨1,233,630,true⟩,0,0,0⟩, +⟨⟨1,233,634,true⟩,0,0,0⟩, +⟨⟨1,233,638,true⟩,0,0,0⟩, +⟨⟨1,233,640,true⟩,0,0,0⟩, +⟨⟨1,233,641,true⟩,0,0,0⟩, +⟨⟨1,233,644,true⟩,0,0,0⟩, +⟨⟨1,233,645,true⟩,0,0,0⟩, +⟨⟨1,233,664,true⟩,0,0,0⟩, +⟨⟨1,233,666,true⟩,0,0,0⟩, +⟨⟨1,233,685,true⟩,0,0,0⟩, +⟨⟨1,233,687,true⟩,0,0,0⟩, +⟨⟨1,233,697,true⟩,0,0,0⟩, +⟨⟨1,233,699,true⟩,0,0,0⟩, +⟨⟨1,233,716,true⟩,0,0,0⟩, +⟨⟨1,233,718,true⟩,0,0,0⟩, +⟨⟨1,233,732,true⟩,0,0,0⟩, +⟨⟨1,233,734,true⟩,0,0,0⟩, +⟨⟨1,233,768,true⟩,0,0,0⟩, +⟨⟨1,233,916,true⟩,0,0,0⟩, +⟨⟨1,233,930,true⟩,0,0,0⟩, +⟨⟨1,233,981,true⟩,0,0,0⟩, +⟨⟨1,233,986,true⟩,0,0,0⟩, +⟨⟨1,234,248,true⟩,0,0,0⟩, +⟨⟨1,234,254,true⟩,0,0,0⟩, +⟨⟨1,234,266,true⟩,0,0,0⟩, +⟨⟨1,234,284,true⟩,0,0,0⟩, +⟨⟨1,234,290,true⟩,0,0,0⟩, +⟨⟨1,234,293,true⟩,0,0,0⟩, +⟨⟨1,234,294,true⟩,0,0,0⟩, +⟨⟨1,234,295,true⟩,0,0,0⟩, +⟨⟨1,234,296,true⟩,0,0,0⟩, +⟨⟨1,234,297,true⟩,0,0,0⟩, +⟨⟨1,234,299,true⟩,0,0,0⟩, +⟨⟨1,234,300,true⟩,0,0,0⟩, +⟨⟨1,234,307,true⟩,0,0,0⟩, +⟨⟨1,234,311,true⟩,0,0,0⟩, +⟨⟨1,234,315,true⟩,0,0,0⟩, +⟨⟨1,234,319,true⟩,0,0,0⟩, +⟨⟨1,234,324,true⟩,0,0,0⟩, +⟨⟨1,234,326,true⟩,0,0,0⟩, +⟨⟨1,234,332,true⟩,0,0,0⟩, +⟨⟨1,234,334,true⟩,0,0,0⟩, +⟨⟨1,234,337,true⟩,0,0,0⟩, +⟨⟨1,234,341,true⟩,0,0,0⟩, +⟨⟨1,234,345,true⟩,0,0,0⟩, +⟨⟨1,234,349,true⟩,0,0,0⟩, +⟨⟨1,234,352,true⟩,0,0,0⟩, +⟨⟨1,234,354,true⟩,0,0,0⟩, +⟨⟨1,234,360,true⟩,0,0,0⟩, +⟨⟨1,234,362,true⟩,0,0,0⟩, +⟨⟨1,234,385,true⟩,0,0,0⟩, +⟨⟨1,234,387,true⟩,0,0,0⟩, +⟨⟨1,234,397,true⟩,0,0,0⟩, +⟨⟨1,234,399,true⟩,0,0,0⟩, +⟨⟨1,234,403,true⟩,0,0,0⟩, +⟨⟨1,234,407,true⟩,0,0,0⟩, +⟨⟨1,234,411,true⟩,0,0,0⟩, +⟨⟨1,234,415,true⟩,0,0,0⟩, +⟨⟨1,234,434,true⟩,0,0,0⟩, +⟨⟨1,234,438,true⟩,0,0,0⟩, +⟨⟨1,234,440,true⟩,0,0,0⟩, +⟨⟨1,234,444,true⟩,0,0,0⟩, +⟨⟨1,234,453,true⟩,0,0,0⟩, +⟨⟨1,234,455,true⟩,0,0,0⟩, +⟨⟨1,234,457,true⟩,0,0,0⟩, +⟨⟨1,234,459,true⟩,0,0,0⟩, +⟨⟨1,234,464,true⟩,0,0,0⟩, +⟨⟨1,234,468,true⟩,0,0,0⟩, +⟨⟨1,234,474,true⟩,0,0,0⟩, +⟨⟨1,234,478,true⟩,0,0,0⟩, +⟨⟨1,234,481,true⟩,0,0,0⟩, +⟨⟨1,234,483,true⟩,0,0,0⟩, +⟨⟨1,234,493,true⟩,0,0,0⟩, +⟨⟨1,234,495,true⟩,0,0,0⟩, +⟨⟨1,234,498,true⟩,0,0,0⟩, +⟨⟨1,234,596,true⟩,0,0,0⟩, +⟨⟨1,234,598,true⟩,0,0,0⟩, +⟨⟨1,234,624,true⟩,0,0,0⟩, +⟨⟨1,234,628,true⟩,0,0,0⟩, +⟨⟨1,234,629,true⟩,0,0,0⟩, +⟨⟨1,234,640,true⟩,0,0,0⟩, +⟨⟨1,234,641,true⟩,0,0,0⟩, +⟨⟨1,234,644,true⟩,0,0,0⟩, +⟨⟨1,234,645,true⟩,0,0,0⟩, +⟨⟨1,234,665,true⟩,0,0,0⟩, +⟨⟨1,234,667,true⟩,0,0,0⟩, +⟨⟨1,234,684,true⟩,0,0,0⟩, +⟨⟨1,234,686,true⟩,0,0,0⟩, +⟨⟨1,234,696,true⟩,0,0,0⟩, +⟨⟨1,234,698,true⟩,0,0,0⟩, +⟨⟨1,234,717,true⟩,0,0,0⟩, +⟨⟨1,234,719,true⟩,0,0,0⟩, +⟨⟨1,234,732,true⟩,0,0,0⟩, +⟨⟨1,234,734,true⟩,0,0,0⟩, +⟨⟨1,234,756,true⟩,0,0,0⟩, +⟨⟨1,234,902,true⟩,0,0,0⟩, +⟨⟨1,234,930,true⟩,0,0,0⟩, +⟨⟨1,234,982,true⟩,0,0,0⟩, +⟨⟨1,234,985,true⟩,0,0,0⟩, +⟨⟨1,235,248,true⟩,0,0,0⟩, +⟨⟨1,235,254,true⟩,0,0,0⟩, +⟨⟨1,235,266,true⟩,0,0,0⟩, +⟨⟨1,235,284,true⟩,0,0,0⟩, +⟨⟨1,235,305,true⟩,0,0,0⟩, +⟨⟨1,235,309,true⟩,0,0,0⟩, +⟨⟨1,235,313,true⟩,0,0,0⟩, +⟨⟨1,235,317,true⟩,0,0,0⟩, +⟨⟨1,235,320,true⟩,0,0,0⟩, +⟨⟨1,235,322,true⟩,0,0,0⟩, +⟨⟨1,235,328,true⟩,0,0,0⟩, +⟨⟨1,235,330,true⟩,0,0,0⟩, +⟨⟨1,235,337,true⟩,0,0,0⟩, +⟨⟨1,235,341,true⟩,0,0,0⟩, +⟨⟨1,235,345,true⟩,0,0,0⟩, +⟨⟨1,235,349,true⟩,0,0,0⟩, +⟨⟨1,235,352,true⟩,0,0,0⟩, +⟨⟨1,235,354,true⟩,0,0,0⟩, +⟨⟨1,235,360,true⟩,0,0,0⟩, +⟨⟨1,235,362,true⟩,0,0,0⟩, +⟨⟨1,235,389,true⟩,0,0,0⟩, +⟨⟨1,235,391,true⟩,0,0,0⟩, +⟨⟨1,235,393,true⟩,0,0,0⟩, +⟨⟨1,235,395,true⟩,0,0,0⟩, +⟨⟨1,235,403,true⟩,0,0,0⟩, +⟨⟨1,235,407,true⟩,0,0,0⟩, +⟨⟨1,235,411,true⟩,0,0,0⟩, +⟨⟨1,235,415,true⟩,0,0,0⟩, +⟨⟨1,235,432,true⟩,0,0,0⟩, +⟨⟨1,235,436,true⟩,0,0,0⟩, +⟨⟨1,235,442,true⟩,0,0,0⟩, +⟨⟨1,235,446,true⟩,0,0,0⟩, +⟨⟨1,235,449,true⟩,0,0,0⟩, +⟨⟨1,235,451,true⟩,0,0,0⟩, +⟨⟨1,235,461,true⟩,0,0,0⟩, +⟨⟨1,235,463,true⟩,0,0,0⟩, +⟨⟨1,235,464,true⟩,0,0,0⟩, +⟨⟨1,235,468,true⟩,0,0,0⟩, +⟨⟨1,235,474,true⟩,0,0,0⟩, +⟨⟨1,235,478,true⟩,0,0,0⟩, +⟨⟨1,235,481,true⟩,0,0,0⟩, +⟨⟨1,235,483,true⟩,0,0,0⟩, +⟨⟨1,235,493,true⟩,0,0,0⟩, +⟨⟨1,235,495,true⟩,0,0,0⟩, +⟨⟨1,235,496,true⟩,0,0,0⟩, +⟨⟨1,235,596,true⟩,0,0,0⟩, +⟨⟨1,235,598,true⟩,0,0,0⟩, +⟨⟨1,235,624,true⟩,0,0,0⟩, +⟨⟨1,235,626,true⟩,0,0,0⟩, +⟨⟨1,235,628,true⟩,0,0,0⟩, +⟨⟨1,235,630,true⟩,0,0,0⟩, +⟨⟨1,235,642,true⟩,0,0,0⟩, +⟨⟨1,235,643,true⟩,0,0,0⟩, +⟨⟨1,235,646,true⟩,0,0,0⟩, +⟨⟨1,235,647,true⟩,0,0,0⟩, +⟨⟨1,235,664,true⟩,0,0,0⟩, +⟨⟨1,235,666,true⟩,0,0,0⟩, +⟨⟨1,235,684,true⟩,0,0,0⟩, +⟨⟨1,235,686,true⟩,0,0,0⟩, +⟨⟨1,235,696,true⟩,0,0,0⟩, +⟨⟨1,235,698,true⟩,0,0,0⟩, +⟨⟨1,235,716,true⟩,0,0,0⟩, +⟨⟨1,235,718,true⟩,0,0,0⟩, +⟨⟨1,235,733,true⟩,0,0,0⟩, +⟨⟨1,235,735,true⟩,0,0,0⟩, +⟨⟨1,235,756,true⟩,0,0,0⟩, +⟨⟨1,235,768,true⟩,0,0,0⟩, +⟨⟨1,235,902,true⟩,0,0,0⟩, +⟨⟨1,235,916,true⟩,0,0,0⟩, +⟨⟨1,236,248,true⟩,0,0,0⟩, +⟨⟨1,236,254,true⟩,0,0,0⟩, +⟨⟨1,236,266,true⟩,0,0,0⟩, +⟨⟨1,236,284,true⟩,0,0,0⟩, +⟨⟨1,236,292,true⟩,0,0,0⟩, +⟨⟨1,236,293,true⟩,0,0,0⟩] +def chunk38 : List Entry := [⟨⟨1,236,294,true⟩,0,0,0⟩, +⟨⟨1,236,295,true⟩,0,0,0⟩, +⟨⟨1,236,297,true⟩,0,0,0⟩, +⟨⟨1,236,299,true⟩,0,0,0⟩, +⟨⟨1,236,300,true⟩,0,0,0⟩, +⟨⟨1,236,302,true⟩,0,0,0⟩, +⟨⟨1,236,307,true⟩,0,0,0⟩, +⟨⟨1,236,311,true⟩,0,0,0⟩, +⟨⟨1,236,315,true⟩,0,0,0⟩, +⟨⟨1,236,319,true⟩,0,0,0⟩, +⟨⟨1,236,324,true⟩,0,0,0⟩, +⟨⟨1,236,326,true⟩,0,0,0⟩, +⟨⟨1,236,332,true⟩,0,0,0⟩, +⟨⟨1,236,334,true⟩,0,0,0⟩, +⟨⟨1,236,339,true⟩,0,0,0⟩, +⟨⟨1,236,343,true⟩,0,0,0⟩, +⟨⟨1,236,347,true⟩,0,0,0⟩, +⟨⟨1,236,351,true⟩,0,0,0⟩, +⟨⟨1,236,356,true⟩,0,0,0⟩, +⟨⟨1,236,358,true⟩,0,0,0⟩, +⟨⟨1,236,364,true⟩,0,0,0⟩, +⟨⟨1,236,366,true⟩,0,0,0⟩, +⟨⟨1,236,389,true⟩,0,0,0⟩, +⟨⟨1,236,391,true⟩,0,0,0⟩, +⟨⟨1,236,393,true⟩,0,0,0⟩, +⟨⟨1,236,395,true⟩,0,0,0⟩, +⟨⟨1,236,401,true⟩,0,0,0⟩, +⟨⟨1,236,405,true⟩,0,0,0⟩, +⟨⟨1,236,409,true⟩,0,0,0⟩, +⟨⟨1,236,413,true⟩,0,0,0⟩, +⟨⟨1,236,432,true⟩,0,0,0⟩, +⟨⟨1,236,436,true⟩,0,0,0⟩, +⟨⟨1,236,442,true⟩,0,0,0⟩, +⟨⟨1,236,446,true⟩,0,0,0⟩, +⟨⟨1,236,449,true⟩,0,0,0⟩, +⟨⟨1,236,451,true⟩,0,0,0⟩, +⟨⟨1,236,461,true⟩,0,0,0⟩, +⟨⟨1,236,463,true⟩,0,0,0⟩, +⟨⟨1,236,464,true⟩,0,0,0⟩, +⟨⟨1,236,468,true⟩,0,0,0⟩, +⟨⟨1,236,474,true⟩,0,0,0⟩, +⟨⟨1,236,478,true⟩,0,0,0⟩, +⟨⟨1,236,481,true⟩,0,0,0⟩, +⟨⟨1,236,483,true⟩,0,0,0⟩, +⟨⟨1,236,493,true⟩,0,0,0⟩, +⟨⟨1,236,495,true⟩,0,0,0⟩, +⟨⟨1,236,511,true⟩,0,0,0⟩, +⟨⟨1,236,592,true⟩,0,0,0⟩, +⟨⟨1,236,594,true⟩,0,0,0⟩, +⟨⟨1,236,624,true⟩,0,0,0⟩, +⟨⟨1,236,626,true⟩,0,0,0⟩, +⟨⟨1,236,629,true⟩,0,0,0⟩, +⟨⟨1,236,634,true⟩,0,0,0⟩, +⟨⟨1,236,639,true⟩,0,0,0⟩, +⟨⟨1,236,642,true⟩,0,0,0⟩, +⟨⟨1,236,643,true⟩,0,0,0⟩, +⟨⟨1,236,646,true⟩,0,0,0⟩, +⟨⟨1,236,647,true⟩,0,0,0⟩, +⟨⟨1,236,664,true⟩,0,0,0⟩, +⟨⟨1,236,666,true⟩,0,0,0⟩, +⟨⟨1,236,684,true⟩,0,0,0⟩, +⟨⟨1,236,686,true⟩,0,0,0⟩, +⟨⟨1,236,696,true⟩,0,0,0⟩, +⟨⟨1,236,698,true⟩,0,0,0⟩, +⟨⟨1,236,716,true⟩,0,0,0⟩, +⟨⟨1,236,718,true⟩,0,0,0⟩, +⟨⟨1,236,733,true⟩,0,0,0⟩, +⟨⟨1,236,735,true⟩,0,0,0⟩, +⟨⟨1,236,742,true⟩,0,0,0⟩, +⟨⟨1,236,806,true⟩,0,0,0⟩, +⟨⟨1,236,902,true⟩,0,0,0⟩, +⟨⟨1,236,916,true⟩,0,0,0⟩, +⟨⟨1,236,981,true⟩,0,0,0⟩, +⟨⟨1,236,985,true⟩,0,0,0⟩, +⟨⟨1,237,248,true⟩,0,0,0⟩, +⟨⟨1,237,254,true⟩,0,0,0⟩, +⟨⟨1,237,266,true⟩,0,0,0⟩, +⟨⟨1,237,284,true⟩,0,0,0⟩, +⟨⟨1,237,305,true⟩,0,0,0⟩, +⟨⟨1,237,309,true⟩,0,0,0⟩, +⟨⟨1,237,313,true⟩,0,0,0⟩, +⟨⟨1,237,317,true⟩,0,0,0⟩, +⟨⟨1,237,320,true⟩,0,0,0⟩, +⟨⟨1,237,322,true⟩,0,0,0⟩, +⟨⟨1,237,328,true⟩,0,0,0⟩, +⟨⟨1,237,330,true⟩,0,0,0⟩, +⟨⟨1,237,339,true⟩,0,0,0⟩, +⟨⟨1,237,343,true⟩,0,0,0⟩, +⟨⟨1,237,347,true⟩,0,0,0⟩, +⟨⟨1,237,351,true⟩,0,0,0⟩, +⟨⟨1,237,356,true⟩,0,0,0⟩, +⟨⟨1,237,358,true⟩,0,0,0⟩, +⟨⟨1,237,364,true⟩,0,0,0⟩, +⟨⟨1,237,366,true⟩,0,0,0⟩, +⟨⟨1,237,385,true⟩,0,0,0⟩, +⟨⟨1,237,387,true⟩,0,0,0⟩, +⟨⟨1,237,397,true⟩,0,0,0⟩, +⟨⟨1,237,399,true⟩,0,0,0⟩, +⟨⟨1,237,401,true⟩,0,0,0⟩, +⟨⟨1,237,405,true⟩,0,0,0⟩, +⟨⟨1,237,409,true⟩,0,0,0⟩, +⟨⟨1,237,413,true⟩,0,0,0⟩, +⟨⟨1,237,434,true⟩,0,0,0⟩, +⟨⟨1,237,438,true⟩,0,0,0⟩, +⟨⟨1,237,440,true⟩,0,0,0⟩, +⟨⟨1,237,444,true⟩,0,0,0⟩, +⟨⟨1,237,453,true⟩,0,0,0⟩, +⟨⟨1,237,455,true⟩,0,0,0⟩, +⟨⟨1,237,457,true⟩,0,0,0⟩, +⟨⟨1,237,459,true⟩,0,0,0⟩, +⟨⟨1,237,464,true⟩,0,0,0⟩, +⟨⟨1,237,468,true⟩,0,0,0⟩, +⟨⟨1,237,474,true⟩,0,0,0⟩, +⟨⟨1,237,478,true⟩,0,0,0⟩, +⟨⟨1,237,481,true⟩,0,0,0⟩, +⟨⟨1,237,483,true⟩,0,0,0⟩, +⟨⟨1,237,493,true⟩,0,0,0⟩, +⟨⟨1,237,495,true⟩,0,0,0⟩, +⟨⟨1,237,509,true⟩,0,0,0⟩, +⟨⟨1,237,592,true⟩,0,0,0⟩, +⟨⟨1,237,594,true⟩,0,0,0⟩, +⟨⟨1,237,624,true⟩,0,0,0⟩, +⟨⟨1,237,626,true⟩,0,0,0⟩, +⟨⟨1,237,628,true⟩,0,0,0⟩, +⟨⟨1,237,630,true⟩,0,0,0⟩, +⟨⟨1,237,640,true⟩,0,0,0⟩, +⟨⟨1,237,641,true⟩,0,0,0⟩, +⟨⟨1,237,644,true⟩,0,0,0⟩, +⟨⟨1,237,645,true⟩,0,0,0⟩, +⟨⟨1,237,665,true⟩,0,0,0⟩, +⟨⟨1,237,667,true⟩,0,0,0⟩, +⟨⟨1,237,684,true⟩,0,0,0⟩, +⟨⟨1,237,686,true⟩,0,0,0⟩, +⟨⟨1,237,696,true⟩,0,0,0⟩, +⟨⟨1,237,698,true⟩,0,0,0⟩, +⟨⟨1,237,717,true⟩,0,0,0⟩, +⟨⟨1,237,719,true⟩,0,0,0⟩, +⟨⟨1,237,732,true⟩,0,0,0⟩, +⟨⟨1,237,734,true⟩,0,0,0⟩, +⟨⟨1,237,742,true⟩,0,0,0⟩, +⟨⟨1,237,768,true⟩,0,0,0⟩, +⟨⟨1,237,806,true⟩,0,0,0⟩, +⟨⟨1,237,902,true⟩,0,0,0⟩, +⟨⟨1,237,930,true⟩,0,0,0⟩, +⟨⟨1,238,248,true⟩,0,0,0⟩, +⟨⟨1,238,254,true⟩,0,0,0⟩, +⟨⟨1,238,266,true⟩,0,0,0⟩, +⟨⟨1,238,284,true⟩,0,0,0⟩, +⟨⟨1,238,307,true⟩,0,0,0⟩, +⟨⟨1,238,311,true⟩,0,0,0⟩, +⟨⟨1,238,315,true⟩,0,0,0⟩, +⟨⟨1,238,319,true⟩,0,0,0⟩, +⟨⟨1,238,324,true⟩,0,0,0⟩, +⟨⟨1,238,326,true⟩,0,0,0⟩, +⟨⟨1,238,332,true⟩,0,0,0⟩, +⟨⟨1,238,334,true⟩,0,0,0⟩, +⟨⟨1,238,337,true⟩,0,0,0⟩, +⟨⟨1,238,341,true⟩,0,0,0⟩, +⟨⟨1,238,345,true⟩,0,0,0⟩, +⟨⟨1,238,349,true⟩,0,0,0⟩, +⟨⟨1,238,352,true⟩,0,0,0⟩, +⟨⟨1,238,354,true⟩,0,0,0⟩, +⟨⟨1,238,360,true⟩,0,0,0⟩, +⟨⟨1,238,362,true⟩,0,0,0⟩, +⟨⟨1,238,385,true⟩,0,0,0⟩, +⟨⟨1,238,387,true⟩,0,0,0⟩, +⟨⟨1,238,397,true⟩,0,0,0⟩, +⟨⟨1,238,399,true⟩,0,0,0⟩, +⟨⟨1,238,401,true⟩,0,0,0⟩, +⟨⟨1,238,405,true⟩,0,0,0⟩, +⟨⟨1,238,409,true⟩,0,0,0⟩, +⟨⟨1,238,413,true⟩,0,0,0⟩, +⟨⟨1,238,432,true⟩,0,0,0⟩, +⟨⟨1,238,436,true⟩,0,0,0⟩, +⟨⟨1,238,442,true⟩,0,0,0⟩, +⟨⟨1,238,446,true⟩,0,0,0⟩, +⟨⟨1,238,449,true⟩,0,0,0⟩, +⟨⟨1,238,451,true⟩,0,0,0⟩, +⟨⟨1,238,461,true⟩,0,0,0⟩, +⟨⟨1,238,463,true⟩,0,0,0⟩, +⟨⟨1,238,466,true⟩,0,0,0⟩, +⟨⟨1,238,470,true⟩,0,0,0⟩, +⟨⟨1,238,472,true⟩,0,0,0⟩, +⟨⟨1,238,476,true⟩,0,0,0⟩, +⟨⟨1,238,485,true⟩,0,0,0⟩, +⟨⟨1,238,487,true⟩,0,0,0⟩, +⟨⟨1,238,489,true⟩,0,0,0⟩, +⟨⟨1,238,491,true⟩,0,0,0⟩, +⟨⟨1,238,507,true⟩,0,0,0⟩, +⟨⟨1,238,592,true⟩,0,0,0⟩, +⟨⟨1,238,594,true⟩,0,0,0⟩, +⟨⟨1,238,624,true⟩,0,0,0⟩, +⟨⟨1,238,626,true⟩,0,0,0⟩, +⟨⟨1,238,628,true⟩,0,0,0⟩, +⟨⟨1,238,630,true⟩,0,0,0⟩, +⟨⟨1,238,640,true⟩,0,0,0⟩, +⟨⟨1,238,641,true⟩,0,0,0⟩, +⟨⟨1,238,644,true⟩,0,0,0⟩, +⟨⟨1,238,645,true⟩,0,0,0⟩, +⟨⟨1,238,664,true⟩,0,0,0⟩] +def chunk39 : List Entry := [⟨⟨1,238,666,true⟩,0,0,0⟩, +⟨⟨1,238,685,true⟩,0,0,0⟩, +⟨⟨1,238,687,true⟩,0,0,0⟩, +⟨⟨1,238,697,true⟩,0,0,0⟩, +⟨⟨1,238,699,true⟩,0,0,0⟩, +⟨⟨1,238,716,true⟩,0,0,0⟩, +⟨⟨1,238,718,true⟩,0,0,0⟩, +⟨⟨1,238,732,true⟩,0,0,0⟩, +⟨⟨1,238,734,true⟩,0,0,0⟩, +⟨⟨1,238,742,true⟩,0,0,0⟩, +⟨⟨1,238,756,true⟩,0,0,0⟩, +⟨⟨1,238,806,true⟩,0,0,0⟩, +⟨⟨1,238,916,true⟩,0,0,0⟩, +⟨⟨1,238,930,true⟩,0,0,0⟩, +⟨⟨1,239,248,true⟩,0,0,0⟩, +⟨⟨1,239,254,true⟩,0,0,0⟩, +⟨⟨1,239,266,true⟩,0,0,0⟩, +⟨⟨1,239,284,true⟩,0,0,0⟩, +⟨⟨1,239,290,true⟩,0,0,0⟩, +⟨⟨1,239,291,true⟩,0,0,0⟩, +⟨⟨1,239,296,true⟩,0,0,0⟩, +⟨⟨1,239,303,true⟩,0,0,0⟩, +⟨⟨1,239,305,true⟩,0,0,0⟩, +⟨⟨1,239,309,true⟩,0,0,0⟩, +⟨⟨1,239,313,true⟩,0,0,0⟩, +⟨⟨1,239,317,true⟩,0,0,0⟩, +⟨⟨1,239,320,true⟩,0,0,0⟩, +⟨⟨1,239,322,true⟩,0,0,0⟩, +⟨⟨1,239,328,true⟩,0,0,0⟩, +⟨⟨1,239,330,true⟩,0,0,0⟩, +⟨⟨1,239,337,true⟩,0,0,0⟩, +⟨⟨1,239,341,true⟩,0,0,0⟩, +⟨⟨1,239,345,true⟩,0,0,0⟩, +⟨⟨1,239,349,true⟩,0,0,0⟩, +⟨⟨1,239,352,true⟩,0,0,0⟩, +⟨⟨1,239,354,true⟩,0,0,0⟩, +⟨⟨1,239,360,true⟩,0,0,0⟩, +⟨⟨1,239,362,true⟩,0,0,0⟩, +⟨⟨1,239,389,true⟩,0,0,0⟩, +⟨⟨1,239,391,true⟩,0,0,0⟩, +⟨⟨1,239,393,true⟩,0,0,0⟩, +⟨⟨1,239,395,true⟩,0,0,0⟩, +⟨⟨1,239,401,true⟩,0,0,0⟩, +⟨⟨1,239,405,true⟩,0,0,0⟩, +⟨⟨1,239,409,true⟩,0,0,0⟩, +⟨⟨1,239,413,true⟩,0,0,0⟩, +⟨⟨1,239,434,true⟩,0,0,0⟩, +⟨⟨1,239,438,true⟩,0,0,0⟩, +⟨⟨1,239,440,true⟩,0,0,0⟩, +⟨⟨1,239,444,true⟩,0,0,0⟩, +⟨⟨1,239,453,true⟩,0,0,0⟩, +⟨⟨1,239,455,true⟩,0,0,0⟩, +⟨⟨1,239,457,true⟩,0,0,0⟩, +⟨⟨1,239,459,true⟩,0,0,0⟩, +⟨⟨1,239,466,true⟩,0,0,0⟩, +⟨⟨1,239,470,true⟩,0,0,0⟩, +⟨⟨1,239,472,true⟩,0,0,0⟩, +⟨⟨1,239,476,true⟩,0,0,0⟩, +⟨⟨1,239,485,true⟩,0,0,0⟩, +⟨⟨1,239,487,true⟩,0,0,0⟩, +⟨⟨1,239,489,true⟩,0,0,0⟩, +⟨⟨1,239,491,true⟩,0,0,0⟩, +⟨⟨1,239,505,true⟩,0,0,0⟩, +⟨⟨1,239,592,true⟩,0,0,0⟩, +⟨⟨1,239,594,true⟩,0,0,0⟩, +⟨⟨1,239,624,true⟩,0,0,0⟩, +⟨⟨1,239,626,true⟩,0,0,0⟩, +⟨⟨1,239,629,true⟩,0,0,0⟩, +⟨⟨1,239,630,true⟩,0,0,0⟩, +⟨⟨1,239,638,true⟩,0,0,0⟩, +⟨⟨1,239,639,true⟩,0,0,0⟩, +⟨⟨1,239,642,true⟩,0,0,0⟩, +⟨⟨1,239,643,true⟩,0,0,0⟩, +⟨⟨1,239,646,true⟩,0,0,0⟩, +⟨⟨1,239,647,true⟩,0,0,0⟩, +⟨⟨1,239,665,true⟩,0,0,0⟩, +⟨⟨1,239,667,true⟩,0,0,0⟩, +⟨⟨1,239,685,true⟩,0,0,0⟩, +⟨⟨1,239,687,true⟩,0,0,0⟩, +⟨⟨1,239,697,true⟩,0,0,0⟩, +⟨⟨1,239,699,true⟩,0,0,0⟩, +⟨⟨1,239,717,true⟩,0,0,0⟩, +⟨⟨1,239,719,true⟩,0,0,0⟩, +⟨⟨1,239,733,true⟩,0,0,0⟩, +⟨⟨1,239,735,true⟩,0,0,0⟩, +⟨⟨1,239,742,true⟩,0,0,0⟩, +⟨⟨1,239,756,true⟩,0,0,0⟩, +⟨⟨1,239,768,true⟩,0,0,0⟩, +⟨⟨1,239,806,true⟩,0,0,0⟩, +⟨⟨1,239,982,true⟩,0,0,0⟩, +⟨⟨1,239,986,true⟩,0,0,0⟩, +⟨⟨0,241,0,false⟩,0,2,1⟩, +⟨⟨1,241,787,true⟩,2,2,0⟩, +⟨⟨1,241,803,true⟩,2,2,0⟩, +⟨⟨1,241,817,true⟩,2,2,0⟩, +⟨⟨1,241,833,true⟩,2,2,0⟩, +⟨⟨0,242,0,false⟩,0,2,1⟩, +⟨⟨1,242,747,true⟩,2,2,0⟩, +⟨⟨1,242,761,true⟩,2,2,0⟩, +⟨⟨1,242,773,true⟩,2,2,0⟩, +⟨⟨0,244,0,false⟩,0,2,1⟩, +⟨⟨1,244,745,true⟩,2,2,0⟩, +⟨⟨0,248,0,true⟩,0,3,1⟩, +⟨⟨1,248,743,true⟩,3,3,0⟩, +⟨⟨1,248,757,true⟩,3,3,0⟩, +⟨⟨1,248,769,true⟩,3,3,0⟩, +⟨⟨1,248,861,true⟩,3,3,0⟩, +⟨⟨1,248,875,true⟩,3,3,0⟩, +⟨⟨1,248,889,true⟩,3,3,0⟩, +⟨⟨0,249,0,true⟩,0,3,1⟩, +⟨⟨1,249,771,true⟩,3,3,0⟩, +⟨⟨1,249,847,true⟩,3,3,0⟩, +⟨⟨1,249,873,true⟩,3,3,0⟩, +⟨⟨0,250,0,true⟩,0,3,1⟩, +⟨⟨1,250,741,true⟩,3,3,0⟩, +⟨⟨1,250,845,true⟩,3,3,0⟩, +⟨⟨1,250,859,true⟩,3,3,0⟩, +⟨⟨1,250,885,true⟩,3,3,0⟩, +⟨⟨0,254,0,false⟩,0,4,1⟩, +⟨⟨1,254,903,true⟩,4,4,0⟩, +⟨⟨1,254,917,true⟩,4,4,0⟩, +⟨⟨0,256,0,false⟩,0,4,1⟩, +⟨⟨1,256,739,true⟩,4,4,0⟩, +⟨⟨1,256,799,true⟩,4,4,0⟩, +⟨⟨1,256,855,true⟩,4,4,0⟩, +⟨⟨1,256,909,true⟩,4,4,0⟩, +⟨⟨0,257,0,false⟩,0,4,1⟩, +⟨⟨1,257,738,true⟩,4,4,0⟩, +⟨⟨1,257,783,true⟩,4,4,0⟩, +⟨⟨1,257,797,true⟩,4,4,0⟩, +⟨⟨1,257,839,true⟩,4,4,0⟩, +⟨⟨1,257,853,true⟩,4,4,0⟩, +⟨⟨1,257,895,true⟩,4,4,0⟩, +⟨⟨0,260,0,true⟩,0,5,1⟩, +⟨⟨1,260,913,true⟩,5,5,0⟩, +⟨⟨0,263,0,true⟩,0,5,1⟩, +⟨⟨1,263,825,true⟩,5,5,0⟩, +⟨⟨1,263,867,true⟩,5,5,0⟩, +⟨⟨0,267,0,false⟩,0,6,1⟩, +⟨⟨1,267,899,true⟩,6,6,0⟩, +⟨⟨0,268,0,false⟩,0,6,1⟩, +⟨⟨1,268,752,true⟩,6,6,0⟩, +⟨⟨1,268,785,true⟩,6,6,0⟩, +⟨⟨1,268,813,true⟩,6,6,0⟩, +⟨⟨1,268,841,true⟩,6,6,0⟩, +⟨⟨1,268,869,true⟩,6,6,0⟩, +⟨⟨1,268,923,true⟩,6,6,0⟩, +⟨⟨0,269,0,false⟩,0,6,1⟩, +⟨⟨1,269,753,true⟩,6,6,0⟩, +⟨⟨1,269,781,true⟩,6,6,0⟩, +⟨⟨1,269,809,true⟩,6,6,0⟩, +⟨⟨1,269,837,true⟩,6,6,0⟩, +⟨⟨1,269,865,true⟩,6,6,0⟩, +⟨⟨1,269,893,true⟩,6,6,0⟩, +⟨⟨0,272,0,true⟩,0,7,1⟩, +⟨⟨1,272,755,true⟩,7,7,0⟩, +⟨⟨1,272,822,true⟩,7,7,0⟩, +⟨⟨1,272,887,true⟩,7,7,0⟩, +⟨⟨1,272,901,true⟩,7,7,0⟩, +⟨⟨1,272,929,true⟩,7,7,0⟩, +⟨⟨0,274,0,true⟩,0,7,1⟩, +⟨⟨1,274,827,true⟩,7,7,0⟩, +⟨⟨1,274,883,true⟩,7,7,0⟩, +⟨⟨0,275,0,true⟩,0,7,1⟩, +⟨⟨1,275,795,true⟩,7,7,0⟩, +⟨⟨1,275,823,true⟩,7,7,0⟩, +⟨⟨1,275,851,true⟩,7,7,0⟩, +⟨⟨1,275,879,true⟩,7,7,0⟩, +⟨⟨0,283,0,true⟩,0,9,1⟩, +⟨⟨1,283,836,true⟩,9,9,0⟩, +⟨⟨0,284,0,true⟩,0,9,1⟩, +⟨⟨1,284,808,true⟩,9,9,0⟩, +⟨⟨1,284,931,true⟩,9,9,0⟩, +⟨⟨0,286,0,true⟩,0,9,1⟩, +⟨⟨1,286,919,true⟩,9,9,0⟩, +⟨⟨1,286,921,true⟩,9,9,0⟩, +⟨⟨0,287,0,true⟩,0,9,1⟩, +⟨⟨1,287,767,true⟩,9,9,0⟩, +⟨⟨0,736,0,false⟩,0,4,1⟩, +⟨⟨1,736,738,true⟩,4,4,0⟩, +⟨⟨1,736,838,true⟩,4,4,0⟩, +⟨⟨1,736,839,true⟩,4,4,0⟩, +⟨⟨1,736,852,true⟩,4,4,0⟩, +⟨⟨1,736,853,true⟩,4,4,0⟩, +⟨⟨0,737,0,false⟩,0,4,1⟩, +⟨⟨1,737,739,true⟩,4,4,0⟩, +⟨⟨1,737,908,true⟩,4,4,0⟩, +⟨⟨1,737,909,true⟩,4,4,0⟩, +⟨⟨0,740,0,true⟩,0,3,1⟩, +⟨⟨1,740,741,true⟩,3,3,0⟩, +⟨⟨0,742,0,true⟩,0,3,1⟩, +⟨⟨1,742,743,true⟩,3,3,0⟩, +⟨⟨1,742,874,true⟩,3,3,0⟩, +⟨⟨1,742,875,true⟩,3,3,0⟩, +⟨⟨1,742,888,true⟩,3,3,0⟩, +⟨⟨1,742,889,true⟩,3,3,0⟩, +⟨⟨0,744,0,false⟩,0,2,1⟩, +⟨⟨1,744,745,true⟩,2,2,0⟩, +⟨⟨0,746,0,false⟩,0,2,1⟩, +⟨⟨1,746,747,true⟩,2,2,0⟩] +def chunk40 : List Entry := [⟨⟨0,748,0,false⟩,0,2,1⟩, +⟨⟨1,748,789,true⟩,2,2,0⟩, +⟨⟨1,748,801,true⟩,2,2,0⟩, +⟨⟨1,748,818,true⟩,2,2,0⟩, +⟨⟨1,748,830,true⟩,2,2,0⟩, +⟨⟨0,749,0,false⟩,0,2,1⟩, +⟨⟨1,749,789,true⟩,2,2,0⟩, +⟨⟨1,749,801,true⟩,2,2,0⟩, +⟨⟨1,749,819,true⟩,2,2,0⟩, +⟨⟨1,749,831,true⟩,2,2,0⟩, +⟨⟨0,750,0,false⟩,0,6,1⟩, +⟨⟨1,750,752,true⟩,6,6,0⟩, +⟨⟨1,750,784,true⟩,6,6,0⟩, +⟨⟨1,750,785,true⟩,6,6,0⟩, +⟨⟨1,750,840,true⟩,6,6,0⟩, +⟨⟨1,750,841,true⟩,6,6,0⟩, +⟨⟨1,750,922,true⟩,6,6,0⟩, +⟨⟨1,750,923,true⟩,6,6,0⟩, +⟨⟨0,756,0,true⟩,0,3,1⟩, +⟨⟨1,756,757,true⟩,3,3,0⟩, +⟨⟨1,756,860,true⟩,3,3,0⟩, +⟨⟨1,756,861,true⟩,3,3,0⟩, +⟨⟨1,756,888,true⟩,3,3,0⟩, +⟨⟨1,756,889,true⟩,3,3,0⟩, +⟨⟨0,760,0,false⟩,0,2,1⟩, +⟨⟨1,760,761,true⟩,2,2,0⟩, +⟨⟨0,762,0,false⟩,0,2,1⟩, +⟨⟨1,762,777,true⟩,2,2,0⟩, +⟨⟨1,762,791,true⟩,2,2,0⟩, +⟨⟨1,762,804,true⟩,2,2,0⟩, +⟨⟨1,762,815,true⟩,2,2,0⟩, +⟨⟨1,762,828,true⟩,2,2,0⟩, +⟨⟨0,763,0,false⟩,0,2,1⟩, +⟨⟨1,763,777,true⟩,2,2,0⟩, +⟨⟨1,763,791,true⟩,2,2,0⟩, +⟨⟨1,763,805,true⟩,2,2,0⟩, +⟨⟨1,763,815,true⟩,2,2,0⟩, +⟨⟨1,763,829,true⟩,2,2,0⟩, +⟨⟨0,764,0,true⟩,0,9,1⟩, +⟨⟨1,764,811,true⟩,9,9,0⟩, +⟨⟨1,764,881,true⟩,9,9,0⟩, +⟨⟨1,764,921,true⟩,9,9,0⟩, +⟨⟨0,765,0,true⟩,0,9,1⟩, +⟨⟨1,765,767,true⟩,9,9,0⟩, +⟨⟨0,766,0,true⟩,0,9,1⟩, +⟨⟨1,766,811,true⟩,9,9,0⟩, +⟨⟨1,766,881,true⟩,9,9,0⟩, +⟨⟨1,766,919,true⟩,9,9,0⟩, +⟨⟨0,768,0,true⟩,0,3,1⟩, +⟨⟨1,768,769,true⟩,3,3,0⟩, +⟨⟨1,768,860,true⟩,3,3,0⟩, +⟨⟨1,768,861,true⟩,3,3,0⟩, +⟨⟨1,768,874,true⟩,3,3,0⟩, +⟨⟨1,768,875,true⟩,3,3,0⟩, +⟨⟨0,770,0,true⟩,0,3,1⟩, +⟨⟨1,770,771,true⟩,3,3,0⟩, +⟨⟨0,772,0,false⟩,0,2,1⟩, +⟨⟨1,772,773,true⟩,2,2,0⟩, +⟨⟨0,776,0,false⟩,0,2,1⟩, +⟨⟨1,776,777,true⟩,2,2,0⟩, +⟨⟨1,776,804,true⟩,2,2,0⟩, +⟨⟨1,776,805,true⟩,2,2,0⟩, +⟨⟨1,776,814,true⟩,2,2,0⟩, +⟨⟨1,776,815,true⟩,2,2,0⟩, +⟨⟨0,779,0,false⟩,0,6,1⟩, +⟨⟨1,779,751,true⟩,6,6,0⟩, +⟨⟨1,779,753,true⟩,6,6,0⟩, +⟨⟨1,779,781,true⟩,6,6,0⟩, +⟨⟨1,779,863,true⟩,6,6,0⟩, +⟨⟨1,779,865,true⟩,6,6,0⟩, +⟨⟨1,779,891,true⟩,6,6,0⟩, +⟨⟨1,779,893,true⟩,6,6,0⟩, +⟨⟨0,782,0,false⟩,0,4,1⟩, +⟨⟨1,782,783,true⟩,4,4,0⟩, +⟨⟨1,782,838,true⟩,4,4,0⟩, +⟨⟨1,782,839,true⟩,4,4,0⟩, +⟨⟨1,782,894,true⟩,4,4,0⟩, +⟨⟨1,782,895,true⟩,4,4,0⟩, +⟨⟨0,786,0,false⟩,0,2,1⟩, +⟨⟨1,786,787,true⟩,2,2,0⟩, +⟨⟨1,786,832,true⟩,2,2,0⟩, +⟨⟨1,786,833,true⟩,2,2,0⟩, +⟨⟨0,788,0,false⟩,0,2,1⟩, +⟨⟨1,788,789,true⟩,2,2,0⟩, +⟨⟨1,788,830,true⟩,2,2,0⟩, +⟨⟨1,788,831,true⟩,2,2,0⟩, +⟨⟨0,790,0,false⟩,0,2,1⟩, +⟨⟨1,790,791,true⟩,2,2,0⟩, +⟨⟨1,790,804,true⟩,2,2,0⟩, +⟨⟨1,790,805,true⟩,2,2,0⟩, +⟨⟨1,790,814,true⟩,2,2,0⟩, +⟨⟨1,790,815,true⟩,2,2,0⟩, +⟨⟨1,790,828,true⟩,2,2,0⟩, +⟨⟨1,790,829,true⟩,2,2,0⟩, +⟨⟨0,792,0,true⟩,0,7,1⟩, +⟨⟨1,792,857,true⟩,7,7,0⟩, +⟨⟨1,792,897,true⟩,7,7,0⟩, +⟨⟨1,792,925,true⟩,7,7,0⟩, +⟨⟨0,793,0,true⟩,0,7,1⟩, +⟨⟨1,793,795,true⟩,7,7,0⟩, +⟨⟨1,793,877,true⟩,7,7,0⟩, +⟨⟨1,793,879,true⟩,7,7,0⟩, +⟨⟨0,794,0,true⟩,0,7,1⟩, +⟨⟨1,794,857,true⟩,7,7,0⟩, +⟨⟨1,794,897,true⟩,7,7,0⟩, +⟨⟨1,794,925,true⟩,7,7,0⟩, +⟨⟨0,796,0,false⟩,0,4,1⟩, +⟨⟨1,796,797,true⟩,4,4,0⟩, +⟨⟨1,796,852,true⟩,4,4,0⟩, +⟨⟨1,796,853,true⟩,4,4,0⟩, +⟨⟨1,796,894,true⟩,4,4,0⟩, +⟨⟨1,796,895,true⟩,4,4,0⟩, +⟨⟨0,798,0,false⟩,0,4,1⟩, +⟨⟨1,798,799,true⟩,4,4,0⟩, +⟨⟨1,798,908,true⟩,4,4,0⟩, +⟨⟨1,798,909,true⟩,4,4,0⟩, +⟨⟨0,800,0,false⟩,0,2,1⟩, +⟨⟨1,800,801,true⟩,2,2,0⟩, +⟨⟨1,800,818,true⟩,2,2,0⟩, +⟨⟨1,800,819,true⟩,2,2,0⟩, +⟨⟨0,802,0,false⟩,0,2,1⟩, +⟨⟨1,802,803,true⟩,2,2,0⟩, +⟨⟨1,802,832,true⟩,2,2,0⟩, +⟨⟨1,802,833,true⟩,2,2,0⟩, +⟨⟨0,806,0,true⟩,0,9,1⟩, +⟨⟨1,806,808,true⟩,9,9,0⟩, +⟨⟨0,807,0,false⟩,0,6,1⟩, +⟨⟨1,807,809,true⟩,6,6,0⟩, +⟨⟨1,807,863,true⟩,6,6,0⟩, +⟨⟨1,807,865,true⟩,6,6,0⟩, +⟨⟨1,807,891,true⟩,6,6,0⟩, +⟨⟨1,807,893,true⟩,6,6,0⟩, +⟨⟨0,810,0,true⟩,0,9,1⟩, +⟨⟨1,810,811,true⟩,9,9,0⟩, +⟨⟨1,810,919,true⟩,9,9,0⟩, +⟨⟨1,810,921,true⟩,9,9,0⟩, +⟨⟨0,812,0,false⟩,0,6,1⟩, +⟨⟨1,812,813,true⟩,6,6,0⟩, +⟨⟨1,812,840,true⟩,6,6,0⟩, +⟨⟨1,812,841,true⟩,6,6,0⟩, +⟨⟨1,812,922,true⟩,6,6,0⟩, +⟨⟨1,812,923,true⟩,6,6,0⟩, +⟨⟨0,816,0,false⟩,0,2,1⟩, +⟨⟨1,816,817,true⟩,2,2,0⟩, +⟨⟨1,816,832,true⟩,2,2,0⟩, +⟨⟨1,816,833,true⟩,2,2,0⟩, +⟨⟨0,820,0,true⟩,0,7,1⟩, +⟨⟨1,820,754,true⟩,7,7,0⟩, +⟨⟨1,820,755,true⟩,7,7,0⟩, +⟨⟨1,820,822,true⟩,7,7,0⟩, +⟨⟨0,821,0,true⟩,0,7,1⟩, +⟨⟨1,821,823,true⟩,7,7,0⟩, +⟨⟨1,821,877,true⟩,7,7,0⟩, +⟨⟨1,821,879,true⟩,7,7,0⟩, +⟨⟨0,824,0,true⟩,0,5,1⟩, +⟨⟨1,824,825,true⟩,5,5,0⟩, +⟨⟨0,826,0,true⟩,0,7,1⟩, +⟨⟨1,826,827,true⟩,7,7,0⟩, +⟨⟨0,834,0,true⟩,0,9,1⟩, +⟨⟨1,834,836,true⟩,9,9,0⟩, +⟨⟨0,835,0,false⟩,0,6,1⟩, +⟨⟨1,835,751,true⟩,6,6,0⟩, +⟨⟨1,835,753,true⟩,6,6,0⟩, +⟨⟨1,835,837,true⟩,6,6,0⟩, +⟨⟨1,835,863,true⟩,6,6,0⟩, +⟨⟨1,835,865,true⟩,6,6,0⟩, +⟨⟨0,844,0,true⟩,0,3,1⟩, +⟨⟨1,844,845,true⟩,3,3,0⟩, +⟨⟨1,844,884,true⟩,3,3,0⟩, +⟨⟨1,844,885,true⟩,3,3,0⟩, +⟨⟨0,846,0,true⟩,0,3,1⟩, +⟨⟨1,846,847,true⟩,3,3,0⟩, +⟨⟨0,849,0,true⟩,0,7,1⟩, +⟨⟨1,849,851,true⟩,7,7,0⟩, +⟨⟨1,849,877,true⟩,7,7,0⟩, +⟨⟨1,849,879,true⟩,7,7,0⟩, +⟨⟨0,854,0,false⟩,0,4,1⟩, +⟨⟨1,854,855,true⟩,4,4,0⟩, +⟨⟨1,854,908,true⟩,4,4,0⟩, +⟨⟨1,854,909,true⟩,4,4,0⟩, +⟨⟨0,858,0,true⟩,0,3,1⟩, +⟨⟨1,858,859,true⟩,3,3,0⟩, +⟨⟨1,858,884,true⟩,3,3,0⟩, +⟨⟨1,858,885,true⟩,3,3,0⟩, +⟨⟨0,866,0,true⟩,0,5,1⟩, +⟨⟨1,866,867,true⟩,5,5,0⟩, +⟨⟨0,868,0,false⟩,0,6,1⟩, +⟨⟨1,868,784,true⟩,6,6,0⟩, +⟨⟨1,868,785,true⟩,6,6,0⟩, +⟨⟨1,868,869,true⟩,6,6,0⟩, +⟨⟨1,868,922,true⟩,6,6,0⟩, +⟨⟨1,868,923,true⟩,6,6,0⟩, +⟨⟨0,872,0,true⟩,0,3,1⟩, +⟨⟨1,872,873,true⟩,3,3,0⟩, +⟨⟨0,880,0,true⟩,0,9,1⟩, +⟨⟨1,880,881,true⟩,9,9,0⟩, +⟨⟨1,880,919,true⟩,9,9,0⟩, +⟨⟨1,880,921,true⟩,9,9,0⟩, +⟨⟨0,882,0,true⟩,0,7,1⟩, +⟨⟨1,882,883,true⟩,7,7,0⟩] +def chunk41 : List Entry := [⟨⟨0,896,0,true⟩,0,7,1⟩, +⟨⟨1,896,856,true⟩,7,7,0⟩, +⟨⟨1,896,857,true⟩,7,7,0⟩, +⟨⟨1,896,897,true⟩,7,7,0⟩, +⟨⟨0,898,0,false⟩,0,6,1⟩, +⟨⟨1,898,899,true⟩,6,6,0⟩, +⟨⟨0,900,0,true⟩,0,7,1⟩, +⟨⟨1,900,754,true⟩,7,7,0⟩, +⟨⟨1,900,755,true⟩,7,7,0⟩, +⟨⟨1,900,886,true⟩,7,7,0⟩, +⟨⟨1,900,887,true⟩,7,7,0⟩, +⟨⟨1,900,901,true⟩,7,7,0⟩, +⟨⟨0,902,0,false⟩,0,4,1⟩, +⟨⟨1,902,903,true⟩,4,4,0⟩, +⟨⟨0,912,0,true⟩,0,5,1⟩, +⟨⟨1,912,913,true⟩,5,5,0⟩, +⟨⟨0,916,0,false⟩,0,4,1⟩, +⟨⟨1,916,917,true⟩,4,4,0⟩, +⟨⟨0,924,0,true⟩,0,7,1⟩, +⟨⟨1,924,856,true⟩,7,7,0⟩, +⟨⟨1,924,857,true⟩,7,7,0⟩, +⟨⟨1,924,925,true⟩,7,7,0⟩, +⟨⟨0,928,0,true⟩,0,7,1⟩, +⟨⟨1,928,886,true⟩,7,7,0⟩, +⟨⟨1,928,887,true⟩,7,7,0⟩, +⟨⟨1,928,929,true⟩,7,7,0⟩, +⟨⟨0,930,0,true⟩,0,9,1⟩, +⟨⟨1,930,931,true⟩,9,9,0⟩, +⟨⟨0,932,0,false⟩,0,464,4⟩, +⟨⟨1,932,938,true⟩,464,464,0⟩, +⟨⟨0,933,0,false⟩,0,464,4⟩, +⟨⟨1,933,938,true⟩,464,464,0⟩, +⟨⟨0,936,0,false⟩,0,470,4⟩, +⟨⟨1,936,961,true⟩,470,470,0⟩, +⟨⟨0,937,0,false⟩,0,464,4⟩, +⟨⟨1,937,938,true⟩,464,464,0⟩, +⟨⟨0,941,0,false⟩,0,458,4⟩, +⟨⟨1,941,949,true⟩,458,458,0⟩, +⟨⟨0,942,0,false⟩,0,462,4⟩, +⟨⟨1,942,953,true⟩,462,462,0⟩, +⟨⟨0,943,0,false⟩,0,460,4⟩, +⟨⟨1,943,958,true⟩,460,460,0⟩, +⟨⟨0,944,0,false⟩,0,462,4⟩, +⟨⟨1,944,953,true⟩,462,462,0⟩, +⟨⟨0,945,0,false⟩,0,460,4⟩, +⟨⟨1,945,958,true⟩,460,460,0⟩, +⟨⟨0,951,0,false⟩,0,462,4⟩, +⟨⟨1,951,953,true⟩,462,462,0⟩, +⟨⟨0,956,0,false⟩,0,460,4⟩, +⟨⟨1,956,958,true⟩,460,460,0⟩, +⟨⟨0,959,0,true⟩,0,471,4⟩, +⟨⟨1,959,978,true⟩,471,471,0⟩, +⟨⟨0,960,0,true⟩,0,471,4⟩, +⟨⟨1,960,978,true⟩,471,471,0⟩, +⟨⟨0,977,0,true⟩,0,471,4⟩, +⟨⟨1,977,978,true⟩,471,471,0⟩, +⟨⟨0,240,0,false⟩,0,2,1⟩, +⟨⟨1,240,0,true⟩,2,2,0⟩, +⟨⟨1,241,0,true⟩,2,2,0⟩, +⟨⟨1,242,0,true⟩,2,2,0⟩, +⟨⟨0,243,0,false⟩,0,2,1⟩, +⟨⟨1,243,0,true⟩,2,2,0⟩, +⟨⟨1,244,0,true⟩,2,2,0⟩, +⟨⟨0,245,0,false⟩,0,2,1⟩, +⟨⟨1,245,0,true⟩,2,2,0⟩, +⟨⟨0,246,0,true⟩,0,3,1⟩, +⟨⟨1,246,1,true⟩,3,3,0⟩, +⟨⟨0,247,0,true⟩,0,3,1⟩, +⟨⟨1,247,1,true⟩,3,3,0⟩, +⟨⟨1,248,1,true⟩,3,3,0⟩, +⟨⟨1,249,1,true⟩,3,3,0⟩, +⟨⟨1,250,1,true⟩,3,3,0⟩, +⟨⟨0,251,0,true⟩,0,3,1⟩, +⟨⟨1,251,1,true⟩,3,3,0⟩, +⟨⟨0,252,0,false⟩,0,4,1⟩, +⟨⟨1,252,2,true⟩,4,4,0⟩, +⟨⟨0,253,0,false⟩,0,4,1⟩, +⟨⟨1,253,2,true⟩,4,4,0⟩, +⟨⟨1,254,2,true⟩,4,4,0⟩, +⟨⟨0,255,0,false⟩,0,4,1⟩, +⟨⟨1,255,2,true⟩,4,4,0⟩, +⟨⟨1,256,2,true⟩,4,4,0⟩, +⟨⟨1,257,2,true⟩,4,4,0⟩, +⟨⟨0,258,0,true⟩,0,5,1⟩, +⟨⟨1,258,3,true⟩,5,5,0⟩, +⟨⟨0,259,0,true⟩,0,5,1⟩, +⟨⟨1,259,3,true⟩,5,5,0⟩, +⟨⟨1,260,3,true⟩,5,5,0⟩, +⟨⟨0,261,0,true⟩,0,5,1⟩, +⟨⟨1,261,3,true⟩,5,5,0⟩, +⟨⟨0,262,0,true⟩,0,5,1⟩, +⟨⟨1,262,3,true⟩,5,5,0⟩, +⟨⟨1,263,3,true⟩,5,5,0⟩, +⟨⟨0,264,0,false⟩,0,6,1⟩, +⟨⟨1,264,4,true⟩,6,6,0⟩, +⟨⟨0,265,0,false⟩,0,6,1⟩, +⟨⟨1,265,4,true⟩,6,6,0⟩, +⟨⟨0,266,0,false⟩,0,6,1⟩, +⟨⟨1,266,4,true⟩,6,6,0⟩, +⟨⟨1,267,4,true⟩,6,6,0⟩, +⟨⟨1,268,4,true⟩,6,6,0⟩, +⟨⟨1,269,4,true⟩,6,6,0⟩, +⟨⟨0,270,0,true⟩,0,7,1⟩, +⟨⟨1,270,5,true⟩,7,7,0⟩, +⟨⟨0,271,0,true⟩,0,7,1⟩, +⟨⟨1,271,5,true⟩,7,7,0⟩, +⟨⟨1,272,5,true⟩,7,7,0⟩, +⟨⟨0,273,0,true⟩,0,7,1⟩, +⟨⟨1,273,5,true⟩,7,7,0⟩, +⟨⟨1,274,5,true⟩,7,7,0⟩, +⟨⟨1,275,5,true⟩,7,7,0⟩, +⟨⟨0,276,0,false⟩,0,8,1⟩, +⟨⟨1,276,6,true⟩,8,8,0⟩, +⟨⟨0,277,0,false⟩,0,8,1⟩, +⟨⟨1,277,6,true⟩,8,8,0⟩, +⟨⟨0,278,0,false⟩,0,8,1⟩, +⟨⟨1,278,6,true⟩,8,8,0⟩, +⟨⟨0,279,0,false⟩,0,8,1⟩, +⟨⟨1,279,6,true⟩,8,8,0⟩, +⟨⟨0,280,0,false⟩,0,8,1⟩, +⟨⟨1,280,6,true⟩,8,8,0⟩, +⟨⟨0,281,0,false⟩,0,8,1⟩, +⟨⟨1,281,6,true⟩,8,8,0⟩, +⟨⟨0,282,0,true⟩,0,9,1⟩, +⟨⟨1,282,7,true⟩,9,9,0⟩, +⟨⟨1,283,7,true⟩,9,9,0⟩, +⟨⟨1,284,7,true⟩,9,9,0⟩, +⟨⟨0,285,0,true⟩,0,9,1⟩, +⟨⟨1,285,7,true⟩,9,9,0⟩, +⟨⟨1,286,7,true⟩,9,9,0⟩, +⟨⟨1,287,7,true⟩,9,9,0⟩, +⟨⟨0,288,0,false⟩,0,10,1⟩, +⟨⟨1,288,8,true⟩,10,10,0⟩, +⟨⟨0,289,0,false⟩,0,10,1⟩, +⟨⟨1,289,8,true⟩,10,10,0⟩, +⟨⟨0,290,0,true⟩,0,11,1⟩, +⟨⟨1,290,9,true⟩,11,11,0⟩, +⟨⟨0,291,0,true⟩,0,11,1⟩, +⟨⟨1,291,9,true⟩,11,11,0⟩, +⟨⟨0,292,0,false⟩,0,12,1⟩, +⟨⟨1,292,10,true⟩,12,12,0⟩, +⟨⟨0,293,0,false⟩,0,12,1⟩, +⟨⟨1,293,10,true⟩,12,12,0⟩, +⟨⟨0,294,0,true⟩,0,13,1⟩, +⟨⟨1,294,11,true⟩,13,13,0⟩, +⟨⟨0,295,0,true⟩,0,13,1⟩, +⟨⟨1,295,11,true⟩,13,13,0⟩, +⟨⟨0,296,0,false⟩,0,14,1⟩, +⟨⟨1,296,12,true⟩,14,14,0⟩, +⟨⟨0,297,0,false⟩,0,14,1⟩, +⟨⟨1,297,12,true⟩,14,14,0⟩, +⟨⟨0,298,0,true⟩,0,15,1⟩, +⟨⟨1,298,13,true⟩,15,15,0⟩, +⟨⟨0,299,0,true⟩,0,15,1⟩, +⟨⟨1,299,13,true⟩,15,15,0⟩, +⟨⟨0,300,0,false⟩,0,16,1⟩, +⟨⟨1,300,14,true⟩,16,16,0⟩, +⟨⟨0,301,0,false⟩,0,16,1⟩, +⟨⟨1,301,14,true⟩,16,16,0⟩, +⟨⟨0,302,0,true⟩,0,17,1⟩, +⟨⟨1,302,15,true⟩,17,17,0⟩, +⟨⟨0,303,0,true⟩,0,17,1⟩, +⟨⟨1,303,15,true⟩,17,17,0⟩, +⟨⟨0,304,0,false⟩,0,18,1⟩, +⟨⟨1,304,16,true⟩,18,18,0⟩, +⟨⟨0,305,0,false⟩,0,18,1⟩, +⟨⟨1,305,16,true⟩,18,18,0⟩, +⟨⟨0,306,0,true⟩,0,19,1⟩, +⟨⟨1,306,17,true⟩,19,19,0⟩, +⟨⟨0,307,0,true⟩,0,19,1⟩, +⟨⟨1,307,17,true⟩,19,19,0⟩, +⟨⟨0,308,0,false⟩,0,20,1⟩, +⟨⟨1,308,18,true⟩,20,20,0⟩, +⟨⟨0,309,0,false⟩,0,20,1⟩, +⟨⟨1,309,18,true⟩,20,20,0⟩, +⟨⟨0,310,0,true⟩,0,21,1⟩, +⟨⟨1,310,19,true⟩,21,21,0⟩, +⟨⟨0,311,0,true⟩,0,21,1⟩, +⟨⟨1,311,19,true⟩,21,21,0⟩, +⟨⟨0,312,0,false⟩,0,22,1⟩, +⟨⟨1,312,20,true⟩,22,22,0⟩, +⟨⟨0,313,0,false⟩,0,22,1⟩, +⟨⟨1,313,20,true⟩,22,22,0⟩, +⟨⟨0,314,0,true⟩,0,23,1⟩, +⟨⟨1,314,21,true⟩,23,23,0⟩, +⟨⟨0,315,0,true⟩,0,23,1⟩, +⟨⟨1,315,21,true⟩,23,23,0⟩, +⟨⟨0,316,0,false⟩,0,24,1⟩, +⟨⟨1,316,22,true⟩,24,24,0⟩, +⟨⟨0,317,0,false⟩,0,24,1⟩, +⟨⟨1,317,22,true⟩,24,24,0⟩, +⟨⟨0,318,0,true⟩,0,25,1⟩, +⟨⟨1,318,23,true⟩,25,25,0⟩, +⟨⟨0,319,0,true⟩,0,25,1⟩, +⟨⟨1,319,23,true⟩,25,25,0⟩, +⟨⟨0,320,0,false⟩,0,26,1⟩, +⟨⟨1,320,24,true⟩,26,26,0⟩, +⟨⟨0,321,0,false⟩,0,26,1⟩, +⟨⟨1,321,24,true⟩,26,26,0⟩, +⟨⟨0,322,0,true⟩,0,27,1⟩] +def chunk42 : List Entry := [⟨⟨1,322,25,true⟩,27,27,0⟩, +⟨⟨0,323,0,true⟩,0,27,1⟩, +⟨⟨1,323,25,true⟩,27,27,0⟩, +⟨⟨0,324,0,false⟩,0,28,1⟩, +⟨⟨1,324,26,true⟩,28,28,0⟩, +⟨⟨0,325,0,false⟩,0,28,1⟩, +⟨⟨1,325,26,true⟩,28,28,0⟩, +⟨⟨0,326,0,true⟩,0,29,1⟩, +⟨⟨1,326,27,true⟩,29,29,0⟩, +⟨⟨0,327,0,true⟩,0,29,1⟩, +⟨⟨1,327,27,true⟩,29,29,0⟩, +⟨⟨0,328,0,false⟩,0,30,1⟩, +⟨⟨1,328,28,true⟩,30,30,0⟩, +⟨⟨0,329,0,false⟩,0,30,1⟩, +⟨⟨1,329,28,true⟩,30,30,0⟩, +⟨⟨0,330,0,true⟩,0,31,1⟩, +⟨⟨1,330,29,true⟩,31,31,0⟩, +⟨⟨0,331,0,true⟩,0,31,1⟩, +⟨⟨1,331,29,true⟩,31,31,0⟩, +⟨⟨0,332,0,false⟩,0,32,1⟩, +⟨⟨1,332,30,true⟩,32,32,0⟩, +⟨⟨0,333,0,false⟩,0,32,1⟩, +⟨⟨1,333,30,true⟩,32,32,0⟩, +⟨⟨0,334,0,true⟩,0,33,1⟩, +⟨⟨1,334,31,true⟩,33,33,0⟩, +⟨⟨0,335,0,true⟩,0,33,1⟩, +⟨⟨1,335,31,true⟩,33,33,0⟩, +⟨⟨0,336,0,false⟩,0,34,1⟩, +⟨⟨1,336,32,true⟩,34,34,0⟩, +⟨⟨0,337,0,false⟩,0,34,1⟩, +⟨⟨1,337,32,true⟩,34,34,0⟩, +⟨⟨0,338,0,true⟩,0,35,1⟩, +⟨⟨1,338,33,true⟩,35,35,0⟩, +⟨⟨0,339,0,true⟩,0,35,1⟩, +⟨⟨1,339,33,true⟩,35,35,0⟩, +⟨⟨0,340,0,false⟩,0,36,1⟩, +⟨⟨1,340,34,true⟩,36,36,0⟩, +⟨⟨0,341,0,false⟩,0,36,1⟩, +⟨⟨1,341,34,true⟩,36,36,0⟩, +⟨⟨0,342,0,true⟩,0,37,1⟩, +⟨⟨1,342,35,true⟩,37,37,0⟩, +⟨⟨0,343,0,true⟩,0,37,1⟩, +⟨⟨1,343,35,true⟩,37,37,0⟩, +⟨⟨0,344,0,false⟩,0,38,1⟩, +⟨⟨1,344,36,true⟩,38,38,0⟩, +⟨⟨0,345,0,false⟩,0,38,1⟩, +⟨⟨1,345,36,true⟩,38,38,0⟩, +⟨⟨0,346,0,true⟩,0,39,1⟩, +⟨⟨1,346,37,true⟩,39,39,0⟩, +⟨⟨0,347,0,true⟩,0,39,1⟩, +⟨⟨1,347,37,true⟩,39,39,0⟩, +⟨⟨0,348,0,false⟩,0,40,1⟩, +⟨⟨1,348,38,true⟩,40,40,0⟩, +⟨⟨0,349,0,false⟩,0,40,1⟩, +⟨⟨1,349,38,true⟩,40,40,0⟩, +⟨⟨0,350,0,true⟩,0,41,1⟩, +⟨⟨1,350,39,true⟩,41,41,0⟩, +⟨⟨0,351,0,true⟩,0,41,1⟩, +⟨⟨1,351,39,true⟩,41,41,0⟩, +⟨⟨0,352,0,false⟩,0,42,1⟩, +⟨⟨1,352,40,true⟩,42,42,0⟩, +⟨⟨0,353,0,false⟩,0,42,1⟩, +⟨⟨1,353,40,true⟩,42,42,0⟩, +⟨⟨0,354,0,true⟩,0,43,1⟩, +⟨⟨1,354,41,true⟩,43,43,0⟩, +⟨⟨0,355,0,true⟩,0,43,1⟩, +⟨⟨1,355,41,true⟩,43,43,0⟩, +⟨⟨0,356,0,false⟩,0,44,1⟩, +⟨⟨1,356,42,true⟩,44,44,0⟩, +⟨⟨0,357,0,false⟩,0,44,1⟩, +⟨⟨1,357,42,true⟩,44,44,0⟩, +⟨⟨0,358,0,true⟩,0,45,1⟩, +⟨⟨1,358,43,true⟩,45,45,0⟩, +⟨⟨0,359,0,true⟩,0,45,1⟩, +⟨⟨1,359,43,true⟩,45,45,0⟩, +⟨⟨0,360,0,false⟩,0,46,1⟩, +⟨⟨1,360,44,true⟩,46,46,0⟩, +⟨⟨0,361,0,false⟩,0,46,1⟩, +⟨⟨1,361,44,true⟩,46,46,0⟩, +⟨⟨0,362,0,true⟩,0,47,1⟩, +⟨⟨1,362,45,true⟩,47,47,0⟩, +⟨⟨0,363,0,true⟩,0,47,1⟩, +⟨⟨1,363,45,true⟩,47,47,0⟩, +⟨⟨0,364,0,false⟩,0,48,1⟩, +⟨⟨1,364,46,true⟩,48,48,0⟩, +⟨⟨0,365,0,false⟩,0,48,1⟩, +⟨⟨1,365,46,true⟩,48,48,0⟩, +⟨⟨0,366,0,true⟩,0,49,1⟩, +⟨⟨1,366,47,true⟩,49,49,0⟩, +⟨⟨0,367,0,true⟩,0,49,1⟩, +⟨⟨1,367,47,true⟩,49,49,0⟩, +⟨⟨0,368,0,false⟩,0,50,1⟩, +⟨⟨1,368,48,true⟩,50,50,0⟩, +⟨⟨0,369,0,false⟩,0,50,1⟩, +⟨⟨1,369,48,true⟩,50,50,0⟩, +⟨⟨0,370,0,true⟩,0,51,1⟩, +⟨⟨1,370,49,true⟩,51,51,0⟩, +⟨⟨0,371,0,true⟩,0,51,1⟩, +⟨⟨1,371,49,true⟩,51,51,0⟩, +⟨⟨0,372,0,false⟩,0,52,1⟩, +⟨⟨1,372,50,true⟩,52,52,0⟩, +⟨⟨0,373,0,false⟩,0,52,1⟩, +⟨⟨1,373,50,true⟩,52,52,0⟩, +⟨⟨0,374,0,true⟩,0,53,1⟩, +⟨⟨1,374,51,true⟩,53,53,0⟩, +⟨⟨0,375,0,true⟩,0,53,1⟩, +⟨⟨1,375,51,true⟩,53,53,0⟩, +⟨⟨0,376,0,false⟩,0,54,1⟩, +⟨⟨1,376,52,true⟩,54,54,0⟩, +⟨⟨0,377,0,false⟩,0,54,1⟩, +⟨⟨1,377,52,true⟩,54,54,0⟩, +⟨⟨0,378,0,true⟩,0,55,1⟩, +⟨⟨1,378,53,true⟩,55,55,0⟩, +⟨⟨0,379,0,true⟩,0,55,1⟩, +⟨⟨1,379,53,true⟩,55,55,0⟩, +⟨⟨0,380,0,false⟩,0,56,1⟩, +⟨⟨1,380,54,true⟩,56,56,0⟩, +⟨⟨0,381,0,false⟩,0,56,1⟩, +⟨⟨1,381,54,true⟩,56,56,0⟩, +⟨⟨0,382,0,true⟩,0,57,1⟩, +⟨⟨1,382,55,true⟩,57,57,0⟩, +⟨⟨0,383,0,true⟩,0,57,1⟩, +⟨⟨1,383,55,true⟩,57,57,0⟩, +⟨⟨0,384,0,false⟩,0,58,1⟩, +⟨⟨1,384,56,true⟩,58,58,0⟩, +⟨⟨0,385,0,false⟩,0,58,1⟩, +⟨⟨1,385,56,true⟩,58,58,0⟩, +⟨⟨0,386,0,true⟩,0,59,1⟩, +⟨⟨1,386,57,true⟩,59,59,0⟩, +⟨⟨0,387,0,true⟩,0,59,1⟩, +⟨⟨1,387,57,true⟩,59,59,0⟩, +⟨⟨0,388,0,false⟩,0,60,1⟩, +⟨⟨1,388,58,true⟩,60,60,0⟩, +⟨⟨0,389,0,false⟩,0,60,1⟩, +⟨⟨1,389,58,true⟩,60,60,0⟩, +⟨⟨0,390,0,true⟩,0,61,1⟩, +⟨⟨1,390,59,true⟩,61,61,0⟩, +⟨⟨0,391,0,true⟩,0,61,1⟩, +⟨⟨1,391,59,true⟩,61,61,0⟩, +⟨⟨0,392,0,false⟩,0,62,1⟩, +⟨⟨1,392,60,true⟩,62,62,0⟩, +⟨⟨0,393,0,false⟩,0,62,1⟩, +⟨⟨1,393,60,true⟩,62,62,0⟩, +⟨⟨0,394,0,true⟩,0,63,1⟩, +⟨⟨1,394,61,true⟩,63,63,0⟩, +⟨⟨0,395,0,true⟩,0,63,1⟩, +⟨⟨1,395,61,true⟩,63,63,0⟩, +⟨⟨0,396,0,false⟩,0,64,1⟩, +⟨⟨1,396,62,true⟩,64,64,0⟩, +⟨⟨0,397,0,false⟩,0,64,1⟩, +⟨⟨1,397,62,true⟩,64,64,0⟩, +⟨⟨0,398,0,true⟩,0,65,1⟩, +⟨⟨1,398,63,true⟩,65,65,0⟩, +⟨⟨0,399,0,true⟩,0,65,1⟩, +⟨⟨1,399,63,true⟩,65,65,0⟩, +⟨⟨0,400,0,false⟩,0,66,1⟩, +⟨⟨1,400,64,true⟩,66,66,0⟩, +⟨⟨0,401,0,false⟩,0,66,1⟩, +⟨⟨1,401,64,true⟩,66,66,0⟩, +⟨⟨0,402,0,true⟩,0,67,1⟩, +⟨⟨1,402,65,true⟩,67,67,0⟩, +⟨⟨0,403,0,true⟩,0,67,1⟩, +⟨⟨1,403,65,true⟩,67,67,0⟩, +⟨⟨0,404,0,false⟩,0,68,1⟩, +⟨⟨1,404,66,true⟩,68,68,0⟩, +⟨⟨0,405,0,false⟩,0,68,1⟩, +⟨⟨1,405,66,true⟩,68,68,0⟩, +⟨⟨0,406,0,true⟩,0,69,1⟩, +⟨⟨1,406,67,true⟩,69,69,0⟩, +⟨⟨0,407,0,true⟩,0,69,1⟩, +⟨⟨1,407,67,true⟩,69,69,0⟩, +⟨⟨0,408,0,false⟩,0,70,1⟩, +⟨⟨1,408,68,true⟩,70,70,0⟩, +⟨⟨0,409,0,false⟩,0,70,1⟩, +⟨⟨1,409,68,true⟩,70,70,0⟩, +⟨⟨0,410,0,true⟩,0,71,1⟩, +⟨⟨1,410,69,true⟩,71,71,0⟩, +⟨⟨0,411,0,true⟩,0,71,1⟩, +⟨⟨1,411,69,true⟩,71,71,0⟩, +⟨⟨0,412,0,false⟩,0,72,1⟩, +⟨⟨1,412,70,true⟩,72,72,0⟩, +⟨⟨0,413,0,false⟩,0,72,1⟩, +⟨⟨1,413,70,true⟩,72,72,0⟩, +⟨⟨0,414,0,true⟩,0,73,1⟩, +⟨⟨1,414,71,true⟩,73,73,0⟩, +⟨⟨0,415,0,true⟩,0,73,1⟩, +⟨⟨1,415,71,true⟩,73,73,0⟩, +⟨⟨0,416,0,false⟩,0,74,1⟩, +⟨⟨1,416,72,true⟩,74,74,0⟩, +⟨⟨0,417,0,false⟩,0,74,1⟩, +⟨⟨1,417,72,true⟩,74,74,0⟩, +⟨⟨0,418,0,true⟩,0,75,1⟩, +⟨⟨1,418,73,true⟩,75,75,0⟩, +⟨⟨0,419,0,true⟩,0,75,1⟩, +⟨⟨1,419,73,true⟩,75,75,0⟩, +⟨⟨0,420,0,false⟩,0,76,1⟩, +⟨⟨1,420,74,true⟩,76,76,0⟩, +⟨⟨0,421,0,false⟩,0,76,1⟩, +⟨⟨1,421,74,true⟩,76,76,0⟩, +⟨⟨0,422,0,true⟩,0,77,1⟩] +def chunk43 : List Entry := [⟨⟨1,422,75,true⟩,77,77,0⟩, +⟨⟨0,423,0,true⟩,0,77,1⟩, +⟨⟨1,423,75,true⟩,77,77,0⟩, +⟨⟨0,424,0,false⟩,0,78,1⟩, +⟨⟨1,424,76,true⟩,78,78,0⟩, +⟨⟨0,425,0,false⟩,0,78,1⟩, +⟨⟨1,425,76,true⟩,78,78,0⟩, +⟨⟨0,426,0,true⟩,0,79,1⟩, +⟨⟨1,426,77,true⟩,79,79,0⟩, +⟨⟨0,427,0,true⟩,0,79,1⟩, +⟨⟨1,427,77,true⟩,79,79,0⟩, +⟨⟨0,428,0,false⟩,0,80,1⟩, +⟨⟨1,428,78,true⟩,80,80,0⟩, +⟨⟨0,429,0,false⟩,0,80,1⟩, +⟨⟨1,429,78,true⟩,80,80,0⟩, +⟨⟨0,430,0,true⟩,0,81,1⟩, +⟨⟨1,430,79,true⟩,81,81,0⟩, +⟨⟨0,431,0,true⟩,0,81,1⟩, +⟨⟨1,431,79,true⟩,81,81,0⟩, +⟨⟨0,432,0,false⟩,0,82,1⟩, +⟨⟨1,432,80,true⟩,82,82,0⟩, +⟨⟨0,433,0,false⟩,0,82,1⟩, +⟨⟨1,433,80,true⟩,82,82,0⟩, +⟨⟨0,434,0,true⟩,0,83,1⟩, +⟨⟨1,434,81,true⟩,83,83,0⟩, +⟨⟨0,435,0,true⟩,0,83,1⟩, +⟨⟨1,435,81,true⟩,83,83,0⟩, +⟨⟨0,436,0,false⟩,0,84,1⟩, +⟨⟨1,436,82,true⟩,84,84,0⟩, +⟨⟨0,437,0,false⟩,0,84,1⟩, +⟨⟨1,437,82,true⟩,84,84,0⟩, +⟨⟨0,438,0,true⟩,0,85,1⟩, +⟨⟨1,438,83,true⟩,85,85,0⟩, +⟨⟨0,439,0,true⟩,0,85,1⟩, +⟨⟨1,439,83,true⟩,85,85,0⟩, +⟨⟨0,440,0,false⟩,0,86,1⟩, +⟨⟨1,440,84,true⟩,86,86,0⟩, +⟨⟨0,441,0,false⟩,0,86,1⟩, +⟨⟨1,441,84,true⟩,86,86,0⟩, +⟨⟨0,442,0,true⟩,0,87,1⟩, +⟨⟨1,442,85,true⟩,87,87,0⟩, +⟨⟨0,443,0,true⟩,0,87,1⟩, +⟨⟨1,443,85,true⟩,87,87,0⟩, +⟨⟨0,444,0,false⟩,0,88,1⟩, +⟨⟨1,444,86,true⟩,88,88,0⟩, +⟨⟨0,445,0,false⟩,0,88,1⟩, +⟨⟨1,445,86,true⟩,88,88,0⟩, +⟨⟨0,446,0,true⟩,0,89,1⟩, +⟨⟨1,446,87,true⟩,89,89,0⟩, +⟨⟨0,447,0,true⟩,0,89,1⟩, +⟨⟨1,447,87,true⟩,89,89,0⟩, +⟨⟨0,448,0,false⟩,0,90,1⟩, +⟨⟨1,448,88,true⟩,90,90,0⟩, +⟨⟨0,449,0,false⟩,0,90,1⟩, +⟨⟨1,449,88,true⟩,90,90,0⟩, +⟨⟨0,450,0,true⟩,0,91,1⟩, +⟨⟨1,450,89,true⟩,91,91,0⟩, +⟨⟨0,451,0,true⟩,0,91,1⟩, +⟨⟨1,451,89,true⟩,91,91,0⟩, +⟨⟨0,452,0,false⟩,0,92,1⟩, +⟨⟨1,452,90,true⟩,92,92,0⟩, +⟨⟨0,453,0,false⟩,0,92,1⟩, +⟨⟨1,453,90,true⟩,92,92,0⟩, +⟨⟨0,454,0,true⟩,0,93,1⟩, +⟨⟨1,454,91,true⟩,93,93,0⟩, +⟨⟨0,455,0,true⟩,0,93,1⟩, +⟨⟨1,455,91,true⟩,93,93,0⟩, +⟨⟨0,456,0,false⟩,0,94,1⟩, +⟨⟨1,456,92,true⟩,94,94,0⟩, +⟨⟨0,457,0,false⟩,0,94,1⟩, +⟨⟨1,457,92,true⟩,94,94,0⟩, +⟨⟨0,458,0,true⟩,0,95,1⟩, +⟨⟨1,458,93,true⟩,95,95,0⟩, +⟨⟨0,459,0,true⟩,0,95,1⟩, +⟨⟨1,459,93,true⟩,95,95,0⟩, +⟨⟨0,460,0,false⟩,0,96,1⟩, +⟨⟨1,460,94,true⟩,96,96,0⟩, +⟨⟨0,461,0,false⟩,0,96,1⟩, +⟨⟨1,461,94,true⟩,96,96,0⟩, +⟨⟨0,462,0,true⟩,0,97,1⟩, +⟨⟨1,462,95,true⟩,97,97,0⟩, +⟨⟨0,463,0,true⟩,0,97,1⟩, +⟨⟨1,463,95,true⟩,97,97,0⟩, +⟨⟨0,464,0,false⟩,0,98,1⟩, +⟨⟨1,464,96,true⟩,98,98,0⟩, +⟨⟨0,465,0,false⟩,0,98,1⟩, +⟨⟨1,465,96,true⟩,98,98,0⟩, +⟨⟨0,466,0,true⟩,0,99,1⟩, +⟨⟨1,466,97,true⟩,99,99,0⟩, +⟨⟨0,467,0,true⟩,0,99,1⟩, +⟨⟨1,467,97,true⟩,99,99,0⟩, +⟨⟨0,468,0,false⟩,0,100,1⟩, +⟨⟨1,468,98,true⟩,100,100,0⟩, +⟨⟨0,469,0,false⟩,0,100,1⟩, +⟨⟨1,469,98,true⟩,100,100,0⟩, +⟨⟨0,470,0,true⟩,0,101,1⟩, +⟨⟨1,470,99,true⟩,101,101,0⟩, +⟨⟨0,471,0,true⟩,0,101,1⟩, +⟨⟨1,471,99,true⟩,101,101,0⟩, +⟨⟨0,472,0,false⟩,0,102,1⟩, +⟨⟨1,472,100,true⟩,102,102,0⟩, +⟨⟨0,473,0,false⟩,0,102,1⟩, +⟨⟨1,473,100,true⟩,102,102,0⟩, +⟨⟨0,474,0,true⟩,0,103,1⟩, +⟨⟨1,474,101,true⟩,103,103,0⟩, +⟨⟨0,475,0,true⟩,0,103,1⟩, +⟨⟨1,475,101,true⟩,103,103,0⟩, +⟨⟨0,476,0,false⟩,0,104,1⟩, +⟨⟨1,476,102,true⟩,104,104,0⟩, +⟨⟨0,477,0,false⟩,0,104,1⟩, +⟨⟨1,477,102,true⟩,104,104,0⟩, +⟨⟨0,478,0,true⟩,0,105,1⟩, +⟨⟨1,478,103,true⟩,105,105,0⟩, +⟨⟨0,479,0,true⟩,0,105,1⟩, +⟨⟨1,479,103,true⟩,105,105,0⟩, +⟨⟨0,480,0,false⟩,0,106,1⟩, +⟨⟨1,480,104,true⟩,106,106,0⟩, +⟨⟨0,481,0,false⟩,0,106,1⟩, +⟨⟨1,481,104,true⟩,106,106,0⟩, +⟨⟨0,482,0,true⟩,0,107,1⟩, +⟨⟨1,482,105,true⟩,107,107,0⟩, +⟨⟨0,483,0,true⟩,0,107,1⟩, +⟨⟨1,483,105,true⟩,107,107,0⟩, +⟨⟨0,484,0,false⟩,0,108,1⟩, +⟨⟨1,484,106,true⟩,108,108,0⟩, +⟨⟨0,485,0,false⟩,0,108,1⟩, +⟨⟨1,485,106,true⟩,108,108,0⟩, +⟨⟨0,486,0,true⟩,0,109,1⟩, +⟨⟨1,486,107,true⟩,109,109,0⟩, +⟨⟨0,487,0,true⟩,0,109,1⟩, +⟨⟨1,487,107,true⟩,109,109,0⟩, +⟨⟨0,488,0,false⟩,0,110,1⟩, +⟨⟨1,488,108,true⟩,110,110,0⟩, +⟨⟨0,489,0,false⟩,0,110,1⟩, +⟨⟨1,489,108,true⟩,110,110,0⟩, +⟨⟨0,490,0,true⟩,0,111,1⟩, +⟨⟨1,490,109,true⟩,111,111,0⟩, +⟨⟨0,491,0,true⟩,0,111,1⟩, +⟨⟨1,491,109,true⟩,111,111,0⟩, +⟨⟨0,492,0,false⟩,0,112,1⟩, +⟨⟨1,492,110,true⟩,112,112,0⟩, +⟨⟨0,493,0,false⟩,0,112,1⟩, +⟨⟨1,493,110,true⟩,112,112,0⟩, +⟨⟨0,494,0,true⟩,0,113,1⟩, +⟨⟨1,494,111,true⟩,113,113,0⟩, +⟨⟨0,495,0,true⟩,0,113,1⟩, +⟨⟨1,495,111,true⟩,113,113,0⟩, +⟨⟨0,496,0,false⟩,0,114,1⟩, +⟨⟨1,496,112,true⟩,114,114,0⟩, +⟨⟨0,497,0,false⟩,0,114,1⟩, +⟨⟨1,497,112,true⟩,114,114,0⟩, +⟨⟨0,498,0,true⟩,0,115,1⟩, +⟨⟨1,498,113,true⟩,115,115,0⟩, +⟨⟨0,499,0,true⟩,0,115,1⟩, +⟨⟨1,499,113,true⟩,115,115,0⟩, +⟨⟨0,500,0,false⟩,0,116,1⟩, +⟨⟨1,500,114,true⟩,116,116,0⟩, +⟨⟨0,501,0,false⟩,0,116,1⟩, +⟨⟨1,501,114,true⟩,116,116,0⟩, +⟨⟨0,502,0,true⟩,0,117,1⟩, +⟨⟨1,502,115,true⟩,117,117,0⟩, +⟨⟨0,503,0,true⟩,0,117,1⟩, +⟨⟨1,503,115,true⟩,117,117,0⟩, +⟨⟨0,504,0,false⟩,0,118,1⟩, +⟨⟨1,504,116,true⟩,118,118,0⟩, +⟨⟨0,505,0,false⟩,0,118,1⟩, +⟨⟨1,505,116,true⟩,118,118,0⟩, +⟨⟨0,506,0,true⟩,0,119,1⟩, +⟨⟨1,506,117,true⟩,119,119,0⟩, +⟨⟨0,507,0,true⟩,0,119,1⟩, +⟨⟨1,507,117,true⟩,119,119,0⟩, +⟨⟨0,508,0,false⟩,0,120,1⟩, +⟨⟨1,508,118,true⟩,120,120,0⟩, +⟨⟨0,509,0,false⟩,0,120,1⟩, +⟨⟨1,509,118,true⟩,120,120,0⟩, +⟨⟨0,510,0,true⟩,0,121,1⟩, +⟨⟨1,510,119,true⟩,121,121,0⟩, +⟨⟨0,511,0,true⟩,0,121,1⟩, +⟨⟨1,511,119,true⟩,121,121,0⟩, +⟨⟨0,512,0,false⟩,0,66,1⟩, +⟨⟨1,512,64,true⟩,66,66,0⟩, +⟨⟨0,512,66,false⟩,66,122,1⟩, +⟨⟨0,67,69,false⟩,69,122,1⟩, +⟨⟨1,512,67,true⟩,122,122,0⟩, +⟨⟨0,513,0,false⟩,0,122,2⟩, +⟨⟨1,513,512,true⟩,122,122,0⟩, +⟨⟨0,514,0,true⟩,0,67,1⟩, +⟨⟨1,514,65,true⟩,67,67,0⟩, +⟨⟨0,514,67,true⟩,67,123,1⟩, +⟨⟨0,66,68,true⟩,68,123,1⟩, +⟨⟨1,514,66,true⟩,123,123,0⟩, +⟨⟨0,515,0,true⟩,0,123,2⟩, +⟨⟨1,515,514,true⟩,123,123,0⟩, +⟨⟨0,516,0,false⟩,0,70,1⟩, +⟨⟨1,516,68,true⟩,70,70,0⟩, +⟨⟨0,516,70,false⟩,70,124,1⟩, +⟨⟨0,71,73,false⟩,73,124,1⟩, +⟨⟨1,516,71,true⟩,124,124,0⟩, +⟨⟨0,517,0,false⟩,0,124,2⟩, +⟨⟨1,517,516,true⟩,124,124,0⟩] +def chunk44 : List Entry := [⟨⟨0,518,0,true⟩,0,71,1⟩, +⟨⟨1,518,69,true⟩,71,71,0⟩, +⟨⟨0,518,71,true⟩,71,125,1⟩, +⟨⟨0,70,72,true⟩,72,125,1⟩, +⟨⟨1,518,70,true⟩,125,125,0⟩, +⟨⟨0,519,0,true⟩,0,125,2⟩, +⟨⟨1,519,518,true⟩,125,125,0⟩, +⟨⟨0,400,66,false⟩,66,126,1⟩, +⟨⟨0,410,71,false⟩,71,126,1⟩, +⟨⟨1,400,410,true⟩,126,126,0⟩, +⟨⟨0,520,0,false⟩,0,126,2⟩, +⟨⟨1,520,400,true⟩,126,126,0⟩, +⟨⟨0,402,67,true⟩,67,127,1⟩, +⟨⟨0,408,70,true⟩,70,127,1⟩, +⟨⟨1,402,408,true⟩,127,127,0⟩, +⟨⟨0,521,0,true⟩,0,127,2⟩, +⟨⟨1,521,402,true⟩,127,127,0⟩, +⟨⟨0,404,68,false⟩,68,128,1⟩, +⟨⟨0,414,73,false⟩,73,128,1⟩, +⟨⟨1,404,414,true⟩,128,128,0⟩, +⟨⟨0,522,0,false⟩,0,128,2⟩, +⟨⟨1,522,404,true⟩,128,128,0⟩, +⟨⟨0,406,69,true⟩,69,129,1⟩, +⟨⟨0,412,72,true⟩,72,129,1⟩, +⟨⟨1,406,412,true⟩,129,129,0⟩, +⟨⟨0,523,0,true⟩,0,129,2⟩, +⟨⟨1,523,406,true⟩,129,129,0⟩, +⟨⟨0,413,72,false⟩,72,130,1⟩, +⟨⟨0,401,66,false⟩,66,130,1⟩, +⟨⟨1,413,401,true⟩,130,130,0⟩, +⟨⟨0,524,0,false⟩,0,130,2⟩, +⟨⟨1,524,413,true⟩,130,130,0⟩, +⟨⟨0,409,70,true⟩,70,131,1⟩, +⟨⟨0,405,68,true⟩,68,131,1⟩, +⟨⟨1,409,405,true⟩,131,131,0⟩, +⟨⟨0,525,0,true⟩,0,131,2⟩, +⟨⟨1,525,409,true⟩,131,131,0⟩, +⟨⟨0,415,73,false⟩,73,132,1⟩, +⟨⟨0,403,67,false⟩,67,132,1⟩, +⟨⟨1,415,403,true⟩,132,132,0⟩, +⟨⟨0,526,0,false⟩,0,132,2⟩, +⟨⟨1,526,415,true⟩,132,132,0⟩, +⟨⟨0,411,71,true⟩,71,133,1⟩, +⟨⟨0,407,69,true⟩,69,133,1⟩, +⟨⟨1,411,407,true⟩,133,133,0⟩, +⟨⟨0,527,0,true⟩,0,133,2⟩, +⟨⟨1,527,411,true⟩,133,133,0⟩, +⟨⟨0,528,0,false⟩,0,34,1⟩, +⟨⟨1,528,32,true⟩,34,34,0⟩, +⟨⟨0,528,34,false⟩,34,134,1⟩, +⟨⟨0,35,37,false⟩,37,134,1⟩, +⟨⟨1,528,35,true⟩,134,134,0⟩, +⟨⟨0,529,0,false⟩,0,134,2⟩, +⟨⟨1,529,528,true⟩,134,134,0⟩, +⟨⟨0,530,0,true⟩,0,35,1⟩, +⟨⟨1,530,33,true⟩,35,35,0⟩, +⟨⟨0,530,35,true⟩,35,135,1⟩, +⟨⟨0,34,36,true⟩,36,135,1⟩, +⟨⟨1,530,34,true⟩,135,135,0⟩, +⟨⟨0,531,0,true⟩,0,135,2⟩, +⟨⟨1,531,530,true⟩,135,135,0⟩, +⟨⟨0,532,0,false⟩,0,38,1⟩, +⟨⟨1,532,36,true⟩,38,38,0⟩, +⟨⟨0,532,38,false⟩,38,136,1⟩, +⟨⟨0,39,41,false⟩,41,136,1⟩, +⟨⟨1,532,39,true⟩,136,136,0⟩, +⟨⟨0,533,0,false⟩,0,136,2⟩, +⟨⟨1,533,532,true⟩,136,136,0⟩, +⟨⟨0,534,0,true⟩,0,39,1⟩, +⟨⟨1,534,37,true⟩,39,39,0⟩, +⟨⟨0,534,39,true⟩,39,137,1⟩, +⟨⟨0,38,40,true⟩,40,137,1⟩, +⟨⟨1,534,38,true⟩,137,137,0⟩, +⟨⟨0,535,0,true⟩,0,137,2⟩, +⟨⟨1,535,534,true⟩,137,137,0⟩, +⟨⟨0,346,39,false⟩,39,138,1⟩, +⟨⟨0,336,34,false⟩,34,138,1⟩, +⟨⟨1,346,336,true⟩,138,138,0⟩, +⟨⟨0,536,0,false⟩,0,138,2⟩, +⟨⟨1,536,346,true⟩,138,138,0⟩, +⟨⟨0,344,38,true⟩,38,139,1⟩, +⟨⟨0,338,35,true⟩,35,139,1⟩, +⟨⟨1,344,338,true⟩,139,139,0⟩, +⟨⟨0,537,0,true⟩,0,139,2⟩, +⟨⟨1,537,344,true⟩,139,139,0⟩, +⟨⟨0,350,41,false⟩,41,140,1⟩, +⟨⟨0,340,36,false⟩,36,140,1⟩, +⟨⟨1,350,340,true⟩,140,140,0⟩, +⟨⟨0,538,0,false⟩,0,140,2⟩, +⟨⟨1,538,350,true⟩,140,140,0⟩, +⟨⟨0,348,40,true⟩,40,141,1⟩, +⟨⟨0,342,37,true⟩,37,141,1⟩, +⟨⟨1,348,342,true⟩,141,141,0⟩, +⟨⟨0,539,0,true⟩,0,141,2⟩, +⟨⟨1,539,348,true⟩,141,141,0⟩, +⟨⟨0,337,34,false⟩,34,142,1⟩, +⟨⟨0,349,40,false⟩,40,142,1⟩, +⟨⟨1,337,349,true⟩,142,142,0⟩, +⟨⟨0,540,0,false⟩,0,142,2⟩, +⟨⟨1,540,337,true⟩,142,142,0⟩, +⟨⟨0,341,36,true⟩,36,143,1⟩, +⟨⟨0,345,38,true⟩,38,143,1⟩, +⟨⟨1,341,345,true⟩,143,143,0⟩, +⟨⟨0,541,0,true⟩,0,143,2⟩, +⟨⟨1,541,341,true⟩,143,143,0⟩, +⟨⟨0,339,35,false⟩,35,144,1⟩, +⟨⟨0,351,41,false⟩,41,144,1⟩, +⟨⟨1,339,351,true⟩,144,144,0⟩, +⟨⟨0,542,0,false⟩,0,144,2⟩, +⟨⟨1,542,339,true⟩,144,144,0⟩, +⟨⟨0,343,37,true⟩,37,145,1⟩, +⟨⟨0,347,39,true⟩,39,145,1⟩, +⟨⟨1,343,347,true⟩,145,145,0⟩, +⟨⟨0,543,0,true⟩,0,145,2⟩, +⟨⟨1,543,343,true⟩,145,145,0⟩, +⟨⟨0,544,0,false⟩,0,26,1⟩, +⟨⟨1,544,24,true⟩,26,26,0⟩, +⟨⟨0,544,26,false⟩,26,146,1⟩, +⟨⟨0,27,29,false⟩,29,146,1⟩, +⟨⟨1,544,27,true⟩,146,146,0⟩, +⟨⟨0,545,0,false⟩,0,146,2⟩, +⟨⟨1,545,544,true⟩,146,146,0⟩, +⟨⟨0,546,0,true⟩,0,27,1⟩, +⟨⟨1,546,25,true⟩,27,27,0⟩, +⟨⟨0,546,27,true⟩,27,147,1⟩, +⟨⟨0,26,28,true⟩,28,147,1⟩, +⟨⟨1,546,26,true⟩,147,147,0⟩, +⟨⟨0,547,0,true⟩,0,147,2⟩, +⟨⟨1,547,546,true⟩,147,147,0⟩, +⟨⟨0,548,0,false⟩,0,30,1⟩, +⟨⟨1,548,28,true⟩,30,30,0⟩, +⟨⟨0,548,30,false⟩,30,148,1⟩, +⟨⟨0,31,33,false⟩,33,148,1⟩, +⟨⟨1,548,31,true⟩,148,148,0⟩, +⟨⟨0,549,0,false⟩,0,148,2⟩, +⟨⟨1,549,548,true⟩,148,148,0⟩, +⟨⟨0,550,0,true⟩,0,31,1⟩, +⟨⟨1,550,29,true⟩,31,31,0⟩, +⟨⟨0,550,31,true⟩,31,149,1⟩, +⟨⟨0,30,32,true⟩,32,149,1⟩, +⟨⟨1,550,30,true⟩,149,149,0⟩, +⟨⟨0,551,0,true⟩,0,149,2⟩, +⟨⟨1,551,550,true⟩,149,149,0⟩, +⟨⟨0,320,26,false⟩,26,150,1⟩, +⟨⟨0,330,31,false⟩,31,150,1⟩, +⟨⟨1,320,330,true⟩,150,150,0⟩, +⟨⟨0,552,0,false⟩,0,150,2⟩, +⟨⟨1,552,320,true⟩,150,150,0⟩, +⟨⟨0,328,30,true⟩,30,151,1⟩, +⟨⟨0,322,27,true⟩,27,151,1⟩, +⟨⟨1,328,322,true⟩,151,151,0⟩, +⟨⟨0,553,0,true⟩,0,151,2⟩, +⟨⟨1,553,328,true⟩,151,151,0⟩, +⟨⟨0,334,33,false⟩,33,152,1⟩, +⟨⟨0,324,28,false⟩,28,152,1⟩, +⟨⟨1,334,324,true⟩,152,152,0⟩, +⟨⟨0,554,0,false⟩,0,152,2⟩, +⟨⟨1,554,334,true⟩,152,152,0⟩, +⟨⟨0,326,29,true⟩,29,153,1⟩, +⟨⟨0,332,32,true⟩,32,153,1⟩, +⟨⟨1,326,332,true⟩,153,153,0⟩, +⟨⟨0,555,0,true⟩,0,153,2⟩, +⟨⟨1,555,326,true⟩,153,153,0⟩, +⟨⟨0,333,32,false⟩,32,154,1⟩, +⟨⟨0,321,26,false⟩,26,154,1⟩, +⟨⟨1,333,321,true⟩,154,154,0⟩, +⟨⟨0,556,0,false⟩,0,154,2⟩, +⟨⟨1,556,333,true⟩,154,154,0⟩, +⟨⟨0,325,28,true⟩,28,155,1⟩, +⟨⟨0,329,30,true⟩,30,155,1⟩, +⟨⟨1,325,329,true⟩,155,155,0⟩, +⟨⟨0,557,0,true⟩,0,155,2⟩, +⟨⟨1,557,325,true⟩,155,155,0⟩, +⟨⟨0,323,27,false⟩,27,156,1⟩, +⟨⟨0,335,33,false⟩,33,156,1⟩, +⟨⟨1,323,335,true⟩,156,156,0⟩, +⟨⟨0,558,0,false⟩,0,156,2⟩, +⟨⟨1,558,323,true⟩,156,156,0⟩, +⟨⟨0,331,31,true⟩,31,157,1⟩, +⟨⟨0,327,29,true⟩,29,157,1⟩, +⟨⟨1,331,327,true⟩,157,157,0⟩, +⟨⟨0,559,0,true⟩,0,157,2⟩, +⟨⟨1,559,331,true⟩,157,157,0⟩, +⟨⟨0,560,0,false⟩,0,18,1⟩, +⟨⟨1,560,16,true⟩,18,18,0⟩, +⟨⟨0,560,18,false⟩,18,158,1⟩, +⟨⟨0,19,21,false⟩,21,158,1⟩, +⟨⟨1,560,19,true⟩,158,158,0⟩, +⟨⟨0,561,0,false⟩,0,158,2⟩, +⟨⟨1,561,560,true⟩,158,158,0⟩, +⟨⟨0,562,0,true⟩,0,19,1⟩, +⟨⟨1,562,17,true⟩,19,19,0⟩, +⟨⟨0,562,19,true⟩,19,159,1⟩, +⟨⟨0,18,20,true⟩,20,159,1⟩, +⟨⟨1,562,18,true⟩,159,159,0⟩, +⟨⟨0,563,0,true⟩,0,159,2⟩, +⟨⟨1,563,562,true⟩,159,159,0⟩, +⟨⟨0,564,0,false⟩,0,22,1⟩, +⟨⟨1,564,20,true⟩,22,22,0⟩, +⟨⟨0,564,22,false⟩,22,160,1⟩] +def chunk45 : List Entry := [⟨⟨0,23,25,false⟩,25,160,1⟩, +⟨⟨1,564,23,true⟩,160,160,0⟩, +⟨⟨0,565,0,false⟩,0,160,2⟩, +⟨⟨1,565,564,true⟩,160,160,0⟩, +⟨⟨0,566,0,true⟩,0,23,1⟩, +⟨⟨1,566,21,true⟩,23,23,0⟩, +⟨⟨0,566,23,true⟩,23,161,1⟩, +⟨⟨0,22,24,true⟩,24,161,1⟩, +⟨⟨1,566,22,true⟩,161,161,0⟩, +⟨⟨0,567,0,true⟩,0,161,2⟩, +⟨⟨1,567,566,true⟩,161,161,0⟩, +⟨⟨0,304,18,false⟩,18,162,1⟩, +⟨⟨0,314,23,false⟩,23,162,1⟩, +⟨⟨1,304,314,true⟩,162,162,0⟩, +⟨⟨0,568,0,false⟩,0,162,2⟩, +⟨⟨1,568,304,true⟩,162,162,0⟩, +⟨⟨0,312,22,true⟩,22,163,1⟩, +⟨⟨0,306,19,true⟩,19,163,1⟩, +⟨⟨1,312,306,true⟩,163,163,0⟩, +⟨⟨0,569,0,true⟩,0,163,2⟩, +⟨⟨1,569,312,true⟩,163,163,0⟩, +⟨⟨0,318,25,false⟩,25,164,1⟩, +⟨⟨0,308,20,false⟩,20,164,1⟩, +⟨⟨1,318,308,true⟩,164,164,0⟩, +⟨⟨0,570,0,false⟩,0,164,2⟩, +⟨⟨1,570,318,true⟩,164,164,0⟩, +⟨⟨0,310,21,true⟩,21,165,1⟩, +⟨⟨0,316,24,true⟩,24,165,1⟩, +⟨⟨1,310,316,true⟩,165,165,0⟩, +⟨⟨0,571,0,true⟩,0,165,2⟩, +⟨⟨1,571,310,true⟩,165,165,0⟩, +⟨⟨0,317,24,false⟩,24,166,1⟩, +⟨⟨0,305,18,false⟩,18,166,1⟩, +⟨⟨1,317,305,true⟩,166,166,0⟩, +⟨⟨0,572,0,false⟩,0,166,2⟩, +⟨⟨1,572,317,true⟩,166,166,0⟩, +⟨⟨0,309,20,true⟩,20,167,1⟩, +⟨⟨0,313,22,true⟩,22,167,1⟩, +⟨⟨1,309,313,true⟩,167,167,0⟩, +⟨⟨0,573,0,true⟩,0,167,2⟩, +⟨⟨1,573,309,true⟩,167,167,0⟩, +⟨⟨0,307,19,false⟩,19,168,1⟩, +⟨⟨0,319,25,false⟩,25,168,1⟩, +⟨⟨1,307,319,true⟩,168,168,0⟩, +⟨⟨0,574,0,false⟩,0,168,2⟩, +⟨⟨1,574,307,true⟩,168,168,0⟩, +⟨⟨0,315,23,true⟩,23,169,1⟩, +⟨⟨0,311,21,true⟩,21,169,1⟩, +⟨⟨1,315,311,true⟩,169,169,0⟩, +⟨⟨0,575,0,true⟩,0,169,2⟩, +⟨⟨1,575,315,true⟩,169,169,0⟩, +⟨⟨0,576,0,false⟩,0,42,1⟩, +⟨⟨1,576,40,true⟩,42,42,0⟩, +⟨⟨0,576,42,false⟩,42,170,1⟩, +⟨⟨0,43,45,false⟩,45,170,1⟩, +⟨⟨1,576,43,true⟩,170,170,0⟩, +⟨⟨0,577,0,false⟩,0,170,2⟩, +⟨⟨1,577,576,true⟩,170,170,0⟩, +⟨⟨0,578,0,true⟩,0,43,1⟩, +⟨⟨1,578,41,true⟩,43,43,0⟩, +⟨⟨0,578,43,true⟩,43,171,1⟩, +⟨⟨0,42,44,true⟩,44,171,1⟩, +⟨⟨1,578,42,true⟩,171,171,0⟩, +⟨⟨0,579,0,true⟩,0,171,2⟩, +⟨⟨1,579,578,true⟩,171,171,0⟩, +⟨⟨0,580,0,false⟩,0,46,1⟩, +⟨⟨1,580,44,true⟩,46,46,0⟩, +⟨⟨0,580,46,false⟩,46,172,1⟩, +⟨⟨0,47,49,false⟩,49,172,1⟩, +⟨⟨1,580,47,true⟩,172,172,0⟩, +⟨⟨0,581,0,false⟩,0,172,2⟩, +⟨⟨1,581,580,true⟩,172,172,0⟩, +⟨⟨0,582,0,true⟩,0,47,1⟩, +⟨⟨1,582,45,true⟩,47,47,0⟩, +⟨⟨0,582,47,true⟩,47,173,1⟩, +⟨⟨0,46,48,true⟩,48,173,1⟩, +⟨⟨1,582,46,true⟩,173,173,0⟩, +⟨⟨0,583,0,true⟩,0,173,2⟩, +⟨⟨1,583,582,true⟩,173,173,0⟩, +⟨⟨0,352,42,false⟩,42,174,1⟩, +⟨⟨0,362,47,false⟩,47,174,1⟩, +⟨⟨1,352,362,true⟩,174,174,0⟩, +⟨⟨0,584,0,false⟩,0,174,2⟩, +⟨⟨1,584,352,true⟩,174,174,0⟩, +⟨⟨0,354,43,true⟩,43,175,1⟩, +⟨⟨0,360,46,true⟩,46,175,1⟩, +⟨⟨1,354,360,true⟩,175,175,0⟩, +⟨⟨0,585,0,true⟩,0,175,2⟩, +⟨⟨1,585,354,true⟩,175,175,0⟩, +⟨⟨0,356,44,false⟩,44,176,1⟩, +⟨⟨0,366,49,false⟩,49,176,1⟩, +⟨⟨1,356,366,true⟩,176,176,0⟩, +⟨⟨0,586,0,false⟩,0,176,2⟩, +⟨⟨1,586,356,true⟩,176,176,0⟩, +⟨⟨0,358,45,true⟩,45,177,1⟩, +⟨⟨0,364,48,true⟩,48,177,1⟩, +⟨⟨1,358,364,true⟩,177,177,0⟩, +⟨⟨0,587,0,true⟩,0,177,2⟩, +⟨⟨1,587,358,true⟩,177,177,0⟩, +⟨⟨0,365,48,false⟩,48,178,1⟩, +⟨⟨0,353,42,false⟩,42,178,1⟩, +⟨⟨1,365,353,true⟩,178,178,0⟩, +⟨⟨0,588,0,false⟩,0,178,2⟩, +⟨⟨1,588,365,true⟩,178,178,0⟩, +⟨⟨0,361,46,true⟩,46,179,1⟩, +⟨⟨0,357,44,true⟩,44,179,1⟩, +⟨⟨1,361,357,true⟩,179,179,0⟩, +⟨⟨0,589,0,true⟩,0,179,2⟩, +⟨⟨1,589,361,true⟩,179,179,0⟩, +⟨⟨0,367,49,false⟩,49,180,1⟩, +⟨⟨0,355,43,false⟩,43,180,1⟩, +⟨⟨1,367,355,true⟩,180,180,0⟩, +⟨⟨0,590,0,false⟩,0,180,2⟩, +⟨⟨1,590,367,true⟩,180,180,0⟩, +⟨⟨0,363,47,true⟩,47,181,1⟩, +⟨⟨0,359,45,true⟩,45,181,1⟩, +⟨⟨1,363,359,true⟩,181,181,0⟩, +⟨⟨0,591,0,true⟩,0,181,2⟩, +⟨⟨1,591,363,true⟩,181,181,0⟩, +⟨⟨0,592,0,false⟩,0,74,1⟩, +⟨⟨1,592,72,true⟩,74,74,0⟩, +⟨⟨0,592,74,false⟩,74,182,1⟩, +⟨⟨0,75,77,false⟩,77,182,1⟩, +⟨⟨1,592,75,true⟩,182,182,0⟩, +⟨⟨0,593,0,false⟩,0,182,2⟩, +⟨⟨1,593,592,true⟩,182,182,0⟩, +⟨⟨0,594,0,true⟩,0,75,1⟩, +⟨⟨1,594,73,true⟩,75,75,0⟩, +⟨⟨0,594,75,true⟩,75,183,1⟩, +⟨⟨0,74,76,true⟩,76,183,1⟩, +⟨⟨1,594,74,true⟩,183,183,0⟩, +⟨⟨0,595,0,true⟩,0,183,2⟩, +⟨⟨1,595,594,true⟩,183,183,0⟩, +⟨⟨0,596,0,false⟩,0,78,1⟩, +⟨⟨1,596,76,true⟩,78,78,0⟩, +⟨⟨0,596,78,false⟩,78,184,1⟩, +⟨⟨0,79,81,false⟩,81,184,1⟩, +⟨⟨1,596,79,true⟩,184,184,0⟩, +⟨⟨0,597,0,false⟩,0,184,2⟩, +⟨⟨1,597,596,true⟩,184,184,0⟩, +⟨⟨0,598,0,true⟩,0,79,1⟩, +⟨⟨1,598,77,true⟩,79,79,0⟩, +⟨⟨0,598,79,true⟩,79,185,1⟩, +⟨⟨0,78,80,true⟩,80,185,1⟩, +⟨⟨1,598,78,true⟩,185,185,0⟩, +⟨⟨0,599,0,true⟩,0,185,2⟩, +⟨⟨1,599,598,true⟩,185,185,0⟩, +⟨⟨0,416,74,false⟩,74,186,1⟩, +⟨⟨0,426,79,false⟩,79,186,1⟩, +⟨⟨1,416,426,true⟩,186,186,0⟩, +⟨⟨0,600,0,false⟩,0,186,2⟩, +⟨⟨1,600,416,true⟩,186,186,0⟩, +⟨⟨0,424,78,true⟩,78,187,1⟩, +⟨⟨0,418,75,true⟩,75,187,1⟩, +⟨⟨1,424,418,true⟩,187,187,0⟩, +⟨⟨0,601,0,true⟩,0,187,2⟩, +⟨⟨1,601,424,true⟩,187,187,0⟩, +⟨⟨0,430,81,false⟩,81,188,1⟩, +⟨⟨0,420,76,false⟩,76,188,1⟩, +⟨⟨1,430,420,true⟩,188,188,0⟩, +⟨⟨0,602,0,false⟩,0,188,2⟩, +⟨⟨1,602,430,true⟩,188,188,0⟩, +⟨⟨0,422,77,true⟩,77,189,1⟩, +⟨⟨0,428,80,true⟩,80,189,1⟩, +⟨⟨1,422,428,true⟩,189,189,0⟩, +⟨⟨0,603,0,true⟩,0,189,2⟩, +⟨⟨1,603,422,true⟩,189,189,0⟩, +⟨⟨0,429,80,false⟩,80,190,1⟩, +⟨⟨0,417,74,false⟩,74,190,1⟩, +⟨⟨1,429,417,true⟩,190,190,0⟩, +⟨⟨0,604,0,false⟩,0,190,2⟩, +⟨⟨1,604,429,true⟩,190,190,0⟩, +⟨⟨0,421,76,true⟩,76,191,1⟩, +⟨⟨0,425,78,true⟩,78,191,1⟩, +⟨⟨1,421,425,true⟩,191,191,0⟩, +⟨⟨0,605,0,true⟩,0,191,2⟩, +⟨⟨1,605,421,true⟩,191,191,0⟩, +⟨⟨0,419,75,false⟩,75,192,1⟩, +⟨⟨0,431,81,false⟩,81,192,1⟩, +⟨⟨1,419,431,true⟩,192,192,0⟩, +⟨⟨0,606,0,false⟩,0,192,2⟩, +⟨⟨1,606,419,true⟩,192,192,0⟩, +⟨⟨0,427,79,true⟩,79,193,1⟩, +⟨⟨0,423,77,true⟩,77,193,1⟩, +⟨⟨1,427,423,true⟩,193,193,0⟩, +⟨⟨0,607,0,true⟩,0,193,2⟩, +⟨⟨1,607,427,true⟩,193,193,0⟩, +⟨⟨0,608,0,false⟩,0,114,1⟩, +⟨⟨1,608,112,true⟩,114,114,0⟩, +⟨⟨0,608,114,false⟩,114,194,1⟩, +⟨⟨0,115,117,false⟩,117,194,1⟩, +⟨⟨1,608,115,true⟩,194,194,0⟩, +⟨⟨0,609,0,false⟩,0,194,2⟩, +⟨⟨1,609,608,true⟩,194,194,0⟩, +⟨⟨0,610,0,true⟩,0,115,1⟩, +⟨⟨1,610,113,true⟩,115,115,0⟩, +⟨⟨0,610,115,true⟩,115,195,1⟩, +⟨⟨0,114,116,true⟩,116,195,1⟩, +⟨⟨1,610,114,true⟩,195,195,0⟩, +⟨⟨0,611,0,true⟩,0,195,2⟩] +def chunk46 : List Entry := [⟨⟨1,611,610,true⟩,195,195,0⟩, +⟨⟨0,612,0,false⟩,0,118,1⟩, +⟨⟨1,612,116,true⟩,118,118,0⟩, +⟨⟨0,612,118,false⟩,118,196,1⟩, +⟨⟨0,119,121,false⟩,121,196,1⟩, +⟨⟨1,612,119,true⟩,196,196,0⟩, +⟨⟨0,613,0,false⟩,0,196,2⟩, +⟨⟨1,613,612,true⟩,196,196,0⟩, +⟨⟨0,614,0,true⟩,0,119,1⟩, +⟨⟨1,614,117,true⟩,119,119,0⟩, +⟨⟨0,614,119,true⟩,119,197,1⟩, +⟨⟨0,118,120,true⟩,120,197,1⟩, +⟨⟨1,614,118,true⟩,197,197,0⟩, +⟨⟨0,615,0,true⟩,0,197,2⟩, +⟨⟨1,615,614,true⟩,197,197,0⟩, +⟨⟨0,506,119,false⟩,119,198,1⟩, +⟨⟨0,496,114,false⟩,114,198,1⟩, +⟨⟨1,506,496,true⟩,198,198,0⟩, +⟨⟨0,616,0,false⟩,0,198,2⟩, +⟨⟨1,616,506,true⟩,198,198,0⟩, +⟨⟨0,504,118,true⟩,118,199,1⟩, +⟨⟨0,498,115,true⟩,115,199,1⟩, +⟨⟨1,504,498,true⟩,199,199,0⟩, +⟨⟨0,617,0,true⟩,0,199,2⟩, +⟨⟨1,617,504,true⟩,199,199,0⟩, +⟨⟨0,510,121,false⟩,121,200,1⟩, +⟨⟨0,500,116,false⟩,116,200,1⟩, +⟨⟨1,510,500,true⟩,200,200,0⟩, +⟨⟨0,618,0,false⟩,0,200,2⟩, +⟨⟨1,618,510,true⟩,200,200,0⟩, +⟨⟨0,508,120,true⟩,120,201,1⟩, +⟨⟨0,502,117,true⟩,117,201,1⟩, +⟨⟨1,508,502,true⟩,201,201,0⟩, +⟨⟨0,619,0,true⟩,0,201,2⟩, +⟨⟨1,619,508,true⟩,201,201,0⟩, +⟨⟨0,497,114,false⟩,114,202,1⟩, +⟨⟨0,509,120,false⟩,120,202,1⟩, +⟨⟨1,497,509,true⟩,202,202,0⟩, +⟨⟨0,620,0,false⟩,0,202,2⟩, +⟨⟨1,620,497,true⟩,202,202,0⟩, +⟨⟨0,501,116,true⟩,116,203,1⟩, +⟨⟨0,505,118,true⟩,118,203,1⟩, +⟨⟨1,501,505,true⟩,203,203,0⟩, +⟨⟨0,621,0,true⟩,0,203,2⟩, +⟨⟨1,621,501,true⟩,203,203,0⟩, +⟨⟨0,499,115,false⟩,115,204,1⟩, +⟨⟨0,511,121,false⟩,121,204,1⟩, +⟨⟨1,499,511,true⟩,204,204,0⟩, +⟨⟨0,622,0,false⟩,0,204,2⟩, +⟨⟨1,622,499,true⟩,204,204,0⟩, +⟨⟨0,503,117,true⟩,117,205,1⟩, +⟨⟨0,507,119,true⟩,119,205,1⟩, +⟨⟨1,503,507,true⟩,205,205,0⟩, +⟨⟨0,623,0,true⟩,0,205,2⟩, +⟨⟨1,623,503,true⟩,205,205,0⟩, +⟨⟨0,624,0,false⟩,0,10,1⟩, +⟨⟨1,624,8,true⟩,10,10,0⟩, +⟨⟨0,624,10,false⟩,10,206,1⟩, +⟨⟨0,11,13,false⟩,13,206,1⟩, +⟨⟨1,624,11,true⟩,206,206,0⟩, +⟨⟨0,625,0,false⟩,0,206,2⟩, +⟨⟨1,625,624,true⟩,206,206,0⟩, +⟨⟨0,626,0,true⟩,0,11,1⟩, +⟨⟨1,626,9,true⟩,11,11,0⟩, +⟨⟨0,626,11,true⟩,11,207,1⟩, +⟨⟨0,10,12,true⟩,12,207,1⟩, +⟨⟨1,626,10,true⟩,207,207,0⟩, +⟨⟨0,627,0,true⟩,0,207,2⟩, +⟨⟨1,627,626,true⟩,207,207,0⟩, +⟨⟨0,628,0,false⟩,0,14,1⟩, +⟨⟨1,628,12,true⟩,14,14,0⟩, +⟨⟨0,628,14,false⟩,14,208,1⟩, +⟨⟨0,15,17,false⟩,17,208,1⟩, +⟨⟨1,628,15,true⟩,208,208,0⟩, +⟨⟨0,629,0,false⟩,0,208,2⟩, +⟨⟨1,629,628,true⟩,208,208,0⟩, +⟨⟨0,630,0,true⟩,0,15,1⟩, +⟨⟨1,630,13,true⟩,15,15,0⟩, +⟨⟨0,630,15,true⟩,15,209,1⟩, +⟨⟨0,14,16,true⟩,16,209,1⟩, +⟨⟨1,630,14,true⟩,209,209,0⟩, +⟨⟨0,631,0,true⟩,0,209,2⟩, +⟨⟨1,631,630,true⟩,209,209,0⟩, +⟨⟨0,288,10,false⟩,10,210,1⟩, +⟨⟨0,298,15,false⟩,15,210,1⟩, +⟨⟨1,288,298,true⟩,210,210,0⟩, +⟨⟨0,632,0,false⟩,0,210,2⟩, +⟨⟨1,632,288,true⟩,210,210,0⟩, +⟨⟨0,290,11,true⟩,11,211,1⟩, +⟨⟨0,296,14,true⟩,14,211,1⟩, +⟨⟨1,290,296,true⟩,211,211,0⟩, +⟨⟨0,633,0,true⟩,0,211,2⟩, +⟨⟨1,633,290,true⟩,211,211,0⟩, +⟨⟨0,292,12,false⟩,12,212,1⟩, +⟨⟨0,302,17,false⟩,17,212,1⟩, +⟨⟨1,292,302,true⟩,212,212,0⟩, +⟨⟨0,634,0,false⟩,0,212,2⟩, +⟨⟨1,634,292,true⟩,212,212,0⟩, +⟨⟨0,294,13,true⟩,13,213,1⟩, +⟨⟨0,300,16,true⟩,16,213,1⟩, +⟨⟨1,294,300,true⟩,213,213,0⟩, +⟨⟨0,635,0,true⟩,0,213,2⟩, +⟨⟨1,635,294,true⟩,213,213,0⟩, +⟨⟨0,301,16,false⟩,16,214,1⟩, +⟨⟨0,289,10,false⟩,10,214,1⟩, +⟨⟨1,301,289,true⟩,214,214,0⟩, +⟨⟨0,636,0,false⟩,0,214,2⟩, +⟨⟨1,636,301,true⟩,214,214,0⟩, +⟨⟨0,297,14,true⟩,14,215,1⟩, +⟨⟨0,293,12,true⟩,12,215,1⟩, +⟨⟨1,297,293,true⟩,215,215,0⟩, +⟨⟨0,637,0,true⟩,0,215,2⟩, +⟨⟨1,637,297,true⟩,215,215,0⟩, +⟨⟨0,303,17,false⟩,17,216,1⟩, +⟨⟨0,291,11,false⟩,11,216,1⟩, +⟨⟨1,303,291,true⟩,216,216,0⟩, +⟨⟨0,638,0,false⟩,0,216,2⟩, +⟨⟨1,638,303,true⟩,216,216,0⟩, +⟨⟨0,299,15,true⟩,15,217,1⟩, +⟨⟨0,295,13,true⟩,13,217,1⟩, +⟨⟨1,299,295,true⟩,217,217,0⟩, +⟨⟨0,639,0,true⟩,0,217,2⟩, +⟨⟨1,639,299,true⟩,217,217,0⟩, +⟨⟨0,640,0,false⟩,0,50,1⟩, +⟨⟨1,640,48,true⟩,50,50,0⟩, +⟨⟨0,640,50,false⟩,50,218,1⟩, +⟨⟨0,51,53,false⟩,53,218,1⟩, +⟨⟨1,640,51,true⟩,218,218,0⟩, +⟨⟨0,641,0,false⟩,0,218,2⟩, +⟨⟨1,641,640,true⟩,218,218,0⟩, +⟨⟨0,642,0,true⟩,0,51,1⟩, +⟨⟨1,642,49,true⟩,51,51,0⟩, +⟨⟨0,642,51,true⟩,51,219,1⟩, +⟨⟨0,50,52,true⟩,52,219,1⟩, +⟨⟨1,642,50,true⟩,219,219,0⟩, +⟨⟨0,643,0,true⟩,0,219,2⟩, +⟨⟨1,643,642,true⟩,219,219,0⟩, +⟨⟨0,644,0,false⟩,0,54,1⟩, +⟨⟨1,644,52,true⟩,54,54,0⟩, +⟨⟨0,644,54,false⟩,54,220,1⟩, +⟨⟨0,55,57,false⟩,57,220,1⟩, +⟨⟨1,644,55,true⟩,220,220,0⟩, +⟨⟨0,645,0,false⟩,0,220,2⟩, +⟨⟨1,645,644,true⟩,220,220,0⟩, +⟨⟨0,646,0,true⟩,0,55,1⟩, +⟨⟨1,646,53,true⟩,55,55,0⟩, +⟨⟨0,646,55,true⟩,55,221,1⟩, +⟨⟨0,54,56,true⟩,56,221,1⟩, +⟨⟨1,646,54,true⟩,221,221,0⟩, +⟨⟨0,647,0,true⟩,0,221,2⟩, +⟨⟨1,647,646,true⟩,221,221,0⟩, +⟨⟨0,368,50,false⟩,50,222,1⟩, +⟨⟨0,378,55,false⟩,55,222,1⟩, +⟨⟨1,368,378,true⟩,222,222,0⟩, +⟨⟨0,648,0,false⟩,0,222,2⟩, +⟨⟨1,648,368,true⟩,222,222,0⟩, +⟨⟨0,376,54,true⟩,54,223,1⟩, +⟨⟨0,370,51,true⟩,51,223,1⟩, +⟨⟨1,376,370,true⟩,223,223,0⟩, +⟨⟨0,649,0,true⟩,0,223,2⟩, +⟨⟨1,649,376,true⟩,223,223,0⟩, +⟨⟨0,382,57,false⟩,57,224,1⟩, +⟨⟨0,372,52,false⟩,52,224,1⟩, +⟨⟨1,382,372,true⟩,224,224,0⟩, +⟨⟨0,650,0,false⟩,0,224,2⟩, +⟨⟨1,650,382,true⟩,224,224,0⟩, +⟨⟨0,374,53,true⟩,53,225,1⟩, +⟨⟨0,380,56,true⟩,56,225,1⟩, +⟨⟨1,374,380,true⟩,225,225,0⟩, +⟨⟨0,651,0,true⟩,0,225,2⟩, +⟨⟨1,651,374,true⟩,225,225,0⟩, +⟨⟨0,381,56,false⟩,56,226,1⟩, +⟨⟨0,369,50,false⟩,50,226,1⟩, +⟨⟨1,381,369,true⟩,226,226,0⟩, +⟨⟨0,652,0,false⟩,0,226,2⟩, +⟨⟨1,652,381,true⟩,226,226,0⟩, +⟨⟨0,373,52,true⟩,52,227,1⟩, +⟨⟨0,377,54,true⟩,54,227,1⟩, +⟨⟨1,373,377,true⟩,227,227,0⟩, +⟨⟨0,653,0,true⟩,0,227,2⟩, +⟨⟨1,653,373,true⟩,227,227,0⟩, +⟨⟨0,371,51,false⟩,51,228,1⟩, +⟨⟨0,383,57,false⟩,57,228,1⟩, +⟨⟨1,371,383,true⟩,228,228,0⟩, +⟨⟨0,654,0,false⟩,0,228,2⟩, +⟨⟨1,654,371,true⟩,228,228,0⟩, +⟨⟨0,379,55,true⟩,55,229,1⟩, +⟨⟨0,375,53,true⟩,53,229,1⟩, +⟨⟨1,379,375,true⟩,229,229,0⟩, +⟨⟨0,655,0,true⟩,0,229,2⟩, +⟨⟨1,655,379,true⟩,229,229,0⟩, +⟨⟨0,656,0,false⟩,0,82,1⟩, +⟨⟨1,656,80,true⟩,82,82,0⟩, +⟨⟨0,656,82,false⟩,82,230,1⟩, +⟨⟨0,83,85,false⟩,85,230,1⟩, +⟨⟨1,656,83,true⟩,230,230,0⟩, +⟨⟨0,657,0,false⟩,0,230,2⟩, +⟨⟨1,657,656,true⟩,230,230,0⟩, +⟨⟨0,658,0,true⟩,0,83,1⟩, +⟨⟨1,658,81,true⟩,83,83,0⟩] +def chunk47 : List Entry := [⟨⟨0,658,83,true⟩,83,231,1⟩, +⟨⟨0,82,84,true⟩,84,231,1⟩, +⟨⟨1,658,82,true⟩,231,231,0⟩, +⟨⟨0,659,0,true⟩,0,231,2⟩, +⟨⟨1,659,658,true⟩,231,231,0⟩, +⟨⟨0,660,0,false⟩,0,86,1⟩, +⟨⟨1,660,84,true⟩,86,86,0⟩, +⟨⟨0,660,86,false⟩,86,232,1⟩, +⟨⟨0,87,89,false⟩,89,232,1⟩, +⟨⟨1,660,87,true⟩,232,232,0⟩, +⟨⟨0,661,0,false⟩,0,232,2⟩, +⟨⟨1,661,660,true⟩,232,232,0⟩, +⟨⟨0,662,0,true⟩,0,87,1⟩, +⟨⟨1,662,85,true⟩,87,87,0⟩, +⟨⟨0,662,87,true⟩,87,233,1⟩, +⟨⟨0,86,88,true⟩,88,233,1⟩, +⟨⟨1,662,86,true⟩,233,233,0⟩, +⟨⟨0,663,0,true⟩,0,233,2⟩, +⟨⟨1,663,662,true⟩,233,233,0⟩, +⟨⟨0,442,87,false⟩,87,234,1⟩, +⟨⟨0,432,82,false⟩,82,234,1⟩, +⟨⟨1,442,432,true⟩,234,234,0⟩, +⟨⟨0,664,0,false⟩,0,234,2⟩, +⟨⟨1,664,442,true⟩,234,234,0⟩, +⟨⟨0,434,83,true⟩,83,235,1⟩, +⟨⟨0,440,86,true⟩,86,235,1⟩, +⟨⟨1,434,440,true⟩,235,235,0⟩, +⟨⟨0,665,0,true⟩,0,235,2⟩, +⟨⟨1,665,434,true⟩,235,235,0⟩, +⟨⟨0,436,84,false⟩,84,236,1⟩, +⟨⟨0,446,89,false⟩,89,236,1⟩, +⟨⟨1,436,446,true⟩,236,236,0⟩, +⟨⟨0,666,0,false⟩,0,236,2⟩, +⟨⟨1,666,436,true⟩,236,236,0⟩, +⟨⟨0,444,88,true⟩,88,237,1⟩, +⟨⟨0,438,85,true⟩,85,237,1⟩, +⟨⟨1,444,438,true⟩,237,237,0⟩, +⟨⟨0,667,0,true⟩,0,237,2⟩, +⟨⟨1,667,444,true⟩,237,237,0⟩, +⟨⟨0,433,82,false⟩,82,238,1⟩, +⟨⟨0,445,88,false⟩,88,238,1⟩, +⟨⟨1,433,445,true⟩,238,238,0⟩, +⟨⟨0,668,0,false⟩,0,238,2⟩, +⟨⟨1,668,433,true⟩,238,238,0⟩, +⟨⟨0,441,86,true⟩,86,239,1⟩, +⟨⟨0,437,84,true⟩,84,239,1⟩, +⟨⟨1,441,437,true⟩,239,239,0⟩, +⟨⟨0,669,0,true⟩,0,239,2⟩, +⟨⟨1,669,441,true⟩,239,239,0⟩, +⟨⟨0,447,89,false⟩,89,240,1⟩, +⟨⟨0,435,83,false⟩,83,240,1⟩, +⟨⟨1,447,435,true⟩,240,240,0⟩, +⟨⟨0,670,0,false⟩,0,240,2⟩, +⟨⟨1,670,447,true⟩,240,240,0⟩, +⟨⟨0,439,85,true⟩,85,241,1⟩, +⟨⟨0,443,87,true⟩,87,241,1⟩, +⟨⟨1,439,443,true⟩,241,241,0⟩, +⟨⟨0,671,0,true⟩,0,241,2⟩, +⟨⟨1,671,439,true⟩,241,241,0⟩, +⟨⟨0,672,0,false⟩,0,106,1⟩, +⟨⟨1,672,104,true⟩,106,106,0⟩, +⟨⟨0,672,106,false⟩,106,242,1⟩, +⟨⟨0,107,109,false⟩,109,242,1⟩, +⟨⟨1,672,107,true⟩,242,242,0⟩, +⟨⟨0,673,0,false⟩,0,242,2⟩, +⟨⟨1,673,672,true⟩,242,242,0⟩, +⟨⟨0,674,0,true⟩,0,107,1⟩, +⟨⟨1,674,105,true⟩,107,107,0⟩, +⟨⟨0,674,107,true⟩,107,243,1⟩, +⟨⟨0,106,108,true⟩,108,243,1⟩, +⟨⟨1,674,106,true⟩,243,243,0⟩, +⟨⟨0,675,0,true⟩,0,243,2⟩, +⟨⟨1,675,674,true⟩,243,243,0⟩, +⟨⟨0,676,0,false⟩,0,110,1⟩, +⟨⟨1,676,108,true⟩,110,110,0⟩, +⟨⟨0,676,110,false⟩,110,244,1⟩, +⟨⟨0,111,113,false⟩,113,244,1⟩, +⟨⟨1,676,111,true⟩,244,244,0⟩, +⟨⟨0,677,0,false⟩,0,244,2⟩, +⟨⟨1,677,676,true⟩,244,244,0⟩, +⟨⟨0,678,0,true⟩,0,111,1⟩, +⟨⟨1,678,109,true⟩,111,111,0⟩, +⟨⟨0,678,111,true⟩,111,245,1⟩, +⟨⟨0,110,112,true⟩,112,245,1⟩, +⟨⟨1,678,110,true⟩,245,245,0⟩, +⟨⟨0,679,0,true⟩,0,245,2⟩, +⟨⟨1,679,678,true⟩,245,245,0⟩, +⟨⟨0,490,111,false⟩,111,246,1⟩, +⟨⟨0,480,106,false⟩,106,246,1⟩, +⟨⟨1,490,480,true⟩,246,246,0⟩, +⟨⟨0,680,0,false⟩,0,246,2⟩, +⟨⟨1,680,490,true⟩,246,246,0⟩, +⟨⟨0,482,107,true⟩,107,247,1⟩, +⟨⟨0,488,110,true⟩,110,247,1⟩, +⟨⟨1,482,488,true⟩,247,247,0⟩, +⟨⟨0,681,0,true⟩,0,247,2⟩, +⟨⟨1,681,482,true⟩,247,247,0⟩, +⟨⟨0,484,108,false⟩,108,248,1⟩, +⟨⟨0,494,113,false⟩,113,248,1⟩, +⟨⟨1,484,494,true⟩,248,248,0⟩, +⟨⟨0,682,0,false⟩,0,248,2⟩, +⟨⟨1,682,484,true⟩,248,248,0⟩, +⟨⟨0,492,112,true⟩,112,249,1⟩, +⟨⟨0,486,109,true⟩,109,249,1⟩, +⟨⟨1,492,486,true⟩,249,249,0⟩, +⟨⟨0,683,0,true⟩,0,249,2⟩, +⟨⟨1,683,492,true⟩,249,249,0⟩, +⟨⟨0,481,106,false⟩,106,250,1⟩, +⟨⟨0,493,112,false⟩,112,250,1⟩, +⟨⟨1,481,493,true⟩,250,250,0⟩, +⟨⟨0,684,0,false⟩,0,250,2⟩, +⟨⟨1,684,481,true⟩,250,250,0⟩, +⟨⟨0,489,110,true⟩,110,251,1⟩, +⟨⟨0,485,108,true⟩,108,251,1⟩, +⟨⟨1,489,485,true⟩,251,251,0⟩, +⟨⟨0,685,0,true⟩,0,251,2⟩, +⟨⟨1,685,489,true⟩,251,251,0⟩, +⟨⟨0,495,113,false⟩,113,252,1⟩, +⟨⟨0,483,107,false⟩,107,252,1⟩, +⟨⟨1,495,483,true⟩,252,252,0⟩, +⟨⟨0,686,0,false⟩,0,252,2⟩, +⟨⟨1,686,495,true⟩,252,252,0⟩, +⟨⟨0,487,109,true⟩,109,253,1⟩, +⟨⟨0,491,111,true⟩,111,253,1⟩, +⟨⟨1,487,491,true⟩,253,253,0⟩, +⟨⟨0,687,0,true⟩,0,253,2⟩, +⟨⟨1,687,487,true⟩,253,253,0⟩, +⟨⟨0,688,0,false⟩,0,98,1⟩, +⟨⟨1,688,96,true⟩,98,98,0⟩, +⟨⟨0,688,98,false⟩,98,254,1⟩, +⟨⟨0,99,101,false⟩,101,254,1⟩, +⟨⟨1,688,99,true⟩,254,254,0⟩, +⟨⟨0,689,0,false⟩,0,254,2⟩, +⟨⟨1,689,688,true⟩,254,254,0⟩, +⟨⟨0,690,0,true⟩,0,99,1⟩, +⟨⟨1,690,97,true⟩,99,99,0⟩, +⟨⟨0,690,99,true⟩,99,255,1⟩, +⟨⟨0,98,100,true⟩,100,255,1⟩, +⟨⟨1,690,98,true⟩,255,255,0⟩, +⟨⟨0,691,0,true⟩,0,255,2⟩, +⟨⟨1,691,690,true⟩,255,255,0⟩, +⟨⟨0,692,0,false⟩,0,102,1⟩, +⟨⟨1,692,100,true⟩,102,102,0⟩, +⟨⟨0,692,102,false⟩,102,256,1⟩, +⟨⟨0,103,105,false⟩,105,256,1⟩, +⟨⟨1,692,103,true⟩,256,256,0⟩, +⟨⟨0,693,0,false⟩,0,256,2⟩, +⟨⟨1,693,692,true⟩,256,256,0⟩, +⟨⟨0,694,0,true⟩,0,103,1⟩, +⟨⟨1,694,101,true⟩,103,103,0⟩, +⟨⟨0,694,103,true⟩,103,257,1⟩, +⟨⟨0,102,104,true⟩,104,257,1⟩, +⟨⟨1,694,102,true⟩,257,257,0⟩, +⟨⟨0,695,0,true⟩,0,257,2⟩, +⟨⟨1,695,694,true⟩,257,257,0⟩, +⟨⟨0,474,103,false⟩,103,258,1⟩, +⟨⟨0,464,98,false⟩,98,258,1⟩, +⟨⟨1,474,464,true⟩,258,258,0⟩, +⟨⟨0,696,0,false⟩,0,258,2⟩, +⟨⟨1,696,474,true⟩,258,258,0⟩, +⟨⟨0,466,99,true⟩,99,259,1⟩, +⟨⟨0,472,102,true⟩,102,259,1⟩, +⟨⟨1,466,472,true⟩,259,259,0⟩, +⟨⟨0,697,0,true⟩,0,259,2⟩, +⟨⟨1,697,466,true⟩,259,259,0⟩, +⟨⟨0,468,100,false⟩,100,260,1⟩, +⟨⟨0,478,105,false⟩,105,260,1⟩, +⟨⟨1,468,478,true⟩,260,260,0⟩, +⟨⟨0,698,0,false⟩,0,260,2⟩, +⟨⟨1,698,468,true⟩,260,260,0⟩, +⟨⟨0,476,104,true⟩,104,261,1⟩, +⟨⟨0,470,101,true⟩,101,261,1⟩, +⟨⟨1,476,470,true⟩,261,261,0⟩, +⟨⟨0,699,0,true⟩,0,261,2⟩, +⟨⟨1,699,476,true⟩,261,261,0⟩, +⟨⟨0,465,98,false⟩,98,262,1⟩, +⟨⟨0,477,104,false⟩,104,262,1⟩, +⟨⟨1,465,477,true⟩,262,262,0⟩, +⟨⟨0,700,0,false⟩,0,262,2⟩, +⟨⟨1,700,465,true⟩,262,262,0⟩, +⟨⟨0,473,102,true⟩,102,263,1⟩, +⟨⟨0,469,100,true⟩,100,263,1⟩, +⟨⟨1,473,469,true⟩,263,263,0⟩, +⟨⟨0,701,0,true⟩,0,263,2⟩, +⟨⟨1,701,473,true⟩,263,263,0⟩, +⟨⟨0,479,105,false⟩,105,264,1⟩, +⟨⟨0,467,99,false⟩,99,264,1⟩, +⟨⟨1,479,467,true⟩,264,264,0⟩, +⟨⟨0,702,0,false⟩,0,264,2⟩, +⟨⟨1,702,479,true⟩,264,264,0⟩, +⟨⟨0,471,101,true⟩,101,265,1⟩, +⟨⟨0,475,103,true⟩,103,265,1⟩, +⟨⟨1,471,475,true⟩,265,265,0⟩, +⟨⟨0,703,0,true⟩,0,265,2⟩, +⟨⟨1,703,471,true⟩,265,265,0⟩, +⟨⟨0,704,0,false⟩,0,90,1⟩, +⟨⟨1,704,88,true⟩,90,90,0⟩, +⟨⟨0,704,90,false⟩,90,266,1⟩, +⟨⟨0,91,93,false⟩,93,266,1⟩, +⟨⟨1,704,91,true⟩,266,266,0⟩] +def chunk48 : List Entry := [⟨⟨0,705,0,false⟩,0,266,2⟩, +⟨⟨1,705,704,true⟩,266,266,0⟩, +⟨⟨0,706,0,true⟩,0,91,1⟩, +⟨⟨1,706,89,true⟩,91,91,0⟩, +⟨⟨0,706,91,true⟩,91,267,1⟩, +⟨⟨0,90,92,true⟩,92,267,1⟩, +⟨⟨1,706,90,true⟩,267,267,0⟩, +⟨⟨0,707,0,true⟩,0,267,2⟩, +⟨⟨1,707,706,true⟩,267,267,0⟩, +⟨⟨0,708,0,false⟩,0,94,1⟩, +⟨⟨1,708,92,true⟩,94,94,0⟩, +⟨⟨0,708,94,false⟩,94,268,1⟩, +⟨⟨0,95,97,false⟩,97,268,1⟩, +⟨⟨1,708,95,true⟩,268,268,0⟩, +⟨⟨0,709,0,false⟩,0,268,2⟩, +⟨⟨1,709,708,true⟩,268,268,0⟩, +⟨⟨0,710,0,true⟩,0,95,1⟩, +⟨⟨1,710,93,true⟩,95,95,0⟩, +⟨⟨0,710,95,true⟩,95,269,1⟩, +⟨⟨0,94,96,true⟩,96,269,1⟩, +⟨⟨1,710,94,true⟩,269,269,0⟩, +⟨⟨0,711,0,true⟩,0,269,2⟩, +⟨⟨1,711,710,true⟩,269,269,0⟩, +⟨⟨0,458,95,false⟩,95,270,1⟩, +⟨⟨0,448,90,false⟩,90,270,1⟩, +⟨⟨1,458,448,true⟩,270,270,0⟩, +⟨⟨0,712,0,false⟩,0,270,2⟩, +⟨⟨1,712,458,true⟩,270,270,0⟩, +⟨⟨0,450,91,true⟩,91,271,1⟩, +⟨⟨0,456,94,true⟩,94,271,1⟩, +⟨⟨1,450,456,true⟩,271,271,0⟩, +⟨⟨0,713,0,true⟩,0,271,2⟩, +⟨⟨1,713,450,true⟩,271,271,0⟩, +⟨⟨0,452,92,false⟩,92,272,1⟩, +⟨⟨0,462,97,false⟩,97,272,1⟩, +⟨⟨1,452,462,true⟩,272,272,0⟩, +⟨⟨0,714,0,false⟩,0,272,2⟩, +⟨⟨1,714,452,true⟩,272,272,0⟩, +⟨⟨0,460,96,true⟩,96,273,1⟩, +⟨⟨0,454,93,true⟩,93,273,1⟩, +⟨⟨1,460,454,true⟩,273,273,0⟩, +⟨⟨0,715,0,true⟩,0,273,2⟩, +⟨⟨1,715,460,true⟩,273,273,0⟩, +⟨⟨0,449,90,false⟩,90,274,1⟩, +⟨⟨0,461,96,false⟩,96,274,1⟩, +⟨⟨1,449,461,true⟩,274,274,0⟩, +⟨⟨0,716,0,false⟩,0,274,2⟩, +⟨⟨1,716,449,true⟩,274,274,0⟩, +⟨⟨0,457,94,true⟩,94,275,1⟩, +⟨⟨0,453,92,true⟩,92,275,1⟩, +⟨⟨1,457,453,true⟩,275,275,0⟩, +⟨⟨0,717,0,true⟩,0,275,2⟩, +⟨⟨1,717,457,true⟩,275,275,0⟩, +⟨⟨0,463,97,false⟩,97,276,1⟩, +⟨⟨0,451,91,false⟩,91,276,1⟩, +⟨⟨1,463,451,true⟩,276,276,0⟩, +⟨⟨0,718,0,false⟩,0,276,2⟩, +⟨⟨1,718,463,true⟩,276,276,0⟩, +⟨⟨0,455,93,true⟩,93,277,1⟩, +⟨⟨0,459,95,true⟩,95,277,1⟩, +⟨⟨1,455,459,true⟩,277,277,0⟩, +⟨⟨0,719,0,true⟩,0,277,2⟩, +⟨⟨1,719,455,true⟩,277,277,0⟩, +⟨⟨0,720,0,false⟩,0,58,1⟩, +⟨⟨1,720,56,true⟩,58,58,0⟩, +⟨⟨0,720,58,false⟩,58,278,1⟩, +⟨⟨0,59,61,false⟩,61,278,1⟩, +⟨⟨1,720,59,true⟩,278,278,0⟩, +⟨⟨0,721,0,false⟩,0,278,2⟩, +⟨⟨1,721,720,true⟩,278,278,0⟩, +⟨⟨0,722,0,true⟩,0,59,1⟩, +⟨⟨1,722,57,true⟩,59,59,0⟩, +⟨⟨0,722,59,true⟩,59,279,1⟩, +⟨⟨0,58,60,true⟩,60,279,1⟩, +⟨⟨1,722,58,true⟩,279,279,0⟩, +⟨⟨0,723,0,true⟩,0,279,2⟩, +⟨⟨1,723,722,true⟩,279,279,0⟩, +⟨⟨0,724,0,false⟩,0,62,1⟩, +⟨⟨1,724,60,true⟩,62,62,0⟩, +⟨⟨0,724,62,false⟩,62,280,1⟩, +⟨⟨0,63,65,false⟩,65,280,1⟩, +⟨⟨1,724,63,true⟩,280,280,0⟩, +⟨⟨0,725,0,false⟩,0,280,2⟩, +⟨⟨1,725,724,true⟩,280,280,0⟩, +⟨⟨0,726,0,true⟩,0,63,1⟩, +⟨⟨1,726,61,true⟩,63,63,0⟩, +⟨⟨0,726,63,true⟩,63,281,1⟩, +⟨⟨0,62,64,true⟩,64,281,1⟩, +⟨⟨1,726,62,true⟩,281,281,0⟩, +⟨⟨0,727,0,true⟩,0,281,2⟩, +⟨⟨1,727,726,true⟩,281,281,0⟩, +⟨⟨0,384,58,false⟩,58,282,1⟩, +⟨⟨0,394,63,false⟩,63,282,1⟩, +⟨⟨1,384,394,true⟩,282,282,0⟩, +⟨⟨0,728,0,false⟩,0,282,2⟩, +⟨⟨1,728,384,true⟩,282,282,0⟩, +⟨⟨0,386,59,true⟩,59,283,1⟩, +⟨⟨0,392,62,true⟩,62,283,1⟩, +⟨⟨1,386,392,true⟩,283,283,0⟩, +⟨⟨0,729,0,true⟩,0,283,2⟩, +⟨⟨1,729,386,true⟩,283,283,0⟩, +⟨⟨0,388,60,false⟩,60,284,1⟩, +⟨⟨0,398,65,false⟩,65,284,1⟩, +⟨⟨1,388,398,true⟩,284,284,0⟩, +⟨⟨0,730,0,false⟩,0,284,2⟩, +⟨⟨1,730,388,true⟩,284,284,0⟩, +⟨⟨0,390,61,true⟩,61,285,1⟩, +⟨⟨0,396,64,true⟩,64,285,1⟩, +⟨⟨1,390,396,true⟩,285,285,0⟩, +⟨⟨0,731,0,true⟩,0,285,2⟩, +⟨⟨1,731,390,true⟩,285,285,0⟩, +⟨⟨0,397,64,false⟩,64,286,1⟩, +⟨⟨0,385,58,false⟩,58,286,1⟩, +⟨⟨1,397,385,true⟩,286,286,0⟩, +⟨⟨0,732,0,false⟩,0,286,2⟩, +⟨⟨1,732,397,true⟩,286,286,0⟩, +⟨⟨0,393,62,true⟩,62,287,1⟩, +⟨⟨0,389,60,true⟩,60,287,1⟩, +⟨⟨1,393,389,true⟩,287,287,0⟩, +⟨⟨0,733,0,true⟩,0,287,2⟩, +⟨⟨1,733,393,true⟩,287,287,0⟩, +⟨⟨0,399,65,false⟩,65,288,1⟩, +⟨⟨0,387,59,false⟩,59,288,1⟩, +⟨⟨1,399,387,true⟩,288,288,0⟩, +⟨⟨0,734,0,false⟩,0,288,2⟩, +⟨⟨1,734,399,true⟩,288,288,0⟩, +⟨⟨0,395,63,true⟩,63,289,1⟩, +⟨⟨0,391,61,true⟩,61,289,1⟩, +⟨⟨1,395,391,true⟩,289,289,0⟩, +⟨⟨0,735,0,true⟩,0,289,2⟩, +⟨⟨1,735,395,true⟩,289,289,0⟩, +⟨⟨0,512,122,false⟩,122,290,1⟩, +⟨⟨0,514,123,false⟩,123,290,1⟩, +⟨⟨1,512,514,true⟩,290,290,0⟩, +⟨⟨0,736,4,false⟩,4,290,2⟩, +⟨⟨1,736,512,true⟩,290,290,0⟩, +⟨⟨0,737,4,false⟩,4,290,2⟩, +⟨⟨1,737,512,true⟩,290,290,0⟩, +⟨⟨0,516,124,true⟩,124,291,1⟩, +⟨⟨0,518,125,true⟩,125,291,1⟩, +⟨⟨1,516,518,true⟩,291,291,0⟩, +⟨⟨0,738,4,true⟩,4,291,2⟩, +⟨⟨1,738,516,true⟩,291,291,0⟩, +⟨⟨0,739,4,true⟩,4,291,2⟩, +⟨⟨1,739,516,true⟩,291,291,0⟩, +⟨⟨0,400,126,false⟩,126,292,1⟩, +⟨⟨0,402,127,false⟩,127,292,1⟩, +⟨⟨1,400,402,true⟩,292,292,0⟩, +⟨⟨0,740,3,false⟩,3,292,2⟩, +⟨⟨1,740,400,true⟩,292,292,0⟩, +⟨⟨0,404,128,true⟩,128,293,1⟩, +⟨⟨0,406,129,true⟩,129,293,1⟩, +⟨⟨1,404,406,true⟩,293,293,0⟩, +⟨⟨0,741,3,true⟩,3,293,2⟩, +⟨⟨1,741,404,true⟩,293,293,0⟩, +⟨⟨0,413,130,false⟩,130,294,1⟩, +⟨⟨0,409,131,false⟩,131,294,1⟩, +⟨⟨1,413,409,true⟩,294,294,0⟩, +⟨⟨0,742,3,false⟩,3,294,2⟩, +⟨⟨1,742,413,true⟩,294,294,0⟩, +⟨⟨0,415,132,true⟩,132,295,1⟩, +⟨⟨0,411,133,true⟩,133,295,1⟩, +⟨⟨1,415,411,true⟩,295,295,0⟩, +⟨⟨0,743,3,true⟩,3,295,2⟩, +⟨⟨1,743,415,true⟩,295,295,0⟩, +⟨⟨0,524,130,false⟩,130,296,1⟩, +⟨⟨0,526,132,false⟩,132,296,1⟩, +⟨⟨1,524,526,true⟩,296,296,0⟩, +⟨⟨0,744,2,false⟩,2,296,2⟩, +⟨⟨1,744,524,true⟩,296,296,0⟩, +⟨⟨0,525,131,true⟩,131,297,1⟩, +⟨⟨0,527,133,true⟩,133,297,1⟩, +⟨⟨1,525,527,true⟩,297,297,0⟩, +⟨⟨0,745,2,true⟩,2,297,2⟩, +⟨⟨1,745,525,true⟩,297,297,0⟩, +⟨⟨0,520,126,false⟩,126,298,1⟩, +⟨⟨0,522,128,false⟩,128,298,1⟩, +⟨⟨1,520,522,true⟩,298,298,0⟩, +⟨⟨0,746,2,false⟩,2,298,2⟩, +⟨⟨1,746,520,true⟩,298,298,0⟩, +⟨⟨0,521,127,true⟩,127,299,1⟩, +⟨⟨0,523,129,true⟩,129,299,1⟩, +⟨⟨1,521,523,true⟩,299,299,0⟩, +⟨⟨0,747,2,true⟩,2,299,2⟩, +⟨⟨1,747,521,true⟩,299,299,0⟩, +⟨⟨0,513,122,false⟩,122,300,1⟩, +⟨⟨0,517,124,false⟩,124,300,1⟩, +⟨⟨1,513,517,true⟩,300,300,0⟩, +⟨⟨0,748,2,false⟩,2,300,2⟩, +⟨⟨1,748,513,true⟩,300,300,0⟩, +⟨⟨0,515,123,true⟩,123,301,1⟩, +⟨⟨0,519,125,true⟩,125,301,1⟩, +⟨⟨1,515,519,true⟩,301,301,0⟩, +⟨⟨0,749,2,true⟩,2,301,2⟩, +⟨⟨1,749,515,true⟩,301,301,0⟩, +⟨⟨0,528,134,false⟩,134,302,1⟩, +⟨⟨0,530,135,false⟩,135,302,1⟩, +⟨⟨1,528,530,true⟩,302,302,0⟩, +⟨⟨0,750,6,false⟩,6,302,2⟩, +⟨⟨1,750,528,true⟩,302,302,0⟩] +def chunk49 : List Entry := [⟨⟨0,751,6,false⟩,6,302,2⟩, +⟨⟨1,751,528,true⟩,302,302,0⟩, +⟨⟨0,532,136,true⟩,136,303,1⟩, +⟨⟨0,534,137,true⟩,137,303,1⟩, +⟨⟨1,532,534,true⟩,303,303,0⟩, +⟨⟨0,752,6,true⟩,6,303,2⟩, +⟨⟨1,752,532,true⟩,303,303,0⟩, +⟨⟨0,753,6,true⟩,6,303,2⟩, +⟨⟨1,753,532,true⟩,303,303,0⟩, +⟨⟨0,346,138,false⟩,138,304,1⟩, +⟨⟨0,344,139,false⟩,139,304,1⟩, +⟨⟨1,346,344,true⟩,304,304,0⟩, +⟨⟨0,754,7,false⟩,7,304,2⟩, +⟨⟨1,754,346,true⟩,304,304,0⟩, +⟨⟨0,350,140,true⟩,140,305,1⟩, +⟨⟨0,348,141,true⟩,141,305,1⟩, +⟨⟨1,350,348,true⟩,305,305,0⟩, +⟨⟨0,755,7,true⟩,7,305,2⟩, +⟨⟨1,755,350,true⟩,305,305,0⟩, +⟨⟨0,337,142,false⟩,142,306,1⟩, +⟨⟨0,341,143,false⟩,143,306,1⟩, +⟨⟨1,337,341,true⟩,306,306,0⟩, +⟨⟨0,756,3,false⟩,3,306,2⟩, +⟨⟨1,756,337,true⟩,306,306,0⟩, +⟨⟨0,339,144,true⟩,144,307,1⟩, +⟨⟨0,343,145,true⟩,145,307,1⟩, +⟨⟨1,339,343,true⟩,307,307,0⟩, +⟨⟨0,757,3,true⟩,3,307,2⟩, +⟨⟨1,757,339,true⟩,307,307,0⟩, +⟨⟨0,540,142,false⟩,142,308,1⟩, +⟨⟨0,542,144,false⟩,144,308,1⟩, +⟨⟨1,540,542,true⟩,308,308,0⟩, +⟨⟨0,758,0,false⟩,0,308,3⟩, +⟨⟨1,758,540,true⟩,308,308,0⟩, +⟨⟨0,541,143,true⟩,143,309,1⟩, +⟨⟨0,543,145,true⟩,145,309,1⟩, +⟨⟨1,541,543,true⟩,309,309,0⟩, +⟨⟨0,759,0,true⟩,0,309,3⟩, +⟨⟨1,759,541,true⟩,309,309,0⟩, +⟨⟨0,536,138,false⟩,138,310,1⟩, +⟨⟨0,538,140,false⟩,140,310,1⟩, +⟨⟨1,536,538,true⟩,310,310,0⟩, +⟨⟨0,760,2,false⟩,2,310,2⟩, +⟨⟨1,760,536,true⟩,310,310,0⟩, +⟨⟨0,537,139,true⟩,139,311,1⟩, +⟨⟨0,539,141,true⟩,141,311,1⟩, +⟨⟨1,537,539,true⟩,311,311,0⟩, +⟨⟨0,761,2,true⟩,2,311,2⟩, +⟨⟨1,761,537,true⟩,311,311,0⟩, +⟨⟨0,529,134,false⟩,134,312,1⟩, +⟨⟨0,533,136,false⟩,136,312,1⟩, +⟨⟨1,529,533,true⟩,312,312,0⟩, +⟨⟨0,762,2,false⟩,2,312,2⟩, +⟨⟨1,762,529,true⟩,312,312,0⟩, +⟨⟨0,531,135,true⟩,135,313,1⟩, +⟨⟨0,535,137,true⟩,137,313,1⟩, +⟨⟨1,531,535,true⟩,313,313,0⟩, +⟨⟨0,763,2,true⟩,2,313,2⟩, +⟨⟨1,763,531,true⟩,313,313,0⟩, +⟨⟨0,544,146,false⟩,146,314,1⟩, +⟨⟨0,546,147,false⟩,147,314,1⟩, +⟨⟨1,544,546,true⟩,314,314,0⟩, +⟨⟨0,764,9,false⟩,9,314,2⟩, +⟨⟨1,764,544,true⟩,314,314,0⟩, +⟨⟨0,765,9,false⟩,9,314,2⟩, +⟨⟨1,765,544,true⟩,314,314,0⟩, +⟨⟨0,548,148,true⟩,148,315,1⟩, +⟨⟨0,550,149,true⟩,149,315,1⟩, +⟨⟨1,548,550,true⟩,315,315,0⟩, +⟨⟨0,766,9,true⟩,9,315,2⟩, +⟨⟨1,766,548,true⟩,315,315,0⟩, +⟨⟨0,767,9,true⟩,9,315,2⟩, +⟨⟨1,767,548,true⟩,315,315,0⟩, +⟨⟨0,320,150,false⟩,150,316,1⟩, +⟨⟨0,328,151,false⟩,151,316,1⟩, +⟨⟨1,320,328,true⟩,316,316,0⟩, +⟨⟨0,768,3,false⟩,3,316,2⟩, +⟨⟨1,768,320,true⟩,316,316,0⟩, +⟨⟨0,334,152,true⟩,152,317,1⟩, +⟨⟨0,326,153,true⟩,153,317,1⟩, +⟨⟨1,334,326,true⟩,317,317,0⟩, +⟨⟨0,769,3,true⟩,3,317,2⟩, +⟨⟨1,769,334,true⟩,317,317,0⟩, +⟨⟨0,333,154,false⟩,154,318,1⟩, +⟨⟨0,325,155,false⟩,155,318,1⟩, +⟨⟨1,333,325,true⟩,318,318,0⟩, +⟨⟨0,770,3,false⟩,3,318,2⟩, +⟨⟨1,770,333,true⟩,318,318,0⟩, +⟨⟨0,323,156,true⟩,156,319,1⟩, +⟨⟨0,331,157,true⟩,157,319,1⟩, +⟨⟨1,323,331,true⟩,319,319,0⟩, +⟨⟨0,771,3,true⟩,3,319,2⟩, +⟨⟨1,771,323,true⟩,319,319,0⟩, +⟨⟨0,552,150,false⟩,150,320,1⟩, +⟨⟨0,554,152,false⟩,152,320,1⟩, +⟨⟨1,552,554,true⟩,320,320,0⟩, +⟨⟨0,772,2,false⟩,2,320,2⟩, +⟨⟨1,772,552,true⟩,320,320,0⟩, +⟨⟨0,553,151,true⟩,151,321,1⟩, +⟨⟨0,555,153,true⟩,153,321,1⟩, +⟨⟨1,553,555,true⟩,321,321,0⟩, +⟨⟨0,773,2,true⟩,2,321,2⟩, +⟨⟨1,773,553,true⟩,321,321,0⟩, +⟨⟨0,556,154,false⟩,154,322,1⟩, +⟨⟨0,558,156,false⟩,156,322,1⟩, +⟨⟨1,556,558,true⟩,322,322,0⟩, +⟨⟨0,774,0,false⟩,0,322,3⟩, +⟨⟨1,774,556,true⟩,322,322,0⟩, +⟨⟨0,557,155,true⟩,155,323,1⟩, +⟨⟨0,559,157,true⟩,157,323,1⟩, +⟨⟨1,557,559,true⟩,323,323,0⟩, +⟨⟨0,775,0,true⟩,0,323,3⟩, +⟨⟨1,775,557,true⟩,323,323,0⟩, +⟨⟨0,545,146,false⟩,146,324,1⟩, +⟨⟨0,549,148,false⟩,148,324,1⟩, +⟨⟨1,545,549,true⟩,324,324,0⟩, +⟨⟨0,776,2,false⟩,2,324,2⟩, +⟨⟨1,776,545,true⟩,324,324,0⟩, +⟨⟨0,547,147,true⟩,147,325,1⟩, +⟨⟨0,551,149,true⟩,149,325,1⟩, +⟨⟨1,547,551,true⟩,325,325,0⟩, +⟨⟨0,777,2,true⟩,2,325,2⟩, +⟨⟨1,777,547,true⟩,325,325,0⟩, +⟨⟨0,560,158,false⟩,158,326,1⟩, +⟨⟨0,562,159,false⟩,159,326,1⟩, +⟨⟨1,560,562,true⟩,326,326,0⟩, +⟨⟨0,778,0,false⟩,0,326,3⟩, +⟨⟨1,778,560,true⟩,326,326,0⟩, +⟨⟨0,779,6,false⟩,6,326,2⟩, +⟨⟨1,779,560,true⟩,326,326,0⟩, +⟨⟨0,564,160,true⟩,160,327,1⟩, +⟨⟨0,566,161,true⟩,161,327,1⟩, +⟨⟨1,564,566,true⟩,327,327,0⟩, +⟨⟨0,780,0,true⟩,0,327,3⟩, +⟨⟨1,780,564,true⟩,327,327,0⟩, +⟨⟨0,781,6,true⟩,6,327,2⟩, +⟨⟨1,781,564,true⟩,327,327,0⟩, +⟨⟨0,304,162,false⟩,162,328,1⟩, +⟨⟨0,312,163,false⟩,163,328,1⟩, +⟨⟨1,304,312,true⟩,328,328,0⟩, +⟨⟨0,782,4,false⟩,4,328,2⟩, +⟨⟨1,782,304,true⟩,328,328,0⟩, +⟨⟨0,318,164,true⟩,164,329,1⟩, +⟨⟨0,310,165,true⟩,165,329,1⟩, +⟨⟨1,318,310,true⟩,329,329,0⟩, +⟨⟨0,783,4,true⟩,4,329,2⟩, +⟨⟨1,783,318,true⟩,329,329,0⟩, +⟨⟨0,317,166,false⟩,166,330,1⟩, +⟨⟨0,309,167,false⟩,167,330,1⟩, +⟨⟨1,317,309,true⟩,330,330,0⟩, +⟨⟨0,784,6,false⟩,6,330,2⟩, +⟨⟨1,784,317,true⟩,330,330,0⟩, +⟨⟨0,307,168,true⟩,168,331,1⟩, +⟨⟨0,315,169,true⟩,169,331,1⟩, +⟨⟨1,307,315,true⟩,331,331,0⟩, +⟨⟨0,785,6,true⟩,6,331,2⟩, +⟨⟨1,785,307,true⟩,331,331,0⟩, +⟨⟨0,572,166,false⟩,166,332,1⟩, +⟨⟨0,574,168,false⟩,168,332,1⟩, +⟨⟨1,572,574,true⟩,332,332,0⟩, +⟨⟨0,786,2,false⟩,2,332,2⟩, +⟨⟨1,786,572,true⟩,332,332,0⟩, +⟨⟨0,573,167,true⟩,167,333,1⟩, +⟨⟨0,575,169,true⟩,169,333,1⟩, +⟨⟨1,573,575,true⟩,333,333,0⟩, +⟨⟨0,787,2,true⟩,2,333,2⟩, +⟨⟨1,787,573,true⟩,333,333,0⟩, +⟨⟨0,568,162,false⟩,162,334,1⟩, +⟨⟨0,570,164,false⟩,164,334,1⟩, +⟨⟨1,568,570,true⟩,334,334,0⟩, +⟨⟨0,788,2,false⟩,2,334,2⟩, +⟨⟨1,788,568,true⟩,334,334,0⟩, +⟨⟨0,569,163,true⟩,163,335,1⟩, +⟨⟨0,571,165,true⟩,165,335,1⟩, +⟨⟨1,569,571,true⟩,335,335,0⟩, +⟨⟨0,789,2,true⟩,2,335,2⟩, +⟨⟨1,789,569,true⟩,335,335,0⟩, +⟨⟨0,561,158,false⟩,158,336,1⟩, +⟨⟨0,565,160,false⟩,160,336,1⟩, +⟨⟨1,561,565,true⟩,336,336,0⟩, +⟨⟨0,790,2,false⟩,2,336,2⟩, +⟨⟨1,790,561,true⟩,336,336,0⟩, +⟨⟨0,563,159,true⟩,159,337,1⟩, +⟨⟨0,567,161,true⟩,161,337,1⟩, +⟨⟨1,563,567,true⟩,337,337,0⟩, +⟨⟨0,791,2,true⟩,2,337,2⟩, +⟨⟨1,791,563,true⟩,337,337,0⟩, +⟨⟨0,576,170,false⟩,170,338,1⟩, +⟨⟨0,578,171,false⟩,171,338,1⟩, +⟨⟨1,576,578,true⟩,338,338,0⟩, +⟨⟨0,792,7,false⟩,7,338,2⟩, +⟨⟨1,792,576,true⟩,338,338,0⟩, +⟨⟨0,793,7,false⟩,7,338,2⟩, +⟨⟨1,793,576,true⟩,338,338,0⟩, +⟨⟨0,580,172,true⟩,172,339,1⟩, +⟨⟨0,582,173,true⟩,173,339,1⟩, +⟨⟨1,580,582,true⟩,339,339,0⟩, +⟨⟨0,794,7,true⟩,7,339,2⟩, +⟨⟨1,794,580,true⟩,339,339,0⟩, +⟨⟨0,795,7,true⟩,7,339,2⟩] +def chunk50 : List Entry := [⟨⟨1,795,580,true⟩,339,339,0⟩, +⟨⟨0,352,174,false⟩,174,340,1⟩, +⟨⟨0,354,175,false⟩,175,340,1⟩, +⟨⟨1,352,354,true⟩,340,340,0⟩, +⟨⟨0,796,4,false⟩,4,340,2⟩, +⟨⟨1,796,352,true⟩,340,340,0⟩, +⟨⟨0,356,176,true⟩,176,341,1⟩, +⟨⟨0,358,177,true⟩,177,341,1⟩, +⟨⟨1,356,358,true⟩,341,341,0⟩, +⟨⟨0,797,4,true⟩,4,341,2⟩, +⟨⟨1,797,356,true⟩,341,341,0⟩, +⟨⟨0,365,178,false⟩,178,342,1⟩, +⟨⟨0,361,179,false⟩,179,342,1⟩, +⟨⟨1,365,361,true⟩,342,342,0⟩, +⟨⟨0,798,4,false⟩,4,342,2⟩, +⟨⟨1,798,365,true⟩,342,342,0⟩, +⟨⟨0,367,180,true⟩,180,343,1⟩, +⟨⟨0,363,181,true⟩,181,343,1⟩, +⟨⟨1,367,363,true⟩,343,343,0⟩, +⟨⟨0,799,4,true⟩,4,343,2⟩, +⟨⟨1,799,367,true⟩,343,343,0⟩, +⟨⟨0,584,174,false⟩,174,344,1⟩, +⟨⟨0,586,176,false⟩,176,344,1⟩, +⟨⟨1,584,586,true⟩,344,344,0⟩, +⟨⟨0,800,2,false⟩,2,344,2⟩, +⟨⟨1,800,584,true⟩,344,344,0⟩, +⟨⟨0,585,175,true⟩,175,345,1⟩, +⟨⟨0,587,177,true⟩,177,345,1⟩, +⟨⟨1,585,587,true⟩,345,345,0⟩, +⟨⟨0,801,2,true⟩,2,345,2⟩, +⟨⟨1,801,585,true⟩,345,345,0⟩, +⟨⟨0,588,178,false⟩,178,346,1⟩, +⟨⟨0,590,180,false⟩,180,346,1⟩, +⟨⟨1,588,590,true⟩,346,346,0⟩, +⟨⟨0,802,2,false⟩,2,346,2⟩, +⟨⟨1,802,588,true⟩,346,346,0⟩, +⟨⟨0,589,179,true⟩,179,347,1⟩, +⟨⟨0,591,181,true⟩,181,347,1⟩, +⟨⟨1,589,591,true⟩,347,347,0⟩, +⟨⟨0,803,2,true⟩,2,347,2⟩, +⟨⟨1,803,589,true⟩,347,347,0⟩, +⟨⟨0,577,170,false⟩,170,348,1⟩, +⟨⟨0,581,172,false⟩,172,348,1⟩, +⟨⟨1,577,581,true⟩,348,348,0⟩, +⟨⟨0,804,2,false⟩,2,348,2⟩, +⟨⟨1,804,577,true⟩,348,348,0⟩, +⟨⟨0,579,171,true⟩,171,349,1⟩, +⟨⟨0,583,173,true⟩,173,349,1⟩, +⟨⟨1,579,583,true⟩,349,349,0⟩, +⟨⟨0,805,2,true⟩,2,349,2⟩, +⟨⟨1,805,579,true⟩,349,349,0⟩, +⟨⟨0,592,182,false⟩,182,350,1⟩, +⟨⟨0,594,183,false⟩,183,350,1⟩, +⟨⟨1,592,594,true⟩,350,350,0⟩, +⟨⟨0,806,9,false⟩,9,350,2⟩, +⟨⟨1,806,592,true⟩,350,350,0⟩, +⟨⟨0,807,6,false⟩,6,350,2⟩, +⟨⟨1,807,592,true⟩,350,350,0⟩, +⟨⟨0,596,184,true⟩,184,351,1⟩, +⟨⟨0,598,185,true⟩,185,351,1⟩, +⟨⟨1,596,598,true⟩,351,351,0⟩, +⟨⟨0,808,9,true⟩,9,351,2⟩, +⟨⟨1,808,596,true⟩,351,351,0⟩, +⟨⟨0,809,6,true⟩,6,351,2⟩, +⟨⟨1,809,596,true⟩,351,351,0⟩, +⟨⟨0,416,186,false⟩,186,352,1⟩, +⟨⟨0,424,187,false⟩,187,352,1⟩, +⟨⟨1,416,424,true⟩,352,352,0⟩, +⟨⟨0,810,9,false⟩,9,352,2⟩, +⟨⟨1,810,416,true⟩,352,352,0⟩, +⟨⟨0,430,188,true⟩,188,353,1⟩, +⟨⟨0,422,189,true⟩,189,353,1⟩, +⟨⟨1,430,422,true⟩,353,353,0⟩, +⟨⟨0,811,9,true⟩,9,353,2⟩, +⟨⟨1,811,430,true⟩,353,353,0⟩, +⟨⟨0,429,190,false⟩,190,354,1⟩, +⟨⟨0,421,191,false⟩,191,354,1⟩, +⟨⟨1,429,421,true⟩,354,354,0⟩, +⟨⟨0,812,6,false⟩,6,354,2⟩, +⟨⟨1,812,429,true⟩,354,354,0⟩, +⟨⟨0,419,192,true⟩,192,355,1⟩, +⟨⟨0,427,193,true⟩,193,355,1⟩, +⟨⟨1,419,427,true⟩,355,355,0⟩, +⟨⟨0,813,6,true⟩,6,355,2⟩, +⟨⟨1,813,419,true⟩,355,355,0⟩, +⟨⟨0,593,182,false⟩,182,356,1⟩, +⟨⟨0,597,184,false⟩,184,356,1⟩, +⟨⟨1,593,597,true⟩,356,356,0⟩, +⟨⟨0,814,2,false⟩,2,356,2⟩, +⟨⟨1,814,593,true⟩,356,356,0⟩, +⟨⟨0,595,183,true⟩,183,357,1⟩, +⟨⟨0,599,185,true⟩,185,357,1⟩, +⟨⟨1,595,599,true⟩,357,357,0⟩, +⟨⟨0,815,2,true⟩,2,357,2⟩, +⟨⟨1,815,595,true⟩,357,357,0⟩, +⟨⟨0,604,190,false⟩,190,358,1⟩, +⟨⟨0,606,192,false⟩,192,358,1⟩, +⟨⟨1,604,606,true⟩,358,358,0⟩, +⟨⟨0,816,2,false⟩,2,358,2⟩, +⟨⟨1,816,604,true⟩,358,358,0⟩, +⟨⟨0,605,191,true⟩,191,359,1⟩, +⟨⟨0,607,193,true⟩,193,359,1⟩, +⟨⟨1,605,607,true⟩,359,359,0⟩, +⟨⟨0,817,2,true⟩,2,359,2⟩, +⟨⟨1,817,605,true⟩,359,359,0⟩, +⟨⟨0,600,186,false⟩,186,360,1⟩, +⟨⟨0,602,188,false⟩,188,360,1⟩, +⟨⟨1,600,602,true⟩,360,360,0⟩, +⟨⟨0,818,2,false⟩,2,360,2⟩, +⟨⟨1,818,600,true⟩,360,360,0⟩, +⟨⟨0,601,187,true⟩,187,361,1⟩, +⟨⟨0,603,189,true⟩,189,361,1⟩, +⟨⟨1,601,603,true⟩,361,361,0⟩, +⟨⟨0,819,2,true⟩,2,361,2⟩, +⟨⟨1,819,601,true⟩,361,361,0⟩, +⟨⟨0,608,194,false⟩,194,362,1⟩, +⟨⟨0,610,195,false⟩,195,362,1⟩, +⟨⟨1,608,610,true⟩,362,362,0⟩, +⟨⟨0,820,7,false⟩,7,362,2⟩, +⟨⟨1,820,608,true⟩,362,362,0⟩, +⟨⟨0,821,7,false⟩,7,362,2⟩, +⟨⟨1,821,608,true⟩,362,362,0⟩, +⟨⟨0,612,196,true⟩,196,363,1⟩, +⟨⟨0,614,197,true⟩,197,363,1⟩, +⟨⟨1,612,614,true⟩,363,363,0⟩, +⟨⟨0,822,7,true⟩,7,363,2⟩, +⟨⟨1,822,612,true⟩,363,363,0⟩, +⟨⟨0,823,7,true⟩,7,363,2⟩, +⟨⟨1,823,612,true⟩,363,363,0⟩, +⟨⟨0,506,198,false⟩,198,364,1⟩, +⟨⟨0,504,199,false⟩,199,364,1⟩, +⟨⟨1,506,504,true⟩,364,364,0⟩, +⟨⟨0,824,5,false⟩,5,364,2⟩, +⟨⟨1,824,506,true⟩,364,364,0⟩, +⟨⟨0,510,200,true⟩,200,365,1⟩, +⟨⟨0,508,201,true⟩,201,365,1⟩, +⟨⟨1,510,508,true⟩,365,365,0⟩, +⟨⟨0,825,5,true⟩,5,365,2⟩, +⟨⟨1,825,510,true⟩,365,365,0⟩, +⟨⟨0,497,202,false⟩,202,366,1⟩, +⟨⟨0,501,203,false⟩,203,366,1⟩, +⟨⟨1,497,501,true⟩,366,366,0⟩, +⟨⟨0,826,7,false⟩,7,366,2⟩, +⟨⟨1,826,497,true⟩,366,366,0⟩, +⟨⟨0,499,204,true⟩,204,367,1⟩, +⟨⟨0,503,205,true⟩,205,367,1⟩, +⟨⟨1,499,503,true⟩,367,367,0⟩, +⟨⟨0,827,7,true⟩,7,367,2⟩, +⟨⟨1,827,499,true⟩,367,367,0⟩, +⟨⟨0,609,194,false⟩,194,368,1⟩, +⟨⟨0,613,196,false⟩,196,368,1⟩, +⟨⟨1,609,613,true⟩,368,368,0⟩, +⟨⟨0,828,2,false⟩,2,368,2⟩, +⟨⟨1,828,609,true⟩,368,368,0⟩, +⟨⟨0,611,195,true⟩,195,369,1⟩, +⟨⟨0,615,197,true⟩,197,369,1⟩, +⟨⟨1,611,615,true⟩,369,369,0⟩, +⟨⟨0,829,2,true⟩,2,369,2⟩, +⟨⟨1,829,611,true⟩,369,369,0⟩, +⟨⟨0,616,198,false⟩,198,370,1⟩, +⟨⟨0,618,200,false⟩,200,370,1⟩, +⟨⟨1,616,618,true⟩,370,370,0⟩, +⟨⟨0,830,2,false⟩,2,370,2⟩, +⟨⟨1,830,616,true⟩,370,370,0⟩, +⟨⟨0,617,199,true⟩,199,371,1⟩, +⟨⟨0,619,201,true⟩,201,371,1⟩, +⟨⟨1,617,619,true⟩,371,371,0⟩, +⟨⟨0,831,2,true⟩,2,371,2⟩, +⟨⟨1,831,617,true⟩,371,371,0⟩, +⟨⟨0,620,202,false⟩,202,372,1⟩, +⟨⟨0,622,204,false⟩,204,372,1⟩, +⟨⟨1,620,622,true⟩,372,372,0⟩, +⟨⟨0,832,2,false⟩,2,372,2⟩, +⟨⟨1,832,620,true⟩,372,372,0⟩, +⟨⟨0,621,203,true⟩,203,373,1⟩, +⟨⟨0,623,205,true⟩,205,373,1⟩, +⟨⟨1,621,623,true⟩,373,373,0⟩, +⟨⟨0,833,2,true⟩,2,373,2⟩, +⟨⟨1,833,621,true⟩,373,373,0⟩, +⟨⟨0,624,206,false⟩,206,374,1⟩, +⟨⟨0,626,207,false⟩,207,374,1⟩, +⟨⟨1,624,626,true⟩,374,374,0⟩, +⟨⟨0,834,9,false⟩,9,374,2⟩, +⟨⟨1,834,624,true⟩,374,374,0⟩, +⟨⟨0,835,6,false⟩,6,374,2⟩, +⟨⟨1,835,624,true⟩,374,374,0⟩, +⟨⟨0,628,208,true⟩,208,375,1⟩, +⟨⟨0,630,209,true⟩,209,375,1⟩, +⟨⟨1,628,630,true⟩,375,375,0⟩, +⟨⟨0,836,9,true⟩,9,375,2⟩, +⟨⟨1,836,628,true⟩,375,375,0⟩, +⟨⟨0,837,6,true⟩,6,375,2⟩, +⟨⟨1,837,628,true⟩,375,375,0⟩, +⟨⟨0,288,210,false⟩,210,376,1⟩, +⟨⟨0,290,211,false⟩,211,376,1⟩, +⟨⟨1,288,290,true⟩,376,376,0⟩, +⟨⟨0,838,4,false⟩,4,376,2⟩, +⟨⟨1,838,288,true⟩,376,376,0⟩, +⟨⟨0,292,212,true⟩,212,377,1⟩, +⟨⟨0,294,213,true⟩,213,377,1⟩] +def chunk51 : List Entry := [⟨⟨1,292,294,true⟩,377,377,0⟩, +⟨⟨0,839,4,true⟩,4,377,2⟩, +⟨⟨1,839,292,true⟩,377,377,0⟩, +⟨⟨0,301,214,false⟩,214,378,1⟩, +⟨⟨0,297,215,false⟩,215,378,1⟩, +⟨⟨1,301,297,true⟩,378,378,0⟩, +⟨⟨0,840,6,false⟩,6,378,2⟩, +⟨⟨1,840,301,true⟩,378,378,0⟩, +⟨⟨0,303,216,true⟩,216,379,1⟩, +⟨⟨0,299,217,true⟩,217,379,1⟩, +⟨⟨1,303,299,true⟩,379,379,0⟩, +⟨⟨0,841,6,true⟩,6,379,2⟩, +⟨⟨1,841,303,true⟩,379,379,0⟩, +⟨⟨0,636,214,false⟩,214,380,1⟩, +⟨⟨0,638,216,false⟩,216,380,1⟩, +⟨⟨1,636,638,true⟩,380,380,0⟩, +⟨⟨0,842,0,false⟩,0,380,3⟩, +⟨⟨1,842,636,true⟩,380,380,0⟩, +⟨⟨0,637,215,true⟩,215,381,1⟩, +⟨⟨0,639,217,true⟩,217,381,1⟩, +⟨⟨1,637,639,true⟩,381,381,0⟩, +⟨⟨0,843,0,true⟩,0,381,3⟩, +⟨⟨1,843,637,true⟩,381,381,0⟩, +⟨⟨0,632,210,false⟩,210,382,1⟩, +⟨⟨0,634,212,false⟩,212,382,1⟩, +⟨⟨1,632,634,true⟩,382,382,0⟩, +⟨⟨0,844,3,false⟩,3,382,2⟩, +⟨⟨1,844,632,true⟩,382,382,0⟩, +⟨⟨0,633,211,true⟩,211,383,1⟩, +⟨⟨0,635,213,true⟩,213,383,1⟩, +⟨⟨1,633,635,true⟩,383,383,0⟩, +⟨⟨0,845,3,true⟩,3,383,2⟩, +⟨⟨1,845,633,true⟩,383,383,0⟩, +⟨⟨0,625,206,false⟩,206,384,1⟩, +⟨⟨0,629,208,false⟩,208,384,1⟩, +⟨⟨1,625,629,true⟩,384,384,0⟩, +⟨⟨0,846,3,false⟩,3,384,2⟩, +⟨⟨1,846,625,true⟩,384,384,0⟩, +⟨⟨0,627,207,true⟩,207,385,1⟩, +⟨⟨0,631,209,true⟩,209,385,1⟩, +⟨⟨1,627,631,true⟩,385,385,0⟩, +⟨⟨0,847,3,true⟩,3,385,2⟩, +⟨⟨1,847,627,true⟩,385,385,0⟩, +⟨⟨0,640,218,false⟩,218,386,1⟩, +⟨⟨0,642,219,false⟩,219,386,1⟩, +⟨⟨1,640,642,true⟩,386,386,0⟩, +⟨⟨0,848,0,false⟩,0,386,3⟩, +⟨⟨1,848,640,true⟩,386,386,0⟩, +⟨⟨0,849,7,false⟩,7,386,2⟩, +⟨⟨1,849,640,true⟩,386,386,0⟩, +⟨⟨0,644,220,true⟩,220,387,1⟩, +⟨⟨0,646,221,true⟩,221,387,1⟩, +⟨⟨1,644,646,true⟩,387,387,0⟩, +⟨⟨0,850,0,true⟩,0,387,3⟩, +⟨⟨1,850,644,true⟩,387,387,0⟩, +⟨⟨0,851,7,true⟩,7,387,2⟩, +⟨⟨1,851,644,true⟩,387,387,0⟩, +⟨⟨0,368,222,false⟩,222,388,1⟩, +⟨⟨0,376,223,false⟩,223,388,1⟩, +⟨⟨1,368,376,true⟩,388,388,0⟩, +⟨⟨0,852,4,false⟩,4,388,2⟩, +⟨⟨1,852,368,true⟩,388,388,0⟩, +⟨⟨0,382,224,true⟩,224,389,1⟩, +⟨⟨0,374,225,true⟩,225,389,1⟩, +⟨⟨1,382,374,true⟩,389,389,0⟩, +⟨⟨0,853,4,true⟩,4,389,2⟩, +⟨⟨1,853,382,true⟩,389,389,0⟩, +⟨⟨0,381,226,false⟩,226,390,1⟩, +⟨⟨0,373,227,false⟩,227,390,1⟩, +⟨⟨1,381,373,true⟩,390,390,0⟩, +⟨⟨0,854,4,false⟩,4,390,2⟩, +⟨⟨1,854,381,true⟩,390,390,0⟩, +⟨⟨0,371,228,true⟩,228,391,1⟩, +⟨⟨0,379,229,true⟩,229,391,1⟩, +⟨⟨1,371,379,true⟩,391,391,0⟩, +⟨⟨0,855,4,true⟩,4,391,2⟩, +⟨⟨1,855,371,true⟩,391,391,0⟩, +⟨⟨0,648,222,false⟩,222,392,1⟩, +⟨⟨0,650,224,false⟩,224,392,1⟩, +⟨⟨1,648,650,true⟩,392,392,0⟩, +⟨⟨0,856,7,false⟩,7,392,2⟩, +⟨⟨1,856,648,true⟩,392,392,0⟩, +⟨⟨0,649,223,true⟩,223,393,1⟩, +⟨⟨0,651,225,true⟩,225,393,1⟩, +⟨⟨1,649,651,true⟩,393,393,0⟩, +⟨⟨0,857,7,true⟩,7,393,2⟩, +⟨⟨1,857,649,true⟩,393,393,0⟩, +⟨⟨0,652,226,false⟩,226,394,1⟩, +⟨⟨0,654,228,false⟩,228,394,1⟩, +⟨⟨1,652,654,true⟩,394,394,0⟩, +⟨⟨0,858,3,false⟩,3,394,2⟩, +⟨⟨1,858,652,true⟩,394,394,0⟩, +⟨⟨0,653,227,true⟩,227,395,1⟩, +⟨⟨0,655,229,true⟩,229,395,1⟩, +⟨⟨1,653,655,true⟩,395,395,0⟩, +⟨⟨0,859,3,true⟩,3,395,2⟩, +⟨⟨1,859,653,true⟩,395,395,0⟩, +⟨⟨0,641,218,false⟩,218,396,1⟩, +⟨⟨0,645,220,false⟩,220,396,1⟩, +⟨⟨1,641,645,true⟩,396,396,0⟩, +⟨⟨0,860,3,false⟩,3,396,2⟩, +⟨⟨1,860,641,true⟩,396,396,0⟩, +⟨⟨0,643,219,true⟩,219,397,1⟩, +⟨⟨0,647,221,true⟩,221,397,1⟩, +⟨⟨1,643,647,true⟩,397,397,0⟩, +⟨⟨0,861,3,true⟩,3,397,2⟩, +⟨⟨1,861,643,true⟩,397,397,0⟩, +⟨⟨0,656,230,false⟩,230,398,1⟩, +⟨⟨0,658,231,false⟩,231,398,1⟩, +⟨⟨1,656,658,true⟩,398,398,0⟩, +⟨⟨0,862,0,false⟩,0,398,3⟩, +⟨⟨1,862,656,true⟩,398,398,0⟩, +⟨⟨0,863,6,false⟩,6,398,2⟩, +⟨⟨1,863,656,true⟩,398,398,0⟩, +⟨⟨0,660,232,true⟩,232,399,1⟩, +⟨⟨0,662,233,true⟩,233,399,1⟩, +⟨⟨1,660,662,true⟩,399,399,0⟩, +⟨⟨0,864,0,true⟩,0,399,3⟩, +⟨⟨1,864,660,true⟩,399,399,0⟩, +⟨⟨0,865,6,true⟩,6,399,2⟩, +⟨⟨1,865,660,true⟩,399,399,0⟩, +⟨⟨0,442,234,false⟩,234,400,1⟩, +⟨⟨0,434,235,false⟩,235,400,1⟩, +⟨⟨1,442,434,true⟩,400,400,0⟩, +⟨⟨0,866,5,false⟩,5,400,2⟩, +⟨⟨1,866,442,true⟩,400,400,0⟩, +⟨⟨0,436,236,true⟩,236,401,1⟩, +⟨⟨0,444,237,true⟩,237,401,1⟩, +⟨⟨1,436,444,true⟩,401,401,0⟩, +⟨⟨0,867,5,true⟩,5,401,2⟩, +⟨⟨1,867,436,true⟩,401,401,0⟩, +⟨⟨0,433,238,false⟩,238,402,1⟩, +⟨⟨0,441,239,false⟩,239,402,1⟩, +⟨⟨1,433,441,true⟩,402,402,0⟩, +⟨⟨0,868,6,false⟩,6,402,2⟩, +⟨⟨1,868,433,true⟩,402,402,0⟩, +⟨⟨0,447,240,true⟩,240,403,1⟩, +⟨⟨0,439,241,true⟩,241,403,1⟩, +⟨⟨1,447,439,true⟩,403,403,0⟩, +⟨⟨0,869,6,true⟩,6,403,2⟩, +⟨⟨1,869,447,true⟩,403,403,0⟩, +⟨⟨0,657,230,false⟩,230,404,1⟩, +⟨⟨0,661,232,false⟩,232,404,1⟩, +⟨⟨1,657,661,true⟩,404,404,0⟩, +⟨⟨0,870,0,false⟩,0,404,3⟩, +⟨⟨1,870,657,true⟩,404,404,0⟩, +⟨⟨0,659,231,true⟩,231,405,1⟩, +⟨⟨0,663,233,true⟩,233,405,1⟩, +⟨⟨1,659,663,true⟩,405,405,0⟩, +⟨⟨0,871,0,true⟩,0,405,3⟩, +⟨⟨1,871,659,true⟩,405,405,0⟩, +⟨⟨0,668,238,false⟩,238,406,1⟩, +⟨⟨0,670,240,false⟩,240,406,1⟩, +⟨⟨1,668,670,true⟩,406,406,0⟩, +⟨⟨0,872,3,false⟩,3,406,2⟩, +⟨⟨1,872,668,true⟩,406,406,0⟩, +⟨⟨0,669,239,true⟩,239,407,1⟩, +⟨⟨0,671,241,true⟩,241,407,1⟩, +⟨⟨1,669,671,true⟩,407,407,0⟩, +⟨⟨0,873,3,true⟩,3,407,2⟩, +⟨⟨1,873,669,true⟩,407,407,0⟩, +⟨⟨0,664,234,false⟩,234,408,1⟩, +⟨⟨0,666,236,false⟩,236,408,1⟩, +⟨⟨1,664,666,true⟩,408,408,0⟩, +⟨⟨0,874,3,false⟩,3,408,2⟩, +⟨⟨1,874,664,true⟩,408,408,0⟩, +⟨⟨0,665,235,true⟩,235,409,1⟩, +⟨⟨0,667,237,true⟩,237,409,1⟩, +⟨⟨1,665,667,true⟩,409,409,0⟩, +⟨⟨0,875,3,true⟩,3,409,2⟩, +⟨⟨1,875,665,true⟩,409,409,0⟩, +⟨⟨0,672,242,false⟩,242,410,1⟩, +⟨⟨0,674,243,false⟩,243,410,1⟩, +⟨⟨1,672,674,true⟩,410,410,0⟩, +⟨⟨0,876,0,false⟩,0,410,3⟩, +⟨⟨1,876,672,true⟩,410,410,0⟩, +⟨⟨0,877,7,false⟩,7,410,2⟩, +⟨⟨1,877,672,true⟩,410,410,0⟩, +⟨⟨0,676,244,true⟩,244,411,1⟩, +⟨⟨0,678,245,true⟩,245,411,1⟩, +⟨⟨1,676,678,true⟩,411,411,0⟩, +⟨⟨0,878,0,true⟩,0,411,3⟩, +⟨⟨1,878,676,true⟩,411,411,0⟩, +⟨⟨0,879,7,true⟩,7,411,2⟩, +⟨⟨1,879,676,true⟩,411,411,0⟩, +⟨⟨0,490,246,false⟩,246,412,1⟩, +⟨⟨0,482,247,false⟩,247,412,1⟩, +⟨⟨1,490,482,true⟩,412,412,0⟩, +⟨⟨0,880,9,false⟩,9,412,2⟩, +⟨⟨1,880,490,true⟩,412,412,0⟩, +⟨⟨0,484,248,true⟩,248,413,1⟩, +⟨⟨0,492,249,true⟩,249,413,1⟩, +⟨⟨1,484,492,true⟩,413,413,0⟩, +⟨⟨0,881,9,true⟩,9,413,2⟩, +⟨⟨1,881,484,true⟩,413,413,0⟩, +⟨⟨0,481,250,false⟩,250,414,1⟩, +⟨⟨0,489,251,false⟩,251,414,1⟩, +⟨⟨1,481,489,true⟩,414,414,0⟩, +⟨⟨0,882,7,false⟩,7,414,2⟩, +⟨⟨1,882,481,true⟩,414,414,0⟩] +def chunk52 : List Entry := [⟨⟨0,495,252,true⟩,252,415,1⟩, +⟨⟨0,487,253,true⟩,253,415,1⟩, +⟨⟨1,495,487,true⟩,415,415,0⟩, +⟨⟨0,883,7,true⟩,7,415,2⟩, +⟨⟨1,883,495,true⟩,415,415,0⟩, +⟨⟨0,673,242,false⟩,242,416,1⟩, +⟨⟨0,677,244,false⟩,244,416,1⟩, +⟨⟨1,673,677,true⟩,416,416,0⟩, +⟨⟨0,884,3,false⟩,3,416,2⟩, +⟨⟨1,884,673,true⟩,416,416,0⟩, +⟨⟨0,675,243,true⟩,243,417,1⟩, +⟨⟨0,679,245,true⟩,245,417,1⟩, +⟨⟨1,675,679,true⟩,417,417,0⟩, +⟨⟨0,885,3,true⟩,3,417,2⟩, +⟨⟨1,885,675,true⟩,417,417,0⟩, +⟨⟨0,680,246,false⟩,246,418,1⟩, +⟨⟨0,682,248,false⟩,248,418,1⟩, +⟨⟨1,680,682,true⟩,418,418,0⟩, +⟨⟨0,886,7,false⟩,7,418,2⟩, +⟨⟨1,886,680,true⟩,418,418,0⟩, +⟨⟨0,681,247,true⟩,247,419,1⟩, +⟨⟨0,683,249,true⟩,249,419,1⟩, +⟨⟨1,681,683,true⟩,419,419,0⟩, +⟨⟨0,887,7,true⟩,7,419,2⟩, +⟨⟨1,887,681,true⟩,419,419,0⟩, +⟨⟨0,684,250,false⟩,250,420,1⟩, +⟨⟨0,686,252,false⟩,252,420,1⟩, +⟨⟨1,684,686,true⟩,420,420,0⟩, +⟨⟨0,888,3,false⟩,3,420,2⟩, +⟨⟨1,888,684,true⟩,420,420,0⟩, +⟨⟨0,685,251,true⟩,251,421,1⟩, +⟨⟨0,687,253,true⟩,253,421,1⟩, +⟨⟨1,685,687,true⟩,421,421,0⟩, +⟨⟨0,889,3,true⟩,3,421,2⟩, +⟨⟨1,889,685,true⟩,421,421,0⟩, +⟨⟨0,688,254,false⟩,254,422,1⟩, +⟨⟨0,690,255,false⟩,255,422,1⟩, +⟨⟨1,688,690,true⟩,422,422,0⟩, +⟨⟨0,890,0,false⟩,0,422,3⟩, +⟨⟨1,890,688,true⟩,422,422,0⟩, +⟨⟨0,891,6,false⟩,6,422,2⟩, +⟨⟨1,891,688,true⟩,422,422,0⟩, +⟨⟨0,692,256,true⟩,256,423,1⟩, +⟨⟨0,694,257,true⟩,257,423,1⟩, +⟨⟨1,692,694,true⟩,423,423,0⟩, +⟨⟨0,892,0,true⟩,0,423,3⟩, +⟨⟨1,892,692,true⟩,423,423,0⟩, +⟨⟨0,893,6,true⟩,6,423,2⟩, +⟨⟨1,893,692,true⟩,423,423,0⟩, +⟨⟨0,689,254,false⟩,254,424,1⟩, +⟨⟨0,693,256,false⟩,256,424,1⟩, +⟨⟨1,689,693,true⟩,424,424,0⟩, +⟨⟨0,894,4,false⟩,4,424,2⟩, +⟨⟨1,894,689,true⟩,424,424,0⟩, +⟨⟨0,691,255,true⟩,255,425,1⟩, +⟨⟨0,695,257,true⟩,257,425,1⟩, +⟨⟨1,691,695,true⟩,425,425,0⟩, +⟨⟨0,895,4,true⟩,4,425,2⟩, +⟨⟨1,895,691,true⟩,425,425,0⟩, +⟨⟨0,474,258,false⟩,258,426,1⟩, +⟨⟨0,466,259,false⟩,259,426,1⟩, +⟨⟨1,474,466,true⟩,426,426,0⟩, +⟨⟨0,896,7,false⟩,7,426,2⟩, +⟨⟨1,896,474,true⟩,426,426,0⟩, +⟨⟨0,468,260,true⟩,260,427,1⟩, +⟨⟨0,476,261,true⟩,261,427,1⟩, +⟨⟨1,468,476,true⟩,427,427,0⟩, +⟨⟨0,897,7,true⟩,7,427,2⟩, +⟨⟨1,897,468,true⟩,427,427,0⟩, +⟨⟨0,465,262,false⟩,262,428,1⟩, +⟨⟨0,473,263,false⟩,263,428,1⟩, +⟨⟨1,465,473,true⟩,428,428,0⟩, +⟨⟨0,898,6,false⟩,6,428,2⟩, +⟨⟨1,898,465,true⟩,428,428,0⟩, +⟨⟨0,479,264,true⟩,264,429,1⟩, +⟨⟨0,471,265,true⟩,265,429,1⟩, +⟨⟨1,479,471,true⟩,429,429,0⟩, +⟨⟨0,899,6,true⟩,6,429,2⟩, +⟨⟨1,899,479,true⟩,429,429,0⟩, +⟨⟨0,700,262,false⟩,262,430,1⟩, +⟨⟨0,702,264,false⟩,264,430,1⟩, +⟨⟨1,700,702,true⟩,430,430,0⟩, +⟨⟨0,900,7,false⟩,7,430,2⟩, +⟨⟨1,900,700,true⟩,430,430,0⟩, +⟨⟨0,701,263,true⟩,263,431,1⟩, +⟨⟨0,703,265,true⟩,265,431,1⟩, +⟨⟨1,701,703,true⟩,431,431,0⟩, +⟨⟨0,901,7,true⟩,7,431,2⟩, +⟨⟨1,901,701,true⟩,431,431,0⟩, +⟨⟨0,696,258,false⟩,258,432,1⟩, +⟨⟨0,698,260,false⟩,260,432,1⟩, +⟨⟨1,696,698,true⟩,432,432,0⟩, +⟨⟨0,902,4,false⟩,4,432,2⟩, +⟨⟨1,902,696,true⟩,432,432,0⟩, +⟨⟨0,697,259,true⟩,259,433,1⟩, +⟨⟨0,699,261,true⟩,261,433,1⟩, +⟨⟨1,697,699,true⟩,433,433,0⟩, +⟨⟨0,903,4,true⟩,4,433,2⟩, +⟨⟨1,903,697,true⟩,433,433,0⟩, +⟨⟨0,704,266,false⟩,266,434,1⟩, +⟨⟨0,706,267,false⟩,267,434,1⟩, +⟨⟨1,704,706,true⟩,434,434,0⟩, +⟨⟨0,904,0,false⟩,0,434,3⟩, +⟨⟨1,904,704,true⟩,434,434,0⟩, +⟨⟨0,905,0,false⟩,0,434,3⟩, +⟨⟨1,905,704,true⟩,434,434,0⟩, +⟨⟨0,708,268,true⟩,268,435,1⟩, +⟨⟨0,710,269,true⟩,269,435,1⟩, +⟨⟨1,708,710,true⟩,435,435,0⟩, +⟨⟨0,906,0,true⟩,0,435,3⟩, +⟨⟨1,906,708,true⟩,435,435,0⟩, +⟨⟨0,907,0,true⟩,0,435,3⟩, +⟨⟨1,907,708,true⟩,435,435,0⟩, +⟨⟨0,705,266,false⟩,266,436,1⟩, +⟨⟨0,709,268,false⟩,268,436,1⟩, +⟨⟨1,705,709,true⟩,436,436,0⟩, +⟨⟨0,908,4,false⟩,4,436,2⟩, +⟨⟨1,908,705,true⟩,436,436,0⟩, +⟨⟨0,707,267,true⟩,267,437,1⟩, +⟨⟨0,711,269,true⟩,269,437,1⟩, +⟨⟨1,707,711,true⟩,437,437,0⟩, +⟨⟨0,909,4,true⟩,4,437,2⟩, +⟨⟨1,909,707,true⟩,437,437,0⟩, +⟨⟨0,458,270,false⟩,270,438,1⟩, +⟨⟨0,450,271,false⟩,271,438,1⟩, +⟨⟨1,458,450,true⟩,438,438,0⟩, +⟨⟨0,910,0,false⟩,0,438,3⟩, +⟨⟨1,910,458,true⟩,438,438,0⟩, +⟨⟨0,452,272,true⟩,272,439,1⟩, +⟨⟨0,460,273,true⟩,273,439,1⟩, +⟨⟨1,452,460,true⟩,439,439,0⟩, +⟨⟨0,911,0,true⟩,0,439,3⟩, +⟨⟨1,911,452,true⟩,439,439,0⟩, +⟨⟨0,449,274,false⟩,274,440,1⟩, +⟨⟨0,457,275,false⟩,275,440,1⟩, +⟨⟨1,449,457,true⟩,440,440,0⟩, +⟨⟨0,912,5,false⟩,5,440,2⟩, +⟨⟨1,912,449,true⟩,440,440,0⟩, +⟨⟨0,463,276,true⟩,276,441,1⟩, +⟨⟨0,455,277,true⟩,277,441,1⟩, +⟨⟨1,463,455,true⟩,441,441,0⟩, +⟨⟨0,913,5,true⟩,5,441,2⟩, +⟨⟨1,913,463,true⟩,441,441,0⟩, +⟨⟨0,712,270,false⟩,270,442,1⟩, +⟨⟨0,714,272,false⟩,272,442,1⟩, +⟨⟨1,712,714,true⟩,442,442,0⟩, +⟨⟨0,914,0,false⟩,0,442,3⟩, +⟨⟨1,914,712,true⟩,442,442,0⟩, +⟨⟨0,713,271,true⟩,271,443,1⟩, +⟨⟨0,715,273,true⟩,273,443,1⟩, +⟨⟨1,713,715,true⟩,443,443,0⟩, +⟨⟨0,915,0,true⟩,0,443,3⟩, +⟨⟨1,915,713,true⟩,443,443,0⟩, +⟨⟨0,716,274,false⟩,274,444,1⟩, +⟨⟨0,718,276,false⟩,276,444,1⟩, +⟨⟨1,716,718,true⟩,444,444,0⟩, +⟨⟨0,916,4,false⟩,4,444,2⟩, +⟨⟨1,916,716,true⟩,444,444,0⟩, +⟨⟨0,717,275,true⟩,275,445,1⟩, +⟨⟨0,719,277,true⟩,277,445,1⟩, +⟨⟨1,717,719,true⟩,445,445,0⟩, +⟨⟨0,917,4,true⟩,4,445,2⟩, +⟨⟨1,917,717,true⟩,445,445,0⟩, +⟨⟨0,720,278,false⟩,278,446,1⟩, +⟨⟨0,722,279,false⟩,279,446,1⟩, +⟨⟨1,720,722,true⟩,446,446,0⟩, +⟨⟨0,918,0,false⟩,0,446,3⟩, +⟨⟨1,918,720,true⟩,446,446,0⟩, +⟨⟨0,919,9,false⟩,9,446,2⟩, +⟨⟨1,919,720,true⟩,446,446,0⟩, +⟨⟨0,724,280,true⟩,280,447,1⟩, +⟨⟨0,726,281,true⟩,281,447,1⟩, +⟨⟨1,724,726,true⟩,447,447,0⟩, +⟨⟨0,920,0,true⟩,0,447,3⟩, +⟨⟨1,920,724,true⟩,447,447,0⟩, +⟨⟨0,921,9,true⟩,9,447,2⟩, +⟨⟨1,921,724,true⟩,447,447,0⟩, +⟨⟨0,721,278,false⟩,278,448,1⟩, +⟨⟨0,725,280,false⟩,280,448,1⟩, +⟨⟨1,721,725,true⟩,448,448,0⟩, +⟨⟨0,922,6,false⟩,6,448,2⟩, +⟨⟨1,922,721,true⟩,448,448,0⟩, +⟨⟨0,723,279,true⟩,279,449,1⟩, +⟨⟨0,727,281,true⟩,281,449,1⟩, +⟨⟨1,723,727,true⟩,449,449,0⟩, +⟨⟨0,923,6,true⟩,6,449,2⟩, +⟨⟨1,923,723,true⟩,449,449,0⟩, +⟨⟨0,384,282,false⟩,282,450,1⟩, +⟨⟨0,386,283,false⟩,283,450,1⟩, +⟨⟨1,384,386,true⟩,450,450,0⟩, +⟨⟨0,924,7,false⟩,7,450,2⟩, +⟨⟨1,924,384,true⟩,450,450,0⟩, +⟨⟨0,388,284,true⟩,284,451,1⟩, +⟨⟨0,390,285,true⟩,285,451,1⟩, +⟨⟨1,388,390,true⟩,451,451,0⟩, +⟨⟨0,925,7,true⟩,7,451,2⟩, +⟨⟨1,925,388,true⟩,451,451,0⟩, +⟨⟨0,728,282,false⟩,282,452,1⟩, +⟨⟨0,730,284,false⟩,284,452,1⟩, +⟨⟨1,728,730,true⟩,452,452,0⟩] +def chunk53 : List Entry := [⟨⟨0,926,0,false⟩,0,452,3⟩, +⟨⟨1,926,728,true⟩,452,452,0⟩, +⟨⟨0,729,283,true⟩,283,453,1⟩, +⟨⟨0,731,285,true⟩,285,453,1⟩, +⟨⟨1,729,731,true⟩,453,453,0⟩, +⟨⟨0,927,0,true⟩,0,453,3⟩, +⟨⟨1,927,729,true⟩,453,453,0⟩, +⟨⟨0,397,286,false⟩,286,454,1⟩, +⟨⟨0,393,287,false⟩,287,454,1⟩, +⟨⟨1,397,393,true⟩,454,454,0⟩, +⟨⟨0,928,7,false⟩,7,454,2⟩, +⟨⟨1,928,397,true⟩,454,454,0⟩, +⟨⟨0,399,288,true⟩,288,455,1⟩, +⟨⟨0,395,289,true⟩,289,455,1⟩, +⟨⟨1,399,395,true⟩,455,455,0⟩, +⟨⟨0,929,7,true⟩,7,455,2⟩, +⟨⟨1,929,399,true⟩,455,455,0⟩, +⟨⟨0,732,286,false⟩,286,456,1⟩, +⟨⟨0,734,288,false⟩,288,456,1⟩, +⟨⟨1,732,734,true⟩,456,456,0⟩, +⟨⟨0,930,9,false⟩,9,456,2⟩, +⟨⟨1,930,732,true⟩,456,456,0⟩, +⟨⟨0,733,287,true⟩,287,457,1⟩, +⟨⟨0,735,289,true⟩,289,457,1⟩, +⟨⟨1,733,735,true⟩,457,457,0⟩, +⟨⟨0,931,9,true⟩,9,457,2⟩, +⟨⟨1,931,733,true⟩,457,457,0⟩, +⟨⟨0,512,290,false⟩,290,458,1⟩, +⟨⟨0,516,291,false⟩,291,458,1⟩, +⟨⟨1,512,516,true⟩,458,458,0⟩, +⟨⟨0,519,301,false⟩,301,458,1⟩, +⟨⟨0,518,291,false⟩,291,458,1⟩, +⟨⟨1,519,518,true⟩,458,458,0⟩, +⟨⟨1,519,512,true⟩,458,458,0⟩, +⟨⟨0,523,299,false⟩,299,458,1⟩, +⟨⟨0,406,293,false⟩,293,458,1⟩, +⟨⟨1,523,406,true⟩,458,458,0⟩, +⟨⟨0,411,295,false⟩,295,458,1⟩, +⟨⟨1,406,411,true⟩,458,458,0⟩, +⟨⟨1,406,518,true⟩,458,458,0⟩, +⟨⟨1,523,512,true⟩,458,458,0⟩, +⟨⟨0,0,2,false⟩,2,458,3⟩, +⟨⟨1,523,0,true⟩,458,458,0⟩, +⟨⟨0,1,3,false⟩,3,458,3⟩, +⟨⟨1,523,1,true⟩,458,458,0⟩, +⟨⟨0,252,4,false⟩,4,458,3⟩, +⟨⟨1,523,252,true⟩,458,458,0⟩, +⟨⟨1,252,0,true⟩,458,458,0⟩, +⟨⟨1,252,1,true⟩,458,458,0⟩, +⟨⟨1,252,512,true⟩,458,458,0⟩, +⟨⟨1,252,523,true⟩,458,458,0⟩, +⟨⟨0,258,5,false⟩,5,458,3⟩, +⟨⟨1,523,258,true⟩,458,458,0⟩, +⟨⟨0,528,302,true⟩,302,459,1⟩, +⟨⟨0,532,303,true⟩,303,459,1⟩, +⟨⟨1,528,532,true⟩,459,459,0⟩, +⟨⟨0,533,312,true⟩,312,459,1⟩, +⟨⟨0,534,303,true⟩,303,459,1⟩, +⟨⟨1,532,533,true⟩,459,459,0⟩, +⟨⟨1,532,534,true⟩,459,459,0⟩, +⟨⟨0,240,2,true⟩,2,459,3⟩, +⟨⟨1,240,528,true⟩,459,459,0⟩, +⟨⟨0,246,3,true⟩,3,459,3⟩, +⟨⟨1,240,246,true⟩,459,459,0⟩, +⟨⟨0,4,6,true⟩,6,459,3⟩, +⟨⟨1,240,4,true⟩,459,459,0⟩, +⟨⟨0,5,7,true⟩,7,459,3⟩, +⟨⟨1,240,5,true⟩,459,459,0⟩, +⟨⟨0,544,314,false⟩,314,460,1⟩, +⟨⟨0,548,315,false⟩,315,460,1⟩, +⟨⟨1,544,548,true⟩,460,460,0⟩, +⟨⟨0,551,325,false⟩,325,460,1⟩, +⟨⟨0,550,315,false⟩,315,460,1⟩, +⟨⟨1,551,550,true⟩,460,460,0⟩, +⟨⟨1,551,544,true⟩,460,460,0⟩, +⟨⟨0,241,2,false⟩,2,460,3⟩, +⟨⟨1,241,544,true⟩,460,460,0⟩, +⟨⟨0,247,3,false⟩,3,460,3⟩, +⟨⟨1,241,247,true⟩,460,460,0⟩, +⟨⟨0,6,8,false⟩,8,460,3⟩, +⟨⟨1,241,6,true⟩,460,460,0⟩, +⟨⟨0,7,9,false⟩,9,460,3⟩, +⟨⟨1,241,7,true⟩,460,460,0⟩, +⟨⟨0,560,326,true⟩,326,461,1⟩, +⟨⟨0,564,327,true⟩,327,461,1⟩, +⟨⟨1,560,564,true⟩,461,461,0⟩, +⟨⟨0,567,337,true⟩,337,461,1⟩, +⟨⟨0,566,327,true⟩,327,461,1⟩, +⟨⟨1,567,566,true⟩,461,461,0⟩, +⟨⟨1,567,560,true⟩,461,461,0⟩, +⟨⟨0,571,335,true⟩,335,461,1⟩, +⟨⟨0,310,329,true⟩,329,461,1⟩, +⟨⟨1,571,310,true⟩,461,461,0⟩, +⟨⟨0,315,331,true⟩,331,461,1⟩, +⟨⟨1,310,315,true⟩,461,461,0⟩, +⟨⟨1,310,566,true⟩,461,461,0⟩, +⟨⟨1,571,560,true⟩,461,461,0⟩, +⟨⟨0,242,2,true⟩,2,461,3⟩, +⟨⟨1,242,560,true⟩,461,461,0⟩, +⟨⟨0,2,4,true⟩,4,461,3⟩, +⟨⟨1,242,2,true⟩,461,461,0⟩, +⟨⟨0,264,6,true⟩,6,461,3⟩, +⟨⟨1,242,264,true⟩,461,461,0⟩, +⟨⟨0,276,8,true⟩,8,461,3⟩, +⟨⟨1,242,276,true⟩,461,461,0⟩, +⟨⟨0,576,338,false⟩,338,462,1⟩, +⟨⟨0,580,339,false⟩,339,462,1⟩, +⟨⟨1,576,580,true⟩,462,462,0⟩, +⟨⟨0,583,349,false⟩,349,462,1⟩, +⟨⟨0,582,339,false⟩,339,462,1⟩, +⟨⟨1,583,582,true⟩,462,462,0⟩, +⟨⟨1,583,576,true⟩,462,462,0⟩, +⟨⟨0,243,2,false⟩,2,462,3⟩, +⟨⟨1,243,576,true⟩,462,462,0⟩, +⟨⟨0,253,4,false⟩,4,462,3⟩, +⟨⟨1,243,253,true⟩,462,462,0⟩, +⟨⟨0,270,7,false⟩,7,462,3⟩, +⟨⟨1,243,270,true⟩,462,462,0⟩, +⟨⟨0,282,9,false⟩,9,462,3⟩, +⟨⟨1,243,282,true⟩,462,462,0⟩, +⟨⟨0,592,350,true⟩,350,463,1⟩, +⟨⟨0,596,351,true⟩,351,463,1⟩, +⟨⟨1,592,596,true⟩,463,463,0⟩, +⟨⟨0,599,357,true⟩,357,463,1⟩, +⟨⟨0,598,351,true⟩,351,463,1⟩, +⟨⟨1,599,598,true⟩,463,463,0⟩, +⟨⟨1,599,592,true⟩,463,463,0⟩, +⟨⟨0,603,361,true⟩,361,463,1⟩, +⟨⟨0,422,353,true⟩,353,463,1⟩, +⟨⟨1,603,422,true⟩,463,463,0⟩, +⟨⟨0,427,355,true⟩,355,463,1⟩, +⟨⟨1,422,427,true⟩,463,463,0⟩, +⟨⟨1,422,598,true⟩,463,463,0⟩, +⟨⟨1,603,592,true⟩,463,463,0⟩, +⟨⟨0,244,2,true⟩,2,463,3⟩, +⟨⟨1,244,592,true⟩,463,463,0⟩, +⟨⟨0,3,5,true⟩,5,463,3⟩, +⟨⟨1,244,3,true⟩,463,463,0⟩, +⟨⟨0,265,6,true⟩,6,463,3⟩, +⟨⟨1,244,265,true⟩,463,463,0⟩, +⟨⟨0,283,9,true⟩,9,463,3⟩, +⟨⟨1,244,283,true⟩,463,463,0⟩, +⟨⟨0,608,362,false⟩,362,464,1⟩, +⟨⟨0,612,363,false⟩,363,464,1⟩, +⟨⟨1,608,612,true⟩,464,464,0⟩, +⟨⟨0,615,369,false⟩,369,464,1⟩, +⟨⟨0,614,363,false⟩,363,464,1⟩, +⟨⟨1,615,614,true⟩,464,464,0⟩, +⟨⟨1,615,608,true⟩,464,464,0⟩, +⟨⟨0,245,2,false⟩,2,464,3⟩, +⟨⟨1,245,608,true⟩,464,464,0⟩, +⟨⟨0,259,5,false⟩,5,464,3⟩, +⟨⟨1,245,259,true⟩,464,464,0⟩, +⟨⟨0,271,7,false⟩,7,464,3⟩, +⟨⟨1,245,271,true⟩,464,464,0⟩, +⟨⟨0,277,8,false⟩,8,464,3⟩, +⟨⟨1,245,277,true⟩,464,464,0⟩, +⟨⟨0,624,374,true⟩,374,465,1⟩, +⟨⟨0,628,375,true⟩,375,465,1⟩, +⟨⟨1,624,628,true⟩,465,465,0⟩, +⟨⟨0,631,385,true⟩,385,465,1⟩, +⟨⟨0,630,375,true⟩,375,465,1⟩, +⟨⟨1,631,630,true⟩,465,465,0⟩, +⟨⟨1,631,624,true⟩,465,465,0⟩, +⟨⟨0,635,383,true⟩,383,465,1⟩, +⟨⟨0,294,377,true⟩,377,465,1⟩, +⟨⟨1,635,294,true⟩,465,465,0⟩, +⟨⟨0,299,379,true⟩,379,465,1⟩, +⟨⟨1,294,299,true⟩,465,465,0⟩, +⟨⟨1,294,630,true⟩,465,465,0⟩, +⟨⟨1,635,624,true⟩,465,465,0⟩, +⟨⟨0,248,3,true⟩,3,465,3⟩, +⟨⟨1,248,624,true⟩,465,465,0⟩, +⟨⟨0,254,4,true⟩,4,465,3⟩, +⟨⟨1,248,254,true⟩,465,465,0⟩, +⟨⟨0,266,6,true⟩,6,465,3⟩, +⟨⟨1,248,266,true⟩,465,465,0⟩, +⟨⟨0,284,9,true⟩,9,465,3⟩, +⟨⟨1,248,284,true⟩,465,465,0⟩, +⟨⟨0,640,386,false⟩,386,466,1⟩, +⟨⟨0,644,387,false⟩,387,466,1⟩, +⟨⟨1,640,644,true⟩,466,466,0⟩, +⟨⟨0,647,397,false⟩,397,466,1⟩, +⟨⟨0,646,387,false⟩,387,466,1⟩, +⟨⟨1,647,646,true⟩,466,466,0⟩, +⟨⟨1,647,640,true⟩,466,466,0⟩, +⟨⟨0,651,393,false⟩,393,466,1⟩, +⟨⟨0,374,389,false⟩,389,466,1⟩, +⟨⟨1,651,374,true⟩,466,466,0⟩, +⟨⟨0,379,391,false⟩,391,466,1⟩, +⟨⟨1,374,379,true⟩,466,466,0⟩, +⟨⟨1,374,646,true⟩,466,466,0⟩, +⟨⟨1,651,640,true⟩,466,466,0⟩, +⟨⟨0,249,3,false⟩,3,466,3⟩, +⟨⟨1,249,640,true⟩,466,466,0⟩, +⟨⟨0,255,4,false⟩,4,466,3⟩, +⟨⟨1,249,255,true⟩,466,466,0⟩, +⟨⟨0,272,7,false⟩,7,466,3⟩, +⟨⟨1,249,272,true⟩,466,466,0⟩, +⟨⟨0,278,8,false⟩,8,466,3⟩] +def chunk54 : List Entry := [⟨⟨1,249,278,true⟩,466,466,0⟩, +⟨⟨0,656,398,true⟩,398,467,1⟩, +⟨⟨0,660,399,true⟩,399,467,1⟩, +⟨⟨1,656,660,true⟩,467,467,0⟩, +⟨⟨0,663,405,true⟩,405,467,1⟩, +⟨⟨0,662,399,true⟩,399,467,1⟩, +⟨⟨1,663,662,true⟩,467,467,0⟩, +⟨⟨1,663,656,true⟩,467,467,0⟩, +⟨⟨0,667,409,true⟩,409,467,1⟩, +⟨⟨0,444,401,true⟩,401,467,1⟩, +⟨⟨1,667,444,true⟩,467,467,0⟩, +⟨⟨0,439,403,true⟩,403,467,1⟩, +⟨⟨1,444,439,true⟩,467,467,0⟩, +⟨⟨1,444,662,true⟩,467,467,0⟩, +⟨⟨1,667,656,true⟩,467,467,0⟩, +⟨⟨0,250,3,true⟩,3,467,3⟩, +⟨⟨1,250,656,true⟩,467,467,0⟩, +⟨⟨0,260,5,true⟩,5,467,3⟩, +⟨⟨1,250,260,true⟩,467,467,0⟩, +⟨⟨0,267,6,true⟩,6,467,3⟩, +⟨⟨1,250,267,true⟩,467,467,0⟩, +⟨⟨0,279,8,true⟩,8,467,3⟩, +⟨⟨1,250,279,true⟩,467,467,0⟩, +⟨⟨0,672,410,false⟩,410,468,1⟩, +⟨⟨0,676,411,false⟩,411,468,1⟩, +⟨⟨1,672,676,true⟩,468,468,0⟩, +⟨⟨0,679,417,false⟩,417,468,1⟩, +⟨⟨0,678,411,false⟩,411,468,1⟩, +⟨⟨1,679,678,true⟩,468,468,0⟩, +⟨⟨1,679,672,true⟩,468,468,0⟩, +⟨⟨0,683,419,false⟩,419,468,1⟩, +⟨⟨0,492,413,false⟩,413,468,1⟩, +⟨⟨1,683,492,true⟩,468,468,0⟩, +⟨⟨0,487,415,false⟩,415,468,1⟩, +⟨⟨1,492,487,true⟩,468,468,0⟩, +⟨⟨1,492,678,true⟩,468,468,0⟩, +⟨⟨1,683,672,true⟩,468,468,0⟩, +⟨⟨0,251,3,false⟩,3,468,3⟩, +⟨⟨1,251,672,true⟩,468,468,0⟩, +⟨⟨0,261,5,false⟩,5,468,3⟩, +⟨⟨1,251,261,true⟩,468,468,0⟩, +⟨⟨0,273,7,false⟩,7,468,3⟩, +⟨⟨1,251,273,true⟩,468,468,0⟩, +⟨⟨0,285,9,false⟩,9,468,3⟩, +⟨⟨1,251,285,true⟩,468,468,0⟩, +⟨⟨0,688,422,true⟩,422,469,1⟩, +⟨⟨0,692,423,true⟩,423,469,1⟩, +⟨⟨1,688,692,true⟩,469,469,0⟩, +⟨⟨0,695,425,true⟩,425,469,1⟩, +⟨⟨0,694,423,true⟩,423,469,1⟩, +⟨⟨1,695,694,true⟩,469,469,0⟩, +⟨⟨1,695,688,true⟩,469,469,0⟩, +⟨⟨0,699,433,true⟩,433,469,1⟩, +⟨⟨0,476,427,true⟩,427,469,1⟩, +⟨⟨1,699,476,true⟩,469,469,0⟩, +⟨⟨0,471,429,true⟩,429,469,1⟩, +⟨⟨1,476,471,true⟩,469,469,0⟩, +⟨⟨1,476,694,true⟩,469,469,0⟩, +⟨⟨1,699,688,true⟩,469,469,0⟩, +⟨⟨0,256,4,true⟩,4,469,3⟩, +⟨⟨1,256,688,true⟩,469,469,0⟩, +⟨⟨0,262,5,true⟩,5,469,3⟩, +⟨⟨1,256,262,true⟩,469,469,0⟩, +⟨⟨0,268,6,true⟩,6,469,3⟩, +⟨⟨1,256,268,true⟩,469,469,0⟩, +⟨⟨0,274,7,true⟩,7,469,3⟩, +⟨⟨1,256,274,true⟩,469,469,0⟩, +⟨⟨0,704,434,false⟩,434,470,1⟩, +⟨⟨0,708,435,false⟩,435,470,1⟩, +⟨⟨1,704,708,true⟩,470,470,0⟩, +⟨⟨0,711,437,false⟩,437,470,1⟩, +⟨⟨0,710,435,false⟩,435,470,1⟩, +⟨⟨1,711,710,true⟩,470,470,0⟩, +⟨⟨0,455,441,false⟩,441,470,1⟩, +⟨⟨0,460,439,false⟩,439,470,1⟩, +⟨⟨1,710,455,true⟩,470,470,0⟩, +⟨⟨1,710,460,true⟩,470,470,0⟩, +⟨⟨1,711,704,true⟩,470,470,0⟩, +⟨⟨0,715,443,false⟩,443,470,1⟩, +⟨⟨1,715,460,true⟩,470,470,0⟩, +⟨⟨1,715,704,true⟩,470,470,0⟩, +⟨⟨0,257,4,false⟩,4,470,3⟩, +⟨⟨1,257,704,true⟩,470,470,0⟩, +⟨⟨0,263,5,false⟩,5,470,3⟩, +⟨⟨1,257,263,true⟩,470,470,0⟩, +⟨⟨0,280,8,false⟩,8,470,3⟩, +⟨⟨1,257,280,true⟩,470,470,0⟩, +⟨⟨0,286,9,false⟩,9,470,3⟩, +⟨⟨1,257,286,true⟩,470,470,0⟩, +⟨⟨0,720,446,true⟩,446,471,1⟩, +⟨⟨0,724,447,true⟩,447,471,1⟩, +⟨⟨1,720,724,true⟩,471,471,0⟩, +⟨⟨0,727,449,true⟩,449,471,1⟩, +⟨⟨0,726,447,true⟩,447,471,1⟩, +⟨⟨1,727,726,true⟩,471,471,0⟩, +⟨⟨1,727,720,true⟩,471,471,0⟩, +⟨⟨0,269,6,true⟩,6,471,3⟩, +⟨⟨1,269,720,true⟩,471,471,0⟩, +⟨⟨0,275,7,true⟩,7,471,3⟩, +⟨⟨1,269,275,true⟩,471,471,0⟩, +⟨⟨0,281,8,true⟩,8,471,3⟩, +⟨⟨1,269,281,true⟩,471,471,0⟩, +⟨⟨0,287,9,true⟩,9,471,3⟩, +⟨⟨1,269,287,true⟩,471,471,0⟩, +⟨⟨0,736,290,false⟩,290,472,2⟩, +⟨⟨0,764,314,false⟩,314,472,2⟩, +⟨⟨1,736,764,true⟩,472,472,0⟩, +⟨⟨0,719,445,false⟩,445,472,2⟩, +⟨⟨0,455,470,false⟩,470,472,1⟩, +⟨⟨1,719,455,true⟩,472,472,0⟩, +⟨⟨1,719,736,true⟩,472,472,0⟩, +⟨⟨0,737,290,true⟩,290,473,2⟩, +⟨⟨0,750,302,true⟩,302,473,2⟩, +⟨⟨1,737,750,true⟩,473,473,0⟩, +⟨⟨0,703,431,true⟩,431,473,2⟩, +⟨⟨0,471,469,true⟩,469,473,1⟩, +⟨⟨1,703,471,true⟩,473,473,0⟩, +⟨⟨1,703,737,true⟩,473,473,0⟩, +⟨⟨0,738,291,false⟩,291,474,2⟩, +⟨⟨0,766,315,false⟩,315,474,2⟩, +⟨⟨1,738,766,true⟩,474,474,0⟩, +⟨⟨0,450,438,false⟩,438,470,1⟩, +⟨⟨0,457,440,false⟩,440,470,1⟩, +⟨⟨0,706,434,false⟩,434,470,1⟩, +⟨⟨1,450,457,true⟩,470,470,0⟩, +⟨⟨1,450,706,true⟩,470,470,0⟩, +⟨⟨0,450,470,false⟩,470,474,1⟩, +⟨⟨1,450,738,true⟩,474,474,0⟩, +⟨⟨0,739,291,true⟩,291,475,2⟩, +⟨⟨0,752,303,true⟩,303,475,2⟩, +⟨⟨1,739,752,true⟩,475,475,0⟩, +⟨⟨0,693,424,true⟩,424,469,1⟩, +⟨⟨1,694,692,true⟩,469,469,0⟩, +⟨⟨1,694,693,true⟩,469,469,0⟩, +⟨⟨0,694,469,true⟩,469,475,1⟩, +⟨⟨1,694,739,true⟩,475,475,0⟩, +⟨⟨0,400,292,false⟩,292,476,2⟩, +⟨⟨0,792,338,false⟩,338,476,2⟩, +⟨⟨1,400,792,true⟩,476,476,0⟩, +⟨⟨0,687,421,false⟩,421,476,2⟩, +⟨⟨0,487,468,false⟩,468,476,1⟩, +⟨⟨1,687,487,true⟩,476,476,0⟩, +⟨⟨1,687,400,true⟩,476,476,0⟩, +⟨⟨0,740,292,true⟩,292,477,2⟩, +⟨⟨0,778,326,true⟩,326,477,2⟩, +⟨⟨1,740,778,true⟩,477,477,0⟩, +⟨⟨0,671,407,true⟩,407,477,2⟩, +⟨⟨0,439,467,true⟩,467,477,1⟩, +⟨⟨1,671,439,true⟩,477,477,0⟩, +⟨⟨1,671,740,true⟩,477,477,0⟩, +⟨⟨0,404,293,false⟩,293,478,2⟩, +⟨⟨0,794,339,false⟩,339,478,2⟩, +⟨⟨1,404,794,true⟩,478,478,0⟩, +⟨⟨0,677,416,false⟩,416,468,1⟩, +⟨⟨1,678,676,true⟩,468,468,0⟩, +⟨⟨1,678,677,true⟩,468,468,0⟩, +⟨⟨0,678,468,false⟩,468,478,1⟩, +⟨⟨1,678,404,true⟩,478,478,0⟩, +⟨⟨0,741,293,true⟩,293,479,2⟩, +⟨⟨0,780,327,true⟩,327,479,2⟩, +⟨⟨1,741,780,true⟩,479,479,0⟩, +⟨⟨0,661,404,true⟩,404,467,1⟩, +⟨⟨1,662,660,true⟩,467,467,0⟩, +⟨⟨1,662,661,true⟩,467,467,0⟩, +⟨⟨0,662,467,true⟩,467,479,1⟩, +⟨⟨1,662,741,true⟩,479,479,0⟩, +⟨⟨0,413,294,false⟩,294,480,2⟩, +⟨⟨0,820,362,false⟩,362,480,2⟩, +⟨⟨1,413,820,true⟩,480,480,0⟩, +⟨⟨0,655,395,false⟩,395,480,2⟩, +⟨⟨0,379,466,false⟩,466,480,1⟩, +⟨⟨1,655,379,true⟩,480,480,0⟩, +⟨⟨1,655,413,true⟩,480,480,0⟩, +⟨⟨0,742,294,true⟩,294,481,2⟩, +⟨⟨0,806,350,true⟩,350,481,2⟩, +⟨⟨1,742,806,true⟩,481,481,0⟩, +⟨⟨0,639,381,true⟩,381,481,2⟩, +⟨⟨0,299,465,true⟩,465,481,1⟩, +⟨⟨1,639,299,true⟩,481,481,0⟩, +⟨⟨1,639,742,true⟩,481,481,0⟩, +⟨⟨0,415,295,false⟩,295,482,2⟩, +⟨⟨0,822,363,false⟩,363,482,2⟩, +⟨⟨1,415,822,true⟩,482,482,0⟩, +⟨⟨0,645,396,false⟩,396,466,1⟩, +⟨⟨1,646,644,true⟩,466,466,0⟩, +⟨⟨1,646,645,true⟩,466,466,0⟩, +⟨⟨0,646,466,false⟩,466,482,1⟩, +⟨⟨1,646,415,true⟩,482,482,0⟩, +⟨⟨0,743,295,true⟩,295,483,2⟩, +⟨⟨0,808,351,true⟩,351,483,2⟩, +⟨⟨1,743,808,true⟩,483,483,0⟩, +⟨⟨0,629,384,true⟩,384,465,1⟩, +⟨⟨1,630,628,true⟩,465,465,0⟩, +⟨⟨1,630,629,true⟩,465,465,0⟩, +⟨⟨0,630,465,true⟩,465,483,1⟩, +⟨⟨1,630,743,true⟩,483,483,0⟩, +⟨⟨0,524,296,false⟩,296,484,2⟩, +⟨⟨0,848,386,false⟩,386,484,2⟩, +⟨⟨1,524,848,true⟩,484,484,0⟩, +⟨⟨0,619,371,false⟩,371,484,2⟩] +def chunk55 : List Entry := [⟨⟨0,508,365,false⟩,365,484,2⟩, +⟨⟨1,619,508,true⟩,484,484,0⟩, +⟨⟨1,619,524,true⟩,484,484,0⟩, +⟨⟨0,744,296,true⟩,296,485,2⟩, +⟨⟨0,834,374,true⟩,374,485,2⟩, +⟨⟨1,744,834,true⟩,485,485,0⟩, +⟨⟨0,607,359,true⟩,359,485,2⟩, +⟨⟨0,427,463,true⟩,463,485,1⟩, +⟨⟨1,607,427,true⟩,485,485,0⟩, +⟨⟨1,607,744,true⟩,485,485,0⟩, +⟨⟨0,525,297,false⟩,297,486,2⟩, +⟨⟨0,850,387,false⟩,387,486,2⟩, +⟨⟨1,525,850,true⟩,486,486,0⟩, +⟨⟨0,623,373,false⟩,373,486,2⟩, +⟨⟨0,503,367,false⟩,367,486,2⟩, +⟨⟨1,623,503,true⟩,486,486,0⟩, +⟨⟨1,623,525,true⟩,486,486,0⟩, +⟨⟨0,745,297,true⟩,297,487,2⟩, +⟨⟨0,836,375,true⟩,375,487,2⟩, +⟨⟨1,745,836,true⟩,487,487,0⟩, +⟨⟨0,597,356,true⟩,356,463,1⟩, +⟨⟨1,598,596,true⟩,463,463,0⟩, +⟨⟨1,598,597,true⟩,463,463,0⟩, +⟨⟨0,598,463,true⟩,463,487,1⟩, +⟨⟨1,598,745,true⟩,487,487,0⟩, +⟨⟨0,520,298,false⟩,298,488,2⟩, +⟨⟨0,876,410,false⟩,410,488,2⟩, +⟨⟨1,520,876,true⟩,488,488,0⟩, +⟨⟨0,587,345,false⟩,345,488,2⟩, +⟨⟨0,358,341,false⟩,341,488,2⟩, +⟨⟨1,587,358,true⟩,488,488,0⟩, +⟨⟨1,587,520,true⟩,488,488,0⟩, +⟨⟨0,746,298,true⟩,298,489,2⟩, +⟨⟨0,862,398,true⟩,398,489,2⟩, +⟨⟨1,746,862,true⟩,489,489,0⟩, +⟨⟨0,575,333,true⟩,333,489,2⟩, +⟨⟨0,315,461,true⟩,461,489,1⟩, +⟨⟨1,575,315,true⟩,489,489,0⟩, +⟨⟨1,575,746,true⟩,489,489,0⟩, +⟨⟨0,521,299,false⟩,299,490,2⟩, +⟨⟨0,878,411,false⟩,411,490,2⟩, +⟨⟨1,521,878,true⟩,490,490,0⟩, +⟨⟨0,591,347,false⟩,347,490,2⟩, +⟨⟨0,363,343,false⟩,343,490,2⟩, +⟨⟨1,591,363,true⟩,490,490,0⟩, +⟨⟨1,591,521,true⟩,490,490,0⟩, +⟨⟨0,747,299,true⟩,299,491,2⟩, +⟨⟨0,864,399,true⟩,399,491,2⟩, +⟨⟨1,747,864,true⟩,491,491,0⟩, +⟨⟨0,565,336,true⟩,336,461,1⟩, +⟨⟨1,566,564,true⟩,461,461,0⟩, +⟨⟨1,566,565,true⟩,461,461,0⟩, +⟨⟨0,566,461,true⟩,461,491,1⟩, +⟨⟨1,566,747,true⟩,491,491,0⟩, +⟨⟨0,513,300,false⟩,300,492,2⟩, +⟨⟨0,904,434,false⟩,434,492,2⟩, +⟨⟨1,513,904,true⟩,492,492,0⟩, +⟨⟨0,555,321,false⟩,321,492,2⟩, +⟨⟨0,326,317,false⟩,317,492,2⟩, +⟨⟨1,555,326,true⟩,492,492,0⟩, +⟨⟨1,555,513,true⟩,492,492,0⟩, +⟨⟨0,748,300,true⟩,300,493,2⟩, +⟨⟨0,890,422,true⟩,422,493,2⟩, +⟨⟨1,748,890,true⟩,493,493,0⟩, +⟨⟨0,535,313,true⟩,313,493,2⟩, +⟨⟨0,534,459,true⟩,459,493,1⟩, +⟨⟨1,535,534,true⟩,493,493,0⟩, +⟨⟨1,535,748,true⟩,493,493,0⟩, +⟨⟨0,515,301,false⟩,301,494,2⟩, +⟨⟨0,906,435,false⟩,435,494,2⟩, +⟨⟨1,515,906,true⟩,494,494,0⟩, +⟨⟨0,559,323,false⟩,323,494,2⟩, +⟨⟨0,331,319,false⟩,319,494,2⟩, +⟨⟨1,559,331,true⟩,494,494,0⟩, +⟨⟨1,559,515,true⟩,494,494,0⟩, +⟨⟨0,749,301,true⟩,301,495,2⟩, +⟨⟨0,892,423,true⟩,423,495,2⟩, +⟨⟨1,749,892,true⟩,495,495,0⟩, +⟨⟨0,539,311,true⟩,311,495,2⟩, +⟨⟨0,348,305,true⟩,305,495,2⟩, +⟨⟨1,539,348,true⟩,495,495,0⟩, +⟨⟨1,539,749,true⟩,495,495,0⟩, +⟨⟨0,751,302,false⟩,302,496,2⟩, +⟨⟨0,765,314,false⟩,314,496,2⟩, +⟨⟨1,751,765,true⟩,496,496,0⟩, +⟨⟨0,731,453,false⟩,453,496,2⟩, +⟨⟨0,390,451,false⟩,451,496,2⟩, +⟨⟨1,731,390,true⟩,496,496,0⟩, +⟨⟨1,731,751,true⟩,496,496,0⟩, +⟨⟨0,753,303,true⟩,303,497,2⟩, +⟨⟨0,767,315,true⟩,315,497,2⟩, +⟨⟨1,753,767,true⟩,497,497,0⟩, +⟨⟨0,735,457,true⟩,457,497,2⟩, +⟨⟨0,395,455,true⟩,455,497,2⟩, +⟨⟨1,735,395,true⟩,497,497,0⟩, +⟨⟨1,735,753,true⟩,497,497,0⟩, +⟨⟨0,346,304,false⟩,304,498,2⟩, +⟨⟨0,416,352,false⟩,352,498,2⟩, +⟨⟨1,346,416,true⟩,498,498,0⟩, +⟨⟨0,482,412,false⟩,412,468,1⟩, +⟨⟨0,489,414,false⟩,414,468,1⟩, +⟨⟨0,674,410,false⟩,410,468,1⟩, +⟨⟨1,482,489,true⟩,468,468,0⟩, +⟨⟨1,482,674,true⟩,468,468,0⟩, +⟨⟨0,482,468,false⟩,468,498,1⟩, +⟨⟨1,482,346,true⟩,498,498,0⟩, +⟨⟨0,754,304,true⟩,304,499,2⟩, +⟨⟨0,304,328,true⟩,328,499,2⟩, +⟨⟨1,754,304,true⟩,499,499,0⟩, +⟨⟨0,373,390,false⟩,390,466,1⟩, +⟨⟨0,376,388,false⟩,388,466,1⟩, +⟨⟨0,642,386,false⟩,386,466,1⟩, +⟨⟨1,373,376,true⟩,466,466,0⟩, +⟨⟨1,373,642,true⟩,466,466,0⟩, +⟨⟨0,373,466,true⟩,466,499,1⟩, +⟨⟨1,373,754,true⟩,499,499,0⟩, +⟨⟨0,350,305,false⟩,305,500,2⟩, +⟨⟨0,430,353,false⟩,353,500,2⟩, +⟨⟨1,350,430,true⟩,500,500,0⟩, +⟨⟨0,682,418,false⟩,418,468,1⟩, +⟨⟨1,682,489,true⟩,468,468,0⟩, +⟨⟨1,682,677,true⟩,468,468,0⟩, +⟨⟨0,682,468,false⟩,468,500,1⟩, +⟨⟨1,682,350,true⟩,500,500,0⟩, +⟨⟨0,755,305,true⟩,305,501,2⟩, +⟨⟨0,318,329,true⟩,329,501,2⟩, +⟨⟨1,755,318,true⟩,501,501,0⟩, +⟨⟨0,654,394,false⟩,394,466,1⟩, +⟨⟨1,654,376,true⟩,466,466,0⟩, +⟨⟨1,654,645,true⟩,466,466,0⟩, +⟨⟨0,654,466,true⟩,466,501,1⟩, +⟨⟨1,654,755,true⟩,501,501,0⟩, +⟨⟨0,337,306,false⟩,306,502,2⟩, +⟨⟨0,506,364,false⟩,364,502,2⟩, +⟨⟨1,337,506,true⟩,502,502,0⟩, +⟨⟨0,434,400,true⟩,400,467,1⟩, +⟨⟨0,441,402,true⟩,402,467,1⟩, +⟨⟨0,658,398,true⟩,398,467,1⟩, +⟨⟨1,434,441,true⟩,467,467,0⟩, +⟨⟨1,434,658,true⟩,467,467,0⟩, +⟨⟨0,434,467,false⟩,467,502,1⟩, +⟨⟨1,434,337,true⟩,502,502,0⟩, +⟨⟨0,756,306,true⟩,306,503,2⟩, +⟨⟨0,352,340,true⟩,340,503,2⟩, +⟨⟨1,756,352,true⟩,503,503,0⟩, +⟨⟨0,290,376,true⟩,376,465,1⟩, +⟨⟨0,297,378,true⟩,378,465,1⟩, +⟨⟨0,626,374,true⟩,374,465,1⟩, +⟨⟨1,290,297,true⟩,465,465,0⟩, +⟨⟨1,290,626,true⟩,465,465,0⟩, +⟨⟨0,290,465,true⟩,465,503,1⟩, +⟨⟨1,290,756,true⟩,503,503,0⟩, +⟨⟨0,339,307,false⟩,307,504,2⟩, +⟨⟨0,510,365,false⟩,365,504,2⟩, +⟨⟨1,339,510,true⟩,504,504,0⟩, +⟨⟨0,666,408,true⟩,408,467,1⟩, +⟨⟨1,666,441,true⟩,467,467,0⟩, +⟨⟨1,666,661,true⟩,467,467,0⟩, +⟨⟨0,666,467,false⟩,467,504,1⟩, +⟨⟨1,666,339,true⟩,504,504,0⟩, +⟨⟨0,757,307,true⟩,307,505,2⟩, +⟨⟨0,356,341,true⟩,341,505,2⟩, +⟨⟨1,757,356,true⟩,505,505,0⟩, +⟨⟨0,634,382,true⟩,382,465,1⟩, +⟨⟨1,634,297,true⟩,465,465,0⟩, +⟨⟨1,634,629,true⟩,465,465,0⟩, +⟨⟨0,634,465,true⟩,465,505,1⟩, +⟨⟨1,634,757,true⟩,505,505,0⟩, +⟨⟨0,540,308,false⟩,308,506,2⟩, +⟨⟨0,442,400,false⟩,400,506,2⟩, +⟨⟨1,540,442,true⟩,506,506,0⟩, +⟨⟨0,613,368,false⟩,368,464,1⟩, +⟨⟨1,614,612,true⟩,464,464,0⟩, +⟨⟨1,614,613,true⟩,464,464,0⟩, +⟨⟨0,614,464,false⟩,464,506,1⟩, +⟨⟨1,614,540,true⟩,506,506,0⟩, +⟨⟨0,758,308,true⟩,308,507,2⟩, +⟨⟨0,288,376,true⟩,376,507,2⟩, +⟨⟨1,758,288,true⟩,507,507,0⟩, +⟨⟨0,581,348,false⟩,348,462,1⟩, +⟨⟨1,582,580,true⟩,462,462,0⟩, +⟨⟨1,582,581,true⟩,462,462,0⟩, +⟨⟨0,582,462,true⟩,462,507,1⟩, +⟨⟨1,582,758,true⟩,507,507,0⟩, +⟨⟨0,541,309,false⟩,309,508,2⟩, +⟨⟨0,436,401,false⟩,401,508,2⟩, +⟨⟨1,541,436,true⟩,508,508,0⟩, +⟨⟨0,501,366,false⟩,366,464,1⟩, +⟨⟨0,504,364,false⟩,364,464,1⟩, +⟨⟨0,610,362,false⟩,362,464,1⟩, +⟨⟨1,501,504,true⟩,464,464,0⟩, +⟨⟨1,501,610,true⟩,464,464,0⟩, +⟨⟨0,501,464,false⟩,464,508,1⟩, +⟨⟨1,501,541,true⟩,508,508,0⟩, +⟨⟨0,759,309,true⟩,309,509,2⟩, +⟨⟨0,292,377,true⟩,377,509,2⟩, +⟨⟨1,759,292,true⟩,509,509,0⟩, +⟨⟨0,354,340,false⟩,340,462,1⟩, +⟨⟨0,361,342,false⟩,342,462,1⟩, +⟨⟨0,578,338,false⟩,338,462,1⟩] +def chunk56 : List Entry := [⟨⟨1,354,361,true⟩,462,462,0⟩, +⟨⟨1,354,578,true⟩,462,462,0⟩, +⟨⟨0,354,462,true⟩,462,509,1⟩, +⟨⟨1,354,759,true⟩,509,509,0⟩, +⟨⟨0,536,310,false⟩,310,510,2⟩, +⟨⟨0,490,412,false⟩,412,510,2⟩, +⟨⟨1,536,490,true⟩,510,510,0⟩, +⟨⟨0,421,354,true⟩,354,463,1⟩, +⟨⟨0,424,352,true⟩,352,463,1⟩, +⟨⟨0,594,350,true⟩,350,463,1⟩, +⟨⟨1,421,424,true⟩,463,463,0⟩, +⟨⟨1,421,594,true⟩,463,463,0⟩, +⟨⟨0,421,463,false⟩,463,510,1⟩, +⟨⟨1,421,536,true⟩,510,510,0⟩, +⟨⟨0,760,310,true⟩,310,511,2⟩, +⟨⟨0,368,388,true⟩,388,511,2⟩, +⟨⟨1,760,368,true⟩,511,511,0⟩, +⟨⟨0,309,330,true⟩,330,461,1⟩, +⟨⟨0,312,328,true⟩,328,461,1⟩, +⟨⟨0,562,326,true⟩,326,461,1⟩, +⟨⟨1,309,312,true⟩,461,461,0⟩, +⟨⟨1,309,562,true⟩,461,461,0⟩, +⟨⟨0,309,461,true⟩,461,511,1⟩, +⟨⟨1,309,760,true⟩,511,511,0⟩, +⟨⟨0,537,311,false⟩,311,512,2⟩, +⟨⟨0,484,413,false⟩,413,512,2⟩, +⟨⟨1,537,484,true⟩,512,512,0⟩, +⟨⟨0,606,358,true⟩,358,463,1⟩, +⟨⟨1,606,424,true⟩,463,463,0⟩, +⟨⟨1,606,597,true⟩,463,463,0⟩, +⟨⟨0,606,463,false⟩,463,512,1⟩, +⟨⟨1,606,537,true⟩,512,512,0⟩, +⟨⟨0,761,311,true⟩,311,513,2⟩, +⟨⟨0,382,389,true⟩,389,513,2⟩, +⟨⟨1,761,382,true⟩,513,513,0⟩, +⟨⟨0,574,332,true⟩,332,461,1⟩, +⟨⟨1,574,312,true⟩,461,461,0⟩, +⟨⟨1,574,565,true⟩,461,461,0⟩, +⟨⟨0,574,461,true⟩,461,513,1⟩, +⟨⟨1,574,761,true⟩,513,513,0⟩, +⟨⟨0,529,312,false⟩,312,514,2⟩, +⟨⟨0,918,446,false⟩,446,514,2⟩, +⟨⟨1,529,918,true⟩,514,514,0⟩, +⟨⟨0,762,312,true⟩,312,515,2⟩, +⟨⟨0,689,424,true⟩,424,515,2⟩, +⟨⟨1,762,689,true⟩,515,515,0⟩, +⟨⟨0,527,297,true⟩,297,515,2⟩, +⟨⟨0,411,458,true⟩,458,515,1⟩, +⟨⟨1,527,411,true⟩,515,515,0⟩, +⟨⟨1,527,762,true⟩,515,515,0⟩, +⟨⟨0,531,313,false⟩,313,516,2⟩, +⟨⟨0,920,447,false⟩,447,516,2⟩, +⟨⟨1,531,920,true⟩,516,516,0⟩, +⟨⟨0,763,313,true⟩,313,517,2⟩, +⟨⟨0,691,425,true⟩,425,517,2⟩, +⟨⟨1,763,691,true⟩,517,517,0⟩, +⟨⟨0,517,300,false⟩,300,458,1⟩, +⟨⟨1,518,516,true⟩,458,458,0⟩, +⟨⟨1,518,517,true⟩,458,458,0⟩, +⟨⟨0,518,458,true⟩,458,517,1⟩, +⟨⟨1,518,763,true⟩,517,517,0⟩, +⟨⟨0,320,316,false⟩,316,518,2⟩, +⟨⟨0,497,366,false⟩,366,518,2⟩, +⟨⟨1,320,497,true⟩,518,518,0⟩, +⟨⟨0,686,420,false⟩,420,468,1⟩, +⟨⟨1,686,489,true⟩,468,468,0⟩, +⟨⟨1,686,674,true⟩,468,468,0⟩, +⟨⟨1,686,677,true⟩,468,468,0⟩, +⟨⟨0,686,468,false⟩,468,518,1⟩, +⟨⟨1,686,320,true⟩,518,518,0⟩, +⟨⟨0,768,316,true⟩,316,519,2⟩, +⟨⟨0,317,330,true⟩,330,519,2⟩, +⟨⟨1,768,317,true⟩,519,519,0⟩, +⟨⟨0,638,380,true⟩,380,465,1⟩, +⟨⟨1,638,297,true⟩,465,465,0⟩, +⟨⟨1,638,626,true⟩,465,465,0⟩, +⟨⟨1,638,629,true⟩,465,465,0⟩, +⟨⟨0,638,465,true⟩,465,519,1⟩, +⟨⟨1,638,768,true⟩,519,519,0⟩, +⟨⟨0,334,317,false⟩,317,520,2⟩, +⟨⟨0,499,367,false⟩,367,520,2⟩, +⟨⟨1,334,499,true⟩,520,520,0⟩, +⟨⟨0,492,468,false⟩,468,520,1⟩, +⟨⟨1,492,334,true⟩,520,520,0⟩, +⟨⟨0,769,317,true⟩,317,521,2⟩, +⟨⟨0,307,331,true⟩,331,521,2⟩, +⟨⟨1,769,307,true⟩,521,521,0⟩, +⟨⟨0,294,465,true⟩,465,521,1⟩, +⟨⟨1,294,769,true⟩,521,521,0⟩, +⟨⟨0,333,318,false⟩,318,522,2⟩, +⟨⟨0,429,354,false⟩,354,522,2⟩, +⟨⟨1,333,429,true⟩,522,522,0⟩, +⟨⟨0,670,406,true⟩,406,467,1⟩, +⟨⟨1,670,441,true⟩,467,467,0⟩, +⟨⟨1,670,658,true⟩,467,467,0⟩, +⟨⟨1,670,661,true⟩,467,467,0⟩, +⟨⟨0,670,467,false⟩,467,522,1⟩, +⟨⟨1,670,333,true⟩,522,522,0⟩, +⟨⟨0,770,318,true⟩,318,523,2⟩, +⟨⟨0,365,342,true⟩,342,523,2⟩, +⟨⟨1,770,365,true⟩,523,523,0⟩, +⟨⟨0,650,392,false⟩,392,466,1⟩, +⟨⟨1,650,376,true⟩,466,466,0⟩, +⟨⟨1,650,642,true⟩,466,466,0⟩, +⟨⟨1,650,645,true⟩,466,466,0⟩, +⟨⟨0,650,466,true⟩,466,523,1⟩, +⟨⟨1,650,770,true⟩,523,523,0⟩, +⟨⟨0,323,319,false⟩,319,524,2⟩, +⟨⟨0,419,355,false⟩,355,524,2⟩, +⟨⟨1,323,419,true⟩,524,524,0⟩, +⟨⟨0,444,467,false⟩,467,524,1⟩, +⟨⟨1,444,323,true⟩,524,524,0⟩, +⟨⟨0,771,319,true⟩,319,525,2⟩, +⟨⟨0,367,343,true⟩,343,525,2⟩, +⟨⟨1,771,367,true⟩,525,525,0⟩, +⟨⟨0,374,466,true⟩,466,525,1⟩, +⟨⟨1,374,771,true⟩,525,525,0⟩, +⟨⟨0,552,320,false⟩,320,526,2⟩, +⟨⟨0,481,414,false⟩,414,526,2⟩, +⟨⟨1,552,481,true⟩,526,526,0⟩, +⟨⟨0,622,372,false⟩,372,464,1⟩, +⟨⟨1,622,504,true⟩,464,464,0⟩, +⟨⟨1,622,613,true⟩,464,464,0⟩, +⟨⟨0,622,464,false⟩,464,526,1⟩, +⟨⟨1,622,552,true⟩,526,526,0⟩, +⟨⟨0,772,320,true⟩,320,527,2⟩, +⟨⟨0,301,378,true⟩,378,527,2⟩, +⟨⟨1,772,301,true⟩,527,527,0⟩, +⟨⟨0,570,334,true⟩,334,461,1⟩, +⟨⟨1,570,312,true⟩,461,461,0⟩, +⟨⟨1,570,562,true⟩,461,461,0⟩, +⟨⟨1,570,565,true⟩,461,461,0⟩, +⟨⟨0,570,461,true⟩,461,527,1⟩, +⟨⟨1,570,772,true⟩,527,527,0⟩, +⟨⟨0,553,321,false⟩,321,528,2⟩, +⟨⟨0,495,415,false⟩,415,528,2⟩, +⟨⟨1,553,495,true⟩,528,528,0⟩, +⟨⟨0,618,370,false⟩,370,464,1⟩, +⟨⟨1,618,504,true⟩,464,464,0⟩, +⟨⟨1,618,610,true⟩,464,464,0⟩, +⟨⟨1,618,613,true⟩,464,464,0⟩, +⟨⟨0,618,464,false⟩,464,528,1⟩, +⟨⟨1,618,553,true⟩,528,528,0⟩, +⟨⟨0,773,321,true⟩,321,529,2⟩, +⟨⟨0,303,379,true⟩,379,529,2⟩, +⟨⟨1,773,303,true⟩,529,529,0⟩, +⟨⟨0,310,461,true⟩,461,529,1⟩, +⟨⟨1,310,773,true⟩,529,529,0⟩, +⟨⟨0,556,322,false⟩,322,530,2⟩, +⟨⟨0,433,402,false⟩,402,530,2⟩, +⟨⟨1,556,433,true⟩,530,530,0⟩, +⟨⟨0,602,360,true⟩,360,463,1⟩, +⟨⟨1,602,424,true⟩,463,463,0⟩, +⟨⟨1,602,594,true⟩,463,463,0⟩, +⟨⟨1,602,597,true⟩,463,463,0⟩, +⟨⟨0,602,463,false⟩,463,530,1⟩, +⟨⟨1,602,556,true⟩,530,530,0⟩, +⟨⟨0,774,322,true⟩,322,531,2⟩, +⟨⟨0,381,390,true⟩,390,531,2⟩, +⟨⟨1,774,381,true⟩,531,531,0⟩, +⟨⟨0,586,344,false⟩,344,462,1⟩, +⟨⟨1,586,361,true⟩,462,462,0⟩, +⟨⟨1,586,581,true⟩,462,462,0⟩, +⟨⟨0,586,462,true⟩,462,531,1⟩, +⟨⟨1,586,774,true⟩,531,531,0⟩, +⟨⟨0,557,323,false⟩,323,532,2⟩, +⟨⟨0,447,403,false⟩,403,532,2⟩, +⟨⟨1,557,447,true⟩,532,532,0⟩, +⟨⟨0,422,463,false⟩,463,532,1⟩, +⟨⟨1,422,557,true⟩,532,532,0⟩, +⟨⟨0,775,323,true⟩,323,533,2⟩, +⟨⟨0,371,391,true⟩,391,533,2⟩, +⟨⟨1,775,371,true⟩,533,533,0⟩, +⟨⟨0,590,346,false⟩,346,462,1⟩, +⟨⟨1,590,361,true⟩,462,462,0⟩, +⟨⟨1,590,578,true⟩,462,462,0⟩, +⟨⟨1,590,581,true⟩,462,462,0⟩, +⟨⟨0,590,462,true⟩,462,533,1⟩, +⟨⟨1,590,775,true⟩,533,533,0⟩, +⟨⟨0,545,324,false⟩,324,534,2⟩, +⟨⟨0,721,448,false⟩,448,534,2⟩, +⟨⟨1,545,721,true⟩,534,534,0⟩, +⟨⟨0,776,324,true⟩,324,535,2⟩, +⟨⟨0,705,436,true⟩,436,535,2⟩, +⟨⟨1,776,705,true⟩,535,535,0⟩, +⟨⟨0,547,325,false⟩,325,536,2⟩, +⟨⟨0,723,449,false⟩,449,536,2⟩, +⟨⟨1,547,723,true⟩,536,536,0⟩, +⟨⟨0,777,325,true⟩,325,537,2⟩, +⟨⟨0,707,437,true⟩,437,537,2⟩, +⟨⟨1,777,707,true⟩,537,537,0⟩, +⟨⟨0,779,326,false⟩,326,538,2⟩, +⟨⟨0,793,338,false⟩,338,538,2⟩, +⟨⟨1,779,793,true⟩,538,538,0⟩, +⟨⟨0,725,448,true⟩,448,471,1⟩, +⟨⟨1,726,724,true⟩,471,471,0⟩, +⟨⟨1,726,725,true⟩,471,471,0⟩, +⟨⟨0,726,471,false⟩,471,538,1⟩, +⟨⟨1,726,779,true⟩,538,538,0⟩, +⟨⟨0,781,327,true⟩,327,539,2⟩] +def chunk57 : List Entry := [⟨⟨0,795,339,true⟩,339,539,2⟩, +⟨⟨1,781,795,true⟩,539,539,0⟩, +⟨⟨0,386,450,true⟩,450,471,1⟩, +⟨⟨0,393,454,true⟩,454,471,1⟩, +⟨⟨0,722,446,true⟩,446,471,1⟩, +⟨⟨1,386,393,true⟩,471,471,0⟩, +⟨⟨1,386,722,true⟩,471,471,0⟩, +⟨⟨0,386,471,true⟩,471,539,1⟩, +⟨⟨1,386,781,true⟩,539,539,0⟩, +⟨⟨0,782,328,false⟩,328,540,2⟩, +⟨⟨0,810,352,false⟩,352,540,2⟩, +⟨⟨1,782,810,true⟩,540,540,0⟩, +⟨⟨0,709,436,false⟩,436,470,1⟩, +⟨⟨0,714,442,false⟩,442,470,1⟩, +⟨⟨1,709,457,true⟩,470,470,0⟩, +⟨⟨1,709,714,true⟩,470,470,0⟩, +⟨⟨0,709,470,false⟩,470,540,1⟩, +⟨⟨1,709,782,true⟩,540,540,0⟩, +⟨⟨0,783,329,true⟩,329,541,2⟩, +⟨⟨0,811,353,true⟩,353,541,2⟩, +⟨⟨1,783,811,true⟩,541,541,0⟩, +⟨⟨0,718,444,false⟩,444,470,1⟩, +⟨⟨1,718,706,true⟩,470,470,0⟩, +⟨⟨1,718,714,true⟩,470,470,0⟩, +⟨⟨0,718,470,true⟩,470,541,1⟩, +⟨⟨1,718,783,true⟩,541,541,0⟩, +⟨⟨0,784,330,false⟩,330,542,2⟩, +⟨⟨0,826,366,false⟩,366,542,2⟩, +⟨⟨1,784,826,true⟩,542,542,0⟩, +⟨⟨0,466,426,true⟩,426,469,1⟩, +⟨⟨0,473,428,true⟩,428,469,1⟩, +⟨⟨0,690,422,true⟩,422,469,1⟩, +⟨⟨1,466,473,true⟩,469,469,0⟩, +⟨⟨1,466,690,true⟩,469,469,0⟩, +⟨⟨0,466,469,false⟩,469,542,1⟩, +⟨⟨1,466,784,true⟩,542,542,0⟩, +⟨⟨0,785,331,true⟩,331,543,2⟩, +⟨⟨0,827,367,true⟩,367,543,2⟩, +⟨⟨1,785,827,true⟩,543,543,0⟩, +⟨⟨0,698,432,true⟩,432,469,1⟩, +⟨⟨1,698,473,true⟩,469,469,0⟩, +⟨⟨1,698,693,true⟩,469,469,0⟩, +⟨⟨0,698,469,true⟩,469,543,1⟩, +⟨⟨1,698,785,true⟩,543,543,0⟩, +⟨⟨0,572,332,false⟩,332,544,2⟩, +⟨⟨0,474,426,false⟩,426,544,2⟩, +⟨⟨1,572,474,true⟩,544,544,0⟩, +⟨⟨0,932,464,false⟩,464,544,1⟩, +⟨⟨1,932,572,true⟩,544,544,0⟩, +⟨⟨0,786,332,true⟩,332,545,2⟩, +⟨⟨0,636,380,true⟩,380,545,2⟩, +⟨⟨1,786,636,true⟩,545,545,0⟩, +⟨⟨0,549,324,false⟩,324,460,1⟩, +⟨⟨1,550,548,true⟩,460,460,0⟩, +⟨⟨1,550,549,true⟩,460,460,0⟩, +⟨⟨0,550,460,true⟩,460,545,1⟩, +⟨⟨1,550,786,true⟩,545,545,0⟩, +⟨⟨0,573,333,false⟩,333,546,2⟩, +⟨⟨0,468,427,false⟩,427,546,2⟩, +⟨⟨1,573,468,true⟩,546,546,0⟩, +⟨⟨0,933,464,false⟩,464,546,1⟩, +⟨⟨1,933,573,true⟩,546,546,0⟩, +⟨⟨0,787,333,true⟩,333,547,2⟩, +⟨⟨0,637,381,true⟩,381,547,2⟩, +⟨⟨1,787,637,true⟩,547,547,0⟩, +⟨⟨0,325,318,false⟩,318,460,1⟩, +⟨⟨0,328,316,false⟩,316,460,1⟩, +⟨⟨0,546,314,false⟩,314,460,1⟩, +⟨⟨1,325,328,true⟩,460,460,0⟩, +⟨⟨1,325,546,true⟩,460,460,0⟩, +⟨⟨0,325,460,true⟩,460,547,1⟩, +⟨⟨1,325,787,true⟩,547,547,0⟩, +⟨⟨0,568,334,false⟩,334,548,2⟩, +⟨⟨0,458,438,false⟩,438,548,2⟩, +⟨⟨1,568,458,true⟩,548,548,0⟩, +⟨⟨0,934,0,false⟩,0,548,5⟩, +⟨⟨1,934,568,true⟩,548,548,0⟩, +⟨⟨0,788,334,true⟩,334,549,2⟩, +⟨⟨0,648,392,true⟩,392,549,2⟩, +⟨⟨1,788,648,true⟩,549,549,0⟩, +⟨⟨0,543,309,true⟩,309,549,2⟩, +⟨⟨0,343,307,true⟩,307,549,2⟩, +⟨⟨1,543,343,true⟩,549,549,0⟩, +⟨⟨1,543,788,true⟩,549,549,0⟩, +⟨⟨0,569,335,false⟩,335,550,2⟩, +⟨⟨0,452,439,false⟩,439,550,2⟩, +⟨⟨1,569,452,true⟩,550,550,0⟩, +⟨⟨0,935,0,false⟩,0,550,5⟩, +⟨⟨1,935,569,true⟩,550,550,0⟩, +⟨⟨0,789,335,true⟩,335,551,2⟩, +⟨⟨0,649,393,true⟩,393,551,2⟩, +⟨⟨1,789,649,true⟩,551,551,0⟩, +⟨⟨0,341,306,true⟩,306,459,1⟩, +⟨⟨0,344,304,true⟩,304,459,1⟩, +⟨⟨0,530,302,true⟩,302,459,1⟩, +⟨⟨1,341,344,true⟩,459,459,0⟩, +⟨⟨1,341,530,true⟩,459,459,0⟩, +⟨⟨0,341,459,true⟩,459,551,1⟩, +⟨⟨1,341,789,true⟩,551,551,0⟩, +⟨⟨0,561,336,false⟩,336,552,2⟩, +⟨⟨0,384,450,false⟩,450,552,2⟩, +⟨⟨1,561,384,true⟩,552,552,0⟩, +⟨⟨0,790,336,true⟩,336,553,2⟩, +⟨⟨0,657,404,true⟩,404,553,2⟩, +⟨⟨1,790,657,true⟩,553,553,0⟩, +⟨⟨0,402,292,false⟩,292,458,1⟩, +⟨⟨0,409,294,false⟩,294,458,1⟩, +⟨⟨0,514,290,false⟩,290,458,1⟩, +⟨⟨1,402,409,true⟩,458,458,0⟩, +⟨⟨1,402,514,true⟩,458,458,0⟩, +⟨⟨0,402,458,true⟩,458,553,1⟩, +⟨⟨1,402,790,true⟩,553,553,0⟩, +⟨⟨0,563,337,false⟩,337,554,2⟩, +⟨⟨0,388,451,false⟩,451,554,2⟩, +⟨⟨1,563,388,true⟩,554,554,0⟩, +⟨⟨0,791,337,true⟩,337,555,2⟩, +⟨⟨0,659,405,true⟩,405,555,2⟩, +⟨⟨1,791,659,true⟩,555,555,0⟩, +⟨⟨0,522,298,false⟩,298,458,1⟩, +⟨⟨1,522,409,true⟩,458,458,0⟩, +⟨⟨1,522,517,true⟩,458,458,0⟩, +⟨⟨0,522,458,true⟩,458,555,1⟩, +⟨⟨1,522,791,true⟩,555,555,0⟩, +⟨⟨0,796,340,false⟩,340,556,2⟩, +⟨⟨0,824,364,false⟩,364,556,2⟩, +⟨⟨1,796,824,true⟩,556,556,0⟩, +⟨⟨0,710,470,false⟩,470,556,1⟩, +⟨⟨1,710,796,true⟩,556,556,0⟩, +⟨⟨0,797,341,true⟩,341,557,2⟩, +⟨⟨0,825,365,true⟩,365,557,2⟩, +⟨⟨1,797,825,true⟩,557,557,0⟩, +⟨⟨0,936,470,true⟩,470,557,1⟩, +⟨⟨1,936,797,true⟩,557,557,0⟩, +⟨⟨0,798,342,false⟩,342,558,2⟩, +⟨⟨0,812,354,false⟩,354,558,2⟩, +⟨⟨1,798,812,true⟩,558,558,0⟩, +⟨⟨0,702,430,true⟩,430,469,1⟩, +⟨⟨1,702,473,true⟩,469,469,0⟩, +⟨⟨1,702,690,true⟩,469,469,0⟩, +⟨⟨1,702,693,true⟩,469,469,0⟩, +⟨⟨0,702,469,false⟩,469,558,1⟩, +⟨⟨1,702,798,true⟩,558,558,0⟩, +⟨⟨0,799,343,true⟩,343,559,2⟩, +⟨⟨0,813,355,true⟩,355,559,2⟩, +⟨⟨1,799,813,true⟩,559,559,0⟩, +⟨⟨0,476,469,true⟩,469,559,1⟩, +⟨⟨1,476,799,true⟩,559,559,0⟩, +⟨⟨0,584,344,false⟩,344,560,2⟩, +⟨⟨0,449,440,false⟩,440,560,2⟩, +⟨⟨1,584,449,true⟩,560,560,0⟩, +⟨⟨0,937,464,false⟩,464,560,1⟩, +⟨⟨1,937,584,true⟩,560,560,0⟩, +⟨⟨0,800,344,true⟩,344,561,2⟩, +⟨⟨0,632,382,true⟩,382,561,2⟩, +⟨⟨1,800,632,true⟩,561,561,0⟩, +⟨⟨0,542,308,true⟩,308,459,1⟩, +⟨⟨1,542,344,true⟩,459,459,0⟩, +⟨⟨1,542,533,true⟩,459,459,0⟩, +⟨⟨0,542,459,true⟩,459,561,1⟩, +⟨⟨1,542,800,true⟩,561,561,0⟩, +⟨⟨0,585,345,false⟩,345,562,2⟩, +⟨⟨0,463,441,false⟩,441,562,2⟩, +⟨⟨1,585,463,true⟩,562,562,0⟩, +⟨⟨0,938,464,false⟩,464,562,1⟩, +⟨⟨1,938,585,true⟩,562,562,0⟩, +⟨⟨0,801,345,true⟩,345,563,2⟩, +⟨⟨0,633,383,true⟩,383,563,2⟩, +⟨⟨1,801,633,true⟩,563,563,0⟩, +⟨⟨0,538,310,true⟩,310,459,1⟩, +⟨⟨1,538,344,true⟩,459,459,0⟩, +⟨⟨1,538,530,true⟩,459,459,0⟩, +⟨⟨1,538,533,true⟩,459,459,0⟩, +⟨⟨0,538,459,true⟩,459,563,1⟩, +⟨⟨1,538,801,true⟩,563,563,0⟩, +⟨⟨0,588,346,false⟩,346,564,2⟩, +⟨⟨0,465,428,false⟩,428,564,2⟩, +⟨⟨1,588,465,true⟩,564,564,0⟩, +⟨⟨0,939,0,false⟩,0,564,5⟩, +⟨⟨1,939,588,true⟩,564,564,0⟩, +⟨⟨0,802,346,true⟩,346,565,2⟩, +⟨⟨0,652,394,true⟩,394,565,2⟩, +⟨⟨1,802,652,true⟩,565,565,0⟩, +⟨⟨0,558,322,false⟩,322,460,1⟩, +⟨⟨1,558,328,true⟩,460,460,0⟩, +⟨⟨1,558,549,true⟩,460,460,0⟩, +⟨⟨0,558,460,true⟩,460,565,1⟩, +⟨⟨1,558,802,true⟩,565,565,0⟩, +⟨⟨0,589,347,false⟩,347,566,2⟩, +⟨⟨0,479,429,false⟩,429,566,2⟩, +⟨⟨1,589,479,true⟩,566,566,0⟩, +⟨⟨0,940,0,false⟩,0,566,5⟩, +⟨⟨1,940,589,true⟩,566,566,0⟩, +⟨⟨0,803,347,true⟩,347,567,2⟩, +⟨⟨0,653,395,true⟩,395,567,2⟩, +⟨⟨1,803,653,true⟩,567,567,0⟩, +⟨⟨0,554,320,false⟩,320,460,1⟩, +⟨⟨1,554,328,true⟩,460,460,0⟩, +⟨⟨1,554,546,true⟩,460,460,0⟩, +⟨⟨1,554,549,true⟩,460,460,0⟩, +⟨⟨0,554,460,true⟩,460,567,1⟩] +def chunk58 : List Entry := [⟨⟨1,554,803,true⟩,567,567,0⟩, +⟨⟨0,577,348,false⟩,348,568,2⟩, +⟨⟨0,728,452,false⟩,452,568,2⟩, +⟨⟨1,577,728,true⟩,568,568,0⟩, +⟨⟨0,804,348,true⟩,348,569,2⟩, +⟨⟨0,673,416,true⟩,416,569,2⟩, +⟨⟨1,804,673,true⟩,569,569,0⟩, +⟨⟨0,526,296,false⟩,296,458,1⟩, +⟨⟨1,526,409,true⟩,458,458,0⟩, +⟨⟨1,526,514,true⟩,458,458,0⟩, +⟨⟨1,526,517,true⟩,458,458,0⟩, +⟨⟨0,526,458,true⟩,458,569,1⟩, +⟨⟨1,526,804,true⟩,569,569,0⟩, +⟨⟨0,579,349,false⟩,349,570,2⟩, +⟨⟨0,729,453,false⟩,453,570,2⟩, +⟨⟨1,579,729,true⟩,570,570,0⟩, +⟨⟨0,805,349,true⟩,349,571,2⟩, +⟨⟨0,675,417,true⟩,417,571,2⟩, +⟨⟨1,805,675,true⟩,571,571,0⟩, +⟨⟨0,406,458,true⟩,458,571,1⟩, +⟨⟨1,406,805,true⟩,571,571,0⟩, +⟨⟨0,807,350,false⟩,350,572,2⟩, +⟨⟨0,821,362,false⟩,362,572,2⟩, +⟨⟨1,807,821,true⟩,572,572,0⟩, +⟨⟨0,730,452,true⟩,452,471,1⟩, +⟨⟨1,730,393,true⟩,471,471,0⟩, +⟨⟨1,730,725,true⟩,471,471,0⟩, +⟨⟨0,730,471,false⟩,471,572,1⟩, +⟨⟨1,730,807,true⟩,572,572,0⟩, +⟨⟨0,809,351,true⟩,351,573,2⟩, +⟨⟨0,823,363,true⟩,363,573,2⟩, +⟨⟨1,809,823,true⟩,573,573,0⟩, +⟨⟨0,734,456,true⟩,456,471,1⟩, +⟨⟨1,734,393,true⟩,471,471,0⟩, +⟨⟨1,734,722,true⟩,471,471,0⟩, +⟨⟨1,734,725,true⟩,471,471,0⟩, +⟨⟨0,734,471,true⟩,471,573,1⟩, +⟨⟨1,734,809,true⟩,573,573,0⟩, +⟨⟨0,593,356,false⟩,356,574,2⟩, +⟨⟨0,397,454,false⟩,454,574,2⟩, +⟨⟨1,593,397,true⟩,574,574,0⟩, +⟨⟨0,814,356,true⟩,356,575,2⟩, +⟨⟨0,625,384,true⟩,384,575,2⟩, +⟨⟨1,814,625,true⟩,575,575,0⟩, +⟨⟨0,252,458,true⟩,458,575,1⟩, +⟨⟨1,252,814,true⟩,575,575,0⟩, +⟨⟨0,595,357,false⟩,357,576,2⟩, +⟨⟨0,399,455,false⟩,455,576,2⟩, +⟨⟨1,595,399,true⟩,576,576,0⟩, +⟨⟨0,815,357,true⟩,357,577,2⟩, +⟨⟨0,627,385,true⟩,385,577,2⟩, +⟨⟨1,815,627,true⟩,577,577,0⟩, +⟨⟨0,941,458,true⟩,458,577,1⟩, +⟨⟨1,941,815,true⟩,577,577,0⟩, +⟨⟨0,604,358,false⟩,358,578,2⟩, +⟨⟨0,700,430,false⟩,430,578,2⟩, +⟨⟨1,604,700,true⟩,578,578,0⟩, +⟨⟨0,942,462,false⟩,462,578,1⟩, +⟨⟨1,942,604,true⟩,578,578,0⟩, +⟨⟨0,816,358,true⟩,358,579,2⟩, +⟨⟨0,668,406,true⟩,406,579,2⟩, +⟨⟨1,816,668,true⟩,579,579,0⟩, +⟨⟨0,943,460,true⟩,460,579,1⟩, +⟨⟨1,943,816,true⟩,579,579,0⟩, +⟨⟨0,605,359,false⟩,359,580,2⟩, +⟨⟨0,701,431,false⟩,431,580,2⟩, +⟨⟨1,605,701,true⟩,580,580,0⟩, +⟨⟨0,944,462,false⟩,462,580,1⟩, +⟨⟨1,944,605,true⟩,580,580,0⟩, +⟨⟨0,817,359,true⟩,359,581,2⟩, +⟨⟨0,669,407,true⟩,407,581,2⟩, +⟨⟨1,817,669,true⟩,581,581,0⟩, +⟨⟨0,945,460,true⟩,460,581,1⟩, +⟨⟨1,945,817,true⟩,581,581,0⟩, +⟨⟨0,600,360,false⟩,360,582,2⟩, +⟨⟨0,712,442,false⟩,442,582,2⟩, +⟨⟨1,600,712,true⟩,582,582,0⟩, +⟨⟨0,946,0,false⟩,0,582,5⟩, +⟨⟨1,946,600,true⟩,582,582,0⟩, +⟨⟨0,818,360,true⟩,360,583,2⟩, +⟨⟨0,680,418,true⟩,418,583,2⟩, +⟨⟨1,818,680,true⟩,583,583,0⟩, +⟨⟨0,532,459,true⟩,459,583,1⟩, +⟨⟨1,532,818,true⟩,583,583,0⟩, +⟨⟨0,601,361,false⟩,361,584,2⟩, +⟨⟨0,713,443,false⟩,443,584,2⟩, +⟨⟨1,601,713,true⟩,584,584,0⟩, +⟨⟨0,947,0,false⟩,0,584,5⟩, +⟨⟨1,947,601,true⟩,584,584,0⟩, +⟨⟨0,819,361,true⟩,361,585,2⟩, +⟨⟨0,681,419,true⟩,419,585,2⟩, +⟨⟨1,819,681,true⟩,585,585,0⟩, +⟨⟨0,948,0,true⟩,0,585,5⟩, +⟨⟨1,948,819,true⟩,585,585,0⟩, +⟨⟨0,609,368,false⟩,368,586,2⟩, +⟨⟨0,732,456,false⟩,456,586,2⟩, +⟨⟨1,609,732,true⟩,586,586,0⟩, +⟨⟨0,828,368,true⟩,368,587,2⟩, +⟨⟨0,641,396,true⟩,396,587,2⟩, +⟨⟨1,828,641,true⟩,587,587,0⟩, +⟨⟨0,949,458,true⟩,458,587,1⟩, +⟨⟨1,949,828,true⟩,587,587,0⟩, +⟨⟨0,611,369,false⟩,369,588,2⟩, +⟨⟨0,733,457,false⟩,457,588,2⟩, +⟨⟨1,611,733,true⟩,588,588,0⟩, +⟨⟨0,829,369,true⟩,369,589,2⟩, +⟨⟨0,643,397,true⟩,397,589,2⟩, +⟨⟨1,829,643,true⟩,589,589,0⟩, +⟨⟨0,950,0,true⟩,0,589,5⟩, +⟨⟨1,950,829,true⟩,589,589,0⟩, +⟨⟨0,616,370,false⟩,370,590,2⟩, +⟨⟨0,716,444,false⟩,444,590,2⟩, +⟨⟨1,616,716,true⟩,590,590,0⟩, +⟨⟨0,951,462,false⟩,462,590,1⟩, +⟨⟨1,951,616,true⟩,590,590,0⟩, +⟨⟨0,830,370,true⟩,370,591,2⟩, +⟨⟨0,664,408,true⟩,408,591,2⟩, +⟨⟨1,830,664,true⟩,591,591,0⟩, +⟨⟨0,952,0,true⟩,0,591,5⟩, +⟨⟨1,952,830,true⟩,591,591,0⟩, +⟨⟨0,617,371,false⟩,371,592,2⟩, +⟨⟨0,717,445,false⟩,445,592,2⟩, +⟨⟨1,617,717,true⟩,592,592,0⟩, +⟨⟨0,953,462,false⟩,462,592,1⟩, +⟨⟨1,953,617,true⟩,592,592,0⟩, +⟨⟨0,831,371,true⟩,371,593,2⟩, +⟨⟨0,665,409,true⟩,409,593,2⟩, +⟨⟨1,831,665,true⟩,593,593,0⟩, +⟨⟨0,954,0,true⟩,0,593,5⟩, +⟨⟨1,954,831,true⟩,593,593,0⟩, +⟨⟨0,620,372,false⟩,372,594,2⟩, +⟨⟨0,696,432,false⟩,432,594,2⟩, +⟨⟨1,620,696,true⟩,594,594,0⟩, +⟨⟨0,955,0,false⟩,0,594,5⟩, +⟨⟨1,955,620,true⟩,594,594,0⟩, +⟨⟨0,832,372,true⟩,372,595,2⟩, +⟨⟨0,684,420,true⟩,420,595,2⟩, +⟨⟨1,832,684,true⟩,595,595,0⟩, +⟨⟨0,956,460,true⟩,460,595,1⟩, +⟨⟨1,956,832,true⟩,595,595,0⟩, +⟨⟨0,621,373,false⟩,373,596,2⟩, +⟨⟨0,697,433,false⟩,433,596,2⟩, +⟨⟨1,621,697,true⟩,596,596,0⟩, +⟨⟨0,957,0,false⟩,0,596,5⟩, +⟨⟨1,957,621,true⟩,596,596,0⟩, +⟨⟨0,833,373,true⟩,373,597,2⟩, +⟨⟨0,685,421,true⟩,421,597,2⟩, +⟨⟨1,833,685,true⟩,597,597,0⟩, +⟨⟨0,958,460,true⟩,460,597,1⟩, +⟨⟨1,958,833,true⟩,597,597,0⟩, +⟨⟨0,835,374,false⟩,374,598,2⟩, +⟨⟨0,849,386,false⟩,386,598,2⟩, +⟨⟨1,835,849,true⟩,598,598,0⟩, +⟨⟨0,959,471,false⟩,471,598,1⟩, +⟨⟨1,959,835,true⟩,598,598,0⟩, +⟨⟨0,837,375,true⟩,375,599,2⟩, +⟨⟨0,851,387,true⟩,387,599,2⟩, +⟨⟨1,837,851,true⟩,599,599,0⟩, +⟨⟨0,960,471,true⟩,471,599,1⟩, +⟨⟨1,960,837,true⟩,599,599,0⟩, +⟨⟨0,838,376,false⟩,376,600,2⟩, +⟨⟨0,866,400,false⟩,400,600,2⟩, +⟨⟨1,838,866,true⟩,600,600,0⟩, +⟨⟨0,961,470,false⟩,470,600,1⟩, +⟨⟨1,961,838,true⟩,600,600,0⟩, +⟨⟨0,839,377,true⟩,377,601,2⟩, +⟨⟨0,867,401,true⟩,401,601,2⟩, +⟨⟨1,839,867,true⟩,601,601,0⟩, +⟨⟨0,962,0,true⟩,0,601,5⟩, +⟨⟨1,962,839,true⟩,601,601,0⟩, +⟨⟨0,840,378,false⟩,378,602,2⟩, +⟨⟨0,882,414,false⟩,414,602,2⟩, +⟨⟨1,840,882,true⟩,602,602,0⟩, +⟨⟨0,963,0,false⟩,0,602,5⟩, +⟨⟨1,963,840,true⟩,602,602,0⟩, +⟨⟨0,841,379,true⟩,379,603,2⟩, +⟨⟨0,883,415,true⟩,415,603,2⟩, +⟨⟨1,841,883,true⟩,603,603,0⟩, +⟨⟨0,964,0,true⟩,0,603,5⟩, +⟨⟨1,964,841,true⟩,603,603,0⟩, +⟨⟨0,842,380,false⟩,380,604,2⟩, +⟨⟨0,896,426,false⟩,426,604,2⟩, +⟨⟨1,842,896,true⟩,604,604,0⟩, +⟨⟨0,965,0,false⟩,0,604,5⟩, +⟨⟨1,965,842,true⟩,604,604,0⟩, +⟨⟨0,843,381,true⟩,381,605,2⟩, +⟨⟨0,897,427,true⟩,427,605,2⟩, +⟨⟨1,843,897,true⟩,605,605,0⟩, +⟨⟨0,966,0,true⟩,0,605,5⟩, +⟨⟨1,966,843,true⟩,605,605,0⟩, +⟨⟨0,844,382,false⟩,382,606,2⟩, +⟨⟨0,912,440,false⟩,440,606,2⟩, +⟨⟨1,844,912,true⟩,606,606,0⟩, +⟨⟨0,967,0,false⟩,0,606,5⟩, +⟨⟨1,967,844,true⟩,606,606,0⟩, +⟨⟨0,845,383,true⟩,383,607,2⟩, +⟨⟨0,913,441,true⟩,441,607,2⟩, +⟨⟨1,845,913,true⟩,607,607,0⟩, +⟨⟨0,968,0,true⟩,0,607,5⟩, +⟨⟨1,968,845,true⟩,607,607,0⟩] +def chunk59 : List Entry := [⟨⟨0,846,384,false⟩,384,608,2⟩, +⟨⟨0,928,454,false⟩,454,608,2⟩, +⟨⟨1,846,928,true⟩,608,608,0⟩, +⟨⟨0,847,385,true⟩,385,609,2⟩, +⟨⟨0,929,455,true⟩,455,609,2⟩, +⟨⟨1,847,929,true⟩,609,609,0⟩, +⟨⟨0,852,388,false⟩,388,610,2⟩, +⟨⟨0,880,412,false⟩,412,610,2⟩, +⟨⟨1,852,880,true⟩,610,610,0⟩, +⟨⟨0,969,0,false⟩,0,610,5⟩, +⟨⟨1,969,852,true⟩,610,610,0⟩, +⟨⟨0,853,389,true⟩,389,611,2⟩, +⟨⟨0,881,413,true⟩,413,611,2⟩, +⟨⟨1,853,881,true⟩,611,611,0⟩, +⟨⟨0,970,0,true⟩,0,611,5⟩, +⟨⟨1,970,853,true⟩,611,611,0⟩, +⟨⟨0,854,390,false⟩,390,612,2⟩, +⟨⟨0,868,402,false⟩,402,612,2⟩, +⟨⟨1,854,868,true⟩,612,612,0⟩, +⟨⟨0,971,0,false⟩,0,612,5⟩, +⟨⟨1,971,854,true⟩,612,612,0⟩, +⟨⟨0,855,391,true⟩,391,613,2⟩, +⟨⟨0,869,403,true⟩,403,613,2⟩, +⟨⟨1,855,869,true⟩,613,613,0⟩, +⟨⟨0,972,0,true⟩,0,613,5⟩, +⟨⟨1,972,855,true⟩,613,613,0⟩, +⟨⟨0,856,392,false⟩,392,614,2⟩, +⟨⟨0,910,438,false⟩,438,614,2⟩, +⟨⟨1,856,910,true⟩,614,614,0⟩, +⟨⟨0,973,0,false⟩,0,614,5⟩, +⟨⟨1,973,856,true⟩,614,614,0⟩, +⟨⟨0,857,393,true⟩,393,615,2⟩, +⟨⟨0,911,439,true⟩,439,615,2⟩, +⟨⟨1,857,911,true⟩,615,615,0⟩, +⟨⟨0,974,0,true⟩,0,615,5⟩, +⟨⟨1,974,857,true⟩,615,615,0⟩, +⟨⟨0,858,394,false⟩,394,616,2⟩, +⟨⟨0,898,428,false⟩,428,616,2⟩, +⟨⟨1,858,898,true⟩,616,616,0⟩, +⟨⟨0,975,0,false⟩,0,616,5⟩, +⟨⟨1,975,858,true⟩,616,616,0⟩, +⟨⟨0,859,395,true⟩,395,617,2⟩, +⟨⟨0,899,429,true⟩,429,617,2⟩, +⟨⟨1,859,899,true⟩,617,617,0⟩, +⟨⟨0,976,0,true⟩,0,617,5⟩, +⟨⟨1,976,859,true⟩,617,617,0⟩, +⟨⟨0,860,396,false⟩,396,618,2⟩, +⟨⟨0,930,456,false⟩,456,618,2⟩, +⟨⟨1,860,930,true⟩,618,618,0⟩, +⟨⟨0,861,397,true⟩,397,619,2⟩, +⟨⟨0,931,457,true⟩,457,619,2⟩, +⟨⟨1,861,931,true⟩,619,619,0⟩, +⟨⟨0,863,398,false⟩,398,620,2⟩, +⟨⟨0,877,410,false⟩,410,620,2⟩, +⟨⟨1,863,877,true⟩,620,620,0⟩, +⟨⟨0,977,471,false⟩,471,620,1⟩, +⟨⟨1,977,863,true⟩,620,620,0⟩, +⟨⟨0,865,399,true⟩,399,621,2⟩, +⟨⟨0,879,411,true⟩,411,621,2⟩, +⟨⟨1,865,879,true⟩,621,621,0⟩, +⟨⟨0,978,471,true⟩,471,621,1⟩, +⟨⟨1,978,865,true⟩,621,621,0⟩, +⟨⟨0,870,404,false⟩,404,622,2⟩, +⟨⟨0,924,450,false⟩,450,622,2⟩, +⟨⟨1,870,924,true⟩,622,622,0⟩, +⟨⟨0,871,405,true⟩,405,623,2⟩, +⟨⟨0,925,451,true⟩,451,623,2⟩, +⟨⟨1,871,925,true⟩,623,623,0⟩, +⟨⟨0,872,406,false⟩,406,624,2⟩, +⟨⟨0,900,430,false⟩,430,624,2⟩, +⟨⟨1,872,900,true⟩,624,624,0⟩, +⟨⟨0,979,0,false⟩,0,624,5⟩, +⟨⟨1,979,872,true⟩,624,624,0⟩, +⟨⟨0,873,407,true⟩,407,625,2⟩, +⟨⟨0,901,431,true⟩,431,625,2⟩, +⟨⟨1,873,901,true⟩,625,625,0⟩, +⟨⟨0,980,0,true⟩,0,625,5⟩, +⟨⟨1,980,873,true⟩,625,625,0⟩, +⟨⟨0,874,408,false⟩,408,626,2⟩, +⟨⟨0,916,444,false⟩,444,626,2⟩, +⟨⟨1,874,916,true⟩,626,626,0⟩, +⟨⟨0,981,0,false⟩,0,626,5⟩, +⟨⟨1,981,874,true⟩,626,626,0⟩, +⟨⟨0,875,409,true⟩,409,627,2⟩, +⟨⟨0,917,445,true⟩,445,627,2⟩, +⟨⟨1,875,917,true⟩,627,627,0⟩, +⟨⟨0,982,0,true⟩,0,627,5⟩, +⟨⟨1,982,875,true⟩,627,627,0⟩, +⟨⟨0,884,416,false⟩,416,628,2⟩, +⟨⟨0,926,452,false⟩,452,628,2⟩, +⟨⟨1,884,926,true⟩,628,628,0⟩, +⟨⟨0,885,417,true⟩,417,629,2⟩, +⟨⟨0,927,453,true⟩,453,629,2⟩, +⟨⟨1,885,927,true⟩,629,629,0⟩, +⟨⟨0,886,418,false⟩,418,630,2⟩, +⟨⟨0,914,442,false⟩,442,630,2⟩, +⟨⟨1,886,914,true⟩,630,630,0⟩, +⟨⟨0,983,0,false⟩,0,630,5⟩, +⟨⟨1,983,886,true⟩,630,630,0⟩, +⟨⟨0,887,419,true⟩,419,631,2⟩, +⟨⟨0,915,443,true⟩,443,631,2⟩, +⟨⟨1,887,915,true⟩,631,631,0⟩, +⟨⟨0,984,0,true⟩,0,631,5⟩, +⟨⟨1,984,887,true⟩,631,631,0⟩, +⟨⟨0,888,420,false⟩,420,632,2⟩, +⟨⟨0,902,432,false⟩,432,632,2⟩, +⟨⟨1,888,902,true⟩,632,632,0⟩, +⟨⟨0,985,0,false⟩,0,632,5⟩, +⟨⟨1,985,888,true⟩,632,632,0⟩, +⟨⟨0,889,421,true⟩,421,633,2⟩, +⟨⟨0,903,433,true⟩,433,633,2⟩, +⟨⟨1,889,903,true⟩,633,633,0⟩, +⟨⟨0,986,0,true⟩,0,633,5⟩, +⟨⟨1,986,889,true⟩,633,633,0⟩, +⟨⟨0,891,422,false⟩,422,634,2⟩, +⟨⟨0,905,434,false⟩,434,634,2⟩, +⟨⟨1,891,905,true⟩,634,634,0⟩, +⟨⟨0,893,423,true⟩,423,635,2⟩, +⟨⟨0,907,435,true⟩,435,635,2⟩, +⟨⟨1,893,907,true⟩,635,635,0⟩, +⟨⟨0,894,424,false⟩,424,636,2⟩, +⟨⟨0,919,446,false⟩,446,636,2⟩, +⟨⟨1,894,919,true⟩,636,636,0⟩, +⟨⟨0,895,425,true⟩,425,637,2⟩, +⟨⟨0,921,447,true⟩,447,637,2⟩, +⟨⟨1,895,921,true⟩,637,637,0⟩, +⟨⟨0,908,436,false⟩,436,638,2⟩, +⟨⟨0,922,448,false⟩,448,638,2⟩, +⟨⟨1,908,922,true⟩,638,638,0⟩, +⟨⟨0,909,437,true⟩,437,639,2⟩, +⟨⟨0,923,449,true⟩,449,639,2⟩, +⟨⟨1,909,923,true⟩,639,639,0⟩, +⟨⟨0,753,497,false⟩,497,640,1⟩, +⟨⟨0,69,71,false⟩,71,640,5⟩, +⟨⟨1,753,69,true⟩,640,640,0⟩, +⟨⟨0,70,125,false⟩,125,640,4⟩, +⟨⟨1,753,70,true⟩,640,640,0⟩, +⟨⟨0,837,599,true⟩,599,641,1⟩, +⟨⟨0,809,573,true⟩,573,641,1⟩, +⟨⟨1,837,809,true⟩,641,641,0⟩, +⟨⟨0,407,133,true⟩,133,641,4⟩, +⟨⟨1,407,837,true⟩,641,641,0⟩, +⟨⟨0,865,621,false⟩,621,642,1⟩, +⟨⟨0,781,539,false⟩,539,642,1⟩, +⟨⟨1,865,781,true⟩,642,642,0⟩, +⟨⟨0,863,620,true⟩,620,643,1⟩, +⟨⟨0,779,538,true⟩,538,643,1⟩, +⟨⟨1,863,779,true⟩,643,643,0⟩, +⟨⟨0,835,598,false⟩,598,644,1⟩, +⟨⟨0,807,572,false⟩,572,644,1⟩, +⟨⟨1,835,807,true⟩,644,644,0⟩, +⟨⟨0,401,130,false⟩,130,644,4⟩, +⟨⟨1,401,835,true⟩,644,644,0⟩, +⟨⟨0,751,496,true⟩,496,645,1⟩, +⟨⟨0,64,66,true⟩,66,645,5⟩, +⟨⟨1,751,64,true⟩,645,645,0⟩, +⟨⟨0,67,122,true⟩,122,645,4⟩, +⟨⟨1,751,67,true⟩,645,645,0⟩, +⟨⟨0,412,129,false⟩,129,642,4⟩, +⟨⟨1,412,865,true⟩,642,642,0⟩, +⟨⟨0,410,126,true⟩,126,643,4⟩, +⟨⟨1,410,863,true⟩,643,643,0⟩, +⟨⟨0,735,497,false⟩,497,646,1⟩, +⟨⟨0,68,70,false⟩,70,646,5⟩, +⟨⟨1,735,68,true⟩,646,646,0⟩, +⟨⟨0,71,124,false⟩,124,646,4⟩, +⟨⟨1,735,71,true⟩,646,646,0⟩, +⟨⟨0,960,599,true⟩,599,647,1⟩, +⟨⟨0,730,572,true⟩,572,647,1⟩, +⟨⟨1,960,730,true⟩,647,647,0⟩, +⟨⟨0,405,131,true⟩,131,647,4⟩, +⟨⟨1,405,960,true⟩,647,647,0⟩, +⟨⟨0,977,620,false⟩,620,648,1⟩, +⟨⟨0,386,539,false⟩,539,648,1⟩, +⟨⟨1,977,386,true⟩,648,648,0⟩, +⟨⟨0,978,621,true⟩,621,649,1⟩, +⟨⟨0,726,538,true⟩,538,649,1⟩, +⟨⟨1,978,726,true⟩,649,649,0⟩, +⟨⟨0,959,598,false⟩,598,650,1⟩, +⟨⟨0,734,573,false⟩,573,650,1⟩, +⟨⟨1,959,734,true⟩,650,650,0⟩, +⟨⟨0,403,132,false⟩,132,650,4⟩, +⟨⟨1,403,959,true⟩,650,650,0⟩, +⟨⟨0,731,496,true⟩,496,651,1⟩, +⟨⟨0,65,67,true⟩,67,651,5⟩, +⟨⟨1,731,65,true⟩,651,651,0⟩, +⟨⟨0,66,123,true⟩,123,651,4⟩, +⟨⟨1,731,66,true⟩,651,651,0⟩, +⟨⟨0,414,128,false⟩,128,648,4⟩, +⟨⟨1,414,977,true⟩,648,648,0⟩, +⟨⟨0,408,127,true⟩,127,649,4⟩, +⟨⟨1,408,978,true⟩,649,649,0⟩, +⟨⟨0,738,474,false⟩,474,652,1⟩, +⟨⟨0,37,39,false⟩,39,652,5⟩, +⟨⟨1,738,37,true⟩,652,652,0⟩, +⟨⟨0,38,137,false⟩,137,652,4⟩, +⟨⟨1,738,38,true⟩,652,652,0⟩, +⟨⟨0,839,601,true⟩,601,653,1⟩, +⟨⟨0,797,557,true⟩,557,653,1⟩, +⟨⟨1,839,797,true⟩,653,653,0⟩] +def chunk60 : List Entry := [⟨⟨0,853,611,false⟩,611,654,1⟩, +⟨⟨0,783,541,false⟩,541,654,1⟩, +⟨⟨1,853,783,true⟩,654,654,0⟩, +⟨⟨0,342,141,false⟩,141,654,4⟩, +⟨⟨1,342,853,true⟩,654,654,0⟩, +⟨⟨0,852,610,true⟩,610,655,1⟩, +⟨⟨0,782,540,true⟩,540,655,1⟩, +⟨⟨1,852,782,true⟩,655,655,0⟩, +⟨⟨0,336,138,true⟩,138,655,4⟩, +⟨⟨1,336,852,true⟩,655,655,0⟩, +⟨⟨0,838,600,false⟩,600,656,1⟩, +⟨⟨0,796,556,false⟩,556,656,1⟩, +⟨⟨1,838,796,true⟩,656,656,0⟩, +⟨⟨0,736,472,true⟩,472,657,1⟩, +⟨⟨0,32,34,true⟩,34,657,5⟩, +⟨⟨1,736,32,true⟩,657,657,0⟩, +⟨⟨0,35,134,true⟩,134,657,4⟩, +⟨⟨1,736,35,true⟩,657,657,0⟩, +⟨⟨0,349,142,false⟩,142,656,4⟩, +⟨⟨1,349,838,true⟩,656,656,0⟩, +⟨⟨0,347,145,true⟩,145,653,4⟩, +⟨⟨1,347,839,true⟩,653,653,0⟩, +⟨⟨0,450,474,false⟩,474,658,1⟩, +⟨⟨0,36,38,false⟩,38,658,5⟩, +⟨⟨1,450,36,true⟩,658,658,0⟩, +⟨⟨0,39,136,false⟩,136,658,4⟩, +⟨⟨1,450,39,true⟩,658,658,0⟩, +⟨⟨0,962,601,true⟩,601,659,1⟩, +⟨⟨0,710,556,true⟩,556,659,1⟩, +⟨⟨1,962,710,true⟩,659,659,0⟩, +⟨⟨0,969,610,false⟩,610,660,1⟩, +⟨⟨0,718,541,false⟩,541,660,1⟩, +⟨⟨1,969,718,true⟩,660,660,0⟩, +⟨⟨0,340,140,false⟩,140,660,4⟩, +⟨⟨1,340,969,true⟩,660,660,0⟩, +⟨⟨0,970,611,true⟩,611,661,1⟩, +⟨⟨0,709,540,true⟩,540,661,1⟩, +⟨⟨1,970,709,true⟩,661,661,0⟩, +⟨⟨0,338,139,true⟩,139,661,4⟩, +⟨⟨1,338,970,true⟩,661,661,0⟩, +⟨⟨0,961,600,false⟩,600,662,1⟩, +⟨⟨0,936,557,false⟩,557,662,1⟩, +⟨⟨1,961,936,true⟩,662,662,0⟩, +⟨⟨0,719,472,true⟩,472,663,1⟩, +⟨⟨0,33,35,true⟩,35,663,5⟩, +⟨⟨1,719,33,true⟩,663,663,0⟩, +⟨⟨0,34,135,true⟩,135,663,4⟩, +⟨⟨1,719,34,true⟩,663,663,0⟩, +⟨⟨0,351,144,false⟩,144,662,4⟩, +⟨⟨1,351,961,true⟩,662,662,0⟩, +⟨⟨0,345,143,true⟩,143,659,4⟩, +⟨⟨1,345,962,true⟩,659,659,0⟩, +⟨⟨0,739,475,false⟩,475,664,1⟩, +⟨⟨0,29,31,false⟩,31,664,5⟩, +⟨⟨1,739,29,true⟩,664,664,0⟩, +⟨⟨0,30,149,false⟩,149,664,4⟩, +⟨⟨1,739,30,true⟩,664,664,0⟩, +⟨⟨0,855,613,true⟩,613,665,1⟩, +⟨⟨0,799,559,true⟩,559,665,1⟩, +⟨⟨1,855,799,true⟩,665,665,0⟩, +⟨⟨0,327,157,true⟩,157,665,4⟩, +⟨⟨1,327,855,true⟩,665,665,0⟩, +⟨⟨0,841,603,false⟩,603,666,1⟩, +⟨⟨0,785,543,false⟩,543,666,1⟩, +⟨⟨1,841,785,true⟩,666,666,0⟩, +⟨⟨0,840,602,true⟩,602,667,1⟩, +⟨⟨0,784,542,true⟩,542,667,1⟩, +⟨⟨1,840,784,true⟩,667,667,0⟩, +⟨⟨0,854,612,false⟩,612,668,1⟩, +⟨⟨0,798,558,false⟩,558,668,1⟩, +⟨⟨1,854,798,true⟩,668,668,0⟩, +⟨⟨0,321,154,false⟩,154,668,4⟩, +⟨⟨1,321,854,true⟩,668,668,0⟩, +⟨⟨0,737,473,true⟩,473,669,1⟩, +⟨⟨0,24,26,true⟩,26,669,5⟩, +⟨⟨1,737,24,true⟩,669,669,0⟩, +⟨⟨0,27,146,true⟩,146,669,4⟩, +⟨⟨1,737,27,true⟩,669,669,0⟩, +⟨⟨0,332,153,false⟩,153,666,4⟩, +⟨⟨1,332,841,true⟩,666,666,0⟩, +⟨⟨0,330,150,true⟩,150,667,4⟩, +⟨⟨1,330,840,true⟩,667,667,0⟩, +⟨⟨0,694,475,false⟩,475,670,1⟩, +⟨⟨0,28,30,false⟩,30,670,5⟩, +⟨⟨1,694,28,true⟩,670,670,0⟩, +⟨⟨0,31,148,false⟩,148,670,4⟩, +⟨⟨1,694,31,true⟩,670,670,0⟩, +⟨⟨0,972,613,true⟩,613,671,1⟩, +⟨⟨0,702,558,true⟩,558,671,1⟩, +⟨⟨1,972,702,true⟩,671,671,0⟩, +⟨⟨0,963,602,false⟩,602,672,1⟩, +⟨⟨0,698,543,false⟩,543,672,1⟩, +⟨⟨1,963,698,true⟩,672,672,0⟩, +⟨⟨0,324,152,false⟩,152,672,4⟩, +⟨⟨1,324,963,true⟩,672,672,0⟩, +⟨⟨0,964,603,true⟩,603,673,1⟩, +⟨⟨0,466,542,true⟩,542,673,1⟩, +⟨⟨1,964,466,true⟩,673,673,0⟩, +⟨⟨0,322,151,true⟩,151,673,4⟩, +⟨⟨1,322,964,true⟩,673,673,0⟩, +⟨⟨0,971,612,false⟩,612,674,1⟩, +⟨⟨0,476,559,false⟩,559,674,1⟩, +⟨⟨1,971,476,true⟩,674,674,0⟩, +⟨⟨0,703,473,true⟩,473,675,1⟩, +⟨⟨0,25,27,true⟩,27,675,5⟩, +⟨⟨1,703,25,true⟩,675,675,0⟩, +⟨⟨0,26,147,true⟩,147,675,4⟩, +⟨⟨1,703,26,true⟩,675,675,0⟩, +⟨⟨0,335,156,false⟩,156,674,4⟩, +⟨⟨1,335,971,true⟩,674,674,0⟩, +⟨⟨0,329,155,true⟩,155,671,4⟩, +⟨⟨1,329,972,true⟩,671,671,0⟩, +⟨⟨0,404,478,false⟩,478,676,1⟩, +⟨⟨0,21,23,false⟩,23,676,5⟩, +⟨⟨1,404,21,true⟩,676,676,0⟩, +⟨⟨0,22,161,false⟩,161,676,4⟩, +⟨⟨1,404,22,true⟩,676,676,0⟩, +⟨⟨0,843,605,true⟩,605,677,1⟩, +⟨⟨0,334,520,true⟩,520,677,1⟩, +⟨⟨1,843,334,true⟩,677,677,0⟩, +⟨⟨0,311,169,true⟩,169,677,4⟩, +⟨⟨1,311,843,true⟩,677,677,0⟩, +⟨⟨0,857,615,false⟩,615,678,1⟩, +⟨⟨0,350,500,false⟩,500,678,1⟩, +⟨⟨1,857,350,true⟩,678,678,0⟩, +⟨⟨0,856,614,true⟩,614,679,1⟩, +⟨⟨0,346,498,true⟩,498,679,1⟩, +⟨⟨1,856,346,true⟩,679,679,0⟩, +⟨⟨0,842,604,false⟩,604,680,1⟩, +⟨⟨0,320,518,false⟩,518,680,1⟩, +⟨⟨1,842,320,true⟩,680,680,0⟩, +⟨⟨0,305,166,false⟩,166,680,4⟩, +⟨⟨1,305,842,true⟩,680,680,0⟩, +⟨⟨0,400,476,true⟩,476,681,1⟩, +⟨⟨0,16,18,true⟩,18,681,5⟩, +⟨⟨1,400,16,true⟩,681,681,0⟩, +⟨⟨0,19,158,true⟩,158,681,4⟩, +⟨⟨1,400,19,true⟩,681,681,0⟩, +⟨⟨0,316,165,false⟩,165,678,4⟩, +⟨⟨1,316,857,true⟩,678,678,0⟩, +⟨⟨0,314,162,true⟩,162,679,4⟩, +⟨⟨1,314,856,true⟩,679,679,0⟩, +⟨⟨0,678,478,false⟩,478,682,1⟩, +⟨⟨0,20,22,false⟩,22,682,5⟩, +⟨⟨1,678,20,true⟩,682,682,0⟩, +⟨⟨0,23,160,false⟩,160,682,4⟩, +⟨⟨1,678,23,true⟩,682,682,0⟩, +⟨⟨0,966,605,true⟩,605,683,1⟩, +⟨⟨0,686,518,true⟩,518,683,1⟩, +⟨⟨1,966,686,true⟩,683,683,0⟩, +⟨⟨0,973,614,false⟩,614,684,1⟩, +⟨⟨0,682,500,false⟩,500,684,1⟩, +⟨⟨1,973,682,true⟩,684,684,0⟩, +⟨⟨0,308,164,false⟩,164,684,4⟩, +⟨⟨1,308,973,true⟩,684,684,0⟩, +⟨⟨0,974,615,true⟩,615,685,1⟩, +⟨⟨0,482,498,true⟩,498,685,1⟩, +⟨⟨1,974,482,true⟩,685,685,0⟩, +⟨⟨0,306,163,true⟩,163,685,4⟩, +⟨⟨1,306,974,true⟩,685,685,0⟩, +⟨⟨0,965,604,false⟩,604,686,1⟩, +⟨⟨0,492,520,false⟩,520,686,1⟩, +⟨⟨1,965,492,true⟩,686,686,0⟩, +⟨⟨0,687,476,true⟩,476,687,1⟩, +⟨⟨0,17,19,true⟩,19,687,5⟩, +⟨⟨1,687,17,true⟩,687,687,0⟩, +⟨⟨0,18,159,true⟩,159,687,4⟩, +⟨⟨1,687,18,true⟩,687,687,0⟩, +⟨⟨0,319,168,false⟩,168,686,4⟩, +⟨⟨1,319,965,true⟩,686,686,0⟩, +⟨⟨0,313,167,true⟩,167,683,4⟩, +⟨⟨1,313,966,true⟩,683,683,0⟩, +⟨⟨0,741,479,false⟩,479,688,1⟩, +⟨⟨0,45,47,false⟩,47,688,5⟩, +⟨⟨1,741,45,true⟩,688,688,0⟩, +⟨⟨0,46,173,false⟩,173,688,4⟩, +⟨⟨1,741,46,true⟩,688,688,0⟩, +⟨⟨0,859,617,true⟩,617,689,1⟩, +⟨⟨0,323,524,true⟩,524,689,1⟩, +⟨⟨1,859,323,true⟩,689,689,0⟩, +⟨⟨0,359,181,true⟩,181,689,4⟩, +⟨⟨1,359,859,true⟩,689,689,0⟩, +⟨⟨0,845,607,false⟩,607,690,1⟩, +⟨⟨0,339,504,false⟩,504,690,1⟩, +⟨⟨1,845,339,true⟩,690,690,0⟩, +⟨⟨0,844,606,true⟩,606,691,1⟩, +⟨⟨0,337,502,true⟩,502,691,1⟩, +⟨⟨1,844,337,true⟩,691,691,0⟩, +⟨⟨0,858,616,false⟩,616,692,1⟩, +⟨⟨0,333,522,false⟩,522,692,1⟩, +⟨⟨1,858,333,true⟩,692,692,0⟩, +⟨⟨0,353,178,false⟩,178,692,4⟩, +⟨⟨1,353,858,true⟩,692,692,0⟩, +⟨⟨0,740,477,true⟩,477,693,1⟩, +⟨⟨0,40,42,true⟩,42,693,5⟩, +⟨⟨1,740,40,true⟩,693,693,0⟩, +⟨⟨0,43,170,true⟩,170,693,4⟩, +⟨⟨1,740,43,true⟩,693,693,0⟩, +⟨⟨0,364,177,false⟩,177,690,4⟩, +⟨⟨1,364,845,true⟩,690,690,0⟩] +def chunk61 : List Entry := [⟨⟨0,362,174,true⟩,174,691,4⟩, +⟨⟨1,362,844,true⟩,691,691,0⟩, +⟨⟨0,662,479,false⟩,479,694,1⟩, +⟨⟨0,44,46,false⟩,46,694,5⟩, +⟨⟨1,662,44,true⟩,694,694,0⟩, +⟨⟨0,47,172,false⟩,172,694,4⟩, +⟨⟨1,662,47,true⟩,694,694,0⟩, +⟨⟨0,976,617,true⟩,617,695,1⟩, +⟨⟨0,670,522,true⟩,522,695,1⟩, +⟨⟨1,976,670,true⟩,695,695,0⟩, +⟨⟨0,357,179,true⟩,179,695,4⟩, +⟨⟨1,357,976,true⟩,695,695,0⟩, +⟨⟨0,967,606,false⟩,606,696,1⟩, +⟨⟨0,666,504,false⟩,504,696,1⟩, +⟨⟨1,967,666,true⟩,696,696,0⟩, +⟨⟨0,968,607,true⟩,607,697,1⟩, +⟨⟨0,434,502,true⟩,502,697,1⟩, +⟨⟨1,968,434,true⟩,697,697,0⟩, +⟨⟨0,975,616,false⟩,616,698,1⟩, +⟨⟨0,444,524,false⟩,524,698,1⟩, +⟨⟨1,975,444,true⟩,698,698,0⟩, +⟨⟨0,355,180,false⟩,180,698,4⟩, +⟨⟨1,355,975,true⟩,698,698,0⟩, +⟨⟨0,671,477,true⟩,477,699,1⟩, +⟨⟨0,41,43,true⟩,43,699,5⟩, +⟨⟨1,671,41,true⟩,699,699,0⟩, +⟨⟨0,42,171,true⟩,171,699,4⟩, +⟨⟨1,671,42,true⟩,699,699,0⟩, +⟨⟨0,366,176,false⟩,176,696,4⟩, +⟨⟨1,366,967,true⟩,696,696,0⟩, +⟨⟨0,360,175,true⟩,175,697,4⟩, +⟨⟨1,360,968,true⟩,697,697,0⟩, +⟨⟨0,415,482,false⟩,482,700,1⟩, +⟨⟨0,77,79,false⟩,79,700,5⟩, +⟨⟨1,415,77,true⟩,700,700,0⟩, +⟨⟨0,78,185,false⟩,185,700,4⟩, +⟨⟨1,415,78,true⟩,700,700,0⟩, +⟨⟨0,873,625,true⟩,625,701,1⟩, +⟨⟨0,771,525,true⟩,525,701,1⟩, +⟨⟨1,873,771,true⟩,701,701,0⟩, +⟨⟨0,423,193,true⟩,193,701,4⟩, +⟨⟨1,423,873,true⟩,701,701,0⟩, +⟨⟨0,887,631,false⟩,631,702,1⟩, +⟨⟨0,755,501,false⟩,501,702,1⟩, +⟨⟨1,887,755,true⟩,702,702,0⟩, +⟨⟨0,886,630,true⟩,630,703,1⟩, +⟨⟨0,754,499,true⟩,499,703,1⟩, +⟨⟨1,886,754,true⟩,703,703,0⟩, +⟨⟨0,872,624,false⟩,624,704,1⟩, +⟨⟨0,770,523,false⟩,523,704,1⟩, +⟨⟨1,872,770,true⟩,704,704,0⟩, +⟨⟨0,417,190,false⟩,190,704,4⟩, +⟨⟨1,417,872,true⟩,704,704,0⟩, +⟨⟨0,413,480,true⟩,480,705,1⟩, +⟨⟨0,72,74,true⟩,74,705,5⟩, +⟨⟨1,413,72,true⟩,705,705,0⟩, +⟨⟨0,75,182,true⟩,182,705,4⟩, +⟨⟨1,413,75,true⟩,705,705,0⟩, +⟨⟨0,428,189,false⟩,189,702,4⟩, +⟨⟨1,428,887,true⟩,702,702,0⟩, +⟨⟨0,426,186,true⟩,186,703,4⟩, +⟨⟨1,426,886,true⟩,703,703,0⟩, +⟨⟨0,646,482,false⟩,482,706,1⟩, +⟨⟨0,76,78,false⟩,78,706,5⟩, +⟨⟨1,646,76,true⟩,706,706,0⟩, +⟨⟨0,79,184,false⟩,184,706,4⟩, +⟨⟨1,646,79,true⟩,706,706,0⟩, +⟨⟨0,980,625,true⟩,625,707,1⟩, +⟨⟨0,650,523,true⟩,523,707,1⟩, +⟨⟨1,980,650,true⟩,707,707,0⟩, +⟨⟨0,983,630,false⟩,630,708,1⟩, +⟨⟨0,654,501,false⟩,501,708,1⟩, +⟨⟨1,983,654,true⟩,708,708,0⟩, +⟨⟨0,420,188,false⟩,188,708,4⟩, +⟨⟨1,420,983,true⟩,708,708,0⟩, +⟨⟨0,984,631,true⟩,631,709,1⟩, +⟨⟨0,373,499,true⟩,499,709,1⟩, +⟨⟨1,984,373,true⟩,709,709,0⟩, +⟨⟨0,418,187,true⟩,187,709,4⟩, +⟨⟨1,418,984,true⟩,709,709,0⟩, +⟨⟨0,979,624,false⟩,624,710,1⟩, +⟨⟨0,374,525,false⟩,525,710,1⟩, +⟨⟨1,979,374,true⟩,710,710,0⟩, +⟨⟨0,655,480,true⟩,480,711,1⟩, +⟨⟨0,73,75,true⟩,75,711,5⟩, +⟨⟨1,655,73,true⟩,711,711,0⟩, +⟨⟨0,74,183,true⟩,183,711,4⟩, +⟨⟨1,655,74,true⟩,711,711,0⟩, +⟨⟨0,431,192,false⟩,192,710,4⟩, +⟨⟨1,431,979,true⟩,710,710,0⟩, +⟨⟨0,425,191,true⟩,191,707,4⟩, +⟨⟨1,425,980,true⟩,707,707,0⟩, +⟨⟨0,743,483,false⟩,483,712,1⟩, +⟨⟨0,117,119,false⟩,119,712,5⟩, +⟨⟨1,743,117,true⟩,712,712,0⟩, +⟨⟨0,118,197,false⟩,197,712,4⟩, +⟨⟨1,743,118,true⟩,712,712,0⟩, +⟨⟨0,889,633,true⟩,633,713,1⟩, +⟨⟨0,769,521,true⟩,521,713,1⟩, +⟨⟨1,889,769,true⟩,713,713,0⟩, +⟨⟨0,875,627,false⟩,627,714,1⟩, +⟨⟨0,757,505,false⟩,505,714,1⟩, +⟨⟨1,875,757,true⟩,714,714,0⟩, +⟨⟨0,502,201,false⟩,201,714,4⟩, +⟨⟨1,502,875,true⟩,714,714,0⟩, +⟨⟨0,874,626,true⟩,626,715,1⟩, +⟨⟨0,756,503,true⟩,503,715,1⟩, +⟨⟨1,874,756,true⟩,715,715,0⟩, +⟨⟨0,496,198,true⟩,198,715,4⟩, +⟨⟨1,496,874,true⟩,715,715,0⟩, +⟨⟨0,888,632,false⟩,632,716,1⟩, +⟨⟨0,768,519,false⟩,519,716,1⟩, +⟨⟨1,888,768,true⟩,716,716,0⟩, +⟨⟨0,742,481,true⟩,481,717,1⟩, +⟨⟨0,112,114,true⟩,114,717,5⟩, +⟨⟨1,742,112,true⟩,717,717,0⟩, +⟨⟨0,115,194,true⟩,194,717,4⟩, +⟨⟨1,742,115,true⟩,717,717,0⟩, +⟨⟨0,509,202,false⟩,202,716,4⟩, +⟨⟨1,509,888,true⟩,716,716,0⟩, +⟨⟨0,507,205,true⟩,205,713,4⟩, +⟨⟨1,507,889,true⟩,713,713,0⟩, +⟨⟨0,630,483,false⟩,483,718,1⟩, +⟨⟨0,116,118,false⟩,118,718,5⟩, +⟨⟨1,630,116,true⟩,718,718,0⟩, +⟨⟨0,119,196,false⟩,196,718,4⟩, +⟨⟨1,630,119,true⟩,718,718,0⟩, +⟨⟨0,986,633,true⟩,633,719,1⟩, +⟨⟨0,638,519,true⟩,519,719,1⟩, +⟨⟨1,986,638,true⟩,719,719,0⟩, +⟨⟨0,981,626,false⟩,626,720,1⟩, +⟨⟨0,634,505,false⟩,505,720,1⟩, +⟨⟨1,981,634,true⟩,720,720,0⟩, +⟨⟨0,500,200,false⟩,200,720,4⟩, +⟨⟨1,500,981,true⟩,720,720,0⟩, +⟨⟨0,982,627,true⟩,627,721,1⟩, +⟨⟨0,290,503,true⟩,503,721,1⟩, +⟨⟨1,982,290,true⟩,721,721,0⟩, +⟨⟨0,498,199,true⟩,199,721,4⟩, +⟨⟨1,498,982,true⟩,721,721,0⟩, +⟨⟨0,985,632,false⟩,632,722,1⟩, +⟨⟨0,294,521,false⟩,521,722,1⟩, +⟨⟨1,985,294,true⟩,722,722,0⟩, +⟨⟨0,639,481,true⟩,481,723,1⟩, +⟨⟨0,113,115,true⟩,115,723,5⟩, +⟨⟨1,639,113,true⟩,723,723,0⟩, +⟨⟨0,114,195,true⟩,195,723,4⟩, +⟨⟨1,639,114,true⟩,723,723,0⟩, +⟨⟨0,511,204,false⟩,204,722,4⟩, +⟨⟨1,511,985,true⟩,722,722,0⟩, +⟨⟨0,505,203,true⟩,203,719,4⟩, +⟨⟨1,505,986,true⟩,719,719,0⟩, +⟨⟨0,525,486,false⟩,486,724,1⟩, +⟨⟨0,13,15,false⟩,15,724,5⟩, +⟨⟨1,525,13,true⟩,724,724,0⟩, +⟨⟨0,14,209,false⟩,209,724,4⟩, +⟨⟨1,525,14,true⟩,724,724,0⟩, +⟨⟨0,573,546,true⟩,546,725,1⟩, +⟨⟨0,553,528,true⟩,528,725,1⟩, +⟨⟨1,573,553,true⟩,725,725,0⟩, +⟨⟨0,295,217,true⟩,217,725,4⟩, +⟨⟨1,295,573,true⟩,725,725,0⟩, +⟨⟨0,585,562,false⟩,562,726,1⟩, +⟨⟨0,541,508,false⟩,508,726,1⟩, +⟨⟨1,585,541,true⟩,726,726,0⟩, +⟨⟨0,584,560,true⟩,560,727,1⟩, +⟨⟨0,540,506,true⟩,506,727,1⟩, +⟨⟨1,584,540,true⟩,727,727,0⟩, +⟨⟨0,572,544,false⟩,544,728,1⟩, +⟨⟨0,552,526,false⟩,526,728,1⟩, +⟨⟨1,572,552,true⟩,728,728,0⟩, +⟨⟨0,289,214,false⟩,214,728,4⟩, +⟨⟨1,289,572,true⟩,728,728,0⟩, +⟨⟨0,524,484,true⟩,484,729,1⟩, +⟨⟨0,8,10,true⟩,10,729,5⟩, +⟨⟨1,524,8,true⟩,729,729,0⟩, +⟨⟨0,11,206,true⟩,206,729,4⟩, +⟨⟨1,524,11,true⟩,729,729,0⟩, +⟨⟨0,300,213,false⟩,213,726,4⟩, +⟨⟨1,300,585,true⟩,726,726,0⟩, +⟨⟨0,298,210,true⟩,210,727,4⟩, +⟨⟨1,298,584,true⟩,727,727,0⟩, +⟨⟨0,623,486,false⟩,486,730,1⟩, +⟨⟨0,12,14,false⟩,14,730,5⟩, +⟨⟨1,623,12,true⟩,730,730,0⟩, +⟨⟨0,15,208,false⟩,208,730,4⟩, +⟨⟨1,623,15,true⟩,730,730,0⟩, +⟨⟨0,933,546,true⟩,546,731,1⟩, +⟨⟨0,622,526,true⟩,526,731,1⟩, +⟨⟨1,933,622,true⟩,731,731,0⟩, +⟨⟨0,293,215,true⟩,215,731,4⟩, +⟨⟨1,293,933,true⟩,731,731,0⟩, +⟨⟨0,937,560,false⟩,560,732,1⟩, +⟨⟨0,501,508,false⟩,508,732,1⟩, +⟨⟨1,937,501,true⟩,732,732,0⟩, +⟨⟨0,938,562,true⟩,562,733,1⟩, +⟨⟨0,614,506,true⟩,506,733,1⟩, +⟨⟨1,938,614,true⟩,733,733,0⟩, +⟨⟨0,932,544,false⟩,544,734,1⟩, +⟨⟨0,618,528,false⟩,528,734,1⟩] +def chunk62 : List Entry := [⟨⟨1,932,618,true⟩,734,734,0⟩, +⟨⟨0,291,216,false⟩,216,734,4⟩, +⟨⟨1,291,932,true⟩,734,734,0⟩, +⟨⟨0,619,484,true⟩,484,735,1⟩, +⟨⟨0,9,11,true⟩,11,735,5⟩, +⟨⟨1,619,9,true⟩,735,735,0⟩, +⟨⟨0,10,207,true⟩,207,735,4⟩, +⟨⟨1,619,10,true⟩,735,735,0⟩, +⟨⟨0,302,212,false⟩,212,732,4⟩, +⟨⟨1,302,937,true⟩,732,732,0⟩, +⟨⟨0,296,211,true⟩,211,733,4⟩, +⟨⟨1,296,938,true⟩,733,733,0⟩, +⟨⟨0,745,487,false⟩,487,736,1⟩, +⟨⟨0,53,55,false⟩,55,736,5⟩, +⟨⟨1,745,53,true⟩,736,736,0⟩, +⟨⟨0,54,221,false⟩,221,736,4⟩, +⟨⟨1,745,54,true⟩,736,736,0⟩, +⟨⟨0,589,566,true⟩,566,737,1⟩, +⟨⟨0,557,532,true⟩,532,737,1⟩, +⟨⟨1,589,557,true⟩,737,737,0⟩, +⟨⟨0,375,229,true⟩,229,737,4⟩, +⟨⟨1,375,589,true⟩,737,737,0⟩, +⟨⟨0,569,550,false⟩,550,738,1⟩, +⟨⟨0,537,512,false⟩,512,738,1⟩, +⟨⟨1,569,537,true⟩,738,738,0⟩, +⟨⟨0,568,548,true⟩,548,739,1⟩, +⟨⟨0,536,510,true⟩,510,739,1⟩, +⟨⟨1,568,536,true⟩,739,739,0⟩, +⟨⟨0,588,564,false⟩,564,740,1⟩, +⟨⟨0,556,530,false⟩,530,740,1⟩, +⟨⟨1,588,556,true⟩,740,740,0⟩, +⟨⟨0,369,226,false⟩,226,740,4⟩, +⟨⟨1,369,588,true⟩,740,740,0⟩, +⟨⟨0,744,485,true⟩,485,741,1⟩, +⟨⟨0,48,50,true⟩,50,741,5⟩, +⟨⟨1,744,48,true⟩,741,741,0⟩, +⟨⟨0,51,218,true⟩,218,741,4⟩, +⟨⟨1,744,51,true⟩,741,741,0⟩, +⟨⟨0,380,225,false⟩,225,738,4⟩, +⟨⟨1,380,569,true⟩,738,738,0⟩, +⟨⟨0,378,222,true⟩,222,739,4⟩, +⟨⟨1,378,568,true⟩,739,739,0⟩, +⟨⟨0,598,487,false⟩,487,742,1⟩, +⟨⟨0,52,54,false⟩,54,742,5⟩, +⟨⟨1,598,52,true⟩,742,742,0⟩, +⟨⟨0,55,220,false⟩,220,742,4⟩, +⟨⟨1,598,55,true⟩,742,742,0⟩, +⟨⟨0,940,566,true⟩,566,743,1⟩, +⟨⟨0,602,530,true⟩,530,743,1⟩, +⟨⟨1,940,602,true⟩,743,743,0⟩, +⟨⟨0,934,548,false⟩,548,744,1⟩, +⟨⟨0,606,512,false⟩,512,744,1⟩, +⟨⟨1,934,606,true⟩,744,744,0⟩, +⟨⟨0,372,224,false⟩,224,744,4⟩, +⟨⟨1,372,934,true⟩,744,744,0⟩, +⟨⟨0,935,550,true⟩,550,745,1⟩, +⟨⟨0,421,510,true⟩,510,745,1⟩, +⟨⟨1,935,421,true⟩,745,745,0⟩, +⟨⟨0,370,223,true⟩,223,745,4⟩, +⟨⟨1,370,935,true⟩,745,745,0⟩, +⟨⟨0,939,564,false⟩,564,746,1⟩, +⟨⟨0,422,532,false⟩,532,746,1⟩, +⟨⟨1,939,422,true⟩,746,746,0⟩, +⟨⟨0,607,485,true⟩,485,747,1⟩, +⟨⟨0,49,51,true⟩,51,747,5⟩, +⟨⟨1,607,49,true⟩,747,747,0⟩, +⟨⟨0,50,219,true⟩,219,747,4⟩, +⟨⟨1,607,50,true⟩,747,747,0⟩, +⟨⟨0,383,228,false⟩,228,746,4⟩, +⟨⟨1,383,939,true⟩,746,746,0⟩, +⟨⟨0,377,227,true⟩,227,743,4⟩, +⟨⟨1,377,940,true⟩,743,743,0⟩, +⟨⟨0,521,490,false⟩,490,748,1⟩, +⟨⟨0,85,87,false⟩,87,748,5⟩, +⟨⟨1,521,85,true⟩,748,748,0⟩, +⟨⟨0,86,233,false⟩,233,748,4⟩, +⟨⟨1,521,86,true⟩,748,748,0⟩, +⟨⟨0,605,580,true⟩,580,749,1⟩, +⟨⟨0,775,533,true⟩,533,749,1⟩, +⟨⟨1,605,775,true⟩,749,749,0⟩, +⟨⟨0,617,592,false⟩,592,750,1⟩, +⟨⟨0,759,509,false⟩,509,750,1⟩, +⟨⟨1,617,759,true⟩,750,750,0⟩, +⟨⟨0,438,237,false⟩,237,750,4⟩, +⟨⟨1,438,617,true⟩,750,750,0⟩, +⟨⟨0,616,590,true⟩,590,751,1⟩, +⟨⟨0,758,507,true⟩,507,751,1⟩, +⟨⟨1,616,758,true⟩,751,751,0⟩, +⟨⟨0,432,234,true⟩,234,751,4⟩, +⟨⟨1,432,616,true⟩,751,751,0⟩, +⟨⟨0,604,578,false⟩,578,752,1⟩, +⟨⟨0,774,531,false⟩,531,752,1⟩, +⟨⟨1,604,774,true⟩,752,752,0⟩, +⟨⟨0,520,488,true⟩,488,753,1⟩, +⟨⟨0,80,82,true⟩,82,753,5⟩, +⟨⟨1,520,80,true⟩,753,753,0⟩, +⟨⟨0,83,230,true⟩,230,753,4⟩, +⟨⟨1,520,83,true⟩,753,753,0⟩, +⟨⟨0,445,238,false⟩,238,752,4⟩, +⟨⟨1,445,604,true⟩,752,752,0⟩, +⟨⟨0,443,241,true⟩,241,749,4⟩, +⟨⟨1,443,605,true⟩,749,749,0⟩, +⟨⟨0,591,490,false⟩,490,754,1⟩, +⟨⟨0,84,86,false⟩,86,754,5⟩, +⟨⟨1,591,84,true⟩,754,754,0⟩, +⟨⟨0,87,232,false⟩,232,754,4⟩, +⟨⟨1,591,87,true⟩,754,754,0⟩, +⟨⟨0,944,580,true⟩,580,755,1⟩, +⟨⟨0,586,531,true⟩,531,755,1⟩, +⟨⟨1,944,586,true⟩,755,755,0⟩, +⟨⟨0,437,239,true⟩,239,755,4⟩, +⟨⟨1,437,944,true⟩,755,755,0⟩, +⟨⟨0,951,590,false⟩,590,756,1⟩, +⟨⟨0,354,509,false⟩,509,756,1⟩, +⟨⟨1,951,354,true⟩,756,756,0⟩, +⟨⟨0,953,592,true⟩,592,757,1⟩, +⟨⟨0,582,507,true⟩,507,757,1⟩, +⟨⟨1,953,582,true⟩,757,757,0⟩, +⟨⟨0,942,578,false⟩,578,758,1⟩, +⟨⟨0,590,533,false⟩,533,758,1⟩, +⟨⟨1,942,590,true⟩,758,758,0⟩, +⟨⟨0,435,240,false⟩,240,758,4⟩, +⟨⟨1,435,942,true⟩,758,758,0⟩, +⟨⟨0,587,488,true⟩,488,759,1⟩, +⟨⟨0,81,83,true⟩,83,759,5⟩, +⟨⟨1,587,81,true⟩,759,759,0⟩, +⟨⟨0,82,231,true⟩,231,759,4⟩, +⟨⟨1,587,82,true⟩,759,759,0⟩, +⟨⟨0,446,236,false⟩,236,756,4⟩, +⟨⟨1,446,951,true⟩,756,756,0⟩, +⟨⟨0,440,235,true⟩,235,757,4⟩, +⟨⟨1,440,953,true⟩,757,757,0⟩, +⟨⟨0,747,491,false⟩,491,760,1⟩, +⟨⟨0,109,111,false⟩,111,760,5⟩, +⟨⟨1,747,109,true⟩,760,760,0⟩, +⟨⟨0,110,245,false⟩,245,760,4⟩, +⟨⟨1,747,110,true⟩,760,760,0⟩, +⟨⟨0,621,596,true⟩,596,761,1⟩, +⟨⟨0,773,529,true⟩,529,761,1⟩, +⟨⟨1,621,773,true⟩,761,761,0⟩, +⟨⟨0,601,584,false⟩,584,762,1⟩, +⟨⟨0,761,513,false⟩,513,762,1⟩, +⟨⟨1,601,761,true⟩,762,762,0⟩, +⟨⟨0,486,249,false⟩,249,762,4⟩, +⟨⟨1,486,601,true⟩,762,762,0⟩, +⟨⟨0,600,582,true⟩,582,763,1⟩, +⟨⟨0,760,511,true⟩,511,763,1⟩, +⟨⟨1,600,760,true⟩,763,763,0⟩, +⟨⟨0,480,246,true⟩,246,763,4⟩, +⟨⟨1,480,600,true⟩,763,763,0⟩, +⟨⟨0,620,594,false⟩,594,764,1⟩, +⟨⟨0,772,527,false⟩,527,764,1⟩, +⟨⟨1,620,772,true⟩,764,764,0⟩, +⟨⟨0,746,489,true⟩,489,765,1⟩, +⟨⟨0,104,106,true⟩,106,765,5⟩, +⟨⟨1,746,104,true⟩,765,765,0⟩, +⟨⟨0,107,242,true⟩,242,765,4⟩, +⟨⟨1,746,107,true⟩,765,765,0⟩, +⟨⟨0,493,250,false⟩,250,764,4⟩, +⟨⟨1,493,620,true⟩,764,764,0⟩, +⟨⟨0,491,253,true⟩,253,761,4⟩, +⟨⟨1,491,621,true⟩,761,761,0⟩, +⟨⟨0,566,491,false⟩,491,766,1⟩, +⟨⟨0,108,110,false⟩,110,766,5⟩, +⟨⟨1,566,108,true⟩,766,766,0⟩, +⟨⟨0,111,244,false⟩,244,766,4⟩, +⟨⟨1,566,111,true⟩,766,766,0⟩, +⟨⟨0,957,596,true⟩,596,767,1⟩, +⟨⟨0,570,527,true⟩,527,767,1⟩, +⟨⟨1,957,570,true⟩,767,767,0⟩, +⟨⟨0,485,251,true⟩,251,767,4⟩, +⟨⟨1,485,957,true⟩,767,767,0⟩, +⟨⟨0,946,582,false⟩,582,768,1⟩, +⟨⟨0,574,513,false⟩,513,768,1⟩, +⟨⟨1,946,574,true⟩,768,768,0⟩, +⟨⟨0,947,584,true⟩,584,769,1⟩, +⟨⟨0,309,511,true⟩,511,769,1⟩, +⟨⟨1,947,309,true⟩,769,769,0⟩, +⟨⟨0,955,594,false⟩,594,770,1⟩, +⟨⟨0,310,529,false⟩,529,770,1⟩, +⟨⟨1,955,310,true⟩,770,770,0⟩, +⟨⟨0,483,252,false⟩,252,770,4⟩, +⟨⟨1,483,955,true⟩,770,770,0⟩, +⟨⟨0,575,489,true⟩,489,771,1⟩, +⟨⟨0,105,107,true⟩,107,771,5⟩, +⟨⟨1,575,105,true⟩,771,771,0⟩, +⟨⟨0,106,243,true⟩,243,771,4⟩, +⟨⟨1,575,106,true⟩,771,771,0⟩, +⟨⟨0,494,248,false⟩,248,768,4⟩, +⟨⟨1,494,946,true⟩,768,768,0⟩, +⟨⟨0,488,247,true⟩,247,769,4⟩, +⟨⟨1,488,947,true⟩,769,769,0⟩, +⟨⟨0,515,494,false⟩,494,772,1⟩, +⟨⟨0,101,103,false⟩,103,772,5⟩, +⟨⟨1,515,101,true⟩,772,772,0⟩, +⟨⟨0,102,257,false⟩,257,772,4⟩, +⟨⟨1,515,102,true⟩,772,772,0⟩, +⟨⟨0,817,581,true⟩,581,773,1⟩, +⟨⟨0,803,567,true⟩,567,773,1⟩, +⟨⟨1,817,803,true⟩,773,773,0⟩] +def chunk63 : List Entry := [⟨⟨0,833,597,false⟩,597,774,1⟩, +⟨⟨0,787,547,false⟩,547,774,1⟩, +⟨⟨1,833,787,true⟩,774,774,0⟩, +⟨⟨0,470,261,false⟩,261,774,4⟩, +⟨⟨1,470,833,true⟩,774,774,0⟩, +⟨⟨0,832,595,true⟩,595,775,1⟩, +⟨⟨0,786,545,true⟩,545,775,1⟩, +⟨⟨1,832,786,true⟩,775,775,0⟩, +⟨⟨0,464,258,true⟩,258,775,4⟩, +⟨⟨1,464,832,true⟩,775,775,0⟩, +⟨⟨0,816,579,false⟩,579,776,1⟩, +⟨⟨0,802,565,false⟩,565,776,1⟩, +⟨⟨1,816,802,true⟩,776,776,0⟩, +⟨⟨0,513,492,true⟩,492,777,1⟩, +⟨⟨0,96,98,true⟩,98,777,5⟩, +⟨⟨1,513,96,true⟩,777,777,0⟩, +⟨⟨0,99,254,true⟩,254,777,4⟩, +⟨⟨1,513,99,true⟩,777,777,0⟩, +⟨⟨0,477,262,false⟩,262,776,4⟩, +⟨⟨1,477,816,true⟩,776,776,0⟩, +⟨⟨0,475,265,true⟩,265,773,4⟩, +⟨⟨1,475,817,true⟩,773,773,0⟩, +⟨⟨0,559,494,false⟩,494,778,1⟩, +⟨⟨0,100,102,false⟩,102,778,5⟩, +⟨⟨1,559,100,true⟩,778,778,0⟩, +⟨⟨0,103,256,false⟩,256,778,4⟩, +⟨⟨1,559,103,true⟩,778,778,0⟩, +⟨⟨0,945,581,true⟩,581,779,1⟩, +⟨⟨0,558,565,true⟩,565,779,1⟩, +⟨⟨1,945,558,true⟩,779,779,0⟩, +⟨⟨0,469,263,true⟩,263,779,4⟩, +⟨⟨1,469,945,true⟩,779,779,0⟩, +⟨⟨0,956,595,false⟩,595,780,1⟩, +⟨⟨0,325,547,false⟩,547,780,1⟩, +⟨⟨1,956,325,true⟩,780,780,0⟩, +⟨⟨0,958,597,true⟩,597,781,1⟩, +⟨⟨0,550,545,true⟩,545,781,1⟩, +⟨⟨1,958,550,true⟩,781,781,0⟩, +⟨⟨0,943,579,false⟩,579,782,1⟩, +⟨⟨0,554,567,false⟩,567,782,1⟩, +⟨⟨1,943,554,true⟩,782,782,0⟩, +⟨⟨0,467,264,false⟩,264,782,4⟩, +⟨⟨1,467,943,true⟩,782,782,0⟩, +⟨⟨0,555,492,true⟩,492,783,1⟩, +⟨⟨0,97,99,true⟩,99,783,5⟩, +⟨⟨1,555,97,true⟩,783,783,0⟩, +⟨⟨0,98,255,true⟩,255,783,4⟩, +⟨⟨1,555,98,true⟩,783,783,0⟩, +⟨⟨0,478,260,false⟩,260,780,4⟩, +⟨⟨1,478,956,true⟩,780,780,0⟩, +⟨⟨0,472,259,true⟩,259,781,4⟩, +⟨⟨1,472,958,true⟩,781,781,0⟩, +⟨⟨0,749,495,false⟩,495,784,1⟩, +⟨⟨0,93,95,false⟩,95,784,5⟩, +⟨⟨1,749,93,true⟩,784,784,0⟩, +⟨⟨0,94,269,false⟩,269,784,4⟩, +⟨⟨1,749,94,true⟩,784,784,0⟩, +⟨⟨0,831,593,true⟩,593,785,1⟩, +⟨⟨0,801,563,true⟩,563,785,1⟩, +⟨⟨1,831,801,true⟩,785,785,0⟩, +⟨⟨0,819,585,false⟩,585,786,1⟩, +⟨⟨0,789,551,false⟩,551,786,1⟩, +⟨⟨1,819,789,true⟩,786,786,0⟩, +⟨⟨0,454,273,false⟩,273,786,4⟩, +⟨⟨1,454,819,true⟩,786,786,0⟩, +⟨⟨0,818,583,true⟩,583,787,1⟩, +⟨⟨0,788,549,true⟩,549,787,1⟩, +⟨⟨1,818,788,true⟩,787,787,0⟩, +⟨⟨0,448,270,true⟩,270,787,4⟩, +⟨⟨1,448,818,true⟩,787,787,0⟩, +⟨⟨0,830,591,false⟩,591,788,1⟩, +⟨⟨0,800,561,false⟩,561,788,1⟩, +⟨⟨1,830,800,true⟩,788,788,0⟩, +⟨⟨0,748,493,true⟩,493,789,1⟩, +⟨⟨0,88,90,true⟩,90,789,5⟩, +⟨⟨1,748,88,true⟩,789,789,0⟩, +⟨⟨0,91,266,true⟩,266,789,4⟩, +⟨⟨1,748,91,true⟩,789,789,0⟩, +⟨⟨0,461,274,false⟩,274,788,4⟩, +⟨⟨1,461,830,true⟩,788,788,0⟩, +⟨⟨0,459,277,true⟩,277,785,4⟩, +⟨⟨1,459,831,true⟩,785,785,0⟩, +⟨⟨0,539,495,false⟩,495,790,1⟩, +⟨⟨0,92,94,false⟩,94,790,5⟩, +⟨⟨1,539,92,true⟩,790,790,0⟩, +⟨⟨0,95,268,false⟩,268,790,4⟩, +⟨⟨1,539,95,true⟩,790,790,0⟩, +⟨⟨0,954,593,true⟩,593,791,1⟩, +⟨⟨0,542,561,true⟩,561,791,1⟩, +⟨⟨1,954,542,true⟩,791,791,0⟩, +⟨⟨0,453,275,true⟩,275,791,4⟩, +⟨⟨1,453,954,true⟩,791,791,0⟩, +⟨⟨0,532,583,false⟩,583,792,1⟩, +⟨⟨0,341,551,false⟩,551,792,1⟩, +⟨⟨1,532,341,true⟩,792,792,0⟩, +⟨⟨0,948,585,true⟩,585,793,1⟩, +⟨⟨0,543,549,true⟩,549,793,1⟩, +⟨⟨1,948,543,true⟩,793,793,0⟩, +⟨⟨0,952,591,false⟩,591,794,1⟩, +⟨⟨0,538,563,false⟩,563,794,1⟩, +⟨⟨1,952,538,true⟩,794,794,0⟩, +⟨⟨0,451,276,false⟩,276,794,4⟩, +⟨⟨1,451,952,true⟩,794,794,0⟩, +⟨⟨0,535,493,true⟩,493,795,1⟩, +⟨⟨0,89,91,true⟩,91,795,5⟩, +⟨⟨1,535,89,true⟩,795,795,0⟩, +⟨⟨0,90,267,true⟩,267,795,4⟩, +⟨⟨1,535,90,true⟩,795,795,0⟩, +⟨⟨0,462,272,false⟩,272,792,4⟩, +⟨⟨1,462,532,true⟩,792,792,0⟩, +⟨⟨0,456,271,true⟩,271,793,4⟩, +⟨⟨1,456,948,true⟩,793,793,0⟩, +⟨⟨0,763,517,false⟩,517,796,1⟩, +⟨⟨0,61,63,false⟩,63,796,5⟩, +⟨⟨1,763,61,true⟩,796,796,0⟩, +⟨⟨0,62,281,false⟩,281,796,4⟩, +⟨⟨1,763,62,true⟩,796,796,0⟩, +⟨⟨0,829,589,true⟩,589,797,1⟩, +⟨⟨0,815,577,true⟩,577,797,1⟩, +⟨⟨1,829,815,true⟩,797,797,0⟩, +⟨⟨0,391,289,true⟩,289,797,4⟩, +⟨⟨1,391,829,true⟩,797,797,0⟩, +⟨⟨0,805,571,false⟩,571,798,1⟩, +⟨⟨0,791,555,false⟩,555,798,1⟩, +⟨⟨1,805,791,true⟩,798,798,0⟩, +⟨⟨0,804,569,true⟩,569,799,1⟩, +⟨⟨0,790,553,true⟩,553,799,1⟩, +⟨⟨1,804,790,true⟩,799,799,0⟩, +⟨⟨0,828,587,false⟩,587,800,1⟩, +⟨⟨0,814,575,false⟩,575,800,1⟩, +⟨⟨1,828,814,true⟩,800,800,0⟩, +⟨⟨0,385,286,false⟩,286,800,4⟩, +⟨⟨1,385,828,true⟩,800,800,0⟩, +⟨⟨0,762,515,true⟩,515,801,1⟩, +⟨⟨0,56,58,true⟩,58,801,5⟩, +⟨⟨1,762,56,true⟩,801,801,0⟩, +⟨⟨0,59,278,true⟩,278,801,4⟩, +⟨⟨1,762,59,true⟩,801,801,0⟩, +⟨⟨0,396,285,false⟩,285,798,4⟩, +⟨⟨1,396,805,true⟩,798,798,0⟩, +⟨⟨0,394,282,true⟩,282,799,4⟩, +⟨⟨1,394,804,true⟩,799,799,0⟩, +⟨⟨0,518,517,false⟩,517,802,1⟩, +⟨⟨0,60,62,false⟩,62,802,5⟩, +⟨⟨1,518,60,true⟩,802,802,0⟩, +⟨⟨0,63,280,false⟩,280,802,4⟩, +⟨⟨1,518,63,true⟩,802,802,0⟩, +⟨⟨0,950,589,true⟩,589,803,1⟩, +⟨⟨0,252,575,true⟩,575,803,1⟩, +⟨⟨1,950,252,true⟩,803,803,0⟩, +⟨⟨0,389,287,true⟩,287,803,4⟩, +⟨⟨1,389,950,true⟩,803,803,0⟩, +⟨⟨0,526,569,false⟩,569,804,1⟩, +⟨⟨0,522,555,false⟩,555,804,1⟩, +⟨⟨1,526,522,true⟩,804,804,0⟩, +⟨⟨0,406,571,true⟩,571,805,1⟩, +⟨⟨0,402,553,true⟩,553,805,1⟩, +⟨⟨1,406,402,true⟩,805,805,0⟩, +⟨⟨0,949,587,false⟩,587,806,1⟩, +⟨⟨0,941,577,false⟩,577,806,1⟩, +⟨⟨1,949,941,true⟩,806,806,0⟩, +⟨⟨0,387,288,false⟩,288,806,4⟩, +⟨⟨1,387,949,true⟩,806,806,0⟩, +⟨⟨0,527,515,true⟩,515,807,1⟩, +⟨⟨0,57,59,true⟩,59,807,5⟩, +⟨⟨1,527,57,true⟩,807,807,0⟩, +⟨⟨0,58,279,true⟩,279,807,4⟩, +⟨⟨1,527,58,true⟩,807,807,0⟩, +⟨⟨0,398,284,false⟩,284,804,4⟩, +⟨⟨1,398,526,true⟩,804,804,0⟩, +⟨⟨0,392,283,true⟩,283,805,4⟩, +⟨⟨1,392,406,true⟩,805,805,0⟩, +⟨⟨0,704,470,false⟩,470,808,2⟩, +⟨⟨0,640,466,false⟩,466,808,2⟩, +⟨⟨1,704,640,true⟩,808,808,0⟩, +⟨⟨0,704,808,false⟩,808,824,1⟩, +⟨⟨0,255,466,false⟩,466,824,3⟩, +⟨⟨1,704,255,true⟩,824,824,0⟩, +⟨⟨0,278,466,false⟩,466,824,3⟩, +⟨⟨1,704,278,true⟩,824,824,0⟩, +⟨⟨0,624,465,true⟩,465,809,2⟩, +⟨⟨0,656,467,true⟩,467,809,2⟩, +⟨⟨1,624,656,true⟩,809,809,0⟩, +⟨⟨0,266,465,true⟩,465,809,2⟩, +⟨⟨1,266,624,true⟩,809,809,0⟩, +⟨⟨0,688,469,false⟩,469,810,2⟩, +⟨⟨0,720,471,false⟩,471,810,2⟩, +⟨⟨1,688,720,true⟩,810,810,0⟩, +⟨⟨0,907,635,false⟩,635,810,1⟩, +⟨⟨0,708,470,false⟩,470,810,2⟩, +⟨⟨1,907,708,true⟩,810,810,0⟩, +⟨⟨1,907,688,true⟩,810,810,0⟩, +⟨⟨0,576,462,true⟩,462,811,2⟩, +⟨⟨0,711,470,true⟩,470,811,2⟩, +⟨⟨1,576,711,true⟩,811,811,0⟩, +⟨⟨0,253,462,true⟩,462,811,2⟩, +⟨⟨1,576,253,true⟩,811,811,0⟩, +⟨⟨0,282,462,true⟩,462,811,2⟩, +⟨⟨1,576,282,true⟩,811,811,0⟩, +⟨⟨0,560,461,false⟩,461,812,2⟩] +def chunk64 : List Entry := [⟨⟨0,592,463,false⟩,463,812,2⟩, +⟨⟨1,560,592,true⟩,812,812,0⟩, +⟨⟨0,264,461,false⟩,461,812,2⟩, +⟨⟨1,560,264,true⟩,812,812,0⟩, +⟨⟨0,810,540,false⟩,540,812,1⟩, +⟨⟨0,811,541,false⟩,541,812,1⟩, +⟨⟨1,592,810,true⟩,812,812,0⟩, +⟨⟨1,592,811,true⟩,812,812,0⟩, +⟨⟨1,592,560,true⟩,812,812,0⟩, +⟨⟨0,544,460,true⟩,460,813,2⟩, +⟨⟨0,727,471,true⟩,471,813,2⟩, +⟨⟨1,544,727,true⟩,813,813,0⟩, +⟨⟨0,6,460,true⟩,460,813,2⟩, +⟨⟨1,544,6,true⟩,813,813,0⟩, +⟨⟨0,7,460,true⟩,460,813,2⟩, +⟨⟨1,544,7,true⟩,813,813,0⟩, +⟨⟨0,599,463,false⟩,463,826,3⟩, +⟨⟨0,608,464,false⟩,464,826,3⟩, +⟨⟨1,599,608,true⟩,826,826,0⟩, +⟨⟨0,3,463,false⟩,463,826,3⟩, +⟨⟨1,599,3,true⟩,826,826,0⟩, +⟨⟨0,663,467,false⟩,467,826,3⟩, +⟨⟨0,672,468,false⟩,468,826,3⟩, +⟨⟨1,663,672,true⟩,826,826,0⟩, +⟨⟨0,567,461,true⟩,461,827,3⟩, +⟨⟨0,583,462,true⟩,462,827,3⟩, +⟨⟨1,567,583,true⟩,827,827,0⟩, +⟨⟨0,2,461,true⟩,461,827,3⟩, +⟨⟨1,567,2,true⟩,827,827,0⟩, +⟨⟨0,631,465,true⟩,465,827,3⟩, +⟨⟨0,647,466,true⟩,466,827,3⟩, +⟨⟨1,631,647,true⟩,827,827,0⟩, +⟨⟨0,512,458,false⟩,458,818,2⟩, +⟨⟨0,551,460,false⟩,460,818,2⟩, +⟨⟨1,512,551,true⟩,818,818,0⟩, +⟨⟨0,512,818,false⟩,818,828,1⟩, +⟨⟨0,1,458,false⟩,458,828,3⟩, +⟨⟨1,512,1,true⟩,828,828,0⟩, +⟨⟨0,640,808,false⟩,808,828,1⟩, +⟨⟨0,679,468,false⟩,468,828,3⟩, +⟨⟨1,640,679,true⟩,828,828,0⟩, +⟨⟨0,551,818,true⟩,818,829,1⟩, +⟨⟨0,715,470,true⟩,470,829,3⟩, +⟨⟨1,551,715,true⟩,829,829,0⟩, +⟨⟨0,280,470,true⟩,470,829,3⟩, +⟨⟨1,551,280,true⟩,829,829,0⟩, +⟨⟨0,286,470,true⟩,470,829,3⟩, +⟨⟨1,551,286,true⟩,829,829,0⟩, +⟨⟨0,603,463,false⟩,463,830,3⟩, +⟨⟨0,695,469,false⟩,469,830,3⟩, +⟨⟨1,603,695,true⟩,830,830,0⟩, +⟨⟨0,262,469,false⟩,469,830,3⟩, +⟨⟨1,603,262,true⟩,830,830,0⟩, +⟨⟨0,265,463,false⟩,463,830,3⟩, +⟨⟨1,603,265,true⟩,830,830,0⟩, +⟨⟨0,519,458,false⟩,458,820,2⟩, +⟨⟨0,528,459,false⟩,459,820,2⟩, +⟨⟨1,519,528,true⟩,820,820,0⟩, +⟨⟨0,519,820,false⟩,820,830,1⟩, +⟨⟨0,246,459,false⟩,459,830,3⟩, +⟨⟨1,519,246,true⟩,830,830,0⟩, +⟨⟨0,635,465,false⟩,465,830,3⟩, +⟨⟨0,683,468,false⟩,468,830,3⟩, +⟨⟨1,635,683,true⟩,830,830,0⟩, +⟨⟨0,528,820,true⟩,820,831,1⟩, +⟨⟨0,699,469,true⟩,469,831,3⟩, +⟨⟨1,528,699,true⟩,831,831,0⟩, +⟨⟨0,4,459,true⟩,459,831,3⟩, +⟨⟨1,528,4,true⟩,831,831,0⟩, +⟨⟨0,5,459,true⟩,459,831,3⟩, +⟨⟨1,528,5,true⟩,831,831,0⟩, +⟨⟨0,571,461,true⟩,461,831,3⟩, +⟨⟨0,615,464,true⟩,464,831,3⟩, +⟨⟨1,571,615,true⟩,831,831,0⟩, +⟨⟨0,276,461,true⟩,461,831,3⟩, +⟨⟨1,571,276,true⟩,831,831,0⟩, +⟨⟨0,651,466,true⟩,466,831,3⟩, +⟨⟨0,667,467,true⟩,467,831,3⟩, +⟨⟨1,651,667,true⟩,831,831,0⟩, +⟨⟨0,64,645,true⟩,645,1,2⟩, +⟨⟨0,119,718,true⟩,718,1,2⟩, +⟨⟨1,64,119,true⟩,1,1,0⟩, +⟨⟨0,32,657,true⟩,657,1,2⟩, +⟨⟨1,32,119,true⟩,1,1,0⟩, +⟨⟨0,16,681,true⟩,681,1,2⟩, +⟨⟨1,16,119,true⟩,1,1,0⟩, +⟨⟨0,9,735,true⟩,735,1,2⟩, +⟨⟨1,9,119,true⟩,1,1,0⟩, +⟨⟨0,8,729,true⟩,729,1,2⟩, +⟨⟨1,8,119,true⟩,1,1,0⟩, +⟨⟨0,118,712,true⟩,712,1,2⟩, +⟨⟨1,64,118,true⟩,1,1,0⟩, +⟨⟨1,32,118,true⟩,1,1,0⟩, +⟨⟨1,16,118,true⟩,1,1,0⟩, +⟨⟨0,1,828,true⟩,828,1,1⟩, +⟨⟨1,1,118,true⟩,1,1,0⟩, +⟨⟨0,0,458,true⟩,458,1,4⟩, +⟨⟨1,0,118,true⟩,1,1,0⟩, +⟨⟨0,117,712,true⟩,712,1,2⟩, +⟨⟨1,64,117,true⟩,1,1,0⟩, +⟨⟨1,32,117,true⟩,1,1,0⟩, +⟨⟨1,16,117,true⟩,1,1,0⟩, +⟨⟨0,2,827,true⟩,827,1,1⟩, +⟨⟨1,2,117,true⟩,1,1,0⟩, +⟨⟨1,0,117,true⟩,1,1,0⟩, +⟨⟨0,116,718,true⟩,718,1,2⟩, +⟨⟨1,64,116,true⟩,1,1,0⟩, +⟨⟨1,32,116,true⟩,1,1,0⟩, +⟨⟨1,16,116,true⟩,1,1,0⟩, +⟨⟨1,9,116,true⟩,1,1,0⟩, +⟨⟨1,8,116,true⟩,1,1,0⟩, +⟨⟨1,2,116,true⟩,1,1,0⟩, +⟨⟨1,1,116,true⟩,1,1,0⟩, +⟨⟨0,115,717,true⟩,717,1,2⟩, +⟨⟨1,64,115,true⟩,1,1,0⟩, +⟨⟨1,32,115,true⟩,1,1,0⟩, +⟨⟨1,16,115,true⟩,1,1,0⟩, +⟨⟨0,4,831,true⟩,831,1,1⟩, +⟨⟨1,4,115,true⟩,1,1,0⟩, +⟨⟨1,0,115,true⟩,1,1,0⟩, +⟨⟨0,114,723,true⟩,723,1,2⟩, +⟨⟨1,64,114,true⟩,1,1,0⟩, +⟨⟨1,32,114,true⟩,1,1,0⟩, +⟨⟨1,16,114,true⟩,1,1,0⟩, +⟨⟨1,9,114,true⟩,1,1,0⟩, +⟨⟨1,8,114,true⟩,1,1,0⟩, +⟨⟨1,4,114,true⟩,1,1,0⟩, +⟨⟨1,1,114,true⟩,1,1,0⟩, +⟨⟨0,113,723,true⟩,723,1,2⟩, +⟨⟨1,64,113,true⟩,1,1,0⟩, +⟨⟨1,32,113,true⟩,1,1,0⟩, +⟨⟨1,16,113,true⟩,1,1,0⟩, +⟨⟨1,9,113,true⟩,1,1,0⟩, +⟨⟨1,8,113,true⟩,1,1,0⟩, +⟨⟨1,4,113,true⟩,1,1,0⟩, +⟨⟨1,2,113,true⟩,1,1,0⟩, +⟨⟨0,112,717,true⟩,717,1,2⟩, +⟨⟨1,64,112,true⟩,1,1,0⟩, +⟨⟨1,32,112,true⟩,1,1,0⟩, +⟨⟨1,16,112,true⟩,1,1,0⟩, +⟨⟨1,4,112,true⟩,1,1,0⟩, +⟨⟨1,2,112,true⟩,1,1,0⟩, +⟨⟨1,1,112,true⟩,1,1,0⟩, +⟨⟨1,0,112,true⟩,1,1,0⟩, +⟨⟨0,111,766,true⟩,766,1,2⟩, +⟨⟨1,64,111,true⟩,1,1,0⟩, +⟨⟨1,32,111,true⟩,1,1,0⟩, +⟨⟨1,9,111,true⟩,1,1,0⟩, +⟨⟨1,1,111,true⟩,1,1,0⟩, +⟨⟨1,0,111,true⟩,1,1,0⟩, +⟨⟨0,110,760,true⟩,760,1,2⟩, +⟨⟨1,64,110,true⟩,1,1,0⟩, +⟨⟨1,32,110,true⟩,1,1,0⟩, +⟨⟨1,8,110,true⟩,1,1,0⟩, +⟨⟨1,1,110,true⟩,1,1,0⟩, +⟨⟨1,0,110,true⟩,1,1,0⟩, +⟨⟨0,109,760,true⟩,760,1,2⟩, +⟨⟨1,64,109,true⟩,1,1,0⟩, +⟨⟨1,32,109,true⟩,1,1,0⟩, +⟨⟨1,8,109,true⟩,1,1,0⟩, +⟨⟨1,2,109,true⟩,1,1,0⟩, +⟨⟨1,1,109,true⟩,1,1,0⟩, +⟨⟨0,108,766,true⟩,766,1,2⟩, +⟨⟨1,64,108,true⟩,1,1,0⟩, +⟨⟨1,32,108,true⟩,1,1,0⟩, +⟨⟨1,9,108,true⟩,1,1,0⟩, +⟨⟨1,2,108,true⟩,1,1,0⟩, +⟨⟨1,1,108,true⟩,1,1,0⟩, +⟨⟨0,107,765,true⟩,765,1,2⟩, +⟨⟨1,64,107,true⟩,1,1,0⟩, +⟨⟨1,32,107,true⟩,1,1,0⟩, +⟨⟨1,8,107,true⟩,1,1,0⟩, +⟨⟨1,4,107,true⟩,1,1,0⟩, +⟨⟨1,1,107,true⟩,1,1,0⟩, +⟨⟨0,106,771,true⟩,771,1,2⟩, +⟨⟨1,64,106,true⟩,1,1,0⟩, +⟨⟨1,32,106,true⟩,1,1,0⟩, +⟨⟨1,9,106,true⟩,1,1,0⟩, +⟨⟨1,4,106,true⟩,1,1,0⟩, +⟨⟨1,1,106,true⟩,1,1,0⟩, +⟨⟨0,105,771,true⟩,771,1,2⟩, +⟨⟨1,64,105,true⟩,1,1,0⟩, +⟨⟨1,32,105,true⟩,1,1,0⟩, +⟨⟨1,9,105,true⟩,1,1,0⟩, +⟨⟨1,4,105,true⟩,1,1,0⟩, +⟨⟨1,2,105,true⟩,1,1,0⟩, +⟨⟨1,1,105,true⟩,1,1,0⟩, +⟨⟨1,0,105,true⟩,1,1,0⟩, +⟨⟨0,104,765,true⟩,765,1,2⟩, +⟨⟨1,64,104,true⟩,1,1,0⟩, +⟨⟨1,32,104,true⟩,1,1,0⟩, +⟨⟨1,8,104,true⟩,1,1,0⟩, +⟨⟨1,4,104,true⟩,1,1,0⟩, +⟨⟨1,2,104,true⟩,1,1,0⟩, +⟨⟨1,1,104,true⟩,1,1,0⟩, +⟨⟨1,0,104,true⟩,1,1,0⟩, +⟨⟨0,103,778,true⟩,778,1,2⟩, +⟨⟨1,64,103,true⟩,1,1,0⟩, +⟨⟨1,32,103,true⟩,1,1,0⟩, +⟨⟨1,2,103,true⟩,1,1,0⟩] +def chunk65 : List Entry := [⟨⟨1,1,103,true⟩,1,1,0⟩, +⟨⟨1,0,103,true⟩,1,1,0⟩, +⟨⟨0,102,772,true⟩,772,1,2⟩, +⟨⟨1,64,102,true⟩,1,1,0⟩, +⟨⟨1,32,102,true⟩,1,1,0⟩, +⟨⟨1,9,102,true⟩,1,1,0⟩, +⟨⟨1,8,102,true⟩,1,1,0⟩, +⟨⟨1,1,102,true⟩,1,1,0⟩, +⟨⟨0,101,772,true⟩,772,1,2⟩, +⟨⟨1,64,101,true⟩,1,1,0⟩, +⟨⟨1,32,101,true⟩,1,1,0⟩, +⟨⟨1,9,101,true⟩,1,1,0⟩, +⟨⟨1,8,101,true⟩,1,1,0⟩, +⟨⟨1,0,101,true⟩,1,1,0⟩, +⟨⟨0,100,778,true⟩,778,1,2⟩, +⟨⟨1,64,100,true⟩,1,1,0⟩, +⟨⟨1,32,100,true⟩,1,1,0⟩, +⟨⟨1,2,100,true⟩,1,1,0⟩, +⟨⟨0,99,777,true⟩,777,1,2⟩, +⟨⟨1,64,99,true⟩,1,1,0⟩, +⟨⟨1,32,99,true⟩,1,1,0⟩, +⟨⟨1,9,99,true⟩,1,1,0⟩, +⟨⟨1,8,99,true⟩,1,1,0⟩, +⟨⟨1,4,99,true⟩,1,1,0⟩, +⟨⟨1,2,99,true⟩,1,1,0⟩, +⟨⟨1,1,99,true⟩,1,1,0⟩, +⟨⟨0,98,783,true⟩,783,1,2⟩, +⟨⟨1,64,98,true⟩,1,1,0⟩, +⟨⟨1,32,98,true⟩,1,1,0⟩, +⟨⟨1,4,98,true⟩,1,1,0⟩, +⟨⟨1,1,98,true⟩,1,1,0⟩, +⟨⟨1,0,98,true⟩,1,1,0⟩, +⟨⟨0,97,783,true⟩,783,1,2⟩, +⟨⟨1,64,97,true⟩,1,1,0⟩, +⟨⟨1,32,97,true⟩,1,1,0⟩, +⟨⟨1,4,97,true⟩,1,1,0⟩, +⟨⟨0,96,777,true⟩,777,1,2⟩, +⟨⟨1,64,96,true⟩,1,1,0⟩, +⟨⟨1,32,96,true⟩,1,1,0⟩, +⟨⟨1,9,96,true⟩,1,1,0⟩, +⟨⟨1,8,96,true⟩,1,1,0⟩, +⟨⟨1,4,96,true⟩,1,1,0⟩, +⟨⟨1,2,96,true⟩,1,1,0⟩, +⟨⟨1,0,96,true⟩,1,1,0⟩, +⟨⟨0,95,790,true⟩,790,1,2⟩, +⟨⟨1,64,95,true⟩,1,1,0⟩, +⟨⟨1,16,95,true⟩,1,1,0⟩, +⟨⟨1,9,95,true⟩,1,1,0⟩, +⟨⟨1,2,95,true⟩,1,1,0⟩, +⟨⟨1,0,95,true⟩,1,1,0⟩, +⟨⟨0,94,784,true⟩,784,1,2⟩, +⟨⟨1,64,94,true⟩,1,1,0⟩, +⟨⟨1,16,94,true⟩,1,1,0⟩, +⟨⟨1,8,94,true⟩,1,1,0⟩, +⟨⟨1,2,94,true⟩,1,1,0⟩, +⟨⟨1,0,94,true⟩,1,1,0⟩, +⟨⟨0,93,784,true⟩,784,1,2⟩, +⟨⟨1,64,93,true⟩,1,1,0⟩, +⟨⟨1,16,93,true⟩,1,1,0⟩, +⟨⟨1,8,93,true⟩,1,1,0⟩, +⟨⟨1,2,93,true⟩,1,1,0⟩, +⟨⟨1,1,93,true⟩,1,1,0⟩, +⟨⟨0,92,790,true⟩,790,1,2⟩, +⟨⟨1,64,92,true⟩,1,1,0⟩, +⟨⟨1,16,92,true⟩,1,1,0⟩, +⟨⟨1,9,92,true⟩,1,1,0⟩, +⟨⟨1,2,92,true⟩,1,1,0⟩, +⟨⟨1,1,92,true⟩,1,1,0⟩, +⟨⟨0,91,789,true⟩,789,1,2⟩, +⟨⟨1,64,91,true⟩,1,1,0⟩, +⟨⟨1,16,91,true⟩,1,1,0⟩, +⟨⟨1,8,91,true⟩,1,1,0⟩, +⟨⟨1,4,91,true⟩,1,1,0⟩, +⟨⟨1,2,91,true⟩,1,1,0⟩, +⟨⟨0,90,795,true⟩,795,1,2⟩, +⟨⟨1,64,90,true⟩,1,1,0⟩, +⟨⟨1,16,90,true⟩,1,1,0⟩, +⟨⟨1,9,90,true⟩,1,1,0⟩, +⟨⟨1,4,90,true⟩,1,1,0⟩, +⟨⟨1,2,90,true⟩,1,1,0⟩, +⟨⟨0,89,795,true⟩,795,1,2⟩, +⟨⟨1,64,89,true⟩,1,1,0⟩, +⟨⟨1,16,89,true⟩,1,1,0⟩, +⟨⟨1,9,89,true⟩,1,1,0⟩, +⟨⟨1,4,89,true⟩,1,1,0⟩, +⟨⟨1,2,89,true⟩,1,1,0⟩, +⟨⟨1,1,89,true⟩,1,1,0⟩, +⟨⟨1,0,89,true⟩,1,1,0⟩, +⟨⟨0,88,789,true⟩,789,1,2⟩, +⟨⟨1,64,88,true⟩,1,1,0⟩, +⟨⟨1,16,88,true⟩,1,1,0⟩, +⟨⟨1,8,88,true⟩,1,1,0⟩, +⟨⟨1,4,88,true⟩,1,1,0⟩, +⟨⟨1,2,88,true⟩,1,1,0⟩, +⟨⟨1,1,88,true⟩,1,1,0⟩, +⟨⟨1,0,88,true⟩,1,1,0⟩, +⟨⟨0,87,754,true⟩,754,1,2⟩, +⟨⟨1,64,87,true⟩,1,1,0⟩, +⟨⟨1,16,87,true⟩,1,1,0⟩, +⟨⟨1,2,87,true⟩,1,1,0⟩, +⟨⟨1,1,87,true⟩,1,1,0⟩, +⟨⟨1,0,87,true⟩,1,1,0⟩, +⟨⟨0,86,748,true⟩,748,1,2⟩, +⟨⟨1,64,86,true⟩,1,1,0⟩, +⟨⟨1,16,86,true⟩,1,1,0⟩, +⟨⟨1,9,86,true⟩,1,1,0⟩, +⟨⟨1,8,86,true⟩,1,1,0⟩, +⟨⟨1,2,86,true⟩,1,1,0⟩, +⟨⟨0,85,748,true⟩,748,1,2⟩, +⟨⟨1,64,85,true⟩,1,1,0⟩, +⟨⟨1,16,85,true⟩,1,1,0⟩, +⟨⟨1,9,85,true⟩,1,1,0⟩, +⟨⟨1,8,85,true⟩,1,1,0⟩, +⟨⟨1,0,85,true⟩,1,1,0⟩, +⟨⟨0,84,754,true⟩,754,1,2⟩, +⟨⟨1,64,84,true⟩,1,1,0⟩, +⟨⟨1,16,84,true⟩,1,1,0⟩, +⟨⟨1,1,84,true⟩,1,1,0⟩, +⟨⟨0,83,753,true⟩,753,1,2⟩, +⟨⟨1,64,83,true⟩,1,1,0⟩, +⟨⟨1,16,83,true⟩,1,1,0⟩, +⟨⟨1,9,83,true⟩,1,1,0⟩, +⟨⟨1,8,83,true⟩,1,1,0⟩, +⟨⟨1,4,83,true⟩,1,1,0⟩, +⟨⟨1,2,83,true⟩,1,1,0⟩, +⟨⟨1,1,83,true⟩,1,1,0⟩, +⟨⟨0,82,759,true⟩,759,1,2⟩, +⟨⟨1,64,82,true⟩,1,1,0⟩, +⟨⟨1,16,82,true⟩,1,1,0⟩, +⟨⟨1,4,82,true⟩,1,1,0⟩, +⟨⟨1,2,82,true⟩,1,1,0⟩, +⟨⟨1,0,82,true⟩,1,1,0⟩, +⟨⟨0,81,759,true⟩,759,1,2⟩, +⟨⟨1,64,81,true⟩,1,1,0⟩, +⟨⟨1,16,81,true⟩,1,1,0⟩, +⟨⟨1,4,81,true⟩,1,1,0⟩, +⟨⟨0,80,753,true⟩,753,1,2⟩, +⟨⟨1,64,80,true⟩,1,1,0⟩, +⟨⟨1,16,80,true⟩,1,1,0⟩, +⟨⟨1,9,80,true⟩,1,1,0⟩, +⟨⟨1,8,80,true⟩,1,1,0⟩, +⟨⟨1,4,80,true⟩,1,1,0⟩, +⟨⟨1,1,80,true⟩,1,1,0⟩, +⟨⟨1,0,80,true⟩,1,1,0⟩, +⟨⟨0,79,706,true⟩,706,1,2⟩, +⟨⟨1,64,79,true⟩,1,1,0⟩, +⟨⟨1,8,79,true⟩,1,1,0⟩, +⟨⟨1,2,79,true⟩,1,1,0⟩, +⟨⟨1,1,79,true⟩,1,1,0⟩, +⟨⟨1,0,79,true⟩,1,1,0⟩, +⟨⟨0,78,700,true⟩,700,1,2⟩, +⟨⟨1,64,78,true⟩,1,1,0⟩, +⟨⟨1,9,78,true⟩,1,1,0⟩, +⟨⟨1,2,78,true⟩,1,1,0⟩, +⟨⟨1,1,78,true⟩,1,1,0⟩, +⟨⟨1,0,78,true⟩,1,1,0⟩, +⟨⟨0,77,700,true⟩,700,1,2⟩, +⟨⟨1,64,77,true⟩,1,1,0⟩, +⟨⟨1,9,77,true⟩,1,1,0⟩, +⟨⟨1,0,77,true⟩,1,1,0⟩, +⟨⟨0,76,706,true⟩,706,1,2⟩, +⟨⟨1,64,76,true⟩,1,1,0⟩, +⟨⟨1,8,76,true⟩,1,1,0⟩, +⟨⟨1,0,76,true⟩,1,1,0⟩, +⟨⟨0,75,705,true⟩,705,1,2⟩, +⟨⟨1,64,75,true⟩,1,1,0⟩, +⟨⟨1,9,75,true⟩,1,1,0⟩, +⟨⟨1,4,75,true⟩,1,1,0⟩, +⟨⟨1,2,75,true⟩,1,1,0⟩, +⟨⟨1,1,75,true⟩,1,1,0⟩, +⟨⟨0,74,711,true⟩,711,1,2⟩, +⟨⟨1,64,74,true⟩,1,1,0⟩, +⟨⟨1,8,74,true⟩,1,1,0⟩, +⟨⟨1,4,74,true⟩,1,1,0⟩, +⟨⟨1,2,74,true⟩,1,1,0⟩, +⟨⟨1,1,74,true⟩,1,1,0⟩, +⟨⟨0,73,711,true⟩,711,1,2⟩, +⟨⟨1,64,73,true⟩,1,1,0⟩, +⟨⟨1,8,73,true⟩,1,1,0⟩, +⟨⟨1,4,73,true⟩,1,1,0⟩, +⟨⟨0,72,705,true⟩,705,1,2⟩, +⟨⟨1,64,72,true⟩,1,1,0⟩, +⟨⟨1,9,72,true⟩,1,1,0⟩, +⟨⟨1,4,72,true⟩,1,1,0⟩, +⟨⟨0,71,646,true⟩,646,1,2⟩, +⟨⟨1,64,71,true⟩,1,1,0⟩, +⟨⟨1,9,71,true⟩,1,1,0⟩, +⟨⟨1,8,71,true⟩,1,1,0⟩, +⟨⟨1,4,71,true⟩,1,1,0⟩, +⟨⟨1,2,71,true⟩,1,1,0⟩, +⟨⟨1,1,71,true⟩,1,1,0⟩, +⟨⟨1,0,71,true⟩,1,1,0⟩, +⟨⟨0,70,640,true⟩,640,1,2⟩, +⟨⟨1,64,70,true⟩,1,1,0⟩, +⟨⟨1,2,70,true⟩,1,1,0⟩, +⟨⟨1,1,70,true⟩,1,1,0⟩, +⟨⟨0,69,640,true⟩,640,1,2⟩, +⟨⟨1,64,69,true⟩,1,1,0⟩, +⟨⟨1,2,69,true⟩,1,1,0⟩, +⟨⟨1,0,69,true⟩,1,1,0⟩] +def chunk66 : List Entry := [⟨⟨0,68,646,true⟩,646,1,2⟩, +⟨⟨1,64,68,true⟩,1,1,0⟩, +⟨⟨1,9,68,true⟩,1,1,0⟩, +⟨⟨1,8,68,true⟩,1,1,0⟩, +⟨⟨1,4,68,true⟩,1,1,0⟩, +⟨⟨1,2,68,true⟩,1,1,0⟩, +⟨⟨0,67,645,true⟩,645,1,2⟩, +⟨⟨1,64,67,true⟩,1,1,0⟩, +⟨⟨1,1,67,true⟩,1,1,0⟩, +⟨⟨1,0,67,true⟩,1,1,0⟩, +⟨⟨0,66,651,true⟩,651,1,2⟩, +⟨⟨1,64,66,true⟩,1,1,0⟩, +⟨⟨1,9,66,true⟩,1,1,0⟩, +⟨⟨1,8,66,true⟩,1,1,0⟩, +⟨⟨1,4,66,true⟩,1,1,0⟩, +⟨⟨1,1,66,true⟩,1,1,0⟩, +⟨⟨0,65,651,true⟩,651,1,2⟩, +⟨⟨1,64,65,true⟩,1,1,0⟩, +⟨⟨1,9,65,true⟩,1,1,0⟩, +⟨⟨1,8,65,true⟩,1,1,0⟩, +⟨⟨1,4,65,true⟩,1,1,0⟩, +⟨⟨1,0,65,true⟩,1,1,0⟩, +⟨⟨1,32,64,true⟩,1,1,0⟩, +⟨⟨1,16,64,true⟩,1,1,0⟩, +⟨⟨1,4,64,true⟩,1,1,0⟩, +⟨⟨1,2,64,true⟩,1,1,0⟩, +⟨⟨1,1,64,true⟩,1,1,0⟩, +⟨⟨0,63,802,true⟩,802,1,2⟩, +⟨⟨1,32,63,true⟩,1,1,0⟩, +⟨⟨1,16,63,true⟩,1,1,0⟩, +⟨⟨1,9,63,true⟩,1,1,0⟩, +⟨⟨1,4,63,true⟩,1,1,0⟩, +⟨⟨1,0,63,true⟩,1,1,0⟩, +⟨⟨0,62,796,true⟩,796,1,2⟩, +⟨⟨1,32,62,true⟩,1,1,0⟩, +⟨⟨1,16,62,true⟩,1,1,0⟩, +⟨⟨1,8,62,true⟩,1,1,0⟩, +⟨⟨1,4,62,true⟩,1,1,0⟩, +⟨⟨1,0,62,true⟩,1,1,0⟩, +⟨⟨0,61,796,true⟩,796,1,2⟩, +⟨⟨1,32,61,true⟩,1,1,0⟩, +⟨⟨1,16,61,true⟩,1,1,0⟩, +⟨⟨1,8,61,true⟩,1,1,0⟩, +⟨⟨1,4,61,true⟩,1,1,0⟩, +⟨⟨1,1,61,true⟩,1,1,0⟩, +⟨⟨0,60,802,true⟩,802,1,2⟩, +⟨⟨1,32,60,true⟩,1,1,0⟩, +⟨⟨1,16,60,true⟩,1,1,0⟩, +⟨⟨1,9,60,true⟩,1,1,0⟩, +⟨⟨1,4,60,true⟩,1,1,0⟩, +⟨⟨1,1,60,true⟩,1,1,0⟩, +⟨⟨0,59,801,true⟩,801,1,2⟩, +⟨⟨1,32,59,true⟩,1,1,0⟩, +⟨⟨1,16,59,true⟩,1,1,0⟩, +⟨⟨1,8,59,true⟩,1,1,0⟩, +⟨⟨1,4,59,true⟩,1,1,0⟩, +⟨⟨1,2,59,true⟩,1,1,0⟩, +⟨⟨0,58,807,true⟩,807,1,2⟩, +⟨⟨1,32,58,true⟩,1,1,0⟩, +⟨⟨1,16,58,true⟩,1,1,0⟩, +⟨⟨1,9,58,true⟩,1,1,0⟩, +⟨⟨1,4,58,true⟩,1,1,0⟩, +⟨⟨1,2,58,true⟩,1,1,0⟩, +⟨⟨0,57,807,true⟩,807,1,2⟩, +⟨⟨1,32,57,true⟩,1,1,0⟩, +⟨⟨1,16,57,true⟩,1,1,0⟩, +⟨⟨1,9,57,true⟩,1,1,0⟩, +⟨⟨1,4,57,true⟩,1,1,0⟩, +⟨⟨1,2,57,true⟩,1,1,0⟩, +⟨⟨1,1,57,true⟩,1,1,0⟩, +⟨⟨1,0,57,true⟩,1,1,0⟩, +⟨⟨0,56,801,true⟩,801,1,2⟩, +⟨⟨1,32,56,true⟩,1,1,0⟩, +⟨⟨1,16,56,true⟩,1,1,0⟩, +⟨⟨1,8,56,true⟩,1,1,0⟩, +⟨⟨1,4,56,true⟩,1,1,0⟩, +⟨⟨1,2,56,true⟩,1,1,0⟩, +⟨⟨1,1,56,true⟩,1,1,0⟩, +⟨⟨1,0,56,true⟩,1,1,0⟩, +⟨⟨0,55,742,true⟩,742,1,2⟩, +⟨⟨1,32,55,true⟩,1,1,0⟩, +⟨⟨1,16,55,true⟩,1,1,0⟩, +⟨⟨1,4,55,true⟩,1,1,0⟩, +⟨⟨1,1,55,true⟩,1,1,0⟩, +⟨⟨1,0,55,true⟩,1,1,0⟩, +⟨⟨0,54,736,true⟩,736,1,2⟩, +⟨⟨1,32,54,true⟩,1,1,0⟩, +⟨⟨1,16,54,true⟩,1,1,0⟩, +⟨⟨1,9,54,true⟩,1,1,0⟩, +⟨⟨1,8,54,true⟩,1,1,0⟩, +⟨⟨1,4,54,true⟩,1,1,0⟩, +⟨⟨0,53,736,true⟩,736,1,2⟩, +⟨⟨1,32,53,true⟩,1,1,0⟩, +⟨⟨1,16,53,true⟩,1,1,0⟩, +⟨⟨1,9,53,true⟩,1,1,0⟩, +⟨⟨1,8,53,true⟩,1,1,0⟩, +⟨⟨1,4,53,true⟩,1,1,0⟩, +⟨⟨1,2,53,true⟩,1,1,0⟩, +⟨⟨1,1,53,true⟩,1,1,0⟩, +⟨⟨0,52,742,true⟩,742,1,2⟩, +⟨⟨1,32,52,true⟩,1,1,0⟩, +⟨⟨1,16,52,true⟩,1,1,0⟩, +⟨⟨1,4,52,true⟩,1,1,0⟩, +⟨⟨1,2,52,true⟩,1,1,0⟩, +⟨⟨1,0,52,true⟩,1,1,0⟩, +⟨⟨0,51,741,true⟩,741,1,2⟩, +⟨⟨1,32,51,true⟩,1,1,0⟩, +⟨⟨1,16,51,true⟩,1,1,0⟩, +⟨⟨1,9,51,true⟩,1,1,0⟩, +⟨⟨1,8,51,true⟩,1,1,0⟩, +⟨⟨1,0,51,true⟩,1,1,0⟩, +⟨⟨0,50,747,true⟩,747,1,2⟩, +⟨⟨1,32,50,true⟩,1,1,0⟩, +⟨⟨1,16,50,true⟩,1,1,0⟩, +⟨⟨1,1,50,true⟩,1,1,0⟩, +⟨⟨0,49,747,true⟩,747,1,2⟩, +⟨⟨1,32,49,true⟩,1,1,0⟩, +⟨⟨1,16,49,true⟩,1,1,0⟩, +⟨⟨1,2,49,true⟩,1,1,0⟩, +⟨⟨0,48,741,true⟩,741,1,2⟩, +⟨⟨1,32,48,true⟩,1,1,0⟩, +⟨⟨1,16,48,true⟩,1,1,0⟩, +⟨⟨1,9,48,true⟩,1,1,0⟩, +⟨⟨1,8,48,true⟩,1,1,0⟩, +⟨⟨1,2,48,true⟩,1,1,0⟩, +⟨⟨1,1,48,true⟩,1,1,0⟩, +⟨⟨1,0,48,true⟩,1,1,0⟩, +⟨⟨0,47,694,true⟩,694,1,2⟩, +⟨⟨1,32,47,true⟩,1,1,0⟩, +⟨⟨1,8,47,true⟩,1,1,0⟩, +⟨⟨1,4,47,true⟩,1,1,0⟩, +⟨⟨1,1,47,true⟩,1,1,0⟩, +⟨⟨1,0,47,true⟩,1,1,0⟩, +⟨⟨0,46,688,true⟩,688,1,2⟩, +⟨⟨1,32,46,true⟩,1,1,0⟩, +⟨⟨1,9,46,true⟩,1,1,0⟩, +⟨⟨1,4,46,true⟩,1,1,0⟩, +⟨⟨1,1,46,true⟩,1,1,0⟩, +⟨⟨1,0,46,true⟩,1,1,0⟩, +⟨⟨0,45,688,true⟩,688,1,2⟩, +⟨⟨1,32,45,true⟩,1,1,0⟩, +⟨⟨1,9,45,true⟩,1,1,0⟩, +⟨⟨1,4,45,true⟩,1,1,0⟩, +⟨⟨1,2,45,true⟩,1,1,0⟩, +⟨⟨1,1,45,true⟩,1,1,0⟩, +⟨⟨0,44,694,true⟩,694,1,2⟩, +⟨⟨1,32,44,true⟩,1,1,0⟩, +⟨⟨1,8,44,true⟩,1,1,0⟩, +⟨⟨1,4,44,true⟩,1,1,0⟩, +⟨⟨1,2,44,true⟩,1,1,0⟩, +⟨⟨1,1,44,true⟩,1,1,0⟩, +⟨⟨0,43,693,true⟩,693,1,2⟩, +⟨⟨1,32,43,true⟩,1,1,0⟩, +⟨⟨1,9,43,true⟩,1,1,0⟩, +⟨⟨1,0,43,true⟩,1,1,0⟩, +⟨⟨0,42,699,true⟩,699,1,2⟩, +⟨⟨1,32,42,true⟩,1,1,0⟩, +⟨⟨1,8,42,true⟩,1,1,0⟩, +⟨⟨1,0,42,true⟩,1,1,0⟩, +⟨⟨0,41,699,true⟩,699,1,2⟩, +⟨⟨1,32,41,true⟩,1,1,0⟩, +⟨⟨1,8,41,true⟩,1,1,0⟩, +⟨⟨1,2,41,true⟩,1,1,0⟩, +⟨⟨0,40,693,true⟩,693,1,2⟩, +⟨⟨1,32,40,true⟩,1,1,0⟩, +⟨⟨1,9,40,true⟩,1,1,0⟩, +⟨⟨1,2,40,true⟩,1,1,0⟩, +⟨⟨0,39,658,true⟩,658,1,2⟩, +⟨⟨1,32,39,true⟩,1,1,0⟩, +⟨⟨1,9,39,true⟩,1,1,0⟩, +⟨⟨1,8,39,true⟩,1,1,0⟩, +⟨⟨1,4,39,true⟩,1,1,0⟩, +⟨⟨1,2,39,true⟩,1,1,0⟩, +⟨⟨1,1,39,true⟩,1,1,0⟩, +⟨⟨1,0,39,true⟩,1,1,0⟩, +⟨⟨0,38,652,true⟩,652,1,2⟩, +⟨⟨1,32,38,true⟩,1,1,0⟩, +⟨⟨1,4,38,true⟩,1,1,0⟩, +⟨⟨1,1,38,true⟩,1,1,0⟩, +⟨⟨0,37,652,true⟩,652,1,2⟩, +⟨⟨1,32,37,true⟩,1,1,0⟩, +⟨⟨1,4,37,true⟩,1,1,0⟩, +⟨⟨1,0,37,true⟩,1,1,0⟩, +⟨⟨0,36,658,true⟩,658,1,2⟩, +⟨⟨1,32,36,true⟩,1,1,0⟩, +⟨⟨1,9,36,true⟩,1,1,0⟩, +⟨⟨1,8,36,true⟩,1,1,0⟩, +⟨⟨1,4,36,true⟩,1,1,0⟩, +⟨⟨1,2,36,true⟩,1,1,0⟩, +⟨⟨0,35,657,true⟩,657,1,2⟩, +⟨⟨1,32,35,true⟩,1,1,0⟩, +⟨⟨1,1,35,true⟩,1,1,0⟩, +⟨⟨1,0,35,true⟩,1,1,0⟩, +⟨⟨0,34,663,true⟩,663,1,2⟩, +⟨⟨1,32,34,true⟩,1,1,0⟩, +⟨⟨1,9,34,true⟩,1,1,0⟩, +⟨⟨1,8,34,true⟩,1,1,0⟩, +⟨⟨1,2,34,true⟩,1,1,0⟩, +⟨⟨1,1,34,true⟩,1,1,0⟩, +⟨⟨0,33,663,true⟩,663,1,2⟩] +def chunk67 : List Entry := [⟨⟨1,32,33,true⟩,1,1,0⟩, +⟨⟨1,9,33,true⟩,1,1,0⟩, +⟨⟨1,8,33,true⟩,1,1,0⟩, +⟨⟨1,2,33,true⟩,1,1,0⟩, +⟨⟨1,0,33,true⟩,1,1,0⟩, +⟨⟨1,64,32,true⟩,1,1,0⟩, +⟨⟨1,8,32,true⟩,1,1,0⟩, +⟨⟨1,2,32,true⟩,1,1,0⟩, +⟨⟨1,0,32,true⟩,1,1,0⟩, +⟨⟨0,31,670,true⟩,670,1,2⟩, +⟨⟨1,16,31,true⟩,1,1,0⟩, +⟨⟨1,8,31,true⟩,1,1,0⟩, +⟨⟨1,4,31,true⟩,1,1,0⟩, +⟨⟨1,2,31,true⟩,1,1,0⟩, +⟨⟨1,0,31,true⟩,1,1,0⟩, +⟨⟨0,30,664,true⟩,664,1,2⟩, +⟨⟨1,16,30,true⟩,1,1,0⟩, +⟨⟨1,9,30,true⟩,1,1,0⟩, +⟨⟨1,4,30,true⟩,1,1,0⟩, +⟨⟨1,2,30,true⟩,1,1,0⟩, +⟨⟨1,0,30,true⟩,1,1,0⟩, +⟨⟨0,29,664,true⟩,664,1,2⟩, +⟨⟨1,16,29,true⟩,1,1,0⟩, +⟨⟨1,9,29,true⟩,1,1,0⟩, +⟨⟨1,4,29,true⟩,1,1,0⟩, +⟨⟨1,2,29,true⟩,1,1,0⟩, +⟨⟨1,1,29,true⟩,1,1,0⟩, +⟨⟨0,28,670,true⟩,670,1,2⟩, +⟨⟨1,16,28,true⟩,1,1,0⟩, +⟨⟨1,8,28,true⟩,1,1,0⟩, +⟨⟨1,4,28,true⟩,1,1,0⟩, +⟨⟨1,2,28,true⟩,1,1,0⟩, +⟨⟨1,1,28,true⟩,1,1,0⟩, +⟨⟨0,27,669,true⟩,669,1,2⟩, +⟨⟨1,16,27,true⟩,1,1,0⟩, +⟨⟨1,9,27,true⟩,1,1,0⟩, +⟨⟨1,0,27,true⟩,1,1,0⟩, +⟨⟨0,26,675,true⟩,675,1,2⟩, +⟨⟨1,16,26,true⟩,1,1,0⟩, +⟨⟨1,8,26,true⟩,1,1,0⟩, +⟨⟨1,0,26,true⟩,1,1,0⟩, +⟨⟨0,25,675,true⟩,675,1,2⟩, +⟨⟨1,16,25,true⟩,1,1,0⟩, +⟨⟨1,8,25,true⟩,1,1,0⟩, +⟨⟨1,1,25,true⟩,1,1,0⟩, +⟨⟨0,24,669,true⟩,669,1,2⟩, +⟨⟨1,16,24,true⟩,1,1,0⟩, +⟨⟨1,9,24,true⟩,1,1,0⟩, +⟨⟨1,1,24,true⟩,1,1,0⟩, +⟨⟨0,23,682,true⟩,682,1,2⟩, +⟨⟨1,16,23,true⟩,1,1,0⟩, +⟨⟨1,9,23,true⟩,1,1,0⟩, +⟨⟨1,8,23,true⟩,1,1,0⟩, +⟨⟨1,4,23,true⟩,1,1,0⟩, +⟨⟨1,2,23,true⟩,1,1,0⟩, +⟨⟨1,1,23,true⟩,1,1,0⟩, +⟨⟨1,0,23,true⟩,1,1,0⟩, +⟨⟨0,22,676,true⟩,676,1,2⟩, +⟨⟨1,16,22,true⟩,1,1,0⟩, +⟨⟨1,4,22,true⟩,1,1,0⟩, +⟨⟨1,2,22,true⟩,1,1,0⟩, +⟨⟨0,21,676,true⟩,676,1,2⟩, +⟨⟨1,16,21,true⟩,1,1,0⟩, +⟨⟨1,4,21,true⟩,1,1,0⟩, +⟨⟨1,0,21,true⟩,1,1,0⟩, +⟨⟨0,20,682,true⟩,682,1,2⟩, +⟨⟨1,16,20,true⟩,1,1,0⟩, +⟨⟨1,9,20,true⟩,1,1,0⟩, +⟨⟨1,8,20,true⟩,1,1,0⟩, +⟨⟨1,4,20,true⟩,1,1,0⟩, +⟨⟨1,1,20,true⟩,1,1,0⟩, +⟨⟨0,19,681,true⟩,681,1,2⟩, +⟨⟨1,16,19,true⟩,1,1,0⟩, +⟨⟨1,2,19,true⟩,1,1,0⟩, +⟨⟨1,0,19,true⟩,1,1,0⟩, +⟨⟨0,18,687,true⟩,687,1,2⟩, +⟨⟨1,16,18,true⟩,1,1,0⟩, +⟨⟨1,9,18,true⟩,1,1,0⟩, +⟨⟨1,8,18,true⟩,1,1,0⟩, +⟨⟨1,2,18,true⟩,1,1,0⟩, +⟨⟨1,1,18,true⟩,1,1,0⟩, +⟨⟨0,17,687,true⟩,687,1,2⟩, +⟨⟨1,16,17,true⟩,1,1,0⟩, +⟨⟨1,9,17,true⟩,1,1,0⟩, +⟨⟨1,8,17,true⟩,1,1,0⟩, +⟨⟨1,1,17,true⟩,1,1,0⟩, +⟨⟨1,0,17,true⟩,1,1,0⟩, +⟨⟨1,64,16,true⟩,1,1,0⟩, +⟨⟨1,8,16,true⟩,1,1,0⟩, +⟨⟨1,1,16,true⟩,1,1,0⟩, +⟨⟨1,0,16,true⟩,1,1,0⟩, +⟨⟨0,15,730,true⟩,730,1,2⟩, +⟨⟨1,9,15,true⟩,1,1,0⟩, +⟨⟨1,4,15,true⟩,1,1,0⟩, +⟨⟨1,2,15,true⟩,1,1,0⟩, +⟨⟨0,14,724,true⟩,724,1,2⟩, +⟨⟨1,8,14,true⟩,1,1,0⟩, +⟨⟨1,4,14,true⟩,1,1,0⟩, +⟨⟨1,2,14,true⟩,1,1,0⟩, +⟨⟨0,13,724,true⟩,724,1,2⟩, +⟨⟨1,8,13,true⟩,1,1,0⟩, +⟨⟨1,4,13,true⟩,1,1,0⟩, +⟨⟨1,1,13,true⟩,1,1,0⟩, +⟨⟨0,12,730,true⟩,730,1,2⟩, +⟨⟨1,9,12,true⟩,1,1,0⟩, +⟨⟨1,4,12,true⟩,1,1,0⟩, +⟨⟨1,1,12,true⟩,1,1,0⟩, +⟨⟨0,11,729,true⟩,729,1,2⟩, +⟨⟨1,8,11,true⟩,1,1,0⟩, +⟨⟨1,2,11,true⟩,1,1,0⟩, +⟨⟨1,1,11,true⟩,1,1,0⟩, +⟨⟨0,10,735,true⟩,735,1,2⟩, +⟨⟨1,9,10,true⟩,1,1,0⟩, +⟨⟨1,2,10,true⟩,1,1,0⟩, +⟨⟨1,1,10,true⟩,1,1,0⟩, +⟨⟨1,8,9,true⟩,1,1,0⟩, +⟨⟨1,4,9,true⟩,1,1,0⟩, +⟨⟨1,0,9,true⟩,1,1,0⟩, +⟨⟨1,9,64,true⟩,1,1,0⟩, +⟨⟨1,64,9,true⟩,1,1,0⟩, +⟨⟨1,9,64,true⟩,1,1,0⟩, +⟨⟨1,32,8,true⟩,1,1,0⟩, +⟨⟨1,16,8,true⟩,1,1,0⟩, +⟨⟨1,0,8,true⟩,1,1,0⟩, +⟨⟨0,7,813,true⟩,813,1,2⟩, +⟨⟨1,4,7,true⟩,1,1,0⟩, +⟨⟨1,2,7,true⟩,1,1,0⟩, +⟨⟨1,1,7,true⟩,1,1,0⟩, +⟨⟨0,6,813,true⟩,813,1,2⟩, +⟨⟨1,4,6,true⟩,1,1,0⟩, +⟨⟨1,2,6,true⟩,1,1,0⟩, +⟨⟨1,0,6,true⟩,1,1,0⟩, +⟨⟨0,5,831,true⟩,831,1,1⟩, +⟨⟨1,4,5,true⟩,1,1,0⟩, +⟨⟨1,1,5,true⟩,1,1,0⟩, +⟨⟨1,0,5,true⟩,1,1,0⟩, +⟨⟨1,64,4,true⟩,1,1,0⟩, +⟨⟨1,2,4,true⟩,1,1,0⟩, +⟨⟨1,4,32,true⟩,1,1,0⟩, +⟨⟨1,32,4,true⟩,1,1,0⟩, +⟨⟨1,4,32,true⟩,1,1,0⟩, +⟨⟨0,3,826,true⟩,826,1,1⟩, +⟨⟨1,2,3,true⟩,1,1,0⟩, +⟨⟨1,1,3,true⟩,1,1,0⟩, +⟨⟨1,0,3,true⟩,1,1,0⟩, +⟨⟨1,32,2,true⟩,1,1,0⟩, +⟨⟨1,1,2,true⟩,1,1,0⟩, +⟨⟨1,2,16,true⟩,1,1,0⟩, +⟨⟨1,16,2,true⟩,1,1,0⟩, +⟨⟨1,2,16,true⟩,1,1,0⟩, +⟨⟨1,16,1,true⟩,1,1,0⟩, +⟨⟨1,0,1,true⟩,1,1,0⟩, +⟨⟨1,1,9,true⟩,1,1,0⟩, +⟨⟨1,9,1,true⟩,1,1,0⟩, +⟨⟨1,1,9,true⟩,1,1,0⟩, +⟨⟨1,64,0,true⟩,1,1,0⟩, +⟨⟨1,32,0,true⟩,1,1,0⟩, +⟨⟨1,16,0,true⟩,1,1,0⟩, +⟨⟨2,0,987,true⟩,1,0,8⟩, +⟨⟨1,120,987,true⟩,0,0,0⟩, +⟨⟨1,121,987,true⟩,0,0,0⟩, +⟨⟨1,122,987,true⟩,0,0,0⟩, +⟨⟨1,123,987,true⟩,0,0,0⟩, +⟨⟨1,124,987,true⟩,0,0,0⟩, +⟨⟨1,125,987,true⟩,0,0,0⟩, +⟨⟨1,126,987,true⟩,0,0,0⟩, +⟨⟨1,127,987,true⟩,0,0,0⟩, +⟨⟨1,128,987,true⟩,0,0,0⟩, +⟨⟨1,129,987,true⟩,0,0,0⟩, +⟨⟨1,130,987,true⟩,0,0,0⟩, +⟨⟨1,131,987,true⟩,0,0,0⟩, +⟨⟨1,132,987,true⟩,0,0,0⟩, +⟨⟨1,133,987,true⟩,0,0,0⟩, +⟨⟨1,134,987,true⟩,0,0,0⟩, +⟨⟨1,135,987,true⟩,0,0,0⟩, +⟨⟨1,136,987,true⟩,0,0,0⟩, +⟨⟨1,137,987,true⟩,0,0,0⟩, +⟨⟨1,138,987,true⟩,0,0,0⟩, +⟨⟨1,139,987,true⟩,0,0,0⟩, +⟨⟨1,140,987,true⟩,0,0,0⟩, +⟨⟨1,141,987,true⟩,0,0,0⟩, +⟨⟨1,142,987,true⟩,0,0,0⟩, +⟨⟨1,143,987,true⟩,0,0,0⟩, +⟨⟨1,144,987,true⟩,0,0,0⟩, +⟨⟨1,145,987,true⟩,0,0,0⟩, +⟨⟨1,146,987,true⟩,0,0,0⟩, +⟨⟨1,147,987,true⟩,0,0,0⟩, +⟨⟨1,148,987,true⟩,0,0,0⟩, +⟨⟨1,149,987,true⟩,0,0,0⟩, +⟨⟨1,150,987,true⟩,0,0,0⟩, +⟨⟨1,151,987,true⟩,0,0,0⟩, +⟨⟨1,152,987,true⟩,0,0,0⟩, +⟨⟨1,153,987,true⟩,0,0,0⟩, +⟨⟨1,154,987,true⟩,0,0,0⟩, +⟨⟨1,155,987,true⟩,0,0,0⟩, +⟨⟨1,156,987,true⟩,0,0,0⟩, +⟨⟨1,157,987,true⟩,0,0,0⟩, +⟨⟨1,158,987,true⟩,0,0,0⟩, +⟨⟨1,159,987,true⟩,0,0,0⟩, +⟨⟨1,160,987,true⟩,0,0,0⟩] +def chunk68 : List Entry := [⟨⟨1,161,987,true⟩,0,0,0⟩, +⟨⟨1,162,987,true⟩,0,0,0⟩, +⟨⟨1,163,987,true⟩,0,0,0⟩, +⟨⟨1,164,987,true⟩,0,0,0⟩, +⟨⟨1,165,987,true⟩,0,0,0⟩, +⟨⟨1,166,987,true⟩,0,0,0⟩, +⟨⟨1,167,987,true⟩,0,0,0⟩, +⟨⟨1,168,987,true⟩,0,0,0⟩, +⟨⟨1,169,987,true⟩,0,0,0⟩, +⟨⟨1,170,987,true⟩,0,0,0⟩, +⟨⟨1,171,987,true⟩,0,0,0⟩, +⟨⟨1,172,987,true⟩,0,0,0⟩, +⟨⟨1,173,987,true⟩,0,0,0⟩, +⟨⟨1,174,987,true⟩,0,0,0⟩, +⟨⟨1,175,987,true⟩,0,0,0⟩, +⟨⟨1,176,987,true⟩,0,0,0⟩, +⟨⟨1,177,987,true⟩,0,0,0⟩, +⟨⟨1,178,987,true⟩,0,0,0⟩, +⟨⟨1,179,987,true⟩,0,0,0⟩, +⟨⟨1,180,987,true⟩,0,0,0⟩, +⟨⟨1,181,987,true⟩,0,0,0⟩, +⟨⟨1,182,987,true⟩,0,0,0⟩, +⟨⟨1,183,987,true⟩,0,0,0⟩, +⟨⟨1,184,987,true⟩,0,0,0⟩, +⟨⟨1,185,987,true⟩,0,0,0⟩, +⟨⟨1,186,987,true⟩,0,0,0⟩, +⟨⟨1,187,987,true⟩,0,0,0⟩, +⟨⟨1,188,987,true⟩,0,0,0⟩, +⟨⟨1,189,987,true⟩,0,0,0⟩, +⟨⟨1,190,987,true⟩,0,0,0⟩, +⟨⟨1,191,987,true⟩,0,0,0⟩, +⟨⟨1,192,987,true⟩,0,0,0⟩, +⟨⟨1,193,987,true⟩,0,0,0⟩, +⟨⟨1,194,987,true⟩,0,0,0⟩, +⟨⟨1,195,987,true⟩,0,0,0⟩, +⟨⟨1,196,987,true⟩,0,0,0⟩, +⟨⟨1,197,987,true⟩,0,0,0⟩, +⟨⟨1,198,987,true⟩,0,0,0⟩, +⟨⟨1,199,987,true⟩,0,0,0⟩, +⟨⟨1,200,987,true⟩,0,0,0⟩, +⟨⟨1,201,987,true⟩,0,0,0⟩, +⟨⟨1,202,987,true⟩,0,0,0⟩, +⟨⟨1,203,987,true⟩,0,0,0⟩, +⟨⟨1,204,987,true⟩,0,0,0⟩, +⟨⟨1,205,987,true⟩,0,0,0⟩, +⟨⟨1,206,987,true⟩,0,0,0⟩, +⟨⟨1,207,987,true⟩,0,0,0⟩, +⟨⟨1,208,987,true⟩,0,0,0⟩, +⟨⟨1,209,987,true⟩,0,0,0⟩, +⟨⟨1,210,987,true⟩,0,0,0⟩, +⟨⟨1,211,987,true⟩,0,0,0⟩, +⟨⟨1,212,987,true⟩,0,0,0⟩, +⟨⟨1,213,987,true⟩,0,0,0⟩, +⟨⟨1,214,987,true⟩,0,0,0⟩, +⟨⟨1,215,987,true⟩,0,0,0⟩, +⟨⟨1,216,987,true⟩,0,0,0⟩, +⟨⟨1,217,987,true⟩,0,0,0⟩, +⟨⟨1,218,987,true⟩,0,0,0⟩, +⟨⟨1,219,987,true⟩,0,0,0⟩, +⟨⟨1,220,987,true⟩,0,0,0⟩, +⟨⟨1,221,987,true⟩,0,0,0⟩, +⟨⟨1,222,987,true⟩,0,0,0⟩, +⟨⟨1,223,987,true⟩,0,0,0⟩, +⟨⟨1,224,987,true⟩,0,0,0⟩, +⟨⟨1,225,987,true⟩,0,0,0⟩, +⟨⟨1,226,987,true⟩,0,0,0⟩, +⟨⟨1,227,987,true⟩,0,0,0⟩, +⟨⟨1,228,987,true⟩,0,0,0⟩, +⟨⟨1,229,987,true⟩,0,0,0⟩, +⟨⟨1,230,987,true⟩,0,0,0⟩, +⟨⟨1,231,987,true⟩,0,0,0⟩, +⟨⟨1,232,987,true⟩,0,0,0⟩, +⟨⟨1,233,987,true⟩,0,0,0⟩, +⟨⟨1,234,987,true⟩,0,0,0⟩, +⟨⟨1,235,987,true⟩,0,0,0⟩, +⟨⟨1,236,987,true⟩,0,0,0⟩, +⟨⟨1,237,987,true⟩,0,0,0⟩, +⟨⟨1,238,987,true⟩,0,0,0⟩, +⟨⟨1,239,987,true⟩,0,0,0⟩, +⟨⟨3,0,987,true⟩,1,0,0⟩, +⟨⟨2,1,987,true⟩,1,0,8⟩, +⟨⟨1,120,987,true⟩,0,0,0⟩, +⟨⟨1,123,987,true⟩,0,0,0⟩, +⟨⟨1,125,987,true⟩,0,0,0⟩, +⟨⟨1,126,987,true⟩,0,0,0⟩, +⟨⟨1,137,987,true⟩,0,0,0⟩, +⟨⟨1,139,987,true⟩,0,0,0⟩, +⟨⟨1,141,987,true⟩,0,0,0⟩, +⟨⟨1,143,987,true⟩,0,0,0⟩, +⟨⟨1,146,987,true⟩,0,0,0⟩, +⟨⟨1,147,987,true⟩,0,0,0⟩, +⟨⟨1,150,987,true⟩,0,0,0⟩, +⟨⟨1,151,987,true⟩,0,0,0⟩, +⟨⟨1,153,987,true⟩,0,0,0⟩, +⟨⟨1,155,987,true⟩,0,0,0⟩, +⟨⟨1,157,987,true⟩,0,0,0⟩, +⟨⟨1,159,987,true⟩,0,0,0⟩, +⟨⟨1,162,987,true⟩,0,0,0⟩, +⟨⟨1,163,987,true⟩,0,0,0⟩, +⟨⟨1,166,987,true⟩,0,0,0⟩, +⟨⟨1,167,987,true⟩,0,0,0⟩, +⟨⟨1,168,987,true⟩,0,0,0⟩, +⟨⟨1,171,987,true⟩,0,0,0⟩, +⟨⟨1,172,987,true⟩,0,0,0⟩, +⟨⟨1,175,987,true⟩,0,0,0⟩, +⟨⟨1,176,987,true⟩,0,0,0⟩, +⟨⟨1,177,987,true⟩,0,0,0⟩, +⟨⟨1,182,987,true⟩,0,0,0⟩, +⟨⟨1,183,987,true⟩,0,0,0⟩, +⟨⟨1,185,987,true⟩,0,0,0⟩, +⟨⟨1,187,987,true⟩,0,0,0⟩, +⟨⟨1,189,987,true⟩,0,0,0⟩, +⟨⟨1,191,987,true⟩,0,0,0⟩, +⟨⟨1,196,987,true⟩,0,0,0⟩, +⟨⟨1,197,987,true⟩,0,0,0⟩, +⟨⟨1,198,987,true⟩,0,0,0⟩, +⟨⟨1,199,987,true⟩,0,0,0⟩, +⟨⟨1,200,987,true⟩,0,0,0⟩, +⟨⟨1,202,987,true⟩,0,0,0⟩, +⟨⟨1,205,987,true⟩,0,0,0⟩, +⟨⟨1,207,987,true⟩,0,0,0⟩, +⟨⟨1,208,987,true⟩,0,0,0⟩, +⟨⟨1,209,987,true⟩,0,0,0⟩, +⟨⟨1,214,987,true⟩,0,0,0⟩, +⟨⟨1,215,987,true⟩,0,0,0⟩, +⟨⟨1,216,987,true⟩,0,0,0⟩, +⟨⟨1,218,987,true⟩,0,0,0⟩, +⟨⟨1,221,987,true⟩,0,0,0⟩, +⟨⟨1,223,987,true⟩,0,0,0⟩, +⟨⟨1,224,987,true⟩,0,0,0⟩, +⟨⟨1,225,987,true⟩,0,0,0⟩, +⟨⟨1,230,987,true⟩,0,0,0⟩, +⟨⟨1,231,987,true⟩,0,0,0⟩, +⟨⟨1,232,987,true⟩,0,0,0⟩, +⟨⟨1,235,987,true⟩,0,0,0⟩, +⟨⟨1,237,987,true⟩,0,0,0⟩, +⟨⟨1,238,987,true⟩,0,0,0⟩, +⟨⟨3,1,987,true⟩,1,0,0⟩, +⟨⟨2,2,987,true⟩,1,0,8⟩, +⟨⟨1,121,987,true⟩,0,0,0⟩, +⟨⟨1,123,987,true⟩,0,0,0⟩, +⟨⟨1,125,987,true⟩,0,0,0⟩, +⟨⟨1,127,987,true⟩,0,0,0⟩, +⟨⟨1,129,987,true⟩,0,0,0⟩, +⟨⟨1,131,987,true⟩,0,0,0⟩, +⟨⟨1,133,987,true⟩,0,0,0⟩, +⟨⟨1,135,987,true⟩,0,0,0⟩, +⟨⟨1,145,987,true⟩,0,0,0⟩, +⟨⟨1,147,987,true⟩,0,0,0⟩, +⟨⟨1,148,987,true⟩,0,0,0⟩, +⟨⟨1,150,987,true⟩,0,0,0⟩, +⟨⟨1,153,987,true⟩,0,0,0⟩, +⟨⟨1,155,987,true⟩,0,0,0⟩, +⟨⟨1,156,987,true⟩,0,0,0⟩, +⟨⟨1,158,987,true⟩,0,0,0⟩, +⟨⟨1,160,987,true⟩,0,0,0⟩, +⟨⟨1,163,987,true⟩,0,0,0⟩, +⟨⟨1,164,987,true⟩,0,0,0⟩, +⟨⟨1,167,987,true⟩,0,0,0⟩, +⟨⟨1,170,987,true⟩,0,0,0⟩, +⟨⟨1,171,987,true⟩,0,0,0⟩, +⟨⟨1,174,987,true⟩,0,0,0⟩, +⟨⟨1,175,987,true⟩,0,0,0⟩, +⟨⟨1,176,987,true⟩,0,0,0⟩, +⟨⟨1,178,987,true⟩,0,0,0⟩, +⟨⟨1,181,987,true⟩,0,0,0⟩, +⟨⟨1,183,987,true⟩,0,0,0⟩, +⟨⟨1,185,987,true⟩,0,0,0⟩, +⟨⟨1,187,987,true⟩,0,0,0⟩, +⟨⟨1,188,987,true⟩,0,0,0⟩, +⟨⟨1,190,987,true⟩,0,0,0⟩, +⟨⟨1,192,987,true⟩,0,0,0⟩, +⟨⟨1,194,987,true⟩,0,0,0⟩, +⟨⟨1,197,987,true⟩,0,0,0⟩, +⟨⟨1,199,987,true⟩,0,0,0⟩, +⟨⟨1,204,987,true⟩,0,0,0⟩, +⟨⟨1,205,987,true⟩,0,0,0⟩, +⟨⟨1,206,987,true⟩,0,0,0⟩, +⟨⟨1,207,987,true⟩,0,0,0⟩, +⟨⟨1,208,987,true⟩,0,0,0⟩, +⟨⟨1,210,987,true⟩,0,0,0⟩, +⟨⟨1,213,987,true⟩,0,0,0⟩, +⟨⟨1,215,987,true⟩,0,0,0⟩, +⟨⟨1,216,987,true⟩,0,0,0⟩, +⟨⟨1,218,987,true⟩,0,0,0⟩, +⟨⟨1,221,987,true⟩,0,0,0⟩, +⟨⟨1,223,987,true⟩,0,0,0⟩, +⟨⟨1,224,987,true⟩,0,0,0⟩, +⟨⟨1,227,987,true⟩,0,0,0⟩, +⟨⟨1,229,987,true⟩,0,0,0⟩, +⟨⟨1,230,987,true⟩,0,0,0⟩, +⟨⟨1,232,987,true⟩,0,0,0⟩, +⟨⟨1,233,987,true⟩,0,0,0⟩, +⟨⟨1,238,987,true⟩,0,0,0⟩, +⟨⟨1,239,987,true⟩,0,0,0⟩, +⟨⟨3,2,987,true⟩,1,0,0⟩, +⟨⟨2,4,987,true⟩,1,0,8⟩, +⟨⟨1,122,987,true⟩,0,0,0⟩, +⟨⟨1,123,987,true⟩,0,0,0⟩, +⟨⟨1,126,987,true⟩,0,0,0⟩] +def chunk69 : List Entry := [⟨⟨1,127,987,true⟩,0,0,0⟩, +⟨⟨1,129,987,true⟩,0,0,0⟩, +⟨⟨1,131,987,true⟩,0,0,0⟩, +⟨⟨1,132,987,true⟩,0,0,0⟩, +⟨⟨1,134,987,true⟩,0,0,0⟩, +⟨⟨1,137,987,true⟩,0,0,0⟩, +⟨⟨1,139,987,true⟩,0,0,0⟩, +⟨⟨1,140,987,true⟩,0,0,0⟩, +⟨⟨1,142,987,true⟩,0,0,0⟩, +⟨⟨1,144,987,true⟩,0,0,0⟩, +⟨⟨1,147,987,true⟩,0,0,0⟩, +⟨⟨1,148,987,true⟩,0,0,0⟩, +⟨⟨1,151,987,true⟩,0,0,0⟩, +⟨⟨1,161,987,true⟩,0,0,0⟩, +⟨⟨1,163,987,true⟩,0,0,0⟩, +⟨⟨1,164,987,true⟩,0,0,0⟩, +⟨⟨1,166,987,true⟩,0,0,0⟩, +⟨⟨1,169,987,true⟩,0,0,0⟩, +⟨⟨1,171,987,true⟩,0,0,0⟩, +⟨⟨1,172,987,true⟩,0,0,0⟩, +⟨⟨1,174,987,true⟩,0,0,0⟩, +⟨⟨1,176,987,true⟩,0,0,0⟩, +⟨⟨1,179,987,true⟩,0,0,0⟩, +⟨⟨1,180,987,true⟩,0,0,0⟩, +⟨⟨1,183,987,true⟩,0,0,0⟩, +⟨⟨1,185,987,true⟩,0,0,0⟩, +⟨⟨1,186,987,true⟩,0,0,0⟩, +⟨⟨1,189,987,true⟩,0,0,0⟩, +⟨⟨1,190,987,true⟩,0,0,0⟩, +⟨⟨1,192,987,true⟩,0,0,0⟩, +⟨⟨1,194,987,true⟩,0,0,0⟩, +⟨⟨1,197,987,true⟩,0,0,0⟩, +⟨⟨1,199,987,true⟩,0,0,0⟩, +⟨⟨1,200,987,true⟩,0,0,0⟩, +⟨⟨1,202,987,true⟩,0,0,0⟩, +⟨⟨1,205,987,true⟩,0,0,0⟩, +⟨⟨1,207,987,true⟩,0,0,0⟩, +⟨⟨1,208,987,true⟩,0,0,0⟩, +⟨⟨1,211,987,true⟩,0,0,0⟩, +⟨⟨1,213,987,true⟩,0,0,0⟩, +⟨⟨1,214,987,true⟩,0,0,0⟩, +⟨⟨1,220,987,true⟩,0,0,0⟩, +⟨⟨1,221,987,true⟩,0,0,0⟩, +⟨⟨1,222,987,true⟩,0,0,0⟩, +⟨⟨1,223,987,true⟩,0,0,0⟩, +⟨⟨1,224,987,true⟩,0,0,0⟩, +⟨⟨1,226,987,true⟩,0,0,0⟩, +⟨⟨1,229,987,true⟩,0,0,0⟩, +⟨⟨1,231,987,true⟩,0,0,0⟩, +⟨⟨1,232,987,true⟩,0,0,0⟩, +⟨⟨1,234,987,true⟩,0,0,0⟩, +⟨⟨1,237,987,true⟩,0,0,0⟩, +⟨⟨1,239,987,true⟩,0,0,0⟩, +⟨⟨3,4,987,true⟩,1,0,0⟩, +⟨⟨2,8,987,true⟩,1,0,8⟩, +⟨⟨1,124,987,true⟩,0,0,0⟩, +⟨⟨1,125,987,true⟩,0,0,0⟩, +⟨⟨1,126,987,true⟩,0,0,0⟩, +⟨⟨1,127,987,true⟩,0,0,0⟩, +⟨⟨1,129,987,true⟩,0,0,0⟩, +⟨⟨1,130,987,true⟩,0,0,0⟩, +⟨⟨1,133,987,true⟩,0,0,0⟩, +⟨⟨1,134,987,true⟩,0,0,0⟩, +⟨⟨1,137,987,true⟩,0,0,0⟩, +⟨⟨1,138,987,true⟩,0,0,0⟩, +⟨⟨1,141,987,true⟩,0,0,0⟩, +⟨⟨1,142,987,true⟩,0,0,0⟩, +⟨⟨1,144,987,true⟩,0,0,0⟩, +⟨⟨1,147,987,true⟩,0,0,0⟩, +⟨⟨1,148,987,true⟩,0,0,0⟩, +⟨⟨1,151,987,true⟩,0,0,0⟩, +⟨⟨1,153,987,true⟩,0,0,0⟩, +⟨⟨1,154,987,true⟩,0,0,0⟩, +⟨⟨1,157,987,true⟩,0,0,0⟩, +⟨⟨1,158,987,true⟩,0,0,0⟩, +⟨⟨1,160,987,true⟩,0,0,0⟩, +⟨⟨1,163,987,true⟩,0,0,0⟩, +⟨⟨1,164,987,true⟩,0,0,0⟩, +⟨⟨1,167,987,true⟩,0,0,0⟩, +⟨⟨1,168,987,true⟩,0,0,0⟩, +⟨⟨1,171,987,true⟩,0,0,0⟩, +⟨⟨1,172,987,true⟩,0,0,0⟩, +⟨⟨1,175,987,true⟩,0,0,0⟩, +⟨⟨1,176,987,true⟩,0,0,0⟩, +⟨⟨1,179,987,true⟩,0,0,0⟩, +⟨⟨1,181,987,true⟩,0,0,0⟩, +⟨⟨1,182,987,true⟩,0,0,0⟩, +⟨⟨1,193,987,true⟩,0,0,0⟩, +⟨⟨1,194,987,true⟩,0,0,0⟩, +⟨⟨1,197,987,true⟩,0,0,0⟩, +⟨⟨1,198,987,true⟩,0,0,0⟩, +⟨⟨1,201,987,true⟩,0,0,0⟩, +⟨⟨1,202,987,true⟩,0,0,0⟩, +⟨⟨1,205,987,true⟩,0,0,0⟩, +⟨⟨1,206,987,true⟩,0,0,0⟩, +⟨⟨1,208,987,true⟩,0,0,0⟩, +⟨⟨1,211,987,true⟩,0,0,0⟩, +⟨⟨1,212,987,true⟩,0,0,0⟩, +⟨⟨1,215,987,true⟩,0,0,0⟩, +⟨⟨1,217,987,true⟩,0,0,0⟩, +⟨⟨1,218,987,true⟩,0,0,0⟩, +⟨⟨1,221,987,true⟩,0,0,0⟩, +⟨⟨1,222,987,true⟩,0,0,0⟩, +⟨⟨1,224,987,true⟩,0,0,0⟩, +⟨⟨1,227,987,true⟩,0,0,0⟩, +⟨⟨1,228,987,true⟩,0,0,0⟩, +⟨⟨1,231,987,true⟩,0,0,0⟩, +⟨⟨1,232,987,true⟩,0,0,0⟩, +⟨⟨1,235,987,true⟩,0,0,0⟩, +⟨⟨1,236,987,true⟩,0,0,0⟩, +⟨⟨1,239,987,true⟩,0,0,0⟩, +⟨⟨3,8,987,true⟩,1,0,0⟩, +⟨⟨2,9,987,true⟩,1,0,8⟩, +⟨⟨1,128,987,true⟩,0,0,0⟩, +⟨⟨1,129,987,true⟩,0,0,0⟩, +⟨⟨1,130,987,true⟩,0,0,0⟩, +⟨⟨1,131,987,true⟩,0,0,0⟩, +⟨⟨1,132,987,true⟩,0,0,0⟩, +⟨⟨1,133,987,true⟩,0,0,0⟩, +⟨⟨1,134,987,true⟩,0,0,0⟩, +⟨⟨1,135,987,true⟩,0,0,0⟩, +⟨⟨1,144,987,true⟩,0,0,0⟩, +⟨⟨1,145,987,true⟩,0,0,0⟩, +⟨⟨1,146,987,true⟩,0,0,0⟩, +⟨⟨1,147,987,true⟩,0,0,0⟩, +⟨⟨1,148,987,true⟩,0,0,0⟩, +⟨⟨1,149,987,true⟩,0,0,0⟩, +⟨⟨1,150,987,true⟩,0,0,0⟩, +⟨⟨1,151,987,true⟩,0,0,0⟩, +⟨⟨1,160,987,true⟩,0,0,0⟩, +⟨⟨1,161,987,true⟩,0,0,0⟩, +⟨⟨1,162,987,true⟩,0,0,0⟩, +⟨⟨1,163,987,true⟩,0,0,0⟩, +⟨⟨1,164,987,true⟩,0,0,0⟩, +⟨⟨1,165,987,true⟩,0,0,0⟩, +⟨⟨1,166,987,true⟩,0,0,0⟩, +⟨⟨1,167,987,true⟩,0,0,0⟩, +⟨⟨1,176,987,true⟩,0,0,0⟩, +⟨⟨1,177,987,true⟩,0,0,0⟩, +⟨⟨1,178,987,true⟩,0,0,0⟩, +⟨⟨1,179,987,true⟩,0,0,0⟩, +⟨⟨1,180,987,true⟩,0,0,0⟩, +⟨⟨1,181,987,true⟩,0,0,0⟩, +⟨⟨1,182,987,true⟩,0,0,0⟩, +⟨⟨1,183,987,true⟩,0,0,0⟩, +⟨⟨1,192,987,true⟩,0,0,0⟩, +⟨⟨1,193,987,true⟩,0,0,0⟩, +⟨⟨1,194,987,true⟩,0,0,0⟩, +⟨⟨1,195,987,true⟩,0,0,0⟩, +⟨⟨1,196,987,true⟩,0,0,0⟩, +⟨⟨1,197,987,true⟩,0,0,0⟩, +⟨⟨1,198,987,true⟩,0,0,0⟩, +⟨⟨1,199,987,true⟩,0,0,0⟩, +⟨⟨1,208,987,true⟩,0,0,0⟩, +⟨⟨1,209,987,true⟩,0,0,0⟩, +⟨⟨1,210,987,true⟩,0,0,0⟩, +⟨⟨1,211,987,true⟩,0,0,0⟩, +⟨⟨1,212,987,true⟩,0,0,0⟩, +⟨⟨1,213,987,true⟩,0,0,0⟩, +⟨⟨1,214,987,true⟩,0,0,0⟩, +⟨⟨1,215,987,true⟩,0,0,0⟩, +⟨⟨1,224,987,true⟩,0,0,0⟩, +⟨⟨1,225,987,true⟩,0,0,0⟩, +⟨⟨1,226,987,true⟩,0,0,0⟩, +⟨⟨1,227,987,true⟩,0,0,0⟩, +⟨⟨1,228,987,true⟩,0,0,0⟩, +⟨⟨1,229,987,true⟩,0,0,0⟩, +⟨⟨1,230,987,true⟩,0,0,0⟩, +⟨⟨1,231,987,true⟩,0,0,0⟩, +⟨⟨3,9,987,true⟩,1,0,0⟩, +⟨⟨2,16,987,true⟩,1,0,8⟩, +⟨⟨1,136,987,true⟩,0,0,0⟩, +⟨⟨1,137,987,true⟩,0,0,0⟩, +⟨⟨1,138,987,true⟩,0,0,0⟩, +⟨⟨1,139,987,true⟩,0,0,0⟩, +⟨⟨1,140,987,true⟩,0,0,0⟩, +⟨⟨1,141,987,true⟩,0,0,0⟩, +⟨⟨1,142,987,true⟩,0,0,0⟩, +⟨⟨1,143,987,true⟩,0,0,0⟩, +⟨⟨1,144,987,true⟩,0,0,0⟩, +⟨⟨1,145,987,true⟩,0,0,0⟩, +⟨⟨1,146,987,true⟩,0,0,0⟩, +⟨⟨1,147,987,true⟩,0,0,0⟩, +⟨⟨1,148,987,true⟩,0,0,0⟩, +⟨⟨1,149,987,true⟩,0,0,0⟩, +⟨⟨1,150,987,true⟩,0,0,0⟩, +⟨⟨1,151,987,true⟩,0,0,0⟩, +⟨⟨1,168,987,true⟩,0,0,0⟩, +⟨⟨1,169,987,true⟩,0,0,0⟩, +⟨⟨1,170,987,true⟩,0,0,0⟩, +⟨⟨1,171,987,true⟩,0,0,0⟩, +⟨⟨1,172,987,true⟩,0,0,0⟩, +⟨⟨1,173,987,true⟩,0,0,0⟩, +⟨⟨1,174,987,true⟩,0,0,0⟩, +⟨⟨1,175,987,true⟩,0,0,0⟩, +⟨⟨1,176,987,true⟩,0,0,0⟩, +⟨⟨1,177,987,true⟩,0,0,0⟩, +⟨⟨1,178,987,true⟩,0,0,0⟩, +⟨⟨1,179,987,true⟩,0,0,0⟩, +⟨⟨1,180,987,true⟩,0,0,0⟩] +def chunk70 : List Entry := [⟨⟨1,181,987,true⟩,0,0,0⟩, +⟨⟨1,182,987,true⟩,0,0,0⟩, +⟨⟨1,183,987,true⟩,0,0,0⟩, +⟨⟨1,200,987,true⟩,0,0,0⟩, +⟨⟨1,201,987,true⟩,0,0,0⟩, +⟨⟨1,202,987,true⟩,0,0,0⟩, +⟨⟨1,203,987,true⟩,0,0,0⟩, +⟨⟨1,204,987,true⟩,0,0,0⟩, +⟨⟨1,205,987,true⟩,0,0,0⟩, +⟨⟨1,206,987,true⟩,0,0,0⟩, +⟨⟨1,207,987,true⟩,0,0,0⟩, +⟨⟨1,208,987,true⟩,0,0,0⟩, +⟨⟨1,209,987,true⟩,0,0,0⟩, +⟨⟨1,210,987,true⟩,0,0,0⟩, +⟨⟨1,211,987,true⟩,0,0,0⟩, +⟨⟨1,212,987,true⟩,0,0,0⟩, +⟨⟨1,213,987,true⟩,0,0,0⟩, +⟨⟨1,214,987,true⟩,0,0,0⟩, +⟨⟨1,215,987,true⟩,0,0,0⟩, +⟨⟨1,232,987,true⟩,0,0,0⟩, +⟨⟨1,233,987,true⟩,0,0,0⟩, +⟨⟨1,234,987,true⟩,0,0,0⟩, +⟨⟨1,235,987,true⟩,0,0,0⟩, +⟨⟨1,236,987,true⟩,0,0,0⟩, +⟨⟨1,237,987,true⟩,0,0,0⟩, +⟨⟨1,238,987,true⟩,0,0,0⟩, +⟨⟨1,239,987,true⟩,0,0,0⟩, +⟨⟨3,16,987,true⟩,1,0,0⟩, +⟨⟨2,32,987,true⟩,1,0,8⟩, +⟨⟨1,152,987,true⟩,0,0,0⟩, +⟨⟨1,153,987,true⟩,0,0,0⟩, +⟨⟨1,154,987,true⟩,0,0,0⟩, +⟨⟨1,155,987,true⟩,0,0,0⟩, +⟨⟨1,156,987,true⟩,0,0,0⟩, +⟨⟨1,157,987,true⟩,0,0,0⟩, +⟨⟨1,158,987,true⟩,0,0,0⟩, +⟨⟨1,159,987,true⟩,0,0,0⟩, +⟨⟨1,160,987,true⟩,0,0,0⟩, +⟨⟨1,161,987,true⟩,0,0,0⟩, +⟨⟨1,162,987,true⟩,0,0,0⟩, +⟨⟨1,163,987,true⟩,0,0,0⟩, +⟨⟨1,164,987,true⟩,0,0,0⟩, +⟨⟨1,165,987,true⟩,0,0,0⟩, +⟨⟨1,166,987,true⟩,0,0,0⟩, +⟨⟨1,167,987,true⟩,0,0,0⟩, +⟨⟨1,168,987,true⟩,0,0,0⟩, +⟨⟨1,169,987,true⟩,0,0,0⟩, +⟨⟨1,170,987,true⟩,0,0,0⟩, +⟨⟨1,171,987,true⟩,0,0,0⟩, +⟨⟨1,172,987,true⟩,0,0,0⟩, +⟨⟨1,173,987,true⟩,0,0,0⟩, +⟨⟨1,174,987,true⟩,0,0,0⟩, +⟨⟨1,175,987,true⟩,0,0,0⟩, +⟨⟨1,176,987,true⟩,0,0,0⟩, +⟨⟨1,177,987,true⟩,0,0,0⟩, +⟨⟨1,178,987,true⟩,0,0,0⟩, +⟨⟨1,179,987,true⟩,0,0,0⟩, +⟨⟨1,180,987,true⟩,0,0,0⟩, +⟨⟨1,181,987,true⟩,0,0,0⟩, +⟨⟨1,182,987,true⟩,0,0,0⟩, +⟨⟨1,183,987,true⟩,0,0,0⟩, +⟨⟨1,216,987,true⟩,0,0,0⟩, +⟨⟨1,217,987,true⟩,0,0,0⟩, +⟨⟨1,218,987,true⟩,0,0,0⟩, +⟨⟨1,219,987,true⟩,0,0,0⟩, +⟨⟨1,220,987,true⟩,0,0,0⟩, +⟨⟨1,221,987,true⟩,0,0,0⟩, +⟨⟨1,222,987,true⟩,0,0,0⟩, +⟨⟨1,223,987,true⟩,0,0,0⟩, +⟨⟨1,224,987,true⟩,0,0,0⟩, +⟨⟨1,225,987,true⟩,0,0,0⟩, +⟨⟨1,226,987,true⟩,0,0,0⟩, +⟨⟨1,227,987,true⟩,0,0,0⟩, +⟨⟨1,228,987,true⟩,0,0,0⟩, +⟨⟨1,229,987,true⟩,0,0,0⟩, +⟨⟨1,230,987,true⟩,0,0,0⟩, +⟨⟨1,231,987,true⟩,0,0,0⟩, +⟨⟨1,232,987,true⟩,0,0,0⟩, +⟨⟨1,233,987,true⟩,0,0,0⟩, +⟨⟨1,234,987,true⟩,0,0,0⟩, +⟨⟨1,235,987,true⟩,0,0,0⟩, +⟨⟨1,236,987,true⟩,0,0,0⟩, +⟨⟨1,237,987,true⟩,0,0,0⟩, +⟨⟨1,238,987,true⟩,0,0,0⟩, +⟨⟨1,239,987,true⟩,0,0,0⟩, +⟨⟨3,32,987,true⟩,1,0,0⟩, +⟨⟨2,64,987,true⟩,1,0,8⟩, +⟨⟨1,184,987,true⟩,0,0,0⟩, +⟨⟨1,185,987,true⟩,0,0,0⟩, +⟨⟨1,186,987,true⟩,0,0,0⟩, +⟨⟨1,187,987,true⟩,0,0,0⟩, +⟨⟨1,188,987,true⟩,0,0,0⟩, +⟨⟨1,189,987,true⟩,0,0,0⟩, +⟨⟨1,190,987,true⟩,0,0,0⟩, +⟨⟨1,191,987,true⟩,0,0,0⟩, +⟨⟨1,192,987,true⟩,0,0,0⟩, +⟨⟨1,193,987,true⟩,0,0,0⟩, +⟨⟨1,194,987,true⟩,0,0,0⟩, +⟨⟨1,195,987,true⟩,0,0,0⟩, +⟨⟨1,196,987,true⟩,0,0,0⟩, +⟨⟨1,197,987,true⟩,0,0,0⟩, +⟨⟨1,198,987,true⟩,0,0,0⟩, +⟨⟨1,199,987,true⟩,0,0,0⟩, +⟨⟨1,200,987,true⟩,0,0,0⟩, +⟨⟨1,201,987,true⟩,0,0,0⟩, +⟨⟨1,202,987,true⟩,0,0,0⟩, +⟨⟨1,203,987,true⟩,0,0,0⟩, +⟨⟨1,204,987,true⟩,0,0,0⟩, +⟨⟨1,205,987,true⟩,0,0,0⟩, +⟨⟨1,206,987,true⟩,0,0,0⟩, +⟨⟨1,207,987,true⟩,0,0,0⟩, +⟨⟨1,208,987,true⟩,0,0,0⟩, +⟨⟨1,209,987,true⟩,0,0,0⟩, +⟨⟨1,210,987,true⟩,0,0,0⟩, +⟨⟨1,211,987,true⟩,0,0,0⟩, +⟨⟨1,212,987,true⟩,0,0,0⟩, +⟨⟨1,213,987,true⟩,0,0,0⟩, +⟨⟨1,214,987,true⟩,0,0,0⟩, +⟨⟨1,215,987,true⟩,0,0,0⟩, +⟨⟨1,216,987,true⟩,0,0,0⟩, +⟨⟨1,217,987,true⟩,0,0,0⟩, +⟨⟨1,218,987,true⟩,0,0,0⟩, +⟨⟨1,219,987,true⟩,0,0,0⟩, +⟨⟨1,220,987,true⟩,0,0,0⟩, +⟨⟨1,221,987,true⟩,0,0,0⟩, +⟨⟨1,222,987,true⟩,0,0,0⟩, +⟨⟨1,223,987,true⟩,0,0,0⟩, +⟨⟨1,224,987,true⟩,0,0,0⟩, +⟨⟨1,225,987,true⟩,0,0,0⟩, +⟨⟨1,226,987,true⟩,0,0,0⟩, +⟨⟨1,227,987,true⟩,0,0,0⟩, +⟨⟨1,228,987,true⟩,0,0,0⟩, +⟨⟨1,229,987,true⟩,0,0,0⟩, +⟨⟨1,230,987,true⟩,0,0,0⟩, +⟨⟨1,231,987,true⟩,0,0,0⟩, +⟨⟨1,232,987,true⟩,0,0,0⟩, +⟨⟨1,233,987,true⟩,0,0,0⟩, +⟨⟨1,234,987,true⟩,0,0,0⟩, +⟨⟨1,235,987,true⟩,0,0,0⟩, +⟨⟨1,236,987,true⟩,0,0,0⟩, +⟨⟨1,237,987,true⟩,0,0,0⟩, +⟨⟨1,238,987,true⟩,0,0,0⟩, +⟨⟨1,239,987,true⟩,0,0,0⟩, +⟨⟨3,64,987,true⟩,1,0,0⟩, +⟨⟨1,16,0,true⟩,1,1,0⟩, +⟨⟨1,32,0,true⟩,1,1,0⟩, +⟨⟨1,64,0,true⟩,1,1,0⟩, +⟨⟨1,1,9,true⟩,1,1,0⟩, +⟨⟨1,9,1,true⟩,1,1,0⟩, +⟨⟨1,1,9,true⟩,1,1,0⟩, +⟨⟨1,0,1,true⟩,1,1,0⟩, +⟨⟨1,16,1,true⟩,1,1,0⟩, +⟨⟨1,2,16,true⟩,1,1,0⟩, +⟨⟨1,16,2,true⟩,1,1,0⟩, +⟨⟨1,2,16,true⟩,1,1,0⟩, +⟨⟨1,1,2,true⟩,1,1,0⟩, +⟨⟨1,32,2,true⟩,1,1,0⟩, +⟨⟨1,0,3,true⟩,1,1,0⟩, +⟨⟨1,1,3,true⟩,1,1,0⟩, +⟨⟨1,2,3,true⟩,1,1,0⟩, +⟨⟨1,4,32,true⟩,1,1,0⟩, +⟨⟨1,32,4,true⟩,1,1,0⟩, +⟨⟨1,4,32,true⟩,1,1,0⟩, +⟨⟨1,2,4,true⟩,1,1,0⟩, +⟨⟨1,64,4,true⟩,1,1,0⟩, +⟨⟨1,0,5,true⟩,1,1,0⟩, +⟨⟨1,1,5,true⟩,1,1,0⟩, +⟨⟨1,4,5,true⟩,1,1,0⟩, +⟨⟨1,0,6,true⟩,1,1,0⟩, +⟨⟨1,2,6,true⟩,1,1,0⟩, +⟨⟨1,4,6,true⟩,1,1,0⟩, +⟨⟨1,1,7,true⟩,1,1,0⟩, +⟨⟨1,2,7,true⟩,1,1,0⟩, +⟨⟨1,4,7,true⟩,1,1,0⟩, +⟨⟨1,0,8,true⟩,1,1,0⟩, +⟨⟨1,16,8,true⟩,1,1,0⟩, +⟨⟨1,32,8,true⟩,1,1,0⟩, +⟨⟨1,9,64,true⟩,1,1,0⟩, +⟨⟨1,64,9,true⟩,1,1,0⟩, +⟨⟨1,9,64,true⟩,1,1,0⟩, +⟨⟨1,0,9,true⟩,1,1,0⟩, +⟨⟨1,4,9,true⟩,1,1,0⟩, +⟨⟨1,8,9,true⟩,1,1,0⟩, +⟨⟨1,1,10,true⟩,1,1,0⟩, +⟨⟨1,2,10,true⟩,1,1,0⟩, +⟨⟨1,9,10,true⟩,1,1,0⟩, +⟨⟨1,1,11,true⟩,1,1,0⟩, +⟨⟨1,2,11,true⟩,1,1,0⟩, +⟨⟨1,8,11,true⟩,1,1,0⟩, +⟨⟨1,1,12,true⟩,1,1,0⟩, +⟨⟨1,4,12,true⟩,1,1,0⟩, +⟨⟨1,9,12,true⟩,1,1,0⟩, +⟨⟨1,1,13,true⟩,1,1,0⟩, +⟨⟨1,4,13,true⟩,1,1,0⟩, +⟨⟨1,8,13,true⟩,1,1,0⟩, +⟨⟨1,2,14,true⟩,1,1,0⟩, +⟨⟨1,4,14,true⟩,1,1,0⟩, +⟨⟨1,8,14,true⟩,1,1,0⟩, +⟨⟨1,2,15,true⟩,1,1,0⟩, +⟨⟨1,4,15,true⟩,1,1,0⟩] +def chunk71 : List Entry := [⟨⟨1,9,15,true⟩,1,1,0⟩, +⟨⟨1,0,16,true⟩,1,1,0⟩, +⟨⟨1,1,16,true⟩,1,1,0⟩, +⟨⟨1,8,16,true⟩,1,1,0⟩, +⟨⟨1,64,16,true⟩,1,1,0⟩, +⟨⟨1,0,17,true⟩,1,1,0⟩, +⟨⟨1,1,17,true⟩,1,1,0⟩, +⟨⟨1,8,17,true⟩,1,1,0⟩, +⟨⟨1,9,17,true⟩,1,1,0⟩, +⟨⟨1,16,17,true⟩,1,1,0⟩, +⟨⟨1,1,18,true⟩,1,1,0⟩, +⟨⟨1,2,18,true⟩,1,1,0⟩, +⟨⟨1,8,18,true⟩,1,1,0⟩, +⟨⟨1,9,18,true⟩,1,1,0⟩, +⟨⟨1,16,18,true⟩,1,1,0⟩, +⟨⟨1,0,19,true⟩,1,1,0⟩, +⟨⟨1,2,19,true⟩,1,1,0⟩, +⟨⟨1,16,19,true⟩,1,1,0⟩, +⟨⟨1,1,20,true⟩,1,1,0⟩, +⟨⟨1,4,20,true⟩,1,1,0⟩, +⟨⟨1,8,20,true⟩,1,1,0⟩, +⟨⟨1,9,20,true⟩,1,1,0⟩, +⟨⟨1,16,20,true⟩,1,1,0⟩, +⟨⟨1,0,21,true⟩,1,1,0⟩, +⟨⟨1,4,21,true⟩,1,1,0⟩, +⟨⟨1,16,21,true⟩,1,1,0⟩, +⟨⟨1,2,22,true⟩,1,1,0⟩, +⟨⟨1,4,22,true⟩,1,1,0⟩, +⟨⟨1,16,22,true⟩,1,1,0⟩, +⟨⟨1,0,23,true⟩,1,1,0⟩, +⟨⟨1,1,23,true⟩,1,1,0⟩, +⟨⟨1,2,23,true⟩,1,1,0⟩, +⟨⟨1,4,23,true⟩,1,1,0⟩, +⟨⟨1,8,23,true⟩,1,1,0⟩, +⟨⟨1,9,23,true⟩,1,1,0⟩, +⟨⟨1,16,23,true⟩,1,1,0⟩, +⟨⟨1,1,24,true⟩,1,1,0⟩, +⟨⟨1,9,24,true⟩,1,1,0⟩, +⟨⟨1,16,24,true⟩,1,1,0⟩, +⟨⟨1,1,25,true⟩,1,1,0⟩, +⟨⟨1,8,25,true⟩,1,1,0⟩, +⟨⟨1,16,25,true⟩,1,1,0⟩, +⟨⟨1,0,26,true⟩,1,1,0⟩, +⟨⟨1,8,26,true⟩,1,1,0⟩, +⟨⟨1,16,26,true⟩,1,1,0⟩, +⟨⟨1,0,27,true⟩,1,1,0⟩, +⟨⟨1,9,27,true⟩,1,1,0⟩, +⟨⟨1,16,27,true⟩,1,1,0⟩, +⟨⟨1,1,28,true⟩,1,1,0⟩, +⟨⟨1,2,28,true⟩,1,1,0⟩, +⟨⟨1,4,28,true⟩,1,1,0⟩, +⟨⟨1,8,28,true⟩,1,1,0⟩, +⟨⟨1,16,28,true⟩,1,1,0⟩, +⟨⟨1,1,29,true⟩,1,1,0⟩, +⟨⟨1,2,29,true⟩,1,1,0⟩, +⟨⟨1,4,29,true⟩,1,1,0⟩, +⟨⟨1,9,29,true⟩,1,1,0⟩, +⟨⟨1,16,29,true⟩,1,1,0⟩, +⟨⟨1,0,30,true⟩,1,1,0⟩, +⟨⟨1,2,30,true⟩,1,1,0⟩, +⟨⟨1,4,30,true⟩,1,1,0⟩, +⟨⟨1,9,30,true⟩,1,1,0⟩, +⟨⟨1,16,30,true⟩,1,1,0⟩, +⟨⟨1,0,31,true⟩,1,1,0⟩, +⟨⟨1,2,31,true⟩,1,1,0⟩, +⟨⟨1,4,31,true⟩,1,1,0⟩, +⟨⟨1,8,31,true⟩,1,1,0⟩, +⟨⟨1,16,31,true⟩,1,1,0⟩, +⟨⟨1,0,32,true⟩,1,1,0⟩, +⟨⟨1,2,32,true⟩,1,1,0⟩, +⟨⟨1,8,32,true⟩,1,1,0⟩, +⟨⟨1,64,32,true⟩,1,1,0⟩, +⟨⟨1,0,33,true⟩,1,1,0⟩, +⟨⟨1,2,33,true⟩,1,1,0⟩, +⟨⟨1,8,33,true⟩,1,1,0⟩, +⟨⟨1,9,33,true⟩,1,1,0⟩, +⟨⟨1,32,33,true⟩,1,1,0⟩, +⟨⟨1,1,34,true⟩,1,1,0⟩, +⟨⟨1,2,34,true⟩,1,1,0⟩, +⟨⟨1,8,34,true⟩,1,1,0⟩, +⟨⟨1,9,34,true⟩,1,1,0⟩, +⟨⟨1,32,34,true⟩,1,1,0⟩, +⟨⟨1,0,35,true⟩,1,1,0⟩, +⟨⟨1,1,35,true⟩,1,1,0⟩, +⟨⟨1,32,35,true⟩,1,1,0⟩, +⟨⟨1,2,36,true⟩,1,1,0⟩, +⟨⟨1,4,36,true⟩,1,1,0⟩, +⟨⟨1,8,36,true⟩,1,1,0⟩, +⟨⟨1,9,36,true⟩,1,1,0⟩, +⟨⟨1,32,36,true⟩,1,1,0⟩, +⟨⟨1,0,37,true⟩,1,1,0⟩, +⟨⟨1,4,37,true⟩,1,1,0⟩, +⟨⟨1,32,37,true⟩,1,1,0⟩, +⟨⟨1,1,38,true⟩,1,1,0⟩, +⟨⟨1,4,38,true⟩,1,1,0⟩, +⟨⟨1,32,38,true⟩,1,1,0⟩, +⟨⟨1,0,39,true⟩,1,1,0⟩, +⟨⟨1,1,39,true⟩,1,1,0⟩, +⟨⟨1,2,39,true⟩,1,1,0⟩, +⟨⟨1,4,39,true⟩,1,1,0⟩, +⟨⟨1,8,39,true⟩,1,1,0⟩, +⟨⟨1,9,39,true⟩,1,1,0⟩, +⟨⟨1,32,39,true⟩,1,1,0⟩, +⟨⟨1,2,40,true⟩,1,1,0⟩, +⟨⟨1,9,40,true⟩,1,1,0⟩, +⟨⟨1,32,40,true⟩,1,1,0⟩, +⟨⟨1,2,41,true⟩,1,1,0⟩, +⟨⟨1,8,41,true⟩,1,1,0⟩, +⟨⟨1,32,41,true⟩,1,1,0⟩, +⟨⟨1,0,42,true⟩,1,1,0⟩, +⟨⟨1,8,42,true⟩,1,1,0⟩, +⟨⟨1,32,42,true⟩,1,1,0⟩, +⟨⟨1,0,43,true⟩,1,1,0⟩, +⟨⟨1,9,43,true⟩,1,1,0⟩, +⟨⟨1,32,43,true⟩,1,1,0⟩, +⟨⟨1,1,44,true⟩,1,1,0⟩, +⟨⟨1,2,44,true⟩,1,1,0⟩, +⟨⟨1,4,44,true⟩,1,1,0⟩, +⟨⟨1,8,44,true⟩,1,1,0⟩, +⟨⟨1,32,44,true⟩,1,1,0⟩, +⟨⟨1,1,45,true⟩,1,1,0⟩, +⟨⟨1,2,45,true⟩,1,1,0⟩, +⟨⟨1,4,45,true⟩,1,1,0⟩, +⟨⟨1,9,45,true⟩,1,1,0⟩, +⟨⟨1,32,45,true⟩,1,1,0⟩, +⟨⟨1,0,46,true⟩,1,1,0⟩, +⟨⟨1,1,46,true⟩,1,1,0⟩, +⟨⟨1,4,46,true⟩,1,1,0⟩, +⟨⟨1,9,46,true⟩,1,1,0⟩, +⟨⟨1,32,46,true⟩,1,1,0⟩, +⟨⟨1,0,47,true⟩,1,1,0⟩, +⟨⟨1,1,47,true⟩,1,1,0⟩, +⟨⟨1,4,47,true⟩,1,1,0⟩, +⟨⟨1,8,47,true⟩,1,1,0⟩, +⟨⟨1,32,47,true⟩,1,1,0⟩, +⟨⟨1,0,48,true⟩,1,1,0⟩, +⟨⟨1,1,48,true⟩,1,1,0⟩, +⟨⟨1,2,48,true⟩,1,1,0⟩, +⟨⟨1,8,48,true⟩,1,1,0⟩, +⟨⟨1,9,48,true⟩,1,1,0⟩, +⟨⟨1,16,48,true⟩,1,1,0⟩, +⟨⟨1,32,48,true⟩,1,1,0⟩, +⟨⟨1,2,49,true⟩,1,1,0⟩, +⟨⟨1,16,49,true⟩,1,1,0⟩, +⟨⟨1,32,49,true⟩,1,1,0⟩, +⟨⟨1,1,50,true⟩,1,1,0⟩, +⟨⟨1,16,50,true⟩,1,1,0⟩, +⟨⟨1,32,50,true⟩,1,1,0⟩, +⟨⟨1,0,51,true⟩,1,1,0⟩, +⟨⟨1,8,51,true⟩,1,1,0⟩, +⟨⟨1,9,51,true⟩,1,1,0⟩, +⟨⟨1,16,51,true⟩,1,1,0⟩, +⟨⟨1,32,51,true⟩,1,1,0⟩, +⟨⟨1,0,52,true⟩,1,1,0⟩, +⟨⟨1,2,52,true⟩,1,1,0⟩, +⟨⟨1,4,52,true⟩,1,1,0⟩, +⟨⟨1,16,52,true⟩,1,1,0⟩, +⟨⟨1,32,52,true⟩,1,1,0⟩, +⟨⟨1,1,53,true⟩,1,1,0⟩, +⟨⟨1,2,53,true⟩,1,1,0⟩, +⟨⟨1,4,53,true⟩,1,1,0⟩, +⟨⟨1,8,53,true⟩,1,1,0⟩, +⟨⟨1,9,53,true⟩,1,1,0⟩, +⟨⟨1,16,53,true⟩,1,1,0⟩, +⟨⟨1,32,53,true⟩,1,1,0⟩, +⟨⟨1,4,54,true⟩,1,1,0⟩, +⟨⟨1,8,54,true⟩,1,1,0⟩, +⟨⟨1,9,54,true⟩,1,1,0⟩, +⟨⟨1,16,54,true⟩,1,1,0⟩, +⟨⟨1,32,54,true⟩,1,1,0⟩, +⟨⟨1,0,55,true⟩,1,1,0⟩, +⟨⟨1,1,55,true⟩,1,1,0⟩, +⟨⟨1,4,55,true⟩,1,1,0⟩, +⟨⟨1,16,55,true⟩,1,1,0⟩, +⟨⟨1,32,55,true⟩,1,1,0⟩, +⟨⟨1,0,56,true⟩,1,1,0⟩, +⟨⟨1,1,56,true⟩,1,1,0⟩, +⟨⟨1,2,56,true⟩,1,1,0⟩, +⟨⟨1,4,56,true⟩,1,1,0⟩, +⟨⟨1,8,56,true⟩,1,1,0⟩, +⟨⟨1,16,56,true⟩,1,1,0⟩, +⟨⟨1,32,56,true⟩,1,1,0⟩, +⟨⟨1,0,57,true⟩,1,1,0⟩, +⟨⟨1,1,57,true⟩,1,1,0⟩, +⟨⟨1,2,57,true⟩,1,1,0⟩, +⟨⟨1,4,57,true⟩,1,1,0⟩, +⟨⟨1,9,57,true⟩,1,1,0⟩, +⟨⟨1,16,57,true⟩,1,1,0⟩, +⟨⟨1,32,57,true⟩,1,1,0⟩, +⟨⟨1,2,58,true⟩,1,1,0⟩, +⟨⟨1,4,58,true⟩,1,1,0⟩, +⟨⟨1,9,58,true⟩,1,1,0⟩, +⟨⟨1,16,58,true⟩,1,1,0⟩, +⟨⟨1,32,58,true⟩,1,1,0⟩, +⟨⟨1,2,59,true⟩,1,1,0⟩, +⟨⟨1,4,59,true⟩,1,1,0⟩, +⟨⟨1,8,59,true⟩,1,1,0⟩, +⟨⟨1,16,59,true⟩,1,1,0⟩, +⟨⟨1,32,59,true⟩,1,1,0⟩, +⟨⟨1,1,60,true⟩,1,1,0⟩] +def chunk72 : List Entry := [⟨⟨1,4,60,true⟩,1,1,0⟩, +⟨⟨1,9,60,true⟩,1,1,0⟩, +⟨⟨1,16,60,true⟩,1,1,0⟩, +⟨⟨1,32,60,true⟩,1,1,0⟩, +⟨⟨1,1,61,true⟩,1,1,0⟩, +⟨⟨1,4,61,true⟩,1,1,0⟩, +⟨⟨1,8,61,true⟩,1,1,0⟩, +⟨⟨1,16,61,true⟩,1,1,0⟩, +⟨⟨1,32,61,true⟩,1,1,0⟩, +⟨⟨1,0,62,true⟩,1,1,0⟩, +⟨⟨1,4,62,true⟩,1,1,0⟩, +⟨⟨1,8,62,true⟩,1,1,0⟩, +⟨⟨1,16,62,true⟩,1,1,0⟩, +⟨⟨1,32,62,true⟩,1,1,0⟩, +⟨⟨1,0,63,true⟩,1,1,0⟩, +⟨⟨1,4,63,true⟩,1,1,0⟩, +⟨⟨1,9,63,true⟩,1,1,0⟩, +⟨⟨1,16,63,true⟩,1,1,0⟩, +⟨⟨1,32,63,true⟩,1,1,0⟩, +⟨⟨1,1,64,true⟩,1,1,0⟩, +⟨⟨1,2,64,true⟩,1,1,0⟩, +⟨⟨1,4,64,true⟩,1,1,0⟩, +⟨⟨1,16,64,true⟩,1,1,0⟩, +⟨⟨1,32,64,true⟩,1,1,0⟩, +⟨⟨1,0,65,true⟩,1,1,0⟩, +⟨⟨1,4,65,true⟩,1,1,0⟩, +⟨⟨1,8,65,true⟩,1,1,0⟩, +⟨⟨1,9,65,true⟩,1,1,0⟩, +⟨⟨1,64,65,true⟩,1,1,0⟩, +⟨⟨1,1,66,true⟩,1,1,0⟩, +⟨⟨1,4,66,true⟩,1,1,0⟩, +⟨⟨1,8,66,true⟩,1,1,0⟩, +⟨⟨1,9,66,true⟩,1,1,0⟩, +⟨⟨1,64,66,true⟩,1,1,0⟩, +⟨⟨1,0,67,true⟩,1,1,0⟩, +⟨⟨1,1,67,true⟩,1,1,0⟩, +⟨⟨1,64,67,true⟩,1,1,0⟩, +⟨⟨1,2,68,true⟩,1,1,0⟩, +⟨⟨1,4,68,true⟩,1,1,0⟩, +⟨⟨1,8,68,true⟩,1,1,0⟩, +⟨⟨1,9,68,true⟩,1,1,0⟩, +⟨⟨1,64,68,true⟩,1,1,0⟩, +⟨⟨1,0,69,true⟩,1,1,0⟩, +⟨⟨1,2,69,true⟩,1,1,0⟩, +⟨⟨1,64,69,true⟩,1,1,0⟩, +⟨⟨1,1,70,true⟩,1,1,0⟩, +⟨⟨1,2,70,true⟩,1,1,0⟩, +⟨⟨1,64,70,true⟩,1,1,0⟩, +⟨⟨1,0,71,true⟩,1,1,0⟩, +⟨⟨1,1,71,true⟩,1,1,0⟩, +⟨⟨1,2,71,true⟩,1,1,0⟩, +⟨⟨1,4,71,true⟩,1,1,0⟩, +⟨⟨1,8,71,true⟩,1,1,0⟩, +⟨⟨1,9,71,true⟩,1,1,0⟩, +⟨⟨1,64,71,true⟩,1,1,0⟩, +⟨⟨1,4,72,true⟩,1,1,0⟩, +⟨⟨1,9,72,true⟩,1,1,0⟩, +⟨⟨1,64,72,true⟩,1,1,0⟩, +⟨⟨1,4,73,true⟩,1,1,0⟩, +⟨⟨1,8,73,true⟩,1,1,0⟩, +⟨⟨1,64,73,true⟩,1,1,0⟩, +⟨⟨1,1,74,true⟩,1,1,0⟩, +⟨⟨1,2,74,true⟩,1,1,0⟩, +⟨⟨1,4,74,true⟩,1,1,0⟩, +⟨⟨1,8,74,true⟩,1,1,0⟩, +⟨⟨1,64,74,true⟩,1,1,0⟩, +⟨⟨1,1,75,true⟩,1,1,0⟩, +⟨⟨1,2,75,true⟩,1,1,0⟩, +⟨⟨1,4,75,true⟩,1,1,0⟩, +⟨⟨1,9,75,true⟩,1,1,0⟩, +⟨⟨1,64,75,true⟩,1,1,0⟩, +⟨⟨1,0,76,true⟩,1,1,0⟩, +⟨⟨1,8,76,true⟩,1,1,0⟩, +⟨⟨1,64,76,true⟩,1,1,0⟩, +⟨⟨1,0,77,true⟩,1,1,0⟩, +⟨⟨1,9,77,true⟩,1,1,0⟩, +⟨⟨1,64,77,true⟩,1,1,0⟩, +⟨⟨1,0,78,true⟩,1,1,0⟩, +⟨⟨1,1,78,true⟩,1,1,0⟩, +⟨⟨1,2,78,true⟩,1,1,0⟩, +⟨⟨1,9,78,true⟩,1,1,0⟩, +⟨⟨1,64,78,true⟩,1,1,0⟩, +⟨⟨1,0,79,true⟩,1,1,0⟩, +⟨⟨1,1,79,true⟩,1,1,0⟩, +⟨⟨1,2,79,true⟩,1,1,0⟩, +⟨⟨1,8,79,true⟩,1,1,0⟩, +⟨⟨1,64,79,true⟩,1,1,0⟩, +⟨⟨1,0,80,true⟩,1,1,0⟩, +⟨⟨1,1,80,true⟩,1,1,0⟩, +⟨⟨1,4,80,true⟩,1,1,0⟩, +⟨⟨1,8,80,true⟩,1,1,0⟩, +⟨⟨1,9,80,true⟩,1,1,0⟩, +⟨⟨1,16,80,true⟩,1,1,0⟩, +⟨⟨1,64,80,true⟩,1,1,0⟩, +⟨⟨1,4,81,true⟩,1,1,0⟩, +⟨⟨1,16,81,true⟩,1,1,0⟩, +⟨⟨1,64,81,true⟩,1,1,0⟩, +⟨⟨1,0,82,true⟩,1,1,0⟩, +⟨⟨1,2,82,true⟩,1,1,0⟩, +⟨⟨1,4,82,true⟩,1,1,0⟩, +⟨⟨1,16,82,true⟩,1,1,0⟩, +⟨⟨1,64,82,true⟩,1,1,0⟩, +⟨⟨1,1,83,true⟩,1,1,0⟩, +⟨⟨1,2,83,true⟩,1,1,0⟩, +⟨⟨1,4,83,true⟩,1,1,0⟩, +⟨⟨1,8,83,true⟩,1,1,0⟩, +⟨⟨1,9,83,true⟩,1,1,0⟩, +⟨⟨1,16,83,true⟩,1,1,0⟩, +⟨⟨1,64,83,true⟩,1,1,0⟩, +⟨⟨1,1,84,true⟩,1,1,0⟩, +⟨⟨1,16,84,true⟩,1,1,0⟩, +⟨⟨1,64,84,true⟩,1,1,0⟩, +⟨⟨1,0,85,true⟩,1,1,0⟩, +⟨⟨1,8,85,true⟩,1,1,0⟩, +⟨⟨1,9,85,true⟩,1,1,0⟩, +⟨⟨1,16,85,true⟩,1,1,0⟩, +⟨⟨1,64,85,true⟩,1,1,0⟩, +⟨⟨1,2,86,true⟩,1,1,0⟩, +⟨⟨1,8,86,true⟩,1,1,0⟩, +⟨⟨1,9,86,true⟩,1,1,0⟩, +⟨⟨1,16,86,true⟩,1,1,0⟩, +⟨⟨1,64,86,true⟩,1,1,0⟩, +⟨⟨1,0,87,true⟩,1,1,0⟩, +⟨⟨1,1,87,true⟩,1,1,0⟩, +⟨⟨1,2,87,true⟩,1,1,0⟩, +⟨⟨1,16,87,true⟩,1,1,0⟩, +⟨⟨1,64,87,true⟩,1,1,0⟩, +⟨⟨1,0,88,true⟩,1,1,0⟩, +⟨⟨1,1,88,true⟩,1,1,0⟩, +⟨⟨1,2,88,true⟩,1,1,0⟩, +⟨⟨1,4,88,true⟩,1,1,0⟩, +⟨⟨1,8,88,true⟩,1,1,0⟩, +⟨⟨1,16,88,true⟩,1,1,0⟩, +⟨⟨1,64,88,true⟩,1,1,0⟩, +⟨⟨1,0,89,true⟩,1,1,0⟩, +⟨⟨1,1,89,true⟩,1,1,0⟩, +⟨⟨1,2,89,true⟩,1,1,0⟩, +⟨⟨1,4,89,true⟩,1,1,0⟩, +⟨⟨1,9,89,true⟩,1,1,0⟩, +⟨⟨1,16,89,true⟩,1,1,0⟩, +⟨⟨1,64,89,true⟩,1,1,0⟩, +⟨⟨1,2,90,true⟩,1,1,0⟩, +⟨⟨1,4,90,true⟩,1,1,0⟩, +⟨⟨1,9,90,true⟩,1,1,0⟩, +⟨⟨1,16,90,true⟩,1,1,0⟩, +⟨⟨1,64,90,true⟩,1,1,0⟩, +⟨⟨1,2,91,true⟩,1,1,0⟩, +⟨⟨1,4,91,true⟩,1,1,0⟩, +⟨⟨1,8,91,true⟩,1,1,0⟩, +⟨⟨1,16,91,true⟩,1,1,0⟩, +⟨⟨1,64,91,true⟩,1,1,0⟩, +⟨⟨1,1,92,true⟩,1,1,0⟩, +⟨⟨1,2,92,true⟩,1,1,0⟩, +⟨⟨1,9,92,true⟩,1,1,0⟩, +⟨⟨1,16,92,true⟩,1,1,0⟩, +⟨⟨1,64,92,true⟩,1,1,0⟩, +⟨⟨1,1,93,true⟩,1,1,0⟩, +⟨⟨1,2,93,true⟩,1,1,0⟩, +⟨⟨1,8,93,true⟩,1,1,0⟩, +⟨⟨1,16,93,true⟩,1,1,0⟩, +⟨⟨1,64,93,true⟩,1,1,0⟩, +⟨⟨1,0,94,true⟩,1,1,0⟩, +⟨⟨1,2,94,true⟩,1,1,0⟩, +⟨⟨1,8,94,true⟩,1,1,0⟩, +⟨⟨1,16,94,true⟩,1,1,0⟩, +⟨⟨1,64,94,true⟩,1,1,0⟩, +⟨⟨1,0,95,true⟩,1,1,0⟩, +⟨⟨1,2,95,true⟩,1,1,0⟩, +⟨⟨1,9,95,true⟩,1,1,0⟩, +⟨⟨1,16,95,true⟩,1,1,0⟩, +⟨⟨1,64,95,true⟩,1,1,0⟩, +⟨⟨1,0,96,true⟩,1,1,0⟩, +⟨⟨1,2,96,true⟩,1,1,0⟩, +⟨⟨1,4,96,true⟩,1,1,0⟩, +⟨⟨1,8,96,true⟩,1,1,0⟩, +⟨⟨1,9,96,true⟩,1,1,0⟩, +⟨⟨1,32,96,true⟩,1,1,0⟩, +⟨⟨1,64,96,true⟩,1,1,0⟩, +⟨⟨1,4,97,true⟩,1,1,0⟩, +⟨⟨1,32,97,true⟩,1,1,0⟩, +⟨⟨1,64,97,true⟩,1,1,0⟩, +⟨⟨1,0,98,true⟩,1,1,0⟩, +⟨⟨1,1,98,true⟩,1,1,0⟩, +⟨⟨1,4,98,true⟩,1,1,0⟩, +⟨⟨1,32,98,true⟩,1,1,0⟩, +⟨⟨1,64,98,true⟩,1,1,0⟩, +⟨⟨1,1,99,true⟩,1,1,0⟩, +⟨⟨1,2,99,true⟩,1,1,0⟩, +⟨⟨1,4,99,true⟩,1,1,0⟩, +⟨⟨1,8,99,true⟩,1,1,0⟩, +⟨⟨1,9,99,true⟩,1,1,0⟩, +⟨⟨1,32,99,true⟩,1,1,0⟩, +⟨⟨1,64,99,true⟩,1,1,0⟩, +⟨⟨1,2,100,true⟩,1,1,0⟩, +⟨⟨1,32,100,true⟩,1,1,0⟩, +⟨⟨1,64,100,true⟩,1,1,0⟩, +⟨⟨1,0,101,true⟩,1,1,0⟩, +⟨⟨1,8,101,true⟩,1,1,0⟩, +⟨⟨1,9,101,true⟩,1,1,0⟩, +⟨⟨1,32,101,true⟩,1,1,0⟩] +def chunk73 : List Entry := [⟨⟨1,64,101,true⟩,1,1,0⟩, +⟨⟨1,1,102,true⟩,1,1,0⟩, +⟨⟨1,8,102,true⟩,1,1,0⟩, +⟨⟨1,9,102,true⟩,1,1,0⟩, +⟨⟨1,32,102,true⟩,1,1,0⟩, +⟨⟨1,64,102,true⟩,1,1,0⟩, +⟨⟨1,0,103,true⟩,1,1,0⟩, +⟨⟨1,1,103,true⟩,1,1,0⟩, +⟨⟨1,2,103,true⟩,1,1,0⟩, +⟨⟨1,32,103,true⟩,1,1,0⟩, +⟨⟨1,64,103,true⟩,1,1,0⟩, +⟨⟨1,0,104,true⟩,1,1,0⟩, +⟨⟨1,1,104,true⟩,1,1,0⟩, +⟨⟨1,2,104,true⟩,1,1,0⟩, +⟨⟨1,4,104,true⟩,1,1,0⟩, +⟨⟨1,8,104,true⟩,1,1,0⟩, +⟨⟨1,32,104,true⟩,1,1,0⟩, +⟨⟨1,64,104,true⟩,1,1,0⟩, +⟨⟨1,0,105,true⟩,1,1,0⟩, +⟨⟨1,1,105,true⟩,1,1,0⟩, +⟨⟨1,2,105,true⟩,1,1,0⟩, +⟨⟨1,4,105,true⟩,1,1,0⟩, +⟨⟨1,9,105,true⟩,1,1,0⟩, +⟨⟨1,32,105,true⟩,1,1,0⟩, +⟨⟨1,64,105,true⟩,1,1,0⟩, +⟨⟨1,1,106,true⟩,1,1,0⟩, +⟨⟨1,4,106,true⟩,1,1,0⟩, +⟨⟨1,9,106,true⟩,1,1,0⟩, +⟨⟨1,32,106,true⟩,1,1,0⟩, +⟨⟨1,64,106,true⟩,1,1,0⟩, +⟨⟨1,1,107,true⟩,1,1,0⟩, +⟨⟨1,4,107,true⟩,1,1,0⟩, +⟨⟨1,8,107,true⟩,1,1,0⟩, +⟨⟨1,32,107,true⟩,1,1,0⟩, +⟨⟨1,64,107,true⟩,1,1,0⟩, +⟨⟨1,1,108,true⟩,1,1,0⟩, +⟨⟨1,2,108,true⟩,1,1,0⟩, +⟨⟨1,9,108,true⟩,1,1,0⟩, +⟨⟨1,32,108,true⟩,1,1,0⟩, +⟨⟨1,64,108,true⟩,1,1,0⟩, +⟨⟨1,1,109,true⟩,1,1,0⟩, +⟨⟨1,2,109,true⟩,1,1,0⟩, +⟨⟨1,8,109,true⟩,1,1,0⟩, +⟨⟨1,32,109,true⟩,1,1,0⟩, +⟨⟨1,64,109,true⟩,1,1,0⟩, +⟨⟨1,0,110,true⟩,1,1,0⟩, +⟨⟨1,1,110,true⟩,1,1,0⟩, +⟨⟨1,8,110,true⟩,1,1,0⟩, +⟨⟨1,32,110,true⟩,1,1,0⟩, +⟨⟨1,64,110,true⟩,1,1,0⟩, +⟨⟨1,0,111,true⟩,1,1,0⟩, +⟨⟨1,1,111,true⟩,1,1,0⟩, +⟨⟨1,9,111,true⟩,1,1,0⟩, +⟨⟨1,32,111,true⟩,1,1,0⟩, +⟨⟨1,64,111,true⟩,1,1,0⟩, +⟨⟨1,0,112,true⟩,1,1,0⟩, +⟨⟨1,1,112,true⟩,1,1,0⟩, +⟨⟨1,2,112,true⟩,1,1,0⟩, +⟨⟨1,4,112,true⟩,1,1,0⟩, +⟨⟨1,16,112,true⟩,1,1,0⟩, +⟨⟨1,32,112,true⟩,1,1,0⟩, +⟨⟨1,64,112,true⟩,1,1,0⟩, +⟨⟨1,2,113,true⟩,1,1,0⟩, +⟨⟨1,4,113,true⟩,1,1,0⟩, +⟨⟨1,8,113,true⟩,1,1,0⟩, +⟨⟨1,9,113,true⟩,1,1,0⟩, +⟨⟨1,16,113,true⟩,1,1,0⟩, +⟨⟨1,32,113,true⟩,1,1,0⟩, +⟨⟨1,64,113,true⟩,1,1,0⟩, +⟨⟨1,1,114,true⟩,1,1,0⟩, +⟨⟨1,4,114,true⟩,1,1,0⟩, +⟨⟨1,8,114,true⟩,1,1,0⟩, +⟨⟨1,9,114,true⟩,1,1,0⟩, +⟨⟨1,16,114,true⟩,1,1,0⟩, +⟨⟨1,32,114,true⟩,1,1,0⟩, +⟨⟨1,64,114,true⟩,1,1,0⟩, +⟨⟨1,0,115,true⟩,1,1,0⟩, +⟨⟨1,4,115,true⟩,1,1,0⟩, +⟨⟨1,16,115,true⟩,1,1,0⟩, +⟨⟨1,32,115,true⟩,1,1,0⟩, +⟨⟨1,64,115,true⟩,1,1,0⟩, +⟨⟨1,1,116,true⟩,1,1,0⟩, +⟨⟨1,2,116,true⟩,1,1,0⟩, +⟨⟨1,8,116,true⟩,1,1,0⟩, +⟨⟨1,9,116,true⟩,1,1,0⟩, +⟨⟨1,16,116,true⟩,1,1,0⟩, +⟨⟨1,32,116,true⟩,1,1,0⟩, +⟨⟨1,64,116,true⟩,1,1,0⟩, +⟨⟨1,0,117,true⟩,1,1,0⟩, +⟨⟨1,2,117,true⟩,1,1,0⟩, +⟨⟨1,16,117,true⟩,1,1,0⟩, +⟨⟨1,32,117,true⟩,1,1,0⟩, +⟨⟨1,64,117,true⟩,1,1,0⟩, +⟨⟨1,0,118,true⟩,1,1,0⟩, +⟨⟨1,1,118,true⟩,1,1,0⟩, +⟨⟨1,16,118,true⟩,1,1,0⟩, +⟨⟨1,32,118,true⟩,1,1,0⟩, +⟨⟨1,64,118,true⟩,1,1,0⟩, +⟨⟨1,8,119,true⟩,1,1,0⟩, +⟨⟨1,9,119,true⟩,1,1,0⟩, +⟨⟨1,16,119,true⟩,1,1,0⟩, +⟨⟨1,32,119,true⟩,1,1,0⟩, +⟨⟨1,64,119,true⟩,1,1,0⟩, +⟨⟨0,125,0,false⟩,0,458,4⟩, +⟨⟨1,125,523,true⟩,458,458,0⟩, +⟨⟨0,127,0,false⟩,0,458,4⟩, +⟨⟨1,127,523,true⟩,458,458,0⟩, +⟨⟨0,176,0,false⟩,0,458,4⟩, +⟨⟨1,176,523,true⟩,458,458,0⟩, +⟨⟨0,177,0,false⟩,0,458,4⟩, +⟨⟨1,177,523,true⟩,458,458,0⟩, +⟨⟨0,178,0,false⟩,0,458,4⟩, +⟨⟨1,178,523,true⟩,458,458,0⟩, +⟨⟨0,179,0,false⟩,0,458,4⟩, +⟨⟨1,179,523,true⟩,458,458,0⟩, +⟨⟨0,180,0,true⟩,0,515,5⟩, +⟨⟨0,523,458,true⟩,458,515,1⟩, +⟨⟨1,180,523,true⟩,515,515,0⟩, +⟨⟨0,181,0,true⟩,0,515,5⟩, +⟨⟨1,181,523,true⟩,515,515,0⟩, +⟨⟨0,182,0,true⟩,0,515,5⟩, +⟨⟨1,182,523,true⟩,515,515,0⟩, +⟨⟨0,183,0,true⟩,0,887,7⟩, +⟨⟨0,523,515,true⟩,515,887,2⟩, +⟨⟨1,183,523,true⟩,887,887,0⟩, +⟨⟨0,122,0,true⟩,0,459,4⟩, +⟨⟨1,122,240,true⟩,459,459,0⟩, +⟨⟨0,123,0,true⟩,0,459,4⟩, +⟨⟨1,123,240,true⟩,459,459,0⟩, +⟨⟨0,208,0,true⟩,0,459,4⟩, +⟨⟨1,208,240,true⟩,459,459,0⟩, +⟨⟨0,209,0,true⟩,0,459,4⟩, +⟨⟨1,209,240,true⟩,459,459,0⟩, +⟨⟨0,210,0,true⟩,0,459,4⟩, +⟨⟨1,210,240,true⟩,459,459,0⟩, +⟨⟨0,211,0,true⟩,0,459,4⟩, +⟨⟨1,211,240,true⟩,459,459,0⟩, +⟨⟨0,212,0,true⟩,0,493,5⟩, +⟨⟨0,240,459,true⟩,459,493,1⟩, +⟨⟨1,212,240,true⟩,493,493,0⟩, +⟨⟨0,213,0,true⟩,0,493,5⟩, +⟨⟨1,213,240,true⟩,493,493,0⟩, +⟨⟨0,214,0,true⟩,0,493,5⟩, +⟨⟨1,214,240,true⟩,493,493,0⟩, +⟨⟨0,215,0,true⟩,0,919,7⟩, +⟨⟨0,240,493,true⟩,493,919,2⟩, +⟨⟨1,215,240,true⟩,919,919,0⟩, +⟨⟨0,216,0,false⟩,0,460,4⟩, +⟨⟨1,216,241,true⟩,460,460,0⟩, +⟨⟨0,217,0,false⟩,0,460,4⟩, +⟨⟨1,217,241,true⟩,460,460,0⟩, +⟨⟨0,218,0,false⟩,0,460,4⟩, +⟨⟨1,218,241,true⟩,460,460,0⟩, +⟨⟨0,219,0,false⟩,0,460,4⟩, +⟨⟨1,219,241,true⟩,460,460,0⟩, +⟨⟨0,220,0,false⟩,0,492,5⟩, +⟨⟨0,241,460,false⟩,460,492,1⟩, +⟨⟨1,220,241,true⟩,492,492,0⟩, +⟨⟨0,221,0,false⟩,0,492,5⟩, +⟨⟨1,221,241,true⟩,492,492,0⟩, +⟨⟨0,222,0,false⟩,0,492,5⟩, +⟨⟨1,222,241,true⟩,492,492,0⟩, +⟨⟨0,223,0,true⟩,0,927,7⟩, +⟨⟨0,241,492,true⟩,492,927,2⟩, +⟨⟨1,223,241,true⟩,927,927,0⟩, +⟨⟨0,224,0,true⟩,0,461,4⟩, +⟨⟨1,224,242,true⟩,461,461,0⟩, +⟨⟨0,225,0,true⟩,0,461,4⟩, +⟨⟨1,225,242,true⟩,461,461,0⟩, +⟨⟨0,226,0,true⟩,0,461,4⟩, +⟨⟨1,226,242,true⟩,461,461,0⟩, +⟨⟨0,227,0,true⟩,0,461,4⟩, +⟨⟨1,227,242,true⟩,461,461,0⟩, +⟨⟨0,228,0,true⟩,0,489,5⟩, +⟨⟨0,242,461,true⟩,461,489,1⟩, +⟨⟨1,228,242,true⟩,489,489,0⟩, +⟨⟨0,229,0,true⟩,0,489,5⟩, +⟨⟨1,229,242,true⟩,489,489,0⟩, +⟨⟨0,230,0,true⟩,0,489,5⟩, +⟨⟨1,230,242,true⟩,489,489,0⟩, +⟨⟨0,231,0,true⟩,0,935,7⟩, +⟨⟨0,242,489,true⟩,489,935,2⟩, +⟨⟨1,231,242,true⟩,935,935,0⟩, +⟨⟨0,126,0,false⟩,0,462,4⟩, +⟨⟨1,126,243,true⟩,462,462,0⟩, +⟨⟨0,200,0,false⟩,0,462,4⟩, +⟨⟨1,200,243,true⟩,462,462,0⟩, +⟨⟨0,201,0,false⟩,0,462,4⟩, +⟨⟨1,201,243,true⟩,462,462,0⟩, +⟨⟨0,202,0,false⟩,0,462,4⟩, +⟨⟨1,202,243,true⟩,462,462,0⟩, +⟨⟨0,203,0,false⟩,0,462,4⟩, +⟨⟨1,203,243,true⟩,462,462,0⟩, +⟨⟨0,204,0,false⟩,0,488,5⟩, +⟨⟨0,243,462,false⟩,462,488,1⟩, +⟨⟨1,204,243,true⟩,488,488,0⟩, +⟨⟨0,205,0,false⟩,0,488,5⟩, +⟨⟨1,205,243,true⟩,488,488,0⟩, +⟨⟨0,206,0,false⟩,0,488,5⟩, +⟨⟨1,206,243,true⟩,488,488,0⟩] +def chunk74 : List Entry := [⟨⟨0,207,0,true⟩,0,911,7⟩, +⟨⟨0,243,488,true⟩,488,911,2⟩, +⟨⟨1,207,243,true⟩,911,911,0⟩, +⟨⟨0,168,0,true⟩,0,463,4⟩, +⟨⟨1,168,244,true⟩,463,463,0⟩, +⟨⟨0,169,0,true⟩,0,463,4⟩, +⟨⟨1,169,244,true⟩,463,463,0⟩, +⟨⟨0,170,0,true⟩,0,463,4⟩, +⟨⟨1,170,244,true⟩,463,463,0⟩, +⟨⟨0,171,0,true⟩,0,463,4⟩, +⟨⟨1,171,244,true⟩,463,463,0⟩, +⟨⟨0,172,0,true⟩,0,485,5⟩, +⟨⟨0,244,463,true⟩,463,485,1⟩, +⟨⟨1,172,244,true⟩,485,485,0⟩, +⟨⟨0,173,0,true⟩,0,485,5⟩, +⟨⟨1,173,244,true⟩,485,485,0⟩, +⟨⟨0,174,0,true⟩,0,485,5⟩, +⟨⟨1,174,244,true⟩,485,485,0⟩, +⟨⟨0,175,0,true⟩,0,879,7⟩, +⟨⟨0,244,485,true⟩,485,879,2⟩, +⟨⟨1,175,244,true⟩,879,879,0⟩, +⟨⟨0,121,0,false⟩,0,464,4⟩, +⟨⟨1,121,245,true⟩,464,464,0⟩, +⟨⟨0,124,0,false⟩,0,464,4⟩, +⟨⟨1,124,245,true⟩,464,464,0⟩, +⟨⟨0,128,0,false⟩,0,464,4⟩, +⟨⟨1,128,245,true⟩,464,464,0⟩, +⟨⟨0,129,0,false⟩,0,464,4⟩, +⟨⟨1,129,245,true⟩,464,464,0⟩, +⟨⟨0,130,0,false⟩,0,464,4⟩, +⟨⟨1,130,245,true⟩,464,464,0⟩, +⟨⟨0,131,0,false⟩,0,464,4⟩, +⟨⟨1,131,245,true⟩,464,464,0⟩, +⟨⟨0,132,0,false⟩,0,484,5⟩, +⟨⟨0,245,464,false⟩,464,484,1⟩, +⟨⟨1,132,245,true⟩,484,484,0⟩, +⟨⟨0,133,0,false⟩,0,484,5⟩, +⟨⟨1,133,245,true⟩,484,484,0⟩, +⟨⟨0,134,0,false⟩,0,484,5⟩, +⟨⟨1,134,245,true⟩,484,484,0⟩, +⟨⟨0,135,0,true⟩,0,839,7⟩, +⟨⟨0,245,484,true⟩,484,839,2⟩, +⟨⟨1,135,245,true⟩,839,839,0⟩, +⟨⟨0,232,0,true⟩,0,465,4⟩, +⟨⟨1,232,248,true⟩,465,465,0⟩, +⟨⟨0,233,0,true⟩,0,465,4⟩, +⟨⟨1,233,248,true⟩,465,465,0⟩, +⟨⟨0,234,0,true⟩,0,465,4⟩, +⟨⟨1,234,248,true⟩,465,465,0⟩, +⟨⟨0,235,0,true⟩,0,465,4⟩, +⟨⟨1,235,248,true⟩,465,465,0⟩, +⟨⟨0,236,0,true⟩,0,481,5⟩, +⟨⟨0,248,465,true⟩,465,481,1⟩, +⟨⟨1,236,248,true⟩,481,481,0⟩, +⟨⟨0,237,0,true⟩,0,481,5⟩, +⟨⟨1,237,248,true⟩,481,481,0⟩, +⟨⟨0,238,0,true⟩,0,481,5⟩, +⟨⟨1,238,248,true⟩,481,481,0⟩, +⟨⟨0,239,0,true⟩,0,943,7⟩, +⟨⟨0,248,481,true⟩,481,943,2⟩, +⟨⟨1,239,248,true⟩,943,943,0⟩, +⟨⟨0,192,0,false⟩,0,466,4⟩, +⟨⟨1,192,249,true⟩,466,466,0⟩, +⟨⟨0,193,0,false⟩,0,466,4⟩, +⟨⟨1,193,249,true⟩,466,466,0⟩, +⟨⟨0,194,0,false⟩,0,466,4⟩, +⟨⟨1,194,249,true⟩,466,466,0⟩, +⟨⟨0,195,0,false⟩,0,466,4⟩, +⟨⟨1,195,249,true⟩,466,466,0⟩, +⟨⟨0,196,0,false⟩,0,480,5⟩, +⟨⟨0,249,466,false⟩,466,480,1⟩, +⟨⟨1,196,249,true⟩,480,480,0⟩, +⟨⟨0,197,0,false⟩,0,480,5⟩, +⟨⟨1,197,249,true⟩,480,480,0⟩, +⟨⟨0,198,0,false⟩,0,480,5⟩, +⟨⟨1,198,249,true⟩,480,480,0⟩, +⟨⟨0,199,0,true⟩,0,903,7⟩, +⟨⟨0,249,480,true⟩,480,903,2⟩, +⟨⟨1,199,249,true⟩,903,903,0⟩, +⟨⟨0,160,0,true⟩,0,467,4⟩, +⟨⟨1,160,250,true⟩,467,467,0⟩, +⟨⟨0,161,0,true⟩,0,467,4⟩, +⟨⟨1,161,250,true⟩,467,467,0⟩, +⟨⟨0,162,0,true⟩,0,467,4⟩, +⟨⟨1,162,250,true⟩,467,467,0⟩, +⟨⟨0,163,0,true⟩,0,467,4⟩, +⟨⟨1,163,250,true⟩,467,467,0⟩, +⟨⟨0,164,0,true⟩,0,477,5⟩, +⟨⟨0,250,467,true⟩,467,477,1⟩, +⟨⟨1,164,250,true⟩,477,477,0⟩, +⟨⟨0,165,0,true⟩,0,477,5⟩, +⟨⟨1,165,250,true⟩,477,477,0⟩, +⟨⟨0,166,0,true⟩,0,477,5⟩, +⟨⟨1,166,250,true⟩,477,477,0⟩, +⟨⟨0,167,0,true⟩,0,871,7⟩, +⟨⟨0,250,477,true⟩,477,871,2⟩, +⟨⟨1,167,250,true⟩,871,871,0⟩, +⟨⟨0,120,0,false⟩,0,468,4⟩, +⟨⟨1,120,251,true⟩,468,468,0⟩, +⟨⟨0,136,0,false⟩,0,468,4⟩, +⟨⟨1,136,251,true⟩,468,468,0⟩, +⟨⟨0,137,0,false⟩,0,468,4⟩, +⟨⟨1,137,251,true⟩,468,468,0⟩, +⟨⟨0,138,0,false⟩,0,468,4⟩, +⟨⟨1,138,251,true⟩,468,468,0⟩, +⟨⟨0,139,0,false⟩,0,468,4⟩, +⟨⟨1,139,251,true⟩,468,468,0⟩, +⟨⟨0,140,0,false⟩,0,476,5⟩, +⟨⟨0,251,468,false⟩,468,476,1⟩, +⟨⟨1,140,251,true⟩,476,476,0⟩, +⟨⟨0,141,0,false⟩,0,476,5⟩, +⟨⟨1,141,251,true⟩,476,476,0⟩, +⟨⟨0,142,0,false⟩,0,476,5⟩, +⟨⟨1,142,251,true⟩,476,476,0⟩, +⟨⟨0,143,0,true⟩,0,847,7⟩, +⟨⟨0,251,476,true⟩,476,847,2⟩, +⟨⟨1,143,251,true⟩,847,847,0⟩, +⟨⟨0,144,0,true⟩,0,469,4⟩, +⟨⟨1,144,256,true⟩,469,469,0⟩, +⟨⟨0,145,0,true⟩,0,469,4⟩, +⟨⟨1,145,256,true⟩,469,469,0⟩, +⟨⟨0,146,0,true⟩,0,469,4⟩, +⟨⟨1,146,256,true⟩,469,469,0⟩, +⟨⟨0,147,0,true⟩,0,469,4⟩, +⟨⟨1,147,256,true⟩,469,469,0⟩, +⟨⟨0,148,0,true⟩,0,473,5⟩, +⟨⟨0,256,469,true⟩,469,473,1⟩, +⟨⟨1,148,256,true⟩,473,473,0⟩, +⟨⟨0,149,0,true⟩,0,473,5⟩, +⟨⟨1,149,256,true⟩,473,473,0⟩, +⟨⟨0,150,0,true⟩,0,473,5⟩, +⟨⟨1,150,256,true⟩,473,473,0⟩, +⟨⟨0,151,0,true⟩,0,855,7⟩, +⟨⟨0,256,473,true⟩,473,855,2⟩, +⟨⟨1,151,256,true⟩,855,855,0⟩, +⟨⟨0,152,0,false⟩,0,470,4⟩, +⟨⟨1,152,257,true⟩,470,470,0⟩, +⟨⟨0,153,0,false⟩,0,470,4⟩, +⟨⟨1,153,257,true⟩,470,470,0⟩, +⟨⟨0,154,0,false⟩,0,470,4⟩, +⟨⟨1,154,257,true⟩,470,470,0⟩, +⟨⟨0,155,0,false⟩,0,470,4⟩, +⟨⟨1,155,257,true⟩,470,470,0⟩, +⟨⟨0,156,0,false⟩,0,472,5⟩, +⟨⟨0,257,470,false⟩,470,472,1⟩, +⟨⟨1,156,257,true⟩,472,472,0⟩, +⟨⟨0,157,0,false⟩,0,472,5⟩, +⟨⟨1,157,257,true⟩,472,472,0⟩, +⟨⟨0,158,0,false⟩,0,472,5⟩, +⟨⟨1,158,257,true⟩,472,472,0⟩, +⟨⟨0,159,0,true⟩,0,863,7⟩, +⟨⟨0,257,472,true⟩,472,863,2⟩, +⟨⟨1,159,257,true⟩,863,863,0⟩, +⟨⟨0,184,0,true⟩,0,471,4⟩, +⟨⟨1,184,269,true⟩,471,471,0⟩, +⟨⟨0,185,0,true⟩,0,471,4⟩, +⟨⟨1,185,269,true⟩,471,471,0⟩, +⟨⟨0,186,0,true⟩,0,471,4⟩, +⟨⟨1,186,269,true⟩,471,471,0⟩, +⟨⟨0,187,0,true⟩,0,471,4⟩, +⟨⟨1,187,269,true⟩,471,471,0⟩, +⟨⟨0,188,0,false⟩,0,496,5⟩, +⟨⟨0,269,471,false⟩,471,496,1⟩, +⟨⟨1,188,269,true⟩,496,496,0⟩, +⟨⟨0,189,0,false⟩,0,496,5⟩, +⟨⟨1,189,269,true⟩,496,496,0⟩, +⟨⟨0,190,0,false⟩,0,496,5⟩, +⟨⟨1,190,269,true⟩,496,496,0⟩, +⟨⟨0,191,0,true⟩,0,895,7⟩, +⟨⟨0,269,496,true⟩,496,895,2⟩, +⟨⟨1,191,269,true⟩,895,895,0⟩, +⟨⟨0,217,460,false⟩,460,514,1⟩, +⟨⟨1,217,529,true⟩,514,514,0⟩, +⟨⟨0,218,460,false⟩,460,514,1⟩, +⟨⟨1,218,529,true⟩,514,514,0⟩, +⟨⟨0,221,492,true⟩,492,777,1⟩, +⟨⟨0,529,514,true⟩,514,777,1⟩, +⟨⟨1,221,529,true⟩,777,777,0⟩, +⟨⟨0,222,492,true⟩,492,777,1⟩, +⟨⟨1,222,529,true⟩,777,777,0⟩, +⟨⟨0,216,460,false⟩,460,516,1⟩, +⟨⟨1,216,531,true⟩,516,516,0⟩, +⟨⟨0,219,460,false⟩,460,516,1⟩, +⟨⟨1,219,531,true⟩,516,516,0⟩, +⟨⟨0,220,492,true⟩,492,783,1⟩, +⟨⟨0,531,516,true⟩,516,783,1⟩, +⟨⟨1,220,531,true⟩,783,783,0⟩, +⟨⟨0,531,783,true⟩,783,927,1⟩, +⟨⟨1,223,531,true⟩,927,927,0⟩, +⟨⟨0,209,459,false⟩,459,534,1⟩, +⟨⟨1,209,545,true⟩,534,534,0⟩, +⟨⟨0,210,459,false⟩,459,534,1⟩, +⟨⟨1,210,545,true⟩,534,534,0⟩, +⟨⟨0,213,493,true⟩,493,789,1⟩, +⟨⟨0,545,534,true⟩,534,789,1⟩, +⟨⟨1,213,545,true⟩,789,789,0⟩, +⟨⟨0,214,493,true⟩,493,789,1⟩, +⟨⟨1,214,545,true⟩,789,789,0⟩, +⟨⟨0,177,458,true⟩,458,535,1⟩, +⟨⟨1,177,776,true⟩,535,535,0⟩] +def chunk75 : List Entry := [⟨⟨0,178,458,true⟩,458,535,1⟩, +⟨⟨1,178,776,true⟩,535,535,0⟩, +⟨⟨0,181,515,true⟩,515,801,1⟩, +⟨⟨0,776,535,true⟩,535,801,1⟩, +⟨⟨1,181,776,true⟩,801,801,0⟩, +⟨⟨0,182,515,true⟩,515,801,1⟩, +⟨⟨1,182,776,true⟩,801,801,0⟩, +⟨⟨0,208,459,false⟩,459,536,1⟩, +⟨⟨1,208,547,true⟩,536,536,0⟩, +⟨⟨0,211,459,false⟩,459,536,1⟩, +⟨⟨1,211,547,true⟩,536,536,0⟩, +⟨⟨0,212,493,true⟩,493,795,1⟩, +⟨⟨0,547,536,true⟩,536,795,1⟩, +⟨⟨1,212,547,true⟩,795,795,0⟩, +⟨⟨0,547,795,true⟩,795,919,1⟩, +⟨⟨1,215,547,true⟩,919,919,0⟩, +⟨⟨0,176,458,true⟩,458,537,1⟩, +⟨⟨1,176,777,true⟩,537,537,0⟩, +⟨⟨0,179,458,true⟩,458,537,1⟩, +⟨⟨1,179,777,true⟩,537,537,0⟩, +⟨⟨0,180,515,true⟩,515,807,1⟩, +⟨⟨0,777,537,true⟩,537,807,1⟩, +⟨⟨1,180,777,true⟩,807,807,0⟩, +⟨⟨0,777,807,true⟩,807,887,1⟩, +⟨⟨1,183,777,true⟩,887,887,0⟩, +⟨⟨0,201,462,false⟩,462,552,1⟩, +⟨⟨1,201,561,true⟩,552,552,0⟩, +⟨⟨0,202,462,false⟩,462,552,1⟩, +⟨⟨1,202,561,true⟩,552,552,0⟩, +⟨⟨0,205,488,true⟩,488,753,1⟩, +⟨⟨0,561,552,true⟩,552,753,1⟩, +⟨⟨1,205,561,true⟩,753,753,0⟩, +⟨⟨0,206,488,true⟩,488,753,1⟩, +⟨⟨1,206,561,true⟩,753,753,0⟩, +⟨⟨0,200,462,false⟩,462,554,1⟩, +⟨⟨1,200,563,true⟩,554,554,0⟩, +⟨⟨0,203,462,false⟩,462,554,1⟩, +⟨⟨1,203,563,true⟩,554,554,0⟩, +⟨⟨0,204,488,true⟩,488,759,1⟩, +⟨⟨0,563,554,true⟩,554,759,1⟩, +⟨⟨1,204,563,true⟩,759,759,0⟩, +⟨⟨0,563,759,true⟩,759,911,1⟩, +⟨⟨1,207,563,true⟩,911,911,0⟩, +⟨⟨0,225,461,false⟩,461,568,1⟩, +⟨⟨1,225,577,true⟩,568,568,0⟩, +⟨⟨0,226,461,false⟩,461,568,1⟩, +⟨⟨1,226,577,true⟩,568,568,0⟩, +⟨⟨0,229,489,true⟩,489,765,1⟩, +⟨⟨0,577,568,true⟩,568,765,1⟩, +⟨⟨1,229,577,true⟩,765,765,0⟩, +⟨⟨0,230,489,true⟩,489,765,1⟩, +⟨⟨1,230,577,true⟩,765,765,0⟩, +⟨⟨0,224,461,false⟩,461,570,1⟩, +⟨⟨1,224,579,true⟩,570,570,0⟩, +⟨⟨0,227,461,false⟩,461,570,1⟩, +⟨⟨1,227,579,true⟩,570,570,0⟩, +⟨⟨0,228,489,true⟩,489,771,1⟩, +⟨⟨0,579,570,true⟩,570,771,1⟩, +⟨⟨1,228,579,true⟩,771,771,0⟩, +⟨⟨0,579,771,true⟩,771,935,1⟩, +⟨⟨1,231,579,true⟩,935,935,0⟩, +⟨⟨0,129,464,false⟩,464,574,1⟩, +⟨⟨1,129,593,true⟩,574,574,0⟩, +⟨⟨0,130,464,false⟩,464,574,1⟩, +⟨⟨1,130,593,true⟩,574,574,0⟩, +⟨⟨0,133,484,true⟩,484,729,1⟩, +⟨⟨0,593,574,true⟩,574,729,1⟩, +⟨⟨1,133,593,true⟩,729,729,0⟩, +⟨⟨0,134,484,true⟩,484,729,1⟩, +⟨⟨1,134,593,true⟩,729,729,0⟩, +⟨⟨0,128,464,false⟩,464,576,1⟩, +⟨⟨1,128,595,true⟩,576,576,0⟩, +⟨⟨0,131,464,false⟩,464,576,1⟩, +⟨⟨1,131,595,true⟩,576,576,0⟩, +⟨⟨0,132,484,true⟩,484,735,1⟩, +⟨⟨0,595,576,true⟩,576,735,1⟩, +⟨⟨1,132,595,true⟩,735,735,0⟩, +⟨⟨0,595,735,true⟩,735,839,1⟩, +⟨⟨1,135,595,true⟩,839,839,0⟩, +⟨⟨0,169,463,false⟩,463,586,1⟩, +⟨⟨1,169,609,true⟩,586,586,0⟩, +⟨⟨0,170,463,false⟩,463,586,1⟩, +⟨⟨1,170,609,true⟩,586,586,0⟩, +⟨⟨0,173,485,true⟩,485,741,1⟩, +⟨⟨0,609,586,true⟩,586,741,1⟩, +⟨⟨1,173,609,true⟩,741,741,0⟩, +⟨⟨0,174,485,true⟩,485,741,1⟩, +⟨⟨1,174,609,true⟩,741,741,0⟩, +⟨⟨0,168,463,false⟩,463,588,1⟩, +⟨⟨1,168,611,true⟩,588,588,0⟩, +⟨⟨0,171,463,false⟩,463,588,1⟩, +⟨⟨1,171,611,true⟩,588,588,0⟩, +⟨⟨0,172,485,true⟩,485,747,1⟩, +⟨⟨0,611,588,true⟩,588,747,1⟩, +⟨⟨1,172,611,true⟩,747,747,0⟩, +⟨⟨0,611,747,true⟩,747,879,1⟩, +⟨⟨1,175,611,true⟩,879,879,0⟩, +⟨⟨0,193,466,false⟩,466,608,1⟩, +⟨⟨1,193,846,true⟩,608,608,0⟩, +⟨⟨0,194,466,false⟩,466,608,1⟩, +⟨⟨1,194,846,true⟩,608,608,0⟩, +⟨⟨0,197,480,true⟩,480,705,1⟩, +⟨⟨0,846,608,true⟩,608,705,1⟩, +⟨⟨1,197,846,true⟩,705,705,0⟩, +⟨⟨0,198,480,true⟩,480,705,1⟩, +⟨⟨1,198,846,true⟩,705,705,0⟩, +⟨⟨0,192,466,true⟩,466,609,1⟩, +⟨⟨1,192,847,true⟩,609,609,0⟩, +⟨⟨0,195,466,true⟩,466,609,1⟩, +⟨⟨1,195,847,true⟩,609,609,0⟩, +⟨⟨0,196,480,true⟩,480,711,1⟩, +⟨⟨0,847,609,true⟩,609,711,1⟩, +⟨⟨1,196,847,true⟩,711,711,0⟩, +⟨⟨0,847,711,true⟩,711,903,1⟩, +⟨⟨1,199,847,true⟩,903,903,0⟩, +⟨⟨0,233,465,false⟩,465,618,1⟩, +⟨⟨1,233,860,true⟩,618,618,0⟩, +⟨⟨0,234,465,false⟩,465,618,1⟩, +⟨⟨1,234,860,true⟩,618,618,0⟩, +⟨⟨0,237,481,true⟩,481,717,1⟩, +⟨⟨0,860,618,true⟩,618,717,1⟩, +⟨⟨1,237,860,true⟩,717,717,0⟩, +⟨⟨0,238,481,true⟩,481,717,1⟩, +⟨⟨1,238,860,true⟩,717,717,0⟩, +⟨⟨0,232,465,true⟩,465,619,1⟩, +⟨⟨1,232,861,true⟩,619,619,0⟩, +⟨⟨0,235,465,true⟩,465,619,1⟩, +⟨⟨1,235,861,true⟩,619,619,0⟩, +⟨⟨0,236,481,true⟩,481,723,1⟩, +⟨⟨0,861,619,true⟩,619,723,1⟩, +⟨⟨1,236,861,true⟩,723,723,0⟩, +⟨⟨0,861,723,true⟩,723,943,1⟩, +⟨⟨1,239,861,true⟩,943,943,0⟩, +⟨⟨0,137,468,false⟩,468,622,1⟩, +⟨⟨1,137,870,true⟩,622,622,0⟩, +⟨⟨0,138,468,false⟩,468,622,1⟩, +⟨⟨1,138,870,true⟩,622,622,0⟩, +⟨⟨0,141,476,true⟩,476,681,1⟩, +⟨⟨0,870,622,true⟩,622,681,1⟩, +⟨⟨1,141,870,true⟩,681,681,0⟩, +⟨⟨0,142,476,true⟩,476,681,1⟩, +⟨⟨1,142,870,true⟩,681,681,0⟩, +⟨⟨0,136,468,true⟩,468,623,1⟩, +⟨⟨1,136,871,true⟩,623,623,0⟩, +⟨⟨0,139,468,true⟩,468,623,1⟩, +⟨⟨1,139,871,true⟩,623,623,0⟩, +⟨⟨0,140,476,true⟩,476,687,1⟩, +⟨⟨0,871,623,true⟩,623,687,1⟩, +⟨⟨1,140,871,true⟩,687,687,0⟩, +⟨⟨0,871,687,true⟩,687,847,1⟩, +⟨⟨1,143,871,true⟩,847,847,0⟩, +⟨⟨0,161,467,false⟩,467,628,1⟩, +⟨⟨1,161,884,true⟩,628,628,0⟩, +⟨⟨0,162,467,false⟩,467,628,1⟩, +⟨⟨1,162,884,true⟩,628,628,0⟩, +⟨⟨0,165,477,true⟩,477,693,1⟩, +⟨⟨0,884,628,true⟩,628,693,1⟩, +⟨⟨1,165,884,true⟩,693,693,0⟩, +⟨⟨0,166,477,true⟩,477,693,1⟩, +⟨⟨1,166,884,true⟩,693,693,0⟩, +⟨⟨0,160,467,true⟩,467,629,1⟩, +⟨⟨1,160,885,true⟩,629,629,0⟩, +⟨⟨0,163,467,true⟩,467,629,1⟩, +⟨⟨1,163,885,true⟩,629,629,0⟩, +⟨⟨0,164,477,true⟩,477,699,1⟩, +⟨⟨0,885,629,true⟩,629,699,1⟩, +⟨⟨1,164,885,true⟩,699,699,0⟩, +⟨⟨0,885,699,true⟩,699,871,1⟩, +⟨⟨1,167,885,true⟩,871,871,0⟩, +⟨⟨0,185,471,false⟩,471,634,1⟩, +⟨⟨1,185,891,true⟩,634,634,0⟩, +⟨⟨0,186,471,false⟩,471,634,1⟩, +⟨⟨1,186,891,true⟩,634,634,0⟩, +⟨⟨0,189,496,true⟩,496,645,1⟩, +⟨⟨0,891,634,true⟩,634,645,1⟩, +⟨⟨1,189,891,true⟩,645,645,0⟩, +⟨⟨0,190,496,true⟩,496,645,1⟩, +⟨⟨1,190,891,true⟩,645,645,0⟩, +⟨⟨0,184,471,true⟩,471,635,1⟩, +⟨⟨1,184,893,true⟩,635,635,0⟩, +⟨⟨0,187,471,true⟩,471,635,1⟩, +⟨⟨1,187,893,true⟩,635,635,0⟩, +⟨⟨0,188,496,true⟩,496,651,1⟩, +⟨⟨0,893,635,true⟩,635,651,1⟩, +⟨⟨1,188,893,true⟩,651,651,0⟩, +⟨⟨0,893,651,true⟩,651,895,1⟩, +⟨⟨1,191,893,true⟩,895,895,0⟩, +⟨⟨0,153,470,false⟩,470,636,1⟩, +⟨⟨1,153,894,true⟩,636,636,0⟩, +⟨⟨0,154,470,false⟩,470,636,1⟩, +⟨⟨1,154,894,true⟩,636,636,0⟩, +⟨⟨0,157,472,true⟩,472,657,1⟩, +⟨⟨0,894,636,true⟩,636,657,1⟩, +⟨⟨1,157,894,true⟩,657,657,0⟩, +⟨⟨0,158,472,true⟩,472,657,1⟩, +⟨⟨1,158,894,true⟩,657,657,0⟩, +⟨⟨0,152,470,true⟩,470,637,1⟩, +⟨⟨1,152,895,true⟩,637,637,0⟩, +⟨⟨0,155,470,true⟩,470,637,1⟩, +⟨⟨1,155,895,true⟩,637,637,0⟩] +def chunk76 : List Entry := [⟨⟨0,156,472,true⟩,472,663,1⟩, +⟨⟨0,895,637,true⟩,637,663,1⟩, +⟨⟨1,156,895,true⟩,663,663,0⟩, +⟨⟨0,895,663,true⟩,663,863,1⟩, +⟨⟨1,159,895,true⟩,863,863,0⟩, +⟨⟨0,145,469,false⟩,469,638,1⟩, +⟨⟨1,145,908,true⟩,638,638,0⟩, +⟨⟨0,146,469,false⟩,469,638,1⟩, +⟨⟨1,146,908,true⟩,638,638,0⟩, +⟨⟨0,149,473,true⟩,473,669,1⟩, +⟨⟨0,908,638,true⟩,638,669,1⟩, +⟨⟨1,149,908,true⟩,669,669,0⟩, +⟨⟨0,150,473,true⟩,473,669,1⟩, +⟨⟨1,150,908,true⟩,669,669,0⟩, +⟨⟨0,144,469,true⟩,469,639,1⟩, +⟨⟨1,144,909,true⟩,639,639,0⟩, +⟨⟨0,147,469,true⟩,469,639,1⟩, +⟨⟨1,147,909,true⟩,639,639,0⟩, +⟨⟨0,148,473,true⟩,473,675,1⟩, +⟨⟨0,909,639,true⟩,639,675,1⟩, +⟨⟨1,148,909,true⟩,675,675,0⟩, +⟨⟨0,909,675,true⟩,675,855,1⟩, +⟨⟨1,151,909,true⟩,855,855,0⟩, +⟨⟨0,184,635,false⟩,635,640,1⟩, +⟨⟨1,184,753,true⟩,640,640,0⟩, +⟨⟨0,187,635,false⟩,635,640,1⟩, +⟨⟨1,187,753,true⟩,640,640,0⟩, +⟨⟨1,189,751,true⟩,645,645,0⟩, +⟨⟨1,190,751,true⟩,645,645,0⟩, +⟨⟨0,185,634,false⟩,634,646,1⟩, +⟨⟨1,185,735,true⟩,646,646,0⟩, +⟨⟨0,186,634,false⟩,634,646,1⟩, +⟨⟨1,186,735,true⟩,646,646,0⟩, +⟨⟨1,188,731,true⟩,651,651,0⟩, +⟨⟨0,731,651,true⟩,651,895,1⟩, +⟨⟨1,191,731,true⟩,895,895,0⟩, +⟨⟨0,152,637,false⟩,637,652,1⟩, +⟨⟨1,152,738,true⟩,652,652,0⟩, +⟨⟨0,155,637,false⟩,637,652,1⟩, +⟨⟨1,155,738,true⟩,652,652,0⟩, +⟨⟨1,157,736,true⟩,657,657,0⟩, +⟨⟨1,158,736,true⟩,657,657,0⟩, +⟨⟨0,153,636,false⟩,636,658,1⟩, +⟨⟨1,153,450,true⟩,658,658,0⟩, +⟨⟨0,154,636,false⟩,636,658,1⟩, +⟨⟨1,154,450,true⟩,658,658,0⟩, +⟨⟨1,156,719,true⟩,663,663,0⟩, +⟨⟨0,719,663,true⟩,663,863,1⟩, +⟨⟨1,159,719,true⟩,863,863,0⟩, +⟨⟨0,144,639,false⟩,639,664,1⟩, +⟨⟨1,144,739,true⟩,664,664,0⟩, +⟨⟨0,147,639,false⟩,639,664,1⟩, +⟨⟨1,147,739,true⟩,664,664,0⟩, +⟨⟨1,149,737,true⟩,669,669,0⟩, +⟨⟨1,150,737,true⟩,669,669,0⟩, +⟨⟨0,145,638,false⟩,638,670,1⟩, +⟨⟨1,145,694,true⟩,670,670,0⟩, +⟨⟨0,146,638,false⟩,638,670,1⟩, +⟨⟨1,146,694,true⟩,670,670,0⟩, +⟨⟨1,148,703,true⟩,675,675,0⟩, +⟨⟨0,703,675,true⟩,675,855,1⟩, +⟨⟨1,151,703,true⟩,855,855,0⟩, +⟨⟨0,136,623,false⟩,623,676,1⟩, +⟨⟨1,136,404,true⟩,676,676,0⟩, +⟨⟨0,139,623,false⟩,623,676,1⟩, +⟨⟨1,139,404,true⟩,676,676,0⟩, +⟨⟨1,141,400,true⟩,681,681,0⟩, +⟨⟨1,142,400,true⟩,681,681,0⟩, +⟨⟨0,137,622,false⟩,622,682,1⟩, +⟨⟨1,137,678,true⟩,682,682,0⟩, +⟨⟨0,138,622,false⟩,622,682,1⟩, +⟨⟨1,138,678,true⟩,682,682,0⟩, +⟨⟨1,140,687,true⟩,687,687,0⟩, +⟨⟨0,687,687,true⟩,687,847,1⟩, +⟨⟨1,143,687,true⟩,847,847,0⟩, +⟨⟨0,160,629,false⟩,629,688,1⟩, +⟨⟨1,160,741,true⟩,688,688,0⟩, +⟨⟨0,163,629,false⟩,629,688,1⟩, +⟨⟨1,163,741,true⟩,688,688,0⟩, +⟨⟨1,165,740,true⟩,693,693,0⟩, +⟨⟨1,166,740,true⟩,693,693,0⟩, +⟨⟨0,161,628,false⟩,628,694,1⟩, +⟨⟨1,161,662,true⟩,694,694,0⟩, +⟨⟨0,162,628,false⟩,628,694,1⟩, +⟨⟨1,162,662,true⟩,694,694,0⟩, +⟨⟨1,164,671,true⟩,699,699,0⟩, +⟨⟨0,671,699,true⟩,699,871,1⟩, +⟨⟨1,167,671,true⟩,871,871,0⟩, +⟨⟨0,192,609,false⟩,609,700,1⟩, +⟨⟨1,192,415,true⟩,700,700,0⟩, +⟨⟨0,195,609,false⟩,609,700,1⟩, +⟨⟨1,195,415,true⟩,700,700,0⟩, +⟨⟨1,197,413,true⟩,705,705,0⟩, +⟨⟨1,198,413,true⟩,705,705,0⟩, +⟨⟨0,193,608,false⟩,608,706,1⟩, +⟨⟨1,193,646,true⟩,706,706,0⟩, +⟨⟨0,194,608,false⟩,608,706,1⟩, +⟨⟨1,194,646,true⟩,706,706,0⟩, +⟨⟨1,196,655,true⟩,711,711,0⟩, +⟨⟨0,655,711,true⟩,711,903,1⟩, +⟨⟨1,199,655,true⟩,903,903,0⟩, +⟨⟨0,232,619,false⟩,619,712,1⟩, +⟨⟨1,232,743,true⟩,712,712,0⟩, +⟨⟨0,235,619,false⟩,619,712,1⟩, +⟨⟨1,235,743,true⟩,712,712,0⟩, +⟨⟨1,237,742,true⟩,717,717,0⟩, +⟨⟨1,238,742,true⟩,717,717,0⟩, +⟨⟨0,233,618,false⟩,618,718,1⟩, +⟨⟨1,233,630,true⟩,718,718,0⟩, +⟨⟨0,234,618,false⟩,618,718,1⟩, +⟨⟨1,234,630,true⟩,718,718,0⟩, +⟨⟨1,236,639,true⟩,723,723,0⟩, +⟨⟨0,639,723,true⟩,723,943,1⟩, +⟨⟨1,239,639,true⟩,943,943,0⟩, +⟨⟨0,128,576,false⟩,576,724,1⟩, +⟨⟨1,128,525,true⟩,724,724,0⟩, +⟨⟨0,131,576,false⟩,576,724,1⟩, +⟨⟨1,131,525,true⟩,724,724,0⟩, +⟨⟨1,133,524,true⟩,729,729,0⟩, +⟨⟨1,134,524,true⟩,729,729,0⟩, +⟨⟨0,129,574,false⟩,574,730,1⟩, +⟨⟨1,129,623,true⟩,730,730,0⟩, +⟨⟨0,130,574,false⟩,574,730,1⟩, +⟨⟨1,130,623,true⟩,730,730,0⟩, +⟨⟨1,132,619,true⟩,735,735,0⟩, +⟨⟨0,619,735,true⟩,735,839,1⟩, +⟨⟨1,135,619,true⟩,839,839,0⟩, +⟨⟨0,168,588,false⟩,588,736,1⟩, +⟨⟨1,168,745,true⟩,736,736,0⟩, +⟨⟨0,171,588,false⟩,588,736,1⟩, +⟨⟨1,171,745,true⟩,736,736,0⟩, +⟨⟨1,173,744,true⟩,741,741,0⟩, +⟨⟨1,174,744,true⟩,741,741,0⟩, +⟨⟨0,169,586,false⟩,586,742,1⟩, +⟨⟨1,169,598,true⟩,742,742,0⟩, +⟨⟨0,170,586,false⟩,586,742,1⟩, +⟨⟨1,170,598,true⟩,742,742,0⟩, +⟨⟨1,172,607,true⟩,747,747,0⟩, +⟨⟨0,607,747,true⟩,747,879,1⟩, +⟨⟨1,175,607,true⟩,879,879,0⟩, +⟨⟨0,200,554,false⟩,554,748,1⟩, +⟨⟨1,200,521,true⟩,748,748,0⟩, +⟨⟨0,203,554,false⟩,554,748,1⟩, +⟨⟨1,203,521,true⟩,748,748,0⟩, +⟨⟨1,205,520,true⟩,753,753,0⟩, +⟨⟨1,206,520,true⟩,753,753,0⟩, +⟨⟨0,201,552,false⟩,552,754,1⟩, +⟨⟨1,201,591,true⟩,754,754,0⟩, +⟨⟨0,202,552,false⟩,552,754,1⟩, +⟨⟨1,202,591,true⟩,754,754,0⟩, +⟨⟨1,204,587,true⟩,759,759,0⟩, +⟨⟨0,587,759,true⟩,759,911,1⟩, +⟨⟨1,207,587,true⟩,911,911,0⟩, +⟨⟨0,224,570,false⟩,570,760,1⟩, +⟨⟨1,224,747,true⟩,760,760,0⟩, +⟨⟨0,227,570,false⟩,570,760,1⟩, +⟨⟨1,227,747,true⟩,760,760,0⟩, +⟨⟨1,229,746,true⟩,765,765,0⟩, +⟨⟨1,230,746,true⟩,765,765,0⟩, +⟨⟨0,225,568,false⟩,568,766,1⟩, +⟨⟨1,225,566,true⟩,766,766,0⟩, +⟨⟨0,226,568,false⟩,568,766,1⟩, +⟨⟨1,226,566,true⟩,766,766,0⟩, +⟨⟨1,228,575,true⟩,771,771,0⟩, +⟨⟨0,575,771,true⟩,771,935,1⟩, +⟨⟨1,231,575,true⟩,935,935,0⟩, +⟨⟨0,216,516,false⟩,516,772,1⟩, +⟨⟨1,216,515,true⟩,772,772,0⟩, +⟨⟨0,219,516,false⟩,516,772,1⟩, +⟨⟨1,219,515,true⟩,772,772,0⟩, +⟨⟨1,221,513,true⟩,777,777,0⟩, +⟨⟨1,222,513,true⟩,777,777,0⟩, +⟨⟨0,217,514,false⟩,514,778,1⟩, +⟨⟨1,217,559,true⟩,778,778,0⟩, +⟨⟨0,218,514,false⟩,514,778,1⟩, +⟨⟨1,218,559,true⟩,778,778,0⟩, +⟨⟨1,220,555,true⟩,783,783,0⟩, +⟨⟨0,555,783,true⟩,783,927,1⟩, +⟨⟨1,223,555,true⟩,927,927,0⟩, +⟨⟨0,208,536,false⟩,536,784,1⟩, +⟨⟨1,208,749,true⟩,784,784,0⟩, +⟨⟨0,211,536,false⟩,536,784,1⟩, +⟨⟨1,211,749,true⟩,784,784,0⟩, +⟨⟨1,213,748,true⟩,789,789,0⟩, +⟨⟨1,214,748,true⟩,789,789,0⟩, +⟨⟨0,209,534,false⟩,534,790,1⟩, +⟨⟨1,209,539,true⟩,790,790,0⟩, +⟨⟨0,210,534,false⟩,534,790,1⟩, +⟨⟨1,210,539,true⟩,790,790,0⟩, +⟨⟨1,212,535,true⟩,795,795,0⟩, +⟨⟨0,535,795,true⟩,795,919,1⟩, +⟨⟨1,215,535,true⟩,919,919,0⟩, +⟨⟨0,176,537,false⟩,537,796,1⟩, +⟨⟨1,176,763,true⟩,796,796,0⟩, +⟨⟨0,179,537,false⟩,537,796,1⟩, +⟨⟨1,179,763,true⟩,796,796,0⟩, +⟨⟨1,181,762,true⟩,801,801,0⟩, +⟨⟨1,182,762,true⟩,801,801,0⟩, +⟨⟨0,177,535,false⟩,535,802,1⟩, +⟨⟨1,177,518,true⟩,802,802,0⟩] +def chunk77 : List Entry := [⟨⟨0,178,535,false⟩,535,802,1⟩, +⟨⟨1,178,518,true⟩,802,802,0⟩, +⟨⟨1,180,527,true⟩,807,807,0⟩, +⟨⟨0,527,807,true⟩,807,887,1⟩, +⟨⟨1,183,527,true⟩,887,887,0⟩, +⟨⟨0,120,468,false⟩,468,824,3⟩, +⟨⟨1,120,704,true⟩,824,824,0⟩, +⟨⟨0,121,464,true⟩,464,811,2⟩, +⟨⟨1,121,576,true⟩,811,811,0⟩, +⟨⟨0,124,464,false⟩,464,828,3⟩, +⟨⟨0,576,811,false⟩,811,828,1⟩, +⟨⟨1,124,576,true⟩,828,828,0⟩, +⟨⟨0,122,459,true⟩,459,813,2⟩, +⟨⟨1,122,544,true⟩,813,813,0⟩, +⟨⟨0,123,459,true⟩,459,827,3⟩, +⟨⟨0,544,813,true⟩,813,827,1⟩, +⟨⟨1,123,544,true⟩,827,827,0⟩, +⟨⟨0,125,458,true⟩,458,829,3⟩, +⟨⟨1,125,551,true⟩,829,829,0⟩, +⟨⟨0,126,462,false⟩,462,830,3⟩, +⟨⟨1,126,603,true⟩,830,830,0⟩, +⟨⟨0,127,458,true⟩,458,831,3⟩, +⟨⟨1,127,528,true⟩,831,831,0⟩, +⟨⟨0,688,810,false⟩,810,824,1⟩, +⟨⟨1,120,688,true⟩,824,824,0⟩, +⟨⟨0,266,809,false⟩,809,824,1⟩, +⟨⟨1,120,266,true⟩,824,824,0⟩, +⟨⟨0,121,811,true⟩,811,825,1⟩, +⟨⟨0,560,812,true⟩,812,825,1⟩, +⟨⟨1,121,560,true⟩,825,825,0⟩, +⟨⟨0,907,810,true⟩,810,825,1⟩, +⟨⟨1,121,907,true⟩,825,825,0⟩, +⟨⟨0,122,813,false⟩,813,826,1⟩, +⟨⟨1,122,599,true⟩,826,826,0⟩, +⟨⟨1,122,663,true⟩,826,826,0⟩, +⟨⟨1,123,567,true⟩,827,827,0⟩, +⟨⟨1,123,631,true⟩,827,827,0⟩, +⟨⟨1,124,512,true⟩,828,828,0⟩, +⟨⟨1,124,640,true⟩,828,828,0⟩, +⟨⟨0,624,809,true⟩,809,829,1⟩, +⟨⟨1,125,624,true⟩,829,829,0⟩, +⟨⟨0,592,812,true⟩,812,829,1⟩, +⟨⟨1,125,592,true⟩,829,829,0⟩, +⟨⟨1,126,635,true⟩,830,830,0⟩, +⟨⟨1,126,519,true⟩,830,830,0⟩, +⟨⟨1,127,571,true⟩,831,831,0⟩, +⟨⟨1,127,651,true⟩,831,831,0⟩, +⟨⟨0,128,724,false⟩,724,832,1⟩, +⟨⟨0,295,725,false⟩,725,832,1⟩, +⟨⟨1,128,295,true⟩,832,832,0⟩, +⟨⟨0,585,726,false⟩,726,832,1⟩, +⟨⟨1,128,585,true⟩,832,832,0⟩, +⟨⟨0,129,730,true⟩,730,833,1⟩, +⟨⟨0,293,731,true⟩,731,833,1⟩, +⟨⟨1,129,293,true⟩,833,833,0⟩, +⟨⟨0,937,732,true⟩,732,833,1⟩, +⟨⟨1,129,937,true⟩,833,833,0⟩, +⟨⟨0,130,730,false⟩,730,834,1⟩, +⟨⟨0,938,733,false⟩,733,834,1⟩, +⟨⟨1,130,938,true⟩,834,834,0⟩, +⟨⟨0,291,734,false⟩,734,834,1⟩, +⟨⟨1,130,291,true⟩,834,834,0⟩, +⟨⟨0,131,724,true⟩,724,835,1⟩, +⟨⟨0,584,727,true⟩,727,835,1⟩, +⟨⟨1,131,584,true⟩,835,835,0⟩, +⟨⟨0,289,728,true⟩,728,835,1⟩, +⟨⟨1,131,289,true⟩,835,835,0⟩, +⟨⟨0,132,735,false⟩,735,836,1⟩, +⟨⟨0,932,734,false⟩,734,836,1⟩, +⟨⟨1,132,932,true⟩,836,836,0⟩, +⟨⟨0,302,732,false⟩,732,836,1⟩, +⟨⟨1,132,302,true⟩,836,836,0⟩, +⟨⟨0,133,729,true⟩,729,837,1⟩, +⟨⟨0,300,726,true⟩,726,837,1⟩, +⟨⟨1,133,300,true⟩,837,837,0⟩, +⟨⟨0,572,728,true⟩,728,837,1⟩, +⟨⟨1,133,572,true⟩,837,837,0⟩, +⟨⟨0,134,729,false⟩,729,838,1⟩, +⟨⟨0,298,727,false⟩,727,838,1⟩, +⟨⟨1,134,298,true⟩,838,838,0⟩, +⟨⟨0,573,725,false⟩,725,838,1⟩, +⟨⟨1,134,573,true⟩,838,838,0⟩, +⟨⟨0,933,731,true⟩,731,839,1⟩, +⟨⟨1,135,933,true⟩,839,839,0⟩, +⟨⟨0,296,733,true⟩,733,839,1⟩, +⟨⟨1,135,296,true⟩,839,839,0⟩, +⟨⟨0,136,676,false⟩,676,840,1⟩, +⟨⟨0,311,677,false⟩,677,840,1⟩, +⟨⟨1,136,311,true⟩,840,840,0⟩, +⟨⟨0,857,678,false⟩,678,840,1⟩, +⟨⟨1,136,857,true⟩,840,840,0⟩, +⟨⟨0,137,682,true⟩,682,841,1⟩, +⟨⟨0,966,683,true⟩,683,841,1⟩, +⟨⟨1,137,966,true⟩,841,841,0⟩, +⟨⟨0,308,684,true⟩,684,841,1⟩, +⟨⟨1,137,308,true⟩,841,841,0⟩, +⟨⟨0,138,682,false⟩,682,842,1⟩, +⟨⟨0,306,685,false⟩,685,842,1⟩, +⟨⟨1,138,306,true⟩,842,842,0⟩, +⟨⟨0,965,686,false⟩,686,842,1⟩, +⟨⟨1,138,965,true⟩,842,842,0⟩, +⟨⟨0,139,676,true⟩,676,843,1⟩, +⟨⟨0,856,679,true⟩,679,843,1⟩, +⟨⟨1,139,856,true⟩,843,843,0⟩, +⟨⟨0,305,680,true⟩,680,843,1⟩, +⟨⟨1,139,305,true⟩,843,843,0⟩, +⟨⟨0,140,687,false⟩,687,844,1⟩, +⟨⟨0,973,684,false⟩,684,844,1⟩, +⟨⟨1,140,973,true⟩,844,844,0⟩, +⟨⟨0,319,686,false⟩,686,844,1⟩, +⟨⟨1,140,319,true⟩,844,844,0⟩, +⟨⟨0,141,681,true⟩,681,845,1⟩, +⟨⟨0,316,678,true⟩,678,845,1⟩, +⟨⟨1,141,316,true⟩,845,845,0⟩, +⟨⟨0,842,680,true⟩,680,845,1⟩, +⟨⟨1,141,842,true⟩,845,845,0⟩, +⟨⟨0,142,681,false⟩,681,846,1⟩, +⟨⟨0,314,679,false⟩,679,846,1⟩, +⟨⟨1,142,314,true⟩,846,846,0⟩, +⟨⟨0,843,677,false⟩,677,846,1⟩, +⟨⟨1,142,843,true⟩,846,846,0⟩, +⟨⟨0,974,685,true⟩,685,847,1⟩, +⟨⟨1,143,974,true⟩,847,847,0⟩, +⟨⟨0,313,683,true⟩,683,847,1⟩, +⟨⟨1,143,313,true⟩,847,847,0⟩, +⟨⟨0,144,664,false⟩,664,848,1⟩, +⟨⟨0,327,665,false⟩,665,848,1⟩, +⟨⟨1,144,327,true⟩,848,848,0⟩, +⟨⟨0,841,666,false⟩,666,848,1⟩, +⟨⟨1,144,841,true⟩,848,848,0⟩, +⟨⟨0,145,670,true⟩,670,849,1⟩, +⟨⟨0,972,671,true⟩,671,849,1⟩, +⟨⟨1,145,972,true⟩,849,849,0⟩, +⟨⟨0,324,672,true⟩,672,849,1⟩, +⟨⟨1,145,324,true⟩,849,849,0⟩, +⟨⟨0,146,670,false⟩,670,850,1⟩, +⟨⟨0,322,673,false⟩,673,850,1⟩, +⟨⟨1,146,322,true⟩,850,850,0⟩, +⟨⟨0,971,674,false⟩,674,850,1⟩, +⟨⟨1,146,971,true⟩,850,850,0⟩, +⟨⟨0,147,664,true⟩,664,851,1⟩, +⟨⟨0,840,667,true⟩,667,851,1⟩, +⟨⟨1,147,840,true⟩,851,851,0⟩, +⟨⟨0,321,668,true⟩,668,851,1⟩, +⟨⟨1,147,321,true⟩,851,851,0⟩, +⟨⟨0,148,675,false⟩,675,852,1⟩, +⟨⟨0,963,672,false⟩,672,852,1⟩, +⟨⟨1,148,963,true⟩,852,852,0⟩, +⟨⟨0,335,674,false⟩,674,852,1⟩, +⟨⟨1,148,335,true⟩,852,852,0⟩, +⟨⟨0,149,669,true⟩,669,853,1⟩, +⟨⟨0,854,668,true⟩,668,853,1⟩, +⟨⟨1,149,854,true⟩,853,853,0⟩, +⟨⟨0,332,666,true⟩,666,853,1⟩, +⟨⟨1,149,332,true⟩,853,853,0⟩, +⟨⟨0,150,669,false⟩,669,854,1⟩, +⟨⟨0,855,665,false⟩,665,854,1⟩, +⟨⟨1,150,855,true⟩,854,854,0⟩, +⟨⟨0,330,667,false⟩,667,854,1⟩, +⟨⟨1,150,330,true⟩,854,854,0⟩, +⟨⟨0,964,673,true⟩,673,855,1⟩, +⟨⟨1,151,964,true⟩,855,855,0⟩, +⟨⟨0,329,671,true⟩,671,855,1⟩, +⟨⟨1,151,329,true⟩,855,855,0⟩, +⟨⟨0,152,652,false⟩,652,856,1⟩, +⟨⟨0,839,653,false⟩,653,856,1⟩, +⟨⟨1,152,839,true⟩,856,856,0⟩, +⟨⟨0,342,654,false⟩,654,856,1⟩, +⟨⟨1,152,342,true⟩,856,856,0⟩, +⟨⟨0,153,658,true⟩,658,857,1⟩, +⟨⟨0,962,659,true⟩,659,857,1⟩, +⟨⟨1,153,962,true⟩,857,857,0⟩, +⟨⟨0,340,660,true⟩,660,857,1⟩, +⟨⟨1,153,340,true⟩,857,857,0⟩, +⟨⟨0,154,658,false⟩,658,858,1⟩, +⟨⟨0,338,661,false⟩,661,858,1⟩, +⟨⟨1,154,338,true⟩,858,858,0⟩, +⟨⟨0,961,662,false⟩,662,858,1⟩, +⟨⟨1,154,961,true⟩,858,858,0⟩, +⟨⟨0,155,652,true⟩,652,859,1⟩, +⟨⟨0,336,655,true⟩,655,859,1⟩, +⟨⟨1,155,336,true⟩,859,859,0⟩, +⟨⟨0,838,656,true⟩,656,859,1⟩, +⟨⟨1,155,838,true⟩,859,859,0⟩, +⟨⟨0,156,663,false⟩,663,860,1⟩, +⟨⟨0,969,660,false⟩,660,860,1⟩, +⟨⟨1,156,969,true⟩,860,860,0⟩, +⟨⟨0,351,662,false⟩,662,860,1⟩, +⟨⟨1,156,351,true⟩,860,860,0⟩, +⟨⟨0,157,657,true⟩,657,861,1⟩, +⟨⟨0,853,654,true⟩,654,861,1⟩, +⟨⟨1,157,853,true⟩,861,861,0⟩, +⟨⟨0,349,656,true⟩,656,861,1⟩, +⟨⟨1,157,349,true⟩,861,861,0⟩, +⟨⟨0,158,657,false⟩,657,862,1⟩, +⟨⟨0,852,655,false⟩,655,862,1⟩, +⟨⟨1,158,852,true⟩,862,862,0⟩, +⟨⟨0,347,653,false⟩,653,862,1⟩, +⟨⟨1,158,347,true⟩,862,862,0⟩, +⟨⟨0,970,661,true⟩,661,863,1⟩] +def chunk78 : List Entry := [⟨⟨1,159,970,true⟩,863,863,0⟩, +⟨⟨0,345,659,true⟩,659,863,1⟩, +⟨⟨1,159,345,true⟩,863,863,0⟩, +⟨⟨0,160,688,false⟩,688,864,1⟩, +⟨⟨0,359,689,false⟩,689,864,1⟩, +⟨⟨1,160,359,true⟩,864,864,0⟩, +⟨⟨0,845,690,false⟩,690,864,1⟩, +⟨⟨1,160,845,true⟩,864,864,0⟩, +⟨⟨0,161,694,true⟩,694,865,1⟩, +⟨⟨0,357,695,true⟩,695,865,1⟩, +⟨⟨1,161,357,true⟩,865,865,0⟩, +⟨⟨0,967,696,true⟩,696,865,1⟩, +⟨⟨1,161,967,true⟩,865,865,0⟩, +⟨⟨0,162,694,false⟩,694,866,1⟩, +⟨⟨0,355,698,false⟩,698,866,1⟩, +⟨⟨1,162,355,true⟩,866,866,0⟩, +⟨⟨0,968,697,false⟩,697,866,1⟩, +⟨⟨1,162,968,true⟩,866,866,0⟩, +⟨⟨0,163,688,true⟩,688,867,1⟩, +⟨⟨0,844,691,true⟩,691,867,1⟩, +⟨⟨1,163,844,true⟩,867,867,0⟩, +⟨⟨0,353,692,true⟩,692,867,1⟩, +⟨⟨1,163,353,true⟩,867,867,0⟩, +⟨⟨0,164,699,false⟩,699,868,1⟩, +⟨⟨0,975,698,false⟩,698,868,1⟩, +⟨⟨1,164,975,true⟩,868,868,0⟩, +⟨⟨0,366,696,false⟩,696,868,1⟩, +⟨⟨1,164,366,true⟩,868,868,0⟩, +⟨⟨0,165,693,true⟩,693,869,1⟩, +⟨⟨0,858,692,true⟩,692,869,1⟩, +⟨⟨1,165,858,true⟩,869,869,0⟩, +⟨⟨0,364,690,true⟩,690,869,1⟩, +⟨⟨1,165,364,true⟩,869,869,0⟩, +⟨⟨0,166,693,false⟩,693,870,1⟩, +⟨⟨0,859,689,false⟩,689,870,1⟩, +⟨⟨1,166,859,true⟩,870,870,0⟩, +⟨⟨0,362,691,false⟩,691,870,1⟩, +⟨⟨1,166,362,true⟩,870,870,0⟩, +⟨⟨0,360,697,true⟩,697,871,1⟩, +⟨⟨1,167,360,true⟩,871,871,0⟩, +⟨⟨0,976,695,true⟩,695,871,1⟩, +⟨⟨1,167,976,true⟩,871,871,0⟩, +⟨⟨0,168,736,false⟩,736,872,1⟩, +⟨⟨0,375,737,false⟩,737,872,1⟩, +⟨⟨1,168,375,true⟩,872,872,0⟩, +⟨⟨0,569,738,false⟩,738,872,1⟩, +⟨⟨1,168,569,true⟩,872,872,0⟩, +⟨⟨0,169,742,true⟩,742,873,1⟩, +⟨⟨0,940,743,true⟩,743,873,1⟩, +⟨⟨1,169,940,true⟩,873,873,0⟩, +⟨⟨0,372,744,true⟩,744,873,1⟩, +⟨⟨1,169,372,true⟩,873,873,0⟩, +⟨⟨0,170,742,false⟩,742,874,1⟩, +⟨⟨0,370,745,false⟩,745,874,1⟩, +⟨⟨1,170,370,true⟩,874,874,0⟩, +⟨⟨0,939,746,false⟩,746,874,1⟩, +⟨⟨1,170,939,true⟩,874,874,0⟩, +⟨⟨0,171,736,true⟩,736,875,1⟩, +⟨⟨0,568,739,true⟩,739,875,1⟩, +⟨⟨1,171,568,true⟩,875,875,0⟩, +⟨⟨0,369,740,true⟩,740,875,1⟩, +⟨⟨1,171,369,true⟩,875,875,0⟩, +⟨⟨0,172,747,false⟩,747,876,1⟩, +⟨⟨0,383,746,false⟩,746,876,1⟩, +⟨⟨1,172,383,true⟩,876,876,0⟩, +⟨⟨0,934,744,false⟩,744,876,1⟩, +⟨⟨1,172,934,true⟩,876,876,0⟩, +⟨⟨0,173,741,true⟩,741,877,1⟩, +⟨⟨0,588,740,true⟩,740,877,1⟩, +⟨⟨1,173,588,true⟩,877,877,0⟩, +⟨⟨0,380,738,true⟩,738,877,1⟩, +⟨⟨1,173,380,true⟩,877,877,0⟩, +⟨⟨0,174,741,false⟩,741,878,1⟩, +⟨⟨0,589,737,false⟩,737,878,1⟩, +⟨⟨1,174,589,true⟩,878,878,0⟩, +⟨⟨0,378,739,false⟩,739,878,1⟩, +⟨⟨1,174,378,true⟩,878,878,0⟩, +⟨⟨0,377,743,true⟩,743,879,1⟩, +⟨⟨1,175,377,true⟩,879,879,0⟩, +⟨⟨0,935,745,true⟩,745,879,1⟩, +⟨⟨1,175,935,true⟩,879,879,0⟩, +⟨⟨0,176,796,false⟩,796,880,1⟩, +⟨⟨0,805,798,false⟩,798,880,1⟩, +⟨⟨1,176,805,true⟩,880,880,0⟩, +⟨⟨0,391,797,false⟩,797,880,1⟩, +⟨⟨1,176,391,true⟩,880,880,0⟩, +⟨⟨0,177,802,true⟩,802,881,1⟩, +⟨⟨0,389,803,true⟩,803,881,1⟩, +⟨⟨1,177,389,true⟩,881,881,0⟩, +⟨⟨0,526,804,true⟩,804,881,1⟩, +⟨⟨1,177,526,true⟩,881,881,0⟩, +⟨⟨0,178,802,false⟩,802,882,1⟩, +⟨⟨0,406,805,false⟩,805,882,1⟩, +⟨⟨1,178,406,true⟩,882,882,0⟩, +⟨⟨0,387,806,false⟩,806,882,1⟩, +⟨⟨1,178,387,true⟩,882,882,0⟩, +⟨⟨0,179,796,true⟩,796,883,1⟩, +⟨⟨0,804,799,true⟩,799,883,1⟩, +⟨⟨1,179,804,true⟩,883,883,0⟩, +⟨⟨0,385,800,true⟩,800,883,1⟩, +⟨⟨1,179,385,true⟩,883,883,0⟩, +⟨⟨0,180,807,false⟩,807,884,1⟩, +⟨⟨0,949,806,false⟩,806,884,1⟩, +⟨⟨1,180,949,true⟩,884,884,0⟩, +⟨⟨0,398,804,false⟩,804,884,1⟩, +⟨⟨1,180,398,true⟩,884,884,0⟩, +⟨⟨0,181,801,true⟩,801,885,1⟩, +⟨⟨0,828,800,true⟩,800,885,1⟩, +⟨⟨1,181,828,true⟩,885,885,0⟩, +⟨⟨0,396,798,true⟩,798,885,1⟩, +⟨⟨1,181,396,true⟩,885,885,0⟩, +⟨⟨0,182,801,false⟩,801,886,1⟩, +⟨⟨0,829,797,false⟩,797,886,1⟩, +⟨⟨1,182,829,true⟩,886,886,0⟩, +⟨⟨0,394,799,false⟩,799,886,1⟩, +⟨⟨1,182,394,true⟩,886,886,0⟩, +⟨⟨0,950,803,true⟩,803,887,1⟩, +⟨⟨1,183,950,true⟩,887,887,0⟩, +⟨⟨0,392,805,true⟩,805,887,1⟩, +⟨⟨1,183,392,true⟩,887,887,0⟩, +⟨⟨0,184,640,false⟩,640,888,1⟩, +⟨⟨0,407,641,false⟩,641,888,1⟩, +⟨⟨1,184,407,true⟩,888,888,0⟩, +⟨⟨0,865,642,false⟩,642,888,1⟩, +⟨⟨1,184,865,true⟩,888,888,0⟩, +⟨⟨0,185,646,true⟩,646,889,1⟩, +⟨⟨0,405,647,true⟩,647,889,1⟩, +⟨⟨1,185,405,true⟩,889,889,0⟩, +⟨⟨0,977,648,true⟩,648,889,1⟩, +⟨⟨1,185,977,true⟩,889,889,0⟩, +⟨⟨0,186,646,false⟩,646,890,1⟩, +⟨⟨0,403,650,false⟩,650,890,1⟩, +⟨⟨1,186,403,true⟩,890,890,0⟩, +⟨⟨0,978,649,false⟩,649,890,1⟩, +⟨⟨1,186,978,true⟩,890,890,0⟩, +⟨⟨0,187,640,true⟩,640,891,1⟩, +⟨⟨0,863,643,true⟩,643,891,1⟩, +⟨⟨1,187,863,true⟩,891,891,0⟩, +⟨⟨0,401,644,true⟩,644,891,1⟩, +⟨⟨1,187,401,true⟩,891,891,0⟩, +⟨⟨0,188,651,false⟩,651,892,1⟩, +⟨⟨0,959,650,false⟩,650,892,1⟩, +⟨⟨1,188,959,true⟩,892,892,0⟩, +⟨⟨0,414,648,false⟩,648,892,1⟩, +⟨⟨1,188,414,true⟩,892,892,0⟩, +⟨⟨0,189,645,true⟩,645,893,1⟩, +⟨⟨0,835,644,true⟩,644,893,1⟩, +⟨⟨1,189,835,true⟩,893,893,0⟩, +⟨⟨0,412,642,true⟩,642,893,1⟩, +⟨⟨1,189,412,true⟩,893,893,0⟩, +⟨⟨0,190,645,false⟩,645,894,1⟩, +⟨⟨0,837,641,false⟩,641,894,1⟩, +⟨⟨1,190,837,true⟩,894,894,0⟩, +⟨⟨0,410,643,false⟩,643,894,1⟩, +⟨⟨1,190,410,true⟩,894,894,0⟩, +⟨⟨0,408,649,true⟩,649,895,1⟩, +⟨⟨1,191,408,true⟩,895,895,0⟩, +⟨⟨0,960,647,true⟩,647,895,1⟩, +⟨⟨1,191,960,true⟩,895,895,0⟩, +⟨⟨0,192,700,false⟩,700,896,1⟩, +⟨⟨0,423,701,false⟩,701,896,1⟩, +⟨⟨1,192,423,true⟩,896,896,0⟩, +⟨⟨0,887,702,false⟩,702,896,1⟩, +⟨⟨1,192,887,true⟩,896,896,0⟩, +⟨⟨0,193,706,true⟩,706,897,1⟩, +⟨⟨0,980,707,true⟩,707,897,1⟩, +⟨⟨1,193,980,true⟩,897,897,0⟩, +⟨⟨0,420,708,true⟩,708,897,1⟩, +⟨⟨1,193,420,true⟩,897,897,0⟩, +⟨⟨0,194,706,false⟩,706,898,1⟩, +⟨⟨0,418,709,false⟩,709,898,1⟩, +⟨⟨1,194,418,true⟩,898,898,0⟩, +⟨⟨0,979,710,false⟩,710,898,1⟩, +⟨⟨1,194,979,true⟩,898,898,0⟩, +⟨⟨0,195,700,true⟩,700,899,1⟩, +⟨⟨0,886,703,true⟩,703,899,1⟩, +⟨⟨1,195,886,true⟩,899,899,0⟩, +⟨⟨0,417,704,true⟩,704,899,1⟩, +⟨⟨1,195,417,true⟩,899,899,0⟩, +⟨⟨0,196,711,false⟩,711,900,1⟩, +⟨⟨0,983,708,false⟩,708,900,1⟩, +⟨⟨1,196,983,true⟩,900,900,0⟩, +⟨⟨0,431,710,false⟩,710,900,1⟩, +⟨⟨1,196,431,true⟩,900,900,0⟩, +⟨⟨0,197,705,true⟩,705,901,1⟩, +⟨⟨0,872,704,true⟩,704,901,1⟩, +⟨⟨1,197,872,true⟩,901,901,0⟩, +⟨⟨0,428,702,true⟩,702,901,1⟩, +⟨⟨1,197,428,true⟩,901,901,0⟩, +⟨⟨0,198,705,false⟩,705,902,1⟩, +⟨⟨0,873,701,false⟩,701,902,1⟩, +⟨⟨1,198,873,true⟩,902,902,0⟩, +⟨⟨0,426,703,false⟩,703,902,1⟩, +⟨⟨1,198,426,true⟩,902,902,0⟩, +⟨⟨0,984,709,true⟩,709,903,1⟩, +⟨⟨1,199,984,true⟩,903,903,0⟩, +⟨⟨0,425,707,true⟩,707,903,1⟩, +⟨⟨1,199,425,true⟩,903,903,0⟩, +⟨⟨0,200,748,false⟩,748,904,1⟩, +⟨⟨0,605,749,false⟩,749,904,1⟩] +def chunk79 : List Entry := [⟨⟨1,200,605,true⟩,904,904,0⟩, +⟨⟨0,438,750,false⟩,750,904,1⟩, +⟨⟨1,200,438,true⟩,904,904,0⟩, +⟨⟨0,201,754,true⟩,754,905,1⟩, +⟨⟨0,437,755,true⟩,755,905,1⟩, +⟨⟨1,201,437,true⟩,905,905,0⟩, +⟨⟨0,951,756,true⟩,756,905,1⟩, +⟨⟨1,201,951,true⟩,905,905,0⟩, +⟨⟨0,202,754,false⟩,754,906,1⟩, +⟨⟨0,953,757,false⟩,757,906,1⟩, +⟨⟨1,202,953,true⟩,906,906,0⟩, +⟨⟨0,435,758,false⟩,758,906,1⟩, +⟨⟨1,202,435,true⟩,906,906,0⟩, +⟨⟨0,203,748,true⟩,748,907,1⟩, +⟨⟨0,432,751,true⟩,751,907,1⟩, +⟨⟨1,203,432,true⟩,907,907,0⟩, +⟨⟨0,604,752,true⟩,752,907,1⟩, +⟨⟨1,203,604,true⟩,907,907,0⟩, +⟨⟨0,204,759,false⟩,759,908,1⟩, +⟨⟨0,942,758,false⟩,758,908,1⟩, +⟨⟨1,204,942,true⟩,908,908,0⟩, +⟨⟨0,446,756,false⟩,756,908,1⟩, +⟨⟨1,204,446,true⟩,908,908,0⟩, +⟨⟨0,205,753,true⟩,753,909,1⟩, +⟨⟨0,617,750,true⟩,750,909,1⟩, +⟨⟨1,205,617,true⟩,909,909,0⟩, +⟨⟨0,445,752,true⟩,752,909,1⟩, +⟨⟨1,205,445,true⟩,909,909,0⟩, +⟨⟨0,206,753,false⟩,753,910,1⟩, +⟨⟨0,616,751,false⟩,751,910,1⟩, +⟨⟨1,206,616,true⟩,910,910,0⟩, +⟨⟨0,443,749,false⟩,749,910,1⟩, +⟨⟨1,206,443,true⟩,910,910,0⟩, +⟨⟨0,944,755,true⟩,755,911,1⟩, +⟨⟨1,207,944,true⟩,911,911,0⟩, +⟨⟨0,440,757,true⟩,757,911,1⟩, +⟨⟨1,207,440,true⟩,911,911,0⟩, +⟨⟨0,208,784,false⟩,784,912,1⟩, +⟨⟨0,831,785,false⟩,785,912,1⟩, +⟨⟨1,208,831,true⟩,912,912,0⟩, +⟨⟨0,454,786,false⟩,786,912,1⟩, +⟨⟨1,208,454,true⟩,912,912,0⟩, +⟨⟨0,209,790,true⟩,790,913,1⟩, +⟨⟨0,453,791,true⟩,791,913,1⟩, +⟨⟨1,209,453,true⟩,913,913,0⟩, +⟨⟨0,532,792,true⟩,792,913,1⟩, +⟨⟨1,209,532,true⟩,913,913,0⟩, +⟨⟨0,210,790,false⟩,790,914,1⟩, +⟨⟨0,451,794,false⟩,794,914,1⟩, +⟨⟨1,210,451,true⟩,914,914,0⟩, +⟨⟨0,948,793,false⟩,793,914,1⟩, +⟨⟨1,210,948,true⟩,914,914,0⟩, +⟨⟨0,211,784,true⟩,784,915,1⟩, +⟨⟨0,448,787,true⟩,787,915,1⟩, +⟨⟨1,211,448,true⟩,915,915,0⟩, +⟨⟨0,830,788,true⟩,788,915,1⟩, +⟨⟨1,211,830,true⟩,915,915,0⟩, +⟨⟨0,212,795,false⟩,795,916,1⟩, +⟨⟨0,952,794,false⟩,794,916,1⟩, +⟨⟨1,212,952,true⟩,916,916,0⟩, +⟨⟨0,462,792,false⟩,792,916,1⟩, +⟨⟨1,212,462,true⟩,916,916,0⟩, +⟨⟨0,213,789,true⟩,789,917,1⟩, +⟨⟨0,819,786,true⟩,786,917,1⟩, +⟨⟨1,213,819,true⟩,917,917,0⟩, +⟨⟨0,461,788,true⟩,788,917,1⟩, +⟨⟨1,213,461,true⟩,917,917,0⟩, +⟨⟨0,214,789,false⟩,789,918,1⟩, +⟨⟨0,818,787,false⟩,787,918,1⟩, +⟨⟨1,214,818,true⟩,918,918,0⟩, +⟨⟨0,459,785,false⟩,785,918,1⟩, +⟨⟨1,214,459,true⟩,918,918,0⟩, +⟨⟨0,456,793,true⟩,793,919,1⟩, +⟨⟨1,215,456,true⟩,919,919,0⟩, +⟨⟨0,954,791,true⟩,791,919,1⟩, +⟨⟨1,215,954,true⟩,919,919,0⟩, +⟨⟨0,216,772,false⟩,772,920,1⟩, +⟨⟨0,817,773,false⟩,773,920,1⟩, +⟨⟨1,216,817,true⟩,920,920,0⟩, +⟨⟨0,470,774,false⟩,774,920,1⟩, +⟨⟨1,216,470,true⟩,920,920,0⟩, +⟨⟨0,217,778,true⟩,778,921,1⟩, +⟨⟨0,469,779,true⟩,779,921,1⟩, +⟨⟨1,217,469,true⟩,921,921,0⟩, +⟨⟨0,956,780,true⟩,780,921,1⟩, +⟨⟨1,217,956,true⟩,921,921,0⟩, +⟨⟨0,218,778,false⟩,778,922,1⟩, +⟨⟨0,958,781,false⟩,781,922,1⟩, +⟨⟨1,218,958,true⟩,922,922,0⟩, +⟨⟨0,467,782,false⟩,782,922,1⟩, +⟨⟨1,218,467,true⟩,922,922,0⟩, +⟨⟨0,219,772,true⟩,772,923,1⟩, +⟨⟨0,464,775,true⟩,775,923,1⟩, +⟨⟨1,219,464,true⟩,923,923,0⟩, +⟨⟨0,816,776,true⟩,776,923,1⟩, +⟨⟨1,219,816,true⟩,923,923,0⟩, +⟨⟨0,220,783,false⟩,783,924,1⟩, +⟨⟨0,943,782,false⟩,782,924,1⟩, +⟨⟨1,220,943,true⟩,924,924,0⟩, +⟨⟨0,478,780,false⟩,780,924,1⟩, +⟨⟨1,220,478,true⟩,924,924,0⟩, +⟨⟨0,221,777,true⟩,777,925,1⟩, +⟨⟨0,477,776,true⟩,776,925,1⟩, +⟨⟨1,221,477,true⟩,925,925,0⟩, +⟨⟨0,833,774,true⟩,774,925,1⟩, +⟨⟨1,221,833,true⟩,925,925,0⟩, +⟨⟨0,222,777,false⟩,777,926,1⟩, +⟨⟨0,475,773,false⟩,773,926,1⟩, +⟨⟨1,222,475,true⟩,926,926,0⟩, +⟨⟨0,832,775,false⟩,775,926,1⟩, +⟨⟨1,222,832,true⟩,926,926,0⟩, +⟨⟨0,945,779,true⟩,779,927,1⟩, +⟨⟨1,223,945,true⟩,927,927,0⟩, +⟨⟨0,472,781,true⟩,781,927,1⟩, +⟨⟨1,223,472,true⟩,927,927,0⟩, +⟨⟨0,224,760,false⟩,760,928,1⟩, +⟨⟨0,621,761,false⟩,761,928,1⟩, +⟨⟨1,224,621,true⟩,928,928,0⟩, +⟨⟨0,486,762,false⟩,762,928,1⟩, +⟨⟨1,224,486,true⟩,928,928,0⟩, +⟨⟨0,225,766,true⟩,766,929,1⟩, +⟨⟨0,485,767,true⟩,767,929,1⟩, +⟨⟨1,225,485,true⟩,929,929,0⟩, +⟨⟨0,946,768,true⟩,768,929,1⟩, +⟨⟨1,225,946,true⟩,929,929,0⟩, +⟨⟨0,226,766,false⟩,766,930,1⟩, +⟨⟨0,947,769,false⟩,769,930,1⟩, +⟨⟨1,226,947,true⟩,930,930,0⟩, +⟨⟨0,483,770,false⟩,770,930,1⟩, +⟨⟨1,226,483,true⟩,930,930,0⟩, +⟨⟨0,227,760,true⟩,760,931,1⟩, +⟨⟨0,480,763,true⟩,763,931,1⟩, +⟨⟨1,227,480,true⟩,931,931,0⟩, +⟨⟨0,620,764,true⟩,764,931,1⟩, +⟨⟨1,227,620,true⟩,931,931,0⟩, +⟨⟨0,228,771,false⟩,771,932,1⟩, +⟨⟨0,955,770,false⟩,770,932,1⟩, +⟨⟨1,228,955,true⟩,932,932,0⟩, +⟨⟨0,494,768,false⟩,768,932,1⟩, +⟨⟨1,228,494,true⟩,932,932,0⟩, +⟨⟨0,229,765,true⟩,765,933,1⟩, +⟨⟨0,601,762,true⟩,762,933,1⟩, +⟨⟨1,229,601,true⟩,933,933,0⟩, +⟨⟨0,493,764,true⟩,764,933,1⟩, +⟨⟨1,229,493,true⟩,933,933,0⟩, +⟨⟨0,230,765,false⟩,765,934,1⟩, +⟨⟨0,600,763,false⟩,763,934,1⟩, +⟨⟨1,230,600,true⟩,934,934,0⟩, +⟨⟨0,491,761,false⟩,761,934,1⟩, +⟨⟨1,230,491,true⟩,934,934,0⟩, +⟨⟨0,957,767,true⟩,767,935,1⟩, +⟨⟨1,231,957,true⟩,935,935,0⟩, +⟨⟨0,488,769,true⟩,769,935,1⟩, +⟨⟨1,231,488,true⟩,935,935,0⟩, +⟨⟨0,232,712,false⟩,712,936,1⟩, +⟨⟨0,889,713,false⟩,713,936,1⟩, +⟨⟨1,232,889,true⟩,936,936,0⟩, +⟨⟨0,502,714,false⟩,714,936,1⟩, +⟨⟨1,232,502,true⟩,936,936,0⟩, +⟨⟨0,233,718,true⟩,718,937,1⟩, +⟨⟨0,986,719,true⟩,719,937,1⟩, +⟨⟨1,233,986,true⟩,937,937,0⟩, +⟨⟨0,500,720,true⟩,720,937,1⟩, +⟨⟨1,233,500,true⟩,937,937,0⟩, +⟨⟨0,234,718,false⟩,718,938,1⟩, +⟨⟨0,498,721,false⟩,721,938,1⟩, +⟨⟨1,234,498,true⟩,938,938,0⟩, +⟨⟨0,985,722,false⟩,722,938,1⟩, +⟨⟨1,234,985,true⟩,938,938,0⟩, +⟨⟨0,235,712,true⟩,712,939,1⟩, +⟨⟨0,496,715,true⟩,715,939,1⟩, +⟨⟨1,235,496,true⟩,939,939,0⟩, +⟨⟨0,888,716,true⟩,716,939,1⟩, +⟨⟨1,235,888,true⟩,939,939,0⟩, +⟨⟨0,236,723,false⟩,723,940,1⟩, +⟨⟨0,981,720,false⟩,720,940,1⟩, +⟨⟨1,236,981,true⟩,940,940,0⟩, +⟨⟨0,511,722,false⟩,722,940,1⟩, +⟨⟨1,236,511,true⟩,940,940,0⟩, +⟨⟨0,237,717,true⟩,717,941,1⟩, +⟨⟨0,875,714,true⟩,714,941,1⟩, +⟨⟨1,237,875,true⟩,941,941,0⟩, +⟨⟨0,509,716,true⟩,716,941,1⟩, +⟨⟨1,237,509,true⟩,941,941,0⟩, +⟨⟨0,238,717,false⟩,717,942,1⟩, +⟨⟨0,874,715,false⟩,715,942,1⟩, +⟨⟨1,238,874,true⟩,942,942,0⟩, +⟨⟨0,507,713,false⟩,713,942,1⟩, +⟨⟨1,238,507,true⟩,942,942,0⟩, +⟨⟨0,982,721,true⟩,721,943,1⟩, +⟨⟨1,239,982,true⟩,943,943,0⟩, +⟨⟨0,505,719,true⟩,719,943,1⟩, +⟨⟨1,239,505,true⟩,943,943,0⟩, +⟨⟨0,651,831,true⟩,831,1,1⟩, +⟨⟨0,667,831,true⟩,831,1,1⟩, +⟨⟨1,651,667,true⟩,1,1,0⟩, +⟨⟨0,571,831,true⟩,831,1,1⟩, +⟨⟨0,276,831,true⟩,831,1,1⟩, +⟨⟨1,571,276,true⟩,1,1,0⟩, +⟨⟨0,615,831,true⟩,831,1,1⟩] +def chunk80 : List Entry := [⟨⟨1,571,615,true⟩,1,1,0⟩, +⟨⟨0,528,831,true⟩,831,1,1⟩, +⟨⟨1,528,5,true⟩,1,1,0⟩, +⟨⟨1,528,4,true⟩,1,1,0⟩, +⟨⟨0,699,831,true⟩,831,1,1⟩, +⟨⟨1,528,699,true⟩,1,1,0⟩, +⟨⟨0,635,830,true⟩,830,1,1⟩, +⟨⟨0,683,830,true⟩,830,1,1⟩, +⟨⟨1,635,683,true⟩,1,1,0⟩, +⟨⟨0,519,830,true⟩,830,1,1⟩, +⟨⟨0,246,830,true⟩,830,1,1⟩, +⟨⟨1,519,246,true⟩,1,1,0⟩, +⟨⟨1,519,528,true⟩,1,1,0⟩, +⟨⟨0,603,830,true⟩,830,1,1⟩, +⟨⟨0,265,830,true⟩,830,1,1⟩, +⟨⟨1,603,265,true⟩,1,1,0⟩, +⟨⟨0,262,830,true⟩,830,1,1⟩, +⟨⟨1,603,262,true⟩,1,1,0⟩, +⟨⟨0,695,830,true⟩,830,1,1⟩, +⟨⟨1,603,695,true⟩,1,1,0⟩, +⟨⟨0,551,829,true⟩,829,1,1⟩, +⟨⟨0,286,829,true⟩,829,1,1⟩, +⟨⟨1,551,286,true⟩,1,1,0⟩, +⟨⟨0,280,829,true⟩,829,1,1⟩, +⟨⟨1,551,280,true⟩,1,1,0⟩, +⟨⟨0,715,829,true⟩,829,1,1⟩, +⟨⟨1,551,715,true⟩,1,1,0⟩, +⟨⟨0,640,828,true⟩,828,1,1⟩, +⟨⟨0,679,828,true⟩,828,1,1⟩, +⟨⟨1,640,679,true⟩,1,1,0⟩, +⟨⟨0,512,828,true⟩,828,1,1⟩, +⟨⟨1,512,1,true⟩,1,1,0⟩, +⟨⟨1,512,551,true⟩,1,1,0⟩, +⟨⟨0,631,827,true⟩,827,1,1⟩, +⟨⟨0,647,827,true⟩,827,1,1⟩, +⟨⟨1,631,647,true⟩,1,1,0⟩, +⟨⟨0,567,827,true⟩,827,1,1⟩, +⟨⟨1,567,2,true⟩,1,1,0⟩, +⟨⟨0,583,827,true⟩,827,1,1⟩, +⟨⟨1,567,583,true⟩,1,1,0⟩, +⟨⟨0,663,826,true⟩,826,1,1⟩, +⟨⟨0,672,826,true⟩,826,1,1⟩, +⟨⟨1,663,672,true⟩,1,1,0⟩, +⟨⟨0,599,826,true⟩,826,1,1⟩, +⟨⟨1,599,3,true⟩,1,1,0⟩, +⟨⟨0,608,826,true⟩,826,1,1⟩, +⟨⟨1,599,608,true⟩,1,1,0⟩, +⟨⟨0,544,827,true⟩,827,1,1⟩, +⟨⟨1,544,7,true⟩,1,1,0⟩, +⟨⟨1,544,6,true⟩,1,1,0⟩, +⟨⟨0,727,813,true⟩,813,1,2⟩, +⟨⟨1,544,727,true⟩,1,1,0⟩, +⟨⟨0,592,829,true⟩,829,1,1⟩, +⟨⟨0,560,825,true⟩,825,1,1⟩, +⟨⟨1,592,560,true⟩,1,1,0⟩, +⟨⟨0,810,812,true⟩,812,1,2⟩, +⟨⟨0,811,812,true⟩,812,1,2⟩, +⟨⟨1,592,810,true⟩,1,1,0⟩, +⟨⟨1,592,811,true⟩,1,1,0⟩, +⟨⟨0,264,812,true⟩,812,1,2⟩, +⟨⟨1,560,264,true⟩,1,1,0⟩, +⟨⟨1,560,592,true⟩,1,1,0⟩, +⟨⟨0,576,828,true⟩,828,1,1⟩, +⟨⟨0,282,811,true⟩,811,1,2⟩, +⟨⟨1,576,282,true⟩,1,1,0⟩, +⟨⟨0,253,811,true⟩,811,1,2⟩, +⟨⟨1,576,253,true⟩,1,1,0⟩, +⟨⟨0,711,811,true⟩,811,1,2⟩, +⟨⟨1,576,711,true⟩,1,1,0⟩, +⟨⟨0,907,825,true⟩,825,1,1⟩, +⟨⟨0,688,824,true⟩,824,1,1⟩, +⟨⟨1,907,688,true⟩,1,1,0⟩, +⟨⟨0,708,810,true⟩,810,1,2⟩, +⟨⟨1,907,708,true⟩,1,1,0⟩, +⟨⟨0,720,810,true⟩,810,1,2⟩, +⟨⟨1,688,720,true⟩,1,1,0⟩, +⟨⟨0,266,824,true⟩,824,1,1⟩, +⟨⟨0,624,829,true⟩,829,1,1⟩, +⟨⟨1,266,624,true⟩,1,1,0⟩, +⟨⟨0,656,809,true⟩,809,1,2⟩, +⟨⟨1,624,656,true⟩,1,1,0⟩, +⟨⟨0,704,824,true⟩,824,1,1⟩, +⟨⟨0,278,824,true⟩,824,1,1⟩, +⟨⟨1,704,278,true⟩,1,1,0⟩, +⟨⟨0,255,824,true⟩,824,1,1⟩, +⟨⟨1,704,255,true⟩,1,1,0⟩, +⟨⟨1,704,640,true⟩,1,1,0⟩, +⟨⟨0,392,887,true⟩,887,1,1⟩, +⟨⟨0,406,882,true⟩,882,1,1⟩, +⟨⟨1,392,406,true⟩,1,1,0⟩, +⟨⟨0,398,884,true⟩,884,1,1⟩, +⟨⟨0,526,881,true⟩,881,1,1⟩, +⟨⟨1,398,526,true⟩,1,1,0⟩, +⟨⟨0,527,887,true⟩,887,1,1⟩, +⟨⟨1,527,58,true⟩,1,1,0⟩, +⟨⟨1,527,57,true⟩,1,1,0⟩, +⟨⟨0,387,882,true⟩,882,1,1⟩, +⟨⟨0,949,884,true⟩,884,1,1⟩, +⟨⟨1,387,949,true⟩,1,1,0⟩, +⟨⟨0,941,806,true⟩,806,1,2⟩, +⟨⟨1,949,941,true⟩,1,1,0⟩, +⟨⟨0,402,805,true⟩,805,1,2⟩, +⟨⟨1,406,402,true⟩,1,1,0⟩, +⟨⟨0,522,804,true⟩,804,1,2⟩, +⟨⟨1,526,522,true⟩,1,1,0⟩, +⟨⟨0,389,881,true⟩,881,1,1⟩, +⟨⟨0,950,887,true⟩,887,1,1⟩, +⟨⟨1,389,950,true⟩,1,1,0⟩, +⟨⟨0,252,803,true⟩,803,1,2⟩, +⟨⟨1,950,252,true⟩,1,1,0⟩, +⟨⟨0,518,802,true⟩,802,1,2⟩, +⟨⟨1,518,63,true⟩,1,1,0⟩, +⟨⟨1,518,60,true⟩,1,1,0⟩, +⟨⟨0,394,886,true⟩,886,1,1⟩, +⟨⟨0,804,883,true⟩,883,1,1⟩, +⟨⟨1,394,804,true⟩,1,1,0⟩, +⟨⟨0,396,885,true⟩,885,1,1⟩, +⟨⟨0,805,880,true⟩,880,1,1⟩, +⟨⟨1,396,805,true⟩,1,1,0⟩, +⟨⟨0,762,801,true⟩,801,1,2⟩, +⟨⟨1,762,59,true⟩,1,1,0⟩, +⟨⟨1,762,56,true⟩,1,1,0⟩, +⟨⟨0,385,883,true⟩,883,1,1⟩, +⟨⟨0,828,885,true⟩,885,1,1⟩, +⟨⟨1,385,828,true⟩,1,1,0⟩, +⟨⟨0,814,800,true⟩,800,1,2⟩, +⟨⟨1,828,814,true⟩,1,1,0⟩, +⟨⟨0,790,799,true⟩,799,1,2⟩, +⟨⟨1,804,790,true⟩,1,1,0⟩, +⟨⟨0,791,798,true⟩,798,1,2⟩, +⟨⟨1,805,791,true⟩,1,1,0⟩, +⟨⟨0,391,880,true⟩,880,1,1⟩, +⟨⟨0,829,886,true⟩,886,1,1⟩, +⟨⟨1,391,829,true⟩,1,1,0⟩, +⟨⟨0,815,797,true⟩,797,1,2⟩, +⟨⟨1,829,815,true⟩,1,1,0⟩, +⟨⟨0,763,796,true⟩,796,1,2⟩, +⟨⟨1,763,62,true⟩,1,1,0⟩, +⟨⟨1,763,61,true⟩,1,1,0⟩, +⟨⟨0,456,919,true⟩,919,1,1⟩, +⟨⟨0,948,914,true⟩,914,1,1⟩, +⟨⟨1,456,948,true⟩,1,1,0⟩, +⟨⟨0,462,916,true⟩,916,1,1⟩, +⟨⟨0,532,913,true⟩,913,1,1⟩, +⟨⟨1,462,532,true⟩,1,1,0⟩, +⟨⟨0,535,919,true⟩,919,1,1⟩, +⟨⟨1,535,90,true⟩,1,1,0⟩, +⟨⟨1,535,89,true⟩,1,1,0⟩, +⟨⟨0,451,914,true⟩,914,1,1⟩, +⟨⟨0,952,916,true⟩,916,1,1⟩, +⟨⟨1,451,952,true⟩,1,1,0⟩, +⟨⟨0,538,794,true⟩,794,1,2⟩, +⟨⟨1,952,538,true⟩,1,1,0⟩, +⟨⟨0,543,793,true⟩,793,1,2⟩, +⟨⟨1,948,543,true⟩,1,1,0⟩, +⟨⟨0,341,792,true⟩,792,1,2⟩, +⟨⟨1,532,341,true⟩,1,1,0⟩, +⟨⟨0,453,913,true⟩,913,1,1⟩, +⟨⟨0,954,919,true⟩,919,1,1⟩, +⟨⟨1,453,954,true⟩,1,1,0⟩, +⟨⟨0,542,791,true⟩,791,1,2⟩, +⟨⟨1,954,542,true⟩,1,1,0⟩, +⟨⟨0,539,790,true⟩,790,1,2⟩, +⟨⟨1,539,95,true⟩,1,1,0⟩, +⟨⟨1,539,92,true⟩,1,1,0⟩, +⟨⟨0,459,918,true⟩,918,1,1⟩, +⟨⟨0,831,912,true⟩,912,1,1⟩, +⟨⟨1,459,831,true⟩,1,1,0⟩, +⟨⟨0,461,917,true⟩,917,1,1⟩, +⟨⟨0,830,915,true⟩,915,1,1⟩, +⟨⟨1,461,830,true⟩,1,1,0⟩, +⟨⟨0,748,789,true⟩,789,1,2⟩, +⟨⟨1,748,91,true⟩,1,1,0⟩, +⟨⟨1,748,88,true⟩,1,1,0⟩, +⟨⟨0,800,788,true⟩,788,1,2⟩, +⟨⟨1,830,800,true⟩,1,1,0⟩, +⟨⟨0,448,915,true⟩,915,1,1⟩, +⟨⟨0,818,918,true⟩,918,1,1⟩, +⟨⟨1,448,818,true⟩,1,1,0⟩, +⟨⟨0,788,787,true⟩,787,1,2⟩, +⟨⟨1,818,788,true⟩,1,1,0⟩, +⟨⟨0,454,912,true⟩,912,1,1⟩, +⟨⟨0,819,917,true⟩,917,1,1⟩, +⟨⟨1,454,819,true⟩,1,1,0⟩, +⟨⟨0,789,786,true⟩,786,1,2⟩, +⟨⟨1,819,789,true⟩,1,1,0⟩, +⟨⟨0,801,785,true⟩,785,1,2⟩, +⟨⟨1,831,801,true⟩,1,1,0⟩, +⟨⟨0,749,784,true⟩,784,1,2⟩, +⟨⟨1,749,94,true⟩,1,1,0⟩, +⟨⟨1,749,93,true⟩,1,1,0⟩, +⟨⟨0,472,927,true⟩,927,1,1⟩, +⟨⟨0,958,922,true⟩,922,1,1⟩, +⟨⟨1,472,958,true⟩,1,1,0⟩, +⟨⟨0,478,924,true⟩,924,1,1⟩, +⟨⟨0,956,921,true⟩,921,1,1⟩, +⟨⟨1,478,956,true⟩,1,1,0⟩, +⟨⟨0,555,927,true⟩,927,1,1⟩, +⟨⟨1,555,98,true⟩,1,1,0⟩, +⟨⟨1,555,97,true⟩,1,1,0⟩] +def chunk81 : List Entry := [⟨⟨0,467,922,true⟩,922,1,1⟩, +⟨⟨0,943,924,true⟩,924,1,1⟩, +⟨⟨1,467,943,true⟩,1,1,0⟩, +⟨⟨0,554,782,true⟩,782,1,2⟩, +⟨⟨1,943,554,true⟩,1,1,0⟩, +⟨⟨0,550,781,true⟩,781,1,2⟩, +⟨⟨1,958,550,true⟩,1,1,0⟩, +⟨⟨0,325,780,true⟩,780,1,2⟩, +⟨⟨1,956,325,true⟩,1,1,0⟩, +⟨⟨0,469,921,true⟩,921,1,1⟩, +⟨⟨0,945,927,true⟩,927,1,1⟩, +⟨⟨1,469,945,true⟩,1,1,0⟩, +⟨⟨0,558,779,true⟩,779,1,2⟩, +⟨⟨1,945,558,true⟩,1,1,0⟩, +⟨⟨0,559,778,true⟩,778,1,2⟩, +⟨⟨1,559,103,true⟩,1,1,0⟩, +⟨⟨1,559,100,true⟩,1,1,0⟩, +⟨⟨0,475,926,true⟩,926,1,1⟩, +⟨⟨0,817,920,true⟩,920,1,1⟩, +⟨⟨1,475,817,true⟩,1,1,0⟩, +⟨⟨0,477,925,true⟩,925,1,1⟩, +⟨⟨0,816,923,true⟩,923,1,1⟩, +⟨⟨1,477,816,true⟩,1,1,0⟩, +⟨⟨0,513,777,true⟩,777,1,2⟩, +⟨⟨1,513,99,true⟩,1,1,0⟩, +⟨⟨1,513,96,true⟩,1,1,0⟩, +⟨⟨0,802,776,true⟩,776,1,2⟩, +⟨⟨1,816,802,true⟩,1,1,0⟩, +⟨⟨0,464,923,true⟩,923,1,1⟩, +⟨⟨0,832,926,true⟩,926,1,1⟩, +⟨⟨1,464,832,true⟩,1,1,0⟩, +⟨⟨0,786,775,true⟩,775,1,2⟩, +⟨⟨1,832,786,true⟩,1,1,0⟩, +⟨⟨0,470,920,true⟩,920,1,1⟩, +⟨⟨0,833,925,true⟩,925,1,1⟩, +⟨⟨1,470,833,true⟩,1,1,0⟩, +⟨⟨0,787,774,true⟩,774,1,2⟩, +⟨⟨1,833,787,true⟩,1,1,0⟩, +⟨⟨0,803,773,true⟩,773,1,2⟩, +⟨⟨1,817,803,true⟩,1,1,0⟩, +⟨⟨0,515,772,true⟩,772,1,2⟩, +⟨⟨1,515,102,true⟩,1,1,0⟩, +⟨⟨1,515,101,true⟩,1,1,0⟩, +⟨⟨0,488,935,true⟩,935,1,1⟩, +⟨⟨0,947,930,true⟩,930,1,1⟩, +⟨⟨1,488,947,true⟩,1,1,0⟩, +⟨⟨0,494,932,true⟩,932,1,1⟩, +⟨⟨0,946,929,true⟩,929,1,1⟩, +⟨⟨1,494,946,true⟩,1,1,0⟩, +⟨⟨0,575,935,true⟩,935,1,1⟩, +⟨⟨1,575,106,true⟩,1,1,0⟩, +⟨⟨1,575,105,true⟩,1,1,0⟩, +⟨⟨0,483,930,true⟩,930,1,1⟩, +⟨⟨0,955,932,true⟩,932,1,1⟩, +⟨⟨1,483,955,true⟩,1,1,0⟩, +⟨⟨0,310,770,true⟩,770,1,2⟩, +⟨⟨1,955,310,true⟩,1,1,0⟩, +⟨⟨0,309,769,true⟩,769,1,2⟩, +⟨⟨1,947,309,true⟩,1,1,0⟩, +⟨⟨0,574,768,true⟩,768,1,2⟩, +⟨⟨1,946,574,true⟩,1,1,0⟩, +⟨⟨0,485,929,true⟩,929,1,1⟩, +⟨⟨0,957,935,true⟩,935,1,1⟩, +⟨⟨1,485,957,true⟩,1,1,0⟩, +⟨⟨0,570,767,true⟩,767,1,2⟩, +⟨⟨1,957,570,true⟩,1,1,0⟩, +⟨⟨0,566,766,true⟩,766,1,2⟩, +⟨⟨1,566,111,true⟩,1,1,0⟩, +⟨⟨1,566,108,true⟩,1,1,0⟩, +⟨⟨0,491,934,true⟩,934,1,1⟩, +⟨⟨0,621,928,true⟩,928,1,1⟩, +⟨⟨1,491,621,true⟩,1,1,0⟩, +⟨⟨0,493,933,true⟩,933,1,1⟩, +⟨⟨0,620,931,true⟩,931,1,1⟩, +⟨⟨1,493,620,true⟩,1,1,0⟩, +⟨⟨0,746,765,true⟩,765,1,2⟩, +⟨⟨1,746,107,true⟩,1,1,0⟩, +⟨⟨1,746,104,true⟩,1,1,0⟩, +⟨⟨0,772,764,true⟩,764,1,2⟩, +⟨⟨1,620,772,true⟩,1,1,0⟩, +⟨⟨0,480,931,true⟩,931,1,1⟩, +⟨⟨0,600,934,true⟩,934,1,1⟩, +⟨⟨1,480,600,true⟩,1,1,0⟩, +⟨⟨0,760,763,true⟩,763,1,2⟩, +⟨⟨1,600,760,true⟩,1,1,0⟩, +⟨⟨0,486,928,true⟩,928,1,1⟩, +⟨⟨0,601,933,true⟩,933,1,1⟩, +⟨⟨1,486,601,true⟩,1,1,0⟩, +⟨⟨0,761,762,true⟩,762,1,2⟩, +⟨⟨1,601,761,true⟩,1,1,0⟩, +⟨⟨0,773,761,true⟩,761,1,2⟩, +⟨⟨1,621,773,true⟩,1,1,0⟩, +⟨⟨0,747,760,true⟩,760,1,2⟩, +⟨⟨1,747,110,true⟩,1,1,0⟩, +⟨⟨1,747,109,true⟩,1,1,0⟩, +⟨⟨0,440,911,true⟩,911,1,1⟩, +⟨⟨0,953,906,true⟩,906,1,1⟩, +⟨⟨1,440,953,true⟩,1,1,0⟩, +⟨⟨0,446,908,true⟩,908,1,1⟩, +⟨⟨0,951,905,true⟩,905,1,1⟩, +⟨⟨1,446,951,true⟩,1,1,0⟩, +⟨⟨0,587,911,true⟩,911,1,1⟩, +⟨⟨1,587,82,true⟩,1,1,0⟩, +⟨⟨1,587,81,true⟩,1,1,0⟩, +⟨⟨0,435,906,true⟩,906,1,1⟩, +⟨⟨0,942,908,true⟩,908,1,1⟩, +⟨⟨1,435,942,true⟩,1,1,0⟩, +⟨⟨0,590,758,true⟩,758,1,2⟩, +⟨⟨1,942,590,true⟩,1,1,0⟩, +⟨⟨0,582,757,true⟩,757,1,2⟩, +⟨⟨1,953,582,true⟩,1,1,0⟩, +⟨⟨0,354,756,true⟩,756,1,2⟩, +⟨⟨1,951,354,true⟩,1,1,0⟩, +⟨⟨0,437,905,true⟩,905,1,1⟩, +⟨⟨0,944,911,true⟩,911,1,1⟩, +⟨⟨1,437,944,true⟩,1,1,0⟩, +⟨⟨0,586,755,true⟩,755,1,2⟩, +⟨⟨1,944,586,true⟩,1,1,0⟩, +⟨⟨0,591,754,true⟩,754,1,2⟩, +⟨⟨1,591,87,true⟩,1,1,0⟩, +⟨⟨1,591,84,true⟩,1,1,0⟩, +⟨⟨0,443,910,true⟩,910,1,1⟩, +⟨⟨0,605,904,true⟩,904,1,1⟩, +⟨⟨1,443,605,true⟩,1,1,0⟩, +⟨⟨0,445,909,true⟩,909,1,1⟩, +⟨⟨0,604,907,true⟩,907,1,1⟩, +⟨⟨1,445,604,true⟩,1,1,0⟩, +⟨⟨0,520,753,true⟩,753,1,2⟩, +⟨⟨1,520,83,true⟩,1,1,0⟩, +⟨⟨1,520,80,true⟩,1,1,0⟩, +⟨⟨0,774,752,true⟩,752,1,2⟩, +⟨⟨1,604,774,true⟩,1,1,0⟩, +⟨⟨0,432,907,true⟩,907,1,1⟩, +⟨⟨0,616,910,true⟩,910,1,1⟩, +⟨⟨1,432,616,true⟩,1,1,0⟩, +⟨⟨0,758,751,true⟩,751,1,2⟩, +⟨⟨1,616,758,true⟩,1,1,0⟩, +⟨⟨0,438,904,true⟩,904,1,1⟩, +⟨⟨0,617,909,true⟩,909,1,1⟩, +⟨⟨1,438,617,true⟩,1,1,0⟩, +⟨⟨0,759,750,true⟩,750,1,2⟩, +⟨⟨1,617,759,true⟩,1,1,0⟩, +⟨⟨0,775,749,true⟩,749,1,2⟩, +⟨⟨1,605,775,true⟩,1,1,0⟩, +⟨⟨0,521,748,true⟩,748,1,2⟩, +⟨⟨1,521,86,true⟩,1,1,0⟩, +⟨⟨1,521,85,true⟩,1,1,0⟩, +⟨⟨0,377,879,true⟩,879,1,1⟩, +⟨⟨0,940,873,true⟩,873,1,1⟩, +⟨⟨1,377,940,true⟩,1,1,0⟩, +⟨⟨0,383,876,true⟩,876,1,1⟩, +⟨⟨0,939,874,true⟩,874,1,1⟩, +⟨⟨1,383,939,true⟩,1,1,0⟩, +⟨⟨0,607,879,true⟩,879,1,1⟩, +⟨⟨1,607,50,true⟩,1,1,0⟩, +⟨⟨1,607,49,true⟩,1,1,0⟩, +⟨⟨0,422,746,true⟩,746,1,2⟩, +⟨⟨1,939,422,true⟩,1,1,0⟩, +⟨⟨0,370,874,true⟩,874,1,1⟩, +⟨⟨0,935,879,true⟩,879,1,1⟩, +⟨⟨1,370,935,true⟩,1,1,0⟩, +⟨⟨0,421,745,true⟩,745,1,2⟩, +⟨⟨1,935,421,true⟩,1,1,0⟩, +⟨⟨0,372,873,true⟩,873,1,1⟩, +⟨⟨0,934,876,true⟩,876,1,1⟩, +⟨⟨1,372,934,true⟩,1,1,0⟩, +⟨⟨0,606,744,true⟩,744,1,2⟩, +⟨⟨1,934,606,true⟩,1,1,0⟩, +⟨⟨0,602,743,true⟩,743,1,2⟩, +⟨⟨1,940,602,true⟩,1,1,0⟩, +⟨⟨0,598,742,true⟩,742,1,2⟩, +⟨⟨1,598,55,true⟩,1,1,0⟩, +⟨⟨1,598,52,true⟩,1,1,0⟩, +⟨⟨0,378,878,true⟩,878,1,1⟩, +⟨⟨0,568,875,true⟩,875,1,1⟩, +⟨⟨1,378,568,true⟩,1,1,0⟩, +⟨⟨0,380,877,true⟩,877,1,1⟩, +⟨⟨0,569,872,true⟩,872,1,1⟩, +⟨⟨1,380,569,true⟩,1,1,0⟩, +⟨⟨0,744,741,true⟩,741,1,2⟩, +⟨⟨1,744,51,true⟩,1,1,0⟩, +⟨⟨1,744,48,true⟩,1,1,0⟩, +⟨⟨0,369,875,true⟩,875,1,1⟩, +⟨⟨0,588,877,true⟩,877,1,1⟩, +⟨⟨1,369,588,true⟩,1,1,0⟩, +⟨⟨0,556,740,true⟩,740,1,2⟩, +⟨⟨1,588,556,true⟩,1,1,0⟩, +⟨⟨0,536,739,true⟩,739,1,2⟩, +⟨⟨1,568,536,true⟩,1,1,0⟩, +⟨⟨0,537,738,true⟩,738,1,2⟩, +⟨⟨1,569,537,true⟩,1,1,0⟩, +⟨⟨0,375,872,true⟩,872,1,1⟩, +⟨⟨0,589,878,true⟩,878,1,1⟩, +⟨⟨1,375,589,true⟩,1,1,0⟩, +⟨⟨0,557,737,true⟩,737,1,2⟩, +⟨⟨1,589,557,true⟩,1,1,0⟩, +⟨⟨0,745,736,true⟩,736,1,2⟩, +⟨⟨1,745,54,true⟩,1,1,0⟩, +⟨⟨1,745,53,true⟩,1,1,0⟩, +⟨⟨0,296,839,true⟩,839,1,1⟩] +def chunk82 : List Entry := [⟨⟨0,938,834,true⟩,834,1,1⟩, +⟨⟨1,296,938,true⟩,1,1,0⟩, +⟨⟨0,302,836,true⟩,836,1,1⟩, +⟨⟨0,937,833,true⟩,833,1,1⟩, +⟨⟨1,302,937,true⟩,1,1,0⟩, +⟨⟨0,619,839,true⟩,839,1,1⟩, +⟨⟨1,619,10,true⟩,1,1,0⟩, +⟨⟨1,619,9,true⟩,1,1,0⟩, +⟨⟨0,291,834,true⟩,834,1,1⟩, +⟨⟨0,932,836,true⟩,836,1,1⟩, +⟨⟨1,291,932,true⟩,1,1,0⟩, +⟨⟨0,618,734,true⟩,734,1,2⟩, +⟨⟨1,932,618,true⟩,1,1,0⟩, +⟨⟨0,614,733,true⟩,733,1,2⟩, +⟨⟨1,938,614,true⟩,1,1,0⟩, +⟨⟨0,501,732,true⟩,732,1,2⟩, +⟨⟨1,937,501,true⟩,1,1,0⟩, +⟨⟨0,293,833,true⟩,833,1,1⟩, +⟨⟨0,933,839,true⟩,839,1,1⟩, +⟨⟨1,293,933,true⟩,1,1,0⟩, +⟨⟨0,622,731,true⟩,731,1,2⟩, +⟨⟨1,933,622,true⟩,1,1,0⟩, +⟨⟨0,623,730,true⟩,730,1,2⟩, +⟨⟨1,623,15,true⟩,1,1,0⟩, +⟨⟨1,623,12,true⟩,1,1,0⟩, +⟨⟨0,298,838,true⟩,838,1,1⟩, +⟨⟨0,584,835,true⟩,835,1,1⟩, +⟨⟨1,298,584,true⟩,1,1,0⟩, +⟨⟨0,300,837,true⟩,837,1,1⟩, +⟨⟨0,585,832,true⟩,832,1,1⟩, +⟨⟨1,300,585,true⟩,1,1,0⟩, +⟨⟨0,524,729,true⟩,729,1,2⟩, +⟨⟨1,524,11,true⟩,1,1,0⟩, +⟨⟨1,524,8,true⟩,1,1,0⟩, +⟨⟨0,289,835,true⟩,835,1,1⟩, +⟨⟨0,572,837,true⟩,837,1,1⟩, +⟨⟨1,289,572,true⟩,1,1,0⟩, +⟨⟨0,552,728,true⟩,728,1,2⟩, +⟨⟨1,572,552,true⟩,1,1,0⟩, +⟨⟨0,540,727,true⟩,727,1,2⟩, +⟨⟨1,584,540,true⟩,1,1,0⟩, +⟨⟨0,541,726,true⟩,726,1,2⟩, +⟨⟨1,585,541,true⟩,1,1,0⟩, +⟨⟨0,295,832,true⟩,832,1,1⟩, +⟨⟨0,573,838,true⟩,838,1,1⟩, +⟨⟨1,295,573,true⟩,1,1,0⟩, +⟨⟨0,553,725,true⟩,725,1,2⟩, +⟨⟨1,573,553,true⟩,1,1,0⟩, +⟨⟨0,525,724,true⟩,724,1,2⟩, +⟨⟨1,525,14,true⟩,1,1,0⟩, +⟨⟨1,525,13,true⟩,1,1,0⟩, +⟨⟨0,505,943,true⟩,943,1,1⟩, +⟨⟨0,986,937,true⟩,937,1,1⟩, +⟨⟨1,505,986,true⟩,1,1,0⟩, +⟨⟨0,511,940,true⟩,940,1,1⟩, +⟨⟨0,985,938,true⟩,938,1,1⟩, +⟨⟨1,511,985,true⟩,1,1,0⟩, +⟨⟨0,639,943,true⟩,943,1,1⟩, +⟨⟨1,639,114,true⟩,1,1,0⟩, +⟨⟨1,639,113,true⟩,1,1,0⟩, +⟨⟨0,294,722,true⟩,722,1,2⟩, +⟨⟨1,985,294,true⟩,1,1,0⟩, +⟨⟨0,498,938,true⟩,938,1,1⟩, +⟨⟨0,982,943,true⟩,943,1,1⟩, +⟨⟨1,498,982,true⟩,1,1,0⟩, +⟨⟨0,290,721,true⟩,721,1,2⟩, +⟨⟨1,982,290,true⟩,1,1,0⟩, +⟨⟨0,500,937,true⟩,937,1,1⟩, +⟨⟨0,981,940,true⟩,940,1,1⟩, +⟨⟨1,500,981,true⟩,1,1,0⟩, +⟨⟨0,634,720,true⟩,720,1,2⟩, +⟨⟨1,981,634,true⟩,1,1,0⟩, +⟨⟨0,638,719,true⟩,719,1,2⟩, +⟨⟨1,986,638,true⟩,1,1,0⟩, +⟨⟨0,630,718,true⟩,718,1,2⟩, +⟨⟨1,630,119,true⟩,1,1,0⟩, +⟨⟨1,630,116,true⟩,1,1,0⟩, +⟨⟨0,507,942,true⟩,942,1,1⟩, +⟨⟨0,889,936,true⟩,936,1,1⟩, +⟨⟨1,507,889,true⟩,1,1,0⟩, +⟨⟨0,509,941,true⟩,941,1,1⟩, +⟨⟨0,888,939,true⟩,939,1,1⟩, +⟨⟨1,509,888,true⟩,1,1,0⟩, +⟨⟨0,742,717,true⟩,717,1,2⟩, +⟨⟨1,742,115,true⟩,1,1,0⟩, +⟨⟨1,742,112,true⟩,1,1,0⟩, +⟨⟨0,768,716,true⟩,716,1,2⟩, +⟨⟨1,888,768,true⟩,1,1,0⟩, +⟨⟨0,496,939,true⟩,939,1,1⟩, +⟨⟨0,874,942,true⟩,942,1,1⟩, +⟨⟨1,496,874,true⟩,1,1,0⟩, +⟨⟨0,756,715,true⟩,715,1,2⟩, +⟨⟨1,874,756,true⟩,1,1,0⟩, +⟨⟨0,502,936,true⟩,936,1,1⟩, +⟨⟨0,875,941,true⟩,941,1,1⟩, +⟨⟨1,502,875,true⟩,1,1,0⟩, +⟨⟨0,757,714,true⟩,714,1,2⟩, +⟨⟨1,875,757,true⟩,1,1,0⟩, +⟨⟨0,769,713,true⟩,713,1,2⟩, +⟨⟨1,889,769,true⟩,1,1,0⟩, +⟨⟨0,743,712,true⟩,712,1,2⟩, +⟨⟨1,743,118,true⟩,1,1,0⟩, +⟨⟨1,743,117,true⟩,1,1,0⟩, +⟨⟨0,425,903,true⟩,903,1,1⟩, +⟨⟨0,980,897,true⟩,897,1,1⟩, +⟨⟨1,425,980,true⟩,1,1,0⟩, +⟨⟨0,431,900,true⟩,900,1,1⟩, +⟨⟨0,979,898,true⟩,898,1,1⟩, +⟨⟨1,431,979,true⟩,1,1,0⟩, +⟨⟨0,655,903,true⟩,903,1,1⟩, +⟨⟨1,655,74,true⟩,1,1,0⟩, +⟨⟨1,655,73,true⟩,1,1,0⟩, +⟨⟨0,374,710,true⟩,710,1,2⟩, +⟨⟨1,979,374,true⟩,1,1,0⟩, +⟨⟨0,418,898,true⟩,898,1,1⟩, +⟨⟨0,984,903,true⟩,903,1,1⟩, +⟨⟨1,418,984,true⟩,1,1,0⟩, +⟨⟨0,373,709,true⟩,709,1,2⟩, +⟨⟨1,984,373,true⟩,1,1,0⟩, +⟨⟨0,420,897,true⟩,897,1,1⟩, +⟨⟨0,983,900,true⟩,900,1,1⟩, +⟨⟨1,420,983,true⟩,1,1,0⟩, +⟨⟨0,654,708,true⟩,708,1,2⟩, +⟨⟨1,983,654,true⟩,1,1,0⟩, +⟨⟨0,650,707,true⟩,707,1,2⟩, +⟨⟨1,980,650,true⟩,1,1,0⟩, +⟨⟨0,646,706,true⟩,706,1,2⟩, +⟨⟨1,646,79,true⟩,1,1,0⟩, +⟨⟨1,646,76,true⟩,1,1,0⟩, +⟨⟨0,426,902,true⟩,902,1,1⟩, +⟨⟨0,886,899,true⟩,899,1,1⟩, +⟨⟨1,426,886,true⟩,1,1,0⟩, +⟨⟨0,428,901,true⟩,901,1,1⟩, +⟨⟨0,887,896,true⟩,896,1,1⟩, +⟨⟨1,428,887,true⟩,1,1,0⟩, +⟨⟨0,413,705,true⟩,705,1,2⟩, +⟨⟨1,413,75,true⟩,1,1,0⟩, +⟨⟨1,413,72,true⟩,1,1,0⟩, +⟨⟨0,417,899,true⟩,899,1,1⟩, +⟨⟨0,872,901,true⟩,901,1,1⟩, +⟨⟨1,417,872,true⟩,1,1,0⟩, +⟨⟨0,770,704,true⟩,704,1,2⟩, +⟨⟨1,872,770,true⟩,1,1,0⟩, +⟨⟨0,754,703,true⟩,703,1,2⟩, +⟨⟨1,886,754,true⟩,1,1,0⟩, +⟨⟨0,755,702,true⟩,702,1,2⟩, +⟨⟨1,887,755,true⟩,1,1,0⟩, +⟨⟨0,423,896,true⟩,896,1,1⟩, +⟨⟨0,873,902,true⟩,902,1,1⟩, +⟨⟨1,423,873,true⟩,1,1,0⟩, +⟨⟨0,771,701,true⟩,701,1,2⟩, +⟨⟨1,873,771,true⟩,1,1,0⟩, +⟨⟨0,415,700,true⟩,700,1,2⟩, +⟨⟨1,415,78,true⟩,1,1,0⟩, +⟨⟨1,415,77,true⟩,1,1,0⟩, +⟨⟨0,360,871,true⟩,871,1,1⟩, +⟨⟨0,968,866,true⟩,866,1,1⟩, +⟨⟨1,360,968,true⟩,1,1,0⟩, +⟨⟨0,366,868,true⟩,868,1,1⟩, +⟨⟨0,967,865,true⟩,865,1,1⟩, +⟨⟨1,366,967,true⟩,1,1,0⟩, +⟨⟨0,671,871,true⟩,871,1,1⟩, +⟨⟨1,671,42,true⟩,1,1,0⟩, +⟨⟨1,671,41,true⟩,1,1,0⟩, +⟨⟨0,355,866,true⟩,866,1,1⟩, +⟨⟨0,975,868,true⟩,868,1,1⟩, +⟨⟨1,355,975,true⟩,1,1,0⟩, +⟨⟨0,444,698,true⟩,698,1,2⟩, +⟨⟨1,975,444,true⟩,1,1,0⟩, +⟨⟨0,434,697,true⟩,697,1,2⟩, +⟨⟨1,968,434,true⟩,1,1,0⟩, +⟨⟨0,666,696,true⟩,696,1,2⟩, +⟨⟨1,967,666,true⟩,1,1,0⟩, +⟨⟨0,357,865,true⟩,865,1,1⟩, +⟨⟨0,976,871,true⟩,871,1,1⟩, +⟨⟨1,357,976,true⟩,1,1,0⟩, +⟨⟨0,670,695,true⟩,695,1,2⟩, +⟨⟨1,976,670,true⟩,1,1,0⟩, +⟨⟨0,662,694,true⟩,694,1,2⟩, +⟨⟨1,662,47,true⟩,1,1,0⟩, +⟨⟨1,662,44,true⟩,1,1,0⟩, +⟨⟨0,362,870,true⟩,870,1,1⟩, +⟨⟨0,844,867,true⟩,867,1,1⟩, +⟨⟨1,362,844,true⟩,1,1,0⟩, +⟨⟨0,364,869,true⟩,869,1,1⟩, +⟨⟨0,845,864,true⟩,864,1,1⟩, +⟨⟨1,364,845,true⟩,1,1,0⟩, +⟨⟨0,740,693,true⟩,693,1,2⟩, +⟨⟨1,740,43,true⟩,1,1,0⟩, +⟨⟨1,740,40,true⟩,1,1,0⟩, +⟨⟨0,353,867,true⟩,867,1,1⟩, +⟨⟨0,858,869,true⟩,869,1,1⟩, +⟨⟨1,353,858,true⟩,1,1,0⟩, +⟨⟨0,333,692,true⟩,692,1,2⟩, +⟨⟨1,858,333,true⟩,1,1,0⟩, +⟨⟨0,337,691,true⟩,691,1,2⟩, +⟨⟨1,844,337,true⟩,1,1,0⟩, +⟨⟨0,339,690,true⟩,690,1,2⟩, +⟨⟨1,845,339,true⟩,1,1,0⟩, +⟨⟨0,359,864,true⟩,864,1,1⟩] +def chunk83 : List Entry := [⟨⟨0,859,870,true⟩,870,1,1⟩, +⟨⟨1,359,859,true⟩,1,1,0⟩, +⟨⟨0,323,689,true⟩,689,1,2⟩, +⟨⟨1,859,323,true⟩,1,1,0⟩, +⟨⟨0,741,688,true⟩,688,1,2⟩, +⟨⟨1,741,46,true⟩,1,1,0⟩, +⟨⟨1,741,45,true⟩,1,1,0⟩, +⟨⟨0,313,847,true⟩,847,1,1⟩, +⟨⟨0,966,841,true⟩,841,1,1⟩, +⟨⟨1,313,966,true⟩,1,1,0⟩, +⟨⟨0,319,844,true⟩,844,1,1⟩, +⟨⟨0,965,842,true⟩,842,1,1⟩, +⟨⟨1,319,965,true⟩,1,1,0⟩, +⟨⟨0,687,847,true⟩,847,1,1⟩, +⟨⟨1,687,18,true⟩,1,1,0⟩, +⟨⟨1,687,17,true⟩,1,1,0⟩, +⟨⟨0,492,686,true⟩,686,1,2⟩, +⟨⟨1,965,492,true⟩,1,1,0⟩, +⟨⟨0,306,842,true⟩,842,1,1⟩, +⟨⟨0,974,847,true⟩,847,1,1⟩, +⟨⟨1,306,974,true⟩,1,1,0⟩, +⟨⟨0,482,685,true⟩,685,1,2⟩, +⟨⟨1,974,482,true⟩,1,1,0⟩, +⟨⟨0,308,841,true⟩,841,1,1⟩, +⟨⟨0,973,844,true⟩,844,1,1⟩, +⟨⟨1,308,973,true⟩,1,1,0⟩, +⟨⟨0,682,684,true⟩,684,1,2⟩, +⟨⟨1,973,682,true⟩,1,1,0⟩, +⟨⟨0,686,683,true⟩,683,1,2⟩, +⟨⟨1,966,686,true⟩,1,1,0⟩, +⟨⟨0,678,682,true⟩,682,1,2⟩, +⟨⟨1,678,23,true⟩,1,1,0⟩, +⟨⟨1,678,20,true⟩,1,1,0⟩, +⟨⟨0,314,846,true⟩,846,1,1⟩, +⟨⟨0,856,843,true⟩,843,1,1⟩, +⟨⟨1,314,856,true⟩,1,1,0⟩, +⟨⟨0,316,845,true⟩,845,1,1⟩, +⟨⟨0,857,840,true⟩,840,1,1⟩, +⟨⟨1,316,857,true⟩,1,1,0⟩, +⟨⟨0,400,681,true⟩,681,1,2⟩, +⟨⟨1,400,19,true⟩,1,1,0⟩, +⟨⟨1,400,16,true⟩,1,1,0⟩, +⟨⟨0,305,843,true⟩,843,1,1⟩, +⟨⟨0,842,845,true⟩,845,1,1⟩, +⟨⟨1,305,842,true⟩,1,1,0⟩, +⟨⟨0,320,680,true⟩,680,1,2⟩, +⟨⟨1,842,320,true⟩,1,1,0⟩, +⟨⟨0,346,679,true⟩,679,1,2⟩, +⟨⟨1,856,346,true⟩,1,1,0⟩, +⟨⟨0,350,678,true⟩,678,1,2⟩, +⟨⟨1,857,350,true⟩,1,1,0⟩, +⟨⟨0,311,840,true⟩,840,1,1⟩, +⟨⟨0,843,846,true⟩,846,1,1⟩, +⟨⟨1,311,843,true⟩,1,1,0⟩, +⟨⟨0,334,677,true⟩,677,1,2⟩, +⟨⟨1,843,334,true⟩,1,1,0⟩, +⟨⟨0,404,676,true⟩,676,1,2⟩, +⟨⟨1,404,22,true⟩,1,1,0⟩, +⟨⟨1,404,21,true⟩,1,1,0⟩, +⟨⟨0,329,855,true⟩,855,1,1⟩, +⟨⟨0,972,849,true⟩,849,1,1⟩, +⟨⟨1,329,972,true⟩,1,1,0⟩, +⟨⟨0,335,852,true⟩,852,1,1⟩, +⟨⟨0,971,850,true⟩,850,1,1⟩, +⟨⟨1,335,971,true⟩,1,1,0⟩, +⟨⟨0,703,855,true⟩,855,1,1⟩, +⟨⟨1,703,26,true⟩,1,1,0⟩, +⟨⟨1,703,25,true⟩,1,1,0⟩, +⟨⟨0,476,674,true⟩,674,1,2⟩, +⟨⟨1,971,476,true⟩,1,1,0⟩, +⟨⟨0,322,850,true⟩,850,1,1⟩, +⟨⟨0,964,855,true⟩,855,1,1⟩, +⟨⟨1,322,964,true⟩,1,1,0⟩, +⟨⟨0,466,673,true⟩,673,1,2⟩, +⟨⟨1,964,466,true⟩,1,1,0⟩, +⟨⟨0,324,849,true⟩,849,1,1⟩, +⟨⟨0,963,852,true⟩,852,1,1⟩, +⟨⟨1,324,963,true⟩,1,1,0⟩, +⟨⟨0,698,672,true⟩,672,1,2⟩, +⟨⟨1,963,698,true⟩,1,1,0⟩, +⟨⟨0,702,671,true⟩,671,1,2⟩, +⟨⟨1,972,702,true⟩,1,1,0⟩, +⟨⟨0,694,670,true⟩,670,1,2⟩, +⟨⟨1,694,31,true⟩,1,1,0⟩, +⟨⟨1,694,28,true⟩,1,1,0⟩, +⟨⟨0,330,854,true⟩,854,1,1⟩, +⟨⟨0,840,851,true⟩,851,1,1⟩, +⟨⟨1,330,840,true⟩,1,1,0⟩, +⟨⟨0,332,853,true⟩,853,1,1⟩, +⟨⟨0,841,848,true⟩,848,1,1⟩, +⟨⟨1,332,841,true⟩,1,1,0⟩, +⟨⟨0,737,669,true⟩,669,1,2⟩, +⟨⟨1,737,27,true⟩,1,1,0⟩, +⟨⟨1,737,24,true⟩,1,1,0⟩, +⟨⟨0,321,851,true⟩,851,1,1⟩, +⟨⟨0,854,853,true⟩,853,1,1⟩, +⟨⟨1,321,854,true⟩,1,1,0⟩, +⟨⟨0,798,668,true⟩,668,1,2⟩, +⟨⟨1,854,798,true⟩,1,1,0⟩, +⟨⟨0,784,667,true⟩,667,1,2⟩, +⟨⟨1,840,784,true⟩,1,1,0⟩, +⟨⟨0,785,666,true⟩,666,1,2⟩, +⟨⟨1,841,785,true⟩,1,1,0⟩, +⟨⟨0,327,848,true⟩,848,1,1⟩, +⟨⟨0,855,854,true⟩,854,1,1⟩, +⟨⟨1,327,855,true⟩,1,1,0⟩, +⟨⟨0,799,665,true⟩,665,1,2⟩, +⟨⟨1,855,799,true⟩,1,1,0⟩, +⟨⟨0,739,664,true⟩,664,1,2⟩, +⟨⟨1,739,30,true⟩,1,1,0⟩, +⟨⟨1,739,29,true⟩,1,1,0⟩, +⟨⟨0,345,863,true⟩,863,1,1⟩, +⟨⟨0,962,857,true⟩,857,1,1⟩, +⟨⟨1,345,962,true⟩,1,1,0⟩, +⟨⟨0,351,860,true⟩,860,1,1⟩, +⟨⟨0,961,858,true⟩,858,1,1⟩, +⟨⟨1,351,961,true⟩,1,1,0⟩, +⟨⟨0,719,863,true⟩,863,1,1⟩, +⟨⟨1,719,34,true⟩,1,1,0⟩, +⟨⟨1,719,33,true⟩,1,1,0⟩, +⟨⟨0,936,662,true⟩,662,1,2⟩, +⟨⟨1,961,936,true⟩,1,1,0⟩, +⟨⟨0,338,858,true⟩,858,1,1⟩, +⟨⟨0,970,863,true⟩,863,1,1⟩, +⟨⟨1,338,970,true⟩,1,1,0⟩, +⟨⟨0,709,661,true⟩,661,1,2⟩, +⟨⟨1,970,709,true⟩,1,1,0⟩, +⟨⟨0,340,857,true⟩,857,1,1⟩, +⟨⟨0,969,860,true⟩,860,1,1⟩, +⟨⟨1,340,969,true⟩,1,1,0⟩, +⟨⟨0,718,660,true⟩,660,1,2⟩, +⟨⟨1,969,718,true⟩,1,1,0⟩, +⟨⟨0,710,659,true⟩,659,1,2⟩, +⟨⟨1,962,710,true⟩,1,1,0⟩, +⟨⟨0,450,658,true⟩,658,1,2⟩, +⟨⟨1,450,39,true⟩,1,1,0⟩, +⟨⟨1,450,36,true⟩,1,1,0⟩, +⟨⟨0,347,862,true⟩,862,1,1⟩, +⟨⟨0,839,856,true⟩,856,1,1⟩, +⟨⟨1,347,839,true⟩,1,1,0⟩, +⟨⟨0,349,861,true⟩,861,1,1⟩, +⟨⟨0,838,859,true⟩,859,1,1⟩, +⟨⟨1,349,838,true⟩,1,1,0⟩, +⟨⟨0,736,657,true⟩,657,1,2⟩, +⟨⟨1,736,35,true⟩,1,1,0⟩, +⟨⟨1,736,32,true⟩,1,1,0⟩, +⟨⟨0,796,656,true⟩,656,1,2⟩, +⟨⟨1,838,796,true⟩,1,1,0⟩, +⟨⟨0,336,859,true⟩,859,1,1⟩, +⟨⟨0,852,862,true⟩,862,1,1⟩, +⟨⟨1,336,852,true⟩,1,1,0⟩, +⟨⟨0,782,655,true⟩,655,1,2⟩, +⟨⟨1,852,782,true⟩,1,1,0⟩, +⟨⟨0,342,856,true⟩,856,1,1⟩, +⟨⟨0,853,861,true⟩,861,1,1⟩, +⟨⟨1,342,853,true⟩,1,1,0⟩, +⟨⟨0,783,654,true⟩,654,1,2⟩, +⟨⟨1,853,783,true⟩,1,1,0⟩, +⟨⟨0,797,653,true⟩,653,1,2⟩, +⟨⟨1,839,797,true⟩,1,1,0⟩, +⟨⟨0,738,652,true⟩,652,1,2⟩, +⟨⟨1,738,38,true⟩,1,1,0⟩, +⟨⟨1,738,37,true⟩,1,1,0⟩, +⟨⟨0,408,895,true⟩,895,1,1⟩, +⟨⟨0,978,890,true⟩,890,1,1⟩, +⟨⟨1,408,978,true⟩,1,1,0⟩, +⟨⟨0,414,892,true⟩,892,1,1⟩, +⟨⟨0,977,889,true⟩,889,1,1⟩, +⟨⟨1,414,977,true⟩,1,1,0⟩, +⟨⟨0,731,895,true⟩,895,1,1⟩, +⟨⟨1,731,66,true⟩,1,1,0⟩, +⟨⟨1,731,65,true⟩,1,1,0⟩, +⟨⟨0,403,890,true⟩,890,1,1⟩, +⟨⟨0,959,892,true⟩,892,1,1⟩, +⟨⟨1,403,959,true⟩,1,1,0⟩, +⟨⟨0,734,650,true⟩,650,1,2⟩, +⟨⟨1,959,734,true⟩,1,1,0⟩, +⟨⟨0,726,649,true⟩,649,1,2⟩, +⟨⟨1,978,726,true⟩,1,1,0⟩, +⟨⟨0,386,648,true⟩,648,1,2⟩, +⟨⟨1,977,386,true⟩,1,1,0⟩, +⟨⟨0,405,889,true⟩,889,1,1⟩, +⟨⟨0,960,895,true⟩,895,1,1⟩, +⟨⟨1,405,960,true⟩,1,1,0⟩, +⟨⟨0,730,647,true⟩,647,1,2⟩, +⟨⟨1,960,730,true⟩,1,1,0⟩, +⟨⟨0,735,646,true⟩,646,1,2⟩, +⟨⟨1,735,71,true⟩,1,1,0⟩, +⟨⟨1,735,68,true⟩,1,1,0⟩, +⟨⟨0,410,894,true⟩,894,1,1⟩, +⟨⟨0,863,891,true⟩,891,1,1⟩, +⟨⟨1,410,863,true⟩,1,1,0⟩, +⟨⟨0,412,893,true⟩,893,1,1⟩, +⟨⟨0,865,888,true⟩,888,1,1⟩, +⟨⟨1,412,865,true⟩,1,1,0⟩, +⟨⟨0,751,645,true⟩,645,1,2⟩, +⟨⟨1,751,67,true⟩,1,1,0⟩, +⟨⟨1,751,64,true⟩,1,1,0⟩, +⟨⟨0,401,891,true⟩,891,1,1⟩, +⟨⟨0,835,893,true⟩,893,1,1⟩] +def chunk84 : List Entry := [⟨⟨1,401,835,true⟩,1,1,0⟩, +⟨⟨0,807,644,true⟩,644,1,2⟩, +⟨⟨1,835,807,true⟩,1,1,0⟩, +⟨⟨0,779,643,true⟩,643,1,2⟩, +⟨⟨1,863,779,true⟩,1,1,0⟩, +⟨⟨0,781,642,true⟩,642,1,2⟩, +⟨⟨1,865,781,true⟩,1,1,0⟩, +⟨⟨0,407,888,true⟩,888,1,1⟩, +⟨⟨0,837,894,true⟩,894,1,1⟩, +⟨⟨1,407,837,true⟩,1,1,0⟩, +⟨⟨0,809,641,true⟩,641,1,2⟩, +⟨⟨1,837,809,true⟩,1,1,0⟩, +⟨⟨0,753,640,true⟩,640,1,2⟩, +⟨⟨1,753,70,true⟩,1,1,0⟩, +⟨⟨1,753,69,true⟩,1,1,0⟩, +⟨⟨0,909,855,true⟩,855,1,1⟩, +⟨⟨0,923,639,true⟩,639,1,3⟩, +⟨⟨1,909,923,true⟩,1,1,0⟩, +⟨⟨0,908,669,true⟩,669,1,2⟩, +⟨⟨0,922,638,true⟩,638,1,3⟩, +⟨⟨1,908,922,true⟩,1,1,0⟩, +⟨⟨0,895,863,true⟩,863,1,1⟩, +⟨⟨0,921,637,true⟩,637,1,3⟩, +⟨⟨1,895,921,true⟩,1,1,0⟩, +⟨⟨0,894,657,true⟩,657,1,2⟩, +⟨⟨0,919,636,true⟩,636,1,3⟩, +⟨⟨1,894,919,true⟩,1,1,0⟩, +⟨⟨0,893,895,true⟩,895,1,1⟩, +⟨⟨1,893,907,true⟩,1,1,0⟩, +⟨⟨0,891,645,true⟩,645,1,2⟩, +⟨⟨0,905,634,true⟩,634,1,3⟩, +⟨⟨1,891,905,true⟩,1,1,0⟩, +⟨⟨1,986,889,true⟩,1,1,0⟩, +⟨⟨0,903,633,true⟩,633,1,3⟩, +⟨⟨1,889,903,true⟩,1,1,0⟩, +⟨⟨1,985,888,true⟩,1,1,0⟩, +⟨⟨0,902,632,true⟩,632,1,3⟩, +⟨⟨1,888,902,true⟩,1,1,0⟩, +⟨⟨1,984,887,true⟩,1,1,0⟩, +⟨⟨0,915,631,true⟩,631,1,3⟩, +⟨⟨1,887,915,true⟩,1,1,0⟩, +⟨⟨1,983,886,true⟩,1,1,0⟩, +⟨⟨0,914,630,true⟩,630,1,3⟩, +⟨⟨1,886,914,true⟩,1,1,0⟩, +⟨⟨0,885,871,true⟩,871,1,1⟩, +⟨⟨0,927,629,true⟩,629,1,3⟩, +⟨⟨1,885,927,true⟩,1,1,0⟩, +⟨⟨0,884,693,true⟩,693,1,2⟩, +⟨⟨0,926,628,true⟩,628,1,3⟩, +⟨⟨1,884,926,true⟩,1,1,0⟩, +⟨⟨1,982,875,true⟩,1,1,0⟩, +⟨⟨0,917,627,true⟩,627,1,3⟩, +⟨⟨1,875,917,true⟩,1,1,0⟩, +⟨⟨1,981,874,true⟩,1,1,0⟩, +⟨⟨0,916,626,true⟩,626,1,3⟩, +⟨⟨1,874,916,true⟩,1,1,0⟩, +⟨⟨1,980,873,true⟩,1,1,0⟩, +⟨⟨0,901,625,true⟩,625,1,3⟩, +⟨⟨1,873,901,true⟩,1,1,0⟩, +⟨⟨1,979,872,true⟩,1,1,0⟩, +⟨⟨0,900,624,true⟩,624,1,3⟩, +⟨⟨1,872,900,true⟩,1,1,0⟩, +⟨⟨0,871,847,true⟩,847,1,1⟩, +⟨⟨0,925,623,true⟩,623,1,3⟩, +⟨⟨1,871,925,true⟩,1,1,0⟩, +⟨⟨0,870,681,true⟩,681,1,2⟩, +⟨⟨0,924,622,true⟩,622,1,3⟩, +⟨⟨1,870,924,true⟩,1,1,0⟩, +⟨⟨1,978,865,true⟩,1,1,0⟩, +⟨⟨0,879,621,true⟩,621,1,3⟩, +⟨⟨1,865,879,true⟩,1,1,0⟩, +⟨⟨1,977,863,true⟩,1,1,0⟩, +⟨⟨0,877,620,true⟩,620,1,3⟩, +⟨⟨1,863,877,true⟩,1,1,0⟩, +⟨⟨0,861,943,true⟩,943,1,1⟩, +⟨⟨0,931,619,true⟩,619,1,3⟩, +⟨⟨1,861,931,true⟩,1,1,0⟩, +⟨⟨0,860,717,true⟩,717,1,2⟩, +⟨⟨0,930,618,true⟩,618,1,3⟩, +⟨⟨1,860,930,true⟩,1,1,0⟩, +⟨⟨1,976,859,true⟩,1,1,0⟩, +⟨⟨0,899,617,true⟩,617,1,3⟩, +⟨⟨1,859,899,true⟩,1,1,0⟩, +⟨⟨1,975,858,true⟩,1,1,0⟩, +⟨⟨0,898,616,true⟩,616,1,3⟩, +⟨⟨1,858,898,true⟩,1,1,0⟩, +⟨⟨1,974,857,true⟩,1,1,0⟩, +⟨⟨0,911,615,true⟩,615,1,3⟩, +⟨⟨1,857,911,true⟩,1,1,0⟩, +⟨⟨1,973,856,true⟩,1,1,0⟩, +⟨⟨0,910,614,true⟩,614,1,3⟩, +⟨⟨1,856,910,true⟩,1,1,0⟩, +⟨⟨1,972,855,true⟩,1,1,0⟩, +⟨⟨0,869,613,true⟩,613,1,3⟩, +⟨⟨1,855,869,true⟩,1,1,0⟩, +⟨⟨1,971,854,true⟩,1,1,0⟩, +⟨⟨0,868,612,true⟩,612,1,3⟩, +⟨⟨1,854,868,true⟩,1,1,0⟩, +⟨⟨1,970,853,true⟩,1,1,0⟩, +⟨⟨0,881,611,true⟩,611,1,3⟩, +⟨⟨1,853,881,true⟩,1,1,0⟩, +⟨⟨1,969,852,true⟩,1,1,0⟩, +⟨⟨0,880,610,true⟩,610,1,3⟩, +⟨⟨1,852,880,true⟩,1,1,0⟩, +⟨⟨0,847,903,true⟩,903,1,1⟩, +⟨⟨0,929,609,true⟩,609,1,3⟩, +⟨⟨1,847,929,true⟩,1,1,0⟩, +⟨⟨0,846,705,true⟩,705,1,2⟩, +⟨⟨0,928,608,true⟩,608,1,3⟩, +⟨⟨1,846,928,true⟩,1,1,0⟩, +⟨⟨1,968,845,true⟩,1,1,0⟩, +⟨⟨0,913,607,true⟩,607,1,3⟩, +⟨⟨1,845,913,true⟩,1,1,0⟩, +⟨⟨1,967,844,true⟩,1,1,0⟩, +⟨⟨0,912,606,true⟩,606,1,3⟩, +⟨⟨1,844,912,true⟩,1,1,0⟩, +⟨⟨1,966,843,true⟩,1,1,0⟩, +⟨⟨0,897,605,true⟩,605,1,3⟩, +⟨⟨1,843,897,true⟩,1,1,0⟩, +⟨⟨1,965,842,true⟩,1,1,0⟩, +⟨⟨0,896,604,true⟩,604,1,3⟩, +⟨⟨1,842,896,true⟩,1,1,0⟩, +⟨⟨1,964,841,true⟩,1,1,0⟩, +⟨⟨0,883,603,true⟩,603,1,3⟩, +⟨⟨1,841,883,true⟩,1,1,0⟩, +⟨⟨1,963,840,true⟩,1,1,0⟩, +⟨⟨0,882,602,true⟩,602,1,3⟩, +⟨⟨1,840,882,true⟩,1,1,0⟩, +⟨⟨1,962,839,true⟩,1,1,0⟩, +⟨⟨0,867,601,true⟩,601,1,3⟩, +⟨⟨1,839,867,true⟩,1,1,0⟩, +⟨⟨1,961,838,true⟩,1,1,0⟩, +⟨⟨0,866,600,true⟩,600,1,3⟩, +⟨⟨1,838,866,true⟩,1,1,0⟩, +⟨⟨1,960,837,true⟩,1,1,0⟩, +⟨⟨0,851,599,true⟩,599,1,3⟩, +⟨⟨1,837,851,true⟩,1,1,0⟩, +⟨⟨1,959,835,true⟩,1,1,0⟩, +⟨⟨0,849,598,true⟩,598,1,3⟩, +⟨⟨1,835,849,true⟩,1,1,0⟩, +⟨⟨1,958,833,true⟩,1,1,0⟩, +⟨⟨0,685,597,true⟩,597,1,3⟩, +⟨⟨1,833,685,true⟩,1,1,0⟩, +⟨⟨1,957,621,true⟩,1,1,0⟩, +⟨⟨0,697,596,true⟩,596,1,3⟩, +⟨⟨1,621,697,true⟩,1,1,0⟩, +⟨⟨1,956,832,true⟩,1,1,0⟩, +⟨⟨0,684,595,true⟩,595,1,3⟩, +⟨⟨1,832,684,true⟩,1,1,0⟩, +⟨⟨1,955,620,true⟩,1,1,0⟩, +⟨⟨0,696,594,true⟩,594,1,3⟩, +⟨⟨1,620,696,true⟩,1,1,0⟩, +⟨⟨1,954,831,true⟩,1,1,0⟩, +⟨⟨0,665,593,true⟩,593,1,3⟩, +⟨⟨1,831,665,true⟩,1,1,0⟩, +⟨⟨1,953,617,true⟩,1,1,0⟩, +⟨⟨0,717,592,true⟩,592,1,3⟩, +⟨⟨1,617,717,true⟩,1,1,0⟩, +⟨⟨1,952,830,true⟩,1,1,0⟩, +⟨⟨0,664,591,true⟩,591,1,3⟩, +⟨⟨1,830,664,true⟩,1,1,0⟩, +⟨⟨1,951,616,true⟩,1,1,0⟩, +⟨⟨0,716,590,true⟩,590,1,3⟩, +⟨⟨1,616,716,true⟩,1,1,0⟩, +⟨⟨1,950,829,true⟩,1,1,0⟩, +⟨⟨0,643,589,true⟩,589,1,3⟩, +⟨⟨1,829,643,true⟩,1,1,0⟩, +⟨⟨0,611,879,true⟩,879,1,1⟩, +⟨⟨0,733,588,true⟩,588,1,3⟩, +⟨⟨1,611,733,true⟩,1,1,0⟩, +⟨⟨1,949,828,true⟩,1,1,0⟩, +⟨⟨0,641,587,true⟩,587,1,3⟩, +⟨⟨1,828,641,true⟩,1,1,0⟩, +⟨⟨0,609,741,true⟩,741,1,2⟩, +⟨⟨0,732,586,true⟩,586,1,3⟩, +⟨⟨1,609,732,true⟩,1,1,0⟩, +⟨⟨1,948,819,true⟩,1,1,0⟩, +⟨⟨0,681,585,true⟩,585,1,3⟩, +⟨⟨1,819,681,true⟩,1,1,0⟩, +⟨⟨1,947,601,true⟩,1,1,0⟩, +⟨⟨0,713,584,true⟩,584,1,3⟩, +⟨⟨1,601,713,true⟩,1,1,0⟩, +⟨⟨1,532,818,true⟩,1,1,0⟩, +⟨⟨0,680,583,true⟩,583,1,3⟩, +⟨⟨1,818,680,true⟩,1,1,0⟩, +⟨⟨1,946,600,true⟩,1,1,0⟩, +⟨⟨0,712,582,true⟩,582,1,3⟩, +⟨⟨1,600,712,true⟩,1,1,0⟩, +⟨⟨1,945,817,true⟩,1,1,0⟩, +⟨⟨0,669,581,true⟩,581,1,3⟩, +⟨⟨1,817,669,true⟩,1,1,0⟩, +⟨⟨1,944,605,true⟩,1,1,0⟩, +⟨⟨0,701,580,true⟩,580,1,3⟩, +⟨⟨1,605,701,true⟩,1,1,0⟩, +⟨⟨1,943,816,true⟩,1,1,0⟩, +⟨⟨0,668,579,true⟩,579,1,3⟩, +⟨⟨1,816,668,true⟩,1,1,0⟩, +⟨⟨1,942,604,true⟩,1,1,0⟩, +⟨⟨0,700,578,true⟩,578,1,3⟩, +⟨⟨1,604,700,true⟩,1,1,0⟩] +def chunk85 : List Entry := [⟨⟨1,941,815,true⟩,1,1,0⟩, +⟨⟨0,627,577,true⟩,577,1,3⟩, +⟨⟨1,815,627,true⟩,1,1,0⟩, +⟨⟨0,595,839,true⟩,839,1,1⟩, +⟨⟨0,399,576,true⟩,576,1,3⟩, +⟨⟨1,595,399,true⟩,1,1,0⟩, +⟨⟨1,252,814,true⟩,1,1,0⟩, +⟨⟨0,625,575,true⟩,575,1,3⟩, +⟨⟨1,814,625,true⟩,1,1,0⟩, +⟨⟨0,593,729,true⟩,729,1,2⟩, +⟨⟨0,397,574,true⟩,574,1,3⟩, +⟨⟨1,593,397,true⟩,1,1,0⟩, +⟨⟨1,734,809,true⟩,1,1,0⟩, +⟨⟨0,393,471,true⟩,471,1,4⟩, +⟨⟨0,722,471,true⟩,471,1,4⟩, +⟨⟨0,725,471,true⟩,471,1,4⟩, +⟨⟨1,734,393,true⟩,1,1,0⟩, +⟨⟨1,734,722,true⟩,1,1,0⟩, +⟨⟨1,734,725,true⟩,1,1,0⟩, +⟨⟨0,823,573,true⟩,573,1,3⟩, +⟨⟨1,809,823,true⟩,1,1,0⟩, +⟨⟨1,730,807,true⟩,1,1,0⟩, +⟨⟨1,730,393,true⟩,1,1,0⟩, +⟨⟨1,730,725,true⟩,1,1,0⟩, +⟨⟨0,821,572,true⟩,572,1,3⟩, +⟨⟨1,807,821,true⟩,1,1,0⟩, +⟨⟨1,406,805,true⟩,1,1,0⟩, +⟨⟨0,675,571,true⟩,571,1,3⟩, +⟨⟨1,805,675,true⟩,1,1,0⟩, +⟨⟨0,579,935,true⟩,935,1,1⟩, +⟨⟨0,729,570,true⟩,570,1,3⟩, +⟨⟨1,579,729,true⟩,1,1,0⟩, +⟨⟨1,526,804,true⟩,1,1,0⟩, +⟨⟨0,409,458,true⟩,458,1,4⟩, +⟨⟨0,514,458,true⟩,458,1,4⟩, +⟨⟨0,517,458,true⟩,458,1,4⟩, +⟨⟨1,526,409,true⟩,1,1,0⟩, +⟨⟨1,526,514,true⟩,1,1,0⟩, +⟨⟨1,526,517,true⟩,1,1,0⟩, +⟨⟨0,673,569,true⟩,569,1,3⟩, +⟨⟨1,804,673,true⟩,1,1,0⟩, +⟨⟨0,577,765,true⟩,765,1,2⟩, +⟨⟨0,728,568,true⟩,568,1,3⟩, +⟨⟨1,577,728,true⟩,1,1,0⟩, +⟨⟨1,554,803,true⟩,1,1,0⟩, +⟨⟨0,328,460,true⟩,460,1,4⟩, +⟨⟨0,546,460,true⟩,460,1,4⟩, +⟨⟨0,549,460,true⟩,460,1,4⟩, +⟨⟨1,554,328,true⟩,1,1,0⟩, +⟨⟨1,554,546,true⟩,1,1,0⟩, +⟨⟨1,554,549,true⟩,1,1,0⟩, +⟨⟨0,653,567,true⟩,567,1,3⟩, +⟨⟨1,803,653,true⟩,1,1,0⟩, +⟨⟨1,940,589,true⟩,1,1,0⟩, +⟨⟨0,479,566,true⟩,566,1,3⟩, +⟨⟨1,589,479,true⟩,1,1,0⟩, +⟨⟨1,558,802,true⟩,1,1,0⟩, +⟨⟨1,558,328,true⟩,1,1,0⟩, +⟨⟨1,558,549,true⟩,1,1,0⟩, +⟨⟨0,652,565,true⟩,565,1,3⟩, +⟨⟨1,802,652,true⟩,1,1,0⟩, +⟨⟨1,939,588,true⟩,1,1,0⟩, +⟨⟨0,465,564,true⟩,564,1,3⟩, +⟨⟨1,588,465,true⟩,1,1,0⟩, +⟨⟨1,538,801,true⟩,1,1,0⟩, +⟨⟨0,344,459,true⟩,459,1,4⟩, +⟨⟨0,530,459,true⟩,459,1,4⟩, +⟨⟨0,533,459,true⟩,459,1,4⟩, +⟨⟨1,538,344,true⟩,1,1,0⟩, +⟨⟨1,538,530,true⟩,1,1,0⟩, +⟨⟨1,538,533,true⟩,1,1,0⟩, +⟨⟨0,633,563,true⟩,563,1,3⟩, +⟨⟨1,801,633,true⟩,1,1,0⟩, +⟨⟨1,938,585,true⟩,1,1,0⟩, +⟨⟨0,463,562,true⟩,562,1,3⟩, +⟨⟨1,585,463,true⟩,1,1,0⟩, +⟨⟨1,542,800,true⟩,1,1,0⟩, +⟨⟨1,542,344,true⟩,1,1,0⟩, +⟨⟨1,542,533,true⟩,1,1,0⟩, +⟨⟨0,632,561,true⟩,561,1,3⟩, +⟨⟨1,800,632,true⟩,1,1,0⟩, +⟨⟨1,937,584,true⟩,1,1,0⟩, +⟨⟨0,449,560,true⟩,560,1,3⟩, +⟨⟨1,584,449,true⟩,1,1,0⟩, +⟨⟨1,476,799,true⟩,1,1,0⟩, +⟨⟨0,813,559,true⟩,559,1,3⟩, +⟨⟨1,799,813,true⟩,1,1,0⟩, +⟨⟨1,702,798,true⟩,1,1,0⟩, +⟨⟨0,473,469,true⟩,469,1,4⟩, +⟨⟨0,690,469,true⟩,469,1,4⟩, +⟨⟨0,693,469,true⟩,469,1,4⟩, +⟨⟨1,702,473,true⟩,1,1,0⟩, +⟨⟨1,702,690,true⟩,1,1,0⟩, +⟨⟨1,702,693,true⟩,1,1,0⟩, +⟨⟨0,812,558,true⟩,558,1,3⟩, +⟨⟨1,798,812,true⟩,1,1,0⟩, +⟨⟨1,936,797,true⟩,1,1,0⟩, +⟨⟨0,825,557,true⟩,557,1,3⟩, +⟨⟨1,797,825,true⟩,1,1,0⟩, +⟨⟨1,710,796,true⟩,1,1,0⟩, +⟨⟨0,824,556,true⟩,556,1,3⟩, +⟨⟨1,796,824,true⟩,1,1,0⟩, +⟨⟨1,522,791,true⟩,1,1,0⟩, +⟨⟨1,522,409,true⟩,1,1,0⟩, +⟨⟨1,522,517,true⟩,1,1,0⟩, +⟨⟨0,659,555,true⟩,555,1,3⟩, +⟨⟨1,791,659,true⟩,1,1,0⟩, +⟨⟨0,563,911,true⟩,911,1,1⟩, +⟨⟨0,388,554,true⟩,554,1,3⟩, +⟨⟨1,563,388,true⟩,1,1,0⟩, +⟨⟨1,402,790,true⟩,1,1,0⟩, +⟨⟨1,402,409,true⟩,1,1,0⟩, +⟨⟨1,402,514,true⟩,1,1,0⟩, +⟨⟨0,657,553,true⟩,553,1,3⟩, +⟨⟨1,790,657,true⟩,1,1,0⟩, +⟨⟨0,561,753,true⟩,753,1,2⟩, +⟨⟨0,384,552,true⟩,552,1,3⟩, +⟨⟨1,561,384,true⟩,1,1,0⟩, +⟨⟨1,341,789,true⟩,1,1,0⟩, +⟨⟨1,341,344,true⟩,1,1,0⟩, +⟨⟨1,341,530,true⟩,1,1,0⟩, +⟨⟨0,649,551,true⟩,551,1,3⟩, +⟨⟨1,789,649,true⟩,1,1,0⟩, +⟨⟨1,935,569,true⟩,1,1,0⟩, +⟨⟨0,452,550,true⟩,550,1,3⟩, +⟨⟨1,569,452,true⟩,1,1,0⟩, +⟨⟨1,543,788,true⟩,1,1,0⟩, +⟨⟨0,343,549,true⟩,549,1,3⟩, +⟨⟨1,543,343,true⟩,1,1,0⟩, +⟨⟨0,648,549,true⟩,549,1,3⟩, +⟨⟨1,788,648,true⟩,1,1,0⟩, +⟨⟨1,934,568,true⟩,1,1,0⟩, +⟨⟨0,458,548,true⟩,548,1,3⟩, +⟨⟨1,568,458,true⟩,1,1,0⟩, +⟨⟨1,325,787,true⟩,1,1,0⟩, +⟨⟨1,325,328,true⟩,1,1,0⟩, +⟨⟨1,325,546,true⟩,1,1,0⟩, +⟨⟨0,637,547,true⟩,547,1,3⟩, +⟨⟨1,787,637,true⟩,1,1,0⟩, +⟨⟨1,933,573,true⟩,1,1,0⟩, +⟨⟨0,468,546,true⟩,546,1,3⟩, +⟨⟨1,573,468,true⟩,1,1,0⟩, +⟨⟨1,550,786,true⟩,1,1,0⟩, +⟨⟨0,548,460,true⟩,460,1,4⟩, +⟨⟨1,550,548,true⟩,1,1,0⟩, +⟨⟨1,550,549,true⟩,1,1,0⟩, +⟨⟨0,636,545,true⟩,545,1,3⟩, +⟨⟨1,786,636,true⟩,1,1,0⟩, +⟨⟨1,932,572,true⟩,1,1,0⟩, +⟨⟨0,474,544,true⟩,544,1,3⟩, +⟨⟨1,572,474,true⟩,1,1,0⟩, +⟨⟨1,698,785,true⟩,1,1,0⟩, +⟨⟨1,698,473,true⟩,1,1,0⟩, +⟨⟨1,698,693,true⟩,1,1,0⟩, +⟨⟨0,827,543,true⟩,543,1,3⟩, +⟨⟨1,785,827,true⟩,1,1,0⟩, +⟨⟨1,466,784,true⟩,1,1,0⟩, +⟨⟨1,466,473,true⟩,1,1,0⟩, +⟨⟨1,466,690,true⟩,1,1,0⟩, +⟨⟨0,826,542,true⟩,542,1,3⟩, +⟨⟨1,784,826,true⟩,1,1,0⟩, +⟨⟨1,718,783,true⟩,1,1,0⟩, +⟨⟨0,706,470,true⟩,470,1,4⟩, +⟨⟨0,714,470,true⟩,470,1,4⟩, +⟨⟨1,718,706,true⟩,1,1,0⟩, +⟨⟨1,718,714,true⟩,1,1,0⟩, +⟨⟨1,783,811,true⟩,1,1,0⟩, +⟨⟨1,709,782,true⟩,1,1,0⟩, +⟨⟨0,457,470,true⟩,470,1,4⟩, +⟨⟨1,709,457,true⟩,1,1,0⟩, +⟨⟨1,709,714,true⟩,1,1,0⟩, +⟨⟨1,782,810,true⟩,1,1,0⟩, +⟨⟨1,386,781,true⟩,1,1,0⟩, +⟨⟨1,386,393,true⟩,1,1,0⟩, +⟨⟨1,386,722,true⟩,1,1,0⟩, +⟨⟨0,795,539,true⟩,539,1,3⟩, +⟨⟨1,781,795,true⟩,1,1,0⟩, +⟨⟨1,726,779,true⟩,1,1,0⟩, +⟨⟨0,724,471,true⟩,471,1,4⟩, +⟨⟨1,726,724,true⟩,1,1,0⟩, +⟨⟨1,726,725,true⟩,1,1,0⟩, +⟨⟨0,793,538,true⟩,538,1,3⟩, +⟨⟨1,779,793,true⟩,1,1,0⟩, +⟨⟨0,777,887,true⟩,887,1,1⟩, +⟨⟨0,707,537,true⟩,537,1,3⟩, +⟨⟨1,777,707,true⟩,1,1,0⟩, +⟨⟨0,547,919,true⟩,919,1,1⟩, +⟨⟨0,723,536,true⟩,536,1,3⟩, +⟨⟨1,547,723,true⟩,1,1,0⟩, +⟨⟨0,776,801,true⟩,801,1,2⟩, +⟨⟨0,705,535,true⟩,535,1,3⟩, +⟨⟨1,776,705,true⟩,1,1,0⟩, +⟨⟨0,545,789,true⟩,789,1,2⟩, +⟨⟨0,721,534,true⟩,534,1,3⟩, +⟨⟨1,545,721,true⟩,1,1,0⟩, +⟨⟨1,590,775,true⟩,1,1,0⟩, +⟨⟨0,361,462,true⟩,462,1,4⟩, +⟨⟨0,578,462,true⟩,462,1,4⟩, +⟨⟨0,581,462,true⟩,462,1,4⟩, +⟨⟨1,590,361,true⟩,1,1,0⟩] +def chunk86 : List Entry := [⟨⟨1,590,578,true⟩,1,1,0⟩, +⟨⟨1,590,581,true⟩,1,1,0⟩, +⟨⟨0,371,533,true⟩,533,1,3⟩, +⟨⟨1,775,371,true⟩,1,1,0⟩, +⟨⟨1,422,557,true⟩,1,1,0⟩, +⟨⟨0,447,532,true⟩,532,1,3⟩, +⟨⟨1,557,447,true⟩,1,1,0⟩, +⟨⟨1,586,774,true⟩,1,1,0⟩, +⟨⟨1,586,361,true⟩,1,1,0⟩, +⟨⟨1,586,581,true⟩,1,1,0⟩, +⟨⟨0,381,531,true⟩,531,1,3⟩, +⟨⟨1,774,381,true⟩,1,1,0⟩, +⟨⟨1,602,556,true⟩,1,1,0⟩, +⟨⟨0,424,463,true⟩,463,1,4⟩, +⟨⟨0,594,463,true⟩,463,1,4⟩, +⟨⟨0,597,463,true⟩,463,1,4⟩, +⟨⟨1,602,424,true⟩,1,1,0⟩, +⟨⟨1,602,594,true⟩,1,1,0⟩, +⟨⟨1,602,597,true⟩,1,1,0⟩, +⟨⟨0,433,530,true⟩,530,1,3⟩, +⟨⟨1,556,433,true⟩,1,1,0⟩, +⟨⟨1,310,773,true⟩,1,1,0⟩, +⟨⟨0,303,529,true⟩,529,1,3⟩, +⟨⟨1,773,303,true⟩,1,1,0⟩, +⟨⟨1,618,553,true⟩,1,1,0⟩, +⟨⟨0,504,464,true⟩,464,1,4⟩, +⟨⟨0,610,464,true⟩,464,1,4⟩, +⟨⟨0,613,464,true⟩,464,1,4⟩, +⟨⟨1,618,504,true⟩,1,1,0⟩, +⟨⟨1,618,610,true⟩,1,1,0⟩, +⟨⟨1,618,613,true⟩,1,1,0⟩, +⟨⟨0,495,528,true⟩,528,1,3⟩, +⟨⟨1,553,495,true⟩,1,1,0⟩, +⟨⟨1,570,772,true⟩,1,1,0⟩, +⟨⟨0,312,461,true⟩,461,1,4⟩, +⟨⟨0,562,461,true⟩,461,1,4⟩, +⟨⟨0,565,461,true⟩,461,1,4⟩, +⟨⟨1,570,312,true⟩,1,1,0⟩, +⟨⟨1,570,562,true⟩,1,1,0⟩, +⟨⟨1,570,565,true⟩,1,1,0⟩, +⟨⟨0,301,527,true⟩,527,1,3⟩, +⟨⟨1,772,301,true⟩,1,1,0⟩, +⟨⟨1,622,552,true⟩,1,1,0⟩, +⟨⟨1,622,504,true⟩,1,1,0⟩, +⟨⟨1,622,613,true⟩,1,1,0⟩, +⟨⟨0,481,526,true⟩,526,1,3⟩, +⟨⟨1,552,481,true⟩,1,1,0⟩, +⟨⟨1,374,771,true⟩,1,1,0⟩, +⟨⟨0,367,525,true⟩,525,1,3⟩, +⟨⟨1,771,367,true⟩,1,1,0⟩, +⟨⟨1,444,323,true⟩,1,1,0⟩, +⟨⟨0,419,524,true⟩,524,1,3⟩, +⟨⟨1,323,419,true⟩,1,1,0⟩, +⟨⟨1,650,770,true⟩,1,1,0⟩, +⟨⟨0,376,466,true⟩,466,1,4⟩, +⟨⟨0,642,466,true⟩,466,1,4⟩, +⟨⟨0,645,466,true⟩,466,1,4⟩, +⟨⟨1,650,376,true⟩,1,1,0⟩, +⟨⟨1,650,642,true⟩,1,1,0⟩, +⟨⟨1,650,645,true⟩,1,1,0⟩, +⟨⟨0,365,523,true⟩,523,1,3⟩, +⟨⟨1,770,365,true⟩,1,1,0⟩, +⟨⟨1,670,333,true⟩,1,1,0⟩, +⟨⟨0,441,467,true⟩,467,1,4⟩, +⟨⟨0,658,467,true⟩,467,1,4⟩, +⟨⟨0,661,467,true⟩,467,1,4⟩, +⟨⟨1,670,441,true⟩,1,1,0⟩, +⟨⟨1,670,658,true⟩,1,1,0⟩, +⟨⟨1,670,661,true⟩,1,1,0⟩, +⟨⟨0,429,522,true⟩,522,1,3⟩, +⟨⟨1,333,429,true⟩,1,1,0⟩, +⟨⟨1,294,769,true⟩,1,1,0⟩, +⟨⟨0,307,521,true⟩,521,1,3⟩, +⟨⟨1,769,307,true⟩,1,1,0⟩, +⟨⟨1,492,334,true⟩,1,1,0⟩, +⟨⟨0,499,520,true⟩,520,1,3⟩, +⟨⟨1,334,499,true⟩,1,1,0⟩, +⟨⟨1,638,768,true⟩,1,1,0⟩, +⟨⟨0,297,465,true⟩,465,1,4⟩, +⟨⟨0,626,465,true⟩,465,1,4⟩, +⟨⟨0,629,465,true⟩,465,1,4⟩, +⟨⟨1,638,297,true⟩,1,1,0⟩, +⟨⟨1,638,626,true⟩,1,1,0⟩, +⟨⟨1,638,629,true⟩,1,1,0⟩, +⟨⟨0,317,519,true⟩,519,1,3⟩, +⟨⟨1,768,317,true⟩,1,1,0⟩, +⟨⟨1,686,320,true⟩,1,1,0⟩, +⟨⟨0,489,468,true⟩,468,1,4⟩, +⟨⟨0,674,468,true⟩,468,1,4⟩, +⟨⟨0,677,468,true⟩,468,1,4⟩, +⟨⟨1,686,489,true⟩,1,1,0⟩, +⟨⟨1,686,674,true⟩,1,1,0⟩, +⟨⟨1,686,677,true⟩,1,1,0⟩, +⟨⟨0,497,518,true⟩,518,1,3⟩, +⟨⟨1,320,497,true⟩,1,1,0⟩, +⟨⟨1,518,763,true⟩,1,1,0⟩, +⟨⟨0,516,458,true⟩,458,1,4⟩, +⟨⟨1,518,516,true⟩,1,1,0⟩, +⟨⟨1,518,517,true⟩,1,1,0⟩, +⟨⟨0,691,517,true⟩,517,1,3⟩, +⟨⟨1,763,691,true⟩,1,1,0⟩, +⟨⟨0,531,927,true⟩,927,1,1⟩, +⟨⟨0,920,516,true⟩,516,1,3⟩, +⟨⟨1,531,920,true⟩,1,1,0⟩, +⟨⟨1,527,762,true⟩,1,1,0⟩, +⟨⟨0,411,515,true⟩,515,1,3⟩, +⟨⟨1,527,411,true⟩,1,1,0⟩, +⟨⟨0,689,515,true⟩,515,1,3⟩, +⟨⟨1,762,689,true⟩,1,1,0⟩, +⟨⟨0,529,777,true⟩,777,1,2⟩, +⟨⟨0,918,514,true⟩,514,1,3⟩, +⟨⟨1,529,918,true⟩,1,1,0⟩, +⟨⟨1,574,761,true⟩,1,1,0⟩, +⟨⟨1,574,312,true⟩,1,1,0⟩, +⟨⟨1,574,565,true⟩,1,1,0⟩, +⟨⟨0,382,513,true⟩,513,1,3⟩, +⟨⟨1,761,382,true⟩,1,1,0⟩, +⟨⟨1,606,537,true⟩,1,1,0⟩, +⟨⟨1,606,424,true⟩,1,1,0⟩, +⟨⟨1,606,597,true⟩,1,1,0⟩, +⟨⟨0,484,512,true⟩,512,1,3⟩, +⟨⟨1,537,484,true⟩,1,1,0⟩, +⟨⟨1,309,760,true⟩,1,1,0⟩, +⟨⟨1,309,312,true⟩,1,1,0⟩, +⟨⟨1,309,562,true⟩,1,1,0⟩, +⟨⟨0,368,511,true⟩,511,1,3⟩, +⟨⟨1,760,368,true⟩,1,1,0⟩, +⟨⟨1,421,536,true⟩,1,1,0⟩, +⟨⟨1,421,424,true⟩,1,1,0⟩, +⟨⟨1,421,594,true⟩,1,1,0⟩, +⟨⟨0,490,510,true⟩,510,1,3⟩, +⟨⟨1,536,490,true⟩,1,1,0⟩, +⟨⟨1,354,759,true⟩,1,1,0⟩, +⟨⟨1,354,361,true⟩,1,1,0⟩, +⟨⟨1,354,578,true⟩,1,1,0⟩, +⟨⟨0,292,509,true⟩,509,1,3⟩, +⟨⟨1,759,292,true⟩,1,1,0⟩, +⟨⟨1,501,541,true⟩,1,1,0⟩, +⟨⟨1,501,504,true⟩,1,1,0⟩, +⟨⟨1,501,610,true⟩,1,1,0⟩, +⟨⟨0,436,508,true⟩,508,1,3⟩, +⟨⟨1,541,436,true⟩,1,1,0⟩, +⟨⟨1,582,758,true⟩,1,1,0⟩, +⟨⟨0,580,462,true⟩,462,1,4⟩, +⟨⟨1,582,580,true⟩,1,1,0⟩, +⟨⟨1,582,581,true⟩,1,1,0⟩, +⟨⟨0,288,507,true⟩,507,1,3⟩, +⟨⟨1,758,288,true⟩,1,1,0⟩, +⟨⟨1,614,540,true⟩,1,1,0⟩, +⟨⟨0,612,464,true⟩,464,1,4⟩, +⟨⟨1,614,612,true⟩,1,1,0⟩, +⟨⟨1,614,613,true⟩,1,1,0⟩, +⟨⟨0,442,506,true⟩,506,1,3⟩, +⟨⟨1,540,442,true⟩,1,1,0⟩, +⟨⟨1,634,757,true⟩,1,1,0⟩, +⟨⟨1,634,297,true⟩,1,1,0⟩, +⟨⟨1,634,629,true⟩,1,1,0⟩, +⟨⟨0,356,505,true⟩,505,1,3⟩, +⟨⟨1,757,356,true⟩,1,1,0⟩, +⟨⟨1,666,339,true⟩,1,1,0⟩, +⟨⟨1,666,441,true⟩,1,1,0⟩, +⟨⟨1,666,661,true⟩,1,1,0⟩, +⟨⟨0,510,504,true⟩,504,1,3⟩, +⟨⟨1,339,510,true⟩,1,1,0⟩, +⟨⟨1,290,756,true⟩,1,1,0⟩, +⟨⟨1,290,297,true⟩,1,1,0⟩, +⟨⟨1,290,626,true⟩,1,1,0⟩, +⟨⟨0,352,503,true⟩,503,1,3⟩, +⟨⟨1,756,352,true⟩,1,1,0⟩, +⟨⟨1,434,337,true⟩,1,1,0⟩, +⟨⟨1,434,441,true⟩,1,1,0⟩, +⟨⟨1,434,658,true⟩,1,1,0⟩, +⟨⟨0,506,502,true⟩,502,1,3⟩, +⟨⟨1,337,506,true⟩,1,1,0⟩, +⟨⟨1,654,755,true⟩,1,1,0⟩, +⟨⟨1,654,376,true⟩,1,1,0⟩, +⟨⟨1,654,645,true⟩,1,1,0⟩, +⟨⟨0,318,501,true⟩,501,1,3⟩, +⟨⟨1,755,318,true⟩,1,1,0⟩, +⟨⟨1,682,350,true⟩,1,1,0⟩, +⟨⟨1,682,489,true⟩,1,1,0⟩, +⟨⟨1,682,677,true⟩,1,1,0⟩, +⟨⟨0,430,500,true⟩,500,1,3⟩, +⟨⟨1,350,430,true⟩,1,1,0⟩, +⟨⟨1,373,754,true⟩,1,1,0⟩, +⟨⟨1,373,376,true⟩,1,1,0⟩, +⟨⟨1,373,642,true⟩,1,1,0⟩, +⟨⟨0,304,499,true⟩,499,1,3⟩, +⟨⟨1,754,304,true⟩,1,1,0⟩, +⟨⟨1,482,346,true⟩,1,1,0⟩, +⟨⟨1,482,489,true⟩,1,1,0⟩, +⟨⟨1,482,674,true⟩,1,1,0⟩, +⟨⟨0,416,498,true⟩,498,1,3⟩, +⟨⟨1,346,416,true⟩,1,1,0⟩, +⟨⟨1,735,753,true⟩,1,1,0⟩, +⟨⟨0,395,497,true⟩,497,1,3⟩, +⟨⟨1,735,395,true⟩,1,1,0⟩, +⟨⟨0,767,497,true⟩,497,1,3⟩, +⟨⟨1,753,767,true⟩,1,1,0⟩, +⟨⟨1,731,751,true⟩,1,1,0⟩] +def chunk87 : List Entry := [⟨⟨0,390,496,true⟩,496,1,3⟩, +⟨⟨1,731,390,true⟩,1,1,0⟩, +⟨⟨0,765,496,true⟩,496,1,3⟩, +⟨⟨1,751,765,true⟩,1,1,0⟩, +⟨⟨1,539,749,true⟩,1,1,0⟩, +⟨⟨0,348,495,true⟩,495,1,3⟩, +⟨⟨1,539,348,true⟩,1,1,0⟩, +⟨⟨0,892,495,true⟩,495,1,3⟩, +⟨⟨1,749,892,true⟩,1,1,0⟩, +⟨⟨1,559,515,true⟩,1,1,0⟩, +⟨⟨0,331,494,true⟩,494,1,3⟩, +⟨⟨1,559,331,true⟩,1,1,0⟩, +⟨⟨0,906,494,true⟩,494,1,3⟩, +⟨⟨1,515,906,true⟩,1,1,0⟩, +⟨⟨1,535,748,true⟩,1,1,0⟩, +⟨⟨0,534,493,true⟩,493,1,3⟩, +⟨⟨1,535,534,true⟩,1,1,0⟩, +⟨⟨0,890,493,true⟩,493,1,3⟩, +⟨⟨1,748,890,true⟩,1,1,0⟩, +⟨⟨1,555,513,true⟩,1,1,0⟩, +⟨⟨0,326,492,true⟩,492,1,3⟩, +⟨⟨1,555,326,true⟩,1,1,0⟩, +⟨⟨0,904,492,true⟩,492,1,3⟩, +⟨⟨1,513,904,true⟩,1,1,0⟩, +⟨⟨1,566,747,true⟩,1,1,0⟩, +⟨⟨0,564,461,true⟩,461,1,4⟩, +⟨⟨1,566,564,true⟩,1,1,0⟩, +⟨⟨1,566,565,true⟩,1,1,0⟩, +⟨⟨0,864,491,true⟩,491,1,3⟩, +⟨⟨1,747,864,true⟩,1,1,0⟩, +⟨⟨1,591,521,true⟩,1,1,0⟩, +⟨⟨0,363,490,true⟩,490,1,3⟩, +⟨⟨1,591,363,true⟩,1,1,0⟩, +⟨⟨0,878,490,true⟩,490,1,3⟩, +⟨⟨1,521,878,true⟩,1,1,0⟩, +⟨⟨1,575,746,true⟩,1,1,0⟩, +⟨⟨0,315,489,true⟩,489,1,3⟩, +⟨⟨1,575,315,true⟩,1,1,0⟩, +⟨⟨0,862,489,true⟩,489,1,3⟩, +⟨⟨1,746,862,true⟩,1,1,0⟩, +⟨⟨1,587,520,true⟩,1,1,0⟩, +⟨⟨0,358,488,true⟩,488,1,3⟩, +⟨⟨1,587,358,true⟩,1,1,0⟩, +⟨⟨0,876,488,true⟩,488,1,3⟩, +⟨⟨1,520,876,true⟩,1,1,0⟩, +⟨⟨1,598,745,true⟩,1,1,0⟩, +⟨⟨0,596,463,true⟩,463,1,4⟩, +⟨⟨1,598,596,true⟩,1,1,0⟩, +⟨⟨1,598,597,true⟩,1,1,0⟩, +⟨⟨0,836,487,true⟩,487,1,3⟩, +⟨⟨1,745,836,true⟩,1,1,0⟩, +⟨⟨1,623,525,true⟩,1,1,0⟩, +⟨⟨0,503,486,true⟩,486,1,3⟩, +⟨⟨1,623,503,true⟩,1,1,0⟩, +⟨⟨0,850,486,true⟩,486,1,3⟩, +⟨⟨1,525,850,true⟩,1,1,0⟩, +⟨⟨1,607,744,true⟩,1,1,0⟩, +⟨⟨0,427,485,true⟩,485,1,3⟩, +⟨⟨1,607,427,true⟩,1,1,0⟩, +⟨⟨0,834,485,true⟩,485,1,3⟩, +⟨⟨1,744,834,true⟩,1,1,0⟩, +⟨⟨1,619,524,true⟩,1,1,0⟩, +⟨⟨0,508,484,true⟩,484,1,3⟩, +⟨⟨1,619,508,true⟩,1,1,0⟩, +⟨⟨0,848,484,true⟩,484,1,3⟩, +⟨⟨1,524,848,true⟩,1,1,0⟩, +⟨⟨1,630,743,true⟩,1,1,0⟩, +⟨⟨0,628,465,true⟩,465,1,4⟩, +⟨⟨1,630,628,true⟩,1,1,0⟩, +⟨⟨1,630,629,true⟩,1,1,0⟩, +⟨⟨0,808,483,true⟩,483,1,3⟩, +⟨⟨1,743,808,true⟩,1,1,0⟩, +⟨⟨1,646,415,true⟩,1,1,0⟩, +⟨⟨0,644,466,true⟩,466,1,4⟩, +⟨⟨1,646,644,true⟩,1,1,0⟩, +⟨⟨1,646,645,true⟩,1,1,0⟩, +⟨⟨0,822,482,true⟩,482,1,3⟩, +⟨⟨1,415,822,true⟩,1,1,0⟩, +⟨⟨1,639,742,true⟩,1,1,0⟩, +⟨⟨0,299,481,true⟩,481,1,3⟩, +⟨⟨1,639,299,true⟩,1,1,0⟩, +⟨⟨0,806,481,true⟩,481,1,3⟩, +⟨⟨1,742,806,true⟩,1,1,0⟩, +⟨⟨1,655,413,true⟩,1,1,0⟩, +⟨⟨0,379,480,true⟩,480,1,3⟩, +⟨⟨1,655,379,true⟩,1,1,0⟩, +⟨⟨0,820,480,true⟩,480,1,3⟩, +⟨⟨1,413,820,true⟩,1,1,0⟩, +⟨⟨1,662,741,true⟩,1,1,0⟩, +⟨⟨0,660,467,true⟩,467,1,4⟩, +⟨⟨1,662,660,true⟩,1,1,0⟩, +⟨⟨1,662,661,true⟩,1,1,0⟩, +⟨⟨0,780,479,true⟩,479,1,3⟩, +⟨⟨1,741,780,true⟩,1,1,0⟩, +⟨⟨1,678,404,true⟩,1,1,0⟩, +⟨⟨0,676,468,true⟩,468,1,4⟩, +⟨⟨1,678,676,true⟩,1,1,0⟩, +⟨⟨1,678,677,true⟩,1,1,0⟩, +⟨⟨0,794,478,true⟩,478,1,3⟩, +⟨⟨1,404,794,true⟩,1,1,0⟩, +⟨⟨1,671,740,true⟩,1,1,0⟩, +⟨⟨0,439,477,true⟩,477,1,3⟩, +⟨⟨1,671,439,true⟩,1,1,0⟩, +⟨⟨0,778,477,true⟩,477,1,3⟩, +⟨⟨1,740,778,true⟩,1,1,0⟩, +⟨⟨1,687,400,true⟩,1,1,0⟩, +⟨⟨0,487,476,true⟩,476,1,3⟩, +⟨⟨1,687,487,true⟩,1,1,0⟩, +⟨⟨0,792,476,true⟩,476,1,3⟩, +⟨⟨1,400,792,true⟩,1,1,0⟩, +⟨⟨1,694,739,true⟩,1,1,0⟩, +⟨⟨0,692,469,true⟩,469,1,4⟩, +⟨⟨1,694,692,true⟩,1,1,0⟩, +⟨⟨1,694,693,true⟩,1,1,0⟩, +⟨⟨0,752,475,true⟩,475,1,3⟩, +⟨⟨1,739,752,true⟩,1,1,0⟩, +⟨⟨1,450,738,true⟩,1,1,0⟩, +⟨⟨1,450,457,true⟩,1,1,0⟩, +⟨⟨1,450,706,true⟩,1,1,0⟩, +⟨⟨0,766,474,true⟩,474,1,3⟩, +⟨⟨1,738,766,true⟩,1,1,0⟩, +⟨⟨1,703,737,true⟩,1,1,0⟩, +⟨⟨0,471,473,true⟩,473,1,3⟩, +⟨⟨1,703,471,true⟩,1,1,0⟩, +⟨⟨0,750,473,true⟩,473,1,3⟩, +⟨⟨1,737,750,true⟩,1,1,0⟩, +⟨⟨1,719,736,true⟩,1,1,0⟩, +⟨⟨0,455,472,true⟩,472,1,3⟩, +⟨⟨1,719,455,true⟩,1,1,0⟩, +⟨⟨0,764,472,true⟩,472,1,3⟩, +⟨⟨1,736,764,true⟩,1,1,0⟩, +⟨⟨0,269,895,true⟩,895,1,1⟩, +⟨⟨0,287,471,true⟩,471,1,4⟩, +⟨⟨1,269,287,true⟩,1,1,0⟩, +⟨⟨0,281,471,true⟩,471,1,4⟩, +⟨⟨1,269,281,true⟩,1,1,0⟩, +⟨⟨0,275,471,true⟩,471,1,4⟩, +⟨⟨1,269,275,true⟩,1,1,0⟩, +⟨⟨1,269,720,true⟩,1,1,0⟩, +⟨⟨1,727,720,true⟩,1,1,0⟩, +⟨⟨1,727,726,true⟩,1,1,0⟩, +⟨⟨1,720,724,true⟩,1,1,0⟩, +⟨⟨0,257,863,true⟩,863,1,1⟩, +⟨⟨1,257,286,true⟩,1,1,0⟩, +⟨⟨1,257,280,true⟩,1,1,0⟩, +⟨⟨0,263,470,true⟩,470,1,4⟩, +⟨⟨1,257,263,true⟩,1,1,0⟩, +⟨⟨1,257,704,true⟩,1,1,0⟩, +⟨⟨1,715,704,true⟩,1,1,0⟩, +⟨⟨0,460,470,true⟩,470,1,4⟩, +⟨⟨1,715,460,true⟩,1,1,0⟩, +⟨⟨1,711,704,true⟩,1,1,0⟩, +⟨⟨1,710,455,true⟩,1,1,0⟩, +⟨⟨1,710,460,true⟩,1,1,0⟩, +⟨⟨1,711,710,true⟩,1,1,0⟩, +⟨⟨1,704,708,true⟩,1,1,0⟩, +⟨⟨0,256,855,true⟩,855,1,1⟩, +⟨⟨0,274,469,true⟩,469,1,4⟩, +⟨⟨1,256,274,true⟩,1,1,0⟩, +⟨⟨0,268,469,true⟩,469,1,4⟩, +⟨⟨1,256,268,true⟩,1,1,0⟩, +⟨⟨1,256,262,true⟩,1,1,0⟩, +⟨⟨1,256,688,true⟩,1,1,0⟩, +⟨⟨1,699,688,true⟩,1,1,0⟩, +⟨⟨1,476,471,true⟩,1,1,0⟩, +⟨⟨1,476,694,true⟩,1,1,0⟩, +⟨⟨1,699,476,true⟩,1,1,0⟩, +⟨⟨1,695,688,true⟩,1,1,0⟩, +⟨⟨1,695,694,true⟩,1,1,0⟩, +⟨⟨1,688,692,true⟩,1,1,0⟩, +⟨⟨0,251,847,true⟩,847,1,1⟩, +⟨⟨0,285,468,true⟩,468,1,4⟩, +⟨⟨1,251,285,true⟩,1,1,0⟩, +⟨⟨0,273,468,true⟩,468,1,4⟩, +⟨⟨1,251,273,true⟩,1,1,0⟩, +⟨⟨0,261,468,true⟩,468,1,4⟩, +⟨⟨1,251,261,true⟩,1,1,0⟩, +⟨⟨1,251,672,true⟩,1,1,0⟩, +⟨⟨1,683,672,true⟩,1,1,0⟩, +⟨⟨1,492,487,true⟩,1,1,0⟩, +⟨⟨1,492,678,true⟩,1,1,0⟩, +⟨⟨1,683,492,true⟩,1,1,0⟩, +⟨⟨1,679,672,true⟩,1,1,0⟩, +⟨⟨1,679,678,true⟩,1,1,0⟩, +⟨⟨1,672,676,true⟩,1,1,0⟩, +⟨⟨0,250,871,true⟩,871,1,1⟩, +⟨⟨0,279,467,true⟩,467,1,4⟩, +⟨⟨1,250,279,true⟩,1,1,0⟩, +⟨⟨0,267,467,true⟩,467,1,4⟩, +⟨⟨1,250,267,true⟩,1,1,0⟩, +⟨⟨0,260,467,true⟩,467,1,4⟩, +⟨⟨1,250,260,true⟩,1,1,0⟩, +⟨⟨1,250,656,true⟩,1,1,0⟩, +⟨⟨1,667,656,true⟩,1,1,0⟩, +⟨⟨1,444,439,true⟩,1,1,0⟩, +⟨⟨1,444,662,true⟩,1,1,0⟩, +⟨⟨1,667,444,true⟩,1,1,0⟩, +⟨⟨1,663,656,true⟩,1,1,0⟩, +⟨⟨1,663,662,true⟩,1,1,0⟩, +⟨⟨1,656,660,true⟩,1,1,0⟩] +def chunk88 : List Entry := [⟨⟨0,249,903,true⟩,903,1,1⟩, +⟨⟨1,249,278,true⟩,1,1,0⟩, +⟨⟨0,272,466,true⟩,466,1,4⟩, +⟨⟨1,249,272,true⟩,1,1,0⟩, +⟨⟨1,249,255,true⟩,1,1,0⟩, +⟨⟨1,249,640,true⟩,1,1,0⟩, +⟨⟨1,651,640,true⟩,1,1,0⟩, +⟨⟨1,374,379,true⟩,1,1,0⟩, +⟨⟨1,374,646,true⟩,1,1,0⟩, +⟨⟨1,651,374,true⟩,1,1,0⟩, +⟨⟨1,647,640,true⟩,1,1,0⟩, +⟨⟨1,647,646,true⟩,1,1,0⟩, +⟨⟨1,640,644,true⟩,1,1,0⟩, +⟨⟨0,248,943,true⟩,943,1,1⟩, +⟨⟨0,284,465,true⟩,465,1,4⟩, +⟨⟨1,248,284,true⟩,1,1,0⟩, +⟨⟨1,248,266,true⟩,1,1,0⟩, +⟨⟨0,254,465,true⟩,465,1,4⟩, +⟨⟨1,248,254,true⟩,1,1,0⟩, +⟨⟨1,248,624,true⟩,1,1,0⟩, +⟨⟨1,635,624,true⟩,1,1,0⟩, +⟨⟨1,294,299,true⟩,1,1,0⟩, +⟨⟨1,294,630,true⟩,1,1,0⟩, +⟨⟨1,635,294,true⟩,1,1,0⟩, +⟨⟨1,631,624,true⟩,1,1,0⟩, +⟨⟨1,631,630,true⟩,1,1,0⟩, +⟨⟨1,624,628,true⟩,1,1,0⟩, +⟨⟨0,245,839,true⟩,839,1,1⟩, +⟨⟨0,277,464,true⟩,464,1,4⟩, +⟨⟨1,245,277,true⟩,1,1,0⟩, +⟨⟨0,271,464,true⟩,464,1,4⟩, +⟨⟨1,245,271,true⟩,1,1,0⟩, +⟨⟨0,259,464,true⟩,464,1,4⟩, +⟨⟨1,245,259,true⟩,1,1,0⟩, +⟨⟨1,245,608,true⟩,1,1,0⟩, +⟨⟨1,615,608,true⟩,1,1,0⟩, +⟨⟨1,615,614,true⟩,1,1,0⟩, +⟨⟨1,608,612,true⟩,1,1,0⟩, +⟨⟨0,244,879,true⟩,879,1,1⟩, +⟨⟨0,283,463,true⟩,463,1,4⟩, +⟨⟨1,244,283,true⟩,1,1,0⟩, +⟨⟨1,244,265,true⟩,1,1,0⟩, +⟨⟨1,244,3,true⟩,1,1,0⟩, +⟨⟨1,244,592,true⟩,1,1,0⟩, +⟨⟨1,603,592,true⟩,1,1,0⟩, +⟨⟨1,422,427,true⟩,1,1,0⟩, +⟨⟨1,422,598,true⟩,1,1,0⟩, +⟨⟨1,603,422,true⟩,1,1,0⟩, +⟨⟨1,599,592,true⟩,1,1,0⟩, +⟨⟨1,599,598,true⟩,1,1,0⟩, +⟨⟨1,592,596,true⟩,1,1,0⟩, +⟨⟨0,243,911,true⟩,911,1,1⟩, +⟨⟨1,243,282,true⟩,1,1,0⟩, +⟨⟨0,270,462,true⟩,462,1,4⟩, +⟨⟨1,243,270,true⟩,1,1,0⟩, +⟨⟨1,243,253,true⟩,1,1,0⟩, +⟨⟨1,243,576,true⟩,1,1,0⟩, +⟨⟨1,583,576,true⟩,1,1,0⟩, +⟨⟨1,583,582,true⟩,1,1,0⟩, +⟨⟨1,576,580,true⟩,1,1,0⟩, +⟨⟨0,242,935,true⟩,935,1,1⟩, +⟨⟨1,242,276,true⟩,1,1,0⟩, +⟨⟨1,242,264,true⟩,1,1,0⟩, +⟨⟨1,242,2,true⟩,1,1,0⟩, +⟨⟨1,242,560,true⟩,1,1,0⟩, +⟨⟨1,571,560,true⟩,1,1,0⟩, +⟨⟨1,310,315,true⟩,1,1,0⟩, +⟨⟨1,310,566,true⟩,1,1,0⟩, +⟨⟨1,571,310,true⟩,1,1,0⟩, +⟨⟨1,567,560,true⟩,1,1,0⟩, +⟨⟨1,567,566,true⟩,1,1,0⟩, +⟨⟨1,560,564,true⟩,1,1,0⟩, +⟨⟨0,241,927,true⟩,927,1,1⟩, +⟨⟨1,241,7,true⟩,1,1,0⟩, +⟨⟨1,241,6,true⟩,1,1,0⟩, +⟨⟨0,247,460,true⟩,460,1,4⟩, +⟨⟨1,241,247,true⟩,1,1,0⟩, +⟨⟨1,241,544,true⟩,1,1,0⟩, +⟨⟨1,551,544,true⟩,1,1,0⟩, +⟨⟨1,551,550,true⟩,1,1,0⟩, +⟨⟨1,544,548,true⟩,1,1,0⟩, +⟨⟨0,240,919,true⟩,919,1,1⟩, +⟨⟨1,240,5,true⟩,1,1,0⟩, +⟨⟨1,240,4,true⟩,1,1,0⟩, +⟨⟨1,240,246,true⟩,1,1,0⟩, +⟨⟨1,240,528,true⟩,1,1,0⟩, +⟨⟨1,532,533,true⟩,1,1,0⟩, +⟨⟨1,532,534,true⟩,1,1,0⟩, +⟨⟨1,528,532,true⟩,1,1,0⟩, +⟨⟨0,523,887,true⟩,887,1,1⟩, +⟨⟨0,258,458,true⟩,458,1,4⟩, +⟨⟨1,523,258,true⟩,1,1,0⟩, +⟨⟨1,252,0,true⟩,1,1,0⟩, +⟨⟨1,252,1,true⟩,1,1,0⟩, +⟨⟨1,252,512,true⟩,1,1,0⟩, +⟨⟨1,252,523,true⟩,1,1,0⟩, +⟨⟨1,523,252,true⟩,1,1,0⟩, +⟨⟨1,523,1,true⟩,1,1,0⟩, +⟨⟨1,523,0,true⟩,1,1,0⟩, +⟨⟨1,523,512,true⟩,1,1,0⟩, +⟨⟨1,406,411,true⟩,1,1,0⟩, +⟨⟨1,406,518,true⟩,1,1,0⟩, +⟨⟨1,523,406,true⟩,1,1,0⟩, +⟨⟨1,519,512,true⟩,1,1,0⟩, +⟨⟨1,519,518,true⟩,1,1,0⟩, +⟨⟨1,512,516,true⟩,1,1,0⟩, +⟨⟨1,931,733,true⟩,1,1,0⟩, +⟨⟨1,733,735,true⟩,1,1,0⟩, +⟨⟨1,930,732,true⟩,1,1,0⟩, +⟨⟨1,732,734,true⟩,1,1,0⟩, +⟨⟨1,929,399,true⟩,1,1,0⟩, +⟨⟨1,399,395,true⟩,1,1,0⟩, +⟨⟨1,928,397,true⟩,1,1,0⟩, +⟨⟨1,397,393,true⟩,1,1,0⟩, +⟨⟨1,927,729,true⟩,1,1,0⟩, +⟨⟨1,729,731,true⟩,1,1,0⟩, +⟨⟨1,926,728,true⟩,1,1,0⟩, +⟨⟨1,728,730,true⟩,1,1,0⟩, +⟨⟨1,925,388,true⟩,1,1,0⟩, +⟨⟨1,388,390,true⟩,1,1,0⟩, +⟨⟨1,924,384,true⟩,1,1,0⟩, +⟨⟨1,384,386,true⟩,1,1,0⟩, +⟨⟨1,923,723,true⟩,1,1,0⟩, +⟨⟨1,723,727,true⟩,1,1,0⟩, +⟨⟨1,922,721,true⟩,1,1,0⟩, +⟨⟨1,721,725,true⟩,1,1,0⟩, +⟨⟨1,921,724,true⟩,1,1,0⟩, +⟨⟨1,920,724,true⟩,1,1,0⟩, +⟨⟨1,724,726,true⟩,1,1,0⟩, +⟨⟨1,919,720,true⟩,1,1,0⟩, +⟨⟨1,918,720,true⟩,1,1,0⟩, +⟨⟨1,720,722,true⟩,1,1,0⟩, +⟨⟨1,917,717,true⟩,1,1,0⟩, +⟨⟨1,717,719,true⟩,1,1,0⟩, +⟨⟨1,916,716,true⟩,1,1,0⟩, +⟨⟨1,716,718,true⟩,1,1,0⟩, +⟨⟨1,915,713,true⟩,1,1,0⟩, +⟨⟨1,713,715,true⟩,1,1,0⟩, +⟨⟨1,914,712,true⟩,1,1,0⟩, +⟨⟨1,712,714,true⟩,1,1,0⟩, +⟨⟨1,913,463,true⟩,1,1,0⟩, +⟨⟨1,463,455,true⟩,1,1,0⟩, +⟨⟨1,912,449,true⟩,1,1,0⟩, +⟨⟨1,449,457,true⟩,1,1,0⟩, +⟨⟨1,911,452,true⟩,1,1,0⟩, +⟨⟨1,452,460,true⟩,1,1,0⟩, +⟨⟨1,910,458,true⟩,1,1,0⟩, +⟨⟨1,458,450,true⟩,1,1,0⟩, +⟨⟨1,909,707,true⟩,1,1,0⟩, +⟨⟨1,707,711,true⟩,1,1,0⟩, +⟨⟨1,908,705,true⟩,1,1,0⟩, +⟨⟨1,705,709,true⟩,1,1,0⟩, +⟨⟨1,907,708,true⟩,1,1,0⟩, +⟨⟨1,906,708,true⟩,1,1,0⟩, +⟨⟨1,708,710,true⟩,1,1,0⟩, +⟨⟨1,905,704,true⟩,1,1,0⟩, +⟨⟨1,904,704,true⟩,1,1,0⟩, +⟨⟨1,704,706,true⟩,1,1,0⟩, +⟨⟨1,903,697,true⟩,1,1,0⟩, +⟨⟨1,697,699,true⟩,1,1,0⟩, +⟨⟨1,902,696,true⟩,1,1,0⟩, +⟨⟨1,696,698,true⟩,1,1,0⟩, +⟨⟨1,901,701,true⟩,1,1,0⟩, +⟨⟨1,701,703,true⟩,1,1,0⟩, +⟨⟨1,900,700,true⟩,1,1,0⟩, +⟨⟨1,700,702,true⟩,1,1,0⟩, +⟨⟨1,899,479,true⟩,1,1,0⟩, +⟨⟨1,479,471,true⟩,1,1,0⟩, +⟨⟨1,898,465,true⟩,1,1,0⟩, +⟨⟨1,465,473,true⟩,1,1,0⟩, +⟨⟨1,897,468,true⟩,1,1,0⟩, +⟨⟨1,468,476,true⟩,1,1,0⟩, +⟨⟨1,896,474,true⟩,1,1,0⟩, +⟨⟨1,474,466,true⟩,1,1,0⟩, +⟨⟨1,895,691,true⟩,1,1,0⟩, +⟨⟨1,691,695,true⟩,1,1,0⟩, +⟨⟨1,894,689,true⟩,1,1,0⟩, +⟨⟨1,689,693,true⟩,1,1,0⟩, +⟨⟨1,893,692,true⟩,1,1,0⟩, +⟨⟨1,892,692,true⟩,1,1,0⟩, +⟨⟨1,692,694,true⟩,1,1,0⟩, +⟨⟨1,891,688,true⟩,1,1,0⟩, +⟨⟨1,890,688,true⟩,1,1,0⟩, +⟨⟨1,688,690,true⟩,1,1,0⟩, +⟨⟨1,889,685,true⟩,1,1,0⟩, +⟨⟨1,685,687,true⟩,1,1,0⟩, +⟨⟨1,888,684,true⟩,1,1,0⟩, +⟨⟨1,684,686,true⟩,1,1,0⟩, +⟨⟨1,887,681,true⟩,1,1,0⟩, +⟨⟨1,681,683,true⟩,1,1,0⟩, +⟨⟨1,886,680,true⟩,1,1,0⟩, +⟨⟨1,680,682,true⟩,1,1,0⟩, +⟨⟨1,885,675,true⟩,1,1,0⟩, +⟨⟨1,675,679,true⟩,1,1,0⟩, +⟨⟨1,884,673,true⟩,1,1,0⟩, +⟨⟨1,673,677,true⟩,1,1,0⟩, +⟨⟨1,883,495,true⟩,1,1,0⟩, +⟨⟨1,495,487,true⟩,1,1,0⟩, +⟨⟨1,882,481,true⟩,1,1,0⟩, +⟨⟨1,481,489,true⟩,1,1,0⟩] +def chunk89 : List Entry := [⟨⟨1,881,484,true⟩,1,1,0⟩, +⟨⟨1,484,492,true⟩,1,1,0⟩, +⟨⟨1,880,490,true⟩,1,1,0⟩, +⟨⟨1,490,482,true⟩,1,1,0⟩, +⟨⟨1,879,676,true⟩,1,1,0⟩, +⟨⟨1,878,676,true⟩,1,1,0⟩, +⟨⟨1,676,678,true⟩,1,1,0⟩, +⟨⟨1,877,672,true⟩,1,1,0⟩, +⟨⟨1,876,672,true⟩,1,1,0⟩, +⟨⟨1,672,674,true⟩,1,1,0⟩, +⟨⟨1,875,665,true⟩,1,1,0⟩, +⟨⟨1,665,667,true⟩,1,1,0⟩, +⟨⟨1,874,664,true⟩,1,1,0⟩, +⟨⟨1,664,666,true⟩,1,1,0⟩, +⟨⟨1,873,669,true⟩,1,1,0⟩, +⟨⟨1,669,671,true⟩,1,1,0⟩, +⟨⟨1,872,668,true⟩,1,1,0⟩, +⟨⟨1,668,670,true⟩,1,1,0⟩, +⟨⟨1,871,659,true⟩,1,1,0⟩, +⟨⟨1,659,663,true⟩,1,1,0⟩, +⟨⟨1,870,657,true⟩,1,1,0⟩, +⟨⟨1,657,661,true⟩,1,1,0⟩, +⟨⟨1,869,447,true⟩,1,1,0⟩, +⟨⟨1,447,439,true⟩,1,1,0⟩, +⟨⟨1,868,433,true⟩,1,1,0⟩, +⟨⟨1,433,441,true⟩,1,1,0⟩, +⟨⟨1,867,436,true⟩,1,1,0⟩, +⟨⟨1,436,444,true⟩,1,1,0⟩, +⟨⟨1,866,442,true⟩,1,1,0⟩, +⟨⟨1,442,434,true⟩,1,1,0⟩, +⟨⟨1,865,660,true⟩,1,1,0⟩, +⟨⟨1,864,660,true⟩,1,1,0⟩, +⟨⟨1,660,662,true⟩,1,1,0⟩, +⟨⟨1,863,656,true⟩,1,1,0⟩, +⟨⟨1,862,656,true⟩,1,1,0⟩, +⟨⟨1,656,658,true⟩,1,1,0⟩, +⟨⟨1,861,643,true⟩,1,1,0⟩, +⟨⟨1,643,647,true⟩,1,1,0⟩, +⟨⟨1,860,641,true⟩,1,1,0⟩, +⟨⟨1,641,645,true⟩,1,1,0⟩, +⟨⟨1,859,653,true⟩,1,1,0⟩, +⟨⟨1,653,655,true⟩,1,1,0⟩, +⟨⟨1,858,652,true⟩,1,1,0⟩, +⟨⟨1,652,654,true⟩,1,1,0⟩, +⟨⟨1,857,649,true⟩,1,1,0⟩, +⟨⟨1,649,651,true⟩,1,1,0⟩, +⟨⟨1,856,648,true⟩,1,1,0⟩, +⟨⟨1,648,650,true⟩,1,1,0⟩, +⟨⟨1,855,371,true⟩,1,1,0⟩, +⟨⟨1,371,379,true⟩,1,1,0⟩, +⟨⟨1,854,381,true⟩,1,1,0⟩, +⟨⟨1,381,373,true⟩,1,1,0⟩, +⟨⟨1,853,382,true⟩,1,1,0⟩, +⟨⟨1,382,374,true⟩,1,1,0⟩, +⟨⟨1,852,368,true⟩,1,1,0⟩, +⟨⟨1,368,376,true⟩,1,1,0⟩, +⟨⟨1,851,644,true⟩,1,1,0⟩, +⟨⟨1,850,644,true⟩,1,1,0⟩, +⟨⟨1,644,646,true⟩,1,1,0⟩, +⟨⟨1,849,640,true⟩,1,1,0⟩, +⟨⟨1,848,640,true⟩,1,1,0⟩, +⟨⟨1,640,642,true⟩,1,1,0⟩, +⟨⟨1,847,627,true⟩,1,1,0⟩, +⟨⟨1,627,631,true⟩,1,1,0⟩, +⟨⟨1,846,625,true⟩,1,1,0⟩, +⟨⟨1,625,629,true⟩,1,1,0⟩, +⟨⟨1,845,633,true⟩,1,1,0⟩, +⟨⟨1,633,635,true⟩,1,1,0⟩, +⟨⟨1,844,632,true⟩,1,1,0⟩, +⟨⟨1,632,634,true⟩,1,1,0⟩, +⟨⟨1,843,637,true⟩,1,1,0⟩, +⟨⟨1,637,639,true⟩,1,1,0⟩, +⟨⟨1,842,636,true⟩,1,1,0⟩, +⟨⟨1,636,638,true⟩,1,1,0⟩, +⟨⟨1,841,303,true⟩,1,1,0⟩, +⟨⟨1,303,299,true⟩,1,1,0⟩, +⟨⟨1,840,301,true⟩,1,1,0⟩, +⟨⟨1,301,297,true⟩,1,1,0⟩, +⟨⟨1,839,292,true⟩,1,1,0⟩, +⟨⟨1,292,294,true⟩,1,1,0⟩, +⟨⟨1,838,288,true⟩,1,1,0⟩, +⟨⟨1,288,290,true⟩,1,1,0⟩, +⟨⟨1,837,628,true⟩,1,1,0⟩, +⟨⟨1,836,628,true⟩,1,1,0⟩, +⟨⟨1,628,630,true⟩,1,1,0⟩, +⟨⟨1,835,624,true⟩,1,1,0⟩, +⟨⟨1,834,624,true⟩,1,1,0⟩, +⟨⟨1,624,626,true⟩,1,1,0⟩, +⟨⟨1,833,621,true⟩,1,1,0⟩, +⟨⟨1,621,623,true⟩,1,1,0⟩, +⟨⟨1,832,620,true⟩,1,1,0⟩, +⟨⟨1,620,622,true⟩,1,1,0⟩, +⟨⟨1,831,617,true⟩,1,1,0⟩, +⟨⟨1,617,619,true⟩,1,1,0⟩, +⟨⟨1,830,616,true⟩,1,1,0⟩, +⟨⟨1,616,618,true⟩,1,1,0⟩, +⟨⟨1,829,611,true⟩,1,1,0⟩, +⟨⟨1,611,615,true⟩,1,1,0⟩, +⟨⟨1,828,609,true⟩,1,1,0⟩, +⟨⟨1,609,613,true⟩,1,1,0⟩, +⟨⟨1,827,499,true⟩,1,1,0⟩, +⟨⟨1,499,503,true⟩,1,1,0⟩, +⟨⟨1,826,497,true⟩,1,1,0⟩, +⟨⟨1,497,501,true⟩,1,1,0⟩, +⟨⟨1,825,510,true⟩,1,1,0⟩, +⟨⟨1,510,508,true⟩,1,1,0⟩, +⟨⟨1,824,506,true⟩,1,1,0⟩, +⟨⟨1,506,504,true⟩,1,1,0⟩, +⟨⟨1,823,612,true⟩,1,1,0⟩, +⟨⟨1,822,612,true⟩,1,1,0⟩, +⟨⟨1,612,614,true⟩,1,1,0⟩, +⟨⟨1,821,608,true⟩,1,1,0⟩, +⟨⟨1,820,608,true⟩,1,1,0⟩, +⟨⟨1,608,610,true⟩,1,1,0⟩, +⟨⟨1,819,601,true⟩,1,1,0⟩, +⟨⟨1,601,603,true⟩,1,1,0⟩, +⟨⟨1,818,600,true⟩,1,1,0⟩, +⟨⟨1,600,602,true⟩,1,1,0⟩, +⟨⟨1,817,605,true⟩,1,1,0⟩, +⟨⟨1,605,607,true⟩,1,1,0⟩, +⟨⟨1,816,604,true⟩,1,1,0⟩, +⟨⟨1,604,606,true⟩,1,1,0⟩, +⟨⟨1,815,595,true⟩,1,1,0⟩, +⟨⟨1,595,599,true⟩,1,1,0⟩, +⟨⟨1,814,593,true⟩,1,1,0⟩, +⟨⟨1,593,597,true⟩,1,1,0⟩, +⟨⟨1,813,419,true⟩,1,1,0⟩, +⟨⟨1,419,427,true⟩,1,1,0⟩, +⟨⟨1,812,429,true⟩,1,1,0⟩, +⟨⟨1,429,421,true⟩,1,1,0⟩, +⟨⟨1,811,430,true⟩,1,1,0⟩, +⟨⟨1,430,422,true⟩,1,1,0⟩, +⟨⟨1,810,416,true⟩,1,1,0⟩, +⟨⟨1,416,424,true⟩,1,1,0⟩, +⟨⟨1,809,596,true⟩,1,1,0⟩, +⟨⟨1,808,596,true⟩,1,1,0⟩, +⟨⟨1,596,598,true⟩,1,1,0⟩, +⟨⟨1,807,592,true⟩,1,1,0⟩, +⟨⟨1,806,592,true⟩,1,1,0⟩, +⟨⟨1,592,594,true⟩,1,1,0⟩, +⟨⟨1,805,579,true⟩,1,1,0⟩, +⟨⟨1,579,583,true⟩,1,1,0⟩, +⟨⟨1,804,577,true⟩,1,1,0⟩, +⟨⟨1,577,581,true⟩,1,1,0⟩, +⟨⟨1,803,589,true⟩,1,1,0⟩, +⟨⟨1,589,591,true⟩,1,1,0⟩, +⟨⟨1,802,588,true⟩,1,1,0⟩, +⟨⟨1,588,590,true⟩,1,1,0⟩, +⟨⟨1,801,585,true⟩,1,1,0⟩, +⟨⟨1,585,587,true⟩,1,1,0⟩, +⟨⟨1,800,584,true⟩,1,1,0⟩, +⟨⟨1,584,586,true⟩,1,1,0⟩, +⟨⟨1,799,367,true⟩,1,1,0⟩, +⟨⟨1,367,363,true⟩,1,1,0⟩, +⟨⟨1,798,365,true⟩,1,1,0⟩, +⟨⟨1,365,361,true⟩,1,1,0⟩, +⟨⟨1,797,356,true⟩,1,1,0⟩, +⟨⟨1,356,358,true⟩,1,1,0⟩, +⟨⟨1,796,352,true⟩,1,1,0⟩, +⟨⟨1,352,354,true⟩,1,1,0⟩, +⟨⟨1,795,580,true⟩,1,1,0⟩, +⟨⟨1,794,580,true⟩,1,1,0⟩, +⟨⟨1,580,582,true⟩,1,1,0⟩, +⟨⟨1,793,576,true⟩,1,1,0⟩, +⟨⟨1,792,576,true⟩,1,1,0⟩, +⟨⟨1,576,578,true⟩,1,1,0⟩, +⟨⟨1,791,563,true⟩,1,1,0⟩, +⟨⟨1,563,567,true⟩,1,1,0⟩, +⟨⟨1,790,561,true⟩,1,1,0⟩, +⟨⟨1,561,565,true⟩,1,1,0⟩, +⟨⟨1,789,569,true⟩,1,1,0⟩, +⟨⟨1,569,571,true⟩,1,1,0⟩, +⟨⟨1,788,568,true⟩,1,1,0⟩, +⟨⟨1,568,570,true⟩,1,1,0⟩, +⟨⟨1,787,573,true⟩,1,1,0⟩, +⟨⟨1,573,575,true⟩,1,1,0⟩, +⟨⟨1,786,572,true⟩,1,1,0⟩, +⟨⟨1,572,574,true⟩,1,1,0⟩, +⟨⟨1,785,307,true⟩,1,1,0⟩, +⟨⟨1,307,315,true⟩,1,1,0⟩, +⟨⟨1,784,317,true⟩,1,1,0⟩, +⟨⟨1,317,309,true⟩,1,1,0⟩, +⟨⟨1,783,318,true⟩,1,1,0⟩, +⟨⟨1,318,310,true⟩,1,1,0⟩, +⟨⟨1,782,304,true⟩,1,1,0⟩, +⟨⟨1,304,312,true⟩,1,1,0⟩, +⟨⟨1,781,564,true⟩,1,1,0⟩, +⟨⟨1,780,564,true⟩,1,1,0⟩, +⟨⟨1,564,566,true⟩,1,1,0⟩, +⟨⟨1,779,560,true⟩,1,1,0⟩, +⟨⟨1,778,560,true⟩,1,1,0⟩, +⟨⟨1,560,562,true⟩,1,1,0⟩, +⟨⟨1,777,547,true⟩,1,1,0⟩, +⟨⟨1,547,551,true⟩,1,1,0⟩, +⟨⟨1,776,545,true⟩,1,1,0⟩, +⟨⟨1,545,549,true⟩,1,1,0⟩, +⟨⟨1,775,557,true⟩,1,1,0⟩, +⟨⟨1,557,559,true⟩,1,1,0⟩, +⟨⟨1,774,556,true⟩,1,1,0⟩, +⟨⟨1,556,558,true⟩,1,1,0⟩] +def chunk90 : List Entry := [⟨⟨1,773,553,true⟩,1,1,0⟩, +⟨⟨1,553,555,true⟩,1,1,0⟩, +⟨⟨1,772,552,true⟩,1,1,0⟩, +⟨⟨1,552,554,true⟩,1,1,0⟩, +⟨⟨1,771,323,true⟩,1,1,0⟩, +⟨⟨1,323,331,true⟩,1,1,0⟩, +⟨⟨1,770,333,true⟩,1,1,0⟩, +⟨⟨1,333,325,true⟩,1,1,0⟩, +⟨⟨1,769,334,true⟩,1,1,0⟩, +⟨⟨1,334,326,true⟩,1,1,0⟩, +⟨⟨1,768,320,true⟩,1,1,0⟩, +⟨⟨1,320,328,true⟩,1,1,0⟩, +⟨⟨1,767,548,true⟩,1,1,0⟩, +⟨⟨1,766,548,true⟩,1,1,0⟩, +⟨⟨1,548,550,true⟩,1,1,0⟩, +⟨⟨1,765,544,true⟩,1,1,0⟩, +⟨⟨1,764,544,true⟩,1,1,0⟩, +⟨⟨1,544,546,true⟩,1,1,0⟩, +⟨⟨1,763,531,true⟩,1,1,0⟩, +⟨⟨1,531,535,true⟩,1,1,0⟩, +⟨⟨1,762,529,true⟩,1,1,0⟩, +⟨⟨1,529,533,true⟩,1,1,0⟩, +⟨⟨1,761,537,true⟩,1,1,0⟩, +⟨⟨1,537,539,true⟩,1,1,0⟩, +⟨⟨1,760,536,true⟩,1,1,0⟩, +⟨⟨1,536,538,true⟩,1,1,0⟩, +⟨⟨1,759,541,true⟩,1,1,0⟩, +⟨⟨1,541,543,true⟩,1,1,0⟩, +⟨⟨1,758,540,true⟩,1,1,0⟩, +⟨⟨1,540,542,true⟩,1,1,0⟩, +⟨⟨1,757,339,true⟩,1,1,0⟩, +⟨⟨1,339,343,true⟩,1,1,0⟩, +⟨⟨1,756,337,true⟩,1,1,0⟩, +⟨⟨1,337,341,true⟩,1,1,0⟩, +⟨⟨1,755,350,true⟩,1,1,0⟩, +⟨⟨1,350,348,true⟩,1,1,0⟩, +⟨⟨1,754,346,true⟩,1,1,0⟩, +⟨⟨1,346,344,true⟩,1,1,0⟩, +⟨⟨1,753,532,true⟩,1,1,0⟩, +⟨⟨1,752,532,true⟩,1,1,0⟩, +⟨⟨1,532,534,true⟩,1,1,0⟩, +⟨⟨1,751,528,true⟩,1,1,0⟩, +⟨⟨1,750,528,true⟩,1,1,0⟩, +⟨⟨1,528,530,true⟩,1,1,0⟩, +⟨⟨1,749,515,true⟩,1,1,0⟩, +⟨⟨1,515,519,true⟩,1,1,0⟩, +⟨⟨1,748,513,true⟩,1,1,0⟩, +⟨⟨1,513,517,true⟩,1,1,0⟩, +⟨⟨1,747,521,true⟩,1,1,0⟩, +⟨⟨1,521,523,true⟩,1,1,0⟩, +⟨⟨1,746,520,true⟩,1,1,0⟩, +⟨⟨1,520,522,true⟩,1,1,0⟩, +⟨⟨1,745,525,true⟩,1,1,0⟩, +⟨⟨1,525,527,true⟩,1,1,0⟩, +⟨⟨1,744,524,true⟩,1,1,0⟩, +⟨⟨1,524,526,true⟩,1,1,0⟩, +⟨⟨1,743,415,true⟩,1,1,0⟩, +⟨⟨1,415,411,true⟩,1,1,0⟩, +⟨⟨1,742,413,true⟩,1,1,0⟩, +⟨⟨1,413,409,true⟩,1,1,0⟩, +⟨⟨1,741,404,true⟩,1,1,0⟩, +⟨⟨1,404,406,true⟩,1,1,0⟩, +⟨⟨1,740,400,true⟩,1,1,0⟩, +⟨⟨1,400,402,true⟩,1,1,0⟩, +⟨⟨1,739,516,true⟩,1,1,0⟩, +⟨⟨1,738,516,true⟩,1,1,0⟩, +⟨⟨1,516,518,true⟩,1,1,0⟩, +⟨⟨1,737,512,true⟩,1,1,0⟩, +⟨⟨1,736,512,true⟩,1,1,0⟩, +⟨⟨1,512,514,true⟩,1,1,0⟩, +⟨⟨1,735,395,true⟩,1,1,0⟩, +⟨⟨1,395,391,true⟩,1,1,0⟩, +⟨⟨1,734,399,true⟩,1,1,0⟩, +⟨⟨1,399,387,true⟩,1,1,0⟩, +⟨⟨1,733,393,true⟩,1,1,0⟩, +⟨⟨1,393,389,true⟩,1,1,0⟩, +⟨⟨1,732,397,true⟩,1,1,0⟩, +⟨⟨1,397,385,true⟩,1,1,0⟩, +⟨⟨1,731,390,true⟩,1,1,0⟩, +⟨⟨1,390,396,true⟩,1,1,0⟩, +⟨⟨1,730,388,true⟩,1,1,0⟩, +⟨⟨1,388,398,true⟩,1,1,0⟩, +⟨⟨1,729,386,true⟩,1,1,0⟩, +⟨⟨1,386,392,true⟩,1,1,0⟩, +⟨⟨1,728,384,true⟩,1,1,0⟩, +⟨⟨1,384,394,true⟩,1,1,0⟩, +⟨⟨1,727,726,true⟩,1,1,0⟩, +⟨⟨1,726,62,true⟩,1,1,0⟩, +⟨⟨1,726,61,true⟩,1,1,0⟩, +⟨⟨1,725,724,true⟩,1,1,0⟩, +⟨⟨1,724,63,true⟩,1,1,0⟩, +⟨⟨1,724,60,true⟩,1,1,0⟩, +⟨⟨1,723,722,true⟩,1,1,0⟩, +⟨⟨1,722,58,true⟩,1,1,0⟩, +⟨⟨1,722,57,true⟩,1,1,0⟩, +⟨⟨1,721,720,true⟩,1,1,0⟩, +⟨⟨1,720,59,true⟩,1,1,0⟩, +⟨⟨1,720,56,true⟩,1,1,0⟩, +⟨⟨1,719,455,true⟩,1,1,0⟩, +⟨⟨1,455,459,true⟩,1,1,0⟩, +⟨⟨1,718,463,true⟩,1,1,0⟩, +⟨⟨1,463,451,true⟩,1,1,0⟩, +⟨⟨1,717,457,true⟩,1,1,0⟩, +⟨⟨1,457,453,true⟩,1,1,0⟩, +⟨⟨1,716,449,true⟩,1,1,0⟩, +⟨⟨1,449,461,true⟩,1,1,0⟩, +⟨⟨1,715,460,true⟩,1,1,0⟩, +⟨⟨1,460,454,true⟩,1,1,0⟩, +⟨⟨1,714,452,true⟩,1,1,0⟩, +⟨⟨1,452,462,true⟩,1,1,0⟩, +⟨⟨1,713,450,true⟩,1,1,0⟩, +⟨⟨1,450,456,true⟩,1,1,0⟩, +⟨⟨1,712,458,true⟩,1,1,0⟩, +⟨⟨1,458,448,true⟩,1,1,0⟩, +⟨⟨1,711,710,true⟩,1,1,0⟩, +⟨⟨1,710,94,true⟩,1,1,0⟩, +⟨⟨1,710,93,true⟩,1,1,0⟩, +⟨⟨1,709,708,true⟩,1,1,0⟩, +⟨⟨1,708,95,true⟩,1,1,0⟩, +⟨⟨1,708,92,true⟩,1,1,0⟩, +⟨⟨1,707,706,true⟩,1,1,0⟩, +⟨⟨1,706,90,true⟩,1,1,0⟩, +⟨⟨1,706,89,true⟩,1,1,0⟩, +⟨⟨1,705,704,true⟩,1,1,0⟩, +⟨⟨1,704,91,true⟩,1,1,0⟩, +⟨⟨1,704,88,true⟩,1,1,0⟩, +⟨⟨1,703,471,true⟩,1,1,0⟩, +⟨⟨1,471,475,true⟩,1,1,0⟩, +⟨⟨1,702,479,true⟩,1,1,0⟩, +⟨⟨1,479,467,true⟩,1,1,0⟩, +⟨⟨1,701,473,true⟩,1,1,0⟩, +⟨⟨1,473,469,true⟩,1,1,0⟩, +⟨⟨1,700,465,true⟩,1,1,0⟩, +⟨⟨1,465,477,true⟩,1,1,0⟩, +⟨⟨1,699,476,true⟩,1,1,0⟩, +⟨⟨1,476,470,true⟩,1,1,0⟩, +⟨⟨1,698,468,true⟩,1,1,0⟩, +⟨⟨1,468,478,true⟩,1,1,0⟩, +⟨⟨1,697,466,true⟩,1,1,0⟩, +⟨⟨1,466,472,true⟩,1,1,0⟩, +⟨⟨1,696,474,true⟩,1,1,0⟩, +⟨⟨1,474,464,true⟩,1,1,0⟩, +⟨⟨1,695,694,true⟩,1,1,0⟩, +⟨⟨1,694,102,true⟩,1,1,0⟩, +⟨⟨1,694,101,true⟩,1,1,0⟩, +⟨⟨1,693,692,true⟩,1,1,0⟩, +⟨⟨1,692,103,true⟩,1,1,0⟩, +⟨⟨1,692,100,true⟩,1,1,0⟩, +⟨⟨1,691,690,true⟩,1,1,0⟩, +⟨⟨1,690,98,true⟩,1,1,0⟩, +⟨⟨1,690,97,true⟩,1,1,0⟩, +⟨⟨1,689,688,true⟩,1,1,0⟩, +⟨⟨1,688,99,true⟩,1,1,0⟩, +⟨⟨1,688,96,true⟩,1,1,0⟩, +⟨⟨1,687,487,true⟩,1,1,0⟩, +⟨⟨1,487,491,true⟩,1,1,0⟩, +⟨⟨1,686,495,true⟩,1,1,0⟩, +⟨⟨1,495,483,true⟩,1,1,0⟩, +⟨⟨1,685,489,true⟩,1,1,0⟩, +⟨⟨1,489,485,true⟩,1,1,0⟩, +⟨⟨1,684,481,true⟩,1,1,0⟩, +⟨⟨1,481,493,true⟩,1,1,0⟩, +⟨⟨1,683,492,true⟩,1,1,0⟩, +⟨⟨1,492,486,true⟩,1,1,0⟩, +⟨⟨1,682,484,true⟩,1,1,0⟩, +⟨⟨1,484,494,true⟩,1,1,0⟩, +⟨⟨1,681,482,true⟩,1,1,0⟩, +⟨⟨1,482,488,true⟩,1,1,0⟩, +⟨⟨1,680,490,true⟩,1,1,0⟩, +⟨⟨1,490,480,true⟩,1,1,0⟩, +⟨⟨1,679,678,true⟩,1,1,0⟩, +⟨⟨1,678,110,true⟩,1,1,0⟩, +⟨⟨1,678,109,true⟩,1,1,0⟩, +⟨⟨1,677,676,true⟩,1,1,0⟩, +⟨⟨1,676,111,true⟩,1,1,0⟩, +⟨⟨1,676,108,true⟩,1,1,0⟩, +⟨⟨1,675,674,true⟩,1,1,0⟩, +⟨⟨1,674,106,true⟩,1,1,0⟩, +⟨⟨1,674,105,true⟩,1,1,0⟩, +⟨⟨1,673,672,true⟩,1,1,0⟩, +⟨⟨1,672,107,true⟩,1,1,0⟩, +⟨⟨1,672,104,true⟩,1,1,0⟩, +⟨⟨1,671,439,true⟩,1,1,0⟩, +⟨⟨1,439,443,true⟩,1,1,0⟩, +⟨⟨1,670,447,true⟩,1,1,0⟩, +⟨⟨1,447,435,true⟩,1,1,0⟩, +⟨⟨1,669,441,true⟩,1,1,0⟩, +⟨⟨1,441,437,true⟩,1,1,0⟩, +⟨⟨1,668,433,true⟩,1,1,0⟩, +⟨⟨1,433,445,true⟩,1,1,0⟩, +⟨⟨1,667,444,true⟩,1,1,0⟩, +⟨⟨1,444,438,true⟩,1,1,0⟩, +⟨⟨1,666,436,true⟩,1,1,0⟩, +⟨⟨1,436,446,true⟩,1,1,0⟩, +⟨⟨1,665,434,true⟩,1,1,0⟩, +⟨⟨1,434,440,true⟩,1,1,0⟩, +⟨⟨1,664,442,true⟩,1,1,0⟩, +⟨⟨1,442,432,true⟩,1,1,0⟩, +⟨⟨1,663,662,true⟩,1,1,0⟩, +⟨⟨1,662,86,true⟩,1,1,0⟩] +def chunk91 : List Entry := [⟨⟨1,662,85,true⟩,1,1,0⟩, +⟨⟨1,661,660,true⟩,1,1,0⟩, +⟨⟨1,660,87,true⟩,1,1,0⟩, +⟨⟨1,660,84,true⟩,1,1,0⟩, +⟨⟨1,659,658,true⟩,1,1,0⟩, +⟨⟨1,658,82,true⟩,1,1,0⟩, +⟨⟨1,658,81,true⟩,1,1,0⟩, +⟨⟨1,657,656,true⟩,1,1,0⟩, +⟨⟨1,656,83,true⟩,1,1,0⟩, +⟨⟨1,656,80,true⟩,1,1,0⟩, +⟨⟨1,655,379,true⟩,1,1,0⟩, +⟨⟨1,379,375,true⟩,1,1,0⟩, +⟨⟨1,654,371,true⟩,1,1,0⟩, +⟨⟨1,371,383,true⟩,1,1,0⟩, +⟨⟨1,653,373,true⟩,1,1,0⟩, +⟨⟨1,373,377,true⟩,1,1,0⟩, +⟨⟨1,652,381,true⟩,1,1,0⟩, +⟨⟨1,381,369,true⟩,1,1,0⟩, +⟨⟨1,651,374,true⟩,1,1,0⟩, +⟨⟨1,374,380,true⟩,1,1,0⟩, +⟨⟨1,650,382,true⟩,1,1,0⟩, +⟨⟨1,382,372,true⟩,1,1,0⟩, +⟨⟨1,649,376,true⟩,1,1,0⟩, +⟨⟨1,376,370,true⟩,1,1,0⟩, +⟨⟨1,648,368,true⟩,1,1,0⟩, +⟨⟨1,368,378,true⟩,1,1,0⟩, +⟨⟨1,647,646,true⟩,1,1,0⟩, +⟨⟨1,646,54,true⟩,1,1,0⟩, +⟨⟨1,646,53,true⟩,1,1,0⟩, +⟨⟨1,645,644,true⟩,1,1,0⟩, +⟨⟨1,644,55,true⟩,1,1,0⟩, +⟨⟨1,644,52,true⟩,1,1,0⟩, +⟨⟨1,643,642,true⟩,1,1,0⟩, +⟨⟨1,642,50,true⟩,1,1,0⟩, +⟨⟨1,642,49,true⟩,1,1,0⟩, +⟨⟨1,641,640,true⟩,1,1,0⟩, +⟨⟨1,640,51,true⟩,1,1,0⟩, +⟨⟨1,640,48,true⟩,1,1,0⟩, +⟨⟨1,639,299,true⟩,1,1,0⟩, +⟨⟨1,299,295,true⟩,1,1,0⟩, +⟨⟨1,638,303,true⟩,1,1,0⟩, +⟨⟨1,303,291,true⟩,1,1,0⟩, +⟨⟨1,637,297,true⟩,1,1,0⟩, +⟨⟨1,297,293,true⟩,1,1,0⟩, +⟨⟨1,636,301,true⟩,1,1,0⟩, +⟨⟨1,301,289,true⟩,1,1,0⟩, +⟨⟨1,635,294,true⟩,1,1,0⟩, +⟨⟨1,294,300,true⟩,1,1,0⟩, +⟨⟨1,634,292,true⟩,1,1,0⟩, +⟨⟨1,292,302,true⟩,1,1,0⟩, +⟨⟨1,633,290,true⟩,1,1,0⟩, +⟨⟨1,290,296,true⟩,1,1,0⟩, +⟨⟨1,632,288,true⟩,1,1,0⟩, +⟨⟨1,288,298,true⟩,1,1,0⟩, +⟨⟨1,631,630,true⟩,1,1,0⟩, +⟨⟨1,630,14,true⟩,1,1,0⟩, +⟨⟨1,630,13,true⟩,1,1,0⟩, +⟨⟨1,629,628,true⟩,1,1,0⟩, +⟨⟨1,628,15,true⟩,1,1,0⟩, +⟨⟨1,628,12,true⟩,1,1,0⟩, +⟨⟨1,627,626,true⟩,1,1,0⟩, +⟨⟨1,626,10,true⟩,1,1,0⟩, +⟨⟨1,626,9,true⟩,1,1,0⟩, +⟨⟨1,625,624,true⟩,1,1,0⟩, +⟨⟨1,624,11,true⟩,1,1,0⟩, +⟨⟨1,624,8,true⟩,1,1,0⟩, +⟨⟨1,623,503,true⟩,1,1,0⟩, +⟨⟨1,503,507,true⟩,1,1,0⟩, +⟨⟨1,622,499,true⟩,1,1,0⟩, +⟨⟨1,499,511,true⟩,1,1,0⟩, +⟨⟨1,621,501,true⟩,1,1,0⟩, +⟨⟨1,501,505,true⟩,1,1,0⟩, +⟨⟨1,620,497,true⟩,1,1,0⟩, +⟨⟨1,497,509,true⟩,1,1,0⟩, +⟨⟨1,619,508,true⟩,1,1,0⟩, +⟨⟨1,508,502,true⟩,1,1,0⟩, +⟨⟨1,618,510,true⟩,1,1,0⟩, +⟨⟨1,510,500,true⟩,1,1,0⟩, +⟨⟨1,617,504,true⟩,1,1,0⟩, +⟨⟨1,504,498,true⟩,1,1,0⟩, +⟨⟨1,616,506,true⟩,1,1,0⟩, +⟨⟨1,506,496,true⟩,1,1,0⟩, +⟨⟨1,615,614,true⟩,1,1,0⟩, +⟨⟨1,614,118,true⟩,1,1,0⟩, +⟨⟨1,614,117,true⟩,1,1,0⟩, +⟨⟨1,613,612,true⟩,1,1,0⟩, +⟨⟨1,612,119,true⟩,1,1,0⟩, +⟨⟨1,612,116,true⟩,1,1,0⟩, +⟨⟨1,611,610,true⟩,1,1,0⟩, +⟨⟨1,610,114,true⟩,1,1,0⟩, +⟨⟨1,610,113,true⟩,1,1,0⟩, +⟨⟨1,609,608,true⟩,1,1,0⟩, +⟨⟨1,608,115,true⟩,1,1,0⟩, +⟨⟨1,608,112,true⟩,1,1,0⟩, +⟨⟨1,607,427,true⟩,1,1,0⟩, +⟨⟨1,427,423,true⟩,1,1,0⟩, +⟨⟨1,606,419,true⟩,1,1,0⟩, +⟨⟨1,419,431,true⟩,1,1,0⟩, +⟨⟨1,605,421,true⟩,1,1,0⟩, +⟨⟨1,421,425,true⟩,1,1,0⟩, +⟨⟨1,604,429,true⟩,1,1,0⟩, +⟨⟨1,429,417,true⟩,1,1,0⟩, +⟨⟨1,603,422,true⟩,1,1,0⟩, +⟨⟨1,422,428,true⟩,1,1,0⟩, +⟨⟨1,602,430,true⟩,1,1,0⟩, +⟨⟨1,430,420,true⟩,1,1,0⟩, +⟨⟨1,601,424,true⟩,1,1,0⟩, +⟨⟨1,424,418,true⟩,1,1,0⟩, +⟨⟨1,600,416,true⟩,1,1,0⟩, +⟨⟨1,416,426,true⟩,1,1,0⟩, +⟨⟨1,599,598,true⟩,1,1,0⟩, +⟨⟨1,598,78,true⟩,1,1,0⟩, +⟨⟨1,598,77,true⟩,1,1,0⟩, +⟨⟨1,597,596,true⟩,1,1,0⟩, +⟨⟨1,596,79,true⟩,1,1,0⟩, +⟨⟨1,596,76,true⟩,1,1,0⟩, +⟨⟨1,595,594,true⟩,1,1,0⟩, +⟨⟨1,594,74,true⟩,1,1,0⟩, +⟨⟨1,594,73,true⟩,1,1,0⟩, +⟨⟨1,593,592,true⟩,1,1,0⟩, +⟨⟨1,592,75,true⟩,1,1,0⟩, +⟨⟨1,592,72,true⟩,1,1,0⟩, +⟨⟨1,591,363,true⟩,1,1,0⟩, +⟨⟨1,363,359,true⟩,1,1,0⟩, +⟨⟨1,590,367,true⟩,1,1,0⟩, +⟨⟨1,367,355,true⟩,1,1,0⟩, +⟨⟨1,589,361,true⟩,1,1,0⟩, +⟨⟨1,361,357,true⟩,1,1,0⟩, +⟨⟨1,588,365,true⟩,1,1,0⟩, +⟨⟨1,365,353,true⟩,1,1,0⟩, +⟨⟨1,587,358,true⟩,1,1,0⟩, +⟨⟨1,358,364,true⟩,1,1,0⟩, +⟨⟨1,586,356,true⟩,1,1,0⟩, +⟨⟨1,356,366,true⟩,1,1,0⟩, +⟨⟨1,585,354,true⟩,1,1,0⟩, +⟨⟨1,354,360,true⟩,1,1,0⟩, +⟨⟨1,584,352,true⟩,1,1,0⟩, +⟨⟨1,352,362,true⟩,1,1,0⟩, +⟨⟨1,583,582,true⟩,1,1,0⟩, +⟨⟨1,582,46,true⟩,1,1,0⟩, +⟨⟨1,582,45,true⟩,1,1,0⟩, +⟨⟨1,581,580,true⟩,1,1,0⟩, +⟨⟨1,580,47,true⟩,1,1,0⟩, +⟨⟨1,580,44,true⟩,1,1,0⟩, +⟨⟨1,579,578,true⟩,1,1,0⟩, +⟨⟨1,578,42,true⟩,1,1,0⟩, +⟨⟨1,578,41,true⟩,1,1,0⟩, +⟨⟨1,577,576,true⟩,1,1,0⟩, +⟨⟨1,576,43,true⟩,1,1,0⟩, +⟨⟨1,576,40,true⟩,1,1,0⟩, +⟨⟨1,575,315,true⟩,1,1,0⟩, +⟨⟨1,315,311,true⟩,1,1,0⟩, +⟨⟨1,574,307,true⟩,1,1,0⟩, +⟨⟨1,307,319,true⟩,1,1,0⟩, +⟨⟨1,573,309,true⟩,1,1,0⟩, +⟨⟨1,309,313,true⟩,1,1,0⟩, +⟨⟨1,572,317,true⟩,1,1,0⟩, +⟨⟨1,317,305,true⟩,1,1,0⟩, +⟨⟨1,571,310,true⟩,1,1,0⟩, +⟨⟨1,310,316,true⟩,1,1,0⟩, +⟨⟨1,570,318,true⟩,1,1,0⟩, +⟨⟨1,318,308,true⟩,1,1,0⟩, +⟨⟨1,569,312,true⟩,1,1,0⟩, +⟨⟨1,312,306,true⟩,1,1,0⟩, +⟨⟨1,568,304,true⟩,1,1,0⟩, +⟨⟨1,304,314,true⟩,1,1,0⟩, +⟨⟨1,567,566,true⟩,1,1,0⟩, +⟨⟨1,566,22,true⟩,1,1,0⟩, +⟨⟨1,566,21,true⟩,1,1,0⟩, +⟨⟨1,565,564,true⟩,1,1,0⟩, +⟨⟨1,564,23,true⟩,1,1,0⟩, +⟨⟨1,564,20,true⟩,1,1,0⟩, +⟨⟨1,563,562,true⟩,1,1,0⟩, +⟨⟨1,562,18,true⟩,1,1,0⟩, +⟨⟨1,562,17,true⟩,1,1,0⟩, +⟨⟨1,561,560,true⟩,1,1,0⟩, +⟨⟨1,560,19,true⟩,1,1,0⟩, +⟨⟨1,560,16,true⟩,1,1,0⟩, +⟨⟨1,559,331,true⟩,1,1,0⟩, +⟨⟨1,331,327,true⟩,1,1,0⟩, +⟨⟨1,558,323,true⟩,1,1,0⟩, +⟨⟨1,323,335,true⟩,1,1,0⟩, +⟨⟨1,557,325,true⟩,1,1,0⟩, +⟨⟨1,325,329,true⟩,1,1,0⟩, +⟨⟨1,556,333,true⟩,1,1,0⟩, +⟨⟨1,333,321,true⟩,1,1,0⟩, +⟨⟨1,555,326,true⟩,1,1,0⟩, +⟨⟨1,326,332,true⟩,1,1,0⟩, +⟨⟨1,554,334,true⟩,1,1,0⟩, +⟨⟨1,334,324,true⟩,1,1,0⟩, +⟨⟨1,553,328,true⟩,1,1,0⟩, +⟨⟨1,328,322,true⟩,1,1,0⟩, +⟨⟨1,552,320,true⟩,1,1,0⟩, +⟨⟨1,320,330,true⟩,1,1,0⟩, +⟨⟨1,551,550,true⟩,1,1,0⟩, +⟨⟨1,550,30,true⟩,1,1,0⟩, +⟨⟨1,550,29,true⟩,1,1,0⟩, +⟨⟨1,549,548,true⟩,1,1,0⟩, +⟨⟨1,548,31,true⟩,1,1,0⟩, +⟨⟨1,548,28,true⟩,1,1,0⟩] +def chunk92 : List Entry := [⟨⟨1,547,546,true⟩,1,1,0⟩, +⟨⟨1,546,26,true⟩,1,1,0⟩, +⟨⟨1,546,25,true⟩,1,1,0⟩, +⟨⟨1,545,544,true⟩,1,1,0⟩, +⟨⟨1,544,27,true⟩,1,1,0⟩, +⟨⟨1,544,24,true⟩,1,1,0⟩, +⟨⟨1,543,343,true⟩,1,1,0⟩, +⟨⟨1,343,347,true⟩,1,1,0⟩, +⟨⟨1,542,339,true⟩,1,1,0⟩, +⟨⟨1,339,351,true⟩,1,1,0⟩, +⟨⟨1,541,341,true⟩,1,1,0⟩, +⟨⟨1,341,345,true⟩,1,1,0⟩, +⟨⟨1,540,337,true⟩,1,1,0⟩, +⟨⟨1,337,349,true⟩,1,1,0⟩, +⟨⟨1,539,348,true⟩,1,1,0⟩, +⟨⟨1,348,342,true⟩,1,1,0⟩, +⟨⟨1,538,350,true⟩,1,1,0⟩, +⟨⟨1,350,340,true⟩,1,1,0⟩, +⟨⟨1,537,344,true⟩,1,1,0⟩, +⟨⟨1,344,338,true⟩,1,1,0⟩, +⟨⟨1,536,346,true⟩,1,1,0⟩, +⟨⟨1,346,336,true⟩,1,1,0⟩, +⟨⟨1,535,534,true⟩,1,1,0⟩, +⟨⟨1,534,38,true⟩,1,1,0⟩, +⟨⟨1,534,37,true⟩,1,1,0⟩, +⟨⟨1,533,532,true⟩,1,1,0⟩, +⟨⟨1,532,39,true⟩,1,1,0⟩, +⟨⟨1,532,36,true⟩,1,1,0⟩, +⟨⟨1,531,530,true⟩,1,1,0⟩, +⟨⟨1,530,34,true⟩,1,1,0⟩, +⟨⟨1,530,33,true⟩,1,1,0⟩, +⟨⟨1,529,528,true⟩,1,1,0⟩, +⟨⟨1,528,35,true⟩,1,1,0⟩, +⟨⟨1,528,32,true⟩,1,1,0⟩, +⟨⟨1,527,411,true⟩,1,1,0⟩, +⟨⟨1,411,407,true⟩,1,1,0⟩, +⟨⟨1,526,415,true⟩,1,1,0⟩, +⟨⟨1,415,403,true⟩,1,1,0⟩, +⟨⟨1,525,409,true⟩,1,1,0⟩, +⟨⟨1,409,405,true⟩,1,1,0⟩, +⟨⟨1,524,413,true⟩,1,1,0⟩, +⟨⟨1,413,401,true⟩,1,1,0⟩, +⟨⟨1,523,406,true⟩,1,1,0⟩, +⟨⟨1,406,412,true⟩,1,1,0⟩, +⟨⟨1,522,404,true⟩,1,1,0⟩, +⟨⟨1,404,414,true⟩,1,1,0⟩, +⟨⟨1,521,402,true⟩,1,1,0⟩, +⟨⟨1,402,408,true⟩,1,1,0⟩, +⟨⟨1,520,400,true⟩,1,1,0⟩, +⟨⟨1,400,410,true⟩,1,1,0⟩, +⟨⟨1,519,518,true⟩,1,1,0⟩, +⟨⟨1,518,70,true⟩,1,1,0⟩, +⟨⟨1,518,69,true⟩,1,1,0⟩, +⟨⟨1,517,516,true⟩,1,1,0⟩, +⟨⟨1,516,71,true⟩,1,1,0⟩, +⟨⟨1,516,68,true⟩,1,1,0⟩, +⟨⟨1,515,514,true⟩,1,1,0⟩, +⟨⟨1,514,66,true⟩,1,1,0⟩, +⟨⟨1,514,65,true⟩,1,1,0⟩, +⟨⟨1,513,512,true⟩,1,1,0⟩, +⟨⟨1,512,67,true⟩,1,1,0⟩, +⟨⟨1,512,64,true⟩,1,1,0⟩, +⟨⟨1,511,119,true⟩,1,1,0⟩, +⟨⟨1,510,119,true⟩,1,1,0⟩, +⟨⟨1,509,118,true⟩,1,1,0⟩, +⟨⟨1,508,118,true⟩,1,1,0⟩, +⟨⟨1,507,117,true⟩,1,1,0⟩, +⟨⟨1,506,117,true⟩,1,1,0⟩, +⟨⟨1,505,116,true⟩,1,1,0⟩, +⟨⟨1,504,116,true⟩,1,1,0⟩, +⟨⟨1,503,115,true⟩,1,1,0⟩, +⟨⟨1,502,115,true⟩,1,1,0⟩, +⟨⟨1,501,114,true⟩,1,1,0⟩, +⟨⟨1,500,114,true⟩,1,1,0⟩, +⟨⟨1,499,113,true⟩,1,1,0⟩, +⟨⟨1,498,113,true⟩,1,1,0⟩, +⟨⟨1,497,112,true⟩,1,1,0⟩, +⟨⟨1,496,112,true⟩,1,1,0⟩, +⟨⟨1,495,111,true⟩,1,1,0⟩, +⟨⟨1,494,111,true⟩,1,1,0⟩, +⟨⟨1,493,110,true⟩,1,1,0⟩, +⟨⟨1,492,110,true⟩,1,1,0⟩, +⟨⟨1,491,109,true⟩,1,1,0⟩, +⟨⟨1,490,109,true⟩,1,1,0⟩, +⟨⟨1,489,108,true⟩,1,1,0⟩, +⟨⟨1,488,108,true⟩,1,1,0⟩, +⟨⟨1,487,107,true⟩,1,1,0⟩, +⟨⟨1,486,107,true⟩,1,1,0⟩, +⟨⟨1,485,106,true⟩,1,1,0⟩, +⟨⟨1,484,106,true⟩,1,1,0⟩, +⟨⟨1,483,105,true⟩,1,1,0⟩, +⟨⟨1,482,105,true⟩,1,1,0⟩, +⟨⟨1,481,104,true⟩,1,1,0⟩, +⟨⟨1,480,104,true⟩,1,1,0⟩, +⟨⟨1,479,103,true⟩,1,1,0⟩, +⟨⟨1,478,103,true⟩,1,1,0⟩, +⟨⟨1,477,102,true⟩,1,1,0⟩, +⟨⟨1,476,102,true⟩,1,1,0⟩, +⟨⟨1,475,101,true⟩,1,1,0⟩, +⟨⟨1,474,101,true⟩,1,1,0⟩, +⟨⟨1,473,100,true⟩,1,1,0⟩, +⟨⟨1,472,100,true⟩,1,1,0⟩, +⟨⟨1,471,99,true⟩,1,1,0⟩, +⟨⟨1,470,99,true⟩,1,1,0⟩, +⟨⟨1,469,98,true⟩,1,1,0⟩, +⟨⟨1,468,98,true⟩,1,1,0⟩, +⟨⟨1,467,97,true⟩,1,1,0⟩, +⟨⟨1,466,97,true⟩,1,1,0⟩, +⟨⟨1,465,96,true⟩,1,1,0⟩, +⟨⟨1,464,96,true⟩,1,1,0⟩, +⟨⟨1,463,95,true⟩,1,1,0⟩, +⟨⟨1,462,95,true⟩,1,1,0⟩, +⟨⟨1,461,94,true⟩,1,1,0⟩, +⟨⟨1,460,94,true⟩,1,1,0⟩, +⟨⟨1,459,93,true⟩,1,1,0⟩, +⟨⟨1,458,93,true⟩,1,1,0⟩, +⟨⟨1,457,92,true⟩,1,1,0⟩, +⟨⟨1,456,92,true⟩,1,1,0⟩, +⟨⟨1,455,91,true⟩,1,1,0⟩, +⟨⟨1,454,91,true⟩,1,1,0⟩, +⟨⟨1,453,90,true⟩,1,1,0⟩, +⟨⟨1,452,90,true⟩,1,1,0⟩, +⟨⟨1,451,89,true⟩,1,1,0⟩, +⟨⟨1,450,89,true⟩,1,1,0⟩, +⟨⟨1,449,88,true⟩,1,1,0⟩, +⟨⟨1,448,88,true⟩,1,1,0⟩, +⟨⟨1,447,87,true⟩,1,1,0⟩, +⟨⟨1,446,87,true⟩,1,1,0⟩, +⟨⟨1,445,86,true⟩,1,1,0⟩, +⟨⟨1,444,86,true⟩,1,1,0⟩, +⟨⟨1,443,85,true⟩,1,1,0⟩, +⟨⟨1,442,85,true⟩,1,1,0⟩, +⟨⟨1,441,84,true⟩,1,1,0⟩, +⟨⟨1,440,84,true⟩,1,1,0⟩, +⟨⟨1,439,83,true⟩,1,1,0⟩, +⟨⟨1,438,83,true⟩,1,1,0⟩, +⟨⟨1,437,82,true⟩,1,1,0⟩, +⟨⟨1,436,82,true⟩,1,1,0⟩, +⟨⟨1,435,81,true⟩,1,1,0⟩, +⟨⟨1,434,81,true⟩,1,1,0⟩, +⟨⟨1,433,80,true⟩,1,1,0⟩, +⟨⟨1,432,80,true⟩,1,1,0⟩, +⟨⟨1,431,79,true⟩,1,1,0⟩, +⟨⟨1,430,79,true⟩,1,1,0⟩, +⟨⟨1,429,78,true⟩,1,1,0⟩, +⟨⟨1,428,78,true⟩,1,1,0⟩, +⟨⟨1,427,77,true⟩,1,1,0⟩, +⟨⟨1,426,77,true⟩,1,1,0⟩, +⟨⟨1,425,76,true⟩,1,1,0⟩, +⟨⟨1,424,76,true⟩,1,1,0⟩, +⟨⟨1,423,75,true⟩,1,1,0⟩, +⟨⟨1,422,75,true⟩,1,1,0⟩, +⟨⟨1,421,74,true⟩,1,1,0⟩, +⟨⟨1,420,74,true⟩,1,1,0⟩, +⟨⟨1,419,73,true⟩,1,1,0⟩, +⟨⟨1,418,73,true⟩,1,1,0⟩, +⟨⟨1,417,72,true⟩,1,1,0⟩, +⟨⟨1,416,72,true⟩,1,1,0⟩, +⟨⟨1,415,71,true⟩,1,1,0⟩, +⟨⟨1,414,71,true⟩,1,1,0⟩, +⟨⟨1,413,70,true⟩,1,1,0⟩, +⟨⟨1,412,70,true⟩,1,1,0⟩, +⟨⟨1,411,69,true⟩,1,1,0⟩, +⟨⟨1,410,69,true⟩,1,1,0⟩, +⟨⟨1,409,68,true⟩,1,1,0⟩, +⟨⟨1,408,68,true⟩,1,1,0⟩, +⟨⟨1,407,67,true⟩,1,1,0⟩, +⟨⟨1,406,67,true⟩,1,1,0⟩, +⟨⟨1,405,66,true⟩,1,1,0⟩, +⟨⟨1,404,66,true⟩,1,1,0⟩, +⟨⟨1,403,65,true⟩,1,1,0⟩, +⟨⟨1,402,65,true⟩,1,1,0⟩, +⟨⟨1,401,64,true⟩,1,1,0⟩, +⟨⟨1,400,64,true⟩,1,1,0⟩, +⟨⟨1,399,63,true⟩,1,1,0⟩, +⟨⟨1,398,63,true⟩,1,1,0⟩, +⟨⟨1,397,62,true⟩,1,1,0⟩, +⟨⟨1,396,62,true⟩,1,1,0⟩, +⟨⟨1,395,61,true⟩,1,1,0⟩, +⟨⟨1,394,61,true⟩,1,1,0⟩, +⟨⟨1,393,60,true⟩,1,1,0⟩, +⟨⟨1,392,60,true⟩,1,1,0⟩, +⟨⟨1,391,59,true⟩,1,1,0⟩, +⟨⟨1,390,59,true⟩,1,1,0⟩, +⟨⟨1,389,58,true⟩,1,1,0⟩, +⟨⟨1,388,58,true⟩,1,1,0⟩, +⟨⟨1,387,57,true⟩,1,1,0⟩, +⟨⟨1,386,57,true⟩,1,1,0⟩, +⟨⟨1,385,56,true⟩,1,1,0⟩, +⟨⟨1,384,56,true⟩,1,1,0⟩, +⟨⟨1,383,55,true⟩,1,1,0⟩, +⟨⟨1,382,55,true⟩,1,1,0⟩, +⟨⟨1,381,54,true⟩,1,1,0⟩, +⟨⟨1,380,54,true⟩,1,1,0⟩, +⟨⟨1,379,53,true⟩,1,1,0⟩, +⟨⟨1,378,53,true⟩,1,1,0⟩, +⟨⟨1,377,52,true⟩,1,1,0⟩, +⟨⟨1,376,52,true⟩,1,1,0⟩, +⟨⟨1,375,51,true⟩,1,1,0⟩, +⟨⟨1,374,51,true⟩,1,1,0⟩] +def chunk93 : List Entry := [⟨⟨1,373,50,true⟩,1,1,0⟩, +⟨⟨1,372,50,true⟩,1,1,0⟩, +⟨⟨1,371,49,true⟩,1,1,0⟩, +⟨⟨1,370,49,true⟩,1,1,0⟩, +⟨⟨1,369,48,true⟩,1,1,0⟩, +⟨⟨1,368,48,true⟩,1,1,0⟩, +⟨⟨1,367,47,true⟩,1,1,0⟩, +⟨⟨1,366,47,true⟩,1,1,0⟩, +⟨⟨1,365,46,true⟩,1,1,0⟩, +⟨⟨1,364,46,true⟩,1,1,0⟩, +⟨⟨1,363,45,true⟩,1,1,0⟩, +⟨⟨1,362,45,true⟩,1,1,0⟩, +⟨⟨1,361,44,true⟩,1,1,0⟩, +⟨⟨1,360,44,true⟩,1,1,0⟩, +⟨⟨1,359,43,true⟩,1,1,0⟩, +⟨⟨1,358,43,true⟩,1,1,0⟩, +⟨⟨1,357,42,true⟩,1,1,0⟩, +⟨⟨1,356,42,true⟩,1,1,0⟩, +⟨⟨1,355,41,true⟩,1,1,0⟩, +⟨⟨1,354,41,true⟩,1,1,0⟩, +⟨⟨1,353,40,true⟩,1,1,0⟩, +⟨⟨1,352,40,true⟩,1,1,0⟩, +⟨⟨1,351,39,true⟩,1,1,0⟩, +⟨⟨1,350,39,true⟩,1,1,0⟩, +⟨⟨1,349,38,true⟩,1,1,0⟩, +⟨⟨1,348,38,true⟩,1,1,0⟩, +⟨⟨1,347,37,true⟩,1,1,0⟩, +⟨⟨1,346,37,true⟩,1,1,0⟩, +⟨⟨1,345,36,true⟩,1,1,0⟩, +⟨⟨1,344,36,true⟩,1,1,0⟩, +⟨⟨1,343,35,true⟩,1,1,0⟩, +⟨⟨1,342,35,true⟩,1,1,0⟩, +⟨⟨1,341,34,true⟩,1,1,0⟩, +⟨⟨1,340,34,true⟩,1,1,0⟩, +⟨⟨1,339,33,true⟩,1,1,0⟩, +⟨⟨1,338,33,true⟩,1,1,0⟩, +⟨⟨1,337,32,true⟩,1,1,0⟩, +⟨⟨1,336,32,true⟩,1,1,0⟩, +⟨⟨1,335,31,true⟩,1,1,0⟩, +⟨⟨1,334,31,true⟩,1,1,0⟩, +⟨⟨1,333,30,true⟩,1,1,0⟩, +⟨⟨1,332,30,true⟩,1,1,0⟩, +⟨⟨1,331,29,true⟩,1,1,0⟩, +⟨⟨1,330,29,true⟩,1,1,0⟩, +⟨⟨1,329,28,true⟩,1,1,0⟩, +⟨⟨1,328,28,true⟩,1,1,0⟩, +⟨⟨1,327,27,true⟩,1,1,0⟩, +⟨⟨1,326,27,true⟩,1,1,0⟩, +⟨⟨1,325,26,true⟩,1,1,0⟩, +⟨⟨1,324,26,true⟩,1,1,0⟩, +⟨⟨1,323,25,true⟩,1,1,0⟩, +⟨⟨1,322,25,true⟩,1,1,0⟩, +⟨⟨1,321,24,true⟩,1,1,0⟩, +⟨⟨1,320,24,true⟩,1,1,0⟩, +⟨⟨1,319,23,true⟩,1,1,0⟩, +⟨⟨1,318,23,true⟩,1,1,0⟩, +⟨⟨1,317,22,true⟩,1,1,0⟩, +⟨⟨1,316,22,true⟩,1,1,0⟩, +⟨⟨1,315,21,true⟩,1,1,0⟩, +⟨⟨1,314,21,true⟩,1,1,0⟩, +⟨⟨1,313,20,true⟩,1,1,0⟩, +⟨⟨1,312,20,true⟩,1,1,0⟩, +⟨⟨1,311,19,true⟩,1,1,0⟩, +⟨⟨1,310,19,true⟩,1,1,0⟩, +⟨⟨1,309,18,true⟩,1,1,0⟩, +⟨⟨1,308,18,true⟩,1,1,0⟩, +⟨⟨1,307,17,true⟩,1,1,0⟩, +⟨⟨1,306,17,true⟩,1,1,0⟩, +⟨⟨1,305,16,true⟩,1,1,0⟩, +⟨⟨1,304,16,true⟩,1,1,0⟩, +⟨⟨1,303,15,true⟩,1,1,0⟩, +⟨⟨1,302,15,true⟩,1,1,0⟩, +⟨⟨1,301,14,true⟩,1,1,0⟩, +⟨⟨1,300,14,true⟩,1,1,0⟩, +⟨⟨1,299,13,true⟩,1,1,0⟩, +⟨⟨1,298,13,true⟩,1,1,0⟩, +⟨⟨1,297,12,true⟩,1,1,0⟩, +⟨⟨1,296,12,true⟩,1,1,0⟩, +⟨⟨1,295,11,true⟩,1,1,0⟩, +⟨⟨1,294,11,true⟩,1,1,0⟩, +⟨⟨1,293,10,true⟩,1,1,0⟩, +⟨⟨1,292,10,true⟩,1,1,0⟩, +⟨⟨1,291,9,true⟩,1,1,0⟩, +⟨⟨1,290,9,true⟩,1,1,0⟩, +⟨⟨1,289,8,true⟩,1,1,0⟩, +⟨⟨1,288,8,true⟩,1,1,0⟩, +⟨⟨1,287,7,true⟩,1,1,0⟩, +⟨⟨1,286,7,true⟩,1,1,0⟩, +⟨⟨1,285,7,true⟩,1,1,0⟩, +⟨⟨1,284,7,true⟩,1,1,0⟩, +⟨⟨1,283,7,true⟩,1,1,0⟩, +⟨⟨1,282,7,true⟩,1,1,0⟩, +⟨⟨1,281,6,true⟩,1,1,0⟩, +⟨⟨1,280,6,true⟩,1,1,0⟩, +⟨⟨1,279,6,true⟩,1,1,0⟩, +⟨⟨1,278,6,true⟩,1,1,0⟩, +⟨⟨1,277,6,true⟩,1,1,0⟩, +⟨⟨1,276,6,true⟩,1,1,0⟩, +⟨⟨1,275,5,true⟩,1,1,0⟩, +⟨⟨1,274,5,true⟩,1,1,0⟩, +⟨⟨1,273,5,true⟩,1,1,0⟩, +⟨⟨1,272,5,true⟩,1,1,0⟩, +⟨⟨1,271,5,true⟩,1,1,0⟩, +⟨⟨1,270,5,true⟩,1,1,0⟩, +⟨⟨1,269,4,true⟩,1,1,0⟩, +⟨⟨1,268,4,true⟩,1,1,0⟩, +⟨⟨1,267,4,true⟩,1,1,0⟩, +⟨⟨1,266,4,true⟩,1,1,0⟩, +⟨⟨1,265,4,true⟩,1,1,0⟩, +⟨⟨1,264,4,true⟩,1,1,0⟩, +⟨⟨1,263,3,true⟩,1,1,0⟩, +⟨⟨1,262,3,true⟩,1,1,0⟩, +⟨⟨1,261,3,true⟩,1,1,0⟩, +⟨⟨1,260,3,true⟩,1,1,0⟩, +⟨⟨1,259,3,true⟩,1,1,0⟩, +⟨⟨1,258,3,true⟩,1,1,0⟩, +⟨⟨1,257,2,true⟩,1,1,0⟩, +⟨⟨1,256,2,true⟩,1,1,0⟩, +⟨⟨1,255,2,true⟩,1,1,0⟩, +⟨⟨1,254,2,true⟩,1,1,0⟩, +⟨⟨1,253,2,true⟩,1,1,0⟩, +⟨⟨1,252,2,true⟩,1,1,0⟩, +⟨⟨1,251,1,true⟩,1,1,0⟩, +⟨⟨1,250,1,true⟩,1,1,0⟩, +⟨⟨1,249,1,true⟩,1,1,0⟩, +⟨⟨1,248,1,true⟩,1,1,0⟩, +⟨⟨1,247,1,true⟩,1,1,0⟩, +⟨⟨1,246,1,true⟩,1,1,0⟩, +⟨⟨1,245,0,true⟩,1,1,0⟩, +⟨⟨1,244,0,true⟩,1,1,0⟩, +⟨⟨1,243,0,true⟩,1,1,0⟩, +⟨⟨1,242,0,true⟩,1,1,0⟩, +⟨⟨1,241,0,true⟩,1,1,0⟩, +⟨⟨1,240,0,true⟩,1,1,0⟩, +⟨⟨1,241,787,true⟩,1,1,0⟩, +⟨⟨1,241,803,true⟩,1,1,0⟩, +⟨⟨1,241,817,true⟩,1,1,0⟩, +⟨⟨1,241,833,true⟩,1,1,0⟩, +⟨⟨1,242,747,true⟩,1,1,0⟩, +⟨⟨1,242,761,true⟩,1,1,0⟩, +⟨⟨1,242,773,true⟩,1,1,0⟩, +⟨⟨1,244,745,true⟩,1,1,0⟩, +⟨⟨1,248,743,true⟩,1,1,0⟩, +⟨⟨1,248,757,true⟩,1,1,0⟩, +⟨⟨1,248,769,true⟩,1,1,0⟩, +⟨⟨1,248,861,true⟩,1,1,0⟩, +⟨⟨1,248,875,true⟩,1,1,0⟩, +⟨⟨1,248,889,true⟩,1,1,0⟩, +⟨⟨1,249,771,true⟩,1,1,0⟩, +⟨⟨1,249,847,true⟩,1,1,0⟩, +⟨⟨1,249,873,true⟩,1,1,0⟩, +⟨⟨1,250,741,true⟩,1,1,0⟩, +⟨⟨1,250,845,true⟩,1,1,0⟩, +⟨⟨1,250,859,true⟩,1,1,0⟩, +⟨⟨1,250,885,true⟩,1,1,0⟩, +⟨⟨1,254,903,true⟩,1,1,0⟩, +⟨⟨1,254,917,true⟩,1,1,0⟩, +⟨⟨1,256,739,true⟩,1,1,0⟩, +⟨⟨1,256,799,true⟩,1,1,0⟩, +⟨⟨1,256,855,true⟩,1,1,0⟩, +⟨⟨1,256,909,true⟩,1,1,0⟩, +⟨⟨1,257,738,true⟩,1,1,0⟩, +⟨⟨1,257,783,true⟩,1,1,0⟩, +⟨⟨1,257,797,true⟩,1,1,0⟩, +⟨⟨1,257,839,true⟩,1,1,0⟩, +⟨⟨1,257,853,true⟩,1,1,0⟩, +⟨⟨1,257,895,true⟩,1,1,0⟩, +⟨⟨1,260,913,true⟩,1,1,0⟩, +⟨⟨1,263,825,true⟩,1,1,0⟩, +⟨⟨1,263,867,true⟩,1,1,0⟩, +⟨⟨1,267,899,true⟩,1,1,0⟩, +⟨⟨1,268,752,true⟩,1,1,0⟩, +⟨⟨1,268,785,true⟩,1,1,0⟩, +⟨⟨1,268,813,true⟩,1,1,0⟩, +⟨⟨1,268,841,true⟩,1,1,0⟩, +⟨⟨1,268,869,true⟩,1,1,0⟩, +⟨⟨1,268,923,true⟩,1,1,0⟩, +⟨⟨1,269,753,true⟩,1,1,0⟩, +⟨⟨1,269,781,true⟩,1,1,0⟩, +⟨⟨1,269,809,true⟩,1,1,0⟩, +⟨⟨1,269,837,true⟩,1,1,0⟩, +⟨⟨1,269,865,true⟩,1,1,0⟩, +⟨⟨1,269,893,true⟩,1,1,0⟩, +⟨⟨1,272,755,true⟩,1,1,0⟩, +⟨⟨1,272,822,true⟩,1,1,0⟩, +⟨⟨1,272,887,true⟩,1,1,0⟩, +⟨⟨1,272,901,true⟩,1,1,0⟩, +⟨⟨1,272,929,true⟩,1,1,0⟩, +⟨⟨1,274,827,true⟩,1,1,0⟩, +⟨⟨1,274,883,true⟩,1,1,0⟩, +⟨⟨1,275,795,true⟩,1,1,0⟩, +⟨⟨1,275,823,true⟩,1,1,0⟩, +⟨⟨1,275,851,true⟩,1,1,0⟩, +⟨⟨1,275,879,true⟩,1,1,0⟩, +⟨⟨1,283,836,true⟩,1,1,0⟩, +⟨⟨1,284,808,true⟩,1,1,0⟩, +⟨⟨1,284,931,true⟩,1,1,0⟩, +⟨⟨1,286,919,true⟩,1,1,0⟩, +⟨⟨1,286,921,true⟩,1,1,0⟩, +⟨⟨1,287,767,true⟩,1,1,0⟩] +def chunk94 : List Entry := [⟨⟨1,736,738,true⟩,1,1,0⟩, +⟨⟨1,736,838,true⟩,1,1,0⟩, +⟨⟨1,736,839,true⟩,1,1,0⟩, +⟨⟨1,736,852,true⟩,1,1,0⟩, +⟨⟨1,736,853,true⟩,1,1,0⟩, +⟨⟨1,737,739,true⟩,1,1,0⟩, +⟨⟨1,737,908,true⟩,1,1,0⟩, +⟨⟨1,737,909,true⟩,1,1,0⟩, +⟨⟨1,740,741,true⟩,1,1,0⟩, +⟨⟨1,742,743,true⟩,1,1,0⟩, +⟨⟨1,742,874,true⟩,1,1,0⟩, +⟨⟨1,742,875,true⟩,1,1,0⟩, +⟨⟨1,742,888,true⟩,1,1,0⟩, +⟨⟨1,742,889,true⟩,1,1,0⟩, +⟨⟨1,744,745,true⟩,1,1,0⟩, +⟨⟨1,746,747,true⟩,1,1,0⟩, +⟨⟨1,748,789,true⟩,1,1,0⟩, +⟨⟨1,748,801,true⟩,1,1,0⟩, +⟨⟨1,748,818,true⟩,1,1,0⟩, +⟨⟨1,748,830,true⟩,1,1,0⟩, +⟨⟨1,749,789,true⟩,1,1,0⟩, +⟨⟨1,749,801,true⟩,1,1,0⟩, +⟨⟨1,749,819,true⟩,1,1,0⟩, +⟨⟨1,749,831,true⟩,1,1,0⟩, +⟨⟨1,750,752,true⟩,1,1,0⟩, +⟨⟨1,750,784,true⟩,1,1,0⟩, +⟨⟨1,750,785,true⟩,1,1,0⟩, +⟨⟨1,750,840,true⟩,1,1,0⟩, +⟨⟨1,750,841,true⟩,1,1,0⟩, +⟨⟨1,750,922,true⟩,1,1,0⟩, +⟨⟨1,750,923,true⟩,1,1,0⟩, +⟨⟨1,756,757,true⟩,1,1,0⟩, +⟨⟨1,756,860,true⟩,1,1,0⟩, +⟨⟨1,756,861,true⟩,1,1,0⟩, +⟨⟨1,756,888,true⟩,1,1,0⟩, +⟨⟨1,756,889,true⟩,1,1,0⟩, +⟨⟨1,760,761,true⟩,1,1,0⟩, +⟨⟨1,762,777,true⟩,1,1,0⟩, +⟨⟨1,762,791,true⟩,1,1,0⟩, +⟨⟨1,762,804,true⟩,1,1,0⟩, +⟨⟨1,762,815,true⟩,1,1,0⟩, +⟨⟨1,762,828,true⟩,1,1,0⟩, +⟨⟨1,763,777,true⟩,1,1,0⟩, +⟨⟨1,763,791,true⟩,1,1,0⟩, +⟨⟨1,763,805,true⟩,1,1,0⟩, +⟨⟨1,763,815,true⟩,1,1,0⟩, +⟨⟨1,763,829,true⟩,1,1,0⟩, +⟨⟨1,764,811,true⟩,1,1,0⟩, +⟨⟨1,764,881,true⟩,1,1,0⟩, +⟨⟨1,764,921,true⟩,1,1,0⟩, +⟨⟨1,765,767,true⟩,1,1,0⟩, +⟨⟨1,766,811,true⟩,1,1,0⟩, +⟨⟨1,766,881,true⟩,1,1,0⟩, +⟨⟨1,766,919,true⟩,1,1,0⟩, +⟨⟨1,768,769,true⟩,1,1,0⟩, +⟨⟨1,768,860,true⟩,1,1,0⟩, +⟨⟨1,768,861,true⟩,1,1,0⟩, +⟨⟨1,768,874,true⟩,1,1,0⟩, +⟨⟨1,768,875,true⟩,1,1,0⟩, +⟨⟨1,770,771,true⟩,1,1,0⟩, +⟨⟨1,772,773,true⟩,1,1,0⟩, +⟨⟨1,776,777,true⟩,1,1,0⟩, +⟨⟨1,776,804,true⟩,1,1,0⟩, +⟨⟨1,776,805,true⟩,1,1,0⟩, +⟨⟨1,776,814,true⟩,1,1,0⟩, +⟨⟨1,776,815,true⟩,1,1,0⟩, +⟨⟨1,779,751,true⟩,1,1,0⟩, +⟨⟨1,779,753,true⟩,1,1,0⟩, +⟨⟨1,779,781,true⟩,1,1,0⟩, +⟨⟨1,779,863,true⟩,1,1,0⟩, +⟨⟨1,779,865,true⟩,1,1,0⟩, +⟨⟨1,779,891,true⟩,1,1,0⟩, +⟨⟨1,779,893,true⟩,1,1,0⟩, +⟨⟨1,782,783,true⟩,1,1,0⟩, +⟨⟨1,782,838,true⟩,1,1,0⟩, +⟨⟨1,782,839,true⟩,1,1,0⟩, +⟨⟨1,782,894,true⟩,1,1,0⟩, +⟨⟨1,782,895,true⟩,1,1,0⟩, +⟨⟨1,786,787,true⟩,1,1,0⟩, +⟨⟨1,786,832,true⟩,1,1,0⟩, +⟨⟨1,786,833,true⟩,1,1,0⟩, +⟨⟨1,788,789,true⟩,1,1,0⟩, +⟨⟨1,788,830,true⟩,1,1,0⟩, +⟨⟨1,788,831,true⟩,1,1,0⟩, +⟨⟨1,790,791,true⟩,1,1,0⟩, +⟨⟨1,790,804,true⟩,1,1,0⟩, +⟨⟨1,790,805,true⟩,1,1,0⟩, +⟨⟨1,790,814,true⟩,1,1,0⟩, +⟨⟨1,790,815,true⟩,1,1,0⟩, +⟨⟨1,790,828,true⟩,1,1,0⟩, +⟨⟨1,790,829,true⟩,1,1,0⟩, +⟨⟨1,792,857,true⟩,1,1,0⟩, +⟨⟨1,792,897,true⟩,1,1,0⟩, +⟨⟨1,792,925,true⟩,1,1,0⟩, +⟨⟨1,793,795,true⟩,1,1,0⟩, +⟨⟨1,793,877,true⟩,1,1,0⟩, +⟨⟨1,793,879,true⟩,1,1,0⟩, +⟨⟨1,794,857,true⟩,1,1,0⟩, +⟨⟨1,794,897,true⟩,1,1,0⟩, +⟨⟨1,794,925,true⟩,1,1,0⟩, +⟨⟨1,796,797,true⟩,1,1,0⟩, +⟨⟨1,796,852,true⟩,1,1,0⟩, +⟨⟨1,796,853,true⟩,1,1,0⟩, +⟨⟨1,796,894,true⟩,1,1,0⟩, +⟨⟨1,796,895,true⟩,1,1,0⟩, +⟨⟨1,798,799,true⟩,1,1,0⟩, +⟨⟨1,798,908,true⟩,1,1,0⟩, +⟨⟨1,798,909,true⟩,1,1,0⟩, +⟨⟨1,800,801,true⟩,1,1,0⟩, +⟨⟨1,800,818,true⟩,1,1,0⟩, +⟨⟨1,800,819,true⟩,1,1,0⟩, +⟨⟨1,802,803,true⟩,1,1,0⟩, +⟨⟨1,802,832,true⟩,1,1,0⟩, +⟨⟨1,802,833,true⟩,1,1,0⟩, +⟨⟨1,806,808,true⟩,1,1,0⟩, +⟨⟨1,807,809,true⟩,1,1,0⟩, +⟨⟨1,807,863,true⟩,1,1,0⟩, +⟨⟨1,807,865,true⟩,1,1,0⟩, +⟨⟨1,807,891,true⟩,1,1,0⟩, +⟨⟨1,807,893,true⟩,1,1,0⟩, +⟨⟨1,810,811,true⟩,1,1,0⟩, +⟨⟨1,810,919,true⟩,1,1,0⟩, +⟨⟨1,810,921,true⟩,1,1,0⟩, +⟨⟨1,812,813,true⟩,1,1,0⟩, +⟨⟨1,812,840,true⟩,1,1,0⟩, +⟨⟨1,812,841,true⟩,1,1,0⟩, +⟨⟨1,812,922,true⟩,1,1,0⟩, +⟨⟨1,812,923,true⟩,1,1,0⟩, +⟨⟨1,816,817,true⟩,1,1,0⟩, +⟨⟨1,816,832,true⟩,1,1,0⟩, +⟨⟨1,816,833,true⟩,1,1,0⟩, +⟨⟨1,820,754,true⟩,1,1,0⟩, +⟨⟨1,820,755,true⟩,1,1,0⟩, +⟨⟨1,820,822,true⟩,1,1,0⟩, +⟨⟨1,821,823,true⟩,1,1,0⟩, +⟨⟨1,821,877,true⟩,1,1,0⟩, +⟨⟨1,821,879,true⟩,1,1,0⟩, +⟨⟨1,824,825,true⟩,1,1,0⟩, +⟨⟨1,826,827,true⟩,1,1,0⟩, +⟨⟨1,834,836,true⟩,1,1,0⟩, +⟨⟨1,835,751,true⟩,1,1,0⟩, +⟨⟨1,835,753,true⟩,1,1,0⟩, +⟨⟨1,835,837,true⟩,1,1,0⟩, +⟨⟨1,835,863,true⟩,1,1,0⟩, +⟨⟨1,835,865,true⟩,1,1,0⟩, +⟨⟨1,844,845,true⟩,1,1,0⟩, +⟨⟨1,844,884,true⟩,1,1,0⟩, +⟨⟨1,844,885,true⟩,1,1,0⟩, +⟨⟨1,846,847,true⟩,1,1,0⟩, +⟨⟨1,849,851,true⟩,1,1,0⟩, +⟨⟨1,849,877,true⟩,1,1,0⟩, +⟨⟨1,849,879,true⟩,1,1,0⟩, +⟨⟨1,854,855,true⟩,1,1,0⟩, +⟨⟨1,854,908,true⟩,1,1,0⟩, +⟨⟨1,854,909,true⟩,1,1,0⟩, +⟨⟨1,858,859,true⟩,1,1,0⟩, +⟨⟨1,858,884,true⟩,1,1,0⟩, +⟨⟨1,858,885,true⟩,1,1,0⟩, +⟨⟨1,866,867,true⟩,1,1,0⟩, +⟨⟨1,868,784,true⟩,1,1,0⟩, +⟨⟨1,868,785,true⟩,1,1,0⟩, +⟨⟨1,868,869,true⟩,1,1,0⟩, +⟨⟨1,868,922,true⟩,1,1,0⟩, +⟨⟨1,868,923,true⟩,1,1,0⟩, +⟨⟨1,872,873,true⟩,1,1,0⟩, +⟨⟨1,880,881,true⟩,1,1,0⟩, +⟨⟨1,880,919,true⟩,1,1,0⟩, +⟨⟨1,880,921,true⟩,1,1,0⟩, +⟨⟨1,882,883,true⟩,1,1,0⟩, +⟨⟨1,896,856,true⟩,1,1,0⟩, +⟨⟨1,896,857,true⟩,1,1,0⟩, +⟨⟨1,896,897,true⟩,1,1,0⟩, +⟨⟨1,898,899,true⟩,1,1,0⟩, +⟨⟨1,900,754,true⟩,1,1,0⟩, +⟨⟨1,900,755,true⟩,1,1,0⟩, +⟨⟨1,900,886,true⟩,1,1,0⟩, +⟨⟨1,900,887,true⟩,1,1,0⟩, +⟨⟨1,900,901,true⟩,1,1,0⟩, +⟨⟨1,902,903,true⟩,1,1,0⟩, +⟨⟨1,912,913,true⟩,1,1,0⟩, +⟨⟨1,916,917,true⟩,1,1,0⟩, +⟨⟨1,924,856,true⟩,1,1,0⟩, +⟨⟨1,924,857,true⟩,1,1,0⟩, +⟨⟨1,924,925,true⟩,1,1,0⟩, +⟨⟨1,928,886,true⟩,1,1,0⟩, +⟨⟨1,928,887,true⟩,1,1,0⟩, +⟨⟨1,928,929,true⟩,1,1,0⟩, +⟨⟨1,930,931,true⟩,1,1,0⟩, +⟨⟨1,932,938,true⟩,1,1,0⟩, +⟨⟨1,933,938,true⟩,1,1,0⟩, +⟨⟨1,936,961,true⟩,1,1,0⟩, +⟨⟨1,937,938,true⟩,1,1,0⟩, +⟨⟨1,941,949,true⟩,1,1,0⟩, +⟨⟨1,942,953,true⟩,1,1,0⟩, +⟨⟨1,943,958,true⟩,1,1,0⟩, +⟨⟨1,944,953,true⟩,1,1,0⟩, +⟨⟨1,945,958,true⟩,1,1,0⟩, +⟨⟨1,951,953,true⟩,1,1,0⟩, +⟨⟨1,956,958,true⟩,1,1,0⟩, +⟨⟨1,959,978,true⟩,1,1,0⟩] +def chunk95 : List Entry := [⟨⟨1,960,978,true⟩,1,1,0⟩, +⟨⟨1,977,978,true⟩,1,1,0⟩] +def chunks : List (List Entry) := [chunk0,chunk1,chunk2,chunk3,chunk4,chunk5,chunk6,chunk7,chunk8,chunk9,chunk10,chunk11,chunk12,chunk13,chunk14,chunk15,chunk16,chunk17,chunk18,chunk19,chunk20,chunk21,chunk22,chunk23,chunk24,chunk25,chunk26,chunk27,chunk28,chunk29,chunk30,chunk31,chunk32,chunk33,chunk34,chunk35,chunk36,chunk37,chunk38,chunk39,chunk40,chunk41,chunk42,chunk43,chunk44,chunk45,chunk46,chunk47,chunk48,chunk49,chunk50,chunk51,chunk52,chunk53,chunk54,chunk55,chunk56,chunk57,chunk58,chunk59,chunk60,chunk61,chunk62,chunk63,chunk64,chunk65,chunk66,chunk67,chunk68,chunk69,chunk70,chunk71,chunk72,chunk73,chunk74,chunk75,chunk76,chunk77,chunk78,chunk79,chunk80,chunk81,chunk82,chunk83,chunk84,chunk85,chunk86,chunk87,chunk88,chunk89,chunk90,chunk91,chunk92,chunk93,chunk94,chunk95] +def forward : List Entry := chunks.flatten +def suffix96 : List Entry := [] +def suffix95 : List Entry := chunk95 ++ suffix96 +def suffix94 : List Entry := chunk94 ++ suffix95 +def suffix93 : List Entry := chunk93 ++ suffix94 +def suffix92 : List Entry := chunk92 ++ suffix93 +def suffix91 : List Entry := chunk91 ++ suffix92 +def suffix90 : List Entry := chunk90 ++ suffix91 +def suffix89 : List Entry := chunk89 ++ suffix90 +def suffix88 : List Entry := chunk88 ++ suffix89 +def suffix87 : List Entry := chunk87 ++ suffix88 +def suffix86 : List Entry := chunk86 ++ suffix87 +def suffix85 : List Entry := chunk85 ++ suffix86 +def suffix84 : List Entry := chunk84 ++ suffix85 +def suffix83 : List Entry := chunk83 ++ suffix84 +def suffix82 : List Entry := chunk82 ++ suffix83 +def suffix81 : List Entry := chunk81 ++ suffix82 +def suffix80 : List Entry := chunk80 ++ suffix81 +def suffix79 : List Entry := chunk79 ++ suffix80 +def suffix78 : List Entry := chunk78 ++ suffix79 +def suffix77 : List Entry := chunk77 ++ suffix78 +def suffix76 : List Entry := chunk76 ++ suffix77 +def suffix75 : List Entry := chunk75 ++ suffix76 +def suffix74 : List Entry := chunk74 ++ suffix75 +def suffix73 : List Entry := chunk73 ++ suffix74 +def suffix72 : List Entry := chunk72 ++ suffix73 +def suffix71 : List Entry := chunk71 ++ suffix72 +def suffix70 : List Entry := chunk70 ++ suffix71 +def suffix69 : List Entry := chunk69 ++ suffix70 +def suffix68 : List Entry := chunk68 ++ suffix69 +def suffix67 : List Entry := chunk67 ++ suffix68 +def suffix66 : List Entry := chunk66 ++ suffix67 +def suffix65 : List Entry := chunk65 ++ suffix66 +def suffix64 : List Entry := chunk64 ++ suffix65 +def suffix63 : List Entry := chunk63 ++ suffix64 +def suffix62 : List Entry := chunk62 ++ suffix63 +def suffix61 : List Entry := chunk61 ++ suffix62 +def suffix60 : List Entry := chunk60 ++ suffix61 +def suffix59 : List Entry := chunk59 ++ suffix60 +def suffix58 : List Entry := chunk58 ++ suffix59 +def suffix57 : List Entry := chunk57 ++ suffix58 +def suffix56 : List Entry := chunk56 ++ suffix57 +def suffix55 : List Entry := chunk55 ++ suffix56 +def suffix54 : List Entry := chunk54 ++ suffix55 +def suffix53 : List Entry := chunk53 ++ suffix54 +def suffix52 : List Entry := chunk52 ++ suffix53 +def suffix51 : List Entry := chunk51 ++ suffix52 +def suffix50 : List Entry := chunk50 ++ suffix51 +def suffix49 : List Entry := chunk49 ++ suffix50 +def suffix48 : List Entry := chunk48 ++ suffix49 +def suffix47 : List Entry := chunk47 ++ suffix48 +def suffix46 : List Entry := chunk46 ++ suffix47 +def suffix45 : List Entry := chunk45 ++ suffix46 +def suffix44 : List Entry := chunk44 ++ suffix45 +def suffix43 : List Entry := chunk43 ++ suffix44 +def suffix42 : List Entry := chunk42 ++ suffix43 +def suffix41 : List Entry := chunk41 ++ suffix42 +def suffix40 : List Entry := chunk40 ++ suffix41 +def suffix39 : List Entry := chunk39 ++ suffix40 +def suffix38 : List Entry := chunk38 ++ suffix39 +def suffix37 : List Entry := chunk37 ++ suffix38 +def suffix36 : List Entry := chunk36 ++ suffix37 +def suffix35 : List Entry := chunk35 ++ suffix36 +def suffix34 : List Entry := chunk34 ++ suffix35 +def suffix33 : List Entry := chunk33 ++ suffix34 +def suffix32 : List Entry := chunk32 ++ suffix33 +def suffix31 : List Entry := chunk31 ++ suffix32 +def suffix30 : List Entry := chunk30 ++ suffix31 +def suffix29 : List Entry := chunk29 ++ suffix30 +def suffix28 : List Entry := chunk28 ++ suffix29 +def suffix27 : List Entry := chunk27 ++ suffix28 +def suffix26 : List Entry := chunk26 ++ suffix27 +def suffix25 : List Entry := chunk25 ++ suffix26 +def suffix24 : List Entry := chunk24 ++ suffix25 +def suffix23 : List Entry := chunk23 ++ suffix24 +def suffix22 : List Entry := chunk22 ++ suffix23 +def suffix21 : List Entry := chunk21 ++ suffix22 +def suffix20 : List Entry := chunk20 ++ suffix21 +def suffix19 : List Entry := chunk19 ++ suffix20 +def suffix18 : List Entry := chunk18 ++ suffix19 +def suffix17 : List Entry := chunk17 ++ suffix18 +def suffix16 : List Entry := chunk16 ++ suffix17 +def suffix15 : List Entry := chunk15 ++ suffix16 +def suffix14 : List Entry := chunk14 ++ suffix15 +def suffix13 : List Entry := chunk13 ++ suffix14 +def suffix12 : List Entry := chunk12 ++ suffix13 +def suffix11 : List Entry := chunk11 ++ suffix12 +def suffix10 : List Entry := chunk10 ++ suffix11 +def suffix9 : List Entry := chunk9 ++ suffix10 +def suffix8 : List Entry := chunk8 ++ suffix9 +def suffix7 : List Entry := chunk7 ++ suffix8 +def suffix6 : List Entry := chunk6 ++ suffix7 +def suffix5 : List Entry := chunk5 ++ suffix6 +def suffix4 : List Entry := chunk4 ++ suffix5 +def suffix3 : List Entry := chunk3 ++ suffix4 +def suffix2 : List Entry := chunk2 ++ suffix3 +def suffix1 : List Entry := chunk1 ++ suffix2 +def suffix0 : List Entry := chunk0 ++ suffix1 +end SourceFrameTrace diff --git a/research/lean-multi-host-source/FrameTraceRefinement.lean b/research/lean-multi-host-source/FrameTraceRefinement.lean new file mode 100644 index 0000000000..86a8743a32 --- /dev/null +++ b/research/lean-multi-host-source/FrameTraceRefinement.lean @@ -0,0 +1,141 @@ +import FrameTraceCore +import PayloadGuards + +/-! +Static frame labels and normalized whole-payload cleanliness imply the +chronological admissibility of the framed interpreter. The labels may be +interpreted by any supplied actual gauge family. Concrete projector and +owner-chart realization are separate from this interpreter theorem. +-/ +namespace FrameTrace +open TreeReplay (Tree) + +def Matches {X : Type} (gauges : Nat → FramedReplay.Gauge X) + (labels : State) (physical : FramedReplay.Store X) : Prop := + physical.map Prod.fst = labels.frames.map gauges + +theorem matches_get {X : Type} (gauges : Nat → FramedReplay.Gauge X) + (labels : State) (physical : FramedReplay.Store X) + (same : Matches gauges labels physical) (i : Nat) : + (physical.get i).1 = gauges (labels.frames.get i) := by + have h := congrArg (fun s => Tree.get s i) same + simpa only [Tree.map_get] using h + +theorem matches_step {X : Type} (gauges : Nat → FramedReplay.Gauge X) + (labels : State) (physical : FramedReplay.Store X) (e : Entry) + (same : Matches gauges labels physical) : + Matches gauges (next labels e) + (FramedReplay.physicalStep physical (toPhysical gauges e)) := by + obtain ⟨⟨op, x, y, odd⟩, oldFrame, newFrame, rank⟩ := e + change physical.map Prod.fst = labels.frames.map gauges at same + cases op with + | zero => + simpa only [Matches, next, toPhysical, FramedReplay.physicalStep, + FramedReplay.reframe, Tree.map_put, Nat.zero_lt_succ, ↓reduceIte] using + congrArg (fun s => s.put x (gauges newFrame)) same + | succ op => + cases op with + | zero => + cases odd with + | false => exact same + | true => + change (physical.put x _).map Prod.fst = labels.frames.map gauges + rw [Tree.map_put] + change (physical.map Prod.fst).put x ((physical.get x).1) = _ + rw [← Tree.map_get Prod.fst physical x, FramedReplay.put_get] + exact same + | succ op => + cases op with + | zero => + simpa [Matches, next, toPhysical, FramedReplay.physicalStep, + FramedReplay.reframe, Tree.map_put] using + congrArg (fun s => s.put y (gauges newFrame)) same + | succ op => + have hn : ¬ op + 1 + 1 + 1 < 3 := by omega + simpa [Matches, next, toPhysical, FramedReplay.physicalStep, + Tree.map_put, hn] using congrArg (fun s => s.put y (gauges 0)) same + +theorem add_frames_equal (labels : State) (e : Entry) + (checked : check labels e = true) (isAdd : e.scalar.op = 1) : + labels.frames.get e.scalar.x = labels.frames.get e.scalar.y := by + simp only [check, isAdd, Bool.and_eq_true, beq_iff_eq] at checked + omega + +/-- The gauge labels at the endpoint are obtained from the same chronological +trace, including the virtual reset on each erased blank temporary. -/ +theorem matches_run {X : Type} (gauges : Nat → FramedReplay.Gauge X) + (entries : List Entry) (labels : State) (physical : FramedReplay.Store X) + (same : Matches gauges labels physical) (flag : Bool) : + Matches gauges (runChecked entries (labels, flag)).1 + (FramedReplay.runPhysical (entries.map (toPhysical gauges)) physical) := by + induction entries generalizing labels physical flag with + | nil => exact same + | cons e es ih => + exact ih (next labels e) (FramedReplay.physicalStep physical (toPhysical gauges e)) + (matches_step _ _ _ _ same) (flag && check labels e) + +theorem valid_step {X : Type} (gauges : Nat → FramedReplay.Gauge X) + (labels : State) (physical : FramedReplay.Store X) (e : Entry) + (same : Matches gauges labels physical) (checked : check labels e = true) + (clean : TreeReplay.PayloadClean (FramedReplay.decode physical) e.scalar) : + FramedReplay.ValidStep physical (toPhysical gauges e) := by + obtain ⟨⟨op, x, y, odd⟩, oldFrame, newFrame, rank⟩ := e + cases op with + | zero => trivial + | succ op => + cases op with + | zero => + change (physical.get x).1 = (physical.get y).1 + rw [matches_get _ _ _ same x, matches_get _ _ _ same y] + exact congrArg gauges (add_frames_equal _ _ checked rfl) + | succ op => + cases op with + | zero => + have h := clean.1 rfl + simpa only [FramedReplay.ValidStep, toPhysical, FramedReplay.decode, + Tree.map_get] using h + | succ op => + cases op with + | zero => + have h := clean.2 rfl + simpa only [FramedReplay.ValidStep, toPhysical, FramedReplay.decode, + Tree.map_get] using h + | succ op => + change false = true at checked + cases checked + +theorem valid_trace {X : Type} (gauges : Nat → FramedReplay.Gauge X) + (entries : List Entry) (labels : State) (physical : FramedReplay.Store X) + (same : Matches gauges labels physical) (checked : Valid entries labels) + (clean : TreeReplay.PayloadCleanRun (entries.map Entry.scalar) + (FramedReplay.decode physical)) : + FramedReplay.ValidTrace (entries.map (toPhysical gauges)) physical := by + induction entries generalizing labels physical with + | nil => trivial + | cons e es ih => + have first := valid_step gauges labels physical e same checked.1 clean.1 + refine ⟨first, ?_⟩ + apply ih (next labels e) (FramedReplay.physicalStep physical (toPhysical gauges e)) + (matches_step _ _ _ _ same) checked.2 + rw [FramedReplay.decode_step _ _ first] + exact clean.2 + +theorem decoded_run {X : Type} (gauges : Nat → FramedReplay.Gauge X) + (entries : List Entry) (labels : State) (physical : FramedReplay.Store X) + (same : Matches gauges labels physical) (checked : Valid entries labels) + (clean : TreeReplay.PayloadCleanRun (entries.map Entry.scalar) + (FramedReplay.decode physical)) : + FramedReplay.decode (FramedReplay.runPhysical (entries.map (toPhysical gauges)) physical) = + TreeReplay.runPayloads (entries.map Entry.scalar) (FramedReplay.decode physical) := by + have h := FramedReplay.decode_run _ _ (valid_trace gauges entries labels physical same checked clean) + simpa only [scalar_projection] using h + +end FrameTrace + +#print axioms FrameTrace.matches_get +#print axioms FrameTrace.matches_step +#print axioms FrameTrace.add_frames_equal +#print axioms FrameTrace.matches_run +#print axioms FrameTrace.valid_step +#print axioms FrameTrace.valid_trace +#print axioms FrameTrace.decoded_run diff --git a/research/lean-multi-host-source/FrameTraceRoutes.lean b/research/lean-multi-host-source/FrameTraceRoutes.lean new file mode 100644 index 0000000000..921ec27e20 --- /dev/null +++ b/research/lean-multi-host-source/FrameTraceRoutes.lean @@ -0,0 +1,38 @@ +import FrameTraceLiterals +import OwnerTransport + +/-! Exact finite-role encoding of the source trace for the independently +proved physical-owner routing interpreter. Only roles0..987 occur. -/ +namespace SourceFrameTrace +set_option maxRecDepth 100000 +set_option maxHeartbeats 0 + +def indicesOK (e : FrameTrace.Entry) : Bool := e.scalar.x < 988 && e.scalar.y < 988 + +theorem indices_checked : forward.all indicesOK = true := by decide + +theorem indices_bound (e : FrameTrace.Entry) (he : e ∈ forward) : + e.scalar.x < 988 ∧ e.scalar.y < 988 := by + have h := List.all_eq_true.mp indices_checked e he + simpa only [indicesOK, Bool.and_eq_true, decide_eq_true_eq] using h + +def toRoute {X : Type} (gauges : Nat → FramedReplay.Gauge X) + (e : FrameTrace.Entry) : OwnerTransport.RouteEvent (Fin 988) X := + ⟨e.scalar.op, ⟨e.scalar.x % 988, Nat.mod_lt _ (by decide)⟩, + ⟨e.scalar.y % 988, Nat.mod_lt _ (by decide)⟩, + e.scalar.odd, gauges (if e.scalar.op < 3 then e.newFrame else 0)⟩ + +theorem route_projection {X : Type} (gauges : Nat → FramedReplay.Gauge X) : + (forward.map (toRoute gauges)).map OwnerTransport.RouteEvent.framed = + forward.map (FrameTrace.toPhysical gauges) := by + rw [List.map_map] + apply List.map_congr_left + intro e he + obtain ⟨hx, hy⟩ := indices_bound e he + simp only [Function.comp_apply, toRoute, OwnerTransport.RouteEvent.framed, + FrameTrace.toPhysical, Nat.mod_eq_of_lt hx, Nat.mod_eq_of_lt hy] + +#print axioms indices_checked +#print axioms indices_bound +#print axioms route_projection +end SourceFrameTrace diff --git a/research/lean-multi-host-source/FrameTraceTables.lean b/research/lean-multi-host-source/FrameTraceTables.lean new file mode 100644 index 0000000000..10bcdffa98 --- /dev/null +++ b/research/lean-multi-host-source/FrameTraceTables.lean @@ -0,0 +1,31 @@ +import FrameTraceLiterals +import OwnershipData + +/-! Small concrete joins between the independently extracted frame trajectory +and the ownership tables. These are finite equalities, not assumptions about +an unexecuted source word. The source-binding replay reproduces both tables. -/ +namespace SourceFrameTrace +set_option maxRecDepth 100000 +set_option maxHeartbeats 0 + +theorem initial_owner_frames : ∀ r : SourceOwnership.Role, + state0.frames.get r.val = SourceOwnership.lookup SourceOwnership.initialFrameTable r.val := by + decide + +theorem helper_final_frames : ∀ h : Fin 747, + state96.frames.get (240 + h.val) = 1 := by + decide + +theorem initial_frame_range : ∀ r : SourceOwnership.Role, + state0.frames.get r.val < 944 := by + decide + +theorem final_frame_range : ∀ r : SourceOwnership.Role, + state96.frames.get r.val < 944 := by + decide + +#print axioms initial_owner_frames +#print axioms helper_final_frames +#print axioms initial_frame_range +#print axioms final_frame_range +end SourceFrameTrace diff --git a/research/lean-multi-host-source/FramedReplay.lean b/research/lean-multi-host-source/FramedReplay.lean new file mode 100644 index 0000000000..20acef964d --- /dev/null +++ b/research/lean-multi-host-source/FramedReplay.lean @@ -0,0 +1,163 @@ +import TreeReplay + +/-! +Literal framed MOVE / XOR / fresh COPY / checked ERASE simulation. +Apache-2.0. Prepared with substantial OpenAI Codex assistance. + +This uses the existing `FramedXor` gauge convention for the actual source +interpreter's copy/erase opcodes and tree register store. A MOVE reindexes +the named row by old.forward ∘ new.inverse. COPY performs the same transport +from the source gauge to the fresh destination gauge. ERASE may clear only +a temporary whose decoded contents equal the still-live source contents. + +This is a generic refinement theorem, not an instantiated source provider. +An actual source certificate must supply the concrete frame gauges and new +frame for every event, prove the chronological admissibility predicate, +and identify distinct tree registers with their actual physical owners. +No source frame or ownership claim follows from the product/tree types. +-/ +namespace FramedReplay + +open TreeReplay (Tree) +/- The same four-field address-gauge interface as main's FramedXor.lean. +It is reproduced here to avoid importing unrelated fanout proofs that do +not compile unchanged with this package's Lean version. No conclusion about +those proofs is used here. -/ +structure Gauge (X : Type) where + forward : X → X + inverse : X → X + inverse_forward : ∀ x, inverse (forward x) = x + forward_inverse : ∀ x, forward (inverse x) = x + +abbrev Row (X : Type) := Gauge X × (X → Bool) +abbrev Store (X : Type) := Tree (Row X) + +def decodeRow {X : Type} (r : Row X) : X → Bool := + fun a => r.2 (r.1.forward a) + +def decode {X : Type} (s : Store X) : Tree (X → Bool) := s.map decodeRow + +def reframe {X : Type} (new : Gauge X) (r : Row X) : Row X := + (new, fun a => r.2 (r.1.forward (new.inverse a))) + +theorem decode_reframe {X : Type} (new : Gauge X) (r : Row X) : + decodeRow (reframe new r) = decodeRow r := by + funext a + simp only [decodeRow, reframe, new.inverse_forward] + +structure Event (X : Type) where + scalar : LinearReplay.Event + /-- Used by MOVE and COPY. After ERASE this is only the gauge attached to + an identically zero/unallocated row; changing it has no physical action. -/ + newFrame : Gauge X + +def physicalStep {X : Type} (s : Store X) (e : Event X) : Store X := + match e.scalar.op with + | 0 => s.put e.scalar.x (reframe e.newFrame (s.get e.scalar.x)) + | 1 => if e.scalar.odd then + s.put e.scalar.x ((s.get e.scalar.x).1, + fun a => (s.get e.scalar.x).2 a ^^ (s.get e.scalar.y).2 a) + else s + | 2 => s.put e.scalar.y (reframe e.newFrame (s.get e.scalar.x)) + | _ => s.put e.scalar.y (e.newFrame, fun _ => false) + +/-- Source-specific range, owner and frame-label checks are additional. +Here the predicates express the semantic common-frame and clean-work rules. -/ +def ValidStep {X : Type} (s : Store X) (e : Event X) : Prop := + match e.scalar.op with + | 0 => True + | 1 => (s.get e.scalar.x).1 = (s.get e.scalar.y).1 + | 2 => decodeRow (s.get e.scalar.y) = fun _ => false + | 3 => decodeRow (s.get e.scalar.x) = decodeRow (s.get e.scalar.y) + | _ => False + +theorem put_get (s : Tree α) (i : Nat) : s.put i (s.get i) = s := by + induction s generalizing i with + | leaf a => rfl + | node l r ihl ihr => + simp only [Tree.put, Tree.get] + split <;> simp_all + +theorem decode_xor {X : Type} (r t : Row X) (common : r.1 = t.1) : + decodeRow (r.1, fun a => r.2 a ^^ t.2 a) = + fun a => decodeRow r a ^^ decodeRow t a := by + funext a + simp only [decodeRow] + rw [common] + +theorem decode_step {X : Type} (s : Store X) (e : Event X) + (valid : ValidStep s e) : + decode (physicalStep s e) = + TreeReplay.step (fun _ : X => false) (fun a b x => a x ^^ b x) + (decode s) e.scalar := by + obtain ⟨⟨op, x, y, odd⟩, newFrame⟩ := e + cases op with + | zero => + simp only [physicalStep, decode, Tree.map_put, decode_reframe, TreeReplay.step] + rw [← Tree.map_get decodeRow s x] + exact put_get _ _ + | succ op => + cases op with + | zero => + change (s.get x).1 = (s.get y).1 at valid + cases odd <;> + simp [physicalStep, decode, TreeReplay.step, Tree.map_put, + Tree.map_get, decode_xor _ _ valid] + | succ op => + cases op with + | zero => + simp [physicalStep, decode, TreeReplay.step, Tree.map_put, + Tree.map_get, decode_reframe] + | succ op => + simp only [physicalStep, decode, TreeReplay.step, Tree.map_put] + rfl + +/-- Decoded blankness is actual physical blankness, since the gauge is a +bijection. COPY therefore does not overwrite arbitrary dirty workspace. -/ +theorem physical_blank_of_decoded_blank {X : Type} (r : Row X) + (blank : decodeRow r = fun _ => false) (a : X) : r.2 a = false := by + have h := congrFun blank (r.1.inverse a) + simpa only [decodeRow, r.1.forward_inverse] using h + +/-- Before ERASE the temporary really is the source transported to its +current frame. This is the physical content of the decoded equality guard. -/ +theorem erase_guard_transport {X : Type} (source temporary : Row X) + (equal : decodeRow source = decodeRow temporary) (a : X) : + temporary.2 a = + source.2 (source.1.forward (temporary.1.inverse a)) := by + have h := congrFun equal (temporary.1.inverse a) + simpa only [decodeRow, temporary.1.forward_inverse] using h.symm + +def runPhysical {X : Type} (events : List (Event X)) (s : Store X) : Store X := + events.foldl physicalStep s + +def scalarWord {X : Type} (events : List (Event X)) : List LinearReplay.Event := + events.map Event.scalar + +def ValidTrace {X : Type} : List (Event X) → Store X → Prop + | [], _ => True + | e :: es, s => ValidStep s e ∧ ValidTrace es (physicalStep s e) + +/-- Chronological simulation, including the actual temporary outputs from +each preceding event. The predicates must be proved on that same execution. -/ +theorem decode_run {X : Type} (events : List (Event X)) (s : Store X) + (valid : ValidTrace events s) : + decode (runPhysical events s) = TreeReplay.runPayloads (scalarWord events) (decode s) := by + induction events generalizing s with + | nil => rfl + | cons e es ih => + change decode (runPhysical es (physicalStep s e)) = + TreeReplay.runPayloads (scalarWord es) + (TreeReplay.step (fun _ : X => false) (fun a b x => a x ^^ b x) + (decode s) e.scalar) + rw [ih _ valid.2, decode_step _ _ valid.1] + +end FramedReplay + +#print axioms FramedReplay.decode_reframe +#print axioms FramedReplay.put_get +#print axioms FramedReplay.decode_xor +#print axioms FramedReplay.decode_step +#print axioms FramedReplay.physical_blank_of_decoded_blank +#print axioms FramedReplay.erase_guard_transport +#print axioms FramedReplay.decode_run diff --git a/research/lean-multi-host-source/HelperGeometryData.lean b/research/lean-multi-host-source/HelperGeometryData.lean new file mode 100644 index 0000000000..1a0a9b15d9 --- /dev/null +++ b/research/lean-multi-host-source/HelperGeometryData.lean @@ -0,0 +1,25 @@ +import FrameData +import OwnershipData + +/-! Kernel joins between the actual helper slot descriptors and the actual +frame matrix table. All displayed coordinate claims are finite checks of +those literal tables, not premises of the physical source theorem. -/ +namespace SelectedGeometry +set_option maxRecDepth 100000 +set_option maxHeartbeats 0 + +theorem tag_frame_bound : ∀ t : SourceOwnership.Tag, + SourceOwnership.lookup SourceOwnership.tagInitialFrame t.val < 944 := by decide + +def tagFrame (t : SourceOwnership.Tag) : Fin 944 := + ⟨SourceOwnership.lookup SourceOwnership.tagInitialFrame t.val, tag_frame_bound t⟩ + +theorem tag_residual_diagonal : ∀ (t : SourceOwnership.Tag) (i j : Fin 8), + FrameGeometry.scaled 1 i j - FrameGeometry.scaled (tagFrame t) i j = + if i = j ∧ SourceOwnership.sourceMask t ⟨i.val, Nat.lt_trans i.isLt (by decide)⟩ = true + then 4 else 0 := by decide + +theorem source_mask_outside : ∀ (t : SourceOwnership.Tag) (i : SourceOwnership.Axis), + 8 ≤ i.val → SourceOwnership.sourceMask t i = false := by decide + +end SelectedGeometry diff --git a/research/lean-multi-host-source/INDEPENDENT-REVIEW.md b/research/lean-multi-host-source/INDEPENDENT-REVIEW.md new file mode 100644 index 0000000000..434bf9d792 --- /dev/null +++ b/research/lean-multi-host-source/INDEPENDENT-REVIEW.md @@ -0,0 +1,209 @@ +# Source-invocation review + +Review snapshot: 2026-10-11, after the shared native-cover correction. +This is a separate agent's source-level review of the execution/contract +connection, not an independent human audit. The reviewer authored the +ownership/layout modules, `SourceInitialPayload`, and the corrective +`SourceCommonCover`; those portions are not independent of their author. + +The principal files reviewed were `SourceInvocation.lean`, +`SourceInvocationComparison.lean`, `SourceNativeInvocation.lean`, +`SourceInitialPayload.lean`, and `SourceMoveGeometry.lean`. The review also +followed their definitions into `SourceInvocationState`, `SourceRaw`, +`SourceRawGuards`, `SelectedGeometry`, and the pinned PR442 source. + +## Result and build qualification + +The raw execution-to-contract connection has the intended arbitrary-input +scope. It does not assume an endpoint contract, injective owner mapping, +helper-relative-frame equation, or clean dirty-helper input in its final +theorem. The concrete arguments are constructed and the intermediate +premises are discharged by named source certificates. + +One material issue was found jointly with the separate interface reviewer: +the first native comparison used two different extensions of the owner +cover charts. The original extension assigned identity to hosted owners +outside its active image; the relocated extension assigned their actual +cover maps. Equal raw payloads therefore did **not** imply equal native +retained inputs. The raw theorem was unaffected, but the stronger native +interpretation required correction. + +`SourceCommonCover` now supplies one shared extension. Its kernel-checked +finite bound excludes the hosted private family 9457 from every selected +original live owner. Its overlap theorem proves that the two active images +overlap only on identical data roles, whose charts agree. Both common-cover +identities then follow. This module and `SourceInitialPayload` passed Lean +with `-t0`. The revised `SourceNativeInvocation` uses this shared extension +and states explicit initialized native input equalities for hosts, data, +and exterior payloads. Its author confirmed the revised module, including +the initialized-state equalities, passed Lean with `-t0`. The separate-cover +issue is resolved. The final coherent replay has subsequently passed. + +At the original review snapshot, the geometry and final invocation modules +were still drafts. The subsequent component builds of `FrameData`, +`FrameGeometry`, `SelectedGeometry`, `SourceMoveGeometry`, and +`SourceInvocation` all passed against the actual source certificates with +`-t 0`. The final bridge source/artifact hashes are archived in +`review-receipts/final-bridge-components.json`. The subsequent coherent +package replay passed all 52 modules and 930 named theorem-closure audits; +`replay-result.json` and `VALIDATION.md` record that integration check. + +## Retained outputs and dirty inputs + +The retained state contains all 747 affected host streams, all 240 active +data streams, and a function on the entire complement of the union of the +two active owner images. Host observations use an invertible fixed family +chart, so they observe complete streams rather than selected coordinates. +`oldResult_framed` also equates every actual original-bank output with the +bank output returned by the contract. These outputs are not assumed restored +or silently projected away during that correspondence. The completion +equation itself compares retained outputs, as its type explicitly states; +old-bank outputs are auxiliary outputs, not equalities to initial bank data. + +All displayed payloads are arbitrary Boolean functions. They can contain +arbitrary correlations. `oldPayload_data`, `newPayload_data`, +`oldPayload_bank`, `newPayload_host`, and `shared_host_input` verify that the +explicit chart embeddings do not constrain or replace those inputs. +Exactly one designated private row is initially blank in each invocation. +The initializer describes that permitted initial state; it is not an +instruction that clears arbitrary dirty storage. Inaccessible tree padding +is not an additional physical allocation. + +The common slot universe and defaults on slots unused by one layout are a +local comparison device. They do not establish equivalence of the complete +global allocations or account for PR442's renumbering of other banks. + +## Literal execution and physical interpretation + +`SourceRaw.final` folds the complete chronological list of 19,002 source +events. `FrameTraceRoutes.route_projection` identifies the finite-register +encoding with the same frame trace; index bounds prevent modulo indexing +from changing an actual operand. `SourceRaw.gather_final` follows that whole +fold, not merely its first or last event. The exterior theorem preserves +every physical row outside its active owner image through the same fold. + +`SourceRawGuards` transports COPY blankness and ERASE equality through the +actual preceding raw/native states. It does not insert a fresh initial +state between guards. `SourceNativeInvocation` returns both private rows +blank. Its native ADD reads the same address in both physical streams: +the route cancellation follows from the common-cover identity, not a +newly assumed cross-stream interface. + +The geometry addresses the remaining distinction between abstract +frame labels and source matrix operators. The selected gauges include the +stage-2 exterior swap on axes 8 through 21. `SourceMoveGeometry` explicitly +cancels this common exterior factor, selects each actual MOVE's certified +nested projectors, and identifies its relative gauge with +`D_(Pnew-Pold)`. COPY is identified with the full local eight-coordinate +swap; ERASE uses the corresponding equality guard. The complete +`actual_matrix_run` theorem carries frame matching and chronological +validity through the entire list. The component build and subsequent coherent +package replay have both passed. + +The chosen helper charts are source-permitted coordinate isometries, not +numeric matrices claimed to have been emitted by the symbolic template. +The actual port bases and data-route matrices are bound separately. The +theorems quantify over any field with `2 ≠ 0` and any invertible common map +`d`, which includes the source's admitted odd fields and cover elements. +This broader identity does not claim that every arbitrary bijection `d` +is an admissible member of the source's orthogonal cover. + +## Source boundary and limits + +The reviewed source is PR442 commit +`4e16d001d505d4f21dd2bcfc44591f9be4c279bd`, stage 2, replica 0, pair 0, +forward orientation. During this review, `check_sources.py` passed: all six +pinned input hashes, the binary-record reconstruction, the identical parent +and hosted local words, all 19,002 events in order, and reproducible +certificate extraction were checked. The original review receipt was a local +artifact and is not included in this package. A separate, later regeneration +is recorded in the shipped [source-binding receipt](../lean-external-review/validation/source-binding.json). +This Python/source extraction boundary is reproducible, not kernel-verified. +The Lean kernel checks the mathematical claims about the embedded literals. + +The completion adds the explicit remaining pending swaps immediately after +this one invocation. It does not identify that completion with the later +recursive child schedule, prove a whole-cover sweep, verify global resource +charging, supply an all-size compiler, or establish any analytic bound. +Nothing here uses PR448's disputed split-helper interface or establishes +its advertised gain. + +## Detailed matrix-operation follow-up + +The following references were checked directly against the PR442 checkout +at the pinned commit above. Line numbers refer to this review snapshot. +The inherited `research/split-centres-global/proofs/PR386-BIT-GEOMETRY.txt` +supplies the operator definitions; its historical R865 ledger is not being +substituted for the selected R747 word. The latter is emitted by +`research/e8-early-reset-kernel/bit_global.py` and bound to the supplied +template and binary records. + +- **Projector identification.** The inherited operator definition is + `D_P = [[I-P,P],[P,I-P]]` (PR386 geometry, lines 37–46). + `FrameGeometry.partialSwap` is exactly this action: + `(x + P(y-x), y - P(y-x))`. The source frame's `B` rows are the image + subspace. `generate_frame_data.py:83–95` binds the complete `[B;A]` + row stack and computes integer witnesses; `FrameGeometry.projector_stack` + proves the supplied projector fixes the `B` columns and kills the + `A` columns. `stack_right_inverse` and `stack_left_inverse` prevent a + deficient spanning family from making those equations vacuous after + reduction to an odd field. Integer casts and denominators 4 and 256 + avoid an invalid rational-field embedding. +- **MOVE direction.** The source advances old frame to new frame and + records their nonnegative dimension difference + (`e8-early-reset-kernel/bit_global.py:91–96`). For payload pullback, + preserving decoded contents requires `old.forward ∘ new.inverse` + (`FramedReplay.lean:35–46`). After cancelling the common exterior + factor, the order is therefore `D_old D_new`, not a sign-reversed + residual. `SourceMoveGeometry:25–56` obtains both absorption equations + from the literal MOVE pair and uses `P_old P_new = P_old` to obtain + exactly `D_(P_new-P_old)`. This agrees with the source's displayed + `D_new D_old` law because the same certified nested projectors commute. + `SourceFrameMoves.move_pair` in `FrameMoveData.lean` binds the selected transition to the literal + old/new labels; a nominal rank equality alone is not used. +- **E2 cancellation.** PR386 geometry lines 48–54 specify the same first + two exterior 7-blocks on every frame of stage 2. They are axes 8–21. + `FrameGeometry.gaugeStage2` includes this actual swap in the forward map + and in the inverse map in reverse order. In the relative map the two + exterior swaps are adjacent and cancel by involution. No unproved + commutation premise is needed for that cancellation, and the other + 56 coordinates remain fixed by the local residual. +- **COPY.** The actual forward emitter checks a fresh blank temporary, + no currently retained center, and a frame difference of eight + (`bit_global.py:104–110`). `SourceFrameLabels.copy_frames` certifies + that every selected COPY uses frame 1 to frame 0. + `SourceMoveGeometry:75–110` identifies this relative transport with + the full swap on local axes 0–7, fixing all exterior axes. + `physicalStep_copy` (lines 158–178) identifies the operational step; + COPY legality is separately discharged along the same run, rather + than being deduced merely from the operator equality. +- **ERASE.** The emitter requires the retained center, the exact source + and temporary frames, and equal scalar columns before returning the + temporary to zero (`bit_global.py:111–116`). `FrameTraceCore:31–42` + checks center lifetime and excludes writes to the center while it is + retained. `SourceRawGuards:62–75` expresses ERASE as equality with the + source transported to the temporary's actual current frame, and its + recursive predicate uses each preceding physical output. + `SourceMoveGeometry:112–124` identifies that transport as the full + local swap. Thus the interpreter's zero assignment represents a + certified uncomputation, not permission to discard arbitrary dirt. + The post-ERASE frame-zero marker replaces the source's unallocated + marker; changing metadata on a zero payload has no address operation. +- **Whole execution.** `SourceMoveGeometry.matrix_run_eq:191–214` + propagates frame matching and chronological checks after each actual + instruction. `actual_matrix_run:218–224` discharges those hypotheses + using the literal trace and initial metadata. The final + `SourceInvocation.selected_call_completion` obtains its endpoint + through `SourceInvocationComparison` and `SelectedGeometry.helper_relative`. + Its companion theorems `selected_matrix_realization` and + `selected_original_matrix_realization` identify those same concrete + raw runs with the whole matrix word. `selected_native_completion` + uses the common-cover native readbacks, while + `selected_native_clean` and `selected_temporary_restoration` provide + legality and the private-row endpoint. The matrix-operation claim is + therefore an explicit companion equality, not an inference from a + module merely being imported. + +No further source-level operator mismatch was found in this follow-up. +The geometry and final invocation component builds have since passed, followed +by the coherent package replay recorded in `replay-result.json`. diff --git a/research/lean-multi-host-source/InvocationPayload.lean b/research/lean-multi-host-source/InvocationPayload.lean new file mode 100644 index 0000000000..0dd84c1eec --- /dev/null +++ b/research/lean-multi-host-source/InvocationPayload.lean @@ -0,0 +1,113 @@ +import SourceRaw +import SourceConnection + +/-! Explicit initial payload construction. Every live role is arbitrary; +only the source's designated private row is blank. Exterior payloads are +independent arbitrary functions, and owner injectivity is used explicitly. -/ +namespace InvocationPayload +open FramedReplay SourceConnection + +noncomputable def extend {R S A : Type} (owner : R → S) (values : R → A) + (outside : S → A) (s : S) : A := by + classical + exact if h : ∃ r, owner r = s then values (Classical.choose h) else outside s + +theorem extend_owner {R S A : Type} (owner : R → S) + (hinj : ∀ {r s}, owner r = owner s → r = s) + (values : R → A) (outside : S → A) (r : R) : + extend owner values outside (owner r) = values r := by + classical + unfold extend + split + · next h => rw [hinj (Classical.choose_spec h)] + · next h => exact False.elim (h ⟨r, rfl⟩) + +theorem extend_outside {R S A : Type} (owner : R → S) + (values : R → A) (outside : S → A) (s : S) + (hs : ∀ r, s ≠ owner r) : extend owner values outside s = outside s := by + classical + apply dif_neg + rintro ⟨r, h⟩ + exact hs r h.symm + +noncomputable def realize {S X : Type} (owner : SourceRaw.Role → S) + (chart : SourceRaw.Role → Gauge X) (input : Nat → X → Bool) + (outside : S → X → Bool) : S → X → Bool := + extend owner (fun r a => input r.val ((chart r).inverse a)) outside + +theorem realize_owner {S X : Type} (owner : SourceRaw.Role → S) + (chart : SourceRaw.Role → Gauge X) + (hinj : ∀ {r s}, owner r = owner s → r = s) + (input : Nat → X → Bool) (outside : S → X → Bool) (r : SourceRaw.Role) : + realize owner chart input outside (owner r) = + fun a => input r.val ((chart r).inverse a) := + extend_owner owner hinj _ outside r + +theorem input_realize {S X : Type} (owner : SourceRaw.Role → S) + (chart : SourceRaw.Role → Gauge X) + (hinj : ∀ {r s}, owner r = owner s → r = s) + (input : Nat → X → Bool) (outside : S → X → Bool) + (blank : ∀ i, 988 ≤ i → input i = fun _ => false) : + SourceRaw.input owner chart (realize owner chart input outside) = input := by + funext i a + unfold SourceRaw.input + split + · next hi => simp only [realize_owner owner chart hinj, (chart ⟨i, hi⟩).inverse_forward] + · next hi => exact (congrFun (blank i (Nat.le_of_not_lt hi)) a).symm + +theorem input_realize_packed {S X : Type} (owner : SourceRaw.Role → S) + (chart : SourceRaw.Role → Gauge X) + (hinj : ∀ {r s}, owner r = owner s → r = s) + (data : Data → X → Bool) (helpers : Host → X → Bool) + (outside : S → X → Bool) : + SourceRaw.input owner chart (realize owner chart (packed data helpers) outside) = + packed data helpers := by + apply input_realize owner chart hinj + intro i hi + simp only [packed, dif_neg (show ¬ i < 240 by omega), + dif_neg (show ¬ i < 987 by omega)] + +/-- The actual complete raw fold, initialized by the displayed payload +construction, realizes the arbitrary-input framed invocation. -/ +theorem realized_gather {S X : Type} (owner : SourceRaw.Role → S) + (chart : SourceRaw.Role → Gauge X) + (hinj : ∀ {r s}, owner r = owner s → r = s) + (gauges : Nat → Gauge X) (data : Data → X → Bool) + (helpers : Host → X → Bool) (outside : S → X → Bool) (r : SourceRaw.Role) : + OwnerTransport.gather owner chart + (SourceRaw.final owner chart gauges + (realize owner chart (packed data helpers) outside)) r = + (SourceFramed.final gauges (packed data helpers)).get r.val := by + have h := SourceRaw.gather_final owner chart hinj gauges + (realize owner chart (packed data helpers) outside) r + rw [input_realize_packed owner chart hinj] at h + exact h + +theorem realized_payload {S X : Type} (owner : SourceRaw.Role → S) + (chart : SourceRaw.Role → Gauge X) + (hinj : ∀ {r s}, owner r = owner s → r = s) + (gauges : Nat → Gauge X) (data : Data → X → Bool) + (helpers : Host → X → Bool) (outside : S → X → Bool) + (r : SourceRaw.Role) (a : X) : + (SourceRaw.final owner chart gauges + (realize owner chart (packed data helpers) outside) (owner r)).2 a = + ((SourceFramed.final gauges (packed data helpers)).get r.val).2 + ((chart r).inverse a) := by + have h := congrArg Prod.snd + (realized_gather owner chart hinj gauges data helpers outside r) + have ha := congrFun h ((chart r).inverse a) + simpa only [OwnerTransport.gather, (chart r).forward_inverse] using ha + +theorem realized_payloads {S X : Type} (owner : SourceRaw.Role → S) + (chart : SourceRaw.Role → Gauge X) + (hinj : ∀ {r s}, owner r = owner s → r = s) + (gauges : Nat → Gauge X) (data : Data → X → Bool) + (helpers : Host → X → Bool) (outside : S → X → Bool) : + (fun r => (SourceRaw.final owner chart gauges + (realize owner chart (packed data helpers) outside) (owner r)).2) = + fun r a => ((SourceFramed.final gauges (packed data helpers)).get r.val).2 + ((chart r).inverse a) := by + funext r a + exact realized_payload owner chart hinj gauges data helpers outside r a + +end InvocationPayload diff --git a/research/lean-multi-host-source/LinearReplay.lean b/research/lean-multi-host-source/LinearReplay.lean new file mode 100644 index 0000000000..b65ad0bedf --- /dev/null +++ b/research/lean-multi-host-source/LinearReplay.lean @@ -0,0 +1,176 @@ +import RowEvaluation + +/-! +Sound symbolic execution of the normalized bit word. The same total gate +semantics runs on coefficient rows and Boolean values. A separate checker +verifies register ranges and the copy/erase clean-temporary preconditions. +Frame operations (opcode 0) act trivially in these normalized coordinates; +identifying those coordinates with physical streams requires a separate +frame invariant, not this linear replay theorem. +-/ +namespace LinearReplay + +structure Event where + op : Nat + x : Nat + y : Nat + odd : Bool + deriving DecidableEq + +def step (zero : α) (xor : α → α → α) (s : Array α) (e : Event) : Array α := + match e.op with + | 0 => s + | 1 => if e.odd then s.setIfInBounds e.x (xor (s.getD e.x zero) (s.getD e.y zero)) else s + | 2 => s.setIfInBounds e.y (s.getD e.x zero) + | _ => s.setIfInBounds e.y zero + +def run (zero : α) (xor : α → α → α) (es : List Event) (s : Array α) : Array α := + es.foldl (step zero xor) s + +def rowStep := step (0 : Nat) (· ^^^ ·) +def boolStep := step false (· ^^ ·) +def runRows := run (0 : Nat) (· ^^^ ·) +def runBools := run false (· ^^ ·) + +def rowChecks (s : Array Nat) (e : Event) : Bool := + match e.op with + | 0 => e.x < 987 + | 1 => e.x < 987 && e.y <= 987 && e.x != e.y + | 2 => e.x < 987 && e.y == 987 && s.getD e.y 0 == 0 + | 3 => e.x < 987 && e.y == 987 && s.getD e.x 0 == s.getD e.y 0 + | _ => false + +def checkedRowStep (s : Array Nat × Bool) (e : Event) : Array Nat × Bool := + (rowStep s.1 e, s.2 && rowChecks s.1 e) + +def runCheckedRows (es : List Event) (s : Array Nat × Bool) : Array Nat × Bool := + es.foldl checkedRowStep s + +def evalRows (n : Nat) (u : Nat → Bool) (s : Array Nat) : Array Bool := + s.map (evalRow n u) + +theorem map_getD (f : α → β) (s : Array α) (i : Nat) (zero : α) : + (s.map f).getD i (f zero) = f (s.getD i zero) := by + simp only [Array.getD_eq_getD_getElem?, Array.getElem?_map] + cases s[i]? <;> rfl + +theorem step_map (zero : α) (zero' : β) (xor : α → α → α) (xor' : β → β → β) + (f : α → β) (hzero : f zero = zero') + (hxor : ∀ a b, f (xor a b) = xor' (f a) (f b)) (s : Array α) (e : Event) : + (step zero xor s e).map f = step zero' xor' (s.map f) e := by + obtain ⟨op, x, y, odd⟩ := e + cases op with + | zero => rfl + | succ op => + cases op with + | zero => + cases odd <;> simp [step, hxor, ← hzero] + | succ op => + cases op with + | zero => simp [step, ← hzero] + | succ op => simp [step, hzero] + +theorem run_map (zero : α) (zero' : β) (xor : α → α → α) (xor' : β → β → β) + (f : α → β) (hzero : f zero = zero') + (hxor : ∀ a b, f (xor a b) = xor' (f a) (f b)) (es : List Event) (s : Array α) : + (run zero xor es s).map f = run zero' xor' es (s.map f) := by + induction es generalizing s with + | nil => rfl + | cons e es ih => + change (run zero xor es (step zero xor s e)).map f = + run zero' xor' es (step zero' xor' (s.map f) e) + rw [ih, step_map zero zero' xor xor' f hzero hxor] + +theorem evalRows_step (n : Nat) (u : Nat → Bool) (s : Array Nat) (e : Event) : + evalRows n u (rowStep s e) = boolStep (evalRows n u s) e := by + exact step_map 0 false (· ^^^ ·) (· ^^ ·) (evalRow n u) + (evalRow_zero n u) (evalRow_xor n u) s e + +theorem evalRows_run (n : Nat) (u : Nat → Bool) (es : List Event) (s : Array Nat) : + evalRows n u (runRows es s) = runBools es (evalRows n u s) := by + exact run_map 0 false (· ^^^ ·) (· ^^ ·) (evalRow n u) + (evalRow_zero n u) (evalRow_xor n u) es s + +theorem checked_projection (es : List Event) (s : Array Nat × Bool) : + (runCheckedRows es s).1 = runRows es s.1 := by + induction es generalizing s with + | nil => rfl + | cons e es ih => + exact ih (checkedRowStep s e) + +def basisRows (n : Nat) : Array Nat := + (Array.range (n + 1)).map fun i => if i < n then 1 <<< i else 0 + +def dirtyInput (n : Nat) (u : Nat → Bool) : Array Bool := + (Array.range (n + 1)).map fun i => if i < n then u i else false + +theorem evalRows_basisRows (n : Nat) (u : Nat → Bool) : + evalRows n u (basisRows n) = dirtyInput n u := by + simp only [evalRows, basisRows, dirtyInput, Array.map_map] + congr 1 + funext i + by_cases h : i < n <;> simp [h, evalRow_shift_basis] + +def boolChecks (s : Array Bool) (e : Event) : Bool := + match e.op with + | 0 => e.x < 987 + | 1 => e.x < 987 && e.y <= 987 && e.x != e.y + | 2 => e.x < 987 && e.y == 987 && !(s.getD e.y false) + | 3 => e.x < 987 && e.y == 987 && s.getD e.x false == s.getD e.y false + | _ => false + +def checkedBoolStep (s : Array Bool × Bool) (e : Event) : Array Bool × Bool := + (boolStep s.1 e, s.2 && boolChecks s.1 e) + +def runCheckedBools (es : List Event) (s : Array Bool × Bool) : Array Bool × Bool := + es.foldl checkedBoolStep s + +theorem evalRows_getD (n : Nat) (u : Nat → Bool) (s : Array Nat) (i : Nat) : + (evalRows n u s).getD i false = evalRow n u (s.getD i 0) := by + simpa [evalRows] using map_getD (evalRow n u) s i 0 + +theorem checks_sound (n : Nat) (u : Nat → Bool) (s : Array Nat) (e : Event) + (h : rowChecks s e = true) : boolChecks (evalRows n u s) e = true := by + obtain ⟨op, x, y, odd⟩ := e + cases op with + | zero => exact h + | succ op => + cases op with + | zero => exact h + | succ op => + cases op with + | zero => + simp only [rowChecks, Bool.and_eq_true, beq_iff_eq] at h + simp only [boolChecks, Bool.and_eq_true, beq_iff_eq, evalRows_getD] + exact ⟨h.1, by simp [h.2]⟩ + | succ op => + cases op with + | zero => + simp only [rowChecks, Bool.and_eq_true, beq_iff_eq] at h + simp only [boolChecks, Bool.and_eq_true, beq_iff_eq, evalRows_getD] + exact ⟨h.1, congrArg (evalRow n u) h.2⟩ + | succ op => cases h + +theorem checked_flag_mono (es : List Event) (s : Array Nat × Bool) + (h : (runCheckedRows es s).2 = true) : s.2 = true := by + induction es generalizing s with + | nil => exact h + | cons e es ih => + have h' := ih (checkedRowStep s e) h + exact (Bool.and_eq_true_iff.mp h').1 + +theorem checked_guards_sound (n : Nat) (u : Nat → Bool) (es : List Event) + (s : Array Nat × Bool) (h : (runCheckedRows es s).2 = true) : + (runCheckedBools es (evalRows n u s.1, s.2)).2 = true := by + induction es generalizing s with + | nil => exact h + | cons e es ih => + have hfirst := checked_flag_mono es (checkedRowStep s e) h + have hparts : s.2 = true ∧ rowChecks s.1 e = true := by + simpa only [checkedRowStep, Bool.and_eq_true] using hfirst + have hb := checks_sound n u s.1 e hparts.2 + have hi := ih (checkedRowStep s e) h + simpa only [runCheckedBools, List.foldl_cons, checkedBoolStep, + evalRows_step, checkedRowStep, hparts.1, hparts.2, hb] using hi + +end LinearReplay diff --git a/research/lean-multi-host-source/MatrixCertificate.lean b/research/lean-multi-host-source/MatrixCertificate.lean new file mode 100644 index 0000000000..d948f4c891 --- /dev/null +++ b/research/lean-multi-host-source/MatrixCertificate.lean @@ -0,0 +1,14 @@ +import MatrixCheckpoints +namespace SourceMatrix +open TreeReplay + +theorem literal_word_checked : runCheckedRows forwardWord (initial,true) = (expected,true) := + (chunks_flatten forwardChunks (initial,true)).symm.trans runFull_checked + +theorem literal_word_rows : runRows forwardWord initial = expected := + (checked_projection forwardWord (initial,true)).symm.trans + (congrArg Prod.fst literal_word_checked) + +#print axioms literal_word_checked +#print axioms literal_word_rows +end SourceMatrix diff --git a/research/lean-multi-host-source/MatrixCheckpoints.lean b/research/lean-multi-host-source/MatrixCheckpoints.lean new file mode 100644 index 0000000000..f61ee07e02 --- /dev/null +++ b/research/lean-multi-host-source/MatrixCheckpoints.lean @@ -0,0 +1,414 @@ +import MatrixData +set_option maxRecDepth 100000 +set_option maxHeartbeats 0 +namespace SourceMatrix +open LinearReplay (Event) +open TreeReplay + +def runCheckedChunks : List (List Event) → (Tree Nat × Bool) → (Tree Nat × Bool) + | [], s => s + | es :: rest, s => runCheckedChunks rest (runCheckedRows es s) + +theorem combine (es : List Event) (rest : List (List Event)) + (s t u : Tree Nat × Bool) (h : runCheckedRows es s = t) + (tail : runCheckedChunks rest t = u) : runCheckedChunks (es :: rest) s = u := by + simp only [runCheckedChunks] + rw [h] + exact tail + +theorem chunks_flatten (chunks : List (List Event)) (s : Tree Nat × Bool) : + runCheckedChunks chunks s = runCheckedRows chunks.flatten s := by + induction chunks generalizing s with + | nil => rfl + | cons es rest ih => + simp only [runCheckedChunks, ih, List.flatten_cons, runCheckedRows, List.foldl_append] + +theorem checkpoint0 : runCheckedRows chunk0 state0 = state1 := by rfl +theorem checkpoint1 : runCheckedRows chunk1 state1 = state2 := by rfl +theorem checkpoint2 : runCheckedRows chunk2 state2 = state3 := by rfl +theorem checkpoint3 : runCheckedRows chunk3 state3 = state4 := by rfl +theorem checkpoint4 : runCheckedRows chunk4 state4 = state5 := by rfl +theorem checkpoint5 : runCheckedRows chunk5 state5 = state6 := by rfl +theorem checkpoint6 : runCheckedRows chunk6 state6 = state7 := by rfl +theorem checkpoint7 : runCheckedRows chunk7 state7 = state8 := by rfl +theorem checkpoint8 : runCheckedRows chunk8 state8 = state9 := by rfl +theorem checkpoint9 : runCheckedRows chunk9 state9 = state10 := by rfl +theorem checkpoint10 : runCheckedRows chunk10 state10 = state11 := by rfl +theorem checkpoint11 : runCheckedRows chunk11 state11 = state12 := by rfl +theorem checkpoint12 : runCheckedRows chunk12 state12 = state13 := by rfl +theorem checkpoint13 : runCheckedRows chunk13 state13 = state14 := by rfl +theorem checkpoint14 : runCheckedRows chunk14 state14 = state15 := by rfl +theorem checkpoint15 : runCheckedRows chunk15 state15 = state16 := by rfl +theorem checkpoint16 : runCheckedRows chunk16 state16 = state17 := by rfl +theorem checkpoint17 : runCheckedRows chunk17 state17 = state18 := by rfl +theorem checkpoint18 : runCheckedRows chunk18 state18 = state19 := by rfl +theorem checkpoint19 : runCheckedRows chunk19 state19 = state20 := by rfl +theorem checkpoint20 : runCheckedRows chunk20 state20 = state21 := by rfl +theorem checkpoint21 : runCheckedRows chunk21 state21 = state22 := by rfl +theorem checkpoint22 : runCheckedRows chunk22 state22 = state23 := by rfl +theorem checkpoint23 : runCheckedRows chunk23 state23 = state24 := by rfl +theorem checkpoint24 : runCheckedRows chunk24 state24 = state25 := by rfl +theorem checkpoint25 : runCheckedRows chunk25 state25 = state26 := by rfl +theorem checkpoint26 : runCheckedRows chunk26 state26 = state27 := by rfl +theorem checkpoint27 : runCheckedRows chunk27 state27 = state28 := by rfl +theorem checkpoint28 : runCheckedRows chunk28 state28 = state29 := by rfl +theorem checkpoint29 : runCheckedRows chunk29 state29 = state30 := by rfl +theorem checkpoint30 : runCheckedRows chunk30 state30 = state31 := by rfl +theorem checkpoint31 : runCheckedRows chunk31 state31 = state32 := by rfl +theorem checkpoint32 : runCheckedRows chunk32 state32 = state33 := by rfl +theorem checkpoint33 : runCheckedRows chunk33 state33 = state34 := by rfl +theorem checkpoint34 : runCheckedRows chunk34 state34 = state35 := by rfl +theorem checkpoint35 : runCheckedRows chunk35 state35 = state36 := by rfl +theorem checkpoint36 : runCheckedRows chunk36 state36 = state37 := by rfl +theorem checkpoint37 : runCheckedRows chunk37 state37 = state38 := by rfl +theorem checkpoint38 : runCheckedRows chunk38 state38 = state39 := by rfl +theorem checkpoint39 : runCheckedRows chunk39 state39 = state40 := by rfl +theorem checkpoint40 : runCheckedRows chunk40 state40 = state41 := by rfl +theorem checkpoint41 : runCheckedRows chunk41 state41 = state42 := by rfl +theorem checkpoint42 : runCheckedRows chunk42 state42 = state43 := by rfl +theorem checkpoint43 : runCheckedRows chunk43 state43 = state44 := by rfl +theorem checkpoint44 : runCheckedRows chunk44 state44 = state45 := by rfl +theorem checkpoint45 : runCheckedRows chunk45 state45 = state46 := by rfl +theorem checkpoint46 : runCheckedRows chunk46 state46 = state47 := by rfl +theorem checkpoint47 : runCheckedRows chunk47 state47 = state48 := by rfl +theorem checkpoint48 : runCheckedRows chunk48 state48 = state49 := by rfl +theorem checkpoint49 : runCheckedRows chunk49 state49 = state50 := by rfl +theorem checkpoint50 : runCheckedRows chunk50 state50 = state51 := by rfl +theorem checkpoint51 : runCheckedRows chunk51 state51 = state52 := by rfl +theorem checkpoint52 : runCheckedRows chunk52 state52 = state53 := by rfl +theorem checkpoint53 : runCheckedRows chunk53 state53 = state54 := by rfl +theorem checkpoint54 : runCheckedRows chunk54 state54 = state55 := by rfl +theorem checkpoint55 : runCheckedRows chunk55 state55 = state56 := by rfl +theorem checkpoint56 : runCheckedRows chunk56 state56 = state57 := by rfl +theorem checkpoint57 : runCheckedRows chunk57 state57 = state58 := by rfl +theorem checkpoint58 : runCheckedRows chunk58 state58 = state59 := by rfl +theorem checkpoint59 : runCheckedRows chunk59 state59 = state60 := by rfl +theorem checkpoint60 : runCheckedRows chunk60 state60 = state61 := by rfl +theorem checkpoint61 : runCheckedRows chunk61 state61 = state62 := by rfl +theorem checkpoint62 : runCheckedRows chunk62 state62 = state63 := by rfl +theorem checkpoint63 : runCheckedRows chunk63 state63 = state64 := by rfl +theorem checkpoint64 : runCheckedRows chunk64 state64 = state65 := by rfl +theorem checkpoint65 : runCheckedRows chunk65 state65 = state66 := by rfl +theorem checkpoint66 : runCheckedRows chunk66 state66 = state67 := by rfl +theorem checkpoint67 : runCheckedRows chunk67 state67 = state68 := by rfl +theorem checkpoint68 : runCheckedRows chunk68 state68 = state69 := by rfl +theorem checkpoint69 : runCheckedRows chunk69 state69 = state70 := by rfl +theorem checkpoint70 : runCheckedRows chunk70 state70 = state71 := by rfl +theorem checkpoint71 : runCheckedRows chunk71 state71 = state72 := by rfl +theorem checkpoint72 : runCheckedRows chunk72 state72 = state73 := by rfl +theorem checkpoint73 : runCheckedRows chunk73 state73 = state74 := by rfl +theorem checkpoint74 : runCheckedRows chunk74 state74 = state75 := by rfl +theorem checkpoint75 : runCheckedRows chunk75 state75 = state76 := by rfl +theorem checkpoint76 : runCheckedRows chunk76 state76 = state77 := by rfl +theorem checkpoint77 : runCheckedRows chunk77 state77 = state78 := by rfl +theorem checkpoint78 : runCheckedRows chunk78 state78 = state79 := by rfl +theorem checkpoint79 : runCheckedRows chunk79 state79 = state80 := by rfl +theorem checkpoint80 : runCheckedRows chunk80 state80 = state81 := by rfl +theorem checkpoint81 : runCheckedRows chunk81 state81 = state82 := by rfl +theorem checkpoint82 : runCheckedRows chunk82 state82 = state83 := by rfl +theorem checkpoint83 : runCheckedRows chunk83 state83 = state84 := by rfl +theorem checkpoint84 : runCheckedRows chunk84 state84 = state85 := by rfl +theorem checkpoint85 : runCheckedRows chunk85 state85 = state86 := by rfl +theorem checkpoint86 : runCheckedRows chunk86 state86 = state87 := by rfl +theorem checkpoint87 : runCheckedRows chunk87 state87 = state88 := by rfl +theorem checkpoint88 : runCheckedRows chunk88 state88 = state89 := by rfl +theorem checkpoint89 : runCheckedRows chunk89 state89 = state90 := by rfl +theorem checkpoint90 : runCheckedRows chunk90 state90 = state91 := by rfl +theorem checkpoint91 : runCheckedRows chunk91 state91 = state92 := by rfl +theorem checkpoint92 : runCheckedRows chunk92 state92 = state93 := by rfl +theorem checkpoint93 : runCheckedRows chunk93 state93 = state94 := by rfl +theorem checkpoint94 : runCheckedRows chunk94 state94 = state95 := by rfl +theorem checkpoint95 : runCheckedRows chunk95 state95 = state96 := by rfl +def suffix96 : List (List Event) := [] +def suffix95 : List (List Event) := chunk95 :: suffix96 +def suffix94 : List (List Event) := chunk94 :: suffix95 +def suffix93 : List (List Event) := chunk93 :: suffix94 +def suffix92 : List (List Event) := chunk92 :: suffix93 +def suffix91 : List (List Event) := chunk91 :: suffix92 +def suffix90 : List (List Event) := chunk90 :: suffix91 +def suffix89 : List (List Event) := chunk89 :: suffix90 +def suffix88 : List (List Event) := chunk88 :: suffix89 +def suffix87 : List (List Event) := chunk87 :: suffix88 +def suffix86 : List (List Event) := chunk86 :: suffix87 +def suffix85 : List (List Event) := chunk85 :: suffix86 +def suffix84 : List (List Event) := chunk84 :: suffix85 +def suffix83 : List (List Event) := chunk83 :: suffix84 +def suffix82 : List (List Event) := chunk82 :: suffix83 +def suffix81 : List (List Event) := chunk81 :: suffix82 +def suffix80 : List (List Event) := chunk80 :: suffix81 +def suffix79 : List (List Event) := chunk79 :: suffix80 +def suffix78 : List (List Event) := chunk78 :: suffix79 +def suffix77 : List (List Event) := chunk77 :: suffix78 +def suffix76 : List (List Event) := chunk76 :: suffix77 +def suffix75 : List (List Event) := chunk75 :: suffix76 +def suffix74 : List (List Event) := chunk74 :: suffix75 +def suffix73 : List (List Event) := chunk73 :: suffix74 +def suffix72 : List (List Event) := chunk72 :: suffix73 +def suffix71 : List (List Event) := chunk71 :: suffix72 +def suffix70 : List (List Event) := chunk70 :: suffix71 +def suffix69 : List (List Event) := chunk69 :: suffix70 +def suffix68 : List (List Event) := chunk68 :: suffix69 +def suffix67 : List (List Event) := chunk67 :: suffix68 +def suffix66 : List (List Event) := chunk66 :: suffix67 +def suffix65 : List (List Event) := chunk65 :: suffix66 +def suffix64 : List (List Event) := chunk64 :: suffix65 +def suffix63 : List (List Event) := chunk63 :: suffix64 +def suffix62 : List (List Event) := chunk62 :: suffix63 +def suffix61 : List (List Event) := chunk61 :: suffix62 +def suffix60 : List (List Event) := chunk60 :: suffix61 +def suffix59 : List (List Event) := chunk59 :: suffix60 +def suffix58 : List (List Event) := chunk58 :: suffix59 +def suffix57 : List (List Event) := chunk57 :: suffix58 +def suffix56 : List (List Event) := chunk56 :: suffix57 +def suffix55 : List (List Event) := chunk55 :: suffix56 +def suffix54 : List (List Event) := chunk54 :: suffix55 +def suffix53 : List (List Event) := chunk53 :: suffix54 +def suffix52 : List (List Event) := chunk52 :: suffix53 +def suffix51 : List (List Event) := chunk51 :: suffix52 +def suffix50 : List (List Event) := chunk50 :: suffix51 +def suffix49 : List (List Event) := chunk49 :: suffix50 +def suffix48 : List (List Event) := chunk48 :: suffix49 +def suffix47 : List (List Event) := chunk47 :: suffix48 +def suffix46 : List (List Event) := chunk46 :: suffix47 +def suffix45 : List (List Event) := chunk45 :: suffix46 +def suffix44 : List (List Event) := chunk44 :: suffix45 +def suffix43 : List (List Event) := chunk43 :: suffix44 +def suffix42 : List (List Event) := chunk42 :: suffix43 +def suffix41 : List (List Event) := chunk41 :: suffix42 +def suffix40 : List (List Event) := chunk40 :: suffix41 +def suffix39 : List (List Event) := chunk39 :: suffix40 +def suffix38 : List (List Event) := chunk38 :: suffix39 +def suffix37 : List (List Event) := chunk37 :: suffix38 +def suffix36 : List (List Event) := chunk36 :: suffix37 +def suffix35 : List (List Event) := chunk35 :: suffix36 +def suffix34 : List (List Event) := chunk34 :: suffix35 +def suffix33 : List (List Event) := chunk33 :: suffix34 +def suffix32 : List (List Event) := chunk32 :: suffix33 +def suffix31 : List (List Event) := chunk31 :: suffix32 +def suffix30 : List (List Event) := chunk30 :: suffix31 +def suffix29 : List (List Event) := chunk29 :: suffix30 +def suffix28 : List (List Event) := chunk28 :: suffix29 +def suffix27 : List (List Event) := chunk27 :: suffix28 +def suffix26 : List (List Event) := chunk26 :: suffix27 +def suffix25 : List (List Event) := chunk25 :: suffix26 +def suffix24 : List (List Event) := chunk24 :: suffix25 +def suffix23 : List (List Event) := chunk23 :: suffix24 +def suffix22 : List (List Event) := chunk22 :: suffix23 +def suffix21 : List (List Event) := chunk21 :: suffix22 +def suffix20 : List (List Event) := chunk20 :: suffix21 +def suffix19 : List (List Event) := chunk19 :: suffix20 +def suffix18 : List (List Event) := chunk18 :: suffix19 +def suffix17 : List (List Event) := chunk17 :: suffix18 +def suffix16 : List (List Event) := chunk16 :: suffix17 +def suffix15 : List (List Event) := chunk15 :: suffix16 +def suffix14 : List (List Event) := chunk14 :: suffix15 +def suffix13 : List (List Event) := chunk13 :: suffix14 +def suffix12 : List (List Event) := chunk12 :: suffix13 +def suffix11 : List (List Event) := chunk11 :: suffix12 +def suffix10 : List (List Event) := chunk10 :: suffix11 +def suffix9 : List (List Event) := chunk9 :: suffix10 +def suffix8 : List (List Event) := chunk8 :: suffix9 +def suffix7 : List (List Event) := chunk7 :: suffix8 +def suffix6 : List (List Event) := chunk6 :: suffix7 +def suffix5 : List (List Event) := chunk5 :: suffix6 +def suffix4 : List (List Event) := chunk4 :: suffix5 +def suffix3 : List (List Event) := chunk3 :: suffix4 +def suffix2 : List (List Event) := chunk2 :: suffix3 +def suffix1 : List (List Event) := chunk1 :: suffix2 +def suffix0 : List (List Event) := chunk0 :: suffix1 +theorem finish96 : runCheckedChunks suffix96 state96 = state96 := rfl +theorem finish95 : runCheckedChunks suffix95 state95 = state96 := + combine chunk95 suffix96 state95 state96 state96 checkpoint95 finish96 +theorem finish94 : runCheckedChunks suffix94 state94 = state96 := + combine chunk94 suffix95 state94 state95 state96 checkpoint94 finish95 +theorem finish93 : runCheckedChunks suffix93 state93 = state96 := + combine chunk93 suffix94 state93 state94 state96 checkpoint93 finish94 +theorem finish92 : runCheckedChunks suffix92 state92 = state96 := + combine chunk92 suffix93 state92 state93 state96 checkpoint92 finish93 +theorem finish91 : runCheckedChunks suffix91 state91 = state96 := + combine chunk91 suffix92 state91 state92 state96 checkpoint91 finish92 +theorem finish90 : runCheckedChunks suffix90 state90 = state96 := + combine chunk90 suffix91 state90 state91 state96 checkpoint90 finish91 +theorem finish89 : runCheckedChunks suffix89 state89 = state96 := + combine chunk89 suffix90 state89 state90 state96 checkpoint89 finish90 +theorem finish88 : runCheckedChunks suffix88 state88 = state96 := + combine chunk88 suffix89 state88 state89 state96 checkpoint88 finish89 +theorem finish87 : runCheckedChunks suffix87 state87 = state96 := + combine chunk87 suffix88 state87 state88 state96 checkpoint87 finish88 +theorem finish86 : runCheckedChunks suffix86 state86 = state96 := + combine chunk86 suffix87 state86 state87 state96 checkpoint86 finish87 +theorem finish85 : runCheckedChunks suffix85 state85 = state96 := + combine chunk85 suffix86 state85 state86 state96 checkpoint85 finish86 +theorem finish84 : runCheckedChunks suffix84 state84 = state96 := + combine chunk84 suffix85 state84 state85 state96 checkpoint84 finish85 +theorem finish83 : runCheckedChunks suffix83 state83 = state96 := + combine chunk83 suffix84 state83 state84 state96 checkpoint83 finish84 +theorem finish82 : runCheckedChunks suffix82 state82 = state96 := + combine chunk82 suffix83 state82 state83 state96 checkpoint82 finish83 +theorem finish81 : runCheckedChunks suffix81 state81 = state96 := + combine chunk81 suffix82 state81 state82 state96 checkpoint81 finish82 +theorem finish80 : runCheckedChunks suffix80 state80 = state96 := + combine chunk80 suffix81 state80 state81 state96 checkpoint80 finish81 +theorem finish79 : runCheckedChunks suffix79 state79 = state96 := + combine chunk79 suffix80 state79 state80 state96 checkpoint79 finish80 +theorem finish78 : runCheckedChunks suffix78 state78 = state96 := + combine chunk78 suffix79 state78 state79 state96 checkpoint78 finish79 +theorem finish77 : runCheckedChunks suffix77 state77 = state96 := + combine chunk77 suffix78 state77 state78 state96 checkpoint77 finish78 +theorem finish76 : runCheckedChunks suffix76 state76 = state96 := + combine chunk76 suffix77 state76 state77 state96 checkpoint76 finish77 +theorem finish75 : runCheckedChunks suffix75 state75 = state96 := + combine chunk75 suffix76 state75 state76 state96 checkpoint75 finish76 +theorem finish74 : runCheckedChunks suffix74 state74 = state96 := + combine chunk74 suffix75 state74 state75 state96 checkpoint74 finish75 +theorem finish73 : runCheckedChunks suffix73 state73 = state96 := + combine chunk73 suffix74 state73 state74 state96 checkpoint73 finish74 +theorem finish72 : runCheckedChunks suffix72 state72 = state96 := + combine chunk72 suffix73 state72 state73 state96 checkpoint72 finish73 +theorem finish71 : runCheckedChunks suffix71 state71 = state96 := + combine chunk71 suffix72 state71 state72 state96 checkpoint71 finish72 +theorem finish70 : runCheckedChunks suffix70 state70 = state96 := + combine chunk70 suffix71 state70 state71 state96 checkpoint70 finish71 +theorem finish69 : runCheckedChunks suffix69 state69 = state96 := + combine chunk69 suffix70 state69 state70 state96 checkpoint69 finish70 +theorem finish68 : runCheckedChunks suffix68 state68 = state96 := + combine chunk68 suffix69 state68 state69 state96 checkpoint68 finish69 +theorem finish67 : runCheckedChunks suffix67 state67 = state96 := + combine chunk67 suffix68 state67 state68 state96 checkpoint67 finish68 +theorem finish66 : runCheckedChunks suffix66 state66 = state96 := + combine chunk66 suffix67 state66 state67 state96 checkpoint66 finish67 +theorem finish65 : runCheckedChunks suffix65 state65 = state96 := + combine chunk65 suffix66 state65 state66 state96 checkpoint65 finish66 +theorem finish64 : runCheckedChunks suffix64 state64 = state96 := + combine chunk64 suffix65 state64 state65 state96 checkpoint64 finish65 +theorem finish63 : runCheckedChunks suffix63 state63 = state96 := + combine chunk63 suffix64 state63 state64 state96 checkpoint63 finish64 +theorem finish62 : runCheckedChunks suffix62 state62 = state96 := + combine chunk62 suffix63 state62 state63 state96 checkpoint62 finish63 +theorem finish61 : runCheckedChunks suffix61 state61 = state96 := + combine chunk61 suffix62 state61 state62 state96 checkpoint61 finish62 +theorem finish60 : runCheckedChunks suffix60 state60 = state96 := + combine chunk60 suffix61 state60 state61 state96 checkpoint60 finish61 +theorem finish59 : runCheckedChunks suffix59 state59 = state96 := + combine chunk59 suffix60 state59 state60 state96 checkpoint59 finish60 +theorem finish58 : runCheckedChunks suffix58 state58 = state96 := + combine chunk58 suffix59 state58 state59 state96 checkpoint58 finish59 +theorem finish57 : runCheckedChunks suffix57 state57 = state96 := + combine chunk57 suffix58 state57 state58 state96 checkpoint57 finish58 +theorem finish56 : runCheckedChunks suffix56 state56 = state96 := + combine chunk56 suffix57 state56 state57 state96 checkpoint56 finish57 +theorem finish55 : runCheckedChunks suffix55 state55 = state96 := + combine chunk55 suffix56 state55 state56 state96 checkpoint55 finish56 +theorem finish54 : runCheckedChunks suffix54 state54 = state96 := + combine chunk54 suffix55 state54 state55 state96 checkpoint54 finish55 +theorem finish53 : runCheckedChunks suffix53 state53 = state96 := + combine chunk53 suffix54 state53 state54 state96 checkpoint53 finish54 +theorem finish52 : runCheckedChunks suffix52 state52 = state96 := + combine chunk52 suffix53 state52 state53 state96 checkpoint52 finish53 +theorem finish51 : runCheckedChunks suffix51 state51 = state96 := + combine chunk51 suffix52 state51 state52 state96 checkpoint51 finish52 +theorem finish50 : runCheckedChunks suffix50 state50 = state96 := + combine chunk50 suffix51 state50 state51 state96 checkpoint50 finish51 +theorem finish49 : runCheckedChunks suffix49 state49 = state96 := + combine chunk49 suffix50 state49 state50 state96 checkpoint49 finish50 +theorem finish48 : runCheckedChunks suffix48 state48 = state96 := + combine chunk48 suffix49 state48 state49 state96 checkpoint48 finish49 +theorem finish47 : runCheckedChunks suffix47 state47 = state96 := + combine chunk47 suffix48 state47 state48 state96 checkpoint47 finish48 +theorem finish46 : runCheckedChunks suffix46 state46 = state96 := + combine chunk46 suffix47 state46 state47 state96 checkpoint46 finish47 +theorem finish45 : runCheckedChunks suffix45 state45 = state96 := + combine chunk45 suffix46 state45 state46 state96 checkpoint45 finish46 +theorem finish44 : runCheckedChunks suffix44 state44 = state96 := + combine chunk44 suffix45 state44 state45 state96 checkpoint44 finish45 +theorem finish43 : runCheckedChunks suffix43 state43 = state96 := + combine chunk43 suffix44 state43 state44 state96 checkpoint43 finish44 +theorem finish42 : runCheckedChunks suffix42 state42 = state96 := + combine chunk42 suffix43 state42 state43 state96 checkpoint42 finish43 +theorem finish41 : runCheckedChunks suffix41 state41 = state96 := + combine chunk41 suffix42 state41 state42 state96 checkpoint41 finish42 +theorem finish40 : runCheckedChunks suffix40 state40 = state96 := + combine chunk40 suffix41 state40 state41 state96 checkpoint40 finish41 +theorem finish39 : runCheckedChunks suffix39 state39 = state96 := + combine chunk39 suffix40 state39 state40 state96 checkpoint39 finish40 +theorem finish38 : runCheckedChunks suffix38 state38 = state96 := + combine chunk38 suffix39 state38 state39 state96 checkpoint38 finish39 +theorem finish37 : runCheckedChunks suffix37 state37 = state96 := + combine chunk37 suffix38 state37 state38 state96 checkpoint37 finish38 +theorem finish36 : runCheckedChunks suffix36 state36 = state96 := + combine chunk36 suffix37 state36 state37 state96 checkpoint36 finish37 +theorem finish35 : runCheckedChunks suffix35 state35 = state96 := + combine chunk35 suffix36 state35 state36 state96 checkpoint35 finish36 +theorem finish34 : runCheckedChunks suffix34 state34 = state96 := + combine chunk34 suffix35 state34 state35 state96 checkpoint34 finish35 +theorem finish33 : runCheckedChunks suffix33 state33 = state96 := + combine chunk33 suffix34 state33 state34 state96 checkpoint33 finish34 +theorem finish32 : runCheckedChunks suffix32 state32 = state96 := + combine chunk32 suffix33 state32 state33 state96 checkpoint32 finish33 +theorem finish31 : runCheckedChunks suffix31 state31 = state96 := + combine chunk31 suffix32 state31 state32 state96 checkpoint31 finish32 +theorem finish30 : runCheckedChunks suffix30 state30 = state96 := + combine chunk30 suffix31 state30 state31 state96 checkpoint30 finish31 +theorem finish29 : runCheckedChunks suffix29 state29 = state96 := + combine chunk29 suffix30 state29 state30 state96 checkpoint29 finish30 +theorem finish28 : runCheckedChunks suffix28 state28 = state96 := + combine chunk28 suffix29 state28 state29 state96 checkpoint28 finish29 +theorem finish27 : runCheckedChunks suffix27 state27 = state96 := + combine chunk27 suffix28 state27 state28 state96 checkpoint27 finish28 +theorem finish26 : runCheckedChunks suffix26 state26 = state96 := + combine chunk26 suffix27 state26 state27 state96 checkpoint26 finish27 +theorem finish25 : runCheckedChunks suffix25 state25 = state96 := + combine chunk25 suffix26 state25 state26 state96 checkpoint25 finish26 +theorem finish24 : runCheckedChunks suffix24 state24 = state96 := + combine chunk24 suffix25 state24 state25 state96 checkpoint24 finish25 +theorem finish23 : runCheckedChunks suffix23 state23 = state96 := + combine chunk23 suffix24 state23 state24 state96 checkpoint23 finish24 +theorem finish22 : runCheckedChunks suffix22 state22 = state96 := + combine chunk22 suffix23 state22 state23 state96 checkpoint22 finish23 +theorem finish21 : runCheckedChunks suffix21 state21 = state96 := + combine chunk21 suffix22 state21 state22 state96 checkpoint21 finish22 +theorem finish20 : runCheckedChunks suffix20 state20 = state96 := + combine chunk20 suffix21 state20 state21 state96 checkpoint20 finish21 +theorem finish19 : runCheckedChunks suffix19 state19 = state96 := + combine chunk19 suffix20 state19 state20 state96 checkpoint19 finish20 +theorem finish18 : runCheckedChunks suffix18 state18 = state96 := + combine chunk18 suffix19 state18 state19 state96 checkpoint18 finish19 +theorem finish17 : runCheckedChunks suffix17 state17 = state96 := + combine chunk17 suffix18 state17 state18 state96 checkpoint17 finish18 +theorem finish16 : runCheckedChunks suffix16 state16 = state96 := + combine chunk16 suffix17 state16 state17 state96 checkpoint16 finish17 +theorem finish15 : runCheckedChunks suffix15 state15 = state96 := + combine chunk15 suffix16 state15 state16 state96 checkpoint15 finish16 +theorem finish14 : runCheckedChunks suffix14 state14 = state96 := + combine chunk14 suffix15 state14 state15 state96 checkpoint14 finish15 +theorem finish13 : runCheckedChunks suffix13 state13 = state96 := + combine chunk13 suffix14 state13 state14 state96 checkpoint13 finish14 +theorem finish12 : runCheckedChunks suffix12 state12 = state96 := + combine chunk12 suffix13 state12 state13 state96 checkpoint12 finish13 +theorem finish11 : runCheckedChunks suffix11 state11 = state96 := + combine chunk11 suffix12 state11 state12 state96 checkpoint11 finish12 +theorem finish10 : runCheckedChunks suffix10 state10 = state96 := + combine chunk10 suffix11 state10 state11 state96 checkpoint10 finish11 +theorem finish9 : runCheckedChunks suffix9 state9 = state96 := + combine chunk9 suffix10 state9 state10 state96 checkpoint9 finish10 +theorem finish8 : runCheckedChunks suffix8 state8 = state96 := + combine chunk8 suffix9 state8 state9 state96 checkpoint8 finish9 +theorem finish7 : runCheckedChunks suffix7 state7 = state96 := + combine chunk7 suffix8 state7 state8 state96 checkpoint7 finish8 +theorem finish6 : runCheckedChunks suffix6 state6 = state96 := + combine chunk6 suffix7 state6 state7 state96 checkpoint6 finish7 +theorem finish5 : runCheckedChunks suffix5 state5 = state96 := + combine chunk5 suffix6 state5 state6 state96 checkpoint5 finish6 +theorem finish4 : runCheckedChunks suffix4 state4 = state96 := + combine chunk4 suffix5 state4 state5 state96 checkpoint4 finish5 +theorem finish3 : runCheckedChunks suffix3 state3 = state96 := + combine chunk3 suffix4 state3 state4 state96 checkpoint3 finish4 +theorem finish2 : runCheckedChunks suffix2 state2 = state96 := + combine chunk2 suffix3 state2 state3 state96 checkpoint2 finish3 +theorem finish1 : runCheckedChunks suffix1 state1 = state96 := + combine chunk1 suffix2 state1 state2 state96 checkpoint1 finish2 +theorem finish0 : runCheckedChunks suffix0 state0 = state96 := + combine chunk0 suffix1 state0 state1 state96 checkpoint0 finish1 +theorem runFull_checked : runCheckedChunks forwardChunks (initial,true) = (expected,true) := finish0 +#print axioms runFull_checked +end SourceMatrix diff --git a/research/lean-multi-host-source/MatrixData.lean b/research/lean-multi-host-source/MatrixData.lean new file mode 100644 index 0000000000..ec15d60282 --- /dev/null +++ b/research/lean-multi-host-source/MatrixData.lean @@ -0,0 +1,40772 @@ +import TreeReplay +/-! +Generated source-bound data. The literal 19,002-event forward word is retained, +including frame events. Node definitions share immutable symbolic matrices; +leaf bit i denotes arbitrary original input variable i. Role 987 and unused +leaves 988..1023 start zero. Their physical interpretation is separate. +-/ +set_option maxRecDepth 100000 +set_option maxHeartbeats 0 +namespace SourceMatrix +open LinearReplay (Event) +open TreeReplay + +def node0 : Tree Nat := .leaf 1 +def node1 : Tree Nat := .leaf 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096 +def node2 : Tree Nat := .node node0 node1 +def node3 : Tree Nat := .leaf 115792089237316195423570985008687907853269984665640564039457584007913129639936 +def node4 : Tree Nat := .leaf 1552518092300708935148979488462502555256886017116696611139052038026050952686376886330878408828646477950487730697131073206171580044114814391444287275041181139204454976020849905550265285631598444825262999193716468750892846853816057856 +def node5 : Tree Nat := .node node3 node4 +def node6 : Tree Nat := .node node2 node5 +def node7 : Tree Nat := .leaf 340282366920938463463374607431768211456 +def node8 : Tree Nat := .leaf 4562440617622195218641171605700291324893228507248559930579192517899275167208677386505912811317371399778642309573594407310688704721375437998252661319722214188251994674360264950082874192246603776 +def node9 : Tree Nat := .node node7 node8 +def node10 : Tree Nat := .leaf 39402006196394479212279040100143613805079739270465446667948293404245721771497210611414266254884915640806627990306816 +def node11 : Tree Nat := .leaf 528294531135665246352339784916516606518847326036121522127960709026673902556724859474417255887657187894674394993257128678882347559502685537250538978462939576908386683999005084168731517676426441053024232908211188404148028292751561738838396898767036476489538580897737998336 +def node12 : Tree Nat := .node node10 node11 +def node13 : Tree Nat := .node node9 node12 +def node14 : Tree Nat := .node node6 node13 +def node15 : Tree Nat := .leaf 18446744073709551616 +def node16 : Tree Nat := .leaf 247330401473104534060502521019647190035131349101211839914063056092897225106531867170316401061243044989597671426016139339351365034306751209967546155101893167916606772148699136 +def node17 : Tree Nat := .node node15 node16 +def node18 : Tree Nat := .leaf 2135987035920910082395021706169552114602704522356652769947041607822219725780640550022962086936576 +def node19 : Tree Nat := .leaf 28638903918474961204418783933674838490721739172170652529441449702311064005352904159345284265824628375429359509218999720074396860757073376700445026041564579620512874307979212102266801261478978776245040008231745247475930553606737583615358787106474295296 +def node20 : Tree Nat := .node node18 node19 +def node21 : Tree Nat := .node node17 node20 +def node22 : Tree Nat := .leaf 6277101735386680763835789423207666416102355444464034512896 +def node23 : Tree Nat := .leaf 84162174424773976115855838126082058648805436845170781751972494449099714468753293153818664580441415219631727501698851483408310916002940861810045036330430093599283578738055113571066620126149163476340692027772502016 +def node24 : Tree Nat := .node node22 node23 +def node25 : Tree Nat := .leaf 726838724295606890549323807888004534353641360687318060281490199180639288113397923326191050713763565560762521606266177933534601628614656 +def node26 : Tree Nat := .leaf 9745314011399999080353382387875188310876226857595007526867906457212948690766426102465615065882010259225304916231408668183459169865203094046577987296312653419531277699956473029870789655490053648352799593479218378873685597925394874945746363615468965612827738803104277547081828589991914110976 +def node27 : Tree Nat := .node node25 node26 +def node28 : Tree Nat := .node node24 node27 +def node29 : Tree Nat := .node node21 node28 +def node30 : Tree Nat := .node node14 node29 +def node31 : Tree Nat := .leaf 4294967296 +def node32 : Tree Nat := .leaf 57586096570152913699974892898380567793532123114264532903689671329431521032595044740083720782129802971518987656109067457577065805510327036019308994315074097345724416 +def node33 : Tree Nat := .node node31 node32 +def node34 : Tree Nat := .leaf 497323236409786642155382248146820840100456150797347717440463976893159497012533375533056 +def node35 : Tree Nat := .leaf 6668014432879854274079851790721257797144758322315908160396257811764037237817632071521432200871554290742929910593433240445888801654119365080363356052330830046095157579514014558463078285911814024728965016135886601981690748037476461291163877376 +def node36 : Tree Nat := .node node34 node35 +def node37 : Tree Nat := .node node33 node36 +def node38 : Tree Nat := .leaf 1461501637330902918203684832716283019655932542976 +def node39 : Tree Nat := .leaf 19595533242629369747791401605606558418088927130487463844933662202465281465266200982457647235235528838735010358900495684567911298014908298340170885513171109743249504533143507682501017145381579984990109696 +def node40 : Tree Nat := .node node38 node39 +def node41 : Tree Nat := .leaf 169230328010303641331690318856389386196071598838855992136870091590247882556495704531248437872567112920983350278405979725889536 +def node42 : Tree Nat := .leaf 2269007733883335972287082669296112915239349672942191252221331572442536403137824056312817862695551072066953619064625508194663368599769448406663254670871573830845597595897613333042429214224697474472410882236254024057110212260250671521235807709272244389361641091086035023229622419456 +def node43 : Tree Nat := .node node41 node42 +def node44 : Tree Nat := .node node40 node43 +def node45 : Tree Nat := .node node37 node44 +def node46 : Tree Nat := .leaf 79228162514264337593543950336 +def node47 : Tree Nat := .leaf 1062275985633534197379176413104937254659186235454063846398888276400807119721704485478325004530458571337778658972493002030693158675305414478819039957533174703887662541670786438063456256 +def node48 : Tree Nat := .node node46 node47 +def node49 : Tree Nat := .leaf 9173994463960286046443283581208347763186259956673124494950355357547691504353939232280074212440502746218496 +def node50 : Tree Nat := .leaf 123003155723136208567847447683223664415731869180715065944930703618254955521953492303010368693540149343822709050322214299552689203876695953600699775494388206142090885899729347827083318884583758435450548517566916626912548274908112766882031433928533568160966639616 +def node51 : Tree Nat := .node node49 node50 +def node52 : Tree Nat := .node node48 node51 +def node53 : Tree Nat := .leaf 26959946667150639794667015087019630673637144422540572481103610249216 +def node54 : Tree Nat := .leaf 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Tree Nat := .leaf 7588550360256754183279148073529370729071901715047420004889892225542594864082845696 +def node67 : Tree Nat := .leaf 101745825697019260773923519755878567461315282017759829107608914364075275235254395622580447400994175578963163918967182013639660669771108475957692810857098847138903161308502419410142185759152435680068435915159402496058513611411689167650816 +def node68 : Tree Nat := .node node66 node67 +def node69 : Tree Nat := .node node65 node68 +def node70 : Tree Nat := .leaf 22300745198530623141535718272648361505980416 +def node71 : Tree Nat := .leaf 299004108316488185848867822351174292268202623451041623610437960853046897358187881202051502002495252055893102400215083077513294952620060704653486412249315029041282722978874323768631243063073425063936 +def node72 : Tree Nat := .node node70 node71 +def node73 : Tree Nat := .leaf 2582249878086908589655919172003011874329705792829223512830659356540647622016841194629645353280137831435903171972747493376 +def node74 : Tree Nat := .leaf 34622310392506957584946940144288832324819178359103260074178033026772100877957520390515409281853501465865381150278099185099233529659567999369251322492547208112268029722558797196081988742442283240850996127872528443254245182193766350116513179157596502523218400437714157458948096 +def node75 : Tree Nat := .node node73 node74 +def node76 : Tree Nat := .node node72 node75 +def node77 : Tree Nat := .node node69 node76 +def node78 : Tree Nat := .leaf 1208925819614629174706176 +def node79 : Tree Nat := .leaf 16209045190941378744189093217543598246142368094697019140608036444104112544581672446873855659949624196438272994575393707743731058888327247296433104820757670652582741419537146576896 +def node80 : Tree Nat := .node node78 node79 +def node81 : Tree Nat := .leaf 139984046386112763159840142535527767382602843577165595931249318810236991948760059086304843329475444736 +def node82 : Tree Nat := .leaf 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436994993873214129706097166956708350993678881411295357199729151951767944417616335439228580716318181998128654620651240845861768505204366709906692902245553277900892247131030458103436298545516643924637451297481464347472084863384057367177715867713536 +def node99 : Tree Nat := .node node97 node98 +def node100 : Tree Nat := .node node96 node99 +def node101 : Tree Nat := .leaf 95780971304118053647396689196894323976171195136475136 +def node102 : Tree Nat := .leaf 1284212866588958375791257295625031412487875928423626430541572486100764686107685747586344369208395617975337638880902885183842634826705030240021439152991181848133599529084092919480386659639727225896311829037056 +def node103 : Tree Nat := .node node101 node102 +def node104 : Tree Nat := .leaf 11090678776483259438313656736572334813745748301503266300681918322458485231222502492159897624416558312389564843845614287315896631296 +def node105 : Tree Nat := .leaf 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node119 node57 +def node121 : Tree Nat := .node node118 node120 +def node122 : Tree Nat := .node node115 node121 +def node123 : Tree Nat := .node node108 node122 +def node124 : Tree Nat := .node node93 node123 +def node125 : Tree Nat := .node node62 node124 +def node126 : Tree Nat := .leaf 256 +def node127 : Tree Nat := .leaf 3432398830065304857490950399540696608634717650071652704697231729592771591698828026061279820330727277488648155695740429018560993999858321906287014145557528576 +def node128 : Tree Nat := .node node126 node127 +def node129 : Tree Nat := .leaf 29642774844752946028434172162224104410437116074403984394101141506025761187823616 +def node130 : Tree Nat := .leaf 397444631628981487398138749046400654145762820381874332451597321734669043887712482900704872660133498355324859058465554740779924491293392484209737542410542371636340473861337575820867913121689201875267327793591416000228568794576910811136 +def node131 : Tree Nat := .node node129 node130 +def node132 : Tree Nat := .node node128 node131 +def node133 : Tree Nat := .leaf 87112285931760246646623899502532662132736 +def node134 : Tree Nat := .leaf 1167984798111281975972139931059274579172666497855631342228273284582214442805421410945513679697247078343332431250840168271536308408672112127552681297848886832192510636636227827221215793215130566656 +def node135 : Tree Nat := .node node133 node134 +def node136 : Tree Nat := .leaf 10086913586276986678343434265636765134100413253239154346994763111486904773503285916522052161250538404046496765518544896 +def node137 : Tree Nat := .leaf 135243399970730303066198984938628251268824915465247109664757941510828519054521564025450817507240240101036645118273824941793880975232687497536137978486512531688546991103745301547195268525165168909574203624502064231461895242944399805142629606084361337981321876709820927574016 +def node138 : Tree Nat := .node node136 node137 +def node139 : Tree Nat := .node node135 node138 +def node140 : Tree Nat := .node node132 node139 +def node141 : Tree Nat := .leaf 4722366482869645213696 +def node142 : Tree Nat := .leaf 63316582777114760719488645381029680648993625369910231018000142359781689627272157995600998671678219517337003885060131670873949448782528309751691815706084650986651333670066978816 +def node143 : Tree Nat := .node node141 node142 +def node144 : Tree Nat := .leaf 546812681195752981093125556779405341338292357723303109106442651602488249799843980805878294255763456 +def node145 : Tree Nat := .leaf 7331559403129590068331208687020758653624765228075687047537011123791632385370343464792392772051104864109916034360063928339045596353810784435313926666640532382851295822842678298180301122938618566718730242107326783353838221723324821405531849499257419595776 +def node146 : Tree Nat := .node node144 node145 +def node147 : Tree Nat := .node node143 node146 +def node148 : Tree Nat := .leaf 1606938044258990275541962092341162602522202993782792835301376 +def node149 : Tree Nat := .leaf 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1099511627776 +def node158 : Tree Nat := .leaf 14742040721959145907193572581985425355144223517251720423344555860334469384344331453461432520225229560708860839963921269139728846210643721220943102544658968920505450496 +def node159 : Tree Nat := .node node157 node158 +def node160 : Tree Nat := .leaf 127314748520905380391777855525586135065716774604121015664758778084648831235208544136462336 +def node161 : Tree Nat := .leaf 1707011694817242694164442058424641996069058130512872489061441999811593532881313810309486643423117898430190057111918909554147533223454557460573019149396692491800360340355587726966548041193424390330615044130786970107312831497593974090537952608256 +def node162 : Tree Nat := .node node160 node161 +def node163 : Tree Nat := .node node159 node162 +def node164 : Tree Nat := .leaf 374144419156711147060143317175368453031918731001856 +def node165 : Tree Nat := .leaf 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Tree Nat := .leaf 1942668892225729070919461906823518906642406839052139521251812409738904285205208498176 +def node192 : Tree Nat := .leaf 26046931378436930758124421057504913270096712196546516251547882077203270460225125279380594534654508948214569963255598595491753131461403769845169359579417304867559209294976619368996399554343023534097519594280807038990979484521392426918608896 +def node193 : Tree Nat := .node node191 node192 +def node194 : Tree Nat := .node node190 node193 +def node195 : Tree Nat := .leaf 5708990770823839524233143877797980545530986496 +def node196 : Tree Nat := .leaf 76545051729020975577310162521900618820659871603466655644272117978380005723696097587725184512638784526308634214455061267843403507870735540391292521535824647434568377082591826884769598224146796816367616 +def node197 : Tree Nat := .node node195 node196 +def node198 : Tree Nat := .leaf 661055968790248598951915308032771039828404682964281219284648795274405791236311345825189210439715284847591212025023358304256 +def node199 : Tree Nat := .leaf 8863311460481781141746416676937941075153709659930434578989576454853657824757125219971944776154496375261537574471193391385403783592849407838528338558092085276740615608975052082196989118065224509657855008735367281473086766641604185629827373864344704645943910512054824309490712576 +def node200 : Tree Nat := .node node198 node199 +def node201 : Tree Nat := .node node197 node200 +def node202 : Tree Nat := .node node194 node201 +def node203 : Tree Nat := .leaf 309485009821345068724781056 +def node204 : Tree Nat := .leaf 4149515568880992958512407863691161151012446232242436899995657329690652811412908146399707048947103794288197886611300789182395151075411775307886874834113963687061181803401509523685376 +def node205 : Tree Nat := .node node203 node204 +def node206 : Tree Nat := .leaf 35835915874844867368919076489095108449946327955754392558399825615420669938882575126094039892345713852416 +def node207 : Tree Nat := .leaf 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111870718431542817204760874740917337854381793641291611443130662899652593770909781872442516663377454591520935582886717656540612737332317877736113382974861639142628415265543797274479692427652260844707187532155254872952853725026318685997495262134665216 +def node224 : Tree Nat := .node node222 node223 +def node225 : Tree Nat := .node node221 node224 +def node226 : Tree Nat := .leaf 24519928653854221733733552434404946937899825954937634816 +def node227 : Tree Nat := .leaf 328758493846773344202561867680008041596896237676448366218642556441795759643567551382104158517349278201686435553511138607063714515636487741445488423165742553122201479445527787386978984867770169829455828233486336 +def node228 : Tree Nat := .node node226 node227 +def node229 : Tree Nat := .leaf 2839213766779714416208296124562517712318911565184836172974571090549372219192960637992933791850638927971728600024477257552869537611776 +def node230 : Tree Nat := .leaf 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2063650512248692368563827284830142994214247367328599695812346519635444931862206482321942405811160890213571855442410658901884170154307365379884917884620857722298385484371113610034107490923540785363375909797699954703703235518560788042337487885808736236287260081631789056 +def node239 : Tree Nat := .node node237 node238 +def node240 : Tree Nat := .node node236 node239 +def node241 : Tree Nat := .leaf 452312848583266388373324160190187140051835877600158453279131187530910662656 +def node242 : Tree Nat := .leaf 6064523798049644277925701126806650606472211004362096137261922023539261533931159712229993784486900304494092698035668254711607734547323493716579247168129613825017402250081444943555723771998431425098683590600454956058175183022718976 +def node243 : Tree Nat := .node node241 node242 +def node244 : Tree Nat := .leaf 52374249726338269920211035149241586435466272736689036631732661889538140742474792878132321477214466514414186946040961136147476104734166288853256441430016 +def node245 : Tree Nat := .node node244 node57 +def node246 : Tree Nat := .node node243 node245 +def node247 : Tree Nat := .node node240 node246 +def node248 : Tree Nat := .node node233 node247 +def node249 : Tree Nat := .node node218 node248 +def node250 : Tree Nat := .node node187 node249 +def node251 : Tree Nat := .node node125 node250 +def node252 : Tree Nat := .leaf 16 +def node253 : Tree Nat := .leaf 214524926879081553593184399971293538039669853129478294043576983099548224481176751628829988770670454843040509730983776813660062124991145119142938384097345536 +def node254 : Tree Nat := .node node252 node253 +def node255 : Tree Nat := .leaf 1852673427797059126777135760139006525652319754650249024631321344126610074238976 +def node256 : Tree Nat := .leaf 24840289476811342962383671815400040884110176273867145778224832608416815242982030181294054541258343647207803691154097171298745280705837030263108596400658898227271279616333598488804244570105575117204207987099463500014285549661056925696 +def node257 : Tree Nat := .node node255 node256 +def node258 : Tree Nat := .node node254 node257 +def node259 : Tree Nat := .leaf 5444517870735015415413993718908291383296 +def node260 : Tree Nat := .leaf 72999049881955123498258745691204661198291656115976958889267080286388402675338838184094604981077942396458276953177510516971019275542007007972042581115555427012031914789764239201325987075945660416 +def node261 : Tree Nat := .node node259 node260 +def node262 : Tree Nat := .leaf 630432099142311667396464641602297820881275828327447146687172694467931548343955369782628260078158650252906047844909056 +def node263 : Tree Nat := .leaf 8452712498170643941637436558664265704301557216577944354047371344426782440907597751590676094202515006314790319892114058862117560952042968596008623655407033230534186943984081346699704282822823056848387726531379014466368452684024987821414350380272583623832617294363807973376 +def node264 : Tree Nat := .node node262 node263 +def node265 : Tree Nat := .node node261 node264 +def node266 : Tree Nat := .node node258 node265 +def node267 : Tree Nat := .leaf 295147905179352825856 +def node268 : Tree Nat := .leaf 3957286423569672544968040336314355040562101585619389438625008897486355601704509874725062416979888719833562742816258229429621840548908019359480738481630290686665708354379186176 +def node269 : Tree Nat := .node node267 node268 +def node270 : Tree Nat := .leaf 34175792574734561318320347298712833833643272357706444319152665725155515612490248800367393390985216 +def node271 : Tree Nat := .leaf 458222462695599379270700542938797415851547826754730440471063195236977024085646466549524548253194054006869752147503995521190349772113174027207120416665033273928205988927667393636268820183663660419920640131707923959614888857707801337845740593703588724736 +def node272 : Tree Nat := .node node270 node271 +def node273 : Tree Nat := .node node269 node272 +def node274 : Tree Nat := .leaf 100433627766186892221372630771322662657637687111424552206336 +def node275 : Tree Nat := .leaf 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+def node284 : Tree Nat := .leaf 921377545122446619199598286374089084696513969828232526459034741270904336521520715841339532514076847544303802497745079321233052888165232576308943909041185557531590656 +def node285 : Tree Nat := .node node283 node284 +def node286 : Tree Nat := .leaf 7957171782556586274486115970349133441607298412757563479047423630290551952200534008528896 +def node287 : Tree Nat := .leaf 106688230926077668385277628651540124754316133157054530566340124988224595805082113144342915213944868651886878569494931847134220826465909841285813696837293280737522521272224232935409252574589024395663440258174185631707051968599623380658622038016 +def node288 : Tree Nat := .node node286 node287 +def node289 : Tree Nat := .node node285 node288 +def node290 : Tree Nat := .leaf 23384026197294446691258957323460528314494920687616 +def node291 : Tree Nat := .leaf 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Tree Nat := .leaf 121416805764108066932466369176469931665150427440758720078238275608681517825325531136 +def node318 : Tree Nat := .leaf 1627933211152308172382776316094057079381044512284157265721742629825204403764070329961287158415906809263410622703474912218234570716337735615323084973713581554222450580936038710562274972146438970881094974642550439936936217782587026682413056 +def node319 : Tree Nat := .node node317 node318 +def node320 : Tree Nat := .node node316 node319 +def node321 : Tree Nat := .leaf 356811923176489970264571492362373784095686656 +def node322 : Tree Nat := .leaf 4784065733063810973581885157618788676291241975216665977767007373648750357731006099232824032039924032894289638403441329240212719241920971274455782595989040464660523567661989180298099889009174801022976 +def node323 : Tree Nat := .node node321 node322 +def node324 : Tree Nat := .leaf 41315998049390537434494706752048189989275292685267576205290549704650361952269459114074325652482205302974450751563959894016 +def node325 : Tree Nat := .leaf 553956966280111321359151042308621317197106853745652161186848528428353614047320326248246548509656023453846098404449586961587736474553087989908021159880755329796288475560940755137311819879076531853615938045960455092067922915100261601864210866521544040371494407003426519343169536 +def node326 : Tree Nat := .node node324 node325 +def node327 : Tree Nat := .node node323 node326 +def node328 : Tree Nat := .node node320 node327 +def node329 : Tree Nat := .leaf 19342813113834066795298816 +def node330 : Tree Nat := .leaf 259344723055062059907025491480697571938277889515152306249728583105665800713306759149981690559193987143012367913206299323899696942213235956742929677132122730441323862712594345230336 +def node331 : Tree Nat := .node node329 node330 +def node332 : Tree Nat := .leaf 2239744742177804210557442280568444278121645497234649534899989100963791871180160945380877493271607115776 +def node333 : Tree Nat := .leaf 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.node node370 node57 +def node372 : Tree Nat := .node node369 node371 +def node373 : Tree Nat := .node node366 node372 +def node374 : Tree Nat := .node node359 node373 +def node375 : Tree Nat := .node node344 node374 +def node376 : Tree Nat := .node node313 node375 +def node377 : Tree Nat := .leaf 4096 +def node378 : Tree Nat := .leaf 54918381281044877719855206392651145738155482401146443275155707673484345467181248416980477125291636439818370491131846864296975903997733150500592226328920457216 +def node379 : Tree Nat := .node node377 node378 +def node380 : Tree Nat := .leaf 474284397516047136454946754595585670566993857190463750305618264096412179005177856 +def node381 : Tree Nat := .leaf 6359114106063703798370219984742410466332205126109989319225557147754704702203399726411277962562135973685197744935448875852478791860694279747355800678568677946181447581781401213133886609947027230004277244697462656003657100713230572978176 +def node382 : Tree Nat := .node node380 node381 +def node383 : Tree Nat := .node node379 node382 +def node384 : Tree Nat := .leaf 1393796574908163946345982392040522594123776 +def node385 : Tree Nat := .leaf 18687756769780511615554238896948393266762663965690101475652372553315431084886742575128218875155953253493318900013442692344580934538753794040842900765582189315080170186179645235539452691442089066496 +def node386 : Tree Nat := .node node384 node385 +def node387 : Tree Nat := .leaf 161390617380431786853494948250188242145606612051826469551916209783790476376052574664352834580008614464743948248296718336 +def node388 : Tree Nat := .leaf 2163894399531684849059183759018052020301198647443953754636127064173256304872345024407213080115843841616586321892381199068702095603722999960578207655784200507016751857659924824755124296402642702553187257992033027703390323887110396882282073697349781407701150027357134841184256 +def node389 : Tree Nat := .node node387 node388 +def node390 : Tree Nat := .node node386 node389 +def node391 : Tree Nat := .node node383 node390 +def node392 : Tree Nat := .leaf 75557863725914323419136 +def node393 : Tree Nat := .leaf 1013065324433836171511818326096474890383898005918563696288002277756507034036354527929615978746851512277392062160962106733983191180520452956027069051297354415786421338721071661056 +def node394 : Tree Nat := .node node392 node393 +def node395 : Tree Nat := .leaf 8749002899132047697490008908470485461412677723572849745703082425639811996797503692894052708092215296 +def node396 : Tree Nat := .leaf 117304950450073441093299338992332138457996243649210992760592177980666118165925495436678284352817677825758656549761022853424729541660972550965022826666248518125620733165482852770884817967017897067499683873717228533661411547573197142488509591988118713532416 +def node397 : Tree Nat := .node node395 node396 +def node398 : Tree Nat := .node node394 node397 +def node399 : Tree Nat := .leaf 25711008708143844408671393477458601640355247900524685364822016 +def node400 : Tree Nat := .leaf 344728266443874206170545512964432112225507069317819522056079337263512430464013488758041250121488036739611555846958495676040441511948045769973944468809441663382665538511073745187088876036706973599091474545756168257536 +def node401 : Tree Nat := .node node399 node400 +def node402 : Tree Nat := .leaf 2977131414714805823690030317109266572712515013375254774912983855843898524112477893944078543723575564536883288499266264815757728270805630976 +def node403 : Tree Nat := .leaf 39916806190694396233127454260736771321349025208709150830050944848744237837379281315699159309852714021786848936883849904879448759767871873214783435965696628406400113459021713530350754428887259743653067134890878479866616209102417407777777105368960883150142418137515120832847169904606880198557696 +def node404 : Tree Nat := .node node402 node403 +def node405 : Tree Nat := .node node401 node404 +def node406 : Tree Nat := .node node398 node405 +def node407 : Tree Nat := .node node391 node406 +def node408 : Tree Nat := .leaf 17592186044416 +def node409 : Tree Nat := .leaf 235872651551346334515097161311766805682307576276027526773512893765351510149509303255382920323603672971341773439422740306235661539370299539535089640714543502728087207936 +def node410 : Tree Nat := .node node408 node409 +def node411 : Tree Nat := .leaf 2037035976334486086268445688409378161051468393665936250636140449354381299763336706183397376 +def node412 : Tree Nat := .leaf 27312187117075883106631072934794271937104930088205959824983071996985496526101020964951786294769886374883040913790702552866360531575272919369168306390347079868805765445689403631464768659094790245289840706092591521717005303961503585448607241732096 +def node413 : Tree Nat := .node node411 node412 +def node414 : Tree Nat := .node node410 node413 +def node415 : Tree Nat := .leaf 5986310706507378352962293074805895248510699696029696 +def node416 : Tree Nat := .leaf 80263304161809898486953580976564463280492245526476651908848280381297792881730359224146523075524726123458602430056430323990164676669064390001339947061948865508349970567755807467524166227482951618519489314816 +def node417 : Tree Nat := .node node415 node416 +def node418 : Tree Nat := .leaf 693167423530203714894603546035770925859109268843954143792619895153655326951406405759993601526034894524347802740350892957243539456 +def node419 : Tree Nat := .leaf 9293855677986144142487890613436878500820376260371215369098574120724629107252527334657301965600977191186242023688706081565341157784655660673692691131889966411143567752796624212141790061464360855438994973639696482537923429417986750550981868377179113018825281909088399455148533430091776 +def node420 : Tree Nat := .node node418 node419 +def node421 : Tree Nat := .node node417 node420 +def node422 : Tree Nat := .node node414 node421 +def node423 : Tree Nat := .leaf 324518553658426726783156020576256 +def node424 : Tree Nat := .leaf 4351082437154956072465106588077822995084026820419845514849846380137705962380101572519219218556758308199541387151331336317719177934050977705242787666055883587123865770683541250307916824576 +def node425 : Tree Nat := .node node423 node424 +def node426 : Tree Nat := .leaf 37576681324381331646231689548629392438010920782533117931316655544515344401833735095419183974156299248510959616 +def node427 : Tree Nat := .leaf 503820925841965910293903145710484129446837736164208910110436162020372297817921504473130470168740451712297816270119789770967814979078946625948466280425014092358004268645291408699733274151255074551605446727954090503833797734023629893148800753371273495187319355867136 +def node428 : Tree Nat := .node node426 node427 +def node429 : Tree Nat := .node node425 node428 +def node430 : Tree Nat := .leaf 110427941548649020598956093796432407239217743554726184882600387580788736 +def node431 : Tree Nat := .leaf 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node442 : Tree Nat := .leaf 31082702275611665134711390509176302506278509424834232340028998555822468563283335970816 +def node443 : Tree Nat := .leaf 416750902054990892129990736920078612321547395144744260024766113235252327363602004470089512554472143171433119412089577527868050103382460317522709753270676877880947348719625909903942392869488376545560313508492912623855671752342278830697742336 +def node444 : Tree Nat := .node node442 node443 +def node445 : Tree Nat := .node node441 node444 +def node446 : Tree Nat := .leaf 91343852333181432387730302044767688728495783936 +def node447 : Tree Nat := .leaf 1224720827664335609236962600350409901130557945655466490308353887654080091579137561403602952202220552420938147431280980285494456125931768646260680344573194358953094033321469230156313571586348749061881856 +def node448 : Tree Nat := .node node446 node447 +def node449 : Tree Nat := .leaf 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573374653997517877902705223825521735199141247292070280934397209846730719022121202017504638277531421638656 +def node458 : Tree Nat := .leaf 7687697232696013035490465480201479025983241823794691621558168976140934720122093268938148043346259333988919315645138393722043075242293497100043735968399262883880680368733084239192707430286484902215659282347932289182034267181757047930126964620533348010060414976 +def node459 : Tree Nat := .node node457 node458 +def node460 : Tree Nat := .node node456 node459 +def node461 : Tree Nat := .leaf 1684996666696914987166688442938726917102321526408785780068975640576 +def node462 : Tree Nat := .leaf 22592111669665739975592870737637022906810831294812620197467215446901550642889587999246991367961839975767182923986271972624986374927027127581012424707895568851446368731861728964581056579941628221790058875830676242925879296 +def node463 : Tree Nat := .node node461 node462 +def node464 : Tree Nat := .leaf 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Nat := .node node494 node57 +def node496 : Tree Nat := .node node493 node495 +def node497 : Tree Nat := .node node490 node496 +def node498 : Tree Nat := .node node483 node497 +def node499 : Tree Nat := .node node468 node498 +def node500 : Tree Nat := .node node438 node499 +def node501 : Tree Nat := .node node376 node500 +def node502 : Tree Nat := .node node251 node501 +def node503 : Tree Nat := .leaf 4 +def node504 : Tree Nat := .leaf 53631231719770388398296099992823384509917463282369573510894245774887056120294187907207497192667613710760127432745944203415015531247786279785734596024336384 +def node505 : Tree Nat := .node node503 node504 +def node506 : Tree Nat := .leaf 463168356949264781694283940034751631413079938662562256157830336031652518559744 +def node507 : Tree Nat := .leaf 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+def node561 : Tree Nat := .node node558 node560 +def node562 : Tree Nat := .node node555 node561 +def node563 : Tree Nat := .node node548 node562 +def node564 : Tree Nat := .node node533 node563 +def node565 : Tree Nat := .leaf 262144 +def node566 : Tree Nat := .leaf 3514776401986872174070733209129673327241950873673372369609965291102998109899599898686750536018664732148375711432438199315006457855854921632037902485050909261824 +def node567 : Tree Nat := .node node565 node566 +def node568 : Tree Nat := .leaf 30354201441027016733116592294117482916287606860189680019559568902170379456331382784 +def node569 : Tree Nat := .leaf 406983302788077043095694079023514269845261128071039316430435657456301100941017582490321789603976702315852655675868728054558642679084433903830771243428395388555612645234009677640568743036609742720273743660637609984234054445646756670603264 +def node570 : Tree Nat := .node node568 node569 +def node571 : Tree Nat := .node node567 node570 +def node572 : Tree Nat := .leaf 89202980794122492566142873090593446023921664 +def node573 : Tree Nat := .leaf 1196016433265952743395471289404697169072810493804166494441751843412187589432751524808206008009981008223572409600860332310053179810480242818613945648997260116165130891915497295074524972252293700255744 +def node574 : Tree Nat := .node node572 node573 +def node575 : Tree Nat := .leaf 10328999512347634358623676688012047497318823171316894051322637426162590488067364778518581413120551325743612687890989973504 +def node576 : Tree Nat := .leaf 138489241570027830339787760577155329299276713436413040296712132107088403511830081562061637127414005863461524601112396740396934118638271997477005289970188832449072118890235188784327954969769132963403984511490113773016980728775065400466052716630386010092873601750856629835792384 +def node577 : Tree Nat := .node node575 node576 +def node578 : Tree Nat := .node node574 node577 +def node579 : Tree Nat := .node node571 node578 +def node580 : Tree Nat := .leaf 4835703278458516698824704 +def node581 : Tree Nat := .leaf 64836180763765514976756372870174392984569472378788076562432145776416450178326689787495422639798496785753091978301574830974924235553308989185732419283030682610330965678148586307584 +def node582 : Tree Nat := .node node580 node581 +def node583 : Tree Nat := .leaf 559936185544451052639360570142111069530411374308662383724997275240947967795040236345219373317901778944 +def node584 : Tree Nat := .leaf 7507516828804700229971157695509256861311759593549503536677899390762631562619231707947410198580331380848554019184705462619182690666302243261761460906639905160039726922590902577336628349889145412319979767917902626154330339044684617119264613887239597666074624 +def node585 : Tree Nat := .node node583 node584 +def node586 : Tree Nat := .node node582 node585 +def node587 : Tree Nat := .leaf 1645504557321206042154969182557350504982735865633579863348609024 +def node588 : Tree Nat := .leaf 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1125899906842624 +def node597 : Tree Nat := .leaf 15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 +def node598 : Tree Nat := .node node596 node597 +def node599 : Tree Nat := .leaf 130370302485407109521180524058200202307293977194619920040712988758680403184853549195737432064 +def node600 : Tree Nat := .leaf 1747979975492856518824388667826833403974715525645181428798916607807071777670465341756914322865272727992514618482604963383447074020817466839626771608982213111603568988524121832413745194182066575698549805189925857389888339453536229468710863470854144 +def node601 : Tree Nat := .node node599 node600 +def node602 : Tree Nat := .node node598 node601 +def node603 : Tree Nat := .leaf 383123885216472214589586756787577295904684780545900544 +def node604 : Tree Nat := .leaf 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Tree Nat := .node node628 node629 +def node631 : Tree Nat := .leaf 118571099379011784113736688648896417641748464297615937576404566024103044751294464 +def node632 : Tree Nat := .leaf 1589778526515925949592554996185602616583051281527497329806389286938676175550849931602819490640533993421299436233862218963119697965173569936838950169642169486545361895445350303283471652486756807501069311174365664000914275178307643244544 +def node633 : Tree Nat := .node node631 node632 +def node634 : Tree Nat := .node node630 node633 +def node635 : Tree Nat := .leaf 348449143727040986586495598010130648530944 +def node636 : Tree Nat := .leaf 4671939192445127903888559724237098316690665991422525368913093138328857771221685643782054718788988313373329725003360673086145233634688448510210725191395547328770042546544911308884863172860522266624 +def node637 : Tree Nat := .node node635 node636 +def node638 : Tree Nat := .leaf 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:= .node node746 node57 +def node748 : Tree Nat := .node node745 node747 +def node749 : Tree Nat := .node node742 node748 +def node750 : Tree Nat := .node node735 node749 +def node751 : Tree Nat := .node node720 node750 +def node752 : Tree Nat := .node node689 node751 +def node753 : Tree Nat := .node node627 node752 +def node754 : Tree Nat := .leaf 64 +def node755 : Tree Nat := .leaf 858099707516326214372737599885174152158679412517913176174307932398192897924707006515319955082681819372162038923935107254640248499964580476571753536389382144 +def node756 : Tree Nat := .node node754 node755 +def node757 : Tree Nat := .leaf 7410693711188236507108543040556026102609279018600996098525285376506440296955904 +def node758 : Tree Nat := .leaf 99361157907245371849534687261600163536440705095468583112899330433667260971928120725176218165033374588831214764616388685194981122823348121052434385602635592909085118465334393955216978280422300468816831948397854000057142198644227702784 +def node759 : Tree Nat := .node node757 node758 +def node760 : Tree Nat := .node node756 node759 +def node761 : Tree Nat := .leaf 21778071482940061661655974875633165533184 +def node762 : Tree Nat := .leaf 291996199527820493993034982764818644793166624463907835557068321145553610701355352736378419924311769585833107812710042067884077102168028031888170324462221708048127659159056956805303948303782641664 +def node763 : Tree Nat := .node node761 node762 +def node764 : Tree Nat := .leaf 2521728396569246669585858566409191283525103313309788586748690777871726193375821479130513040312634601011624191379636224 +def node765 : Tree Nat := .leaf 33810849992682575766549746234657062817206228866311777416189485377707129763630391006362704376810060025259161279568456235448470243808171874384034494621628132922136747775936325386798817131291292227393550906125516057865473810736099951285657401521090334495330469177455231893504 +def node766 : Tree Nat := .node node764 node765 +def node767 : Tree Nat := .node node763 node766 +def node768 : Tree Nat := .node node760 node767 +def node769 : Tree Nat := .leaf 1180591620717411303424 +def node770 : Tree Nat := .leaf 15829145694278690179872161345257420162248406342477557754500035589945422406818039498900249667919554879334250971265032917718487362195632077437922953926521162746662833417516744704 +def node771 : Tree Nat := .node node769 node770 +def node772 : Tree Nat := .leaf 136703170298938245273281389194851335334573089430825777276610662900622062449960995201469573563940864 +def node773 : Tree Nat := .leaf 1832889850782397517082802171755189663406191307018921761884252780947908096342585866198098193012776216027479008590015982084761399088452696108828481666660133095712823955710669574545075280734654641679682560526831695838459555430831205351382962374814354898944 +def node774 : Tree Nat := .node node772 node773 +def node775 : Tree Nat := .node node771 node774 +def node776 : Tree Nat := .leaf 401734511064747568885490523085290650630550748445698208825344 +def node777 : Tree Nat := .leaf 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Tree Nat := .leaf 485667223056432267729865476705879726660601709763034880312953102434726071301302124544 +def node820 : Tree Nat := .leaf 6511732844609232689531105264376228317524178049136629062886970519300817615056281319845148633663627237053642490813899648872938282865350942461292339894854326216889802323744154842249099888585755883524379898570201759747744871130348106729652224 +def node821 : Tree Nat := .node node819 node820 +def node822 : Tree Nat := .node node818 node821 +def node823 : Tree Nat := .leaf 1427247692705959881058285969449495136382746624 +def node824 : Tree Nat := .leaf 19136262932255243894327540630475154705164967900866663911068029494595001430924024396931296128159696131577158553613765316960850876967683885097823130383956161858642094270647956721192399556036699204091904 +def node825 : Tree Nat := .node node823 node824 +def node826 : Tree Nat := .leaf 165263992197562149737978827008192759957101170741070304821162198818601447809077836456297302609928821211897803006255839576064 +def node827 : Tree Nat := .leaf 2215827865120445285436604169234485268788427414982608644747394113713414456189281304992986194038624093815384393617798347846350945898212351959632084639523021319185153902243763020549247279516306127414463752183841820368271691660401046407456843466086176161485977628013706077372678144 +def node828 : Tree Nat := .node node826 node827 +def node829 : Tree Nat := .node node825 node828 +def node830 : Tree Nat := .node node822 node829 +def node831 : Tree Nat := .leaf 77371252455336267181195264 +def node832 : Tree Nat := .leaf 1037378892220248239628101965922790287753111558060609224998914332422663202853227036599926762236775948572049471652825197295598787768852943826971718708528490921765295450850377380921344 +def node833 : Tree Nat := .node node831 node832 +def node834 : Tree Nat := .leaf 8958978968711216842229769122273777112486581988938598139599956403855167484720643781523509973086428463104 +def node835 : Tree Nat := .leaf 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.node node872 node57 +def node874 : Tree Nat := .node node871 node873 +def node875 : Tree Nat := .node node868 node874 +def node876 : Tree Nat := .node node861 node875 +def node877 : Tree Nat := .node node846 node876 +def node878 : Tree Nat := .node node815 node877 +def node879 : Tree Nat := .leaf 16384 +def node880 : Tree Nat := .leaf 219673525124179510879420825570604582952621929604585773100622830693937381868724993667921908501166545759273481964527387457187903615990932602002368905315681828864 +def node881 : Tree Nat := .node node879 node880 +def node882 : Tree Nat := .leaf 1897137590064188545819787018382342682267975428761855001222473056385648716020711424 +def node883 : Tree Nat := .leaf 25436456424254815193480879938969641865328820504439957276902228591018818808813598905645111850248543894740790979741795503409915167442777118989423202714274711784725790327125604852535546439788108920017108978789850624014628402852922291912704 +def node884 : Tree Nat := .node node882 node883 +def node885 : Tree Nat := .node node881 node884 +def node886 : Tree Nat := .leaf 5575186299632655785383929568162090376495104 +def node887 : Tree Nat := .leaf 74751027079122046462216955587793573067050655862760405902609490213261724339546970300512875500623813013973275600053770769378323738155015176163371603062328757260320680744718580942157810765768356265984 +def node888 : Tree Nat := .node node886 node887 +def node889 : Tree Nat := .leaf 645562469521727147413979793000752968582426448207305878207664839135161905504210298657411338320034457858975792993186873344 +def node890 : Tree Nat := .leaf 8655577598126739396236735036072208081204794589775815018544508256693025219489380097628852320463375366466345287569524796274808382414891999842312830623136802028067007430639699299020497185610570810212749031968132110813561295548441587529128294789399125630804600109428539364737024 +def node891 : Tree Nat := .node node889 node890 +def node892 : Tree Nat := .node node888 node891 +def node893 : Tree Nat := .node node885 node892 +def node894 : Tree Nat := .leaf 302231454903657293676544 +def node895 : Tree Nat := .leaf 4052261297735344686047273304385899561535592023674254785152009111026028136145418111718463914987406049109568248643848426935932764722081811824108276205189417663145685354884286644224 +def node896 : Tree Nat := .node node894 node895 +def node897 : Tree Nat := .leaf 34996011596528190789960035633881941845650710894291398982812329702559247987190014771576210832368861184 +def node898 : Tree Nat := .leaf 469219801800293764373197355969328553831984974596843971042368711922664472663701981746713137411270711303034626199044091413698918166643890203860091306664994072502482932661931411083539271868071588269998735494868914134645646190292788569954038367952474854129664 +def node899 : Tree Nat := .node node897 node898 +def node900 : Tree Nat := .node node896 node899 +def node901 : Tree Nat := .leaf 102844034832575377634685573909834406561420991602098741459288064 +def node902 : Tree Nat := .leaf 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70368744177664 +def node911 : Tree Nat := .leaf 943490606205385338060388645247067222729230305104110107094051575061406040598037213021531681294414691885367093757690961224942646157481198158140358562858174010912348831744 +def node912 : Tree Nat := .node node910 node911 +def node913 : Tree Nat := .leaf 8148143905337944345073782753637512644205873574663745002544561797417525199053346824733589504 +def node914 : Tree Nat := .leaf 109248748468303532426524291739177087748419720352823839299932287987941986104404083859807145179079545499532163655162810211465442126301091677476673225561388319475223061782757614525859074636379160981159362824370366086868021215846014341794428966928384 +def node915 : Tree Nat := .node node913 node914 +def node916 : Tree Nat := .node node912 node915 +def node917 : Tree Nat := .leaf 23945242826029513411849172299223580994042798784118784 +def node918 : Tree Nat := .leaf 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node944 : Tree Nat := .leaf 124330809102446660538845562036705210025114037699336929360115994223289874253133343883264 +def node945 : Tree Nat := .leaf 1667003608219963568519962947680314449286189580578977040099064452941009309454408017880358050217888572685732477648358310111472200413529841270090839013082707511523789394878503639615769571477953506182241254033971650495422687009369115322790969344 +def node946 : Tree Nat := .node node944 node945 +def node947 : Tree Nat := .node node943 node946 +def node948 : Tree Nat := .leaf 365375409332725729550921208179070754913983135744 +def node949 : Tree Nat := .leaf 4898883310657342436947850401401639604522231782621865961233415550616320366316550245614411808808882209683752589725123921141977824503727074585042721378292777435812376133285876920625254286345394996247527424 +def node950 : Tree Nat := .node node948 node949 +def node951 : Tree Nat := .leaf 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Tree Nat := .node node996 node57 +def node998 : Tree Nat := .node node995 node997 +def node999 : Tree Nat := .node node992 node998 +def node1000 : Tree Nat := .node node985 node999 +def node1001 : Tree Nat := .node node970 node1000 +def node1002 : Tree Nat := .node node940 node1001 +def node1003 : Tree Nat := .node node878 node1002 +def node1004 : Tree Nat := .node node753 node1003 +def node1005 : Tree Nat := .node node502 node1004 +def node1006 : Tree Nat := .leaf 2 +def node1007 : Tree Nat := .leaf 26815615859885194199148049996411692254958731641184786755447122887443528060147093953603748596333806855380063716372972101707507765623893139892867298012168192 +def node1008 : Tree Nat := .node node1006 node1007 +def node1009 : Tree Nat := .leaf 231584178474632390847141970017375815706539969331281128078915168015826259279872 +def node1010 : Tree Nat := .leaf 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node57 +def node1064 : Tree Nat := .node node1061 node1063 +def node1065 : Tree Nat := .node node1058 node1064 +def node1066 : Tree Nat := .node node1051 node1065 +def node1067 : Tree Nat := .node node1036 node1066 +def node1068 : Tree Nat := .leaf 131072 +def node1069 : Tree Nat := .leaf 1757388200993436087035366604564836663620975436836686184804982645551499054949799949343375268009332366074187855716219099657503228927927460816018951242525454630912 +def node1070 : Tree Nat := .node node1068 node1069 +def node1071 : Tree Nat := .leaf 15177100720513508366558296147058741458143803430094840009779784451085189728165691392 +def node1072 : Tree Nat := .leaf 203491651394038521547847039511757134922630564035519658215217828728150550470508791245160894801988351157926327837934364027279321339542216951915385621714197694277806322617004838820284371518304871360136871830318804992117027222823378335301632 +def node1073 : Tree Nat := .node node1071 node1072 +def node1074 : Tree Nat := .node node1070 node1073 +def node1075 : Tree Nat := .leaf 44601490397061246283071436545296723011960832 +def node1076 : Tree Nat := .leaf 598008216632976371697735644702348584536405246902083247220875921706093794716375762404103004004990504111786204800430166155026589905240121409306972824498630058082565445957748647537262486126146850127872 +def node1077 : Tree Nat := .node node1075 node1076 +def node1078 : Tree Nat := .leaf 5164499756173817179311838344006023748659411585658447025661318713081295244033682389259290706560275662871806343945494986752 +def node1079 : Tree Nat := .leaf 69244620785013915169893880288577664649638356718206520148356066053544201755915040781030818563707002931730762300556198370198467059319135998738502644985094416224536059445117594392163977484884566481701992255745056886508490364387532700233026358315193005046436800875428314917896192 +def node1080 : Tree Nat := .node node1078 node1079 +def node1081 : Tree Nat := .node node1077 node1080 +def node1082 : Tree Nat := .node node1074 node1081 +def node1083 : Tree Nat := .leaf 2417851639229258349412352 +def node1084 : Tree Nat := .leaf 32418090381882757488378186435087196492284736189394038281216072888208225089163344893747711319899248392876545989150787415487462117776654494592866209641515341305165482839074293153792 +def node1085 : Tree Nat := .node node1083 node1084 +def node1086 : Tree Nat := .leaf 279968092772225526319680285071055534765205687154331191862498637620473983897520118172609686658950889472 +def node1087 : Tree Nat := .leaf 3753758414402350114985578847754628430655879796774751768338949695381315781309615853973705099290165690424277009592352731309591345333151121630880730453319952580019863461295451288668314174944572706159989883958951313077165169522342308559632306943619798833037312 +def node1088 : Tree Nat := .node node1086 node1087 +def node1089 : Tree Nat := .node node1085 node1088 +def node1090 : Tree Nat := .leaf 822752278660603021077484591278675252491367932816789931674304512 +def node1091 : Tree Nat := .leaf 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Tree Nat := .leaf 562949953421312 +def node1100 : Tree Nat := .leaf 7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653952 +def node1101 : Tree Nat := .node node1099 node1100 +def node1102 : Tree Nat := .leaf 65185151242703554760590262029100101153646988597309960020356494379340201592426774597868716032 +def node1103 : Tree Nat := .leaf 873989987746428259412194333913416701987357762822590714399458303903535888835232670878457161432636363996257309241302481691723537010408733419813385804491106555801784494262060916206872597091033287849274902594962928694944169726768114734355431735427072 +def node1104 : Tree Nat := .node node1102 node1103 +def node1105 : Tree Nat := .node node1101 node1104 +def node1106 : Tree Nat := .leaf 191561942608236107294793378393788647952342390272950272 +def node1107 : Tree Nat := .leaf 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.leaf 139234637988958594318883410818490335842688858253435056475195084164406590796163250320615014993816265862385324388842602762167013693889631286567769205313788274787963704661873320009853338386432 +def node1116 : Tree Nat := .node node1114 node1115 +def node1117 : Tree Nat := .leaf 1202453802380202612679414065556140558016349465041059773802132977424491020858679523053413887173001575952350707712 +def node1118 : Tree Nat := .leaf 16122269626942909129404900662735492142298807557254685123533957184651913530173488143140175045399694454793530120643833272670970079330526292030350920973600450955456136596649325078391464772840162385651374295294530896122681527488756156580761624107880751845994219387748352 +def node1119 : Tree Nat := .node node1117 node1118 +def node1120 : Tree Nat := .node node1116 node1119 +def node1121 : Tree Nat := .leaf 3533694129556768659166595001485837031654967793751237916243212402585239552 +def node1122 : Tree Nat := .leaf 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:= .leaf 2199023255552 +def node1163 : Tree Nat := .leaf 29484081443918291814387145163970850710288447034503440846689111720668938768688662906922865040450459121417721679927842538279457692421287442441886205089317937841010900992 +def node1164 : Tree Nat := .node node1162 node1163 +def node1165 : Tree Nat := .leaf 254629497041810760783555711051172270131433549208242031329517556169297662470417088272924672 +def node1166 : Tree Nat := .leaf 3414023389634485388328884116849283992138116261025744978122883999623187065762627620618973286846235796860380114223837819108295066446909114921146038298793384983600720680711175453933096082386848780661230088261573940214625662995187948181075905216512 +def node1167 : Tree Nat := .node node1165 node1166 +def node1168 : Tree Nat := .node node1164 node1167 +def node1169 : Tree Nat := .leaf 748288838313422294120286634350736906063837462003712 +def node1170 : Tree Nat := .leaf 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node1193 node1194 +def node1196 : Tree Nat := .leaf 3885337784451458141838923813647037813284813678104279042503624819477808570410416996352 +def node1197 : Tree Nat := .leaf 52093862756873861516248842115009826540193424393093032503095764154406540920450250558761189069309017896429139926511197190983506262922807539690338719158834609735118418589953238737992799108686047068195039188561614077981958969042784853837217792 +def node1198 : Tree Nat := .node node1196 node1197 +def node1199 : Tree Nat := .node node1195 node1198 +def node1200 : Tree Nat := .leaf 11417981541647679048466287755595961091061972992 +def node1201 : Tree Nat := .leaf 153090103458041951154620325043801237641319743206933311288544235956760011447392195175450369025277569052617268428910122535686807015741471080782585043071649294869136754165183653769539196448293593632735232 +def node1202 : Tree Nat := .node node1200 node1201 +def node1203 : Tree Nat := .leaf 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71671831749689734737838152978190216899892655911508785116799651230841339877765150252188079784691427704832 +def node1212 : Tree Nat := .leaf 960962154087001629436308185025184878247905227974336452694771122017616840015261658617268505418282416748614914455642299215255384405286687137505466996049907860485085046091635529899088428785810612776957410293491536147754283397719630991265870577566668501257551872 +def node1213 : Tree Nat := .node node1211 node1212 +def node1214 : Tree Nat := .node node1210 node1213 +def node1215 : Tree Nat := .leaf 210624583337114373395836055367340864637790190801098222508621955072 +def node1216 : Tree Nat := .leaf 2824013958708217496949108842204627863351353911851577524683401930862693830361198499905873920995229996970897865498283996578123296865878390947626553088486946106430796091482716120572632072492703527723757359478834530365734912 +def node1217 : Tree Nat := .node node1215 node1216 +def node1218 : Tree Nat := .leaf 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node1227 : Tree Nat := .leaf 16687398718132110018711107079449625895333629080911349765211262561111091607661254297054391304192 +def node1228 : Tree Nat := .leaf 223741436863085634409521749481834675708763587282583222886261325799305187541819563744885033326754909183041871165773435313081225474664635755472226765949723278285256830531087594548959384855304521689414375064310509745905707450052637371994990524269330432 +def node1229 : Tree Nat := .node node1227 node1228 +def node1230 : Tree Nat := .node node1226 node1229 +def node1231 : Tree Nat := .leaf 49039857307708443467467104868809893875799651909875269632 +def node1232 : Tree Nat := .leaf 657516987693546688405123735360016083193792475352896732437285112883591519287135102764208317034698556403372871107022277214127429031272975482890976846331485106244402958891055574773957969735540339658911656466972672 +def node1233 : Tree Nat := .node node1231 node1232 +def node1234 : Tree Nat := .leaf 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307828173409331868845930000782371982852185463050511302093346042220669701339821957901673955116288403443801781174272 +def node1243 : Tree Nat := .leaf 4127301024497384737127654569660285988428494734657199391624693039270889863724412964643884811622321780427143710884821317803768340308614730759769835769241715444596770968742227220068214981847081570726751819595399909407406471037121576084674975771617472472574520163263578112 +def node1244 : Tree Nat := .node node1242 node1243 +def node1245 : Tree Nat := .node node1241 node1244 +def node1246 : Tree Nat := .leaf 904625697166532776746648320380374280103671755200316906558262375061821325312 +def node1247 : Tree Nat := .leaf 12129047596099288555851402253613301212944422008724192274523844047078523067862319424459987568973800608988185396071336509423215469094646987433158494336259227650034804500162889887111447543996862850197367181200909912116350366045437952 +def node1248 : Tree Nat := .node node1246 node1247 +def node1249 : Tree Nat := .leaf 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16905424996341287883274873117328531408603114433155888708094742688853564881815195503181352188405030012629580639784228117724235121904085937192017247310814066461068373887968162693399408565645646113696775453062758028932736905368049975642828700760545167247665234588727615946752 +def node1269 : Tree Nat := .node node1267 node1268 +def node1270 : Tree Nat := .node node1266 node1269 +def node1271 : Tree Nat := .node node1263 node1270 +def node1272 : Tree Nat := .leaf 590295810358705651712 +def node1273 : Tree Nat := .leaf 7914572847139345089936080672628710081124203171238778877250017794972711203409019749450124833959777439667125485632516458859243681097816038718961476963260581373331416708758372352 +def node1274 : Tree Nat := .node node1272 node1273 +def node1275 : Tree Nat := .leaf 68351585149469122636640694597425667667286544715412888638305331450311031224980497600734786781970432 +def node1276 : Tree Nat := .leaf 916444925391198758541401085877594831703095653509460880942126390473954048171292933099049096506388108013739504295007991042380699544226348054414240833330066547856411977855334787272537640367327320839841280263415847919229777715415602675691481187407177449472 +def node1277 : Tree Nat := .node node1275 node1276 +def node1278 : Tree Nat := .node node1274 node1277 +def node1279 : Tree Nat := .leaf 200867255532373784442745261542645325315275374222849104412672 +def node1280 : Tree Nat := .leaf 2693189581592767235707386820034625876761773979045465016063119822371190863000105380922197266574125287028215280054363247469065949312094107577921441162573762995177074519617763634274131844036773231242902144888720064512 +def node1281 : Tree Nat := .node node1279 node1280 +def node1282 : Tree Nat := .leaf 23258839177459420497578361852416145099316523541994177929007686373780457219628733546438113622840434097944400691400517693873107252115668992 +def node1283 : Tree Nat := .leaf 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node1313 node57 +def node1315 : Tree Nat := .node node1312 node1314 +def node1316 : Tree Nat := .node node1309 node1315 +def node1317 : Tree Nat := .node node1302 node1316 +def node1318 : Tree Nat := .node node1287 node1317 +def node1319 : Tree Nat := .leaf 2097152 +def node1320 : Tree Nat := .leaf 28118211215894977392565865673037386617935606989386978956879722328823984879196799189494004288149317857187005691459505594520051662846839373056303219880407274094592 +def node1321 : Tree Nat := .node node1319 node1320 +def node1322 : Tree Nat := .leaf 242833611528216133864932738352939863330300854881517440156476551217363035650651062272 +def node1323 : Tree Nat := .leaf 3255866422304616344765552632188114158762089024568314531443485259650408807528140659922574316831813618526821245406949824436469141432675471230646169947427163108444901161872077421124549944292877941762189949285100879873872435565174053364826112 +def node1324 : Tree Nat := .node node1322 node1323 +def node1325 : Tree Nat := .node node1321 node1324 +def node1326 : Tree Nat := .leaf 713623846352979940529142984724747568191373312 +def node1327 : Tree Nat := .leaf 9568131466127621947163770315237577352582483950433331955534014747297500715462012198465648064079848065788579276806882658480425438483841942548911565191978080929321047135323978360596199778018349602045952 +def node1328 : Tree Nat := .node node1326 node1327 +def node1329 : Tree Nat := .leaf 82631996098781074868989413504096379978550585370535152410581099409300723904538918228148651304964410605948901503127919788032 +def node1330 : Tree Nat := .leaf 1107913932560222642718302084617242634394213707491304322373697056856707228094640652496493097019312046907692196808899173923175472949106175979816042319761510659592576951121881510274623639758153063707231876091920910184135845830200523203728421733043088080742988814006853038686339072 +def node1331 : Tree Nat := .node node1329 node1330 +def node1332 : Tree Nat := .node node1328 node1331 +def node1333 : Tree Nat := .node node1325 node1332 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node1350 : Tree Nat := .leaf 9007199254740992 +def node1351 : Tree Nat := .leaf 120766797594289323271729746591624604509341479053326093708038601607859973196548763266756055205685080561326988000984443036792658708157593364241965896045846273396780650463232 +def node1352 : Tree Nat := .node node1350 node1351 +def node1353 : Tree Nat := .leaf 1042962419883256876169444192465601618458351817556959360325703910069443225478828393565899456512 +def node1354 : Tree Nat := .leaf 13983839803942852150595109342614667231797724205161451430391332862456574221363722734055314582922181823940116947860839707067576592166539734717014172871857704892828551908192974659309961553456532605588398441519406859119106715628289835749686907766833152 +def node1355 : Tree Nat := .node node1353 node1354 +def node1356 : Tree Nat := .node node1352 node1355 +def node1357 : Tree Nat := .leaf 3064991081731777716716694054300618367237478244367204352 +def node1358 : Tree Nat := .leaf 41094811730846668025320233460001005199612029709556045777330319555224469955445943922763019814668659775210804444188892325882964314454560967680686052895717819140275184930690973423372373108471271228681978529185792 +def node1359 : Tree Nat := .node node1357 node1358 +def node1360 : Tree Nat := .leaf 354901720847464302026037015570314714039863945648104521621821386318671527399120079749116723981329865996466075003059657194108692201472 +def node1361 : Tree Nat := .leaf 4758454107128905800953799994079681792420032645310062268978469949811010102913293995344538606387700321887355916128617513761454672785743698264930657859527662802505506689431871596616596511469752757984765426503524599059416795862009216282102716609115705865638544337453260521036049116206989312 +def node1362 : Tree Nat := .node node1360 node1361 +def node1363 : Tree Nat := .node node1359 node1362 +def node1364 : Tree Nat := .node node1356 node1363 +def node1365 : Tree Nat := .leaf 166153499473114484112975882535043072 +def node1366 : Tree Nat := .leaf 2227754207823337509102134573095845373483021732054960903603121346630505452738612005129840239901060253798165190221481644194672219102234100585084307285020612396607419274589973120157653414182912 +def node1367 : Tree Nat := .node node1365 node1366 +def node1368 : Tree Nat := .leaf 19239260838083241802870625048898248928261591440656956380834127638791856333738872368854622194768025215237611323392 +def node1369 : Tree Nat := .leaf 257956314031086546070478410603767874276780920916074961976543314954430616482775810290242800726395111276696481930301332362735521269288420672485614735577607215287298185546389201254263436365442598170421988724712494337962904439820098505292185985726092029535907510203973632 +def node1370 : Tree Nat := .node node1368 node1369 +def node1371 : Tree Nat := .node node1367 node1370 +def node1372 : Tree Nat := .leaf 56539106072908298546665520023773392506479484700019806659891398441363832832 +def node1373 : Tree Nat := .leaf 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689456532887748412341091025928864224451014138635639044112158674527024860928026977516082500242976073479223111693916991352080883023896091539947888937618883326765331077022147490374177752073413947198182949091512336515072 +def node1406 : Tree Nat := .node node1404 node1405 +def node1407 : Tree Nat := .leaf 5954262829429611647380060634218533145425030026750509549825967711687797048224955787888157087447151129073766576998532529631515456541611261952 +def node1408 : Tree Nat := .leaf 79833612381388792466254908521473542642698050417418301660101889697488475674758562631398318619705428043573697873767699809758897519535743746429566871931393256812800226918043427060701508857774519487306134269781756959733232418204834815555554210737921766300284836275030241665694339809213760397115392 +def node1409 : Tree Nat := .node node1407 node1408 +def node1410 : Tree Nat := .node node1406 node1409 +def node1411 : Tree Nat := .node node1403 node1410 +def node1412 : Tree Nat := .node node1396 node1411 +def node1413 : Tree Nat := .leaf 35184372088832 +def node1414 : Tree Nat := .leaf 471745303102692669030194322623533611364615152552055053547025787530703020299018606510765840647207345942683546878845480612471323078740599079070179281429087005456174415872 +def node1415 : Tree Nat := .node node1413 node1414 +def node1416 : Tree Nat := .leaf 4074071952668972172536891376818756322102936787331872501272280898708762599526673412366794752 +def node1417 : Tree Nat := .leaf 54624374234151766213262145869588543874209860176411919649966143993970993052202041929903572589539772749766081827581405105732721063150545838738336612780694159737611530891378807262929537318189580490579681412185183043434010607923007170897214483464192 +def node1418 : Tree Nat := .node node1416 node1417 +def node1419 : Tree Nat := .node node1415 node1418 +def node1420 : Tree Nat := .leaf 11972621413014756705924586149611790497021399392059392 +def node1421 : Tree Nat := .leaf 160526608323619796973907161953128926560984491052953303817696560762595585763460718448293046151049452246917204860112860647980329353338128780002679894123897731016699941135511614935048332454965903237038978629632 +def node1422 : Tree Nat := .node node1420 node1421 +def node1423 : Tree Nat := .leaf 1386334847060407429789207092071541851718218537687908287585239790307310653902812811519987203052069789048695605480701785914487078912 +def node1424 : Tree Nat := .leaf 18587711355972288284975781226873757001640752520742430738197148241449258214505054669314603931201954382372484047377412163130682315569311321347385382263779932822287135505593248424283580122928721710877989947279392965075846858835973501101963736754358226037650563818176798910297066860183552 +def node1425 : Tree Nat := .node node1423 node1424 +def node1426 : Tree Nat := .node node1422 node1425 +def node1427 : Tree Nat := .node node1419 node1426 +def node1428 : Tree Nat := .leaf 649037107316853453566312041152512 +def node1429 : Tree Nat := .leaf 8702164874309912144930213176155645990168053640839691029699692760275411924760203145038438437113516616399082774302662672635438355868101955410485575332111767174247731541367082500615833649152 +def node1430 : Tree Nat := .node node1428 node1429 +def node1431 : Tree Nat := .leaf 75153362648762663292463379097258784876021841565066235862633311089030688803667470190838367948312598497021919232 +def node1432 : Tree Nat := .leaf 1007641851683931820587806291420968258893675472328417820220872324040744595635843008946260940337480903424595632540239579541935629958157893251896932560850028184716008537290582817399466548302510149103210893455908181007667595468047259786297601506742546990374638711734272 +def node1433 : Tree Nat := .node node1431 node1432 +def node1434 : Tree Nat := .node node1430 node1433 +def node1435 : Tree Nat := .leaf 220855883097298041197912187592864814478435487109452369765200775161577472 +def node1436 : Tree Nat := .leaf 2961193260766427870080908753323559866441509279473679754522422863056280045864824078237301652581494289303756200212728639995902214134435299666298460531313288000496778442422580538845568248046109094286466596972878396512780851085312 +def node1437 : Tree Nat := .node node1435 node1436 +def node1438 : Tree Nat := .leaf 25573364124188608359478044506465618376692515984711443667838213813251045284411519960025547596296126227741302219746563054759509816764729633229129121792 +def node1439 : Tree Nat := .node node1438 node57 +def node1440 : Tree Nat := .node node1437 node1439 +def node1441 : Tree Nat := .node node1434 node1440 +def node1442 : Tree Nat := .node node1427 node1441 +def node1443 : Tree Nat := .node node1412 node1442 +def node1444 : Tree Nat := .leaf 536870912 +def node1445 : Tree Nat := .leaf 7198262071269114212496861612297570974191515389283066612961208916178940129074380592510465097766225371439873457013633432197133225688790879502413624289384262168215552 +def node1446 : Tree Nat := .node node1444 node1445 +def node1447 : Tree Nat := .leaf 62165404551223330269422781018352605012557018849668464680057997111644937126566671941632 +def node1448 : Tree Nat := .leaf 833501804109981784259981473840157224643094790289488520049532226470504654727204008940179025108944286342866238824179155055736100206764920635045419506541353755761894697439251819807884785738976753091120627016985825247711343504684557661395484672 +def node1449 : Tree Nat := .node node1447 node1448 +def node1450 : Tree Nat := .node node1446 node1449 +def node1451 : Tree Nat := .leaf 182687704666362864775460604089535377456991567872 +def node1452 : Tree Nat := .leaf 2449441655328671218473925200700819802261115891310932980616707775308160183158275122807205904404441104841876294862561960570988912251863537292521360689146388717906188066642938460312627143172697498123763712 +def node1453 : Tree Nat := .node node1451 node1452 +def node1454 : Tree Nat := .leaf 21153791001287955166461289857048673274508949854856999017108761448780985319561963066406054734070889115122918784800747465736192 +def node1455 : Tree Nat := .leaf 283625966735416996535885333662014114404918709117773906527666446555317050392228007039102232836943884008369202383078188524332921074971181050832906833858946728855699699487201666630303651778087184309051360279531753007138776532531333940154475963659030548670205136385754377903702802432 +def node1456 : Tree Nat := .node node1454 node1455 +def node1457 : Tree Nat := .node node1453 node1456 +def node1458 : Tree Nat := .node node1450 node1457 +def node1459 : Tree Nat := .leaf 9903520314283042199192993792 +def node1460 : Tree Nat := .leaf 132784498204191774672397051638117156832398279431757980799861034550100889965213060684790625566307321417222332371561625253836644834413176809852379994691646837985957817708848304757932032 +def node1461 : Tree Nat := .node node1459 node1460 +def node1462 : Tree Nat := .leaf 1146749307995035755805410447651043470398282494584140561868794419693461438044242404035009276555062843277312 +def node1463 : Tree Nat := .leaf 15375394465392026070980930960402958051966483647589383243116337952281869440244186537876296086692518667977838631290276787444086150484586994200087471936798525767761360737466168478385414860572969804431318564695864578364068534363514095860253929241066696020120829952 +def node1464 : Tree Nat := .node node1462 node1463 +def node1465 : Tree Nat := .node node1461 node1464 +def node1466 : Tree Nat := .leaf 3369993333393829974333376885877453834204643052817571560137951281152 +def node1467 : Tree Nat := .leaf 45184223339331479951185741475274045813621662589625240394934430893803101285779175998493982735923679951534365847972543945249972749854054255162024849415791137702892737463723457929162113159883256443580117751661352485851758592 +def node1468 : Tree Nat := .node node1466 node1467 +def node1469 : Tree Nat := .leaf 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node1500 : Tree Nat := .node node1499 node57 +def node1501 : Tree Nat := .node node1498 node1500 +def node1502 : Tree Nat := .node node1495 node1501 +def node1503 : Tree Nat := .node node1488 node1502 +def node1504 : Tree Nat := .node node1473 node1503 +def node1505 : Tree Nat := .node node1443 node1504 +def node1506 : Tree Nat := .node node1381 node1505 +def node1507 : Tree Nat := .node node1256 node1506 +def node1508 : Tree Nat := .leaf 8 +def node1509 : Tree Nat := .leaf 107262463439540776796592199985646769019834926564739147021788491549774112240588375814414994385335227421520254865491888406830031062495572559571469192048672768 +def node1510 : Tree Nat := .node node1508 node1509 +def node1511 : Tree Nat := .leaf 926336713898529563388567880069503262826159877325124512315660672063305037119488 +def node1512 : Tree Nat := .leaf 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node1564 node57 +def node1566 : Tree Nat := .node node1563 node1565 +def node1567 : Tree Nat := .node node1560 node1566 +def node1568 : Tree Nat := .node node1553 node1567 +def node1569 : Tree Nat := .node node1538 node1568 +def node1570 : Tree Nat := .leaf 524288 +def node1571 : Tree Nat := .leaf 7029552803973744348141466418259346654483901747346744739219930582205996219799199797373501072037329464296751422864876398630012915711709843264075804970101818523648 +def node1572 : Tree Nat := .node node1570 node1571 +def node1573 : Tree Nat := .leaf 60708402882054033466233184588234965832575213720379360039119137804340758912662765568 +def node1574 : Tree Nat := .leaf 813966605576154086191388158047028539690522256142078632860871314912602201882035164980643579207953404631705311351737456109117285358168867807661542486856790777111225290468019355281137486073219485440547487321275219968468108891293513341206528 +def node1575 : Tree Nat := .node node1573 node1574 +def node1576 : Tree Nat := .node node1572 node1575 +def node1577 : Tree Nat := .leaf 178405961588244985132285746181186892047843328 +def node1578 : Tree Nat := .leaf 2392032866531905486790942578809394338145620987608332988883503686824375178865503049616412016019962016447144819201720664620106359620960485637227891297994520232330261783830994590149049944504587400511488 +def node1579 : Tree Nat := .node node1577 node1578 +def node1580 : Tree Nat := .leaf 20657999024695268717247353376024094994637646342633788102645274852325180976134729557037162826241102651487225375781979947008 +def node1581 : Tree Nat := .leaf 276978483140055660679575521154310658598553426872826080593424264214176807023660163124123274254828011726923049202224793480793868237276543994954010579940377664898144237780470377568655909939538265926807969022980227546033961457550130800932105433260772020185747203501713259671584768 +def node1582 : Tree Nat := .node node1580 node1581 +def node1583 : Tree Nat := .node node1579 node1582 +def node1584 : Tree Nat := .node node1576 node1583 +def node1585 : Tree Nat := .leaf 9671406556917033397649408 +def node1586 : Tree Nat := .leaf 129672361527531029953512745740348785969138944757576153124864291552832900356653379574990845279596993571506183956603149661949848471106617978371464838566061365220661931356297172615168 +def node1587 : Tree Nat := .node node1585 node1586 +def node1588 : Tree Nat := .leaf 1119872371088902105278721140284222139060822748617324767449994550481895935590080472690438746635803557888 +def node1589 : Tree Nat := .leaf 15015033657609400459942315391018513722623519187099007073355798781525263125238463415894820397160662761697108038369410925238365381332604486523522921813279810320079453845181805154673256699778290824639959535835805252308660678089369234238529227774479195332149248 +def node1590 : Tree Nat := .node node1588 node1589 +def node1591 : Tree Nat := .node node1587 node1590 +def node1592 : Tree Nat := .leaf 3291009114642412084309938365114701009965471731267159726697218048 +def node1593 : Tree Nat := .leaf 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Tree Nat := .leaf 2251799813685248 +def node1602 : Tree Nat := .leaf 30191699398572330817932436647906151127335369763331523427009650401964993299137190816689013801421270140331747000246110759198164677039398341060491474011461568349195162615808 +def node1603 : Tree Nat := .node node1601 node1602 +def node1604 : Tree Nat := .leaf 260740604970814219042361048116400404614587954389239840081425977517360806369707098391474864128 +def node1605 : Tree Nat := .leaf 3495959950985713037648777335653666807949431051290362857597833215614143555340930683513828645730545455985029236965209926766894148041634933679253543217964426223207137977048243664827490388364133151397099610379851714779776678907072458937421726941708288 +def node1606 : Tree Nat := .node node1604 node1605 +def node1607 : Tree Nat := .node node1603 node1606 +def node1608 : Tree Nat := .leaf 766247770432944429179173513575154591809369561091801088 +def node1609 : Tree Nat := .leaf 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:= .leaf 556938551955834377275533643273961343370755433013740225900780336657626363184653001282460059975265063449541297555370411048668054775558525146271076821255153099151854818647493280039413353545728 +def node1618 : Tree Nat := .node node1616 node1617 +def node1619 : Tree Nat := .leaf 4809815209520810450717656262224562232065397860164239095208531909697964083434718092213655548692006303809402830848 +def node1620 : Tree Nat := .leaf 64489078507771636517619602650941968569195230229018740494135828738607654120693952572560700181598777819174120482575333090683880317322105168121403683894401803821824546386597300313565859091360649542605497181178123584490726109955024626323046496431523007383976877550993408 +def node1621 : Tree Nat := .node node1619 node1620 +def node1622 : Tree Nat := .node node1618 node1621 +def node1623 : Tree Nat := .leaf 14134776518227074636666380005943348126619871175004951664972849610340958208 +def node1624 : Tree Nat := .leaf 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Nat := .leaf 8796093022208 +def node1665 : Tree Nat := .leaf 117936325775673167257548580655883402841153788138013763386756446882675755074754651627691460161801836485670886719711370153117830769685149769767544820357271751364043603968 +def node1666 : Tree Nat := .node node1664 node1665 +def node1667 : Tree Nat := .leaf 1018517988167243043134222844204689080525734196832968125318070224677190649881668353091698688 +def node1668 : Tree Nat := .leaf 13656093558537941553315536467397135968552465044102979912491535998492748263050510482475893147384943187441520456895351276433180265787636459684584153195173539934402882722844701815732384329547395122644920353046295760858502651980751792724303620866048 +def node1669 : Tree Nat := .node node1667 node1668 +def node1670 : Tree Nat := .node node1666 node1669 +def node1671 : Tree Nat := .leaf 2993155353253689176481146537402947624255349848014848 +def node1672 : Tree Nat := .leaf 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node1695 node1696 +def node1698 : Tree Nat := .leaf 15541351137805832567355695254588151253139254712417116170014499277911234281641667985408 +def node1699 : Tree Nat := .leaf 208375451027495446064995368460039306160773697572372130012383056617626163681801002235044756277236071585716559706044788763934025051691230158761354876635338438940473674359812954951971196434744188272780156754246456311927835876171139415348871168 +def node1700 : Tree Nat := .node node1698 node1699 +def node1701 : Tree Nat := .node node1697 node1700 +def node1702 : Tree Nat := .leaf 45671926166590716193865151022383844364247891968 +def node1703 : Tree Nat := .leaf 612360413832167804618481300175204950565278972827733245154176943827040045789568780701801476101110276210469073715640490142747228062965884323130340172286597179476547016660734615078156785793174374530940928 +def node1704 : Tree Nat := .node node1702 node1703 +def node1705 : Tree Nat := .leaf 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node1751 : Tree Nat := .node node1750 node57 +def node1752 : Tree Nat := .node node1749 node1751 +def node1753 : Tree Nat := .node node1746 node1752 +def node1754 : Tree Nat := .node node1739 node1753 +def node1755 : Tree Nat := .node node1724 node1754 +def node1756 : Tree Nat := .node node1694 node1755 +def node1757 : Tree Nat := .node node1632 node1756 +def node1758 : Tree Nat := .leaf 128 +def node1759 : Tree Nat := .leaf 1716199415032652428745475199770348304317358825035826352348615864796385795849414013030639910165363638744324077847870214509280496999929160953143507072778764288 +def node1760 : Tree Nat := .node node1758 node1759 +def node1761 : Tree Nat := .leaf 14821387422376473014217086081112052205218558037201992197050570753012880593911808 +def node1762 : Tree Nat := .leaf 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node1822 node1825 +def node1827 : Tree Nat := .leaf 2854495385411919762116571938898990272765493248 +def node1828 : Tree Nat := .leaf 38272525864510487788655081260950309410329935801733327822136058989190002861848048793862592256319392263154317107227530633921701753935367770195646260767912323717284188541295913442384799112073398408183808 +def node1829 : Tree Nat := .node node1827 node1828 +def node1830 : Tree Nat := .leaf 330527984395124299475957654016385519914202341482140609642324397637202895618155672912594605219857642423795606012511679152128 +def node1831 : Tree Nat := .leaf 4431655730240890570873208338468970537576854829965217289494788227426828912378562609985972388077248187630768787235596695692701891796424703919264169279046042638370307804487526041098494559032612254828927504367683640736543383320802092814913686932172352322971955256027412154745356288 +def node1832 : Tree Nat := .node node1830 node1831 +def node1833 : Tree Nat := .node node1829 node1832 +def node1834 : Tree Nat := .node node1826 node1833 +def node1835 : Tree Nat := .leaf 154742504910672534362390528 +def node1836 : Tree Nat := .leaf 2074757784440496479256203931845580575506223116121218449997828664845326405706454073199853524473551897144098943305650394591197575537705887653943437417056981843530590901700754761842688 +def node1837 : Tree Nat := .node node1835 node1836 +def node1838 : Tree Nat := .leaf 17917957937422433684459538244547554224973163977877196279199912807710334969441287563047019946172856926208 +def node1839 : Tree Nat := .leaf 240240538521750407359077046256296219561976306993584113173692780504404210003815414654317126354570604187153728613910574803813846101321671784376366749012476965121271261522908882474772107196452653194239352573372884036938570849429907747816467644391667125314387968 +def node1840 : Tree Nat := .node node1838 node1839 +def node1841 : Tree Nat := .node node1837 node1840 +def node1842 : Tree Nat := .leaf 52656145834278593348959013841835216159447547700274555627155488768 +def node1843 : Tree Nat := .leaf 706003489677054374237277210551156965837838477962894381170850482715673457590299624976468480248807499242724466374570999144530824216469597736906638272121736526607699022870679030143158018123175881930939339869708632591433728 +def node1844 : Tree Nat := .node node1842 node1843 +def node1845 : Tree Nat := .leaf 6097165137335922326917182089439777940915230747392521779021790936768304177382354726797472857545882756171536974846497310342671827498609932238848 +def node1846 : Tree Nat := .leaf 81749619078542123485445026325988907666122803627436340899944335050228199090952768134551878266578358316619466622738124605193111060004601596343876476857746694976307432364076469310158345070361107955001481492256519126766829996241750851128887511795631888691491672345630967465671003964634890646646161408 +def node1847 : Tree Nat := .node node1845 node1846 +def node1848 : Tree Nat := .node node1844 node1847 +def node1849 : Tree Nat := .node node1841 node1848 +def node1850 : Tree Nat := .node node1834 node1849 +def node1851 : Tree Nat := .leaf 36028797018963968 +def node1852 : Tree Nat := .leaf 483067190377157293086918986366498418037365916213304374832154406431439892786195053067024220822740322245307952003937772147170634832630373456967863584183385093587122601852928 +def node1853 : Tree Nat := .node node1851 node1852 +def node1854 : Tree Nat := .leaf 4171849679533027504677776769862406473833407270227837441302815640277772901915313574263597826048 +def node1855 : Tree Nat := .leaf 55935359215771408602380437370458668927190896820645805721565331449826296885454890936221258331688727295760467791443358828270306368666158938868056691487430819571314207632771898637239846213826130422353593766077627436476426862513159342998747631067332608 +def node1856 : Tree Nat := .node node1854 node1855 +def node1857 : Tree Nat := .node node1853 node1856 +def node1858 : Tree Nat := .leaf 12259964326927110866866776217202473468949912977468817408 +def node1859 : Tree Nat := .leaf 164379246923386672101280933840004020798448118838224183109321278220897879821783775691052079258674639100843217776755569303531857257818243870722744211582871276561100739722763893693489492433885084914727914116743168 +def node1860 : Tree Nat := .node node1858 node1859 +def node1861 : Tree Nat := .leaf 1419606883389857208104148062281258856159455782592418086487285545274686109596480318996466895925319463985864300012238628776434768805888 +def node1862 : Tree Nat := .leaf 19033816428515623203815199976318727169680130581240249075913879799244040411653175981378154425550801287549423664514470055045818691142974793059722631438110651210022026757727486386466386045879011031939061706014098396237667183448036865128410866436462823462554177349813042084144196464827957248 +def node1863 : Tree Nat := .node node1861 node1862 +def node1864 : Tree Nat := .node node1860 node1863 +def node1865 : Tree Nat := .node node1857 node1864 +def node1866 : Tree Nat := .leaf 664613997892457936451903530140172288 +def node1867 : Tree Nat := .leaf 8911016831293350036408538292383381493932086928219843614412485386522021810954448020519360959604241015192660760885926576778688876408936402340337229140082449586429677098359892480630613656731648 +def node1868 : Tree Nat := .node node1866 node1867 +def node1869 : Tree Nat := .leaf 76957043352332967211482500195592995713046365762627825523336510555167425334955489475418488779072100860950445293568 +def node1870 : Tree Nat := .leaf 1031825256124346184281913642415071497107123683664299847906173259817722465931103241160971202905580445106785927721205329450942085077153682689942458942310428861149192742185556805017053745461770392681687954898849977351851617759280394021168743942904368118143630040815894528 +def node1871 : Tree Nat := .node node1869 node1870 +def node1872 : Tree Nat := .node node1868 node1871 +def node1873 : Tree Nat := .leaf 226156424291633194186662080095093570025917938800079226639565593765455331328 +def node1874 : Tree Nat := .leaf 3032261899024822138962850563403325303236105502181048068630961011769630766965579856114996892243450152247046349017834127355803867273661746858289623584064806912508701125040722471777861885999215712549341795300227478029087591511359488 +def node1875 : Tree Nat := .node node1873 node1874 +def node1876 : Tree Nat := .leaf 26187124863169134960105517574620793217733136368344518315866330944769070371237396439066160738607233257207093473020480568073738052367083144426628220715008 +def node1877 : Tree Nat := .node node1876 node57 +def node1878 : Tree Nat := .node node1875 node1877 +def node1879 : Tree Nat := .node node1872 node1878 +def node1880 : Tree Nat := .node node1865 node1879 +def node1881 : Tree Nat := .node node1850 node1880 +def node1882 : Tree Nat := .node node1819 node1881 +def node1883 : Tree Nat := .leaf 32768 +def node1884 : Tree Nat := .leaf 439347050248359021758841651141209165905243859209171546201245661387874763737449987335843817002333091518546963929054774914375807231981865204004737810631363657728 +def node1885 : Tree Nat := .node node1883 node1884 +def node1886 : Tree Nat := .leaf 3794275180128377091639574036764685364535950857523710002444946112771297432041422848 +def node1887 : Tree Nat := .leaf 50872912848509630386961759877939283730657641008879914553804457182037637617627197811290223700497087789481581959483591006819830334885554237978846405428549423569451580654251209705071092879576217840034217957579701248029256805705844583825408 +def node1888 : Tree Nat := .node node1886 node1887 +def node1889 : Tree Nat := .node node1885 node1888 +def node1890 : Tree Nat := .leaf 11150372599265311570767859136324180752990208 +def node1891 : Tree Nat := .leaf 149502054158244092924433911175587146134101311725520811805218980426523448679093940601025751001247626027946551200107541538756647476310030352326743206124657514520641361489437161884315621531536712531968 +def node1892 : Tree Nat := .node node1890 node1891 +def node1893 : Tree Nat := .leaf 1291124939043454294827959586001505937164852896414611756415329678270323811008420597314822676640068915717951585986373746688 +def node1894 : Tree Nat := .leaf 17311155196253478792473470072144416162409589179551630037089016513386050438978760195257704640926750732932690575139049592549616764829783999684625661246273604056134014861279398598040994371221141620425498063936264221627122591096883175058256589578798251261609200218857078729474048 +def node1895 : Tree Nat := .node node1893 node1894 +def node1896 : Tree Nat := .node node1892 node1895 +def node1897 : Tree Nat := .node node1889 node1896 +def node1898 : Tree Nat := .leaf 604462909807314587353088 +def node1899 : Tree Nat := .leaf 8104522595470689372094546608771799123071184047348509570304018222052056272290836223436927829974812098219136497287696853871865529444163623648216552410378835326291370709768573288448 +def node1900 : Tree Nat := .node node1898 node1899 +def node1901 : Tree Nat := .leaf 69992023193056381579920071267763883691301421788582797965624659405118495974380029543152421664737722368 +def node1902 : Tree Nat := .leaf 938439603600587528746394711938657107663969949193687942084737423845328945327403963493426274822541422606069252398088182827397836333287780407720182613329988145004965865323862822167078543736143176539997470989737828269291292380585577139908076735904949708259328 +def node1903 : Tree Nat := .node node1901 node1902 +def node1904 : Tree Nat := .node node1900 node1903 +def node1905 : Tree Nat := .leaf 205688069665150755269371147819668813122841983204197482918576128 +def node1906 : Tree Nat := .leaf 2757826131550993649364364103715456897804056554542556176448634698108099443712107910064330000971904293916892446775667965408323532095584366159791555750475533307061324308088589961496711008293655788792731796366049346060288 +def node1907 : Tree Nat := .node node1905 node1906 +def node1908 : Tree Nat := .leaf 23817051317718446589520242536874132581700120107002038199303870846751188192899823151552628349788604516295066307994130118526061826166445047808 +def node1909 : Tree Nat := .leaf 319334449525555169865019634085894170570792201669673206640407558789953902699034250525593274478821712174294791495070799239035590078142974985718267487725573027251200907672173708242806035431098077949224537079127027838932929672819339262222216842951687065201139345100120966662777359236855041588461568 +def node1910 : Tree Nat := .node node1908 node1909 +def node1911 : Tree Nat := .node node1907 node1910 +def node1912 : Tree Nat := .node node1904 node1911 +def node1913 : Tree Nat := .node node1897 node1912 +def node1914 : Tree Nat := .leaf 140737488355328 +def node1915 : Tree Nat := .leaf 1886981212410770676120777290494134445458460610208220214188103150122812081196074426043063362588829383770734187515381922449885292314962396316280717125716348021824697663488 +def node1916 : Tree Nat := .node node1914 node1915 +def node1917 : Tree Nat := .leaf 16296287810675888690147565507275025288411747149327490005089123594835050398106693649467179008 +def node1918 : Tree Nat := .leaf 218497496936607064853048583478354175496839440705647678599864575975883972208808167719614290358159090999064327310325620422930884252602183354953346451122776638950446123565515229051718149272758321962318725648740732173736042431692028683588857933856768 +def node1919 : Tree Nat := .node node1917 node1918 +def node1920 : Tree Nat := .node node1916 node1919 +def node1921 : Tree Nat := .leaf 47890485652059026823698344598447161988085597568237568 +def node1922 : Tree Nat := .leaf 642106433294479187895628647812515706243937964211813215270786243050382343053842873793172184604197808987668819440451442591921317413352515120010719576495590924066799764542046459740193329819863612948155914518528 +def node1923 : Tree Nat := .node node1921 node1922 +def node1924 : Tree Nat := .leaf 5545339388241629719156828368286167406872874150751633150340959161229242615611251246079948812208279156194782421922807143657948315648 +def node1925 : Tree Nat := .leaf 74350845423889153139903124907495028006563010082969722952788592965797032858020218677258415724807817529489936189509648652522729262277245285389541529055119731289148542022372993697134320491714886843511959789117571860303387435343894004407854947017432904150602255272707195641188267440734208 +def node1926 : Tree Nat := .node node1924 node1925 +def node1927 : Tree Nat := .node node1923 node1926 +def node1928 : Tree Nat := .node node1920 node1927 +def node1929 : Tree Nat := .leaf 2596148429267413814265248164610048 +def node1930 : Tree Nat := .leaf 34808659497239648579720852704622583960672214563358764118798771041101647699040812580153753748454066465596331097210650690541753423472407821641942301328447068696990926165468330002463334596608 +def node1931 : Tree Nat := .node node1929 node1930 +def node1932 : Tree Nat := .leaf 300613450595050653169853516389035139504087366260264943450533244356122755214669880763353471793250393988087676928 +def node1933 : Tree Nat := .leaf 4030567406735727282351225165683873035574701889313671280883489296162978382543372035785043761349923613698382530160958318167742519832631573007587730243400112738864034149162331269597866193210040596412843573823632724030670381872189039145190406026970187961498554846937088 +def node1934 : Tree Nat := .node node1932 node1933 +def node1935 : Tree Nat := .node node1931 node1934 +def node1936 : Tree Nat := .leaf 883423532389192164791648750371459257913741948437809479060803100646309888 +def node1937 : Tree Nat := .leaf 11844773043065711480323635013294239465766037117894719018089691452225120183459296312949206610325977157215024800850914559983608856537741198665193842125253152001987113769690322155382272992184436377145866387891513586051123404341248 +def node1938 : Tree Nat := .node node1936 node1937 +def node1939 : Tree Nat := .leaf 102293456496754433437912178025862473506770063938845774671352855253004181137646079840102190385184504910965208878986252219038039267058918532916516487168 +def node1940 : Tree Nat := .node node1939 node57 +def node1941 : Tree Nat := .node node1938 node1940 +def node1942 : Tree Nat := .node node1935 node1941 +def node1943 : Tree Nat := .node node1928 node1942 +def node1944 : Tree Nat := .node node1913 node1943 +def node1945 : Tree Nat := .leaf 2147483648 +def node1946 : Tree Nat := .leaf 28793048285076456849987446449190283896766061557132266451844835664715760516297522370041860391064901485759493828054533728788532902755163518009654497157537048672862208 +def node1947 : Tree Nat := .node node1945 node1946 +def node1948 : Tree Nat := .leaf 248661618204893321077691124073410420050228075398673858720231988446579748506266687766528 +def node1949 : Tree Nat := .leaf 3334007216439927137039925895360628898572379161157954080198128905882018618908816035760716100435777145371464955296716620222944400827059682540181678026165415023047578789757007279231539142955907012364482508067943300990845374018738230645581938688 +def node1950 : Tree Nat := .node node1948 node1949 +def node1951 : Tree Nat := .node node1947 node1950 +def node1952 : Tree Nat := .leaf 730750818665451459101842416358141509827966271488 +def node1953 : Tree Nat := .leaf 9797766621314684873895700802803279209044463565243731922466831101232640732633100491228823617617764419367505179450247842283955649007454149170085442756585554871624752266571753841250508572690789992495054848 +def node1954 : Tree Nat := .node node1952 node1953 +def node1955 : Tree Nat := .leaf 84615164005151820665845159428194693098035799419427996068435045795123941278247852265624218936283556460491675139202989862944768 +def node1956 : Tree Nat := .leaf 1134503866941667986143541334648056457619674836471095626110665786221268201568912028156408931347775536033476809532312754097331684299884724203331627335435786915422798797948806666521214607112348737236205441118127012028555106130125335760617903854636122194680820545543017511614811209728 +def node1957 : Tree Nat := .node node1955 node1956 +def node1958 : Tree Nat := .node node1954 node1957 +def node1959 : Tree Nat := .node node1951 node1958 +def node1960 : Tree Nat := .leaf 39614081257132168796771975168 +def node1961 : Tree Nat := .leaf 531137992816767098689588206552468627329593117727031923199444138200403559860852242739162502265229285668889329486246501015346579337652707239409519978766587351943831270835393219031728128 +def node1962 : Tree Nat := .node node1960 node1961 +def node1963 : Tree Nat := .leaf 4586997231980143023221641790604173881593129978336562247475177678773845752176969616140037106220251373109248 +def node1964 : Tree Nat := .leaf 61501577861568104283923723841611832207865934590357532972465351809127477760976746151505184346770074671911354525161107149776344601938347976800349887747194103071045442949864673913541659442291879217725274258783458313456274137454056383441015716964266784080483319808 +def node1965 : Tree Nat := .node node1963 node1964 +def node1966 : Tree Nat := .node node1962 node1965 +def node1967 : Tree Nat := .leaf 13479973333575319897333507543509815336818572211270286240551805124608 +def node1968 : Tree Nat := .leaf 180736893357325919804742965901096183254486650358500961579737723575212405143116703993975930943694719806137463391890175780999890999416217020648099397663164550811570949854893831716648452639533025774320471006645409943407034368 +def node1969 : Tree Nat := .node node1967 node1968 +def node1970 : Tree Nat := .leaf 1560874275157996115690798614896583152874299071332485575429578479812685869409882810060153051531745985579913465560703311447723987839644142653145088 +def node1971 : Tree Nat := .node node1970 node57 +def node1972 : Tree Nat := .node node1969 node1971 +def node1973 : Tree Nat := .node node1966 node1972 +def node1974 : Tree Nat := .node node1959 node1973 +def node1975 : Tree Nat := .leaf 9223372036854775808 +def node1976 : Tree Nat := .leaf 123665200736552267030251260509823595017565674550605919957031528046448612553265933585158200530621522494798835713008069669675682517153375604983773077550946583958303386074349568 +def node1977 : Tree Nat := .node node1975 node1976 +def node1978 : Tree Nat := .leaf 1067993517960455041197510853084776057301352261178326384973520803911109862890320275011481043468288 +def node1979 : Tree Nat := .leaf 14319451959237480602209391966837419245360869586085326264720724851155532002676452079672642132912314187714679754609499860037198430378536688350222513020782289810256437153989606051133400630739489388122520004115872623737965276803368791807679393553237147648 +def node1980 : Tree Nat := .node node1978 node1979 +def node1981 : Tree Nat := .node node1977 node1980 +def node1982 : Tree Nat := .leaf 3138550867693340381917894711603833208051177722232017256448 +def node1983 : Tree Nat := .leaf 42081087212386988057927919063041029324402718422585390875986247224549857234376646576909332290220707609815863750849425741704155458001470430905022518165215046799641789369027556785533310063074581738170346013886251008 +def node1984 : Tree Nat := .node node1982 node1983 +def node1985 : Tree Nat := .leaf 363419362147803445274661903944002267176820680343659030140745099590319644056698961663095525356881782780381260803133088966767300814307328 +def node1986 : Tree Nat := .leaf 4872657005699999540176691193937594155438113428797503763433953228606474345383213051232807532941005129612652458115704334091729584932601547023288993648156326709765638849978236514935394827745026824176399796739609189436842798962697437472873181807734482806413869401552138773540914294995957055488 +def node1987 : Tree Nat := .node node1985 node1986 +def node1988 : Tree Nat := .node node1984 node1987 +def node1989 : Tree Nat := .node node1981 node1988 +def node1990 : Tree Nat := .leaf 170141183460469231731687303715884105728 +def node1991 : Tree Nat := .leaf 2281220308811097609320585802850145662446614253624279965289596258949637583604338693252956405658685699889321154786797203655344352360687718999126330659861107094125997337180132475041437096123301888 +def node1992 : Tree Nat := .node node1990 node1991 +def node1993 : Tree Nat := .leaf 19701003098197239606139520050071806902539869635232723333974146702122860885748605305707133127442457820403313995153408 +def node1994 : Tree Nat := .leaf 264147265567832623176169892458258303259423663018060761063980354513336951278362429737208627943828593947337197496628564339441173779751342768625269489231469788454193341999502542084365758838213220526512116454105594202074014146375780869419198449383518238244769290448868999168 +def node1995 : Tree Nat := .node node1993 node1994 +def node1996 : Tree Nat := .node node1992 node1995 +def node1997 : Tree Nat := .leaf 57896044618658097711785492504343953926634992332820282019728792003956564819968 +def node1998 : Tree Nat := .leaf 776259046150354467574489744231251277628443008558348305569526019013025476343188443165439204414323238975243865348565536603085790022057407195722143637520590569602227488010424952775132642815799222412631499596858234375446423426908028928 +def node1999 : Tree Nat := .node node1997 node1998 +def node2000 : Tree Nat := .leaf 6703903964971298549787012499102923063739682910296196688861780721860882015036773488400937149083451713845015929093243025426876941405973284973216824503042048 +def node2001 : Tree Nat := .node node2000 node57 +def node2002 : Tree Nat := .node node1999 node2001 +def node2003 : Tree Nat := .node node1996 node2002 +def node2004 : Tree Nat := .node node1989 node2003 +def node2005 : Tree Nat := .node node1974 node2004 +def node2006 : Tree Nat := .node node1944 node2005 +def node2007 : Tree Nat := .node node1882 node2006 +def node2008 : Tree Nat := .node node1757 node2007 +def node2009 : Tree Nat := .node node1507 node2008 +def node2010 : Tree Nat := .node node1005 node2009 +def node2011 : Tree Nat := .leaf 468837596257654785485714567836825287797216999011290225314876832561941490196892712413000809714458310517483176007983386841105428133203049499878352226978873295886886612109912281310141678387756614710705668987677453263568896 +def node2012 : Tree Nat := .node node2011 node235 +def node2013 : Tree Nat := .node node2012 node239 +def node2014 : Tree Nat := .node node2013 node246 +def node2015 : Tree Nat := .node node233 node2014 +def node2016 : Tree Nat := .node node218 node2015 +def node2017 : Tree Nat := .node node187 node2016 +def node2018 : Tree Nat := .node node125 node2017 +def node2019 : Tree Nat := .leaf 17926543156650705493745156729723227086574128068473552473659540154970077439176188202568893103141175937287205588304377392190185369369475267917001639732154358328899734084597219304625978558416683920238348160431141421056 +def node2020 : Tree Nat := .node node2019 node485 +def node2021 : Tree Nat := .node node2020 node489 +def node2022 : Tree Nat := .node node2021 node496 +def node2023 : Tree Nat := .node node483 node2022 +def node2024 : Tree Nat := .node node468 node2023 +def node2025 : Tree Nat := .node node438 node2024 +def node2026 : Tree Nat := .node node376 node2025 +def node2027 : Tree Nat := .node node2018 node2026 +def node2028 : Tree Nat := .leaf 1174833932040724960313232606750625274616384720429471888776451919860092366200491702340667794169296118804398355566270771080656304851059944022032590696334448917359572673155626758359554958083022082656036815126615964084338688 +def node2029 : Tree Nat := .node node2028 node737 +def node2030 : Tree Nat := .node node2029 node741 +def node2031 : Tree Nat := .node node2030 node748 +def node2032 : Tree Nat := .node node735 node2031 +def node2033 : Tree Nat := .node node720 node2032 +def node2034 : Tree Nat := .node node689 node2033 +def node2035 : Tree Nat := .node node627 node2034 +def node2036 : Tree Nat := .node node2035 node1003 +def node2037 : Tree Nat := .node node2027 node2036 +def node2038 : Tree Nat := .leaf 1081947199765842424529591879509026010150599323721976877786911901102607643345088549071012028586067969415086892678226327950891943481813958187189058352707702921661272309510797616656978764698096947630881447428301830436959628321604570912209493886309420406585308103865622174105600 +def node2039 : Tree Nat := .node node2038 node1240 +def node2040 : Tree Nat := .node node2039 node1244 +def node2041 : Tree Nat := .node node2040 node1251 +def node2042 : Tree Nat := .node node1238 node2041 +def node2043 : Tree Nat := .node node1223 node2042 +def node2044 : Tree Nat := .node node1192 node2043 +def node2045 : Tree Nat := .node node1130 node2044 +def node2046 : Tree Nat := .leaf 12265838598041424932662211800746456264892248528636915848700250083271096680854451408693025484194569951020610662418735741116292517827976557850985588716273805352473985024 +def node2047 : Tree Nat := .node node2046 node1490 +def node2048 : Tree Nat := .node node2047 node1494 +def node2049 : Tree Nat := .node node2048 node1501 +def node2050 : Tree Nat := .node node1488 node2049 +def node2051 : Tree Nat := .node node1473 node2050 +def node2052 : Tree Nat := .node node1443 node2051 +def node2053 : Tree Nat := .node node1381 node2052 +def node2054 : Tree Nat := .node node2045 node2053 +def node2055 : Tree Nat := .leaf 1174833932040723294629220079997464680937933805781821401243985445075573084210780894769804100209656106251896829950546403362887871301176856649286481267126524720761980671939482040735062037418460003427932135323694311835435008 +def node2056 : Tree Nat := .node node2055 node1741 +def node2057 : Tree Nat := .node node2056 node1745 +def node2058 : Tree Nat := .node node2057 node1752 +def node2059 : Tree Nat := .node node1739 node2058 +def node2060 : Tree Nat := .node node1724 node2059 +def node2061 : Tree Nat := .node node1694 node2060 +def node2062 : Tree Nat := .node node1632 node2061 +def node2063 : Tree Nat := .node node2062 node2007 +def node2064 : Tree Nat := .node node2054 node2063 +def node2065 : Tree Nat := .node node2037 node2064 +def node2066 : Tree Nat := .leaf 7507516828804700229971157695509256861311759593549503536677899755757881062691615256630906892622143669048765587635950989016785553242771871920041144482488516403958696424541355426923166035466523350467695506195964986883515035653151194577774143095278493476323328 +def node2067 : Tree Nat := .node node2066 node8 +def node2068 : Tree Nat := .node node2067 node12 +def node2069 : Tree Nat := .node node6 node2068 +def node2070 : Tree Nat := .node node2069 node29 +def node2071 : Tree Nat := .node node2070 node61 +def node2072 : Tree Nat := .node node2071 node124 +def node2073 : Tree Nat := .node node2072 node2017 +def node2074 : Tree Nat := .node node2073 node2026 +def node2075 : Tree Nat := .leaf 273579137855854662637703584477554704905474600149037125472103942208734233739212779909899012926853449381586694951578066665825364326401150344902364034516509246267139574666783592800550159095424721382800764962865152 +def node2076 : Tree Nat := .node node2075 node987 +def node2077 : Tree Nat := .node node2076 node991 +def node2078 : Tree Nat := .node node2077 node998 +def node2079 : Tree Nat := .node node985 node2078 +def node2080 : Tree Nat := .node node970 node2079 +def node2081 : Tree Nat := .node node940 node2080 +def node2082 : Tree Nat := .node node878 node2081 +def node2083 : Tree Nat := .node node2035 node2082 +def node2084 : Tree Nat := .node node2074 node2083 +def node2085 : Tree Nat := .leaf 3817079555632202118852736812188664416678190481860523062554763186928420483835729749332671896572236125722699394517866482154175725426502302433280 +def node2086 : Tree Nat := .node node2085 node1014 +def node2087 : Tree Nat := .node node2086 node1018 +def node2088 : Tree Nat := .node node1012 node2087 +def node2089 : Tree Nat := .node node2088 node1035 +def node2090 : Tree Nat := .node node2089 node1066 +def node2091 : Tree Nat := .node node2090 node1129 +def node2092 : Tree Nat := .node node2091 node2044 +def node2093 : Tree Nat := .leaf 6828046779268970776657768233878085902324275438521959671787668942028781287039163393246395227370680568936631177633751398183847755896434749212611613699815207199423526999689055146138073928553989707314316414176701463176675357109177790752949645869056 +def node2094 : Tree Nat := .node node2093 node1490 +def node2095 : Tree Nat := .node node2094 node1494 +def node2096 : Tree Nat := .node node2095 node1501 +def node2097 : Tree Nat := .node node1488 node2096 +def node2098 : Tree Nat := .node node1473 node2097 +def node2099 : Tree Nat := .node node1443 node2098 +def node2100 : Tree Nat := .node node1381 node2099 +def node2101 : Tree Nat := .node node2092 node2100 +def node2102 : Tree Nat := .leaf 2739226045072033710287658726391013369481562983073862426076014871121501917116897813478243768409544927272652705989782486018374878784366859763845742616822186473850268648721702202620786213851226595574270626849882112 +def node2103 : Tree Nat := .node node2102 node1991 +def node2104 : Tree Nat := .node node2103 node1995 +def node2105 : Tree Nat := .node node2104 node2002 +def node2106 : Tree Nat := .node node1989 node2105 +def node2107 : Tree Nat := .node node1974 node2106 +def node2108 : Tree Nat := .node node1944 node2107 +def node2109 : Tree Nat := .node node1882 node2108 +def node2110 : Tree Nat := .node node2062 node2109 +def node2111 : Tree Nat := .node node2101 node2110 +def node2112 : Tree Nat := .node node2084 node2111 +def node2113 : Tree Nat := .leaf 105796154684141381155274736610525587442662427694440757135209251527544209035205378763885930082777625399120688702591835100413952 +def node2114 : Tree Nat := .node node2113 node260 +def node2115 : Tree Nat := .node node2114 node264 +def node2116 : Tree Nat := .node node258 node2115 +def node2117 : Tree Nat := .node node2116 node281 +def node2118 : Tree Nat := .node node2117 node312 +def node2119 : Tree Nat := .node node2118 node375 +def node2120 : Tree Nat := .node node2119 node2025 +def node2121 : Tree Nat := .node node2073 node2120 +def node2122 : Tree Nat := .leaf 36304123742133375556593330216254635448529824738232755544798166470840175999708721578904841561045755026793346261350008872879909556370672936013382894168378543194507926213841472487214390311393061541483299565880754275502469841512321511300826214601285896648702734006221749603783820705792 +def node2123 : Tree Nat := .node node2122 node511 +def node2124 : Tree Nat := .node node2123 node515 +def node2125 : Tree Nat := .node node509 node2124 +def node2126 : Tree Nat := .node node2125 node532 +def node2127 : Tree Nat := .node node2126 node563 +def node2128 : Tree Nat := .node node2127 node626 +def node2129 : Tree Nat := .node node2128 node2034 +def node2130 : Tree Nat := .node node2129 node2082 +def node2131 : Tree Nat := .node node2121 node2130 +def node2132 : Tree Nat := .leaf 1234340207232534768924172979604602254694906452051709736717661236720499396856479823312072673064313071630115411980215128677346294207804374260756924346473570570601804001752727042444247368600918518930609367174255504442510088617885444184082760394641158027040293629031386591871015652950016 +def node2133 : Tree Nat := .node node2132 node1014 +def node2134 : Tree Nat := .node node2133 node1018 +def node2135 : Tree Nat := .node node1012 node2134 +def node2136 : Tree Nat := .node node2135 node1035 +def node2137 : Tree Nat := .node node2136 node1066 +def node2138 : Tree Nat := .node node2137 node1129 +def node2139 : Tree Nat := .node node2138 node2044 +def node2140 : Tree Nat := .node node2139 node2100 +def node2141 : Tree Nat := .leaf 7507516828804700229971157695509256861311759593549503536677899755757881062691614939970702182859795639737729241335368268839526962869220176380869024994616278906372529249382147856492585955442967754510945820115799159267379988939256829520312060678046440337965056 +def node2142 : Tree Nat := .node node2141 node1516 +def node2143 : Tree Nat := .node node2142 node1520 +def node2144 : Tree Nat := .node node1514 node2143 +def node2145 : Tree Nat := .node node2144 node1537 +def node2146 : Tree Nat := .node node2145 node1568 +def node2147 : Tree Nat := .node node2146 node1631 +def node2148 : Tree Nat := .node node2147 node2061 +def node2149 : Tree Nat := .node node2148 node2109 +def node2150 : Tree Nat := .node node2140 node2149 +def node2151 : Tree Nat := .node node2131 node2150 +def node2152 : Tree Nat := .leaf 1198036083490401393367579651265226826447551684806266405050177285577599119244146985902642702006115315422144908141997955354442654161558858392652635956895807234053333644930642165096742786396124080735141558700451638583991144045229014311750217410052338483131077371848404557776182283599872 +def node2153 : Tree Nat := .node node2152 node260 +def node2154 : Tree Nat := .node node2153 node264 +def node2155 : Tree Nat := .node node258 node2154 +def node2156 : Tree Nat := .node node2155 node281 +def node2157 : Tree Nat := .node node2156 node312 +def node2158 : Tree Nat := .node node2157 node375 +def node2159 : Tree Nat := .node node2158 node2025 +def node2160 : Tree Nat := .node node2073 node2159 +def node2161 : Tree Nat := .leaf 1876879207201175057492789423877314215327939898387375884169474870502861069060069777085350899625385307944621763169733298966004217108175076334941498697493526348261090679838701955844679066557945412331335633104200459721278357402016461217985288214373752801067008 +def node2162 : Tree Nat := .node node2161 node762 +def node2163 : Tree Nat := .node node2162 node766 +def node2164 : Tree Nat := .node node760 node2163 +def node2165 : Tree Nat := .node node2164 node783 +def node2166 : Tree Nat := .node node2165 node814 +def node2167 : Tree Nat := .node node2166 node877 +def node2168 : Tree Nat := .node node2167 node2081 +def node2169 : Tree Nat := .node node2129 node2168 +def node2170 : Tree Nat := .node node2160 node2169 +def node2171 : Tree Nat := .leaf 1876879207201175057492789423877314215327939898387375884169474870502861069060070093590973961046635783876384798228441414893615363744802625114903901272193891965773159178991235475926452926225260928752525353097635840536846069882588357951942737629732306648301568 +def node2172 : Tree Nat := .node node2171 node1265 +def node2173 : Tree Nat := .node node2172 node1269 +def node2174 : Tree Nat := .node node1263 node2173 +def node2175 : Tree Nat := .node node2174 node1286 +def node2176 : Tree Nat := .node node2175 node1317 +def node2177 : Tree Nat := .node node2176 node1380 +def node2178 : Tree Nat := .node node2177 node2099 +def node2179 : Tree Nat := .node node2139 node2178 +def node2180 : Tree Nat := .leaf 5358672883264439887174515571660366814788868341446333581496815546408313980226089180297111583026461534014254259822919680 +def node2181 : Tree Nat := .node node2180 node1766 +def node2182 : Tree Nat := .node node2181 node1770 +def node2183 : Tree Nat := .node node1764 node2182 +def node2184 : Tree Nat := .node node2183 node1787 +def node2185 : Tree Nat := .node node2184 node1818 +def node2186 : Tree Nat := .node node2185 node1881 +def node2187 : Tree Nat := .node node2186 node2108 +def node2188 : Tree Nat := .node node2148 node2187 +def node2189 : Tree Nat := .node node2179 node2188 +def node2190 : Tree Nat := .node node2170 node2189 +def node2191 : Tree Nat := .leaf 17311155196269223196464683982066137460447416991840732818070830393671261811490375849033411404231964381810464754670324811932353562430335537915041855151722693554378390873491324469124433380221578326735867175047542352811765745130236894818601834286493700075393513200972209986732032 +def node2192 : Tree Nat := .node node2191 node134 +def node2193 : Tree Nat := .node node2192 node138 +def node2194 : Tree Nat := .node node132 node2193 +def node2195 : Tree Nat := .node node2194 node155 +def node2196 : Tree Nat := .node node2195 node186 +def node2197 : Tree Nat := .node node2196 node2016 +def node2198 : Tree Nat := .node node2072 node2197 +def node2199 : Tree Nat := .node node2198 node2159 +def node2200 : Tree Nat := .leaf 36579752000384710793674020277211081973674073206503860298248682067554828102488498910478851330984753758208 +def node2201 : Tree Nat := .node node2200 node636 +def node2202 : Tree Nat := .node node2201 node640 +def node2203 : Tree Nat := .node node634 node2202 +def node2204 : Tree Nat := .node node2203 node657 +def node2205 : Tree Nat := .node node2204 node688 +def node2206 : Tree Nat := .node node2205 node2033 +def node2207 : Tree Nat := .node node2128 node2206 +def node2208 : Tree Nat := .node node2207 node2168 +def node2209 : Tree Nat := .node node2199 node2208 +def node2210 : Tree Nat := .leaf 80457312478118534229036470300930434235522628172007171743766890685245679184089647933239416792566688702726199162643349219304756178487690587881148635952103739212572069218136512981418747960205101428061079815665262519843036191502184975837112522252962909937375153777109796767115111085276719187230720 +def node2211 : Tree Nat := .node node2210 node1139 +def node2212 : Tree Nat := .node node2211 node1143 +def node2213 : Tree Nat := .node node1137 node2212 +def node2214 : Tree Nat := .node node2213 node1160 +def node2215 : Tree Nat := .node node2214 node1191 +def node2216 : Tree Nat := .node node2215 node2043 +def node2217 : Tree Nat := .node node2138 node2216 +def node2218 : Tree Nat := .node node2217 node2178 +def node2219 : Tree Nat := .leaf 72608247484266751113186647294354820488834247026939543948396825646101063287786253971485042109138266243244020558325693611899195180836380228795842510795805830184899484320891698888933334758724964010824766196053363935991772905653606246796970257905614633451343421084568691049424014540800 +def node2220 : Tree Nat := .node node2219 node1766 +def node2221 : Tree Nat := .node node2220 node1770 +def node2222 : Tree Nat := .node node1764 node2221 +def node2223 : Tree Nat := .node node2222 node1787 +def node2224 : Tree Nat := .node node2223 node1818 +def node2225 : Tree Nat := .node node2224 node1881 +def node2226 : Tree Nat := .node node2225 node2108 +def node2227 : Tree Nat := .node node2148 node2226 +def node2228 : Tree Nat := .node node2218 node2227 +def node2229 : Tree Nat := .node node2209 node2228 +def node2230 : Tree Nat := .leaf 80145462429753592445482322650559168134091064725027669358396684983451368644923776130938100240910653658101242071565417656836259861823657472707729412812233908292102307548806815514861582499591286511208356178336207009271225452082097782481502387044477048311498076921331516806121434146036450307604480 +def node2231 : Tree Nat := .node node2230 node385 +def node2232 : Tree Nat := .node node2231 node389 +def node2233 : Tree Nat := .node node383 node2232 +def node2234 : Tree Nat := .node node2233 node406 +def node2235 : Tree Nat := .node node2234 node437 +def node2236 : Tree Nat := .node node2235 node2024 +def node2237 : Tree Nat := .node node2158 node2236 +def node2238 : Tree Nat := .node node2198 node2237 +def node2239 : Tree Nat := .leaf 159979074811142526733376176478649845913726400468227039400546995978457108606195822085848242502208871814147841939303516298562461715320792416588692211721032574627857094924207395842199566855284999841253009260713314861888938826657348399093729138641345229856783627437768866059583779386597517025083392 +def node2240 : Tree Nat := .node node2239 node636 +def node2241 : Tree Nat := .node node2240 node640 +def node2242 : Tree Nat := .node node634 node2241 +def node2243 : Tree Nat := .node node2242 node657 +def node2244 : Tree Nat := .node node2243 node688 +def node2245 : Tree Nat := .node node2244 node2033 +def node2246 : Tree Nat := .node node2128 node2245 +def node2247 : Tree Nat := .node node2246 node2168 +def node2248 : Tree Nat := .node node2238 node2247 +def node2249 : Tree Nat := .leaf 15180809685871891150942957405172300992695016077440977636989365291607024240787718144 +def node2250 : Tree Nat := .node node2249 node1390 +def node2251 : Tree Nat := .node node2250 node1394 +def node2252 : Tree Nat := .node node1388 node2251 +def node2253 : Tree Nat := .node node2252 node1411 +def node2254 : Tree Nat := .node node2253 node1442 +def node2255 : Tree Nat := .node node2254 node2098 +def node2256 : Tree Nat := .node node2177 node2255 +def node2257 : Tree Nat := .node node2217 node2256 +def node2258 : Tree Nat := .leaf 8656105892673619465444975048166327535575816414642870886433951036774960517713398590419113722066179432147823147253351950962798170215546662598092199921108283620759921794391459779472859766165906862099710146520716755861149392119382741038929864129243772519307543194074059523489792 +def node2259 : Tree Nat := .node node2258 node1641 +def node2260 : Tree Nat := .node node2259 node1645 +def node2261 : Tree Nat := .node node1639 node2260 +def node2262 : Tree Nat := .node node2261 node1662 +def node2263 : Tree Nat := .node node2262 node1693 +def node2264 : Tree Nat := .node node2263 node2060 +def node2265 : Tree Nat := .node node2147 node2264 +def node2266 : Tree Nat := .node node2265 node2226 +def node2267 : Tree Nat := .node node2257 node2266 +def node2268 : Tree Nat := .node node2248 node2267 +def node2269 : Tree Nat := .leaf 481810883316472689157478868621150384599757151392261010109718725329574893937754112 +def node2270 : Tree Nat := .node node2269 node71 +def node2271 : Tree Nat := .node node2270 node75 +def node2272 : Tree Nat := .node node69 node2271 +def node2273 : Tree Nat := .node node2272 node92 +def node2274 : Tree Nat := .node node2273 node123 +def node2275 : Tree Nat := .node node2071 node2274 +def node2276 : Tree Nat := .node node2275 node2197 +def node2277 : Tree Nat := .node node2276 node2237 +def node2278 : Tree Nat := .leaf 141821638945306632879540928499235702789523804660839184782518748770858768217330637056927231610528714797648669947982388910771338890716884623321751781272675432160266887218119868172972824147326488661501869817027060846856350006731859710772130540812896817838513895280656967914024337408 +def node2279 : Tree Nat := .node node2278 node887 +def node2280 : Tree Nat := .node node2279 node891 +def node2281 : Tree Nat := .node node885 node2280 +def node2282 : Tree Nat := .node node2281 node908 +def node2283 : Tree Nat := .node node2282 node939 +def node2284 : Tree Nat := .node node2283 node2080 +def node2285 : Tree Nat := .node node2167 node2284 +def node2286 : Tree Nat := .node node2246 node2285 +def node2287 : Tree Nat := .node node2277 node2286 +def node2288 : Tree Nat := .leaf 141830295051199290754602382260373947395761342649441538550624200908015257966475838851543722998600295523153339307542856779229583930645813040756871935928954994184077134748546386712448692686860792090461209352870009684666016952950219644231626722392007632518005223417883344385427374080 +def node2289 : Tree Nat := .node node2288 node1390 +def node2290 : Tree Nat := .node node2289 node1394 +def node2291 : Tree Nat := .node node1388 node2290 +def node2292 : Tree Nat := .node node2291 node1411 +def node2293 : Tree Nat := .node node2292 node1442 +def node2294 : Tree Nat := .node node2293 node2098 +def node2295 : Tree Nat := .node node2177 node2294 +def node2296 : Tree Nat := .node node2217 node2295 +def node2297 : Tree Nat := .leaf 160290924859507184890963588712040320533756863335788821184229948264768520609423743754511922078006017603983437319396672369196710285824121217747960377139064043842851939963770279939992922224534680114065829533015236208406364399917226924053716704235227880827350299198351580318921267902962916831264768 +def node2298 : Tree Nat := .node node2297 node1891 +def node2299 : Tree Nat := .node node2298 node1895 +def node2300 : Tree Nat := .node node1889 node2299 +def node2301 : Tree Nat := .node node2300 node1912 +def node2302 : Tree Nat := .node node2301 node1943 +def node2303 : Tree Nat := .node node2302 node2107 +def node2304 : Tree Nat := .node node2225 node2303 +def node2305 : Tree Nat := .node node2265 node2304 +def node2306 : Tree Nat := .node node2296 node2305 +def node2307 : Tree Nat := .node node2287 node2306 +def node2308 : Tree Nat := .leaf 1125210230865546156491849650849141005172147100623948788746598902420821053428050286487299832733803496144141082012950154579985768502758488851419781728238585222574812589266531793180956534193688241016149195968941694751080448 +def node2309 : Tree Nat := .node node2308 node71 +def node2310 : Tree Nat := .node node2309 node75 +def node2311 : Tree Nat := .node node69 node2310 +def node2312 : Tree Nat := .node node2311 node92 +def node2313 : Tree Nat := .node node2312 node123 +def node2314 : Tree Nat := .node node2071 node2313 +def node2315 : Tree Nat := .node node2314 node2197 +def node2316 : Tree Nat := .node node2315 node2237 +def node2317 : Tree Nat := .leaf 20114328119529598101849381248576356844260372121771258500328082453509786552587602388615402985422003286694629844743189464679972790247107178046857054806744177249097321093177889564539159850498167825446728415712806013666883199524892261241736205001162508566973353664497782619137029286078471557087232 +def node2318 : Tree Nat := .node node2317 node573 +def node2319 : Tree Nat := .node node2318 node577 +def node2320 : Tree Nat := .node node571 node2319 +def node2321 : Tree Nat := .node node2320 node594 +def node2322 : Tree Nat := .node node2321 node625 +def node2323 : Tree Nat := .node node2127 node2322 +def node2324 : Tree Nat := .node node2323 node2245 +def node2325 : Tree Nat := .node node2324 node2285 +def node2326 : Tree Nat := .node node2316 node2325 +def node2327 : Tree Nat := .leaf 39994768702785596225770281352084312081721853282407026069857556488069756134593827504028143467174470452474990943962669938400409793704882481838592406687053585316228198534298970086021145454035509544876989239109957934797546575222738120312819642958921720009038193726087052370931232860868943030517760 +def node2328 : Tree Nat := .node node2327 node1076 +def node2329 : Tree Nat := .node node2328 node1080 +def node2330 : Tree Nat := .node node1074 node2329 +def node2331 : Tree Nat := .node node2330 node1097 +def node2332 : Tree Nat := .node node2331 node1128 +def node2333 : Tree Nat := .node node2137 node2332 +def node2334 : Tree Nat := .node node2333 node2216 +def node2335 : Tree Nat := .node node2334 node2295 +def node2336 : Tree Nat := .leaf 5253600824962731304332606217058373276783251298667640713640712128886814987776539586958775481131246172722345512271872 +def node2337 : Tree Nat := .node node2336 node1578 +def node2338 : Tree Nat := .node node2337 node1582 +def node2339 : Tree Nat := .node node1576 node2338 +def node2340 : Tree Nat := .node node2339 node1599 +def node2341 : Tree Nat := .node node2340 node1630 +def node2342 : Tree Nat := .node node2146 node2341 +def node2343 : Tree Nat := .node node2342 node2264 +def node2344 : Tree Nat := .node node2343 node2304 +def node2345 : Tree Nat := .node node2335 node2344 +def node2346 : Tree Nat := .node node2326 node2345 +def node2347 : Tree Nat := .leaf 20036365607438398109206554221717894591659180118237426039412854667412122224214503810828260586009694292471602677085437682769966064655111192062970664211417467949647261595047783935418163656787200077547300458755866726888308095984177535042959544840056549823002389952364327697533244672721282706440192 +def node2348 : Tree Nat := .node node2347 node322 +def node2349 : Tree Nat := .node node2348 node326 +def node2350 : Tree Nat := .node node320 node2349 +def node2351 : Tree Nat := .node node2350 node343 +def node2352 : Tree Nat := .node node2351 node374 +def node2353 : Tree Nat := .node node2157 node2352 +def node2354 : Tree Nat := .node node2353 node2236 +def node2355 : Tree Nat := .node node2315 node2354 +def node2356 : Tree Nat := .leaf 436451664819679261516780642764882623031870302877831935108197012898612232919960128220834664064130097429467055322753502124259177618610847081563571617792 +def node2357 : Tree Nat := .node node2356 node824 +def node2358 : Tree Nat := .node node2357 node828 +def node2359 : Tree Nat := .node node822 node2358 +def node2360 : Tree Nat := .node node2359 node845 +def node2361 : Tree Nat := .node node2360 node876 +def node2362 : Tree Nat := .node node2166 node2361 +def node2363 : Tree Nat := .node node2362 node2284 +def node2364 : Tree Nat := .node node2324 node2363 +def node2365 : Tree Nat := .node node2355 node2364 +def node2366 : Tree Nat := .leaf 1968170611839440239603092822138809854884193543195732940825840228588103579073369240675251808050747348422514460808850067699488827088718515501890242824204507273016030536139841159468466415661238827549579507217206306017314388508105954794190762656805872900237936295936 +def node2367 : Tree Nat := .node node2366 node1327 +def node2368 : Tree Nat := .node node2367 node1331 +def node2369 : Tree Nat := .node node1325 node2368 +def node2370 : Tree Nat := .node node2369 node1348 +def node2371 : Tree Nat := .node node2370 node1379 +def node2372 : Tree Nat := .node node2176 node2371 +def node2373 : Tree Nat := .node node2372 node2294 +def node2374 : Tree Nat := .node node2334 node2373 +def node2375 : Tree Nat := .leaf 32246507424497658146532278144464391913490075163096718785559364785344191354011248318908866205655535483151498720787432408330540408855682523067846012624874617360028222110378708653747845669032547654340269655198609248879860651614387508816138652468090456182584341986017280 +def node2376 : Tree Nat := .node node2375 node1578 +def node2377 : Tree Nat := .node node2376 node1582 +def node2378 : Tree Nat := .node node1576 node2377 +def node2379 : Tree Nat := .node node2378 node1599 +def node2380 : Tree Nat := .node node2379 node1630 +def node2381 : Tree Nat := .node node2146 node2380 +def node2382 : Tree Nat := .node node2381 node2264 +def node2383 : Tree Nat := .node node2382 node2304 +def node2384 : Tree Nat := .node node2374 node2383 +def node2385 : Tree Nat := .node node2365 node2384 +def node2386 : Tree Nat := .leaf 388129523075618493122339836630096054427223634588105293390099477028266276159473090555861521249404160932011661038651793952929479422758812987550487914612078970202667472208588016059109786710000848622674377424703671094924499941314265088 +def node2387 : Tree Nat := .node node2386 node196 +def node2388 : Tree Nat := .node node2387 node200 +def node2389 : Tree Nat := .node node194 node2388 +def node2390 : Tree Nat := .node node2389 node217 +def node2391 : Tree Nat := .node node2390 node2015 +def node2392 : Tree Nat := .node node2196 node2391 +def node2393 : Tree Nat := .node node2314 node2392 +def node2394 : Tree Nat := .node node2393 node2354 +def node2395 : Tree Nat := .leaf 32244539253885818706292675051642253103647037187929130507437185080316792066156221825285406495653496851657776485678441071675117668035146022414305557196886535259051522490754145579969797895179315256401775808449739259697302398814583691307272482893883714426925276110782464 +def node2396 : Tree Nat := .node node2395 node824 +def node2397 : Tree Nat := .node node2396 node828 +def node2398 : Tree Nat := .node node822 node2397 +def node2399 : Tree Nat := .node node2398 node845 +def node2400 : Tree Nat := .node node2399 node876 +def node2401 : Tree Nat := .node node2166 node2400 +def node2402 : Tree Nat := .node node2401 node2284 +def node2403 : Tree Nat := .node node2324 node2402 +def node2404 : Tree Nat := .node node2394 node2403 +def node2405 : Tree Nat := .leaf 420876366980065917456444544752487169846064065902810401434505213070877754129577188242448560599098962206740493205571899655611207848748222129570498010141918055440761677481059161093889747509405231911860786245989826560 +def node2406 : Tree Nat := .node node2405 node1201 +def node2407 : Tree Nat := .node node2406 node1205 +def node2408 : Tree Nat := .node node1199 node2407 +def node2409 : Tree Nat := .node node2408 node1222 +def node2410 : Tree Nat := .node node2409 node2042 +def node2411 : Tree Nat := .node node2215 node2410 +def node2412 : Tree Nat := .node node2333 node2411 +def node2413 : Tree Nat := .node node2412 node2373 +def node2414 : Tree Nat := .leaf 40072731214876796218413108378942774334323045285940858530772784274179266683592954082168903349767324293130424338184606348085645673785155640043888534828777831355789397249513415866641676312060666906692242301348507838518265495255970418332236727578522906659536277871716450590027128851476183917789184 +def node2415 : Tree Nat := .node node2414 node1828 +def node2416 : Tree Nat := .node node2415 node1832 +def node2417 : Tree Nat := .node node1826 node2416 +def node2418 : Tree Nat := .node node2417 node1849 +def node2419 : Tree Nat := .node node2418 node1880 +def node2420 : Tree Nat := .node node2224 node2419 +def node2421 : Tree Nat := .node node2420 node2303 +def node2422 : Tree Nat := .node node2382 node2421 +def node2423 : Tree Nat := .node node2413 node2422 +def node2424 : Tree Nat := .node node2404 node2423 +def node2425 : Tree Nat := .leaf 4989600774417665509015065799559216404602780166926639091188048129501138449035341986869698100080542248342583753843428313671635575063230559098187536994539972933005997472758539794579254625311002825115066060503208231882468157064164019707657553381209589556765296582543197548591073060530122555129856 +def node2426 : Tree Nat := .node node2425 node447 +def node2427 : Tree Nat := .node node2426 node451 +def node2428 : Tree Nat := .node node445 node2427 +def node2429 : Tree Nat := .node node2428 node467 +def node2430 : Tree Nat := .node node2429 node2023 +def node2431 : Tree Nat := .node node2235 node2430 +def node2432 : Tree Nat := .node node2353 node2431 +def node2433 : Tree Nat := .node node2393 node2432 +def node2434 : Tree Nat := .leaf 9979201548254465038155997574090178006299953753319660660381375882742818927998918350738505463023658415398099156132278510137744736367289781369040026320175171618009363958374242511544740415411849804989814965072301583613655066486254536116781414466088205360887914150299725759228762909747926779559936 +def node2435 : Tree Nat := .node node2434 node698 +def node2436 : Tree Nat := .node node2435 node702 +def node2437 : Tree Nat := .node node696 node2436 +def node2438 : Tree Nat := .node node2437 node719 +def node2439 : Tree Nat := .node node2438 node2032 +def node2440 : Tree Nat := .node node2244 node2439 +def node2441 : Tree Nat := .node node2323 node2440 +def node2442 : Tree Nat := .node node2441 node2402 +def node2443 : Tree Nat := .node node2433 node2442 +def node2444 : Tree Nat := .leaf 5028582029882399525462345320204731981883587735092193063525305450952575249177172116263568223105123230548636787193461383948712621880603312140714785232842096368941520430405193310267830029669133521379494745372248628101557109290324128865943274367303488588767248036060856896913215580757391187116032 +def node2445 : Tree Nat := .node node2444 node1201 +def node2446 : Tree Nat := .node node2445 node1205 +def node2447 : Tree Nat := .node node1199 node2446 +def node2448 : Tree Nat := .node node2447 node1222 +def node2449 : Tree Nat := .node node2448 node2042 +def node2450 : Tree Nat := .node node2215 node2449 +def node2451 : Tree Nat := .node node2333 node2450 +def node2452 : Tree Nat := .leaf 129927638196001957593015637195327996046280422511275907690240514561481232955215713411268608 +def node2453 : Tree Nat := .node node2452 node1452 +def node2454 : Tree Nat := .node node2453 node1456 +def node2455 : Tree Nat := .node node1450 node2454 +def node2456 : Tree Nat := .node node2455 node1472 +def node2457 : Tree Nat := .node node2456 node2097 +def node2458 : Tree Nat := .node node2293 node2457 +def node2459 : Tree Nat := .node node2372 node2458 +def node2460 : Tree Nat := .node node2451 node2459 +def node2461 : Tree Nat := .leaf 8061626826094347221414268616256904040889269236057812766754246782462871110468075123339448563158751726354989189573569737571599367519269569620284662933113569979541605607989935830180299252965061165383688056254087483958299437229146069493081951295017410176889823703334912 +def node2462 : Tree Nat := .node node2461 node1703 +def node2463 : Tree Nat := .node node2462 node1707 +def node2464 : Tree Nat := .node node1701 node2463 +def node2465 : Tree Nat := .node node2464 node1723 +def node2466 : Tree Nat := .node node2465 node2059 +def node2467 : Tree Nat := .node node2263 node2466 +def node2468 : Tree Nat := .node node2381 node2467 +def node2469 : Tree Nat := .node node2468 node2421 +def node2470 : Tree Nat := .node node2460 node2469 +def node2471 : Tree Nat := .node node2443 node2470 +def node2472 : Tree Nat := .leaf 206754148749679101171755793584395662397653506844855490880041968654023455554584034810494485715171576435949688998375398047744 +def node2473 : Tree Nat := .node node2472 node39 +def node2474 : Tree Nat := .node node2473 node43 +def node2475 : Tree Nat := .node node37 node2474 +def node2476 : Tree Nat := .node node2475 node60 +def node2477 : Tree Nat := .node node2070 node2476 +def node2478 : Tree Nat := .node node2477 node2313 +def node2479 : Tree Nat := .node node2478 node2392 +def node2480 : Tree Nat := .node node2479 node2432 +def node2481 : Tree Nat := .leaf 8061134813471454564709278378172451595382697492350202586319113003583328947243921783642977354659505911468918994647359185488933685101789674268739788968642849918860900085764455761008810428089234894369044556895150358232326421657180740554750436339772122811552951470915584 +def node2482 : Tree Nat := .node node2481 node949 +def node2483 : Tree Nat := .node node2482 node953 +def node2484 : Tree Nat := .node node947 node2483 +def node2485 : Tree Nat := .node node2484 node969 +def node2486 : Tree Nat := .node node2485 node2079 +def node2487 : Tree Nat := .node node2283 node2486 +def node2488 : Tree Nat := .node node2401 node2487 +def node2489 : Tree Nat := .node node2441 node2488 +def node2490 : Tree Nat := .node node2480 node2489 +def node2491 : Tree Nat := .leaf 492012622892656704990238084452251441810928680478211353074222523471479393502725184660276873998006663998813145330047983509730321495612895498074327544186461058746881903333247832437633860389101362010104528074175179849629936774732877071702005934438231595714565111808 +def node2492 : Tree Nat := .node node2491 node1452 +def node2493 : Tree Nat := .node node2492 node1456 +def node2494 : Tree Nat := .node node1450 node2493 +def node2495 : Tree Nat := .node node2494 node1472 +def node2496 : Tree Nat := .node node2495 node2097 +def node2497 : Tree Nat := .node node2293 node2496 +def node2498 : Tree Nat := .node node2372 node2497 +def node2499 : Tree Nat := .node node2451 node2498 +def node2500 : Tree Nat := .leaf 10018182803719199054603277094735693583580761321485214632718632621999971839155334720690115850865904002970821504265768528967295833113652456910114441206157042932473873922526613546371820348768222940859757187900010682191860799649298422014767388486092887903545081961399194603239154599914557971365888 +def node2501 : Tree Nat := .node node2500 node1953 +def node2502 : Tree Nat := .node node2501 node1957 +def node2503 : Tree Nat := .node node1951 node2502 +def node2504 : Tree Nat := .node node2503 node1973 +def node2505 : Tree Nat := .node node2504 node2106 +def node2506 : Tree Nat := .node node2302 node2505 +def node2507 : Tree Nat := .node node2420 node2506 +def node2508 : Tree Nat := .node node2468 node2507 +def node2509 : Tree Nat := .node node2499 node2508 +def node2510 : Tree Nat := .node node2490 node2509 +def node2511 : Tree Nat := .leaf 1134503866941667986143541334648056457619674842830209732174383704661281727402804754416548424845268597132444970383912631563207990827489845178429108122191373230708943107068998149163237322978318337638638205048320699552232994768557237690514401021484899385820239497037206160401244356608 +def node2512 : Tree Nat := .node node2511 node39 +def node2513 : Tree Nat := .node node2512 node43 +def node2514 : Tree Nat := .node node37 node2513 +def node2515 : Tree Nat := .node node2514 node60 +def node2516 : Tree Nat := .node node2070 node2515 +def node2517 : Tree Nat := .node node2516 node2313 +def node2518 : Tree Nat := .node node2517 node2392 +def node2519 : Tree Nat := .node node2518 node2432 +def node2520 : Tree Nat := .leaf 321829249912474136881525683989307835131953557306589263343752782944593437589520939150189555629080100264798835086290555977713254120225443146180701228171476451892310277561050909123407951909422647174765070431906078761372756650335197093869944677908587267228944404943551694123201041417101176326848512 +def node2521 : Tree Nat := .node node2520 node542 +def node2522 : Tree Nat := .node node2521 node546 +def node2523 : Tree Nat := .node node540 node2522 +def node2524 : Tree Nat := .node node2523 node562 +def node2525 : Tree Nat := .node node2126 node2524 +def node2526 : Tree Nat := .node node2525 node2322 +def node2527 : Tree Nat := .node node2526 node2440 +def node2528 : Tree Nat := .node node2527 node2488 +def node2529 : Tree Nat := .node node2519 node2528 +def node2530 : Tree Nat := .leaf 639916299244570106898880282343936394601108129500086289847591281966445774086874148613579531170258849978937705569952856868184947918664318708362504720753564462941279276757510887279018182132657416178492560489528341474355086250189390618367775718725920126516888684173487710115671916730597705496133632 +def node2531 : Tree Nat := .node node2530 node1045 +def node2532 : Tree Nat := .node node2531 node1049 +def node2533 : Tree Nat := .node node1043 node2532 +def node2534 : Tree Nat := .node node2533 node1065 +def node2535 : Tree Nat := .node node2136 node2534 +def node2536 : Tree Nat := .node node2535 node2332 +def node2537 : Tree Nat := .node node2536 node2450 +def node2538 : Tree Nat := .node node2537 node2498 +def node2539 : Tree Nat := .leaf 19571188189497153960147916309566839526594175068066195184065914478120408381495685291517811323313419527913472 +def node2540 : Tree Nat := .node node2539 node1547 +def node2541 : Tree Nat := .node node2540 node1551 +def node2542 : Tree Nat := .node node1545 node2541 +def node2543 : Tree Nat := .node node2542 node1567 +def node2544 : Tree Nat := .node node2145 node2543 +def node2545 : Tree Nat := .node node2544 node2380 +def node2546 : Tree Nat := .node node2545 node2467 +def node2547 : Tree Nat := .node node2546 node2507 +def node2548 : Tree Nat := .node node2538 node2547 +def node2549 : Tree Nat := .node node2529 node2548 +def node2550 : Tree Nat := .leaf 320581849719015504285796232270159840383892969391784817983639634828399285715423821179807476921894270412460028816508423648153232402599709517290130818817670178154070101218375702613277248737488700294725089103305924473206939663798042759485596102028104174913448812074834518158009158631623777048330240 +def node2551 : Tree Nat := .node node2550 node291 +def node2552 : Tree Nat := .node node2551 node295 +def node2553 : Tree Nat := .node node289 node2552 +def node2554 : Tree Nat := .node node2553 node311 +def node2555 : Tree Nat := .node node2156 node2554 +def node2556 : Tree Nat := .node node2555 node2352 +def node2557 : Tree Nat := .node node2556 node2431 +def node2558 : Tree Nat := .node node2518 node2557 +def node2559 : Tree Nat := .leaf 498294809852580943905802398904238954219916016715507267358650523645440979495938882011136 +def node2560 : Tree Nat := .node node2559 node793 +def node2561 : Tree Nat := .node node2560 node797 +def node2562 : Tree Nat := .node node791 node2561 +def node2563 : Tree Nat := .node node2562 node813 +def node2564 : Tree Nat := .node node2165 node2563 +def node2565 : Tree Nat := .node node2564 node2400 +def node2566 : Tree Nat := .node node2565 node2487 +def node2567 : Tree Nat := .node node2527 node2566 +def node2568 : Tree Nat := .node node2558 node2567 +def node2569 : Tree Nat := .leaf 567251935584012117616353577041561371734776462270766013478031382293311805960637328517293275040758938467665397012245017271704235428691565005120448078904513563400770836461779074694694144052535420247984686086107917111790830968012852440975383044205583507424471282321336593690709196800 +def node2570 : Tree Nat := .node node2569 node1296 +def node2571 : Tree Nat := .node node2570 node1300 +def node2572 : Tree Nat := .node node1294 node2571 +def node2573 : Tree Nat := .node node2572 node1316 +def node2574 : Tree Nat := .node node2175 node2573 +def node2575 : Tree Nat := .node node2574 node2371 +def node2576 : Tree Nat := .node node2575 node2497 +def node2577 : Tree Nat := .node node2537 node2576 +def node2578 : Tree Nat := .leaf 1134538491365238617645709308610684339450379797753347501667578239658343657726760624906612719539297292415998002462756517118968397271384190568611747957444814147151601701445989250704496154691965982943906131784209193584487661492056650093046168263805178561691266399015313926690684534784 +def node2579 : Tree Nat := .node node2578 node1547 +def node2580 : Tree Nat := .node node2579 node1551 +def node2581 : Tree Nat := .node node1545 node2580 +def node2582 : Tree Nat := .node node2581 node1567 +def node2583 : Tree Nat := .node node2145 node2582 +def node2584 : Tree Nat := .node node2583 node2380 +def node2585 : Tree Nat := .node node2584 node2467 +def node2586 : Tree Nat := .node node2585 node2507 +def node2587 : Tree Nat := .node node2577 node2586 +def node2588 : Tree Nat := .node node2568 node2587 +def node2589 : Tree Nat := .leaf 225921116696657399755928707376375798670333560260644071634548162212369334107823776038057071519881333252061364655668791715358213179274623608611407031717239351202907673747076056987966624041448656492470108764953984353506951168 +def node2590 : Tree Nat := .node node2589 node165 +def node2591 : Tree Nat := .node node2590 node169 +def node2592 : Tree Nat := .node node163 node2591 +def node2593 : Tree Nat := .node node2592 node185 +def node2594 : Tree Nat := .node node2195 node2593 +def node2595 : Tree Nat := .node node2594 node2391 +def node2596 : Tree Nat := .node node2517 node2595 +def node2597 : Tree Nat := .node node2596 node2557 +def node2598 : Tree Nat := .leaf 567286555781226500029355731569122967715603332303024435169262119354790718260422894252365794277193656171034240881504545882039792440605577976305040582381114750828792298657564703515972443248396882185269925306943303416431680051002886638100427216309143252535485277326058616232270102528 +def node2599 : Tree Nat := .node node2598 node793 +def node2600 : Tree Nat := .node node2599 node797 +def node2601 : Tree Nat := .node node791 node2600 +def node2602 : Tree Nat := .node node2601 node813 +def node2603 : Tree Nat := .node node2165 node2602 +def node2604 : Tree Nat := .node node2603 node2400 +def node2605 : Tree Nat := .node node2604 node2487 +def node2606 : Tree Nat := .node node2527 node2605 +def node2607 : Tree Nat := .node node2597 node2606 +def node2608 : Tree Nat := .leaf 28269553036454149273333508300725009675533862636644254066851763058143920128 +def node2609 : Tree Nat := .node node2608 node1170 +def node2610 : Tree Nat := .node node2609 node1174 +def node2611 : Tree Nat := .node node1168 node2610 +def node2612 : Tree Nat := .node node2611 node1190 +def node2613 : Tree Nat := .node node2214 node2612 +def node2614 : Tree Nat := .node node2613 node2449 +def node2615 : Tree Nat := .node node2536 node2614 +def node2616 : Tree Nat := .node node2615 node2576 +def node2617 : Tree Nat := .leaf 641163699438029873998476675731070532890503365471348354882531362507106952652341177184586026177890229202314479090694496935628738694544632002740895571643276383782576266711859013453263643358330239817921192358353938733289475637851398127272992259463923911283983766309090658348073546397034786236399616 +def node2618 : Tree Nat := .node node2617 node1797 +def node2619 : Tree Nat := .node node2618 node1801 +def node2620 : Tree Nat := .node node1795 node2619 +def node2621 : Tree Nat := .node node2620 node1817 +def node2622 : Tree Nat := .node node2223 node2621 +def node2623 : Tree Nat := .node node2622 node2419 +def node2624 : Tree Nat := .node node2623 node2506 +def node2625 : Tree Nat := .node node2585 node2624 +def node2626 : Tree Nat := .node node2616 node2625 +def node2627 : Tree Nat := .node node2607 node2626 +def node2628 : Tree Nat := .leaf 4937360828930139075696691888388341703560824888322208164833617614595517561556605024501045357416203106568280468781367495212908167983181339073273592438566943336108922629372796776202083052275359055708099265239702556857507176525057421565370904417591513469277601010930743354191333797396480 +def node2629 : Tree Nat := .node node2628 node667 +def node2630 : Tree Nat := .node node2629 node671 +def node2631 : Tree Nat := .node node665 node2630 +def node2632 : Tree Nat := .node node2631 node687 +def node2633 : Tree Nat := .node node2243 node2632 +def node2634 : Tree Nat := .node node2633 node2439 +def node2635 : Tree Nat := .node node2526 node2634 +def node2636 : Tree Nat := .node node2635 node2605 +def node2637 : Tree Nat := .node node2597 node2636 +def node2638 : Tree Nat := .leaf 9439072172954677644714263904271829727395694639439515609240739454321509785382047952225675997004176433832325951903502590804545085859770249562327929855799949684973133695024869043544004569598801240538962845537402306902327473008038635379576778779074562467705110792716095388313543174520832 +def node2639 : Tree Nat := .node node2638 node1170 +def node2640 : Tree Nat := .node node2639 node1174 +def node2641 : Tree Nat := .node node1168 node2640 +def node2642 : Tree Nat := .node node2641 node1190 +def node2643 : Tree Nat := .node node2214 node2642 +def node2644 : Tree Nat := .node node2643 node2449 +def node2645 : Tree Nat := .node node2536 node2644 +def node2646 : Tree Nat := .node node2645 node2576 +def node2647 : Tree Nat := .leaf 4831851268154607294990378905814491072350628645150914666842950171959208900874551690351197585222671992070425098101625845086671046610682614427476362523952927701437205312438272 +def node2648 : Tree Nat := .node node2647 node1672 +def node2649 : Tree Nat := .node node2648 node1676 +def node2650 : Tree Nat := .node node1670 node2649 +def node2651 : Tree Nat := .node node2650 node1692 +def node2652 : Tree Nat := .node node2262 node2651 +def node2653 : Tree Nat := .node node2652 node2466 +def node2654 : Tree Nat := .node node2584 node2653 +def node2655 : Tree Nat := .node node2654 node2624 +def node2656 : Tree Nat := .node node2646 node2655 +def node2657 : Tree Nat := .node node2637 node2656 +def node2658 : Tree Nat := .leaf 4792144333961605573470318597553505032601180409098725599827279743563115417912112873870037829428216777831309210655101407571163493262736114679447454578921403231388587583565533846240720862956847408963542982250236474540534393570768670284273869653759790297106208150123446861535251227738112 +def node2659 : Tree Nat := .node node2658 node416 +def node2660 : Tree Nat := .node node2659 node420 +def node2661 : Tree Nat := .node node414 node2660 +def node2662 : Tree Nat := .node node2661 node436 +def node2663 : Tree Nat := .node node2234 node2662 +def node2664 : Tree Nat := .node node2663 node2430 +def node2665 : Tree Nat := .node node2556 node2664 +def node2666 : Tree Nat := .node node2596 node2665 +def node2667 : Tree Nat := .leaf 104033814531196299259318050976128469961908184544211664628003893345906670014769258584400451803766626850273321607686769388711866084482745536348160 +def node2668 : Tree Nat := .node node2667 node918 +def node2669 : Tree Nat := .node node2668 node922 +def node2670 : Tree Nat := .node node916 node2669 +def node2671 : Tree Nat := .node node2670 node938 +def node2672 : Tree Nat := .node node2282 node2671 +def node2673 : Tree Nat := .node node2672 node2486 +def node2674 : Tree Nat := .node node2604 node2673 +def node2675 : Tree Nat := .node node2635 node2674 +def node2676 : Tree Nat := .node node2666 node2675 +def node2677 : Tree Nat := .leaf 114555615673899844817675135827349603920186156328588973012815230098216247591936145623178599818602061805628440424236441183793286810769621760146212077663227459888103895663369975594942529988997020774105405362937139803083602009554464800692999342913126137856 +def node2678 : Tree Nat := .node node2677 node1421 +def node2679 : Tree Nat := .node node2678 node1425 +def node2680 : Tree Nat := .node node1419 node2679 +def node2681 : Tree Nat := .node node2680 node1441 +def node2682 : Tree Nat := .node node2292 node2681 +def node2683 : Tree Nat := .node node2682 node2496 +def node2684 : Tree Nat := .node node2575 node2683 +def node2685 : Tree Nat := .node node2645 node2684 +def node2686 : Tree Nat := .leaf 225921116696657399755928707376375798670333555195312617614099150595166526000831197939208375616448768444844308775376678197259415801619655891592005693734934921697417155233432635558002928230857937610471723584776381395869106176 +def node2687 : Tree Nat := .node node2686 node1672 +def node2688 : Tree Nat := .node node2687 node1676 +def node2689 : Tree Nat := .node node1670 node2688 +def node2690 : Tree Nat := .node node2689 node1692 +def node2691 : Tree Nat := .node node2262 node2690 +def node2692 : Tree Nat := .node node2691 node2466 +def node2693 : Tree Nat := .node node2584 node2692 +def node2694 : Tree Nat := .node node2693 node2624 +def node2695 : Tree Nat := .node node2685 node2694 +def node2696 : Tree Nat := .node node2676 node2695 +def node2697 : Tree Nat := .leaf 48516190384397171392751175090678259260270162528013642586385209916290288086478333150780021580175739629118289543847768199510899830187141888180207452226534790820321120216919046882785569607977848325115572050133012699573930366104240128 +def node2698 : Tree Nat := .node node2697 node102 +def node2699 : Tree Nat := .node node2698 node106 +def node2700 : Tree Nat := .node node100 node2699 +def node2701 : Tree Nat := .node node2700 node122 +def node2702 : Tree Nat := .node node2312 node2701 +def node2703 : Tree Nat := .node node2516 node2702 +def node2704 : Tree Nat := .node node2703 node2595 +def node2705 : Tree Nat := .node node2704 node2665 +def node2706 : Tree Nat := .leaf 114555615673899844817675135827349603920186156328588973012815230098216247597001467415855239037616505603637170860454974156046109455801580026176644352441657784801933346009161319638632059810916765995044128687677992717900953077222877186178719421456915103744 +def node2707 : Tree Nat := .node node2706 node918 +def node2708 : Tree Nat := .node node2707 node922 +def node2709 : Tree Nat := .node node916 node2708 +def node2710 : Tree Nat := .node node2709 node938 +def node2711 : Tree Nat := .node node2282 node2710 +def node2712 : Tree Nat := .node node2711 node2486 +def node2713 : Tree Nat := .node node2604 node2712 +def node2714 : Tree Nat := .node node2635 node2713 +def node2715 : Tree Nat := .node node2705 node2714 +def node2716 : Tree Nat := .leaf 69834024122222457494083773416407443204537254041236423104231356814990992587150109094858084210853447215565889941297139817408148734017706838317188734169300357554966366667884890283802709983232 +def node2717 : Tree Nat := .node node2716 node1107 +def node2718 : Tree Nat := .node node2717 node1111 +def node2719 : Tree Nat := .node node1105 node2718 +def node2720 : Tree Nat := .node node2719 node1127 +def node2721 : Tree Nat := .node node2331 node2720 +def node2722 : Tree Nat := .node node2535 node2721 +def node2723 : Tree Nat := .node node2722 node2644 +def node2724 : Tree Nat := .node node2723 node2684 +def node2725 : Tree Nat := .leaf 9584288667923211146940637195106895509586686918352633524518732024561752301339197280802709155441220641788786764210402813327422804732093548427479683312030666151796693172219442849825974286000413401897406023848754974361654848085862909785912343346992327217019229975372613847542561899544576 +def node2726 : Tree Nat := .node node2725 node1922 +def node2727 : Tree Nat := .node node2726 node1926 +def node2728 : Tree Nat := .node node1920 node2727 +def node2729 : Tree Nat := .node node2728 node1942 +def node2730 : Tree Nat := .node node2301 node2729 +def node2731 : Tree Nat := .node node2730 node2505 +def node2732 : Tree Nat := .node node2623 node2731 +def node2733 : Tree Nat := .node node2693 node2732 +def node2734 : Tree Nat := .node node2724 node2733 +def node2735 : Tree Nat := .node node2715 node2734 +def node2736 : Tree Nat := .leaf 22724544930726588110725806962783727643142673088265530472678316555569854358164337572876794349550923195104626125959269260141286643344862051856090222283281233314923472460247591753253530698233814808788992 +def node2737 : Tree Nat := .node node2736 node353 +def node2738 : Tree Nat := .node node2737 node357 +def node2739 : Tree Nat := .node node351 node2738 +def node2740 : Tree Nat := .node node2739 node373 +def node2741 : Tree Nat := .node node2351 node2740 +def node2742 : Tree Nat := .node node2555 node2741 +def node2743 : Tree Nat := .node node2742 node2664 +def node2744 : Tree Nat := .node node2704 node2743 +def node2745 : Tree Nat := .leaf 18587711355972288284975781226873757001640752527254561075954200296864920133568817487707092950860057205891604452303042089454261995933702318684836888461722869150513792971597610852869053192966382049615296070527169379437005615326909340540045362780284770418596130319539492465740224013533184 +def node2746 : Tree Nat := .node node2745 node604 +def node2747 : Tree Nat := .node node2746 node608 +def node2748 : Tree Nat := .node node602 node2747 +def node2749 : Tree Nat := .node node2748 node624 +def node2750 : Tree Nat := .node node2321 node2749 +def node2751 : Tree Nat := .node node2525 node2750 +def node2752 : Tree Nat := .node node2751 node2634 +def node2753 : Tree Nat := .node node2752 node2713 +def node2754 : Tree Nat := .node node2744 node2753 +def node2755 : Tree Nat := .leaf 9516908214257811601907599988159363584840065290620124935450087718987904762481275522191874685950243732024609872161685536783436920631949828444073824651566436158632700981972424500129421206791459829592797996473299888060732951885525870173416992842012546755806726101377942289406746870713155584 +def node2756 : Tree Nat := .node node2755 node1107 +def node2757 : Tree Nat := .node node2756 node1111 +def node2758 : Tree Nat := .node node1105 node2757 +def node2759 : Tree Nat := .node node2758 node1127 +def node2760 : Tree Nat := .node node2331 node2759 +def node2761 : Tree Nat := .node node2535 node2760 +def node2762 : Tree Nat := .node node2761 node2644 +def node2763 : Tree Nat := .node node2762 node2684 +def node2764 : Tree Nat := .leaf 6511732893125423073928276657127400410040102860476731377848561062811134572353652677596114027250812584288330251989403902611627946281703492177380333199712947485677694181111595751837530378006434692568839243109796242971786043761919877000986624 +def node2765 : Tree Nat := .node node2764 node1609 +def node2766 : Tree Nat := .node node2765 node1613 +def node2767 : Tree Nat := .node node1607 node2766 +def node2768 : Tree Nat := .node node2767 node1629 +def node2769 : Tree Nat := .node node2379 node2768 +def node2770 : Tree Nat := .node node2583 node2769 +def node2771 : Tree Nat := .node node2770 node2692 +def node2772 : Tree Nat := .node node2771 node2732 +def node2773 : Tree Nat := .node node2763 node2772 +def node2774 : Tree Nat := .node node2754 node2773 +def node2775 : Tree Nat := .leaf 3946994756128544269578066891768983879112377101272772882477760140748241979636027752448 +def node2776 : Tree Nat := .node node2775 node227 +def node2777 : Tree Nat := .node node2776 node231 +def node2778 : Tree Nat := .node node225 node2777 +def node2779 : Tree Nat := .node node2778 node2014 +def node2780 : Tree Nat := .node node2390 node2779 +def node2781 : Tree Nat := .node node2594 node2780 +def node2782 : Tree Nat := .node node2703 node2781 +def node2783 : Tree Nat := .leaf 18587711355972288284975781226873757001640752520742430762455243433647852495356937686061563313740224455898572328929311704065567065391092933311837846148791088729398392233347632277708175404638606175464530453434801214177405834470295458207525426731480014236825693038484629435769815534927872 +def node2784 : Tree Nat := .node node2783 node353 +def node2785 : Tree Nat := .node node2784 node357 +def node2786 : Tree Nat := .node node351 node2785 +def node2787 : Tree Nat := .node node2786 node373 +def node2788 : Tree Nat := .node node2351 node2787 +def node2789 : Tree Nat := .node node2555 node2788 +def node2790 : Tree Nat := .node node2789 node2664 +def node2791 : Tree Nat := .node node2782 node2790 +def node2792 : Tree Nat := .leaf 6512130313498956863217084807164470744461190538033039686479754608152295293285303498932704226690161011840344628306615244958143754424581746160005740030721115414831250524732072120471607767215869506335382602385818777000225356731587806598529024 +def node2793 : Tree Nat := .node node2792 node855 +def node2794 : Tree Nat := .node node2793 node859 +def node2795 : Tree Nat := .node node853 node2794 +def node2796 : Tree Nat := .node node2795 node875 +def node2797 : Tree Nat := .node node2399 node2796 +def node2798 : Tree Nat := .node node2603 node2797 +def node2799 : Tree Nat := .node node2798 node2712 +def node2800 : Tree Nat := .node node2752 node2799 +def node2801 : Tree Nat := .node node2791 node2800 +def node2802 : Tree Nat := .leaf 397468889724173685979542788245425099345541698338619579376990907177671153860196467700470072948073273624394463306874264394576519767311383244340052479607909691946642178912766603519238872485298262736058053565703231285977499605674229760000 +def node2803 : Tree Nat := .node node2802 node1358 +def node2804 : Tree Nat := .node node2803 node1362 +def node2805 : Tree Nat := .node node1356 node2804 +def node2806 : Tree Nat := .node node2805 node1378 +def node2807 : Tree Nat := .node node2370 node2806 +def node2808 : Tree Nat := .node node2574 node2807 +def node2809 : Tree Nat := .node node2808 node2683 +def node2810 : Tree Nat := .node node2762 node2809 +def node2811 : Tree Nat := .leaf 9516908214257811601907599988159363584840065290626636270825807227503749905371816105021419189398839454839689918914562806248206411829822979351300064714670728090477351428117358393598991669469351841968509351516504407542994913425616382779636326741406417431494079439248169515839300427386454016 +def node2812 : Tree Nat := .node node2811 node1859 +def node2813 : Tree Nat := .node node2812 node1863 +def node2814 : Tree Nat := .node node1857 node2813 +def node2815 : Tree Nat := .node node2814 node1879 +def node2816 : Tree Nat := .node node2418 node2815 +def node2817 : Tree Nat := .node node2622 node2816 +def node2818 : Tree Nat := .node node2817 node2731 +def node2819 : Tree Nat := .node node2771 node2818 +def node2820 : Tree Nat := .node node2810 node2819 +def node2821 : Tree Nat := .node node2801 node2820 +def node2822 : Tree Nat := .leaf 1081947199765842424529591879509026010150599323721976877786900707526989651739900452381302641357895255978501721913515669361826438869198939157555349872519364529282686887865300640437034619865895573149131335640835183649031013298945249799126030690691237418553763965387271414218752 +def node2823 : Tree Nat := .node node2822 node227 +def node2824 : Tree Nat := .node node2823 node231 +def node2825 : Tree Nat := .node node225 node2824 +def node2826 : Tree Nat := .node node2825 node2014 +def node2827 : Tree Nat := .node node2390 node2826 +def node2828 : Tree Nat := .node node2594 node2827 +def node2829 : Tree Nat := .node node2703 node2828 +def node2830 : Tree Nat := .leaf 1081947199765842428283579405142723924825813715812836346492076121543015060372064209641751433262088109426091034646786981282793600926032542135675913792410103233849786744018307384196898778351908756611216034530149932423844497084601131852442098816003756397745129645091740801040384 +def node2831 : Tree Nat := .node node2830 node477 +def node2832 : Tree Nat := .node node2831 node481 +def node2833 : Tree Nat := .node node475 node2832 +def node2834 : Tree Nat := .node node2833 node2022 +def node2835 : Tree Nat := .node node2429 node2834 +def node2836 : Tree Nat := .node node2663 node2835 +def node2837 : Tree Nat := .node node2789 node2836 +def node2838 : Tree Nat := .node node2829 node2837 +def node2839 : Tree Nat := .leaf 4872657005699999810663491135398204041823608939751973073340296112092162650589745671020362028981173928417388251915025194266042170442037274997643866993603969714391782314214918113366669399820314066283330081797497310614275602110739527794279828745667685699620948636905853379476976799170359721984 +def node2840 : Tree Nat := .node node2839 node729 +def node2841 : Tree Nat := .node node2840 node733 +def node2842 : Tree Nat := .node node727 node2841 +def node2843 : Tree Nat := .node node2842 node2031 +def node2844 : Tree Nat := .node node2438 node2843 +def node2845 : Tree Nat := .node node2633 node2844 +def node2846 : Tree Nat := .node node2751 node2845 +def node2847 : Tree Nat := .node node2846 node2799 +def node2848 : Tree Nat := .node node2838 node2847 +def node2849 : Tree Nat := .leaf 1277347543416232079459429376525906018077612080889412371381485013669145509714721103929373520155488338893598791020415041613409168073371303333206532275245895985772137920110930531605961111337859276429609669873223001089364622090072996023559092105177471052211626349662736489225388094709670766987706368 +def node2850 : Tree Nat := .node node2849 node1232 +def node2851 : Tree Nat := .node node2850 node1236 +def node2852 : Tree Nat := .node node1230 node2851 +def node2853 : Tree Nat := .node node2852 node2041 +def node2854 : Tree Nat := .node node2448 node2853 +def node2855 : Tree Nat := .node node2643 node2854 +def node2856 : Tree Nat := .node node2761 node2855 +def node2857 : Tree Nat := .node node2856 node2809 +def node2858 : Tree Nat := .leaf 1081947199765842428283579419127417286713116607617159638942613056013073795264965194137452593836483412298566698713689968775822544520768080289377703883248676138220521111569333297870668621177238560967042745988186232887228049401282685593731614212234989812617936179897629910499328 +def node2859 : Tree Nat := .node node2858 node1733 +def node2860 : Tree Nat := .node node2859 node1737 +def node2861 : Tree Nat := .node node1731 node2860 +def node2862 : Tree Nat := .node node2861 node2058 +def node2863 : Tree Nat := .node node2465 node2862 +def node2864 : Tree Nat := .node node2691 node2863 +def node2865 : Tree Nat := .node node2770 node2864 +def node2866 : Tree Nat := .node node2865 node2818 +def node2867 : Tree Nat := .node node2857 node2866 +def node2868 : Tree Nat := .node node2848 node2867 +def node2869 : Tree Nat := .leaf 276978483140055660679575521154310658598553426872826080593424479721944743637335064583130340808000721892441268569379212308399932662694284205702097585169193435032414605838253575203503260866196031433458804951352921717574925866750570369867543297795471900803549689214968312956452864 +def node2870 : Tree Nat := .node node2869 node23 +def node2871 : Tree Nat := .node node2870 node27 +def node2872 : Tree Nat := .node node21 node2871 +def node2873 : Tree Nat := .node node2069 node2872 +def node2874 : Tree Nat := .node node2873 node2515 +def node2875 : Tree Nat := .node node2874 node2702 +def node2876 : Tree Nat := .node node2875 node2828 +def node2877 : Tree Nat := .leaf 1277342670759226379460700660234536462305607824197264347990219482828857053616974461436967345783191853911950530066003400769902543076803619525702886840821972807467189310119954914441588863863238364207919223494656759721532371568606469678750184742073157127139805893085889175187628107506806903111942144 +def node2878 : Tree Nat := .node node2877 node477 +def node2879 : Tree Nat := .node node2878 node481 +def node2880 : Tree Nat := .node node475 node2879 +def node2881 : Tree Nat := .node node2880 node2022 +def node2882 : Tree Nat := .node node2429 node2881 +def node2883 : Tree Nat := .node node2663 node2882 +def node2884 : Tree Nat := .node node2789 node2883 +def node2885 : Tree Nat := .node node2876 node2884 +def node2886 : Tree Nat := .leaf 270486799941460606132397969877256554634692338922149125534990864827253047922381898296765922036845598671568204247815885628137567517818175826095693888262472651812408910495712160756593870939223671596717691837567818862928306520659828178036690529606204965015036497709941991145472 +def node2887 : Tree Nat := .node node2886 node979 +def node2888 : Tree Nat := .node node2887 node983 +def node2889 : Tree Nat := .node node977 node2888 +def node2890 : Tree Nat := .node node2889 node2078 +def node2891 : Tree Nat := .node node2485 node2890 +def node2892 : Tree Nat := .node node2711 node2891 +def node2893 : Tree Nat := .node node2798 node2892 +def node2894 : Tree Nat := .node node2846 node2893 +def node2895 : Tree Nat := .node node2885 node2894 +def node2896 : Tree Nat := .leaf 2258409667001035898343208751322206821385858914707798140037538705686029881515079305806254936189499867136 +def node2897 : Tree Nat := .node node2896 node1029 +def node2898 : Tree Nat := .node node2897 node1033 +def node2899 : Tree Nat := .node node1027 node2898 +def node2900 : Tree Nat := .node node2135 node2899 +def node2901 : Tree Nat := .node node2900 node2534 +def node2902 : Tree Nat := .node node2901 node2760 +def node2903 : Tree Nat := .node node2902 node2855 +def node2904 : Tree Nat := .leaf 270486799941460609886385509495647727003124994963545150394648763308944639969102659393676275592250940467361807953988974708791626313912197649469725030384215454103215939714398451354197695534910753912172065410386729530974690402527933667380203914260281870715639370715960036032512 +def node2905 : Tree Nat := .node node2904 node1482 +def node2906 : Tree Nat := .node node2905 node1486 +def node2907 : Tree Nat := .node node1480 node2906 +def node2908 : Tree Nat := .node node2907 node2096 +def node2909 : Tree Nat := .node node2495 node2908 +def node2910 : Tree Nat := .node node2682 node2909 +def node2911 : Tree Nat := .node node2808 node2910 +def node2912 : Tree Nat := .node node2903 node2911 +def node2913 : Tree Nat := .leaf 9745314011400000162300582153717612840468120351314379564770510113036312714024121089520989186893633952103646779539050048426379727856838138252855638408405920573308883103035584518742055194901059732900103093998568260455003750990349021753782911846133295858913413634714893276474919782063527690240 +def node2914 : Tree Nat := .node node2913 node1983 +def node2915 : Tree Nat := .node node2914 node1987 +def node2916 : Tree Nat := .node node1981 node2915 +def node2917 : Tree Nat := .node node2916 node2105 +def node2918 : Tree Nat := .node node2504 node2917 +def node2919 : Tree Nat := .node node2730 node2918 +def node2920 : Tree Nat := .node node2817 node2919 +def node2921 : Tree Nat := .node node2865 node2920 +def node2922 : Tree Nat := .node node2912 node2921 +def node2923 : Tree Nat := .node node2895 node2922 +def node2924 : Tree Nat := .leaf 168608589349493131958015087616540679668592803278962431331060101814331015260871777495148119299778999483168145679854451622674939147754434619637275616256377777392408477111434973918618393799252678538302702349285742709182101189207206478668919921086858129216098575736383705351846341888997113995729043456 +def node2925 : Tree Nat := .node node2924 node526 +def node2926 : Tree Nat := .node node2925 node530 +def node2927 : Tree Nat := .node node524 node2926 +def node2928 : Tree Nat := .node node2125 node2927 +def node2929 : Tree Nat := .node node2928 node2524 +def node2930 : Tree Nat := .node node2929 node2750 +def node2931 : Tree Nat := .node node2930 node2845 +def node2932 : Tree Nat := .node node2931 node2893 +def node2933 : Tree Nat := .node node2885 node2932 +def node2934 : Tree Nat := .leaf 91968321463359891190271877741643521241811080357357754374850699790700430936706816559365054036878295092464935961604259661610452401777491444353936885094292892669342129114234833723624367198344907828786407901963416781473772858743134249540649602208935560444346072946865932678419219184521135123735773184 +def node2935 : Tree Nat := .node node2934 node1029 +def node2936 : Tree Nat := .node node2935 node1033 +def node2937 : Tree Nat := .node node1027 node2936 +def node2938 : Tree Nat := .node node2135 node2937 +def node2939 : Tree Nat := .node node2938 node2534 +def node2940 : Tree Nat := .node node2939 node2760 +def node2941 : Tree Nat := .node node2940 node2855 +def node2942 : Tree Nat := .node node2941 node2911 +def node2943 : Tree Nat := .leaf 26300704596148022627941559149523057717701372056357747728297816288775812747739779378434227152869262029520856657695428264964216366692057936387711106578883398136681548910067462004614136509076779991080611912597110784 +def node2944 : Tree Nat := .node node2943 node1531 +def node2945 : Tree Nat := .node node2944 node1535 +def node2946 : Tree Nat := .node node1529 node2945 +def node2947 : Tree Nat := .node node2144 node2946 +def node2948 : Tree Nat := .node node2947 node2582 +def node2949 : Tree Nat := .node node2948 node2769 +def node2950 : Tree Nat := .node node2949 node2864 +def node2951 : Tree Nat := .node node2950 node2920 +def node2952 : Tree Nat := .node node2942 node2951 +def node2953 : Tree Nat := .node node2933 node2952 +def node2954 : Tree Nat := .leaf 86858970270951006203423838165645771885047073375041211488604415337194479134408200026866468221203321374509304249163184904583451743670206537702115563266644027668708487191084016195953265499820484379492289712844829686163969286747579215443403244899357270621071917752457405118571341027053397170209161216 +def node2955 : Tree Nat := .node node2954 node275 +def node2956 : Tree Nat := .node node2955 node279 +def node2957 : Tree Nat := .node node273 node2956 +def node2958 : Tree Nat := .node node2155 node2957 +def node2959 : Tree Nat := .node node2958 node2554 +def node2960 : Tree Nat := .node node2959 node2788 +def node2961 : Tree Nat := .node node2960 node2883 +def node2962 : Tree Nat := .node node2876 node2961 +def node2963 : Tree Nat := .leaf 1062275985633534197379176413104937309055784302134591804243203517880050540862725951677782028739713834020723043102400272789639940438561977354730803066432123755105364480299043701898870784 +def node2964 : Tree Nat := .node node2963 node777 +def node2965 : Tree Nat := .node node2964 node781 +def node2966 : Tree Nat := .node node775 node2965 +def node2967 : Tree Nat := .node node2164 node2966 +def node2968 : Tree Nat := .node node2967 node2602 +def node2969 : Tree Nat := .node node2968 node2797 +def node2970 : Tree Nat := .node node2969 node2892 +def node2971 : Tree Nat := .node node2931 node2970 +def node2972 : Tree Nat := .node node2962 node2971 +def node2973 : Tree Nat := .leaf 2269284720819188557607214520797381970144826882205520724559655836291846687190913726402047483367509812685079604712967947551928284951134268102634086871681161675151596075755869694094988418475794112983556045632761878673528386101109976751347744536084823942553335974290549936971396939776 +def node2974 : Tree Nat := .node node2973 node1280 +def node2975 : Tree Nat := .node node2974 node1284 +def node2976 : Tree Nat := .node node1278 node2975 +def node2977 : Tree Nat := .node node2174 node2976 +def node2978 : Tree Nat := .node node2977 node2573 +def node2979 : Tree Nat := .node node2978 node2807 +def node2980 : Tree Nat := .node node2979 node2910 +def node2981 : Tree Nat := .node node2941 node2980 +def node2982 : Tree Nat := .leaf 138497694282557489791594520883107362511587926461792414802412290885116654711244934379385276898882351777722071648826508466570935182983877595422721801033778925029865199276330556817049578766433639737180896404553634105254771648607715184818862878788982837595487849699395077767430144 +def node2983 : Tree Nat := .node node2982 node1531 +def node2984 : Tree Nat := .node node2983 node1535 +def node2985 : Tree Nat := .node node1529 node2984 +def node2986 : Tree Nat := .node node2144 node2985 +def node2987 : Tree Nat := .node node2986 node2582 +def node2988 : Tree Nat := .node node2987 node2769 +def node2989 : Tree Nat := .node node2988 node2864 +def node2990 : Tree Nat := .node node2989 node2920 +def node2991 : Tree Nat := .node node2981 node2990 +def node2992 : Tree Nat := .node node2972 node2991 +def node2993 : Tree Nat := .leaf 2015283703367863641175612582842135243135427334428804184044917736999987313807108150565911656580400360071894370193173689646129889958808112504284773750881602853973553365132356026392074963350514880265968068991716688117422993563050756771474897800964273178369612299894784 +def node2994 : Tree Nat := .node node2993 node149 +def node2995 : Tree Nat := .node node2994 node153 +def node2996 : Tree Nat := .node node147 node2995 +def node2997 : Tree Nat := .node node2194 node2996 +def node2998 : Tree Nat := .node node2997 node2593 +def node2999 : Tree Nat := .node node2998 node2827 +def node3000 : Tree Nat := .node node2875 node2999 +def node3001 : Tree Nat := .node node3000 node2961 +def node3002 : Tree Nat := .leaf 2269146223124906000117422926276498862782315294279058932144853424001014171895230212411404973000048044792172692986741420723191826847732454366742485245184723751556231813275184199818286288664587407927686291209969248876865125372494088416703025341267711009436503035510800019187558252544 +def node3003 : Tree Nat := .node node3002 node777 +def node3004 : Tree Nat := .node node3003 node781 +def node3005 : Tree Nat := .node node775 node3004 +def node3006 : Tree Nat := .node node2164 node3005 +def node3007 : Tree Nat := .node node3006 node2602 +def node3008 : Tree Nat := .node node3007 node2797 +def node3009 : Tree Nat := .node node3008 node2892 +def node3010 : Tree Nat := .node node2931 node3009 +def node3011 : Tree Nat := .node node3001 node3010 +def node3012 : Tree Nat := .leaf 5426784091427692294449002872834001191861345797073879325485401925211495949028586085117973647966784806542156079863244232903884800 +def node3013 : Tree Nat := .node node3012 node1154 +def node3014 : Tree Nat := .node node3013 node1158 +def node3015 : Tree Nat := .node node1152 node3014 +def node3016 : Tree Nat := .node node2213 node3015 +def node3017 : Tree Nat := .node node3016 node2642 +def node3018 : Tree Nat := .node node3017 node2854 +def node3019 : Tree Nat := .node node2940 node3018 +def node3020 : Tree Nat := .node node3019 node2980 +def node3021 : Tree Nat := .leaf 173717940541902012406847659425866484451190533229463526990882236840893119072742199839856502876068937588389229049516035492492906865262399953583505161180764870181157579673159550819488672200170647667420217060905152992175436413411303170551637600442427329845432512562951393434993202899550138548902428672 +def node3022 : Tree Nat := .node node3021 node1781 +def node3023 : Tree Nat := .node node3022 node1785 +def node3024 : Tree Nat := .node node1779 node3023 +def node3025 : Tree Nat := .node node2222 node3024 +def node3026 : Tree Nat := .node node3025 node2621 +def node3027 : Tree Nat := .node node3026 node2816 +def node3028 : Tree Nat := .node node3027 node2919 +def node3029 : Tree Nat := .node node2989 node3028 +def node3030 : Tree Nat := .node node3020 node3029 +def node3031 : Tree Nat := .node node3011 node3030 +def node3032 : Tree Nat := .leaf 7964944355277567400889522414977037647226486648590379644400413818214409026365355710218240 +def node3033 : Tree Nat := .node node3032 node400 +def node3034 : Tree Nat := .node node3033 node404 +def node3035 : Tree Nat := .node node398 node3034 +def node3036 : Tree Nat := .node node2233 node3035 +def node3037 : Tree Nat := .node node3036 node2662 +def node3038 : Tree Nat := .node node3037 node2882 +def node3039 : Tree Nat := .node node2960 node3038 +def node3040 : Tree Nat := .node node3000 node3039 +def node3041 : Tree Nat := .leaf 37175422711944576571966846157115377644457117624326996718013592867814909517272922286185664988388014749487763295594273489954555800867105990784175189628038510374413617503462222491871385824278346527407119254668977871877140251560080523816850153173163401473122539585747587483907989595750400 +def node3042 : Tree Nat := .node node3041 node651 +def node3043 : Tree Nat := .node node3042 node655 +def node3044 : Tree Nat := .node node649 node3043 +def node3045 : Tree Nat := .node node2242 node3044 +def node3046 : Tree Nat := .node node3045 node2632 +def node3047 : Tree Nat := .node node3046 node2844 +def node3048 : Tree Nat := .node node2930 node3047 +def node3049 : Tree Nat := .node node3048 node3009 +def node3050 : Tree Nat := .node node3040 node3049 +def node3051 : Tree Nat := .leaf 19182518119363401510097021509837085089334432213989030557701434505264689708377241855498476855145954111770111954865225270101930396867267044285639372698380683619098369523605745502539474917124134063916692376392100250429637189441522266501064957788075144987938715838451986854756081358340096000 +def node3052 : Tree Nat := .node node3051 node1154 +def node3053 : Tree Nat := .node node3052 node1158 +def node3054 : Tree Nat := .node node1152 node3053 +def node3055 : Tree Nat := .node node2213 node3054 +def node3056 : Tree Nat := .node node3055 node2642 +def node3057 : Tree Nat := .node node3056 node2854 +def node3058 : Tree Nat := .node node2940 node3057 +def node3059 : Tree Nat := .node node3058 node2980 +def node3060 : Tree Nat := .leaf 2015283703367863641175612582842035880461389139542819912243331976362067957714186995885281003401944813791902549089772943823362393928515275778861986212803546325673972774730408460574291099939738563564768712940745341811620167108343010492239283895175733762267438913683456 +def node3061 : Tree Nat := .node node3060 node1656 +def node3062 : Tree Nat := .node node3061 node1660 +def node3063 : Tree Nat := .node node1654 node3062 +def node3064 : Tree Nat := .node node2261 node3063 +def node3065 : Tree Nat := .node node3064 node2690 +def node3066 : Tree Nat := .node node3065 node2863 +def node3067 : Tree Nat := .node node2988 node3066 +def node3068 : Tree Nat := .node node3067 node3028 +def node3069 : Tree Nat := .node node3059 node3068 +def node3070 : Tree Nat := .node node3050 node3069 +def node3071 : Tree Nat := .leaf 19070991851227567780385655359698316649593705989427444620245069009852873381868266799619284790372586035931953043278025883202425015142334914992320745639743023782957160290155831262614110372560209147570684874137322521731381072630438671218798334986687041176250400540474604879039624807849132032 +def node3072 : Tree Nat := .node node3071 node400 +def node3073 : Tree Nat := .node node3072 node404 +def node3074 : Tree Nat := .node node398 node3073 +def node3075 : Tree Nat := .node node2233 node3074 +def node3076 : Tree Nat := .node node3075 node2662 +def node3077 : Tree Nat := .node node3076 node2882 +def node3078 : Tree Nat := .node node2960 node3077 +def node3079 : Tree Nat := .node node3000 node3078 +def node3080 : Tree Nat := .leaf 13680631785650431133738452164010503310375293534170028390549037955891717037865253816288400046754357063764740923769182219620837144325719834458511641738981805487332345774080 +def node3081 : Tree Nat := .node node3080 node902 +def node3082 : Tree Nat := .node node3081 node906 +def node3083 : Tree Nat := .node node900 node3082 +def node3084 : Tree Nat := .node node2281 node3083 +def node3085 : Tree Nat := .node node3084 node2710 +def node3086 : Tree Nat := .node node3085 node2891 +def node3087 : Tree Nat := .node node3008 node3086 +def node3088 : Tree Nat := .node node3048 node3087 +def node3089 : Tree Nat := .node node3079 node3088 +def node3090 : Tree Nat := .leaf 503820925841965910293903145710583493637006880564327892725666673368473246240567669475682352989106934593376810395043683004339709682878398364814850018495420126823091912531784710277140623037246438902106649274332563816113930590028247814086601834530830047331569195024384 +def node3091 : Tree Nat := .node node3090 node1405 +def node3092 : Tree Nat := .node node3091 node1409 +def node3093 : Tree Nat := .node node1403 node3092 +def node3094 : Tree Nat := .node node2291 node3093 +def node3095 : Tree Nat := .node node3094 node2681 +def node3096 : Tree Nat := .node node3095 node2909 +def node3097 : Tree Nat := .node node2979 node3096 +def node3098 : Tree Nat := .node node3058 node3097 +def node3099 : Tree Nat := .node node3098 node3068 +def node3100 : Tree Nat := .node node3089 node3099 +def node3101 : Tree Nat := .leaf 33018408195979077897021236557282287907427960838451981092487189987679470573908052333928986881956429041035710718910443876958184790166011882350154566339868106858294749432546375864417740428279671221168030005380294700000841809675947608112270072119711011021731982319990865920 +def node3102 : Tree Nat := .node node3101 node86 +def node3103 : Tree Nat := .node node3102 node90 +def node3104 : Tree Nat := .node node84 node3103 +def node3105 : Tree Nat := .node node2311 node3104 +def node3106 : Tree Nat := .node node3105 node2701 +def node3107 : Tree Nat := .node node2874 node3106 +def node3108 : Tree Nat := .node node3107 node2999 +def node3109 : Tree Nat := .node node3108 node3078 +def node3110 : Tree Nat := .leaf 503820925841965910293903145710682853278783176422042742899963128541361843967736281426486644995877983155568212169833255435184329347739794588698106462461282403652790728932768240966668038923127871765125284449793408086921060505933784890175830612362935065730007691165696 +def node3111 : Tree Nat := .node node3110 node902 +def node3112 : Tree Nat := .node node3111 node906 +def node3113 : Tree Nat := .node node900 node3112 +def node3114 : Tree Nat := .node node2281 node3113 +def node3115 : Tree Nat := .node node3114 node2710 +def node3116 : Tree Nat := .node node3115 node2891 +def node3117 : Tree Nat := .node node3008 node3116 +def node3118 : Tree Nat := .node node3048 node3117 +def node3119 : Tree Nat := .node node3109 node3118 +def node3120 : Tree Nat := .leaf 3121748573623855157871539313632482308408977085151040576371274208782248126476023315017321253671272308254208472291375379995766757901330068117913600 +def node3121 : Tree Nat := .node node3120 node1091 +def node3122 : Tree Nat := .node node3121 node1095 +def node3123 : Tree Nat := .node node1089 node3122 +def node3124 : Tree Nat := .node node2330 node3123 +def node3125 : Tree Nat := .node node3124 node2759 +def node3126 : Tree Nat := .node node2939 node3125 +def node3127 : Tree Nat := .node node3126 node3057 +def node3128 : Tree Nat := .node node3127 node3097 +def node3129 : Tree Nat := .leaf 148701690847778306280310070740832021923419923311650029397698061862645982565585358253925509580443099392097636026797386502591340007597866141510220585781267578938273216270938198148028688929417347711928562238815532716661821702988252074193821279163473319304143965052005009034220979926073344 +def node3130 : Tree Nat := .node node3129 node1906 +def node3131 : Tree Nat := .node node3130 node1910 +def node3132 : Tree Nat := .node node1904 node3131 +def node3133 : Tree Nat := .node node2300 node3132 +def node3134 : Tree Nat := .node node3133 node2729 +def node3135 : Tree Nat := .node node3134 node2918 +def node3136 : Tree Nat := .node node3027 node3135 +def node3137 : Tree Nat := .node node3067 node3136 +def node3138 : Tree Nat := .node node3128 node3137 +def node3139 : Tree Nat := .node node3119 node3138 +def node3140 : Tree Nat := .leaf 114845059217176999652199161716909580259015855316846175740438722537414721536 +def node3141 : Tree Nat := .node node3140 node337 +def node3142 : Tree Nat := .node node3141 node341 +def node3143 : Tree Nat := .node node335 node3142 +def node3144 : Tree Nat := .node node2350 node3143 +def node3145 : Tree Nat := .node node3144 node2787 +def node3146 : Tree Nat := .node node2959 node3145 +def node3147 : Tree Nat := .node node3146 node3077 +def node3148 : Tree Nat := .node node3108 node3147 +def node3149 : Tree Nat := .leaf 40446859910595699341125708145656373132591514042419445126956107720017105848770028401130341546201483200632496178089575328505341280298665416420738783615214685575516665677543978420028481860981334107678969827397592415521936031525211183633406223766682073246559280167614029697992209031921401856 +def node3150 : Tree Nat := .node node3149 node588 +def node3151 : Tree Nat := .node node3150 node592 +def node3152 : Tree Nat := .node node586 node3151 +def node3153 : Tree Nat := .node node2320 node3152 +def node3154 : Tree Nat := .node node3153 node2749 +def node3155 : Tree Nat := .node node2929 node3154 +def node3156 : Tree Nat := .node node3155 node3047 +def node3157 : Tree Nat := .node node3156 node3117 +def node3158 : Tree Nat := .node node3148 node3157 +def node3159 : Tree Nat := .leaf 152270531428124985663540008006528895254462281213872294947618853506483312281637601006710476254648951477568578231959350517633987616622943568599590373193859195360868939825216653169583071331114913603895493890080653363050630102702956458529979846094068988950630236848710628703269671191875420160 +def node3160 : Tree Nat := .node node3159 node1091 +def node3161 : Tree Nat := .node node3160 node1095 +def node3162 : Tree Nat := .node node1089 node3161 +def node3163 : Tree Nat := .node node2330 node3162 +def node3164 : Tree Nat := .node node3163 node2759 +def node3165 : Tree Nat := .node node2939 node3164 +def node3166 : Tree Nat := .node node3165 node3057 +def node3167 : Tree Nat := .node node3166 node3097 +def node3168 : Tree Nat := .leaf 33018408195979077897021236563951930273518967420704215659524541816820944659071993167455629007494867542162264158717584922876283407033358596609923679208455290439931457594477923970132687088832368158479239626062853660846677676937234292923601138618686647043740346805456470016 +def node3169 : Tree Nat := .node node3168 node1593 +def node3170 : Tree Nat := .node node3169 node1597 +def node3171 : Tree Nat := .node node1591 node3170 +def node3172 : Tree Nat := .node node2378 node3171 +def node3173 : Tree Nat := .node node3172 node2768 +def node3174 : Tree Nat := .node node2987 node3173 +def node3175 : Tree Nat := .node node3174 node3066 +def node3176 : Tree Nat := .node node3175 node3136 +def node3177 : Tree Nat := .node node3167 node3176 +def node3178 : Tree Nat := .node node3158 node3177 +def node3179 : Tree Nat := .leaf 38067632857031246415885002001632223813615570301801070128684750548400235182831352333308404133180821172702099111877852160800355136763992239695518951053977240173283467367941175228282463341185918534820004623241488810812315249396333941409644421671105928803014371937217565094105033883999272960 +def node3180 : Tree Nat := .node node3179 node337 +def node3181 : Tree Nat := .node node3180 node341 +def node3182 : Tree Nat := .node node335 node3181 +def node3183 : Tree Nat := .node node2350 node3182 +def node3184 : Tree Nat := .node node3183 node2787 +def node3185 : Tree Nat := .node node2959 node3184 +def node3186 : Tree Nat := .node node3185 node3077 +def node3187 : Tree Nat := .node node3108 node3186 +def node3188 : Tree Nat := .leaf 20748211015063410780906421896822158626924498190588287285775620026209456615471791988689968758453153894901983719879896477313606312650243469291863244584224718465017803241537802531241984 +def node3189 : Tree Nat := .node node3188 node839 +def node3190 : Tree Nat := .node node3189 node843 +def node3191 : Tree Nat := .node node837 node3190 +def node3192 : Tree Nat := .node node2398 node3191 +def node3193 : Tree Nat := .node node3192 node2796 +def node3194 : Tree Nat := .node node3007 node3193 +def node3195 : Tree Nat := .node node3194 node3116 +def node3196 : Tree Nat := .node node3156 node3195 +def node3197 : Tree Nat := .node node3187 node3196 +def node3198 : Tree Nat := .leaf 8254602048994769474255309145988586409736845223991162255450003588722430659544893995193483422244551447177666524461011845455872219001318037887812636521618309039280170203022832835315547568235962024216265884681913660902540744509496526225359714031110042071845719941272567808 +def node3199 : Tree Nat := .node node3198 node1342 +def node3200 : Tree Nat := .node node3199 node1346 +def node3201 : Tree Nat := .node node1340 node3200 +def node3202 : Tree Nat := .node node2369 node3201 +def node3203 : Tree Nat := .node node3202 node2806 +def node3204 : Tree Nat := .node node2978 node3203 +def node3205 : Tree Nat := .node node3204 node3096 +def node3206 : Tree Nat := .node node3166 node3205 +def node3207 : Tree Nat := .node node3206 node3176 +def node3208 : Tree Nat := .node node3197 node3207 +def node3209 : Tree Nat := .leaf 8863852434081664062958681472877695588158784959592295567428676745533724054444448707009155594945536400548669592693422271275626349022051805379194444516422601761535311722779303668492240133077151516401604992088085099140856217169796100269094434467468012032514533422092127754149429248 +def node3210 : Tree Nat := .node node3209 node211 +def node3211 : Tree Nat := .node node3210 node215 +def node3212 : Tree Nat := .node node209 node3211 +def node3213 : Tree Nat := .node node2389 node3212 +def node3214 : Tree Nat := .node node3213 node2826 +def node3215 : Tree Nat := .node node2998 node3214 +def node3216 : Tree Nat := .node node3107 node3215 +def node3217 : Tree Nat := .node node3216 node3186 +def node3218 : Tree Nat := .leaf 8254602048994769474255309139322199910068143258083693241044839823575153550594486940739435416735876022684849312314722302358075980517169046263441500479711629410651914192877422095937077620632807849196598684646854079044997768909947805864291995304362525388298948685349257216 +def node3219 : Tree Nat := .node node3218 node839 +def node3220 : Tree Nat := .node node3219 node843 +def node3221 : Tree Nat := .node node837 node3220 +def node3222 : Tree Nat := .node node2398 node3221 +def node3223 : Tree Nat := .node node3222 node2796 +def node3224 : Tree Nat := .node node3007 node3223 +def node3225 : Tree Nat := .node node3224 node3116 +def node3226 : Tree Nat := .node node3156 node3225 +def node3227 : Tree Nat := .node node3217 node3226 +def node3228 : Tree Nat := .leaf 30167106578526653722750210521455750217352698652216812734343755334767121140995525450042802590677309223436705898510265056214806368878592 +def node3229 : Tree Nat := .node node3228 node1216 +def node3230 : Tree Nat := .node node3229 node1220 +def node3231 : Tree Nat := .node node1214 node3230 +def node3232 : Tree Nat := .node node2447 node3231 +def node3233 : Tree Nat := .node node3232 node2853 +def node3234 : Tree Nat := .node node3056 node3233 +def node3235 : Tree Nat := .node node3165 node3234 +def node3236 : Tree Nat := .node node3235 node3205 +def node3237 : Tree Nat := .leaf 154649758481689438539253101856584427727906370118567238084748270901022217271244407098556404626491896659290190412922964660798727172120946886784235702852196485941661076272352594379896806449531432218916554131709942067149968839391080282890680995224406801313306735649347994140613857766604275712 +def node3238 : Tree Nat := .node node3237 node1843 +def node3239 : Tree Nat := .node node3238 node1847 +def node3240 : Tree Nat := .node node1841 node3239 +def node3241 : Tree Nat := .node node2417 node3240 +def node3242 : Tree Nat := .node node3241 node2815 +def node3243 : Tree Nat := .node node3026 node3242 +def node3244 : Tree Nat := .node node3243 node3135 +def node3245 : Tree Nat := .node node3175 node3244 +def node3246 : Tree Nat := .node node3236 node3245 +def node3247 : Tree Nat := .node node3227 node3246 +def node3248 : Tree Nat := .leaf 334201214867376853218536976941293147291168796603667662419815488624194146587008665374425088 +def node3249 : Tree Nat := .node node3248 node462 +def node3250 : Tree Nat := .node node3249 node465 +def node3251 : Tree Nat := .node node460 node3250 +def node3252 : Tree Nat := .node node2428 node3251 +def node3253 : Tree Nat := .node node3252 node2881 +def node3254 : Tree Nat := .node node3076 node3253 +def node3255 : Tree Nat := .node node3185 node3254 +def node3256 : Tree Nat := .node node3216 node3255 +def node3257 : Tree Nat := .leaf 74350847640257991860231331556363993181239786870752635029752400361930165761785448651591505484970839553341940157553410627684958321052340855584422428792356060817975930476681643200448303206502130554636552985996031068956834435954675543855893812783291068692455694282091485301269818255605760 +def node3258 : Tree Nat := .node node3257 node713 +def node3259 : Tree Nat := .node node3258 node717 +def node3260 : Tree Nat := .node node711 node3259 +def node3261 : Tree Nat := .node node2437 node3260 +def node3262 : Tree Nat := .node node3261 node2843 +def node3263 : Tree Nat := .node node3046 node3262 +def node3264 : Tree Nat := .node node3155 node3263 +def node3265 : Tree Nat := .node node3264 node3225 +def node3266 : Tree Nat := .node node3256 node3265 +def node3267 : Tree Nat := .leaf 609379529096411867973366339948478118506964670448485409767219194677177969197692491102901687804714868502153666615462946466893632205431910779071873488141615126635493261638544082572070444531516089408435267139195634070617346717681514684276536853985436580045941268986704134129271039549681696768 +def node3268 : Tree Nat := .node node3267 node1216 +def node3269 : Tree Nat := .node node3268 node1220 +def node3270 : Tree Nat := .node node1214 node3269 +def node3271 : Tree Nat := .node node2447 node3270 +def node3272 : Tree Nat := .node node3271 node2853 +def node3273 : Tree Nat := .node node3056 node3272 +def node3274 : Tree Nat := .node node3165 node3273 +def node3275 : Tree Nat := .node node3274 node3205 +def node3276 : Tree Nat := .leaf 8863852434081664062958681472878132609825122888544206837958136310848772034852094046130035258833550989519909403882847570816487973164325535839060701421719436933990676260863165478072794424471089493802230452903266840236962920064251966253162705858599248256413391027797770579797344256 +def node3277 : Tree Nat := .node node3276 node1718 +def node3278 : Tree Nat := .node node3277 node1721 +def node3279 : Tree Nat := .node node1716 node3278 +def node3280 : Tree Nat := .node node2464 node3279 +def node3281 : Tree Nat := .node node3280 node2862 +def node3282 : Tree Nat := .node node3065 node3281 +def node3283 : Tree Nat := .node node3174 node3282 +def node3284 : Tree Nat := .node node3283 node3244 +def node3285 : Tree Nat := .node node3275 node3284 +def node3286 : Tree Nat := .node node3266 node3285 +def node3287 : Tree Nat := .leaf 609156476566787278379108054239156247333694058308169791851172548092041729379507673387366203849147725996730025406920568452273150403897892308531071537704644186156703520144043236917508273800981481956093727732268419714023411839396981673670438107794104211234348615754786277726904399948031197184 +def node3288 : Tree Nat := .node node3287 node462 +def node3289 : Tree Nat := .node node3288 node465 +def node3290 : Tree Nat := .node node460 node3289 +def node3291 : Tree Nat := .node node2428 node3290 +def node3292 : Tree Nat := .node node3291 node2881 +def node3293 : Tree Nat := .node node3076 node3292 +def node3294 : Tree Nat := .node node3185 node3293 +def node3295 : Tree Nat := .node node3216 node3294 +def node3296 : Tree Nat := .leaf 285174294677505597696929517968117162742859243835309547566973143959939968586652321188380066451490673669948493632720856144851889209619427657005695662671967746949118816330126340532587358888919040 +def node3297 : Tree Nat := .node node3296 node964 +def node3298 : Tree Nat := .node node3297 node967 +def node3299 : Tree Nat := .node node962 node3298 +def node3300 : Tree Nat := .node node2484 node3299 +def node3301 : Tree Nat := .node node3300 node2890 +def node3302 : Tree Nat := .node node3115 node3301 +def node3303 : Tree Nat := .node node3224 node3302 +def node3304 : Tree Nat := .node node3264 node3303 +def node3305 : Tree Nat := .node node3295 node3304 +def node3306 : Tree Nat := .leaf 2215963108520416015739670368219860918705627185547197085343450321573077336868309251077102326174225549155407086842882886153507097866022858011143218203355784684139059833755154934588180336648220194811903249793435037512778837937724462381679612300118268217587874856115163562608951296 +def node3307 : Tree Nat := .node node3306 node1467 +def node3308 : Tree Nat := .node node3307 node1470 +def node3309 : Tree Nat := .node node1465 node3308 +def node3310 : Tree Nat := .node node2494 node3309 +def node3311 : Tree Nat := .node node3310 node2908 +def node3312 : Tree Nat := .node node3095 node3311 +def node3313 : Tree Nat := .node node3204 node3312 +def node3314 : Tree Nat := .node node3274 node3313 +def node3315 : Tree Nat := .node node3314 node3284 +def node3316 : Tree Nat := .node node3305 node3315 +def node3317 : Tree Nat := .leaf 123003155723136208567847447683223664415745989465967061144775319672827615245282853070109007218536306674745708410782905388586055064621515797122191070561722069598184336831924337253385042086151271460696227772647207623375333095605399243438411704696025136440067227648 +def node3318 : Tree Nat := .node node3317 node54 +def node3319 : Tree Nat := .node node3318 node58 +def node3320 : Tree Nat := .node node52 node3319 +def node3321 : Tree Nat := .node node2514 node3320 +def node3322 : Tree Nat := .node node2873 node3321 +def node3323 : Tree Nat := .node node3322 node3106 +def node3324 : Tree Nat := .node node3323 node3215 +def node3325 : Tree Nat := .node node3324 node3294 +def node3326 : Tree Nat := .leaf 2215963108520416015739670368219423897040103223200861968900182144416075582367312816110528302486423822293081034527335103821046647224874906191755096497613522479383626210196778033937866111658809070779601974003567415185610612313815382293752246012734944525208758807204983703200595968 +def node3327 : Tree Nat := .node node3326 node964 +def node3328 : Tree Nat := .node node3327 node967 +def node3329 : Tree Nat := .node node962 node3328 +def node3330 : Tree Nat := .node node2484 node3329 +def node3331 : Tree Nat := .node node3330 node2890 +def node3332 : Tree Nat := .node node3115 node3331 +def node3333 : Tree Nat := .node node3224 node3332 +def node3334 : Tree Nat := .node node3264 node3333 +def node3335 : Tree Nat := .node node3325 node3334 +def node3336 : Tree Nat := .leaf 756639114940576652872440497549345693020992785872306026333515008241567627040562698603178517571988745643777377048184413009116009735942832128 +def node3337 : Tree Nat := .node node3336 node1060 +def node3338 : Tree Nat := .node node3337 node1063 +def node3339 : Tree Nat := .node node1058 node3338 +def node3340 : Tree Nat := .node node2533 node3339 +def node3341 : Tree Nat := .node node2938 node3340 +def node3342 : Tree Nat := .node node3341 node3164 +def node3343 : Tree Nat := .node node3342 node3273 +def node3344 : Tree Nat := .node node3343 node3313 +def node3345 : Tree Nat := .leaf 297403390559003316441364371679462987949131770409322091479259371325373453793164064587149053478616722460716689797178803623935715975742154320267602450005467807086740497647693172174975943133796607630875584672064863927162867892548431439440543355712961411972610691668516073001438323176112128 +def node3346 : Tree Nat := .node node3345 node1968 +def node3347 : Tree Nat := .node node3346 node1971 +def node3348 : Tree Nat := .node node1966 node3347 +def node3349 : Tree Nat := .node node2503 node3348 +def node3350 : Tree Nat := .node node3349 node2917 +def node3351 : Tree Nat := .node node3134 node3350 +def node3352 : Tree Nat := .node node3243 node3351 +def node3353 : Tree Nat := .node node3283 node3352 +def node3354 : Tree Nat := .node node3344 node3353 +def node3355 : Tree Nat := .node node3335 node3354 +def node3356 : Tree Nat := .leaf 3978707337726839157882554740189643922864093980309715973361556260758507809766316452085760 +def node3357 : Tree Nat := .node node3356 node306 +def node3358 : Tree Nat := .node node3357 node309 +def node3359 : Tree Nat := .node node304 node3358 +def node3360 : Tree Nat := .node node2553 node3359 +def node3361 : Tree Nat := .node node2958 node3360 +def node3362 : Tree Nat := .node node3361 node3184 +def node3363 : Tree Nat := .node node3362 node3293 +def node3364 : Tree Nat := .node node3324 node3363 +def node3365 : Tree Nat := .leaf 305730676383032197711281649742622710886123306029018948465096423214894378187525711710577125145017308736797642166709708925119651563701120884476865237687147190834701536676069687533883080766034579488107378925052481974792132810804528819213223678255519999183931524425391943649623999058886524928 +def node3366 : Tree Nat := .node node3365 node557 +def node3367 : Tree Nat := .node node3366 node560 +def node3368 : Tree Nat := .node node555 node3367 +def node3369 : Tree Nat := .node node2523 node3368 +def node3370 : Tree Nat := .node node2928 node3369 +def node3371 : Tree Nat := .node node3370 node3154 +def node3372 : Tree Nat := .node node3371 node3263 +def node3373 : Tree Nat := .node node3372 node3333 +def node3374 : Tree Nat := .node node3364 node3373 +def node3375 : Tree Nat := .leaf 1218759058188390998269292023606661654806717069847887146350174569787895234894393803710342248917586552091505598663909792279820342266659040293446632428157702443356617321741665090067496469685042973419493452164641674827539035806476143598059428512651241732077559017628245651222258864616399437824 +def node3376 : Tree Nat := .node node3375 node1060 +def node3377 : Tree Nat := .node node3376 node1063 +def node3378 : Tree Nat := .node node1058 node3377 +def node3379 : Tree Nat := .node node2533 node3378 +def node3380 : Tree Nat := .node node2938 node3379 +def node3381 : Tree Nat := .node node3380 node3164 +def node3382 : Tree Nat := .node node3381 node3273 +def node3383 : Tree Nat := .node node3382 node3313 +def node3384 : Tree Nat := .leaf 123003155723136208567847447708070018416355381964899431605122243912527778097675492900439533338605641464139113673047619645997955107023597622533631865752384565045090165295010437231576649888568431557609663563836632543763696941308742116380327089660849966709347450880 +def node3385 : Tree Nat := .node node3384 node1562 +def node3386 : Tree Nat := .node node3385 node1565 +def node3387 : Tree Nat := .node node1560 node3386 +def node3388 : Tree Nat := .node node2581 node3387 +def node3389 : Tree Nat := .node node2986 node3388 +def node3390 : Tree Nat := .node node3389 node3173 +def node3391 : Tree Nat := .node node3390 node3282 +def node3392 : Tree Nat := .node node3391 node3352 +def node3393 : Tree Nat := .node node3383 node3392 +def node3394 : Tree Nat := .node node3374 node3393 +def node3395 : Tree Nat := .leaf 305135869619641084486162424651110383869718645522469604919050302005727267917819995841479478538868055680940285189690738651919013376267824941051617314061007409483742210675248527715269648201148996333276918982055879758765585967492508679507501528971337673078090043435055574271729634129811079168 +def node3396 : Tree Nat := .node node3395 node306 +def node3397 : Tree Nat := .node node3396 node309 +def node3398 : Tree Nat := .node node304 node3397 +def node3399 : Tree Nat := .node node2553 node3398 +def node3400 : Tree Nat := .node node2958 node3399 +def node3401 : Tree Nat := .node node3400 node3184 +def node3402 : Tree Nat := .node node3401 node3293 +def node3403 : Tree Nat := .node node3324 node3402 +def node3404 : Tree Nat := .leaf 1124745611186432219120852645541230153857174661685817753619098995078759793402993066561690753717083484401470826737403450717811278374969336507466167070703991935467520 +def node3405 : Tree Nat := .node node3404 node808 +def node3406 : Tree Nat := .node node3405 node811 +def node3407 : Tree Nat := .node node806 node3406 +def node3408 : Tree Nat := .node node2601 node3407 +def node3409 : Tree Nat := .node node3006 node3408 +def node3410 : Tree Nat := .node node3409 node3223 +def node3411 : Tree Nat := .node node3410 node3332 +def node3412 : Tree Nat := .node node3372 node3411 +def node3413 : Tree Nat := .node node3403 node3412 +def node3414 : Tree Nat := .leaf 30750788930784052141961861945646205950900528103719502925379297944556910045507410279399120945204228792313382002610787910988188490091825741111533237413584381112438465983917439245016505154253351048330085848699459150767942317836070135067586943261631549653278261248 +def node3415 : Tree Nat := .node node3414 node1311 +def node3416 : Tree Nat := .node node3415 node1314 +def node3417 : Tree Nat := .node node1309 node3416 +def node3418 : Tree Nat := .node node2572 node3417 +def node3419 : Tree Nat := .node node2977 node3418 +def node3420 : Tree Nat := .node node3419 node3203 +def node3421 : Tree Nat := .node node3420 node3312 +def node3422 : Tree Nat := .node node3382 node3421 +def node3423 : Tree Nat := .node node3422 node3392 +def node3424 : Tree Nat := .node node3413 node3423 +def node3425 : Tree Nat := .leaf 225924563982610226070265215820544374824657167771312989075437813652077668501960498285146510074899144885499114984200464467326910359101686978775252846219264264892966590051920900182865697594634932453259309048250060922253475840 +def node3426 : Tree Nat := .node node3425 node180 +def node3427 : Tree Nat := .node node3426 node183 +def node3428 : Tree Nat := .node node178 node3427 +def node3429 : Tree Nat := .node node2592 node3428 +def node3430 : Tree Nat := .node node2997 node3429 +def node3431 : Tree Nat := .node node3430 node3214 +def node3432 : Tree Nat := .node node3323 node3431 +def node3433 : Tree Nat := .node node3432 node3402 +def node3434 : Tree Nat := .leaf 30750788930784052141961861920811980997887234677887817339864608149478746012353383005245511535615183867402719086846186378172349218606166225793694462505817694549368294893849779989912882483817193565211203275397663375979504164983291109865107550718284446247010959360 +def node3435 : Tree Nat := .node node3434 node808 +def node3436 : Tree Nat := .node node3435 node811 +def node3437 : Tree Nat := .node node806 node3436 +def node3438 : Tree Nat := .node node2601 node3437 +def node3439 : Tree Nat := .node node3006 node3438 +def node3440 : Tree Nat := .node node3439 node3223 +def node3441 : Tree Nat := .node node3440 node3332 +def node3442 : Tree Nat := .node node3372 node3441 +def node3443 : Tree Nat := .node node3433 node3442 +def node3444 : Tree Nat := .leaf 1614300194054904032231230069590596278140639345625913276370617277966333712853859790957696726547384160288084583581942284288 +def node3445 : Tree Nat := .node node3444 node1185 +def node3446 : Tree Nat := .node node3445 node1188 +def node3447 : Tree Nat := .node node1183 node3446 +def node3448 : Tree Nat := .node node2641 node3447 +def node3449 : Tree Nat := .node node3055 node3448 +def node3450 : Tree Nat := .node node3449 node3272 +def node3451 : Tree Nat := .node node3381 node3450 +def node3452 : Tree Nat := .node node3451 node3421 +def node3453 : Tree Nat := .leaf 1219353864951782111494411248513669248238417417502665318371385195113776976654427429269755729120838114140898916494294983697473193877894337772409732609568290886049967825033721765654481278587565869435907257226035585937681628243558338676960072350451946772779061807631319253040020352662948020224 +def node3454 : Tree Nat := .node node3453 node1812 +def node3455 : Tree Nat := .node node3454 node1815 +def node3456 : Tree Nat := .node node1810 node3455 +def node3457 : Tree Nat := .node node2620 node3456 +def node3458 : Tree Nat := .node node3025 node3457 +def node3459 : Tree Nat := .node node3458 node3242 +def node3460 : Tree Nat := .node node3459 node3351 +def node3461 : Tree Nat := .node node3391 node3460 +def node3462 : Tree Nat := .node node3452 node3461 +def node3463 : Tree Nat := .node node3443 node3462 +def node3464 : Tree Nat := .leaf 23902598168545870313190697279186551945593047349981765538359991320021372759057826886713344 +def node3465 : Tree Nat := .node node3464 node431 +def node3466 : Tree Nat := .node node3465 node434 +def node3467 : Tree Nat := .node node429 node3466 +def node3468 : Tree Nat := .node node2661 node3467 +def node3469 : Tree Nat := .node node3075 node3468 +def node3470 : Tree Nat := .node node3469 node3292 +def node3471 : Tree Nat := .node node3401 node3470 +def node3472 : Tree Nat := .node node3432 node3471 +def node3473 : Tree Nat := .leaf 367873285853439564760533587811143966328459060057661429664211016701021150139241504673514450146755572907776759555882616850812232166675443291171532706989528100542462706662124705638869494300965106051153893667243031562928615940775818537943818489297006017639786694337997085515615741192857612847614525440 +def node3474 : Tree Nat := .node node3473 node682 +def node3475 : Tree Nat := .node node3474 node685 +def node3476 : Tree Nat := .node node680 node3475 +def node3477 : Tree Nat := .node node2631 node3476 +def node3478 : Tree Nat := .node node3045 node3477 +def node3479 : Tree Nat := .node node3478 node3262 +def node3480 : Tree Nat := .node node3371 node3479 +def node3481 : Tree Nat := .node node3480 node3441 +def node3482 : Tree Nat := .node node3472 node3481 +def node3483 : Tree Nat := .leaf 674434357397972527831506359689032488715202958153110094699136562788445821639287146625768890659898391528336492751750116100773007205770255670840498810443826188440795773504687095619308580575390114318856694211300531962836965496574777555039307766611604994364863540195758840085856922720439252541830594560 +def node3484 : Tree Nat := .node node3483 node1185 +def node3485 : Tree Nat := .node node3484 node1188 +def node3486 : Tree Nat := .node node1183 node3485 +def node3487 : Tree Nat := .node node2641 node3486 +def node3488 : Tree Nat := .node node3055 node3487 +def node3489 : Tree Nat := .node node3488 node3272 +def node3490 : Tree Nat := .node node3381 node3489 +def node3491 : Tree Nat := .node node3490 node3421 +def node3492 : Tree Nat := .leaf 553990777130104003934917592054855974259924061527415598228274596169714978873108889622872645198406642054558278952365671633092016626097594910422476814009311811588144432308231332280759118191506643479319278552639471085147961488712709541928083778730940338402020934120883322395557888 +def node3493 : Tree Nat := .node node3492 node1687 +def node3494 : Tree Nat := .node node3493 node1690 +def node3495 : Tree Nat := .node node1685 node3494 +def node3496 : Tree Nat := .node node2689 node3495 +def node3497 : Tree Nat := .node node3064 node3496 +def node3498 : Tree Nat := .node node3497 node3281 +def node3499 : Tree Nat := .node node3390 node3498 +def node3500 : Tree Nat := .node node3499 node3460 +def node3501 : Tree Nat := .node node3491 node3500 +def node3502 : Tree Nat := .node node3482 node3501 +def node3503 : Tree Nat := .leaf 347435881083804024813695352662582961584956833008659305225776271727755038173984289085997064519319836027896598150277906664489114558658205249325521407903002537796268903234728220188901475585127554123903957158063485043643369761486045258142528445235487148116499512002201080201254868760538573756249931776 +def node3504 : Tree Nat := .node node3503 node431 +def node3505 : Tree Nat := .node node3504 node434 +def node3506 : Tree Nat := .node node429 node3505 +def node3507 : Tree Nat := .node node2661 node3506 +def node3508 : Tree Nat := .node node3075 node3507 +def node3509 : Tree Nat := .node node3508 node3292 +def node3510 : Tree Nat := .node node3401 node3509 +def node3511 : Tree Nat := .node node3432 node3510 +def node3512 : Tree Nat := .leaf 76545284419409946423878098706159761389024225897941522277007614789152672935126794109495346091152475877559497453826600114383610078769329946729298024493969054019615952058065384281731363452164600508710912 +def node3513 : Tree Nat := .node node3512 node933 +def node3514 : Tree Nat := .node node3513 node936 +def node3515 : Tree Nat := .node node931 node3514 +def node3516 : Tree Nat := .node node2709 node3515 +def node3517 : Tree Nat := .node node3114 node3516 +def node3518 : Tree Nat := .node node3517 node3331 +def node3519 : Tree Nat := .node node3440 node3518 +def node3520 : Tree Nat := .node node3480 node3519 +def node3521 : Tree Nat := .node node3511 node3520 +def node3522 : Tree Nat := .leaf 9076030969344193881830906443734197896041214432680857066853762215856310823831566669886141577485648253891936520286387185970107498991864168418146640176962795664917808271276761143081364339715242438384420450311516277979483685930617190356347810880755682323778084205330946013767139328000 +def node3523 : Tree Nat := .node node3522 node1436 +def node3524 : Tree Nat := .node node3523 node1439 +def node3525 : Tree Nat := .node node1434 node3524 +def node3526 : Tree Nat := .node node2680 node3525 +def node3527 : Tree Nat := .node node3094 node3526 +def node3528 : Tree Nat := .node node3527 node3311 +def node3529 : Tree Nat := .node node3420 node3528 +def node3530 : Tree Nat := .node node3490 node3529 +def node3531 : Tree Nat := .node node3530 node3500 +def node3532 : Tree Nat := .node node3521 node3531 +def node3533 : Tree Nat := .leaf 4327788799063369938358906039786514733686659991111267002964750199774241231704086128711648433962413955584303182974979549405715530762430078814852912465377306534215350030291850950715526940601521297047749872166048782515897426340433349468738567280986331168819527095179048220884992 +def node3534 : Tree Nat := .node node3533 node4 +def node3535 : Tree Nat := .node node2 node3534 +def node3536 : Tree Nat := .node node3535 node2068 +def node3537 : Tree Nat := .node node3536 node2872 +def node3538 : Tree Nat := .leaf 90095700615208749952205140752626349712100267269774297252850104458456255020586311837977132474920250650954782098409275539135756009140090338604097935226436652318673855705128169417757152056157457027474294811634729175424005842532765642251939581988099049127936000 +def node3539 : Tree Nat := .node node3317 node3538 +def node3540 : Tree Nat := .node node3539 node58 +def node3541 : Tree Nat := .node node52 node3540 +def node3542 : Tree Nat := .node node2514 node3541 +def node3543 : Tree Nat := .node node3537 node3542 +def node3544 : Tree Nat := .leaf 4538015484673128766171577568051408829129253711688905441017270071213568949015601252517454566735934103205789848084469788332364839965613848223691087111498988025028718775827143512882654997922784868541227627112076097602987810689029292312260857121809678250509706534069867051881762652160 +def node3545 : Tree Nat := .node node3544 node67 +def node3546 : Tree Nat := .node node65 node3545 +def node3547 : Tree Nat := .node node3546 node2310 +def node3548 : Tree Nat := .node node3547 node3104 +def node3549 : Tree Nat := .node node3548 node2701 +def node3550 : Tree Nat := .node node3543 node3549 +def node3551 : Tree Nat := .leaf 277611868196852612820085195624083737478891494950657476986477143411526254299827257334747029929515089622227143769943309999615832575103309343715480674810620750046572978977116925516772023254322727589356243466207349673073204789248 +def node3552 : Tree Nat := .node node3425 node3551 +def node3553 : Tree Nat := .node node3552 node183 +def node3554 : Tree Nat := .node node178 node3553 +def node3555 : Tree Nat := .node node2592 node3554 +def node3556 : Tree Nat := .node node2997 node3555 +def node3557 : Tree Nat := .leaf 4127552950335700185474827592214072194001970501836583918977266660048293214675395339397828890805210218063420076089665893252592400998382560742555297555176633156508586729658050673393437568761396341196472410418471994093143082686944831614089455694705112702037908491683758080 +def node3558 : Tree Nat := .node node3557 node242 +def node3559 : Tree Nat := .node node3558 node245 +def node3560 : Tree Nat := .node node2013 node3559 +def node3561 : Tree Nat := .node node2825 node3560 +def node3562 : Tree Nat := .node node3213 node3561 +def node3563 : Tree Nat := .node node3556 node3562 +def node3564 : Tree Nat := .node node3550 node3563 +def node3565 : Tree Nat := .leaf 69244620785013915169893880288577664649638356718206520148356066053544201755915040781030818563707002931730762300556198370198467059319135998738502644985094416224536059445117594392163977484884566481703844929172853945635267500147671706758678678069843254071068122219554924992135168 +def node3566 : Tree Nat := .node node3565 node256 +def node3567 : Tree Nat := .node node254 node3566 +def node3568 : Tree Nat := .node node3567 node2154 +def node3569 : Tree Nat := .node node3568 node2957 +def node3570 : Tree Nat := .leaf 17350741762303288301255324726505233592430718434416092311654821463220390893739203583421689370594693101389196485621456874975989535943956833982217542175663796877910811186069807844798251453395170474334765216637959354567075299328 +def node3571 : Tree Nat := .node node3395 node3570 +def node3572 : Tree Nat := .node node3571 node309 +def node3573 : Tree Nat := .node node304 node3572 +def node3574 : Tree Nat := .node node2553 node3573 +def node3575 : Tree Nat := .node node3569 node3574 +def node3576 : Tree Nat := .leaf 185074578797901741880056797082722491652594329967104984657651428941017502866551504889831353286343393081484762513295539999743888383402206229143653783207108769584085106800684616437859902199135058135254172214134845481269485109248 +def node3577 : Tree Nat := .node node3576 node368 +def node3578 : Tree Nat := .node node3577 node371 +def node3579 : Tree Nat := .node node366 node3578 +def node3580 : Tree Nat := .node node2786 node3579 +def node3581 : Tree Nat := .node node3183 node3580 +def node3582 : Tree Nat := .node node3575 node3581 +def node3583 : Tree Nat := .leaf 70906491683854253070072331218981063655902577448435742967067236238248175601478738248918999512888940417370844905815175098223849718145899221368344070297458002192578743016374594256826799000631354426195534712996854019179512934085564995663054180435628132340881422198874009160329986048 +def node3584 : Tree Nat := .node node3583 node381 +def node3585 : Tree Nat := .node node379 node3584 +def node3586 : Tree Nat := .node node3585 node2232 +def node3587 : Tree Nat := .node node3586 node3074 +def node3588 : Tree Nat := .node node3587 node3507 +def node3589 : Tree Nat := .leaf 18152061871066687778296661354368903323621809078354772711935094637964933221171650581015415390625850576347222485398317875866793592221273485683496094478891500200912313990635464124912452863194272287610730100521231584558141129784606065006780015229799157562234958782104722839658267934720 +def node3590 : Tree Nat := .node node3589 node443 +def node3591 : Tree Nat := .node node441 node3590 +def node3592 : Tree Nat := .node node3591 node2427 +def node3593 : Tree Nat := .node node3592 node3290 +def node3594 : Tree Nat := .node node3593 node2881 +def node3595 : Tree Nat := .node node3588 node3594 +def node3596 : Tree Nat := .node node3582 node3595 +def node3597 : Tree Nat := .node node3564 node3596 +def node3598 : Tree Nat := .leaf 64489078507771637412585350103284506207282228156357443329190177868940545665739255769781450348877032798714253789594969822851364980415846420446305582552944825710731610185490413454593181246065229179470053335512802636265709283484670470135556316201641397534318430959697920 +def node3599 : Tree Nat := .node node3598 node569 +def node3600 : Tree Nat := .node node567 node3599 +def node3601 : Tree Nat := .node node3600 node2319 +def node3602 : Tree Nat := .node node3601 node3152 +def node3603 : Tree Nat := .leaf 49692708741517100404930162553280883400323263580120335617144127691486424773101934148218588629411074240398167893643315732289073775856322241122475267870269188510521661549621084010459068489150180782849196848584279628992773002688542539776 +def node3604 : Tree Nat := .node node3603 node619 +def node3605 : Tree Nat := .node node3604 node622 +def node3606 : Tree Nat := .node node617 node3605 +def node3607 : Tree Nat := .node node2748 node3606 +def node3608 : Tree Nat := .node node3602 node3607 +def node3609 : Tree Nat := .node node3370 node3608 +def node3610 : Tree Nat := .leaf 1110447472787410451280340782496334949915565979802629907945908573646105017199309029338988119718060358488908575079773239998463330300413237374861922699242483000186291915908467702067088093017290910357424973864829398692292819156992 +def node3611 : Tree Nat := .node node3473 node3610 +def node3612 : Tree Nat := .node node3611 node685 +def node3613 : Tree Nat := .node node680 node3612 +def node3614 : Tree Nat := .node node2631 node3613 +def node3615 : Tree Nat := .node node3045 node3614 +def node3616 : Tree Nat := .leaf 257956317875169772319385075231187213055505109751773041230046415222586106579360230874766909130404030621746093094006436657873295790476388149177752823499062326111512108516004589725025843145699535201381121900283479086178354114154084056723016302218508900817544254354096128 +def node3617 : Tree Nat := .node node3616 node744 +def node3618 : Tree Nat := .node node3617 node747 +def node3619 : Tree Nat := .node node2030 node3618 +def node3620 : Tree Nat := .node node2842 node3619 +def node3621 : Tree Nat := .node node3261 node3620 +def node3622 : Tree Nat := .node node3615 node3621 +def node3623 : Tree Nat := .node node3609 node3622 +def node3624 : Tree Nat := .leaf 6191329402440458580124202281849711845739827299690889293332775591049148980830917257817055802950478472598785642570998141504795070010913887728396620560358834413291924860272968574486183201596404500051228945121390573958218961096988695430114222597052103715820589002713464832 +def node3625 : Tree Nat := .node node3434 node3624 +def node3626 : Tree Nat := .node node3625 node811 +def node3627 : Tree Nat := .node node806 node3626 +def node3628 : Tree Nat := .node node2601 node3627 +def node3629 : Tree Nat := .node node3006 node3628 +def node3630 : Tree Nat := .node node3629 node3223 +def node3631 : Tree Nat := .leaf 9076584892499624000469689828226760282701348722326821713643608315639232502580756490540189131484592466369882212749188672534231992940101449934755636487247161484782176778148646014730649729773003381487614761759138543577896610204126782187795157983712958817578555626555688756037833195520 +def node3632 : Tree Nat := .node node3631 node933 +def node3633 : Tree Nat := .node node3632 node936 +def node3634 : Tree Nat := .node node931 node3633 +def node3635 : Tree Nat := .node node2709 node3634 +def node3636 : Tree Nat := .node node3114 node3635 +def node3637 : Tree Nat := .leaf 22158278651204452854366041692344852687884274149826086447473941137134144561892813049929861940386240938153843936177983478463509458982123519596320846395230213191851539022437630205492472795163061398475446624285078742528278953309220489188606133997791121730853999570011313907070664704 +def node3638 : Tree Nat := .node node3637 node945 +def node3639 : Tree Nat := .node node943 node3638 +def node3640 : Tree Nat := .node node3639 node2483 +def node3641 : Tree Nat := .node node3640 node3329 +def node3642 : Tree Nat := .leaf 1107981554260208007869835184109711948519848119949036945928529435827462642354167913278505822428065667027742715131458310835646369889593792323564810388750753915858421224617433382925397237392415646291686692141755470545300432670568247575607956365342296671552989339341209927432536064 +def node3643 : Tree Nat := .node node3642 node994 +def node3644 : Tree Nat := .node node3643 node997 +def node3645 : Tree Nat := .node node2077 node3644 +def node3646 : Tree Nat := .node node2889 node3645 +def node3647 : Tree Nat := .node node3641 node3646 +def node3648 : Tree Nat := .node node3636 node3647 +def node3649 : Tree Nat := .node node3630 node3648 +def node3650 : Tree Nat := .node node3623 node3649 +def node3651 : Tree Nat := .node node3597 node3650 +def node3652 : Tree Nat := .leaf 264147265567892686976580031625726659363614910878666845535570007101838667417133359551525753716459600010124949597967474383030247018866723567629094481178798724970631006998331577673670915950541322205371192038855985702395455421466371177941843730407534277651613515738402258944 +def node3653 : Tree Nat := .node node3652 node1010 +def node3654 : Tree Nat := .node node1008 node3653 +def node3655 : Tree Nat := .node node3654 node2134 +def node3656 : Tree Nat := .node node3655 node2937 +def node3657 : Tree Nat := .leaf 6491683198595054547177551277054156060903595942331864878646248339038165009476353095145304330080538694868990560431615101454209149145248879400353496861748724270318093376495394472085361213548341069647515037267115314529168069537965523615899011752564830632523582990270272664240128 +def node3658 : Tree Nat := .node node3375 node3657 +def node3659 : Tree Nat := .node node3658 node1063 +def node3660 : Tree Nat := .node node1058 node3659 +def node3661 : Tree Nat := .node node2533 node3660 +def node3662 : Tree Nat := .node node3656 node3661 +def node3663 : Tree Nat := .leaf 57278681880282598266741390408408596112073575107801884750380706224728954912021854056104385596147127637774357555095311732689303106074376692652622954979648160308715047559991058126855927576744512779217681303684731971486625110250447625670398125889921482752 +def node3664 : Tree Nat := .node node3663 node1122 +def node3665 : Tree Nat := .node node3664 node1125 +def node3666 : Tree Nat := .node node1120 node3665 +def node3667 : Tree Nat := .node node2758 node3666 +def node3668 : Tree Nat := .node node3163 node3667 +def node3669 : Tree Nat := .node node3662 node3668 +def node3670 : Tree Nat := .leaf 62977616668685342387325421960217648264250230355977254793400162357726016160706066959434384680823039694200140654924873146729788871606308563376915741358958747515091597100758845709529810885099968320599190713012881073322486147882951892977927282736051327953256977530880 +def node3671 : Tree Nat := .node node3670 node1247 +def node3672 : Tree Nat := .node node3671 node1250 +def node3673 : Tree Nat := .node node2040 node3672 +def node3674 : Tree Nat := .node node2852 node3673 +def node3675 : Tree Nat := .node node3271 node3674 +def node3676 : Tree Nat := .node node3488 node3675 +def node3677 : Tree Nat := .node node3669 node3676 +def node3678 : Tree Nat := .leaf 66036816637964468156759819055481632075417978298957646183090756945133772865340002359174299416448252603766528494444140705221200120529708040432346663027636608041504158084147899646743114732500752828806843890381313734913430309552540681989121982042682908194427282730006872064 +def node3679 : Tree Nat := .node node3678 node1386 +def node3680 : Tree Nat := .node node1384 node3679 +def node3681 : Tree Nat := .node node3680 node2290 +def node3682 : Tree Nat := .node node3681 node3093 +def node3683 : Tree Nat := .node node3682 node3526 +def node3684 : Tree Nat := .node node3683 node3311 +def node3685 : Tree Nat := .node node3420 node3684 +def node3686 : Tree Nat := .node node3677 node3685 +def node3687 : Tree Nat := .leaf 4030567421750760995895985049773048056469099047391227855212699350938280458006096623232860680325798628881305858591549929533692822230915488655287349367107025111430694718027481321432317981837273175297969030494103705199223505613847628336802853825632439246623709258055680 +def node3688 : Tree Nat := .node node3687 node1574 +def node3689 : Tree Nat := .node node1572 node3688 +def node3690 : Tree Nat := .node node3689 node2377 +def node3691 : Tree Nat := .node node3690 node3171 +def node3692 : Tree Nat := .node node3691 node2768 +def node3693 : Tree Nat := .node node3389 node3692 +def node3694 : Tree Nat := .leaf 4226356249085321970818718279332132852150778608288972177023685672213391220453798875795338047101257503157395159946057029431058780476021484298004311827703516615267093471992040673349852141411411765566392621289257734706561524134847777407635770422011444621048356853271406575616 +def node3695 : Tree Nat := .node node3694 node1637 +def node3696 : Tree Nat := .node node1635 node3695 +def node3697 : Tree Nat := .node node3696 node2260 +def node3698 : Tree Nat := .node node3697 node3063 +def node3699 : Tree Nat := .node node3698 node3496 +def node3700 : Tree Nat := .leaf 458222462695599379270700542938797415851547826754730440471063195236977024085646466549524548253194054006869752147503995521190349772113174027207120416665033273928205988943208744774074652751019355674508791384847178672032005027722300615756974875345256710144 +def node3701 : Tree Nat := .node node3700 node1699 +def node3702 : Tree Nat := .node node1697 node3701 +def node3703 : Tree Nat := .node node3702 node2463 +def node3704 : Tree Nat := .node node3703 node3279 +def node3705 : Tree Nat := .node node3704 node2862 +def node3706 : Tree Nat := .node node3699 node3705 +def node3707 : Tree Nat := .node node3693 node3706 +def node3708 : Tree Nat := .leaf 984025245785313409979642667100198837075336788121429291146728212168925905501427243611624769112066079783908427311760756267587287066326648854280262839710577875902676810476120039447197653492606449244932706879310828502416901927568845044498501159371016548692596359168 +def node3709 : Tree Nat := .node node3708 node1762 +def node3710 : Tree Nat := .node node1760 node3709 +def node3711 : Tree Nat := .node node3710 node2221 +def node3712 : Tree Nat := .node node3711 node3024 +def node3713 : Tree Nat := .node node3712 node3457 +def node3714 : Tree Nat := .node node3713 node3242 +def node3715 : Tree Nat := .leaf 694871762167608049626282723770905715162043830833208898076279771632803262962607377701488142089040871141567657864678296095251240318970110686340489458480483915643121487203692938742159498012962646179451956129936101160535614917185381276544808818351698618788122820825572984266275196057600993769868492800 +def node3716 : Tree Nat := .node node3715 node1937 +def node3717 : Tree Nat := .node node3716 node1940 +def node3718 : Tree Nat := .node node1935 node3717 +def node3719 : Tree Nat := .node node2728 node3718 +def node3720 : Tree Nat := .node node3133 node3719 +def node3721 : Tree Nat := .leaf 776259046150354467574489744231251277628443008558348305569526019013025476343188443165439204414323238975243865348565536603085790022057407195722143886182208774495548565701549026185552693043874621086490219828846680955194929693595795456 +def node3722 : Tree Nat := .node node3721 node1949 +def node3723 : Tree Nat := .node node1947 node3722 +def node3724 : Tree Nat := .node node3723 node2502 +def node3725 : Tree Nat := .node node3724 node3348 +def node3726 : Tree Nat := .node node3725 node2917 +def node3727 : Tree Nat := .node node3720 node3726 +def node3728 : Tree Nat := .node node3714 node3727 +def node3729 : Tree Nat := .node node3707 node3728 +def node3730 : Tree Nat := .node node3686 node3729 +def node3731 : Tree Nat := .node node3651 node3730 +def node3732 : Tree Nat := .leaf 377888757473172520759533830679308359076483153975433513596157183529873416825652844724488084226799455715083388091195770378633513302968788313144741234746284281797287187968249088639342657279149778733338794573529262470599789198653743480002972095328569399975081146318848 +def node3733 : Tree Nat := .node node3533 node3732 +def node3734 : Tree Nat := .node node2 node3733 +def node3735 : Tree Nat := .node node3734 node2068 +def node3736 : Tree Nat := .node node3735 node2872 +def node3737 : Tree Nat := .leaf 5243959930521868196035988243035872375697538011210511234121231012194650625123109478166957532892420798640416084237546670450062559728857362876975555917014796327300845251045104039284910971781057462537723602464825979829470963432852800835516463904194560 +def node3738 : Tree Nat := .node node34 node3737 +def node3739 : Tree Nat := .node node33 node3738 +def node3740 : Tree Nat := .node node3739 node2513 +def node3741 : Tree Nat := .node node3740 node3541 +def node3742 : Tree Nat := .node node3736 node3741 +def node3743 : Tree Nat := .leaf 85918022740406503255645470092525385597218198553156191474395948294389047319891965327042170483216034080834072913620861113945728167576735743201464798203400475521372325600679029398174714093332572878666893937049128186820834077074802903018177894467026026496 +def node3744 : Tree Nat := .node node97 node3743 +def node3745 : Tree Nat := .node node96 node3744 +def node3746 : Tree Nat := .node node3745 node2699 +def node3747 : Tree Nat := .leaf 22158278651228636258806456056038960038878377388039534658809823164819445497669790920225122172600951200721943477860173773644475208891129974715316635833275739573311939698870814410387446782780648471303897765416895265125658712948194486365801568895732904051021597407906052102808403968 +def node3748 : Tree Nat := .node node112 node3747 +def node3749 : Tree Nat := .node node111 node3748 +def node3750 : Tree Nat := .node node3749 node121 +def node3751 : Tree Nat := .node node3746 node3750 +def node3752 : Tree Nat := .node node3548 node3751 +def node3753 : Tree Nat := .node node3742 node3752 +def node3754 : Tree Nat := .leaf 328066310098881164179615652565680299866661311420379969952641507336145424065831505050517601731582585722532552096262890007113125705605012535427757295227306050895113380026998537697967464394323853756030146399511422800879959051444527601908993499332608 +def node3755 : Tree Nat := .node node129 node3754 +def node3756 : Tree Nat := .node node128 node3755 +def node3757 : Tree Nat := .node node3756 node2193 +def node3758 : Tree Nat := .node node3757 node2996 +def node3759 : Tree Nat := .leaf 94466423595368608180106839820715774271282075530789170645706780378819805840860282088711963156638834696055840550647460582056465308577302492365337427579690142317125800370992139131199988903360326478426021261491391969468837075129430604965400141257113780347622379225088 +def node3760 : Tree Nat := .node node175 node3759 +def node3761 : Tree Nat := .node node174 node3760 +def node3762 : Tree Nat := .node node3761 node3553 +def node3763 : Tree Nat := .node node2592 node3762 +def node3764 : Tree Nat := .node node3758 node3763 +def node3765 : Tree Nat := .leaf 283625967792006058808176788520780685867414277271872180408915520460270309811540679986766115142045205324378049948305486052875173941726172978001747862728566971514576073431486346258644074521221272496670890023661006055707107150675225085339451244327824784234534939426919600627354959872 +def node3766 : Tree Nat := .node node191 node3765 +def node3767 : Tree Nat := .node node190 node3766 +def node3768 : Tree Nat := .node node3767 node2388 +def node3769 : Tree Nat := .node node3768 node3212 +def node3770 : Tree Nat := .leaf 335612155294628451614282624222752013563145380923874834329391988698957781312729345617327549990132363774562806748660152969621838211996953633208340148924584917427885245796631391823439077282956782534121562596465764618858561175078956057992485786403995648 +def node3771 : Tree Nat := .node node222 node3770 +def node3772 : Tree Nat := .node node221 node3771 +def node3773 : Tree Nat := .node node3772 node2824 +def node3774 : Tree Nat := .leaf 18193571394148932833777103380419951819416633013086288411785766070617784601793479136689981353460700913482278094107004764134823203641970481149737741504388841475052206750244334830667171315995294275296050771801364868174525549068156928 +def node3775 : Tree Nat := .node node3557 node3774 +def node3776 : Tree Nat := .node node3775 node245 +def node3777 : Tree Nat := .node node2013 node3776 +def node3778 : Tree Nat := .node node3773 node3777 +def node3779 : Tree Nat := .node node3769 node3778 +def node3780 : Tree Nat := .node node3764 node3779 +def node3781 : Tree Nat := .node node3753 node3780 +def node3782 : Tree Nat := .leaf 74520868430434028887151015446200122652330528821601437334674497825250445728946090543882163623775030941623411073462291513896235842117511090789325789201976694681813838849000795466412733710316725351612623961298390500042856648983170777088 +def node3783 : Tree Nat := .node node3565 node3782 +def node3784 : Tree Nat := .node node254 node3783 +def node3785 : Tree Nat := .node node3784 node2154 +def node3786 : Tree Nat := .node node3785 node2957 +def node3787 : Tree Nat := .leaf 106359737525781379605108474833793304158522309951378197960786959903126326889461660261747255647108909874379240409407194963301747559922682255118158738270267697700517530020343833132154265682223961112434983274328737786561600469468525776667285887269294744296323930255103398507790204928 +def node3788 : Tree Nat := .node node301 node3787 +def node3789 : Tree Nat := .node node300 node3788 +def node3790 : Tree Nat := .node node3789 node3572 +def node3791 : Tree Nat := .node node2553 node3790 +def node3792 : Tree Nat := .node node3786 node3791 +def node3793 : Tree Nat := .leaf 21479177938861104702947544874773277196989586550366132530617939748530463231904153732720255410358355143047267352342040021923908070304459736237482782738019403970305796475647076428442909062240920907100219323086452220530875566524863996364866851409902960640 +def node3794 : Tree Nat := .node node317 node3793 +def node3795 : Tree Nat := .node node316 node3794 +def node3796 : Tree Nat := .node node3795 node2349 +def node3797 : Tree Nat := .node node3796 node3182 +def node3798 : Tree Nat := .leaf 34959599509857130376772047909570245155022077753222690323156717046970908809843459429991689341708477671361073328299922719442102075636771286232142044736550051000036031981488512296322594614113899245700170655610943620849267582380120915439444231121272832 +def node3799 : Tree Nat := .node node348 node3798 +def node3800 : Tree Nat := .node node347 node3799 +def node3801 : Tree Nat := .node node3800 node2785 +def node3802 : Tree Nat := .leaf 6190951559809168803779520960961825423248316278147658867123225492542117970998137146895424917273663411058907179831602016087110815463642615673627887334875468869851371554983005091373433799192768949541773198961967982081823272309034871564489610621044687874722732121893371904 +def node3803 : Tree Nat := .node node3576 node3802 +def node3804 : Tree Nat := .node node3803 node371 +def node3805 : Tree Nat := .node node366 node3804 +def node3806 : Tree Nat := .node node3801 node3805 +def node3807 : Tree Nat := .node node3797 node3806 +def node3808 : Tree Nat := .node node3792 node3807 +def node3809 : Tree Nat := .leaf 386934471046981733957067836228931709432148377789486431695762605409927701258105713789861977575902701768103175928929274513752564972492905197353405021019305891410946023873960664080891603106476551709534036778271240558565508345331131992580998570016603573079825621446557696 +def node3810 : Tree Nat := .node node395 node3809 +def node3811 : Tree Nat := .node node394 node3810 +def node3812 : Tree Nat := .node node3811 node3073 +def node3813 : Tree Nat := .node node3586 node3812 +def node3814 : Tree Nat := .leaf 106359737525781373700957022117933584227176072140440595903369682715355389438936909868576183637967103570658423573895531705298322042521420623376866451941552683834835419068238732412880189011909769061225491713938670587838718640260712419060396825661366776741703027250962735307872534528 +def node3815 : Tree Nat := .node node411 node3814 +def node3816 : Tree Nat := .node node410 node3815 +def node3817 : Tree Nat := .node node3816 node2660 +def node3818 : Tree Nat := .leaf 7161473972933517889805535017187635973373048257470963709225479198264171918743498650832301792621832275057311905678445468161400744857603340455942286865064552610498742550512352864233015503300429093695148902046942483001977974817691787083024760666207551488 +def node3819 : Tree Nat := .node node3503 node3818 +def node3820 : Tree Nat := .node node3819 node434 +def node3821 : Tree Nat := .node node429 node3820 +def node3822 : Tree Nat := .node node3817 node3821 +def node3823 : Tree Nat := .node node3813 node3822 +def node3824 : Tree Nat := .leaf 396220898351839024966200495091397361487646578285816854921853361649410203895667028964638671035944016825479566234923297695055393564692743703462168593349949970522317072813742419109431759721890712376125722155818058238934501180714204208722812627352275547990827647337389621248 +def node3825 : Tree Nat := .node node3589 node3824 +def node3826 : Tree Nat := .node node441 node3825 +def node3827 : Tree Nat := .node node3826 node2427 +def node3828 : Tree Nat := .node node3827 node3290 +def node3829 : Tree Nat := .leaf 17726622920979684553119776263005300707063713350041753661841669300413629377192852866157530908057924956512928646284290973327497340797237127828634503631396437823291311380750968637900998634214042841661346845758480105627100730671345278059471452982609966868254961824679170070353543168 +def node3830 : Tree Nat := .node node491 node3829 +def node3831 : Tree Nat := .node node3830 node495 +def node3832 : Tree Nat := .node node2021 node3831 +def node3833 : Tree Nat := .node node2880 node3832 +def node3834 : Tree Nat := .node node3828 node3833 +def node3835 : Tree Nat := .node node3823 node3834 +def node3836 : Tree Nat := .node node3808 node3835 +def node3837 : Tree Nat := .node node3781 node3836 +def node3838 : Tree Nat := .leaf 18630217107608507221787753861550030663082632205400359333668624456312611432236522635970540905943757735405852768365572878474058960529377772697331447300494173670453459712250198866603183427579181337903155990324597625010714162245792694272 +def node3839 : Tree Nat := .node node506 node3838 +def node3840 : Tree Nat := .node node505 node3839 +def node3841 : Tree Nat := .node node3840 node2124 +def node3842 : Tree Nat := .leaf 572778078369499224088375678673496769814434783443413050588828994046221280107058083186905685316492567508587190184379994401487937215141467534008900520831291592410257486159584242045336025229579575524900800164634904949518611072134751672307175742129485905920 +def node3843 : Tree Nat := .node node521 node3842 +def node3844 : Tree Nat := .node node520 node3843 +def node3845 : Tree Nat := .node node3844 node2926 +def node3846 : Tree Nat := .node node3841 node3845 +def node3847 : Tree Nat := .leaf 85916711835441056807814603089982736960820311082249057456115247031688285757227159331847437655731071536746730016572158087344389467621885749950767459089054011489508583477079527260968578485993875759676888321442815936058430884600501727295793896813389414400 +def node3848 : Tree Nat := .node node537 node3847 +def node3849 : Tree Nat := .node node536 node3848 +def node3850 : Tree Nat := .node node3849 node2522 +def node3851 : Tree Nat := .leaf 1476037868677634502814169372198683972988782430168580791339168443419059466263441907636124424322481792125872508603866571594632270446520351443208397305932658473705090630796752173924999826615005101225406582210802999522950579298897353202584377207142402817931599675392 +def node3852 : Tree Nat := .node node552 node3851 +def node3853 : Tree Nat := .node node551 node3852 +def node3854 : Tree Nat := .node node3853 node3367 +def node3855 : Tree Nat := .node node3850 node3854 +def node3856 : Tree Nat := .node node3846 node3855 +def node3857 : Tree Nat := .leaf 85916711755426104563164716032153802554402288059321493371708562224882483323031081381338675850221356091656890457763946718190218188455383806029372331426405231175268908110103303144736105813469858034964229853923396563658773573650165453009413301589434695680 +def node3858 : Tree Nat := .node node3598 node3857 +def node3859 : Tree Nat := .node node567 node3858 +def node3860 : Tree Nat := .node node3859 node2319 +def node3861 : Tree Nat := .node node3860 node3152 +def node3862 : Tree Nat := .leaf 96733617761657454776429403976412952853792845343528110741203743107911481181040928858841050272398166728761180723862999636025820475983157752182105525841602705732736819579895950470348788637040974313908245771767185376736089164932536939484569744647284511075965316326490112 +def node3863 : Tree Nat := .node node614 node3862 +def node3864 : Tree Nat := .node node613 node3863 +def node3865 : Tree Nat := .node node3864 node3605 +def node3866 : Tree Nat := .node node2748 node3865 +def node3867 : Tree Nat := .node node3861 node3866 +def node3868 : Tree Nat := .node node3856 node3867 +def node3869 : Tree Nat := .leaf 22158278651204452854366041692344873172024611956738416420778642232838097390590379204399730677690238677276238511943707192303230536396904681877006189422144862962250220477127157081722265555472962878468721788891141802259211237696694431455098004104503049368837747407826147229158080512 +def node3870 : Tree Nat := .node node662 node3869 +def node3871 : Tree Nat := .node node661 node3870 +def node3872 : Tree Nat := .node node3871 node2630 +def node3873 : Tree Nat := .node node3872 node3613 +def node3874 : Tree Nat := .node node3045 node3873 +def node3875 : Tree Nat := .leaf 283625967792006058808176788520780685867492418066007491201189893723442824551350970123355754690799848970609659759686161428713315725330136504846391572618333767301051332825870557568179582599959524411273567651545935913814096349338254155941743803110667205351507877880483777908110786560 +def node3876 : Tree Nat := .node node693 node3875 +def node3877 : Tree Nat := .node node692 node3876 +def node3878 : Tree Nat := .node node3877 node2436 +def node3879 : Tree Nat := .leaf 386934476812402743627727392523500921566280650861543810810833688600272656829864755526934152793203699424739223387141485277957077195464937440448544928399212799230394441230094078431208333942694469970496659748813203267893573546255848144256064926184361509703872272851271680 +def node3880 : Tree Nat := .node node708 node3879 +def node3881 : Tree Nat := .node node707 node3880 +def node3882 : Tree Nat := .node node3881 node3259 +def node3883 : Tree Nat := .node node3878 node3882 +def node3884 : Tree Nat := .leaf 1342448621178513806457130496891008054252581523695499337317567954795831125250917382469310199960529455098251226994640611878487352847987814532833360595698339669711540983186525567293756309131827130136486250385863058475434244700315824231969943145615982592 +def node3885 : Tree Nat := .node node724 node3884 +def node3886 : Tree Nat := .node node723 node3885 +def node3887 : Tree Nat := .node node3886 node2841 +def node3888 : Tree Nat := .leaf 1790150099102876869021435248250019995303683645961087837873023903202429601313653915871270409447693384026195235419427974469326868836788545837468724169759452914345396290085828876473465373760937127713522365137019312905795752414634069627897879810082340864 +def node3889 : Tree Nat := .node node3616 node3888 +def node3890 : Tree Nat := .node node3889 node747 +def node3891 : Tree Nat := .node node2030 node3890 +def node3892 : Tree Nat := .node node3887 node3891 +def node3893 : Tree Nat := .node node3883 node3892 +def node3894 : Tree Nat := .node node3874 node3893 +def node3895 : Tree Nat := .node node3868 node3894 +def node3896 : Tree Nat := .leaf 2133764618521553367705552573030802495086322663141090611326802499764491916101642262886858304278897373037737571389898636942684416529318196825716273936745865614750450425444484658708185051491780487913268805163483712634141039371992467613172440760320 +def node3897 : Tree Nat := .node node788 node3896 +def node3898 : Tree Nat := .node node787 node3897 +def node3899 : Tree Nat := .node node3898 node2600 +def node3900 : Tree Nat := .node node3899 node3627 +def node3901 : Tree Nat := .node node3006 node3900 +def node3902 : Tree Nat := .leaf 5370122551043688113192634414340729018687074301844027826099173202256324203193672610220328498265936146765100341841324571901821048067611455652691449087295010375368994793149683765662534084505722681461718934272819259218265083265309975383166342165419786240 +def node3903 : Tree Nat := .node node819 node3902 +def node3904 : Tree Nat := .node node818 node3903 +def node3905 : Tree Nat := .node node3904 node2397 +def node3906 : Tree Nat := .leaf 6491683198595054907538359059679767099519165326776190606872841682895938675156205829827954246070653506325448497533049877936699207677031205602503774949860278085600379091695222156172265173571251819817722568655078874469199831720657246054702495236910965947804916669572092495134720 +def node3907 : Tree Nat := .node node834 node3906 +def node3908 : Tree Nat := .node node833 node3907 +def node3909 : Tree Nat := .node node3908 node3220 +def node3910 : Tree Nat := .node node3905 node3909 +def node3911 : Tree Nat := .node node3910 node2796 +def node3912 : Tree Nat := .node node3901 node3911 +def node3913 : Tree Nat := .leaf 396220898351748940262924391034580082446911282557105712257184269735696308556763500769409061650186262571756801724068211526934337185306644629595040724591803238912237341311010068534628648213463908602364998261936873948798022164385518870834400336120765455401249618883243933696 +def node3914 : Tree Nat := .node node882 node3913 +def node3915 : Tree Nat := .node node881 node3914 +def node3916 : Tree Nat := .node node3915 node2280 +def node3917 : Tree Nat := .leaf 1407659405400881293119592067907985661495954923790531913127106135767993417991105945240139412233812133909103878597132274241096754499931670611580273919994982217507448797985794233250617815604214764809996206484606742403936938570878365709862115103857424562388992 +def node3918 : Tree Nat := .node node897 node3917 +def node3919 : Tree Nat := .node node896 node3918 +def node3920 : Tree Nat := .node node3919 node3112 +def node3921 : Tree Nat := .node node3916 node3920 +def node3922 : Tree Nat := .leaf 106359737525781373700957022117933502290615026150268396679865807767377546568936562432141426383331230177709482720886973175926764122445281329797387784268544023861283739517889897255530235402099396925075884488091706668575396008252642462527799214285489968599249047065005752362161143808 +def node3923 : Tree Nat := .node node3631 node3922 +def node3924 : Tree Nat := .node node3923 node936 +def node3925 : Tree Nat := .node node931 node3924 +def node3926 : Tree Nat := .node node2709 node3925 +def node3927 : Tree Nat := .node node3921 node3926 +def node3928 : Tree Nat := .leaf 6491683198595054547177551277054161061914420602222566823797224233463116773185776810152759537540890347877687328901197238280256940476887057079167568042282935937651496162503584746782412137330462679027746409487017930418885405521849737370608323007000830491164478189417372896460800 +def node3929 : Tree Nat := .node node3637 node3928 +def node3930 : Tree Nat := .node node943 node3929 +def node3931 : Tree Nat := .node node3930 node2483 +def node3932 : Tree Nat := .node node3931 node3329 +def node3933 : Tree Nat := .leaf 4431655730257012840500151247598389094333148860437198935663687543473576294143884265310279872035561008209194541707385439878087331595002717726213210409974759413892464193445561772877042655512009941244785796256264491421379937999613740670655100590829722248160933947389342391207985152 +def node3934 : Tree Nat := .node node3642 node3933 +def node3935 : Tree Nat := .node node3934 node997 +def node3936 : Tree Nat := .node node2077 node3935 +def node3937 : Tree Nat := .node node2889 node3936 +def node3938 : Tree Nat := .node node3932 node3937 +def node3939 : Tree Nat := .node node3927 node3938 +def node3940 : Tree Nat := .node node3912 node3939 +def node3941 : Tree Nat := .node node3895 node3940 +def node3942 : Tree Nat := .node node3837 node3941 +def node3943 : Tree Nat := .leaf 5038209277188451174950782032032735533241519514921488084978120461898471455085793951279383971555930013573806614822582945671441806338746192925240270958653793190179805586552231393474589184854121620238917998079490324833094542726062146543199550331874269669972187723857920 +def node3944 : Tree Nat := .node node1086 node3943 +def node3945 : Tree Nat := .node node1085 node3944 +def node3946 : Tree Nat := .node node3945 node3161 +def node3947 : Tree Nat := .node node2330 node3946 +def node3948 : Tree Nat := .node node3947 node3667 +def node3949 : Tree Nat := .node node3662 node3948 +def node3950 : Tree Nat := .leaf 5038209258419659102939031717574155078837684942886299676153494321170844943644377560210125473720109119374230956507143244254767631936489098815470617721781455537617741138146509881170381417104643695282248157243536448468573318315432241739558397443507580165797462744760320 +def node3951 : Tree Nat := .node node1196 node3950 +def node3952 : Tree Nat := .node node1195 node3951 +def node3953 : Tree Nat := .node node3952 node2446 +def node3954 : Tree Nat := .node node3953 node3270 +def node3955 : Tree Nat := .node node3954 node3674 +def node3956 : Tree Nat := .node node3488 node3955 +def node3957 : Tree Nat := .node node3949 node3956 +def node3958 : Tree Nat := .leaf 5038209258419659172858230476819102047443924074715425260092982646010980130135879357014175808506018187399551077312107017410262889094988001597367623636948814508650907045741438551140092282477424042065862234562203932980330184937270594527021585675161913700307732392837120 +def node3959 : Tree Nat := .node node1353 node3958 +def node3960 : Tree Nat := .node node1352 node3959 +def node3961 : Tree Nat := .node node3960 node2804 +def node3962 : Tree Nat := .node node3961 node1378 +def node3963 : Tree Nat := .node node3202 node3962 +def node3964 : Tree Nat := .node node3419 node3963 +def node3965 : Tree Nat := .leaf 14322947932527751047429056869870802812671392806493648684794573761204384728699272417221811301540877574054683416252504293890528058998992608462213168098171746946388397845725945668276129812253577065622376876694192743782897644792128205655531424696722522112 +def node3966 : Tree Nat := .node node3522 node3965 +def node3967 : Tree Nat := .node node3966 node1439 +def node3968 : Tree Nat := .node node1434 node3967 +def node3969 : Tree Nat := .node node2680 node3968 +def node3970 : Tree Nat := .node node3682 node3969 +def node3971 : Tree Nat := .leaf 970323807687943084468112180289064097035553760697935381961907523766281845428985553956799005517904048719054831685706920753857237527571758994652679546900738212002784360013031190968915803519749028015789374496072792969308029283635036160 +def node3972 : Tree Nat := .node node1496 node3971 +def node3973 : Tree Nat := .node node3972 node1500 +def node3974 : Tree Nat := .node node2095 node3973 +def node3975 : Tree Nat := .node node2907 node3974 +def node3976 : Tree Nat := .node node3310 node3975 +def node3977 : Tree Nat := .node node3970 node3976 +def node3978 : Tree Nat := .node node3964 node3977 +def node3979 : Tree Nat := .node node3957 node3978 +def node3980 : Tree Nat := .leaf 307507890453396678158617067384810577610188427909214633367327926694492705727511880445237178556119005118142824939461480863674763442553400389408688761326571475062093088275831667856087407567891456483354370795329668807916141508489389790806521387003615660278410117120 +def node3981 : Tree Nat := .node node1526 node3980 +def node3982 : Tree Nat := .node node1525 node3981 +def node3983 : Tree Nat := .node node3982 node2984 +def node3984 : Tree Nat := .node node2144 node3983 +def node3985 : Tree Nat := .node node3984 node3388 +def node3986 : Tree Nat := .node node3985 node3692 +def node3987 : Tree Nat := .leaf 82546020797455584050393612812824354874414380115598372038388889121945788621835792202920314527460317177612264211353432306557373706427003467767285013132777633397685504510053816246182691595555420345373396869606250768392722766956838141838778905626007500983506362361142312960 +def node3988 : Tree Nat := .node node3694 node3987 +def node3989 : Tree Nat := .node node1635 node3988 +def node3990 : Tree Nat := .node node3989 node2260 +def node3991 : Tree Nat := .node node3990 node3063 +def node3992 : Tree Nat := .node node3991 node3496 +def node3993 : Tree Nat := .leaf 3580081700695792870399535724574524629625619903045113380443533919954444474421853919006620866540372510284318831770441627686884890560469131366002810521360229952787048660529569360389442997012951655592084656402937374747621778084508957027713885394949898240 +def node3994 : Tree Nat := .node node1747 node3993 +def node3995 : Tree Nat := .node node3994 node1751 +def node3996 : Tree Nat := .node node2057 node3995 +def node3997 : Tree Nat := .node node2861 node3996 +def node3998 : Tree Nat := .node node3704 node3997 +def node3999 : Tree Nat := .node node3992 node3998 +def node4000 : Tree Nat := .node node3986 node3999 +def node4001 : Tree Nat := .leaf 82546020797455584050393617080353576019735791143578806845886515820389882602306870751366426518956189545677773350969807539675648630529160404684410484755416806264299586162619632642418898705550779514963749896904472465626396814561412535931206700919506778257759550012569681920 +def node4002 : Tree Nat := .node node1792 node4001 +def node4003 : Tree Nat := .node node1791 node4002 +def node4004 : Tree Nat := .node node4003 node2619 +def node4005 : Tree Nat := .node node4004 node3456 +def node4006 : Tree Nat := .node node3712 node4005 +def node4007 : Tree Nat := .node node4006 node3242 +def node4008 : Tree Nat := .node node4007 node3727 +def node4009 : Tree Nat := .node node4000 node4008 +def node4010 : Tree Nat := .node node3979 node4009 +def node4011 : Tree Nat := .node node3942 node4010 +def node4012 : Tree Nat := .leaf 4327788799063369938358906039786514733686659991111267002964750199774241231704086128711648433962413955584303182974979549405715530762430078814852912465377306534215350030291850950715526940601521297047749872166048782515897426340433349468738567280986331168819527095179048220884996 +def node4013 : Tree Nat := .node node4012 node3732 +def node4014 : Tree Nat := .node node2 node4013 +def node4015 : Tree Nat := .leaf 1584883593408437182288149857193704281834079755425736424225843631759063864353201003683274660150897466442150608604894308408330506127330939688359546966095076931219234913787742880075332006324127955802251414643799001327884322182476316641611770142788008235334965745445100322816 +def node4016 : Tree Nat := .node node10 node4015 +def node4017 : Tree Nat := .node node2067 node4016 +def node4018 : Tree Nat := .node node4014 node4017 +def node4019 : Tree Nat := .leaf 2135987035920910082395021706169552114602704522356652769947041607822219725780640550022962103713792 +def node4020 : Tree Nat := .node node4019 node19 +def node4021 : Tree Nat := .node node17 node4020 +def node4022 : Tree Nat := .leaf 2554685341518452758919237426069541239754648489584243248130787338226088434540964770630848661445639579404617557265482625320952904084313665088840186479791880530663026792655089622415478154238440113647444649432609701929842311068152639492652680489977111990574727588539770837579765955723430324621803520 +def node4023 : Tree Nat := .node node25 node4022 +def node4024 : Tree Nat := .node node2870 node4023 +def node4025 : Tree Nat := .node node4021 node4024 +def node4026 : Tree Nat := .node node4018 node4025 +def node4027 : Tree Nat := .leaf 497323236409786642155382248146820840100456150797347717440463976893159497012533375533312 +def node4028 : Tree Nat := .node node4027 node3737 +def node4029 : Tree Nat := .node node33 node4028 +def node4030 : Tree Nat := .leaf 6807023201651555654745434527164761616181671626072234442189491167099468469303198752637350242948394673005219227861536703475571913793484758347605494536649635180950258430984563788240565977881618004035425302297784604103678911746779791990346343718848486283999279825435320514750091100160 +def node4031 : Tree Nat := .node node41 node4030 +def node4032 : Tree Nat := .node node2512 node4031 +def node4033 : Tree Nat := .node node4029 node4032 +def node4034 : Tree Nat := .node node4033 node3541 +def node4035 : Tree Nat := .node node4026 node4034 +def node4036 : Tree Nat := .leaf 4538015484673128766171577568051408829129253711688905441017270071213568949015601252517454566735934103205789848084469788332364839965613848223691087111498988025028718775827143512882654997922784868541227627112076097602987810689029292312260857121809678250509706534069867051881762652192 +def node4037 : Tree Nat := .node node4036 node67 +def node4038 : Tree Nat := .node node65 node4037 +def node4039 : Tree Nat := .leaf 103866931177520872754840820432866496974457535077309780222534099080316302633872561171546227845560504397596143450834297555297700588978703998107753967477641624336804089167676391588245966227326849722552988383617585329762735546581299050349539537472789507569655201313142472376844288 +def node4040 : Tree Nat := .node node73 node4039 +def node4041 : Tree Nat := .node node2309 node4040 +def node4042 : Tree Nat := .node node4038 node4041 +def node4043 : Tree Nat := .node node4042 node3104 +def node4044 : Tree Nat := .leaf 32592575621351777380295131014550050576823494298654980010178247189670100796213387298934423552 +def node4045 : Tree Nat := .node node4044 node3743 +def node4046 : Tree Nat := .node node96 node4045 +def node4047 : Tree Nat := .leaf 76283967404910271121540606155089898734733648345126935749561096382907755712328744362867134533652820785256674530436899517488320223096453662809669608810552844302666404114954691533259812824499473901443270743634628728671275508662835248522459175639886159658517913909797582727859162394193297408 +def node4048 : Tree Nat := .node node104 node4047 +def node4049 : Tree Nat := .node node2698 node4048 +def node4050 : Tree Nat := .node node4046 node4049 +def node4051 : Tree Nat := .leaf 1766847064778384329583297500742918515827483896875618958121606201292619777 +def node4052 : Tree Nat := .node node4051 node117 +def node4053 : Tree Nat := .node node4052 node120 +def node4054 : Tree Nat := .node node3749 node4053 +def node4055 : Tree Nat := .node node4050 node4054 +def node4056 : Tree Nat := .node node4043 node4055 +def node4057 : Tree Nat := .node node4035 node4056 +def node4058 : Tree Nat := .leaf 29642774844752946028434172162224104410437116074403984394101141506025761187823632 +def node4059 : Tree Nat := .node node4058 node3754 +def node4060 : Tree Nat := .node node128 node4059 +def node4061 : Tree Nat := .node node4060 node2193 +def node4062 : Tree Nat := .node node4061 node2996 +def node4063 : Tree Nat := .leaf 127314748520905380391777855525586135065716774604121015664758778084648831235208544136466432 +def node4064 : Tree Nat := .node node4063 node161 +def node4065 : Tree Nat := .node node159 node4064 +def node4066 : Tree Nat := .leaf 19490628603665978034840773681243539961557360016463531326936773483086779926822171408214188547845393368511684281602943816911048437564228549634134766698418502582185456096385930609530592569841986138228152651895622610228401354471004088515664636667304704799350041282788674412188623126767167602688 +def node4067 : Tree Nat := .node node167 node4066 +def node4068 : Tree Nat := .node node2590 node4067 +def node4069 : Tree Nat := .node node4065 node4068 +def node4070 : Tree Nat := .node node4069 node3762 +def node4071 : Tree Nat := .node node4062 node4070 +def node4072 : Tree Nat := .leaf 1942668892225729070919461906823518906642406839052139521251812409738904285205208498240 +def node4073 : Tree Nat := .node node4072 node3765 +def node4074 : Tree Nat := .node node190 node4073 +def node4075 : Tree Nat := .node node4074 node2388 +def node4076 : Tree Nat := .node node4075 node3212 +def node4077 : Tree Nat := .leaf 8343699359066055009355553539724812947666814540455674882605631280555545803830627148527196700672 +def node4078 : Tree Nat := .node node4077 node3770 +def node4079 : Tree Nat := .node node221 node4078 +def node4080 : Tree Nat := .node node4079 node2824 +def node4081 : Tree Nat := .leaf 4127552950335700185474827592214072194001970501836583918977266660048293214675395339397828890805210218063420076089665893252592400998382560742555297555176633156508586729658050673393437568761396341196472410418471994093143082686944831614089455694705112702037908491683758082 +def node4082 : Tree Nat := .node node4081 node3774 +def node4083 : Tree Nat := .node node4082 node245 +def node4084 : Tree Nat := .node node2013 node4083 +def node4085 : Tree Nat := .node node4080 node4084 +def node4086 : Tree Nat := .node node4076 node4085 +def node4087 : Tree Nat := .node node4071 node4086 +def node4088 : Tree Nat := .node node4057 node4087 +def node4089 : Tree Nat := .leaf 69244620785013915169893880288577664649638356718206520148356066053544201755915040781030818563707002931730762300556198370198467059319135998738502644985094416224536059445117594392163977484884566481703844929172853945635267500147671706758678678069843254071068122219554924992135176 +def node4090 : Tree Nat := .node node4089 node3782 +def node4091 : Tree Nat := .node node254 node4090 +def node4092 : Tree Nat := .leaf 25359685232396118344188732546456419720150332619533882545491048820937314225483437088018660568885159823764625991970808387603640606764703284135512557815229785756843724227678079281095406393738872832209833759217215790932864864653265696481747855757525416820001132555114351951872 +def node4093 : Tree Nat := .node node262 node4092 +def node4094 : Tree Nat := .node node2153 node4093 +def node4095 : Tree Nat := .node node4091 node4094 +def node4096 : Tree Nat := .node node4095 node2957 +def node4097 : Tree Nat := .leaf 7957171782556586274486115970349133441607298412757563479047423630290551952200534008529920 +def node4098 : Tree Nat := .node node4097 node287 +def node4099 : Tree Nat := .node node285 node4098 +def node4100 : Tree Nat := .leaf 2359768043238669411178565976067957431848923659859878902310184835340237859263337018565330577203373114949631763827210528522449903343760226342929784857706436784079421499733517866364126382793685373451307317525704185019394620750660698382085240017643134164936106734729476424158807316234240 +def node4101 : Tree Nat := .node node293 node4100 +def node4102 : Tree Nat := .node node2551 node4101 +def node4103 : Tree Nat := .node node4099 node4102 +def node4104 : Tree Nat := .node node4103 node3790 +def node4105 : Tree Nat := .node node4096 node4104 +def node4106 : Tree Nat := .leaf 121416805764108066932466369176469931665150427440758720078238275608681517825325531200 +def node4107 : Tree Nat := .node node4106 node3793 +def node4108 : Tree Nat := .node node316 node4107 +def node4109 : Tree Nat := .leaf 1661870898840333964077453126925863951591320561236956483560545585285060842141960978744739645528968070361538295213348760884763209423659263969724063479642265989388865426682822265411935459637229595560847814137881365276203768745300784805592632599564632121114483221010279558029508608 +def node4110 : Tree Nat := .node node324 node4109 +def node4111 : Tree Nat := .node node2348 node4110 +def node4112 : Tree Nat := .node node4108 node4111 +def node4113 : Tree Nat := .node node4112 node3182 +def node4114 : Tree Nat := .leaf 521481209941628438084722096232800809229175908778479680162851955034721612739414196782949990400 +def node4115 : Tree Nat := .node node4114 node3798 +def node4116 : Tree Nat := .node node347 node4115 +def node4117 : Tree Nat := .node node4116 node2785 +def node4118 : Tree Nat := .leaf 185074578797901741880056797082722491652594329967104984657651428941017502866551504889831353286343393081484762513295539999743888383402206229143653783207108769584085106800684616437859902199135058135254172214134845481269485109249 +def node4119 : Tree Nat := .node node4118 node3802 +def node4120 : Tree Nat := .node node4119 node371 +def node4121 : Tree Nat := .node node366 node4120 +def node4122 : Tree Nat := .node node4117 node4121 +def node4123 : Tree Nat := .node node4113 node4122 +def node4124 : Tree Nat := .node node4105 node4123 +def node4125 : Tree Nat := .leaf 70906491683854253070072331218981063655902577448435742967067236238248175601478738248918999512888940417370844905815175098223849718145899221368344070297458002192578743016374594256826799000631354426195534712996854019179512934085564995663054180435628132340881422198874009160329986064 +def node4126 : Tree Nat := .node node4125 node381 +def node4127 : Tree Nat := .node node379 node4126 +def node4128 : Tree Nat := .node node4127 node2232 +def node4129 : Tree Nat := .node node4128 node3812 +def node4130 : Tree Nat := .leaf 2037035976334486086268445688409378161051468393665936250636140449354381299763336706183413760 +def node4131 : Tree Nat := .node node4130 node3814 +def node4132 : Tree Nat := .node node410 node4131 +def node4133 : Tree Nat := .node node4132 node2660 +def node4134 : Tree Nat := .node node4133 node3821 +def node4135 : Tree Nat := .node node4129 node4134 +def node4136 : Tree Nat := .leaf 18152061871066687778296661354368903323621809078354772711935094637964933221171650581015415390625850576347222485398317875866793592221273485683496094478891500200912313990635464124912452863194272287610730100521231584558141129784606065006780015229799157562234958782104722839658267934848 +def node4137 : Tree Nat := .node node4136 node3824 +def node4138 : Tree Nat := .node node441 node4137 +def node4139 : Tree Nat := .leaf 425438950103125494805269443724151674051532525954198637108871527674937080267384167241679774515438718500479706332744706411622303984140235025072243327396350123989807749724877361736183105236268229758425673062476345429873600914237238214453345370585125269492206510444981569607440531456 +def node4140 : Tree Nat := .node node449 node4139 +def node4141 : Tree Nat := .node node2426 node4140 +def node4142 : Tree Nat := .node node4138 node4141 +def node4143 : Tree Nat := .node node4142 node3290 +def node4144 : Tree Nat := .leaf 133499189745056880149688856635597007162669032647290798121690100488888732861290034376435134627840 +def node4145 : Tree Nat := .node node4144 node473 +def node4146 : Tree Nat := .node node471 node4145 +def node4147 : Tree Nat := .leaf 3045410628562499712610431996210996347148820892998439852146220767879046465864508157020504708088128206007907786322315208807330990582875966889555621030097704193603524281236397821834621767340641765110249872962255743398026749351685898420545738629834051754008668375970086733463071434372473159680 +def node4148 : Tree Nat := .node node479 node4147 +def node4149 : Tree Nat := .node node2878 node4148 +def node4150 : Tree Nat := .node node4146 node4149 +def node4151 : Tree Nat := .leaf 7237005577332262213973186563042994240829374041602535252466099000494570602500 +def node4152 : Tree Nat := .node node4151 node3829 +def node4153 : Tree Nat := .node node4152 node495 +def node4154 : Tree Nat := .node node2021 node4153 +def node4155 : Tree Nat := .node node4150 node4154 +def node4156 : Tree Nat := .node node4143 node4155 +def node4157 : Tree Nat := .node node4135 node4156 +def node4158 : Tree Nat := .node node4124 node4157 +def node4159 : Tree Nat := .node node4088 node4158 +def node4160 : Tree Nat := .leaf 463168356949264781694283940034751631413079938662562256157830336031652518559752 +def node4161 : Tree Nat := .node node4160 node3838 +def node4162 : Tree Nat := .node node505 node4161 +def node4163 : Tree Nat := .leaf 6339534373627982956228077418998199278226167912433458265535528508320086830680698313693007070651886254736092739919085544146588170714032226447006467741555274922900640207988061010024778212117117292636290794898534260849776339513018740866060762785204437717874462970772855980032 +def node4164 : Tree Nat := .node node513 node4163 +def node4165 : Tree Nat := .node node2123 node4164 +def node4166 : Tree Nat := .node node4162 node4165 +def node4167 : Tree Nat := .node node4166 node3845 +def node4168 : Tree Nat := .leaf 1989292945639146568621528992587283360401824603189390869761855907572637988050133502132736 +def node4169 : Tree Nat := .node node4168 node3847 +def node4170 : Tree Nat := .node node536 node4169 +def node4171 : Tree Nat := .leaf 27228092806600031667444992031553354982872196075306295026655978869310436837653888675753814352346612864803443428775506098335960423197233380879959056050458885970147171150771359996509150570696369693668930586835048288685322547123008058254829692511266932672339693093032420278755469033472 +def node4172 : Tree Nat := .node node544 node4171 +def node4173 : Tree Nat := .node node2521 node4172 +def node4174 : Tree Nat := .node node4170 node4173 +def node4175 : Tree Nat := .node node4174 node3854 +def node4176 : Tree Nat := .node node4167 node4175 +def node4177 : Tree Nat := .leaf 64489078507771637412585350103284506207282228156357443329190177868940545665739255769781450348877032798714253789594969822851364980415846420446305582552944825710731610185490413454593181246065229179470053335512802636265709283484670470135556316201641397534318430959697952 +def node4178 : Tree Nat := .node node4177 node3857 +def node4179 : Tree Nat := .node node567 node4178 +def node4180 : Tree Nat := .node node4179 node2319 +def node4181 : Tree Nat := .node node4180 node3152 +def node4182 : Tree Nat := .leaf 130370302485407109521180524058200202307293977194619920040712988758680403184853549195737563136 +def node4183 : Tree Nat := .node node4182 node600 +def node4184 : Tree Nat := .node node598 node4183 +def node4185 : Tree Nat := .node node4184 node2747 +def node4186 : Tree Nat := .leaf 49692708741517100404930162553280883400323263580120335617144127691486424773101934148218588629411074240398167893643315732289073775856322241122475267870269188510521661549621084010459068489150180782849196848584279628992773002688542539777 +def node4187 : Tree Nat := .node node4186 node619 +def node4188 : Tree Nat := .node node4187 node622 +def node4189 : Tree Nat := .node node3864 node4188 +def node4190 : Tree Nat := .node node4185 node4189 +def node4191 : Tree Nat := .node node4181 node4190 +def node4192 : Tree Nat := .node node4176 node4191 +def node4193 : Tree Nat := .leaf 118571099379011784113736688648896417641748464297615937576404566024103044751294480 +def node4194 : Tree Nat := .node node4193 node632 +def node4195 : Tree Nat := .node node630 node4194 +def node4196 : Tree Nat := .node node4195 node2241 +def node4197 : Tree Nat := .node node4196 node3044 +def node4198 : Tree Nat := .leaf 509258994083621521567111422102344540262867098416484062659035112338595324940834176545857536 +def node4199 : Tree Nat := .node node4198 node3869 +def node4200 : Tree Nat := .node node661 node4199 +def node4201 : Tree Nat := .node node4200 node2630 +def node4202 : Tree Nat := .node node4201 node3613 +def node4203 : Tree Nat := .node node4197 node4202 +def node4204 : Tree Nat := .leaf 7770675568902916283677847627294075626569627356208558085007249638955617140820833992832 +def node4205 : Tree Nat := .node node4204 node3875 +def node4206 : Tree Nat := .node node692 node4205 +def node4207 : Tree Nat := .node node4206 node2436 +def node4208 : Tree Nat := .node node4207 node3882 +def node4209 : Tree Nat := .leaf 33374797436264220037422214158899251790667258161822699530422525122222183215322508594108784705536 +def node4210 : Tree Nat := .node node4209 node3884 +def node4211 : Tree Nat := .node node723 node4210 +def node4212 : Tree Nat := .node node4211 node2841 +def node4213 : Tree Nat := .leaf 257956317875169772319385075231187213055505109751773041230046415222586106579360230874766909130404030621746093094006436657873295790476388149177752823499062326111512108516004589725025843145699535201381121900283479086178354114154084056723016302218508900817544254354096130 +def node4214 : Tree Nat := .node node4213 node3888 +def node4215 : Tree Nat := .node node4214 node747 +def node4216 : Tree Nat := .node node2030 node4215 +def node4217 : Tree Nat := .node node4212 node4216 +def node4218 : Tree Nat := .node node4208 node4217 +def node4219 : Tree Nat := .node node4203 node4218 +def node4220 : Tree Nat := .node node4192 node4219 +def node4221 : Tree Nat := .leaf 7410693711188236507108543040556026102609279018600996098525285376506440296955912 +def node4222 : Tree Nat := .node node4221 node758 +def node4223 : Tree Nat := .node node756 node4222 +def node4224 : Tree Nat := .leaf 101432549978047727299649238703971188451618686598935332248568456133121389290891173019088113130430180075777483838705368706345410731424515623152103483864884398766410243327808976160396451393873876682180652718376548173596421432208299853856972204563271003485991407532365695680512 +def node4225 : Tree Nat := .node node764 node4224 +def node4226 : Tree Nat := .node node2162 node4225 +def node4227 : Tree Nat := .node node4223 node4226 +def node4228 : Tree Nat := .node node4227 node3005 +def node4229 : Tree Nat := .leaf 31828687130226345097944463881396533766429193651030253916189694521162207808802136034117632 +def node4230 : Tree Nat := .node node4229 node3896 +def node4231 : Tree Nat := .node node787 node4230 +def node4232 : Tree Nat := .node node4231 node2600 +def node4233 : Tree Nat := .node node4232 node3627 +def node4234 : Tree Nat := .node node4228 node4233 +def node4235 : Tree Nat := .leaf 485667223056432267729865476705879726660601709763034880312953102434726071301302124608 +def node4236 : Tree Nat := .node node4235 node3902 +def node4237 : Tree Nat := .node node818 node4236 +def node4238 : Tree Nat := .node node4237 node2397 +def node4239 : Tree Nat := .node node4238 node3909 +def node4240 : Tree Nat := .leaf 2085924839766513752338888384931203236916703635113918720651407820138886450957656787131799437312 +def node4241 : Tree Nat := .node node4240 node851 +def node4242 : Tree Nat := .node node849 node4241 +def node4243 : Tree Nat := .node node4242 node2794 +def node4244 : Tree Nat := .leaf 113078212145816597093331040047546785012958969400039613319782796882727665666 +def node4245 : Tree Nat := .node node4244 node870 +def node4246 : Tree Nat := .node node4245 node873 +def node4247 : Tree Nat := .node node868 node4246 +def node4248 : Tree Nat := .node node4243 node4247 +def node4249 : Tree Nat := .node node4239 node4248 +def node4250 : Tree Nat := .node node4234 node4249 +def node4251 : Tree Nat := .leaf 1897137590064188545819787018382342682267975428761855001222473056385648716020711456 +def node4252 : Tree Nat := .node node4251 node3913 +def node4253 : Tree Nat := .node node881 node4252 +def node4254 : Tree Nat := .node node4253 node2280 +def node4255 : Tree Nat := .node node4254 node3920 +def node4256 : Tree Nat := .leaf 8148143905337944345073782753637512644205873574663745002544561797417525199053346824733622272 +def node4257 : Tree Nat := .node node4256 node914 +def node4258 : Tree Nat := .node node912 node4257 +def node4259 : Tree Nat := .leaf 76172441136774437391830751467728656192723803830002481165131913493459060163041714034851246910065609058962439626152635044509536129203037794881585296516970164705732681301921132042714111343761901571178002803950952370880820427509819407515847393219360010302292010526888521934397379993032196096 +def node4260 : Tree Nat := .node node920 node4259 +def node4261 : Tree Nat := .node node2707 node4260 +def node4262 : Tree Nat := .node node4258 node4261 +def node4263 : Tree Nat := .node node4262 node3925 +def node4264 : Tree Nat := .node node4255 node4263 +def node4265 : Tree Nat := .leaf 22158278651204452854366041692344852687884274149826086447473941137134144561892813049929861940386240938153843936177983478463509458982123519596320846395230213191851539022437630205492472795163061398475446624285078742528278953309220489188606133997791121730853999570011313907070664832 +def node4266 : Tree Nat := .node node4265 node3928 +def node4267 : Tree Nat := .node node943 node4266 +def node4268 : Tree Nat := .node node4267 node2483 +def node4269 : Tree Nat := .node node4268 node3329 +def node4270 : Tree Nat := .leaf 533996758980227520598755426542388028650676130589163192486760401955554931445160137505740530122752 +def node4271 : Tree Nat := .node node4270 node975 +def node4272 : Tree Nat := .node node973 node4271 +def node4273 : Tree Nat := .node node4272 node2888 +def node4274 : Tree Nat := .leaf 1107981554260208007869835184109711948519848119949036945928529435827462642354167913278505822428065667027742715131458310835646369889593792323564810388750753915858421224617433382925397237392415646291686692141755470545300432670568247575607956365342296671552989339341209927432536068 +def node4275 : Tree Nat := .node node4274 node3933 +def node4276 : Tree Nat := .node node4275 node997 +def node4277 : Tree Nat := .node node2077 node4276 +def node4278 : Tree Nat := .node node4273 node4277 +def node4279 : Tree Nat := .node node4269 node4278 +def node4280 : Tree Nat := .node node4264 node4279 +def node4281 : Tree Nat := .node node4250 node4280 +def node4282 : Tree Nat := .node node4220 node4281 +def node4283 : Tree Nat := .node node4159 node4282 +def node4284 : Tree Nat := .leaf 264147265567892686976580031625726659363614910878666845535570007101838667417133359551525753716459600010124949597967474383030247018866723567629094481178798724970631006998331577673670915950541322205371192038855985702395455421466371177941843730407534277651613515738402258948 +def node4285 : Tree Nat := .node node4284 node1010 +def node4286 : Tree Nat := .node node1008 node4285 +def node4287 : Tree Nat := .node node4286 node2134 +def node4288 : Tree Nat := .leaf 4271974071841820164790043412339104229205409044713305539894083215644439451561281100045924190650368 +def node4289 : Tree Nat := .node node4288 node1025 +def node4290 : Tree Nat := .node node1023 node4289 +def node4291 : Tree Nat := .node node4290 node2936 +def node4292 : Tree Nat := .node node4287 node4291 +def node4293 : Tree Nat := .leaf 994646472819573284310764496293641680200912301594695434880927953786318994025066751066368 +def node4294 : Tree Nat := .node node4293 node1041 +def node4295 : Tree Nat := .node node1039 node4294 +def node4296 : Tree Nat := .node node4295 node2532 +def node4297 : Tree Nat := .node node4296 node3660 +def node4298 : Tree Nat := .node node4292 node4297 +def node4299 : Tree Nat := .leaf 15177100720513508366558296147058741458143803430094840009779784451085189728165691424 +def node4300 : Tree Nat := .node node4299 node1072 +def node4301 : Tree Nat := .node node1070 node4300 +def node4302 : Tree Nat := .node node4301 node2329 +def node4303 : Tree Nat := .leaf 3832013394306662038380235609030730046849506420036078479684890705479446832388411006307119293745860546091537497940849590868427080937715699828619209852706876327014410892066084498913672425173176935390694444949524334067195156073832071146666602115420244782413672141201451599953328310842260499061538816 +def node4304 : Tree Nat := .node node1093 node4303 +def node4305 : Tree Nat := .node node3160 node4304 +def node4306 : Tree Nat := .node node3945 node4305 +def node4307 : Tree Nat := .node node4302 node4306 +def node4308 : Tree Nat := .leaf 65185151242703554760590262029100101153646988597309960020356494379340201592426774597868781568 +def node4309 : Tree Nat := .node node4308 node1103 +def node4310 : Tree Nat := .node node1101 node4309 +def node4311 : Tree Nat := .leaf 2436625906231695326700905209468427057831082966439083760608787768675100360823038606491112800133401796076444188802610205640474883383349882492786054990194383833807976019157207749442485951154480271635573946208961065005862613031090094312454222323655311134823537109797160215553021900567741464576 +def node4312 : Tree Nat := .node node1109 node4311 +def node4313 : Tree Nat := .node node2756 node4312 +def node4314 : Tree Nat := .node node4310 node4313 +def node4315 : Tree Nat := .leaf 57278681880282598266741390408408596112073575107801884750380706224728954912021854056104385596147127637774357555095311732689303106074376692652622954979648160308715047559991058126855927576744512779217681303684731971486625110250447625670398125889921482753 +def node4316 : Tree Nat := .node node4315 node1122 +def node4317 : Tree Nat := .node node4316 node1125 +def node4318 : Tree Nat := .node node1120 node4317 +def node4319 : Tree Nat := .node node4314 node4318 +def node4320 : Tree Nat := .node node4307 node4319 +def node4321 : Tree Nat := .node node4298 node4320 +def node4322 : Tree Nat := .leaf 59285549689505892056868344324448208820874232148807968788202283012051522375647248 +def node4323 : Tree Nat := .node node4322 node1135 +def node4324 : Tree Nat := .node node1133 node4323 +def node4325 : Tree Nat := .node node4324 node2212 +def node4326 : Tree Nat := .node node4325 node3054 +def node4327 : Tree Nat := .leaf 254629497041810760783555711051172270131433549208242031329517556169297662470417088272928768 +def node4328 : Tree Nat := .node node4327 node1166 +def node4329 : Tree Nat := .node node1164 node4328 +def node4330 : Tree Nat := .leaf 3485195879244804053432958980038829437807641097639205763411965295271735915219697750496488237100366446694840758883264780587002934169245872752634759174458737404178837907298734079553171273049135320789623115114886180951721286031745031456618200641442167382059480715908149795680700036284416 +def node4331 : Tree Nat := .node node1172 node4330 +def node4332 : Tree Nat := .node node2639 node4331 +def node4333 : Tree Nat := .node node4329 node4332 +def node4334 : Tree Nat := .node node4333 node3486 +def node4335 : Tree Nat := .node node4326 node4334 +def node4336 : Tree Nat := .leaf 3885337784451458141838923813647037813284813678104279042503624819477808570410416996416 +def node4337 : Tree Nat := .node node4336 node3950 +def node4338 : Tree Nat := .node node1195 node4337 +def node4339 : Tree Nat := .node node4338 node2446 +def node4340 : Tree Nat := .node node4339 node3270 +def node4341 : Tree Nat := .leaf 16687398718132110018711107079449625895333629080911349765211262561111091607661254297054392352768 +def node4342 : Tree Nat := .node node4341 node1228 +def node4343 : Tree Nat := .node node1226 node4342 +def node4344 : Tree Nat := .node node4343 node2851 +def node4345 : Tree Nat := .leaf 62977616668685342387325421960217648264250230355977254793400162357726016160706066959434384680823039694200140654924873146729788871606308563376915741358958747515091597100758845709529810885099968320599190713012881073322486147882951892977927282736051327953256977530882 +def node4346 : Tree Nat := .node node4345 node1247 +def node4347 : Tree Nat := .node node4346 node1250 +def node4348 : Tree Nat := .node node2040 node4347 +def node4349 : Tree Nat := .node node4344 node4348 +def node4350 : Tree Nat := .node node4340 node4349 +def node4351 : Tree Nat := .node node4335 node4350 +def node4352 : Tree Nat := .node node4321 node4351 +def node4353 : Tree Nat := .leaf 3705346855594118253554271520278013051304639509300498049262642688253220148477960 +def node4354 : Tree Nat := .node node4353 node1261 +def node4355 : Tree Nat := .node node1259 node4354 +def node4356 : Tree Nat := .node node4355 node2173 +def node4357 : Tree Nat := .node node4356 node2976 +def node4358 : Tree Nat := .leaf 15914343565113172548972231940698266883214596825515126958094847260581103904401068017058816 +def node4359 : Tree Nat := .node node4358 node1292 +def node4360 : Tree Nat := .node node1290 node4359 +def node4361 : Tree Nat := .leaf 2396072166980802786735159298776695238492753254626953962345726140499318441713542203466335663006501932102703021732244536653564517241356537517436396932440381965372951061267879679692805250221280533042865891641484249404308384146824709126425012940991490075165892992186852984530481274945536 +def node4362 : Tree Nat := .node node1298 node4361 +def node4363 : Tree Nat := .node node2570 node4362 +def node4364 : Tree Nat := .node node4360 node4363 +def node4365 : Tree Nat := .node node4364 node3417 +def node4366 : Tree Nat := .node node4357 node4365 +def node4367 : Tree Nat := .leaf 242833611528216133864932738352939863330300854881517440156476551217363035650651062336 +def node4368 : Tree Nat := .node node4367 node1323 +def node4369 : Tree Nat := .node node1321 node4368 +def node4370 : Tree Nat := .node node4369 node2368 +def node4371 : Tree Nat := .node node4370 node3201 +def node4372 : Tree Nat := .leaf 1042962419883256876169444192465601618458351817556959360325703910069443225478828393565899718656 +def node4373 : Tree Nat := .node node4372 node3958 +def node4374 : Tree Nat := .node node1352 node4373 +def node4375 : Tree Nat := .node node4374 node2804 +def node4376 : Tree Nat := .leaf 56539106072908298546665520023773392506479484700019806659891398441363832833 +def node4377 : Tree Nat := .node node4376 node1373 +def node4378 : Tree Nat := .node node4377 node1376 +def node4379 : Tree Nat := .node node1371 node4378 +def node4380 : Tree Nat := .node node4375 node4379 +def node4381 : Tree Nat := .node node4371 node4380 +def node4382 : Tree Nat := .node node4366 node4381 +def node4383 : Tree Nat := .leaf 66036816637964468156759819055481632075417978298957646183090756945133772865340002359174299416448252603766528494444140705221200120529708040432346663027636608041504158084147899646743114732500752828806843890381313734913430309552540681989121982042682908194427282730006872080 +def node4384 : Tree Nat := .node node4383 node1386 +def node4385 : Tree Nat := .node node1384 node4384 +def node4386 : Tree Nat := .node node4385 node2290 +def node4387 : Tree Nat := .node node4386 node3093 +def node4388 : Tree Nat := .leaf 4074071952668972172536891376818756322102936787331872501272280898708762599526673412366811136 +def node4389 : Tree Nat := .node node4388 node1417 +def node4390 : Tree Nat := .node node1415 node4389 +def node4391 : Tree Nat := .leaf 4777041818484878089238775775306555549421673397830804699716667098052459361127799050013853210318902276269728400175994925924585355101313009586278043241791442735327793824937464845040880091592681479695643416450803992024492642720845189783204680345870064091676194901271437319946346183067172864 +def node4392 : Tree Nat := .node node1423 node4391 +def node4393 : Tree Nat := .node node2678 node4392 +def node4394 : Tree Nat := .node node4390 node4393 +def node4395 : Tree Nat := .node node4394 node3968 +def node4396 : Tree Nat := .node node4387 node4395 +def node4397 : Tree Nat := .leaf 62165404551223330269422781018352605012557018849668464680057997111644937126566671941760 +def node4398 : Tree Nat := .node node4397 node1448 +def node4399 : Tree Nat := .node node1446 node4398 +def node4400 : Tree Nat := .node node4399 node2493 +def node4401 : Tree Nat := .node node4400 node3309 +def node4402 : Tree Nat := .leaf 266998379490113760299377713271194014325338065294581596243380200977777465722580068752870265061376 +def node4403 : Tree Nat := .node node4402 node1478 +def node4404 : Tree Nat := .node node1476 node4403 +def node4405 : Tree Nat := .node node4404 node2906 +def node4406 : Tree Nat := .leaf 14474011154664524427946373126085988481658748083205070504932198000989141204996 +def node4407 : Tree Nat := .node node4406 node3971 +def node4408 : Tree Nat := .node node4407 node1500 +def node4409 : Tree Nat := .node node2095 node4408 +def node4410 : Tree Nat := .node node4405 node4409 +def node4411 : Tree Nat := .node node4401 node4410 +def node4412 : Tree Nat := .node node4396 node4411 +def node4413 : Tree Nat := .node node4382 node4412 +def node4414 : Tree Nat := .node node4352 node4413 +def node4415 : Tree Nat := .leaf 926336713898529563388567880069503262826159877325124512315660672063305037119496 +def node4416 : Tree Nat := .node node4415 node1512 +def node4417 : Tree Nat := .node node1510 node4416 +def node4418 : Tree Nat := .node node4417 node2143 +def node4419 : Tree Nat := .node node4418 node3983 +def node4420 : Tree Nat := .leaf 3978585891278293137243057985174566720803649206378781739523711815145275976100267004264960 +def node4421 : Tree Nat := .node node4420 node1543 +def node4422 : Tree Nat := .node node1541 node4421 +def node4423 : Tree Nat := .node node4422 node2580 +def node4424 : Tree Nat := .node node4423 node3387 +def node4425 : Tree Nat := .node node4419 node4424 +def node4426 : Tree Nat := .leaf 4030567421750760995895985049773048056469099047391227855212699350938280458006096623232860680325798628881305858591549929533692822230915488655287349367107025111430694718027481321432317981837273175297969030494103705199223505613847628336802853825632439246623709258055712 +def node4427 : Tree Nat := .node node4426 node1574 +def node4428 : Tree Nat := .node node1572 node4427 +def node4429 : Tree Nat := .node node4428 node2377 +def node4430 : Tree Nat := .node node4429 node3171 +def node4431 : Tree Nat := .leaf 260740604970814219042361048116400404614587954389239840081425977517360806369707098391474995200 +def node4432 : Tree Nat := .node node4431 node1605 +def node4433 : Tree Nat := .node node1603 node4432 +def node4434 : Tree Nat := .node node4433 node2766 +def node4435 : Tree Nat := .leaf 14134776518227074636666380005943348126619871175004951664972849610340958209 +def node4436 : Tree Nat := .node node4435 node1624 +def node4437 : Tree Nat := .node node4436 node1627 +def node4438 : Tree Nat := .node node1622 node4437 +def node4439 : Tree Nat := .node node4434 node4438 +def node4440 : Tree Nat := .node node4430 node4439 +def node4441 : Tree Nat := .node node4425 node4440 +def node4442 : Tree Nat := .leaf 4226356249085321970818718279332132852150778608288972177023685672213391220453798875795338047101257503157395159946057029431058780476021484298004311827703516615267093471992040673349852141411411765566392621289257734706561524134847777407635770422011444621048356853271406575632 +def node4443 : Tree Nat := .node node4442 node3987 +def node4444 : Tree Nat := .node node1635 node4443 +def node4445 : Tree Nat := .node node4444 node2260 +def node4446 : Tree Nat := .node node4445 node3063 +def node4447 : Tree Nat := .leaf 1018517988167243043134222844204689080525734196832968125318070224677190649881668353091706880 +def node4448 : Tree Nat := .node node4447 node1668 +def node4449 : Tree Nat := .node node1666 node4448 +def node4450 : Tree Nat := .node node4449 node2688 +def node4451 : Tree Nat := .node node4450 node3495 +def node4452 : Tree Nat := .node node4446 node4451 +def node4453 : Tree Nat := .leaf 458222462695599379270700542938797415851547826754730440471063195236977024085646466549524548253194054006869752147503995521190349772113174027207120416665033273928205988943208744774074652751019355674508791384847178672032005027722300615756974875345256710272 +def node4454 : Tree Nat := .node node4453 node1699 +def node4455 : Tree Nat := .node node1697 node4454 +def node4456 : Tree Nat := .node node4455 node2463 +def node4457 : Tree Nat := .node node4456 node3279 +def node4458 : Tree Nat := .leaf 66749594872528440074844428317798503581334516323645399060845050244444366430645017188217567313920 +def node4459 : Tree Nat := .node node4458 node1729 +def node4460 : Tree Nat := .node node1727 node4459 +def node4461 : Tree Nat := .node node4460 node2860 +def node4462 : Tree Nat := .leaf 3618502788666131106986593281521497120414687020801267626233049500247285301250 +def node4463 : Tree Nat := .node node4462 node3993 +def node4464 : Tree Nat := .node node4463 node1751 +def node4465 : Tree Nat := .node node2057 node4464 +def node4466 : Tree Nat := .node node4461 node4465 +def node4467 : Tree Nat := .node node4457 node4466 +def node4468 : Tree Nat := .node node4452 node4467 +def node4469 : Tree Nat := .node node4441 node4468 +def node4470 : Tree Nat := .leaf 984025245785313409979642667100198837075336788121429291146728212168925905501427243611624769112066079783908427311760756267587287066326648854280262839710577875902676810476120039447197653492606449244932706879310828502416901927568845044498501159371016548692596359176 +def node4471 : Tree Nat := .node node4470 node1762 +def node4472 : Tree Nat := .node node1760 node4471 +def node4473 : Tree Nat := .node node4472 node2221 +def node4474 : Tree Nat := .node node4473 node3024 +def node4475 : Tree Nat := .leaf 63657374260452690195888927762793067532858387302060507832379389042324415617604272068233216 +def node4476 : Tree Nat := .node node4475 node4001 +def node4477 : Tree Nat := .node node1791 node4476 +def node4478 : Tree Nat := .node node4477 node2619 +def node4479 : Tree Nat := .node node4478 node3456 +def node4480 : Tree Nat := .node node4474 node4479 +def node4481 : Tree Nat := .leaf 971334446112864535459730953411759453321203419526069760625906204869452142602604249152 +def node4482 : Tree Nat := .node node4481 node1824 +def node4483 : Tree Nat := .node node1822 node4482 +def node4484 : Tree Nat := .node node4483 node2416 +def node4485 : Tree Nat := .node node4484 node3240 +def node4486 : Tree Nat := .leaf 4171849679533027504677776769862406473833407270227837441302815640277772901915313574263598350336 +def node4487 : Tree Nat := .node node4486 node1855 +def node4488 : Tree Nat := .node node1853 node4487 +def node4489 : Tree Nat := .leaf 95169082142578116019075999881593635848400652906201245379569398996220202058265879906890772127754006437747118322572350275229093455714873965298613157190553256050110133788637431932331930229395055159695308530070491981188335917240184325642054332182314117312770886749065210420720982324139786240 +def node4490 : Tree Nat := .node node1861 node4489 +def node4491 : Tree Nat := .node node2812 node4490 +def node4492 : Tree Nat := .node node4488 node4491 +def node4493 : Tree Nat := .leaf 226156424291633194186662080095093570025917938800079226639565593765455331330 +def node4494 : Tree Nat := .node node4493 node1874 +def node4495 : Tree Nat := .node node4494 node1877 +def node4496 : Tree Nat := .node node1872 node4495 +def node4497 : Tree Nat := .node node4492 node4496 +def node4498 : Tree Nat := .node node4485 node4497 +def node4499 : Tree Nat := .node node4480 node4498 +def node4500 : Tree Nat := .leaf 3794275180128377091639574036764685364535950857523710002444946112771297432041422880 +def node4501 : Tree Nat := .node node4500 node1887 +def node4502 : Tree Nat := .node node1885 node4501 +def node4503 : Tree Nat := .node node4502 node2299 +def node4504 : Tree Nat := .node node4503 node3132 +def node4505 : Tree Nat := .leaf 16296287810675888690147565507275025288411747149327490005089123594835050398106693649467211776 +def node4506 : Tree Nat := .node node4505 node1918 +def node4507 : Tree Nat := .node node1916 node4506 +def node4508 : Tree Nat := .leaf 2436402853695423659241485500093704572747063277408834851439929402896202969724464545835081024886227372623855718994041676694517315195563050756929886365607218474614108573531140630461394548193005126975043410329593712290281702868784062630440998758814258836111085303031342093966098335765419261952 +def node4509 : Tree Nat := .node node1924 node4508 +def node4510 : Tree Nat := .node node2726 node4509 +def node4511 : Tree Nat := .node node4507 node4510 +def node4512 : Tree Nat := .node node4511 node3718 +def node4513 : Tree Nat := .node node4504 node4512 +def node4514 : Tree Nat := .leaf 776259046150354467574489744231251277628443008558348305569526019013025476343188443165439204414323238975243865348565536603085790022057407195722143886182208774495548565701549026185552693043874621086490219828846680955194929693595795584 +def node4515 : Tree Nat := .node node4514 node1949 +def node4516 : Tree Nat := .node node1947 node4515 +def node4517 : Tree Nat := .node node4516 node2502 +def node4518 : Tree Nat := .node node4517 node3348 +def node4519 : Tree Nat := .leaf 1067993517960455041197510853084776057301352261178326384973520803911109862890320275011481051856896 +def node4520 : Tree Nat := .node node4519 node1979 +def node4521 : Tree Nat := .node node1977 node4520 +def node4522 : Tree Nat := .leaf 2554680468861447058919697249378347302160493051470814450627023904272859828066619387417797428638106638399487944613024509616618812354728732487293163190798232374336317027016239644178963218843612368620620473032812962320652874225353676795215207616795304256091921174670369285440992414809135328664748032 +def node4523 : Tree Nat := .node node1985 node4522 +def node4524 : Tree Nat := .node node2914 node4523 +def node4525 : Tree Nat := .node node4521 node4524 +def node4526 : Tree Nat := .leaf 57896044618658097711785492504343953926634992332820282019728792003956564819972 +def node4527 : Tree Nat := .node node4526 node1998 +def node4528 : Tree Nat := .node node4527 node2001 +def node4529 : Tree Nat := .node node2104 node4528 +def node4530 : Tree Nat := .node node4525 node4529 +def node4531 : Tree Nat := .node node4518 node4530 +def node4532 : Tree Nat := .node node4513 node4531 +def node4533 : Tree Nat := .node node4499 node4532 +def node4534 : Tree Nat := .node node4469 node4533 +def node4535 : Tree Nat := .node node4414 node4534 +def node4536 : Tree Nat := .node node4283 node4535 +def node4537 : Tree Nat := .leaf 39402006196394479212279040100143613805079739270465446667948293404245721771497210611414266254884915712864222028234752 +def node4538 : Tree Nat := .node node4537 node4015 +def node4539 : Tree Nat := .node node2067 node4538 +def node4540 : Tree Nat := .node node4014 node4539 +def node4541 : Tree Nat := .node node4540 node4025 +def node4542 : Tree Nat := .leaf 169230328010303641331690318856389386196071598838855992136870091590247882556495704531248437872567112920988072644888849371103232 +def node4543 : Tree Nat := .node node4542 node4030 +def node4544 : Tree Nat := .node node2512 node4543 +def node4545 : Tree Nat := .node node4029 node4544 +def node4546 : Tree Nat := .leaf 9173994463960286046443283581208347763186259956673124494950355357547691504353939232280074212441602257846272 +def node4547 : Tree Nat := .node node4546 node50 +def node4548 : Tree Nat := .node node48 node4547 +def node4549 : Tree Nat := .node node4548 node3540 +def node4550 : Tree Nat := .node node4545 node4549 +def node4551 : Tree Nat := .node node4541 node4550 +def node4552 : Tree Nat := .leaf 2582249878086908589655919172003011874329705792829223512830659356540647622016841194629645353280137831454349916046457044992 +def node4553 : Tree Nat := .node node4552 node4039 +def node4554 : Tree Nat := .node node2309 node4553 +def node4555 : Tree Nat := .node node4038 node4554 +def node4556 : Tree Nat := .leaf 139984046386112763159840142535527767382602843577165595931249318810236991948760059086304843333770412032 +def node4557 : Tree Nat := .node node4556 node82 +def node4558 : Tree Nat := .node node80 node4557 +def node4559 : Tree Nat := .node node4558 node3103 +def node4560 : Tree Nat := .node node4555 node4559 +def node4561 : Tree Nat := .leaf 601226901190101306339707032778070279008174732520529886901066488712245510429339761526706943586501069451152064512 +def node4562 : Tree Nat := .node node4561 node3747 +def node4563 : Tree Nat := .node node111 node4562 +def node4564 : Tree Nat := .node node4563 node4053 +def node4565 : Tree Nat := .node node4050 node4564 +def node4566 : Tree Nat := .node node4560 node4565 +def node4567 : Tree Nat := .node node4551 node4566 +def node4568 : Tree Nat := .leaf 10086913586276986678343434265636765134100413253239154346994763111486904773503285916522052161250538405199418270125391872 +def node4569 : Tree Nat := .node node4568 node137 +def node4570 : Tree Nat := .node node2192 node4569 +def node4571 : Tree Nat := .node node4060 node4570 +def node4572 : Tree Nat := .leaf 546812681195752981093125556779405341338292357723303109106442651602488249799843980805878294524198912 +def node4573 : Tree Nat := .node node4572 node145 +def node4574 : Tree Nat := .node node143 node4573 +def node4575 : Tree Nat := .node node4574 node2995 +def node4576 : Tree Nat := .node node4571 node4575 +def node4577 : Tree Nat := .leaf 2348542582773833227889480596789337027375682548908319870707290971532209025114608443463698998384786295217979392 +def node4578 : Tree Nat := .node node4577 node3759 +def node4579 : Tree Nat := .node node174 node4578 +def node4580 : Tree Nat := .node node4579 node3553 +def node4581 : Tree Nat := .node node4069 node4580 +def node4582 : Tree Nat := .node node4576 node4581 +def node4583 : Tree Nat := .leaf 661055968790248598951915308032771039828404682964281219284648795274405791236311345825189210439715284847886359930202711130112 +def node4584 : Tree Nat := .node node4583 node199 +def node4585 : Tree Nat := .node node2387 node4584 +def node4586 : Tree Nat := .node node4074 node4585 +def node4587 : Tree Nat := .leaf 35835915874844867368919076489095108449946327955754392558399825615420669938882575126094039892414433329152 +def node4588 : Tree Nat := .node node4587 node207 +def node4589 : Tree Nat := .node node205 node4588 +def node4590 : Tree Nat := .node node4589 node3211 +def node4591 : Tree Nat := .node node4586 node4590 +def node4592 : Tree Nat := .leaf 153914086704665934422965000391185991426092731525255651046673021110334850669910978950836977558144206225500517957632 +def node4593 : Tree Nat := .node node4592 node238 +def node4594 : Tree Nat := .node node2012 node4593 +def node4595 : Tree Nat := .node node4594 node4083 +def node4596 : Tree Nat := .node node4080 node4595 +def node4597 : Tree Nat := .node node4591 node4596 +def node4598 : Tree Nat := .node node4582 node4597 +def node4599 : Tree Nat := .node node4567 node4598 +def node4600 : Tree Nat := .leaf 630432099142311667396464641602297820881275828327447146687172694467931548343955369782628260078158650541136423996620800 +def node4601 : Tree Nat := .node node4600 node4092 +def node4602 : Tree Nat := .node node2153 node4601 +def node4603 : Tree Nat := .node node4091 node4602 +def node4604 : Tree Nat := .leaf 34175792574734561318320347298712833833643272357706444319152665725155515612490248800367393458094080 +def node4605 : Tree Nat := .node node4604 node271 +def node4606 : Tree Nat := .node node269 node4605 +def node4607 : Tree Nat := .node node4606 node2956 +def node4608 : Tree Nat := .node node4603 node4607 +def node4609 : Tree Nat := .leaf 2707685248164858261307045101702230179137145581421695874189921465443966120903931272499975005961073806735752493920427154195087360 +def node4610 : Tree Nat := .node node4609 node4100 +def node4611 : Tree Nat := .node node2551 node4610 +def node4612 : Tree Nat := .node node4099 node4611 +def node4613 : Tree Nat := .leaf 146783911423364576743092537299333564210980159306769991919205685720763064069663027716481187399052441986007040 +def node4614 : Tree Nat := .node node4613 node3787 +def node4615 : Tree Nat := .node node300 node4614 +def node4616 : Tree Nat := .node node4615 node3572 +def node4617 : Tree Nat := .node node4612 node4616 +def node4618 : Tree Nat := .node node4608 node4617 +def node4619 : Tree Nat := .leaf 41315998049390537434494706752048189989275292685267576205290549704650361952269459114074325652482205303048237727858798100480 +def node4620 : Tree Nat := .node node4619 node4109 +def node4621 : Tree Nat := .node node2348 node4620 +def node4622 : Tree Nat := .node node4108 node4621 +def node4623 : Tree Nat := .leaf 2239744742177804210557442280568444278121645497234649534899989100963791871180160945380877493288786984960 +def node4624 : Tree Nat := .node node4623 node333 +def node4625 : Tree Nat := .node node331 node4624 +def node4626 : Tree Nat := .node node4625 node3181 +def node4627 : Tree Nat := .node node4622 node4626 +def node4628 : Tree Nat := .leaf 9619630419041620901435312524449124464130795720328478190417063819395928166869436184427311097384013733518712504320 +def node4629 : Tree Nat := .node node4628 node364 +def node4630 : Tree Nat := .node node362 node4629 +def node4631 : Tree Nat := .node node4630 node4120 +def node4632 : Tree Nat := .node node4117 node4631 +def node4633 : Tree Nat := .node node4627 node4632 +def node4634 : Tree Nat := .node node4618 node4633 +def node4635 : Tree Nat := .leaf 161390617380431786853494948250188242145606612051826469551916209783790476376052574664352834580008614469355634266724106240 +def node4636 : Tree Nat := .node node4635 node388 +def node4637 : Tree Nat := .node node2231 node4636 +def node4638 : Tree Nat := .node node4127 node4637 +def node4639 : Tree Nat := .leaf 8749002899132047697490008908470485461412677723572849745703082425639811996797503692894052709165957120 +def node4640 : Tree Nat := .node node4639 node3809 +def node4641 : Tree Nat := .node node394 node4640 +def node4642 : Tree Nat := .node node4641 node3073 +def node4643 : Tree Nat := .node node4638 node4642 +def node4644 : Tree Nat := .leaf 37576681324381331646231689548629392438010920782533117931316655544515344401833735095419183974156369617255137280 +def node4645 : Tree Nat := .node node4644 node427 +def node4646 : Tree Nat := .node node425 node4645 +def node4647 : Tree Nat := .node node4646 node3820 +def node4648 : Tree Nat := .node node4133 node4647 +def node4649 : Tree Nat := .node node4643 node4648 +def node4650 : Tree Nat := .leaf 10576895500643977583230644928524336637254474927428499508554380724390492659780981533203027367035444557562639984021091144171520 +def node4651 : Tree Nat := .node node4650 node4139 +def node4652 : Tree Nat := .node node2426 node4651 +def node4653 : Tree Nat := .node node4138 node4652 +def node4654 : Tree Nat := .leaf 573374653997517877902705223825521735199141247292070280934397209846730719022121202017504638277806299545600 +def node4655 : Tree Nat := .node node4654 node458 +def node4656 : Tree Nat := .node node456 node4655 +def node4657 : Tree Nat := .node node4656 node3289 +def node4658 : Tree Nat := .node node4653 node4657 +def node4659 : Tree Nat := .leaf 2462625387274654950767440006258975862817483704404090416746768337765357610718575663213391640930307245564812758876160 +def node4660 : Tree Nat := .node node4659 node488 +def node4661 : Tree Nat := .node node2020 node4660 +def node4662 : Tree Nat := .node node4661 node4153 +def node4663 : Tree Nat := .node node4150 node4662 +def node4664 : Tree Nat := .node node4658 node4663 +def node4665 : Tree Nat := .node node4649 node4664 +def node4666 : Tree Nat := .node node4634 node4665 +def node4667 : Tree Nat := .node node4599 node4666 +def node4668 : Tree Nat := .leaf 157608024785577916849116160400574455220318957081861786671793173616982887085988842445657065019539662707341700037083136 +def node4669 : Tree Nat := .node node4668 node4163 +def node4670 : Tree Nat := .node node2123 node4669 +def node4671 : Tree Nat := .node node4162 node4670 +def node4672 : Tree Nat := .leaf 8543948143683640329580086824678208458410818089426611079788166431288878903122562200091848381300736 +def node4673 : Tree Nat := .node node4672 node3842 +def node4674 : Tree Nat := .node node520 node4673 +def node4675 : Tree Nat := .node node4674 node2926 +def node4676 : Tree Nat := .node node4671 node4675 +def node4677 : Tree Nat := .leaf 676921312041214565326761275425557544784286395355423968547480366360991530225982818124993751490268451683942845846589658193985536 +def node4678 : Tree Nat := .node node4677 node4171 +def node4679 : Tree Nat := .node node2521 node4678 +def node4680 : Tree Nat := .node node4170 node4679 +def node4681 : Tree Nat := .leaf 36695977855841144185773134324833391052745039826692497979801421430190766017415756929120296849764210008129536 +def node4682 : Tree Nat := .node node4681 node3851 +def node4683 : Tree Nat := .node node551 node4682 +def node4684 : Tree Nat := .node node4683 node3367 +def node4685 : Tree Nat := .node node4680 node4684 +def node4686 : Tree Nat := .node node4676 node4685 +def node4687 : Tree Nat := .leaf 10328999512347634358623676688012047497318823171316894051322637426162590488067364778518581413120551325780506176038409076736 +def node4688 : Tree Nat := .node node4687 node576 +def node4689 : Tree Nat := .node node2318 node4688 +def node4690 : Tree Nat := .node node4179 node4689 +def node4691 : Tree Nat := .leaf 559936185544451052639360570142111069530411374308662383724997275240947967795040236345219373326491713536 +def node4692 : Tree Nat := .node node4691 node584 +def node4693 : Tree Nat := .node node582 node4692 +def node4694 : Tree Nat := .node node4693 node3151 +def node4695 : Tree Nat := .node node4690 node4694 +def node4696 : Tree Nat := .leaf 2404907604760405225358828131112281116032698930082119547604265954848982041717359046106827774346003714854654836736 +def node4697 : Tree Nat := .node node4696 node3862 +def node4698 : Tree Nat := .node node613 node4697 +def node4699 : Tree Nat := .node node4698 node4188 +def node4700 : Tree Nat := .node node4185 node4699 +def node4701 : Tree Nat := .node node4695 node4700 +def node4702 : Tree Nat := .node node4686 node4701 +def node4703 : Tree Nat := .leaf 40347654345107946713373737062547060536401653012956617387979052445947619094013143666088208645002153618491830071287873536 +def node4704 : Tree Nat := .node node4703 node639 +def node4705 : Tree Nat := .node node2240 node4704 +def node4706 : Tree Nat := .node node4195 node4705 +def node4707 : Tree Nat := .leaf 2187250724783011924372502227117621365353169430893212436425770606409952999199375923223513177559924736 +def node4708 : Tree Nat := .node node4707 node647 +def node4709 : Tree Nat := .node node645 node4708 +def node4710 : Tree Nat := .node node4709 node3043 +def node4711 : Tree Nat := .node node4706 node4710 +def node4712 : Tree Nat := .leaf 9394170331095332911557922387157348109502730195633279482829163886128836100458433773854795993539109996499828736 +def node4713 : Tree Nat := .node node4712 node678 +def node4714 : Tree Nat := .node node676 node4713 +def node4715 : Tree Nat := .node node4714 node3612 +def node4716 : Tree Nat := .node node4201 node4715 +def node4717 : Tree Nat := .node node4711 node4716 +def node4718 : Tree Nat := .leaf 2644223875160994395807661232131084159313618731857124877138595181097623164945245383300756841758861139390955143910452138868736 +def node4719 : Tree Nat := .node node4718 node701 +def node4720 : Tree Nat := .node node2435 node4719 +def node4721 : Tree Nat := .node node4206 node4720 +def node4722 : Tree Nat := .leaf 143343663499379469475676305956380433799785311823017570233599302461682679755530300504376159569520294363136 +def node4723 : Tree Nat := .node node4722 node3879 +def node4724 : Tree Nat := .node node707 node4723 +def node4725 : Tree Nat := .node node4724 node3259 +def node4726 : Tree Nat := .node node4721 node4725 +def node4727 : Tree Nat := .leaf 615656346818663737691860001564743965704370926101022604186692084441339402679643915803347910232576815894802817089536 +def node4728 : Tree Nat := .node node4727 node740 +def node4729 : Tree Nat := .node node2029 node4728 +def node4730 : Tree Nat := .node node4729 node4215 +def node4731 : Tree Nat := .node node4212 node4730 +def node4732 : Tree Nat := .node node4726 node4731 +def node4733 : Tree Nat := .node node4717 node4732 +def node4734 : Tree Nat := .node node4702 node4733 +def node4735 : Tree Nat := .leaf 2521728396569246669585858566409191283525103313309788586748690777871726193375821479130513040312634601588084943683059712 +def node4736 : Tree Nat := .node node4735 node4224 +def node4737 : Tree Nat := .node node2162 node4736 +def node4738 : Tree Nat := .node node4223 node4737 +def node4739 : Tree Nat := .leaf 136703170298938245273281389194851335334573089430825777276610662900622062449960995201469573698158592 +def node4740 : Tree Nat := .node node4739 node773 +def node4741 : Tree Nat := .node node771 node4740 +def node4742 : Tree Nat := .node node4741 node3004 +def node4743 : Tree Nat := .node node4738 node4742 +def node4744 : Tree Nat := .leaf 587135645693458306972370149197334256843920637227079967676822742883052256278652110865924749596200971851005952 +def node4745 : Tree Nat := .node node4744 node804 +def node4746 : Tree Nat := .node node802 node4745 +def node4747 : Tree Nat := .node node4746 node3626 +def node4748 : Tree Nat := .node node4232 node4747 +def node4749 : Tree Nat := .node node4743 node4748 +def node4750 : Tree Nat := .leaf 165263992197562149737978827008192759957101170741070304821162198818601447809077836456297302609928821212045376958845515988992 +def node4751 : Tree Nat := .node node4750 node827 +def node4752 : Tree Nat := .node node2396 node4751 +def node4753 : Tree Nat := .node node4237 node4752 +def node4754 : Tree Nat := .leaf 8958978968711216842229769122273777112486581988938598139599956403855167484720643781523509973120788201472 +def node4755 : Tree Nat := .node node4754 node3906 +def node4756 : Tree Nat := .node node833 node4755 +def node4757 : Tree Nat := .node node4756 node3220 +def node4758 : Tree Nat := .node node4753 node4757 +def node4759 : Tree Nat := .leaf 38478521676166483605741250097796497856523182881313912761668255277583712667477744737709244389536052682275036332032 +def node4760 : Tree Nat := .node node4759 node866 +def node4761 : Tree Nat := .node node864 node4760 +def node4762 : Tree Nat := .node node4761 node4246 +def node4763 : Tree Nat := .node node4243 node4762 +def node4764 : Tree Nat := .node node4758 node4763 +def node4765 : Tree Nat := .node node4749 node4764 +def node4766 : Tree Nat := .leaf 645562469521727147413979793000752968582426448207305878207664839135161905504210298657411338320034457868199165030041649152 +def node4767 : Tree Nat := .node node4766 node890 +def node4768 : Tree Nat := .node node2279 node4767 +def node4769 : Tree Nat := .node node4253 node4768 +def node4770 : Tree Nat := .leaf 34996011596528190789960035633881941845650710894291398982812329702559247987190014771576210834516344832 +def node4771 : Tree Nat := .node node4770 node3917 +def node4772 : Tree Nat := .node node896 node4771 +def node4773 : Tree Nat := .node node4772 node3112 +def node4774 : Tree Nat := .node node4769 node4773 +def node4775 : Tree Nat := .leaf 150306725297525326584926758194517569752043683130132471725266622178061377607334940381676735896625337731532193792 +def node4776 : Tree Nat := .node node4775 node929 +def node4777 : Tree Nat := .node node927 node4776 +def node4778 : Tree Nat := .node node4777 node3924 +def node4779 : Tree Nat := .node node4262 node4778 +def node4780 : Tree Nat := .node node4774 node4779 +def node4781 : Tree Nat := .leaf 42307582002575910332922579714097346549017899709713998034217522897561970639123926132812109468141778230248198752842929754079232 +def node4782 : Tree Nat := .node node4781 node952 +def node4783 : Tree Nat := .node node2482 node4782 +def node4784 : Tree Nat := .node node4267 node4783 +def node4785 : Tree Nat := .leaf 2293498615990071511610820895302086940796564989168281123737588839386922876088484808070018553110675442368512 +def node4786 : Tree Nat := .node node4785 node960 +def node4787 : Tree Nat := .node node958 node4786 +def node4788 : Tree Nat := .node node4787 node3328 +def node4789 : Tree Nat := .node node4784 node4788 +def node4790 : Tree Nat := .leaf 9850501549098619803069760025035903451269934817616361666987073351061430442874302652853566563721228946230454016540672 +def node4791 : Tree Nat := .node node4790 node990 +def node4792 : Tree Nat := .node node2076 node4791 +def node4793 : Tree Nat := .node node4792 node4276 +def node4794 : Tree Nat := .node node4273 node4793 +def node4795 : Tree Nat := .node node4789 node4794 +def node4796 : Tree Nat := .node node4780 node4795 +def node4797 : Tree Nat := .node node4765 node4796 +def node4798 : Tree Nat := .node node4734 node4797 +def node4799 : Tree Nat := .node node4667 node4798 +def node4800 : Tree Nat := .leaf 78804012392788958424558080200287227610159478540930893335896586808491443542994421222828532509769831353670850018541568 +def node4801 : Tree Nat := .node node4800 node1017 +def node4802 : Tree Nat := .node node2133 node4801 +def node4803 : Tree Nat := .node node4286 node4802 +def node4804 : Tree Nat := .node node4803 node4291 +def node4805 : Tree Nat := .leaf 338460656020607282663380637712778772392143197677711984273740183180495765112991409062496875745134225841971422923294829096992768 +def node4806 : Tree Nat := .node node4805 node1048 +def node4807 : Tree Nat := .node node2531 node4806 +def node4808 : Tree Nat := .node node4295 node4807 +def node4809 : Tree Nat := .leaf 18347988927920572092886567162416695526372519913346248989900710715095383008707878464560148424882105004064768 +def node4810 : Tree Nat := .node node4809 node1056 +def node4811 : Tree Nat := .node node1054 node4810 +def node4812 : Tree Nat := .node node4811 node3659 +def node4813 : Tree Nat := .node node4808 node4812 +def node4814 : Tree Nat := .node node4804 node4813 +def node4815 : Tree Nat := .leaf 5164499756173817179311838344006023748659411585658447025661318713081295244033682389259290706560275662890253088019204538368 +def node4816 : Tree Nat := .node node4815 node1079 +def node4817 : Tree Nat := .node node2328 node4816 +def node4818 : Tree Nat := .node node4301 node4817 +def node4819 : Tree Nat := .leaf 279968092772225526319680285071055534765205687154331191862498637620473983897520118172609686663245856768 +def node4820 : Tree Nat := .node node4819 node3943 +def node4821 : Tree Nat := .node node1085 node4820 +def node4822 : Tree Nat := .node node4821 node4305 +def node4823 : Tree Nat := .node node4818 node4822 +def node4824 : Tree Nat := .leaf 1202453802380202612679414065556140558016349465041059773802132977424491020858679523053413887173001857427327418368 +def node4825 : Tree Nat := .node node4824 node1118 +def node4826 : Tree Nat := .node node1116 node4825 +def node4827 : Tree Nat := .node node4826 node4317 +def node4828 : Tree Nat := .node node4314 node4827 +def node4829 : Tree Nat := .node node4823 node4828 +def node4830 : Tree Nat := .node node4814 node4829 +def node4831 : Tree Nat := .leaf 20173827172553973356686868531273530268200826506478308693989526222973809547006571833044104322501076809245915035643936768 +def node4832 : Tree Nat := .node node4831 node1142 +def node4833 : Tree Nat := .node node2211 node4832 +def node4834 : Tree Nat := .node node4324 node4833 +def node4835 : Tree Nat := .leaf 1093625362391505962186251113558810682676584715446606218212885303204976499599687961611756588779962368 +def node4836 : Tree Nat := .node node4835 node1150 +def node4837 : Tree Nat := .node node1148 node4836 +def node4838 : Tree Nat := .node node4837 node3053 +def node4839 : Tree Nat := .node node4834 node4838 +def node4840 : Tree Nat := .leaf 4697085165547666455778961193578674054751365097816639741414581943064418050229216886927397996769554998249914368 +def node4841 : Tree Nat := .node node4840 node1181 +def node4842 : Tree Nat := .node node1179 node4841 +def node4843 : Tree Nat := .node node4842 node3485 +def node4844 : Tree Nat := .node node4333 node4843 +def node4845 : Tree Nat := .node node4839 node4844 +def node4846 : Tree Nat := .leaf 1322111937580497197903830616065542079656809365928562438569297590548811582472622691650378420879430569695477571955226069434368 +def node4847 : Tree Nat := .node node4846 node1204 +def node4848 : Tree Nat := .node node2445 node4847 +def node4849 : Tree Nat := .node node4338 node4848 +def node4850 : Tree Nat := .leaf 71671831749689734737838152978190216899892655911508785116799651230841339877765150252188079784760147181568 +def node4851 : Tree Nat := .node node4850 node1212 +def node4852 : Tree Nat := .node node1210 node4851 +def node4853 : Tree Nat := .node node4852 node3269 +def node4854 : Tree Nat := .node node4849 node4853 +def node4855 : Tree Nat := .leaf 307828173409331868845930000782371982852185463050511302093346042220669701339821957901673955116288407947401408544768 +def node4856 : Tree Nat := .node node4855 node1243 +def node4857 : Tree Nat := .node node2039 node4856 +def node4858 : Tree Nat := .node node4857 node4347 +def node4859 : Tree Nat := .node node4344 node4858 +def node4860 : Tree Nat := .node node4854 node4859 +def node4861 : Tree Nat := .node node4845 node4860 +def node4862 : Tree Nat := .node node4830 node4861 +def node4863 : Tree Nat := .leaf 1260864198284623334792929283204595641762551656654894293374345388935863096687910739565256520156317300794042471841529856 +def node4864 : Tree Nat := .node node4863 node1268 +def node4865 : Tree Nat := .node node2172 node4864 +def node4866 : Tree Nat := .node node4355 node4865 +def node4867 : Tree Nat := .leaf 68351585149469122636640694597425667667286544715412888638305331450311031224980497600734786849079296 +def node4868 : Tree Nat := .node node4867 node1276 +def node4869 : Tree Nat := .node node1274 node4868 +def node4870 : Tree Nat := .node node4869 node2975 +def node4871 : Tree Nat := .node node4866 node4870 +def node4872 : Tree Nat := .leaf 5415370496329716522614090203404460358274291162843391748379842930887932241807862544999950011922147613471486098374922829809319936 +def node4873 : Tree Nat := .node node4872 node4361 +def node4874 : Tree Nat := .node node2570 node4873 +def node4875 : Tree Nat := .node node4360 node4874 +def node4876 : Tree Nat := .leaf 293567822846729153486185074598667128421960318613539983838411371441526128139326055432962374798100485925502976 +def node4877 : Tree Nat := .node node4876 node1307 +def node4878 : Tree Nat := .node node1305 node4877 +def node4879 : Tree Nat := .node node4878 node3416 +def node4880 : Tree Nat := .node node4875 node4879 +def node4881 : Tree Nat := .node node4871 node4880 +def node4882 : Tree Nat := .leaf 82631996098781074868989413504096379978550585370535152410581099409300723904538918228148651304964410606022688479422757994496 +def node4883 : Tree Nat := .node node4882 node1330 +def node4884 : Tree Nat := .node node2367 node4883 +def node4885 : Tree Nat := .node node4369 node4884 +def node4886 : Tree Nat := .leaf 4479489484355608421114884561136888556243290994469299069799978201927583742360321890761754986560394100736 +def node4887 : Tree Nat := .node node4886 node1338 +def node4888 : Tree Nat := .node node1336 node4887 +def node4889 : Tree Nat := .node node4888 node3200 +def node4890 : Tree Nat := .node node4885 node4889 +def node4891 : Tree Nat := .leaf 19239260838083241802870625048898248928261591440656956380834127638791856333738872368854622194768026341137518166016 +def node4892 : Tree Nat := .node node4891 node1369 +def node4893 : Tree Nat := .node node1367 node4892 +def node4894 : Tree Nat := .node node4893 node4378 +def node4895 : Tree Nat := .node node4375 node4894 +def node4896 : Tree Nat := .node node4890 node4895 +def node4897 : Tree Nat := .node node4881 node4896 +def node4898 : Tree Nat := .leaf 322781234760863573706989896500376484291213224103652939103832419567580952752105149328705669160017228934099582515020824576 +def node4899 : Tree Nat := .node node4898 node1393 +def node4900 : Tree Nat := .node node2289 node4899 +def node4901 : Tree Nat := .node node4385 node4900 +def node4902 : Tree Nat := .leaf 17498005798264095394980017816940970922825355447145699491406164851279623993595007385788105417258172416 +def node4903 : Tree Nat := .node node4902 node1401 +def node4904 : Tree Nat := .node node1399 node4903 +def node4905 : Tree Nat := .node node4904 node3092 +def node4906 : Tree Nat := .node node4901 node4905 +def node4907 : Tree Nat := .leaf 75153362648762663292463379097258784876021841565066235862633311089030688803667470190838367948312668865766096896 +def node4908 : Tree Nat := .node node4907 node1432 +def node4909 : Tree Nat := .node node1430 node4908 +def node4910 : Tree Nat := .node node4909 node3967 +def node4911 : Tree Nat := .node node4394 node4910 +def node4912 : Tree Nat := .node node4906 node4911 +def node4913 : Tree Nat := .leaf 21153791001287955166461289857048673274508949854856999017108761448780985319561963066406054734070889115124099376421464877039616 +def node4914 : Tree Nat := .node node4913 node1455 +def node4915 : Tree Nat := .node node2492 node4914 +def node4916 : Tree Nat := .node node4399 node4915 +def node4917 : Tree Nat := .leaf 1146749307995035755805410447651043470398282494584140561868794419693461438044242404035009276555337721184256 +def node4918 : Tree Nat := .node node4917 node1463 +def node4919 : Tree Nat := .node node1461 node4918 +def node4920 : Tree Nat := .node node4919 node3308 +def node4921 : Tree Nat := .node node4916 node4920 +def node4922 : Tree Nat := .leaf 4925250774549309901534880012517951725634967408808180833493536675530715221437151326426783281860614473115227008270336 +def node4923 : Tree Nat := .node node4922 node1493 +def node4924 : Tree Nat := .node node2094 node4923 +def node4925 : Tree Nat := .node node4924 node4408 +def node4926 : Tree Nat := .node node4405 node4925 +def node4927 : Tree Nat := .node node4921 node4926 +def node4928 : Tree Nat := .node node4912 node4927 +def node4929 : Tree Nat := .node node4897 node4928 +def node4930 : Tree Nat := .node node4862 node4929 +def node4931 : Tree Nat := .leaf 315216049571155833698232320801148910440637914163723573343586347233965774171977684891314130039079325270568211998310400 +def node4932 : Tree Nat := .node node4931 node1519 +def node4933 : Tree Nat := .node node2142 node4932 +def node4934 : Tree Nat := .node node4417 node4933 +def node4935 : Tree Nat := .leaf 17087896287367280659160173649356416916821636178853222159576332862577757806245124400183696729047040 +def node4936 : Tree Nat := .node node4935 node3980 +def node4937 : Tree Nat := .node node1525 node4936 +def node4938 : Tree Nat := .node node4937 node2984 +def node4939 : Tree Nat := .node node4934 node4938 +def node4940 : Tree Nat := .leaf 1353842624082429130653522550851115089568572790710847937094960732721983060451965636249987502980536903367876246960213577097543680 +def node4941 : Tree Nat := .node node4940 node1550 +def node4942 : Tree Nat := .node node2579 node4941 +def node4943 : Tree Nat := .node node4422 node4942 +def node4944 : Tree Nat := .leaf 73391955711682288371546268649666782105490079653384995959602842860381532034831513858240593699526220993003520 +def node4945 : Tree Nat := .node node4944 node1558 +def node4946 : Tree Nat := .node node1556 node4945 +def node4947 : Tree Nat := .node node4946 node3386 +def node4948 : Tree Nat := .node node4943 node4947 +def node4949 : Tree Nat := .node node4939 node4948 +def node4950 : Tree Nat := .leaf 20657999024695268717247353376024094994637646342633788102645274852325180976134729557037162826241102651524118863929399050240 +def node4951 : Tree Nat := .node node4950 node1581 +def node4952 : Tree Nat := .node node2376 node4951 +def node4953 : Tree Nat := .node node4428 node4952 +def node4954 : Tree Nat := .leaf 1119872371088902105278721140284222139060822748617324767449994550481895935590080472690438746644393492480 +def node4955 : Tree Nat := .node node4954 node1589 +def node4956 : Tree Nat := .node node1587 node4955 +def node4957 : Tree Nat := .node node4956 node3170 +def node4958 : Tree Nat := .node node4953 node4957 +def node4959 : Tree Nat := .leaf 4809815209520810450717656262224562232065397860164239095208531909697964083434718092213655548692006866759356252160 +def node4960 : Tree Nat := .node node4959 node1620 +def node4961 : Tree Nat := .node node1618 node4960 +def node4962 : Tree Nat := .node node4961 node4437 +def node4963 : Tree Nat := .node node4434 node4962 +def node4964 : Tree Nat := .node node4958 node4963 +def node4965 : Tree Nat := .node node4949 node4964 +def node4966 : Tree Nat := .leaf 80695308690215893426747474125094121072803306025913234775958104891895238188026287332176417290004307234677817133362053120 +def node4967 : Tree Nat := .node node4966 node1644 +def node4968 : Tree Nat := .node node2259 node4967 +def node4969 : Tree Nat := .node node4444 node4968 +def node4970 : Tree Nat := .leaf 4374501449566023848745004454235242730706338861786424872851541212819905998398751846447026354582978560 +def node4971 : Tree Nat := .node node4970 node1652 +def node4972 : Tree Nat := .node node1650 node4971 +def node4973 : Tree Nat := .node node4972 node3062 +def node4974 : Tree Nat := .node node4969 node4973 +def node4975 : Tree Nat := .leaf 18788340662190665823115844774314696219005460391266558965658327772257672200916867547709591987078184808627568640 +def node4976 : Tree Nat := .node node4975 node1683 +def node4977 : Tree Nat := .node node1681 node4976 +def node4978 : Tree Nat := .node node4977 node3494 +def node4979 : Tree Nat := .node node4450 node4978 +def node4980 : Tree Nat := .node node4974 node4979 +def node4981 : Tree Nat := .leaf 5288447750321988791615322464262168318627237463714249754277190362195246329890490766601513683517722278781319992010545572085760 +def node4982 : Tree Nat := .node node4981 node1706 +def node4983 : Tree Nat := .node node2462 node4982 +def node4984 : Tree Nat := .node node4455 node4983 +def node4985 : Tree Nat := .leaf 286687326998758938951352611912760867599570623646035140467198604923365359511060601008752319138903149772800 +def node4986 : Tree Nat := .node node4985 node1714 +def node4987 : Tree Nat := .node node1712 node4986 +def node4988 : Tree Nat := .node node4987 node3278 +def node4989 : Tree Nat := .node node4984 node4988 +def node4990 : Tree Nat := .leaf 1231312693637327475383720003129487931408741852202045208373384168882678805359287831606695820465153622782406379438080 +def node4991 : Tree Nat := .node node4990 node1744 +def node4992 : Tree Nat := .node node2056 node4991 +def node4993 : Tree Nat := .node node4992 node4464 +def node4994 : Tree Nat := .node node4461 node4993 +def node4995 : Tree Nat := .node node4989 node4994 +def node4996 : Tree Nat := .node node4980 node4995 +def node4997 : Tree Nat := .node node4965 node4996 +def node4998 : Tree Nat := .leaf 5043456793138493339171717132818382567050206626619577173497381555743452386751642958261026080625269202599709135062695936 +def node4999 : Tree Nat := .node node4998 node1769 +def node5000 : Tree Nat := .node node2220 node4999 +def node5001 : Tree Nat := .node node4472 node5000 +def node5002 : Tree Nat := .leaf 273406340597876490546562778389702670669146178861651554553221325801244124899921990402939147262099456 +def node5003 : Tree Nat := .node node5002 node1777 +def node5004 : Tree Nat := .node node1775 node5003 +def node5005 : Tree Nat := .node node5004 node3023 +def node5006 : Tree Nat := .node node5001 node5005 +def node5007 : Tree Nat := .leaf 1174271291386916613944740298394668513687841274454159935353645485766104512557304221731849499192393147608989696 +def node5008 : Tree Nat := .node node5007 node1808 +def node5009 : Tree Nat := .node node1806 node5008 +def node5010 : Tree Nat := .node node5009 node3455 +def node5011 : Tree Nat := .node node4478 node5010 +def node5012 : Tree Nat := .node node5006 node5011 +def node5013 : Tree Nat := .leaf 330527984395124299475957654016385519914202341482140609642324397637202895618155672912594605219857642423943179965101355565056 +def node5014 : Tree Nat := .node node5013 node1831 +def node5015 : Tree Nat := .node node2415 node5014 +def node5016 : Tree Nat := .node node4483 node5015 +def node5017 : Tree Nat := .leaf 17917957937422433684459538244547554224973163977877196279199912807710334969441287563047019946207216664576 +def node5018 : Tree Nat := .node node5017 node1839 +def node5019 : Tree Nat := .node node1837 node5018 +def node5020 : Tree Nat := .node node5019 node3239 +def node5021 : Tree Nat := .node node5016 node5020 +def node5022 : Tree Nat := .leaf 76957043352332967211482500195592995713046365762627825523336510555167425334955489475418488779072103112750258978816 +def node5023 : Tree Nat := .node node5022 node1870 +def node5024 : Tree Nat := .node node1868 node5023 +def node5025 : Tree Nat := .node node5024 node4495 +def node5026 : Tree Nat := .node node4492 node5025 +def node5027 : Tree Nat := .node node5021 node5026 +def node5028 : Tree Nat := .node node5012 node5027 +def node5029 : Tree Nat := .leaf 1291124939043454294827959586001505937164852896414611756415329678270323811008420597314822676640068915727174958023228522496 +def node5030 : Tree Nat := .node node5029 node1894 +def node5031 : Tree Nat := .node node2298 node5030 +def node5032 : Tree Nat := .node node4502 node5031 +def node5033 : Tree Nat := .leaf 69992023193056381579920071267763883691301421788582797965624659405118495974380029543152421666885206016 +def node5034 : Tree Nat := .node node5033 node1902 +def node5035 : Tree Nat := .node node1900 node5034 +def node5036 : Tree Nat := .node node5035 node3131 +def node5037 : Tree Nat := .node node5032 node5036 +def node5038 : Tree Nat := .leaf 300613450595050653169853516389035139504087366260264943450533244356122755214669880763353471793250534725576032256 +def node5039 : Tree Nat := .node node5038 node1933 +def node5040 : Tree Nat := .node node1931 node5039 +def node5041 : Tree Nat := .node node5040 node3717 +def node5042 : Tree Nat := .node node4511 node5041 +def node5043 : Tree Nat := .node node5037 node5042 +def node5044 : Tree Nat := .leaf 84615164005151820665845159428194693098035799419427996068435045795123941278247852265624218936283556460494036322444424685551616 +def node5045 : Tree Nat := .node node5044 node1956 +def node5046 : Tree Nat := .node node2501 node5045 +def node5047 : Tree Nat := .node node4516 node5046 +def node5048 : Tree Nat := .leaf 4586997231980143023221641790604173881593129978336562247475177678773845752176969616140037106220801128923136 +def node5049 : Tree Nat := .node node5048 node1964 +def node5050 : Tree Nat := .node node1962 node5049 +def node5051 : Tree Nat := .node node5050 node3347 +def node5052 : Tree Nat := .node node5047 node5051 +def node5053 : Tree Nat := .leaf 19701003098197239606139520050071806902539869635232723333974146702122860885748605305707133127442457856432111014117376 +def node5054 : Tree Nat := .node node5053 node1994 +def node5055 : Tree Nat := .node node2103 node5054 +def node5056 : Tree Nat := .node node5055 node4528 +def node5057 : Tree Nat := .node node4525 node5056 +def node5058 : Tree Nat := .node node5052 node5057 +def node5059 : Tree Nat := .node node5043 node5058 +def node5060 : Tree Nat := .node node5028 node5059 +def node5061 : Tree Nat := .node node4997 node5060 +def node5062 : Tree Nat := .node node4930 node5061 +def node5063 : Tree Nat := .node node4799 node5062 +def node5064 : Tree Nat := .leaf 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946735967130312392048640 +def node5065 : Tree Nat := .node node0 node5064 +def node5066 : Tree Nat := .node node5065 node4013 +def node5067 : Tree Nat := .node node5066 node4539 +def node5068 : Tree Nat := .leaf 726838724295606890549323807888004534353641360687318060281490199180639288113397923326191050713763565560762521915751187754879670353395712 +def node5069 : Tree Nat := .node node5068 node4022 +def node5070 : Tree Nat := .node node2870 node5069 +def node5071 : Tree Nat := .node node4021 node5070 +def node5072 : Tree Nat := .node node5067 node5071 +def node5073 : Tree Nat := .leaf 3121748550315992231381597229793166305748598142664971150859156959625371738819765620120306103063491971159826931121426905305051627349712232557576192 +def node5074 : Tree Nat := .node node5073 node57 +def node5075 : Tree Nat := .node node3539 node5074 +def node5076 : Tree Nat := .node node4548 node5075 +def node5077 : Tree Nat := .node node4545 node5076 +def node5078 : Tree Nat := .node node5072 node5077 +def node5079 : Tree Nat := .leaf 47634102635436893179040485073748265163400240214004076398607741693502376385799646303105256699577209032590132616067488399566387989926434045952 +def node5080 : Tree Nat := .node node5079 node89 +def node5081 : Tree Nat := .node node3102 node5080 +def node5082 : Tree Nat := .node node4558 node5081 +def node5083 : Tree Nat := .node node4555 node5082 +def node5084 : Tree Nat := .leaf 11090678776483259438313656736572334813745748301503266300681918322458485231222502492159897624416558312389566052771433901945071337472 +def node5085 : Tree Nat := .node node5084 node4047 +def node5086 : Tree Nat := .node node2698 node5085 +def node5087 : Tree Nat := .node node4046 node5086 +def node5088 : Tree Nat := .leaf 204586912993508866875824356051724947013540127877691549342705710506008362275292159680204380770369009821930417757972509630372937068945465596329362194432 +def node5089 : Tree Nat := .node node5088 node57 +def node5090 : Tree Nat := .node node4052 node5089 +def node5091 : Tree Nat := .node node4563 node5090 +def node5092 : Tree Nat := .node node5087 node5091 +def node5093 : Tree Nat := .node node5083 node5092 +def node5094 : Tree Nat := .node node5078 node5093 +def node5095 : Tree Nat := .leaf 186070713419675363980626894819329160794532188335953423432061490990243657757029868371504908982723472783555205536155901708126379116521848832 +def node5096 : Tree Nat := .node node5095 node152 +def node5097 : Tree Nat := .node node2994 node5096 +def node5098 : Tree Nat := .node node4574 node5097 +def node5099 : Tree Nat := .node node4571 node5098 +def node5100 : Tree Nat := .leaf 43322963970637732180912721627235682866194329302747133987038743447103457934462900359999600095377180907771813229135656724151140352 +def node5101 : Tree Nat := .node node5100 node4066 +def node5102 : Tree Nat := .node node2590 node5101 +def node5103 : Tree Nat := .node node4065 node5102 +def node5104 : Tree Nat := .leaf 799167628880894011233688890827050574271641124522232614619944181664095165137859998750798362384253944616915694367080419979788340200624584194430861312 +def node5105 : Tree Nat := .node node5104 node57 +def node5106 : Tree Nat := .node node3552 node5105 +def node5107 : Tree Nat := .node node4579 node5106 +def node5108 : Tree Nat := .node node5103 node5107 +def node5109 : Tree Nat := .node node5099 node5108 +def node5110 : Tree Nat := .leaf 12194330274671844653834364178879555881830461494785043558043581873536608354764709453594945715091765512343073949694262271285571884398716567683072 +def node5111 : Tree Nat := .node node5110 node214 +def node5112 : Tree Nat := .node node3210 node5111 +def node5113 : Tree Nat := .node node4589 node5112 +def node5114 : Tree Nat := .node node4586 node5113 +def node5115 : Tree Nat := .leaf 2839213766779714416208296124562517712318911565184836172974571090549372219192960637992933791850638927971728619367290371386936332910592 +def node5116 : Tree Nat := .node node5115 node230 +def node5117 : Tree Nat := .node node2823 node5116 +def node5118 : Tree Nat := .node node4079 node5117 +def node5119 : Tree Nat := .leaf 52374249726338269920211035149241586435466272736689036631732661889538140742474792878132321477214466514414186946040961219224225841291408345341197708951552 +def node5120 : Tree Nat := .node node5119 node57 +def node5121 : Tree Nat := .node node4082 node5120 +def node5122 : Tree Nat := .node node4594 node5121 +def node5123 : Tree Nat := .node node5118 node5122 +def node5124 : Tree Nat := .node node5114 node5123 +def node5125 : Tree Nat := .node node5109 node5124 +def node5126 : Tree Nat := .node node5094 node5125 +def node5127 : Tree Nat := .leaf 214524926879081553593184399971293538039669853129478294043576983099548224481176751628829988770670454843040509730983776813660062124991147775474084998272778240 +def node5128 : Tree Nat := .node node252 node5127 +def node5129 : Tree Nat := .node node5128 node4090 +def node5130 : Tree Nat := .node node5129 node4602 +def node5131 : Tree Nat := .leaf 11629419588729710248789180926208072549658261770997088964503843186890228609814366773219056811420217048972200346938198886221933900956958720 +def node5132 : Tree Nat := .node node5131 node278 +def node5133 : Tree Nat := .node node2955 node5132 +def node5134 : Tree Nat := .node node4606 node5133 +def node5135 : Tree Nat := .node node5130 node5134 +def node5136 : Tree Nat := .leaf 49947976805055875702105555676690660891977570282639538413746511354005947821116249921924897649015871538557230897942587095965582217550308353905786880 +def node5137 : Tree Nat := .node node5136 node57 +def node5138 : Tree Nat := .node node3571 node5137 +def node5139 : Tree Nat := .node node4615 node5138 +def node5140 : Tree Nat := .node node4612 node5139 +def node5141 : Tree Nat := .node node5135 node5140 +def node5142 : Tree Nat := .leaf 762145642166990290864647761179972242614403843424065222377723867096038022172794340849684107193235344521442121856129076442891035787700417331200 +def node5143 : Tree Nat := .node node5142 node340 +def node5144 : Tree Nat := .node node3180 node5143 +def node5145 : Tree Nat := .node node4625 node5144 +def node5146 : Tree Nat := .node node4622 node5145 +def node5147 : Tree Nat := .leaf 177450860423732151013018507785157357019931972824052260810910693159335763699560039874558361990664932998233042337233107055571044925440 +def node5148 : Tree Nat := .node node5147 node356 +def node5149 : Tree Nat := .node node2784 node5148 +def node5150 : Tree Nat := .node node4116 node5149 +def node5151 : Tree Nat := .leaf 3273390607896141870013189696827599152216642046043064789483291368096133796404674554883270092325904157150886684127560091778404690685195907175313844469760 +def node5152 : Tree Nat := .node node5151 node57 +def node5153 : Tree Nat := .node node4119 node5152 +def node5154 : Tree Nat := .node node4630 node5153 +def node5155 : Tree Nat := .node node5150 node5154 +def node5156 : Tree Nat := .node node5146 node5155 +def node5157 : Tree Nat := .node node5141 node5156 +def node5158 : Tree Nat := .leaf 2977131414714805823690030317109266572712515013375254774912983855843898524112477893944078543723575564536883288519073305444323812669191618560 +def node5159 : Tree Nat := .node node5158 node403 +def node5160 : Tree Nat := .node node3072 node5159 +def node5161 : Tree Nat := .node node4641 node5160 +def node5162 : Tree Nat := .node node4638 node5161 +def node5163 : Tree Nat := .leaf 693167423530203714894603546035770925859109268843954143792619895153655326951406405759993601526034894524348104971805796614537216000 +def node5164 : Tree Nat := .node node5163 node419 +def node5165 : Tree Nat := .node node2659 node5164 +def node5166 : Tree Nat := .node node4132 node5165 +def node5167 : Tree Nat := .leaf 12786682062094304179739022253232809188346257992355721833919106906625522642205759980012773798148063113870651109873282825453969542089271949238646865920 +def node5168 : Tree Nat := .node node5167 node57 +def node5169 : Tree Nat := .node node3819 node5168 +def node5170 : Tree Nat := .node node4646 node5169 +def node5171 : Tree Nat := .node node5166 node5170 +def node5172 : Tree Nat := .node node5162 node5171 +def node5173 : Tree Nat := .leaf 195109284394749514461349826862072894109287383916560696928697309976585733676235351257519131441468248197489183195092984533366411397561504644464640 +def node5174 : Tree Nat := .node node5173 node57 +def node5175 : Tree Nat := .node node3288 node5174 +def node5176 : Tree Nat := .node node4656 node5175 +def node5177 : Tree Nat := .node node4653 node5176 +def node5178 : Tree Nat := .leaf 45427420268475430659332737993000283397102585042957378767593137448789955507087370207886940669610222847547657677762888576182179782983680 +def node5179 : Tree Nat := .node node5178 node4147 +def node5180 : Tree Nat := .node node2878 node5179 +def node5181 : Tree Nat := .node node4146 node5180 +def node5182 : Tree Nat := .leaf 837987995621412318723376562387865382967460363787024586107722590232610251879596686050117143635431464230626991136655378510666616621975628847603868132966400 +def node5183 : Tree Nat := .node node5182 node57 +def node5184 : Tree Nat := .node node4152 node5183 +def node5185 : Tree Nat := .node node4661 node5184 +def node5186 : Tree Nat := .node node5181 node5185 +def node5187 : Tree Nat := .node node5177 node5186 +def node5188 : Tree Nat := .node node5172 node5187 +def node5189 : Tree Nat := .node node5157 node5188 +def node5190 : Tree Nat := .node node5126 node5189 +def node5191 : Tree Nat := .leaf 53631231719770388398296099992823384509917463282369573510894245774887056120294187907207497192667613710760127432745944203415015531247786390466199038281646080 +def node5192 : Tree Nat := .node node503 node5191 +def node5193 : Tree Nat := .node node5192 node4161 +def node5194 : Tree Nat := .node node5193 node4670 +def node5195 : Tree Nat := .leaf 2907354897182427562197295231552018137414565442749272241125960796722557152453591693304764202855054262243050087044034731376828543964020736 +def node5196 : Tree Nat := .node node5195 node529 +def node5197 : Tree Nat := .node node2925 node5196 +def node5198 : Tree Nat := .node node4674 node5197 +def node5199 : Tree Nat := .node node5194 node5198 +def node5200 : Tree Nat := .leaf 12486994201263968925526388919172665222994392570659884603436627838501486955279062480481224412253967884639307724485667056400999206058001035727732736 +def node5201 : Tree Nat := .node node5200 node57 +def node5202 : Tree Nat := .node node3366 node5201 +def node5203 : Tree Nat := .node node4683 node5202 +def node5204 : Tree Nat := .node node4680 node5203 +def node5205 : Tree Nat := .node node5199 node5204 +def node5206 : Tree Nat := .leaf 190536410541747572716161940294993060653600960856016305594430966774009505543198585212421026798308836130360530464111497273237023284518648283136 +def node5207 : Tree Nat := .node node5206 node591 +def node5208 : Tree Nat := .node node3150 node5207 +def node5209 : Tree Nat := .node node4693 node5208 +def node5210 : Tree Nat := .node node4690 node5209 +def node5211 : Tree Nat := .leaf 44362715105933037753254626946289339254982993206013065202727673289833940924890009968639590497666233249558261793234096378521935937536 +def node5212 : Tree Nat := .node node5211 node607 +def node5213 : Tree Nat := .node node2746 node5212 +def node5214 : Tree Nat := .node node4184 node5213 +def node5215 : Tree Nat := .leaf 818347651974035467503297424206899788054160511510766197370822842024033449101168638720817523081476039287721671031890028136898031206126605324324790337536 +def node5216 : Tree Nat := .node node5215 node57 +def node5217 : Tree Nat := .node node4187 node5216 +def node5218 : Tree Nat := .node node4698 node5217 +def node5219 : Tree Nat := .node node5214 node5218 +def node5220 : Tree Nat := .node node5210 node5219 +def node5221 : Tree Nat := .node node5205 node5220 +def node5222 : Tree Nat := .leaf 744282853678701455922507579277316643178128753343813693728245963960974631028119473486019635930893891134220822134720086518222474266894401536 +def node5223 : Tree Nat := .node node5222 node654 +def node5224 : Tree Nat := .node node3042 node5223 +def node5225 : Tree Nat := .node node4709 node5224 +def node5226 : Tree Nat := .node node4706 node5225 +def node5227 : Tree Nat := .leaf 173291855882550928723650886508942731464777317210988535948154973788413831737851601439998400381508723631087101800815175067957723136 +def node5228 : Tree Nat := .node node5227 node670 +def node5229 : Tree Nat := .node node2629 node5228 +def node5230 : Tree Nat := .node node4200 node5229 +def node5231 : Tree Nat := .leaf 3196670515523576044934755563308202297086564498088930458479776726656380660551439995003193449537015778467662777468321030882046043949044770465682292736 +def node5232 : Tree Nat := .node node5231 node57 +def node5233 : Tree Nat := .node node3611 node5232 +def node5234 : Tree Nat := .node node4714 node5233 +def node5235 : Tree Nat := .node node5230 node5234 +def node5236 : Tree Nat := .node node5226 node5235 +def node5237 : Tree Nat := .leaf 48777321098687378615337456715518223527321845979140174232174327494146433419058837814379782860367062049372295798774513783941831078791872864321536 +def node5238 : Tree Nat := .node node5237 node716 +def node5239 : Tree Nat := .node node3258 node5238 +def node5240 : Tree Nat := .node node4724 node5239 +def node5241 : Tree Nat := .node node4721 node5240 +def node5242 : Tree Nat := .leaf 11356855067118857664833184498250070849275646260739344691898284362197488876771842551971735167402555711886914438783535257879611741044736 +def node5243 : Tree Nat := .node node5242 node732 +def node5244 : Tree Nat := .node node2840 node5243 +def node5245 : Tree Nat := .node node4211 node5244 +def node5246 : Tree Nat := .leaf 209496998905353079680844140596966345741865090946756146526930647558152562969899171512529285908857866057656747784163844710743403892051149268388908300763136 +def node5247 : Tree Nat := .node node5246 node57 +def node5248 : Tree Nat := .node node4214 node5247 +def node5249 : Tree Nat := .node node4729 node5248 +def node5250 : Tree Nat := .node node5245 node5249 +def node5251 : Tree Nat := .node node5241 node5250 +def node5252 : Tree Nat := .node node5236 node5251 +def node5253 : Tree Nat := .node node5221 node5252 +def node5254 : Tree Nat := .leaf 46517678354918840995156723704832290198633047083988355858015372747560914439257467092876227245680868195888801385276915466316975054029586432 +def node5255 : Tree Nat := .node node5254 node780 +def node5256 : Tree Nat := .node node3003 node5255 +def node5257 : Tree Nat := .node node4741 node5256 +def node5258 : Tree Nat := .node node4738 node5257 +def node5259 : Tree Nat := .leaf 10830740992659433045228180406808920716548582325686783496759685861775864483615725089999900023844295226942972196749845659618639872 +def node5260 : Tree Nat := .node node5259 node796 +def node5261 : Tree Nat := .node node2599 node5260 +def node5262 : Tree Nat := .node node4231 node5261 +def node5263 : Tree Nat := .leaf 199791907220223502808422222706762643567910281130558153654986045416023791284464999687699590596063486154228923591770186124585499656837841837612859392 +def node5264 : Tree Nat := .node node5263 node57 +def node5265 : Tree Nat := .node node3625 node5264 +def node5266 : Tree Nat := .node node4746 node5265 +def node5267 : Tree Nat := .node node5262 node5266 +def node5268 : Tree Nat := .node node5258 node5267 +def node5269 : Tree Nat := .leaf 3048582568667961163458591044719888970457615373696260889510895468384152088691177363398736428772941378085768487423882480471450028450053317722112 +def node5270 : Tree Nat := .node node5269 node842 +def node5271 : Tree Nat := .node node3219 node5270 +def node5272 : Tree Nat := .node node4756 node5271 +def node5273 : Tree Nat := .node node4753 node5272 +def node5274 : Tree Nat := .leaf 709803441694928604052074031140629428079727891296209043243642772637343054798240159498233447962659731992932159677525871305250782052352 +def node5275 : Tree Nat := .node node5274 node858 +def node5276 : Tree Nat := .node node2793 node5275 +def node5277 : Tree Nat := .node node4242 node5276 +def node5278 : Tree Nat := .leaf 13093562431584567480052758787310396608866568184172259157933165472384535185618698219533080369303616628603546736510240325575243894462162600457284744118272 +def node5279 : Tree Nat := .node node5278 node57 +def node5280 : Tree Nat := .node node4245 node5279 +def node5281 : Tree Nat := .node node4761 node5280 +def node5282 : Tree Nat := .node node5277 node5281 +def node5283 : Tree Nat := .node node5273 node5282 +def node5284 : Tree Nat := .node node5268 node5283 +def node5285 : Tree Nat := .leaf 11908525658859223294760121268437066290850060053501019099651935423375594096449911575776314174894302258147533154036679140520163081879994499072 +def node5286 : Tree Nat := .node node5285 node905 +def node5287 : Tree Nat := .node node3111 node5286 +def node5288 : Tree Nat := .node node4772 node5287 +def node5289 : Tree Nat := .node node4769 node5288 +def node5290 : Tree Nat := .leaf 2772669694120814859578414184143083703436437075375816575170479580614621307805625623039974406104139578097391815424313379143561510912 +def node5291 : Tree Nat := .node node5290 node4259 +def node5292 : Tree Nat := .node node2707 node5291 +def node5293 : Tree Nat := .node node4258 node5292 +def node5294 : Tree Nat := .leaf 51146728248377216718956089012931236753385031969422887335676427626502090568823039920051095192592252455482604439493128705667448900943273531706422853632 +def node5295 : Tree Nat := .node node5294 node57 +def node5296 : Tree Nat := .node node3923 node5295 +def node5297 : Tree Nat := .node node4777 node5296 +def node5298 : Tree Nat := .node node5293 node5297 +def node5299 : Tree Nat := .node node5289 node5298 +def node5300 : Tree Nat := .leaf 780437137578998057845399307448291576437149535666242787714789239906342934704941405030076525765872992789956732780361796928663819755034044952215552 +def node5301 : Tree Nat := .node node5300 node57 +def node5302 : Tree Nat := .node node3327 node5301 +def node5303 : Tree Nat := .node node4787 node5302 +def node5304 : Tree Nat := .node node4784 node5303 +def node5305 : Tree Nat := .leaf 181709681073901722637330951972001133588410340171829515070372549795159822028349480831547762678440891390190630556309049394056184769544192 +def node5306 : Tree Nat := .node node5305 node982 +def node5307 : Tree Nat := .node node2887 node5306 +def node5308 : Tree Nat := .node node4272 node5307 +def node5309 : Tree Nat := .leaf 3351951982485649274893506249551461531869841455148098344430890360930441007518386744200468574541725856922507964546621513378052468595444578938511942391693312 +def node5310 : Tree Nat := .node node5309 node57 +def node5311 : Tree Nat := .node node4275 node5310 +def node5312 : Tree Nat := .node node4792 node5311 +def node5313 : Tree Nat := .node node5308 node5312 +def node5314 : Tree Nat := .node node5304 node5313 +def node5315 : Tree Nat := .node node5299 node5314 +def node5316 : Tree Nat := .node node5284 node5315 +def node5317 : Tree Nat := .node node5253 node5316 +def node5318 : Tree Nat := .node node5190 node5317 +def node5319 : Tree Nat := .leaf 40223423789827791298722074994617538382438097461777180133170684331165292090220640930405622894500710283070095574559458152561261648435839875859997610404216832 +def node5320 : Tree Nat := .node node1006 node5319 +def node5321 : Tree Nat := .node node5320 node4285 +def node5322 : Tree Nat := .node node5321 node4802 +def node5323 : Tree Nat := .leaf 1453677448591213781098647615776009068707282721374636120562980398361278576226795846652382101427527131121525043522017365688414271982010368 +def node5324 : Tree Nat := .node node5323 node1032 +def node5325 : Tree Nat := .node node2935 node5324 +def node5326 : Tree Nat := .node node4290 node5325 +def node5327 : Tree Nat := .node node5322 node5326 +def node5328 : Tree Nat := .leaf 6243497100631984462763194459586332611497196285329942301718313919250743477639531240240612206126983942319653862242833528200499603029000517863866368 +def node5329 : Tree Nat := .node node5328 node57 +def node5330 : Tree Nat := .node node3658 node5329 +def node5331 : Tree Nat := .node node4811 node5330 +def node5332 : Tree Nat := .node node4808 node5331 +def node5333 : Tree Nat := .node node5327 node5332 +def node5334 : Tree Nat := .leaf 95268205270873786358080970147496530326800480428008152797215483387004752771599292606210513399154418065180265232055748636618511642259324141568 +def node5335 : Tree Nat := .node node5334 node4303 +def node5336 : Tree Nat := .node node3160 node5335 +def node5337 : Tree Nat := .node node4821 node5336 +def node5338 : Tree Nat := .node node4818 node5337 +def node5339 : Tree Nat := .leaf 22181357552966518876627313473144669627491496603006532601363836644916970462445004984319795248833116624779130896617048189260967968768 +def node5340 : Tree Nat := .node node5339 node4311 +def node5341 : Tree Nat := .node node2756 node5340 +def node5342 : Tree Nat := .node node4310 node5341 +def node5343 : Tree Nat := .leaf 409173825987017733751648712103449894027080255755383098685411421012016724550584319360408761540738019643860835515945014068449015603063302662162395168768 +def node5344 : Tree Nat := .node node5343 node57 +def node5345 : Tree Nat := .node node4316 node5344 +def node5346 : Tree Nat := .node node4826 node5345 +def node5347 : Tree Nat := .node node5342 node5346 +def node5348 : Tree Nat := .node node5338 node5347 +def node5349 : Tree Nat := .node node5333 node5348 +def node5350 : Tree Nat := .leaf 372141426839350727961253789638658321589064376671906846864122981980487315514059736743009817965446945567110411067360043259111237133447200768 +def node5351 : Tree Nat := .node node5350 node1157 +def node5352 : Tree Nat := .node node3052 node5351 +def node5353 : Tree Nat := .node node4837 node5352 +def node5354 : Tree Nat := .node node4834 node5353 +def node5355 : Tree Nat := .leaf 86645927941275464361825443254471365732388658605494267974077486894206915868925800719999200190754361815543550900407587533978861568 +def node5356 : Tree Nat := .node node5355 node4330 +def node5357 : Tree Nat := .node node2639 node5356 +def node5358 : Tree Nat := .node node4329 node5357 +def node5359 : Tree Nat := .leaf 1598335257761788022467377781654101148543282249044465229239888363328190330275719997501596724768507889233831388734160515441023021974522385232841146368 +def node5360 : Tree Nat := .node node5359 node57 +def node5361 : Tree Nat := .node node3484 node5360 +def node5362 : Tree Nat := .node node4842 node5361 +def node5363 : Tree Nat := .node node5358 node5362 +def node5364 : Tree Nat := .node node5354 node5363 +def node5365 : Tree Nat := .leaf 24388660549343689307668728357759111763660922989570087116087163747073216709529418907189891430183531024686147899387256891970915539395936432160768 +def node5366 : Tree Nat := .node node5365 node1219 +def node5367 : Tree Nat := .node node3268 node5366 +def node5368 : Tree Nat := .node node4852 node5367 +def node5369 : Tree Nat := .node node4849 node5368 +def node5370 : Tree Nat := .leaf 5678427533559428832416592249125035424637823130369672345949142181098744438385921275985867583701277855943457219391767628939805870522368 +def node5371 : Tree Nat := .node node5370 node1235 +def node5372 : Tree Nat := .node node2850 node5371 +def node5373 : Tree Nat := .node node4343 node5372 +def node5374 : Tree Nat := .leaf 104748499452676539840422070298483172870932545473378073263465323779076281484949585756264642954428933028828373892081922355371701946025574634194454150381568 +def node5375 : Tree Nat := .node node5374 node57 +def node5376 : Tree Nat := .node node4346 node5375 +def node5377 : Tree Nat := .node node4857 node5376 +def node5378 : Tree Nat := .node node5373 node5377 +def node5379 : Tree Nat := .node node5369 node5378 +def node5380 : Tree Nat := .node node5364 node5379 +def node5381 : Tree Nat := .node node5349 node5380 +def node5382 : Tree Nat := .leaf 643574780637244660779553199913880614119009559388434882130730949298644673443530254886489966312011364529121529192951330440980186374973438013759961766467469312 +def node5383 : Tree Nat := .node node1257 node5382 +def node5384 : Tree Nat := .node node5383 node4354 +def node5385 : Tree Nat := .node node5384 node4865 +def node5386 : Tree Nat := .leaf 23258839177459420497578361852416145099316523541994177929007686373780457219628733546438113622840434097944400692638457733158487527014793216 +def node5387 : Tree Nat := .node node5386 node1283 +def node5388 : Tree Nat := .node node2974 node5387 +def node5389 : Tree Nat := .node node4869 node5388 +def node5390 : Tree Nat := .node node5385 node5389 +def node5391 : Tree Nat := .leaf 99895953610111751404211111353381321783955140565279076827493022708011895642232499843849795298031743077114461795885093062292749828418920918806429696 +def node5392 : Tree Nat := .node node5391 node57 +def node5393 : Tree Nat := .node node3415 node5392 +def node5394 : Tree Nat := .node node4878 node5393 +def node5395 : Tree Nat := .node node4875 node5394 +def node5396 : Tree Nat := .node node5390 node5395 +def node5397 : Tree Nat := .leaf 1524291284333980581729295522359944485228807686848130444755447734192076044345588681699368214386470689042884243711941240235725014225026658861056 +def node5398 : Tree Nat := .node node5397 node1345 +def node5399 : Tree Nat := .node node3199 node5398 +def node5400 : Tree Nat := .node node4888 node5399 +def node5401 : Tree Nat := .node node4885 node5400 +def node5402 : Tree Nat := .leaf 354901720847464302026037015570314714039863945648104521621821386318671527399120079749116723981329865996466079838762935652625391026176 +def node5403 : Tree Nat := .node node5402 node1361 +def node5404 : Tree Nat := .node node2803 node5403 +def node5405 : Tree Nat := .node node4374 node5404 +def node5406 : Tree Nat := .leaf 6546781215792283740026379393655198304433284092086129578966582736192267592809349109766540184651808314301773368255120162787621947231081300228642372059136 +def node5407 : Tree Nat := .node node5406 node57 +def node5408 : Tree Nat := .node node4377 node5407 +def node5409 : Tree Nat := .node node4893 node5408 +def node5410 : Tree Nat := .node node5405 node5409 +def node5411 : Tree Nat := .node node5401 node5410 +def node5412 : Tree Nat := .node node5396 node5411 +def node5413 : Tree Nat := .leaf 5954262829429611647380060634218533145425030026750509549825967711687797048224955787888157087447151129073766577018339570260081540939997249536 +def node5414 : Tree Nat := .node node5413 node1408 +def node5415 : Tree Nat := .node node3091 node5414 +def node5416 : Tree Nat := .node node4904 node5415 +def node5417 : Tree Nat := .node node4901 node5416 +def node5418 : Tree Nat := .leaf 1386334847060407429789207092071541851718218537687908287585239790307310653902812811519987203052069789048695907712156689571780755456 +def node5419 : Tree Nat := .node node5418 node4391 +def node5420 : Tree Nat := .node node2678 node5419 +def node5421 : Tree Nat := .node node4390 node5420 +def node5422 : Tree Nat := .leaf 25573364124188608359478044506465618376692515984711443667838213813251045284411519960025547596296126227741302219746564352833724450471636765853211426816 +def node5423 : Tree Nat := .node node5422 node57 +def node5424 : Tree Nat := .node node3966 node5423 +def node5425 : Tree Nat := .node node4909 node5424 +def node5426 : Tree Nat := .node node5421 node5425 +def node5427 : Tree Nat := .node node5417 node5426 +def node5428 : Tree Nat := .leaf 390218568789499028922699653724145788218574767833121393857394619953171467352470702515038262882936496394978366390180898464331909877517022476107776 +def node5429 : Tree Nat := .node node5428 node57 +def node5430 : Tree Nat := .node node3307 node5429 +def node5431 : Tree Nat := .node node4919 node5430 +def node5432 : Tree Nat := .node node4916 node5431 +def node5433 : Tree Nat := .leaf 90854840536950861318665475986000566794205170085914757535186274897579911014174740415773881339220445695095315278154524697028092384772096 +def node5434 : Tree Nat := .node node5433 node1485 +def node5435 : Tree Nat := .node node2905 node5434 +def node5436 : Tree Nat := .node node4404 node5435 +def node5437 : Tree Nat := .leaf 1675975991242824637446753124775730765934920727574049172215445180465220503759193372100234287270862928461253982273310756689026234297722289469255971195846656 +def node5438 : Tree Nat := .node node5437 node57 +def node5439 : Tree Nat := .node node4407 node5438 +def node5440 : Tree Nat := .node node4924 node5439 +def node5441 : Tree Nat := .node node5436 node5440 +def node5442 : Tree Nat := .node node5432 node5441 +def node5443 : Tree Nat := .node node5427 node5442 +def node5444 : Tree Nat := .node node5412 node5443 +def node5445 : Tree Nat := .node node5381 node5444 +def node5446 : Tree Nat := .leaf 160893695159311165194888299978470153529752389847108720532682737324661168360882563721622491578002841132280382298237832610245046593743358950037668230330318848 +def node5447 : Tree Nat := .node node1508 node5446 +def node5448 : Tree Nat := .node node5447 node4416 +def node5449 : Tree Nat := .node node5448 node4933 +def node5450 : Tree Nat := .leaf 5814709794364855124394590463104036274829130885498544482251921593445114304907183386609528405710108524486100173469099443110966950478479360 +def node5451 : Tree Nat := .node node5450 node1534 +def node5452 : Tree Nat := .node node2983 node5451 +def node5453 : Tree Nat := .node node4937 node5452 +def node5454 : Tree Nat := .node node5449 node5453 +def node5455 : Tree Nat := .leaf 24973988402527937851052777838345330445988785141319769206873255677002973910558124960962448824507935769278615448971293547982791108775154176952893440 +def node5456 : Tree Nat := .node node5455 node57 +def node5457 : Tree Nat := .node node3385 node5456 +def node5458 : Tree Nat := .node node4946 node5457 +def node5459 : Tree Nat := .node node4943 node5458 +def node5460 : Tree Nat := .node node5454 node5459 +def node5461 : Tree Nat := .leaf 381072821083495145432323880589986121307201921712032611188861933548019011086397170424842053596617672260721060928064538221445517893850208665600 +def node5462 : Tree Nat := .node node5461 node1596 +def node5463 : Tree Nat := .node node3169 node5462 +def node5464 : Tree Nat := .node node4956 node5463 +def node5465 : Tree Nat := .node node4953 node5464 +def node5466 : Tree Nat := .leaf 88725430211866075506509253892578678509965986412026130405455346579667881849780019937279180995332466499116521168616553527785522462720 +def node5467 : Tree Nat := .node node5466 node1612 +def node5468 : Tree Nat := .node node2765 node5467 +def node5469 : Tree Nat := .node node4433 node5468 +def node5470 : Tree Nat := .leaf 1636695303948070935006594848413799576108321023021532394741645684048066898202337277441635046162952078575443342063780045889202345342597953587656922234880 +def node5471 : Tree Nat := .node node5470 node57 +def node5472 : Tree Nat := .node node4436 node5471 +def node5473 : Tree Nat := .node node4961 node5472 +def node5474 : Tree Nat := .node node5469 node5473 +def node5475 : Tree Nat := .node node5465 node5474 +def node5476 : Tree Nat := .node node5460 node5475 +def node5477 : Tree Nat := .leaf 1488565707357402911845015158554633286356257506687627387456491927921949262056238946972039271861787782268441644259536652722161906334595809280 +def node5478 : Tree Nat := .node node5477 node1659 +def node5479 : Tree Nat := .node node3061 node5478 +def node5480 : Tree Nat := .node node4972 node5479 +def node5481 : Tree Nat := .node node4969 node5480 +def node5482 : Tree Nat := .leaf 346583711765101857447301773017885462929554634421977071896309947576827663475703202879996800763017447262174052485902898307268608000 +def node5483 : Tree Nat := .node node5482 node1675 +def node5484 : Tree Nat := .node node2687 node5483 +def node5485 : Tree Nat := .node node4449 node5484 +def node5486 : Tree Nat := .leaf 6393341031047152089869511126616404594173128996177860916959553453312761321102879990006386899074031556935325554936641412726984771044635974619323432960 +def node5487 : Tree Nat := .node node5486 node57 +def node5488 : Tree Nat := .node node3493 node5487 +def node5489 : Tree Nat := .node node4977 node5488 +def node5490 : Tree Nat := .node node5485 node5489 +def node5491 : Tree Nat := .node node5481 node5490 +def node5492 : Tree Nat := .leaf 97554642197374757230674913431036447054643691958280348464348654988292866838117675628759565720734124098744591597546492266683205698780752322232320 +def node5493 : Tree Nat := .node node5492 node57 +def node5494 : Tree Nat := .node node3277 node5493 +def node5495 : Tree Nat := .node node4987 node5494 +def node5496 : Tree Nat := .node node4984 node5495 +def node5497 : Tree Nat := .leaf 22713710134237715329666368996500141698551292521478689383796568724394977753543685103943470334805111423773828838881444288091089891491840 +def node5498 : Tree Nat := .node node5497 node1736 +def node5499 : Tree Nat := .node node2859 node5498 +def node5500 : Tree Nat := .node node4460 node5499 +def node5501 : Tree Nat := .leaf 418993997810706159361688281193932691483730181893512293053861295116305125939798343025058571817715732115313495568327689255333308310987814423801934066483200 +def node5502 : Tree Nat := .node node5501 node57 +def node5503 : Tree Nat := .node node4463 node5502 +def node5504 : Tree Nat := .node node4992 node5503 +def node5505 : Tree Nat := .node node5500 node5504 +def node5506 : Tree Nat := .node node5496 node5505 +def node5507 : Tree Nat := .node node5491 node5506 +def node5508 : Tree Nat := .node node5476 node5507 +def node5509 : Tree Nat := .leaf 93035356709837681990313447409664580397266094167976711716030745495121828878514934185752454491361736391777602768077950854063189558260924416 +def node5510 : Tree Nat := .node node5509 node1784 +def node5511 : Tree Nat := .node node3022 node5510 +def node5512 : Tree Nat := .node node5004 node5511 +def node5513 : Tree Nat := .node node5001 node5512 +def node5514 : Tree Nat := .leaf 21661481985318866090456360813617841433097164651373566993519371723551728967231450179999800047688590453885906614567828362075570176 +def node5515 : Tree Nat := .node node5514 node1800 +def node5516 : Tree Nat := .node node2618 node5515 +def node5517 : Tree Nat := .node node4477 node5516 +def node5518 : Tree Nat := .leaf 399583814440447005616844445413525287135820562261116307309972090832047582568929999375399181192126972308457847183540209989894170100312292097215430656 +def node5519 : Tree Nat := .node node5518 node57 +def node5520 : Tree Nat := .node node3454 node5519 +def node5521 : Tree Nat := .node node5009 node5520 +def node5522 : Tree Nat := .node node5517 node5521 +def node5523 : Tree Nat := .node node5513 node5522 +def node5524 : Tree Nat := .leaf 6097165137335922326917182089439777940915230747392521779021790936768304177382354726797472857545882756171536974847131135642785942199358283841536 +def node5525 : Tree Nat := .node node5524 node1846 +def node5526 : Tree Nat := .node node3238 node5525 +def node5527 : Tree Nat := .node node5019 node5526 +def node5528 : Tree Nat := .node node5016 node5527 +def node5529 : Tree Nat := .leaf 1419606883389857208104148062281258856159455782592418086487285545274686109596480318996466895925319463985864309683645185693468166455296 +def node5530 : Tree Nat := .node node5529 node4489 +def node5531 : Tree Nat := .node node2812 node5530 +def node5532 : Tree Nat := .node node4488 node5531 +def node5533 : Tree Nat := .leaf 26187124863169134960105517574620793217733136368344518315866330944769070371237396439066160738607233257207093473020480609612112920645704172670598854475776 +def node5534 : Tree Nat := .node node5533 node57 +def node5535 : Tree Nat := .node node4494 node5534 +def node5536 : Tree Nat := .node node5024 node5535 +def node5537 : Tree Nat := .node node5532 node5536 +def node5538 : Tree Nat := .node node5528 node5537 +def node5539 : Tree Nat := .node node5523 node5538 +def node5540 : Tree Nat := .leaf 23817051317718446589520242536874132581700120107002038199303870846751188192899823151552628349788604516295066308033744199783193994963217022976 +def node5541 : Tree Nat := .node node5540 node1909 +def node5542 : Tree Nat := .node node3130 node5541 +def node5543 : Tree Nat := .node node5035 node5542 +def node5544 : Tree Nat := .node node5032 node5543 +def node5545 : Tree Nat := .leaf 5545339388241629719156828368286167406872874150751633150340959161229242615611251246079948812208279156194783026385716950972535668736 +def node5546 : Tree Nat := .node node5545 node4508 +def node5547 : Tree Nat := .node node2726 node5546 +def node5548 : Tree Nat := .node node4507 node5547 +def node5549 : Tree Nat := .leaf 102293456496754433437912178025862473506770063938845774671352855253004181137646079840102190385184504910965208878986254815186468534472732798164681097216 +def node5550 : Tree Nat := .node node5549 node57 +def node5551 : Tree Nat := .node node3716 node5550 +def node5552 : Tree Nat := .node node5040 node5551 +def node5553 : Tree Nat := .node node5548 node5552 +def node5554 : Tree Nat := .node node5544 node5553 +def node5555 : Tree Nat := .leaf 1560874275157996115690798614896583152874299071332485575429578479812685869409882810060153051531745985579913465560713452652525813674856116278788096 +def node5556 : Tree Nat := .node node5555 node57 +def node5557 : Tree Nat := .node node3346 node5556 +def node5558 : Tree Nat := .node node5050 node5557 +def node5559 : Tree Nat := .node node5047 node5558 +def node5560 : Tree Nat := .leaf 363419362147803445274661903944002267176820680343659030140745099590319644056698961663095525356881782780381260957875593877439835176697856 +def node5561 : Tree Nat := .node node5560 node4522 +def node5562 : Tree Nat := .node node2914 node5561 +def node5563 : Tree Nat := .node node4521 node5562 +def node5564 : Tree Nat := .leaf 6703903964971298549787012499102923063739682910296196688861780721860882015036773488400937149083451713845015929093243026091490939298431221425120354643214336 +def node5565 : Tree Nat := .node node5564 node57 +def node5566 : Tree Nat := .node node4527 node5565 +def node5567 : Tree Nat := .node node5055 node5566 +def node5568 : Tree Nat := .node node5563 node5567 +def node5569 : Tree Nat := .node node5559 node5568 +def node5570 : Tree Nat := .node node5554 node5569 +def node5571 : Tree Nat := .node node5539 node5570 +def node5572 : Tree Nat := .node node5508 node5571 +def node5573 : Tree Nat := .node node5445 node5572 +def node5574 : Tree Nat := .node node5318 node5573 +def node5575 : Tree Nat := .leaf 2189386711818932834454897248823790917467772135415569089195717648017775218925156563773536139663638528 +def node5576 : Tree Nat := .node node5575 node19 +def node5577 : Tree Nat := .node node17 node5576 +def node5578 : Tree Nat := .node node5577 node5070 +def node5579 : Tree Nat := .node node5067 node5578 +def node5580 : Tree Nat := .leaf 57586096570152913699974892898380567793532123114264532903689671329431521032595044740083720782129802971518987656109067457577065805510327036019308994315074097496719360 +def node5581 : Tree Nat := .node node31 node5580 +def node5582 : Tree Nat := .node node5581 node4028 +def node5583 : Tree Nat := .node node5582 node4544 +def node5584 : Tree Nat := .node node5583 node5076 +def node5585 : Tree Nat := .node node5579 node5584 +def node5586 : Tree Nat := .leaf 878694100496718043517683302282418331810487718418343092402491322775749527474899974671687634004666183037093927858109549828751614463963730408009475621301382021120 +def node5587 : Tree Nat := .node node63 node5586 +def node5588 : Tree Nat := .node node5587 node4037 +def node5589 : Tree Nat := .leaf 2646806125039081304397317151303087171187948437649954100651425840454163812567262224495386487112141277222409493826498595913728 +def node5590 : Tree Nat := .node node5589 node4039 +def node5591 : Tree Nat := .node node2309 node5590 +def node5592 : Tree Nat := .node node5588 node5591 +def node5593 : Tree Nat := .node node5592 node5082 +def node5594 : Tree Nat := .leaf 3773962424821541352241554580988268890916921220416440428376206300245624162392148852086126725177658767541468375030763844899770584629924792632561434251432696043649395916800 +def node5595 : Tree Nat := .node node94 node5594 +def node5596 : Tree Nat := .node node5595 node4045 +def node5597 : Tree Nat := .node node5596 node5086 +def node5598 : Tree Nat := .node node5597 node5091 +def node5599 : Tree Nat := .node node5593 node5598 +def node5600 : Tree Nat := .node node5585 node5599 +def node5601 : Tree Nat := .leaf 3432398830065304857490950399540699255440842689152957102014383032679942779647265676015380471756567731652460722957964924405048106141135544315780840644153442304 +def node5602 : Tree Nat := .node node126 node5601 +def node5603 : Tree Nat := .node node5602 node4059 +def node5604 : Tree Nat := .node node5603 node4570 +def node5605 : Tree Nat := .leaf 555356629339436621422705643604083549796703175812729720186230818033777128702966543005970142905499648 +def node5606 : Tree Nat := .node node5605 node145 +def node5607 : Tree Nat := .node node143 node5606 +def node5608 : Tree Nat := .node node5607 node5097 +def node5609 : Tree Nat := .node node5604 node5608 +def node5610 : Tree Nat := .leaf 14742040721959145907193572581985425355144223517251720423344555860336658771056150386295887417474053351626328612099336838228924563858661496439868259108432505060169089024 +def node5611 : Tree Nat := .node node157 node5610 +def node5612 : Tree Nat := .node node5611 node4064 +def node5613 : Tree Nat := .node node5612 node5102 +def node5614 : Tree Nat := .node node5613 node5107 +def node5615 : Tree Nat := .node node5609 node5614 +def node5616 : Tree Nat := .leaf 224945689727159819140526925384299092943484855915095831655181262278137644615813229662050950266761710772162640267505575307940906219522194045013888223456112257531904 +def node5617 : Tree Nat := .node node188 node5616 +def node5618 : Tree Nat := .node node5617 node4073 +def node5619 : Tree Nat := .node node5618 node4585 +def node5620 : Tree Nat := .leaf 36395852060389318421558437059237219519476739330063054942124822890661617906677615362439259265740925042688 +def node5621 : Tree Nat := .node node5620 node207 +def node5622 : Tree Nat := .node node205 node5621 +def node5623 : Tree Nat := .node node5622 node5112 +def node5624 : Tree Nat := .node node5619 node5623 +def node5625 : Tree Nat := .node node5624 node5123 +def node5626 : Tree Nat := .node node5615 node5625 +def node5627 : Tree Nat := .node node5600 node5626 +def node5628 : Tree Nat := .leaf 921377545122446619199598286374089084696513969828232526459034741270904336521520715841339532514076847544303802497745079321233052888165232576308943909041185559947509760 +def node5629 : Tree Nat := .node node283 node5628 +def node5630 : Tree Nat := .node node5629 node4098 +def node5631 : Tree Nat := .node node5630 node4611 +def node5632 : Tree Nat := .node node5631 node5139 +def node5633 : Tree Nat := .node node5135 node5632 +def node5634 : Tree Nat := .leaf 14059105607947488696282932836518693308967803494693489478439861164411992439598399594747002144074658928593502845729752797260025831423419686528151609940822112337920 +def node5635 : Tree Nat := .node node314 node5634 +def node5636 : Tree Nat := .node node5635 node4107 +def node5637 : Tree Nat := .leaf 42348898000625300870357074420849394739007175002399265610422813447266621001076195591926183793794260435551246990570788552179712 +def node5638 : Tree Nat := .node node5637 node4109 +def node5639 : Tree Nat := .node node2348 node5638 +def node5640 : Tree Nat := .node node5636 node5639 +def node5641 : Tree Nat := .node node5640 node5145 +def node5642 : Tree Nat := .leaf 60383398797144661635864873295812302254670739526663046854019300803929986598274381633378027602842540280663494000492221518396329354078796682120982948022923136698390326280192 +def node5643 : Tree Nat := .node node345 node5642 +def node5644 : Tree Nat := .node node5643 node4115 +def node5645 : Tree Nat := .node node5644 node5149 +def node5646 : Tree Nat := .node node5645 node5154 +def node5647 : Tree Nat := .node node5641 node5646 +def node5648 : Tree Nat := .node node5633 node5647 +def node5649 : Tree Nat := .leaf 54918381281044877719855206392651166897110983445275426915757403066163643724790514859637941259714403933884985297128595659611000681447123937490221735813002035200 +def node5650 : Tree Nat := .node node377 node5649 +def node5651 : Tree Nat := .node node5650 node4126 +def node5652 : Tree Nat := .node node5651 node4637 +def node5653 : Tree Nat := .node node5652 node5161 +def node5654 : Tree Nat := .leaf 235872651551346334515097161311766805682307576276027526773512893765369012427281639192598065131464026281368828000278930719032607598304794807968136209381431654069536030720 +def node5655 : Tree Nat := .node node408 node5654 +def node5656 : Tree Nat := .node node5655 node4131 +def node5657 : Tree Nat := .node node5656 node5165 +def node5658 : Tree Nat := .node node5657 node5170 +def node5659 : Tree Nat := .node node5653 node5658 +def node5660 : Tree Nat := .leaf 3599131035634557106248430806148785487095757694641533306481751487365557872518522026383168663409045733420208023399877373016897694756423579675359994030934132051148800 +def node5661 : Tree Nat := .node node439 node5660 +def node5662 : Tree Nat := .node node5661 node4137 +def node5663 : Tree Nat := .node node5662 node4652 +def node5664 : Tree Nat := .leaf 582333632966229094744934992947795512311627829281008879073997166250585886506841845799028148250927087747072 +def node5665 : Tree Nat := .node node5664 node458 +def node5666 : Tree Nat := .node node456 node5665 +def node5667 : Tree Nat := .node node5666 node5175 +def node5668 : Tree Nat := .node node5663 node5667 +def node5669 : Tree Nat := .node node5668 node5186 +def node5670 : Tree Nat := .node node5659 node5669 +def node5671 : Tree Nat := .node node5648 node5670 +def node5672 : Tree Nat := .node node5627 node5671 +def node5673 : Tree Nat := .leaf 230344386280611654799899571593522271174128492457058131614758685317726084130380178960334883128519211886075950624436269830308263222041308144077235977260296389483560960 +def node5674 : Tree Nat := .node node534 node5673 +def node5675 : Tree Nat := .node node5674 node4169 +def node5676 : Tree Nat := .node node5675 node4679 +def node5677 : Tree Nat := .node node5676 node5203 +def node5678 : Tree Nat := .node node5199 node5677 +def node5679 : Tree Nat := .leaf 3514776401986872174070733209129673327241950873673372369609965291102998109899599898686750536018664732148375711432438199315006457855854921632037902485076679065600 +def node5680 : Tree Nat := .node node565 node5679 +def node5681 : Tree Nat := .node node5680 node4178 +def node5682 : Tree Nat := .leaf 671384968302596233310538984720783087325723506135598113335971432700568381724378710603707791852835836173666866106241120206848 +def node5683 : Tree Nat := .node node5682 node576 +def node5684 : Tree Nat := .node node2318 node5683 +def node5685 : Tree Nat := .node node5681 node5684 +def node5686 : Tree Nat := .node node5685 node5209 +def node5687 : Tree Nat := .leaf 15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581701120 +def node5688 : Tree Nat := .node node596 node5687 +def node5689 : Tree Nat := .node node5688 node4183 +def node5690 : Tree Nat := .node node5689 node5213 +def node5691 : Tree Nat := .node node5690 node5218 +def node5692 : Tree Nat := .node node5686 node5691 +def node5693 : Tree Nat := .node node5678 node5692 +def node5694 : Tree Nat := .leaf 13729595320261219429963801598162828783436871225587481175863347767765825373970314503510729704136356376575593698978553642258037770259868838872138627370782294016 +def node5695 : Tree Nat := .node node628 node5694 +def node5696 : Tree Nat := .node node5695 node4194 +def node5697 : Tree Nat := .node node5696 node4705 +def node5698 : Tree Nat := .node node5697 node5225 +def node5699 : Tree Nat := .leaf 58968162887836583628774290327941701420576894069006881693378223441372907724766428739197008436882098897514927714022334181986046867210859288386574915199012453909996240896 +def node5700 : Tree Nat := .node node659 node5699 +def node5701 : Tree Nat := .node node5700 node4199 +def node5702 : Tree Nat := .node node5701 node5229 +def node5703 : Tree Nat := .node node5702 node5234 +def node5704 : Tree Nat := .node node5698 node5703 +def node5705 : Tree Nat := .leaf 899782758908639276562107701537196371773939423660383326622446852883099765450118952401390792605852858064649697899976667853129539879058524906817102466776997000380416 +def node5706 : Tree Nat := .node node690 node5705 +def node5707 : Tree Nat := .node node5706 node4205 +def node5708 : Tree Nat := .node node5707 node4720 +def node5709 : Tree Nat := .leaf 143483647545765582238836146098915961567167914666594735829530551780492916747479060563462464412854064775168 +def node5710 : Tree Nat := .node node5709 node3879 +def node5711 : Tree Nat := .node node707 node5710 +def node5712 : Tree Nat := .node node5711 node5239 +def node5713 : Tree Nat := .node node5708 node5712 +def node5714 : Tree Nat := .node node5713 node5250 +def node5715 : Tree Nat := .node node5704 node5714 +def node5716 : Tree Nat := .node node5693 node5715 +def node5717 : Tree Nat := .leaf 858099707516326214372737599885174152158679412517913176174307932398192897924707006515319955082681819372162038923935107254640248499964582247459184612506337280 +def node5718 : Tree Nat := .node node754 node5717 +def node5719 : Tree Nat := .node node5718 node4222 +def node5720 : Tree Nat := .node node5719 node4737 +def node5721 : Tree Nat := .leaf 8885706069430985942763290297665336796747250813003675522979693088540434059247464688095522282864115712 +def node5722 : Tree Nat := .node node5721 node773 +def node5723 : Tree Nat := .node node771 node5722 +def node5724 : Tree Nat := .node node5723 node5256 +def node5725 : Tree Nat := .node node5720 node5724 +def node5726 : Tree Nat := .leaf 3685510180489786476798393145496356338786055879312930105836138965083617346086082863365358130056307390177215209990980317284932211552660930305235775636164742231736975360 +def node5727 : Tree Nat := .node node785 node5726 +def node5728 : Tree Nat := .node node5727 node4230 +def node5729 : Tree Nat := .node node5728 node5261 +def node5730 : Tree Nat := .node node5729 node5266 +def node5731 : Tree Nat := .node node5725 node5730 +def node5732 : Tree Nat := .leaf 56236422431789954785131731346074773235871213978773957913759444657647969758393598378988008576298635714374011382919011189040103325693678746112606439761226865049600 +def node5733 : Tree Nat := .node node816 node5732 +def node5734 : Tree Nat := .node node5733 node4236 +def node5735 : Tree Nat := .leaf 10742159492841539732968623755532529397211576098169569813375542923209094107590059369659324669645373378774685360979936660160512 +def node5736 : Tree Nat := .node node5735 node827 +def node5737 : Tree Nat := .node node2396 node5736 +def node5738 : Tree Nat := .node node5734 node5737 +def node5739 : Tree Nat := .node node5738 node5272 +def node5740 : Tree Nat := .node node5739 node5282 +def node5741 : Tree Nat := .node node5731 node5740 +def node5742 : Tree Nat := .leaf 219673525124179510879420825570604667588443933781101707663029612264654574899162059438551765038857615735539941188514382638444002725788495747562810213669766430720 +def node5743 : Tree Nat := .node node879 node5742 +def node5744 : Tree Nat := .node node5743 node4252 +def node5745 : Tree Nat := .node node5744 node4768 +def node5746 : Tree Nat := .leaf 35030187389102925351278355981180654679484354166649105427131482368284403502802505020376578227974438912 +def node5747 : Tree Nat := .node node5746 node3917 +def node5748 : Tree Nat := .node node896 node5747 +def node5749 : Tree Nat := .node node5748 node5287 +def node5750 : Tree Nat := .node node5745 node5749 +def node5751 : Tree Nat := .leaf 943490606205385338060388645247067222729230305104110107094051575061476049709126556770392260525856105125475312001115722876130430393219179231872544837525726616275963084800 +def node5752 : Tree Nat := .node node910 node5751 +def node5753 : Tree Nat := .node node5752 node4257 +def node5754 : Tree Nat := .node node5753 node5292 +def node5755 : Tree Nat := .node node5754 node5297 +def node5756 : Tree Nat := .node node5750 node5755 +def node5757 : Tree Nat := .leaf 14396524142538228424993723224595141948383030778566133225927005949462231490074088105532674653636182933680832093599509492067590779025694318701439976123735969858846720 +def node5758 : Tree Nat := .node node941 node5757 +def node5759 : Tree Nat := .node node5758 node4266 +def node5760 : Tree Nat := .node node5759 node4783 +def node5761 : Tree Nat := .leaf 2295738360732249315821378337582655385074686634665515773272488828487886667959664969015399430603964229353472 +def node5762 : Tree Nat := .node node5761 node960 +def node5763 : Tree Nat := .node node958 node5762 +def node5764 : Tree Nat := .node node5763 node5302 +def node5765 : Tree Nat := .node node5760 node5764 +def node5766 : Tree Nat := .node node5765 node5313 +def node5767 : Tree Nat := .node node5756 node5766 +def node5768 : Tree Nat := .node node5741 node5767 +def node5769 : Tree Nat := .node node5716 node5768 +def node5770 : Tree Nat := .node node5672 node5769 +def node5771 : Tree Nat := .leaf 172758289710458741099924678695141703380596369342793598711069013988294563097785134220251162346389408914556962968327202372731197416530981108057926982945222292188168192 +def node5772 : Tree Nat := .node node1037 node5771 +def node5773 : Tree Nat := .node node5772 node4294 +def node5774 : Tree Nat := .node node5773 node4807 +def node5775 : Tree Nat := .node node5774 node5331 +def node5776 : Tree Nat := .node node5327 node5775 +def node5777 : Tree Nat := .leaf 2636082301490154130553049906847254995431463155255029277207473968327248582424699924015062902013998549111281783574328649486254843391891191224028426863826836652032 +def node5778 : Tree Nat := .node node1068 node5777 +def node5779 : Tree Nat := .node node5778 node4300 +def node5780 : Tree Nat := .node node5779 node4817 +def node5781 : Tree Nat := .leaf 1147029276087807981331730127936114525933047700271294893060656918331081912028139924153181886242000967041024 +def node5782 : Tree Nat := .node node5781 node3943 +def node5783 : Tree Nat := .node node1085 node5782 +def node5784 : Tree Nat := .node node5783 node5336 +def node5785 : Tree Nat := .node node5780 node5784 +def node5786 : Tree Nat := .leaf 11321887274464624056724663742964806672750763661249321285128618900736872487176446556258380175532976302624405125092291534699311753889774377897684302754298088130948186570752 +def node5787 : Tree Nat := .node node1099 node5786 +def node5788 : Tree Nat := .node node5787 node4309 +def node5789 : Tree Nat := .node node5788 node5341 +def node5790 : Tree Nat := .node node5789 node5346 +def node5791 : Tree Nat := .node node5785 node5790 +def node5792 : Tree Nat := .node node5776 node5791 +def node5793 : Tree Nat := .leaf 6864797660130609714981900799081393888654403602739538719933448179968630509121162187720672976632887255545678035770191461744913840835552817479440134532235264000 +def node5794 : Tree Nat := .node node1131 node5793 +def node5795 : Tree Nat := .node node5794 node4323 +def node5796 : Tree Nat := .node node5795 node4833 +def node5797 : Tree Nat := .node node5796 node5353 +def node5798 : Tree Nat := .leaf 29484081443918291814387145163970850710288447034503440846689111720669494125318002343544287746094063204967518383103655267999643923239321219570589171632323907983916400640 +def node5799 : Tree Nat := .node node1162 node5798 +def node5800 : Tree Nat := .node node5799 node4328 +def node5801 : Tree Nat := .node node5800 node5357 +def node5802 : Tree Nat := .node node5801 node5362 +def node5803 : Tree Nat := .node node5797 node5802 +def node5804 : Tree Nat := .leaf 449891379454319638281053850768598185886969711830191663310111953113244147385570345468963305829908562454322154118294214335211488223456107584263290777352257310556160 +def node5805 : Tree Nat := .node node1193 node5804 +def node5806 : Tree Nat := .node node5805 node4337 +def node5807 : Tree Nat := .leaf 1404743933679278272772820029569638459635359951299097590979878689958112306377161609878527072184394980301500260434648827428864 +def node5808 : Tree Nat := .node node5807 node1204 +def node5809 : Tree Nat := .node node2445 node5808 +def node5810 : Tree Nat := .node node5806 node5809 +def node5811 : Tree Nat := .node node5810 node5368 +def node5812 : Tree Nat := .node node5811 node5378 +def node5813 : Tree Nat := .node node5803 node5812 +def node5814 : Tree Nat := .node node5792 node5813 +def node5815 : Tree Nat := .leaf 1161976947540975084822891808156236350343871260162019106851190634655287530824668459212491375629041664 +def node5816 : Tree Nat := .node node5815 node1276 +def node5817 : Tree Nat := .node node1274 node5816 +def node5818 : Tree Nat := .node node5817 node5388 +def node5819 : Tree Nat := .node node5385 node5818 +def node5820 : Tree Nat := .leaf 2764132635367339857598794859122267254089541909484697579377104223812713009564562147524018597542230542632911407493235237963699158664495697728926831727123556675010691072 +def node5821 : Tree Nat := .node node1288 node5820 +def node5822 : Tree Nat := .node node5821 node4359 +def node5823 : Tree Nat := .node node5822 node4874 +def node5824 : Tree Nat := .node node5823 node5394 +def node5825 : Tree Nat := .node node5819 node5824 +def node5826 : Tree Nat := .leaf 42177316823842466088848798509556079926903410484080468435319583493235977318795198784241006432223976785780508537189258391780077494270259059584454829821229386432512 +def node5827 : Tree Nat := .node node1319 node5826 +def node5828 : Tree Nat := .node node5827 node4368 +def node5829 : Tree Nat := .node node5828 node4884 +def node5830 : Tree Nat := .leaf 76151321234045343158953037539327105456135946905978084186599629432768923620125472142949834771320541282304 +def node5831 : Tree Nat := .node node5830 node1338 +def node5832 : Tree Nat := .node node1336 node5831 +def node5833 : Tree Nat := .node node5832 node5399 +def node5834 : Tree Nat := .node node5829 node5833 +def node5835 : Tree Nat := .node node5834 node5410 +def node5836 : Tree Nat := .node node5825 node5835 +def node5837 : Tree Nat := .leaf 109836762562089755439710412785302292881054898481571159323131444916607150569722448133058545230461962837749047359425303607121023992390446602501444887306668343296 +def node5838 : Tree Nat := .node node1382 node5837 +def node5839 : Tree Nat := .node node5838 node4384 +def node5840 : Tree Nat := .node node5839 node4900 +def node5841 : Tree Nat := .leaf 17502277772335937215144807860353310027054560856190412796946058934495268433046568666888151341448822784 +def node5842 : Tree Nat := .node node5841 node1401 +def node5843 : Tree Nat := .node node1399 node5842 +def node5844 : Tree Nat := .node node5843 node5415 +def node5845 : Tree Nat := .node node5840 node5844 +def node5846 : Tree Nat := .leaf 471745303102692669030194322623533611364615152552055053547025787530704182275966147485850663539015502179033890750105642631578174269375254366601003949888299496831803457536 +def node5847 : Tree Nat := .node node1413 node5846 +def node5848 : Tree Nat := .node node5847 node4389 +def node5849 : Tree Nat := .node node5848 node5420 +def node5850 : Tree Nat := .node node5849 node5425 +def node5851 : Tree Nat := .node node5845 node5850 +def node5852 : Tree Nat := .leaf 7198262071269114212496861612297570974191515389283066612961285067500174174417539545548004424871681507386779435097820031826565994612411004974556574124155582709497856 +def node5853 : Tree Nat := .node node1444 node5852 +def node5854 : Tree Nat := .node node5853 node4398 +def node5855 : Tree Nat := .leaf 21158955501044128983640601695392679298257609266442657464134422767494066614805996748795314024777449390786989629509484081577984 +def node5856 : Tree Nat := .node node5855 node1455 +def node5857 : Tree Nat := .node node2492 node5856 +def node5858 : Tree Nat := .node node5854 node5857 +def node5859 : Tree Nat := .node node5858 node5431 +def node5860 : Tree Nat := .node node5859 node5441 +def node5861 : Tree Nat := .node node5851 node5860 +def node5862 : Tree Nat := .node node5836 node5861 +def node5863 : Tree Nat := .node node5814 node5862 +def node5864 : Tree Nat := .leaf 70009111089343748860579231441413240108218243424761651187784235737981073732186274667552605363614253056 +def node5865 : Tree Nat := .node node5864 node3980 +def node5866 : Tree Nat := .node node1525 node5865 +def node5867 : Tree Nat := .node node5866 node5452 +def node5868 : Tree Nat := .node node5449 node5867 +def node5869 : Tree Nat := .leaf 691033158841834964399698714780566813522385477371174394844276055953178252391140536881004649385557635658227851873308809490924789666123924432231707931780889168249356288 +def node5870 : Tree Nat := .node node1539 node5869 +def node5871 : Tree Nat := .node node5870 node4421 +def node5872 : Tree Nat := .node node5871 node4942 +def node5873 : Tree Nat := .node node5872 node5458 +def node5874 : Tree Nat := .node node5868 node5873 +def node5875 : Tree Nat := .leaf 10544329205960616522212199627389019981725852621020117108829895873308994329698799696060251608055994196445127134297314597945019373567564764896113707455178497589248 +def node5876 : Tree Nat := .node node1570 node5875 +def node5877 : Tree Nat := .node node5876 node4427 +def node5878 : Tree Nat := .node node5877 node4952 +def node5879 : Tree Nat := .leaf 4588117104351231925326920511744458103732190801085179572242627673324327648112559696612727544967445522415616 +def node5880 : Tree Nat := .node node5879 node1589 +def node5881 : Tree Nat := .node node1587 node5880 +def node5882 : Tree Nat := .node node5881 node5463 +def node5883 : Tree Nat := .node node5878 node5882 +def node5884 : Tree Nat := .leaf 45287549097858496226898654971859226691003054644997285140514475602947489948705786225033520702131905210497620500369166138797247015559097511590737211017192352523792744316928 +def node5885 : Tree Nat := .node node1601 node5884 +def node5886 : Tree Nat := .node node5885 node4432 +def node5887 : Tree Nat := .node node5886 node5468 +def node5888 : Tree Nat := .node node5887 node5473 +def node5889 : Tree Nat := .node node5883 node5888 +def node5890 : Tree Nat := .node node5874 node5889 +def node5891 : Tree Nat := .leaf 27459190640522438859927603196325583611237234042112954606201609369271569945166722378060051938188741429003292835625293091473157597372245349935657093101120389120 +def node5892 : Tree Nat := .node node1633 node5891 +def node5893 : Tree Nat := .node node5892 node4443 +def node5894 : Tree Nat := .node node5893 node4968 +def node5895 : Tree Nat := .leaf 4647907790163900339291567232624945401375485040648076427404762538621150123298673836849965501845078016 +def node5896 : Tree Nat := .node node5895 node1652 +def node5897 : Tree Nat := .node node1650 node5896 +def node5898 : Tree Nat := .node node5897 node5479 +def node5899 : Tree Nat := .node node5894 node5898 +def node5900 : Tree Nat := .leaf 117936325775673167257548580655883402841153788138013763386756446882684640780824082613634223452099501822467633970524373828640810462773690203826792285045367273646907719680 +def node5901 : Tree Nat := .node node1664 node5900 +def node5902 : Tree Nat := .node node5901 node4448 +def node5903 : Tree Nat := .node node5902 node5484 +def node5904 : Tree Nat := .node node5903 node5489 +def node5905 : Tree Nat := .node node5899 node5904 +def node5906 : Tree Nat := .leaf 1799565517817278553124215403074392743547878847320766653240884562677701261363340083120564069953867970689249373132482355215533892308704561721402434220596992629800960 +def node5907 : Tree Nat := .node node1695 node5906 +def node5908 : Tree Nat := .node node5907 node4454 +def node5909 : Tree Nat := .leaf 5618975734717113091091280118278553838541439805196390363919514759832449225508646439514108288737579921205263171975646927650816 +def node5910 : Tree Nat := .node node5909 node1706 +def node5911 : Tree Nat := .node node2462 node5910 +def node5912 : Tree Nat := .node node5908 node5911 +def node5913 : Tree Nat := .node node5912 node5495 +def node5914 : Tree Nat := .node node5913 node5505 +def node5915 : Tree Nat := .node node5905 node5914 +def node5916 : Tree Nat := .node node5890 node5915 +def node5917 : Tree Nat := .leaf 2574299122548978643118212799655522456476038237553739528522923797194578693774121019545959865248045458116486116771805321763920745499893743200602691685285101568 +def node5918 : Tree Nat := .node node1758 node5917 +def node5919 : Tree Nat := .node node5918 node4471 +def node5920 : Tree Nat := .node node5919 node5000 +def node5921 : Tree Nat := .node node5920 node5512 +def node5922 : Tree Nat := .leaf 11056530541469359430395179436489069016358167637938790317508416895250852038258248590096074390168922170531645629972940951854796634657982790915707326908494226691989700608 +def node5923 : Tree Nat := .node node1789 node5922 +def node5924 : Tree Nat := .node node5923 node4476 +def node5925 : Tree Nat := .node node5924 node5516 +def node5926 : Tree Nat := .node node5925 node5521 +def node5927 : Tree Nat := .node node5921 node5926 +def node5928 : Tree Nat := .leaf 168709267295369864355395194038224319707613641936321873741278333972943909275180795136964025728895907143122034148757033567120309977081036238337819319282855961427968 +def node5929 : Tree Nat := .node node1820 node5928 +def node5930 : Tree Nat := .node node5929 node4482 +def node5931 : Tree Nat := .node node5930 node5015 +def node5932 : Tree Nat := .leaf 304605284936181372635812150157308421824543787623912336746398517731075694480501888571799339085110366437376 +def node5933 : Tree Nat := .node node5932 node1839 +def node5934 : Tree Nat := .node node1837 node5933 +def node5935 : Tree Nat := .node node5934 node5526 +def node5936 : Tree Nat := .node node5931 node5935 +def node5937 : Tree Nat := .node node5936 node5537 +def node5938 : Tree Nat := .node node5927 node5937 +def node5939 : Tree Nat := .leaf 439347050248359021758841651141209171524219593926284637292525779666428602278889792532234180921847851350996189437701214428484095969561786409267909786278291308544 +def node5940 : Tree Nat := .node node1883 node5939 +def node5941 : Tree Nat := .node node5940 node4501 +def node5942 : Tree Nat := .node node5941 node5031 +def node5943 : Tree Nat := .node node5942 node5543 +def node5944 : Tree Nat := .leaf 1886981212410770676120777290494134445458460610208220214188103150122816729103864589943402654156062008716135563000422570526312697077501017466404015799553197987326542741504 +def node5945 : Tree Nat := .node node1914 node5944 +def node5946 : Tree Nat := .node node5945 node4506 +def node5947 : Tree Nat := .node node5946 node5547 +def node5948 : Tree Nat := .node node5947 node5552 +def node5949 : Tree Nat := .node node5943 node5948 +def node5950 : Tree Nat := .leaf 28793048285076456849987446449190283896766061557132266451845140270000696697670158182192017699486726029547117740391280127306263978449644019898226296496622159039299584 +def node5951 : Tree Nat := .node node1945 node5950 +def node5952 : Tree Nat := .node node5951 node4515 +def node5953 : Tree Nat := .leaf 84635822004176515934562406781570717193030437065770629856537691069976266459223986995181256099109797563145560441308354084601856 +def node5954 : Tree Nat := .node node5953 node1956 +def node5955 : Tree Nat := .node node2501 node5954 +def node5956 : Tree Nat := .node node5952 node5955 +def node5957 : Tree Nat := .node node5956 node5558 +def node5958 : Tree Nat := .node node5957 node5568 +def node5959 : Tree Nat := .node node5949 node5958 +def node5960 : Tree Nat := .node node5938 node5959 +def node5961 : Tree Nat := .node node5916 node5960 +def node5962 : Tree Nat := .node node5863 node5961 +def node5963 : Tree Nat := .node node5770 node5962 +def node5964 : Tree Nat := .leaf 247330401473104534060502521019647190035131349101211839914063056092897225106531867170316401061243044989597671426016139339351365034306751209967546155101893167916616667753349120 +def node5965 : Tree Nat := .node node15 node5964 +def node5966 : Tree Nat := .node node5965 node5576 +def node5967 : Tree Nat := .node node5966 node5070 +def node5968 : Tree Nat := .node node5067 node5967 +def node5969 : Tree Nat := .leaf 173461086210561232364982576827799120850973388809827391940291843880004079620408097144529648819381290744008089873460063917328826368 +def node5970 : Tree Nat := .node node5969 node4030 +def node5971 : Tree Nat := .node node2512 node5970 +def node5972 : Tree Nat := .node node5582 node5971 +def node5973 : Tree Nat := .leaf 1062275985633534197379176413104937254659186235454063846398888276400807119721704485478325004530458571337778658972493002030693158675305414478819039957579905375614475990327560905026437120 +def node5974 : Tree Nat := .node node46 node5973 +def node5975 : Tree Nat := .leaf 9403344325559293197604365670738556457265916455589952607324114241486383791962787713087076067751551598757675008 +def node5976 : Tree Nat := .node node5975 node50 +def node5977 : Tree Nat := .node node5974 node5976 +def node5978 : Tree Nat := .node node5977 node5075 +def node5979 : Tree Nat := .node node5972 node5978 +def node5980 : Tree Nat := .node node5968 node5979 +def node5981 : Tree Nat := .leaf 16209045190941378744189093217543598246142368094697019140608036444104112544581672446873855659949624196438272994575393707743731058888327247296433104820757670695084039765363953500160 +def node5982 : Tree Nat := .node node78 node5981 +def node5983 : Tree Nat := .node node5982 node4557 +def node5984 : Tree Nat := .node node5983 node5081 +def node5985 : Tree Nat := .node node5592 node5984 +def node5986 : Tree Nat := .leaf 33407390011885571814802509289913801841244081656121354510432703369411853316118721981407719129088 +def node5987 : Tree Nat := .node node5986 node3743 +def node5988 : Tree Nat := .node node5595 node5987 +def node5989 : Tree Nat := .node node5988 node5086 +def node5990 : Tree Nat := .node node5989 node5091 +def node5991 : Tree Nat := .node node5985 node5990 +def node5992 : Tree Nat := .node node5980 node5991 +def node5993 : Tree Nat := .leaf 63316582777114760719488645381029680648993625369910231018000142359791092971597717288798603037348958073794269801515721623481273563024014693543654603419171727054402885268824653824 +def node5994 : Tree Nat := .node node141 node5993 +def node5995 : Tree Nat := .node node5994 node5606 +def node5996 : Tree Nat := .node node5995 node5097 +def node5997 : Tree Nat := .node node5604 node5996 +def node5998 : Tree Nat := .leaf 43999885282678946746239482902661240410978615698102557955586223813464449464688883178124593846867449359455756074982246382345125888 +def node5999 : Tree Nat := .node node5998 node4066 +def node6000 : Tree Nat := .node node2590 node5999 +def node6001 : Tree Nat := .node node5612 node6000 +def node6002 : Tree Nat := .node node6001 node5107 +def node6003 : Tree Nat := .node node5997 node6002 +def node6004 : Tree Nat := .leaf 4149515568880992958512407863691161151012446232242437073456743540251885176395484974198827899920492604115589826903144669186474771483508919837535694215404707695151055263465426852511744 +def node6005 : Tree Nat := .node node203 node6004 +def node6006 : Tree Nat := .node node6005 node5621 +def node6007 : Tree Nat := .node node6006 node5112 +def node6008 : Tree Nat := .node node5619 node6007 +def node6009 : Tree Nat := .leaf 966134380754314586173837972732996836074731832426608749664308812862879785572423513524060327217295446999905817809716788375997391019771179617305139021682888909155652922834944 +def node6010 : Tree Nat := .node node219 node6009 +def node6011 : Tree Nat := .leaf 8474069661551462118876734063783013149974108517650294802646344269314226207015480697722934263808 +def node6012 : Tree Nat := .node node6011 node3770 +def node6013 : Tree Nat := .node node6010 node6012 +def node6014 : Tree Nat := .node node6013 node5117 +def node6015 : Tree Nat := .node node6014 node5122 +def node6016 : Tree Nat := .node node6008 node6015 +def node6017 : Tree Nat := .node node6003 node6016 +def node6018 : Tree Nat := .node node5992 node6017 +def node6019 : Tree Nat := .leaf 3957286423569672544968040336314355040562101585619389438625008897486355601704509874725062416979888719833562742816258229429621840548908019359480738481630290686665866684053585920 +def node6020 : Tree Nat := .node node267 node6019 +def node6021 : Tree Nat := .node node6020 node4605 +def node6022 : Tree Nat := .node node6021 node5133 +def node6023 : Tree Nat := .node node5130 node6022 +def node6024 : Tree Nat := .leaf 150453509208948691161669850731816903316254663289439241717185827863782140671404603409393217084024390173518200832 +def node6025 : Tree Nat := .node node6024 node3787 +def node6026 : Tree Nat := .node node300 node6025 +def node6027 : Tree Nat := .node node6026 node5138 +def node6028 : Tree Nat := .node node5631 node6027 +def node6029 : Tree Nat := .node node6023 node6028 +def node6030 : Tree Nat := .leaf 259344723055062059907025491480697571938277889515152306249728583105665800713306759149981690559193987143012367913206299323899696942213235956742929677132122731121344636245823256002560 +def node6031 : Tree Nat := .node node329 node6030 +def node6032 : Tree Nat := .node node6031 node4624 +def node6033 : Tree Nat := .node node6032 node5144 +def node6034 : Tree Nat := .node node5640 node6033 +def node6035 : Tree Nat := .leaf 60383398797144661635864873295812302254670739526663046854019300803929986598274381633378027602842540280663494000492221518396329354078796682120982948022923136698390334668800 +def node6036 : Tree Nat := .node node345 node6035 +def node6037 : Tree Nat := .node node6036 node4115 +def node6038 : Tree Nat := .node node6037 node5149 +def node6039 : Tree Nat := .node node6038 node5154 +def node6040 : Tree Nat := .node node6034 node6039 +def node6041 : Tree Nat := .node node6029 node6040 +def node6042 : Tree Nat := .leaf 1013065324433836171511818326096474890383898005918563696288002277756582205746992218513480535012515933478963610375047086316094814392320198740213745229366657343883158889691841822720 +def node6043 : Tree Nat := .node node392 node6042 +def node6044 : Tree Nat := .node node6043 node4640 +def node6045 : Tree Nat := .node node6044 node5160 +def node6046 : Tree Nat := .node node5652 node6045 +def node6047 : Tree Nat := .node node6046 node5658 +def node6048 : Tree Nat := .leaf 66392249102095887336198525819058578416199139715878991786603824991478482054477003051649943273764341594197165755294343117409472085132391333975889925160746693530858043934408553256714240 +def node6049 : Tree Nat := .node node454 node6048 +def node6050 : Tree Nat := .node node6049 node5665 +def node6051 : Tree Nat := .node node6050 node5175 +def node6052 : Tree Nat := .node node5663 node6051 +def node6053 : Tree Nat := .leaf 15458150092069033378781407563727949377195709318825739994628941005806076569158508761709416422791544450153387687240435200421743493550375351180443791499792495490315391393136640 +def node6054 : Tree Nat := .node node469 node6053 +def node6055 : Tree Nat := .node node6054 node4145 +def node6056 : Tree Nat := .node node6055 node5180 +def node6057 : Tree Nat := .node node6056 node5185 +def node6058 : Tree Nat := .node node6052 node6057 +def node6059 : Tree Nat := .node node6047 node6058 +def node6060 : Tree Nat := .node node6041 node6059 +def node6061 : Tree Nat := .node node6018 node6060 +def node6062 : Tree Nat := .leaf 989321605892418136242010084078588760140525396404847359656252224371588900426127468681265604244972179958390685704064557357405460137227004839870184620407572671666433685664563200 +def node6063 : Tree Nat := .node node518 node6062 +def node6064 : Tree Nat := .node node6063 node4673 +def node6065 : Tree Nat := .node node6064 node5197 +def node6066 : Tree Nat := .node node5194 node6065 +def node6067 : Tree Nat := .leaf 4249103942534136789516705652419749018636744941816255385595553105603228478886817941913300018121834285351114635889972008122772634701221657915276159830163852596701859132454328730229145600 +def node6068 : Tree Nat := .node node549 node6067 +def node6069 : Tree Nat := .leaf 2385238560629674372075253731114170418428427588735012368687092392962399791132024200392819295234550505226108928 +def node6070 : Tree Nat := .node node6069 node3851 +def node6071 : Tree Nat := .node node6068 node6070 +def node6072 : Tree Nat := .node node6071 node5202 +def node6073 : Tree Nat := .node node5676 node6072 +def node6074 : Tree Nat := .node node6066 node6073 +def node6075 : Tree Nat := .leaf 64836180763765514976756372870174392984569472378788076562432145776416450178326689787495422639798496785753091978301574830974924235553308989185732419283030682638665164575366457589760 +def node6076 : Tree Nat := .node node580 node6075 +def node6077 : Tree Nat := .node node6076 node4692 +def node6078 : Tree Nat := .node node6077 node5208 +def node6079 : Tree Nat := .node node5685 node6078 +def node6080 : Tree Nat := .node node6079 node5691 +def node6081 : Tree Nat := .node node6074 node6080 +def node6082 : Tree Nat := .leaf 253266331108459042877954581524118722595974501479640924072000569439277212018297580673565664537444694972664270203529965925212983622993895379678171866233731821030629724853786116096 +def node6083 : Tree Nat := .node node643 node6082 +def node6084 : Tree Nat := .node node6083 node4708 +def node6085 : Tree Nat := .node node6084 node5224 +def node6086 : Tree Nat := .node node5697 node6085 +def node6087 : Tree Nat := .node node6086 node5703 +def node6088 : Tree Nat := .leaf 16598062275523971834049631454764644604049784928969750375360008687742329085372861830384761811362636134391062591114705236794854530831201413705928609437107758875812645447412335851339776 +def node6089 : Tree Nat := .node node705 node6088 +def node6090 : Tree Nat := .node node6089 node5710 +def node6091 : Tree Nat := .node node6090 node5239 +def node6092 : Tree Nat := .node node5708 node6091 +def node6093 : Tree Nat := .leaf 3864537523017258344695351890931987344298927329706434998657235251451519142290094942776383935730959418111102236860962082483863020333209910909653498326524980300399504294936576 +def node6094 : Tree Nat := .node node721 node6093 +def node6095 : Tree Nat := .node node6094 node4210 +def node6096 : Tree Nat := .node node6095 node5244 +def node6097 : Tree Nat := .node node6096 node5249 +def node6098 : Tree Nat := .node node6092 node6097 +def node6099 : Tree Nat := .node node6087 node6098 +def node6100 : Tree Nat := .node node6081 node6099 +def node6101 : Tree Nat := .leaf 15829145694278690179872161345257420162248406342477557754500035589945422406818039498900249667919554879334250971265032917718487362195632077437922953926521162746662938970633011200 +def node6102 : Tree Nat := .node node769 node6101 +def node6103 : Tree Nat := .node node6102 node5722 +def node6104 : Tree Nat := .node node6103 node5256 +def node6105 : Tree Nat := .node node5720 node6104 +def node6106 : Tree Nat := .leaf 703998164522863147939831726442579846575657851169640927289379581015431191435022130849993501549879189751291077168555642274155855872 +def node6107 : Tree Nat := .node node6106 node796 +def node6108 : Tree Nat := .node node2599 node6107 +def node6109 : Tree Nat := .node node5728 node6108 +def node6110 : Tree Nat := .leaf 38163816970074789953204059697826726694854841419760197898993478287398396658112387206285108723752570589106143232 +def node6111 : Tree Nat := .node node6110 node804 +def node6112 : Tree Nat := .node node802 node6111 +def node6113 : Tree Nat := .node node6112 node5265 +def node6114 : Tree Nat := .node node6109 node6113 +def node6115 : Tree Nat := .node node6105 node6114 +def node6116 : Tree Nat := .leaf 1037378892220248239628101965922790287753111558060609224998914332422663202853227036599926762236775948572049471652825197295598787768852943826971718708528490922218642633205863321436160 +def node6117 : Tree Nat := .node node831 node6116 +def node6118 : Tree Nat := .node node6117 node4755 +def node6119 : Tree Nat := .node node6118 node5271 +def node6120 : Tree Nat := .node node5738 node6119 +def node6121 : Tree Nat := .leaf 241533595188578646543459493183249209018682958106652187416077203215719946393097526533512110411370161122653976001968886073585317416315186728483931792091692546793561307217920 +def node6122 : Tree Nat := .node node847 node6121 +def node6123 : Tree Nat := .leaf 135585114584823393902027745020528210399585736282404716842341508309027619312247691163566934065152 +def node6124 : Tree Nat := .node node6123 node851 +def node6125 : Tree Nat := .node node6122 node6124 +def node6126 : Tree Nat := .node node6125 node5276 +def node6127 : Tree Nat := .node node6126 node5281 +def node6128 : Tree Nat := .node node6120 node6127 +def node6129 : Tree Nat := .node node6115 node6128 +def node6130 : Tree Nat := .leaf 4052261297735344686047273304385899561535592023674254785152009111026328822987968874053922140050063733915854441500188345264379257569280794960854980917466629375532635415830855680000 +def node6131 : Tree Nat := .node node894 node6130 +def node6132 : Tree Nat := .node node6131 node5747 +def node6133 : Tree Nat := .node node6132 node5287 +def node6134 : Tree Nat := .node node5745 node6133 +def node6135 : Tree Nat := .leaf 2775377379368979717839721229244785933615574220957238271044669502080065273926529554312474381110100651904127567918233806297756598272 +def node6136 : Tree Nat := .node node6135 node4259 +def node6137 : Tree Nat := .node node2707 node6136 +def node6138 : Tree Nat := .node node5753 node6137 +def node6139 : Tree Nat := .node node6138 node5297 +def node6140 : Tree Nat := .node node6134 node6139 +def node6141 : Tree Nat := .leaf 265568996408383549344794103276234313664796558863515967146415299965913928217908012206599773095057366376788663021177372469637888340529565335903559700642986774122818268094861159149076480 +def node6142 : Tree Nat := .node node956 node6141 +def node6143 : Tree Nat := .node node6142 node5762 +def node6144 : Tree Nat := .node node6143 node5302 +def node6145 : Tree Nat := .node node5760 node6144 +def node6146 : Tree Nat := .leaf 61832600368276133515125630254911797508782837275302959978515764023224306276634035046837665691166177800613550748961740801686973974201501404721775165999169981961261565564026880 +def node6147 : Tree Nat := .node node971 node6146 +def node6148 : Tree Nat := .leaf 534518240190169149036840148638620829459905306497941672166923253910589653057899551702523480113152 +def node6149 : Tree Nat := .node node6148 node975 +def node6150 : Tree Nat := .node node6147 node6149 +def node6151 : Tree Nat := .node node6150 node5307 +def node6152 : Tree Nat := .node node6151 node5312 +def node6153 : Tree Nat := .node node6145 node6152 +def node6154 : Tree Nat := .node node6140 node6153 +def node6155 : Tree Nat := .node node6129 node6154 +def node6156 : Tree Nat := .node node6100 node6155 +def node6157 : Tree Nat := .node node6061 node6156 +def node6158 : Tree Nat := .leaf 741991204419313602181507563058941570105394047303635519742189168278691675319595601510949203183729134968793014278048418018054095102920253629902638465305679503749830212050747392 +def node6159 : Tree Nat := .node node1021 node6158 +def node6160 : Tree Nat := .node node6159 node4289 +def node6161 : Tree Nat := .node node6160 node5325 +def node6162 : Tree Nat := .node node5322 node6161 +def node6163 : Tree Nat := .leaf 3186827956900602592137529239314811763977558706362191539196664829202421359165113456434975013591375714013335976917479006092079476025916243436457119872646254783389801073669133781153349632 +def node6164 : Tree Nat := .node node1052 node6163 +def node6165 : Tree Nat := .node node6164 node4810 +def node6166 : Tree Nat := .node node6165 node5330 +def node6167 : Tree Nat := .node node5774 node6166 +def node6168 : Tree Nat := .node node6162 node6167 +def node6169 : Tree Nat := .leaf 48627135572824136232567279652630794738427104284091057421824109332312337633745017340621566979848872589314818983726181123231193176664981741889299314462273012000249522604438246653952 +def node6170 : Tree Nat := .node node1083 node6169 +def node6171 : Tree Nat := .node node6170 node5782 +def node6172 : Tree Nat := .node node6171 node5336 +def node6173 : Tree Nat := .node node5780 node6172 +def node6174 : Tree Nat := .node node6173 node5790 +def node6175 : Tree Nat := .node node6168 node6174 +def node6176 : Tree Nat := .leaf 126633165554229521438977290762059361297987250739820462036000284719565764493104945665574072597087553205092436197708998354116585989958019019294515655612562121268537217845360066560 +def node6177 : Tree Nat := .node node1146 node6176 +def node6178 : Tree Nat := .node node6177 node4836 +def node6179 : Tree Nat := .node node6178 node5352 +def node6180 : Tree Nat := .node node5796 node6179 +def node6181 : Tree Nat := .leaf 4990652988394395609265146268177341183173325416430179725252993314505944178368542942360360371567655484175417344 +def node6182 : Tree Nat := .node node6181 node1181 +def node6183 : Tree Nat := .node node1179 node6182 +def node6184 : Tree Nat := .node node6183 node5361 +def node6185 : Tree Nat := .node node5801 node6184 +def node6186 : Tree Nat := .node node6180 node6185 +def node6187 : Tree Nat := .leaf 8299031137761985917024815727382322302024892464484873843991199942060252369065299195460654508872823286678953728808825391829239766839706728740367596535677286829878438589049401392496640 +def node6188 : Tree Nat := .node node1208 node6187 +def node6189 : Tree Nat := .node node6188 node4851 +def node6190 : Tree Nat := .node node6189 node5367 +def node6191 : Tree Nat := .node node5810 node6190 +def node6192 : Tree Nat := .leaf 1932268761508629172347675945465993672149463664853217499328617625725759571144788686337758434753080165715295591028901062697200189625324140172140768562940555855046213341675520 +def node6193 : Tree Nat := .node node1224 node6192 +def node6194 : Tree Nat := .node node6193 node4342 +def node6195 : Tree Nat := .node node6194 node5372 +def node6196 : Tree Nat := .node node6195 node5377 +def node6197 : Tree Nat := .node node6191 node6196 +def node6198 : Tree Nat := .node node6186 node6197 +def node6199 : Tree Nat := .node node6175 node6198 +def node6200 : Tree Nat := .leaf 11871859270709017634904121008943065121686304756858168315875026692459066805113529624175187250939666159500688228448774688288865521646724058078442215444890872059997283392811958272 +def node6201 : Tree Nat := .node node1272 node6200 +def node6202 : Tree Nat := .node node6201 node5816 +def node6203 : Tree Nat := .node node6202 node5388 +def node6204 : Tree Nat := .node node5385 node6203 +def node6205 : Tree Nat := .leaf 92061298437605180884439533457875826090662949768337659722457329825094848110733663264999150202676509429015036998782510363788181504 +def node6206 : Tree Nat := .node node6205 node4361 +def node6207 : Tree Nat := .node node2570 node6206 +def node6208 : Tree Nat := .node node5822 node6207 +def node6209 : Tree Nat := .node node6208 node5394 +def node6210 : Tree Nat := .node node6204 node6209 +def node6211 : Tree Nat := .leaf 778034169165186179721076474442092715814833668545456918749185749316997402139920277449945071677581961429037103739618897971699090826639707870228789031396368192003992361671011946463232 +def node6212 : Tree Nat := .node node1334 node6211 +def node6213 : Tree Nat := .node node6212 node5831 +def node6214 : Tree Nat := .node node6213 node5399 +def node6215 : Tree Nat := .node node5829 node6214 +def node6216 : Tree Nat := .leaf 181150196391433984907594619887436906764012218579989140562057902411789959794823144900134082808527620841990482001476664555188988062236390046362948844068769410095170985132032 +def node6217 : Tree Nat := .node node1350 node6216 +def node6218 : Tree Nat := .leaf 17730361138015366894880551271915227513791980898468309125536966471180534833140082690620292071424 +def node6219 : Tree Nat := .node node6218 node3958 +def node6220 : Tree Nat := .node node6217 node6219 +def node6221 : Tree Nat := .node node6220 node5404 +def node6222 : Tree Nat := .node node6221 node5409 +def node6223 : Tree Nat := .node node6215 node6222 +def node6224 : Tree Nat := .node node6210 node6223 +def node6225 : Tree Nat := .leaf 2026130648867672343023636652192949780767796011837127392576004555513019058725697450254841222639971201895967297647340643647691635354355411856232506645537069191944410332926318739456 +def node6226 : Tree Nat := .node node1397 node6225 +def node6227 : Tree Nat := .node node6226 node5842 +def node6228 : Tree Nat := .node node6227 node5415 +def node6229 : Tree Nat := .node node5840 node6228 +def node6230 : Tree Nat := .leaf 1386673307716428037071870472709254630490610680885585999569513530490491149667925802929049699927814923274537879135079984400877748224 +def node6231 : Tree Nat := .node node6230 node4391 +def node6232 : Tree Nat := .node node2678 node6231 +def node6233 : Tree Nat := .node node5848 node6232 +def node6234 : Tree Nat := .leaf 75171710637690583864556265664421201571548214084979582111623211799745784186676178069302928096737550970770161664 +def node6235 : Tree Nat := .node node6234 node1432 +def node6236 : Tree Nat := .node node1430 node6235 +def node6237 : Tree Nat := .node node6236 node5424 +def node6238 : Tree Nat := .node node6233 node6237 +def node6239 : Tree Nat := .node node6229 node6238 +def node6240 : Tree Nat := .leaf 132784498204191774672397051638117156832398279431757980891922332987706070849652594142666451656970271185559992094018955078931492945146840074851530197368156267000994816491358668546113536 +def node6241 : Tree Nat := .node node1459 node6240 +def node6242 : Tree Nat := .node node6241 node4918 +def node6243 : Tree Nat := .node node6242 node5430 +def node6244 : Tree Nat := .node node5858 node6243 +def node6245 : Tree Nat := .leaf 30916300184138066757562815127455898754391418637651479989257882011612153138316501126650688148022275504250980843479531209399819097597469438212414449922569786072266466810658816 +def node6246 : Tree Nat := .node node1474 node6245 +def node6247 : Tree Nat := .leaf 267063564641356463854138303533223114426491712283178906203400557472156805924172495527468133842944 +def node6248 : Tree Nat := .node node6247 node1478 +def node6249 : Tree Nat := .node node6246 node6248 +def node6250 : Tree Nat := .node node6249 node5435 +def node6251 : Tree Nat := .node node6250 node5440 +def node6252 : Tree Nat := .node node6244 node6251 +def node6253 : Tree Nat := .node node6239 node6252 +def node6254 : Tree Nat := .node node6224 node6253 +def node6255 : Tree Nat := .node node6199 node6254 +def node6256 : Tree Nat := .leaf 2967964817677254408726030252235766280421576189214542078968756673114766701278382406043796812734916539875172057112193672072216380411681014519610553861222718014999287862854156288 +def node6257 : Tree Nat := .node node1523 node6256 +def node6258 : Tree Nat := .node node6257 node5865 +def node6259 : Tree Nat := .node node6258 node5452 +def node6260 : Tree Nat := .node node5449 node6259 +def node6261 : Tree Nat := .leaf 5546693230865712148287481890837018521962442723542343998278054121961964598671703211716198799711259693098150902632677164549633212416 +def node6262 : Tree Nat := .node node6261 node1550 +def node6263 : Tree Nat := .node node2579 node6262 +def node6264 : Tree Nat := .node node5871 node6263 +def node6265 : Tree Nat := .node node6264 node5458 +def node6266 : Tree Nat := .node node6260 node6265 +def node6267 : Tree Nat := .leaf 194508542291296544930269118610523178953708417136364229687296437329249350534980069362486267919395490357259275934904724492924772706659926967557197257849092047859327095931663630204928 +def node6268 : Tree Nat := .node node1585 node6267 +def node6269 : Tree Nat := .node node6268 node5880 +def node6270 : Tree Nat := .node node6269 node5463 +def node6271 : Tree Nat := .node node5878 node6270 +def node6272 : Tree Nat := .leaf 1068254258565425855416553214132892457705966849132715624813602229888627223696689982109872526852096 +def node6273 : Tree Nat := .node node6272 node1605 +def node6274 : Tree Nat := .node node5885 node6273 +def node6275 : Tree Nat := .node node6274 node5468 +def node6276 : Tree Nat := .node node6275 node5473 +def node6277 : Tree Nat := .node node6271 node6276 +def node6278 : Tree Nat := .node node6266 node6277 +def node6279 : Tree Nat := .leaf 506532662216918085755909163048237445191949002959281848144001138878291680835147338754761193433123582865390885921900813564890589068547624874671646912854962316616963239949641973760 +def node6280 : Tree Nat := .node node1648 node6279 +def node6281 : Tree Nat := .node node6280 node5896 +def node6282 : Tree Nat := .node node6281 node5479 +def node6283 : Tree Nat := .node node5894 node6282 +def node6284 : Tree Nat := .leaf 368245193750420723537758133831503304362651799073350638889829319300379392442934653059996600810706037716059959100470726669344178176 +def node6285 : Tree Nat := .node node6284 node1675 +def node6286 : Tree Nat := .node node2687 node6285 +def node6287 : Tree Nat := .node node5902 node6286 +def node6288 : Tree Nat := .leaf 19962611953577582437060585072709364732693301665720718901011973258023776713474171769441441486270577956236558336 +def node6289 : Tree Nat := .node node6288 node1683 +def node6290 : Tree Nat := .node node1681 node6289 +def node6291 : Tree Nat := .node node6290 node5488 +def node6292 : Tree Nat := .node node6287 node6291 +def node6293 : Tree Nat := .node node6283 node6292 +def node6294 : Tree Nat := .leaf 33196124551047943668099262909529289208099569857939495903963423160388370431134991613777502967234681523946510382269987328890352643625425052456596548552101460787566622982854350345338880 +def node6295 : Tree Nat := .node node1710 node6294 +def node6296 : Tree Nat := .node node6295 node4986 +def node6297 : Tree Nat := .node node6296 node5494 +def node6298 : Tree Nat := .node node5912 node6297 +def node6299 : Tree Nat := .leaf 7729075046034516689390703781863974688597854659412869997314470502903038284579256434186972356557747183669947760273403940091012562038928316819794844966246409188557528563712000 +def node6300 : Tree Nat := .node node1725 node6299 +def node6301 : Tree Nat := .leaf 70921444552061467579522205087660910055167923593873236502147865884722139332560330762481165664256 +def node6302 : Tree Nat := .node node6301 node1729 +def node6303 : Tree Nat := .node node6300 node6302 +def node6304 : Tree Nat := .node node6303 node5499 +def node6305 : Tree Nat := .node node6304 node5504 +def node6306 : Tree Nat := .node node6298 node6305 +def node6307 : Tree Nat := .node node6293 node6306 +def node6308 : Tree Nat := .node node6278 node6307 +def node6309 : Tree Nat := .leaf 47487437082836070539616484035772260486745219027432673263500106769836267220454118496700749003758664638002752913795098753155462086586896232313768861779563488239988605805666500608 +def node6310 : Tree Nat := .node node1773 node6309 +def node6311 : Tree Nat := .node node6310 node5003 +def node6312 : Tree Nat := .node node6311 node5511 +def node6313 : Tree Nat := .node node5920 node6312 +def node6314 : Tree Nat := .node node6313 node5926 +def node6315 : Tree Nat := .leaf 3112136676660744718884305897768370863259334674181827674996742997267989608559681109799780286710327845716148414958475591886796363306558831480915156125585472765749233534906618083278848 +def node6316 : Tree Nat := .node node1835 node6315 +def node6317 : Tree Nat := .node node6316 node5933 +def node6318 : Tree Nat := .node node6317 node5526 +def node6319 : Tree Nat := .node node5931 node6318 +def node6320 : Tree Nat := .leaf 724600785565735939630378479549747627056048874319956562248231609647159839179292579600536331234110483367961928005906658220755952248945560185451795376275077640380683909070848 +def node6321 : Tree Nat := .node node1851 node6320 +def node6322 : Tree Nat := .node node6321 node4487 +def node6323 : Tree Nat := .node node6322 node5531 +def node6324 : Tree Nat := .node node6323 node5536 +def node6325 : Tree Nat := .node node6319 node6324 +def node6326 : Tree Nat := .node node6314 node6325 +def node6327 : Tree Nat := .leaf 8104522595470689372094546608771799123071184047348509570304018222052076234902789801019364890559884807583869190589362574590766541417421647424930026582148276767777641287724809846784 +def node6328 : Tree Nat := .node node1898 node6327 +def node6329 : Tree Nat := .node node6328 node5034 +def node6330 : Tree Nat := .node node6329 node5542 +def node6331 : Tree Nat := .node node5942 node6330 +def node6332 : Tree Nat := .leaf 300686842550762335458225062657684806286192856339918328446492847198983136746704712277211712386950060946569035776 +def node6333 : Tree Nat := .node node6332 node1933 +def node6334 : Tree Nat := .node node1931 node6333 +def node6335 : Tree Nat := .node node6334 node5551 +def node6336 : Tree Nat := .node node5947 node6335 +def node6337 : Tree Nat := .node node6331 node6336 +def node6338 : Tree Nat := .leaf 531137992816767098689588206552468627329593117727031923567689331950824283398610376570665806627881084742239968376075820315725971780587360299406120789472625068003790371306119888375906304 +def node6339 : Tree Nat := .node node1960 node6338 +def node6340 : Tree Nat := .node node6339 node5049 +def node6341 : Tree Nat := .node node6340 node5557 +def node6342 : Tree Nat := .node node5956 node6341 +def node6343 : Tree Nat := .leaf 123665200736552267030251260509823595017565674550605919957031528046448612553266004506602752592089102017003923373918124837599276390389877752849657799690279144289065867240013824 +def node6344 : Tree Nat := .node node1975 node6343 +def node6345 : Tree Nat := .node node6344 node4520 +def node6346 : Tree Nat := .node node6345 node5562 +def node6347 : Tree Nat := .node node6346 node5567 +def node6348 : Tree Nat := .node node6342 node6347 +def node6349 : Tree Nat := .node node6337 node6348 +def node6350 : Tree Nat := .node node6326 node6349 +def node6351 : Tree Nat := .node node6308 node6350 +def node6352 : Tree Nat := .node node6255 node6351 +def node6353 : Tree Nat := .node node6157 node6352 +def node6354 : Tree Nat := .leaf 4562440617622195218641171605700291324893228507248559930579192517899275167208677386505912811317371399778642309573594407310688704721375437998252661319722214188251994674360264950085407467036999680 +def node6355 : Tree Nat := .node node2066 node6354 +def node6356 : Tree Nat := .node node6355 node4538 +def node6357 : Tree Nat := .node node5066 node6356 +def node6358 : Tree Nat := .node node6357 node5967 +def node6359 : Tree Nat := .leaf 509756317320031308209266804350491361102967554567281410376475576315488484437846709921390848 +def node6360 : Tree Nat := .node node6359 node3737 +def node6361 : Tree Nat := .node node5581 node6360 +def node6362 : Tree Nat := .node node6361 node5971 +def node6363 : Tree Nat := .node node6362 node5978 +def node6364 : Tree Nat := .node node6358 node6363 +def node6365 : Tree Nat := .leaf 299004108316488185848867822351174292268202623451041623610437960853046897358187881202051502002495252055893102400215083077513294952620060704653486412249315029041282722978874334648963619594735997419520 +def node6366 : Tree Nat := .node node2308 node6365 +def node6367 : Tree Nat := .node node6366 node5590 +def node6368 : Tree Nat := .node node5588 node6367 +def node6369 : Tree Nat := .node node6368 node5984 +def node6370 : Tree Nat := .leaf 69617318994479297159441705409245167921344429126717528237597542082203295398081625160307507496908132931192662194421301381083506846944815643283884602656894137393981852330936660004926669195520 +def node6371 : Tree Nat := .node node109 node6370 +def node6372 : Tree Nat := .leaf 616257573719853838998199708597522035983379100833543134073593150930051648190073255564874617176163316964253969154048 +def node6373 : Tree Nat := .node node6372 node3747 +def node6374 : Tree Nat := .node node6371 node6373 +def node6375 : Tree Nat := .node node6374 node5090 +def node6376 : Tree Nat := .node node5989 node6375 +def node6377 : Tree Nat := .node node6369 node6376 +def node6378 : Tree Nat := .node node6364 node6377 +def node6379 : Tree Nat := .leaf 1167984798111281975972139931059274579172666497855631342228273284582214442805421411561771253417100917341532139848362204254915409242215246201145832227900535022265766201510845003384532757469099720704 +def node6380 : Tree Nat := .node node2191 node6379 +def node6381 : Tree Nat := .node node6380 node4569 +def node6382 : Tree Nat := .node node5603 node6381 +def node6383 : Tree Nat := .node node6382 node5996 +def node6384 : Tree Nat := .leaf 271942652322184754529069161754864146894337494622828892398080351776677311527387422916289277433150662921042668871421880729347738249113253585255876150945713097972070730762455313381907759104 +def node6385 : Tree Nat := .node node172 node6384 +def node6386 : Tree Nat := .node node6385 node4578 +def node6387 : Tree Nat := .node node6386 node5106 +def node6388 : Tree Nat := .node node6001 node6387 +def node6389 : Tree Nat := .node node6383 node6388 +def node6390 : Tree Nat := .leaf 17822033662586700072817076584766762987864173856439687228824970773044043621908896041038721919208482030895077839091884461766644557168364165783642012847446309549334930512208269399107937234854144 +def node6391 : Tree Nat := .node node2011 node6390 +def node6392 : Tree Nat := .leaf 156318994309426339648323828522298272542125430455337770594277287065183832711628337996943805332490209940355172794368 +def node6393 : Tree Nat := .node node6392 node238 +def node6394 : Tree Nat := .node node6391 node6393 +def node6395 : Tree Nat := .leaf 53192597378312305387714332573448486223520433248199802829103484731562174191575961516853139000295942553701908617072851247361123872497534950665522499289088 +def node6396 : Tree Nat := .node node6395 node57 +def node6397 : Tree Nat := .node node4082 node6396 +def node6398 : Tree Nat := .node node6394 node6397 +def node6399 : Tree Nat := .node node6014 node6398 +def node6400 : Tree Nat := .node node6008 node6399 +def node6401 : Tree Nat := .node node6389 node6400 +def node6402 : Tree Nat := .node node6378 node6401 +def node6403 : Tree Nat := .leaf 72999049881955123498258745691204661198291656115976958889267080286388402675338838184094604981077942396458276953177510516971019275542007007972042581115555427012031914789764239201366519472591994880 +def node6404 : Tree Nat := .node node2152 node6403 +def node6405 : Tree Nat := .node node6404 node4601 +def node6406 : Tree Nat := .node node5129 node6405 +def node6407 : Tree Nat := .node node6406 node6022 +def node6408 : Tree Nat := .leaf 8156101077120500931348268869607861777647480873076502566023609221047815751005547358742152192 +def node6409 : Tree Nat := .node node6408 node287 +def node6410 : Tree Nat := .node node5629 node6409 +def node6411 : Tree Nat := .node node6410 node4611 +def node6412 : Tree Nat := .leaf 16996415770136547158066822609678996074546979767265021542382212422412913915547271767653200072487337141404458543559888032491090538804886631661104639321278486009831615845240974480422993920 +def node6413 : Tree Nat := .node node298 node6412 +def node6414 : Tree Nat := .node node6413 node6025 +def node6415 : Tree Nat := .node node6414 node5138 +def node6416 : Tree Nat := .node node6411 node6415 +def node6417 : Tree Nat := .node node6407 node6416 +def node6418 : Tree Nat := .leaf 1113877103911668754551067286547922686741510866027480451801560673315252726369306002564920119950530126899082595110740822097336109551117050292542153642510306198303709637294986560078826707128320 +def node6419 : Tree Nat := .node node360 node6418 +def node6420 : Tree Nat := .node node6419 node4629 +def node6421 : Tree Nat := .node node6420 node5153 +def node6422 : Tree Nat := .node node6038 node6421 +def node6423 : Tree Nat := .node node6034 node6422 +def node6424 : Tree Nat := .node node6417 node6423 +def node6425 : Tree Nat := .leaf 18687756769780511615554238896948393266762663965690101475652372553315431084886742580054672103507643357640878326596950558537564692811975687308181709273721901773090176136016340983326927664096424755200 +def node6426 : Tree Nat := .node node2230 node6425 +def node6427 : Tree Nat := .node node6426 node4636 +def node6428 : Tree Nat := .node node5651 node6427 +def node6429 : Tree Nat := .node node6428 node6045 +def node6430 : Tree Nat := .leaf 4351082437154956072465106588077824671469191889231500695354619867971921791327909402323774532687350194432061870895287755912415210337717458603085896492757586681807179096036313168441507840000 +def node6431 : Tree Nat := .node node423 node6430 +def node6432 : Tree Nat := .node node6431 node4645 +def node6433 : Tree Nat := .node node6432 node5169 +def node6434 : Tree Nat := .node node5657 node6433 +def node6435 : Tree Nat := .node node6429 node6434 +def node6436 : Tree Nat := .leaf 285152538601387201165073225356268207805826781703034995661199532368704697950542336656619550707335712490240210947491442202739246186401014838673929032116105583472911493810065477900878116133290240 +def node6437 : Tree Nat := .node node2019 node6436 +def node6438 : Tree Nat := .node node6437 node4660 +def node6439 : Tree Nat := .leaf 851081558052996886203429321175175779576326931971196845265655755704994787065215384269650224004735080859230537873165618836241860516437791448061152877084672 +def node6440 : Tree Nat := .node node6439 node57 +def node6441 : Tree Nat := .node node4152 node6440 +def node6442 : Tree Nat := .node node6438 node6441 +def node6443 : Tree Nat := .node node6056 node6442 +def node6444 : Tree Nat := .node node6052 node6443 +def node6445 : Tree Nat := .node node6435 node6444 +def node6446 : Tree Nat := .node node6424 node6445 +def node6447 : Tree Nat := .node node6402 node6446 +def node6448 : Tree Nat := .leaf 18249762470488780874564686422801165299572914028994239722316770071597100668834709546023651245269485599114569238294377629242754818885501751993010645278888856753007978697441059800333185618846679040 +def node6449 : Tree Nat := .node node2122 node6448 +def node6450 : Tree Nat := .node node6449 node4669 +def node6451 : Tree Nat := .node node5193 node6450 +def node6452 : Tree Nat := .node node6451 node6065 +def node6453 : Tree Nat := .leaf 129304041466544526960399384518173418426118599207310406534520633992221469223258677638599168 +def node6454 : Tree Nat := .node node6453 node3847 +def node6455 : Tree Nat := .node node5674 node6454 +def node6456 : Tree Nat := .node node6455 node4679 +def node6457 : Tree Nat := .node node6456 node6072 +def node6458 : Tree Nat := .node node6452 node6457 +def node6459 : Tree Nat := .leaf 1196016433265952743395471289404697169072810493804166494441751843412187589432751524808206008009981008223572409600860332310053179810480242818613945648997260116165130891915497297492376611481552049668096 +def node6460 : Tree Nat := .node node2317 node6459 +def node6461 : Tree Nat := .node node6460 node5683 +def node6462 : Tree Nat := .node node5681 node6461 +def node6463 : Tree Nat := .node node6462 node6078 +def node6464 : Tree Nat := .leaf 278469275977917188637766821636980671685377716506870112950390168328813181592326500641230029987632531724770648777685205524334027387779262573135538410627576549575927409323746640019706676774400 +def node6465 : Tree Nat := .node node611 node6464 +def node6466 : Tree Nat := .node node6465 node4697 +def node6467 : Tree Nat := .node node6466 node5217 +def node6468 : Tree Nat := .node node5690 node6467 +def node6469 : Tree Nat := .node node6463 node6468 +def node6470 : Tree Nat := .node node6458 node6469 +def node6471 : Tree Nat := .leaf 4671939192445127903888559724237098316690665991422525368913093138328857771221685653642175898306649737344525062563713248820210846971378593687701140072221918369942131584538786127497823136833251311616 +def node6472 : Tree Nat := .node node2239 node6471 +def node6473 : Tree Nat := .node node6472 node4704 +def node6474 : Tree Nat := .node node5696 node6473 +def node6475 : Tree Nat := .node node6474 node6085 +def node6476 : Tree Nat := .leaf 1087770609288739018116276647019459103996379798650378142231900843323557512653122587271214025012841875587026661579251589431274428535273824085161927665587440727654252572445730999833215369216 +def node6477 : Tree Nat := .node node674 node6476 +def node6478 : Tree Nat := .node node6477 node4713 +def node6479 : Tree Nat := .node node6478 node5233 +def node6480 : Tree Nat := .node node5702 node6479 +def node6481 : Tree Nat := .node node6475 node6480 +def node6482 : Tree Nat := .leaf 71288134650346800291268306339067051951456695425758748915299883092176174487635584164154887676833928129697387164207913545577779880879352996370178706197162162715046637834694890850592267996005376 +def node6483 : Tree Nat := .node node2028 node6482 +def node6484 : Tree Nat := .node node6483 node4728 +def node6485 : Tree Nat := .leaf 209701585818346588547719964953018070688878631074633838076273353268658571332174463672209490289628235067478678201921817220373776829120094733985237662957568 +def node6486 : Tree Nat := .node node6485 node57 +def node6487 : Tree Nat := .node node4214 node6486 +def node6488 : Tree Nat := .node node6484 node6487 +def node6489 : Tree Nat := .node node6096 node6488 +def node6490 : Tree Nat := .node node6092 node6489 +def node6491 : Tree Nat := .node node6481 node6490 +def node6492 : Tree Nat := .node node6470 node6491 +def node6493 : Tree Nat := .leaf 291996199527820493993034982764818644793166624463907835557068321145553610701355352736378419924311769585833107812710042067884077102168028031888170324462221708048127659159056956805330969901546864640 +def node6494 : Tree Nat := .node node2161 node6493 +def node6495 : Tree Nat := .node node6494 node4736 +def node6496 : Tree Nat := .node node5719 node6495 +def node6497 : Tree Nat := .node node6496 node6104 +def node6498 : Tree Nat := .leaf 2068864663464712431366390152290774694817897587316966504552330143875543507572138842217531392 +def node6499 : Tree Nat := .node node6498 node3896 +def node6500 : Tree Nat := .node node5727 node6499 +def node6501 : Tree Nat := .node node6500 node6108 +def node6502 : Tree Nat := .leaf 67985663080546188632267290438715984298187919069060086169528849689651655662189087070612800289949348565617834174239552129964362155219546526644418557282621641547229746119269259683666329600 +def node6503 : Tree Nat := .node node800 node6502 +def node6504 : Tree Nat := .node node6503 node6111 +def node6505 : Tree Nat := .node node6504 node5265 +def node6506 : Tree Nat := .node node6501 node6505 +def node6507 : Tree Nat := .node node6497 node6506 +def node6508 : Tree Nat := .leaf 4455508415646675018204269146191690746966043464109921807206242693261010905477224010259680479802120507596330380442963288389344438204468201170168614570041224793214838549179946240315306828390400 +def node6509 : Tree Nat := .node node862 node6508 +def node6510 : Tree Nat := .leaf 2501103908950821434373181256356772360674006887285404329508436593042941323386053407951100885319843298247087795208192 +def node6511 : Tree Nat := .node node6510 node866 +def node6512 : Tree Nat := .node node6509 node6511 +def node6513 : Tree Nat := .node node6512 node5280 +def node6514 : Tree Nat := .node node6126 node6513 +def node6515 : Tree Nat := .node node6120 node6514 +def node6516 : Tree Nat := .node node6507 node6515 +def node6517 : Tree Nat := .leaf 74751027079122046462216955587793573067050655862760405902609490213261724339546970320218688414030573430563513306387802234150258771247902749232726837094887607092360704544065363933307674064638726635520 +def node6518 : Tree Nat := .node node2278 node6517 +def node6519 : Tree Nat := .node node6518 node4767 +def node6520 : Tree Nat := .node node5744 node6519 +def node6521 : Tree Nat := .node node6520 node6133 +def node6522 : Tree Nat := .leaf 17404329748619824289860426352311298685876767556926002781418479471887687165311637609295098130749400777728247483581151023649660841350869834412343585971029671728637106856553543709243232747520 +def node6523 : Tree Nat := .node node925 node6522 +def node6524 : Tree Nat := .node node6523 node4776 +def node6525 : Tree Nat := .node node6524 node5296 +def node6526 : Tree Nat := .node node6138 node6525 +def node6527 : Tree Nat := .node node6521 node6526 +def node6528 : Tree Nat := .leaf 1140610154405548804660292901425072831223307126812139982644798129474818791802169346626478202829342849960960843789965768810956984745604059354695716128464422333891645975240261911603512464533127680 +def node6529 : Tree Nat := .node node2075 node6528 +def node6530 : Tree Nat := .leaf 9860121179517661423971195337560352575734065613336690145177490414880826371041172089037993874818612959963972729044992 +def node6531 : Tree Nat := .node node6530 node990 +def node6532 : Tree Nat := .node node6529 node6531 +def node6533 : Tree Nat := .leaf 3355225373093545416763519439248289131022058097194141409220373652298537141314791418755351844634051761079658851230749073469830873286129774845687256236163072 +def node6534 : Tree Nat := .node node6533 node57 +def node6535 : Tree Nat := .node node4275 node6534 +def node6536 : Tree Nat := .node node6532 node6535 +def node6537 : Tree Nat := .node node6151 node6536 +def node6538 : Tree Nat := .node node6145 node6537 +def node6539 : Tree Nat := .node node6527 node6538 +def node6540 : Tree Nat := .node node6516 node6539 +def node6541 : Tree Nat := .node node6492 node6540 +def node6542 : Tree Nat := .node node6447 node6541 +def node6543 : Tree Nat := .leaf 13687321852866585655923514817100873974679685521745679791737577553697825501626032159517738433952114199335926928720783221932066114164126313994757983959166642564755984023080794850251155851530207232 +def node6544 : Tree Nat := .node node2132 node6543 +def node6545 : Tree Nat := .node node6544 node4801 +def node6546 : Tree Nat := .node node5321 node6545 +def node6547 : Tree Nat := .node node6546 node6161 +def node6548 : Tree Nat := .node node6547 node6167 +def node6549 : Tree Nat := .leaf 897012324949464557546603467053522876804607870353124870831313882559140692074563643606154506007485756167679307200645249232539884857860182113960459236747945087123848168936622982186226105720882847547392 +def node6550 : Tree Nat := .node node2327 node6549 +def node6551 : Tree Nat := .node node6550 node4816 +def node6552 : Tree Nat := .node node5779 node6551 +def node6553 : Tree Nat := .node node6552 node6172 +def node6554 : Tree Nat := .leaf 208851956983437891478325116227735503764033287380152584712792626246609886194244875480922522490724398793577986583263904143250520540834446929851653807970682412181945556992809980014780007581952 +def node6555 : Tree Nat := .node node1114 node6554 +def node6556 : Tree Nat := .node node6555 node4825 +def node6557 : Tree Nat := .leaf 1676385165068811655180504773487834215828947807829804555314130591886232520483743956419594696032403666480897843108826701703094683313325352771918133591015424 +def node6558 : Tree Nat := .node node6557 node57 +def node6559 : Tree Nat := .node node4316 node6558 +def node6560 : Tree Nat := .node node6556 node6559 +def node6561 : Tree Nat := .node node5789 node6560 +def node6562 : Tree Nat := .node node6553 node6561 +def node6563 : Tree Nat := .node node6548 node6562 +def node6564 : Tree Nat := .leaf 2335969596222563951944279862118549158345332995711262684456546569164428885610842822047346353703920496334988691023978609085198047272681994849382649660881606376013359270216260986932641526785433927680 +def node6565 : Tree Nat := .node node2210 node6564 +def node6566 : Tree Nat := .node node6565 node4832 +def node6567 : Tree Nat := .node node5795 node6566 +def node6568 : Tree Nat := .node node6567 node6179 +def node6569 : Tree Nat := .leaf 270543840606923933332527942991870537014648146033757158287612403429878766374818156289987584 +def node6570 : Tree Nat := .node node6569 node1166 +def node6571 : Tree Nat := .node node5799 node6570 +def node6572 : Tree Nat := .node node6571 node5357 +def node6573 : Tree Nat := .leaf 543885304644369509058138323509727927578100730864786077070563370965699468817945944764705231423079520087116864969877933892853897537698925915063965531108232809514355718870393321810988892160 +def node6574 : Tree Nat := .node node1177 node6573 +def node6575 : Tree Nat := .node node6574 node6182 +def node6576 : Tree Nat := .node node6575 node5361 +def node6577 : Tree Nat := .node node6572 node6576 +def node6578 : Tree Nat := .node node6568 node6577 +def node6579 : Tree Nat := .leaf 35644067325173400145634153169533525975728347712879374457649941546088087243817792082077443838416964060899947085010250834075154890153919027787467515767640204880239342385661039145781132265525760 +def node6580 : Tree Nat := .node node2038 node6579 +def node6581 : Tree Nat := .node node6580 node4856 +def node6582 : Tree Nat := .node node6581 node5376 +def node6583 : Tree Nat := .node node6195 node6582 +def node6584 : Tree Nat := .node node6191 node6583 +def node6585 : Tree Nat := .node node6578 node6584 +def node6586 : Tree Nat := .node node6563 node6585 +def node6587 : Tree Nat := .leaf 218997149645865370494776237073613983594874968347930876667801240859165208026016514552283814943233827189374830859532531550913057826626021023916127743346666281036095744369292717604018493624483315712 +def node6588 : Tree Nat := .node node2171 node6587 +def node6589 : Tree Nat := .node node6588 node4864 +def node6590 : Tree Nat := .node node5384 node6589 +def node6591 : Tree Nat := .node node6590 node6203 +def node6592 : Tree Nat := .leaf 50989247310409641474200467829036988223640939301795064627146637267238741746641815302959600217462011424213375630679664097473271616414659894983313917962340076534236817178706140498453594112 +def node6593 : Tree Nat := .node node1303 node6592 +def node6594 : Tree Nat := .node node6593 node4877 +def node6595 : Tree Nat := .node node6594 node5393 +def node6596 : Tree Nat := .node node6208 node6595 +def node6597 : Tree Nat := .node node6591 node6596 +def node6598 : Tree Nat := .leaf 3341631311735006263653201859643768060224532598082441355404682019945758179107918007694760359851590380697247785332222466292008328653351150877626460927530918594911128911884959680236480121311232 +def node6599 : Tree Nat := .node node1365 node6598 +def node6600 : Tree Nat := .leaf 327067434247415110648800625831270231780447054491168258474180169859461557673560830270528577311056434288538926710784 +def node6601 : Tree Nat := .node node6600 node1369 +def node6602 : Tree Nat := .node node6599 node6601 +def node6603 : Tree Nat := .leaf 111295280668468823580448449692138371175365829565464202842431906515268549077758934866031183139080741343130147260337042518159323893256655934423096522440704 +def node6604 : Tree Nat := .node node6603 node57 +def node6605 : Tree Nat := .node node4377 node6604 +def node6606 : Tree Nat := .node node6602 node6605 +def node6607 : Tree Nat := .node node6221 node6606 +def node6608 : Tree Nat := .node node6215 node6607 +def node6609 : Tree Nat := .node node6597 node6608 +def node6610 : Tree Nat := .leaf 37375513539561023231108477793896786533525327931380202951304745106630862169773485150583505184559321617635438425858155616469608923568675846555865971390625936303721170642887867782135339671423104843776 +def node6611 : Tree Nat := .node node2288 node6610 +def node6612 : Tree Nat := .node node6611 node4899 +def node6613 : Tree Nat := .node node5839 node6612 +def node6614 : Tree Nat := .node node6613 node6228 +def node6615 : Tree Nat := .leaf 4075066599141791745821202141315049963783137699633467196707161826662548918520698479117877504 +def node6616 : Tree Nat := .node node6615 node1417 +def node6617 : Tree Nat := .node node5847 node6616 +def node6618 : Tree Nat := .node node6617 node6232 +def node6619 : Tree Nat := .leaf 8702164874309912144930213176155646101463334309308514610148142452413783100126032710502641279545423131667631852061597538666621494948843298540632835669154285333571624798023016923712356089856 +def node6620 : Tree Nat := .node node1428 node6619 +def node6621 : Tree Nat := .node node6620 node6235 +def node6622 : Tree Nat := .node node6621 node5424 +def node6623 : Tree Nat := .node node6618 node6622 +def node6624 : Tree Nat := .node node6614 node6623 +def node6625 : Tree Nat := .leaf 570305077202774402330146450712536415611653563406069991322399064737409395901084673313239101414671424972600832537306224847168616033163800286796230810999033931819111737724911885135177430320813056 +def node6626 : Tree Nat := .node node2093 node6625 +def node6627 : Tree Nat := .leaf 4926453228351690104147559426583507866192983758273221893267338808508139712458010005949836695747787474972654335688704 +def node6628 : Tree Nat := .node node6627 node1493 +def node6629 : Tree Nat := .node node6626 node6628 +def node6630 : Tree Nat := .node node6629 node5439 +def node6631 : Tree Nat := .node node6250 node6630 +def node6632 : Tree Nat := .node node6244 node6631 +def node6633 : Tree Nat := .node node6624 node6632 +def node6634 : Tree Nat := .node node6609 node6633 +def node6635 : Tree Nat := .node node6586 node6634 +def node6636 : Tree Nat := .leaf 54749287411466342623694059268403495898718742086982719166950310214791302006504128638070953735808456797343707714883132887728264456656505255979031935836666570259023936092323179400996179156819509248 +def node6637 : Tree Nat := .node node2141 node6636 +def node6638 : Tree Nat := .node node6637 node4932 +def node6639 : Tree Nat := .node node5448 node6638 +def node6640 : Tree Nat := .node node6639 node6259 +def node6641 : Tree Nat := .leaf 12747311827602410368550116957259247055910234825448766156786659316809685436660453825739900054365502856053343907669916024368317904103664973745828479490429250227803159465820620234736795648 +def node6642 : Tree Nat := .node node1554 node6641 +def node6643 : Tree Nat := .node node6642 node4945 +def node6644 : Tree Nat := .node node6643 node5457 +def node6645 : Tree Nat := .node node6264 node6644 +def node6646 : Tree Nat := .node node6640 node6645 +def node6647 : Tree Nat := .leaf 835407827933751565913300464910942015056133149520610338851170504986439544776979501923690089962897595174311946333055616573002082163337787719406615231882729648727782227971239920059120030320128 +def node6648 : Tree Nat := .node node1616 node6647 +def node6649 : Tree Nat := .leaf 19705812913406760416590237706334031464771935033092887573069355234032558849832040023799346782991149863298870370369536 +def node6650 : Tree Nat := .node node6649 node1620 +def node6651 : Tree Nat := .node node6648 node6650 +def node6652 : Tree Nat := .leaf 6705540660275246620722019093951336863315791231319218221256522367544930081934975825678378784129614665923591372435306806137380141643773819378708011565449216 +def node6653 : Tree Nat := .node node6652 node57 +def node6654 : Tree Nat := .node node4436 node6653 +def node6655 : Tree Nat := .node node6651 node6654 +def node6656 : Tree Nat := .node node6275 node6655 +def node6657 : Tree Nat := .node node6271 node6656 +def node6658 : Tree Nat := .node node6646 node6657 +def node6659 : Tree Nat := .leaf 9343878384890255807777119448474196633381331982845050737826186276657715542443371290065213346528798061119840706363493706846297354554781226528858043425732418043593493044190707937613024592808839741440 +def node6660 : Tree Nat := .node node2258 node6659 +def node6661 : Tree Nat := .node node6660 node4967 +def node6662 : Tree Nat := .node node5893 node6661 +def node6663 : Tree Nat := .node node6662 node6282 +def node6664 : Tree Nat := .leaf 1082175362427695733330111771967482148058592584135028633150449613719515065499272625159940096 +def node6665 : Tree Nat := .node node6664 node1668 +def node6666 : Tree Nat := .node node5901 node6665 +def node6667 : Tree Nat := .node node6666 node6286 +def node6668 : Tree Nat := .leaf 2175541218577478036232553294038912348623571463206808960854244365244632557516982757456454874934134859094557758791049937809083593702106348083159266998646778035422449323133218686306835496960 +def node6669 : Tree Nat := .node node1679 node6668 +def node6670 : Tree Nat := .node node6669 node6289 +def node6671 : Tree Nat := .node node6670 node5488 +def node6672 : Tree Nat := .node node6667 node6671 +def node6673 : Tree Nat := .node node6663 node6672 +def node6674 : Tree Nat := .leaf 142576269300693600582536612678134103902913390851517497830599766184352348975271168328309775353667856245151436837639537659825412174833757132263293253558285697935204977449301787262228660725237760 +def node6675 : Tree Nat := .node node2055 node6674 +def node6676 : Tree Nat := .leaf 1308269736989660442595202503325080927121788217964673033896720679437846230694243321082114309244225725895156638416896 +def node6677 : Tree Nat := .node node6676 node1744 +def node6678 : Tree Nat := .node node6675 node6677 +def node6679 : Tree Nat := .node node6678 node5503 +def node6680 : Tree Nat := .node node6304 node6679 +def node6681 : Tree Nat := .node node6298 node6680 +def node6682 : Tree Nat := .node node6673 node6681 +def node6683 : Tree Nat := .node node6658 node6682 +def node6684 : Tree Nat := .leaf 875988598583461481979104948294455934379499873391723506671204963436660832104066058209135259772935308757499323438130126203652231306504084095664510973386665124144382977477170870415938866509112147968 +def node6685 : Tree Nat := .node node2219 node6684 +def node6686 : Tree Nat := .node node6685 node4999 +def node6687 : Tree Nat := .node node5919 node6686 +def node6688 : Tree Nat := .node node6687 node6312 +def node6689 : Tree Nat := .leaf 203956989241638565896801871316147952894563757207180258508586549068954966986567261211838400869848045696853502522718656389893086465658639579933255671846868003644850551453129923755788730368 +def node6690 : Tree Nat := .node node1804 node6689 +def node6691 : Tree Nat := .node node6690 node5008 +def node6692 : Tree Nat := .node node6691 node5520 +def node6693 : Tree Nat := .node node5925 node6692 +def node6694 : Tree Nat := .node node6688 node6693 +def node6695 : Tree Nat := .leaf 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149502054158244092924433911175587146134101311725520811805218980426523448679093940602334020738237286470541753703432622465878435694274703386223463885562503745214884682571551471128541347426693350948864 +def node6706 : Tree Nat := .node node2297 node6705 +def node6707 : Tree Nat := .node node6706 node5030 +def node6708 : Tree Nat := .node node5941 node6707 +def node6709 : Tree Nat := .node node6708 node6330 +def node6710 : Tree Nat := .leaf 16300266396567166983284808565260199855132550798533868786828647306650195674082793916471476736 +def node6711 : Tree Nat := .node node6710 node1918 +def node6712 : Tree Nat := .node node5945 node6711 +def node6713 : Tree Nat := .node node6712 node5547 +def node6714 : Tree Nat := .leaf 34808659497239648579720852704622584405853337237234058440592569809655132400504130842010565118181692526670527408246390154666485979795373194162531342676616933642412157798986926474996255555584 +def node6715 : Tree Nat := .node node1929 node6714 +def node6716 : Tree Nat := .node node6715 node6333 +def node6717 : Tree Nat := .node node6716 node5551 +def node6718 : Tree Nat := .node node6713 node6717 +def node6719 : Tree Nat := .node node6709 node6718 +def node6720 : Tree Nat := .leaf 2281220308811097609320585802850145662446614253624279965289596258949637583604338693252956405658685699890403330149224899388674464132655201147184923243996135727276446950899647540540709721283241984 +def node6721 : Tree Nat := .node node2102 node6720 +def node6722 : Tree Nat := .node node6721 node5054 +def node6723 : Tree Nat := .node node6722 node5566 +def node6724 : Tree Nat := .node node6346 node6723 +def node6725 : Tree Nat := .node node6342 node6724 +def node6726 : Tree Nat := .node node6719 node6725 +def node6727 : Tree Nat := .node node6704 node6726 +def node6728 : Tree Nat := .node node6683 node6727 +def node6729 : Tree Nat := .node node6635 node6728 +def node6730 : Tree Nat := .node node6542 node6729 +def node6731 : Tree Nat := .leaf 84162174424773976115855838126082058648805436845170781751972494449099714468753293153818664580441415219631727501698851483408310916002940861810045036330430093599283578738055113571066620128934528564732797646295531520 +def node6732 : Tree Nat := .node node2869 node6731 +def node6733 : Tree Nat := .node node6732 node5069 +def node6734 : Tree Nat := .node node5966 node6733 +def node6735 : Tree Nat := .node node6357 node6734 +def node6736 : Tree Nat := .leaf 19595533242629369747791401605606558418088927130487463844933662202465281465266200982457647235235528838735010358900495684567911298014908298340170885513171109743249504533143690224187450010415395510251683840 +def node6737 : Tree Nat := .node node2511 node6736 +def node6738 : Tree Nat := .node node6737 node5970 +def node6739 : Tree Nat := .node node6361 node6738 +def node6740 : Tree Nat := .node node6739 node5978 +def node6741 : Tree Nat := .node node6735 node6740 +def node6742 : Tree Nat := .leaf 1284212866588958375791257295625031412487875928423626430541572486100764686107685747586344369208395617975337638880902885183842634826705030240021439152991181848133599529084092919481099713102355604934653724590080 +def node6743 : Tree Nat := .node node2697 node6742 +def node6744 : Tree Nat := .node node6743 node5085 +def node6745 : Tree Nat := .node node5988 node6744 +def node6746 : Tree Nat := .node node6745 node6375 +def node6747 : Tree Nat := .node node6369 node6746 +def node6748 : Tree Nat := .node node6741 node6747 +def node6749 : Tree Nat := .leaf 5016456510113118655434598811035278955030765345404790744306217316095185947145313588669695687683687695812394247308157531133001298324106784135707060447011883364710695764884180424507611484794078958855707951104 +def node6750 : Tree Nat := .node node2589 node6749 +def node6751 : Tree Nat := .node node6750 node5999 +def node6752 : Tree Nat := .node node5612 node6751 +def node6753 : Tree Nat := .node node6752 node6387 +def node6754 : Tree Nat := .node node6383 node6753 +def node6755 : Tree Nat := .leaf 76545051729020975577310162521900618820659871603466655644272117978391373669441992928649456010793771169492723606464102115801602474151255487753295586590288542499595349352791130889605904915928353628749824 +def node6756 : Tree Nat := .node node2386 node6755 +def node6757 : Tree Nat := .node node6756 node4584 +def node6758 : Tree Nat := .node node5618 node6757 +def node6759 : Tree Nat := .node node6758 node6007 +def node6760 : Tree Nat := .leaf 328758493846773344202561867680008041596896237676448366218642556441844584598768874197612675014549870173478920799730492785372287450872327677240933060626425441239268118703932673318369566140111567296237627531853824 +def node6761 : Tree Nat := .node node2822 node6760 +def node6762 : Tree Nat := .node node6761 node5116 +def node6763 : Tree Nat := .node node6013 node6762 +def node6764 : Tree Nat := .node node6763 node6398 +def node6765 : Tree Nat := .node node6759 node6764 +def node6766 : Tree Nat := .node node6754 node6765 +def node6767 : Tree Nat := .node node6748 node6766 +def node6768 : Tree Nat := .leaf 313528531882069915964662425689704934689422834087799421518938595239444503444259215719322355763768461419760165742407930953086580768238532773442734168210737755891992072530299043586999200166646328164026941440 +def node6769 : Tree Nat := .node node2550 node6768 +def node6770 : Tree Nat := .node node6769 node4610 +def node6771 : Tree Nat := .node node6410 node6770 +def node6772 : Tree Nat := .leaf 51196676225182272594658194568607927414277009539705526874090174137856096516644156169973020090241268327021161670391071292763414483160823840060328640512 +def node6773 : Tree Nat := .node node6772 node57 +def node6774 : Tree Nat := .node node3571 node6773 +def node6775 : Tree Nat := .node node6414 node6774 +def node6776 : Tree Nat := .node node6771 node6775 +def node6777 : Tree Nat := .node node6407 node6776 +def node6778 : Tree Nat := .leaf 4784065733063810973581885157618788676291241975216665977767007373648750357731006099232824032039924032894289638403441329240212719241920971274455782595989040464660523567661989354383417913515775958712320 +def node6779 : Tree Nat := .node node2347 node6778 +def node6780 : Tree Nat := .node node6779 node5638 +def node6781 : Tree Nat := .node node5636 node6780 +def node6782 : Tree Nat := .leaf 781199283221165048136263955209471548679763939509666852937166963773438972727114199370926209873066228134478174902217926005106710790821745369546752 +def node6783 : Tree Nat := .node node6782 node340 +def node6784 : Tree Nat := .node node3180 node6783 +def node6785 : Tree Nat := .node node6032 node6784 +def node6786 : Tree Nat := .node node6781 node6785 +def node6787 : Tree Nat := .leaf 20547405865423334012660116730000502599806014854778022888665159777612234977722971961381509907334329887605402222094446162941482157227280483840343026447858909570137592465345486711697595409637689678954459593441280 +def node6788 : Tree Nat := .node node2783 node6787 +def node6789 : Tree Nat := .leaf 181887131934325454788343970479786290945430272144653567331183460488319157792049040871422321040431556323188863598646282501111755814469632 +def node6790 : Tree Nat := .node node6789 node356 +def node6791 : Tree Nat := .node node6788 node6790 +def node6792 : Tree Nat := .node node6037 node6791 +def node6793 : Tree Nat := .node node6792 node6421 +def node6794 : Tree Nat := .node node6786 node6793 +def node6795 : Tree Nat := .node node6777 node6794 +def node6796 : Tree Nat := .leaf 80263304161809898486953580976564463280492245526476651908873859988919082122074300031847448280234030136639599203666570256117334972696953549492605735270451118720033592441364614653886091177557617384890564608000 +def node6797 : Tree Nat := .node node2658 node6796 +def node6798 : Tree Nat := .node node6797 node5164 +def node6799 : Tree Nat := .node node5656 node6798 +def node6800 : Tree Nat := .leaf 12986473969314527682547444475939571831914168273486279987574092952041546433490224979700473388744126600024880033465053011578555041746109791076259725312 +def node6801 : Tree Nat := .node node6800 node57 +def node6802 : Tree Nat := .node node3819 node6801 +def node6803 : Tree Nat := .node node6432 node6802 +def node6804 : Tree Nat := .node node6799 node6803 +def node6805 : Tree Nat := .node node6429 node6804 +def node6806 : Tree Nat := .leaf 1224720827664335609236962600350409901130557945655466490308353887654170968601032065231440494305520026132401980092863498049562243764665993474245317529993952560087563312133189324565364713331566102414622720 +def node6807 : Tree Nat := .node node2425 node6806 +def node6808 : Tree Nat := .node node6807 node4651 +def node6809 : Tree Nat := .node node5662 node6808 +def node6810 : Tree Nat := .leaf 198157866963417475624808417906792783079744999290256957818208205444969885764926528620917867870241189575574951682516867013837861426011557962186752 +def node6811 : Tree Nat := .node node6810 node57 +def node6812 : Tree Nat := .node node3288 node6811 +def node6813 : Tree Nat := .node node6050 node6812 +def node6814 : Tree Nat := .node node6809 node6813 +def node6815 : Tree Nat := .leaf 5260135901548373507240989882880128665550339802823173859498280903069122468134075592016375594012282744511731870424491767115029624085620362335233057072459525323351559321941488144847076712097291245660452533536030720 +def node6816 : Tree Nat := .node node2877 node6815 +def node6817 : Tree Nat := .leaf 46137223710170359263384812024140912825182312934253587810836780221427298561885610367385174117572882579540589837440414447487430565036032 +def node6818 : Tree Nat := .node node6817 node4147 +def node6819 : Tree Nat := .node node6816 node6818 +def node6820 : Tree Nat := .node node6055 node6819 +def node6821 : Tree Nat := .node node6820 node6442 +def node6822 : Tree Nat := .node node6814 node6821 +def node6823 : Tree Nat := .node node6805 node6822 +def node6824 : Tree Nat := .node node6795 node6823 +def node6825 : Tree Nat := .node node6767 node6824 +def node6826 : Tree Nat := .leaf 78382132970517478991165606422426233672355708521949855379734648809861125861064803929830588940942115354940041435601982738271645192059633193360683542052684438972998018132574152424461690491548863623468154880 +def node6827 : Tree Nat := .node node2520 node6826 +def node6828 : Tree Nat := .node node6827 node4678 +def node6829 : Tree Nat := .node node6455 node6828 +def node6830 : Tree Nat := .leaf 811654623082157980159215279746223239494635517092892499223380809502596652093139061231279586796507912501555002091566087036189339406682585230158594048 +def node6831 : Tree Nat := .node node6830 node57 +def node6832 : Tree Nat := .node node3366 node6831 +def node6833 : Tree Nat := .node node6071 node6832 +def node6834 : Tree Nat := .node node6829 node6833 +def node6835 : Tree Nat := .node node6452 node6834 +def node6836 : Tree Nat := .leaf 1196016433265952743395471289404697169072810493804166494441751843412187589432751524808206008009981008223572409600860332310053179810480242818613945648997260116165130891915497302328079889940068748492800 +def node6837 : Tree Nat := .node node2317 node6836 +def node6838 : Tree Nat := .node node6837 node5683 +def node6839 : Tree Nat := .node node5681 node6838 +def node6840 : Tree Nat := .leaf 12384866685213592226550526119174548942484062455641059863638012840310617860307908038807366741890074348473434480158373768558808907683235215966208 +def node6841 : Tree Nat := .node node6840 node591 +def node6842 : Tree Nat := .node node3150 node6841 +def node6843 : Tree Nat := .node node6077 node6842 +def node6844 : Tree Nat := .node node6839 node6843 +def node6845 : Tree Nat := .leaf 5136851466355833503165029182500125649951503713694505722166289944403058744430742990345377476833582471901350555523611540735370539306820120960085756611964727392534398116336371677922022007533994489610808579850240 +def node6846 : Tree Nat := .node node2745 node6845 +def node6847 : Tree Nat := .leaf 2883576481885647453961550751508807051573894558390849238177298763839206160117850647961573382348305161221286881160524467765458268848128 +def node6848 : Tree Nat := .node node6847 node607 +def node6849 : Tree Nat := .node node6846 node6848 +def node6850 : Tree Nat := .node node5689 node6849 +def node6851 : Tree Nat := .node node6850 node6467 +def node6852 : Tree Nat := .node node6844 node6851 +def node6853 : Tree Nat := .node node6835 node6852 +def node6854 : Tree Nat := .leaf 20065826040452474621738395244141115820123061381619162977263266771549630493027248000605238696295458540404356134388197755135397265683910253670308006855728484704108654312330023159644456040031561744690200969216 +def node6855 : Tree Nat := .node node2628 node6854 +def node6856 : Tree Nat := .node node6855 node5228 +def node6857 : Tree Nat := .node node5701 node6856 +def node6858 : Tree Nat := .leaf 3199792264073892037166137160537995463392313096231595429630635883616006032290259760623313755640079270438822604399442457787351095576394482698239868928 +def node6859 : Tree Nat := .node node6858 node57 +def node6860 : Tree Nat := .node node3611 node6859 +def node6861 : Tree Nat := .node node6478 node6860 +def node6862 : Tree Nat := .node node6857 node6861 +def node6863 : Tree Nat := .node node6475 node6862 +def node6864 : Tree Nat := .leaf 306180206916083902309240650087602475282639486413866622577088471913701910026718715805689082021034924396179967129964898638704797491971261319357219127014720910778705064653556171137724675397698943079940096 +def node6865 : Tree Nat := .node node2434 node6864 +def node6866 : Tree Nat := .node node6865 node4719 +def node6867 : Tree Nat := .node node5707 node6866 +def node6868 : Tree Nat := .leaf 48824955201322815508516497200591971792485246219354178308572935235839935795444637460682888117066639258404885931390581272341397466781799298367488 +def node6869 : Tree Nat := .node node6868 node716 +def node6870 : Tree Nat := .node node3258 node6869 +def node6871 : Tree Nat := .node node6090 node6870 +def node6872 : Tree Nat := .node node6867 node6871 +def node6873 : Tree Nat := .leaf 1315033975387093376810247470720032166387584950705793464874570225767964237857491370576552898024606584355425506153554221281192025026319389938509067892033896422361872145916589324450133865476187390108645058303492096 +def node6874 : Tree Nat := .node node2839 node6873 +def node6875 : Tree Nat := .leaf 11367945745895340924271498154986643184089392009040847958198966280519947362003065054463895065026972270199304004836306691781556812382208 +def node6876 : Tree Nat := .node node6875 node732 +def node6877 : Tree Nat := .node node6874 node6876 +def node6878 : Tree Nat := .node node6095 node6877 +def node6879 : Tree Nat := .node node6878 node6488 +def node6880 : Tree Nat := .node node6872 node6879 +def node6881 : Tree Nat := .node node6863 node6880 +def node6882 : Tree Nat := .node node6853 node6881 +def node6883 : Tree Nat := .leaf 1254114127528279663858649702758819738757691336351197686075754380957778013777036862877289423055073845679040662969631723812346323072954131093770936672842951023567968290121186438791387047864781817975490478080 +def node6884 : Tree Nat := .node node2598 node6883 +def node6885 : Tree Nat := .node node6884 node6107 +def node6886 : Tree Nat := .node node6500 node6885 +def node6887 : Tree Nat := .node node6886 node6505 +def node6888 : Tree Nat := .node node6497 node6887 +def node6889 : Tree Nat := .leaf 19136262932255243894327540630475154705164967900866663911068029494595001430924024396931296128159696131577158553613765316960850876967683885097823130383956161858642094270647956837249278239041099975884800 +def node6890 : Tree Nat := .node node2395 node6889 +def node6891 : Tree Nat := .node node6890 node5736 +def node6892 : Tree Nat := .node node5734 node6891 +def node6893 : Tree Nat := .node node6892 node6119 +def node6894 : Tree Nat := .leaf 82189623461693336050640466920002010399224059419112091554660639110448939910891887845526039629337319550421608888377784651765928628909121935361372105791435638280550369861381946846752352120543911833772937277603840 +def node6895 : Tree Nat := .node node2792 node6894 +def node6896 : Tree Nat := .node node6895 node5275 +def node6897 : Tree Nat := .node node6125 node6896 +def node6898 : Tree Nat := .node node6897 node6513 +def node6899 : Tree Nat := .node node6893 node6898 +def node6900 : Tree Nat := .node node6888 node6899 +def node6901 : Tree Nat := .leaf 321053216647239593947814323906257853121968982105906607635495439955676328488297200127389793120936120546558396814666281024469339890787814197970422941081804474880134369765458455978831116235513314426419591249920 +def node6902 : Tree Nat := .node node2706 node6901 +def node6903 : Tree Nat := .node node6902 node6136 +def node6904 : Tree Nat := .node node5753 node6903 +def node6905 : Tree Nat := .node node6904 node6525 +def node6906 : Tree Nat := .node node6521 node6905 +def node6907 : Tree Nat := .leaf 4898883310657342436947850401401639604522231782621865961233415550616683874404128260925761977222080104529607920371453992198248975058663973896981270119975810240350253248532757298104298496776362616946688000 +def node6908 : Tree Nat := .node node2481 node6907 +def node6909 : Tree Nat := .node node6908 node4782 +def node6910 : Tree Nat := .node node5759 node6909 +def node6911 : Tree Nat := .node node6910 node6144 +def node6912 : Tree Nat := .leaf 21040543606193494028963959531520514662201359211292695437993123612276489872536302368065502376049130978046927481697967068460118496342481449340932228289838101293406237287765952579388296548728038128277922973430579200 +def node6913 : Tree Nat := .node node2886 node6912 +def node6914 : Tree Nat := .node node6913 node5306 +def node6915 : Tree Nat := .node node6150 node6914 +def node6916 : Tree Nat := .node node6915 node6536 +def node6917 : Tree Nat := .node node6911 node6916 +def node6918 : Tree Nat := .node node6906 node6917 +def node6919 : Tree Nat := .node node6900 node6918 +def node6920 : Tree Nat := .node node6882 node6919 +def node6921 : Tree Nat := .node node6825 node6920 +def node6922 : Tree Nat := .leaf 58786599727888109243374204816819675254266781391462391534800986607395844395798602947372941705706586516205031076701487053703733894044724895020512656539513329229748513599430705589189484301178555480231903232 +def node6923 : Tree Nat := .node node2530 node6922 +def node6924 : Tree Nat := .node node6923 node4806 +def node6925 : Tree Nat := .node node5773 node6924 +def node6926 : Tree Nat := .leaf 25579607621289240343940807700925204709304013180996773610139932127170296027889159491265788208502253211683621873608807186361924950074665766371075293184 +def node6927 : Tree Nat := .node node6926 node57 +def node6928 : Tree Nat := .node node3658 node6927 +def node6929 : Tree Nat := .node node6165 node6928 +def node6930 : Tree Nat := .node node6925 node6929 +def node6931 : Tree Nat := .node node6547 node6930 +def node6932 : Tree Nat := .leaf 390313836994769902709057734694293284748901568313549402010191835436558472105242301807644473396335650813043546655412954212968528389159281800249344 +def node6933 : Tree Nat := .node node6932 node4303 +def node6934 : Tree Nat := .node node3160 node6933 +def node6935 : Tree Nat := .node node6171 node6934 +def node6936 : Tree Nat := .node node6552 node6935 +def node6937 : Tree Nat := .leaf 3852638599766875127373771886875094237463627785270879291624717458302294058323057242759033107625186853926012916642708655551527904480115090720064317458973545544400798587252278758441873032381810056727277382664192 +def node6938 : Tree Nat := .node node2755 node6937 +def node6939 : Tree Nat := .leaf 90877021894503827837542103299473711463832661582517764067787638734224827984637185420758201134469278811720094409051141745217353352740864 +def node6940 : Tree Nat := .node node6939 node4311 +def node6941 : Tree Nat := .node node6938 node6940 +def node6942 : Tree Nat := .node node5788 node6941 +def node6943 : Tree Nat := .node node6942 node6560 +def node6944 : Tree Nat := .node node6936 node6943 +def node6945 : Tree Nat := .node node6931 node6944 +def node6946 : Tree Nat := .leaf 10032913020226237310869197622070557910061530690809581488606846702285306268196454118298061607680085400949418196256277171308273181235726187811398772969540116101045301323061042020476710117842051537545094758400 +def node6947 : Tree Nat := .node node2638 node6946 +def node6948 : Tree Nat := .node node6947 node5356 +def node6949 : Tree Nat := .node node6571 node6948 +def node6950 : Tree Nat := .leaf 1698231211371899773871588893007482470327237389609744306067381386036202225917952497345446520066539632310945850530045608503315771802941306151647576064 +def node6951 : Tree Nat := .node node6950 node57 +def node6952 : Tree Nat := .node node3484 node6951 +def node6953 : Tree Nat := .node node6575 node6952 +def node6954 : Tree Nat := .node node6949 node6953 +def node6955 : Tree Nat := .node node6568 node6954 +def node6956 : Tree Nat := .leaf 153090103458041951154620325043801237641319743206933311288544235956762895023874080822904330576029077859668842323468513384924984314505310286942702893719610868251485059326404940650699720916059051901583360 +def node6957 : Tree Nat := .node node2444 node6956 +def node6958 : Tree Nat := .node node6957 node5808 +def node6959 : Tree Nat := .node node5806 node6958 +def node6960 : Tree Nat := .leaf 25912951833677669889398023880119056248889730676418217560842611481265292753875007588889259644570001713729032143099198132206640553620963091021824 +def node6961 : Tree Nat := .node node6960 node1219 +def node6962 : Tree Nat := .node node3268 node6961 +def node6963 : Tree Nat := .node node6189 node6962 +def node6964 : Tree Nat := .node node6959 node6963 +def node6965 : Tree Nat := .leaf 657516987693546688405123735360016083193792475352896732437285112883603904153820316356434867560817730952315355169477918273991067044113286100751284754370292472986293033239529009254116343504099148566594891682938880 +def node6966 : Tree Nat := .node node2849 node6965 +def node6967 : Tree Nat := .leaf 6033329254406893134442629264695350138677687076017776867570963567417415965785041355734984307682607721939923299230530564592431261548544 +def node6968 : Tree Nat := .node node6967 node1235 +def node6969 : Tree Nat := .node node6966 node6968 +def node6970 : Tree Nat := .node node6194 node6969 +def node6971 : Tree Nat := .node node6970 node6582 +def node6972 : Tree Nat := .node node6964 node6971 +def node6973 : Tree Nat := .node node6955 node6972 +def node6974 : Tree Nat := .node node6945 node6973 +def node6975 : Tree Nat := .leaf 940585595646209747893987277069114804068268502263398264556815785718333510332777647157967067291305384259280497227223792859259742304715598320328202504632213267675976217590891289427031748818856887683710451712 +def node6976 : Tree Nat := .node node2569 node6975 +def node6977 : Tree Nat := .node node6976 node6206 +def node6978 : Tree Nat := .node node5822 node6977 +def node6979 : Tree Nat := .node node6978 node6595 +def node6980 : Tree Nat := .node node6591 node6979 +def node6981 : Tree Nat := .leaf 14352197199191432920745655472856366028873725925649997933301022120946251073193018297698472096119772098682868915210323987720638157725762913823367347787967121393981570702985967714979617691534125560758272 +def node6982 : Tree Nat := .node node2366 node6981 +def node6983 : Tree Nat := .node node6982 node4883 +def node6984 : Tree Nat := .node node5828 node6983 +def node6985 : Tree Nat := .node node6984 node6214 +def node6986 : Tree Nat := .leaf 61642217596270002037980350190001507799418044564334068665995479332836704933168915884144529722002989662816206666283338488824446471681841451521029079343576728710412777396036460135069968518108960907636438122627072 +def node6987 : Tree Nat := .node node2802 node6986 +def node6988 : Tree Nat := .node node6987 node5403 +def node6989 : Tree Nat := .node node6220 node6988 +def node6990 : Tree Nat := .node node6989 node6606 +def node6991 : Tree Nat := .node node6985 node6990 +def node6992 : Tree Nat := .node node6980 node6991 +def node6993 : Tree Nat := .leaf 160526608323619796973907161953128926560984491052953303817698258993806957663234590037186053633519779484306814604418928029366365555564046732500025340643964270649010886986041660543551648226768844543190626205696 +def node6994 : Tree Nat := .node node2677 node6993 +def node6995 : Tree Nat := .node node6994 node6231 +def node6996 : Tree Nat := .node node6617 node6995 +def node6997 : Tree Nat := .node node6996 node6622 +def node6998 : Tree Nat := .node node6614 node6997 +def node6999 : Tree Nat := .leaf 2449441655328671218473925200700819802261115891310932980616707775308166216487529529700340347033705800192014972549637978347856483215430954708487145730502123702213870674364878383611857673737289929385312256 +def node7000 : Tree Nat := .node node2491 node6999 +def node7001 : Tree Nat := .node node7000 node5856 +def node7002 : Tree Nat := .node node5854 node7001 +def node7003 : Tree Nat := .node node7002 node6243 +def node7004 : Tree Nat := .leaf 10520271803096747014481979765760257331100679605646347718996561806137490221545995321897222470579057021510214827443032853643599707111848873019009504548892650959555017343970618228526426713900852075096207466562584576 +def node7005 : Tree Nat := .node node2904 node7004 +def node7006 : Tree Nat := .node node7005 node5434 +def node7007 : Tree Nat := .node node6249 node7006 +def node7008 : Tree Nat := .node node7007 node6630 +def node7009 : Tree Nat := .node node7003 node7008 +def node7010 : Tree Nat := .node node6998 node7009 +def node7011 : Tree Nat := .node node6992 node7010 +def node7012 : Tree Nat := .node node6974 node7011 +def node7013 : Tree Nat := .leaf 235146398911552436973496819267278701017067125565849566139203946429583377583194411789491766822826346064820124306805948214814935576178899580082050626158053316918994054397722213884469827654601503503389032448 +def node7014 : Tree Nat := .node node2578 node7013 +def node7015 : Tree Nat := .node node7014 node6262 +def node7016 : Tree Nat := .node node5871 node7015 +def node7017 : Tree Nat := .node node7016 node6644 +def node7018 : Tree Nat := .node node6640 node7017 +def node7019 : Tree Nat := .leaf 3588049299797858230186413868214091507218431481412499483325255530236562768298254574424618024029943024670717228802580996930159539431440728455841836946991780348495392675746491892477129834444656149004288 +def node7020 : Tree Nat := .node node2375 node7019 +def node7021 : Tree Nat := .node node7020 node4951 +def node7022 : Tree Nat := .node node5877 node7021 +def node7023 : Tree Nat := .node node7022 node6270 +def node7024 : Tree Nat := .leaf 15410554399067500509495087547500376949854511141083517166498869833209176233292228971036132430500747415704051666570834622206111617920460362880257269835894182177603194349009115033765115284651812296781303212146688 +def node7025 : Tree Nat := .node node2764 node7024 +def node7026 : Tree Nat := .node node7025 node5467 +def node7027 : Tree Nat := .node node6274 node7026 +def node7028 : Tree Nat := .node node7027 node6655 +def node7029 : Tree Nat := .node node7023 node7028 +def node7030 : Tree Nat := .node node7018 node7029 +def node7031 : Tree Nat := .leaf 40131652080904949243476790488282231640246122763238325954437126664618210968547727056549201109594277230002787495015789254947123884768022419980370446919718559354199865317342956745340638155487585600336004382720 +def node7032 : Tree Nat := .node node2686 node7031 +def node7033 : Tree Nat := .node node7032 node6285 +def node7034 : Tree Nat := .node node6666 node7033 +def node7035 : Tree Nat := .node node7034 node6671 +def node7036 : Tree Nat := .node node6663 node7035 +def node7037 : Tree Nat := .leaf 612360413832167804618481300175204950565278972827733245154176943827086183013278951061064860913134417123294256028574743730558064843187311621692225782653982353594119899240275204915597200240661805095976960 +def node7038 : Tree Nat := .node node2461 node7037 +def node7039 : Tree Nat := .node node7038 node5910 +def node7040 : Tree Nat := .node node5908 node7039 +def node7041 : Tree Nat := .node node7040 node6297 +def node7042 : Tree Nat := .leaf 2630067950774186753620494941440064332775169901411586929749140451534564235015503828532458076556701018396571229427379365814327924330536871817328833913946858292847853025139797250778348745955999220061658183830077440 +def node7043 : Tree Nat := .node node2858 node7042 +def node7044 : Tree Nat := .node node7043 node5498 +def node7045 : Tree Nat := .node node6303 node7044 +def node7046 : Tree Nat := .node node7045 node6679 +def node7047 : Tree Nat := .node node7041 node7046 +def node7048 : Tree Nat := .node node7036 node7047 +def node7049 : Tree Nat := .node node7030 node7048 +def node7050 : Tree Nat := .leaf 3762342382584838991575949108276459216273074009053593058227263142873334041331110588631868269165221537037121988908895171437038969218862393281312810018528853070703904870363555422151517242473624056054224519168 +def node7051 : Tree Nat := .node node2617 node7050 +def node7052 : Tree Nat := .node node7051 node5515 +def node7053 : Tree Nat := .node node5924 node7052 +def node7054 : Tree Nat := .leaf 6792924845487599095486355572029929881308949558438977224269525544144808903671809989381786080266158529243783402120181622716878941144948266716538863616 +def node7055 : Tree Nat := .node node7054 node57 +def node7056 : Tree Nat := .node node3454 node7055 +def node7057 : Tree Nat := .node node6691 node7056 +def node7058 : Tree Nat := .node node7053 node7057 +def node7059 : Tree Nat := .node node6688 node7058 +def node7060 : Tree Nat := .leaf 57408788796765731682982621891425464115494903702599991733204088483785004292772073190793888384479088394731475660841295950882552630903051655293469391151868485575926282811943870279634077351114498384068608 +def node7061 : Tree Nat := .node node2414 node7060 +def node7062 : Tree Nat := .node node7061 node5014 +def node7063 : Tree Nat := .node node5930 node7062 +def node7064 : Tree Nat := .leaf 103651807334710679557592095520476224995558922705672870243370445925061171015500030355557038578280006854916128572393623402325991640980110606073856 +def node7065 : Tree Nat := .node node7064 node1846 +def node7066 : Tree Nat := .node node3238 node7065 +def node7067 : Tree Nat := .node node6317 node7066 +def node7068 : Tree Nat := .node node7063 node7067 +def node7069 : Tree Nat := .leaf 246568870385080008151921400760006031197672178257336274663981917331346819732675663536578118888011958651264826665133353955297785886727365806084116317374306914841651109584145840540241844554428996748500851394347008 +def node7070 : Tree Nat := .node node2811 node7069 +def node7071 : Tree Nat := .leaf 24133317017627572537770517058781400554710748304071107470283854269669663863140165422939937230730430887759693148565089473784558057947136 +def node7072 : Tree Nat := .node node7071 node4489 +def node7073 : Tree Nat := .node node7070 node7072 +def node7074 : Tree Nat := .node node6322 node7073 +def node7075 : Tree Nat := .node node7074 node6701 +def node7076 : Tree Nat := .node node7068 node7075 +def node7077 : Tree Nat := .node node7059 node7076 +def node7078 : Tree Nat := .leaf 642106433294479187895628647812515706243937964211813215270793035975227830652938360148744214534079117937227258417675712117465462222256186930000101362575857082596043547944166641362910208761008561214872453382144 +def node7079 : Tree Nat := .node node2725 node7078 +def node7080 : Tree Nat := .node node7079 node5546 +def node7081 : Tree Nat := .node node6712 node7080 +def node7082 : Tree Nat := .leaf 102318430485156961375763230803700818837216052723987094440559728508681184111556637965063152834009012846734487494435226108734451325581507952341633990656 +def node7083 : Tree Nat := .node node7082 node57 +def node7084 : Tree Nat := .node node3716 node7083 +def node7085 : Tree Nat := .node node6716 node7084 +def node7086 : Tree Nat := .node node7081 node7085 +def node7087 : Tree Nat := .node node6709 node7086 +def node7088 : Tree Nat := .leaf 9797766621314684873895700802803279209044463565243731922466831101232664865950118118801361388134823200768059890198551913391425932861723818833948582922008494808855482697459513534399073662164574550553001984 +def node7089 : Tree Nat := .node node2500 node7088 +def node7090 : Tree Nat := .node node7089 node5954 +def node7091 : Tree Nat := .node node5952 node7090 +def node7092 : Tree Nat := .leaf 1561255347979079610836230938777173138995606273254197608040767341746233888420969207230577893585342603252174186621641517190747259192749966487453696 +def node7093 : Tree Nat := .node node7092 node57 +def node7094 : Tree Nat := .node node3346 node7093 +def node7095 : Tree Nat := .node node6340 node7094 +def node7096 : Tree Nat := .node node7091 node7095 +def node7097 : Tree Nat := .leaf 42081087212386988057927919063041029324402718422585390875986247224549960886183981287588889882316228086040859309772131414574398828447395492076038018195570603838220069375882472914105703686476907729811326124492324864 +def node7098 : Tree Nat := .node node2913 node7097 +def node7099 : Tree Nat := .leaf 363508087578015311350168413197894845855330646330071056271150554936899311938548741683032804537877115246880377479044210430967620699160576 +def node7100 : Tree Nat := .node node7099 node4522 +def node7101 : Tree Nat := .node node7098 node7100 +def node7102 : Tree Nat := .node node6345 node7101 +def node7103 : Tree Nat := .node node7102 node6723 +def node7104 : Tree Nat := .node node7096 node7103 +def node7105 : Tree Nat := .node node7087 node7104 +def node7106 : Tree Nat := .node node7077 node7105 +def node7107 : Tree Nat := .node node7049 node7106 +def node7108 : Tree Nat := .node node7012 node7107 +def node7109 : Tree Nat := .node node6921 node7108 +def node7110 : Tree Nat := .leaf 67039039649712985497870124991029230637396829102961966888617807218608820150367734884009371490834517138450159290932430254268769414059733126433329350673694720 +def node7111 : Tree Nat := .node node0 node7110 +def node7112 : Tree Nat := .node node7111 node4013 +def node7113 : Tree Nat := .leaf 40387056351304341192586016102647204150206732752227082834647000739351864815784640876699622911257038534204694293316108288 +def node7114 : Tree Nat := .node node7113 node4015 +def node7115 : Tree Nat := .node node6355 node7114 +def node7116 : Tree Nat := .node node7112 node7115 +def node7117 : Tree Nat := .node node7116 node6734 +def node7118 : Tree Nat := .leaf 90095700615208749952205140752626349712100267269774297252850104458456255020586311837977132474920250651021821138058988524633626134131119569241494764329398619207291662923736989568124886940166828518308811950084888466356436096801535056311672708421428399801630720 +def node7119 : Tree Nat := .node node3317 node7118 +def node7120 : Tree Nat := .node node7119 node5074 +def node7121 : Tree Nat := .node node5977 node7120 +def node7122 : Tree Nat := .node node6739 node7121 +def node7123 : Tree Nat := .node node7117 node7122 +def node7124 : Tree Nat := .leaf 4393470502483590217588416511412091659052438592091715462012456613878747637374499873358438170023330915185469639290547749143758072319818652040047378106378061086720 +def node7125 : Tree Nat := .node node63 node7124 +def node7126 : Tree Nat := .node node7125 node4037 +def node7127 : Tree Nat := .leaf 3318191093341677537707856136023870258513671943785552213987397273154732194291640935099094278964977113396076359932739716120576 +def node7128 : Tree Nat := .node node7127 node4039 +def node7129 : Tree Nat := .node node6366 node7128 +def node7130 : Tree Nat := .node node7126 node7129 +def node7131 : Tree Nat := .leaf 5515652263101987298728728207430913795608113109085112352897269396216198887424215820128660001943808587833784893551335930816647064191168732319583111500951066614122648616177179922993422016587311577585464241250445033472000 +def node7132 : Tree Nat := .node node3101 node7131 +def node7133 : Tree Nat := .node node7132 node5080 +def node7134 : Tree Nat := .node node5983 node7133 +def node7135 : Tree Nat := .node node7130 node7134 +def node7136 : Tree Nat := .node node7135 node6746 +def node7137 : Tree Nat := .node node7123 node7136 +def node7138 : Tree Nat := .leaf 17161994150326524287454751997703528038877713914740438277877730800445768153617580179526110175892924108228054421936518566663085876401004383187919468014935736320 +def node7139 : Tree Nat := .node node126 node7138 +def node7140 : Tree Nat := .node node7139 node4059 +def node7141 : Tree Nat := .node node7140 node6381 +def node7142 : Tree Nat := .leaf 21545516652742137885659094560277007014094191832363720128504958578969526904001588057069981129655815353128807445082618462147232095508541388077531684570906336832825941983923716728892836336950821687649194513047008313344 +def node7143 : Tree Nat := .node node2993 node7142 +def node7144 : Tree Nat := .node node7143 node5096 +def node7145 : Tree Nat := .node node5995 node7144 +def node7146 : Tree Nat := .node node7141 node7145 +def node7147 : Tree Nat := .leaf 277611868196852612820085195624083737478891494950657476986477143411800846206232481723346305961478345456712698687169687134194619590434127562339433249108810456345144998646541852002415001552377730996591863151260381622555973255168 +def node7148 : Tree Nat := .node node3425 node7147 +def node7149 : Tree Nat := .node node7148 node5105 +def node7150 : Tree Nat := .node node6386 node7149 +def node7151 : Tree Nat := .node node6752 node7150 +def node7152 : Tree Nat := .node node7146 node7151 +def node7153 : Tree Nat := .leaf 1412006979354108748474554421102313931675676955925788762341700965431346915180599249952936960497614998525835989100446339481647664535586399624020009296470555887862398785093222876070956912945974675118917213944111558498975744 +def node7154 : Tree Nat := .node node3209 node7153 +def node7155 : Tree Nat := .node node7154 node5111 +def node7156 : Tree Nat := .node node6006 node7155 +def node7157 : Tree Nat := .node node6758 node7156 +def node7158 : Tree Nat := .node node7157 node6764 +def node7159 : Tree Nat := .node node7152 node7158 +def node7160 : Tree Nat := .node node7137 node7159 +def node7161 : Tree Nat := .leaf 1072624634395407767965921999856467690198349265647391470217884915497741122405883758144149943853352274215202548654918884068300310624955730022933269610779115520 +def node7162 : Tree Nat := .node node252 node7161 +def node7163 : Tree Nat := .node node7162 node4090 +def node7164 : Tree Nat := .leaf 646192901620869459081376257642355266403307724035633325354352011829629837052554254027193966580112616518740301454038269952 +def node7165 : Tree Nat := .node node7164 node4092 +def node7166 : Tree Nat := .node node6404 node7165 +def node7167 : Tree Nat := .node node7163 node7166 +def node7168 : Tree Nat := .leaf 1346594790796383617853693410017312938380886989522732508031559911185595431500052690461098633287062643514107640027181623734532974656047053788960720581286881497588537259808881817137065922062952457035724762340728504320 +def node7169 : Tree Nat := .node node2954 node7168 +def node7170 : Tree Nat := .leaf 11920155078447953005008910449363274363399718315272016188616439266562484325059725942549533231705722475196505354383617339406385015780951457792 +def node7171 : Tree Nat := .node node7170 node278 +def node7172 : Tree Nat := .node node7169 node7171 +def node7173 : Tree Nat := .node node6021 node7172 +def node7174 : Tree Nat := .node node7167 node7173 +def node7175 : Tree Nat := .leaf 17350741762303288301255324726505233592430718434416092311654821463220390893739203583421689370594693104707387578963134412683845671967827092495889485961216010865308084340802002136439186552489449439311878612714319287306791419904 +def node7176 : Tree Nat := .node node3395 node7175 +def node7177 : Tree Nat := .node node7176 node6773 +def node7178 : Tree Nat := .node node6414 node7177 +def node7179 : Tree Nat := .node node6771 node7178 +def node7180 : Tree Nat := .node node7174 node7179 +def node7181 : Tree Nat := .leaf 53091057493466840603325698176381924136218751100568835423798356370475715108666254961585508463439633814325932351550725212340224 +def node7182 : Tree Nat := .node node7181 node4109 +def node7183 : Tree Nat := .node node6779 node7182 +def node7184 : Tree Nat := .node node5636 node7183 +def node7185 : Tree Nat := .leaf 88250436209631796779659651318894620729729809745361797646356310339459182198787453122058560031100937405340558296821374893066353027058699717113329784015217065825962377858834878767894752265396985241367427860007120535552000 +def node7186 : Tree Nat := .node node3179 node7185 +def node7187 : Tree Nat := .node node7186 node6783 +def node7188 : Tree Nat := .node node6032 node7187 +def node7189 : Tree Nat := .node node7184 node7188 +def node7190 : Tree Nat := .node node7189 node6793 +def node7191 : Tree Nat := .node node7180 node7190 +def node7192 : Tree Nat := .leaf 274591906405224388599276031963255834485554917226377134578787015330818218623952574298189706298572019669424926485642978298055003407235619685053031949482768465920 +def node7193 : Tree Nat := .node node377 node7192 +def node7194 : Tree Nat := .node node7193 node4126 +def node7195 : Tree Nat := .node node7194 node6427 +def node7196 : Tree Nat := .leaf 344728266443874206170545512964432112225507069317819522056079337263512430464019444474548128324349197898893390156112989413349913396133992300666030627136242845966400347980622323843293764138768835186717244500968147517440 +def node7197 : Tree Nat := .node node3071 node7196 +def node7198 : Tree Nat := .leaf 3023649093069724664685187040814098862911148060459243130770999228591459438551735361036954770969256432732772089904350220910640787723221204992 +def node7199 : Tree Nat := .node node7198 node403 +def node7200 : Tree Nat := .node node7197 node7199 +def node7201 : Tree Nat := .node node6044 node7200 +def node7202 : Tree Nat := .node node7195 node7201 +def node7203 : Tree Nat := .leaf 7161473972933517889805535017187635973373048257470963709225479198264171918743498650832301792622516073261738978130523743436309243010104788112792498927328454244128552516046103760049911092506941168507340526814453271595519422841101064972644720043079237632 +def node7204 : Tree Nat := .node node3503 node7203 +def node7205 : Tree Nat := .node node7204 node6801 +def node7206 : Tree Nat := .node node6432 node7205 +def node7207 : Tree Nat := .node node6799 node7206 +def node7208 : Tree Nat := .node node7202 node7207 +def node7209 : Tree Nat := .leaf 22592111669665739975592870737637022906810831294812620197467215446901550642889587999246991367961839976090042962759528335290400829507603899099835808290089438848614684886251173160229200329870125914317057641283929607965245440 +def node7210 : Tree Nat := .node node3287 node7209 +def node7211 : Tree Nat := .node node7210 node6811 +def node7212 : Tree Nat := .node node6050 node7211 +def node7213 : Tree Nat := .node node6809 node7212 +def node7214 : Tree Nat := .node node7213 node6821 +def node7215 : Tree Nat := .node node7208 node7214 +def node7216 : Tree Nat := .node node7191 node7215 +def node7217 : Tree Nat := .node node7160 node7216 +def node7218 : Tree Nat := .leaf 10244521611062564595192550426037339589320732210321016133666556285103887660589274758967709226270078067906759970162475008 +def node7219 : Tree Nat := .node node7218 node4163 +def node7220 : Tree Nat := .node node6449 node7219 +def node7221 : Tree Nat := .node node5193 node7220 +def node7222 : Tree Nat := .leaf 336648697699095904463423352504328234595221747380683127007889977796398857875013172615274658321765660878526910006795405933633243664011763447240180145321720374397134314952220454284266480506453563964290838523438694400 +def node7223 : Tree Nat := .node node2924 node7222 +def node7224 : Tree Nat := .leaf 188978068316857791542824190050881178931946753778702695673187451786966214909483460064809673185578527045798255623199936439503207660485869568 +def node7225 : Tree Nat := .node node7224 node529 +def node7226 : Tree Nat := .node node7223 node7225 +def node7227 : Tree Nat := .node node6064 node7226 +def node7228 : Tree Nat := .node node7221 node7227 +def node7229 : Tree Nat := .leaf 1445895146858607358437943727208769466035893202868007692637901788602771865779329039719773369549414226139298056400768797718217012910827477287590678939449466350345919873054353202388106505184564516819519498076096549158035390464 +def node7230 : Tree Nat := .node node3365 node7229 +def node7231 : Tree Nat := .node node7230 node6831 +def node7232 : Tree Nat := .node node6071 node7231 +def node7233 : Tree Nat := .node node6829 node7232 +def node7234 : Tree Nat := .node node7228 node7233 +def node7235 : Tree Nat := .leaf 22062609052407949194914912829723655182432452436340449411589077584864795549696863280514640007775234351335139574205343723266588256764674929278332446003804266456490594464708719691973688066349246310341854803273958996049920 +def node7236 : Tree Nat := .node node3149 node7235 +def node7237 : Tree Nat := .node node7236 node6841 +def node7238 : Tree Nat := .node node6077 node7237 +def node7239 : Tree Nat := .node node6839 node7238 +def node7240 : Tree Nat := .node node7239 node6851 +def node7241 : Tree Nat := .node node7234 node7240 +def node7242 : Tree Nat := .leaf 86182066610968551542636378241108028056376767329454880514019834315878107616015292344588760483377018095352252236103023637325382394175627881760048601527420141788215917859474158771968724363560360739179253652219993522176 +def node7243 : Tree Nat := .node node3041 node7242 +def node7244 : Tree Nat := .leaf 745009692402997062813056903085204647712482394704501011788527454160155270316232871409345826981607654699781584656635837705977353937247797248 +def node7245 : Tree Nat := .node node7244 node654 +def node7246 : Tree Nat := .node node7243 node7245 +def node7247 : Tree Nat := .node node6084 node7246 +def node7248 : Tree Nat := .node node6474 node7247 +def node7249 : Tree Nat := .leaf 1110447472787410451280340782496334949915565979802629907945908573646122179193459355863275574470058062016947452793687980436741208031213683143015540279422009110362184840016695756489024611583953996233825978248017318160307754893312 +def node7250 : Tree Nat := .node node3473 node7249 +def node7251 : Tree Nat := .node node7250 node6859 +def node7252 : Tree Nat := .node node6478 node7251 +def node7253 : Tree Nat := .node node6857 node7252 +def node7254 : Tree Nat := .node node7248 node7253 +def node7255 : Tree Nat := .leaf 5648027917416434993898217684409255726702707823703155049366803861725387660722396999811747841990459994587988632617437452237622851374112048298560830212607217567213604012595269293699518172179373635560131237697970514769739776 +def node7256 : Tree Nat := .node node3257 node7255 +def node7257 : Tree Nat := .node node7256 node6869 +def node7258 : Tree Nat := .node node6090 node7257 +def node7259 : Tree Nat := .node node6867 node7258 +def node7260 : Tree Nat := .node node7259 node6879 +def node7261 : Tree Nat := .node node7254 node7260 +def node7262 : Tree Nat := .node node7241 node7261 +def node7263 : Tree Nat := .leaf 163912345777001033523080806816597433429131715365136258138664900561662202569428396143483347620321249070943719210407165952 +def node7264 : Tree Nat := .node node7263 node4224 +def node7265 : Tree Nat := .node node6494 node7264 +def node7266 : Tree Nat := .node node5719 node7265 +def node7267 : Tree Nat := .leaf 5386379163185534471414773640069251753523547958090930032126239644742381726000210761844394533148250574056430560108726494938131898624188215155842882325147525990354149039235527268548263688103257023428653416375019110400 +def node7268 : Tree Nat := .node node3002 node7267 +def node7269 : Tree Nat := .node node7268 node5255 +def node7270 : Tree Nat := .node node6103 node7269 +def node7271 : Tree Nat := .node node7266 node7270 +def node7272 : Tree Nat := .leaf 6191329402440458580124202281849711845739827299690889293332775591049148980830917257817055802950478472598785642570998141504795070010913887728396643124058269136699181273694693536803941094565622241806284059422848026137140144255347369271211184441423192205710533135622471680 +def node7273 : Tree Nat := .node node3434 node7272 +def node7274 : Tree Nat := .node node7273 node5264 +def node7275 : Tree Nat := .node node6504 node7274 +def node7276 : Tree Nat := .node node6886 node7275 +def node7277 : Tree Nat := .node node7271 node7276 +def node7278 : Tree Nat := .leaf 353001744838527187118638605275578482918919238981447190585425241357836728795149812488234240124403749621362233187285499572265412108234798868453319136060868263303849511435339515071579009061587940965469676852383343936798720 +def node7279 : Tree Nat := .node node3218 node7278 +def node7280 : Tree Nat := .node node7279 node5270 +def node7281 : Tree Nat := .node node6118 node7280 +def node7282 : Tree Nat := .node node6892 node7281 +def node7283 : Tree Nat := .node node7282 node6898 +def node7284 : Tree Nat := .node node7277 node7283 +def node7285 : Tree Nat := .leaf 1378913065775496824682182051857728448902028277271278088224317349054049721856077777898192513297396791595573560624451957653399653584535969202664122508544971383865601391922489295373175056555035107695592203144938368532480 +def node7286 : Tree Nat := .node node3110 node7285 +def node7287 : Tree Nat := .node node7286 node5286 +def node7288 : Tree Nat := .node node6132 node7287 +def node7289 : Tree Nat := .node node6520 node7288 +def node7290 : Tree Nat := .leaf 106359737525781373700957022117933502290615026150268396679865807767377546568936562432141426383331230177709482720886973180320234624928871547385804295680635682913722331609605359267986849280847034299575757846529876691906311193722281753075548358043562288417901087112383858740222230528 +def node7291 : Tree Nat := .node node3631 node7290 +def node7292 : Tree Nat := .node node7291 node5295 +def node7293 : Tree Nat := .node node6524 node7292 +def node7294 : Tree Nat := .node node6904 node7293 +def node7295 : Tree Nat := .node node7289 node7294 +def node7296 : Tree Nat := .leaf 90368446678662959902371482950548091627243325179250480789868861787606202571558351996987965471847359904360171851038113341161603318030415596399343233160357755394458739545004692640916801319480503657268230555768231206930350080 +def node7297 : Tree Nat := .node node3326 node7296 +def node7298 : Tree Nat := .node node7297 node5301 +def node7299 : Tree Nat := .node node6143 node7298 +def node7300 : Tree Nat := .node node6910 node7299 +def node7301 : Tree Nat := .node node7300 node6916 +def node7302 : Tree Nat := .node node7295 node7301 +def node7303 : Tree Nat := .node node7284 node7302 +def node7304 : Tree Nat := .node node7262 node7303 +def node7305 : Tree Nat := .node node7217 node7304 +def node7306 : Tree Nat := .leaf 683798204427072452078275274908498152501447656850212062263901633629809965533750895816895589206512074812191624767510788593541448023409277889619959376871686144 +def node7307 : Tree Nat := .node node1006 node7306 +def node7308 : Tree Nat := .node node7307 node4285 +def node7309 : Tree Nat := .node node7308 node6545 +def node7310 : Tree Nat := .leaf 252486523274321928347567514378246175946416310535512345255917483347299143406259879461455993741324245658895182505096554450224932748008822585430135108991290280797850736214165340713199860381232855517414181701840535552 +def node7311 : Tree Nat := .node node2934 node7310 +def node7312 : Tree Nat := .leaf 5955716506878202861161159281834309154493737309471884185946530692086158326801182583734809469548578656204888102061861587625769955211979259904 +def node7313 : Tree Nat := .node node7312 node1032 +def node7314 : Tree Nat := .node node7311 node7313 +def node7315 : Tree Nat := .node node6160 node7314 +def node7316 : Tree Nat := .node node7309 node7315 +def node7317 : Tree Nat := .leaf 6491683198595054547177551277054156060903595942331864878646248339038165009476353095145304330080538694868990560431615101521248188794961864898223621852777954907714922479457361360703168432157161220015249921276486805363685207988124814548329266021334244692256709423599623337934848 +def node7318 : Tree Nat := .node node3375 node7317 +def node7319 : Tree Nat := .node node7318 node6927 +def node7320 : Tree Nat := .node node6165 node7319 +def node7321 : Tree Nat := .node node6925 node7320 +def node7322 : Tree Nat := .node node7316 node7321 +def node7323 : Tree Nat := .leaf 16546956789305961896186184622292741386824339327255337058691808188648596662272647460385980005831425763501354680654007792449941192573506196958749334502853199842367945848531539768980266049761934732756391426714642417713152 +def node7324 : Tree Nat := .node node3159 node7323 +def node7325 : Tree Nat := .node node7324 node6933 +def node7326 : Tree Nat := .node node6171 node7325 +def node7327 : Tree Nat := .node node6552 node7326 +def node7328 : Tree Nat := .node node7327 node6943 +def node7329 : Tree Nat := .node node7322 node7328 +def node7330 : Tree Nat := .leaf 34323988300653048574909503995406977499891637644852493326135057549240200454287884565780724914821628684548970871395484553218071438207798167415097227633355653120 +def node7331 : Tree Nat := .node node1131 node7330 +def node7332 : Tree Nat := .node node7331 node4323 +def node7333 : Tree Nat := .leaf 21434691370838596691479797814478125909963378163133202987363871611909672643694482572609360842657394110039957507485466624 +def node7334 : Tree Nat := .node node7333 node1142 +def node7335 : Tree Nat := .node node6565 node7334 +def node7336 : Tree Nat := .node node7332 node7335 +def node7337 : Tree Nat := .leaf 43091033305484275771318189120554014028188383664727440257009917157939053808001875072823473122977547416641495362048743906258833891689178908698530024816089691382898001987069796675431907760211571636325937525880006901760 +def node7338 : Tree Nat := .node node3051 node7337 +def node7339 : Tree Nat := .leaf 395400266016810148458832151491074466688380900213901024793130668354267772733688470289447931588287379665054811759998500992269724660461993984 +def node7340 : Tree Nat := .node node7339 node1157 +def node7341 : Tree Nat := .node node7338 node7340 +def node7342 : Tree Nat := .node node6178 node7341 +def node7343 : Tree Nat := .node node7336 node7342 +def node7344 : Tree Nat := .leaf 185074578797901741880056797082722491652594329967104984657651428941566686679361953667029905350269904545890037005703395796359545607985241981992266023872373226183358466840156520474974533538486938354856395322574254455633762844672 +def node7345 : Tree Nat := .node node3483 node7344 +def node7346 : Tree Nat := .node node7345 node6951 +def node7347 : Tree Nat := .node node6575 node7346 +def node7348 : Tree Nat := .node node6949 node7347 +def node7349 : Tree Nat := .node node7343 node7348 +def node7350 : Tree Nat := .leaf 2824013958708217496949108842204627863351353911851577524683401930862693830361198499905873920995229996981142387109346561173315847291915730536947285298807962240097352376586603781161906831460412753993835427385594500528209920 +def node7351 : Tree Nat := .node node3267 node7350 +def node7352 : Tree Nat := .node node7351 node6961 +def node7353 : Tree Nat := .node node6189 node7352 +def node7354 : Tree Nat := .node node6959 node7353 +def node7355 : Tree Nat := .node node7354 node6971 +def node7356 : Tree Nat := .node node7349 node7355 +def node7357 : Tree Nat := .node node7329 node7356 +def node7358 : Tree Nat := .leaf 4039784372389150853561080230051938815142660968568197524094679733556786294500158071383295899861187930542322920081544871203598923968141161366882161743860644492765611779426645451411197766099725688278626907229448568832 +def node7359 : Tree Nat := .node node2973 node7358 +def node7360 : Tree Nat := .node node7359 node5387 +def node7361 : Tree Nat := .node node6202 node7360 +def node7362 : Tree Nat := .node node6590 node7361 +def node7363 : Tree Nat := .leaf 11567161174868858867503549817670155728287145622944061541103214308813593929159469055614459580396462120683855150547811853309691200344562025540229462019277955050296911266428313896120462554438577089190324470357657787103262539776 +def node7364 : Tree Nat := .node node3414 node7363 +def node7365 : Tree Nat := .node node7364 node5392 +def node7366 : Tree Nat := .node node6594 node7365 +def node7367 : Tree Nat := .node node6978 node7366 +def node7368 : Tree Nat := .node node7362 node7367 +def node7369 : Tree Nat := .leaf 264751308628895390338978953956683862189189429236085392939068931018377546596362359366175680093302812216021674890464124679199059081176099151339989352045651197477887133576504636303684256796190955724102262827434278683410432 +def node7370 : Tree Nat := .node node3198 node7369 +def node7371 : Tree Nat := .node node7370 node5398 +def node7372 : Tree Nat := .node node6213 node7371 +def node7373 : Tree Nat := .node node6984 node7372 +def node7374 : Tree Nat := .node node7373 node6990 +def node7375 : Tree Nat := .node node7368 node7374 +def node7376 : Tree Nat := .leaf 549183812810448777198552063926511464405274492407855796615657224583035752848612240665292726152309814188745236797126518035605119961952233011769354673584959651840 +def node7377 : Tree Nat := .node node1382 node7376 +def node7378 : Tree Nat := .node node7377 node4384 +def node7379 : Tree Nat := .leaf 322860038773256362665414454580576771518823383582193869997168316154389444195648143749928497692526998765453253365039366144 +def node7380 : Tree Nat := .node node7379 node1393 +def node7381 : Tree Nat := .node node6611 node7380 +def node7382 : Tree Nat := .node node7378 node7381 +def node7383 : Tree Nat := .leaf 689456532887748412341091025928864224451014138635639044112158674527024860928027372916348517053124532311374602768383679732981096924920884670616243205391617015235620524953735777753842806885173945699175218816172798509056 +def node7384 : Tree Nat := .node node3090 node7383 +def node7385 : Tree Nat := .node node7384 node5414 +def node7386 : Tree Nat := .node node6227 node7385 +def node7387 : Tree Nat := .node node7382 node7386 +def node7388 : Tree Nat := .leaf 14322947932527751047429056869870802812671392806493648684794573761204384728699272417221811301543612766872391706060817394990162051608998399089614016347227353480907637707860949251543712169079625364871143375764235898157063436885765307806171784612337942528 +def node7389 : Tree Nat := .node node3522 node7388 +def node7390 : Tree Nat := .node node7389 node5423 +def node7391 : Tree Nat := .node node6621 node7390 +def node7392 : Tree Nat := .node node6996 node7391 +def node7393 : Tree Nat := .node node7387 node7392 +def node7394 : Tree Nat := .leaf 22563699434723407256413421724962317757892969217741755055114301457452178921183158358673841096961844371088489889944132909006848 +def node7395 : Tree Nat := .node node7394 node1455 +def node7396 : Tree Nat := .node node7000 node7395 +def node7397 : Tree Nat := .node node5854 node7396 +def node7398 : Tree Nat := .leaf 45184223339331479951185741475274045813621662589625240394934430893803101285779175998493982735923679951555800539343382541941452547668532381071988227578924340690256609075633130572856595732492617286237511861701309993337225216 +def node7399 : Tree Nat := .node node3306 node7398 +def node7400 : Tree Nat := .node node7399 node5429 +def node7401 : Tree Nat := .node node6242 node7400 +def node7402 : Tree Nat := .node node7397 node7401 +def node7403 : Tree Nat := .node node7402 node7008 +def node7404 : Tree Nat := .node node7393 node7403 +def node7405 : Tree Nat := .node node7375 node7404 +def node7406 : Tree Nat := .node node7357 node7405 +def node7407 : Tree Nat := .leaf 2735192817708289808313101099633992610005790627400848249055606534519239862135003583267582356826048299248766499070043154374165792093637102150640359915615420416 +def node7408 : Tree Nat := .node node1508 node7407 +def node7409 : Tree Nat := .node node7408 node4416 +def node7410 : Tree Nat := .node node7409 node6638 +def node7411 : Tree Nat := .leaf 1009946093097287713390270057512984703785665242142049381023669933389196573625039517845823974965296982635580730020386217800899730992035290341720540435965161123191402944856661362852799441515646871775016374745618710528 +def node7412 : Tree Nat := .node node2982 node7411 +def node7413 : Tree Nat := .node node7412 node5451 +def node7414 : Tree Nat := .node node6258 node7413 +def node7415 : Tree Nat := .node node7410 node7414 +def node7416 : Tree Nat := .leaf 2891790293717214716875887454417538932071786405736015385275803577204471106924262671671580817098971984588397763535890203966216140906157213452775474120754782756838487471893503856121294126300828723014083266129259828705291665408 +def node7417 : Tree Nat := .node node3384 node7416 +def node7418 : Tree Nat := .node node7417 node5456 +def node7419 : Tree Nat := .node node6643 node7418 +def node7420 : Tree Nat := .node node7016 node7419 +def node7421 : Tree Nat := .node node7415 node7420 +def node7422 : Tree Nat := .leaf 66187827157223847584744738489170965547297357309021348234767232754594386649090589841543920023325703054005418722616031169799764770294024787834997338011412799369471783394126159075921064199047738931025563545130748533014528 +def node7423 : Tree Nat := .node node3168 node7422 +def node7424 : Tree Nat := .node node7423 node5462 +def node7425 : Tree Nat := .node node6269 node7424 +def node7426 : Tree Nat := .node node7022 node7425 +def node7427 : Tree Nat := .node node7426 node7028 +def node7428 : Tree Nat := .node node7421 node7427 +def node7429 : Tree Nat := .leaf 85738765483354386765919191257912503639853512652532811949455486447638690574777930290437443370629576437277526268424749056 +def node7430 : Tree Nat := .node node7429 node1644 +def node7431 : Tree Nat := .node node6660 node7430 +def node7432 : Tree Nat := .node node5893 node7431 +def node7433 : Tree Nat := .leaf 172364133221937103085272756482216056112753534658909761028039668631756215232009768028113694785408703556846592022342158986080679999104793884215563693843272567052369724026506129026277210108257837020456378060601305333760 +def node7434 : Tree Nat := .node node3060 node7433 +def node7435 : Tree Nat := .node node7434 node5478 +def node7436 : Tree Nat := .node node6281 node7435 +def node7437 : Tree Nat := .node node7432 node7436 +def node7438 : Tree Nat := .leaf 740298315191606967520227188330889966610377319868419938630605715764104335454506672607900322649368979303438941690827012492301688591158065117028903017394102725039016239290194105582787546564745345009824447410634696355828568424448 +def node7439 : Tree Nat := .node node3492 node7438 +def node7440 : Tree Nat := .node node7439 node5487 +def node7441 : Tree Nat := .node node6670 node7440 +def node7442 : Tree Nat := .node node7034 node7441 +def node7443 : Tree Nat := .node node7437 node7442 +def node7444 : Tree Nat := .leaf 11296055834832869987796435368818511453405415647406310098733607723450775321444793999623495683980919988047503807770137019835573994280110997219637927719084042564388084927593067051718924433454161731216278508859057331870105600 +def node7445 : Tree Nat := .node node3276 node7444 +def node7446 : Tree Nat := .node node7445 node5493 +def node7447 : Tree Nat := .node node6296 node7446 +def node7448 : Tree Nat := .node node7040 node7447 +def node7449 : Tree Nat := .node node7448 node7046 +def node7450 : Tree Nat := .node node7443 node7449 +def node7451 : Tree Nat := .node node7428 node7450 +def node7452 : Tree Nat := .leaf 16159137489556603414244320920207755260570643874272790096378718934227145178000632285533183599444751722169291680326179484814395695872564645467528646975442577971062447117706581805644791064250349948400261995929899368448 +def node7453 : Tree Nat := .node node3021 node7452 +def node7454 : Tree Nat := .leaf 1581601064067240593835328605964297866753523600855604099172522673417071090934753881157791726353149518660219247027614603576225095892856733696 +def node7455 : Tree Nat := .node node7454 node1784 +def node7456 : Tree Nat := .node node7453 node7455 +def node7457 : Tree Nat := .node node6311 node7456 +def node7458 : Tree Nat := .node node6687 node7457 +def node7459 : Tree Nat := .leaf 46268644699475435470014199270680622913148582491776246164412857235254375716637876222457838321585848360625988367217514025589658995699822588857790316768790345464967992971568505652095438571084842445603524928524838229513213050880 +def node7460 : Tree Nat := .node node3453 node7459 +def node7461 : Tree Nat := .node node7460 node7055 +def node7462 : Tree Nat := .node node6691 node7461 +def node7463 : Tree Nat := .node node7053 node7462 +def node7464 : Tree Nat := .node node7458 node7463 +def node7465 : Tree Nat := .leaf 1059005234515581561355915815826735448756757716944341571756275724073510186385449437464702720373211248864086699561856498716796236324704396605359957408182604789911548534306018545214737027184763822896409016722091976528232448 +def node7466 : Tree Nat := .node node3237 node7465 +def node7467 : Tree Nat := .node node7466 node7065 +def node7468 : Tree Nat := .node node6317 node7467 +def node7469 : Tree Nat := .node node7063 node7468 +def node7470 : Tree Nat := .node node7469 node7075 +def node7471 : Tree Nat := .node node7464 node7470 +def node7472 : Tree Nat := .leaf 1291440155093025450661657818322307086075293534328775479988673264617557776782592574999713990770107995052445526235226832896 +def node7473 : Tree Nat := .node node7472 node1894 +def node7474 : Tree Nat := .node node6706 node7473 +def node7475 : Tree Nat := .node node5941 node7474 +def node7476 : Tree Nat := .leaf 2757826131550993649364364103715456897804056554542556176448634698108099443712109491665394068212498129245498411073534718931924387699683538682464972821566468060942482099814943111015371227540683403396308021461942202793984 +def node7477 : Tree Nat := .node node3129 node7476 +def node7478 : Tree Nat := .leaf 23822866027512811444644637127337236617974949237887536743786122768344633307204730334939237878194314624819552408207213299226304961913695502336 +def node7479 : Tree Nat := .node node7478 node1909 +def node7480 : Tree Nat := .node node7477 node7479 +def node7481 : Tree Nat := .node node6329 node7480 +def node7482 : Tree Nat := .node node7475 node7481 +def node7483 : Tree Nat := .node node7482 node7086 +def node7484 : Tree Nat := .leaf 90254797738893629025653686899849271031571876870967020220457205829808715684732633434695364387847377484350823613284001012252672 +def node7485 : Tree Nat := .node node7484 node1956 +def node7486 : Tree Nat := .node node7089 node7485 +def node7487 : Tree Nat := .node node5952 node7486 +def node7488 : Tree Nat := .leaf 180736893357325919804742965901096183254486650358500961579737723575212405143116703993975930943694719806223202157373530167765810190674129524287952910315697362761026436302532522291426382929970469144950047443922936211831783424 +def node7489 : Tree Nat := .node node3345 node7488 +def node7490 : Tree Nat := .node node7489 node7093 +def node7491 : Tree Nat := .node node6340 node7490 +def node7492 : Tree Nat := .node node7487 node7491 +def node7493 : Tree Nat := .node node7492 node7103 +def node7494 : Tree Nat := .node node7483 node7493 +def node7495 : Tree Nat := .node node7471 node7494 +def node7496 : Tree Nat := .node node7451 node7495 +def node7497 : Tree Nat := .node node7406 node7496 +def node7498 : Tree Nat := .node node7305 node7497 +def node7499 : Tree Nat := .leaf 377888757473172520759533830679308359076483153975433513596157183529873416825652844724488084226799455715083388091195770378633513302968788313144741234746284281797287190712992429797712113156752671161213261838004573698898598580602209531555319723451676179481363715457024 +def node7500 : Tree Nat := .node node4012 node7499 +def node7501 : Tree Nat := .node node7111 node7500 +def node7502 : Tree Nat := .node node7501 node7115 +def node7503 : Tree Nat := .leaf 1236652007365522670302512605098235950175656745506059199570315280464486125532659335851582005306215224947988357130080696696756825171533756049837730775509465839583050353417912320 +def node7504 : Tree Nat := .node node15 node7503 +def node7505 : Tree Nat := .leaf 2744743341158369455877602892427874467264475311228298809381948466051552347628123106779506282569138176 +def node7506 : Tree Nat := .node node7505 node19 +def node7507 : Tree Nat := .node node7504 node7506 +def node7508 : Tree Nat := .node node7507 node6733 +def node7509 : Tree Nat := .node node7502 node7508 +def node7510 : Tree Nat := .leaf 287930482850764568499874464491902838967660615571322664518448356647157605162975223700418603910649014857594938280545337287885329027551635180096544971575370486980280320 +def node7511 : Tree Nat := .node node31 node7510 +def node7512 : Tree Nat := .node node7511 node6360 +def node7513 : Tree Nat := .node node7512 node6738 +def node7514 : Tree Nat := .node node7513 node7121 +def node7515 : Tree Nat := .node node7509 node7514 +def node7516 : Tree Nat := .leaf 101745825697019260773923519755878567461315282017759829107608914364075275235254395622580447400994175578963163918967182013639660669771108475957977604782878218969652180163307557752082469452334082895397373439102739836815826189629777593565184 +def node7517 : Tree Nat := .node node4036 node7516 +def node7518 : Tree Nat := .node node7125 node7517 +def node7519 : Tree Nat := .node node7518 node7129 +def node7520 : Tree Nat := .node node7519 node7134 +def node7521 : Tree Nat := .leaf 18869812124107706761207772904941344454584606102082202141881031501228120811960744260430633625888293837707341875153819224498852923149623963162807171257163480218246977617920 +def node7522 : Tree Nat := .node node94 node7521 +def node7523 : Tree Nat := .leaf 41881459673437033933679243353696814991218190173771649313079047638726079523134202679130653392896 +def node7524 : Tree Nat := .node node7523 node3743 +def node7525 : Tree Nat := .node node7522 node7524 +def node7526 : Tree Nat := .node node7525 node6744 +def node7527 : Tree Nat := .leaf 23689546086131422960647270026588478931532074235789438036179382904520535894958330069379827884834547780974888619175296567359417018897542359528379682224241314724347522182348158539413309970669001911408831208423785221804295786070016 +def node7528 : Tree Nat := .node node4051 node7527 +def node7529 : Tree Nat := .node node7528 node5089 +def node7530 : Tree Nat := .node node6374 node7529 +def node7531 : Tree Nat := .node node7526 node7530 +def node7532 : Tree Nat := .node node7520 node7531 +def node7533 : Tree Nat := .node node7515 node7532 +def node7534 : Tree Nat := .leaf 328066310098881164179615652565680299866661311420379969952641507336145424065831507987408526809381184421252089913671847477251404533096190623600995096234878713242395124296758426317919011862694315318470482829867503827558796036203237670687960698191872 +def node7535 : Tree Nat := .node node4058 node7534 +def node7536 : Tree Nat := .node node7139 node7535 +def node7537 : Tree Nat := .node node7536 node6381 +def node7538 : Tree Nat := .node node7537 node7145 +def node7539 : Tree Nat := .leaf 73710203609795729535967862909927126775721117586258602116722779301709566495822579125492895854356152249141256326121671020214971431069520784826443174307444958970165329920 +def node7540 : Tree Nat := .node node157 node7539 +def node7541 : Tree Nat := .node node7540 node4064 +def node7542 : Tree Nat := .node node7541 node6751 +def node7543 : Tree Nat := .node node7542 node7150 +def node7544 : Tree Nat := .node node7538 node7543 +def node7545 : Tree Nat := .leaf 1124728448635799095702634626921495464717424279575479158277628115161237410065932182063441742872614568836812338167482243161070446098580718951830990690233109257912320 +def node7546 : Tree Nat := .node node188 node7545 +def node7547 : Tree Nat := .leaf 283625967792006058808176788520780685867414277271872180408915520460270309811540679986766115142045205324379286600312851575545476454331271213951923519474073030714146388711950832384176733857072854501977105248608994412837187847371981910510985000377662515010044405266502650980772872192 +def node7548 : Tree Nat := .node node4072 node7547 +def node7549 : Tree Nat := .node node7546 node7548 +def node7550 : Tree Nat := .node node7549 node6757 +def node7551 : Tree Nat := .node node7550 node7156 +def node7552 : Tree Nat := .leaf 4830671903771572930869189863664984180373659162133043748321544064314398927862518456300444262948254865111008054670678870859860411352981090526958637348207869209555157217771520 +def node7553 : Tree Nat := .node node219 node7552 +def node7554 : Tree Nat := .node node7553 node6012 +def node7555 : Tree Nat := .node node7554 node6762 +def node7556 : Tree Nat := .leaf 18193571394148932833777103380419951819416633013086288411785766070618909330242114935785683988087622408946995518386580243293100831757131718559803673686452283217924821319081147168834653559156364721394631490753195858864758658326069248 +def node7557 : Tree Nat := .node node4081 node7556 +def node7558 : Tree Nat := .node node7557 node6396 +def node7559 : Tree Nat := .node node6394 node7558 +def node7560 : Tree Nat := .node node7555 node7559 +def node7561 : Tree Nat := .node node7551 node7560 +def node7562 : Tree Nat := .node node7544 node7561 +def node7563 : Tree Nat := .node node7533 node7562 +def node7564 : Tree Nat := .leaf 74520868430434028887151015446200122652330528821601437334674497825324155932555886273418131486684958068399132191048550116012958621419220657285148368327469590536169991098142051792534404730531696782682144746124833674350301607953336107008 +def node7565 : Tree Nat := .node node4089 node7564 +def node7566 : Tree Nat := .node node7162 node7565 +def node7567 : Tree Nat := .node node7566 node7166 +def node7568 : Tree Nat := .leaf 19786432117848362724840201681571775202810507928096947193125044487431778008522549373625312084899443599167813714081291147148109202744540096797403692408151453433328805654686597120 +def node7569 : Tree Nat := .node node267 node7568 +def node7570 : Tree Nat := .node node7569 node4605 +def node7571 : Tree Nat := .node node7570 node7172 +def node7572 : Tree Nat := .node node7567 node7571 +def node7573 : Tree Nat := .leaf 4606887725612233095997991431870445423482569849141162632295173706354521682607603579206697662570384237721519012488725396606165264440826162881544719545205927791684485120 +def node7574 : Tree Nat := .node node283 node7573 +def node7575 : Tree Nat := .node node7574 node6409 +def node7576 : Tree Nat := .node node7575 node6770 +def node7577 : Tree Nat := .node node7576 node7178 +def node7578 : Tree Nat := .node node7572 node7577 +def node7579 : Tree Nat := .leaf 70295528039737443481414664182593466544839017473467447392199305822059962197991997973735010720373294642967514228648763986300129157117098432640758049702048977387520 +def node7580 : Tree Nat := .node node314 node7579 +def node7581 : Tree Nat := .leaf 21479177938861104702947544874773277196989586550366132530617939748530463231904158563392159181931286012237131017326220395583070203348208057781547097136947266488762096919910024683308020070295591585971079183497805201621402525162212204234076406567120732160 +def node7582 : Tree Nat := .node node4106 node7581 +def node7583 : Tree Nat := .node node7580 node7582 +def node7584 : Tree Nat := .node node7583 node7183 +def node7585 : Tree Nat := .node node7584 node7188 +def node7586 : Tree Nat := .leaf 301916993985723308179324366479061511273353697633315234270096504019649932991371908166890138014212701403317470002461107591981646770393983410604914740114615683491951641886720 +def node7587 : Tree Nat := .node node345 node7586 +def node7588 : Tree Nat := .node node7587 node4115 +def node7589 : Tree Nat := .node node7588 node6791 +def node7590 : Tree Nat := .leaf 6190951559809168803779520960961825423248316278147658867123225492542117970998137146895424917273663411058907179831602016087110815463642615673627887334875468869851372778163602413226758289875934424983404588145615159354800519565582635415325258886440984006443745443401695232 +def node7591 : Tree Nat := .node node4118 node7590 +def node7592 : Tree Nat := .node node7591 node5152 +def node7593 : Tree Nat := .node node6420 node7592 +def node7594 : Tree Nat := .node node7589 node7593 +def node7595 : Tree Nat := .node node7585 node7594 +def node7596 : Tree Nat := .node node7578 node7595 +def node7597 : Tree Nat := .leaf 6359114106063703798370219984742410466332205126109989319225557148056621696189123034590602329041197484958551442568764110122575295880344212738727708845458815960394148985098871215594994201928674000398260655302377396118272784205182214864896 +def node7598 : Tree Nat := .node node4125 node7597 +def node7599 : Tree Nat := .node node7193 node7598 +def node7600 : Tree Nat := .node node7599 node6427 +def node7601 : Tree Nat := .node node7600 node7201 +def node7602 : Tree Nat := .leaf 1179363257756731672575485806558834028411537881380137633867564468826845062136408195962990325657320131406844140001394653595163037991523974039840681046907158270345499115520 +def node7603 : Tree Nat := .node node408 node7602 +def node7604 : Tree Nat := .node node7603 node4131 +def node7605 : Tree Nat := .node node7604 node6798 +def node7606 : Tree Nat := .node node7605 node7206 +def node7607 : Tree Nat := .node node7601 node7606 +def node7608 : Tree Nat := .leaf 17995655178172785531242154030743927435478788473207666532408757436827789362592610131915843317045228667101040116999386865084488473782117898376799970154670101909995520 +def node7609 : Tree Nat := .node node439 node7608 +def node7610 : Tree Nat := .node node7609 node4137 +def node7611 : Tree Nat := .node node7610 node6808 +def node7612 : Tree Nat := .node node7611 node7212 +def node7613 : Tree Nat := .leaf 77290750460345166893907037818639746885978546594128699973144705029030382845792543808547082113957722250766938436202176002108717467751876755902218957498962477451576956957163520 +def node7614 : Tree Nat := .node node469 node7613 +def node7615 : Tree Nat := .node node7614 node4145 +def node7616 : Tree Nat := .node node7615 node6819 +def node7617 : Tree Nat := .leaf 17726622920979684553119776263005300707063713350041753661841669300413629377192852866157530908057924956512928646284578903810348105365737002293126406470364098438862634045269416994548156239377018065361765449669129120484695668951890615347356782010161602048351506796254540557333823488 +def node7618 : Tree Nat := .node node4151 node7617 +def node7619 : Tree Nat := .node node7618 node6440 +def node7620 : Tree Nat := .node node6438 node7619 +def node7621 : Tree Nat := .node node7616 node7620 +def node7622 : Tree Nat := .node node7612 node7621 +def node7623 : Tree Nat := .node node7607 node7622 +def node7624 : Tree Nat := .node node7596 node7623 +def node7625 : Tree Nat := .node node7563 node7624 +def node7626 : Tree Nat := .leaf 18630217107608507221787753861550030663082632205400359333668624456312611432236522635970540905943757735405852768365572878474058960529396436952051324212794141370121969258627597298719535859482978587472306546288468862136814804962870558720 +def node7627 : Tree Nat := .node node4160 node7626 +def node7628 : Tree Nat := .node node5192 node7627 +def node7629 : Tree Nat := .node node7628 node7220 +def node7630 : Tree Nat := .node node7629 node7227 +def node7631 : Tree Nat := .node node7630 node7233 +def node7632 : Tree Nat := .leaf 85916711755426104563164716032153802554402288059321493371708562224882483323031158672089136195388249998694709097510832696736812317155356950734401361809251023719077455192217260866986872751906060210966338571391148440414675792607664415486864878546391859200 +def node7633 : Tree Nat := .node node4177 node7632 +def node7634 : Tree Nat := .node node5680 node7633 +def node7635 : Tree Nat := .node node7634 node6838 +def node7636 : Tree Nat := .node node7635 node7238 +def node7637 : Tree Nat := .leaf 94758184344525691842589080106353915726128296943157752144717531617800961467674370503593652882607817257720198406807316479869050731801535744222211131585183369196983554811519235033829839312146645551821087779058010412087582224547840 +def node7638 : Tree Nat := .node node4186 node7637 +def node7639 : Tree Nat := .node node7638 node5216 +def node7640 : Tree Nat := .node node6466 node7639 +def node7641 : Tree Nat := .node node6850 node7640 +def node7642 : Tree Nat := .node node7636 node7641 +def node7643 : Tree Nat := .node node7631 node7642 +def node7644 : Tree Nat := .leaf 1589778526515925949592554996185602616583051281527497329806389286957545987674957638364027263545475337875884042335944421105000729466401690748799694430072803112433655733152692178437290876985609730650693274337172835258077755396554620862464 +def node7645 : Tree Nat := .node node4193 node7644 +def node7646 : Tree Nat := .node node5695 node7645 +def node7647 : Tree Nat := .node node7646 node6473 +def node7648 : Tree Nat := .node node7647 node7247 +def node7649 : Tree Nat := .node node7648 node7253 +def node7650 : Tree Nat := .leaf 283625967792006058808176788520780685867492418066007491201189893723442824551350970123355754690799848970629446191804009791438155927011708280049202080546430714494176377313302335576702131973584836496173011250713749627895387496486363358686283899908070897759659331313812583562797383680 +def node7651 : Tree Nat := .node node4204 node7650 +def node7652 : Tree Nat := .node node5706 node7651 +def node7653 : Tree Nat := .node node7652 node6866 +def node7654 : Tree Nat := .leaf 179879499606154900660394583158153181086644653996657790771655374671154534654156675925901723678594989817856 +def node7655 : Tree Nat := .node node7654 node3879 +def node7656 : Tree Nat := .node node6089 node7655 +def node7657 : Tree Nat := .node node7656 node7257 +def node7658 : Tree Nat := .node node7653 node7657 +def node7659 : Tree Nat := .leaf 1790150099102876869021435248250019995303683645961087837873023903202429601313653915871270454261092509358815454821276390872661791171662185172966436696816914477571297509984537132542799611736272019503843128724060579238133414564884878111154564866305425408 +def node7660 : Tree Nat := .node node4213 node7659 +def node7661 : Tree Nat := .node node7660 node6486 +def node7662 : Tree Nat := .node node6484 node7661 +def node7663 : Tree Nat := .node node6878 node7662 +def node7664 : Tree Nat := .node node7658 node7663 +def node7665 : Tree Nat := .node node7649 node7664 +def node7666 : Tree Nat := .node node7643 node7665 +def node7667 : Tree Nat := .leaf 99361157907245371849534687261600163536440705095468583112899330434846624229684852397751703971592208617242752645996526319062545591650193183188842581565625918566405249872178533956611631875585338460340805988238535046964300468989726818304 +def node7668 : Tree Nat := .node node4221 node7667 +def node7669 : Tree Nat := .node node5718 node7668 +def node7670 : Tree Nat := .node node7669 node7265 +def node7671 : Tree Nat := .node node7670 node7270 +def node7672 : Tree Nat := .node node7671 node7276 +def node7673 : Tree Nat := .leaf 5370122551043688113192634414340729018687074301844027826099173202256324203193672802692412164164545111084383972243038008664803289306073302839212761614127292374960451185612667826259678699392849250417808822572635385382689343898456798450664568284591489024 +def node7674 : Tree Nat := .node node4235 node7673 +def node7675 : Tree Nat := .node node5733 node7674 +def node7676 : Tree Nat := .node node7675 node6891 +def node7677 : Tree Nat := .node node7676 node7281 +def node7678 : Tree Nat := .leaf 1516130949512411069481425281701662651618052751090524034315480505902811038660962713588740600152469003559001962982124730210310691073658662791737421923948246773299579229621401352888317808084096330056788796026913709169213897665675264 +def node7679 : Tree Nat := .node node4244 node7678 +def node7680 : Tree Nat := .node node7679 node5279 +def node7681 : Tree Nat := .node node6512 node7680 +def node7682 : Tree Nat := .node node6897 node7681 +def node7683 : Tree Nat := .node node7677 node7682 +def node7684 : Tree Nat := .node node7672 node7683 +def node7685 : Tree Nat := .leaf 396220898351748940262924391034580082446911282557105712257184269735696308556763500769409061650186262571756801724068211526934337185306644629595040724591803238912237341311010068576510107886900942536044241615633688940016212338157168183913447974846844978535452298013897326592 +def node7686 : Tree Nat := .node node4251 node7685 +def node7687 : Tree Nat := .node node5743 node7686 +def node7688 : Tree Nat := .node node7687 node6519 +def node7689 : Tree Nat := .leaf 43915893458533911294041646278845991476231604979652780950111175456824837562049969708472100510838554624 +def node7690 : Tree Nat := .node node7689 node3917 +def node7691 : Tree Nat := .node node6131 node7690 +def node7692 : Tree Nat := .node node7691 node7287 +def node7693 : Tree Nat := .node node7688 node7692 +def node7694 : Tree Nat := .node node7693 node7294 +def node7695 : Tree Nat := .leaf 2878071993698478410566313330530450897386314463946524652346485994738472554466506814814427578854891317100544 +def node7696 : Tree Nat := .node node7695 node960 +def node7697 : Tree Nat := .node node6142 node7696 +def node7698 : Tree Nat := .node node7697 node7298 +def node7699 : Tree Nat := .node node6910 node7698 +def node7700 : Tree Nat := .leaf 670103354774992542938867893659149039859491042780346389009264762219617272370147242866090414178304 +def node7701 : Tree Nat := .node node7700 node975 +def node7702 : Tree Nat := .node node6147 node7701 +def node7703 : Tree Nat := .node node7702 node6914 +def node7704 : Tree Nat := .leaf 4431655730257012840500151247598389094333148860437198935663687543473576294143884265310279872035561008209194541711992327603699564691000709158083655833457329263033626825740735479231564338119613520451483458826648729142898950488339137276820365031655885129705653492595270182892470272 +def node7705 : Tree Nat := .node node4274 node7704 +def node7706 : Tree Nat := .node node7705 node6534 +def node7707 : Tree Nat := .node node6532 node7706 +def node7708 : Tree Nat := .node node7703 node7707 +def node7709 : Tree Nat := .node node7699 node7708 +def node7710 : Tree Nat := .node node7694 node7709 +def node7711 : Tree Nat := .node node7684 node7710 +def node7712 : Tree Nat := .node node7666 node7711 +def node7713 : Tree Nat := .node node7625 node7712 +def node7714 : Tree Nat := .leaf 3105036184601417870297958976925005110513772034233393222278104076052101905372753772661756817657292955900975461394262146412343160088273544676347108461376403924687755943517931416080183352213308065107350835949482907210257794218470670336 +def node7715 : Tree Nat := .node node4284 node7714 +def node7716 : Tree Nat := .node node7307 node7715 +def node7717 : Tree Nat := .node node7716 node6545 +def node7718 : Tree Nat := .node node7717 node7315 +def node7719 : Tree Nat := .leaf 2936890925077798598698719537817408957470138278827491178088173237801007572662347281744269759888619951547468370461562440336430356081026678836984758710068778967198859264 +def node7720 : Tree Nat := .node node1037 node7719 +def node7721 : Tree Nat := .node node7720 node4294 +def node7722 : Tree Nat := .node node7721 node6924 +def node7723 : Tree Nat := .node node7722 node7320 +def node7724 : Tree Nat := .node node7718 node7723 +def node7725 : Tree Nat := .leaf 44813399125332620219401848416403334922334873639335497712527057461563225901219898708256069334237975334891790320763587041266332337662150250808483256685056223084544 +def node7726 : Tree Nat := .node node1068 node7725 +def node7727 : Tree Nat := .leaf 203491651394038521547847039511757134922630564035519658215217828728150550470508791245160894801988351157926327837934364027279321339542216951916524797417315181600802398036225392188045506291031460221452621926092154355146277535695732027817984 +def node7728 : Tree Nat := .node node4299 node7727 +def node7729 : Tree Nat := .node node7726 node7728 +def node7730 : Tree Nat := .node node7729 node6551 +def node7731 : Tree Nat := .leaf 1223180597321853324490683165475441631389183647177272977247256547763850835648265396296131721013321508323328 +def node7732 : Tree Nat := .node node7731 node3943 +def node7733 : Tree Nat := .node node6170 node7732 +def node7734 : Tree Nat := .node node7733 node7325 +def node7735 : Tree Nat := .node node7730 node7734 +def node7736 : Tree Nat := .leaf 192472083665898608964319283630401713436762982241238461847186521312526832281999591456392462984060597144614887126568956089888299816126164424260633146823067498226119171702784 +def node7737 : Tree Nat := .node node1099 node7736 +def node7738 : Tree Nat := .node node7737 node4309 +def node7739 : Tree Nat := .node node7738 node6941 +def node7740 : Tree Nat := .leaf 47379092172262845921294540053176957863064148471578876072358765808970776261876922695278241105486502095404938220877125687326634731973024756858767366474747618728321749721728802850177855955037874665700563984206812393906542594752512 +def node7741 : Tree Nat := .node node4315 node7740 +def node7742 : Tree Nat := .node node7741 node6558 +def node7743 : Tree Nat := .node node6556 node7742 +def node7744 : Tree Nat := .node node7739 node7743 +def node7745 : Tree Nat := .node node7735 node7744 +def node7746 : Tree Nat := .node node7724 node7745 +def node7747 : Tree Nat := .leaf 794889263257962974796277498092801308291525640763748664903194643469349835339125276995804540198418266346479598670046419446272201675537988998710124473948061822312235427528865025123582076004724125174858762302530771035297412705014060679168 +def node7748 : Tree Nat := .node node4322 node7747 +def node7749 : Tree Nat := .node node7331 node7748 +def node7750 : Tree Nat := .node node7749 node7335 +def node7751 : Tree Nat := .node node7750 node7342 +def node7752 : Tree Nat := .leaf 147420407219591459071935725819854253551442235172517204233445558603354134906142084957178511198193565027435152353628029096640454386013011423397381456677691181630824120320 +def node7753 : Tree Nat := .node node1162 node7752 +def node7754 : Tree Nat := .node node7753 node6570 +def node7755 : Tree Nat := .node node7754 node6948 +def node7756 : Tree Nat := .node node7755 node7347 +def node7757 : Tree Nat := .node node7751 node7756 +def node7758 : Tree Nat := .leaf 2249456897271598191405269253842990929434848559150958316550996515790945408748910428589527375783776533143571527250776569550745380532160669305665724997949249940357120 +def node7759 : Tree Nat := .node node1193 node7758 +def node7760 : Tree Nat := .leaf 5038209258419659102939031717574155078837684942886299676153494321170844943644377560210125474956761126739753626809655849353003582112145844321529817292096736002103866670805845732752386723319868643270605287324233145225398489849188291577289172952973419748847816162672640 +def node7761 : Tree Nat := .node node4336 node7760 +def node7762 : Tree Nat := .node node7759 node7761 +def node7763 : Tree Nat := .node node7762 node6958 +def node7764 : Tree Nat := .node node7763 node7353 +def node7765 : Tree Nat := .leaf 9661343807543145861738379727329968360747318324266087496643088128628797855724045120524730791310827349385243351302305002788212751664252456991935613529186965043603741905387520 +def node7766 : Tree Nat := .node node1224 node7765 +def node7767 : Tree Nat := .node node7766 node4342 +def node7768 : Tree Nat := .node node7767 node6969 +def node7769 : Tree Nat := .leaf 12129047596099288555851402253613301212944422008724192274523844047080772524759591022651392838227643599917620244630487467739766465610437932841907404764848755025818581033306461414362224113547608230729527850506575637114299615985795072 +def node7770 : Tree Nat := .node node4345 node7769 +def node7771 : Tree Nat := .node node7770 node5375 +def node7772 : Tree Nat := .node node6581 node7771 +def node7773 : Tree Nat := .node node7768 node7772 +def node7774 : Tree Nat := .node node7764 node7773 +def node7775 : Tree Nat := .node node7757 node7774 +def node7776 : Tree Nat := .node node7746 node7775 +def node7777 : Tree Nat := .leaf 49680578953622685924767343630800081768220352547734291556449665216981050893183651821660044808336541547967049617480711546830936120015028195432359277758496307652736124260102349331236518236851604620421427397596308456706262280952937971712 +def node7778 : Tree Nat := .node node4353 node7777 +def node7779 : Tree Nat := .node node5383 node7778 +def node7780 : Tree Nat := .node node7779 node6589 +def node7781 : Tree Nat := .node node7780 node7361 +def node7782 : Tree Nat := .node node7781 node7367 +def node7783 : Tree Nat := .leaf 3255866422304616344765552632188114158762089024568314531443485259660070151335683805784312696559143586887568563731215911933112229561304269086370215067951893899755728511257320772426854947081090693426442406277036493403059400608777795270213632 +def node7784 : Tree Nat := .node node4367 node7783 +def node7785 : Tree Nat := .node node5827 node7784 +def node7786 : Tree Nat := .node node7785 node6983 +def node7787 : Tree Nat := .node node7786 node7372 +def node7788 : Tree Nat := .leaf 758065474756205534740712640850831325809026375545262017157740252942407691741394964028749223060862538061761587254458531838955859540804724127870368628678103494652732015848889709853454497690859331479928510410241396391324453766692864 +def node7789 : Tree Nat := .node node4376 node7788 +def node7790 : Tree Nat := .node node7789 node6604 +def node7791 : Tree Nat := .node node6602 node7790 +def node7792 : Tree Nat := .node node6989 node7791 +def node7793 : Tree Nat := .node node7787 node7792 +def node7794 : Tree Nat := .node node7782 node7793 +def node7795 : Tree Nat := .leaf 12718228212127407596740439969484820932664410252219978638451114295811326398392522761001880291603333458643749187504212985975054087741038492486083509524027493906575596566880272428728880811875701230402537899999840052121929884918412787843072 +def node7796 : Tree Nat := .node node4383 node7795 +def node7797 : Tree Nat := .node node7377 node7796 +def node7798 : Tree Nat := .node node7797 node7381 +def node7799 : Tree Nat := .leaf 18664254719876912299967699668509546377398432116352431903797249569150555963871237126100642717077864448 +def node7800 : Tree Nat := .node node7799 node1401 +def node7801 : Tree Nat := .node node6226 node7800 +def node7802 : Tree Nat := .node node7801 node7385 +def node7803 : Tree Nat := .node node7798 node7802 +def node7804 : Tree Nat := .leaf 2358726515513463345150971613117668056823075762760275267735128937653520911379830737429253317695077510895169453750528213157890871346876271833005019749441497484158346199040 +def node7805 : Tree Nat := .node node1413 node7804 +def node7806 : Tree Nat := .node node7805 node6616 +def node7807 : Tree Nat := .node node7806 node6995 +def node7808 : Tree Nat := .node node7807 node7391 +def node7809 : Tree Nat := .node node7803 node7808 +def node7810 : Tree Nat := .leaf 35991310356345571062484308061487854870957576946415333064806425337500870872087697727740022124358407536933897175489100159132829973062055024872782870620777741748797440 +def node7811 : Tree Nat := .node node1444 node7810 +def node7812 : Tree Nat := .node node7811 node4398 +def node7813 : Tree Nat := .node node7812 node7396 +def node7814 : Tree Nat := .node node7813 node7401 +def node7815 : Tree Nat := .leaf 154581500920690333787814075637279493771957093188257399946289410058060765691582505633253440740111377521254904217397656046999095487987347191062072249612848930361332334050672640 +def node7816 : Tree Nat := .node node1474 node7815 +def node7817 : Tree Nat := .leaf 284793925779371830749018854805138341940283693181647215328937523943337340757312578218088425914368 +def node7818 : Tree Nat := .node node7817 node1478 +def node7819 : Tree Nat := .node node7816 node7818 +def node7820 : Tree Nat := .node node7819 node7006 +def node7821 : Tree Nat := .leaf 970323807687943084468112180289064097035553760697935381961907523766569775911836318525298879982395951558022492301278243418375685884218916599815654770601156815913433374870626129249461140807634357043341009676169337940883399770615316480 +def node7822 : Tree Nat := .node node4406 node7821 +def node7823 : Tree Nat := .node node7822 node5438 +def node7824 : Tree Nat := .node node6629 node7823 +def node7825 : Tree Nat := .node node7820 node7824 +def node7826 : Tree Nat := .node node7814 node7825 +def node7827 : Tree Nat := .node node7809 node7826 +def node7828 : Tree Nat := .node node7794 node7827 +def node7829 : Tree Nat := .node node7776 node7828 +def node7830 : Tree Nat := .leaf 12420144738405671481191835907700020442055088136933572889112416304208407621491015090647027270629171823603901845577048585649372640352993172150433805849529319912309677993676392972867532012667976556878706217405216698511545345695987793920 +def node7831 : Tree Nat := .node node4415 node7830 +def node7832 : Tree Nat := .node node7408 node7831 +def node7833 : Tree Nat := .node node7832 node6638 +def node7834 : Tree Nat := .leaf 74657018879507649199870798674038185509593728465409727615188998276602223855484948504402570865459331072 +def node7835 : Tree Nat := .node node7834 node3980 +def node7836 : Tree Nat := .node node6257 node7835 +def node7837 : Tree Nat := .node node7836 node7413 +def node7838 : Tree Nat := .node node7833 node7837 +def node7839 : Tree Nat := .leaf 11747563700311194394794878151269635829880553115309964712352692951204030290649389126977079039554479806189873481846249761345721424324106715347939034840275115860239056896 +def node7840 : Tree Nat := .node node1539 node7839 +def node7841 : Tree Nat := .node node7840 node4421 +def node7842 : Tree Nat := .node node7841 node7015 +def node7843 : Tree Nat := .node node7842 node7419 +def node7844 : Tree Nat := .node node7838 node7843 +def node7845 : Tree Nat := .leaf 179253596501330480877607393665613339689339494557341990850108229846252903604879594833024277336951901339567161283054348165065329350648601003233933026738034459017216 +def node7846 : Tree Nat := .node node1570 node7845 +def node7847 : Tree Nat := .leaf 813966605576154086191388158047028539690522256142078632860871315067183702802725498768457654845232898403662404539994856055406695416229633499244048120110231517222602811722923572678793533072314973427894678383347469581317039252625847391879168 +def node7848 : Tree Nat := .node node4426 node7847 +def node7849 : Tree Nat := .node node7846 node7848 +def node7850 : Tree Nat := .node node7849 node7021 +def node7851 : Tree Nat := .leaf 4892722389287413297962732661901766525556734588709091908989026191055403342593061585184526884052555888852992 +def node7852 : Tree Nat := .node node7851 node1589 +def node7853 : Tree Nat := .node node6268 node7852 +def node7854 : Tree Nat := .node node7853 node7424 +def node7855 : Tree Nat := .node node7850 node7854 +def node7856 : Tree Nat := .leaf 769888334663594435857277134521606853747051928964953847388746085250107329127998365825569851936242388578459548506275824359553199264504657697042532587292269992904476653387776 +def node7857 : Tree Nat := .node node1601 node7856 +def node7858 : Tree Nat := .leaf 1139175703117487322996075419220553367761134772726588861315750095773349363029250312872353692516352 +def node7859 : Tree Nat := .node node7858 node1605 +def node7860 : Tree Nat := .node node7857 node7859 +def node7861 : Tree Nat := .node node7860 node7026 +def node7862 : Tree Nat := .leaf 189516368689051383685178160212707831452256593886315504289435063235601922935348741007187305765215634515440396813614632959740619776597557657053667787334580882929180134778991679138462853869689454588800369021078644955672865786560512 +def node7863 : Tree Nat := .node node4435 node7862 +def node7864 : Tree Nat := .node node7863 node6653 +def node7865 : Tree Nat := .node node6651 node7864 +def node7866 : Tree Nat := .node node7861 node7865 +def node7867 : Tree Nat := .node node7855 node7866 +def node7868 : Tree Nat := .node node7844 node7867 +def node7869 : Tree Nat := .leaf 82546020797455584050393612812824354874414380115598372038388889121945788621835792202920314527460317196482076335461139067765146611368347922351891115214979775278717005738174628206926952026189046233667234576948125922211947265809761291462742068433178758146986580608119930880 +def node7870 : Tree Nat := .node node4442 node7869 +def node7871 : Tree Nat := .node node5892 node7870 +def node7872 : Tree Nat := .node node7871 node7431 +def node7873 : Tree Nat := .node node7872 node7436 +def node7874 : Tree Nat := .node node7873 node7442 +def node7875 : Tree Nat := .leaf 3580081700695792870399535724574524629625619903045113380443533919954444474421853919006621045793969011614799709377835293300224579899963688707993660629590076205690653540124402384666779948914291222753367710751102440076972426685512190960740623429408915456 +def node7876 : Tree Nat := .node node4462 node7875 +def node7877 : Tree Nat := .node node7876 node5502 +def node7878 : Tree Nat := .node node6678 node7877 +def node7879 : Tree Nat := .node node7045 node7878 +def node7880 : Tree Nat := .node node7448 node7879 +def node7881 : Tree Nat := .node node7874 node7880 +def node7882 : Tree Nat := .node node7868 node7881 +def node7883 : Tree Nat := .leaf 198722315814490743699069374523200327072881410190937166225798660869693248459369704795503407943184417234485505291993052638125091183300217153484699508634524503513247747825838241660962169718735472284509935729800727749555781881446801604608 +def node7884 : Tree Nat := .node node4470 node7883 +def node7885 : Tree Nat := .node node5918 node7884 +def node7886 : Tree Nat := .node node7885 node6686 +def node7887 : Tree Nat := .node node7886 node7457 +def node7888 : Tree Nat := .node node7887 node7463 +def node7889 : Tree Nat := .leaf 13023465689218465379062210528752456635048356098273258125773941038602405118447226234126154544461776080961032033556764251593265311815951992251712678155534222285715847036066769233004475601531064966313264454837446052082782012253600690112692224 +def node7890 : Tree Nat := .node node4481 node7889 +def node7891 : Tree Nat := .node node5929 node7890 +def node7892 : Tree Nat := .node node7891 node7062 +def node7893 : Tree Nat := .node node7892 node7468 +def node7894 : Tree Nat := .leaf 3032261899024822138962850563403325303236105502181048068630961011805622077321925427177481200304938007118003925964249460420610292611162617730377321311804829036867108661974619647266962045132045685611396820173010348649865333260156928 +def node7895 : Tree Nat := .node node4493 node7894 +def node7896 : Tree Nat := .node node7895 node6699 +def node7897 : Tree Nat := .node node6697 node7896 +def node7898 : Tree Nat := .node node7074 node7897 +def node7899 : Tree Nat := .node node7893 node7898 +def node7900 : Tree Nat := .node node7888 node7899 +def node7901 : Tree Nat := .leaf 50872912848509630386961759877939283730657641008879914553804457182037637617627197811290223700497087789481581959483591006819830334885554237979516508783324416112390448547910358744930583922356564229043482719799318520399404048571934998003712 +def node7902 : Tree Nat := .node node4500 node7901 +def node7903 : Tree Nat := .node node5940 node7902 +def node7904 : Tree Nat := .node node7903 node7474 +def node7905 : Tree Nat := .node node7904 node7481 +def node7906 : Tree Nat := .leaf 11844773043065711480323635013294239465766037117894719018089691452229513653961779903166795026837389248874077239443006275445621313151619946302568341998611590172010444684875791794672820741328194449465685039931560964157501465427968 +def node7907 : Tree Nat := .node node3715 node7906 +def node7908 : Tree Nat := .node node7907 node7083 +def node7909 : Tree Nat := .node node6716 node7908 +def node7910 : Tree Nat := .node node7081 node7909 +def node7911 : Tree Nat := .node node7905 node7910 +def node7912 : Tree Nat := .leaf 776259046150354467574489744231251277628443008558348305569526019017632364068800676261437195846193684398726435197706699235380963728411928878329747216727288232172611725731943965263858039421964486853457662478402953920652351218592514048 +def node7913 : Tree Nat := .node node4526 node7912 +def node7914 : Tree Nat := .node node7913 node5565 +def node7915 : Tree Nat := .node node6722 node7914 +def node7916 : Tree Nat := .node node7102 node7915 +def node7917 : Tree Nat := .node node7492 node7916 +def node7918 : Tree Nat := .node node7911 node7917 +def node7919 : Tree Nat := .node node7900 node7918 +def node7920 : Tree Nat := .node node7882 node7919 +def node7921 : Tree Nat := .node node7829 node7920 +def node7922 : Tree Nat := .node node7713 node7921 +def node7923 : Tree Nat := .leaf 28638903918474961204418783933674838490721739172170652529441449724066476191127684521670817206213751732775318955376503196847496200616682333339992037660437243057263846468288566578705580823555030464832333023661227711263188964051023536205215664791214882816 +def node7924 : Tree Nat := .node node7505 node7923 +def node7925 : Tree Nat := .node node7504 node7924 +def node7926 : Tree Nat := .node node7925 node6733 +def node7927 : Tree Nat := .node node7502 node7926 +def node7928 : Tree Nat := .leaf 639060358786575835169666188868664779529086153774591816910996210307709953661105387559990016 +def node7929 : Tree Nat := .leaf 5243959930521868196035988243035872375697538011210511234121231012194650941706023363740761130335647703788819329205673520001217649729569161945280545812312758691568420044698150497824916017468606156794909620374899201655940616336400885868126586514964480 +def node7930 : Tree Nat := .node node7928 node7929 +def node7931 : Tree Nat := .node node7511 node7930 +def node7932 : Tree Nat := .leaf 217460971493240179111222059730460361261952004507929949895878067693468529085096980322654242666248740103463845948442310299673952256 +def node7933 : Tree Nat := .node node7932 node4030 +def node7934 : Tree Nat := .node node6737 node7933 +def node7935 : Tree Nat := .node node7931 node7934 +def node7936 : Tree Nat := .leaf 5311379928167670986895882065524686273295931177270319231994441382004035598608522427391625022652292856688893294862465010153465793376527072394095199787743757972316335122781889635255582720 +def node7937 : Tree Nat := .node node46 node7936 +def node7938 : Tree Nat := .leaf 11788582886188967569679619401852726875694344044324964976011206634448783583094811913479895362986102103983783936 +def node7939 : Tree Nat := .node node7938 node50 +def node7940 : Tree Nat := .node node7937 node7939 +def node7941 : Tree Nat := .node node7940 node7120 +def node7942 : Tree Nat := .node node7935 node7941 +def node7943 : Tree Nat := .node node7927 node7942 +def node7944 : Tree Nat := .leaf 81045225954706893720945466087717991230711840473485095703040182220520562722908362234369278299748120982191364972876968538718655294441636236482165524103788353333749204340730411089920 +def node7945 : Tree Nat := .node node78 node7944 +def node7946 : Tree Nat := .node node7945 node4557 +def node7947 : Tree Nat := .node node7946 node7133 +def node7948 : Tree Nat := .node node7519 node7947 +def node7949 : Tree Nat := .leaf 85918022740406503255645470092525385597218198553156191474395948294389379281137475806478851475845129373726153909319440508904661186701693135611737183218658725237741147308650015226951185808919620239092555893719007636446637810542456579330207164179431817216 +def node7950 : Tree Nat := .node node7523 node7949 +def node7951 : Tree Nat := .node node7522 node7950 +def node7952 : Tree Nat := .node node7951 node6744 +def node7953 : Tree Nat := .leaf 348086594972396485797208527046225839606722145633587641187987710411016476990408125801537537484540664655963310972106506905417534234724078216419423013284470686969909261654683300024633345969920 +def node7954 : Tree Nat := .node node109 node7953 +def node7955 : Tree Nat := .node node7954 node6373 +def node7956 : Tree Nat := .node node7955 node7529 +def node7957 : Tree Nat := .node node7952 node7956 +def node7958 : Tree Nat := .node node7948 node7957 +def node7959 : Tree Nat := .node node7943 node7958 +def node7960 : Tree Nat := .leaf 316582913885573803597443226905148403244968126849551155090000711799068304989895297962364267574793653046458540005045687548694257186017910073221826469652903548085032610122610769920 +def node7961 : Tree Nat := .node node141 node7960 +def node7962 : Tree Nat := .node node7961 node5606 +def node7963 : Tree Nat := .node node7962 node7144 +def node7964 : Tree Nat := .node node7537 node7963 +def node7965 : Tree Nat := .leaf 1707011694817242694164442058424641996069058130512872489061442001108317148156624109844614100826605758121579504687680440802790448751783561027106814899305145287770296055417427292998044660691909101396794827845435355767926484837581243542224530046976 +def node7966 : Tree Nat := .node node4063 node7965 +def node7967 : Tree Nat := .node node7540 node7966 +def node7968 : Tree Nat := .node node7967 node6751 +def node7969 : Tree Nat := .leaf 1359713261610923772645345808774323250890717293273207034629981195100234824180510010187503302445992538508069330450673470160622166784387077670417803816533153825626323303208186313215123128320 +def node7970 : Tree Nat := .node node172 node7969 +def node7971 : Tree Nat := .node node7970 node4578 +def node7972 : Tree Nat := .node node7971 node7149 +def node7973 : Tree Nat := .node node7968 node7972 +def node7974 : Tree Nat := .node node7964 node7973 +def node7975 : Tree Nat := .leaf 20747577844404964792562039318455805755062231161212187448816752227994214261768346804583589711283128738506652418017849905981329302314710333543464303652512466570963700710877762703851520 +def node7976 : Tree Nat := .node node203 node7975 +def node7977 : Tree Nat := .node node7976 node5621 +def node7978 : Tree Nat := .node node7977 node7155 +def node7979 : Tree Nat := .node node7550 node7978 +def node7980 : Tree Nat := .leaf 335612155294628451614282624222752013563145380923874834329391988698957781312729345617327549990132626668746003407554088403919364678553866032272662982565490294265885466542155142248628139912246706711742743183284759287326296075780573687677136546566242304 +def node7981 : Tree Nat := .node node6011 node7980 +def node7982 : Tree Nat := .node node7553 node7981 +def node7983 : Tree Nat := .node node7982 node6762 +def node7984 : Tree Nat := .node node7983 node7559 +def node7985 : Tree Nat := .node node7979 node7984 +def node7986 : Tree Nat := .node node7974 node7985 +def node7987 : Tree Nat := .node node7959 node7986 +def node7988 : Tree Nat := .leaf 458222462695599379270700542938797415851547826754730440471063200806362543643990239304860980992807487714424082284906254528993716348376805873737133241265633026578840484340642947340379306864211416005172102842476136511145880376255987812778540987837124243456 +def node7989 : Tree Nat := .node node4604 node7988 +def node7990 : Tree Nat := .node node7569 node7989 +def node7991 : Tree Nat := .node node7990 node7172 +def node7992 : Tree Nat := .node node7567 node7991 +def node7993 : Tree Nat := .leaf 106688230926077668385277628651540124754316133157054530566340124988237209655557241475580000842516870658578670268299093650969838042326647599766246822062979417191645916566693714178136075680895944012413084569882530485617248520163370494263484743680 +def node7994 : Tree Nat := .node node6408 node7993 +def node7995 : Tree Nat := .node node7574 node7994 +def node7996 : Tree Nat := .node node7995 node6770 +def node7997 : Tree Nat := .leaf 84982078850682735790334113048394980372734898836325107711911062112064569577736358838266000362436685707022292717799440162455452694024433158305523196603900127557061361964510234164089323520 +def node7998 : Tree Nat := .node node298 node7997 +def node7999 : Tree Nat := .leaf 188617326179023481114873910429643630011109504709199439616179306151180537329516990615678325807776960762624344064 +def node8000 : Tree Nat := .node node7999 node3787 +def node8001 : Tree Nat := .node node7998 node8000 +def node8002 : Tree Nat := .node node8001 node7177 +def node8003 : Tree Nat := .node node7996 node8002 +def node8004 : Tree Nat := .node node7992 node8003 +def node8005 : Tree Nat := .leaf 1296723615275310299535127457403487859691389447575761531248642915528329003566533795749908452795969935715061839566031496619498484711066179783714648385660613653339987269451686577438720 +def node8006 : Tree Nat := .node node329 node8005 +def node8007 : Tree Nat := .node node8006 node4624 +def node8008 : Tree Nat := .node node8007 node7187 +def node8009 : Tree Nat := .node node7584 node8008 +def node8010 : Tree Nat := .leaf 34959599509857130376772047909570245155022077753222690323156717052282288738011130416887571407233163944657004505570241951436543457640806884840664472128175073652328888670381807158787604767579692622227243049706143408593025554696456038221333866376855552 +def node8011 : Tree Nat := .node node4114 node8010 +def node8012 : Tree Nat := .node node7587 node8011 +def node8013 : Tree Nat := .node node8012 node6791 +def node8014 : Tree Nat := .leaf 5569385519558343772755336432739613433707554330137402259007803366576263631846530012824600599752650634495412975553704110486680547755585251462710768212551530991518548186474932800394133535518720 +def node8015 : Tree Nat := .node node360 node8014 +def node8016 : Tree Nat := .node node8015 node4629 +def node8017 : Tree Nat := .node node8016 node7592 +def node8018 : Tree Nat := .node node8013 node8017 +def node8019 : Tree Nat := .node node8009 node8018 +def node8020 : Tree Nat := .node node8004 node8019 +def node8021 : Tree Nat := .leaf 5065326622169180857559091630482374451919490029592818481440011388782911028734961092567402675062579667394818051875235431580474071961600993701068726146833286719415794305522697502720 +def node8022 : Tree Nat := .node node392 node8021 +def node8023 : Tree Nat := .node node8022 node4640 +def node8024 : Tree Nat := .node node8023 node7200 +def node8025 : Tree Nat := .node node7600 node8024 +def node8026 : Tree Nat := .leaf 106359737525781373700957022117933584227176072140440595903369682715355389438936909868576183637967103570658423573895531705298322042521420623376866451943031418440989452286195042419047319468491042691879415373230641448154304638039371885254445675791858209445255943384825230072538464256 +def node8027 : Tree Nat := .node node4130 node8026 +def node8028 : Tree Nat := .node node7603 node8027 +def node8029 : Tree Nat := .node node8028 node6798 +def node8030 : Tree Nat := .leaf 21755412185774780362325532940389123357345959446157503476773099339859608956639547011618872663436750972160309354476438779562076051688587293015429482463787258410444285952589856877684740587520 +def node8031 : Tree Nat := .node node423 node8030 +def node8032 : Tree Nat := .node node8031 node4645 +def node8033 : Tree Nat := .node node8032 node7205 +def node8034 : Tree Nat := .node node8029 node8033 +def node8035 : Tree Nat := .node node8025 node8034 +def node8036 : Tree Nat := .leaf 396220898351839024966200495091397361487646578285816854921853361649410203895667028964638671035944016825479566234923297695055393564692743703462168593349949970522328861396628608077001439341292565103001416499862383203910512387348652992305907439265755443353813749441373405184 +def node8037 : Tree Nat := .node node4136 node8036 +def node8038 : Tree Nat := .node node7609 node8037 +def node8039 : Tree Nat := .node node8038 node6808 +def node8040 : Tree Nat := .leaf 331961245510479436680992629095292892080995698579394958933019124957392410272385015258249716368821707970985828776471715587047360425661956669879449625803733467653676312029269712405790720 +def node8041 : Tree Nat := .node node454 node8040 +def node8042 : Tree Nat := .node node8041 node5665 +def node8043 : Tree Nat := .node node8042 node7211 +def node8044 : Tree Nat := .node node8039 node8043 +def node8045 : Tree Nat := .leaf 1789931494904685075276173995854677405670108698260665783090090606448617575601866754025418263682391073451953467334344738670993105893758249149584742886992361457335441782475412363988818182407787265955891138934255115802231990918047717228335198473761587200 +def node8046 : Tree Nat := .node node4144 node8045 +def node8047 : Tree Nat := .node node7614 node8046 +def node8048 : Tree Nat := .node node8047 node6819 +def node8049 : Tree Nat := .node node8048 node7620 +def node8050 : Tree Nat := .node node8044 node8049 +def node8051 : Tree Nat := .node node8035 node8050 +def node8052 : Tree Nat := .node node8020 node8051 +def node8053 : Tree Nat := .node node7987 node8052 +def node8054 : Tree Nat := .leaf 572778078369499224088375678673496769814434783443413050588828994394307875079454568984114212362718407115309335817967635589475647626157944524417026322368829076950922142122895214151842930647113810248979016584057918233989298042044013326990475766762831875840 +def node8055 : Tree Nat := .node node4672 node8054 +def node8056 : Tree Nat := .node node6063 node8055 +def node8057 : Tree Nat := .node node8056 node7226 +def node8058 : Tree Nat := .node node7629 node8057 +def node8059 : Tree Nat := .leaf 85916711835441056807814603089982736960820311082249057456115247031688285762292485954016618513290163167229104468491648116937207949061897138733678487824015104056911258539659194655786630361229307340150960283043809637127157031433788446711588202336086917120 +def node8060 : Tree Nat := .node node6453 node8059 +def node8061 : Tree Nat := .node node5674 node8060 +def node8062 : Tree Nat := .node node8061 node6828 +def node8063 : Tree Nat := .node node8062 node7232 +def node8064 : Tree Nat := .node node8058 node8063 +def node8065 : Tree Nat := .leaf 1747979975492856518824388667826833403974715525645181428798916607827819355514870306549476362183728533747576849643817150832263826248811681101395118413565802822886697727030774250431595100163395878013260138733390161042400806024499930179588626174705664 +def node8066 : Tree Nat := .node node4182 node8065 +def node8067 : Tree Nat := .node node5688 node8066 +def node8068 : Tree Nat := .node node8067 node6849 +def node8069 : Tree Nat := .node node8068 node7640 +def node8070 : Tree Nat := .node node7636 node8069 +def node8071 : Tree Nat := .node node8064 node8070 +def node8072 : Tree Nat := .leaf 22158278651204452854366041692344873172024611956738416420778642232838097390590379204399730677690238677276238511943707192303230536396904681877006189422362323933743460656238379141452725916734914882976651738787019869952679766781791411777752246770751789472301593356268457528832032768 +def node8073 : Tree Nat := .node node4198 node8072 +def node8074 : Tree Nat := .node node5700 node8073 +def node8075 : Tree Nat := .node node8074 node6856 +def node8076 : Tree Nat := .node node8075 node7252 +def node8077 : Tree Nat := .node node7648 node8076 +def node8078 : Tree Nat := .leaf 1342448621178513806457130496891008054252581523695499337317567954795831125250917382469310199960531242778696964275119372831710532820574818846470755864456496232209942484256087070185041935010998614544310278376232222219655498707522406240676284375729438720 +def node8079 : Tree Nat := .node node4209 node8078 +def node8080 : Tree Nat := .node node6094 node8079 +def node8081 : Tree Nat := .node node8080 node6877 +def node8082 : Tree Nat := .leaf 262894183196658893935434297526466556912399064322833640905376838000220745523750425189062629289924177621180586818994668467734900701617629684650760162246656 +def node8083 : Tree Nat := .node node8082 node57 +def node8084 : Tree Nat := .node node7660 node8083 +def node8085 : Tree Nat := .node node6484 node8084 +def node8086 : Tree Nat := .node node8081 node8085 +def node8087 : Tree Nat := .node node7658 node8086 +def node8088 : Tree Nat := .node node8077 node8087 +def node8089 : Tree Nat := .node node8071 node8088 +def node8090 : Tree Nat := .leaf 1832889850782397517082802171755189663406191307018921761884252780947908096342585866198098193012776216027479008590015982084761399088452696108828481666660133095712824594771028361120910450400843510344462089612985470430276466427041513061336623480201914888960 +def node8091 : Tree Nat := .node node5721 node8090 +def node8092 : Tree Nat := .node node6102 node8091 +def node8093 : Tree Nat := .node node8092 node7269 +def node8094 : Tree Nat := .node node7670 node8093 +def node8095 : Tree Nat := .leaf 2133764618521553367705552573030802495086322663141090611326802499845537142056349156607803770366615364268449411863383732645724598749838759548624636171115143914498571407635849631585153590210435782354905041645649236737929392705741671953902851850240 +def node8096 : Tree Nat := .node node6498 node8095 +def node8097 : Tree Nat := .node node5727 node8096 +def node8098 : Tree Nat := .node node8097 node6885 +def node8099 : Tree Nat := .node node8098 node7275 +def node8100 : Tree Nat := .node node8094 node8099 +def node8101 : Tree Nat := .leaf 27967679607885704301190218685229334463595448410322902860782665809895227293410181258444742214239344020615132732046787126046215296397649047170387184009715772222342810838678667118060085562365759235609955188562010322138340988317941636009607979622989824 +def node8102 : Tree Nat := .node node6123 node8101 +def node8103 : Tree Nat := .node node6122 node8102 +def node8104 : Tree Nat := .node node8103 node6896 +def node8105 : Tree Nat := .node node8104 node7681 +def node8106 : Tree Nat := .node node7677 node8105 +def node8107 : Tree Nat := .node node8100 node8106 +def node8108 : Tree Nat := .leaf 109248748468303532426524291739177087748419720352823839299932287988768647409142094175760788933174269010085424427992358187636451984950401417250338520351954958132653895801109537249204153731309444984464052436488454432726662419850256226069879160045568 +def node8109 : Tree Nat := .node node4256 node8108 +def node8110 : Tree Nat := .node node5752 node8109 +def node8111 : Tree Nat := .leaf 3479375543891842865779552955687365780191232072126879198334049083095496465361551685162467882659979841655418645086789448571912454144 +def node8112 : Tree Nat := .node node8111 node4259 +def node8113 : Tree Nat := .node node6902 node8112 +def node8114 : Tree Nat := .node node8110 node8113 +def node8115 : Tree Nat := .node node8114 node7293 +def node8116 : Tree Nat := .node node7693 node8115 +def node8117 : Tree Nat := .leaf 6491683198595054547177551277054161061914420602222566823797224233463116773185776810152759537540890347877687328901197238280256940476887057079167568042282935937651496242665948372867391611151874611626289164208557431828647242398054851622336688051721842154452946494623827842039808 +def node8118 : Tree Nat := .node node4265 node8117 +def node8119 : Tree Nat := .node node5758 node8118 +def node8120 : Tree Nat := .node node8119 node6909 +def node8121 : Tree Nat := .node node8120 node7698 +def node8122 : Tree Nat := .leaf 7159725979618740301104695983418709622680434793042663132360362426937479262949149812481666875230480344748057170577956964648580410289503168355621266697894447351120757085064133476240170475991911478448337672475740128402136464028007699112026009991741702144 +def node8123 : Tree Nat := .node node7700 node8122 +def node8124 : Tree Nat := .node node6147 node8123 +def node8125 : Tree Nat := .node node8124 node6914 +def node8126 : Tree Nat := .leaf 4206306931146542302966948760423464910598385029165338254486029408003531928380006803025002068638786841938889389103914692306072733802567566293748409113247744 +def node8127 : Tree Nat := .node node8126 node57 +def node8128 : Tree Nat := .node node7705 node8127 +def node8129 : Tree Nat := .node node6532 node8128 +def node8130 : Tree Nat := .node node8125 node8129 +def node8131 : Tree Nat := .node node8121 node8130 +def node8132 : Tree Nat := .node node8116 node8131 +def node8133 : Tree Nat := .node node8107 node8132 +def node8134 : Tree Nat := .node node8089 node8133 +def node8135 : Tree Nat := .node node8053 node8134 +def node8136 : Tree Nat := .leaf 12613850475128331237085628572002006691791698804161803835617215860737758480433125225686136454123395294469481242726823106306919616749644311708344853910196551563747113604862705664 +def node8137 : Tree Nat := .node node1021 node8136 +def node8138 : Tree Nat := .leaf 57277807836949922408837567867349676981443478344341305058882899448132952382255369043341634412427487258175390564980572490889505983583062254031053604596335556968141406954117684512521295856065432296706572719627668840723080083197257764240660972921560236032 +def node8139 : Tree Nat := .node node4288 node8138 +def node8140 : Tree Nat := .node node8137 node8139 +def node8141 : Tree Nat := .node node8140 node7314 +def node8142 : Tree Nat := .node node7717 node8141 +def node8143 : Tree Nat := .leaf 13336028865759708548159703581442515594289516644631816320792515624161240303406411750237750855553405387975796074885968791071779026906096175488978996524996926122401451229511351236535968490830803107963573926237935772430905933960453380377329795072 +def node8144 : Tree Nat := .node node4293 node8143 +def node8145 : Tree Nat := .node node7720 node8144 +def node8146 : Tree Nat := .node node8145 node6924 +def node8147 : Tree Nat := .leaf 54176075267310244066337997068351799987618498008157256166343302096441163105806928759394575231053387138226711607597143103565351092440576138419771037834986331317626618252375274279606943744 +def node8148 : Tree Nat := .node node1052 node8147 +def node8149 : Tree Nat := .node node8148 node4810 +def node8150 : Tree Nat := .node node8149 node7319 +def node8151 : Tree Nat := .node node8146 node8150 +def node8152 : Tree Nat := .node node8142 node8151 +def node8153 : Tree Nat := .leaf 826661304738010315953643754094723510553260772829547976171009858649309739773665294790566638657430834018351922723345079094930284003304689612118088345858641204004241884275450193117184 +def node8154 : Tree Nat := .node node1083 node8153 +def node8155 : Tree Nat := .node node8154 node7732 +def node8156 : Tree Nat := .node node8155 node7325 +def node8157 : Tree Nat := .node node7730 node8156 +def node8158 : Tree Nat := .leaf 873989987746428259412194333913416701987357762822590714399458304567458379856191544240442419623222148158248706400092386151335201948939087668076356517823364840653140422062021386301647991748498013583475276852613915535725504731553302531833988657446912 +def node8159 : Tree Nat := .node node4308 node8158 +def node8160 : Tree Nat := .node node7737 node8159 +def node8161 : Tree Nat := .node node8160 node6941 +def node8162 : Tree Nat := .leaf 1787680445737280478760953223179972587004313637395268758156562498401501069561502891285625879171484407824027990369163744221254007206582008706341230113456128 +def node8163 : Tree Nat := .node node8162 node57 +def node8164 : Tree Nat := .node node7741 node8163 +def node8165 : Tree Nat := .node node6556 node8164 +def node8166 : Tree Nat := .node node8161 node8165 +def node8167 : Tree Nat := .node node8157 node8166 +def node8168 : Tree Nat := .node node8152 node8167 +def node8169 : Tree Nat := .leaf 633165827771147607194886453810296806489936253699102310180001423597857445328252284420335266030211136070483322119609811919007175058505643893966162568467524437885500457795002040320 +def node8170 : Tree Nat := .node node1146 node8169 +def node8171 : Tree Nat := .node node8170 node4836 +def node8172 : Tree Nat := .node node8171 node7341 +def node8173 : Tree Nat := .node node7750 node8172 +def node8174 : Tree Nat := .leaf 3414023389634485388328884116849283992138116261025744978122884000919910681037937920154100744249723656551769561799599350356937981975238118487679834048701837779570656395773015019964592701885333491727409871976222325875239316335175217632762482655232 +def node8175 : Tree Nat := .node node6569 node8174 +def node8176 : Tree Nat := .node node7753 node8175 +def node8177 : Tree Nat := .node node8176 node6948 +def node8178 : Tree Nat := .leaf 2719426523221847545290691617548640276201672194071595037924807736210332026334928702221160106357214379181674623760927871701937491239805273998223232529755010844936805042003612008117824389120 +def node8179 : Tree Nat := .node node1177 node8178 +def node8180 : Tree Nat := .node node8179 node6182 +def node8181 : Tree Nat := .node node8180 node7346 +def node8182 : Tree Nat := .node node8177 node8181 +def node8183 : Tree Nat := .node node8173 node8182 +def node8184 : Tree Nat := .leaf 41495155688809929585124078636911611510124462322424369747954623102448622800200290809238157476107504810625464111078812720719592410465131781196964145087778747617445061571903751737835520 +def node8185 : Tree Nat := .node node1208 node8184 +def node8186 : Tree Nat := .node node8185 node4851 +def node8187 : Tree Nat := .node node8186 node7352 +def node8188 : Tree Nat := .node node7763 node8187 +def node8189 : Tree Nat := .leaf 223741436863085634409521749481834675708763587282583222886261325799305187541819563744885033326759115489973017708076402261841648939575234140501392104204209307693260362459467601351984386923943308531353264453414424438211780183855204938288738933382578176 +def node8190 : Tree Nat := .node node4341 node8189 +def node8191 : Tree Nat := .node node7766 node8190 +def node8192 : Tree Nat := .node node8191 node6969 +def node8193 : Tree Nat := .node node8192 node7772 +def node8194 : Tree Nat := .node node8188 node8193 +def node8195 : Tree Nat := .node node8183 node8194 +def node8196 : Tree Nat := .node node8168 node8195 +def node8197 : Tree Nat := .leaf 916444925391198758541401085877594831703095653509460880942126396043339567729636705854385529246001541721293834432410250050184066120489979900944253657930666300507046473268310340976648127047875076425092742974184060470760769233963789150624281581540712968192 +def node8198 : Tree Nat := .node node5815 node8197 +def node8199 : Tree Nat := .node node6201 node8198 +def node8200 : Tree Nat := .node node8199 node7360 +def node8201 : Tree Nat := .node node7780 node8200 +def node8202 : Tree Nat := .leaf 213376461852155336770555257303080249508632266314109061132680249976499647012064739613634172942177745330540923934206510909610910516374770716493359894577331107291538623722326390841725797574405727258325457763181750679054890143454234654985764732928 +def node8203 : Tree Nat := .node node4358 node8202 +def node8204 : Tree Nat := .node node5821 node8203 +def node8205 : Tree Nat := .node node8204 node6977 +def node8206 : Tree Nat := .node node8205 node7366 +def node8207 : Tree Nat := .node node8201 node8206 +def node8208 : Tree Nat := .leaf 5038209258419659172858230476819102047443924074715425260092982646010980130135879362325555736673689174295433142836793290706194066365307233591809005640984413117173334437366461203432948971370718904530872388027997309507402579032470382270779557991497036482197367648419840 +def node8209 : Tree Nat := .node node6218 node8208 +def node8210 : Tree Nat := .node node6217 node8209 +def node8211 : Tree Nat := .node node8210 node6988 +def node8212 : Tree Nat := .node node8211 node7791 +def node8213 : Tree Nat := .node node7787 node8212 +def node8214 : Tree Nat := .node node8207 node8213 +def node8215 : Tree Nat := .leaf 10130653244338361715118183260964748903838980059185636962880022777565095293628487251274206113199856009479836488236703218238458176771777059281162533227685345959722051620651128586240 +def node8216 : Tree Nat := .node node1397 node8215 +def node8217 : Tree Nat := .node node8216 node7800 +def node8218 : Tree Nat := .node node8217 node7385 +def node8219 : Tree Nat := .node node7798 node8218 +def node8220 : Tree Nat := .leaf 54624374234151766213262145869588543874209860176411919649966143993970993052202041929903572589539772749766081827581411020671145679283417663978361281302520484832134146586015975146370799662180695128444457607585705009164824818784740318788433460854784 +def node8221 : Tree Nat := .node node6615 node8220 +def node8222 : Tree Nat := .node node7805 node8221 +def node8223 : Tree Nat := .leaf 1478734606154033217956310006167130456581273630653923659291970860315585997778659466194048850130491432703552916133862494764665929728 +def node8224 : Tree Nat := .node node8223 node4391 +def node8225 : Tree Nat := .node node6994 node8224 +def node8226 : Tree Nat := .node node8222 node8225 +def node8227 : Tree Nat := .leaf 43510824371549560724651065880778230507316671546542573050740712262068915500630163552513206397727115658338159260307987693333107474744216492703164178345771218975983782597009943398708611645440 +def node8228 : Tree Nat := .node node1428 node8227 +def node8229 : Tree Nat := .leaf 80162363626084979473821411932598542754721539501409761836876205114251728365044721011663288468305206454945579008 +def node8230 : Tree Nat := .node node8229 node1432 +def node8231 : Tree Nat := .node node8228 node8230 +def node8232 : Tree Nat := .node node8231 node7390 +def node8233 : Tree Nat := .node node8226 node8232 +def node8234 : Tree Nat := .node node8219 node8233 +def node8235 : Tree Nat := .leaf 833501804109981784259981473840157224643094790289488520049532226470504654727204008940179025108944286342866238824179155055736100206953537961224442987656227666191538327450361324517084225355156059242301164346502815863389669312461518424019828736 +def node8236 : Tree Nat := .node node4397 node8235 +def node8237 : Tree Nat := .node node7811 node8236 +def node8238 : Tree Nat := .node node8237 node7396 +def node8239 : Tree Nat := .leaf 663922491020958873361985258190585784161991397158789904459611664938530354248262970713332258284851355927799960470094775394657464725734200374257650986840781335004785187797478556922019840 +def node8240 : Tree Nat := .node node1459 node8239 +def node8241 : Tree Nat := .node node8240 node4918 +def node8242 : Tree Nat := .node node8241 node7400 +def node8243 : Tree Nat := .node node8238 node8242 +def node8244 : Tree Nat := .leaf 3579862989809370150552347991709354811340217396521331566180181213005587301738353996183512521501485746879143930685003989674672815980398824510783343292773873376777657841404247943171922571946276716792934554708052307271788573073495908870870392378834812928 +def node8245 : Tree Nat := .node node7817 node8244 +def node8246 : Tree Nat := .node node7816 node8245 +def node8247 : Tree Nat := .node node8246 node7006 +def node8248 : Tree Nat := .node node8247 node7824 +def node8249 : Tree Nat := .node node8243 node8248 +def node8250 : Tree Nat := .node node8234 node8249 +def node8251 : Tree Nat := .node node8214 node8250 +def node8252 : Tree Nat := .node node8196 node8251 +def node8253 : Tree Nat := .leaf 50455401900513324948342514288008026767166795216647215342468863442951033921732500902744545816493581177877924970907292425227678466998577246833379415640786206254987893668520656896 +def node8254 : Tree Nat := .node node1523 node8253 +def node8255 : Tree Nat := .leaf 307507890453396678158617067384810577610188427909214633367327926694492706075598475417633664353327532164368664546183626497262404630541110800425165751734697276599630572816496323819398379674398361900888605519407885227339154792960076760715783041686915684911756087040 +def node8256 : Tree Nat := .node node7834 node8255 +def node8257 : Tree Nat := .node node8254 node8256 +def node8258 : Tree Nat := .node node8257 node7413 +def node8259 : Tree Nat := .node node7833 node8258 +def node8260 : Tree Nat := .leaf 53344115463038834192638814325770062377158066578527265283170062504242951146879418287289640867937183229782419343933102886447133190798050214271394099692852753568617270115948604704407844525752688969608779410249626043538871944021863310980439605248 +def node8261 : Tree Nat := .node node4420 node8260 +def node8262 : Tree Nat := .node node7840 node8261 +def node8263 : Tree Nat := .leaf 5914938424616132871825240024668521826325094522615694637167883441262343991114637864776195400521965730814210861733147891218977390592 +def node8264 : Tree Nat := .node node8263 node1550 +def node8265 : Tree Nat := .node node7014 node8264 +def node8266 : Tree Nat := .node node8262 node8265 +def node8267 : Tree Nat := .leaf 216704301069240976265351988273407199950473992032629024665373208385764652423227715037578300924213548552906846430388572414261404369762304553679084151337297253872653710918950543990525526016 +def node8268 : Tree Nat := .node node1554 node8267 +def node8269 : Tree Nat := .node node8268 node4945 +def node8270 : Tree Nat := .node node8269 node7418 +def node8271 : Tree Nat := .node node8266 node8270 +def node8272 : Tree Nat := .node node8259 node8271 +def node8273 : Tree Nat := .leaf 3306645218952041263814575016378894042213043091318191904684039434597238959094661179162266554629723336073407690893380316379721136013218758448472353383434564813608560630838281713483776 +def node8274 : Tree Nat := .node node1585 node8273 +def node8275 : Tree Nat := .node node8274 node7852 +def node8276 : Tree Nat := .node node8275 node7424 +def node8277 : Tree Nat := .node node7850 node8276 +def node8278 : Tree Nat := .leaf 3495959950985713037648777335653666807949431051290362857597833215655638711029740613098952724367457067495153699287634296514848771144083556479453834027202583699314642787673707775906303109083725561862231391576815859867555426524517520509325478679543808 +def node8279 : Tree Nat := .node node7858 node8278 +def node8280 : Tree Nat := .node node7857 node8279 +def node8281 : Tree Nat := .node node8280 node7026 +def node8282 : Tree Nat := .leaf 7150721782949121915043812892719890348017254549581075032626249993606004278246011565142503516685937631296111961476654976002325562875407337975180544486408192 +def node8283 : Tree Nat := .node node8282 node57 +def node8284 : Tree Nat := .node node7863 node8283 +def node8285 : Tree Nat := .node node6651 node8284 +def node8286 : Tree Nat := .node node8281 node8285 +def node8287 : Tree Nat := .node node8277 node8286 +def node8288 : Tree Nat := .node node8272 node8287 +def node8289 : Tree Nat := .leaf 13656093558537941553315536467397135968552465044102979912491535998492748263050510482475893147384943187441520456895354755808724157630502239237539840560953731166475009602043035864815479826012756674330082820928955740700158070625838582172875533320192 +def node8290 : Tree Nat := .node node6664 node8289 +def node8291 : Tree Nat := .node node5901 node8290 +def node8292 : Tree Nat := .node node8291 node7033 +def node8293 : Tree Nat := .node node8292 node7441 +def node8294 : Tree Nat := .node node7873 node8293 +def node8295 : Tree Nat := .leaf 208375451027495446064995368460039306160773697572372130012383056637412595799649364959884957958807846788527067634141735957059069539123008167283904250260650523839917273527626669033262343582853391017320253551650148720079289309499945070035468288 +def node8296 : Tree Nat := .node node4453 node8295 +def node8297 : Tree Nat := .node node5907 node8296 +def node8298 : Tree Nat := .node node8297 node7039 +def node8299 : Tree Nat := .node node8298 node7447 +def node8300 : Tree Nat := .leaf 894965747452342537638086997927338702835054349130332891545045303197220750167278254979540133307026787453950433785008785065217621789006560276438488138831519363134633326402596389760980042937904024388953612218718693959625155363085956825955142641563729920 +def node8301 : Tree Nat := .node node6301 node8300 +def node8302 : Tree Nat := .node node6300 node8301 +def node8303 : Tree Nat := .node node8302 node7044 +def node8304 : Tree Nat := .node node8303 node7878 +def node8305 : Tree Nat := .node node8299 node8304 +def node8306 : Tree Nat := .node node8294 node8305 +def node8307 : Tree Nat := .node node8288 node8306 +def node8308 : Tree Nat := .leaf 82546020797455584050393617080353576019735791143578806845886515820389882602306870751366426600001415500384667071915273627393639861241000878169506187795599026784862309070981867011697198453671761706328722773873011184281691256197649018096730804707860112006963890742980771840 +def node8309 : Tree Nat := .node node4475 node8308 +def node8310 : Tree Nat := .node node5923 node8309 +def node8311 : Tree Nat := .node node8310 node7052 +def node8312 : Tree Nat := .node node8311 node7462 +def node8313 : Tree Nat := .node node7887 node8312 +def node8314 : Tree Nat := .leaf 55935359215771408602380437370458668927190896820645805721565331534808375736137626726555371380083707668495366627768466540181368480730728516604415529753431182007999914655064616436680008669278824446786752071600824040376554419574521307508981795156656128 +def node8315 : Tree Nat := .node node4486 node8314 +def node8316 : Tree Nat := .node node6321 node8315 +def node8317 : Tree Nat := .node node8316 node7073 +def node8318 : Tree Nat := .node node8317 node7897 +def node8319 : Tree Nat := .node node7893 node8318 +def node8320 : Tree Nat := .node node8313 node8319 +def node8321 : Tree Nat := .leaf 218497496936607064853048583478354175496839440705647678599864575979190617427760208983428865374537985041277370401643812327614923687199422314048007630285043193580169459638922919945098465652479457975537484097213085557170607245300589314427139647340544 +def node8322 : Tree Nat := .node node6710 node8321 +def node8323 : Tree Nat := .node node5945 node8322 +def node8324 : Tree Nat := .node node8323 node7080 +def node8325 : Tree Nat := .leaf 320649454504339917895285647730394171018886158005639047347504820457006913460178884046653153873220638902805594112 +def node8326 : Tree Nat := .node node8325 node1933 +def node8327 : Tree Nat := .node node6715 node8326 +def node8328 : Tree Nat := .node node8327 node7908 +def node8329 : Tree Nat := .node node8324 node8328 +def node8330 : Tree Nat := .node node7905 node8329 +def node8331 : Tree Nat := .leaf 3334007216439927137039925895360628898572379161157954080198128905882018618908816035760716100435777145371464955296716620222944400827380331994686017944060700670777972960775893437237178190303411832821489421528122185037498527891958869548387532800 +def node8332 : Tree Nat := .node node4514 node8331 +def node8333 : Tree Nat := .node node5951 node8332 +def node8334 : Tree Nat := .node node8333 node7486 +def node8335 : Tree Nat := .node node8334 node7491 +def node8336 : Tree Nat := .leaf 14319451959237480602209391966837419245360869586085326264720724853874958525898299624963333750460954463916351948681094897962006166588868714685151215241942396167470816335664229812061272332676980627927794002339105153492976121740173833811291401671061536768 +def node8337 : Tree Nat := .node node4519 node8336 +def node8338 : Tree Nat := .node node6344 node8337 +def node8339 : Tree Nat := .node node8338 node7101 +def node8340 : Tree Nat := .node node8339 node7915 +def node8341 : Tree Nat := .node node8335 node8340 +def node8342 : Tree Nat := .node node8330 node8341 +def node8343 : Tree Nat := .node node8320 node8342 +def node8344 : Tree Nat := .node node8307 node8343 +def node8345 : Tree Nat := .node node8252 node8344 +def node8346 : Tree Nat := .node node8135 node8345 +def node8347 : Tree Nat := .leaf 22812203088110976093205858028501456624466142536242799652895962589496375836043386932529564056586856998893211547867972036553443523606877189991263306598611070941259973371801324750418593085883678720 +def node8348 : Tree Nat := .node node2066 node8347 +def node8349 : Tree Nat := .node node8348 node7114 +def node8350 : Tree Nat := .node node7501 node8349 +def node8351 : Tree Nat := .node node8350 node7926 +def node8352 : Tree Nat := .leaf 97977666213146848738957008028032792090444635652437319224668311012326407326331004912288236176177644193675051794502478422839556490074541491700854427565855548716247522665717842648649140501964259133719838720 +def node8353 : Tree Nat := .node node2511 node8352 +def node8354 : Tree Nat := .node node8353 node7933 +def node8355 : Tree Nat := .node node7931 node8354 +def node8356 : Tree Nat := .leaf 123003155723136208567847447683223664415731869180715065944930727538583620841008360212436156787483530800032585133652103134589557447628484608631195939614548405762255357347921365033729519948179968040306920796479896572114871577525951076828223066624686125036901236736 +def node8357 : Tree Nat := .node node7938 node8356 +def node8358 : Tree Nat := .node node7937 node8357 +def node8359 : Tree Nat := .node node8358 node7120 +def node8360 : Tree Nat := .node node8355 node8359 +def node8361 : Tree Nat := .node node8351 node8360 +def node8362 : Tree Nat := .leaf 1495020541582440929244339111755871461341013117255208118052189804265234486790939406010257510012476260279465512001075415387566474763100303523267432061246575145206413614894371636977043509534804745912320 +def node8363 : Tree Nat := .node node2308 node8362 +def node8364 : Tree Nat := .node node8363 node7128 +def node8365 : Tree Nat := .node node7518 node8364 +def node8366 : Tree Nat := .leaf 1876879207201175057492789423877314215327939898387375884169474870502860978765784020192710578146539469678281041038976018550758262162951396858827297756224032876866930623859273512306193640915809959957184933242782255149653526021144526081140903890402985300197376 +def node8367 : Tree Nat := .node node4556 node8366 +def node8368 : Tree Nat := .node node7945 node8367 +def node8369 : Tree Nat := .node node8368 node7133 +def node8370 : Tree Nat := .node node8365 node8369 +def node8371 : Tree Nat := .leaf 772576568029280178646523537119820308525504531288880904667870437995235480901701593561818422508653526904609141948416 +def node8372 : Tree Nat := .leaf 22158278651228636258806456056038960038878377388039534658809823164819445497669790920225122172600951200721943477860173773644475208895141421602472685850601092013596158401757763023711934711634665164422500449800294086980252055384781669306179175386741448874562032390983120031206866944 +def node8373 : Tree Nat := .node node8371 node8372 +def node8374 : Tree Nat := .node node7954 node8373 +def node8375 : Tree Nat := .node node8374 node7529 +def node8376 : Tree Nat := .node node7952 node8375 +def node8377 : Tree Nat := .node node8370 node8376 +def node8378 : Tree Nat := .node node8361 node8377 +def node8379 : Tree Nat := .leaf 5839923990556409879860699655296372895863332489278156711141366422911072214027107065203947151723750654686057202412075453075126256213593839888846972300122453392207897786049631130882355894302351032320 +def node8380 : Tree Nat := .node node2191 node8379 +def node8381 : Tree Nat := .node node8380 node4569 +def node8382 : Tree Nat := .node node7536 node8381 +def node8383 : Tree Nat := .leaf 7331559403129590068331208687020758653624765228075687047537011123791632385370343464792392772051104864109916034360063928339045596353810784435313926666640532382851300168453118046895980276668702873639231039893172450578193216497554913833216745015892827460864 +def node8384 : Tree Nat := .node node5605 node8383 +def node8385 : Tree Nat := .node node7961 node8384 +def node8386 : Tree Nat := .node node8385 node7144 +def node8387 : Tree Nat := .node node8382 node8386 +def node8388 : Tree Nat := .leaf 94466423595368608180106839820715774271282075530789170645706786502423944162538328273524964908688340348845568827979912123825903579432145497525663584782161669917256462380892603448690236714579149808393392488079041939231637512945991270912022810920323888276341740535808 +def node8389 : Tree Nat := .node node4577 node8388 +def node8390 : Tree Nat := .node node7970 node8389 +def node8391 : Tree Nat := .node node8390 node7149 +def node8392 : Tree Nat := .node node7968 node8391 +def node8393 : Tree Nat := .node node8387 node8392 +def node8394 : Tree Nat := .leaf 382725258645104877886550812609503094103299358017333278221360589892093283696160708734338538031828695565672690736429000754506399966122516807110514713605009453278300414006347302027330580313627296708689920 +def node8395 : Tree Nat := .node node2386 node8394 +def node8396 : Tree Nat := .node node8395 node4584 +def node8397 : Tree Nat := .node node7549 node8396 +def node8398 : Tree Nat := .leaf 480481077043500814718154092512592439123952613987168226347385566848732410564040709169333908005514104237639946505977860748994115113715557595859798701972105653993197209103020177024997289519161519982318593993718068196330533906757601545264066171139228552979808256 +def node8399 : Tree Nat := .node node5620 node8398 +def node8400 : Tree Nat := .node node7976 node8399 +def node8401 : Tree Nat := .node node8400 node7155 +def node8402 : Tree Nat := .node node8397 node8401 +def node8403 : Tree Nat := .leaf 89110168312933500364085382923833814939320869282198436144124853865220218109544480205193609596042410160592465003299798007344424438047717162153820719044608472264381568346903160249700205230859520 +def node8404 : Tree Nat := .node node2011 node8403 +def node8405 : Tree Nat := .node node8404 node6393 +def node8406 : Tree Nat := .node node8405 node7558 +def node8407 : Tree Nat := .node node7983 node8406 +def node8408 : Tree Nat := .node node8402 node8407 +def node8409 : Tree Nat := .node node8393 node8408 +def node8410 : Tree Nat := .node node8378 node8409 +def node8411 : Tree Nat := .leaf 364995249409775617491293728456023305991458280579884794446335401431942013376694190920473024905389711982291384765887552584855096377710035039860212905577777135060159573948821196006697489374138859520 +def node8412 : Tree Nat := .node node2152 node8411 +def node8413 : Tree Nat := .node node8412 node7165 +def node8414 : Tree Nat := .node node7566 node8413 +def node8415 : Tree Nat := .node node8414 node7991 +def node8416 : Tree Nat := .leaf 10224965740585213362714659021898636472465378460393469070575939364923359258577686200959683584 +def node8417 : Tree Nat := .node node8416 node7993 +def node8418 : Tree Nat := .node node7574 node8417 +def node8419 : Tree Nat := .leaf 1567642659410349579823312128448524673447114170438997107594692976197222517221296078596611778818842307098800828712039654765432903841192663867213670841053688779459960362651485482378386248031428146139517419520 +def node8420 : Tree Nat := .node node2550 node8419 +def node8421 : Tree Nat := .node node8420 node4610 +def node8422 : Tree Nat := .node node8418 node8421 +def node8423 : Tree Nat := .leaf 106359737525781379605108474833793304158522309951378197960786959903126326889461660261747255647108909874379240409407194963301747559922682255118158835180618846611238502005076397301215868192572619647975918632931039428805550891695302269852728039155828404314032211927413208292404494336 +def node8424 : Tree Nat := .node node7999 node8423 +def node8425 : Tree Nat := .node node7998 node8424 +def node8426 : Tree Nat := .leaf 64183150194496800277205639044547499246191177813191806861664267089897642950134381149673493478985394927046041703856124304341969524906933631136588365824 +def node8427 : Tree Nat := .node node8426 node57 +def node8428 : Tree Nat := .node node7176 node8427 +def node8429 : Tree Nat := .node node8425 node8428 +def node8430 : Tree Nat := .node node8422 node8429 +def node8431 : Tree Nat := .node node8415 node8430 +def node8432 : Tree Nat := .leaf 23920328665319054867909425788093943381456209876083329888835036868243751788655030496164120160199620164471448192017206646201063596209604856372278912979945202323302617838309946191632696152556875934597120 +def node8433 : Tree Nat := .node node2347 node8432 +def node8434 : Tree Nat := .node node8433 node7182 +def node8435 : Tree Nat := .node node7583 node8434 +def node8436 : Tree Nat := .leaf 30030067315218800919884630782037027445247038374198014146711597563050526250476926831789640794321325523394216076738821850476730762665208973047046616203127649920337554213900730129655038904087870530184586942109605740098223057772300286899567109075862999806246912 +def node8437 : Tree Nat := .node node4623 node8436 +def node8438 : Tree Nat := .node node8006 node8437 +def node8439 : Tree Nat := .node node8438 node7187 +def node8440 : Tree Nat := .node node8435 node8439 +def node8441 : Tree Nat := .leaf 228024355644495814051728782503927203770612585078907155142020240709746456353934651238807495158004438902729453436086696948599186379505664 +def node8442 : Tree Nat := .node node8441 node356 +def node8443 : Tree Nat := .node node6788 node8442 +def node8444 : Tree Nat := .node node8012 node8443 +def node8445 : Tree Nat := .node node8444 node8017 +def node8446 : Tree Nat := .node node8440 node8445 +def node8447 : Tree Nat := .node node8431 node8446 +def node8448 : Tree Nat := .leaf 93438783848902558077771194484741966333813319828450507378261862766577155424433712900273360517538216788204391632984752792687823464059878436540908546368609508865450880680081704916634601728735151390720 +def node8449 : Tree Nat := .node node2230 node8448 +def node8450 : Tree Nat := .node node8449 node4636 +def node8451 : Tree Nat := .node node7599 node8450 +def node8452 : Tree Nat := .leaf 386934471046981733957067836228931709432148377789486431695762605409927701258194823958174911076266787151027009743868595383034763408637030051218625239128850371616139633470003074241484068109776349716878461216318957720719329064375740464845380138363506733329525826677417216 +def node8453 : Tree Nat := .node node4639 node8452 +def node8454 : Tree Nat := .node node8022 node8453 +def node8455 : Tree Nat := .node node8454 node7200 +def node8456 : Tree Nat := .node node8451 node8455 +def node8457 : Tree Nat := .leaf 503820925841965910293903145710484129446837736164208910110436259998038510964770243430138498201532542156933468707439014439278827305486272956953378568661190270002197943697085911178156113707745149093097147582381656359382513981546295610991449402511775459446453075705856 +def node8458 : Tree Nat := .node node4644 node8457 +def node8459 : Tree Nat := .node node8031 node8458 +def node8460 : Tree Nat := .node node8459 node7205 +def node8461 : Tree Nat := .node node8029 node8460 +def node8462 : Tree Nat := .node node8456 node8461 +def node8463 : Tree Nat := .leaf 6123604138321678046184813001752049505652789728277332451541769438270854843005160326157202471527600130662009900464317490247811218823329967371226587649969762800437816560665946622669663210107928719361310720 +def node8464 : Tree Nat := .node node2425 node8463 +def node8465 : Tree Nat := .node node8464 node4651 +def node8466 : Tree Nat := .node node8038 node8465 +def node8467 : Tree Nat := .leaf 7687697232696013035490465480201479025983241823794691621558168976373619191620825225088847795236974191558473969514814950181581893655156530627686282680200816261066621757443842027446022203131608843005806620258818016487867190782608776322500477074802997486073937920 +def node8468 : Tree Nat := .node node5664 node8467 +def node8469 : Tree Nat := .node node8041 node8468 +def node8470 : Tree Nat := .node node8469 node7211 +def node8471 : Tree Nat := .node node8466 node8470 +def node8472 : Tree Nat := .leaf 1425762693006936005825366126781341039029133908515174978305997661843523489752711683283097753536678562451201054737457211013696230932005074193369645160580527917364557469050327389504390580666417920 +def node8473 : Tree Nat := .node node2019 node8472 +def node8474 : Tree Nat := .node node8473 node4660 +def node8475 : Tree Nat := .node node8474 node7619 +def node8476 : Tree Nat := .node node8048 node8475 +def node8477 : Tree Nat := .node node8471 node8476 +def node8478 : Tree Nat := .node node8462 node8477 +def node8479 : Tree Nat := .node node8447 node8478 +def node8480 : Tree Nat := .node node8410 node8479 +def node8481 : Tree Nat := .leaf 1476037868677634502814169372198683972988782430168580791339168443419059466263441907636124424322481792125872508603866571594632270460771873670989385684165707380200540866460038741356697022991270145584560104331718701948419026674174784623175263203973562364946680905728 +def node8482 : Tree Nat := .node node6069 node8481 +def node8483 : Tree Nat := .node node6068 node8482 +def node8484 : Tree Nat := .node node8483 node7231 +def node8485 : Tree Nat := .node node8062 node8484 +def node8486 : Tree Nat := .node node8058 node8485 +def node8487 : Tree Nat := .leaf 7507516828804700229971157695509256861311759593549503536677899755757880972394849199241138654603637372306834599069499908954584122608315619955952381379664810549751709213975668464889213204985523122355019628130808203931465399204258565940460620584728971804934144 +def node8488 : Tree Nat := .node node4691 node8487 +def node8489 : Tree Nat := .node node6076 node8488 +def node8490 : Tree Nat := .node node8489 node7237 +def node8491 : Tree Nat := .node node7635 node8490 +def node8492 : Tree Nat := .leaf 96733617761657454776429403976412952853792845343528110741203743107911481181040928858841050272398166728761180723862999663303659308644297869994502119774289885363987390186413866677662301843539228121020234383001913945528933159500261078337364609888006388683037839049359360 +def node8493 : Tree Nat := .node node4696 node8492 +def node8494 : Tree Nat := .node node6465 node8493 +def node8495 : Tree Nat := .node node8494 node7639 +def node8496 : Tree Nat := .node node8068 node8495 +def node8497 : Tree Nat := .node node8491 node8496 +def node8498 : Tree Nat := .node node8486 node8497 +def node8499 : Tree Nat := .leaf 29326237612518360273324834748083034614499060912302748190148045920929222548417379684535697869545458485573572652615234019353844228938732890452938989764315666209967634492425450649932218187985406271949114338074467713943270251450768335949516902387610344801024 +def node8500 : Tree Nat := .node node4707 node8499 +def node8501 : Tree Nat := .node node6083 node8500 +def node8502 : Tree Nat := .node node8501 node7246 +def node8503 : Tree Nat := .node node7647 node8502 +def node8504 : Tree Nat := .leaf 125955231460491477573475786427621032361709434041052227527609040887818333099585254004833430151688207031373812084863225664102543636863020352647825304444791554918196632834013588603934073044213734760418168792503236230967902711806321479634502215673398687424126547656704 +def node8505 : Tree Nat := .node node4712 node8504 +def node8506 : Tree Nat := .node node6477 node8505 +def node8507 : Tree Nat := .leaf 4011446887156050017325352440284218702886948613324487928854016693118602684383398821854593342436587182940377606491008544823540434983077067928398462976 +def node8508 : Tree Nat := .node node8507 node57 +def node8509 : Tree Nat := .node node7250 node8508 +def node8510 : Tree Nat := .node node8506 node8509 +def node8511 : Tree Nat := .node node8075 node8510 +def node8512 : Tree Nat := .node node8503 node8511 +def node8513 : Tree Nat := .leaf 386934476812402743627727392523500921566280650861543810810833688600272750268648604429492230564398184166705557200461313728464455457327704017603969362112113072590911979446882282822841318695487157793960719627249744176439942155764713595136745007889278144305601008002662400 +def node8514 : Tree Nat := .node node7654 node8513 +def node8515 : Tree Nat := .node node6089 node8514 +def node8516 : Tree Nat := .node node8515 node7257 +def node8517 : Tree Nat := .node node7653 node8516 +def node8518 : Tree Nat := .leaf 14251522227780988378233048906495450235663286567431697196376265044359153522120915702425468447375277431420590885996831159547015081230336 +def node8519 : Tree Nat := .node node8518 node732 +def node8520 : Tree Nat := .node node6874 node8519 +def node8521 : Tree Nat := .node node8080 node8520 +def node8522 : Tree Nat := .node node8521 node8085 +def node8523 : Tree Nat := .node node8517 node8522 +def node8524 : Tree Nat := .node node8512 node8523 +def node8525 : Tree Nat := .node node8498 node8524 +def node8526 : Tree Nat := .leaf 7872201966280717348342236651726314522606839627565764220475565046817526677545920985684922536296458463682987175223744519303708112553500306298026726936267447320351671548130900671902569361791403123491931042452089688837469570699538089003040708937269945617310273241088 +def node8527 : Tree Nat := .node node6110 node8526 +def node8528 : Tree Nat := .node node6503 node8527 +def node8529 : Tree Nat := .node node8528 node7274 +def node8530 : Tree Nat := .node node8098 node8529 +def node8531 : Tree Nat := .node node8094 node8530 +def node8532 : Tree Nat := .leaf 6491683198595054907538359059679767099519165326776190606872841682895938675156205829827954246070653506325448497533049877936699207677031205602503774949860278085605632612357821261387061533623666597915695999467843264620941350699024847324834066073131331220863760578833285757534208 +def node8533 : Tree Nat := .node node4754 node8532 +def node8534 : Tree Nat := .node node6117 node8533 +def node8535 : Tree Nat := .node node8534 node7280 +def node8536 : Tree Nat := .node node7676 node8535 +def node8537 : Tree Nat := .node node8536 node8105 +def node8538 : Tree Nat := .node node8531 node8537 +def node8539 : Tree Nat := .leaf 1407659405400881293119592067907985661495954923790531913127106135771543901259824389395270939209683637473092444482594868181214229146124038676882436803170665099849763577476620005166104186039473614004181804292084857139438539577971440178739884764108684691282176 +def node8540 : Tree Nat := .node node7689 node8539 +def node8541 : Tree Nat := .node node6131 node8540 +def node8542 : Tree Nat := .node node8541 node7287 +def node8543 : Tree Nat := .node node7688 node8542 +def node8544 : Tree Nat := .leaf 2015283703367863641175612582841936517787350944656835640441746215724148601621265841204650329199635253963361704077586753776847457138833007799872461733478875211739115875409877674453698529508861490870289000582657415704114650896457171058077581399733125408895416940888064 +def node8545 : Tree Nat := .node node4775 node8544 +def node8546 : Tree Nat := .node node6523 node8545 +def node8547 : Tree Nat := .node node8546 node7292 +def node8548 : Tree Nat := .node node8114 node8547 +def node8549 : Tree Nat := .node node8543 node8548 +def node8550 : Tree Nat := .leaf 30750788930784052141961861920805916103932967295178766486232677399584280462929302320091703929256498676968794517788671627077976566203660779339580954131107064011783000940444338032186217287620702709166160396823790403303282275140643086092144835525642926844987572224 +def node8551 : Tree Nat := .node node7695 node8550 +def node8552 : Tree Nat := .node node6142 node8551 +def node8553 : Tree Nat := .node node8552 node7298 +def node8554 : Tree Nat := .node node8120 node8553 +def node8555 : Tree Nat := .leaf 12361225088468482858344376593917124936408072500622094474685927007923767694427225496989094760138456258211060524253184 +def node8556 : Tree Nat := .node node8555 node990 +def node8557 : Tree Nat := .node node6529 node8556 +def node8558 : Tree Nat := .node node8557 node8128 +def node8559 : Tree Nat := .node node8125 node8558 +def node8560 : Tree Nat := .node node8554 node8559 +def node8561 : Tree Nat := .node node8549 node8560 +def node8562 : Tree Nat := .node node8538 node8561 +def node8563 : Tree Nat := .node node8525 node8562 +def node8564 : Tree Nat := .node node8480 node8563 +def node8565 : Tree Nat := .leaf 232684471498731956150699751890714857569554653869676556459538818412863033527642546711801553377185941388710757788253314772845123940790147337910885727305832923600851728392373512454269649476013522944 +def node8566 : Tree Nat := .node node2132 node8565 +def node8567 : Tree Nat := .node node8566 node4801 +def node8568 : Tree Nat := .node node7716 node8567 +def node8569 : Tree Nat := .node node8568 node8141 +def node8570 : Tree Nat := .leaf 246006311446272417135694895366447328831463738361430131889861431156838576362961852515446525481023680143855294183974317434142246651505180562231895715108936611904346243247650712860812838832763726475757469314046813199027419852434063843710254500553219693197867876352 +def node8571 : Tree Nat := .node node4809 node8570 +def node8572 : Tree Nat := .node node8148 node8571 +def node8573 : Tree Nat := .leaf 27277838832661140117812396593932687179631250570606517916207313513206498253807111988611234728568792843994567724138852794865240721877607072522722869248 +def node8574 : Tree Nat := .node node8573 node57 +def node8575 : Tree Nat := .node node7318 node8574 +def node8576 : Tree Nat := .node node8572 node8575 +def node8577 : Tree Nat := .node node8146 node8576 +def node8578 : Tree Nat := .node node8569 node8577 +def node8579 : Tree Nat := .leaf 15249209524140897478292258939909888905678333796003122804132336003505391765267581941304626602127257854850548222410969236953178042583623095937327807024715066481105418871922590697165843797255008408305664 +def node8580 : Tree Nat := .node node2327 node8579 +def node8581 : Tree Nat := .node node8580 node4816 +def node8582 : Tree Nat := .node node7729 node8581 +def node8583 : Tree Nat := .leaf 5038209277188451174950782032032735533241519514921488084978120461898471477897997039390360064761788042075263239288725481914241459234708782421616107002040725719743862173409230286686137052826158173682441604956680316096401141337133087803172922133199020088565273607536640 +def node8584 : Tree Nat := .node node7731 node8583 +def node8585 : Tree Nat := .node node8154 node8584 +def node8586 : Tree Nat := .node node8585 node7325 +def node8587 : Tree Nat := .node node8582 node8586 +def node8588 : Tree Nat := .leaf 96910351148910720971984732564169061602510348658535540935358602301642243950422226776493185442151886533660017708281672309809784614289408 +def node8589 : Tree Nat := .node node8588 node4311 +def node8590 : Tree Nat := .node node6938 node8589 +def node8591 : Tree Nat := .node node8160 node8590 +def node8592 : Tree Nat := .leaf 3550483268718444155131526975871503563988565885462593940117474646192368065302162883175682882342314779490825771915486370435258849194185597807478114735501601007093074468877769660251260128893184 +def node8593 : Tree Nat := .node node1114 node8592 +def node8594 : Tree Nat := .leaf 16122269626942909129404900662735492142298807557254685123533957184651913530173488143140175045399694454793530120643833336854120273827326569235989965521099697146633949788456186742658554670483112520032523968788009881517608573530460012705065966077405658779625355976114176 +def node8595 : Tree Nat := .node node4824 node8594 +def node8596 : Tree Nat := .node node8593 node8595 +def node8597 : Tree Nat := .node node8596 node8164 +def node8598 : Tree Nat := .node node8591 node8597 +def node8599 : Tree Nat := .node node8587 node8598 +def node8600 : Tree Nat := .node node8578 node8599 +def node8601 : Tree Nat := .leaf 11679847981112819759721399310592745791726664978556313422282732845822144428054214112112559700232718557454829397387472315931495401827463221378240693086614024419606852314406968924545666119594273669120 +def node8602 : Tree Nat := .node node2210 node8601 +def node8603 : Tree Nat := .node node8602 node7334 +def node8604 : Tree Nat := .node node7749 node8603 +def node8605 : Tree Nat := .leaf 14663118806259180136662417374041517307249530456151374095074022247583264770740686929584785544102209728219832068720127856678091192707621568870627853333281064765702609028127115591223318860797574361119463675358036235605096422543570012521803281065056470608384 +def node8606 : Tree Nat := .node node4835 node8605 +def node8607 : Tree Nat := .node node8170 node8606 +def node8608 : Tree Nat := .node node8607 node7341 +def node8609 : Tree Nat := .node node8604 node8608 +def node8610 : Tree Nat := .leaf 62977615730245738786737893213810516180854717020526113763804532499754813870596280428767312275191567769616683588429876804909853413215950765891206786754861930073751493655524174277358398551322961473724223276722913823597735786106325561035518105102745088762894857797632 +def node8611 : Tree Nat := .node node6181 node8610 +def node8612 : Tree Nat := .node node8179 node8611 +def node8613 : Tree Nat := .node node8612 node7346 +def node8614 : Tree Nat := .node node8177 node8613 +def node8615 : Tree Nat := .node node8609 node8614 +def node8616 : Tree Nat := .leaf 765450517290209755773101625219006188206598716034666556442721179783849078037153031883969191489163494982963098352043257115483049157692621908634928676373593221845604958566680145566296921156720856997560320 +def node8617 : Tree Nat := .node node2444 node8616 +def node8618 : Tree Nat := .node node8617 node5808 +def node8619 : Tree Nat := .node node7762 node8618 +def node8620 : Tree Nat := .leaf 960962154087001629436308185025184878247905227974336452694771133697464821128081418338667816011028208475279893011955721497988230227431115191719579108609608093203642500921032917371404360281212440240178788534184622761778703004571945398234795123232788095531220992 +def node8621 : Tree Nat := .node node4850 node8620 +def node8622 : Tree Nat := .node node8185 node8621 +def node8623 : Tree Nat := .node node8622 node7352 +def node8624 : Tree Nat := .node node8619 node8623 +def node8625 : Tree Nat := .leaf 178220336625867000728170765847667629878641738564396872288249707730440436219088960410387219192084820306051383922649788493900567064987676160050760769325925902815444319834962826408009792990763520 +def node8626 : Tree Nat := .node node2038 node8625 +def node8627 : Tree Nat := .node node8626 node4856 +def node8628 : Tree Nat := .node node8627 node7771 +def node8629 : Tree Nat := .node node8192 node8628 +def node8630 : Tree Nat := .node node8624 node8629 +def node8631 : Tree Nat := .node node8615 node8630 +def node8632 : Tree Nat := .node node8600 node8631 +def node8633 : Tree Nat := .leaf 3936100983140358674171118325863157261303419813782882110237782515784158576702511753696331798193284779002326689610310857585686054911695675110865276703759352853223154758832733764608829945741089476503393354251048438033943313404605743180295633495012978933329689575424 +def node8634 : Tree Nat := .node node4876 node8633 +def node8635 : Tree Nat := .node node6593 node8634 +def node8636 : Tree Nat := .node node8635 node7365 +def node8637 : Tree Nat := .node node8205 node8636 +def node8638 : Tree Nat := .node node8201 node8637 +def node8639 : Tree Nat := .leaf 60060134630437601839769261564074054890494076748396028293423195126101052500953853663579281588642651046788432153477643700953461525330417946094104048478207709763176159757321137743629434871613785393034524070351144776929069937854466031714255367356127841852850176 +def node8640 : Tree Nat := .node node5830 node8639 +def node8641 : Tree Nat := .node node6212 node8640 +def node8642 : Tree Nat := .node node8641 node7371 +def node8643 : Tree Nat := .node node7786 node8642 +def node8644 : Tree Nat := .node node8643 node8212 +def node8645 : Tree Nat := .node node8638 node8644 +def node8646 : Tree Nat := .leaf 186877567697805116155542388969483932667626639656901014756523725533154310848867425752917525922796608088177192129290778082348044617843379232779329856953129681518605853214439338910676687098116455792640 +def node8647 : Tree Nat := .node node2288 node8646 +def node8648 : Tree Nat := .node node8647 node7380 +def node8649 : Tree Nat := .node node7797 node8648 +def node8650 : Tree Nat := .leaf 234609900900146882186598677984664276915992487298421985521184356139552572957717991601527334553302985530159051663918917995099166813762381321019006063719716228336061772382349628191558129834602859122675527798195226393248725910590714119939845591986030417828352 +def node8651 : Tree Nat := .node node7799 node8650 +def node8652 : Tree Nat := .node node8216 node8651 +def node8653 : Tree Nat := .node node8652 node7385 +def node8654 : Tree Nat := .node node8649 node8653 +def node8655 : Tree Nat := .leaf 4345610439748715679153730084306920500797785845667224354994774230092427684895516635407865088 +def node8656 : Tree Nat := .node node8655 node8220 +def node8657 : Tree Nat := .node node7805 node8656 +def node8658 : Tree Nat := .node node8657 node8225 +def node8659 : Tree Nat := .leaf 1007641851683931820587806291420968258893675472328417820220872422018410808782691747903268968370272993869231284977558804210246642284565219582901844849086204362360202212342377319877889387859000223644702594310335746863216311715569925504140250155883048954633772431572992 +def node8660 : Tree Nat := .node node8229 node8659 +def node8661 : Tree Nat := .node node8228 node8660 +def node8662 : Tree Nat := .node node8661 node7390 +def node8663 : Tree Nat := .node node8658 node8662 +def node8664 : Tree Nat := .node node8654 node8663 +def node8665 : Tree Nat := .leaf 12247208276643356092369626003504099011305579456554664903083538876540831082437647648501701735168529000960074862748189891739282416077154773542435728652510618511069353371824391918010931335901864479938314240 +def node8666 : Tree Nat := .node node2491 node8665 +def node8667 : Tree Nat := .node node8666 node7395 +def node8668 : Tree Nat := .node node8237 node8667 +def node8669 : Tree Nat := .leaf 15375394465392026070980930960402958051966483647589383243116337953212607326239114362479095094255378098256057246768983013282241424136039128310657658784004739276505126292309199631398673951953465567591907916339407487587400228766921009429747979058001741686052487168 +def node8670 : Tree Nat := .node node4917 node8669 +def node8671 : Tree Nat := .node node8240 node8670 +def node8672 : Tree Nat := .node node8671 node7400 +def node8673 : Tree Nat := .node node8668 node8672 +def node8674 : Tree Nat := .leaf 2851525386013872011650732253562682078058267817030349956611995323687046979505423366566195507073357124863004162686531124235843080165819001433981154054995169659095558688624559425675887151604055040 +def node8675 : Tree Nat := .node node2093 node8674 +def node8676 : Tree Nat := .leaf 5253520662599105214796360052414778097973430812764390151741518978367601270131570836220365273058843909261193262399488 +def node8677 : Tree Nat := .node node8676 node1493 +def node8678 : Tree Nat := .node node8675 node8677 +def node8679 : Tree Nat := .node node8678 node7823 +def node8680 : Tree Nat := .node node8247 node8679 +def node8681 : Tree Nat := .node node8673 node8680 +def node8682 : Tree Nat := .node node8664 node8681 +def node8683 : Tree Nat := .node node8645 node8682 +def node8684 : Tree Nat := .node node8632 node8683 +def node8685 : Tree Nat := .leaf 930737885994927824602799007562859430278218615478706225838155273651452134110570186847206213508743765554843031153013259091380495763160589351643542909223331694403406913569494049816935045665931657216 +def node8686 : Tree Nat := .node node2141 node8685 +def node8687 : Tree Nat := .node node8686 node4932 +def node8688 : Tree Nat := .node node7832 node8687 +def node8689 : Tree Nat := .node node8688 node8258 +def node8690 : Tree Nat := .leaf 984025245785089668542779581465789315325854953445720527559445628946039644175627938424082949548321194750581672402577714396421513859037923273301412255683888153063930857810419861523821693096910777230060742075186571822795544203703804864509687558125217144474112622592 +def node8691 : Tree Nat := .node node4944 node8690 +def node8692 : Tree Nat := .node node8268 node8691 +def node8693 : Tree Nat := .node node8692 node7418 +def node8694 : Tree Nat := .node node8266 node8693 +def node8695 : Tree Nat := .node node8689 node8694 +def node8696 : Tree Nat := .leaf 60996838096563589913169035759639555622713335184012491216529344014021567061070327765218506408509031419402192889643876947812712170334492383749311228098860265924421675487690362172111207185559154533072896 +def node8697 : Tree Nat := .node node2375 node8696 +def node8698 : Tree Nat := .node node8697 node4951 +def node8699 : Tree Nat := .node node7849 node8698 +def node8700 : Tree Nat := .leaf 15015033657609400459942315391018513722623519187099007073355799146520512535014080907188548853183968753155388618254205371573766813274617863217713842286304715709791436136566571042225841554874668534674999396048710830085795738248943183059725234471968569471008768 +def node8701 : Tree Nat := .node node7851 node8700 +def node8702 : Tree Nat := .node node8274 node8701 +def node8703 : Tree Nat := .node node8702 node7424 +def node8704 : Tree Nat := .node node8699 node8703 +def node8705 : Tree Nat := .leaf 14201933074873776620526107903486014255954263541850375760469898584769472261208651532702731529369259117963303087661945481741035396776742391229912458942006404028372297875511078641005040515442176 +def node8706 : Tree Nat := .node node1616 node8705 +def node8707 : Tree Nat := .leaf 21014082650396420859185440209659112391893723251057560606966075913470405080526283344881461092235375589194027008786432 +def node8708 : Tree Nat := .node node8707 node1620 +def node8709 : Tree Nat := .node node8706 node8708 +def node8710 : Tree Nat := .node node8709 node8284 +def node8711 : Tree Nat := .node node8281 node8710 +def node8712 : Tree Nat := .node node8704 node8711 +def node8713 : Tree Nat := .node node8695 node8712 +def node8714 : Tree Nat := .leaf 58652475225036720546649669496166069228998121824605496380296091841858445096834759369071395739090916971147145305230468038707688457877465780905877979528631332419935229586904112916566644826589114352751275918012669262000364869345287195803680471881210960821248 +def node8715 : Tree Nat := .node node5895 node8714 +def node8716 : Tree Nat := .node node6280 node8715 +def node8717 : Tree Nat := .node node8716 node7435 +def node8718 : Tree Nat := .node node7872 node8717 +def node8719 : Tree Nat := .leaf 251910462920982955146951572855242064723418868082104455055218081775636666199170508009666860303376414062747624169726451328205087273388551350127265024181698535342497117285744056393123752558676694968424631998905721625510120712616773513254545942982557904314516675493888 +def node8720 : Tree Nat := .node node6288 node8719 +def node8721 : Tree Nat := .node node6669 node8720 +def node8722 : Tree Nat := .node node8721 node7440 +def node8723 : Tree Nat := .node node8292 node8722 +def node8724 : Tree Nat := .node node8718 node8723 +def node8725 : Tree Nat := .leaf 3843848616348006517745232740100739512991620911897345810779084674948035057866162790011462991157062334621099314723583953384747070775457597417447620901725554238548428361558671410374436063187860294487062420503823097720698652196731738404402392986953772121486000128 +def node8726 : Tree Nat := .node node4985 node8725 +def node8727 : Tree Nat := .node node6295 node8726 +def node8728 : Tree Nat := .node node8727 node7446 +def node8729 : Tree Nat := .node node8298 node8728 +def node8730 : Tree Nat := .node node8729 node8304 +def node8731 : Tree Nat := .node node8724 node8730 +def node8732 : Tree Nat := .node node8713 node8731 +def node8733 : Tree Nat := .leaf 3665779701564795034165604343510379326812382614037843523768505561895816192685171732396196386025552432054958017180031964169522798176905392217656963333320266191425658136387079734303513276128331181995837586432123785145989686801027334062024502435829669481472 +def node8734 : Tree Nat := .node node5002 node8733 +def node8735 : Tree Nat := .node node6310 node8734 +def node8736 : Tree Nat := .node node8735 node7456 +def node8737 : Tree Nat := .node node7886 node8736 +def node8738 : Tree Nat := .leaf 15744403932561434696684473303452629045213679255131528440951130124133472403373636927954362952412694738722641942453734646872088232117784143131217336481788098895219052797358246165743612629938891414230053959559793427105072103609913921851262195654059482283758262943744 +def node8739 : Tree Nat := .node node5007 node8738 +def node8740 : Tree Nat := .node node6690 node8739 +def node8741 : Tree Nat := .node node8740 node7461 +def node8742 : Tree Nat := .node node8311 node8741 +def node8743 : Tree Nat := .node node8737 node8742 +def node8744 : Tree Nat := .leaf 240240538521750407359077046256296219561976306993584113173692780504404210003815414654317126354570604187153728613910574803813846101321671784376387763095127361542130446963118541587164000919703710754846318649286354442019097132774789208908703019980861152323174400 +def node8745 : Tree Nat := .node node5932 node8744 +def node8746 : Tree Nat := .node node6316 node8745 +def node8747 : Tree Nat := .node node8746 node7467 +def node8748 : Tree Nat := .node node7892 node8747 +def node8749 : Tree Nat := .node node8748 node8318 +def node8750 : Tree Nat := .node node8743 node8749 +def node8751 : Tree Nat := .leaf 938439603600587528746394711938657107663969949193687942084737423859530878402277740113952382726027436862023515939938558587867734918057252668928834146032719674374224983287165909829024025477178573316739862219650287211297696408957875015419155376909990223701504 +def node8752 : Tree Nat := .node node5033 node8751 +def node8753 : Tree Nat := .node node6328 node8752 +def node8754 : Tree Nat := .node node8753 node7480 +def node8755 : Tree Nat := .node node7904 node8754 +def node8756 : Tree Nat := .leaf 17382441758994862716614920337227682003191143382668897419979096920369710739582066541631416832 +def node8757 : Tree Nat := .node node8756 node8321 +def node8758 : Tree Nat := .node node5945 node8757 +def node8759 : Tree Nat := .node node8758 node7080 +def node8760 : Tree Nat := .leaf 4030567406735727282351225165683873035574701889313671280883490863805637792892951859097172209874597060812552969158065912860718717055148794303666326855178931581171132949991043309252631626113881789076710787494473777719449841832551690630672784413218219389644694364356608 +def node8761 : Tree Nat := .node node8325 node8760 +def node8762 : Tree Nat := .node node6715 node8761 +def node8763 : Tree Nat := .node node8762 node7908 +def node8764 : Tree Nat := .node node8759 node8763 +def node8765 : Tree Nat := .node node8755 node8764 +def node8766 : Tree Nat := .leaf 61501577861568104283923723841611832207865934590357532972465353304148019343417675395844296102641536012924471780369225201966148867172834767739755898004704115547305722415376674988957047008766642318028797526215519560031419343867671277812652694007776318885229232128 +def node8767 : Tree Nat := .node node5048 node8766 +def node8768 : Tree Nat := .node node6339 node8767 +def node8769 : Tree Nat := .node node8768 node7490 +def node8770 : Tree Nat := .node node8334 node8769 +def node8771 : Tree Nat := .leaf 387641404595642883887938930256676246410041394634142163741434409206568975801688907105972741768607546134640070627609299904752178757107712 +def node8772 : Tree Nat := .node node8771 node4522 +def node8773 : Tree Nat := .node node7098 node8772 +def node8774 : Tree Nat := .node node8338 node8773 +def node8775 : Tree Nat := .node node8774 node7915 +def node8776 : Tree Nat := .node node8770 node8775 +def node8777 : Tree Nat := .node node8765 node8776 +def node8778 : Tree Nat := .node node8750 node8777 +def node8779 : Tree Nat := .node node8732 node8778 +def node8780 : Tree Nat := .node node8684 node8779 +def node8781 : Tree Nat := .node node8564 node8780 +def node8782 : Tree Nat := .leaf 50631577962366905787778566528684543739527464962548098968313557024455752476373915635667332137527116602111454263478583296 +def node8783 : Tree Nat := .leaf 1584883593408437182288149857193704281834079755425736424225843631759063864353201003683274660150897466442150608604894308408330506188540761574895954701162100250985755648757051555070570178535076031952805070396344500818139181139189923519932181691743049135541340210479614656512 +def node8784 : Tree Nat := .node node8782 node8783 +def node8785 : Tree Nat := .node node8348 node8784 +def node8786 : Tree Nat := .node node7501 node8785 +def node8787 : Tree Nat := .leaf 420810872123869880579279190630410293244027184225853908759862472245498572343766465769093322902207076098158637508494257417041554580014704309050225181652150467996417893690275567855333100635388092529023636169734225920 +def node8788 : Tree Nat := .node node2869 node8787 +def node8789 : Tree Nat := .node node8788 node5069 +def node8790 : Tree Nat := .node node7925 node8789 +def node8791 : Tree Nat := .node node8786 node8790 +def node8792 : Tree Nat := .node node8791 node8360 +def node8793 : Tree Nat := .leaf 103866931177520872754840820432866496974457535077309780222534099080316302633872561171546227845560504397596143450834297555297700588978704004458870740372654633956795522493060012770364175913112060462214348824043684864633789570838700187215575407415703329429743819352822344818098176 +def node8794 : Tree Nat := .node node7127 node8793 +def node8795 : Tree Nat := .node node8363 node8794 +def node8796 : Tree Nat := .node node7518 node8795 +def node8797 : Tree Nat := .leaf 27578261315509936493643641037154568978040565545425561764486346981080994437121079100643300009719042939168924467756679654083235320955843661597915557504755333070613243080885899614967110082936557887927319044524404029521920 +def node8798 : Tree Nat := .node node3101 node8797 +def node8799 : Tree Nat := .node node8798 node5080 +def node8800 : Tree Nat := .node node8368 node8799 +def node8801 : Tree Nat := .node node8796 node8800 +def node8802 : Tree Nat := .leaf 6421064332944791878956286478125157062439379642118132152707862430503823430538428737931721846041978089876688194404514425919213174133525151200107195764955909240667997645420464597403121720636350094545462304440320 +def node8803 : Tree Nat := .node node2697 node8802 +def node8804 : Tree Nat := .node node8803 node5085 +def node8805 : Tree Nat := .node node7951 node8804 +def node8806 : Tree Nat := .node node8805 node8375 +def node8807 : Tree Nat := .node node8801 node8806 +def node8808 : Tree Nat := .node node8792 node8807 +def node8809 : Tree Nat := .leaf 135243399970730303066198984938628251268824915465247109664758362321700642924402143304641447917533484128220870972182584804266126473805031264001907071809414738764645149741253795804612310079745183613883253849683716381929891660838090080710484939184996726073850900345990661799936 +def node8810 : Tree Nat := .node node4568 node8809 +def node8811 : Tree Nat := .node node8380 node8810 +def node8812 : Tree Nat := .node node7536 node8811 +def node8813 : Tree Nat := .leaf 107727583263710689428295472801385035070470959161818600642524792894847634520016880401658741613032833448481059681185642099472614489684169269837580286098326478621041859843397875500861560700511182426828448165267001835520 +def node8814 : Tree Nat := .node node2993 node8813 +def node8815 : Tree Nat := .node node8814 node5096 +def node8816 : Tree Nat := .node node8385 node8815 +def node8817 : Tree Nat := .node node8812 node8816 +def node8818 : Tree Nat := .leaf 25082282550565593277172994055176394775153826727023953721569484087644816440172561589274934383979146236216750381696355286268398564008017037806015067302740368068819350077214203584152067524825640703545908920320 +def node8819 : Tree Nat := .node node2589 node8818 +def node8820 : Tree Nat := .node node8819 node5999 +def node8821 : Tree Nat := .node node7967 node8820 +def node8822 : Tree Nat := .node node8821 node8391 +def node8823 : Tree Nat := .node node8817 node8822 +def node8824 : Tree Nat := .leaf 8863311460481781141746416676937941075153709659930434578990017707034705983741023518228539249258145024310264383459425172937101079503843345104138631358247589963767318400459158956662320883200518008243421657655443366802216578530898360023666847625671689572150747616767214773963063296 +def node8825 : Tree Nat := .node node4583 node8824 +def node8826 : Tree Nat := .node node8395 node8825 +def node8827 : Tree Nat := .node node7549 node8826 +def node8828 : Tree Nat := .leaf 7060034896770543742372772105511569658378384779628943811708504827156734575902996249764684802488074993113824621717883791719270515909698447922580839509077773455076002797688492169770475085125348310679048451642082073268715520 +def node8829 : Tree Nat := .node node3209 node8828 +def node8830 : Tree Nat := .node node8829 node5111 +def node8831 : Tree Nat := .node node8400 node8830 +def node8832 : Tree Nat := .node node8827 node8831 +def node8833 : Tree Nat := .leaf 1643792469233866721012809338400040207984481188382241831093212782209808822456260244774165573039156454528904426953284714066564312477191717615750000952660321863601140264620521997768503431616298957404882685835345920 +def node8834 : Tree Nat := .node node2822 node8833 +def node8835 : Tree Nat := .node node8834 node5116 +def node8836 : Tree Nat := .node node7982 node8835 +def node8837 : Tree Nat := .leaf 2063650512248692368563827284830142994214247367328599695812346920951965740911698917089847288633477292674799487825670203271184114749717975751385077121862258892449068682367131942885388077598404270131123372826376306959296835686522994865408120603016149307219071391787646976 +def node8838 : Tree Nat := .node node6392 node8837 +def node8839 : Tree Nat := .node node8404 node8838 +def node8840 : Tree Nat := .node node8839 node7558 +def node8841 : Tree Nat := .node node8836 node8840 +def node8842 : Tree Nat := .node node8832 node8841 +def node8843 : Tree Nat := .node node8823 node8842 +def node8844 : Tree Nat := .node node8808 node8843 +def node8845 : Tree Nat := .leaf 810105247397870492604457064458952699832439439400769583493016912391292039621982650170677314200433865589684020664445435904 +def node8846 : Tree Nat := .leaf 25359685232396118344188732546456419720150332619533882545491075121616821967350973292968074969528487575463640107840105879008155952377043954513472639693199847170566282887030201739930981541859300934021509924502578088559481622449875403922472091130786242149375070930621318561792 +def node8847 : Tree Nat := .node node8845 node8846 +def node8848 : Tree Nat := .node node8412 node8847 +def node8849 : Tree Nat := .node node7566 node8848 +def node8850 : Tree Nat := .leaf 6732973953981918089268467050086564691904434947613662540157799555927977157500263452305493166435313217570538200135908118672664873280235268944803602906434407487942686299044409085685329610166209480464378178715747614720 +def node8851 : Tree Nat := .node node2954 node8850 +def node8852 : Tree Nat := .leaf 14943804171517677669694097490177373226310866375731259319387438495153943763611461303586488002674978907929277444287967560317025803504172662784 +def node8853 : Tree Nat := .node node8852 node278 +def node8854 : Tree Nat := .node node8851 node8853 +def node8855 : Tree Nat := .node node7990 node8854 +def node8856 : Tree Nat := .node node8849 node8855 +def node8857 : Tree Nat := .node node8856 node8430 +def node8858 : Tree Nat := .leaf 1661870898840333964077453126925863951591320561236956483560547308926393061512991831472304467689529197896884884310959041281449526985811584066946436220283887735378359893633602830359002209204210265522351144291017046490433600747040687917211849068385325925057365530457925464545558528 +def node8859 : Tree Nat := .node node7181 node8858 +def node8860 : Tree Nat := .node node8433 node8859 +def node8861 : Tree Nat := .node node7583 node8860 +def node8862 : Tree Nat := .leaf 441252181048158983898298256594473103648649048726808988231781551697295910993937265610292800155504687026702791484106874465331765135293498585566648920076085329129811889294174393839473761326984926206837104712390464472350720 +def node8863 : Tree Nat := .node node3179 node8862 +def node8864 : Tree Nat := .leaf 979357150184582523761072373116264331759508938799923810755375169218408858492040727991844077743307417710053126584734793018944572216833303331733504 +def node8865 : Tree Nat := .node node8864 node340 +def node8866 : Tree Nat := .node node8863 node8865 +def node8867 : Tree Nat := .node node8438 node8866 +def node8868 : Tree Nat := .node node8861 node8867 +def node8869 : Tree Nat := .leaf 102737029327116670063300583650002512999030074273890114443325798888061174888614859806907549536671649438027011110472230814707410786136402419201715132239294547850687962326727433558449947530181601512727396871045120 +def node8870 : Tree Nat := .node node2783 node8869 +def node8871 : Tree Nat := .node node8870 node8442 +def node8872 : Tree Nat := .node node8012 node8871 +def node8873 : Tree Nat := .leaf 128978157015543273035239205301883937138390460458037480988271658476587503615485762282482882249132034960883524620011322272984532960373565064819057473128812604655619868258722904552411631146197497845534209711071408340708049125634780442968088009084279134803396919044341760 +def node8874 : Tree Nat := .node node4628 node8873 +def node8875 : Tree Nat := .node node8015 node8874 +def node8876 : Tree Nat := .node node8875 node7592 +def node8877 : Tree Nat := .node node8872 node8876 +def node8878 : Tree Nat := .node node8868 node8877 +def node8879 : Tree Nat := .node node8857 node8878 +def node8880 : Tree Nat := .leaf 2163894399531684849059183759018052020301198647443953754636131356444151968345126933054957510300834930693865425602250549665918999689160906378529052407677803019192953075762511466180778120259358852537139570288885879638163887349626037693074198094976262366244946068446066130288640 +def node8881 : Tree Nat := .node node4635 node8880 +def node8882 : Tree Nat := .node node8449 node8881 +def node8883 : Tree Nat := .node node7599 node8882 +def node8884 : Tree Nat := .leaf 1723641332219371030852727564822160561127535346589097610280396686317562152320097222372740641621745989494466950780564947066749566980669961503330153135681214229832001739903111619216468820693803942882309447645906516049920 +def node8885 : Tree Nat := .node node3071 node8884 +def node8886 : Tree Nat := .node node8885 node7199 +def node8887 : Tree Nat := .node node8454 node8886 +def node8888 : Tree Nat := .node node8883 node8887 +def node8889 : Tree Nat := .leaf 401316520809049492434767904882822316402461227632383259544369299944595410610371500159237241401170150683197996018332851280586674863484767747463028676352255593600167962206823070632717207413070931811310155857920 +def node8890 : Tree Nat := .node node2658 node8889 +def node8891 : Tree Nat := .node node8890 node5164 +def node8892 : Tree Nat := .node node8028 node8891 +def node8893 : Tree Nat := .node node8892 node8460 +def node8894 : Tree Nat := .node node8888 node8893 +def node8895 : Tree Nat := .leaf 425438950103125494805269443724151674051532525954198637108871527674937080267384167241679774515438718500479706332744706411622303984140235025072243327396350123989858381302839728641970883802796914302165200527438893528841914471261693966929719286220792601629733627047093023870919114752 +def node8896 : Tree Nat := .node node4650 node8895 +def node8897 : Tree Nat := .node node8464 node8896 +def node8898 : Tree Nat := .node node8038 node8897 +def node8899 : Tree Nat := .node node8898 node8470 +def node8900 : Tree Nat := .leaf 26300679507741867536204949414400643327751699014115869297491404515345612340670377960081877970061413722558659352122458835575148120428101811676165285362297626616757796609707440724235373260825329373938375506966609920 +def node8901 : Tree Nat := .node node2877 node8900 +def node8902 : Tree Nat := .node node8901 node6818 +def node8903 : Tree Nat := .node node8047 node8902 +def node8904 : Tree Nat := .leaf 33018408195979077897021236557282287907427957877257595132997647051196446026465367017734728495491573273491423577193013868229034783643806460937965593703470395206212194761048289991360427265562788968233216271895438569807102456259299336110958256120469961382108888702979670016 +def node8905 : Tree Nat := .node node4659 node8904 +def node8906 : Tree Nat := .node node8473 node8905 +def node8907 : Tree Nat := .node node8906 node7619 +def node8908 : Tree Nat := .node node8903 node8907 +def node8909 : Tree Nat := .node node8899 node8908 +def node8910 : Tree Nat := .node node8894 node8909 +def node8911 : Tree Nat := .node node8879 node8910 +def node8912 : Tree Nat := .node node8844 node8911 +def node8913 : Tree Nat := .leaf 6339534373627982956228077418998199278226167912433458265535528508320086830680698313693007070651886254736092739919085544146588171130259015275454040340011033497312981205779359999992397783151564210460055654015843657383509380418671267638639561297356782893043405751017747251200 +def node8914 : Tree Nat := .node node7218 node8913 +def node8915 : Tree Nat := .node node6449 node8914 +def node8916 : Tree Nat := .node node7628 node8915 +def node8917 : Tree Nat := .node node8916 node8057 +def node8918 : Tree Nat := .node node8917 node8485 +def node8919 : Tree Nat := .leaf 138489241570027830339787760577155329299276713436413040296712239834671667222519509857534438512449076334420686419713039265189828966272792014357406948711801865282520599949916374426427427584258817132673822091776212099495601770634908798341553578191086521275300430199021896837627904 +def node8920 : Tree Nat := .node node5682 node8919 +def node8921 : Tree Nat := .node node6837 node8920 +def node8922 : Tree Nat := .node node7634 node8921 +def node8923 : Tree Nat := .node node8922 node8490 +def node8924 : Tree Nat := .node node8923 node8496 +def node8925 : Tree Nat := .node node8918 node8924 +def node8926 : Tree Nat := .leaf 540973599882921212264795939754513005075299661860988438659038499017268058136175524568853356593652864839094194135635457566731451878088250253596857407112485439971758502615117114307453738973940910907241618100914691333335523658076643629656203753947611561405751885017999457910784 +def node8927 : Tree Nat := .node node4703 node8926 +def node8928 : Tree Nat := .node node6472 node8927 +def node8929 : Tree Nat := .node node7646 node8928 +def node8930 : Tree Nat := .leaf 933987760719854854355881093136085826644429148483203707461714905947121485225716331474155500167186181745579840279835774145480561597733666816 +def node8931 : Tree Nat := .node node8930 node654 +def node8932 : Tree Nat := .node node7243 node8931 +def node8933 : Tree Nat := .node node8501 node8932 +def node8934 : Tree Nat := .node node8929 node8933 +def node8935 : Tree Nat := .node node8934 node8511 +def node8936 : Tree Nat := .leaf 35453245841927124566985666707751764300614838639721738315958587117680049500380736045026358081221561514814713638614771326280822160514656266360939915892467475344941985465471326461259605472534647643979718773628017630289667321645841778695382159980224771474232500702473446159063973888 +def node8937 : Tree Nat := .node node4718 node8936 +def node8938 : Tree Nat := .node node6865 node8937 +def node8939 : Tree Nat := .node node7652 node8938 +def node8940 : Tree Nat := .leaf 61209821886536407735067023319766520734969308674995238172210948076150553655752545499490254858956713606878320411548955040900206374465034514333696 +def node8941 : Tree Nat := .node node8940 node716 +def node8942 : Tree Nat := .node node7256 node8941 +def node8943 : Tree Nat := .node node8515 node8942 +def node8944 : Tree Nat := .node node8939 node8943 +def node8945 : Tree Nat := .leaf 8254602048994769474255309139320571976856989469314398783249392499606112672240704885574247748401706000233929539901795343469967184440659999948277603260329472867283418625678858954562349176868296666604703746386564774724053610071888572633947354664955581295243585788831596544 +def node8946 : Tree Nat := .node node4727 node8945 +def node8947 : Tree Nat := .node node6483 node8946 +def node8948 : Tree Nat := .node node8947 node8084 +def node8949 : Tree Nat := .node node8521 node8948 +def node8950 : Tree Nat := .node node8944 node8949 +def node8951 : Tree Nat := .node node8935 node8950 +def node8952 : Tree Nat := .node node8925 node8951 +def node8953 : Tree Nat := .leaf 101432549978047727299649238703971188451618686598935332248568457776913858524757894031897451530470388060258672220947199799558192941233338079412348258030457437922864772232235929445110517958186353873898268468377500833918285033348564474378969973066702619784948812415051531026432 +def node8954 : Tree Nat := .node node7263 node8953 +def node8955 : Tree Nat := .node node6494 node8954 +def node8956 : Tree Nat := .node node7669 node8955 +def node8957 : Tree Nat := .node node8956 node8093 +def node8958 : Tree Nat := .node node8957 node8530 +def node8959 : Tree Nat := .leaf 2215827865120445285436604169234485268788427414982608644747421691974729966125774948634023348607602134380929819179562834193332026892649473038732727939532740362124322826711519700203330514837261971076061667741346575701342304903481932307071810576169112719373904947058230481402200064 +def node8960 : Tree Nat := .node node5735 node8959 +def node8961 : Tree Nat := .node node6890 node8960 +def node8962 : Tree Nat := .node node7675 node8961 +def node8963 : Tree Nat := .node node8962 node8535 +def node8964 : Tree Nat := .leaf 515912628062173092140956821207535748553561841832149923953086654991143783531144897753479656629184997707219690884556386294955130183393281517532818746089598409720832587843160098863813141129449204357881783464492291416293877698990274224787956123519708884712518566316867584 +def node8965 : Tree Nat := .node node6510 node8964 +def node8966 : Tree Nat := .node node6509 node8965 +def node8967 : Tree Nat := .node node8966 node7680 +def node8968 : Tree Nat := .node node8104 node8967 +def node8969 : Tree Nat := .node node8963 node8968 +def node8970 : Tree Nat := .node node8958 node8969 +def node8971 : Tree Nat := .leaf 8655577598126739396236735036072208081204794589775815018544508256693025219489380097628852320463375366466345287569524796274808382414892000776300591342991656383948100566725525943449645668814278271927654979089617336529892769703941754715310040369239405466578745589990137098403840 +def node8972 : Tree Nat := .node node4766 node8971 +def node8973 : Tree Nat := .node node6518 node8972 +def node8974 : Tree Nat := .node node7687 node8973 +def node8975 : Tree Nat := .node node8974 node8542 +def node8976 : Tree Nat := .node node8975 node8548 +def node8977 : Tree Nat := .leaf 132073632783916311588084946229129151629711831509030380531990242751524671676058380222726390848516333855340948353262239789917378028874662876285761648178564522403613413219334197089327255393482772219798299320449599651311261886763873723448492736533309609893349008939939790848 +def node8978 : Tree Nat := .node node8555 node8977 +def node8979 : Tree Nat := .node node6529 node8978 +def node8980 : Tree Nat := .node node8979 node8128 +def node8981 : Tree Nat := .node node8125 node8980 +def node8982 : Tree Nat := .node node8554 node8981 +def node8983 : Tree Nat := .node node8976 node8982 +def node8984 : Tree Nat := .node node8970 node8983 +def node8985 : Tree Nat := .node node8952 node8984 +def node8986 : Tree Nat := .node node8912 node8985 +def node8987 : Tree Nat := .leaf 1056589062271330492704679569833033213037694652072243044255921418053347805113449718948834511775314375789348789986514257357764696098362521259083601717998252270081105127506948968261273790728022100514906957857150368652373799892920833530803378532327091897551293995098807730176 +def node8988 : Tree Nat := .node node4800 node8987 +def node8989 : Tree Nat := .node node8566 node8988 +def node8990 : Tree Nat := .node node7716 node8989 +def node8991 : Tree Nat := .leaf 4292270895663472781908647744430184991089077279103709869350597216904085437906417950844751893602512176201218102586641425653823856716149983952312296852851934773563462515640810792124397626480958543796041088931289104384 +def node8992 : Tree Nat := .node node2934 node8991 +def node8993 : Tree Nat := .leaf 6351116772895013009619991433325383621182118209685785210739661360440426099534871054024257401136866035869942913821860088618039679872441253888 +def node8994 : Tree Nat := .node node8993 node1032 +def node8995 : Tree Nat := .node node8992 node8994 +def node8996 : Tree Nat := .node node8140 node8995 +def node8997 : Tree Nat := .node node8990 node8996 +def node8998 : Tree Nat := .leaf 999372195374097857137361481885934479322535283654860656091616772325729354728576250105340008997011970775485528303925279912963476198760323215348715161171726596905724731190321995016221233120035443163942354944 +def node8999 : Tree Nat := .node node2530 node8998 +def node9000 : Tree Nat := .node node8999 node4806 +def node9001 : Tree Nat := .node node8145 node9000 +def node9002 : Tree Nat := .node node9001 node8576 +def node9003 : Tree Nat := .node node8997 node9002 +def node9004 : Tree Nat := .leaf 69244620785013915169893880288577664649638356718206520148356066053544201755915040781030818563707002931730762300556198370198467059319136024142969736565146454704501792746652079120636816228025409440347434017449455025992706461417137247697169838086848239874339603405486121470132224 +def node9005 : Tree Nat := .node node4815 node9004 +def node9006 : Tree Nat := .node node8580 node9005 +def node9007 : Tree Nat := .node node7729 node9006 +def node9008 : Tree Nat := .leaf 281298265418201352235165138578976603576013768563340729997760739207026143258635006826561660099134237979523029571118132471649000273749605348298738686548504397320255079425036176072664522845952890456858654254148921101123584 +def node9009 : Tree Nat := .node node3159 node9008 +def node9010 : Tree Nat := .leaf 416226788828447572598455758574412340997791298989967619571034446917823764859117309396533733040905652526772578798512152345175168942780244891271168 +def node9011 : Tree Nat := .node node9010 node4303 +def node9012 : Tree Nat := .node node9009 node9011 +def node9013 : Tree Nat := .node node8585 node9012 +def node9014 : Tree Nat := .node node9007 node9013 +def node9015 : Tree Nat := .leaf 65494856196036877165354122076876602036881672349604947957620196791138998991491973126903562829628176516742219582926047144375974376161956542241093396802550274254813575983288738893511841550490770964363715505291264 +def node9016 : Tree Nat := .node node2755 node9015 +def node9017 : Tree Nat := .node node9016 node8589 +def node9018 : Tree Nat := .node node8160 node9017 +def node9019 : Tree Nat := .node node9018 node8597 +def node9020 : Tree Nat := .node node9014 node9019 +def node9021 : Tree Nat := .node node9003 node9020 +def node9022 : Tree Nat := .leaf 270486799941460606132397969877256502537649830930494219329516303832529161978923707330092265424773724229257516090456409746060007449037718761538045050295927270453192140844999097351807578604910352523457457474185780613391786903782489885853114545269358064055172777055811589373952 +def node9023 : Tree Nat := .node node7333 node9022 +def node9024 : Tree Nat := .node node8602 node9023 +def node9025 : Tree Nat := .node node7749 node9024 +def node9026 : Tree Nat := .leaf 215455166527421378856590945602770070140941918323637201285049585789695269040011643100937167908386250973488087384390902892339513890793972792914093718659362258435267726013575925701709117868469408656782315586481312235520 +def node9027 : Tree Nat := .node node3051 node9026 +def node9028 : Tree Nat := .node node9027 node7340 +def node9029 : Tree Nat := .node node8607 node9028 +def node9030 : Tree Nat := .node node9025 node9029 +def node9031 : Tree Nat := .leaf 50164565101131186554345988110352789550307653454047907443043973366903517236744181174847262717274362630952205691272066426255397066003748607791769219889258675455245166640403998765817348273329637137881099141120 +def node9032 : Tree Nat := .node node2638 node9031 +def node9033 : Tree Nat := .node node9032 node5356 +def node9034 : Tree Nat := .node node8176 node9033 +def node9035 : Tree Nat := .node node9034 node8613 +def node9036 : Tree Nat := .node node9030 node9035 +def node9037 : Tree Nat := .leaf 17726622920963562283492833353875882150307419319860869157979594161888363808498148738200484025412641399571801957930618564322504863096692752942666969916339675240507934009434211038859310001265742517901276666390810648275303345172502545653494221490016394218094658128822039083453775872 +def node9038 : Tree Nat := .node node5807 node9037 +def node9039 : Tree Nat := .node node8617 node9038 +def node9040 : Tree Nat := .node node7762 node9039 +def node9041 : Tree Nat := .node node9040 node8623 +def node9042 : Tree Nat := .leaf 3287584938467733442025618676800080415968962376764483662186425564418168139169324144888892944117518749348886584596857284088318991374650157918080118668317150765834146058379326260032465089460098368628253075513016320 +def node9043 : Tree Nat := .node node2849 node9042 +def node9044 : Tree Nat := .node node9043 node6968 +def node9045 : Tree Nat := .node node8191 node9044 +def node9046 : Tree Nat := .leaf 4127301024497384737127654569660285988428494734657199391624693841903931481823397834179694577266954585349598975651340406295063309343403046932720021699509883043494192502815249314708361813674859390960414319722103129228759716091556506292976882233474460249980278226343165952 +def node9047 : Tree Nat := .node node4855 node9046 +def node9048 : Tree Nat := .node node8626 node9047 +def node9049 : Tree Nat := .node node9048 node7771 +def node9050 : Tree Nat := .node node9045 node9049 +def node9051 : Tree Nat := .node node9041 node9050 +def node9052 : Tree Nat := .node node9036 node9051 +def node9053 : Tree Nat := .node node9021 node9052 +def node9054 : Tree Nat := .leaf 16905424996341287883274873117328531408603114433155888708094795290212580365550267913080180989691685516027608871522823100533265809355193667168626733423166961746175924962105377857667626564181205358061870500585502492187534680454769828733971332890945545007470142122318670856192 +def node9055 : Tree Nat := .node node4863 node9054 +def node9056 : Tree Nat := .node node6588 node9055 +def node9057 : Tree Nat := .node node7779 node9056 +def node9058 : Tree Nat := .node node9057 node8200 +def node9059 : Tree Nat := .node node9058 node8637 +def node9060 : Tree Nat := .leaf 1107913932560222642718302084617242634394213707491304322373700504139371666836702357951622741340434301978385375004119734716548108073410816116680624062346776282254133824135723428673288545242777668130584957307947868269212023932825291882617190947077513938092084297247131153687642112 +def node9061 : Tree Nat := .node node4882 node9060 +def node9062 : Tree Nat := .node node6982 node9061 +def node9063 : Tree Nat := .node node7785 node9062 +def node9064 : Tree Nat := .node node9063 node8642 +def node9065 : Tree Nat := .leaf 257956314031086546070478410603767874276780920916074961976543318951919397979167238839688728270133028566837616549743956729202610572205839586790615156937643203335181287488502416955383088219347393211714850119573139024869292062719023266569822021713162157761467067817525248 +def node9066 : Tree Nat := .node node6600 node9065 +def node9067 : Tree Nat := .node node6599 node9066 +def node9068 : Tree Nat := .node node9067 node7790 +def node9069 : Tree Nat := .node node8211 node9068 +def node9070 : Tree Nat := .node node9064 node9069 +def node9071 : Tree Nat := .node node9059 node9070 +def node9072 : Tree Nat := .leaf 4327788799063369698118367518036104040602397294887907509272271297430095263635817683405403880971652039542289058624239800526271807549197625592959794319142811062738308587730196215212863888232150005042183765171477463145874901624283357007732644985205328812222475333084945200447488 +def node9073 : Tree Nat := .node node7379 node9072 +def node9074 : Tree Nat := .node node8647 node9073 +def node9075 : Tree Nat := .node node7797 node9074 +def node9076 : Tree Nat := .leaf 3447282664438742061705455129644321122255070693178195220560793372635124304640136864581742585265622661556873013841918398664905484624604423353081216026958085076178102624768678888769214034425857349095483240278115001303040 +def node9077 : Tree Nat := .node node3090 node9076 +def node9078 : Tree Nat := .node node9077 node5414 +def node9079 : Tree Nat := .node node8652 node9078 +def node9080 : Tree Nat := .node node9075 node9079 +def node9081 : Tree Nat := .leaf 802633041618098984869535809765644632804922455264766519088491294969034788316172950185930268167598897421534073022094640146831827777820233662500126703219821353245054434930208301906461856987777405758063079587840 +def node9082 : Tree Nat := .node node2677 node9081 +def node9083 : Tree Nat := .node node9082 node8224 +def node9084 : Tree Nat := .node node8657 node9083 +def node9085 : Tree Nat := .node node9084 node8662 +def node9086 : Tree Nat := .node node9080 node9085 +def node9087 : Tree Nat := .leaf 283625966735416996535885333662014114404918709117773906527666446555317050392228007039102232836943884008369202383078188524332921074971181050832906833858946728856509804734599537122908108842546137008883799718932522590631793444922625979776458613829707862870639001975438398568148238336 +def node9088 : Tree Nat := .node node7394 node9087 +def node9089 : Tree Nat := .node node8666 node9088 +def node9090 : Tree Nat := .node node8237 node9089 +def node9091 : Tree Nat := .node node9090 node8672 +def node9092 : Tree Nat := .leaf 52601359015483735072409898828801286655503398028231738594982809030687451107729976609486112352895285107551074137215164268217998535559244365095047522744463254797775086719853091142632130400377759804907533591054909440 +def node9093 : Tree Nat := .node node2904 node9092 +def node9094 : Tree Nat := .node node9093 node5434 +def node9095 : Tree Nat := .node node8246 node9094 +def node9096 : Tree Nat := .leaf 66036816391958155794042473114564575814855915754515190265995191365363564936260670734885806988470147516908573264271584410659181506112724307016124279857404118762986362510986107751906147120339441534047230828658637845066354224556271944788358062293409741162705050009088294912 +def node9097 : Tree Nat := .node node8676 node9096 +def node9098 : Tree Nat := .node node8675 node9097 +def node9099 : Tree Nat := .node node9098 node7823 +def node9100 : Tree Nat := .node node9095 node9099 +def node9101 : Tree Nat := .node node9091 node9100 +def node9102 : Tree Nat := .node node9086 node9101 +def node9103 : Tree Nat := .node node9071 node9102 +def node9104 : Tree Nat := .node node9053 node9103 +def node9105 : Tree Nat := .leaf 4226356249085321970818718279332132852150778608288972177023685672213391220453798875795338047101257503157395159946057029431058782140928639611794602221526550912916457463157236633220330425549199199719253299734927093368116389964622601001022369225276884885167142377258997514240 +def node9106 : Tree Nat := .node node4931 node9105 +def node9107 : Tree Nat := .node node8686 node9106 +def node9108 : Tree Nat := .node node7832 node9107 +def node9109 : Tree Nat := .leaf 17169083582653891127634590977720739964356309116414839477402388867616341751625671803379007574410048704804872410346565702615295426864599935809249187411407739094253850062563243168497590505765996820175278370675518078976 +def node9110 : Tree Nat := .node node2982 node9109 +def node9111 : Tree Nat := .node node9110 node5451 +def node9112 : Tree Nat := .node node8257 node9111 +def node9113 : Tree Nat := .node node9108 node9112 +def node9114 : Tree Nat := .leaf 3997488781496391428549445927543737917290141134619442624366467089302917418914305000421360035988047883101942113215701119651853904795041292861394860644686906387622898924761277636035987070128225559557613551616 +def node9115 : Tree Nat := .node node2578 node9114 +def node9116 : Tree Nat := .node node9115 node8264 +def node9117 : Tree Nat := .node node8262 node9116 +def node9118 : Tree Nat := .node node9117 node8693 +def node9119 : Tree Nat := .node node9113 node9118 +def node9120 : Tree Nat := .leaf 276978483140055660679575521154310658598553426872826080593424479669343334445039019715068877024898152668841372839426078530379657932545584006597111517108286051149117725867854768471548249453429059899600883116698886908292396725276144376857807142378640489594403985817299740983820288 +def node9121 : Tree Nat := .node node4950 node9120 +def node9122 : Tree Nat := .node node8697 node9121 +def node9123 : Tree Nat := .node node7849 node9122 +def node9124 : Tree Nat := .leaf 1125193061672805408940660554315906414304055074253362919991042956828104573034540027306246640396536951918092118284472529886596001094998421393194954746194017589281020317700144704290658091383811561827434580267222725061246976 +def node9125 : Tree Nat := .node node3168 node9124 +def node9126 : Tree Nat := .node node9125 node5462 +def node9127 : Tree Nat := .node node8702 node9126 +def node9128 : Tree Nat := .node node9123 node9127 +def node9129 : Tree Nat := .leaf 261979424784147508661416488307506408147526689398419791830480787164555995965967892507614251318512706066968878331704188577503897504647826168964373587210201097019254303933154955574006959839080809045282154606493696 +def node9130 : Tree Nat := .node node2764 node9129 +def node9131 : Tree Nat := .node node9130 node5467 +def node9132 : Tree Nat := .node node8280 node9131 +def node9133 : Tree Nat := .leaf 64489078507771636517619602650941968569195230229018740494135828738607654120693952572560700181598777819174120482575333199795235647966665639370990059625150522346826828812668965142819911917353664771053451626117037859662102088225921181730777947761789733840195935723847680 +def node9134 : Tree Nat := .node node8707 node9133 +def node9135 : Tree Nat := .node node8706 node9134 +def node9136 : Tree Nat := .node node9135 node8284 +def node9137 : Tree Nat := .node node9132 node9136 +def node9138 : Tree Nat := .node node9128 node9137 +def node9139 : Tree Nat := .node node9119 node9138 +def node9140 : Tree Nat := .leaf 1081947199765842424529591879509026010150599323721976877318070265060582134354261780670656626622613825243240774608730757333906975779019000243741409321058535566725946467030098320496234813074601586545538432598922948259183104629854242850226722178285056913331039391857283168206848 +def node9141 : Tree Nat := .node node7429 node9140 +def node9142 : Tree Nat := .node node6660 node9141 +def node9143 : Tree Nat := .node node7871 node9142 +def node9144 : Tree Nat := .node node9143 node8717 +def node9145 : Tree Nat := .node node9144 node8723 +def node9146 : Tree Nat := .leaf 70906491683854249133971333415503528601229677279443476631917736831890935403465942420329874115650275057166553958689538174040058373315829802735532955105133219165843016990084889187462508945616794498656035024629132269373975153450533629742909649006141448729378718676705817200986947584 +def node9147 : Tree Nat := .node node5909 node9146 +def node9148 : Tree Nat := .node node7038 node9147 +def node9149 : Tree Nat := .node node8297 node9148 +def node9150 : Tree Nat := .node node9149 node8728 +def node9151 : Tree Nat := .leaf 16509204097989538948510618278641143953713978938628797566498778578147892399689530814862017371646349561088216961671437979077503865057889461467817274798812903756476960563163313394698779140562459808058207385577364593538866552146131724803297306208190526240392626115358752768 +def node9152 : Tree Nat := .node node6676 node9151 +def node9153 : Tree Nat := .node node6675 node9152 +def node9154 : Tree Nat := .node node9153 node7877 +def node9155 : Tree Nat := .node node8303 node9154 +def node9156 : Tree Nat := .node node9150 node9155 +def node9157 : Tree Nat := .node node9145 node9156 +def node9158 : Tree Nat := .node node9139 node9157 +def node9159 : Tree Nat := .leaf 67621699985365151533099492469314125634412457732623554832378974042999197994994224038344085553700536019480699323620574657322504905784482918092213878136200383363022844438457247630881722581573959104945019892369700432881713455618258281897574835507270129089029566607985976803328 +def node9160 : Tree Nat := .node node4998 node9159 +def node9161 : Tree Nat := .node node6685 node9160 +def node9162 : Tree Nat := .node node7885 node9161 +def node9163 : Tree Nat := .node node9162 node8736 +def node9164 : Tree Nat := .node node9163 node8742 +def node9165 : Tree Nat := .leaf 4431655730240890570873208338468970537576854829965217289494815805688144422315056253627009542646226228196314212797361182039682972790861824998364812579055761681309476728955282720752577794353568098490525419925188396069613996563882978714528654042255288880859882575071936558774878208 +def node9166 : Tree Nat := .node node5013 node9165 +def node9167 : Tree Nat := .node node7061 node9166 +def node9168 : Tree Nat := .node node7891 node9167 +def node9169 : Tree Nat := .node node9168 node8747 +def node9170 : Tree Nat := .leaf 1031825256124346184281913642415071497107123683664299847906173309982287567062289795506959313258369995414439381769112772494915451980670919434123633789573146135511823694391248077083480000858836396430295746668069866610527073004447034425167509760252641447780767921915035648 +def node9171 : Tree Nat := .node node5022 node9170 +def node9172 : Tree Nat := .node node6696 node9171 +def node9173 : Tree Nat := .node node9172 node7896 +def node9174 : Tree Nat := .node node8317 node9173 +def node9175 : Tree Nat := .node node9169 node9174 +def node9176 : Tree Nat := .node node9164 node9175 +def node9177 : Tree Nat := .leaf 17311155196253478792473470072144416162409589179551630037089016513386050438978760195257704640926750732932690575139049592549616764829784014628429832763951273750231505038652624908907370102480461007863993217880027833088426177584885850037164518856242539229169517244660582902136832 +def node9178 : Tree Nat := .node node7472 node9177 +def node9179 : Tree Nat := .node node6706 node9178 +def node9180 : Tree Nat := .node node7903 node9179 +def node9181 : Tree Nat := .leaf 25404467091580052038479965733301534484728472838743140842958645441761704398139484216097029604547464143479771655234827902802530057806552236032 +def node9182 : Tree Nat := .node node9181 node1909 +def node9183 : Tree Nat := .node node7477 node9182 +def node9184 : Tree Nat := .node node8753 node9183 +def node9185 : Tree Nat := .node node9180 node9184 +def node9186 : Tree Nat := .leaf 109111355330644560471249586375730748718525002282426071664829254052825993015228447954444938914275171375978270896555407731451330266726456219058172854272 +def node9187 : Tree Nat := .node node9186 node57 +def node9188 : Tree Nat := .node node7907 node9187 +def node9189 : Tree Nat := .node node8762 node9188 +def node9190 : Tree Nat := .node node8759 node9189 +def node9191 : Tree Nat := .node node9185 node9190 +def node9192 : Tree Nat := .leaf 1664907155313790290393823034297649363991165195959870478284137787671295059436469237586134932163622610107090315194035140593073250833730077093527552 +def node9193 : Tree Nat := .node node9192 node57 +def node9194 : Tree Nat := .node node7489 node9193 +def node9195 : Tree Nat := .node node8768 node9194 +def node9196 : Tree Nat := .node node8334 node9195 +def node9197 : Tree Nat := .leaf 264147265567832623176169892458258303259423663018060761063980616492761735425871091153696935450236741474026595916420394820228338335747308736517777103482788301160260310877834246272943262735717868352681080827692804403171033400679714024374772456343357319053814572603475492864 +def node9198 : Tree Nat := .node node5053 node9197 +def node9199 : Tree Nat := .node node6721 node9198 +def node9200 : Tree Nat := .node node9199 node7914 +def node9201 : Tree Nat := .node node8774 node9200 +def node9202 : Tree Nat := .node node9196 node9201 +def node9203 : Tree Nat := .node node9191 node9202 +def node9204 : Tree Nat := .node node9176 node9203 +def node9205 : Tree Nat := .node node9158 node9204 +def node9206 : Tree Nat := .node node9104 node9205 +def node9207 : Tree Nat := .node node8986 node9206 +def node9208 : Tree Nat := .leaf 1139663674045120753463792124847496920835746094750353437106502722716349942556251493028159315344186791353652707945851314322569080039015463149366598961452810240 +def node9209 : Tree Nat := .node node0 node9208 +def node9210 : Tree Nat := .node node9209 node7500 +def node9211 : Tree Nat := .leaf 387807452497886593584499586484524762615924423116127594099231364021438389212737577853002588961976568981184596313755524621408539901316912229851476212176388206001419547320622520757116082460022538240 +def node9212 : Tree Nat := .node node2066 node9211 +def node9213 : Tree Nat := .node node9212 node8784 +def node9214 : Tree Nat := .node node9210 node9213 +def node9215 : Tree Nat := .leaf 21023084125213885395142714286670011152986164673603006392695359767896264134055208709476894090205658824115802071211371843844866027916073852847241423183660919272911856008104509440 +def node9216 : Tree Nat := .node node15 node9215 +def node9217 : Tree Nat := .node node9216 node7924 +def node9218 : Tree Nat := .node node9217 node8789 +def node9219 : Tree Nat := .node node9214 node9218 +def node9220 : Tree Nat := .leaf 4894818208462997664497865896362348262450230464712485296813622063001679287770578802907116266481033252579113950769270733894050593468377798061641264516781298278664765440 +def node9221 : Tree Nat := .node node31 node9220 +def node9222 : Tree Nat := .node node9221 node7930 +def node9223 : Tree Nat := .leaf 6807023201651555654745434527164761616181671626072234442189491167099468469303198752637350242948394673005219227861536703475571913793484758347605494536649635180950602725714707883199922872134013058932854089059529931176663443934546091107185686345171024142534464218310813725622615932928 +def node9224 : Tree Nat := .node node7932 node9223 +def node9225 : Tree Nat := .node node8353 node9224 +def node9226 : Tree Nat := .node node9222 node9225 +def node9227 : Tree Nat := .leaf 90293458778850406777229995113919666646030830013595426943905503494068605176344881265657625385088978563711186012661905172608918487400960230699618396391643885529377697087292123799344906240 +def node9228 : Tree Nat := .node node46 node9227 +def node9229 : Tree Nat := .node node9228 node8357 +def node9230 : Tree Nat := .node node9229 node7120 +def node9231 : Tree Nat := .node node9226 node9230 +def node9232 : Tree Nat := .node node9219 node9231 +def node9233 : Tree Nat := .leaf 74688998542221033699003080694005558203891456065559162854211762435938709835366497847093448890396625558152983867939311735443887229436917084680805427808427038474240 +def node9234 : Tree Nat := .node node63 node9233 +def node9235 : Tree Nat := .node node9234 node7517 +def node9236 : Tree Nat := .node node9235 node8795 +def node9237 : Tree Nat := .leaf 1377768841230017193256072923491205850922101288049246626951683097748849566289442157984277731095718056697253204538908465158217140005507816020196813909764402006673736473792416988528640 +def node9238 : Tree Nat := .node node78 node9237 +def node9239 : Tree Nat := .node node9238 node8367 +def node9240 : Tree Nat := .node node9239 node8799 +def node9241 : Tree Nat := .node node9236 node9240 +def node9242 : Tree Nat := .leaf 320786806109831014940532139384002855727938303735397436411977535520878053803332652427320771640100995241024811877614926816480499693543607373767721911371779163710198619504640 +def node9243 : Tree Nat := .node node94 node9242 +def node9244 : Tree Nat := .node node9243 node7950 +def node9245 : Tree Nat := .node node9244 node8804 +def node9246 : Tree Nat := .leaf 5917472114530740258552544959785839273314276475770989900195791076987280108836938138626138137237191299151376286525810617392098081990309329679130191225836001678488457448129616100418766881488640 +def node9247 : Tree Nat := .node node109 node9246 +def node9248 : Tree Nat := .node node9247 node8373 +def node9249 : Tree Nat := .leaf 74688998542221033699003080694005558203891456065559162854211762435938709835366497847093563735455836153134406782276860025147416015890213999913083332211511058759731 +def node9250 : Tree Nat := .node node9249 node7527 +def node9251 : Tree Nat := .node node9250 node5089 +def node9252 : Tree Nat := .node node9248 node9251 +def node9253 : Tree Nat := .node node9245 node9252 +def node9254 : Tree Nat := .node node9241 node9253 +def node9255 : Tree Nat := .node node9232 node9254 +def node9256 : Tree Nat := .leaf 18153169852625075539254866889738487863162542998668723719382859751319737950474053042143369297705148585435795696884057714039558177798692147647807942045813883239663457881954728771163173548296357292202069827936286583548971006257388104363651435602244565418996241418328226479889017012118 +def node9257 : Tree Nat := .node node9256 node7556 +def node9258 : Tree Nat := .node node9257 node6396 +def node9259 : Tree Nat := .node node8839 node9258 +def node9260 : Tree Nat := .node node8836 node9259 +def node9261 : Tree Nat := .node node8832 node9260 +def node9262 : Tree Nat := .node node8823 node9261 +def node9263 : Tree Nat := .node node9255 node9262 +def node9264 : Tree Nat := .node node314 node1320 +def node9265 : Tree Nat := .node node9264 node7582 +def node9266 : Tree Nat := .node node9265 node8860 +def node9267 : Tree Nat := .node node9266 node8867 +def node9268 : Tree Nat := .leaf 458222462695599379270700543123871994649449568634787237553785686889571355430520292437193170450284480364627107959436636856780369805281034289352226705851079641608143313804919284519937650749461677560677737778731921942213121735347267705911306200554105995417 +def node9269 : Tree Nat := .node node9268 node7590 +def node9270 : Tree Nat := .node node9269 node5152 +def node9271 : Tree Nat := .node node8875 node9270 +def node9272 : Tree Nat := .node node8872 node9271 +def node9273 : Tree Nat := .node node9267 node9272 +def node9274 : Tree Nat := .node node8857 node9273 +def node9275 : Tree Nat := .leaf 112960558348328699877964353688185114534054156474063100987336077234507753214447939996234956839809199880450214813797641676452004147538019495499179041450447194243073424431255865801146001649350629571585288197052160814895595520 +def node9276 : Tree Nat := .node node3287 node9275 +def node9277 : Tree Nat := .node node9276 node6811 +def node9278 : Tree Nat := .node node8469 node9277 +def node9279 : Tree Nat := .node node8898 node9278 +def node9280 : Tree Nat := .node node1634 node7617 +def node9281 : Tree Nat := .node node9280 node6440 +def node9282 : Tree Nat := .node node8906 node9281 +def node9283 : Tree Nat := .node node8903 node9282 +def node9284 : Tree Nat := .node node9279 node9283 +def node9285 : Tree Nat := .node node8894 node9284 +def node9286 : Tree Nat := .node node9274 node9285 +def node9287 : Tree Nat := .node node9263 node9286 +def node9288 : Tree Nat := .leaf 27228092806600031667444992031553354982872196075306295026656091829868785166353766640107502537461146918959917491876493434413194930950447828819955291007298695170027621365585157638185602574843907713164429765876498735879565620547439314120630838512916283301911278381229472439570364628992 +def node9289 : Tree Nat := .node node4677 node9288 +def node9290 : Tree Nat := .node node6827 node9289 +def node9291 : Tree Nat := .node node8061 node9290 +def node9292 : Tree Nat := .node node9291 node8484 +def node9293 : Tree Nat := .node node8917 node9292 +def node9294 : Tree Nat := .leaf 49692708741517100404930162553280883400323263580120335617144128012273230882932949088750728013413929968336471629040752144266609296734376044455127695191162275060055855394311456428734517125419435191013403740368823377522124256473675399253 +def node9295 : Tree Nat := .node node9294 node7637 +def node9296 : Tree Nat := .node node9295 node5216 +def node9297 : Tree Nat := .node node8494 node9296 +def node9298 : Tree Nat := .node node8068 node9297 +def node9299 : Tree Nat := .node node8923 node9298 +def node9300 : Tree Nat := .node node9293 node9299 +def node9301 : Tree Nat := .node node9300 node8951 +def node9302 : Tree Nat := .leaf 4455508415646675018204269146191690746966043464109921807206242693261010905477224010259680479802120510747370406335371453085846362462725044046658786022036362495994596144238519311726774205808640 +def node9303 : Tree Nat := .node node9302 node8095 +def node9304 : Tree Nat := .node node5727 node9303 +def node9305 : Tree Nat := .leaf 1037378892220248239628101965922790287753111558060610297242272605706534680443087310683077700546426191563615650861725513106182665725636853817074079293755958272272659431137920617021440 +def node9306 : Tree Nat := .node node9305 node796 +def node9307 : Tree Nat := .node node6884 node9306 +def node9308 : Tree Nat := .node node9304 node9307 +def node9309 : Tree Nat := .node node9308 node8529 +def node9310 : Tree Nat := .node node8957 node9309 +def node9311 : Tree Nat := .leaf 858099707516326214372737599885190513293906971170737236078181743481428650940610372475497250140364860915495137629744280687598631453264558359069372864507412480 +def node9312 : Tree Nat := .node node9311 node8959 +def node9313 : Tree Nat := .node node6890 node9312 +def node9314 : Tree Nat := .node node7675 node9313 +def node9315 : Tree Nat := .node node9314 node8535 +def node9316 : Tree Nat := .leaf 241533595188578646543459493183249209018682958106652187416077203215719946393304033092648995272851711072762165122423639733461595369659676102677681550736500568719609393315840 +def node9317 : Tree Nat := .node node9316 node8101 +def node9318 : Tree Nat := .node node6122 node9317 +def node9319 : Tree Nat := .node node9318 node6896 +def node9320 : Tree Nat := .leaf 291996199527820493993034982764818644793166624463907835557068321145553610701355356545752065864793646554216867494563329863679182352245391437045442805249775788344856692374251520874296565350824673280 +def node9321 : Tree Nat := .node node9320 node8964 +def node9322 : Tree Nat := .node node6509 node9321 +def node9323 : Tree Nat := .node node9322 node7680 +def node9324 : Tree Nat := .node node9319 node9323 +def node9325 : Tree Nat := .node node9315 node9324 +def node9326 : Tree Nat := .node node9310 node9325 +def node9327 : Tree Nat := .leaf 567251933470833993071770667324028228809837418235547813055339953145530871328198386850309977243546146401518033709968085553492998884518265097915578352520381532704513223596121217052326574072084067066025301398572583787732629067860356372478722402403186445651089321223150837880674320384 +def node9328 : Tree Nat := .node node4781 node9327 +def node9329 : Tree Nat := .node node6908 node9328 +def node9330 : Tree Nat := .node node8119 node9329 +def node9331 : Tree Nat := .node node9330 node8553 +def node9332 : Tree Nat := .node node9331 node8981 +def node9333 : Tree Nat := .node node8976 node9332 +def node9334 : Tree Nat := .node node9326 node9333 +def node9335 : Tree Nat := .node node9301 node9334 +def node9336 : Tree Nat := .node node9287 node9335 +def node9337 : Tree Nat := .leaf 4538015467766671944574165338592225830478699345884382504442663144885072806275648112625635725391102144133907238129251016389326737199538896813326509341743147661692572370715803045922286005458975168534536911519489356406158553271566539509828985923834640212864019753661793098962896420864 +def node9338 : Tree Nat := .node node4805 node9337 +def node9339 : Tree Nat := .node node8999 node9338 +def node9340 : Tree Nat := .node node8145 node9339 +def node9341 : Tree Nat := .node node9340 node8576 +def node9342 : Tree Nat := .node node8997 node9341 +def node9343 : Tree Nat := .leaf 57278681880282598266741390408408596112073575107801884750380706224728954912021854056109280414355590635438855420991674080951753336539089177949436577042649839596485626362898174393563117253615259924173614117673876134980920847112168116826745017934041579715 +def node9344 : Tree Nat := .node node9343 node7740 +def node9345 : Tree Nat := .node node9344 node8163 +def node9346 : Tree Nat := .node node8596 node9345 +def node9347 : Tree Nat := .node node9018 node9346 +def node9348 : Tree Nat := .node node9014 node9347 +def node9349 : Tree Nat := .node node9342 node9348 +def node9350 : Tree Nat := .leaf 14120069793541087484745544211023139316756769559257887623417009654313469151805992499529369604976149985028646194879483581008889841572026727756585213017892004804485437304179670832880831264914574485210113936244651832398315520 +def node9351 : Tree Nat := .node node3267 node9350 +def node9352 : Tree Nat := .node node9351 node6961 +def node9353 : Tree Nat := .node node8622 node9352 +def node9354 : Tree Nat := .node node9040 node9353 +def node9355 : Tree Nat := .leaf 4538015484673128829149194236736751216454675671906553705267500427190823742415763610243858534894498949233759028493994007295121419313603122547579190081828989791157197712638893616936228667662815174384794036891349002722153533643547334351267347137397983108577893810607103091555327541286 +def node9356 : Tree Nat := .node node9355 node7769 +def node9357 : Tree Nat := .node node9356 node5375 +def node9358 : Tree Nat := .node node9048 node9357 +def node9359 : Tree Nat := .node node9045 node9358 +def node9360 : Tree Nat := .node node9354 node9359 +def node9361 : Tree Nat := .node node9036 node9360 +def node9362 : Tree Nat := .node node9349 node9361 +def node9363 : Tree Nat := .leaf 90293458778850406777229995113919666646030830013595426943905503494068605176344881265657625385088978563957814825763502688167962486905210368921491420797041845512831316737989918628438343785 +def node9364 : Tree Nat := .node node9363 node7788 +def node9365 : Tree Nat := .node node9364 node6604 +def node9366 : Tree Nat := .node node9067 node9365 +def node9367 : Tree Nat := .node node8211 node9366 +def node9368 : Tree Nat := .node node9064 node9367 +def node9369 : Tree Nat := .node node9059 node9368 +def node9370 : Tree Nat := .leaf 344294730144094959356894252395054897428786761745327072984532187766299116839342626322537858535184392875493210872524832768 +def node9371 : Tree Nat := .node node9370 node9072 +def node9372 : Tree Nat := .node node8647 node9371 +def node9373 : Tree Nat := .node node7797 node9372 +def node9374 : Tree Nat := .node node9373 node9079 +def node9375 : Tree Nat := .node node9374 node9085 +def node9376 : Tree Nat := .leaf 225921116696657399755928707376370229068108312948126201974672154469015506428895879992469913679618399757779002696716912709707262738342661905359941137894621703451283045378165652864282978662463086431187559305624246205169008640 +def node9377 : Tree Nat := .node node3306 node9376 +def node9378 : Tree Nat := .node node9377 node5429 +def node9379 : Tree Nat := .node node8671 node9378 +def node9380 : Tree Nat := .node node9090 node9379 +def node9381 : Tree Nat := .node node9380 node9100 +def node9382 : Tree Nat := .node node9375 node9381 +def node9383 : Tree Nat := .node node9369 node9382 +def node9384 : Tree Nat := .node node9362 node9383 +def node9385 : Tree Nat := .leaf 18152061871066687778296661354368903321914797383537530017770878500656987882502348379209919271793476684848577078718978737711775964304584483133298507280652209046522559769877623577049140976535922457684646999027926814160332981127383537822750744652840418201324316287993904432042148364288 +def node9386 : Tree Nat := .node node8263 node9385 +def node9387 : Tree Nat := .node node9115 node9386 +def node9388 : Tree Nat := .node node8262 node9387 +def node9389 : Tree Nat := .node node9388 node8693 +def node9390 : Tree Nat := .node node9113 node9389 +def node9391 : Tree Nat := .leaf 21023084125213885395142714286670011152986164673603006392695359767896264134055208709476894097978231545096928474617790760740363503259901014269929317572208487882085496144441376933 +def node9392 : Tree Nat := .node node9391 node7862 +def node9393 : Tree Nat := .node node9392 node8283 +def node9394 : Tree Nat := .node node9135 node9393 +def node9395 : Tree Nat := .node node9132 node9394 +def node9396 : Tree Nat := .node node9128 node9395 +def node9397 : Tree Nat := .node node9390 node9396 +def node9398 : Tree Nat := .leaf 28598854314567559613391395321173069789913487295323575074684356559458522676146876171923760404587048919519964551306400400380369736202673448696097744273002201103 +def node9399 : Tree Nat := .node node1633 node9398 +def node9400 : Tree Nat := .node node9399 node7870 +def node9401 : Tree Nat := .leaf 9731685837388142401361619034958721395997256405961178331925417640679153931656108865417112026539953195727844046320476870793699007170693809250272926594967482863541504640410445138526842428181067071488 +def node9402 : Tree Nat := .node node2258 node9401 +def node9403 : Tree Nat := .node node9402 node9141 +def node9404 : Tree Nat := .node node9400 node9403 +def node9405 : Tree Nat := .node node9404 node8717 +def node9406 : Tree Nat := .node node9405 node8723 +def node9407 : Tree Nat := .leaf 34573893392277960861355335833020495059021671145988741826916941735274072057592707329181934122672548411002836297429314778617378348608802018483291812582676111503163190901004493178011648 +def node9408 : Tree Nat := .node node1710 node9407 +def node9409 : Tree Nat := .node node9408 node8726 +def node9410 : Tree Nat := .node node9409 node7446 +def node9411 : Tree Nat := .node node9149 node9410 +def node9412 : Tree Nat := .leaf 8049861852144347704331235921247977544325792963148267433726448038423916338382453501499708304803946151165952043940619281171210657015629582685253539258305940661104160249151488 +def node9413 : Tree Nat := .node node1725 node9412 +def node9414 : Tree Nat := .node node9413 node8301 +def node9415 : Tree Nat := .node node9414 node7044 +def node9416 : Tree Nat := .leaf 148493741415224340841089157637919943176227667327288487730795557261339629084108106466935913490905047542233948460700635845851120104533291767124525857467155195061363291021887895790508585389195008 +def node9417 : Tree Nat := .node node2055 node9416 +def node9418 : Tree Nat := .node node9417 node9152 +def node9419 : Tree Nat := .node node9418 node7877 +def node9420 : Tree Nat := .node node9415 node9419 +def node9421 : Tree Nat := .node node9411 node9420 +def node9422 : Tree Nat := .node node9406 node9421 +def node9423 : Tree Nat := .node node9397 node9422 +def node9424 : Tree Nat := .leaf 2855863089077773182209267324617845225153104919786179789455118587512735738405665506058799225509550430097976785793721528831849577038944624102510106034231574528 +def node9425 : Tree Nat := .node node1758 node9424 +def node9426 : Tree Nat := .node node9425 node7884 +def node9427 : Tree Nat := .leaf 971799851553527581570569552014162052202257672043943265213368006312545610615448283325759428810600108152850811939175608757176694105652968293627816861100831622097674865638736434367723979067587821568 +def node9428 : Tree Nat := .node node2219 node9427 +def node9429 : Tree Nat := .node node9428 node9160 +def node9430 : Tree Nat := .node node9426 node9429 +def node9431 : Tree Nat := .leaf 52681375513771265754887036977184851477482977358558121901695430947787108947691287707277393426044768582784304013741437679281840752307338007723087331036703244766237522843137998848 +def node9432 : Tree Nat := .node node1773 node9431 +def node9433 : Tree Nat := .node node9432 node8734 +def node9434 : Tree Nat := .node node9433 node7456 +def node9435 : Tree Nat := .node node9430 node9434 +def node9436 : Tree Nat := .leaf 12265838569442570618094652187355060940022342223338345508485899993168913979942744529637832526593648032933544370751231368463915016573699658672112815789110782738917490688 +def node9437 : Tree Nat := .node node1789 node9436 +def node9438 : Tree Nat := .node node9437 node8309 +def node9439 : Tree Nat := .node node9438 node7052 +def node9440 : Tree Nat := .leaf 226264784939942784041764575991351635242406668151715599282963202873371916500723055406883225964987675694946854361141009432537642797840053283988455510955890247626998502421152787871467307008 +def node9441 : Tree Nat := .node node1804 node9440 +def node9442 : Tree Nat := .node node9441 node8739 +def node9443 : Tree Nat := .node node9442 node7461 +def node9444 : Tree Nat := .node node9439 node9443 +def node9445 : Tree Nat := .node node9435 node9444 +def node9446 : Tree Nat := .leaf 3452526625670513672512276855336786426428324404170465076949511762594175971995896231184131255569269953841352147844558859749414715543213703674140251326821383850204327375493171750371328 +def node9447 : Tree Nat := .node node1835 node9446 +def node9448 : Tree Nat := .node node9447 node8745 +def node9449 : Tree Nat := .node node9448 node7467 +def node9450 : Tree Nat := .node node9168 node9449 +def node9451 : Tree Nat := .leaf 803853996486988308027451125750501273765304219948701811244131941952317946589527705494344992462841317486332763881552698963651134526173980830735585495555164257297321221357568 +def node9452 : Tree Nat := .node node1851 node9451 +def node9453 : Tree Nat := .node node9452 node8315 +def node9454 : Tree Nat := .node node9453 node7073 +def node9455 : Tree Nat := .leaf 14828488945824090294961083252169220767246363403990833514608276463509301919791386159145499096841432314344037047411737194170786958399245732019467420365918451264918134546489508581049380538220288 +def node9456 : Tree Nat := .node node1866 node9455 +def node9457 : Tree Nat := .node node9456 node9171 +def node9458 : Tree Nat := .node node9457 node7896 +def node9459 : Tree Nat := .node node9454 node9458 +def node9460 : Tree Nat := .node node9450 node9459 +def node9461 : Tree Nat := .node node9445 node9460 +def node9462 : Tree Nat := .leaf 1377178920576379837427577009580219589715147046981308291938128751065196467357370505290151434140737571489723052503651581952 +def node9463 : Tree Nat := .node node9462 node9177 +def node9464 : Tree Nat := .node node6706 node9463 +def node9465 : Tree Nat := .node node7903 node9464 +def node9466 : Tree Nat := .node node9465 node9184 +def node9467 : Tree Nat := .node node9466 node9190 +def node9468 : Tree Nat := .leaf 1134503866941667986143541334648056457619674836471095626110679906291061742656396773700619954487092292803036067419936171106985997769036530195831156705040763065407827444143686150102223496953920763963962026331144904033359591567429515431450784685901036769166030659479262163447209525248 +def node9469 : Tree Nat := .node node7484 node9468 +def node9470 : Tree Nat := .node node7089 node9469 +def node9471 : Tree Nat := .node node8333 node9470 +def node9472 : Tree Nat := .node node9471 node9195 +def node9473 : Tree Nat := .node node9472 node9201 +def node9474 : Tree Nat := .node node9467 node9473 +def node9475 : Tree Nat := .node node9461 node9474 +def node9476 : Tree Nat := .node node9423 node9475 +def node9477 : Tree Nat := .node node9384 node9476 +def node9478 : Tree Nat := .node node9336 node9477 +def node9479 : Tree Nat := .leaf 70910819472717805518518461762433435520739548614634136462226558431777249178673042942175392673962812409345367711250780339809446437160831581425893922918914524353048616819643521417267881686267175752698925030312603131862052993148303050282082346650219129053601226360487285938983010364 +def node9480 : Tree Nat := .node node9479 node7499 +def node9481 : Tree Nat := .node node9209 node9480 +def node9482 : Tree Nat := .node node9481 node9213 +def node9483 : Tree Nat := .leaf 7153784826105787969847746240716974985148462131839516448917662028173475729844029918074586489337520293668696837644402376089706427860249973253853828088086557955939104192734684653540662710801597572993401814885481840640 +def node9484 : Tree Nat := .node node2869 node9483 +def node9485 : Tree Nat := .node node9484 node5069 +def node9486 : Tree Nat := .node node9217 node9485 +def node9487 : Tree Nat := .node node9482 node9486 +def node9488 : Tree Nat := .leaf 1665620325623496428562269136476557465537558806091434426819361287209548924547627083508900014995019951292475880506542133188272460331267205358914525268619544328176207885317203325027035388533392405273237258240 +def node9489 : Tree Nat := .node node2511 node9488 +def node9490 : Tree Nat := .node node9489 node9224 +def node9491 : Tree Nat := .node node9222 node9490 +def node9492 : Tree Nat := .leaf 17726622920979684553209871963620509457015918490794380011553769567683403674445702970615987163078511268350905778759499154461369926503795990817760032604495218008104128809598815613755447902300755054929890336609295949003004480901975503813713218106963137104663179504675968957135454208 +def node9493 : Tree Nat := .node node3317 node9492 +def node9494 : Tree Nat := .node node9493 node5074 +def node9495 : Tree Nat := .node node9229 node9494 +def node9496 : Tree Nat := .node node9491 node9495 +def node9497 : Tree Nat := .node node9487 node9496 +def node9498 : Tree Nat := .leaf 25415349206901495797153764899849814842797222993338538006887226672508986275445969902174377670212096424750913704018282061588630070972705159895546345041191777468509031453204317828609739662091680680509440 +def node9499 : Tree Nat := .node node2308 node9498 +def node9500 : Tree Nat := .leaf 283625967792006058808176788520780685867414277271872180408915520460270309811540679986766115142045205324379286600312851575545476454331271213951923519474073034032337482053628370092032869880943113015649049034161208400234461002104176202151920099471941479987157801342862583720488992768 +def node9501 : Tree Nat := .node node9500 node8793 +def node9502 : Tree Nat := .node node9499 node9501 +def node9503 : Tree Nat := .node node9235 node9502 +def node9504 : Tree Nat := .leaf 468830442363668920391941897631627672626689614272234549996267898678376905431058344710936100165223729965871715951863554119415000456249342247164564477580840662200425132375060293454440871409921484094764423756914868501872640 +def node9505 : Tree Nat := .node node3101 node9504 +def node9506 : Tree Nat := .node node9505 node5080 +def node9507 : Tree Nat := .node node9239 node9506 +def node9508 : Tree Nat := .node node9503 node9507 +def node9509 : Tree Nat := .leaf 109158093660061461942256870128127670061469453916008246596033661318564998319153288544839271382713627527903699304876745240626623960269927570401822328004250457091355959972147898155853069250817951607272859175485440 +def node9510 : Tree Nat := .node node2697 node9509 +def node9511 : Tree Nat := .node node9510 node5085 +def node9512 : Tree Nat := .node node9244 node9511 +def node9513 : Tree Nat := .node node9512 node9252 +def node9514 : Tree Nat := .node node9508 node9513 +def node9515 : Tree Nat := .node node9497 node9514 +def node9516 : Tree Nat := .node node9515 node9262 +def node9517 : Tree Nat := .leaf 1589778526533276691354858284486857941309556515119928048240805379269200809138178029257766467128897027246478735440651808683963863879085536420767521522568692598394871744018000262778092879122048917203182723776484713870792074683861412282368 +def node9518 : Tree Nat := .node node3395 node9517 +def node9519 : Tree Nat := .node node9518 node8427 +def node9520 : Tree Nat := .node node8425 node9519 +def node9521 : Tree Nat := .node node8422 node9520 +def node9522 : Tree Nat := .node node8856 node9521 +def node9523 : Tree Nat := .leaf 283625967792006058808176788520780685867492418066007491201189893723442824551350970123355754690799848970629446191804009791438155927011708280049202080546430767585233870780142938902400308355508972714924111819549173426251757972201472024941245485416534337393473657246164134288009723904 +def node9524 : Tree Nat := .node node9523 node8858 +def node9525 : Tree Nat := .node node8433 node9524 +def node9526 : Tree Nat := .node node9265 node9525 +def node9527 : Tree Nat := .node node9526 node8867 +def node9528 : Tree Nat := .node node9527 node9272 +def node9529 : Tree Nat := .node node9522 node9528 +def node9530 : Tree Nat := .leaf 1876879207201175057492789423877314215327939898387375884169474870502860978765784020192710578146539744270187446263364617826790225418785882413744524133358611663882261442077897464880491830622108531976854358169267898127951581024551761700825956922352468068663296 +def node9531 : Tree Nat := .node node377 node9530 +def node9532 : Tree Nat := .node node9531 node7598 +def node9533 : Tree Nat := .node node9532 node8882 +def node9534 : Tree Nat := .node node9533 node8887 +def node9535 : Tree Nat := .leaf 1254114127528279663858649702758819738757691336351197686095533779772580140555070662925258924768296963510965920181475342308532678410116166062853196141853236152836631725706416854345623471208391694740021575680 +def node9536 : Tree Nat := .node node9535 node57 +def node9537 : Tree Nat := .node node7204 node9536 +def node9538 : Tree Nat := .node node8459 node9537 +def node9539 : Tree Nat := .node node8892 node9538 +def node9540 : Tree Nat := .node node9534 node9539 +def node9541 : Tree Nat := .leaf 82189623461693336050640466920002010399224059419112091554660639110750749585190016000708440142764588558496912810373714479827507280279152992141798664767910544729071566291873027101646363078904797918545148704194560 +def node9542 : Tree Nat := .node node9541 node57 +def node9543 : Tree Nat := .node node9276 node9542 +def node9544 : Tree Nat := .node node8469 node9543 +def node9545 : Tree Nat := .node node8898 node9544 +def node9546 : Tree Nat := .leaf 19136262932255243894327540630475154705164967900866663911068029494665271971651822328732451457242618444957051614852090012241971511458780847522848906174281273206945407737948239571798211680470220259983360 +def node9547 : Tree Nat := .node node9546 node4147 +def node9548 : Tree Nat := .node node8901 node9547 +def node9549 : Tree Nat := .node node8047 node9548 +def node9550 : Tree Nat := .node node9549 node9282 +def node9551 : Tree Nat := .node node9545 node9550 +def node9552 : Tree Nat := .node node9540 node9551 +def node9553 : Tree Nat := .node node9529 node9552 +def node9554 : Tree Nat := .node node9516 node9553 +def node9555 : Tree Nat := .leaf 4431655730257012840500151247598389094333148860437198937109582690668832350280923896982472690575782445672423981730577243214361408266728606753454576332479881664099000446578398849864310836572938192520243965657529212453711128294084259391013231211339949825259812532616407161424052224 +def node9556 : Tree Nat := .node node9555 node529 +def node9557 : Tree Nat := .node node7223 node9556 +def node9558 : Tree Nat := .node node8056 node9557 +def node9559 : Tree Nat := .node node8916 node9558 +def node9560 : Tree Nat := .leaf 4431655730257012840500151247598389094333148860437198937109582690332183652581827992519049338071454211077202234349894116206471430470329748877857025382871555402331683226509533197448577248947090808042162398276115079488818823542692339664926870216220401949225151568691819340927860736 +def node9561 : Tree Nat := .node node3365 node9560 +def node9562 : Tree Nat := .node node9561 node6831 +def node9563 : Tree Nat := .node node8483 node9562 +def node9564 : Tree Nat := .node node9291 node9563 +def node9565 : Tree Nat := .node node9559 node9564 +def node9566 : Tree Nat := .node node9565 node9299 +def node9567 : Tree Nat := .leaf 69248847399219318367034471326242072013677720552319918872306130969262830369747016508473746272318167084537800132305034744227673313979795037371697784750120913142388030320313791373592830766070104072092022707012505723279952904650805767362098928086246511469012680508186734037565530 +def node9568 : Tree Nat := .node node9567 node7659 +def node9569 : Tree Nat := .node node9568 node8083 +def node9570 : Tree Nat := .node node8947 node9569 +def node9571 : Tree Nat := .node node8521 node9570 +def node9572 : Tree Nat := .node node8944 node9571 +def node9573 : Tree Nat := .node node8935 node9572 +def node9574 : Tree Nat := .node node9566 node9573 +def node9575 : Tree Nat := .leaf 27967679607885704301190218685229334463595448410322903006780765573805474289927672640854064610822656252569050510580947698823110901873064308988622799852500414409928289070570668080319093852209583895379850053107559710590017945330770862274866132526563328 +def node9576 : Tree Nat := .node node2161 node9575 +def node9577 : Tree Nat := .node node9576 node8954 +def node9578 : Tree Nat := .node node7669 node9577 +def node9579 : Tree Nat := .leaf 5386379163185534471414773640069251753523547958090930032126239644742381726004816012001531498406771089703208956838391166599446745854131737057851412854634015232548895536557933219941255024970848965872679525696342589440 +def node9580 : Tree Nat := .node node3002 node9579 +def node9581 : Tree Nat := .node node9580 node5255 +def node9582 : Tree Nat := .node node8092 node9581 +def node9583 : Tree Nat := .node node9578 node9582 +def node9584 : Tree Nat := .leaf 283625967792006058808176788520780685867492418066007491201189893723442824551978027187119894522729173822008856061182855459613754770049585470528091087434949199023878582307679861741920639840324834621097273356026238973137226308622947536725229630477126583233506205898374693807693234176 +def node9585 : Tree Nat := .node node2598 node9584 +def node9586 : Tree Nat := .node node9585 node9306 +def node9587 : Tree Nat := .node node9304 node9586 +def node9588 : Tree Nat := .leaf 6191329402440458580124204415614330367293195005243462324135270677371812121921528584619555648487620528947942250374768508120159338460325751112129288848657018975458729898330864651947855593137029877655915644576438236572922499160389014920447922370815897947382487038474321920 +def node9589 : Tree Nat := .node node3434 node9588 +def node9590 : Tree Nat := .node node9589 node5264 +def node9591 : Tree Nat := .node node8528 node9590 +def node9592 : Tree Nat := .node node9587 node9591 +def node9593 : Tree Nat := .node node9583 node9592 +def node9594 : Tree Nat := .leaf 6359114106075270959545088843609914025718006747965898412012271524835302263080420578953093753630826691836448620151460163738771171813501969727651547677881703902838865423991110675772987707802875392273746367715546081184830220010635079450624 +def node9595 : Tree Nat := .node node2395 node9594 +def node9596 : Tree Nat := .node node9595 node9312 +def node9597 : Tree Nat := .node node7675 node9596 +def node9598 : Tree Nat := .node node9597 node8535 +def node9599 : Tree Nat := .leaf 23692437876425140216458957644889564495784379482196179251176688417653786143395573887275969421097590675722496831607492232774187679227340842624796772152923037187790413565537871183544616195486276163504218400161185710314979606921216 +def node9600 : Tree Nat := .node node2792 node9599 +def node9601 : Tree Nat := .node node9600 node5275 +def node9602 : Tree Nat := .node node9318 node9601 +def node9603 : Tree Nat := .leaf 1707011694817242694210710703124117431539072329783553114202344791423430903423171540175713850026265366398998246612387635793921889857613080182536713796065221674793276593667861833135231755897578192133197551437132594820949284356079201929391157280768 +def node9604 : Tree Nat := .node node862 node9603 +def node9605 : Tree Nat := .node node9604 node9321 +def node9606 : Tree Nat := .node node9605 node7680 +def node9607 : Tree Nat := .node node9602 node9606 +def node9608 : Tree Nat := .node node9598 node9607 +def node9609 : Tree Nat := .node node9593 node9608 +def node9610 : Tree Nat := .node node9609 node9333 +def node9611 : Tree Nat := .node node9574 node9610 +def node9612 : Tree Nat := .node node9554 node9611 +def node9613 : Tree Nat := .leaf 22158278915351719406283974454238294293253600613639834401477574801287227636565480605836873234056213251386675190208529309257073181946602535894361398425560037988433397372343350750903237034660444658407064468342277185322991397778127512448970732101282128690299419324947478428759621836 +def node9614 : Tree Nat := .node node9613 node7714 +def node9615 : Tree Nat := .node node7307 node9614 +def node9616 : Tree Nat := .node node9615 node8989 +def node9617 : Tree Nat := .node node9616 node8996 +def node9618 : Tree Nat := .leaf 106366229208979968755504199669210556446675929746210728544744454015716584733946038785236571687661310716404351711447404795421755873117666509250702519302488460868630046532084816629347552449279191460795773096451153178711674878930269877890096687309583622662593343821807458363560165376 +def node9619 : Tree Nat := .node node3375 node9618 +def node9620 : Tree Nat := .node node9619 node8574 +def node9621 : Tree Nat := .node node8572 node9620 +def node9622 : Tree Nat := .node node9340 node9621 +def node9623 : Tree Nat := .node node9617 node9622 +def node9624 : Tree Nat := .node node9623 node9348 +def node9625 : Tree Nat := .leaf 4538015484673128829149194236736751216454675671906553705267500427190823742415763610243858534894498949233759028493994007295121419313603122547579190081828989791157197712638893616936228667662815174385279704114405434989883399120253214077927948847161017988890846913041829162856629665894 +def node9626 : Tree Nat := .node node9625 node7769 +def node9627 : Tree Nat := .node node9626 node5375 +def node9628 : Tree Nat := .node node9048 node9627 +def node9629 : Tree Nat := .node node9045 node9628 +def node9630 : Tree Nat := .node node9354 node9629 +def node9631 : Tree Nat := .node node9036 node9630 +def node9632 : Tree Nat := .node node9624 node9631 +def node9633 : Tree Nat := .leaf 6359114106075270959545088843609914016149875281838276464848501209597724910497936628519761798096811944538947904689447965273123107733653903939072270870999045422413426940149168126861422515824794462952699232391567720588630441992285477404672 +def node9634 : Tree Nat := .node node3414 node9633 +def node9635 : Tree Nat := .node node9634 node5392 +def node9636 : Tree Nat := .node node8635 node9635 +def node9637 : Tree Nat := .node node8205 node9636 +def node9638 : Tree Nat := .node node9058 node9637 +def node9639 : Tree Nat := .node node9638 node9368 +def node9640 : Tree Nat := .leaf 66040847205386218917755715040531405124250706444155860708962823057636354365324083092028507272312376655958431544544599075221604076110973130996411039455535123385653242355042749324242940282797301225406729407614481103583595099680297269679637968713074805490434321411779592432 +def node9641 : Tree Nat := .node node9640 node7795 +def node9642 : Tree Nat := .node node7377 node9641 +def node9643 : Tree Nat := .node node9642 node9372 +def node9644 : Tree Nat := .node node9643 node9079 +def node9645 : Tree Nat := .node node9644 node9085 +def node9646 : Tree Nat := .leaf 34959599509857130376772047909570245155022077753222690323156717052282288738011130416887571407233163944657004505570241951436566021340241608247920885549900035970086781639599548913842719069037144801148426208064817249689987399067544528111277999285862400 +def node9647 : Tree Nat := .node node9646 node9087 +def node9648 : Tree Nat := .node node8666 node9647 +def node9649 : Tree Nat := .node node8237 node9648 +def node9650 : Tree Nat := .node node9649 node9379 +def node9651 : Tree Nat := .node node9650 node9100 +def node9652 : Tree Nat := .node node9645 node9651 +def node9653 : Tree Nat := .node node9639 node9652 +def node9654 : Tree Nat := .node node9632 node9653 +def node9655 : Tree Nat := .leaf 23692437876425140175364145914042896470464146022195174051564658708097740366065254332051499465651646752959477016938832457563383235038448516741832457698362069507104360669820052043269431264795302740131845291689914481633001077735424 +def node9656 : Tree Nat := .node node3384 node9655 +def node9657 : Tree Nat := .node node9656 node5456 +def node9658 : Tree Nat := .node node8692 node9657 +def node9659 : Tree Nat := .node node9388 node9658 +def node9660 : Tree Nat := .node node9113 node9659 +def node9661 : Tree Nat := .node node9660 node9396 +def node9662 : Tree Nat := .leaf 179517918048042891055120502722933031097901996790749277476957330659929690961850774297095211550081538663474474761123650214109927183834272858240826062492807389647271873448271557247085100729155084372539139087763565969408 +def node9663 : Tree Nat := .node node3060 node9662 +def node9664 : Tree Nat := .node node9663 node5478 +def node9665 : Tree Nat := .node node8716 node9664 +def node9666 : Tree Nat := .node node9404 node9665 +def node9667 : Tree Nat := .leaf 41797272406528445672039059624758789105783681569329760381243501477858445365412806695582161552757383013021777095534757295183354798665799400359584498799593977082351193169195107058789118502274868214532981915648 +def node9668 : Tree Nat := .node node2686 node9667 +def node9669 : Tree Nat := .node node9668 node6285 +def node9670 : Tree Nat := .node node8291 node9669 +def node9671 : Tree Nat := .node node9670 node8722 +def node9672 : Tree Nat := .node node9666 node9671 +def node9673 : Tree Nat := .leaf 637775763039069300415635065075054765408076195821071783161064170499549032065014750603975853771322372635219987419658772204335858133938589483025886517327788956945056048113938932906766525455266055211450368 +def node9674 : Tree Nat := .node node2461 node9673 +def node9675 : Tree Nat := .node node9674 node9147 +def node9676 : Tree Nat := .node node8297 node9675 +def node9677 : Tree Nat := .node node9676 node9410 +def node9678 : Tree Nat := .leaf 2739226044434248215562751811568192002836639355327595176345174112852931075467693699601672539521507853141395183732965854097136340085361829501965729713330190882068967795536370197251684948192979310242919485043376128 +def node9679 : Tree Nat := .node node2858 node9678 +def node9680 : Tree Nat := .node node9679 node5498 +def node9681 : Tree Nat := .node node9414 node9680 +def node9682 : Tree Nat := .leaf 1665620325623496428562269136476557465537558806091434426819361287209548924547627083508900014995019951292475880506542133250453045692176407519488249244377321641725918963469959166394129173505152475035508670634 +def node9683 : Tree Nat := .node node9682 node7875 +def node9684 : Tree Nat := .node node9683 node5502 +def node9685 : Tree Nat := .node node9418 node9684 +def node9686 : Tree Nat := .node node9681 node9685 +def node9687 : Tree Nat := .node node9677 node9686 +def node9688 : Tree Nat := .node node9672 node9687 +def node9689 : Tree Nat := .node node9661 node9688 +def node9690 : Tree Nat := .leaf 17926543152476856912677293520855478492195558048021376513170141317658239181844451441763375555634021441781557957861855365965970225108626403565539592738381609936647402271205739190637190086948690497965010394440362098688 +def node9691 : Tree Nat := .node node3021 node9690 +def node9692 : Tree Nat := .node node9691 node7455 +def node9693 : Tree Nat := .node node9433 node9692 +def node9694 : Tree Nat := .node node9430 node9693 +def node9695 : Tree Nat := .leaf 4173848580680055756279568541994196943052941478793829798970870049125104952101700809263478861105167642650557206445805580812965106477175467546456398614305446375312144465559572308387165583142234643351971299328 +def node9696 : Tree Nat := .node node2617 node9695 +def node9697 : Tree Nat := .node node9696 node5515 +def node9698 : Tree Nat := .node node9438 node9697 +def node9699 : Tree Nat := .leaf 1707011694817242694210710703124117431539072329783553111974590583600093394321036967079868476543243634344037343009266289163416437119001075052696473895004967876628086372186217638463012653663477607048890266416520198213530009766106081771737743097856 +def node9700 : Tree Nat := .node node3453 node9699 +def node9701 : Tree Nat := .node node9700 node7055 +def node9702 : Tree Nat := .node node9442 node9701 +def node9703 : Tree Nat := .node node9698 node9702 +def node9704 : Tree Nat := .node node9694 node9703 +def node9705 : Tree Nat := .leaf 63687875071411983585808846160800124253127158795071865829023285661698989137294018696036969926531488687905230811245812695510331824908072930091192605809104101185793219994500231270994538774165079088693248 +def node9706 : Tree Nat := .node node2414 node9705 +def node9707 : Tree Nat := .node node9706 node9166 +def node9708 : Tree Nat := .node node7891 node9707 +def node9709 : Tree Nat := .leaf 1174833932040723294629219108182784638464528092235128931167118381394050363021357969687404580414031229208596182326434553263945824672718939984071202749702577188808124155245739323597598889533097366025703763626623501093306368 +def node9710 : Tree Nat := .node node3237 node9709 +def node9711 : Tree Nat := .node node9710 node7065 +def node9712 : Tree Nat := .node node9448 node9711 +def node9713 : Tree Nat := .node node9708 node9712 +def node9714 : Tree Nat := .leaf 273537340583448134043537803968131690859917572754232429705354939539462878140937064235891350641388266628746917081632314544158481218088171441124566539587121733652456699694911791849342561684703036522000773292228608 +def node9715 : Tree Nat := .node node2811 node9714 +def node9716 : Tree Nat := .node node9715 node7072 +def node9717 : Tree Nat := .node node9453 node9716 +def node9718 : Tree Nat := .node node9717 node9458 +def node9719 : Tree Nat := .node node9713 node9718 +def node9720 : Tree Nat := .node node9704 node9719 +def node9721 : Tree Nat := .leaf 34959599509857130376772047909570245155022077753222839825210875296375213171922306004033705508544889465468809724550668474885245115280842633998922133175927982521286889181138305561319029099389471544354550865579337891051476836229428843732809535998394368 +def node9722 : Tree Nat := .node node2297 node9721 +def node9723 : Tree Nat := .node node9722 node9463 +def node9724 : Tree Nat := .node node7903 node9723 +def node9725 : Tree Nat := .leaf 17726622920979684553209871963620509457015918490794380011553772325509535225439352334980090878535409072407460321315675603096068034603239702925670096934496189912398045702045591281720856225832850639296050128165046424536311542226283592403674714817971430760451972236472335006481514496 +def node9726 : Tree Nat := .node node3129 node9725 +def node9727 : Tree Nat := .node node9726 node9182 +def node9728 : Tree Nat := .node node8753 node9727 +def node9729 : Tree Nat := .node node9724 node9728 +def node9730 : Tree Nat := .leaf 283625967792006058808176788520780685867414277271872180408915520460270310453647113281245303037673853136894992844250815787358691725117514264334266573316946827204522086251437357760852310332385704936966462386676328410954037497695100268951684641518401220180487621206475531876403511296 +def node9731 : Tree Nat := .node node2725 node9730 +def node9732 : Tree Nat := .node node9731 node5546 +def node9733 : Tree Nat := .node node8758 node9732 +def node9734 : Tree Nat := .node node9733 node9189 +def node9735 : Tree Nat := .node node9729 node9734 +def node9736 : Tree Nat := .leaf 1589778526533276691354858284486867739076177829804801943941608182548409853601743272989688933959998259887211368541143037507581481643504903925946971770410976554043879198167170348220849464676920541955449295530325964379364765473853907337216 +def node9737 : Tree Nat := .node node2500 node9736 +def node9738 : Tree Nat := .leaf 27967679607885704301190218685229334463595448410322902860782665809895227293410181258444742214239344020615132732046787126046305551195387940799412837696615621493374382715549634138280542768195567951294687821996705686526188365802292459622891980635242496 +def node9739 : Tree Nat := .node node9738 node9468 +def node9740 : Tree Nat := .node node9737 node9739 +def node9741 : Tree Nat := .node node8333 node9740 +def node9742 : Tree Nat := .node node9741 node9195 +def node9743 : Tree Nat := .leaf 106366229208979968755504199669210556446675929746210728544744454015758665821158425773294499606724351745728754429869990186297742120342216366485079165879397793158850754141900680380196978190983346918797243527356175696876889925729911667259124244095116932725667925559977804377446416384 +def node9744 : Tree Nat := .node node2913 node9743 +def node9745 : Tree Nat := .node node9744 node8772 +def node9746 : Tree Nat := .node node8338 node9745 +def node9747 : Tree Nat := .leaf 6191329402440458580124204415614330367293195005243462324135270677371812121923809804928366746096941114750792396037215122373783618425615347371078926432261357668711686303989550351837176747923827081311259996937125955572048829820250122014573919707996030422423924134597623808 +def node9748 : Tree Nat := .node node2102 node9747 +def node9749 : Tree Nat := .node node9748 node9198 +def node9750 : Tree Nat := .node node9749 node7914 +def node9751 : Tree Nat := .node node9746 node9750 +def node9752 : Tree Nat := .node node9742 node9751 +def node9753 : Tree Nat := .node node9735 node9752 +def node9754 : Tree Nat := .node node9720 node9753 +def node9755 : Tree Nat := .node node9689 node9754 +def node9756 : Tree Nat := .node node9654 node9755 +def node9757 : Tree Nat := .node node9612 node9756 +def node9758 : Tree Nat := .leaf 503820925841965910293903145710484129446837736164208910110436259998038510964770243430138498201532542156933485869433164765803114760238270660481417446375105010440475821427886356946309731287924675203273040506489884413804450500112958696867850406894963378914468011442176 +def node9759 : Tree Nat := .node node126 node9758 +def node9760 : Tree Nat := .node node9759 node7535 +def node9761 : Tree Nat := .node node9760 node8811 +def node9762 : Tree Nat := .node node9761 node8816 +def node9763 : Tree Nat := .leaf 572778078369499224088375678951108638011287396263498246212912731873199370030112045970591355774519253321541817541313941550953993082870643211586713456563448667385049704462328463260653386992258808895520868586472919786367029038635876478250857389318805131008 +def node9764 : Tree Nat := .node node3425 node9763 +def node9765 : Tree Nat := .node node9764 node5105 +def node9766 : Tree Nat := .node node8390 node9765 +def node9767 : Tree Nat := .node node8821 node9766 +def node9768 : Tree Nat := .node node9762 node9767 +def node9769 : Tree Nat := .node node9768 node9261 +def node9770 : Tree Nat := .node node9515 node9769 +def node9771 : Tree Nat := .leaf 6190951559809168803779520960961825423248316278147658867123225492542117970998137146895424917273663411058907179831602016087110815463642615673627887334875468869863161361049791380796437909277787151859098932189940124330811726200031418998420070799920879369429847547385479168 +def node9772 : Tree Nat := .node node9268 node9771 +def node9773 : Tree Nat := .node node9772 node5152 +def node9774 : Tree Nat := .node node8875 node9773 +def node9775 : Tree Nat := .node node8872 node9774 +def node9776 : Tree Nat := .node node9527 node9775 +def node9777 : Tree Nat := .node node9522 node9776 +def node9778 : Tree Nat := .leaf 8254602048994769481416783112254089866662524486502034756622440757077076381466184083838419667145204651066231332524311416731706162571183743384586846270434260980075917553007313198690901692914400426654614838893505943231394136886341844229466777506056646267888305831910834176 +def node9779 : Tree Nat := .node node3503 node9778 +def node9780 : Tree Nat := .node node9779 node9536 +def node9781 : Tree Nat := .node node8459 node9780 +def node9782 : Tree Nat := .node node8892 node9781 +def node9783 : Tree Nat := .node node9534 node9782 +def node9784 : Tree Nat := .leaf 17995655178172785531242154030758178957706569461585899581315252887063452649160041829112219582089587820623161032701812333531863751213538489262796801314217116991225856 +def node9785 : Tree Nat := .node node439 node9784 +def node9786 : Tree Nat := .node node9785 node8037 +def node9787 : Tree Nat := .node node9786 node8897 +def node9788 : Tree Nat := .node node9787 node9544 +def node9789 : Tree Nat := .node node9788 node9550 +def node9790 : Tree Nat := .node node9783 node9789 +def node9791 : Tree Nat := .node node9777 node9790 +def node9792 : Tree Nat := .node node9770 node9791 +def node9793 : Tree Nat := .leaf 6190951559809168803779520960961825423248316278147658867123225492542117970998137425364700895190852048825728816812273701464827322333755566063796216148057061196363802591079779013328562527808638305524916193544837947548825628483683114139791779764752303351667944087990829056 +def node9794 : Tree Nat := .node node9793 node8059 +def node9795 : Tree Nat := .node node5674 node9794 +def node9796 : Tree Nat := .node node9795 node9290 +def node9797 : Tree Nat := .leaf 78382132970517478991165606422426233672355708521949855382244534644315183615313069074077534829875210501252638208309597598712957178119783906275532174658619735763527784574968349798084012877840090220881510400 +def node9798 : Tree Nat := .node node9797 node57 +def node9799 : Tree Nat := .node node9561 node9798 +def node9800 : Tree Nat := .node node8483 node9799 +def node9801 : Tree Nat := .node node9796 node9800 +def node9802 : Tree Nat := .node node9559 node9801 +def node9803 : Tree Nat := .leaf 1196016433265952743395471289404697169072810494067060677638410737356538792695510622309009252350241986916522682559980387105027308962188677881618288251121661172954563078459873527440160264918356262387712 +def node9804 : Tree Nat := .node node9803 node607 +def node9805 : Tree Nat := .node node6846 node9804 +def node9806 : Tree Nat := .node node8067 node9805 +def node9807 : Tree Nat := .leaf 94758184344525691842589080106353915726128296943157752144717531617800961467674370503593652882607817257720198406807316479869050731801577625681884568619117048440337251626510453224003610961459724599459813858581144614766712877940736 +def node9808 : Tree Nat := .node node9294 node9807 +def node9809 : Tree Nat := .node node9808 node5216 +def node9810 : Tree Nat := .node node8494 node9809 +def node9811 : Tree Nat := .node node9806 node9810 +def node9812 : Tree Nat := .node node8923 node9811 +def node9813 : Tree Nat := .node node9802 node9812 +def node9814 : Tree Nat := .leaf 21006411636098684369632382521210230624191329883882561241821780788479335903137376612200105088922870717887005735400158572019133419943328750957391616292313441635744039001583488362143794339273282753602407890944 +def node9815 : Tree Nat := .node node2628 node9814 +def node9816 : Tree Nat := .node node9815 node5228 +def node9817 : Tree Nat := .node node8074 node9816 +def node9818 : Tree Nat := .leaf 30750788930784052141961861920805917214380440082589217766573459895919230378495282122721611875165072323090973711248027490353551036261722796287033747819087500752991032154127481047726496709629813071351000413519546892327893859094639319918123083542961087152742465536 +def node9819 : Tree Nat := .node node3473 node9818 +def node9820 : Tree Nat := .node node9819 node8508 +def node9821 : Tree Nat := .node node8506 node9820 +def node9822 : Tree Nat := .node node9817 node9821 +def node9823 : Tree Nat := .node node8934 node9822 +def node9824 : Tree Nat := .leaf 320532404115275335229986305560458841311513212343722927441536036337621143189589605907120381775589622821876830553552735064334915182815000452373867450006301431775339338727147857181844874225696229191319552 +def node9825 : Tree Nat := .node node2434 node9824 +def node9826 : Tree Nat := .node node9825 node8937 +def node9827 : Tree Nat := .node node7652 node9826 +def node9828 : Tree Nat := .leaf 217460971493240179111222239609959967416852664902513108049059154338122525742887751978028913820783394260139771850165988894663770112 +def node9829 : Tree Nat := .node node9828 node8513 +def node9830 : Tree Nat := .node node6089 node9829 +def node9831 : Tree Nat := .node node9830 node8942 +def node9832 : Tree Nat := .node node9827 node9831 +def node9833 : Tree Nat := .leaf 758065474756205534740712640850831325883656141507343823712661761141118511753076192052590413331567103173883519921202034199422833756513723753409457848468793450964552877572904010295213962029846900594489296265025821073932120798265344 +def node9834 : Tree Nat := .node node2028 node9833 +def node9835 : Tree Nat := .node node9834 node8946 +def node9836 : Tree Nat := .node node9835 node9569 +def node9837 : Tree Nat := .node node8521 node9836 +def node9838 : Tree Nat := .node node9832 node9837 +def node9839 : Tree Nat := .node node9823 node9838 +def node9840 : Tree Nat := .node node9813 node9839 +def node9841 : Tree Nat := .leaf 1516130949512411069481425281701662651618052751090524042230053353042156128597043386217450681276672174797780840232142525183021894482678412242501316242512262275594731051006524991661085059674726865929261969595205036161735993984037632 +def node9842 : Tree Nat := .node node769 node9841 +def node9843 : Tree Nat := .node node9842 node8091 +def node9844 : Tree Nat := .node node9843 node9581 +def node9845 : Tree Nat := .node node9578 node9844 +def node9846 : Tree Nat := .leaf 33992831540273094316151640874536164934625201688560801263722131414287413730675858788193463597623834324638029306701865652802804238642475075655741142392275129013667998134779383135021826048 +def node9847 : Tree Nat := .node node800 node9846 +def node9848 : Tree Nat := .node node9847 node8527 +def node9849 : Tree Nat := .node node9848 node9590 +def node9850 : Tree Nat := .node node9587 node9849 +def node9851 : Tree Nat := .node node9845 node9850 +def node9852 : Tree Nat := .leaf 458222462695599379270700543123871994649449568634787237553785692458956874129784670072636529748425157355181179828491938909568233393724009090772130464238696934527463584720883257237488359460168530644722507743922583535492172995357844018000520868659577548800 +def node9853 : Tree Nat := .node node831 node9852 +def node9854 : Tree Nat := .node node9853 node8533 +def node9855 : Tree Nat := .node node9854 node7280 +def node9856 : Tree Nat := .node node9597 node9855 +def node9857 : Tree Nat := .leaf 123003155723136208567847447683223665156030184372322033465157915869473587451385680080856095538856044158426243859888522334114484606338942965396231338480162505923917145054749748818687743027363254406311161071117038947561126299864660328618566523105655877646120124416 +def node9858 : Tree Nat := .node node847 node9857 +def node9859 : Tree Nat := .node node9858 node9317 +def node9860 : Tree Nat := .node node9859 node9601 +def node9861 : Tree Nat := .leaf 1516130949512411069481425281701662651618052751090524034315480505902811038660962713588740600152469003559001962982124730210310691073658662792376482282734822608469245418490066132417403961858688146967785006334623662830319285225665280 +def node9862 : Tree Nat := .node node4244 node9861 +def node9863 : Tree Nat := .node node9862 node5279 +def node9864 : Tree Nat := .node node9605 node9863 +def node9865 : Tree Nat := .node node9860 node9864 +def node9866 : Tree Nat := .node node9856 node9865 +def node9867 : Tree Nat := .node node9851 node9866 +def node9868 : Tree Nat := .leaf 189516368689051383685178160212782801476485361798148216021259930422652568466179849343966583056669755404987969800449560250963903010195628972374212412915763048082369150359702090433146618364783744489305364755432194018846881383972864 +def node9869 : Tree Nat := .node node2278 node9868 +def node9870 : Tree Nat := .node node9869 node8972 +def node9871 : Tree Nat := .node node7687 node9870 +def node9872 : Tree Nat := .node node9871 node8542 +def node9873 : Tree Nat := .node node9872 node8548 +def node9874 : Tree Nat := .leaf 3479375543891842865779555833759359478669642638440209728784946469409960411886204031648462621132534308162233459514368303463229554688 +def node9875 : Tree Nat := .node node9874 node8550 +def node9876 : Tree Nat := .node node6142 node9875 +def node9877 : Tree Nat := .node node9876 node7298 +def node9878 : Tree Nat := .node node9330 node9877 +def node9879 : Tree Nat := .node node9878 node8981 +def node9880 : Tree Nat := .node node9873 node9879 +def node9881 : Tree Nat := .node node9867 node9880 +def node9882 : Tree Nat := .node node9840 node9881 +def node9883 : Tree Nat := .node node9792 node9882 +def node9884 : Tree Nat := .leaf 135243399970730303066198984938628251268824915465247109664758362321700642924402143304641447917533484128220870972182585488064330900877483342277181980307567240212301999953316059706245939889710717364779070745272922894004703852462857591499078480633020135351740520305367533486080 +def node9885 : Tree Nat := .node node1006 node9884 +def node9886 : Tree Nat := .node node9885 node9614 +def node9887 : Tree Nat := .node node9886 node8989 +def node9888 : Tree Nat := .node node9887 node8996 +def node9889 : Tree Nat := .node node9888 node9622 +def node9890 : Tree Nat := .leaf 262894183196658893935434297526466556912399064324056821502698691324711428689225866820451812937101450598427843366758519303383166097913761405664081670569984 +def node9891 : Tree Nat := .node node9890 node8583 +def node9892 : Tree Nat := .node node8154 node9891 +def node9893 : Tree Nat := .node node9892 node9012 +def node9894 : Tree Nat := .node node9007 node9893 +def node9895 : Tree Nat := .leaf 776306425242526730420411038771304454586306072706819884445598377783441334845062553184132474087299170900821840135927576361068290363143901903086605984093762979791340047481665694066708217277919524728123363042387160733046257761187266560 +def node9896 : Tree Nat := .node node9343 node9895 +def node9897 : Tree Nat := .node node9896 node8163 +def node9898 : Tree Nat := .node node8596 node9897 +def node9899 : Tree Nat := .node node9018 node9898 +def node9900 : Tree Nat := .node node9894 node9899 +def node9901 : Tree Nat := .node node9889 node9900 +def node9902 : Tree Nat := .leaf 2015283703367863641175612582841936517787350944656835640441746215724148601621265841204650329199635253963361738401575054429896032048337003206849961625116520064232442010467426914654152817393427271595203822211341964674986046381010389129515789197900540506123050296541184 +def node9903 : Tree Nat := .node node1131 node9902 +def node9904 : Tree Nat := .node node9903 node7748 +def node9905 : Tree Nat := .node node9904 node9024 +def node9906 : Tree Nat := .node node9905 node9029 +def node9907 : Tree Nat := .leaf 458222462695599379270700543123871994649449568634787237553785692458956873611095223962512409934374174393786035951936159879263620894266842879440529037625178634564082466332908971212752533047569882845328623317450670049632818731112383135352795443470887088128 +def node9908 : Tree Nat := .node node3483 node9907 +def node9909 : Tree Nat := .node node9908 node6951 +def node9910 : Tree Nat := .node node8612 node9909 +def node9911 : Tree Nat := .node node9034 node9910 +def node9912 : Tree Nat := .node node9906 node9911 +def node9913 : Tree Nat := .node node9912 node9630 +def node9914 : Tree Nat := .node node9901 node9913 +def node9915 : Tree Nat := .leaf 94758184344525691842589080106353933975890767431938626709403954418966261040588399497833375199377888854820867241517345889948852842737473864705476431501068863680102643157330903691573535240701666775705983682284491579796326848856064 +def node9916 : Tree Nat := .node node9915 node9065 +def node9917 : Tree Nat := .node node6599 node9916 +def node9918 : Tree Nat := .leaf 758065474756205534740712640850831325809026375545262017157740252942407691741394964028749223060862538061761587254458532027573185719828205242744279058321733505762236725048329326032760648871396660996919126088567204168285216391036928 +def node9919 : Tree Nat := .node node9363 node9918 +def node9920 : Tree Nat := .leaf 4249103942534136789552696962776259077577276031006939427604420765221094426996941958460243036970247720957266013151423046438199843211846397625444404135665696461000950475253452438893494272 +def node9921 : Tree Nat := .node node9920 node57 +def node9922 : Tree Nat := .node node9919 node9921 +def node9923 : Tree Nat := .node node9917 node9922 +def node9924 : Tree Nat := .node node8211 node9923 +def node9925 : Tree Nat := .node node9064 node9924 +def node9926 : Tree Nat := .node node9638 node9925 +def node9927 : Tree Nat := .leaf 7507516828804700229971157695509256861311759593549503536677899755757880972394849199241138654603637921490647409518277107506648049119780025230444789235461426206976292249728517077129878497711675432169208373367605330449501004324220518173472389939402556764585984 +def node9928 : Tree Nat := .node node1382 node9927 +def node9929 : Tree Nat := .node node9928 node9641 +def node9930 : Tree Nat := .node node9929 node9372 +def node9931 : Tree Nat := .node node9930 node9079 +def node9932 : Tree Nat := .leaf 33018408195979077911344184489810038954857014747128397945669039857690094711259940778939113224190845690713234878736626635101426489704623855928127645312468794295826211108275643472268064973423738219776928440975063934678245832023535234268021693006235269188280673315317612544 +def node9933 : Tree Nat := .node node3522 node9932 +def node9934 : Tree Nat := .node node9933 node5423 +def node9935 : Tree Nat := .node node8661 node9934 +def node9936 : Tree Nat := .node node9084 node9935 +def node9937 : Tree Nat := .node node9931 node9936 +def node9938 : Tree Nat := .leaf 35991310356345571062484308061715879226602072760467061847310352541271483457166604882882042365068153993287831826727907654290834411964784478308869567569376928128303104 +def node9939 : Tree Nat := .node node1444 node9938 +def node9940 : Tree Nat := .node node9939 node8236 +def node9941 : Tree Nat := .node node9940 node9648 +def node9942 : Tree Nat := .node node9941 node9379 +def node9943 : Tree Nat := .node node9942 node9100 +def node9944 : Tree Nat := .node node9937 node9943 +def node9945 : Tree Nat := .node node9926 node9944 +def node9946 : Tree Nat := .node node9914 node9945 +def node9947 : Tree Nat := .leaf 540973599882921212264795939754513005075299661860988438659038499017268058136175524568853356593652864839094194135635460301924269586378058566697957041105095445762385903463366169913988258213803045910824885683271517381634772424575713672810577919739705198507902525377915073331200 +def node9948 : Tree Nat := .node node1508 node9947 +def node9949 : Tree Nat := .node node9948 node7831 +def node9950 : Tree Nat := .node node9949 node9107 +def node9951 : Tree Nat := .node node9950 node9112 +def node9952 : Tree Nat := .node node9951 node9659 +def node9953 : Tree Nat := .leaf 4206306931146542302966948760423464910598385029170230976875316821301494661041908569550558803227495933847878415294970095648665795387752093177800965002100736 +def node9954 : Tree Nat := .node node9953 node8700 +def node9955 : Tree Nat := .node node8274 node9954 +def node9956 : Tree Nat := .node node9955 node9126 +def node9957 : Tree Nat := .node node9123 node9956 +def node9958 : Tree Nat := .leaf 189516368689051383685178160212707831452256593886315504289435063235601922935348741007187305765215634515440396813614632959740619776598227760408442779877519750822839283818851170181243200258698719351019986293448792198538956200738816 +def node9959 : Tree Nat := .node node9391 node9958 +def node9960 : Tree Nat := .node node9959 node8283 +def node9961 : Tree Nat := .node node9135 node9960 +def node9962 : Tree Nat := .node node9132 node9961 +def node9963 : Tree Nat := .node node9957 node9962 +def node9964 : Tree Nat := .node node9952 node9963 +def node9965 : Tree Nat := .leaf 503820925841965910293903145710484129446837736164208910110436259998038510964770243430139004734194759075019241778596213003248306709241229942329561447513983263957493998691851164935683157044063371234353521559856876009394710726590972231393499084102856589583828547272704 +def node9966 : Tree Nat := .node node1648 node9965 +def node9967 : Tree Nat := .node node9966 node8715 +def node9968 : Tree Nat := .node node9967 node9664 +def node9969 : Tree Nat := .node node9404 node9968 +def node9970 : Tree Nat := .leaf 135243399970730303066198984938628251268824915465247109664758362321700642924402143304641447917533484128220988908508361161231588449458139225680023134095705253975688756400198735461320694541338408824940872581758593780724415222615975422268763630402787680172097792056731577090048 +def node9971 : Tree Nat := .node node1664 node9970 +def node9972 : Tree Nat := .node node9971 node8290 +def node9973 : Tree Nat := .node node9972 node9669 +def node9974 : Tree Nat := .leaf 1876879207201175057492789423877314215327939898387375884169474870502863154307002597670746810699833783181684988276774827749547650341975951266725714184144871273491539821231997235574067496290267391565821383658120519521784608966345323633711298692977622027075584 +def node9975 : Tree Nat := .node node1679 node9974 +def node9976 : Tree Nat := .node node9975 node8720 +def node9977 : Tree Nat := .leaf 123003155723136208567847447683223665156030184372322033465157915869473587451385680080856095418089246564136920588158775742489880096997463912070137630441560898063943948505986482062632537342282693079323160086674002154902418142271296086652670477259382480865469661184 +def node9978 : Tree Nat := .node node3492 node9977 +def node9979 : Tree Nat := .node node9978 node5487 +def node9980 : Tree Nat := .node node9976 node9979 +def node9981 : Tree Nat := .node node9973 node9980 +def node9982 : Tree Nat := .node node9969 node9981 +def node9983 : Tree Nat := .leaf 33018408195979077911344184489810038954857014747128397945669039857690094711259940778939113224190845690713236678302144452379979613920026930320871193191316115062479451410504688207300333568571865836051369997317923903042499240381584517574443890726110872594353019380859666432 +def node9984 : Tree Nat := .node node1695 node9983 +def node9985 : Tree Nat := .node node9984 node8296 +def node9986 : Tree Nat := .node node9985 node9675 +def node9987 : Tree Nat := .leaf 970335652472282206014425373911873826643838038188458692328331923556755613148941055626646840777046284631252286366401277886644267491844561407225470902733661639857553169741034189407186678110666213527761289472104298939762895393543684096 +def node9988 : Tree Nat := .node node3276 node9987 +def node9989 : Tree Nat := .node node9988 node5493 +def node9990 : Tree Nat := .node node9409 node9989 +def node9991 : Tree Nat := .node node9986 node9990 +def node9992 : Tree Nat := .node node9991 node9686 +def node9993 : Tree Nat := .node node9982 node9992 +def node9994 : Tree Nat := .node node9964 node9993 +def node9995 : Tree Nat := .leaf 8254602048994769481416783112254089866662524486502034756622440757077076381466184083838419667145204651066231444997156280311615732834646435534133318012862218527991745071896628494630418480111158402671767436164934691254159974908719924436118164863548871480767827461007212544 +def node9996 : Tree Nat := .node node1820 node9995 +def node9997 : Tree Nat := .node node9996 node7890 +def node9998 : Tree Nat := .node node9997 node9707 +def node9999 : Tree Nat := .node node9998 node9712 +def node10000 : Tree Nat := .leaf 3032261899024822138962850563403325303236105502181048068630961011805622077321925427177481200304938007118003925964249460420610292611162617740602287052390042399581767683873256119732340505525514756187336185096369607227551534219840512 +def node10001 : Tree Nat := .node node4493 node10000 +def node10002 : Tree Nat := .node node10001 node6699 +def node10003 : Tree Nat := .node node9457 node10002 +def node10004 : Tree Nat := .node node9717 node10003 +def node10005 : Tree Nat := .node node9999 node10004 +def node10006 : Tree Nat := .node node9704 node10005 +def node10007 : Tree Nat := .leaf 2015283703367863641175612582841936517787350944656835640441746215724148601621265841204658433722230724652733832948183826229019103232384351716420265643338572120504732846690863842484127629491646408092491519065213830204430210004658605681926168033226831876832818869829632 +def node10008 : Tree Nat := .node node1898 node10007 +def node10009 : Tree Nat := .node node10008 node8752 +def node10010 : Tree Nat := .node node10009 node9727 +def node10011 : Tree Nat := .node node9724 node10010 +def node10012 : Tree Nat := .leaf 540973599882921212264795939754513005075299661860988438659038499017268058136175524568853356593652864839096081116847871072600390363668552701143415501715303665976574006613488981995184332639846109273413715067042251569150154347025598965125540316055985915633618873399739770994688 +def node10013 : Tree Nat := .node node1914 node10012 +def node10014 : Tree Nat := .node node10013 node8757 +def node10015 : Tree Nat := .node node10014 node9732 +def node10016 : Tree Nat := .leaf 7507516828804700229971157695509256861311759593549503536677899755757915781054346438889718375456342544074608081732840466270766847890821126878143830048041579960724746316194113408227089148402217185592680781189247272750829451392917509099637858269405020099182592 +def node10017 : Tree Nat := .node node1929 node10016 +def node10018 : Tree Nat := .node node10017 node8761 +def node10019 : Tree Nat := .leaf 970335652460986150179592503924077391275019526735053276680925613458022005425490280305202046777422788947271366378517686424651131505532068219761957338943155427503605385315311005041255813628375685237790475361209269501847557272080744448 +def node10020 : Tree Nat := .node node3715 node10019 +def node10021 : Tree Nat := .node node10020 node9187 +def node10022 : Tree Nat := .node node10018 node10021 +def node10023 : Tree Nat := .node node10015 node10022 +def node10024 : Tree Nat := .node node10011 node10023 +def node10025 : Tree Nat := .leaf 572778078369499224088375678951108638011287396263498246212912731873199901168104862737690045362725805790169147134431668582877192527008843615146574308806187829887314933747997352590139633493274155474858521293712329306345795625987820309521692782537836859136 +def node10026 : Tree Nat := .node node1960 node10025 +def node10027 : Tree Nat := .node node10026 node8767 +def node10028 : Tree Nat := .leaf 776306425423263623777736958576047420487402255961306534804099339363179058420274958327249178081275101844516559942065039752958466144143792902502823004741862377454504598293236643921602048994567977367656388816707631739691667704594300928 +def node10029 : Tree Nat := .node node3345 node10028 +def node10030 : Tree Nat := .node node10029 node9193 +def node10031 : Tree Nat := .node node10027 node10030 +def node10032 : Tree Nat := .node node9741 node10031 +def node10033 : Tree Nat := .leaf 30750788930784052141961861920805917214380440082589217766573459895919230378495282122721735540365808875358003962508537313948568601936273402206990779347133949365544298087712639248257118232124611907064008483189222574845047234699623092995674030126919390538816815104 +def node10034 : Tree Nat := .node node1975 node10033 +def node10035 : Tree Nat := .node node10034 node8337 +def node10036 : Tree Nat := .node node10035 node9745 +def node10037 : Tree Nat := .node node10036 node9750 +def node10038 : Tree Nat := .node node10032 node10037 +def node10039 : Tree Nat := .node node10024 node10038 +def node10040 : Tree Nat := .node node10006 node10039 +def node10041 : Tree Nat := .node node9994 node10040 +def node10042 : Tree Nat := .node node9946 node10041 +def node10043 : Tree Nat := .node node9883 node10042 +def node10044 : Tree Nat := .leaf 377888757473172520759533830679308359076483153975433513596157183529873416825652844724488084226799455715083388091195770378633513302968788313144741234746284281797287190713277223723491484987501690016018400179944857392080245795931147055498657064208988757699452141371392 +def node10045 : Tree Nat := .node node9479 node10044 +def node10046 : Tree Nat := .node node9209 node10045 +def node10047 : Tree Nat := .node node10046 node9213 +def node10048 : Tree Nat := .leaf 1787680445737280478760953223179972587004313637395268760901305839559870525439105783713500346435959719052326799751112210272806354834705115485847512682594304 +def node10049 : Tree Nat := .node node10048 node7923 +def node10050 : Tree Nat := .node node9216 node10049 +def node10051 : Tree Nat := .node node10050 node9485 +def node10052 : Tree Nat := .node node10047 node10051 +def node10053 : Tree Nat := .node node10052 node9496 +def node10054 : Tree Nat := .node node10053 node9514 +def node10055 : Tree Nat := .leaf 328066310098881164179615652565684592137556974893161878600385937521136513143110611697277877406598088506689996331622692229145007045272391841703581737660532537099111274280710738614771863797467878780986123640659628225185276994747033711776891987296256 +def node10056 : Tree Nat := .node node4058 node10055 +def node10057 : Tree Nat := .node node9759 node10056 +def node10058 : Tree Nat := .node node10057 node8811 +def node10059 : Tree Nat := .node node10058 node8816 +def node10060 : Tree Nat := .leaf 73710203609795729563245701742588266893533514180191289296354029872316084412029892638699394108163264237752491054690463864209539155208373579691683896185052031492888199168 +def node10061 : Tree Nat := .node node157 node10060 +def node10062 : Tree Nat := .node node10061 node7966 +def node10063 : Tree Nat := .node node10062 node8820 +def node10064 : Tree Nat := .node node10063 node9766 +def node10065 : Tree Nat := .node node10059 node10064 +def node10066 : Tree Nat := .leaf 1124728448635803107149521782971512790069864563794182045226241439649166264082625300666126126271436423430154774754665183538676937107125542492265973767301037656375296 +def node10067 : Tree Nat := .node node188 node10066 +def node10068 : Tree Nat := .node node10067 node7548 +def node10069 : Tree Nat := .node node10068 node8826 +def node10070 : Tree Nat := .node node10069 node8831 +def node10071 : Tree Nat := .leaf 18193571394148932833777103380419951819416633013086288411785766070618909330242114935785683988087622408946995518386581015869668861037310365083340793506760808722456110199985815039272648794637266422988193309175704512391663267468017664 +def node10072 : Tree Nat := .node node9256 node10071 +def node10073 : Tree Nat := .node node10072 node6396 +def node10074 : Tree Nat := .node node8839 node10073 +def node10075 : Tree Nat := .node node8836 node10074 +def node10076 : Tree Nat := .node node10070 node10075 +def node10077 : Tree Nat := .node node10065 node10076 +def node10078 : Tree Nat := .node node10054 node10077 +def node10079 : Tree Nat := .leaf 74520868430434028887151015446200122652330528821601437334674497825324155932555886273418131486684958068399132191048550116012958621419220657285152713937909339251849144828226358713035202516377364007037139520354926102035197124588743972096 +def node10080 : Tree Nat := .node node4089 node10079 +def node10081 : Tree Nat := .node node7162 node10080 +def node10082 : Tree Nat := .node node10081 node8848 +def node10083 : Tree Nat := .node node10082 node8855 +def node10084 : Tree Nat := .node node10083 node9521 +def node10085 : Tree Nat := .node node10084 node9776 +def node10086 : Tree Nat := .leaf 1179363257756731672575485806558834125321889030290858605852297032995906664646756854498531261015922433049088090423621430088348480143410507699858389328579468080130113404928 +def node10087 : Tree Nat := .node node408 node10086 +def node10088 : Tree Nat := .node node10087 node8027 +def node10089 : Tree Nat := .node node10088 node8891 +def node10090 : Tree Nat := .leaf 1254114127528279663858649702758819738757691336351204836817316728894495184367963382815606942022846544586042462324927482224104966067960154557846113684464185045748219556139244017470548848254838975795346538496 +def node10091 : Tree Nat := .node node10090 node57 +def node10092 : Tree Nat := .node node9779 node10091 +def node10093 : Tree Nat := .node node8459 node10092 +def node10094 : Tree Nat := .node node10089 node10093 +def node10095 : Tree Nat := .node node9534 node10094 +def node10096 : Tree Nat := .leaf 19136262932255243894327540630475154705164967900866663911068029494665277886590246944865323282482643188135896819454261827807407353380407619460568486221873664591344206305902909267608449230932304696705024 +def node10097 : Tree Nat := .node node10096 node4147 +def node10098 : Tree Nat := .node node8901 node10097 +def node10099 : Tree Nat := .node node8047 node10098 +def node10100 : Tree Nat := .node node10099 node9282 +def node10101 : Tree Nat := .node node9788 node10100 +def node10102 : Tree Nat := .node node10095 node10101 +def node10103 : Tree Nat := .node node10085 node10102 +def node10104 : Tree Nat := .node node10078 node10103 +def node10105 : Tree Nat := .leaf 18630217107608507221787753861550030663082632205400359333668624456312611432236522635970540905943757735405852768365572878474139122893022521931525145624726739912876690798129007060556412064597230315837351267300132150605120011417816137728 +def node10106 : Tree Nat := .node node4160 node10105 +def node10107 : Tree Nat := .node node5192 node10106 +def node10108 : Tree Nat := .node node10107 node8915 +def node10109 : Tree Nat := .node node10108 node9558 +def node10110 : Tree Nat := .leaf 3032261899024822138962850563403325303236105502181048069620282617698040213563935511256069960445463403522851285620501684799575084586314156403208291296653733959574206393103005571077886350220863565558087948257121945696142830774307840 +def node10111 : Tree Nat := .node node10110 node8481 +def node10112 : Tree Nat := .node node6068 node10111 +def node10113 : Tree Nat := .node node10112 node9799 +def node10114 : Tree Nat := .node node9796 node10113 +def node10115 : Tree Nat := .node node10109 node10114 +def node10116 : Tree Nat := .node node10115 node9812 +def node10117 : Tree Nat := .leaf 18630217107608507221787753861550030667991818309961841388926525104046124897821636509769991391246968884665472848282109756370941481697601911712863436808565170455368780870356894118443977590628536535196924571849457387997420325356557041664 +def node10118 : Tree Nat := .node node2239 node10117 +def node10119 : Tree Nat := .node node10118 node8927 +def node10120 : Tree Nat := .node node7646 node10119 +def node10121 : Tree Nat := .leaf 99361157907245371849534687261600163536440705095468583113164468625225792290197711100284765759309869423479251738384401920447807523725697902678552750915056555013184194393963856491357712381141733973846624833224791159270404068458320887808 +def node10122 : Tree Nat := .node node643 node10121 +def node10123 : Tree Nat := .node node10122 node8500 +def node10124 : Tree Nat := .node node10123 node8932 +def node10125 : Tree Nat := .node node10120 node10124 +def node10126 : Tree Nat := .leaf 1143008960541682796527414227720507353612301942356793663981667428693133659351055029601669960922881791868769847635204755371889564350235459812587860098798053483700215021407430386374628343808 +def node10127 : Tree Nat := .node node674 node10126 +def node10128 : Tree Nat := .node node10127 node8505 +def node10129 : Tree Nat := .node node10128 node9820 +def node10130 : Tree Nat := .node node9817 node10129 +def node10131 : Tree Nat := .node node10125 node10130 +def node10132 : Tree Nat := .leaf 17440932625454102892005221033749487198655746904019317303701802724120541980963587606948089473513130821969426664851898611152401632012365957170080388262936375594123247479124333149814784 +def node10133 : Tree Nat := .node node705 node10132 +def node10134 : Tree Nat := .node node10133 node9829 +def node10135 : Tree Nat := .node node10134 node8942 +def node10136 : Tree Nat := .node node9827 node10135 +def node10137 : Tree Nat := .leaf 74520868430434028887151015446200122652330528821601437334674501886107725040534381285330860630062284695006365359138451048810937685710819391780309868461986241568399902150601734424811729685118392775683610336362059908531172491584520344832 +def node10138 : Tree Nat := .node node721 node10137 +def node10139 : Tree Nat := .node node10138 node8079 +def node10140 : Tree Nat := .node node10139 node8520 +def node10141 : Tree Nat := .leaf 1790150099102876869021435248250019995303749140817283874750189257324506477915690797543620059209050129555606593820267882845788694734491813349483178916399840524715673484360699089085040705133074569778097942300043867977026926406435368882118928581810716672 +def node10142 : Tree Nat := .node node9567 node10141 +def node10143 : Tree Nat := .node node10142 node8083 +def node10144 : Tree Nat := .node node9835 node10143 +def node10145 : Tree Nat := .node node10140 node10144 +def node10146 : Tree Nat := .node node10136 node10145 +def node10147 : Tree Nat := .node node10131 node10146 +def node10148 : Tree Nat := .node node10116 node10147 +def node10149 : Tree Nat := .leaf 3580081700695792870399535724574524629625881882469897527952195336442751980830001445696019465586228542255722428480987629992674781227361541120319586096008934360467253886591403714093404300042842333536467984517003148659866557895333562008071782352210100224 +def node10150 : Tree Nat := .node node754 node10149 +def node10151 : Tree Nat := .leaf 99361157907245371849534687261600163536440705095468583112899330434846624229684852397751703971592208617242752645996526324316066254249298397985202633980404016539836062636568685698130610243186608591911642208603808105808209730182989217792 +def node10152 : Tree Nat := .node node4221 node10151 +def node10153 : Tree Nat := .node node10150 node10152 +def node10154 : Tree Nat := .node node10153 node9577 +def node10155 : Tree Nat := .node node10154 node9844 +def node10156 : Tree Nat := .leaf 3105036184601417870297958976925005110513776489741808868953122280321248097063500738705220927579100162143668722405167623636353419768753347936033558949270062292216261010433761902259002737588191417219942603894990174979882393346368995328 +def node10157 : Tree Nat := .node node10156 node8095 +def node10158 : Tree Nat := .node node5727 node10157 +def node10159 : Tree Nat := .leaf 1037378892222606966143615429267941259366229226505074777600675764862208739637417078004498925917997608622745137579189658361622101044767486457028501700229033919631400833374257720328192 +def node10160 : Tree Nat := .node node10159 node796 +def node10161 : Tree Nat := .node node9585 node10160 +def node10162 : Tree Nat := .node node10158 node10161 +def node10163 : Tree Nat := .node node10162 node9849 +def node10164 : Tree Nat := .node node10155 node10163 +def node10165 : Tree Nat := .leaf 82551059006714003709496551844541929029493217800541434838937461879860518786082074369721984112554764681204108801708627641978897189856704185316274846907082553131312752354631566758713821812346592761878535616367102080112890334057146269258850151576614466401702855582430461952 +def node10166 : Tree Nat := .node node3218 node10165 +def node10167 : Tree Nat := .node node10166 node5270 +def node10168 : Tree Nat := .node node9854 node10167 +def node10169 : Tree Nat := .node node9597 node10168 +def node10170 : Tree Nat := .leaf 49680578953622685924767343630800081768220352547734291556449665458514646081762298365119537991585750566650007724132898962908139335734974588736409752849250575367163811942604699436879442841829643177517509172198228903946413067103962704384 +def node10171 : Tree Nat := .node node10170 node8101 +def node10172 : Tree Nat := .node node9858 node10171 +def node10173 : Tree Nat := .node node10172 node9601 +def node10174 : Tree Nat := .leaf 12420144738405671481191835907700020442347084336461393383105451286973226266284181715110935106186240144749455456278403942195445355672291158622545958991823043947007746503927423457260479638374759258683741793826121373259062549949618061312 +def node10175 : Tree Nat := .node node10174 node8964 +def node10176 : Tree Nat := .node node9604 node10175 +def node10177 : Tree Nat := .node node10176 node9863 +def node10178 : Tree Nat := .node node10173 node10177 +def node10179 : Tree Nat := .node node10169 node10178 +def node10180 : Tree Nat := .node node10164 node10179 +def node10181 : Tree Nat := .leaf 198722315814490743699069374523200327072881410190937166229863783348305194581188124230982329158601836088313023092820593049082338303043134938212527576345153445003467692623156463316788864733519804778744942471736108165567237534013829677056 +def node10182 : Tree Nat := .node node894 node10181 +def node10183 : Tree Nat := .leaf 7150721782949121915043812892719890348017254549581075076542143452139915572287657843988494992917542610948892911587830432827163124925377046447281055324962816 +def node10184 : Tree Nat := .node node10183 node8539 +def node10185 : Tree Nat := .node node10182 node10184 +def node10186 : Tree Nat := .node node10185 node7287 +def node10187 : Tree Nat := .node node9871 node10186 +def node10188 : Tree Nat := .leaf 322072184375856321174699476789749394159709606316691957543114134358696373785218137347343185263952332678830987998941013741323432919616291095481803709608274964545894040963922233750817879056241020147215714222080 +def node10189 : Tree Nat := .node node2706 node10188 +def node10190 : Tree Nat := .node node10189 node8112 +def node10191 : Tree Nat := .node node8110 node10190 +def node10192 : Tree Nat := .leaf 17455318995930233931408337023750131456856251576282691500653492196783603419875066702670176644482377413353334444895955468838025604317917511873445056117050116595304207897784721641828941561856 +def node10193 : Tree Nat := .node node925 node10192 +def node10194 : Tree Nat := .node node10193 node8545 +def node10195 : Tree Nat := .node node10194 node7292 +def node10196 : Tree Nat := .node node10191 node10195 +def node10197 : Tree Nat := .node node10187 node10196 +def node10198 : Tree Nat := .leaf 4914431524289799822611991528163900667720178319041320125661158324581048347874743043795436315911784559172447750684491737249038596320248041162573466349780407704014182257491587353482312239001177971849428992 +def node10199 : Tree Nat := .node node2481 node10198 +def node10200 : Tree Nat := .node node10199 node9328 +def node10201 : Tree Nat := .node node8119 node10200 +def node10202 : Tree Nat := .leaf 266347030577548735526764636647948068755166856282704692244238264104560076874016225094308765650729564362552735590668141387711087408690791837490831573198297513044390036357361003566989312 +def node10203 : Tree Nat := .node node956 node10202 +def node10204 : Tree Nat := .node node10203 node9875 +def node10205 : Tree Nat := .node node10204 node7298 +def node10206 : Tree Nat := .node node10201 node10205 +def node10207 : Tree Nat := .leaf 12129047596099288555851402253613301212944422008724192274585857797645440092259624247526192072643190449411503193749577650890491030329725143884308783215221987396508808141757514781720828493800575897338924374336159860224565135974334464 +def node10208 : Tree Nat := .node node971 node10207 +def node10209 : Tree Nat := .node node10208 node8123 +def node10210 : Tree Nat := .node node10209 node6914 +def node10211 : Tree Nat := .leaf 377888757473172520759533830679308359076483153975433513596157183529873417969883099717749812339383325821436968046412807505362807416121989976238104397615875416611480409895350097376897549670102106121873444817005162553206519632269134379244092055558373056286259762495488 +def node10212 : Tree Nat := .node node2075 node10211 +def node10213 : Tree Nat := .node node10212 node8978 +def node10214 : Tree Nat := .node node10213 node8128 +def node10215 : Tree Nat := .node node10210 node10214 +def node10216 : Tree Nat := .node node10206 node10215 +def node10217 : Tree Nat := .node node10197 node10216 +def node10218 : Tree Nat := .node node10180 node10217 +def node10219 : Tree Nat := .node node10148 node10218 +def node10220 : Tree Nat := .node node10104 node10219 +def node10221 : Tree Nat := .leaf 3105036184601417870297958976925005110513772034233393222278104076052101905372753772661756817657292955900975461394262146412343160088273545815522811578863726920763175164071299177214956078802169380857446609298845936460570666572163186688 +def node10222 : Tree Nat := .node node9613 node10221 +def node10223 : Tree Nat := .node node9885 node10222 +def node10224 : Tree Nat := .node node10223 node8989 +def node10225 : Tree Nat := .node node10224 node8996 +def node10226 : Tree Nat := .leaf 281298265418201352235165138578976603576013768563340732934651664284824741957354544643970617569272516807014207659291370272656572936096887092568498575168455944788625540987476512503020603872631727441617364322927888299982848 +def node10227 : Tree Nat := .node node1037 node10226 +def node10228 : Tree Nat := .node node10227 node8144 +def node10229 : Tree Nat := .node node10228 node9339 +def node10230 : Tree Nat := .node node10229 node9621 +def node10231 : Tree Nat := .node node10225 node10230 +def node10232 : Tree Nat := .leaf 2215827865120445285436604169234485268788427414982608644747421691974729966125774948634023348607602134380929819179562879006731152225269692440581144342867662696997962162209232227260792078063163190974769923810680813676677196693802695894113076908506774869624713430314915537625284608 +def node10233 : Tree Nat := .node node1068 node10232 +def node10234 : Tree Nat := .node node10233 node7728 +def node10235 : Tree Nat := .node node10234 node9006 +def node10236 : Tree Nat := .node node10235 node9893 +def node10237 : Tree Nat := .node node10236 node9899 +def node10238 : Tree Nat := .node node10231 node10237 +def node10239 : Tree Nat := .leaf 794889263257962974813446581675455199419160231741469404867550952585764674816527665863420881950043938149858606244456468151077074085884554701325419900812661758121484614940272764217835926067287368343356352808296767855472691075689578758144 +def node10240 : Tree Nat := .node node4322 node10239 +def node10241 : Tree Nat := .node node9903 node10240 +def node10242 : Tree Nat := .node node10241 node9024 +def node10243 : Tree Nat := .node node10242 node9029 +def node10244 : Tree Nat := .leaf 147420407219591459181047081150498814022691821548247952951970560885780206570971339010004504213422012981880091267903200472618725282568419154848711723404147400688996974592 +def node10245 : Tree Nat := .node node1162 node10244 +def node10246 : Tree Nat := .node node10245 node8175 +def node10247 : Tree Nat := .node node10246 node9033 +def node10248 : Tree Nat := .node node10247 node9910 +def node10249 : Tree Nat := .node node10243 node10248 +def node10250 : Tree Nat := .leaf 2249456897271662374555463750643268135073893106650204507728809707597807073016000326232477510164926206637050512645703615592449236656465011275190631931580386528722944 +def node10251 : Tree Nat := .node node1193 node10250 +def node10252 : Tree Nat := .node node10251 node7761 +def node10253 : Tree Nat := .node node10252 node9039 +def node10254 : Tree Nat := .node node10253 node9353 +def node10255 : Tree Nat := .leaf 12129047596099288555851402253613301212944422008724192274523844047080772524759591022651392838227643599917620244630499828964854934093296277218501321889785163098319203127781147341370147881242035456226516945266714093372510676510048256 +def node10256 : Tree Nat := .node node9625 node10255 +def node10257 : Tree Nat := .node node10256 node5375 +def node10258 : Tree Nat := .node node9048 node10257 +def node10259 : Tree Nat := .node node9045 node10258 +def node10260 : Tree Nat := .node node10254 node10259 +def node10261 : Tree Nat := .node node10249 node10260 +def node10262 : Tree Nat := .node node10238 node10261 +def node10263 : Tree Nat := .leaf 49680578953622685924767343630800081768220352547734291556449665216981050893183651821660044808336541547967049617480711546830936120015028195432376660200255302515452739180439577013239709380234273517841406494516678167445844347494569388544 +def node10264 : Tree Nat := .node node4353 node10263 +def node10265 : Tree Nat := .node node5383 node10264 +def node10266 : Tree Nat := .node node10265 node9056 +def node10267 : Tree Nat := .node node10266 node8200 +def node10268 : Tree Nat := .leaf 64836180763765516101484821505977500134091255350301002693480429854726126083584489973728188363989263892096896293291636820427274412764935651606719070367361645489928571386885857869824 +def node10269 : Tree Nat := .node node10268 node4361 +def node10270 : Tree Nat := .node node6976 node10269 +def node10271 : Tree Nat := .node node8204 node10270 +def node10272 : Tree Nat := .node node10271 node9636 +def node10273 : Tree Nat := .node node10267 node10272 +def node10274 : Tree Nat := .leaf 18193571394148932833777103380419951819416633013086288411785781166468608616407523902004007941163186076631877184148294520694869843533959959883179937580490533114811611771726601860741663995579714305469464049673750398739226208273170432 +def node10275 : Tree Nat := .node node10274 node8208 +def node10276 : Tree Nat := .node node6217 node10275 +def node10277 : Tree Nat := .node node10276 node6988 +def node10278 : Tree Nat := .node node10277 node9923 +def node10279 : Tree Nat := .node node9064 node10278 +def node10280 : Tree Nat := .node node10273 node10279 +def node10281 : Tree Nat := .leaf 1478734606154033217956310006185794711301150542953891358960480406692984429895011898097846099699641988667424153259963137481743794176 +def node10282 : Tree Nat := .node node10281 node8650 +def node10283 : Tree Nat := .node node8216 node10282 +def node10284 : Tree Nat := .node node10283 node9078 +def node10285 : Tree Nat := .node node9930 node10284 +def node10286 : Tree Nat := .leaf 2358726515513463345150971613117668444464480358403159155674059194329767321421225371571417059129486717464145255439435319130632639954422406473075647358741402236337103306752 +def node10287 : Tree Nat := .node node1413 node10286 +def node10288 : Tree Nat := .node node10287 node8656 +def node10289 : Tree Nat := .node node10288 node9083 +def node10290 : Tree Nat := .node node10289 node9935 +def node10291 : Tree Nat := .node node10285 node10290 +def node10292 : Tree Nat := .node node10291 node9943 +def node10293 : Tree Nat := .node node10280 node10292 +def node10294 : Tree Nat := .node node10262 node10293 +def node10295 : Tree Nat := .leaf 12420144738405671481191835907700020442055088136933572889112416304208407621491015090647027270629171823603901845577048585649693289807497512068329091497259714083328564151682032020215036833124983470338885101451869852384765984598793388032 +def node10296 : Tree Nat := .node node4415 node10295 +def node10297 : Tree Nat := .node node9948 node10296 +def node10298 : Tree Nat := .node node10297 node9107 +def node10299 : Tree Nat := .leaf 5914938424616132871825240024743178845204602171815565435841921626771937719580047592391384398798567954669695810237550462084436721664 +def node10300 : Tree Nat := .node node10299 node8255 +def node10301 : Tree Nat := .node node8254 node10300 +def node10302 : Tree Nat := .node node10301 node9111 +def node10303 : Tree Nat := .node node10298 node10302 +def node10304 : Tree Nat := .leaf 1125193061672805408940660554315906414304055074253362931738606657139298967829418178575882470277090067228056830637165481090626291744387548370273994300673823779154502163949906050012082415490526909766469420542338585300303872 +def node10305 : Tree Nat := .node node1539 node10304 +def node10306 : Tree Nat := .node node10305 node8261 +def node10307 : Tree Nat := .node node10306 node9387 +def node10308 : Tree Nat := .node node10307 node9658 +def node10309 : Tree Nat := .node node10303 node10308 +def node10310 : Tree Nat := .leaf 8863311460481781141746416676937941075153709659930434578990017707034705983741023518228539249258145024310264383459425352190697580834324222711532296971587279303261875742450009064892167136104122887838254681932780318703556145692181414371831912955022338173153981549793952808422080512 +def node10311 : Tree Nat := .node node1570 node10310 +def node10312 : Tree Nat := .node node10311 node7848 +def node10313 : Tree Nat := .node node10312 node9122 +def node10314 : Tree Nat := .node node10313 node9956 +def node10315 : Tree Nat := .node node10314 node9962 +def node10316 : Tree Nat := .node node10309 node10315 +def node10317 : Tree Nat := .leaf 82551059006714003709496551844541929029493217800541258338065042616266959466779436580480524652935273957608816089087948723614499614950460068196212645032271872014719109604845434052659704412912366102310505182235450155357172664299610479754319357606131731566735428424282603520 +def node10318 : Tree Nat := .node node4442 node10317 +def node10319 : Tree Nat := .node node9399 node10318 +def node10320 : Tree Nat := .node node10319 node9403 +def node10321 : Tree Nat := .node node10320 node9968 +def node10322 : Tree Nat := .node node10321 node9981 +def node10323 : Tree Nat := .leaf 3580081700695792870399535724574524629625881882469897527952195336442751980830001445696019465585799492401964265373801261192732194151282201414060629507921780394268157437629050210835744322501501423850386965055035595032546433645351271769785905584015409152 +def node10324 : Tree Nat := .node node9682 node10323 +def node10325 : Tree Nat := .node node10324 node5502 +def node10326 : Tree Nat := .node node9418 node10325 +def node10327 : Tree Nat := .node node9681 node10326 +def node10328 : Tree Nat := .node node9991 node10327 +def node10329 : Tree Nat := .node node10322 node10328 +def node10330 : Tree Nat := .node node10316 node10329 +def node10331 : Tree Nat := .leaf 198722315814490743699069374523200327072881410190937166225798660869693248459369704795503407943184417234485505291993052659139173833696638012670139718293636895406970998883398848627038083189140552810793280611261819984931371075473810391040 +def node10332 : Tree Nat := .node node4470 node10331 +def node10333 : Tree Nat := .node node9425 node10332 +def node10334 : Tree Nat := .node node10333 node9429 +def node10335 : Tree Nat := .node node10334 node9693 +def node10336 : Tree Nat := .node node10335 node9703 +def node10337 : Tree Nat := .node node10336 node10005 +def node10338 : Tree Nat := .leaf 1790150099102876869021435248250019995303749140817283874750189257324506477915690797543620059648397179803965615579109533986997860639735672558654725117645501912590437221810686424928857707466166088325061871354818782352834158388300572886856739213174374400 +def node10339 : Tree Nat := .node node1883 node10338 +def node10340 : Tree Nat := .node node10339 node7902 +def node10341 : Tree Nat := .node node10340 node9723 +def node10342 : Tree Nat := .node node10341 node10010 +def node10343 : Tree Nat := .node node10342 node10023 +def node10344 : Tree Nat := .node node10343 node10038 +def node10345 : Tree Nat := .node node10337 node10344 +def node10346 : Tree Nat := .node node10330 node10345 +def node10347 : Tree Nat := .node node10294 node10346 +def node10348 : Tree Nat := .node node10220 node10347 +def node10349 : Tree Nat := .leaf 5243959930521868196035988243035872375697538011210511234210341180507584442070108746664594945274968573071017765349798373866437867839113642150474155408355168852160885047997948505169340455516323318948730339419507673920322184683304046117826791745824000 +def node10350 : Tree Nat := .node node7928 node10349 +def node10351 : Tree Nat := .node node9221 node10350 +def node10352 : Tree Nat := .node node10351 node9490 +def node10353 : Tree Nat := .node node10352 node9495 +def node10354 : Tree Nat := .node node10052 node10353 +def node10355 : Tree Nat := .leaf 1342448621178615552282827516151781977772337402262960652599585714624938734165281457744545454356153823226097958450698335995629500002588458507140526972932454209814725362475056722365205242568750697013762612459127619593094601447359222066865914153323003904 +def node10356 : Tree Nat := .node node4036 node10355 +def node10357 : Tree Nat := .node node9234 node10356 +def node10358 : Tree Nat := .node node10357 node9502 +def node10359 : Tree Nat := .node node10358 node9507 +def node10360 : Tree Nat := .node node10359 node9513 +def node10361 : Tree Nat := .node node10354 node10360 +def node10362 : Tree Nat := .leaf 316582913885573803597443226905148403251319243622446168099620703232393688611077416172050052785533314406898966104580558602718514587154776109091769383474763636703072289995052023808 +def node10363 : Tree Nat := .node node141 node10362 +def node10364 : Tree Nat := .node node10363 node8384 +def node10365 : Tree Nat := .node node10364 node8815 +def node10366 : Tree Nat := .node node10058 node10365 +def node10367 : Tree Nat := .leaf 19490628603665978034840773681243539961557583757901227914375292986620521742971720329026114225858569118357533119016956141129520526606495487774733684002469445223271476900381241943878047499907414790523502139924273616157203700182445116049551145991000420388134755878835919286439373384124570009600 +def node10368 : Tree Nat := .node node5998 node10367 +def node10369 : Tree Nat := .node node8819 node10368 +def node10370 : Tree Nat := .node node10062 node10369 +def node10371 : Tree Nat := .node node10370 node9766 +def node10372 : Tree Nat := .node node10366 node10371 +def node10373 : Tree Nat := .leaf 4830671903771572930869189863664985114361419881987898104202637200400225572291666939504151724663160812232493280387010345015360578539162836106798917183982014690116754951438336 +def node10374 : Tree Nat := .node node219 node10373 +def node10375 : Tree Nat := .node node10374 node7981 +def node10376 : Tree Nat := .node node10375 node8835 +def node10377 : Tree Nat := .node node10376 node10074 +def node10378 : Tree Nat := .node node10070 node10377 +def node10379 : Tree Nat := .node node10372 node10378 +def node10380 : Tree Nat := .node node10361 node10379 +def node10381 : Tree Nat := .leaf 2359768043238669411178565976067957431848923659859878902310184835340237859263337018565330577203373114949631763904501278982795070237667264161630741565571519785943188496197989416129478537261224420170600379559576989442085602452326955349759421376398210478704019274592160250200798787731456 +def node10382 : Tree Nat := .node node4609 node10381 +def node10383 : Tree Nat := .node node8420 node10382 +def node10384 : Tree Nat := .node node8418 node10383 +def node10385 : Tree Nat := .node node10384 node9520 +def node10386 : Tree Nat := .node node10083 node10385 +def node10387 : Tree Nat := .leaf 21479177938861104702947544874773277196989586550366132536457863739086873111764858218688532077794618501515287728467586818494142417375315122985494248860697921174819299331985477758434276283889431474818051483620258593829300311211843335116432300869471764480 +def node10388 : Tree Nat := .node node4106 node10387 +def node10389 : Tree Nat := .node node9264 node10388 +def node10390 : Tree Nat := .node node10389 node9525 +def node10391 : Tree Nat := .node node10390 node8867 +def node10392 : Tree Nat := .node node10391 node9775 +def node10393 : Tree Nat := .node node10386 node10392 +def node10394 : Tree Nat := .leaf 5065326622169180857559091630482374868146278858040391079895769963195252026526260082535022246097026585218582910992544828114207112867253520473647524658985631894584737085767588773888 +def node10395 : Tree Nat := .node node392 node10394 +def node10396 : Tree Nat := .node node10395 node8453 +def node10397 : Tree Nat := .node node10396 node8886 +def node10398 : Tree Nat := .node node9533 node10397 +def node10399 : Tree Nat := .leaf 9293855677986144142487890613436878500820376260371215369098574120724629107252527334657301965600977191186252154341950419927056275967916625424261437267262942338500270809871838671426583744675505539836332617320471378462629370222360140891376255543550590746088107848121372340499261652205568 +def node10400 : Tree Nat := .node node5163 node10399 +def node10401 : Tree Nat := .node node8890 node10400 +def node10402 : Tree Nat := .node node10088 node10401 +def node10403 : Tree Nat := .node node10402 node10093 +def node10404 : Tree Nat := .node node10398 node10403 +def node10405 : Tree Nat := .leaf 396220898351839024966536107246691989939260860910039606935416507030334078729996420953337628817256746171096893784913430321724139568100297791866087958028503836554601524379194098371267324807834720245250044639774629910622255130531937751593233735341536017041490885987939647488 +def node10406 : Tree Nat := .node node4136 node10405 +def node10407 : Tree Nat := .node node9785 node10406 +def node10408 : Tree Nat := .node node10407 node8897 +def node10409 : Tree Nat := .leaf 54627708241368206140399185795483904585298056017266413654686809042878885470045010165051424860300847637662202877726723737999808766448833602807268777694179025360312204838129743181606701608281543269348845388880260232996225396217430196203130552582144 +def node10410 : Tree Nat := .node node10409 node57 +def node10411 : Tree Nat := .node node9276 node10410 +def node10412 : Tree Nat := .node node8469 node10411 +def node10413 : Tree Nat := .node node10408 node10412 +def node10414 : Tree Nat := .leaf 77290750460345166893907037818700956707865083001863766996464471549765352154467539046719293062033872804422690981701666256967674181358755076313767912539862683826041991471497216 +def node10415 : Tree Nat := .node node469 node10414 +def node10416 : Tree Nat := .node node10415 node8046 +def node10417 : Tree Nat := .node node10416 node10098 +def node10418 : Tree Nat := .node node10417 node9282 +def node10419 : Tree Nat := .node node10413 node10418 +def node10420 : Tree Nat := .node node10404 node10419 +def node10421 : Tree Nat := .node node10393 node10420 +def node10422 : Tree Nat := .node node10380 node10421 +def node10423 : Tree Nat := .leaf 208388169255707573472614171509061198930901276895454073646203940204144747575459346560230824634649146985266226023337015404428058945766855710786329270267454691762386291943651572693177990955143535742526387109193567875369225268964320781798473728 +def node10424 : Tree Nat := .node node10423 node8913 +def node10425 : Tree Nat := .node node6449 node10424 +def node10426 : Tree Nat := .node node10107 node10425 +def node10427 : Tree Nat := .node node10426 node9558 +def node10428 : Tree Nat := .leaf 85916711835441056807814603089982736960820311082249057549554030880590843840063680438758584847103482995679611846753510883514363373495610039007039005362231892261302891524411987343610094421107743881059506651653318502578037711515493363346189931071238307840 +def node10429 : Tree Nat := .node node9793 node10428 +def node10430 : Tree Nat := .node node5674 node10429 +def node10431 : Tree Nat := .node node10430 node9290 +def node10432 : Tree Nat := .node node10431 node10113 +def node10433 : Tree Nat := .node node10427 node10432 +def node10434 : Tree Nat := .leaf 85916711755426104563164716032153802554402288059321493371709987987575490259036984038215917536427279132603224272489138694398655840645109662417684459562787702281528656246954718078000568982838065285159708216551728968332040350076714742876369269127058277120 +def node10435 : Tree Nat := .node node4177 node10434 +def node10436 : Tree Nat := .node node5680 node10435 +def node10437 : Tree Nat := .leaf 5370122551043688113192634414340729018687074301844043075308697343153802495452612712581317842498394745438907874967439810156561382348653426910971764528852051459379296172053372626905174135531576850616281766612182917239840319251218225040397823978008805376 +def node10438 : Tree Nat := .node node10437 node8919 +def node10439 : Tree Nat := .node node6837 node10438 +def node10440 : Tree Nat := .node node10436 node10439 +def node10441 : Tree Nat := .leaf 1342448621178615552282827516151781977772342539114427008433088879654121234290931409248259148861875989516042399807261285629881961328615291383217619697281109880632885213638685118396779511240990358367541606933306158431395777555228370883185975044276027392 +def node10442 : Tree Nat := .node node10441 node591 +def node10443 : Tree Nat := .node node7236 node10442 +def node10444 : Tree Nat := .node node8489 node10443 +def node10445 : Tree Nat := .node node10440 node10444 +def node10446 : Tree Nat := .node node10445 node9811 +def node10447 : Tree Nat := .node node10433 node10446 +def node10448 : Tree Nat := .leaf 13023465689218465379062210528752456635109352936369821715687110074362044674069939583683337136576769515718408398694545381658298282478649854485223157748107782007324616701211911943811486046651530565352537356415277444077466145361937812695678976 +def node10449 : Tree Nat := .node node628 node10448 +def node10450 : Tree Nat := .node node10449 node7645 +def node10451 : Tree Nat := .node node10450 node10119 +def node10452 : Tree Nat := .node node10451 node10124 +def node10453 : Tree Nat := .leaf 61962639909484535141172984758657490945840564470948637404370086350503902175090710502302784623196452735583711775315818419500240519915430071388281949446402277112362827776 +def node10454 : Tree Nat := .node node659 node10453 +def node10455 : Tree Nat := .node node10454 node8073 +def node10456 : Tree Nat := .leaf 2323463919496536035621972653359219625205094065092803842274643530181157276813131833664325491400244297796561139088004291538942484332617725465229688123693282285148110419588487212015260496123349292266621913191436365660998606650631791842408520202332224188930022829612787894302734911799296 +def node10457 : Tree Nat := .node node5227 node10456 +def node10458 : Tree Nat := .node node9815 node10457 +def node10459 : Tree Nat := .node node10455 node10458 +def node10460 : Tree Nat := .node node10459 node10129 +def node10461 : Tree Nat := .node node10452 node10460 +def node10462 : Tree Nat := .leaf 13336028865759708548159703581442515594289516644631994541129141491161968474172260363342481631760584609875317580475824259592783134003673990120968600844433174741633622395792045418577278075636057409222166967426200308067244292821319737925821291008 +def node10463 : Tree Nat := .node node690 node10462 +def node10464 : Tree Nat := .node node10463 node7651 +def node10465 : Tree Nat := .node node10464 node9826 +def node10466 : Tree Nat := .node node10465 node10135 +def node10467 : Tree Nat := .leaf 894965747452546029289481036448886549875942782458238885487929050676346001670193408525280769631812514053853248991909205357186142978804329290852520958333949865919627955693679688841800240309058432305961498603966501398279527098031501872816813144099389440 +def node10468 : Tree Nat := .node node2839 node10467 +def node10469 : Tree Nat := .node node10468 node8519 +def node10470 : Tree Nat := .node node10139 node10469 +def node10471 : Tree Nat := .node node10470 node10144 +def node10472 : Tree Nat := .node node10466 node10471 +def node10473 : Tree Nat := .node node10461 node10472 +def node10474 : Tree Nat := .node node10447 node10473 +def node10475 : Tree Nat := .leaf 396220898351839024966536107246691989939260860910039606940802886193519613201411194593406880570780294129187823817039669966466521294105113803867619456435274926257810481217585264970714070661966457303101457494408645143171150667089870971534488760312384982914170411684282236928 +def node10476 : Tree Nat := .node node3002 node10475 +def node10477 : Tree Nat := .node node10476 node5255 +def node10478 : Tree Nat := .node node9843 node10477 +def node10479 : Tree Nat := .node node10154 node10478 +def node10480 : Tree Nat := .leaf 85916711755426104563164716032153802554402288059321493371709987987575490259036984038217760291517524025841623469061886872568048868584766127470602529045329510954571697678637397143028722677926672890155198375194195074108370815229332630694451640242121458432 +def node10481 : Tree Nat := .node node785 node10480 +def node10482 : Tree Nat := .node node10481 node10157 +def node10483 : Tree Nat := .leaf 145216494968533502226373290834951226575318379068300240142165220636322329800820739604020343212515268612285031624966704428230028521254434561691433413297200607162016350340084453714941042002047577870386021126281069772148333971666387992719670232556259747718062213811520931603450786283520 +def node10484 : Tree Nat := .node node10159 node10483 +def node10485 : Tree Nat := .node node9585 node10484 +def node10486 : Tree Nat := .node node10482 node10485 +def node10487 : Tree Nat := .node node10486 node9849 +def node10488 : Tree Nat := .node node10479 node10487 +def node10489 : Tree Nat := .leaf 5370122551043688113192634414340729018687074301844043075308697343153802495452612712581317842498341114207188104579041514056568556888014607465814888871982142923182862154849621004302262322488786578224833537639116490801561266489153964294461823292999794688 +def node10490 : Tree Nat := .node node4235 node10489 +def node10491 : Tree Nat := .node node5733 node10490 +def node10492 : Tree Nat := .node node10491 node9596 +def node10493 : Tree Nat := .node node10492 node10168 +def node10494 : Tree Nat := .node node10493 node10178 +def node10495 : Tree Nat := .node node10488 node10494 +def node10496 : Tree Nat := .leaf 22158279047425351206114981955269264206604694403649698977884354490022367126286687761163231447099300327462501083700508916371442063331241867183650819017403048525546699568475720452462794493245022769877594274831261485586368706798003749934920430684199764319146571891720755542729359360 +def node10497 : Tree Nat := .node node4251 node10496 +def node10498 : Tree Nat := .node node5743 node10497 +def node10499 : Tree Nat := .node node10498 node9870 +def node10500 : Tree Nat := .leaf 13656093609410854401825166855824327627575913246889902774822791357490205711436261751968436032022891116268576329792333263731410739802136913893655855237128909172175034562304895702943551816971555040783562724571866507898495571041346257902074090749952 +def node10501 : Tree Nat := .node node3110 node10500 +def node10502 : Tree Nat := .node node10501 node5286 +def node10503 : Tree Nat := .node node10185 node10502 +def node10504 : Tree Nat := .node node10499 node10503 +def node10505 : Tree Nat := .leaf 85916711835441056807814603089982736960820311082249057549554030880590843840063680439704839585944235673597599286859700373497683220509204843680467684647521210336623349878949689172652034172765763992844277495467634285279746418245667999142046074160218636288 +def node10506 : Tree Nat := .node node910 node10505 +def node10507 : Tree Nat := .node node10506 node8109 +def node10508 : Tree Nat := .node node10507 node10190 +def node10509 : Tree Nat := .node node10508 node10195 +def node10510 : Tree Nat := .node node10504 node10509 +def node10511 : Tree Nat := .leaf 5243959930521868196035988243035872375697538011210511234210341180507584442070108746679033646734330643962100337372903071894747802028163855844836517337162696708872189910751923402457266842722265984140371214701769192058193440059690916330648477785695488 +def node10512 : Tree Nat := .node node941 node10511 +def node10513 : Tree Nat := .leaf 106366229208979968755504199669210638388237986561042818470193479939588852555710095645386336397504644461006301261224432902536602299461897510433945619511073701376927103782437708367420186860102194566491041662394850005586133285281769940106068012479909931287410396331319853900380504064 +def node10514 : Tree Nat := .node node4265 node10513 +def node10515 : Tree Nat := .node node10512 node10514 +def node10516 : Tree Nat := .node node10515 node10200 +def node10517 : Tree Nat := .node node10516 node10205 +def node10518 : Tree Nat := .leaf 106366229208979968755504199669210638388237986561042818470193479939609959878385351765250841502415537477301951989984003626548983584843451265983111355215683583058198951451675602296070637296809433722455993038601017223719515817290923694571060066923254295256347529776247367020419481600 +def node10519 : Tree Nat := .node node2886 node10518 +def node10520 : Tree Nat := .node node10519 node5306 +def node10521 : Tree Nat := .node node10209 node10520 +def node10522 : Tree Nat := .node node10521 node10214 +def node10523 : Tree Nat := .node node10517 node10522 +def node10524 : Tree Nat := .node node10510 node10523 +def node10525 : Tree Nat := .node node10495 node10524 +def node10526 : Tree Nat := .node node10474 node10525 +def node10527 : Tree Nat := .node node10422 node10526 +def node10528 : Tree Nat := .leaf 13336028865759708548159703581442515594289516644631994541129141491161968474172259417867629497291969784848084324593699231507998115866506562708171081345302977506324101018005251803600956166990853868732899852140751216750740896786861390170320558592 +def node10529 : Tree Nat := .node node4293 node10528 +def node10530 : Tree Nat := .node node10227 node10529 +def node10531 : Tree Nat := .node node10530 node9339 +def node10532 : Tree Nat := .node node10531 node9621 +def node10533 : Tree Nat := .node node10225 node10532 +def node10534 : Tree Nat := .leaf 894965747452546029289481036448886549874566106265255522109080822855435967996006405530010642098271948348752422136166711393055556153033839597778030355783435887932050641584197192159016268330092069895244643678940146581551247517441103103490838373591547904 +def node10535 : Tree Nat := .node node4299 node10534 +def node10536 : Tree Nat := .node node10233 node10535 +def node10537 : Tree Nat := .node node10536 node9006 +def node10538 : Tree Nat := .node node10537 node9893 +def node10539 : Tree Nat := .leaf 192472083665898608964319283630401713436762982241238512478764483679432620060566120140936202511525559692713855440125980545640776190041800091592770673939669609680382650286080 +def node10540 : Tree Nat := .node node1099 node10539 +def node10541 : Tree Nat := .node node10540 node8159 +def node10542 : Tree Nat := .node node10541 node9017 +def node10543 : Tree Nat := .node node10542 node9898 +def node10544 : Tree Nat := .node node10538 node10543 +def node10545 : Tree Nat := .node node10533 node10544 +def node10546 : Tree Nat := .leaf 633165827771147607194886453810296806515340720790682362218481389331158979812980757259078406873169781512245026517749296135104204663053108037445934223702352340688030515601554276352 +def node10547 : Tree Nat := .node node1146 node10546 +def node10548 : Tree Nat := .node node10547 node8606 +def node10549 : Tree Nat := .node node10548 node9028 +def node10550 : Tree Nat := .node node10242 node10549 +def node10551 : Tree Nat := .leaf 3485195879244804053432958980038829437807641097639205763411965295271735915219697750496488237100366446694841075466178666160806531612472777901038010493702359850346937528001966473241782350465307370842408648429293079917825866590347749971205355417551259151442955479544852867970695088308224 +def node10552 : Tree Nat := .node node5355 node10551 +def node10553 : Tree Nat := .node node9032 node10552 +def node10554 : Tree Nat := .node node10246 node10553 +def node10555 : Tree Nat := .node node10554 node9910 +def node10556 : Tree Nat := .node node10550 node10555 +def node10557 : Tree Nat := .leaf 9661343807543145861738379727329983304551489841943757190740578306002024166590420851784050178749322503329006962763608589276215426643160386269379901496747282069407246078050304 +def node10558 : Tree Nat := .node node1224 node10557 +def node10559 : Tree Nat := .node node10558 node8190 +def node10560 : Tree Nat := .node node10559 node9044 +def node10561 : Tree Nat := .node node10560 node10258 +def node10562 : Tree Nat := .node node10254 node10561 +def node10563 : Tree Nat := .node node10556 node10562 +def node10564 : Tree Nat := .node node10545 node10563 +def node10565 : Tree Nat := .leaf 813966605576154086191388158047028539690522258993604018874743326717915956595751963107337126675482426609179999401170328017888193597183825892044590690374984870334207627845535524714320027464487685768749012209278961810747444407270906275838976 +def node10566 : Tree Nat := .node node10565 node8197 +def node10567 : Tree Nat := .node node6201 node10566 +def node10568 : Tree Nat := .leaf 22158279047425351206114981955269264206604694403649698977884354580244218109644390157360689918259267198981929381723586954485956112766135777699496635255476241912211557614541951103719683922440241938439768070116292529600843458068981320424012033729176705647623937434752899310098251776 +def node10569 : Tree Nat := .node node2973 node10568 +def node10570 : Tree Nat := .node node10569 node5387 +def node10571 : Tree Nat := .node node10567 node10570 +def node10572 : Tree Nat := .node node10266 node10571 +def node10573 : Tree Nat := .leaf 2396072166980802786735159298776695238492753254626953962345726140499318441713542203466335663006501932102703021886826037574254851029170613155695247854582057677391423380673554069513079880603709977051681800971270629151253329536324833868827918638391807721972935623980355562696118657351680 +def node10574 : Tree Nat := .node node10268 node10573 +def node10575 : Tree Nat := .node node6976 node10574 +def node10576 : Tree Nat := .node node8204 node10575 +def node10577 : Tree Nat := .node node10576 node9636 +def node10578 : Tree Nat := .node node10572 node10577 +def node10579 : Tree Nat := .leaf 3255866422304616344765552632188114158762100704416295644263244981059380744081475532449291252872565869620414385875643966147224342121004501804927669897349281372071660006659148235648233187774177307450862013129350900371983946274897389543882752 +def node10580 : Tree Nat := .node node4367 node10579 +def node10581 : Tree Nat := .node node5827 node10580 +def node10582 : Tree Nat := .node node10581 node9062 +def node10583 : Tree Nat := .leaf 3255866422304616344765552632188114158762100704416295644263244981059380744081479047225693239744739940353623515548971208098098015493374224317392067330120761483444945321520142513066617604624738470102500450128733558381121373271419338710712320 +def node10584 : Tree Nat := .node node10583 node8639 +def node10585 : Tree Nat := .node node6212 node10584 +def node10586 : Tree Nat := .node node10585 node7371 +def node10587 : Tree Nat := .node node10582 node10586 +def node10588 : Tree Nat := .node node10587 node10278 +def node10589 : Tree Nat := .node node10578 node10588 +def node10590 : Tree Nat := .leaf 208388169255707573472592108900008790981706361982624349991021507751708407126047757482645959839099450121985711383329240170045044593210749205776390333770174551333823849124193549305691072463665266718550656089550148560131411239384863482823311360 +def node10591 : Tree Nat := .node node9640 node10590 +def node10592 : Tree Nat := .node node9928 node10591 +def node10593 : Tree Nat := .node node10592 node9372 +def node10594 : Tree Nat := .leaf 10130653244338361715118183260964750568746135372975927356703057075214459284793683211144684397337643680774895924705940804373390340394387166371477727262825939032972885350728222113792 +def node10595 : Tree Nat := .node node1397 node10594 +def node10596 : Tree Nat := .node node10595 node10282 +def node10597 : Tree Nat := .node node10596 node9078 +def node10598 : Tree Nat := .node node10593 node10597 +def node10599 : Tree Nat := .node node10598 node10290 +def node10600 : Tree Nat := .leaf 223741437696587438519503533741816149548920811925678013175749845848837414012324218472089042266938140598917304050942641086020803995311334347454930065428652295349488028651005928802345711441027533886509323695715588784714596047244874250750257357402406912 +def node10601 : Tree Nat := .node node4397 node10600 +def node10602 : Tree Nat := .node node9939 node10601 +def node10603 : Tree Nat := .node node10602 node9648 +def node10604 : Tree Nat := .node node10603 node9379 +def node10605 : Tree Nat := .leaf 154581500920690333787814075638258850922141675712018472319405674389820274630382429444008815909329786379746944945389500124742402905697400317646807042631793502578165637382406144 +def node10606 : Tree Nat := .node node1474 node10605 +def node10607 : Tree Nat := .node node10606 node8245 +def node10608 : Tree Nat := .node node10607 node9094 +def node10609 : Tree Nat := .node node10608 node9099 +def node10610 : Tree Nat := .node node10604 node10609 +def node10611 : Tree Nat := .node node10599 node10610 +def node10612 : Tree Nat := .node node10589 node10611 +def node10613 : Tree Nat := .node node10564 node10612 +def node10614 : Tree Nat := .leaf 53344115463038834192638814325770062377158066765404832980975178659785340116363350954916280524838197986306144877087413735314558943715576137068002187870044882859395352463993222547787077305082545922738460928855479257978210854698550409096895397888 +def node10615 : Tree Nat := .node node4420 node10614 +def node10616 : Tree Nat := .node node10305 node10615 +def node10617 : Tree Nat := .node node10616 node9387 +def node10618 : Tree Nat := .node node10617 node9658 +def node10619 : Tree Nat := .node node10303 node10618 +def node10620 : Tree Nat := .leaf 813966605576154086191388158047028539690522258993604018874743326717915956365407576826725471875582855015657728227041835560830061982425140572601172983114394203753727047566003738497794967053469028423064337478906158205876464928512998995934208 +def node10621 : Tree Nat := .node node4426 node10620 +def node10622 : Tree Nat := .node node10311 node10621 +def node10623 : Tree Nat := .node node10622 node9122 +def node10624 : Tree Nat := .node node10623 node9956 +def node10625 : Tree Nat := .leaf 769888334663594435857277134521606853747051928964954657493993483120599933585062824778269684375681789348043041523188215651592821247154828374356733021157859676925141098823680 +def node10626 : Tree Nat := .node node1601 node10625 +def node10627 : Tree Nat := .node node10626 node8279 +def node10628 : Tree Nat := .node node10627 node9131 +def node10629 : Tree Nat := .node node10628 node9961 +def node10630 : Tree Nat := .node node10624 node10629 +def node10631 : Tree Nat := .node node10619 node10630 +def node10632 : Tree Nat := .leaf 4646927838993072071243945306718439250410188130185607684549287060362314553626263667328650982800488595593126077170975209963528137983958312711714491844803023596651679646361507358097421290814715449965594513405066824179954259537107582388358187709063204034071626586438784464660034303819776 +def node10633 : Tree Nat := .node node6284 node10632 +def node10634 : Tree Nat := .node node9668 node10633 +def node10635 : Tree Nat := .node node9972 node10634 +def node10636 : Tree Nat := .node node10635 node9980 +def node10637 : Tree Nat := .node node10321 node10636 +def node10638 : Tree Nat := .node node10637 node10328 +def node10639 : Tree Nat := .node node10631 node10638 +def node10640 : Tree Nat := .leaf 290432989937067004452746581669902453150636758136600480284330441272644659601641479208040686425030537224570063249933408856460057042508869123382879902423051292291993683015472812631455106011182128516518771675563018408317069932920675230933610029947233551218191556406294552380637747740672 +def node10641 : Tree Nat := .node node5514 node10640 +def node10642 : Tree Nat := .node node9696 node10641 +def node10643 : Tree Nat := .node node9438 node10642 +def node10644 : Tree Nat := .node node10643 node9702 +def node10645 : Tree Nat := .node node10335 node10644 +def node10646 : Tree Nat := .leaf 13023465689218465379062210528752456635109352936369821715687110074362044674069939569310167035678305424975053600617834579358483818224461023671114871045178099233528559206401261616753786829629925232237686130325136414254893219439159844645765120 +def node10647 : Tree Nat := .node node4481 node10646 +def node10648 : Tree Nat := .node node9996 node10647 +def node10649 : Tree Nat := .node node10648 node9707 +def node10650 : Tree Nat := .node node10649 node9712 +def node10651 : Tree Nat := .node node10650 node10004 +def node10652 : Tree Nat := .node node10645 node10651 +def node10653 : Tree Nat := .leaf 13656093609410854401825166854358895846491748774760620921371450552297205445088148100103090958675166887938608246376936715292315164450332574123094078540470239949799425714433484412725838570943340596686647049972438460499476591025242630744810531323904 +def node10654 : Tree Nat := .node node4500 node10653 +def node10655 : Tree Nat := .node node10339 node10654 +def node10656 : Tree Nat := .node node10655 node9723 +def node10657 : Tree Nat := .node node10656 node10010 +def node10658 : Tree Nat := .node node10657 node10023 +def node10659 : Tree Nat := .leaf 21479177938861104702947544874773277196989586550366132536457863739086873111764858218688560870842903577972137715914036008778039183436872255251946093696362636935335596854355519618825341185375190968646106017349047126732055474729852989613589837918144626688 +def node10660 : Tree Nat := .node node1945 node10659 +def node10661 : Tree Nat := .leaf 54627708241368206140399185795483904503108432555573077604046342122876875070820950745939333305640208526911453292536707737291368623684245044310355967320464545532804924558976751039808036840370998540277279097007233131349862317312632277657981848387584 +def node10662 : Tree Nat := .node node4514 node10661 +def node10663 : Tree Nat := .node node10660 node10662 +def node10664 : Tree Nat := .node node10663 node9740 +def node10665 : Tree Nat := .node node10664 node10031 +def node10666 : Tree Nat := .node node10665 node10037 +def node10667 : Tree Nat := .node node10658 node10666 +def node10668 : Tree Nat := .node node10652 node10667 +def node10669 : Tree Nat := .node node10639 node10668 +def node10670 : Tree Nat := .node node10613 node10669 +def node10671 : Tree Nat := .node node10527 node10670 +def node10672 : Tree Nat := .leaf 28638903918474961204418783933674838490721739573487173338490942158834381073950000924132044838597011277144618899971913807218996359853923734510142720858433261390115127054963430063473328286583706817087926623829189918086259596768230949276147476101370740736 +def node10673 : Tree Nat := .node node10048 node10672 +def node10674 : Tree Nat := .node node9216 node10673 +def node10675 : Tree Nat := .leaf 2554685341518452758919237426069541239769664439686778039789488195018192825858419992913601177979876320677534113140064435864847307323026879843537296391880518312486843789995827975613092940778402760023536592615649541282409129271154355902404104978768797004720994087557947984428641814476980434805780480 +def node10676 : Tree Nat := .node node5068 node10675 +def node10677 : Tree Nat := .node node9484 node10676 +def node10678 : Tree Nat := .node node10674 node10677 +def node10679 : Tree Nat := .node node10047 node10678 +def node10680 : Tree Nat := .node node10679 node10353 +def node10681 : Tree Nat := .leaf 85918022740406503255645470092525385597218198553162315078534269972435564094139227855984504265573406706177695678757711363747666347027850338083264783349320735138205464798897826445774515776290846826742525656519445453007303757165126242540315092898793127936 +def node10682 : Tree Nat := .node node7523 node10681 +def node10683 : Tree Nat := .node node9243 node10682 +def node10684 : Tree Nat := .leaf 76283967404910271121540606155089898734733648345126935749561096382907755712381345721882618268725230684086139739583423874389913946949627057624519051315441610816612128132788506995059149932427970427946120635121673054236417806801955968045968462733996901787990825645180127720564174542170226688 +def node10685 : Tree Nat := .node node5084 node10684 +def node10686 : Tree Nat := .node node9510 node10685 +def node10687 : Tree Nat := .node node10683 node10686 +def node10688 : Tree Nat := .node node10687 node9252 +def node10689 : Tree Nat := .node node10359 node10688 +def node10690 : Tree Nat := .node node10680 node10689 +def node10691 : Tree Nat := .leaf 96733617761664786335832533566481284062479866102181735506431818794959018192164720491226420615862959121533231828727109579338019372572636915590855930558725199290654030718796717977830754961586124101296903085875553176568826331950839271553862164801839605428053731876820224 +def node10692 : Tree Nat := .node node5605 node10691 +def node10693 : Tree Nat := .node node10363 node10692 +def node10694 : Tree Nat := .leaf 2494800386918399833815086676309963377712804265022133458703139449237699290108263623073821198302019763532049195219961542387255182594993347804550075730910981413468910470097693121167720962177249082951194696338438973530655660352958973101493058300892529287302465131033649046332397116510081900370432 +def node10695 : Tree Nat := .node node5095 node10694 +def node10696 : Tree Nat := .node node8814 node10695 +def node10697 : Tree Nat := .node node10693 node10696 +def node10698 : Tree Nat := .node node10058 node10697 +def node10699 : Tree Nat := .leaf 1723641332219371030852727564823520274389146270361742956089171009568452869613370429407370622816846224318647460790752450369195559519178030833780826605841836396616388817573529423033001974519430266185517633959121639178240 +def node10700 : Tree Nat := .node node172 node10699 +def node10701 : Tree Nat := .node node10700 node8389 +def node10702 : Tree Nat := .node node10701 node9765 +def node10703 : Tree Nat := .node node10370 node10702 +def node10704 : Tree Nat := .node node10698 node10703 +def node10705 : Tree Nat := .leaf 107727583263710689428295472801385055818048803566783393204564111350653389582248041613846190429785061442695321449532446683062325772812907776489998303948232459950344174553731418965165213212977753390529159043029705687040 +def node10706 : Tree Nat := .node node203 node10705 +def node10707 : Tree Nat := .node node10706 node8399 +def node10708 : Tree Nat := .node node10707 node8830 +def node10709 : Tree Nat := .node node10069 node10708 +def node10710 : Tree Nat := .leaf 38067632857031246407630399952637454346519987142099238452932455581906790445986786755799354708720610106914213142790699425667407556874447264145723794044070360352320624513692479666585867485218142105735309497846836668681627359695095723418764414801944075741251166029661113860628030218106306560 +def node10711 : Tree Nat := .node node5115 node10710 +def node10712 : Tree Nat := .node node8834 node10711 +def node10713 : Tree Nat := .node node10375 node10712 +def node10714 : Tree Nat := .node node10713 node10074 +def node10715 : Tree Nat := .node node10709 node10714 +def node10716 : Tree Nat := .node node10704 node10715 +def node10717 : Tree Nat := .node node10690 node10716 +def node10718 : Tree Nat := .leaf 155925024182399985285654182695081520760319266147381951508517489884678925378252842231429953756840307089140715991143407219297951436065941808298279660696778278056231006896984762499082834647950735808312545343706527006867059481055518477289265155307627911331521974171186215064846378700862820231680 +def node10719 : Tree Nat := .node node8852 node10718 +def node10720 : Tree Nat := .node node8851 node10719 +def node10721 : Tree Nat := .node node7990 node10720 +def node10722 : Tree Nat := .node node10082 node10721 +def node10723 : Tree Nat := .leaf 106688230926077668385277628651540124755315505352428628423477486470123144134879776759234861498608487430904399623027669901075178051323659570541732350366904697104609392765454037393484790842067670609318809301072852480633469753283405937427427098624 +def node10724 : Tree Nat := .node node8416 node10723 +def node10725 : Tree Nat := .node node7574 node10724 +def node10726 : Tree Nat := .node node10725 node10383 +def node10727 : Tree Nat := .node node10726 node9520 +def node10728 : Tree Nat := .node node10722 node10727 +def node10729 : Tree Nat := .leaf 1747979975492856518824388667826833403974740607927731994392193780821874531909645460376231504348665998209057060325930360780471036790185047226588214886276323163052162924784276271757550433087885624072788463677987426908831797465081059040172579357720576 +def node10730 : Tree Nat := .node node314 node10729 +def node10731 : Tree Nat := .node node10730 node10388 +def node10732 : Tree Nat := .node node10731 node9525 +def node10733 : Tree Nat := .node node10732 node8867 +def node10734 : Tree Nat := .leaf 2379227053564452900476899997039840896213512282606016847526883752241158718264596478888124767182634548505321707128128047801479743165146749243933849532568702441948776963122736629150383041967770234758123611436502011054222492809308222961589044941301309196685593412599421110664487917882179584 +def node10735 : Tree Nat := .node node8441 node10734 +def node10736 : Tree Nat := .node node8870 node10735 +def node10737 : Tree Nat := .node node8012 node10736 +def node10738 : Tree Nat := .node node10737 node9774 +def node10739 : Tree Nat := .node node10733 node10738 +def node10740 : Tree Nat := .node node10728 node10739 +def node10741 : Tree Nat := .leaf 103866931564455343801822554389934333203389244509458158012020530776078908043800262429741051803735415473862930601861307299166295972013467413095900791591279873085645894109199646240367250154596128571990698540922146080952747291558029251591315872261083467793250552682348171495515392 +def node10742 : Tree Nat := .node node4639 node10741 +def node10743 : Tree Nat := .node node10395 node10742 +def node10744 : Tree Nat := .node node10743 node8886 +def node10745 : Tree Nat := .node node9533 node10744 +def node10746 : Tree Nat := .leaf 1643792469233866721012831093812225982764843513915182220216570128169254979959737017873505432648113094075916045825948150817536472786546194054529563028712010450894155694102985785026913875902251547261760370575933440 +def node10747 : Tree Nat := .node node423 node10746 +def node10748 : Tree Nat := .node node10747 node8458 +def node10749 : Tree Nat := .node node10748 node10092 +def node10750 : Tree Nat := .node node10402 node10749 +def node10751 : Tree Nat := .node node10745 node10750 +def node10752 : Tree Nat := .leaf 26300679507741867536204949414732604573262178450796861926586697407426608039249772919014897095018806132831044367380708551943969828399087640452637000949344987042419753279586890350039106728479005685967645219372400640 +def node10753 : Tree Nat := .node node454 node10752 +def node10754 : Tree Nat := .node node10753 node8468 +def node10755 : Tree Nat := .node node10754 node10411 +def node10756 : Tree Nat := .node node10408 node10755 +def node10757 : Tree Nat := .leaf 1789931494904685075276173995854677405670108698260665783322775077947349531752566505916133121251945727321630023793883557083856139421400795861386296264178302846046199570728727136833942123197934603866776866240088039403083719310421229682604847949775110144 +def node10758 : Tree Nat := .node node4144 node10757 +def node10759 : Tree Nat := .node node10415 node10758 +def node10760 : Tree Nat := .leaf 3045410628562499712610431996210996347177459796916914813350639551812721304355229896593991881426619148166742167396265209731463035421472978166700239930069618000822520641090321556344764488199075026500365000017219173461500077638269605237633665253663241672094927972738317682739218910473843900416 +def node10761 : Tree Nat := .node node10096 node10760 +def node10762 : Tree Nat := .node node8901 node10761 +def node10763 : Tree Nat := .node node10759 node10762 +def node10764 : Tree Nat := .leaf 109248748468303532426524291739177087748419720352823839303482771257487091564273621151632319956353475417986878295713029159401689127993764873647658980548106479796213258340804397923025648743714951977187733095422203927771735755303276182434303749167360 +def node10765 : Tree Nat := .node node10764 node7617 +def node10766 : Tree Nat := .node node10765 node6440 +def node10767 : Tree Nat := .node node8906 node10766 +def node10768 : Tree Nat := .node node10763 node10767 +def node10769 : Tree Nat := .node node10756 node10768 +def node10770 : Tree Nat := .node node10751 node10769 +def node10771 : Tree Nat := .node node10740 node10770 +def node10772 : Tree Nat := .node node10717 node10771 +def node10773 : Tree Nat := .leaf 38981256045599996321413529552484778492955776800487604723103019487688029043323807551459749416242586242972663796034889354678354260236946480643847680761704091706685832250032696592824010108344411642647276371827774942895166445059971423854009612716795191801004446877954131808477033940271438547968 +def node10774 : Tree Nat := .node node9555 node10773 +def node10775 : Tree Nat := .node node7223 node10774 +def node10776 : Tree Nat := .node node8056 node10775 +def node10777 : Tree Nat := .node node10426 node10776 +def node10778 : Tree Nat := .node node10777 node10432 +def node10779 : Tree Nat := .leaf 1747979975492856518824388667826833403974740607927731994392193780821874531909645460376203386137450103231664494460257323393853101183195660247631335163947499178172966125594782267469401115230698618381328958083467375245984958092024755820292172083625984 +def node10780 : Tree Nat := .node node4182 node10779 +def node10781 : Tree Nat := .node node5688 node10780 +def node10782 : Tree Nat := .leaf 594806763391113225119224999259960224052504080663757783622308743726376370591745013128756754093935341620975307564880756003575038662329312936505914480482571696503618121240426644898524096380402157073868491220717064880731047715211102379437393307558428398418031019935048094288549169231560704 +def node10783 : Tree Nat := .node node9803 node10782 +def node10784 : Tree Nat := .node node6846 node10783 +def node10785 : Tree Nat := .node node10781 node10784 +def node10786 : Tree Nat := .node node10785 node9810 +def node10787 : Tree Nat := .node node10445 node10786 +def node10788 : Tree Nat := .node node10778 node10787 +def node10789 : Tree Nat := .leaf 1584883593408437211614387469712064555158914503508771038724904544061812054501246924612497208568277150977848478150352793981903158803774780928740183639894990703924745413072717765038204670960526681885023258381750772767253519213657637463202433142511385085058242598089959457536 +def node10790 : Tree Nat := .node node4707 node10789 +def node10791 : Tree Nat := .node node10122 node10790 +def node10792 : Tree Nat := .node node10791 node8932 +def node10793 : Tree Nat := .node node10451 node10792 +def node10794 : Tree Nat := .leaf 53344115463038834192638814325770062377158066765404832980975178659785340116425313594825765059979370971064802368033254299785507581119946223418506090045135593361698137087189675283370789080398364342238701448770909329366492804144952686209258225664 +def node10795 : Tree Nat := .node node659 node10794 +def node10796 : Tree Nat := .node node10795 node8073 +def node10797 : Tree Nat := .node node10796 node10458 +def node10798 : Tree Nat := .node node10797 node10129 +def node10799 : Tree Nat := .node node10793 node10798 +def node10800 : Tree Nat := .leaf 82551059006714003709566475310830395121783235067659435050372654133420130779075372570317644052991028430001268377850854185891664814666544108925181759608065456196858222579027535181170397676002996622961039718013094544349280105350379173480586509699793236632682402576341139456 +def node10801 : Tree Nat := .node node3257 node10800 +def node10802 : Tree Nat := .node node10801 node8941 +def node10803 : Tree Nat := .node node10134 node10802 +def node10804 : Tree Nat := .node node10465 node10803 +def node10805 : Tree Nat := .leaf 152270531428124985630521599810549817371760496609159473209520430360789742538586277437111327119644425364026120943639279071518089878320787474950575721365763956720219533682572574968371467103957447521335353240892500031120302422169910477631454527052653346151976220684244467405601694246682755072 +def node10806 : Tree Nat := .node node8518 node10805 +def node10807 : Tree Nat := .node node10468 node10806 +def node10808 : Tree Nat := .node node10139 node10807 +def node10809 : Tree Nat := .node node10808 node10144 +def node10810 : Tree Nat := .node node10804 node10809 +def node10811 : Tree Nat := .node node10799 node10810 +def node10812 : Tree Nat := .node node10788 node10811 +def node10813 : Tree Nat := .leaf 1476037870510524353596566889281486144743972093574772098358090205303312247211350003978710290520579985138648724631345580184648252545533272759442081792994189046860673962172863336127725384112180595985403614676180791561404497104451251050216776265310185845148595794688 +def node10814 : Tree Nat := .node node5721 node10813 +def node10815 : Tree Nat := .node node9842 node10814 +def node10816 : Tree Nat := .leaf 623700096729599941143673061886283382447435673680950235479233377409867028482305313800458208401858198151226794247420228508602131400450429247485901188292840378816773832392678307087689622607501714882775677360302111264997430051671536717931416989295603894752143531276288050714468795635792271653888 +def node10817 : Tree Nat := .node node5254 node10816 +def node10818 : Tree Nat := .node node10476 node10817 +def node10819 : Tree Nat := .node node10815 node10818 +def node10820 : Tree Nat := .node node10154 node10819 +def node10821 : Tree Nat := .node node10820 node10487 +def node10822 : Tree Nat := .leaf 213376461852155336770555257303080249512629755095605452561229695904043384929354880748254473666251728746058214090720701100545564459333989336831380189536513655594333138889843180953261023080008128783578100968630626946544141771941529587407885697024 +def node10823 : Tree Nat := .node node10822 node8959 +def node10824 : Tree Nat := .node node9595 node10823 +def node10825 : Tree Nat := .node node10491 node10824 +def node10826 : Tree Nat := .node node10825 node10168 +def node10827 : Tree Nat := .leaf 9516908214257811601907599988159363588419928280429494688509287891331375017166805387210408779886319742775226958598388031269281297351191758887711472242214588931135963469832754551222749824457144447590219847424556232671251926830884501000682897149615413406472575317896479729877536277180448768 +def node10828 : Tree Nat := .node node5274 node10827 +def node10829 : Tree Nat := .node node9600 node10828 +def node10830 : Tree Nat := .node node10172 node10829 +def node10831 : Tree Nat := .node node10830 node10177 +def node10832 : Tree Nat := .node node10826 node10831 +def node10833 : Tree Nat := .node node10821 node10832 +def node10834 : Tree Nat := .leaf 106688230926077668385277628651540124755315505352428628423477486470123144134879776759455232229745023956832998297898181274066994845806710355433223617396271263368695227945897090875725775513959799831620499092688322592723167021216679524437904588800 +def node10835 : Tree Nat := .node node879 node10834 +def node10836 : Tree Nat := .node node10835 node10497 +def node10837 : Tree Nat := .node node10836 node9870 +def node10838 : Tree Nat := .node node10837 node10503 +def node10839 : Tree Nat := .leaf 109248748468303532426524291739177087748419720352823839303482771257487091564273621151632292497162834895548018368109832833828820050252564300426021402694269737623479667716595907684463002925495042791942167171990055439819736888728025886321139288938752 +def node10840 : Tree Nat := .node node4256 node10839 +def node10841 : Tree Nat := .node node10506 node10840 +def node10842 : Tree Nat := .leaf 76172441136774437391830751467728656192723803830002481165131913493459060163068014714358988777601814008377172230725897222960332991129624492289011904556219937624747578396939938175545155711142610123121972632350040011333457428459164394558267146498946900652331117255367527620365025212404596736 +def node10843 : Tree Nat := .node node8111 node10842 +def node10844 : Tree Nat := .node node10189 node10843 +def node10845 : Tree Nat := .node node10841 node10844 +def node10846 : Tree Nat := .node node10845 node10195 +def node10847 : Tree Nat := .node node10838 node10846 +def node10848 : Tree Nat := .leaf 55938773239161043087768766345230778807527298178812208283877953563424242707741571296695045277037402305856329616964921931480163369661667111596524615843028647028613981701385322573240387107737698665234058122079742099654834360850925244548233298356207616 +def node10849 : Tree Nat := .node node3326 node10848 +def node10850 : Tree Nat := .node node10849 node5301 +def node10851 : Tree Nat := .node node10204 node10850 +def node10852 : Tree Nat := .node node10516 node10851 +def node10853 : Tree Nat := .leaf 7159725979618740301104695983418709622680434793043045857619007531815365813761759315575770174588497678026278531167849057932276570998237506893653095393460120041857186085818639876206292992799021993161942681929018428816142811330035029692339637288450392064 +def node10854 : Tree Nat := .node node7700 node10853 +def node10855 : Tree Nat := .node node10208 node10854 +def node10856 : Tree Nat := .leaf 2436328502849999770088345596968797077776334522235701804125814182170586849673050004763378113147484449123994991205752168894128882143494779858311182358093524161945275594502448679097648440002921991150981452155750057051176357837540854252964516868549345174138316690435184138788523878482618351616 +def node10857 : Tree Nat := .node node5305 node10856 +def node10858 : Tree Nat := .node node10519 node10857 +def node10859 : Tree Nat := .node node10855 node10858 +def node10860 : Tree Nat := .node node10859 node10214 +def node10861 : Tree Nat := .node node10852 node10860 +def node10862 : Tree Nat := .node node10847 node10861 +def node10863 : Tree Nat := .node node10833 node10862 +def node10864 : Tree Nat := .node node10812 node10863 +def node10865 : Tree Nat := .node node10772 node10864 +def node10866 : Tree Nat := .leaf 7060034896770543742372772105511569658378384792242794286836836064242363147905002941556383606649878828731040482455642272152395741595834902045976133978559016181899109104608108919414786793470202220875600015389195678131421184 +def node10867 : Tree Nat := .node node1021 node10866 +def node10868 : Tree Nat := .leaf 57277807836949922408837567867349676981443479146974346676981884317668762147900001848264089677194006346666685534015360807062456169513330421629951026130408579062781553785945462332754958356192135516527925964682103770931381989659114752018066730984639823872 +def node10869 : Tree Nat := .node node4288 node10868 +def node10870 : Tree Nat := .node node10867 node10869 +def node10871 : Tree Nat := .leaf 19490628022799998160706764777226414492262978068786581943017299059169869475107624303289320337067332765661959836441527626887498324869054912724501554777273559384595828159355027852735768357840781258878462523086162141859551791836193364567673518792342428330106728656425331359473843025132424016640 +def node10872 : Tree Nat := .node node8993 node10871 +def node10873 : Tree Nat := .node node8992 node10872 +def node10874 : Tree Nat := .node node10870 node10873 +def node10875 : Tree Nat := .node node10224 node10874 +def node10876 : Tree Nat := .leaf 112960558348328699877964353688185114588230231741373345053674074302859553202066438004392213006152501976891377919604570435846579378591406633725890649047590297808424516871832004220917039484336960889211906449427435094502539264 +def node10877 : Tree Nat := .node node1052 node10876 +def node10878 : Tree Nat := .node node10877 node8571 +def node10879 : Tree Nat := .node node10878 node9620 +def node10880 : Tree Nat := .node node10531 node10879 +def node10881 : Tree Nat := .node node10875 node10880 +def node10882 : Tree Nat := .leaf 826661304738010315953643754094723510553260772829547976171010202944039883868624651684819033712328262805113668050418063627118050302421528954744410883717176388397117377486322717949952 +def node10883 : Tree Nat := .node node1083 node10882 +def node10884 : Tree Nat := .node node10883 node9891 +def node10885 : Tree Nat := .node node10884 node9012 +def node10886 : Tree Nat := .node node10537 node10885 +def node10887 : Tree Nat := .leaf 873989987746428259412194333913416701987357775069798991042814396937084383360290555546021876177887051241787582940923468588982850450640822836605357477898227588843032161344437463456421534184226666094093787921967287360117422742484638433698468595761152 +def node10888 : Tree Nat := .node node4308 node10887 +def node10889 : Tree Nat := .node node10540 node10888 +def node10890 : Tree Nat := .leaf 2436625906231695326700905209468427057831083840429071507037047180869434274239740593848887869932392838890841125886993565931030429405226060379837296777777324757276565002007658390265322556511958169863162789241122409443326069452624278539120316417443233102110897227219902700191455599036337225728 +def node10891 : Tree Nat := .node node8588 node10890 +def node10892 : Tree Nat := .node node9016 node10891 +def node10893 : Tree Nat := .node node10889 node10892 +def node10894 : Tree Nat := .node node10893 node9898 +def node10895 : Tree Nat := .node node10886 node10894 +def node10896 : Tree Nat := .node node10881 node10895 +def node10897 : Tree Nat := .leaf 64489078507786299636425861831078630986569271746325990024591980112702728142941535837331440868528362604718222692303553031863955775823343730563697681194021150200160109877434667751848039032944888089914249200478157323337460124461526278153321517774311537121260992194456064 +def node10898 : Tree Nat := .node node4835 node10897 +def node10899 : Tree Nat := .node node10547 node10898 +def node10900 : Tree Nat := .node node10899 node9028 +def node10901 : Tree Nat := .node node10242 node10900 +def node10902 : Tree Nat := .leaf 55938773239161043087768766254575518211183034936906831466543454418809295646818664664475525480827957392151918397330266139531725418712703754722903209587479883845779485311460389451699973261980709780278479481472800262702429658890856482726614557639311360 +def node10903 : Tree Nat := .node node6569 node10902 +def node10904 : Tree Nat := .node node10245 node10903 +def node10905 : Tree Nat := .node node10904 node10553 +def node10906 : Tree Nat := .leaf 3447282664438742061705455129647040548778292540723485912178342012911325976834208459619667393001832993583207942544139558771262699003786097976842143898660022567417907898766902121298969045270794154137486852286232825692160 +def node10907 : Tree Nat := .node node1177 node10906 +def node10908 : Tree Nat := .node node10907 node8611 +def node10909 : Tree Nat := .node node10908 node9909 +def node10910 : Tree Nat := .node node10905 node10909 +def node10911 : Tree Nat := .node node10901 node10910 +def node10912 : Tree Nat := .leaf 215455166527421378856590945602770111636097607133566786409128222701306779164473965525306915863009353422110887584681712130496989998298783418378204797472082978027678191145357122665854205647217026101843887490233050071040 +def node10913 : Tree Nat := .node node1208 node10912 +def node10914 : Tree Nat := .node node10913 node8621 +def node10915 : Tree Nat := .node node10914 node9352 +def node10916 : Tree Nat := .node node10253 node10915 +def node10917 : Tree Nat := .leaf 76135265714062492815260799905274908678720522324960996303655519196976165093895368364254679407658334797238243436350420943669186942913912083564867359960902224507481108863903528753808088323074815390455250610154370427094567393814714878421542232647972592819261980193406305823429072092137521152 +def node10918 : Tree Nat := .node node6967 node10917 +def node10919 : Tree Nat := .node node9043 node10918 +def node10920 : Tree Nat := .node node10559 node10919 +def node10921 : Tree Nat := .node node10920 node10258 +def node10922 : Tree Nat := .node node10916 node10921 +def node10923 : Tree Nat := .node node10911 node10922 +def node10924 : Tree Nat := .node node10896 node10923 +def node10925 : Tree Nat := .leaf 15015950102534791658700856792104391317455222282752516534236741272916555874581810543894403238713214754697109912088637781823816997340738353197614786539962646376091943183039839352566818203001716409751424488791685014146266499018177146848875858753550110183976960 +def node10926 : Tree Nat := .node node10565 node10925 +def node10927 : Tree Nat := .node node6201 node10926 +def node10928 : Tree Nat := .leaf 311850048364799970572893120005414463159653646912752305414931921134323129143250539822961494162725575219822254527973354532848541913836851803472398752285779690353741070038502127659790014388754434512327791662295514805842962391994386771031137154908664537073690074841848266591676757477831211008768 +def node10929 : Tree Nat := .node node5386 node10928 +def node10930 : Tree Nat := .node node10569 node10929 +def node10931 : Tree Nat := .node node10927 node10930 +def node10932 : Tree Nat := .node node10266 node10931 +def node10933 : Tree Nat := .leaf 213376461852155336770555257303080249512629755095605452561229695904043384929354880748253615566544212419843841353120815910032270552362818599595302007793032226943392528517367683703120658219092633645948356687943028315090877213582460214543378284544 +def node10934 : Tree Nat := .node node4358 node10933 +def node10935 : Tree Nat := .node node5821 node10934 +def node10936 : Tree Nat := .node node10935 node10575 +def node10937 : Tree Nat := .node node10936 node9636 +def node10938 : Tree Nat := .node node10932 node10937 +def node10939 : Tree Nat := .leaf 4758454107128905800953799994079681794209964140214747344254643945665687508583402693605204389710475399834705447881184019677587794037689425586560681653411219886361646110832667458002892775648055604030964997232251735893358919059943820148879582849203745268722263647874490203640897065982099456 +def node10940 : Tree Nat := .node node5402 node10939 +def node10941 : Tree Nat := .node node6987 node10940 +def node10942 : Tree Nat := .node node10276 node10941 +def node10943 : Tree Nat := .node node10942 node9923 +def node10944 : Tree Nat := .node node10587 node10943 +def node10945 : Tree Nat := .node node10938 node10944 +def node10946 : Tree Nat := .leaf 69244620785013915170128490189477811531824955396191184425272058540842623741436225137170371136664720923332289635109501355728626110983054942138068903378908836025520798810371795348972878000407759068538992147284057885115381989215332474090418563997438953994279448997472151887960576 +def node10947 : Tree Nat := .node node10281 node10946 +def node10948 : Tree Nat := .node node10595 node10947 +def node10949 : Tree Nat := .node node10948 node9078 +def node10950 : Tree Nat := .node node10593 node10949 +def node10951 : Tree Nat := .leaf 4777041818484878089238775775306555549421891895327741306781520146635937715303295889454558857997516342778782464570043212241472269980943501834861170987953556446240178220885872918887630830752335782007186888998104860426178776583274411632410130288909283581261737806392248987901778363229955584 +def node10952 : Tree Nat := .node node8223 node10951 +def node10953 : Tree Nat := .node node9082 node10952 +def node10954 : Tree Nat := .node node10288 node10953 +def node10955 : Tree Nat := .leaf 3287584938467733442025662187624451965529687027830364440416932881089714681742374885601155013033019379512439097803255011203977329533910465905773451775791894982326849222557672031251441073242695378571651784124661760 +def node10956 : Tree Nat := .node node1428 node10955 +def node10957 : Tree Nat := .node node10956 node8660 +def node10958 : Tree Nat := .node node10957 node9934 +def node10959 : Tree Nat := .node node10954 node10958 +def node10960 : Tree Nat := .node node10950 node10959 +def node10961 : Tree Nat := .leaf 52601359015483735072409898829465209146524356901593723853173394814849442504888766513945724017833815461799337107928496526502849891487044325565142298139120719523509287094110742129472911735382544992705012147976929280 +def node10962 : Tree Nat := .node node1459 node10961 +def node10963 : Tree Nat := .node node10962 node8670 +def node10964 : Tree Nat := .node node10963 node9378 +def node10965 : Tree Nat := .node node10603 node10964 +def node10966 : Tree Nat := .leaf 3579862989809370150552347991709354811340217396521331567110919099000515126341153003746371951779704362357850156523159263326124950090969011357989556801517638931620688994417507034552418335106866068436477463931384001675195486642989958687805438044766470144 +def node10967 : Tree Nat := .node node7817 node10966 +def node10968 : Tree Nat := .node node10606 node10967 +def node10969 : Tree Nat := .leaf 1218164251424999885044172798484398538859528357199375940858488307151618586345806550393140350968693308065350738980891613209960226597590803688703338126720824052327010867507592148113361146034059961055303926514436207825116473192450151263200622301156178373634718791461277388763800225533113925632 +def node10970 : Tree Nat := .node node5433 node10969 +def node10971 : Tree Nat := .node node9093 node10970 +def node10972 : Tree Nat := .node node10968 node10971 +def node10973 : Tree Nat := .node node10972 node9099 +def node10974 : Tree Nat := .node node10965 node10973 +def node10975 : Tree Nat := .node node10960 node10974 +def node10976 : Tree Nat := .node node10945 node10975 +def node10977 : Tree Nat := .node node10924 node10976 +def node10978 : Tree Nat := .leaf 14120069793541087484745544211023139316756769609713289523930334602655983439814019266696164821623365327497509637830517502741390744316572544250166390895816975711777862531858137831458078098293990125996320191232545500918972416 +def node10979 : Tree Nat := .node node1523 node10978 +def node10980 : Tree Nat := .leaf 5038516785078904571628940649100120343819129703349397299611487789825165970604072637865777698426141369607427607953271665540738721639339323532416532167792460417020461803982046783009956451205832572044342493562199723981628480491926047879933637916240707004250185363623680 +def node10981 : Tree Nat := .node node10299 node10980 +def node10982 : Tree Nat := .node node10979 node10981 +def node10983 : Tree Nat := .leaf 77962512091199992642827155836619268151796150693293626696227314137569691707866915251543715486074274238522930556271885208426794892153453479482203236389873799993165812455582342964165607897951147983540374578588708617113586080306244875119147477750083675741893464286999022216260056773667189708032 +def node10984 : Tree Nat := .node node5450 node10983 +def node10985 : Tree Nat := .node node9110 node10984 +def node10986 : Tree Nat := .node node10982 node10985 +def node10987 : Tree Nat := .node node10298 node10986 +def node10988 : Tree Nat := .leaf 225921116696657399755928707376370229284812614017367178240024142742422706379369872025098938344991608143543655119944627747285563662556210458266787568283194117712687415140470206543367129999760340303841270224574790195694534656 +def node10989 : Tree Nat := .node node1554 node10988 +def node10990 : Tree Nat := .node node10989 node8691 +def node10991 : Tree Nat := .node node10990 node9657 +def node10992 : Tree Nat := .node node10617 node10991 +def node10993 : Tree Nat := .node node10987 node10992 +def node10994 : Tree Nat := .leaf 3306645218952041263814575016378894042213043091318191904684040811776159535474498606739276134849313051220454672201672254508472201209686115818977643534868705551180050353890785365065728 +def node10995 : Tree Nat := .node node1585 node10994 +def node10996 : Tree Nat := .node node10995 node9954 +def node10997 : Tree Nat := .node node10996 node9126 +def node10998 : Tree Nat := .node node10623 node10997 +def node10999 : Tree Nat := .leaf 3495959950985713037648777335653666807949481215855463988784387561643749063819290920752406772274900111468520602804871040696023618406800830842084786232893855765740898184739711524514094878303614820537686636743456263866321243872790850146463359778684928 +def node11000 : Tree Nat := .node node7858 node10999 +def node11001 : Tree Nat := .node node10626 node11000 +def node11002 : Tree Nat := .leaf 1189613526782226450238449998519920448105008161327515567244617487452752741183490026257513508187870683241950615129761512007150077324658625873011828938847441007542239681711390010041733809579568686486189655409299527969651671048480331748716824509401592320615283301389416974146502512101818368 +def node11003 : Tree Nat := .node node5466 node11002 +def node11004 : Tree Nat := .node node9130 node11003 +def node11005 : Tree Nat := .node node11001 node11004 +def node11006 : Tree Nat := .node node11005 node9961 +def node11007 : Tree Nat := .node node10998 node11006 +def node11008 : Tree Nat := .node node10993 node11007 +def node11009 : Tree Nat := .leaf 1056589062271330551357154794869753759687364148238312273254043242658844185409541560807279608610073744860744529077431228504910001328830559966772059595464033175959084656138281388196503377632135017081551784446264721403649717905590095531168247877614287701231765876309768551424 +def node11010 : Tree Nat := .node node5895 node11009 +def node11011 : Tree Nat := .node node9966 node11010 +def node11012 : Tree Nat := .node node11011 node9664 +def node11013 : Tree Nat := .node node10320 node11012 +def node11014 : Tree Nat := .node node11013 node10636 +def node11015 : Tree Nat := .leaf 304541062856249971261043199621099634714882089299843985214622076787904646586452459494519704675533833431884590858214285724247014240507813259083731357989730156378225933556287895277538092779890124661842523769012120533857204498197301852505468018677508161185893751472910924893568903807823249408 +def node11016 : Tree Nat := .node node5497 node11015 +def node11017 : Tree Nat := .node node9679 node11016 +def node11018 : Tree Nat := .node node9414 node11017 +def node11019 : Tree Nat := .node node11018 node10326 +def node11020 : Tree Nat := .node node9991 node11019 +def node11021 : Tree Nat := .node node11014 node11020 +def node11022 : Tree Nat := .node node11008 node11021 +def node11023 : Tree Nat := .leaf 984025249450869370107574615631393658836234280258103141597289152714545206071444131109254681944517580776134104457535731576453478028560721450206804473340851486384197049236077997910901427400424053358391924071024158254919329349693491665537021620149719580303782104064 +def node11024 : Tree Nat := .node node5002 node11023 +def node11025 : Tree Nat := .node node9432 node11024 +def node11026 : Tree Nat := .leaf 1247400193459199986152164510103367905614711427706494166828336535981415444438633317194506772233159742921890833013035783390413375604053295204257954387395432733600795136874301633469355185102373107356408502561468524486530297456596624945802826100809279189757822827880815319277026741867136501720320 +def node11027 : Tree Nat := .node node7454 node11026 +def node11028 : Tree Nat := .node node9691 node11027 +def node11029 : Tree Nat := .node node11025 node11028 +def node11030 : Tree Nat := .node node10334 node11029 +def node11031 : Tree Nat := .leaf 82551059006714003709566475310830395121783235067653522271146608803035893582437006630728752155738089189558962505058110420684346055307366185403097996801240011197979482405419233472900631402643132425233253646261039181591198658776681488479001584265851609043446088110629191680 +def node11032 : Tree Nat := .node node4475 node11031 +def node11033 : Tree Nat := .node node9437 node11032 +def node11034 : Tree Nat := .node node11033 node10642 +def node11035 : Tree Nat := .node node11034 node9702 +def node11036 : Tree Nat := .node node11030 node11035 +def node11037 : Tree Nat := .leaf 95169082142578116019075999881593635848400652906201245379569398996220203781907212126261802980481571261267392711718620636972049544885883533751482770560982663420732950634861750579792720981845424355254827708101325762014941759076580942030871905711737150314745406179331395938354941445778964480 +def node11038 : Tree Nat := .node node7071 node11037 +def node11039 : Tree Nat := .node node9715 node11038 +def node11040 : Tree Nat := .node node9453 node11039 +def node11041 : Tree Nat := .node node11040 node10003 +def node11042 : Tree Nat := .node node10650 node11041 +def node11043 : Tree Nat := .node node11036 node11042 +def node11044 : Tree Nat := .leaf 218497496936607064853048583478354175496839440705647678614066509054064394048286316886914879630492248583127746162113710912384395948408073846750739159654302311543472547300868401686133862429221849205449943039219489585542905120811667955432180162782720 +def node11045 : Tree Nat := .node node8756 node11044 +def node11046 : Tree Nat := .node node10013 node11045 +def node11047 : Tree Nat := .leaf 2436402853695423659241485500093704572832981300149241354695574872988728355321682744388243339964761642596291283088180904550501819461136457463107582044364929838361774920558990968544659331542325862113248875128491538736056218645074909457183524415333704289118389060196468336506413428664212389888 +def node11048 : Tree Nat := .node node5545 node11047 +def node11049 : Tree Nat := .node node9731 node11048 +def node11050 : Tree Nat := .node node11046 node11049 +def node11051 : Tree Nat := .node node11050 node10022 +def node11052 : Tree Nat := .node node10657 node11051 +def node11053 : Tree Nat := .leaf 14319451959237480602209391966837419245360869586086091715238015063630731627523518631151540349176989130472794669860878747040043319620752683876640378736925359265822859592779712861218964954585615556604167595560950758451542801885740130732448122528059097088 +def node11054 : Tree Nat := .node node4519 node11053 +def node11055 : Tree Nat := .node node10034 node11054 +def node11056 : Tree Nat := .leaf 2554680468861447058919697249383385818945571956042443391276124024616678957769968784717408916427931804370092017250890287315044953724336160095246434856338971095975656350548656176346755679260632830424602519815822918771858706797398019288777407340776932736583847222550302923357233121813385514028371712 +def node11057 : Tree Nat := .node node8771 node11056 +def node11058 : Tree Nat := .node node9744 node11057 +def node11059 : Tree Nat := .node node11055 node11058 +def node11060 : Tree Nat := .node node11059 node9750 +def node11061 : Tree Nat := .node node10665 node11060 +def node11062 : Tree Nat := .node node11052 node11061 +def node11063 : Tree Nat := .node node11043 node11062 +def node11064 : Tree Nat := .node node11022 node11063 +def node11065 : Tree Nat := .node node10977 node11064 +def node11066 : Tree Nat := .node node10865 node11065 +def node11067 : Tree Nat := .leaf 2554685341518452758919237508620600246483668149253253350619883316801427893517855043286255311400007099752906683457708488855875737324295257694391482283545332979030952715177587583678549137636625339051071773786047217285405752232194073915498649328048902355100167568144457684221878447159383011146919936 +def node11068 : Tree Nat := .node node5068 node11067 +def node11069 : Tree Nat := .node node9484 node11068 +def node11070 : Tree Nat := .node node10674 node11069 +def node11071 : Tree Nat := .node node10047 node11070 +def node11072 : Tree Nat := .node node11071 node10353 +def node11073 : Tree Nat := .leaf 638668899051110339730043494528037430307403838405632263158900008459255607361866436634204573127948553095500436194351489747037328708508230649565280757817240367889084385404166360484145889045213551683510656047351015251501641786798707938600222306116436473701931909301205614612832872569859463660437504 +def node11074 : Tree Nat := .node node5079 node11073 +def node11075 : Tree Nat := .node node9505 node11074 +def node11076 : Tree Nat := .node node9239 node11075 +def node11077 : Tree Nat := .node node10358 node11076 +def node11078 : Tree Nat := .node node11077 node10688 +def node11079 : Tree Nat := .node node11072 node11078 +def node11080 : Tree Nat := .leaf 25359685326862541939557340726563259540866106890815958076280245767323608469774917455506403243053452484151980456685674706988068076202947533945618137218863431952727952804286664120823584990549537648600659732895970576638523561681512916868463362042809053069698959206963059097600 +def node11081 : Tree Nat := .node node4577 node11080 +def node11082 : Tree Nat := .node node10700 node11081 +def node11083 : Tree Nat := .node node11082 node9765 +def node11084 : Tree Nat := .node node10370 node11083 +def node11085 : Tree Nat := .node node10698 node11084 +def node11086 : Tree Nat := .leaf 2554675596204441358920157155234181557867294149299169136804610260329945488780656810431192698101188848322993184617960894559274858525751158067667913842687243683593514224337475929545962042497366330775037117621256315181996258567253372708797541371099867345416135622814627179689575844509694256521084928 +def node11087 : Tree Nat := .node node11086 node8824 +def node11088 : Tree Nat := .node node8395 node11087 +def node11089 : Tree Nat := .node node10068 node11088 +def node11090 : Tree Nat := .leaf 8655577598126739876717812079573022799358887102368254142497122243861251566874946946361262884504084535800253293083629033914754888392752749770415705058549252243746802538831179936646854771834455296924944498251137318848486763422009951045843947126840950730644916729218690078212096 +def node11091 : Tree Nat := .node node5620 node11090 +def node11092 : Tree Nat := .node node10706 node11091 +def node11093 : Tree Nat := .leaf 163499238157084246971167031136149696249049528960308906100902295024436347946163260596679273177584043220016291918008106676313433488263068652987245384142954425939882895679384858461038954002101894372865759311049947314292097272030496335834137286927066994764288186258808085181189053362867848956191178752 +def node11094 : Tree Nat := .node node5110 node11093 +def node11095 : Tree Nat := .node node8829 node11094 +def node11096 : Tree Nat := .node node11092 node11095 +def node11097 : Tree Nat := .node node11089 node11096 +def node11098 : Tree Nat := .leaf 101434613628559975992017802531256018594612900846302660848264270123834810490498805730814541377759021537551347020435025469761464125348087797388099643107579300181757221300918296577053403346263952278168399591750327210225244330184250997373835381187305635934256031486443318673408 +def node11099 : Tree Nat := .node node6392 node11098 +def node11100 : Tree Nat := .node node8404 node11099 +def node11101 : Tree Nat := .node node11100 node10073 +def node11102 : Tree Nat := .node node10713 node11101 +def node11103 : Tree Nat := .node node11097 node11102 +def node11104 : Tree Nat := .node node11085 node11103 +def node11105 : Tree Nat := .node node11079 node11104 +def node11106 : Tree Nat := .leaf 22158278651228636258836486123354178839798262018821571686255070203193643511816502517788172698851428127553733118654495099167869424971880243452949416613266300986643205017960890673632272265848565894552155488704381957510436642326891275046277398444513749161461599500058983031013113856 +def node11107 : Tree Nat := .node node4623 node11106 +def node11108 : Tree Nat := .node node8006 node11107 +def node11109 : Tree Nat := .leaf 10218702384817765435680645196173672777168963974041446678917664294909138896974824637728038800435160094659217004303684034646930101677216339049673522749832601919118813623008873037518294171650174351246698378332906430449763134362193166116879849422958038592051299340097797396858985710810246544359424000 +def node11110 : Tree Nat := .node node8864 node11109 +def node11111 : Tree Nat := .node node8863 node11110 +def node11112 : Tree Nat := .node node11108 node11111 +def node11113 : Tree Nat := .node node10732 node11112 +def node11114 : Tree Nat := .leaf 567251933470962971228786210597063468015139302172686203515797990626519142986674974353925463005828629283767165744928969078113010206791249630875951917585200590177642036200776836920585296976636478697171498896418117997443700476201064421604357182846154533660173600357954234799718662144 +def node11115 : Tree Nat := .node node4628 node11114 +def node11116 : Tree Nat := .node node8015 node11115 +def node11117 : Tree Nat := .node node11116 node9773 +def node11118 : Tree Nat := .node node10737 node11117 +def node11119 : Tree Nat := .node node11113 node11118 +def node11120 : Tree Nat := .node node10728 node11119 +def node11121 : Tree Nat := .leaf 35455409736326656251834725891510782352635139838369182269713223249036493652349081171959413038731862349745407504040373576830488079514345427267318444944875153147961178418547088972725786250654907002832255913198306516169305485533191404733075234178319747736598745648541892225194262528 +def node11122 : Tree Nat := .node node4635 node11121 +def node11123 : Tree Nat := .node node8449 node11122 +def node11124 : Tree Nat := .node node9532 node11123 +def node11125 : Tree Nat := .leaf 39916806190694396233127454260740707662572704089133729307453854262301760819169371191393510266061278684767761452452960890994768399117478387058122360733857118275157910455804363183442276876867844440542346831774028896976358218282631555978346803093349268482644156655484625375045202864401362211307520 +def node11126 : Tree Nat := .node node7198 node11125 +def node11127 : Tree Nat := .node node8885 node11126 +def node11128 : Tree Nat := .node node10743 node11127 +def node11129 : Tree Nat := .node node11124 node11128 +def node11130 : Tree Nat := .node node11129 node10750 +def node11131 : Tree Nat := .leaf 4030813413047173554768361068967408738611106825644141611024171706943156614093664811971195408108485210540454307098209726277602981287511682813479305691439277706115473717553149066777298247703992176505290231379250780857696569336263241611700499356692651978222466199715840 +def node11132 : Tree Nat := .node node11131 node8895 +def node11133 : Tree Nat := .node node8464 node11132 +def node11134 : Tree Nat := .node node10407 node11133 +def node11135 : Tree Nat := .leaf 27228092806600031667452679728786050995907686540786496505682075071692579857975324809083876156652767744185006339671730408604753404919962643770136872900953851700655307648265358454446669196601351555191875788079630344722571427167698132137118705703698892078233778858304275437056438566912 +def node11136 : Tree Nat := .node node5664 node11135 +def node11137 : Tree Nat := .node node10753 node11136 +def node11138 : Tree Nat := .node node11137 node10411 +def node11139 : Tree Nat := .node node11134 node11138 +def node11140 : Tree Nat := .node node11139 node10768 +def node11141 : Tree Nat := .node node11130 node11140 +def node11142 : Tree Nat := .node node11120 node11141 +def node11143 : Tree Nat := .node node11105 node11142 +def node11144 : Tree Nat := .leaf 4431655730257012840500151247598389094333148860437198937109582690332183652581827992519049338071454211077202234349894116206471430470329748877857025382871555402331683226509533197448577248947090808042162398276115079488818823542692339664926870216220401949225151568691819753244721152 +def node11145 : Tree Nat := .node node3365 node11144 +def node11146 : Tree Nat := .node node11145 node9798 +def node11147 : Tree Nat := .node node10112 node11146 +def node11148 : Tree Nat := .node node10431 node11147 +def node11149 : Tree Nat := .node node10777 node11148 +def node11150 : Tree Nat := .leaf 2554675596204441358920157155234181557867294149299169136804610260329945488780656810431192698101188848322993184617960894559274858525751158067667913842687243683593514224337475268489993252248767378859729084850216486777313294286034088060002266965308631034070310433604187464404727958149764053809954816 +def node11151 : Tree Nat := .node node10441 node11150 +def node11152 : Tree Nat := .node node7236 node11151 +def node11153 : Tree Nat := .node node8489 node11152 +def node11154 : Tree Nat := .node node10440 node11153 +def node11155 : Tree Nat := .node node11154 node10786 +def node11156 : Tree Nat := .node node11149 node11155 +def node11157 : Tree Nat := .leaf 9979201547673599058281863581306462517340300062019790210017489918558921907093582200854775305538287161721252878314991185198838233378149135735961349323188131882388122931163339997791434232063474487545613283702412034079201443921913713766978228210993571247065555093910777999872818611904917878603776 +def node11158 : Tree Nat := .node node8930 node11157 +def node11159 : Tree Nat := .node node7243 node11158 +def node11160 : Tree Nat := .node node10791 node11159 +def node11161 : Tree Nat := .node node10451 node11160 +def node11162 : Tree Nat := .leaf 1661870898840459919308913618403437427377748182269318192994588361153920670553879649805404052943534031327036572517990415093534390211475686610583299240636535560682804685188521026991836222792814199595395358025777464659226103983271655819923655389864960427273038929145349591093215232 +def node11163 : Tree Nat := .node node4712 node11162 +def node11164 : Tree Nat := .node node10127 node11163 +def node11165 : Tree Nat := .node node11164 node9820 +def node11166 : Tree Nat := .node node10797 node11165 +def node11167 : Tree Nat := .node node11161 node11166 +def node11168 : Tree Nat := .leaf 82550051303360741916107859754326784219622491917202995329887288771575546074290011407674718492856896677897222798209608533306636892746287980925430569795279255834022343002859263911076269844696080063543704484216278781013788423784644324876651172445034780556095974095692169216 +def node11169 : Tree Nat := .node node11168 node8936 +def node11170 : Tree Nat := .node node9825 node11169 +def node11171 : Tree Nat := .node node10464 node11170 +def node11172 : Tree Nat := .leaf 6339921308104795358971705146390722779147734193084319809346339342008687103430966962297436562882450652920259445476286005460316635585716342979471644309373145610385572117758806882275220624470259697617849614735470907127685820360827032352234698042364672171187711352025749913600 +def node11173 : Tree Nat := .node node9828 node11172 +def node11174 : Tree Nat := .node node10133 node11173 +def node11175 : Tree Nat := .leaf 653996952628336987883560278233738547718631346856110851083340600802711820085834176847013762973728793009003169160170245119347862546085735366977009543661942653636780598059209912381160006629227494600074732134483096401768604305914313498453636105307270443881771782632860129228971580996626011385489260544 +def node11176 : Tree Nat := .node node8940 node11175 +def node11177 : Tree Nat := .node node10801 node11176 +def node11178 : Tree Nat := .node node11174 node11177 +def node11179 : Tree Nat := .node node11171 node11178 +def node11180 : Tree Nat := .node node11179 node10809 +def node11181 : Tree Nat := .node node11167 node11180 +def node11182 : Tree Nat := .node node11156 node11181 +def node11183 : Tree Nat := .leaf 425438950103125502677471410004869022393769177680513159715711155240701300742949214059206452061359704185402242629203170094609479207884754328780355880896656422016585317570287048993642431933697586204734562318842017020772956923351382804399289985758881604670442564317038641181192355840 +def node11184 : Tree Nat := .node node6110 node11183 +def node11185 : Tree Nat := .node node9847 node11184 +def node11186 : Tree Nat := .node node11185 node9590 +def node11187 : Tree Nat := .node node10486 node11186 +def node11188 : Tree Nat := .node node10820 node11187 +def node11189 : Tree Nat := .leaf 106366229208979974660016013192852983925621829116704974151393832744809222828136816467577083601354980527885565857904728013179684259130359286323761338955568706889324107637688755122477255254106243314573834328930507272070171833046001294700052873221901535645253075687992041578162028544 +def node11190 : Tree Nat := .node node4754 node11189 +def node11191 : Tree Nat := .node node9853 node11190 +def node11192 : Tree Nat := .leaf 40874809539271061743830427095554928386242624881290560035939236474670127286718166675870366018207657152927555223217506271435244281420483280512656072953612368692107728795735138202357488057851619903291315035427430355266558632123791718465654685552266746349075643893406252216870568837468890993686216704 +def node11193 : Tree Nat := .node node5269 node11192 +def node11194 : Tree Nat := .node node10166 node11193 +def node11195 : Tree Nat := .node node11191 node11194 +def node11196 : Tree Nat := .node node10825 node11195 +def node11197 : Tree Nat := .leaf 138489242085940458401960852718112150506812461989974882128862163787758322213663293388679336265928732963605684126932730149746215261227922197750688466244620611372119009670748962269587526448071958262123026449657995563987893186928786497331827802979042644795009314911540463154495488 +def node11198 : Tree Nat := .node node10174 node11197 +def node11199 : Tree Nat := .node node9604 node11198 +def node11200 : Tree Nat := .node node11199 node9863 +def node11201 : Tree Nat := .node node10830 node11200 +def node11202 : Tree Nat := .node node11196 node11201 +def node11203 : Tree Nat := .node node11188 node11202 +def node11204 : Tree Nat := .leaf 6807023201651555654745435934824167017062964745664302350175152663054392259835111879743486014492295932829608623132475913159209386885929240942473675750878781304989279608151511053865022721897590535552859255163715970650277448116350383192042825783710602113974642958195577834307307215104 +def node11205 : Tree Nat := .node node10183 node11204 +def node11206 : Tree Nat := .node node10182 node11205 +def node11207 : Tree Nat := .leaf 159667224762777584949820972239200565038831724993982648918921553599713459634511369750519140373160749979869921516543568691118301625238745560688643520648292026242260514031153319591213631363809757087162139563076892298734818335502137704378323133245352144416437195978248420795353320095876199227588608 +def node11208 : Tree Nat := .node node5285 node11207 +def node11209 : Tree Nat := .node node10501 node11208 +def node11210 : Tree Nat := .node node11206 node11209 +def node11211 : Tree Nat := .node node10837 node11210 +def node11212 : Tree Nat := .node node11211 node10846 +def node11213 : Tree Nat := .leaf 3832013394306662038380235609031737750202768213424770570108423684605880289199288185993934337564133537943793606752632195885238204148580290598299373660791471920714069307820811795528718155916841318274802605260080922074197171005804881985850017003585680794207785153038579316361378835290376868274896896 +def node11214 : Tree Nat := .node node11213 node9327 +def node11215 : Tree Nat := .node node10199 node11214 +def node11216 : Tree Nat := .node node10515 node11215 +def node11217 : Tree Nat := .node node11216 node10851 +def node11218 : Tree Nat := .leaf 4431655862314523354789519926553916766706006459677048798525196337678387173839727929685389765372617076712648068138309535301922762708239853873027688864817409859873999132568695940086774883680823491973297639723487716519213647875144865478402377490748025414169492468420945498714669056 +def node11219 : Tree Nat := .node node8555 node11218 +def node11220 : Tree Nat := .node node10212 node11219 +def node11221 : Tree Nat := .node node11220 node8128 +def node11222 : Tree Nat := .node node10859 node11221 +def node11223 : Tree Nat := .node node11217 node11222 +def node11224 : Tree Nat := .node node11212 node11223 +def node11225 : Tree Nat := .node node11203 node11224 +def node11226 : Tree Nat := .node node11182 node11225 +def node11227 : Tree Nat := .node node11143 node11226 +def node11228 : Tree Nat := .leaf 4030813413047173554768361068967408738611106825644141611024171706943156614093664811971195408108485210540454307098209726277602981287511682813468728795938633728532243072624624730140043772776563676996735850654860288197915587803060214244665054799130011994201375055544320 +def node11229 : Tree Nat := .node node4809 node11228 +def node11230 : Tree Nat := .node node10877 node11229 +def node11231 : Tree Nat := .node node11230 node9620 +def node11232 : Tree Nat := .node node10531 node11231 +def node11233 : Tree Nat := .node node10875 node11232 +def node11234 : Tree Nat := .leaf 82546020489966464680251183349328047143419795363974241586668681842931793211176474663509693808981297054193577257227116044943395939965977926410631676009464925660782129250707718536868931306854130319053920728228618424751815720773433956647745414038818917528131839123246812928 +def node11235 : Tree Nat := .node node11234 node9004 +def node11236 : Tree Nat := .node node8580 node11235 +def node11237 : Tree Nat := .node node10536 node11236 +def node11238 : Tree Nat := .leaf 3832013394306662038380235609031737750202768213424770570108423684605880289199288185993934337564133537943793606752632195885238204148580290598299373660791471920714069307820769487946715580006508395695088507913531904174487457007770664462952455032946556868074973043570437538131130636537533938520817664 +def node11239 : Tree Nat := .node node9010 node11238 +def node11240 : Tree Nat := .node node9009 node11239 +def node11241 : Tree Nat := .node node10884 node11240 +def node11242 : Tree Nat := .node node11237 node11241 +def node11243 : Tree Nat := .leaf 776306425242526730420411038771304454586306072706819884445598377783441334845062553184132474087299170900821840135927576361068290363143901903086605984093762979791340047481665694066708217277919524728123363042387162503933688837304221696 +def node11244 : Tree Nat := .node node9343 node11243 +def node11245 : Tree Nat := .node node11244 node8163 +def node11246 : Tree Nat := .node node8596 node11245 +def node11247 : Tree Nat := .node node10893 node11246 +def node11248 : Tree Nat := .node node11242 node11247 +def node11249 : Tree Nat := .node node11233 node11248 +def node11250 : Tree Nat := .leaf 4989600773836821687419583011228355251654751505267483652018386927664715984742613358105906730234107040896054968538608791843049749466083152021272901375955531500216627448678700834498862264501581100228899240427254362138815730519759686408864465062395156671166246780938551565705396297058891037933568 +def node11251 : Tree Nat := .node node7339 node11250 +def node11252 : Tree Nat := .node node9027 node11251 +def node11253 : Tree Nat := .node node10899 node11252 +def node11254 : Tree Nat := .node node10242 node11253 +def node11255 : Tree Nat := .leaf 16905425059318903613520611904066424622413630614010605728620909054017112865305081783676461418458997791219176641139506688963142614265047080384577499314373748501037855035856871513191800841539603909384831974309725768910448504052505614840296893926463650110215230885213528653824 +def node11256 : Tree Nat := .node node6181 node11255 +def node11257 : Tree Nat := .node node10907 node11256 +def node11258 : Tree Nat := .node node11257 node9909 +def node11259 : Tree Nat := .node node10905 node11258 +def node11260 : Tree Nat := .node node11254 node11259 +def node11261 : Tree Nat := .leaf 17311155196253479753435624159146045598717774204736508284994244487722503133749893892722525769008169071600506586167258067829509776785505512616660060195066465469810613648260718112549871023513378379268353499092468073267214711769508611815867523428187937463964640477448678433357824 +def node11262 : Tree Nat := .node node4850 node11261 +def node11263 : Tree Nat := .node node10913 node11262 +def node11264 : Tree Nat := .leaf 326998476314168493941780206738569259224467206527547894855795934813813642666471920802477636901123923765283597305493876179793981791365426820400975668895112127993027117555948984819933562038665732738302503022429422771019598153366595154842760272426857739016964063217905057168319950114571049029903319040 +def node11265 : Tree Nat := .node node6960 node11264 +def node11266 : Tree Nat := .node node9351 node11265 +def node11267 : Tree Nat := .node node11263 node11266 +def node11268 : Tree Nat := .node node10253 node11267 +def node11269 : Tree Nat := .leaf 67625827286389648917836620123883785920400886227358212031770598736841101926476047436178265248277802974066048922596225997728799969093826321139146598157899893246066338630960062880196430943387633964335980306689422536010942215334349838403867812389503603549279546886212319969280 +def node11270 : Tree Nat := .node node4855 node11269 +def node11271 : Tree Nat := .node node8626 node11270 +def node11272 : Tree Nat := .node node11271 node10257 +def node11273 : Tree Nat := .node node10920 node11272 +def node11274 : Tree Nat := .node node11268 node11273 +def node11275 : Tree Nat := .node node11260 node11274 +def node11276 : Tree Nat := .node node11249 node11275 +def node11277 : Tree Nat := .leaf 15015950158473564897861899879873157572030740493935551471143572739460010293391106190713067903188740235525067304240556179154083136872463771910318541262865855963571827028819324664027207654701689671732134269070164495619066761720606805739732341480164667823288320 +def node11278 : Tree Nat := .node node10565 node11277 +def node11279 : Tree Nat := .node node6201 node11278 +def node11280 : Tree Nat := .node node11279 node10930 +def node11281 : Tree Nat := .node node10266 node11280 +def node11282 : Tree Nat := .node node11281 node10937 +def node11283 : Tree Nat := .leaf 2554685341518452758919237508620600246483668149253253350619883316801427893517855043286255311400007099752906683457708488855875737324295257694391482283545332979030952715177587666310545236417700208040485277882427195835991122767346484496598058628772806894018395716795762648632484469847862433904914432 +def node11284 : Tree Nat := .node node11283 node9060 +def node11285 : Tree Nat := .node node6982 node11284 +def node11286 : Tree Nat := .node node10581 node11285 +def node11287 : Tree Nat := .leaf 16122269687003043759842502502504753706372862447748761871929985478075108656274540644094028708978976043436181167432265490331763974780788094566407911615203745624841659551632346499979692414112547391646309361822533951868753350459529950559531997791661026135753197828964352 +def node11288 : Tree Nat := .node node10583 node11287 +def node11289 : Tree Nat := .node node6212 node11288 +def node11290 : Tree Nat := .leaf 20437404769635530873023127480337686835839614525262522652363831944826367965732780394791890237198469228960270708628065182625314337519140814179503509425912360354660157331655652888222390952778798015742206595856943981287102857086215177441447981932179627992796573476272702293690789920304072252754755584 +def node11291 : Tree Nat := .node node5397 node11290 +def node11292 : Tree Nat := .node node7370 node11291 +def node11293 : Tree Nat := .node node11289 node11292 +def node11294 : Tree Nat := .node node11286 node11293 +def node11295 : Tree Nat := .leaf 1134503866941925942457572421194126936030278604345372407031595981253038285975348693098599121725931981531306200448503008723535741725765732806403362544627553680564765087347021331389711999370876147052181373724356618883479164706454384723513503709167606591187743821637023630515027050496 +def node11296 : Tree Nat := .node node9915 node11295 +def node11297 : Tree Nat := .node node6599 node11296 +def node11298 : Tree Nat := .node node11297 node9922 +def node11299 : Tree Nat := .node node10942 node11298 +def node11300 : Tree Nat := .node node11294 node11299 +def node11301 : Tree Nat := .node node11282 node11300 +def node11302 : Tree Nat := .leaf 70910819472653312503669451783021564705270279676738364539427009103188365498729578238013279519531246709206096247748162413840584645123379000361125914899452361976905755298672619383677721809505026648661077208394303746837121028352157913099917381651126654058190941152038902146187395072 +def node11303 : Tree Nat := .node node9370 node11302 +def node11304 : Tree Nat := .node node8647 node11303 +def node11305 : Tree Nat := .node node10592 node11304 +def node11306 : Tree Nat := .leaf 79833612381388792474910486119600282519415862496991324459460776799856729817255684875259570186580374989934960758271784345559150812619372780344321760324146006583215931976592679304448311396605699423952989041616212256658176916455972134404040974159931717346128783401871192396339256538432450475327488 +def node11307 : Tree Nat := .node node5413 node11306 +def node11308 : Tree Nat := .node node9077 node11307 +def node11309 : Tree Nat := .node node10948 node11308 +def node11310 : Tree Nat := .node node11305 node11309 +def node11311 : Tree Nat := .node node11310 node10959 +def node11312 : Tree Nat := .leaf 18152061871066687778312036748834295347985778314497932975822844984304577265745464717163131879119715799211056173813234115810032021551353466146580748704788248174833217428661628316325646102828231657316045672979880279727924889043722945310338144881607339210754064267051906173728200851456 +def node11313 : Tree Nat := .node node4917 node11312 +def node11314 : Tree Nat := .node node10962 node11313 +def node11315 : Tree Nat := .node node11314 node9378 +def node11316 : Tree Nat := .node node10603 node11315 +def node11317 : Tree Nat := .leaf 1082013236582234382685385921982140574726414179637731392508336260251947497919198041341391512429602295390757683181995028918317634960525112968048425445338392970844709453392609306603986719221721925987072479829751606897028170984078799122171510536347350323072202096907292256501760 +def node11318 : Tree Nat := .node node8676 node11317 +def node11319 : Tree Nat := .node node8675 node11318 +def node11320 : Tree Nat := .node node11319 node7823 +def node11321 : Tree Nat := .node node10972 node11320 +def node11322 : Tree Nat := .node node11316 node11321 +def node11323 : Tree Nat := .node node11311 node11322 +def node11324 : Tree Nat := .node node11301 node11323 +def node11325 : Tree Nat := .node node11276 node11324 +def node11326 : Tree Nat := .leaf 82546020489966464680251183349328047143419795363974241586668681842931793211176474663509693808981297054193577257227116044943395939965977926410631676004300425904608312071395880192862907558194718733395473702567299711670520476739751567388454707478543254637878751104042274560 +def node11327 : Tree Nat := .node node10299 node11326 +def node11328 : Tree Nat := .node node10979 node11327 +def node11329 : Tree Nat := .node node11328 node10985 +def node11330 : Tree Nat := .node node10298 node11329 +def node11331 : Tree Nat := .node node11330 node10992 +def node11332 : Tree Nat := .leaf 2554680468861447058919697249383385818945571956098382164515285067704447724115199563524936214606744012653969970814314530022786525021031205372283837162195300712940578282028819566666421815552426163514984542868531895110890372004426509041789958331191966993393146359367963525310809890480482741783629568 +def node11333 : Tree Nat := .node node11332 node9120 +def node11334 : Tree Nat := .node node8697 node11333 +def node11335 : Tree Nat := .node node10622 node11334 +def node11336 : Tree Nat := .leaf 5109351192408882717840339505059633591674614784055497869506061806746153259142624288655259715269617169706172170324375841277053593230744285446199267871685371383553160140891998195316849294850373533851713416851022994960575475424842324166132108010788674556135097984963978275657507446748887628474482688 +def node11337 : Tree Nat := .node node5461 node11336 +def node11338 : Tree Nat := .node node9125 node11337 +def node11339 : Tree Nat := .node node10996 node11338 +def node11340 : Tree Nat := .node node11335 node11339 +def node11341 : Tree Nat := .node node11340 node11006 +def node11342 : Tree Nat := .node node11331 node11341 +def node11343 : Tree Nat := .leaf 19958403095347304482792936110343045676687705457338501036854589129346270312522385467072407791742824587977025823422452838005582284611949116291650848342134637964539012298217746089283014903198752349081787673688753813767637035058480774060721598685775141627944430970293205669499272944345018261307392 +def node11344 : Tree Nat := .node node5477 node11343 +def node11345 : Tree Nat := .node node9663 node11344 +def node11346 : Tree Nat := .node node11011 node11345 +def node11347 : Tree Nat := .node node10320 node11346 +def node11348 : Tree Nat := .leaf 1107913932560474553181223067572389585967068949556027741241782608594426884918477994617821911848443968838688751418182482340717834524739021203954012613696903547278315522671065925790574289299170791883143634002916292901210929654450802003329807720590768484035066855151445670363136000 +def node11349 : Tree Nat := .node node6288 node11348 +def node11350 : Tree Nat := .node node9975 node11349 +def node11351 : Tree Nat := .node node11350 node9979 +def node11352 : Tree Nat := .node node10635 node11351 +def node11353 : Tree Nat := .node node11347 node11352 +def node11354 : Tree Nat := .leaf 4226356249089165819435066285849878084890879347801963797935583018024170305128746910853204209891268966148552222280678128745782366094313386682570059818943998533818183017395785061581889096959573635782441160029414155788620213062343299653219100963681287278154096149380483514368 +def node11355 : Tree Nat := .node node4985 node11354 +def node11356 : Tree Nat := .node node9408 node11355 +def node11357 : Tree Nat := .leaf 970335652472282206014425373911873826643838038188458692328331923556755613148941055626646840777046284631252286366401277886644267491844561407225470902733661639857553169741034189407186678110666213527761289472104299050443359835800993792 +def node11358 : Tree Nat := .node node3276 node11357 +def node11359 : Tree Nat := .node node11358 node5493 +def node11360 : Tree Nat := .node node11356 node11359 +def node11361 : Tree Nat := .node node9986 node11360 +def node11362 : Tree Nat := .leaf 270503309145558595671346480495535143681603544909432848127082802611107309871323396860907127442145370578818604307418081184039084952902776650999512867570726083356948617805562260665202277384050914983265515681571357977985325770334636017577917842575566254581413169681926948126720 +def node11363 : Tree Nat := .node node6676 node11362 +def node11364 : Tree Nat := .node node9417 node11363 +def node11365 : Tree Nat := .node node11364 node10325 +def node11366 : Tree Nat := .node node11018 node11365 +def node11367 : Tree Nat := .node node11361 node11366 +def node11368 : Tree Nat := .node node11353 node11367 +def node11369 : Tree Nat := .node node11342 node11368 +def node11370 : Tree Nat := .leaf 984025249451093111545271203069913162369976096407652062409214830727720955917292968523267006162989669818401042598134648880504420669646742254202115807688306416449625701531427485939552433329226399069832951604910667578615044938478206261584266494400469837661184510976 +def node11371 : Tree Nat := .node node5002 node11370 +def node11372 : Tree Nat := .node node9432 node11371 +def node11373 : Tree Nat := .node node11372 node11028 +def node11374 : Tree Nat := .node node10334 node11373 +def node11375 : Tree Nat := .leaf 283625966735417012280289266223448811089392012570402951741345701686845491343358131172574636210580811962732154795772927246974863528705827922921138951643089860073846286522698432341960906200792302752496429657823936820685753004716053084848562223743629714132834656034920682326411182080 +def node11376 : Tree Nat := .node node5007 node11375 +def node11377 : Tree Nat := .node node9441 node11376 +def node11378 : Tree Nat := .node node11377 node9701 +def node11379 : Tree Nat := .node node11034 node11378 +def node11380 : Tree Nat := .node node11374 node11379 +def node11381 : Tree Nat := .leaf 15015950158473564897861899879873157572030740493935551471143572739460010293391106190713067903188740235525067304240556179154083136872464102438302936387165331921225843414339238866368689795311331996129771471965782651291979356325826663382156284660129769178853376 +def node11382 : Tree Nat := .node node11381 node9165 +def node11383 : Tree Nat := .node node9706 node11382 +def node11384 : Tree Nat := .node node10648 node11383 +def node11385 : Tree Nat := .leaf 3936341223678880424578477402909413557522981790089875694350956208564662980912515569110986115319639349606513843338924768160489868757796996782649653091522447980584696889279696883150417109742009180214148200569697724388385332501738517969504542198032959794482012749824 +def node11386 : Tree Nat := .node node5932 node11385 +def node11387 : Tree Nat := .node node9447 node11386 +def node11388 : Tree Nat := .leaf 81749619078542123485583515568074848124524764480154453050451147512218173973081630298339636588792021610008145959004053338156716744131534326493622692118974617174058120830321089921530464080031856917271069018704591085028953022691408846692875404982560675188823500148610010110466013279546431109800656896 +def node11389 : Tree Nat := .node node7064 node11388 +def node11390 : Tree Nat := .node node9710 node11389 +def node11391 : Tree Nat := .node node11387 node11390 +def node11392 : Tree Nat := .node node11384 node11391 +def node11393 : Tree Nat := .leaf 276978484171880916803921705436224301013624923979949764257724327575516644427326586777358672531857465927211368253865460299492430427461035987268030951231919840722263861379678462862796326536909060758437279546994633576362263335803217381304841567546150249847045433598067662898855936 +def node11394 : Tree Nat := .node node5022 node11393 +def node11395 : Tree Nat := .node node9456 node11394 +def node11396 : Tree Nat := .node node11395 node10002 +def node11397 : Tree Nat := .node node11040 node11396 +def node11398 : Tree Nat := .node node11392 node11397 +def node11399 : Tree Nat := .node node11380 node11398 +def node11400 : Tree Nat := .leaf 4538015467766671944574166277031829431066228092279094443099770808855021999963590197363059584921980546411647352081633742416763599223054836751885097209478065718945241299549949078641960379683958455700446740543514833584731870011428759160116197221531049170739035172817170008953120122368 +def node11401 : Tree Nat := .node node5033 node11400 +def node11402 : Tree Nat := .node node10008 node11401 +def node11403 : Tree Nat := .leaf 319334449525555169865025974007202275366151173374819597363186706524146987018843596864935283165925143141257088931633681689688510337588451271723727804361158743594180379316483081388416421003215836756106812299751498098630547522434074733129344528772047892233491579798163331334948546948207067338375168 +def node11404 : Tree Nat := .node node9181 node11403 +def node11405 : Tree Nat := .node node9726 node11404 +def node11406 : Tree Nat := .node node11402 node11405 +def node11407 : Tree Nat := .node node10656 node11406 +def node11408 : Tree Nat := .leaf 970335652460986150179592503924077391275019526735053276680925613458022005425490280305202046777422788947271366378517686424651131505532068219761957338943155427503605385315311005041255813628375685237790475361209269667868253935466708992 +def node11409 : Tree Nat := .node node3715 node11408 +def node11410 : Tree Nat := .node node11409 node9187 +def node11411 : Tree Nat := .node node10018 node11410 +def node11412 : Tree Nat := .node node11050 node11411 +def node11413 : Tree Nat := .node node11407 node11412 +def node11414 : Tree Nat := .leaf 82550051303360741916107859754326784219622491917202995329887288771575546074290011407674718492856896677897222798209608533306636892746287980925430567151055380673027947195198031779992110531077348206418827345621097683390623478539261024119809413583895389600952063643553300480 +def node11415 : Tree Nat := .node node5048 node11414 +def node11416 : Tree Nat := .node node10026 node11415 +def node11417 : Tree Nat := .leaf 776306425423263623777736958576047420487402255961306534804099339363179058420274958327249178081275101844516559942065039752958466144143792902502823004741862377454504598293236643921602048994567977367656388816707634396022814318769733632 +def node11418 : Tree Nat := .node node3345 node11417 +def node11419 : Tree Nat := .node node11418 node9193 +def node11420 : Tree Nat := .node node11416 node11419 +def node11421 : Tree Nat := .node node10664 node11420 +def node11422 : Tree Nat := .leaf 2554680468861447058919697249383385818945571956098382164515285067704447724115199563524936214606744012653969970814314530022786525021031205372283837162195300712940578282028819546008422790857157446267631166844436900473244029370638406396515106006010990858663589322205137284208158366361618812384579328 +def node11423 : Tree Nat := .node node8771 node11422 +def node11424 : Tree Nat := .node node9744 node11423 +def node11425 : Tree Nat := .node node11055 node11424 +def node11426 : Tree Nat := .leaf 17726623185110827851325456530045774608565722579284532176040355225868980301259884164071575179109576849808543431957214480742899683325031088689975706434116778723296235169694521916693556274209005253619145019071891475968107748343535946333208245864788850561451977182636611686929268736 +def node11427 : Tree Nat := .node node5053 node11426 +def node11428 : Tree Nat := .node node9748 node11427 +def node11429 : Tree Nat := .node node11428 node7914 +def node11430 : Tree Nat := .node node11425 node11429 +def node11431 : Tree Nat := .node node11421 node11430 +def node11432 : Tree Nat := .node node11413 node11431 +def node11433 : Tree Nat := .node node11399 node11432 +def node11434 : Tree Nat := .node node11369 node11433 +def node11435 : Tree Nat := .node node11325 node11434 +def node11436 : Tree Nat := .node node11227 node11435 +def node11437 : Tree Nat := .leaf 17726622920979684553209871963620509457015918490794380011553769567683403674445702970615987163078511268350905778759499154461369926503795990817760032604495218008104128809598815613755447902300755054929890336609295949003004480901975503813713218106963137104663179504675968995790159872 +def node11438 : Tree Nat := .node node3317 node11437 +def node11439 : Tree Nat := .node node11438 node5074 +def node11440 : Tree Nat := .node node9229 node11439 +def node11441 : Tree Nat := .node node10352 node11440 +def node11442 : Tree Nat := .node node11071 node11441 +def node11443 : Tree Nat := .leaf 283625967792006058808176788520780685867414277271872180408915520460270309811540679986766115142045205324379286600312851575545476454331271213951923519474073034032337482053628370092032869880943113015649049034161208400234461002104176202151920099471941479987157801342862583720489582592 +def node11444 : Tree Nat := .node node11443 node8793 +def node11445 : Tree Nat := .node node9499 node11444 +def node11446 : Tree Nat := .node node10357 node11445 +def node11447 : Tree Nat := .leaf 396245081756219384693933737670634408122819097769191542418947721514317564179091680265178246578708546329999037058612292570338875071443958542840208923128486826541561350715250105215153578879300314862394334803113974359494039692763310278617226982199648677917810460360059322368 +def node11448 : Tree Nat := .node node11447 node8366 +def node11449 : Tree Nat := .node node9238 node11448 +def node11450 : Tree Nat := .node node11449 node11075 +def node11451 : Tree Nat := .node node11446 node11450 +def node11452 : Tree Nat := .node node11451 node10688 +def node11453 : Tree Nat := .node node11442 node11452 +def node11454 : Tree Nat := .leaf 96733617761664787678281154745096836345307382253963713278769221057919670791750435116165154781144416866078686184880932805435977823270972911220355933147183706431181003651250927792556117436642846466502145654626250190331438791078458864648463612161061672293967885199824128 +def node11455 : Tree Nat := .node node5605 node11454 +def node11456 : Tree Nat := .node node10363 node11455 +def node11457 : Tree Nat := .node node11456 node10696 +def node11458 : Tree Nat := .node node10058 node11457 +def node11459 : Tree Nat := .node node11458 node11084 +def node11460 : Tree Nat := .leaf 8655577598126739876717812079573022799358887102368254142497122243861251566874946946361262884504084535800253293083629033914754888392752749770415705276010223736986981650053419546606822188687120199438052547310291656971012506309761929074757767910235210870416766895207584741982208 +def node11461 : Tree Nat := .node node5620 node11460 +def node11462 : Tree Nat := .node node10706 node11461 +def node11463 : Tree Nat := .node node11462 node11095 +def node11464 : Tree Nat := .node node11089 node11463 +def node11465 : Tree Nat := .node node11464 node11102 +def node11466 : Tree Nat := .node node11459 node11465 +def node11467 : Tree Nat := .node node11453 node11466 +def node11468 : Tree Nat := .leaf 77962512091199992642827155836619268151797045659041079242256603618606140594416791194326173724959762167573606902273555401835320172923085291996257089638865709198522998598561147293456460418909481967582086781278963615122775179259387767194725796955131961395957468969612666208381673954204747191552 +def node11469 : Tree Nat := .node node11468 node7988 +def node11470 : Tree Nat := .node node7569 node11469 +def node11471 : Tree Nat := .leaf 155925024182399985285654182695081520760320608596003130124069772712195077160230614573969068183848740178020370112377698150707199695214803684287795703096585539341860888858313377790466052267648016918193178228920165691985456260566759467647632696914561217489953369948741443435729564675907096259072 +def node11472 : Tree Nat := .node node8852 node11471 +def node11473 : Tree Nat := .node node8851 node11472 +def node11474 : Tree Nat := .node node11470 node11473 +def node11475 : Tree Nat := .node node10082 node11474 +def node11476 : Tree Nat := .leaf 1589778526533276691354858284486857941309556515119928048240805379269200809138178029257766467128897027246478735440651808683963863879085536420767521522568692598394871744018000262778092879122048917203182723776484713870792074693757016932352 +def node11477 : Tree Nat := .node node3395 node11476 +def node11478 : Tree Nat := .node node11477 node8427 +def node11479 : Tree Nat := .node node8425 node11478 +def node11480 : Tree Nat := .node node10726 node11479 +def node11481 : Tree Nat := .node node11475 node11480 +def node11482 : Tree Nat := .leaf 283625967792006058808176788520780685867492418066007491201189893723442824551350970123355754690799848970629446191804009791438155927011708280049202080546430767585233870780142938902400308355508972714924111819549173426251757972201472024941245485416534337393473657246164134288016015360 +def node11483 : Tree Nat := .node node11482 node8858 +def node11484 : Tree Nat := .node node8433 node11483 +def node11485 : Tree Nat := .node node10731 node11484 +def node11486 : Tree Nat := .leaf 4989600773836821687419583011228355251654751505281139745627797782066541151598437685733482643480996943670877759896098997554486011218051588053295792492224107830008960712410111574300999178395239195210770327403639954143401194666981359871333254752713619384839077080708227297692123432454253915668480 +def node11487 : Tree Nat := .leaf 396245081756219384693933737670634408122819097769191542418947721514317564179091680265178246578708546329999037058612292570338875071443958542840208923128486826541561350715110121168767466116140474719858807035731371515916874096832060959806989990250888618831505617026288910336 +def node11488 : Tree Nat := .node node11486 node11487 +def node11489 : Tree Nat := .node node8006 node11488 +def node11490 : Tree Nat := .node node11489 node11111 +def node11491 : Tree Nat := .node node11485 node11490 +def node11492 : Tree Nat := .leaf 79833612381388792474910486119600282519415862496991324459460776799856729817255684875259591192992011088619330390654305555789775003949256662905563582104934485919119069353204879409537234267323586429688389721669441331706558329929025758821142516777476239864810529742188370912291269235382835833208832 +def node11493 : Tree Nat := .node node11492 node8010 +def node11494 : Tree Nat := .node node7587 node11493 +def node11495 : Tree Nat := .node node11494 node10736 +def node11496 : Tree Nat := .node node11495 node11117 +def node11497 : Tree Nat := .node node11491 node11496 +def node11498 : Tree Nat := .node node11481 node11497 +def node11499 : Tree Nat := .leaf 64489078507786300531391609283624660276050308195212539899158086377958250252022358692767408864534768134728864790575501380616377911990055123619253834227860747978190465669619558583030728314632089157401002991982904942154953549104755285344381032012918333506152074951961088 +def node11500 : Tree Nat := .leaf 103866931564455343801822554389934333203389244509458158012020530776078908043800262429741051803735415473862930601861307299166558866196664071989836225888806339642558293173523703061869948845920840000679924407742597893889848742156457094958074391564466633891164314088012253166085376 +def node11501 : Tree Nat := .node node11499 node11500 +def node11502 : Tree Nat := .node node10395 node11501 +def node11503 : Tree Nat := .leaf 39916806190694502599356663240709463166772373299772117545440415305120231012649310801353388651413043935609263867990438192946758383121104936041707204185123101386513126139387421382393728552470140511179643641207751352969396819299855275494164094017043839542711079909779881722574979111768382630789120 +def node11504 : Tree Nat := .node node7198 node11503 +def node11505 : Tree Nat := .node node8885 node11504 +def node11506 : Tree Nat := .node node11502 node11505 +def node11507 : Tree Nat := .node node11124 node11506 +def node11508 : Tree Nat := .leaf 69244620785013915170128490189477811531824955396191184425272058540842623741436225137170371136664720923332289635109501355732832417914201484441035852139332300936119183877118707650229526467940943278210293154845537470875995854379866433900733061479839844801215516331642734145198592 +def node11509 : Tree Nat := .node node11508 node8457 +def node11510 : Tree Nat := .node node10747 node11509 +def node11511 : Tree Nat := .node node11510 node10092 +def node11512 : Tree Nat := .node node10402 node11511 +def node11513 : Tree Nat := .node node11507 node11512 +def node11514 : Tree Nat := .leaf 17311155196253479753435624159146045598717774204736508284994244487722503133749893892722525769008169071600506586167258067829509776785505512616660063674442009361653479427816551871909483192345761876358231972895573080234789267006187551076610346062984988430285444880128576797540352 +def node11515 : Tree Nat := .node node11514 node10757 +def node11516 : Tree Nat := .node node10415 node11515 +def node11517 : Tree Nat := .node node11516 node10762 +def node11518 : Tree Nat := .node node11517 node10767 +def node11519 : Tree Nat := .node node11139 node11518 +def node11520 : Tree Nat := .node node11513 node11519 +def node11521 : Tree Nat := .node node11498 node11520 +def node11522 : Tree Nat := .node node11467 node11521 +def node11523 : Tree Nat := .leaf 155925024182399985285654182695081520760320608596003130124069772712195077160230614573969068183848740178020370112377698150707199695214803684287795703096585539341860888858313377790466052267648016926737126372603806021565543085244967926058450786341172297278119801237620346558291764767755477559808 +def node11524 : Tree Nat := .node node11523 node8054 +def node11525 : Tree Nat := .node node6063 node11524 +def node11526 : Tree Nat := .leaf 4431655730257012840500151247598389094333148860437198937109582690668832350280923896982472690575782445672423981730577243214361408266728606753454576332479881664099000446578398849864310836572938192520243965657529212453711128294084259391013231211339949825259812532616407779899342848 +def node11527 : Tree Nat := .leaf 38981256045599996321809750450836617517922312907734296713042280348598068650264610437653269029443997437566070676605669648807542084053986150610314202055809205510553451706467971519081820589561996907617990442489741400198267902554380068997180763383885062772538935638266516791391204351955720784896 +def node11528 : Tree Nat := .node node11526 node11527 +def node11529 : Tree Nat := .node node7223 node11528 +def node11530 : Tree Nat := .node node11525 node11529 +def node11531 : Tree Nat := .node node10426 node11530 +def node11532 : Tree Nat := .node node11531 node11148 +def node11533 : Tree Nat := .leaf 9979201547673621216560911006657668632322255331283996814711893568257899791448162445072884949928444522411171137582190167128219956965103621692074115458965831379023378407405252209349048774014578767165721268395403113207841702325512845021810605854697720256374525218584220664046598584177554468569088 +def node11534 : Tree Nat := .node node11533 node8487 +def node11535 : Tree Nat := .node node6076 node11534 +def node11536 : Tree Nat := .node node11535 node11152 +def node11537 : Tree Nat := .node node10440 node11536 +def node11538 : Tree Nat := .leaf 159667224762777584949820972239200565038831724993982648918921553599713459634511369750519140451542882950387400507709175113544535297594454082638498902892826670557444129344222393668748461239020258339800348003044793497099105976466568038110700099159065102564141811659586977559769382789515615846662144 +def node11539 : Tree Nat := .node node11538 node10779 +def node11540 : Tree Nat := .node node5688 node11539 +def node11541 : Tree Nat := .node node11540 node10784 +def node11542 : Tree Nat := .node node11541 node9810 +def node11543 : Tree Nat := .node node11537 node11542 +def node11544 : Tree Nat := .node node11532 node11543 +def node11545 : Tree Nat := .leaf 96733617761664787678281154745096836345307382253963713278769221057919670791750435116165154781144416866078686184880932805435977823270972911220355933147183706431181003653438178517339129361015348693619767019979419621224651227504229471058416611360437595517481062759748864 +def node11546 : Tree Nat := .leaf 1584883593408437211614387469712064555158914503508771038724904544061812054501246924612497208568277150977848478150352795769583604541055259689693406819867577708238382808341478666344044230831052120990806971882097208726972571540457388575412705948866219790173728445602642051840 +def node11547 : Tree Nat := .node node11545 node11546 +def node11548 : Tree Nat := .node node10122 node11547 +def node11549 : Tree Nat := .leaf 9979201547673621216560911006657668632322255331283996814711893568257899791448162445072884949928444522411171137582190167128219956965103621692074115458965831379023378407405252209349048774014578207229535723944350473847271560214443314610436297192313995259099284270616425623810253364804227976855552 +def node11550 : Tree Nat := .node node8930 node11549 +def node11551 : Tree Nat := .node node7243 node11550 +def node11552 : Tree Nat := .node node11548 node11551 +def node11553 : Tree Nat := .node node10451 node11552 +def node11554 : Tree Nat := .node node11553 node11166 +def node11555 : Tree Nat := .leaf 6339921308104795358971705146390722779147734193084319809346339342008687103430966962297436562882450652920259445476286005460316635585716342979473123043979299643603528427764992676986521775013213588976810095142163891557580832258924878451934340031032096324447674489507493707776 +def node11556 : Tree Nat := .node node9828 node11555 +def node11557 : Tree Nat := .node node10133 node11556 +def node11558 : Tree Nat := .node node11557 node11177 +def node11559 : Tree Nat := .node node11171 node11558 +def node11560 : Tree Nat := .leaf 8655577598126739876717812079573022799358887102368254142497122243861251566874946946361262884504084535800253293083629033914754888392752749770415705276010223736986981650053419546606855563484556463658089969524450556222803173567923751774288190435357433053632089403801693526687744 +def node11561 : Tree Nat := .node node11560 node8078 +def node11562 : Tree Nat := .node node10138 node11561 +def node11563 : Tree Nat := .node node11562 node10807 +def node11564 : Tree Nat := .node node11563 node10144 +def node11565 : Tree Nat := .node node11559 node11564 +def node11566 : Tree Nat := .node node11554 node11565 +def node11567 : Tree Nat := .node node11544 node11566 +def node11568 : Tree Nat := .leaf 396220899827876895477060460843258879220747005654011700510188605388424284033308668164687632795967036691676878923562154953069719752748550337399360717470585629548790571239868060544130660935560104357430640625178244586803046691936434856044484785558312282351676731136535442176 +def node11569 : Tree Nat := .node node5721 node11568 +def node11570 : Tree Nat := .node node9842 node11569 +def node11571 : Tree Nat := .leaf 623700096729599941143673061886283382447435673680950235479233377409867028482305313800780280586234054472401493724209977902761841006767121205029015322651536752601991969740021492351641955286332702881716691101625544184613721147153340427539691953841497935716065765027105929770709815783007985875968 +def node11572 : Tree Nat := .node node5254 node11571 +def node11573 : Tree Nat := .node node10476 node11572 +def node11574 : Tree Nat := .node node11570 node11573 +def node11575 : Tree Nat := .node node10154 node11574 +def node11576 : Tree Nat := .leaf 283625967792006058808176788520780685867492418066007491201189893723442824551978027187119894522729173822008856061182855459613754770049585470528091087434949199023878582307679861741920639840324834621097273356026238973137226308622947536725229630477126583233506205898374693807702671360 +def node11577 : Tree Nat := .node node2598 node11576 +def node11578 : Tree Nat := .node node11577 node10484 +def node11579 : Tree Nat := .node node10482 node11578 +def node11580 : Tree Nat := .node node11579 node11186 +def node11581 : Tree Nat := .node node11575 node11580 +def node11582 : Tree Nat := .leaf 16122269687003043759856158596114164560774687614603120767776477226849869277195912094646325914424064191536284258390940657219702583027165031281700226779654078198964762589151785451146334069596103149836147686975466231063579597465906244187516195026467792276471129148489728 +def node11583 : Tree Nat := .leaf 5904511857512998928198048976647532699003309661005525248051846672763490302092671016919565265813889165235272183539790248670633263363826497656421434336293579253968221172534864633793061036658128590324136002376985948117308970220515354456741563412829831969241718325248 +def node11584 : Tree Nat := .node node11582 node11583 +def node11585 : Tree Nat := .node node9853 node11584 +def node11586 : Tree Nat := .node node11585 node11194 +def node11587 : Tree Nat := .node node10825 node11586 +def node11588 : Tree Nat := .leaf 23692437876425140216458957644889564495784379482196179251176688417653786143395573887275969421097590675722496831607492232774187679227340842624796772152923037187790413565537871183544616195486276163504218400161185710314982022840320 +def node11589 : Tree Nat := .node node2792 node11588 +def node11590 : Tree Nat := .node node11589 node10828 +def node11591 : Tree Nat := .node node10172 node11590 +def node11592 : Tree Nat := .node node11591 node11200 +def node11593 : Tree Nat := .node node11587 node11592 +def node11594 : Tree Nat := .node node11581 node11593 +def node11595 : Tree Nat := .leaf 159667224762777584949820972239200565038831724993982648918921553599713459634511369750519140451542882950387400507709175113544535297594454082638498902892826670557444129344222393668748461239020258339800347872674491011691996455286043979910497791865087907944221770946598218879366197935966420109099008 +def node11596 : Tree Nat := .node node5285 node11595 +def node11597 : Tree Nat := .node node10501 node11596 +def node11598 : Tree Nat := .node node11206 node11597 +def node11599 : Tree Nat := .node node10837 node11598 +def node11600 : Tree Nat := .node node11599 node10846 +def node11601 : Tree Nat := .node node11600 node11223 +def node11602 : Tree Nat := .node node11594 node11601 +def node11603 : Tree Nat := .node node11567 node11602 +def node11604 : Tree Nat := .node node11522 node11603 +def node11605 : Tree Nat := .leaf 5904511857512998928198048976647532699003309661005525248051846672763490302092671016919565265813889165235272183539790248670633263363826497656421434336293579253968221176806838705634881201448172002663240231582394992830614510114598570101181014974110932015165908975616 +def node11606 : Tree Nat := .node node11605 node10868 +def node11607 : Tree Nat := .node node10867 node11606 +def node11608 : Tree Nat := .leaf 580865979874134008906969201210315654396307779749920966216938596455013640222452974299397860847118273290532849095283182172014738024312923289594492390929742194259910377677130657235787981455990766289093562242522013100317058980834239210321466986266930529322844140457585902049289337582336 +def node11609 : Tree Nat := .node node8993 node11608 +def node11610 : Tree Nat := .node node8992 node11609 +def node11611 : Tree Nat := .node node11607 node11610 +def node11612 : Tree Nat := .node node10224 node11611 +def node11613 : Tree Nat := .leaf 6339921308104795358971705146390722779147734193084319809346339342008687103430966962297436562882450652920259445476286005460316635585716342979473123043979299643603528446112981604907093867899780751393505621514683804903829822159635593547317348738910560884596099371612497772544 +def node11614 : Tree Nat := .node node11613 node11228 +def node11615 : Tree Nat := .node node10877 node11614 +def node11616 : Tree Nat := .leaf 106366229208979968755504199669210556446675929746210728544744454015716584733946038785236571687661310716404351711447404795421755873117666509250702519302488460868630046532084816629347552449279191460795773096451153178711674878930269877890096687309583622662593343821807458363711160320 +def node11617 : Tree Nat := .node node3375 node11616 +def node11618 : Tree Nat := .node node11617 node8574 +def node11619 : Tree Nat := .node node11615 node11618 +def node11620 : Tree Nat := .node node10531 node11619 +def node11621 : Tree Nat := .node node11612 node11620 +def node11622 : Tree Nat := .leaf 1584883593408437211614387469712064555158914503508771038724904544061812054501246924612497208568277150977848478150352795769583604541055259689693406819867577708238382808341478666344109415982294824545567562144126308828126218529054698535433062443245559991766155220200510833408 +def node11623 : Tree Nat := .node node11622 node10887 +def node11624 : Tree Nat := .node node10540 node11623 +def node11625 : Tree Nat := .node node11624 node10892 +def node11626 : Tree Nat := .node node11625 node11246 +def node11627 : Tree Nat := .node node11242 node11626 +def node11628 : Tree Nat := .node node11621 node11627 +def node11629 : Tree Nat := .leaf 39916806190694502599356663240709463166772373299772117545440415305120231012649310801353388651413043935609263867990438192946758383121104936041707204185123101386513126139387421382393728552470140512273269003599257315155647932858665958170748809463650057755596383114756381322262940723524971410751488 +def node11630 : Tree Nat := .leaf 64489078507786300531391609283624660276050308195212539899158086377958250252022358692767408864534768134728864790575501380616377911990055123619253834227860747978190465660870555683898680617142080248930517530570227218582103803401672859704569035215414640612099365786003968 +def node11631 : Tree Nat := .node node11629 node11630 +def node11632 : Tree Nat := .node node10547 node11631 +def node11633 : Tree Nat := .leaf 4989600773836821687419583011228355251654751505281139745627797782066541151598437685733482643480996943670877759896098997554486011218051588053295792492224107830008960712410111574300999178395236955466028149599429396701120626222703238225836020103178719395738113288837047136746742554960965128683520 +def node11634 : Tree Nat := .node node7339 node11633 +def node11635 : Tree Nat := .node node9027 node11634 +def node11636 : Tree Nat := .node node11632 node11635 +def node11637 : Tree Nat := .node node10242 node11636 +def node11638 : Tree Nat := .node node11637 node11259 +def node11639 : Tree Nat := .leaf 38981256045599996321809750450836617517922312907734296713042280348598068650264610437653269029443997437566070676605669648807542084053986150610314202055809205510553451706467971519081820589633668739367680177227579553176458119454272724908689548500684714003380275516031667043579284136715867966464 +def node11640 : Tree Nat := .leaf 17311155196253479753435624159146045598717774204736508284994244487722503133749893892722525769008169071600506586167258067829509776785505512616660063674442009361653479427816551871909349693156016819478082284038937483227626597973540260278488655962496099697424154845752141662912512 +def node11641 : Tree Nat := .node node11639 node11640 +def node11642 : Tree Nat := .node node10913 node11641 +def node11643 : Tree Nat := .node node11642 node11266 +def node11644 : Tree Nat := .node node10253 node11643 +def node11645 : Tree Nat := .leaf 623700096729599941143673061886283382447435673680950235479233377409867028482305313800780280586234054472401493724209977902761841006767121205029015322651536752601991969740021492351641955286332702881733378500343676294632432254232790053435025582922409285481277027588217021378371070080062378228736 +def node11646 : Tree Nat := .node node11645 node8189 +def node11647 : Tree Nat := .node node10558 node11646 +def node11648 : Tree Nat := .node node11647 node10919 +def node11649 : Tree Nat := .node node11648 node11272 +def node11650 : Tree Nat := .node node11644 node11649 +def node11651 : Tree Nat := .node node11638 node11650 +def node11652 : Tree Nat := .node node11628 node11651 +def node11653 : Tree Nat := .leaf 311850048364799970572893120005414463159653646912752305414931921134323129143250539822962748276853103499486113177676113352587299605173203008309216069014674185538109033421317734601812860933340476974652719144519619771910922546552232884715601339954412756629829318859318815439931596453626557547264 +def node11654 : Tree Nat := .node node5386 node11653 +def node11655 : Tree Nat := .node node10569 node11654 +def node11656 : Tree Nat := .node node11279 node11655 +def node11657 : Tree Nat := .node node10266 node11656 +def node11658 : Tree Nat := .leaf 6359114106075270959545088843609914016149875281838276464848501209597724910497936628519761798096811944538947904689447965273123107733653903939072270870999045422413426940149168126861422515824794462952699232391567720588630442097838593671168 +def node11659 : Tree Nat := .node node3414 node11658 +def node11660 : Tree Nat := .node node11659 node5392 +def node11661 : Tree Nat := .node node8635 node11660 +def node11662 : Tree Nat := .node node10936 node11661 +def node11663 : Tree Nat := .node node11657 node11662 +def node11664 : Tree Nat := .leaf 16122269687003043759856158596114164560774687614603120767776477226849869277195912094646325914424064191536284258390940657219702583027165031281700226779654078198964753630172816739929491839826980876059035200393477292465439997509502389020031474382686268766498008360288256 +def node11665 : Tree Nat := .node node10583 node11664 +def node11666 : Tree Nat := .node node6212 node11665 +def node11667 : Tree Nat := .node node11666 node11292 +def node11668 : Tree Nat := .node node11286 node11667 +def node11669 : Tree Nat := .node node11668 node11299 +def node11670 : Tree Nat := .node node11663 node11669 +def node11671 : Tree Nat := .leaf 69244620785013915170128490189477811531824955396191184425272058540842623741436225137170371136664720923332289635109501355732832417914201484441035852139332300936119183839542026325848194821709253729580900716834616688342877923063210889385388659646104749382031542175273116890061312 +def node11672 : Tree Nat := .node node10281 node11671 +def node11673 : Tree Nat := .node node10595 node11672 +def node11674 : Tree Nat := .leaf 79833612381388792474910486119600282519415862496991324459460776799856729817255684875259591192992011088619330390654305555789775003949256662905563582104934485919119069353204879409537234267323586429688389200188231390078120245206929526020333287601567461385130366890233336190678529821186052883218432 +def node11675 : Tree Nat := .node node5413 node11674 +def node11676 : Tree Nat := .node node9077 node11675 +def node11677 : Tree Nat := .node node11673 node11676 +def node11678 : Tree Nat := .node node11305 node11677 +def node11679 : Tree Nat := .node node11678 node10959 +def node11680 : Tree Nat := .leaf 396220899827876895477060460843258879220747005654011700510188605388424284033308668164687632795967036691676878923562154953069719752748550337399360717470585629548790572386617368539166416740970552008474111023460739170943608560730854549505922829800716317360953286474256626432 +def node11681 : Tree Nat := .node node11680 node11312 +def node11682 : Tree Nat := .node node10962 node11681 +def node11683 : Tree Nat := .node node11682 node9378 +def node11684 : Tree Nat := .node node10603 node11683 +def node11685 : Tree Nat := .node node11684 node11321 +def node11686 : Tree Nat := .node node11679 node11685 +def node11687 : Tree Nat := .node node11670 node11686 +def node11688 : Tree Nat := .node node11652 node11687 +def node11689 : Tree Nat := .leaf 77962512091199992642827155836619268151797045659041079242256603618606140594416791194326173724959762167573606902273555401835320172923085291996257089638865709198522998598561147293456460418909481933406294206544402296802427880546553933551453439248687642243291743814097053718132873586811289097472 +def node11690 : Tree Nat := .node node5450 node11689 +def node11691 : Tree Nat := .node node9110 node11690 +def node11692 : Tree Nat := .node node11328 node11691 +def node11693 : Tree Nat := .node node10298 node11692 +def node11694 : Tree Nat := .leaf 23692437876425140175364145914042896470464146022195174051564658708097740366065254332051499465651646752959477016938832457563383235038448516741832457698362069507104360669820052043269431264795302740131845291689914481633002688348160 +def node11695 : Tree Nat := .node node3384 node11694 +def node11696 : Tree Nat := .node node11695 node5456 +def node11697 : Tree Nat := .node node10990 node11696 +def node11698 : Tree Nat := .node node10617 node11697 +def node11699 : Tree Nat := .node node11693 node11698 +def node11700 : Tree Nat := .node node11699 node11341 +def node11701 : Tree Nat := .leaf 1056589062271330551357154794869753759687364148238312273254043242658844185409541560807279608610073744860744529077431235655631784277952475010584952315354381193213634237213357930339955517547707304739395772941257638946260666798501683361601075040739213078278213157365093514240 +def node11702 : Tree Nat := .node node5895 node11701 +def node11703 : Tree Nat := .node node9966 node11702 +def node11704 : Tree Nat := .leaf 19958403095347304482792936110343045676687705457393128745095957335486669498317869371657705847760091001631712632465331723475627294777000541151951695979796840842265736036217554855731848506006021126775966699049066018605766778240087475669003141955123987016824691203289431065716703140548148813889536 +def node11705 : Tree Nat := .node node5477 node11704 +def node11706 : Tree Nat := .node node9663 node11705 +def node11707 : Tree Nat := .node node11703 node11706 +def node11708 : Tree Nat := .node node10320 node11707 +def node11709 : Tree Nat := .node node11708 node11352 +def node11710 : Tree Nat := .leaf 984025249451093111545271203069913162369976096407652062409214830727720955917292968523267006162989669818401042598134648880504420669646742254202115807688306416736313028530186424890905045241987266669403575250945808045813649861843565772644867503152788976564334283776 +def node11711 : Tree Nat := .leaf 4226356249089165819435066285849878084890879347801963797935583018024170305128746910853204209891268966148552222280678128745782366094313386682575974757368614666690008257420528240427093699131389201218283081656186093508200260654734684052017668918350983088391646611464920236032 +def node11712 : Tree Nat := .node node11710 node11711 +def node11713 : Tree Nat := .node node9408 node11712 +def node11714 : Tree Nat := .node node11713 node11359 +def node11715 : Tree Nat := .node node9986 node11714 +def node11716 : Tree Nat := .node node11715 node11366 +def node11717 : Tree Nat := .node node11709 node11716 +def node11718 : Tree Nat := .node node11700 node11717 +def node11719 : Tree Nat := .leaf 3936341223678880479206185644277619697922167585573780197459388764137740584958857691987861186140590095545847148979133295071943161294504734074018276775767492290940664483150583013831832215281538609724855710086875126317218982730297450563491759432655640391611123236864 +def node11720 : Tree Nat := .node node11719 node11370 +def node11721 : Tree Nat := .node node9432 node11720 +def node11722 : Tree Nat := .node node11721 node11028 +def node11723 : Tree Nat := .node node10334 node11722 +def node11724 : Tree Nat := .leaf 4226356249089165819435066285849878084890879347801963797935583018024170305128746910853204209891268966148552222280678128745782366094313386682575974757368614666690009431691819627343707643871687595886796769497460547668135614300220450156530226222572714937890839004612529225728 +def node11725 : Tree Nat := .node node11724 node11375 +def node11726 : Tree Nat := .node node9441 node11725 +def node11727 : Tree Nat := .node node11726 node9701 +def node11728 : Tree Nat := .node node11034 node11727 +def node11729 : Tree Nat := .node node11723 node11728 +def node11730 : Tree Nat := .leaf 3936341223678880479206185644277619697922167585573780197459388764137740584958857691987861186140590095545847148979133295071943161294504734074018276775767492290940664209744242415955341668718760220022185040940696264665664429508971649319366859510665237452463861137408 +def node11731 : Tree Nat := .node node5932 node11730 +def node11732 : Tree Nat := .node node9447 node11731 +def node11733 : Tree Nat := .node node11732 node11390 +def node11734 : Tree Nat := .node node11384 node11733 +def node11735 : Tree Nat := .leaf 1056589062271330551357154794869753759687364148238312273254043242658844185409541560807279608610073744860744529077431235655631784277952475010584952315354381193213634237213357930344127367227240332244073549711120045420094074068729520802903890681016985980193526731628691864576 +def node11736 : Tree Nat := .node node11735 node8314 +def node11737 : Tree Nat := .node node9452 node11736 +def node11738 : Tree Nat := .node node11737 node11039 +def node11739 : Tree Nat := .node node11738 node11396 +def node11740 : Tree Nat := .node node11734 node11739 +def node11741 : Tree Nat := .node node11729 node11740 +def node11742 : Tree Nat := .leaf 19958403095347304482792936110343045676687705457393128745095957335486669498317869371657705847760091001631712632465331723475627294777000541151951695979796840842265736036217554855731848506006021196767989892105447598525838046003971166970424930537921952641484096321785405445746246292969815699095552 +def node11743 : Tree Nat := .node node11742 node11400 +def node11744 : Tree Nat := .node node10008 node11743 +def node11745 : Tree Nat := .leaf 17726622920979684553209871963620509457015918490794380011553772325509535225439352334980090878535409072407460321315675603096068034603239702925670096934496189912398045702045591281720856225832850639296050128165046424536311542226283592403674714817971430760451972236472335032251318272 +def node11746 : Tree Nat := .node node3129 node11745 +def node11747 : Tree Nat := .node node11746 node11404 +def node11748 : Tree Nat := .node node11744 node11747 +def node11749 : Tree Nat := .node node10656 node11748 +def node11750 : Tree Nat := .leaf 283625967792006058808176788520780685867414277271872180408915520460270310453647113281245303037673853136894992844250815787358691725117514264334266573316946827204522086251437357760852310332385704936966462386676328410954037497695100268951684641518401220180487621206475531876403904512 +def node11751 : Tree Nat := .node node2725 node11750 +def node11752 : Tree Nat := .node node11751 node11048 +def node11753 : Tree Nat := .node node11046 node11752 +def node11754 : Tree Nat := .node node11753 node11411 +def node11755 : Tree Nat := .node node11749 node11754 +def node11756 : Tree Nat := .leaf 580865979874134008906969201210315654396307779749920966216938596455013640222452974299397860847118273290532849095283182172014738024312923289594492390929742194259910377677130657240374978687970909312315204033126186981910188959170801457796644665040776281499813756597623008270090466505472 +def node11757 : Tree Nat := .node node11756 node11414 +def node11758 : Tree Nat := .node node10026 node11757 +def node11759 : Tree Nat := .node node11758 node11419 +def node11760 : Tree Nat := .node node10664 node11759 +def node11761 : Tree Nat := .leaf 311850048364799970572893120005414463159653646912752305414931921134323129143250539822962748276853103499486113177676113352587299605173203008309216069014674185538109033421317734601812860933340476975720712662480074813108433399637008942016953601132739141603350122770428678330251871465107609404160 +def node11762 : Tree Nat := .node node11761 node11053 +def node11763 : Tree Nat := .node node10034 node11762 +def node11764 : Tree Nat := .leaf 106366229208979968755504199669210556446675929746210728544744454015758665821158425773294499606724351745728754429869990186297742120342216366485079165879397793158850754141900680380196978190983346918797243527356175696876889925729911667259124244095116932725667925559977804377547079680 +def node11765 : Tree Nat := .node node2913 node11764 +def node11766 : Tree Nat := .node node11765 node11423 +def node11767 : Tree Nat := .node node11763 node11766 +def node11768 : Tree Nat := .node node11767 node11429 +def node11769 : Tree Nat := .node node11760 node11768 +def node11770 : Tree Nat := .node node11755 node11769 +def node11771 : Tree Nat := .node node11741 node11770 +def node11772 : Tree Nat := .node node11718 node11771 +def node11773 : Tree Nat := .node node11688 node11772 +def node11774 : Tree Nat := .node node11604 node11773 +def node11775 : Tree Nat := .leaf 638668899051110339730043494528037430307403838405632263158900008459255607361866436634204573132862984619790236016963481275201229376228408968606600883478398692470132733278909404279582204956998110855958406731842752500540238107046749101173688655896844177716114166792792968095145111571037435509866496 +def node11776 : Tree Nat := .node node5079 node11775 +def node11777 : Tree Nat := .node node9505 node11776 +def node11778 : Tree Nat := .node node11449 node11777 +def node11779 : Tree Nat := .node node11446 node11778 +def node11780 : Tree Nat := .leaf 1661870905031411479118082422182958388339573605517634471142247228277146163095997620803541199838958948600699983576897594925136406503173415067734781790088778947283220568591810265733176946294962614881544785177036077053546998683093203950372832360794661600130987244040793467840888832 +def node11781 : Tree Nat := .node node11780 node57 +def node11782 : Tree Nat := .node node9250 node11781 +def node11783 : Tree Nat := .node node9248 node11782 +def node11784 : Tree Nat := .node node10687 node11783 +def node11785 : Tree Nat := .node node11779 node11784 +def node11786 : Tree Nat := .node node11442 node11785 +def node11787 : Tree Nat := .leaf 316582913885591799252621399690679645405350001801403874669082289131975003863964479624699212827362426626481055692401181763751216399488307972842982921964026433504386507112043249664 +def node11788 : Tree Nat := .node node141 node11787 +def node11789 : Tree Nat := .node node11788 node11455 +def node11790 : Tree Nat := .leaf 2494800386918399833815086676309963377712804265022133458703139449237699290108263623073821198303215779965315147963357013676659879764066158298617136408549392150825449262793203743476730214527491069867717378898419360635682969315147650983111346552014190460257028209493522573772557381428438162758144 +def node11791 : Tree Nat := .node node5095 node11790 +def node11792 : Tree Nat := .node node8814 node11791 +def node11793 : Tree Nat := .node node11789 node11792 +def node11794 : Tree Nat := .node node10058 node11793 +def node11795 : Tree Nat := .leaf 2494800386918399833815086676309963377712804265022133458703139449237699290108263623073821198303215779965315147963357013676659879764066158298617136408549392150825449262793203743476730216876033652641550606787899957425019996690830199891431217259305161992466053324101966037471555766214733380737536 +def node11796 : Tree Nat := .leaf 25359685326862541939557340726563259540884737107923566583502033521185158500438000087711803602387121108608293068117911229624038617108891291681023989987229004831202091927179686642755110136174264388513536423694099583699079973746110147184300713310109185220304079218380875235328 +def node11797 : Tree Nat := .node node11795 node11796 +def node11798 : Tree Nat := .node node10700 node11797 +def node11799 : Tree Nat := .node node11798 node9765 +def node11800 : Tree Nat := .node node10370 node11799 +def node11801 : Tree Nat := .node node11794 node11800 +def node11802 : Tree Nat := .leaf 163499238157084246971167031136149696249049528960308906100902295024436442704347605122371115766664149573950267808775538614940142892217487619248285972542452259315082273568239679328280471347991843225708496784914652790723598340894176438477294617830758568299528887925583791164871337854447645283040034816 +def node11803 : Tree Nat := .node node5110 node11802 +def node11804 : Tree Nat := .node node8829 node11803 +def node11805 : Tree Nat := .node node11462 node11804 +def node11806 : Tree Nat := .node node11089 node11805 +def node11807 : Tree Nat := .leaf 101434614006448733465190323290789849273921259922785814823697783719991994020372222556467386102247105764350802735518413560957234503981601100356887956252320534928041503098205487290330627069755437265670089607768727390170101722264496793304982436685962700143244789185895460044800 +def node11808 : Tree Nat := .node node6392 node11807 +def node11809 : Tree Nat := .node node8404 node11808 +def node11810 : Tree Nat := .node node11809 node10073 +def node11811 : Tree Nat := .node node10713 node11810 +def node11812 : Tree Nat := .node node11806 node11811 +def node11813 : Tree Nat := .node node11801 node11812 +def node11814 : Tree Nat := .node node11786 node11813 +def node11815 : Tree Nat := .leaf 81749619078542123485583515568074848124524764480154453050451147512218363489450319349723321766952234392809622444365851486372738004061956979062088871968318583757114790585728785576579078498544127865382966877856102443023290481613681137308679073193897753079688258899060389281957197967485705145379717120 +def node11816 : Tree Nat := .node node11815 node10381 +def node11817 : Tree Nat := .node node8420 node11816 +def node11818 : Tree Nat := .node node10725 node11817 +def node11819 : Tree Nat := .node node11818 node11479 +def node11820 : Tree Nat := .node node11475 node11819 +def node11821 : Tree Nat := .leaf 10218702384817765435680645196173672777168963974041446678917664313539356004583331859515792661985190762651035314265525423573455205723341236871310032519823993166087698288481721319628050542591656048848610091196343239014933589730974036473773967866935629220587834537022369246316373708230571900916465664 +def node11822 : Tree Nat := .node node8864 node11821 +def node11823 : Tree Nat := .node node8863 node11822 +def node11824 : Tree Nat := .node node11489 node11823 +def node11825 : Tree Nat := .node node11485 node11824 +def node11826 : Tree Nat := .leaf 20437404769635530873023127480337686835839614525262522652363831944827126031207536600326630949839320060286154364769572526449026999280281932691256588891355558664133594448019233235742745203620266892563509802901721535269368055211734613589113211846631992841510547936958969994646500937285179687397490688 +def node11827 : Tree Nat := .node node11826 node57 +def node11828 : Tree Nat := .node node9772 node11827 +def node11829 : Tree Nat := .node node11116 node11828 +def node11830 : Tree Nat := .node node11495 node11829 +def node11831 : Tree Nat := .node node11825 node11830 +def node11832 : Tree Nat := .node node11820 node11831 +def node11833 : Tree Nat := .leaf 1876879207201175057492789423877314215327939898387375884169474870502860978765784020192710578146539744270187446263364617826790225418785882413744524133358611663882261442077897464880491830622108531976854358169267898127951581024551761700825956922352468068665600 +def node11834 : Tree Nat := .node node377 node11833 +def node11835 : Tree Nat := .node node11834 node7598 +def node11836 : Tree Nat := .node node11835 node11123 +def node11837 : Tree Nat := .node node11836 node11506 +def node11838 : Tree Nat := .leaf 633165827771183598505242799381359290823402436669908964291241856393006290165522028742537610514028998040696363117430993345091984039101064808108535148630015591555363229235865993216 +def node11839 : Tree Nat := .node node11838 node8026 +def node11840 : Tree Nat := .node node10087 node11839 +def node11841 : Tree Nat := .leaf 276978484171880916803921705436224301013624923980139280626413378959201822587539294608810929125743781431500803317101062222427779168468223293033246586440527661066082209234022628675165480156426772382268943090437368013836441457390866341557141812932064760488599197602403233636810752 +def node11842 : Tree Nat := .node node11841 node10399 +def node11843 : Tree Nat := .node node8890 node11842 +def node11844 : Tree Nat := .node node11840 node11843 +def node11845 : Tree Nat := .node node11844 node11511 +def node11846 : Tree Nat := .node node11837 node11845 +def node11847 : Tree Nat := .leaf 77290824170548776689636601064402699296131976535377947187753767903795224470551951076611931761427980967686928734192720947431538390897910284687347604223758868878073484359696384 +def node11848 : Tree Nat := .node node469 node11847 +def node11849 : Tree Nat := .node node11848 node11515 +def node11850 : Tree Nat := .node node11849 node10762 +def node11851 : Tree Nat := .node node11850 node10767 +def node11852 : Tree Nat := .node node11139 node11851 +def node11853 : Tree Nat := .node node11846 node11852 +def node11854 : Tree Nat := .node node11832 node11853 +def node11855 : Tree Nat := .node node11814 node11854 +def node11856 : Tree Nat := .leaf 163499238157084246971167031136149696249049528960308906100902295024436442704347605122371115766664149573950267808775538614940142892217487619248285972542452259315082273568240356249592512562557169986983922342459437077118953764862723918843655609360984551117653881677074059616555280700294234941234020352 +def node11857 : Tree Nat := .node node11856 node9288 +def node11858 : Tree Nat := .node node6827 node11857 +def node11859 : Tree Nat := .node node10430 node11858 +def node11860 : Tree Nat := .node node11859 node11147 +def node11861 : Tree Nat := .node node11531 node11860 +def node11862 : Tree Nat := .leaf 40874809539271061743830427101745879946051793685070080996901061897918443564865825542993591510749775123925692648582207166626096330246212097324929775236787342999898762362828778557314337308375934005137291419578834907108646038817346632828015714577131662554429789923226168879654078315742159406467383296 +def node11863 : Tree Nat := .node node11862 node57 +def node11864 : Tree Nat := .node node9808 node11863 +def node11865 : Tree Nat := .node node8494 node11864 +def node11866 : Tree Nat := .node node11541 node11865 +def node11867 : Tree Nat := .node node11537 node11866 +def node11868 : Tree Nat := .node node11861 node11867 +def node11869 : Tree Nat := .leaf 316582913885591799252621399690679645405350001801403874669082289131975003863964479624699722086356510248002622803823284108291479266586724456905641957076365028829327341288589107200 +def node11870 : Tree Nat := .node node11869 node8072 +def node11871 : Tree Nat := .node node10795 node11870 +def node11872 : Tree Nat := .leaf 138489242085940458401960852718112150506812461990069640313206689479600911293769647304405464562871890715750401658550531111213889631731515850633296283675632665661477254874268899510331835538531160041730679446253306604028235378004391548291687909087226089740692260341482243990159360 +def node11873 : Tree Nat := .leaf 2323463919496536035621972653359219625205094065092803842274643530181157276813131833664325491400244331789392679361098607690583358868782660090431376684494546007279524707002217887874048689586946916100946551220743067526651409454870434317484175943474616464059036497610922673685869933625344 +def node11874 : Tree Nat := .node node11872 node11873 +def node11875 : Tree Nat := .node node9815 node11874 +def node11876 : Tree Nat := .node node11871 node11875 +def node11877 : Tree Nat := .leaf 103866931564455343801822554389934333203389244509458158012020530776078908043800262429741051803735415473862930601861307299166558866196664071989836225888806339642558293182917873392965281757478762387837272517245328089523128224985620981086910492022900407745960307627122249665914112 +def node11878 : Tree Nat := .leaf 1661870905031411479118082422182958388339573605517634471142247228277146163095997620803541199838958948600699983576897594925136406298586502074225914914264422895558273555051682388041627603589252108873182509884876396849166228314083382019955074388285031227193918298575197138478694400 +def node11879 : Tree Nat := .node node11877 node11878 +def node11880 : Tree Nat := .node node10127 node11879 +def node11881 : Tree Nat := .node node11880 node9820 +def node11882 : Tree Nat := .node node11876 node11881 +def node11883 : Tree Nat := .node node11553 node11882 +def node11884 : Tree Nat := .leaf 653996952628336987883560278233738925607388820028631610617171280111070896568988152280527359130912322882421139043269962869160201929411556803945055956469448016444196720049186150485557622504644106080484627484580473299318274408020435371898453110469823650401404051767239373321027139369682297645251756032 +def node11885 : Tree Nat := .node node8940 node11884 +def node11886 : Tree Nat := .node node10801 node11885 +def node11887 : Tree Nat := .node node11557 node11886 +def node11888 : Tree Nat := .node node11171 node11887 +def node11889 : Tree Nat := .node node11888 node11564 +def node11890 : Tree Nat := .node node11883 node11889 +def node11891 : Tree Nat := .node node11868 node11890 +def node11892 : Tree Nat := .leaf 27967679607885704301190218685229334463595448410322903006780765573805474289927672640854064610822656252569050510580947698823110901873064308988622799852500414409928289070570668080319093852209583895379850053107559710590017945331450883048399361437335552 +def node11893 : Tree Nat := .node node2161 node11892 +def node11894 : Tree Nat := .node node11893 node8954 +def node11895 : Tree Nat := .node node10153 node11894 +def node11896 : Tree Nat := .node node11895 node11574 +def node11897 : Tree Nat := .leaf 6191329402440458580124204415614330367293195005243462324135270677371812121921528584619555648487620528947942250374768508120159338460325751112129288848657018975458729898330864651947855593137029877655915644576438236572922499160389014920494653042542711396039261505437302784 +def node11898 : Tree Nat := .node node3434 node11897 +def node11899 : Tree Nat := .node node11898 node5264 +def node11900 : Tree Nat := .node node11185 node11899 +def node11901 : Tree Nat := .node node11579 node11900 +def node11902 : Tree Nat := .node node11896 node11901 +def node11903 : Tree Nat := .leaf 6359114106075270959545088843609914025718006747965898412012271524835302263080420578953093753630826691836448620151460163738771171813501969727651547677881703902838865423991110675772987707802875392273746367715546081184830220168964753850368 +def node11904 : Tree Nat := .node node2395 node11903 +def node11905 : Tree Nat := .node node11904 node10823 +def node11906 : Tree Nat := .node node10491 node11905 +def node11907 : Tree Nat := .leaf 40874809539271061743830427101745879946051793685070080996901061897918443564865825542993591510749775123925692648582207166626096330246212097324929774418439691025863294859531354350414549254215422494371094048755992883075196937648707912010492633101092374832758758033198031981622872189136835081677045760 +def node11908 : Tree Nat := .node node5269 node11907 +def node11909 : Tree Nat := .node node10166 node11908 +def node11910 : Tree Nat := .node node11585 node11909 +def node11911 : Tree Nat := .node node11906 node11910 +def node11912 : Tree Nat := .leaf 1707011694817242694210710703124117431539072329783553114202344791423430903423171540175713850026265366398998246612387635793921889857613080182536713796065221674793276593667861833135231755897578192133197551437133342511696913371257710320862564974592 +def node11913 : Tree Nat := .node node862 node11912 +def node11914 : Tree Nat := .leaf 138489242085940458401960852718112150506812461990069640313206689479600911293769647304405464562871890715750401658550531111213889631731515850633296283502340809778926326150618013001389104073753842830742143498098332815614403640152790108293287527578502458653590459526307176032436224 +def node11915 : Tree Nat := .node node10174 node11914 +def node11916 : Tree Nat := .node node11913 node11915 +def node11917 : Tree Nat := .leaf 1107913932560474553181223067572389585967068949556785806716538814129167597559328825943630938223989230855846491671124890032459242582330202011582355204517452444929382921266823283769560427707387455476650986206898062706628562597112166198937714621913262854018096221920188171498291200 +def node11918 : Tree Nat := .node node11917 node57 +def node11919 : Tree Nat := .node node9862 node11918 +def node11920 : Tree Nat := .node node11916 node11919 +def node11921 : Tree Nat := .node node11591 node11920 +def node11922 : Tree Nat := .node node11911 node11921 +def node11923 : Tree Nat := .node node11902 node11922 +def node11924 : Tree Nat := .leaf 1247400193459199986152164510103367905614711427706494166828336535981415444438633317194506772553692147037166168243022088950872216915566507547980881828931469071221938326463907540589737110998721226758565641040961783339015232315280207452142001373732889026474768889969054177857797592901097225233664 +def node11925 : Tree Nat := .node node11924 node8544 +def node11926 : Tree Nat := .node node10193 node11925 +def node11927 : Tree Nat := .node node11926 node7292 +def node11928 : Tree Nat := .node node10845 node11927 +def node11929 : Tree Nat := .node node11599 node11928 +def node11930 : Tree Nat := .node node11929 node11223 +def node11931 : Tree Nat := .node node11923 node11930 +def node11932 : Tree Nat := .node node11891 node11931 +def node11933 : Tree Nat := .node node11855 node11932 +def node11934 : Tree Nat := .leaf 77290824170548776689636601064402699296131976535377947187753767903795224470551951076612926407900800540971239498689014589111739303199504980122228532177545187872098551110762752 +def node11935 : Tree Nat := .node node11934 node10528 +def node11936 : Tree Nat := .node node10227 node11935 +def node11937 : Tree Nat := .leaf 25359685326862541939557340726563259540884737107923566583502033521185158500438000087711803602387121108608293068117911229624038617108891291681023990325689660851809374590560324355533882528317462066225520697434282764194845086737519209681176458444335027191727002513209972228096 +def node11938 : Tree Nat := .node node11937 node9337 +def node11939 : Tree Nat := .node node8999 node11938 +def node11940 : Tree Nat := .node node11936 node11939 +def node11941 : Tree Nat := .node node11940 node11619 +def node11942 : Tree Nat := .node node11612 node11941 +def node11943 : Tree Nat := .node node11942 node11627 +def node11944 : Tree Nat := .leaf 633165827771183598505242799381359290823402436669908964291241856393006290165522028742535573478052663554610094671742583966930932570707398871857899008180661210255599892529682579456 +def node11945 : Tree Nat := .node node1146 node11944 +def node11946 : Tree Nat := .node node11945 node11631 +def node11947 : Tree Nat := .node node11946 node11635 +def node11948 : Tree Nat := .node node10242 node11947 +def node11949 : Tree Nat := .leaf 10218702384817765435680645196173672777168963974041446678917664313539356004583331859515792661985190762651035314265525423573455205723341236871310032519823993166087698288568367247569326006953481492103081456928731897620427857705051523367980883735861429940587034727776731061859924608638159434895327232 +def node11950 : Tree Nat := .leaf 3485195879244804053432958980038829437807641097639205763411965295271735915219697750496488237100366450943945018000315455713503494388731855478314041500641787454767702749096393470183740810708344341090129605695306231340872304790190961817602980861955394817139416480495328121423133981802496 +def node11951 : Tree Nat := .node node11949 node11950 +def node11952 : Tree Nat := .node node9032 node11951 +def node11953 : Tree Nat := .node node10904 node11952 +def node11954 : Tree Nat := .leaf 16905425059318903613520611904066424622426050758749011400102100889924812885747136871813394991348110207523385048760997704053789641535676252208181401159950797086687548325664369025260129933036863623468160538461407800930663540885630598310635779027915519962599996869812322041856 +def node11955 : Tree Nat := .node node6181 node11954 +def node11956 : Tree Nat := .node node10907 node11955 +def node11957 : Tree Nat := .node node11956 node9909 +def node11958 : Tree Nat := .node node11953 node11957 +def node11959 : Tree Nat := .node node11948 node11958 +def node11960 : Tree Nat := .leaf 326998476314168493941780206738569259224467206527547894855795934816918678851073338672775595878048928875797373795235685048747104071686674917464476407600333055572127279699617707225101185675019152507055850958462981720289660445582856165276522174685860476605155480437847661063310125094453442376272314368 +def node11961 : Tree Nat := .node node6960 node11960 +def node11962 : Tree Nat := .node node9351 node11961 +def node11963 : Tree Nat := .node node11642 node11962 +def node11964 : Tree Nat := .node node10253 node11963 +def node11965 : Tree Nat := .leaf 67625827286389648917836620123883785920403991263542813449640896695818026931586561208212498641500081078142101024501598751501461725911483614095047573619294155392478681791048336426011953754966497691256743481853493835188157171413152007784725258998802449485740117552784483155968 +def node11966 : Tree Nat := .node node4855 node11965 +def node11967 : Tree Nat := .node node8626 node11966 +def node11968 : Tree Nat := .leaf 653996952628336987883560278233738925607388820028631610617171280111070896568988152280527359130912322882421139043269962869160201929411556803945056061217947469120736560471256448968730493437189579458557890949904252375599759357606191636541407539402852478775296133689594745022973164944316492099402137600 +def node11969 : Tree Nat := .node node11968 node57 +def node11970 : Tree Nat := .node node10256 node11969 +def node11971 : Tree Nat := .node node11967 node11970 +def node11972 : Tree Nat := .node node11648 node11971 +def node11973 : Tree Nat := .node node11964 node11972 +def node11974 : Tree Nat := .node node11959 node11973 +def node11975 : Tree Nat := .node node11943 node11974 +def node11976 : Tree Nat := .leaf 2396072166980802786735159298776695238492753254626953962345726140499318441713542203466335663006519387421698952120757445911278601160627469407271530546082711169588206984093429136215750057248192354480949478981279757169063587081341018263915960520023984796663087092459244188739015615972352 +def node11977 : Tree Nat := .node node11976 node10933 +def node11978 : Tree Nat := .node node5821 node11977 +def node11979 : Tree Nat := .leaf 2396072166980802786735159298776695238492753254626953962345726140499318441713542203466335663006519387421698952120757445911278601160627469407271530546082711169588206984093429136215750057248192354465035135416166584620091355140642751380701363694508857838568239831878140284337947598913536 +def node11980 : Tree Nat := .node node10268 node11979 +def node11981 : Tree Nat := .node node6976 node11980 +def node11982 : Tree Nat := .node node11978 node11981 +def node11983 : Tree Nat := .leaf 638668899051110339730043494528037430307403838405632263158900008459255607361866436634204573132862984619790236016963481275201229376228408968606600883478398692470132733278909404279582204957291678678805135885328937575138905235468709419787228639735255549157640294932119023528107486369137921435369472 +def node11984 : Tree Nat := .node node11983 node8633 +def node11985 : Tree Nat := .node node6593 node11984 +def node11986 : Tree Nat := .node node11985 node11660 +def node11987 : Tree Nat := .node node11982 node11986 +def node11988 : Tree Nat := .node node11657 node11987 +def node11989 : Tree Nat := .leaf 20437404769635530873023127480337686835839614525262522652363831944827126031207536600326630949839320060286154364769572526449026999280281932691256585617964950767991724434829536408143592986978220849498720319610353439135571650537179730319020885942474841954826420376867191589955815741378004373553020928 +def node11990 : Tree Nat := .node node5397 node11989 +def node11991 : Tree Nat := .node node7370 node11990 +def node11992 : Tree Nat := .node node11666 node11991 +def node11993 : Tree Nat := .node node11286 node11992 +def node11994 : Tree Nat := .node node11993 node11299 +def node11995 : Tree Nat := .node node11988 node11994 +def node11996 : Tree Nat := .leaf 7507516828804700229971157695509256861311759593549503536677899755757880972394849199241138654603637921490647409518277107506648049119780025230444789235461426206976292249728517077129878497711675432169208373367605330449501004324220518173472389939402556764610560 +def node11997 : Tree Nat := .node node1382 node11996 +def node11998 : Tree Nat := .node node11997 node10591 +def node11999 : Tree Nat := .node node11998 node11304 +def node12000 : Tree Nat := .node node11999 node11677 +def node12001 : Tree Nat := .node node12000 node10959 +def node12002 : Tree Nat := .leaf 34959599509857130376772047909570245155022077753222690323156717052282288738011130416887571407233163944657004505570241951436566021340241608247920885549900035970086781639599548913842719069037144801148426208064817249689987399067587029409623826092785664 +def node12003 : Tree Nat := .node node12002 node9087 +def node12004 : Tree Nat := .node node8666 node12003 +def node12005 : Tree Nat := .node node10602 node12004 +def node12006 : Tree Nat := .node node12005 node11683 +def node12007 : Tree Nat := .leaf 154581648341097553379273256685340001420955698403840020567358626360381160410589000415347825913833999801759926825480768027942875524422682886065961891343516906725566326379380736 +def node12008 : Tree Nat := .node node1474 node12007 +def node12009 : Tree Nat := .node node12008 node10967 +def node12010 : Tree Nat := .node node12009 node10971 +def node12011 : Tree Nat := .leaf 101434614006448733465190323290789849273921259922785814823697783719991994020372222556467386102247105764350802735518413562633210495224425737803641081028051300862962230672254659505775807534975941024863461708003014661033030183518479066615739125712196997865534258441866655891456 +def node12012 : Tree Nat := .node node12011 node57 +def node12013 : Tree Nat := .node node7822 node12012 +def node12014 : Tree Nat := .node node11319 node12013 +def node12015 : Tree Nat := .node node12010 node12014 +def node12016 : Tree Nat := .node node12006 node12015 +def node12017 : Tree Nat := .node node12001 node12016 +def node12018 : Tree Nat := .node node11995 node12017 +def node12019 : Tree Nat := .node node11975 node12018 +def node12020 : Tree Nat := .leaf 319334449525555169865025974007202275366151173374819597363186706524146987018843596864935283165944279404189344175528009230318985492293616239624594468272226773088845657203073328333281744285771871899954391407577306195087621657919972432243298010953524399685217318138897754460797589878665593028083712 +def node12021 : Tree Nat := .node node12020 node8690 +def node12022 : Tree Nat := .node node10989 node12021 +def node12023 : Tree Nat := .node node12022 node11696 +def node12024 : Tree Nat := .node node10617 node12023 +def node12025 : Tree Nat := .node node11693 node12024 +def node12026 : Tree Nat := .leaf 5109351192408882717840339505059633591674614784055497869506061819166297997548295769847095622969637612053256506785769224382504880203970551730380982982620477569793304890347454473720791490295729206142872039396981986783619422432588828093555565271268312930894356668705772101778880705811437578092544000 +def node12027 : Tree Nat := .node node5461 node12026 +def node12028 : Tree Nat := .node node9125 node12027 +def node12029 : Tree Nat := .node node10996 node12028 +def node12030 : Tree Nat := .node node11335 node12029 +def node12031 : Tree Nat := .node node12030 node11006 +def node12032 : Tree Nat := .node node12025 node12031 +def node12033 : Tree Nat := .leaf 1107913932560474553181223067572389585967068949556785806716538814129167597559328825943630938223989230855846491671124890032459229488767770427014875151758665134532774054698639111510402494541915070941465367508678529626259258980483562652201204381587687610123634059319730886754172928 +def node12034 : Tree Nat := .node node6288 node12033 +def node12035 : Tree Nat := .node node9975 node12034 +def node12036 : Tree Nat := .node node12035 node9979 +def node12037 : Tree Nat := .node node10635 node12036 +def node12038 : Tree Nat := .node node11708 node12037 +def node12039 : Tree Nat := .leaf 67625827286389648917836620123883785920403991263542813449640896695818026931586561208212498641500081078142101024501598751920455723722189773456735854813226846876208863684560629479873248871271623631055086506912065652903889286726647576112414514332110760473554541354718549639168 +def node12040 : Tree Nat := .node node12039 node57 +def node12041 : Tree Nat := .node node10324 node12040 +def node12042 : Tree Nat := .node node11364 node12041 +def node12043 : Tree Nat := .node node11018 node12042 +def node12044 : Tree Nat := .node node11715 node12043 +def node12045 : Tree Nat := .node node12038 node12044 +def node12046 : Tree Nat := .node node12032 node12045 +def node12047 : Tree Nat := .leaf 1247400193459199986152164510103367905614711427706494166828336535981415444438633317194506772553692147037166168243022088950872216915566507547980881828931469071221938326463907540589736960691995929233239056114203588821445480271597077319670276107110710965097161555028672501121900967563365693039872 +def node12048 : Tree Nat := .node node7454 node12047 +def node12049 : Tree Nat := .node node9691 node12048 +def node12050 : Tree Nat := .node node11721 node12049 +def node12051 : Tree Nat := .node node10334 node12050 +def node12052 : Tree Nat := .leaf 154581648341097553379273256685340001420955698403840020567358626360381160410589000415411483288094452491955815753243561095475733911724743393898341280385841322343170598447613952 +def node12053 : Tree Nat := .node node12052 node11031 +def node12054 : Tree Nat := .node node9437 node12053 +def node12055 : Tree Nat := .leaf 16905425059318903613520611904066424622426050758749011400102100889924812885747136871813394991348110207523385048760997704053789641535676252208181422821432782405553638782025182643101563030201514997035154057833131352659630772335810598110683467618369405869214564698174397612032 +def node12056 : Tree Nat := .node node12055 node10640 +def node12057 : Tree Nat := .node node9696 node12056 +def node12058 : Tree Nat := .node node12054 node12057 +def node12059 : Tree Nat := .leaf 1707011694817242694210710703124117431539072329783553111974590583600093394321036967079868476543243634344037343009266289163416437119001075052696473895004967876628086372186217638463012653663477607048890266416520696674028429109558420699385348227072 +def node12060 : Tree Nat := .node node3453 node12059 +def node12061 : Tree Nat := .node node12060 node7055 +def node12062 : Tree Nat := .node node11726 node12061 +def node12063 : Tree Nat := .node node12058 node12062 +def node12064 : Tree Nat := .node node12051 node12063 +def node12065 : Tree Nat := .leaf 81749619078542123485583515568074848124524764480154453050451147512218363489450319349723321766952234392809622444365851486372738004061956979062088871968318583757114790585726077891330913640282820820281264647676965297441868785739491215843235107072993821807188283893099315475221445473565277991184629760 +def node12066 : Tree Nat := .node node7064 node12065 +def node12067 : Tree Nat := .node node9710 node12066 +def node12068 : Tree Nat := .node node11732 node12067 +def node12069 : Tree Nat := .node node11384 node12068 +def node12070 : Tree Nat := .leaf 276978484171880916803921705436224301013624923980139280626413378959201822587539294608810929125743781431500803317101062222427779168468223293033246585747360237535878494339419082639394554297317503538314799297817472860181114505984460581563540286897170236140494225796606619099594752 +def node12071 : Tree Nat := .node node5022 node12070 +def node12072 : Tree Nat := .node node9456 node12071 +def node12073 : Tree Nat := .node node12072 node10002 +def node12074 : Tree Nat := .node node11738 node12073 +def node12075 : Tree Nat := .node node12069 node12074 +def node12076 : Tree Nat := .node node12064 node12075 +def node12077 : Tree Nat := .leaf 34959599509857130376772047909570245155022077753222839825210875296375213171922306004033705508544889465468809724550668474885245115280842633998922133175927982521286889181138305561319029099389471544354550865579337891051476836229457177931706753869676544 +def node12078 : Tree Nat := .node node2297 node12077 +def node12079 : Tree Nat := .node node12078 node9463 +def node12080 : Tree Nat := .node node10655 node12079 +def node12081 : Tree Nat := .leaf 319334449525555169865025974007202275366151173374819597363186706524146987018843596864935283165944279404189344175528009230318985492293616239624594468272226773088845657203073328333281744285698479944242709119205759926437954875814482352589913014993921556824835786104066240602556996179139372035080192 +def node12082 : Tree Nat := .node node9181 node12081 +def node12083 : Tree Nat := .node node11746 node12082 +def node12084 : Tree Nat := .node node11744 node12083 +def node12085 : Tree Nat := .node node12080 node12084 +def node12086 : Tree Nat := .leaf 5109351192408882717840339505059633591674614784055497869506061819166297997548295769847095622969637612053256506785769224382504880203970551730380982982620477569793304895892793861962421209452557574429039446269856137535252572773547989322798180882519559010843168876984928296561907091528388550628212736 +def node12087 : Tree Nat := .node node12086 node11047 +def node12088 : Tree Nat := .node node11751 node12087 +def node12089 : Tree Nat := .node node11046 node12088 +def node12090 : Tree Nat := .leaf 7507516828804700229971157695509256861311759593549503536677899755757915781054346438889718375456342544074608081732840466270766847890821126878143830048041579960724746316194113408227089148402217185592680781189247272750829451392917509099637858269405020099219456 +def node12091 : Tree Nat := .node node1929 node12090 +def node12092 : Tree Nat := .node node12091 node8761 +def node12093 : Tree Nat := .node node12092 node11410 +def node12094 : Tree Nat := .node node12089 node12093 +def node12095 : Tree Nat := .node node12085 node12094 +def node12096 : Tree Nat := .leaf 1589778526533276691354858284486867739076177829804801943941608182548409853601743272989688933959998259887211368541143037507581481643504903925946971770410976554043879198167170348220849464676920541955449295530325964379364765480450977103872 +def node12097 : Tree Nat := .node node2500 node12096 +def node12098 : Tree Nat := .leaf 27967679607885704301190218685229334463595448410322902860782665809895227293410181258444742214239344020615132732046787126046305551195387940799412837696615621493374382715549634138280542768195567951294687821996705686526188365802745806805247466575757312 +def node12099 : Tree Nat := .node node12098 node9468 +def node12100 : Tree Nat := .node node12097 node12099 +def node12101 : Tree Nat := .node node10663 node12100 +def node12102 : Tree Nat := .node node12101 node11759 +def node12103 : Tree Nat := .leaf 6191329402440458580124204415614330367293195005243462324135270677371812121923809804928366746096941114750792396037215122373783618425615347371078926432261357668711686303989550351837176747923827081311259996937125955572048829820250122014605073489147239388195107112572944384 +def node12104 : Tree Nat := .node node2102 node12103 +def node12105 : Tree Nat := .node node12104 node11427 +def node12106 : Tree Nat := .leaf 326998476314168493941780206738569259224467206527547894855795934816918678851073338672775595878048928875797373795235685048747104071686674917464483111504298026870677066712116810148164925357929448703744712739184842602304697219071257102425605626399705492534248723463939152002608556315878562730915528704 +def node12107 : Tree Nat := .node node12106 node57 +def node12108 : Tree Nat := .node node7913 node12107 +def node12109 : Tree Nat := .node node12105 node12108 +def node12110 : Tree Nat := .node node11767 node12109 +def node12111 : Tree Nat := .node node12102 node12110 +def node12112 : Tree Nat := .node node12095 node12111 +def node12113 : Tree Nat := .node node12076 node12112 +def node12114 : Tree Nat := .node node12046 node12113 +def node12115 : Tree Nat := .node node12019 node12114 +def node12116 : Tree Nat := .node node11933 node12115 +def node12117 : Tree Nat := .leaf 18193571394149040561360367091109380114889434398142106460589332854012113894353465589178387984679552247368806900677816877496866991626658398559972763374162670459579824052566071486510694497216058519322833192234146668900418529731280896 +def node12118 : Tree Nat := .node node12117 node57 +def node12119 : Tree Nat := .node node11438 node12118 +def node12120 : Tree Nat := .node node9229 node12119 +def node12121 : Tree Nat := .node node10352 node12120 +def node12122 : Tree Nat := .node node11071 node12121 +def node12123 : Tree Nat := .leaf 1516130949514134710813644652732515379182876271364913180585842248858900209670531166458353970581876385272497585689702815984758180096362672097643961816834904116993409713371913743737469651179345565500616826166861951898180351936180992 +def node12124 : Tree Nat := .leaf 76283967404910271121540606155089898734733648345126935848922254290153127561916032983482781805165935779554722852747892499615706237147338157909284810625311034295863866517190427442866673658125873106498871550178228067420612200765812459403680843875730875634615658869971286990968243000491114496 +def node12125 : Tree Nat := .node node12123 node12124 +def node12126 : Tree Nat := .node node9510 node12125 +def node12127 : Tree Nat := .node node10683 node12126 +def node12128 : Tree Nat := .node node12127 node11783 +def node12129 : Tree Nat := .node node11779 node12128 +def node12130 : Tree Nat := .node node12122 node12129 +def node12131 : Tree Nat := .leaf 503820925841965910293903145710484129446837736164208910110436259998038510964770243430138498201532542156933485869433164765803114760238270660481417446375105010440475821427886356946309731287924675203273040506489884413804450500112958696867850417775295755446130583797760 +def node12132 : Tree Nat := .node node126 node12131 +def node12133 : Tree Nat := .node node12132 node10056 +def node12134 : Tree Nat := .node node12133 node8811 +def node12135 : Tree Nat := .node node12134 node11793 +def node12136 : Tree Nat := .leaf 2323463919496536035621972653359219625205094065092803842274643530181157276813131833664325491400244331789392679361098607690583358868782660090431376684494546007279524707002217887874048689586946916228261299741648447918429264980456569383200950547595632128817814582259753908894414070091776 +def node12137 : Tree Nat := .node node12136 node7965 +def node12138 : Tree Nat := .node node10061 node12137 +def node12139 : Tree Nat := .node node12138 node10369 +def node12140 : Tree Nat := .leaf 1516130949514134710813644652732515379182876271364913180585842248858900209670531166458353970581876374181818809206443377671101443524027858351895660313568603435075087254886682521234977491281721148942304436600809180464278406864843520 +def node12141 : Tree Nat := .node node172 node12140 +def node12142 : Tree Nat := .node node12141 node11797 +def node12143 : Tree Nat := .leaf 572778078369499224088375678951108638011287396263498246212912731873199370030112045970591355774519253321541817541313941550953993082870643211586713456563448667385049704462328463260653386992258808895520868586472919786367029038635876478250859922593595526912 +def node12144 : Tree Nat := .node node3425 node12143 +def node12145 : Tree Nat := .leaf 1189613526782226450238449998519920448105008161327515567262811058846901674017267129637933460007287316255036903541547293173618685941066149775815004508891521095407805756686735105008244777635761260989313774653885226222323281571005295993712433121897000993165167330851507573510312914805850112 +def node12146 : Tree Nat := .node node12145 node57 +def node12147 : Tree Nat := .node node12144 node12146 +def node12148 : Tree Nat := .node node12142 node12147 +def node12149 : Tree Nat := .node node12139 node12148 +def node12150 : Tree Nat := .node node12135 node12149 +def node12151 : Tree Nat := .leaf 18193571394149040561360367091109380114889434398142106460589332854012113894353465589175266236129236255137425303448023711191118393483993427409113606414537298720760058432445765383447202526056231588201406286929095041550706297173704704 +def node12152 : Tree Nat := .node node203 node12151 +def node12153 : Tree Nat := .node node12152 node11461 +def node12154 : Tree Nat := .node node12153 node11804 +def node12155 : Tree Nat := .node node11089 node12154 +def node12156 : Tree Nat := .leaf 4830671904896301379504992970814506897332932672057762667996819245626467011940833203586777025329286938503929703817165119770025762077839773213924459676247988457417792607813632 +def node12157 : Tree Nat := .node node219 node12156 +def node12158 : Tree Nat := .node node12157 node7981 +def node12159 : Tree Nat := .leaf 76135265714062492815260799905274908678720522324960996303657035327925677504964849789536381070309952849989333960392650997022229099042509126951084810642178899521492656483850087487287234780075206121609317111233055663941252674237940596373841310641439170324119213891620878149962195022454469376 +def node12160 : Tree Nat := .node node12159 node10710 +def node12161 : Tree Nat := .node node8834 node12160 +def node12162 : Tree Nat := .node node12158 node12161 +def node12163 : Tree Nat := .node node12162 node11810 +def node12164 : Tree Nat := .node node12155 node12163 +def node12165 : Tree Nat := .node node12150 node12164 +def node12166 : Tree Nat := .node node12130 node12165 +def node12167 : Tree Nat := .leaf 2359768043238669411178565976067957431848923659859878902310184835340237859263337018565330577203374257958592305587297806397022790745020876463573098359235501453371881629857340471159080207222147301962469149407212194197457492016677190809572009236497008532187719489613567680587173416075264 +def node12168 : Tree Nat := .node node11815 node12167 +def node12169 : Tree Nat := .node node8420 node12168 +def node12170 : Tree Nat := .node node10725 node12169 +def node12171 : Tree Nat := .node node12170 node11479 +def node12172 : Tree Nat := .node node11475 node12171 +def node12173 : Tree Nat := .leaf 145216494968533502226373290834951226575318379068300240142165220636322329800820739604020343212515268878632062202515439954994665169202503316858289696001892851400280454900170947361585177931714663912474832803480791236010050160944213747330903651554702382200002569298941302697973065777152 +def node12174 : Tree Nat := .node node12173 node11114 +def node12175 : Tree Nat := .node node8015 node12174 +def node12176 : Tree Nat := .node node12175 node11828 +def node12177 : Tree Nat := .node node11495 node12176 +def node12178 : Tree Nat := .node node11825 node12177 +def node12179 : Tree Nat := .node node12172 node12178 +def node12180 : Tree Nat := .leaf 5065326623348544115315823303057860674705112983362280110186628569047549059522166747181779100595557846234505344041632918537828542955602000617058032358844021223164205165897702178816 +def node12181 : Tree Nat := .node node392 node12180 +def node12182 : Tree Nat := .node node12181 node11501 +def node12183 : Tree Nat := .node node12182 node11505 +def node12184 : Tree Nat := .node node11836 node12183 +def node12185 : Tree Nat := .leaf 9293855677986144142487890613436878500820376260371215369098574120724629107252527334657301965600977191203693086967404522819061497001666112622917184171282259642202073533992380652390171351623595013349463439289898043314527981374761772903742212713630979009024483442244619819623594802020352 +def node12186 : Tree Nat := .node node11841 node12185 +def node12187 : Tree Nat := .node node8890 node12186 +def node12188 : Tree Nat := .node node11840 node12187 +def node12189 : Tree Nat := .leaf 74520868430434028887152659238669356519051541652695249560657262668838071114776102843546300741664917805417005696481198229107034537465046605435970250410695885445903674391255070723486096672071466992822166434230828353582458884959319905536 +def node12190 : Tree Nat := .node node423 node12189 +def node12191 : Tree Nat := .node node12190 node11509 +def node12192 : Tree Nat := .node node12191 node10092 +def node12193 : Tree Nat := .node node12188 node12192 +def node12194 : Tree Nat := .node node12184 node12193 +def node12195 : Tree Nat := .leaf 99361157907245371849560987941107905403976910044883315717472592613297421091611439095159130579631458390161767543091545130448897298616679106537146603808803104180288699637518030685173029996466195482261681315332287111494177375402361618432 +def node12196 : Tree Nat := .node node454 node12195 +def node12197 : Tree Nat := .node node12196 node11136 +def node12198 : Tree Nat := .node node12197 node10411 +def node12199 : Tree Nat := .node node11134 node12198 +def node12200 : Tree Nat := .leaf 9661343809792602759010042101885447055194757977017650297393245439118108529138995364806309480844617497198337259817405870259684399846328198589058304412868221246552445365649408 +def node12201 : Tree Nat := .node node12200 node8904 +def node12202 : Tree Nat := .node node8473 node12201 +def node12203 : Tree Nat := .node node12202 node10766 +def node12204 : Tree Nat := .node node11850 node12203 +def node12205 : Tree Nat := .node node12199 node12204 +def node12206 : Tree Nat := .node node12194 node12205 +def node12207 : Tree Nat := .node node12179 node12206 +def node12208 : Tree Nat := .node node12166 node12207 +def node12209 : Tree Nat := .leaf 594806763391113225119224999259960224052504080663757783634437791322475659147596415382370055306879763629699499839466613801220478754588937184032106553125762145915121314990004295789015126710127300958177274435939052277239855856968617161158221801359004295756955394271207954513114305205895168 +def node12210 : Tree Nat := .node node9803 node12209 +def node12211 : Tree Nat := .node node6846 node12210 +def node12212 : Tree Nat := .node node11540 node12211 +def node12213 : Tree Nat := .leaf 290432989937067004452746581669902453150636758136600480284330441272644659601641479208040686425030537224634899430697174372561541864014846623516971157773352294985474112870201343622644356390135675708639147848775947400538788872895553909653394663595669980631660029670569127482378260447232 +def node12214 : Tree Nat := .node node12213 node8492 +def node12215 : Tree Nat := .node node6465 node12214 +def node12216 : Tree Nat := .node node12215 node11864 +def node12217 : Tree Nat := .node node12212 node12216 +def node12218 : Tree Nat := .node node11537 node12217 +def node12219 : Tree Nat := .node node11861 node12218 +def node12220 : Tree Nat := .leaf 30750788930784052141961861920805917214380440082589217766573459895919230378495282122721611875165072323090973711248027490353551036261722796287033747819087500752991032154127481047726496709629813071351000413519546892327893859094639502459809516407994902678004039680 +def node12221 : Tree Nat := .node node3473 node12220 +def node12222 : Tree Nat := .node node12221 node8508 +def node12223 : Tree Nat := .node node11880 node12222 +def node12224 : Tree Nat := .node node11876 node12223 +def node12225 : Tree Nat := .node node11553 node12224 +def node12226 : Tree Nat := .leaf 4830671904896301379504992970814506897332932672057762667997434901973285675678525063588341769294991309430030726421351811854467101480519417129727807586480565273312595424903168 +def node12227 : Tree Nat := .node node12226 node8945 +def node12228 : Tree Nat := .node node9834 node12227 +def node12229 : Tree Nat := .node node12228 node10143 +def node12230 : Tree Nat := .node node11563 node12229 +def node12231 : Tree Nat := .node node11888 node12230 +def node12232 : Tree Nat := .node node12225 node12231 +def node12233 : Tree Nat := .node node12219 node12232 +def node12234 : Tree Nat := .leaf 145216494968533502226373290834951226575318379068300240142165220636322329800820739604020343212515268878632062202515439954994665169202503316858289696001892851400280454900161327731166136310813228599950383679016660440289721682753796683511507723387832946015575258201557288964454353272832 +def node12235 : Tree Nat := .node node10159 node12234 +def node12236 : Tree Nat := .node node11577 node12235 +def node12237 : Tree Nat := .node node10482 node12236 +def node12238 : Tree Nat := .leaf 12129047596099504011017929674992157803890024778835828372130977613867181652982292329630349219413392409641905476690684583420349896935984927863485666089227332587581674898458765615624779392593624902202350286878315594097842747172978688 +def node12239 : Tree Nat := .node node12238 node57 +def node12240 : Tree Nat := .node node11898 node12239 +def node12241 : Tree Nat := .node node11185 node12240 +def node12242 : Tree Nat := .node node12237 node12241 +def node12243 : Tree Nat := .node node11896 node12242 +def node12244 : Tree Nat := .leaf 458222462695599379270700543123871994649449568634787237553785692458956874129784670072636529748425157355181179828491938909568233393724009090772130464238696934527463584720883257237488359460168530644722507743922583535492172995357844018000561401056223883264 +def node12245 : Tree Nat := .node node831 node12244 +def node12246 : Tree Nat := .node node12245 node11584 +def node12247 : Tree Nat := .node node12246 node11909 +def node12248 : Tree Nat := .node node11906 node12247 +def node12249 : Tree Nat := .leaf 123003155723136208567847447683223665156030184372322033465157915869473587451385680080856095538856044158426243859888522334114484606338942965396231338480162505923917145054749748818687743027363254406311161071117038947561126299864663249285549448946196926050305310720 +def node12250 : Tree Nat := .node node847 node12249 +def node12251 : Tree Nat := .node node12250 node10171 +def node12252 : Tree Nat := .leaf 3032261899028269421627289305465030758365752542729826361171684497717800419334836753154315408764558384314447453886436720437185572799361960167497369359410128186253065049495472267790605641094776384964599911410184619951143017827585024 +def node12253 : Tree Nat := .node node12252 node10827 +def node12254 : Tree Nat := .node node11589 node12253 +def node12255 : Tree Nat := .node node12251 node12254 +def node12256 : Tree Nat := .node node12255 node11920 +def node12257 : Tree Nat := .node node12248 node12256 +def node12258 : Tree Nat := .node node12243 node12257 +def node12259 : Tree Nat := .leaf 3485195879244804053432958980038829437807641097639205763411965295271735915219697750496488237100366450943945018000315455713503494388731855478314041500641787454767702749096393470183740810708344349238273511033250576414655058427703606023476555525700397361701213898020527174769958715424768 +def node12260 : Tree Nat := .node node12259 node10839 +def node12261 : Tree Nat := .node node10506 node12260 +def node12262 : Tree Nat := .leaf 76172441136774437391830751467728656192723803830002481363854229307949803862137389237559315850483224199314338460589680571265527572317748723271341063158056025937770671217532987257883458754277548335649548977503485014801150051615627711347131880018751679397273588991475693187602559226234273792 +def node12263 : Tree Nat := .node node8111 node12262 +def node12264 : Tree Nat := .node node10189 node12263 +def node12265 : Tree Nat := .node node12261 node12264 +def node12266 : Tree Nat := .leaf 594806763391113225119224999259960224052504080663757783634437791322475659147596415382370055306879763629699499839466613801220478754588937235178834801502978864871210327921241049174047096133014636634604900938029621100279775908063809753410677283963443788885661061720108897786646011628748800 +def node12267 : Tree Nat := .node node12266 node57 +def node12268 : Tree Nat := .node node7291 node12267 +def node12269 : Tree Nat := .node node11926 node12268 +def node12270 : Tree Nat := .node node12265 node12269 +def node12271 : Tree Nat := .node node11599 node12270 +def node12272 : Tree Nat := .leaf 95169082142578116019075999881593635848400652906201245379572431258119228604046174976825206305784807366769573759788240919589747585099447469262738840521428308533936875822204889595544268067565326921998207828913049868524311125291712297082781339824636454771693684758144826933445140461322816512 +def node12273 : Tree Nat := .node node12272 node10856 +def node12274 : Tree Nat := .node node10519 node12273 +def node12275 : Tree Nat := .node node10855 node12274 +def node12276 : Tree Nat := .node node12275 node11221 +def node12277 : Tree Nat := .node node11217 node12276 +def node12278 : Tree Nat := .node node12271 node12277 +def node12279 : Tree Nat := .node node12258 node12278 +def node12280 : Tree Nat := .node node12233 node12279 +def node12281 : Tree Nat := .node node12208 node12280 +def node12282 : Tree Nat := .leaf 874043331861891298246386972727742472049734933136564395875795372115744168700406918896976792458411889439773889085800556002718165009584538412742425480086097633725891556696901456678969321261531748640016526382896142839375400953339336984107565491159040 +def node12283 : Tree Nat := .node node11622 node12282 +def node12284 : Tree Nat := .node node10540 node12283 +def node12285 : Tree Nat := .node node12284 node10892 +def node12286 : Tree Nat := .leaf 5065326623348544115315823303057860674705112983362280110186628569048751513324546949794458514661113986792521693506673978311630675933026491637916711881897435110337207023325029597184 +def node12287 : Tree Nat := .node node12286 node8594 +def node12288 : Tree Nat := .node node8593 node12287 +def node12289 : Tree Nat := .node node12288 node11245 +def node12290 : Tree Nat := .node node12285 node12289 +def node12291 : Tree Nat := .node node11242 node12290 +def node12292 : Tree Nat := .node node11942 node12291 +def node12293 : Tree Nat := .leaf 2015283703367863641175612582841936517787350944656835640441746215724148601621265841204650329199635253963361738401575054429896032048337003206849961625116520064232442010467426914654152817393427271595203822211341964674986046381010389129515789313957419189127451068334080 +def node12294 : Tree Nat := .node node1131 node12293 +def node12295 : Tree Nat := .node node12294 node10240 +def node12296 : Tree Nat := .node node12295 node9024 +def node12297 : Tree Nat := .node node12296 node11947 +def node12298 : Tree Nat := .leaf 3032261899028269421627289305465030758365752542729826361171684497717800419334836753154315408764557674511005758957832668363154432169933880439606073150366884543480427706440674027631107407646813725232606979250507094079837767045532672 +def node12299 : Tree Nat := .node node1177 node12298 +def node12300 : Tree Nat := .node node12299 node11955 +def node12301 : Tree Nat := .leaf 458222462695599379270700543123871994649449568634787237553785692458956873611095223962512409934374174393786035951936159879263620894266842879440529037625178634564082466332908971212752533047569882845328623317450670049632818731112383135352822465068651311104 +def node12302 : Tree Nat := .node node3483 node12301 +def node12303 : Tree Nat := .node node12302 node6951 +def node12304 : Tree Nat := .node node12300 node12303 +def node12305 : Tree Nat := .node node11953 node12304 +def node12306 : Tree Nat := .node node12297 node12305 +def node12307 : Tree Nat := .leaf 12129047596099504011017929674992157803890024778835828372130977613867181652982292329430557312193168906833483253983921939852439615805426774208499620673203541303116675210759175019561293238364701310432164162292815937260000909560119296 +def node12308 : Tree Nat := .node node1208 node12307 +def node12309 : Tree Nat := .node node12308 node11641 +def node12310 : Tree Nat := .node node12309 node11962 +def node12311 : Tree Nat := .node node10253 node12310 +def node12312 : Tree Nat := .leaf 9661343809792602759010042101885447055194757977017650297390782813730833874188227924800050504981800013493933169400659101921919042235609622925844912771937914000987632606773248 +def node12313 : Tree Nat := .node node1224 node12312 +def node12314 : Tree Nat := .node node12313 node11646 +def node12315 : Tree Nat := .leaf 76135265714062492815260799905274908678720522324960996303657035327925677504964849789536381070309952849989333960392650997022229099042509126951084810642178896682278889704135671278991110217557493802697751926396882689370162124865721403413203317707647319685191242163001510859590808086121558784 +def node12316 : Tree Nat := .node node6967 node12315 +def node12317 : Tree Nat := .node node9043 node12316 +def node12318 : Tree Nat := .node node12314 node12317 +def node12319 : Tree Nat := .leaf 9293855677986144142487890613436878500820376260371215369098574120724629107252527334657301965600977191203693086967404522819061497001666112622917184171282259642202073533992688480563580683492440943350245811272750228777578492676855118945962882414970800966926157397360908227570996210565120 +def node12320 : Tree Nat := .node node12319 node11965 +def node12321 : Tree Nat := .node node8626 node12320 +def node12322 : Tree Nat := .node node12321 node11970 +def node12323 : Tree Nat := .node node12318 node12322 +def node12324 : Tree Nat := .node node12311 node12323 +def node12325 : Tree Nat := .node node12306 node12324 +def node12326 : Tree Nat := .node node12292 node12325 +def node12327 : Tree Nat := .leaf 1218164251424999885044172798484398538859528357199375940933009175582052615232957565839340473621023836886952176315566115096067951638125184974034298652736718859084780437757396578246082786885444631912441287999130461289158607842895735483310383729351685611114214220885630047123391638036440700160 +def node12328 : Tree Nat := .node node12327 node57 +def node12329 : Tree Nat := .node node11659 node12328 +def node12330 : Tree Nat := .node node11985 node12329 +def node12331 : Tree Nat := .node node11982 node12330 +def node12332 : Tree Nat := .node node11657 node12331 +def node12333 : Tree Nat := .leaf 76283967404910271121540606155089898734733648345126935848922254290153127561916032983482781805165935779554722852747892499615706237147338157909284810625311034650765587364654729468903689228440587146362817198282749689241998519437339858523760592992454856964481655336051125753903895625882140672 +def node12334 : Tree Nat := .node node12333 node10939 +def node12335 : Tree Nat := .node node6987 node12334 +def node12336 : Tree Nat := .node node10276 node12335 +def node12337 : Tree Nat := .node node12336 node11298 +def node12338 : Tree Nat := .node node11993 node12337 +def node12339 : Tree Nat := .node node12332 node12338 +def node12340 : Tree Nat := .leaf 10130653246697088230631646606115722181863803817440407715106216230888518479123450532565909768909060739904382642170086059812825659525019806325900133735901586391714287587065325420544 +def node12341 : Tree Nat := .node node1397 node12340 +def node12342 : Tree Nat := .node node12341 node11672 +def node12343 : Tree Nat := .node node12342 node11676 +def node12344 : Tree Nat := .node node11999 node12343 +def node12345 : Tree Nat := .leaf 49680578953622685924770631215738549501662378209921916008415194904008881257624068754541134523018283922852650772493744566210448559112831450443580637529789212981358512632215368908222036229456831189872657935589920862824415999278694050304 +def node12346 : Tree Nat := .node node1428 node12345 +def node12347 : Tree Nat := .node node12346 node8660 +def node12348 : Tree Nat := .leaf 74520868430434028887152659238669356519051541652695249560657262668838071114776102843571874105789106413776483740987663847483727053449758049103808464223946930730315194351280618319782222899812769212568730787064552804054095650812531332352 +def node12349 : Tree Nat := .node node12348 node57 +def node12350 : Tree Nat := .node node9933 node12349 +def node12351 : Tree Nat := .node node12347 node12350 +def node12352 : Tree Nat := .node node10954 node12351 +def node12353 : Tree Nat := .node node12344 node12352 +def node12354 : Tree Nat := .leaf 198722315814490743699121975882215810807953820089766631434945185226594842183222878190318257385689306000999451016010886474600973170804566509196642568185123939732536141181537969346561592476234663552922753522997202529924076087621787320320 +def node12355 : Tree Nat := .node node1459 node12354 +def node12356 : Tree Nat := .node node12355 node11681 +def node12357 : Tree Nat := .node node12356 node9378 +def node12358 : Tree Nat := .node node12005 node12357 +def node12359 : Tree Nat := .leaf 99361157907245371849560987941107905403976910044883315717472592613297421091611439095159130579631458481016608080042406449114373284617245900742316689723560639366563597217429044859913445770347534702707376410647565266018874403494746390528 +def node12360 : Tree Nat := .leaf 1218164251424999885044172798484398538859528357199375940933009175582052615232957565839340473621023836886952176315566115096067951638125184974034198756783108747333376226646043196924298831744879352835613794976422449393516375343051885688012351986274571149318329127823337297294972717117634270464 +def node12361 : Tree Nat := .node node12359 node12360 +def node12362 : Tree Nat := .node node9093 node12361 +def node12363 : Tree Nat := .node node12009 node12362 +def node12364 : Tree Nat := .node node12363 node12014 +def node12365 : Tree Nat := .node node12358 node12364 +def node12366 : Tree Nat := .node node12353 node12365 +def node12367 : Tree Nat := .node node12339 node12366 +def node12368 : Tree Nat := .node node12326 node12367 +def node12369 : Tree Nat := .leaf 540973599882921212264795939754513005075299661860988438659038499017268058136175524568853356593652864839094194135635460301924269586378058566697957041105095445762385903463366169913988258213803045910824885683271517381634772424575713672810577919747311102109271901786895292563456 +def node12370 : Tree Nat := .node node1508 node12369 +def node12371 : Tree Nat := .node node12370 node10296 +def node12372 : Tree Nat := .node node12371 node9107 +def node12373 : Tree Nat := .node node12372 node11692 +def node12374 : Tree Nat := .leaf 2359768043238669411178565976067957431848923659859878902310184835340237859263337018565330577203374257958592305587297806397022790745020876463573098359235501453371881629857340471159080207222147301966447735298490487334700550001851757530375658442875790271711431304758843656687440420340224 +def node12375 : Tree Nat := .node node12374 node10614 +def node12376 : Tree Nat := .node node10305 node12375 +def node12377 : Tree Nat := .node node12376 node9387 +def node12378 : Tree Nat := .leaf 304541062856249971261043199621099634714882089299843985264302655741527332511219803125319786443754185979618882414663951182761660322270111624203294323563883250966084710467025203516123417300006033167459149873939698874931574565762963738209418796276429954152374217219122619948757125088738847232 +def node12379 : Tree Nat := .node node12378 node57 +def node12380 : Tree Nat := .node node11695 node12379 +def node12381 : Tree Nat := .node node12022 node12380 +def node12382 : Tree Nat := .node node12377 node12381 +def node12383 : Tree Nat := .node node12373 node12382 +def node12384 : Tree Nat := .leaf 76172441136774437391830751467728656192723803830002481363854229307949803862137389237559315850483224199314338460589680571265527572317748723271341063158056026026496101429399062764392712646856226845615535389529615420256496631283509561127151817297932674729740088107996861804156087011756736512 +def node12385 : Tree Nat := .leaf 1189613526782226450238449998519920448105008161327515567262811058846901674017267129637933460007287316255036903541547293173618685941066149775015836880010627084174116865859684530736603653113528646369369592989790061084463282820206933609458488504981306626084747351063167372885728720374988800 +def node12386 : Tree Nat := .node node12384 node12385 +def node12387 : Tree Nat := .node node9130 node12386 +def node12388 : Tree Nat := .node node11001 node12387 +def node12389 : Tree Nat := .node node12388 node9961 +def node12390 : Tree Nat := .node node12030 node12389 +def node12391 : Tree Nat := .node node12383 node12390 +def node12392 : Tree Nat := .leaf 503820925841965910293903145710484129446837736164208910110436259998038510964770243430139004734194759075019241778596213003248306709241229942329561447513983263957493998691851164935683157044063371234353521559856876009394710726590972231393499091356411507271603595509760 +def node12393 : Tree Nat := .node node1648 node12392 +def node12394 : Tree Nat := .node node12393 node11702 +def node12395 : Tree Nat := .node node12394 node11706 +def node12396 : Tree Nat := .node node10320 node12395 +def node12397 : Tree Nat := .leaf 4646927838993072071243945306718439250410188130185607684549287060362314553626263667328650982800488595594163456063197816929671753413226253971080721071308098374252355411223716097734838368819214375883592122027811961759143917898729683433125674166091705734300660506070185298034292024147968 +def node12398 : Tree Nat := .node node6284 node12397 +def node12399 : Tree Nat := .node node9668 node12398 +def node12400 : Tree Nat := .node node9972 node12399 +def node12401 : Tree Nat := .leaf 1876879207201175057492789423877314215327939898387375884169474870502863154307002597670746810699833783181684988276774827749547650341975951266725714184144871273491539821231997235574067496290267391565821383658120519521784608966345323633711298692977622027077120 +def node12402 : Tree Nat := .node node1679 node12401 +def node12403 : Tree Nat := .node node12402 node12034 +def node12404 : Tree Nat := .leaf 123003155723136208567847447683223665156030184372322033465157915869473587451385680080856095418089246564136920588158775742489880096997463912070137630441560898063943948505986482062632537342282693079323160086674002154902418142271298033763992427819743179801593118720 +def node12405 : Tree Nat := .node node3492 node12404 +def node12406 : Tree Nat := .leaf 49680578953622685924770631215738549501662378209921916008415194904008881257624068754547527864049331074942520283620360970804621688109009311360540190983101974302461392622221755807296067786392156744809299348316905633869051973898017483264 +def node12407 : Tree Nat := .node node12406 node57 +def node12408 : Tree Nat := .node node12405 node12407 +def node12409 : Tree Nat := .node node12403 node12408 +def node12410 : Tree Nat := .node node12400 node12409 +def node12411 : Tree Nat := .node node12396 node12410 +def node12412 : Tree Nat := .leaf 198722315814490743699121975882215810807953820089766631434945185226594842183222878190318257385689306023713161150248601804267342167304708207747935089663813323529104865576515722890246696419704998358034177296826041411368364178711678812160 +def node12413 : Tree Nat := .leaf 304541062856249971261043199621099634714882089299843985264302655741527332511219803125319786443754185979618882414663951182761660322270111624203269349575480723028233657689186858185677428514864713398252276618262695901021016440802001289384910860507151338703402923671139828839981970911785953792 +def node12414 : Tree Nat := .node node12412 node12413 +def node12415 : Tree Nat := .node node9679 node12414 +def node12416 : Tree Nat := .node node9414 node12415 +def node12417 : Tree Nat := .node node12416 node12042 +def node12418 : Tree Nat := .node node11715 node12417 +def node12419 : Tree Nat := .node node12411 node12418 +def node12420 : Tree Nat := .node node12391 node12419 +def node12421 : Tree Nat := .leaf 290432989937067004452746581669902453150636758136600480284330441272644659601641479208040686425030537224634899430697174372561541864014846623516971157773352294985474112870198938715039595984910316880508035567659914701608706753347949643698545681553952621585553201896223123767523605610496 +def node12422 : Tree Nat := .node node12055 node12421 +def node12423 : Tree Nat := .node node9696 node12422 +def node12424 : Tree Nat := .node node12054 node12423 +def node12425 : Tree Nat := .node node12424 node12062 +def node12426 : Tree Nat := .node node12051 node12425 +def node12427 : Tree Nat := .leaf 95169082142578116019075999881593635848400652906201245379572431258119228604046174976825206305784807366769573759788240919589747585099447469262738840521428126824255801920482252264592296066431738511658035999397979495974515965469683947601949792061958013880303494127588517884051084276553272320 +def node12428 : Tree Nat := .node node7071 node12427 +def node12429 : Tree Nat := .node node9715 node12428 +def node12430 : Tree Nat := .node node11737 node12429 +def node12431 : Tree Nat := .leaf 10130653246697088230631646606115722181863803817440407715106216230965475522475783499777392269104653735617429007932713885336162170080187231660855623211320075170786390699815584399360 +def node12432 : Tree Nat := .node node12431 node12070 +def node12433 : Tree Nat := .node node9456 node12432 +def node12434 : Tree Nat := .node node12433 node10002 +def node12435 : Tree Nat := .node node12430 node12434 +def node12436 : Tree Nat := .node node12069 node12435 +def node12437 : Tree Nat := .node node12426 node12436 +def node12438 : Tree Nat := .leaf 2015283703367863641175612582841936517787350944656835640441746215724148601621265841204658433722230724652733832948183826229019103232384351716420265643338572120504732846690863842484127629491646408092491519065213830204430210004658605681926168207312149901339420027518976 +def node12439 : Tree Nat := .node node1898 node12438 +def node12440 : Tree Nat := .node node12439 node11743 +def node12441 : Tree Nat := .node node12440 node12083 +def node12442 : Tree Nat := .node node12080 node12441 +def node12443 : Tree Nat := .node node12442 node12094 +def node12444 : Tree Nat := .leaf 572778078369499224088375678951108638011287396263498246212912731873199901168104862737690045362725805790169147134431668582877192527008843615146574308806187829887314933747997352590139633493274155474858521293712329306345795625987820309521694471387697123072 +def node12445 : Tree Nat := .node node1960 node12444 +def node12446 : Tree Nat := .node node12445 node11757 +def node12447 : Tree Nat := .node node12446 node11419 +def node12448 : Tree Nat := .node node12101 node12447 +def node12449 : Tree Nat := .leaf 30750788930784052141961861920805917214380440082589217766573459895919230378495282122721735540365808875358003962508537313948568601936273402206990779347133949365544298087712639248257118232124611907064008483189222574845047234699623214690131652036941934222324531200 +def node12450 : Tree Nat := .node node1975 node12449 +def node12451 : Tree Nat := .node node12450 node11762 +def node12452 : Tree Nat := .node node12451 node11766 +def node12453 : Tree Nat := .leaf 4646927838993072071243945306718439250410188130185607684549287060362314553626263667328650982800488595594163456063197816929671753413226253971080721071308098374252355411243417100833035608425353895933663928930351831394376641232703830135248535051840311040007793633512643154466403038265344 +def node12454 : Tree Nat := .node node12453 node11426 +def node12455 : Tree Nat := .node node12104 node12454 +def node12456 : Tree Nat := .node node12455 node12108 +def node12457 : Tree Nat := .node node12452 node12456 +def node12458 : Tree Nat := .node node12448 node12457 +def node12459 : Tree Nat := .node node12443 node12458 +def node12460 : Tree Nat := .node node12437 node12459 +def node12461 : Tree Nat := .node node12420 node12460 +def node12462 : Tree Nat := .node node12368 node12461 +def node12463 : Tree Nat := .node node12281 node12462 +def node12464 : Tree Nat := .leaf 17926543152476856912677293520855478492216581132146590398565284031944909192997437606436978562026716801549454221995910574675447119206602737973032322247935353835732717051777428881351737678344671561125737392258441805956 +def node12465 : Tree Nat := .node node15 node12464 +def node12466 : Tree Nat := .leaf 57277807836951143358745932098478964063680549288467361651318030741787743322281176643657393843375033658889124154023053061468858478984886643526937128338091804430618034685959723936940294746463814549757554823917428391466438839631470524921799171015480427264 +def node12467 : Tree Nat := .node node10048 node12466 +def node12468 : Tree Nat := .node node12465 node12467 +def node12469 : Tree Nat := .leaf 7153784826105787970235553693214861578732961718324041211533586451289603323943261282096024878550257871521699426606378945070891024174491165156214844875791433374281952635915628495940109471255455215914035972603371323460 +def node12470 : Tree Nat := .node node2869 node12469 +def node12471 : Tree Nat := .leaf 21480925918836597559466369263441104030393561290974060268452255932867694986296767864148908281180755951618519392962047802656260566083388867969549768200396222315358159616171354030900926324292775571359759003629055824770107058691851111060007472711908786176 +def node12472 : Tree Nat := .node node12471 node11067 +def node12473 : Tree Nat := .node node12470 node12472 +def node12474 : Tree Nat := .node node12468 node12473 +def node12475 : Tree Nat := .node node10047 node12474 +def node12476 : Tree Nat := .node node12475 node12121 +def node12477 : Tree Nat := .leaf 57277807836951143358745932098478964063680549288467361651318030741787743322281176643657393843375033658889124154070687164104295372163927128600685393501492044644622111084567465630442671132263460852862811523494637424056571455698958924488187160941914473216 +def node12478 : Tree Nat := .node node12477 node11775 +def node12479 : Tree Nat := .node node9505 node12478 +def node12480 : Tree Nat := .node node11449 node12479 +def node12481 : Tree Nat := .node node11446 node12480 +def node12482 : Tree Nat := .leaf 1311064997792836947369580459091613708074602387457451439602639160023902085483338671383517729119449281150470197223926815648555981020116887633632462165149676431110475434541175783802628524718050331792258782292470729758147040194104194352301331185664000 +def node12483 : Tree Nat := .node node7523 node12482 +def node12484 : Tree Nat := .node node9243 node12483 +def node12485 : Tree Nat := .leaf 468830442472827014052003359573884542754817284333704003912276145274410566749623343030089388710063001348585343479767253424291745696875966207434492047982662990204675589466416253426588769565774553345582375364187727677358080 +def node12486 : Tree Nat := .node node2697 node12485 +def node12487 : Tree Nat := .node node12486 node12125 +def node12488 : Tree Nat := .node node12484 node12487 +def node12489 : Tree Nat := .leaf 25415349212818967911684505158402359802583062266652814482658216572704777352433250011011315808838234561988105003169658348114440688364803241885855674720321968694345033131692775276739355762510447561998080 +def node12490 : Tree Nat := .node node109 node12489 +def node12491 : Tree Nat := .node node12490 node8373 +def node12492 : Tree Nat := .node node12491 node11782 +def node12493 : Tree Nat := .node node12488 node12492 +def node12494 : Tree Nat := .node node12481 node12493 +def node12495 : Tree Nat := .node node12476 node12494 +def node12496 : Tree Nat := .leaf 5370122337667226261037297643785471715606824797209265542696027639022998446597614421607746013381207555911162013478139622897535094357344667294908013203655797080985465581430526841104662501502584395379799872310026139090246791128402660988633307021531742208 +def node12497 : Tree Nat := .node node12496 node8809 +def node12498 : Tree Nat := .node node8380 node12497 +def node12499 : Tree Nat := .node node12133 node12498 +def node12500 : Tree Nat := .leaf 2379227053564452900476899997039840917692690221467121550474428627014435915254183029254257303640498287592194818892986266490040614008050327216071565446790781933407635763975618775915805899124939358429673889224083120869807335941529059979199971273071908712296273678608312432380704952548655104 +def node12501 : Tree Nat := .node node12500 node11790 +def node12502 : Tree Nat := .node node8814 node12501 +def node12503 : Tree Nat := .node node11789 node12502 +def node12504 : Tree Nat := .node node12499 node12503 +def node12505 : Tree Nat := .node node12504 node12149 +def node12506 : Tree Nat := .leaf 2436328502849999770088345596968797077747695618317228063871303762468041298264565336134016996401428638302326225443377536294965505371713790382435367802473742428887581673893285478646026746712454678408545210646052479321746230234261065633085270302582071601416914985499837720593424769015410311936 +def node12507 : Tree Nat := .node node12506 node11802 +def node12508 : Tree Nat := .node node8829 node12507 +def node12509 : Tree Nat := .node node12153 node12508 +def node12510 : Tree Nat := .node node11089 node12509 +def node12511 : Tree Nat := .leaf 38067632857031246407630399952637454346519987155435267318692164130066494027429302350088871353352604648043354633952667899839667920216928895906308403919387940828144884106475613670259857606186742950168484239480459064473672778272373799054821824024111043167451474096905406681947768143927597568 +def node12512 : Tree Nat := .node node12159 node12511 +def node12513 : Tree Nat := .node node8834 node12512 +def node12514 : Tree Nat := .node node12158 node12513 +def node12515 : Tree Nat := .node node12514 node11810 +def node12516 : Tree Nat := .node node12510 node12515 +def node12517 : Tree Nat := .node node12505 node12516 +def node12518 : Tree Nat := .node node12495 node12517 +def node12519 : Tree Nat := .leaf 5370122444355457187114966029063100367146949548527282113628264633951038989126565237296868313047372184925938231709683998094374763694751005857654776842087099615500997784413971225307833845155072271114455355631045275526042483708519780378620999403182817280 +def node12520 : Tree Nat := .node node8416 node12519 +def node12521 : Tree Nat := .node node7574 node12520 +def node12522 : Tree Nat := .node node12521 node12169 +def node12523 : Tree Nat := .node node12522 node11479 +def node12524 : Tree Nat := .node node11475 node12523 +def node12525 : Tree Nat := .leaf 1747979978748722941129005012592386036162854766689832698808489425085119512969026204457710551574359237953797000679553876329442244888283062719962439203668390493172924408229221593277692946154503228697526933780487877037565355846202432311591918068432896 +def node12526 : Tree Nat := .node node314 node12525 +def node12527 : Tree Nat := .node node12526 node10388 +def node12528 : Tree Nat := .node node12527 node11484 +def node12529 : Tree Nat := .node node12528 node11824 +def node12530 : Tree Nat := .leaf 2379227053564452900476899997039840917692690221467121550474428627014435915254183029254257303640498287592194818892986266490040614008050327216071565446604711219987960399994991881096476738330407170093720465792021629879563678184499191607695062290348435928741068142452410724254325836026806272 +def node12531 : Tree Nat := .node node8441 node12530 +def node12532 : Tree Nat := .node node8870 node12531 +def node12533 : Tree Nat := .node node11494 node12532 +def node12534 : Tree Nat := .node node12533 node12176 +def node12535 : Tree Nat := .node node12529 node12534 +def node12536 : Tree Nat := .node node12524 node12535 +def node12537 : Tree Nat := .leaf 213389485317844555235934319513609001969264864448541822382945383014117746974028950687822925733579890725268816406721433744611790426798423492405826617612327593284771663688625911434289328215706054047556646948737706286085140721271255008654748155904 +def node12538 : Tree Nat := .node node12537 node11121 +def node12539 : Tree Nat := .node node8449 node12538 +def node12540 : Tree Nat := .node node11835 node12539 +def node12541 : Tree Nat := .node node12540 node12183 +def node12542 : Tree Nat := .leaf 8254602048994769481416783112254089866662524486502034756622440757077076381466184083838419667145204651066231332524311416731706162571183743384586846270434260980075917553007313198690901692914400426654614838893505943231394136886341844229466777508842011356280411450433863680 +def node12543 : Tree Nat := .node node3503 node12542 +def node12544 : Tree Nat := .node node12543 node10091 +def node12545 : Tree Nat := .node node12191 node12544 +def node12546 : Tree Nat := .node node12188 node12545 +def node12547 : Tree Nat := .node node12541 node12546 +def node12548 : Tree Nat := .leaf 1790040743653153378808600520146416582757857117981018607162078560718607018844130779537284753544442890156525571812251666916689968241451048425686722285580997115783823050396443732741626586200860098909568808407260029458523539047309957708491169089064048896 +def node12549 : Tree Nat := .node node11514 node12548 +def node12550 : Tree Nat := .node node11848 node12549 +def node12551 : Tree Nat := .leaf 3045410628562499712610431996210996347177459796916915627317245127966807495743387943622531571948878141770761042139591927647419631173436085503826915412496227180821921811418339444538361672024967071091055375002089507669127923173794319557661129741349010421107137251700128430183626181380119739392 +def node12552 : Tree Nat := .node node10096 node12551 +def node12553 : Tree Nat := .node node8901 node12552 +def node12554 : Tree Nat := .node node12550 node12553 +def node12555 : Tree Nat := .node node12554 node12203 +def node12556 : Tree Nat := .node node12199 node12555 +def node12557 : Tree Nat := .node node12547 node12556 +def node12558 : Tree Nat := .node node12536 node12557 +def node12559 : Tree Nat := .node node12518 node12558 +def node12560 : Tree Nat := .leaf 21480925918836597559466369263441104030393561290974060268452255932867694986296767864148908281180755951618519392962047075817536270476498318645741880195861868673997472298111072540701745685004662173436432812578342061204546296169935359872252593041555390464 +def node12561 : Tree Nat := .node node11538 node12560 +def node12562 : Tree Nat := .node node5688 node12561 +def node12563 : Tree Nat := .node node12562 node12211 +def node12564 : Tree Nat := .node node12563 node12216 +def node12565 : Tree Nat := .node node11537 node12564 +def node12566 : Tree Nat := .node node11861 node12565 +def node12567 : Tree Nat := .leaf 25415349212818967911684505158402359802583062266652814482658216572704777352433250011011315808838234561988105003169658348233011787743815025999592363369218386336093497429308712853143921786613492313292560 +def node12568 : Tree Nat := .node node12567 node7644 +def node12569 : Tree Nat := .node node10449 node12568 +def node12570 : Tree Nat := .leaf 5370122444355457187114966029063100367146949548527282113628264633951038989126565237296868313047372184925938231709683998094374763694791353511999884788800473352563544844950372878320790462543051323560402974725058419192130692353521933997112829474470690816 +def node12571 : Tree Nat := .node node12570 node8926 +def node12572 : Tree Nat := .node node10118 node12571 +def node12573 : Tree Nat := .node node12569 node12572 +def node12574 : Tree Nat := .node node12573 node11552 +def node12575 : Tree Nat := .node node12574 node12224 +def node12576 : Tree Nat := .leaf 152270531428124985630521599810549817371765740569089995077716466349032778410961974975122537630878635705206628528081349180264768911967521805594537821703136859792114281484600738824216303621294610218044225430803251954522759689012632743615594898267355115344034414124304158321932342724468450560 +def node12577 : Tree Nat := .node node8518 node12576 +def node12578 : Tree Nat := .node node10468 node12577 +def node12579 : Tree Nat := .node node11562 node12578 +def node12580 : Tree Nat := .leaf 1790150099102876869021435248250019995303749140817283874750189257324506477915690797543620059209050129555606593820267882845788694734491813349483178916399840524715673484360699089085040705133074569778097942300043867977026926406435368882767446928152068096 +def node12581 : Tree Nat := .node node9567 node12580 +def node12582 : Tree Nat := .node node12581 node8083 +def node12583 : Tree Nat := .node node12228 node12582 +def node12584 : Tree Nat := .node node12579 node12583 +def node12585 : Tree Nat := .node node11888 node12584 +def node12586 : Tree Nat := .node node12575 node12585 +def node12587 : Tree Nat := .node node12566 node12586 +def node12588 : Tree Nat := .leaf 3580081700695792870399535724574524629625881882469897527952195336442751980830001445696019465586228542255722428480987629992674781227361541120319586096008934360467253886591403714093404300042842333536467984517003148659866557895333562018448075893671723008 +def node12589 : Tree Nat := .node node754 node12588 +def node12590 : Tree Nat := .node node12589 node10152 +def node12591 : Tree Nat := .node node12590 node11894 +def node12592 : Tree Nat := .leaf 3495959954241579459953393680419219440137595374617564693200683205906994044878671664833882304724191364341086472471803104926586425549181896667921578236454572747078535414826744278734157553209315101188091189875186472884473529521690262738335803352154112 +def node12593 : Tree Nat := .node node12592 node11571 +def node12594 : Tree Nat := .node node10476 node12593 +def node12595 : Tree Nat := .node node11570 node12594 +def node12596 : Tree Nat := .node node12591 node12595 +def node12597 : Tree Nat := .node node12596 node12242 +def node12598 : Tree Nat := .leaf 5370122337667226261037297643785471715606824797209265542696027639022998446597614421607746013381207555911162013478139622897535094357334580381321736216977453646719828816296426427851423347155589632268312967536522853173724738967152122583433888751406350336 +def node12599 : Tree Nat := .node node12598 node8959 +def node12600 : Tree Nat := .node node11904 node12599 +def node12601 : Tree Nat := .node node10491 node12600 +def node12602 : Tree Nat := .leaf 57277807836950736375443144021435868369601526175514037199240877921687636891226719764220455084770833072138561119918959033458644374807482296411822421728596553932025557691044684443954613051107996710231408206651904921037348319699801099933023694036953480192 +def node12603 : Tree Nat := .node node12602 node11907 +def node12604 : Tree Nat := .node node10166 node12603 +def node12605 : Tree Nat := .node node12246 node12604 +def node12606 : Tree Nat := .node node12601 node12605 +def node12607 : Tree Nat := .leaf 9516908214257811601907599988159363588420037529177962992041714415623114194254553806930761603725623225546484445689952304890432929671148112363129459120510301960295365158960748316096397483437692554070016060682897037069174952479628215952660084882710835610400347053651783006059970580929616128 +def node12608 : Tree Nat := .node node12252 node12607 +def node12609 : Tree Nat := .node node11589 node12608 +def node12610 : Tree Nat := .node node12251 node12609 +def node12611 : Tree Nat := .node node12610 node11920 +def node12612 : Tree Nat := .node node12606 node12611 +def node12613 : Tree Nat := .node node12597 node12612 +def node12614 : Tree Nat := .leaf 106701254391766886850656690862068877211950614705364998245193173580197506179553846699037628417320326237027157599897048055410927257611855589977807319516145162533095589454630140895288184354723595549476729212108633128627337014384532725596743401472 +def node12615 : Tree Nat := .node node879 node12614 +def node12616 : Tree Nat := .node node12615 node10497 +def node12617 : Tree Nat := .leaf 106701254391766886850656690862068877211950614705364998245193173580197506179553846699037628417320326237027157599897048055411572820081377317125221299309145915501678015902837446773495849193858757454980939510766044466947371472252731890626785050624 +def node12618 : Tree Nat := .node node12617 node8971 +def node12619 : Tree Nat := .node node9869 node12618 +def node12620 : Tree Nat := .node node12616 node12619 +def node12621 : Tree Nat := .leaf 1747979978748722941129005012592386036162854766689832698808489425085119512969026204457710551574359237953797012588079535188665539648404331157028730053728443994192024060164644968871789396066079005011701828082746024570719392525342952474673798062931968 +def node12622 : Tree Nat := .node node12621 node11595 +def node12623 : Tree Nat := .node node10501 node12622 +def node12624 : Tree Nat := .node node11206 node12623 +def node12625 : Tree Nat := .node node12620 node12624 +def node12626 : Tree Nat := .node node12625 node12270 +def node12627 : Tree Nat := .leaf 3045410628562499712610431996210996347177459796916915627317245127966807495743387943622531571948878141770761042139591927647419631173436085503826916192933364759819979656817646892829938109174502737333843089791329414012062628115199349634186895614341800377839917613497057094003381215425071954944 +def node12628 : Tree Nat := .node node12627 node57 +def node12629 : Tree Nat := .node node10849 node12628 +def node12630 : Tree Nat := .node node10204 node12629 +def node12631 : Tree Nat := .node node11216 node12630 +def node12632 : Tree Nat := .leaf 7164969939549262169300731971661745495056132331054256368853217872995873398203829424322434769533772646599349548933198856306143008866076620535803569548868475210709346970866637824711462333254538316480891412268437936490063133514718333738457464080196216064 +def node12633 : Tree Nat := .node node7700 node12632 +def node12634 : Tree Nat := .node node10208 node12633 +def node12635 : Tree Nat := .leaf 2436328502849999770088345596968797077747695618317228063871303762468041298264565336134016996401428638302326225443377536294965505371713790382435367790279412154215737020058921299766470864881993183623501652602470605785137875469551612038139555210816559258342965291237566435021540370298842628864 +def node12636 : Tree Nat := .node node12272 node12635 +def node12637 : Tree Nat := .node node10519 node12636 +def node12638 : Tree Nat := .node node12634 node12637 +def node12639 : Tree Nat := .node node12638 node11221 +def node12640 : Tree Nat := .node node12631 node12639 +def node12641 : Tree Nat := .node node12626 node12640 +def node12642 : Tree Nat := .node node12613 node12641 +def node12643 : Tree Nat := .node node12587 node12642 +def node12644 : Tree Nat := .node node12559 node12643 +def node12645 : Tree Nat := .leaf 135243399970730303066198984938628251268824915465247109664758362321700642924402143304641447917533484128220870972182585488064330900877483342277181980307567240212301999953316059706245939889710717364779070745272922894004703852462857591499078480633733188814368899343709429039104 +def node12646 : Tree Nat := .node node1006 node12645 +def node12647 : Tree Nat := .node node12646 node10222 +def node12648 : Tree Nat := .leaf 1790040743653153378808600520146416582757857117981018607162078560718607018844130779537284753544442890156525571812251666916689968241451127229699115074539421673864023337624053892220167517094195995496377299850803023879746367579819727539844839939082590464 +def node12649 : Tree Nat := .node node12648 node8987 +def node12650 : Tree Nat := .node node8566 node12649 +def node12651 : Tree Nat := .node node12647 node12650 +def node12652 : Tree Nat := .leaf 57277807836950736375443144021435868369601526175514037199240877921687636891226719764220455084770833072138561116870376464790683211348891251691933451270981180235764668180149216059802524359930633311494979433710526835268860895817320628482995243983635758080 +def node12653 : Tree Nat := .node node11605 node12652 +def node12654 : Tree Nat := .node node10867 node12653 +def node12655 : Tree Nat := .node node12654 node11610 +def node12656 : Tree Nat := .node node12651 node12655 +def node12657 : Tree Nat := .node node12656 node11941 +def node12658 : Tree Nat := .leaf 2436625906231695326700905209468427057917000552264512563844861783959417011200560904931136927481946869771431969727057246370735268991170296053434896064637025130774248222516863233945790241159479380199786139120072098615978103625390042531964593912910867387390643645465570699333501673196555862016 +def node12659 : Tree Nat := .node node8588 node12658 +def node12660 : Tree Nat := .node node9016 node12659 +def node12661 : Tree Nat := .node node12284 node12660 +def node12662 : Tree Nat := .node node12661 node12289 +def node12663 : Tree Nat := .node node11242 node12662 +def node12664 : Tree Nat := .node node12657 node12663 +def node12665 : Tree Nat := .node node12664 node12325 +def node12666 : Tree Nat := .leaf 9516908214257811601907599988159363588420037529177962992041714415623114194254553806930761603725623225546484445689952304890432929671148112363129459120510301960295365158962009180294682106772485483353220656324659588725829846773002561341595947979398746349965603573808100306854013052771145984 +def node12667 : Tree Nat := .node node12666 node9054 +def node12668 : Tree Nat := .node node6588 node12667 +def node12669 : Tree Nat := .node node10265 node12668 +def node12670 : Tree Nat := .leaf 152270531428124985630521599810549817371765740569089995077716466349032778410961974975122537630878635705206628528081349180264768911967521805594537821703160118631291740905098317186068719766393926741586219608732259640896540146232261477162033011890195549441978814816942616055090830251483243776 +def node12671 : Tree Nat := .node node12670 node11653 +def node12672 : Tree Nat := .node node10569 node12671 +def node12673 : Tree Nat := .node node11279 node12672 +def node12674 : Tree Nat := .node node12669 node12673 +def node12675 : Tree Nat := .leaf 213389485317844555235934319513609001969264864448541822382945383014117746974028950687822925733579890725268816406721433744611629036181043060618973122664077405042626057076574084964737412005922263571180594374073353451505132106801899374388024049664 +def node12676 : Tree Nat := .node node11976 node12675 +def node12677 : Tree Nat := .node node5821 node12676 +def node12678 : Tree Nat := .node node12677 node11981 +def node12679 : Tree Nat := .node node12678 node12330 +def node12680 : Tree Nat := .node node12674 node12679 +def node12681 : Tree Nat := .leaf 2436625906231695326700905209468427057917000552264512563844861783959417011200560904931136927481946869771431969727057246370735268991170296053434896066161316415108228804246158756305734726388287067047916583875519832808054147970978724231332808299381556430274887357406810935058515898223214723072 +def node12682 : Tree Nat := .node node12681 node11989 +def node12683 : Tree Nat := .node node7370 node12682 +def node12684 : Tree Nat := .node node11666 node12683 +def node12685 : Tree Nat := .node node11286 node12684 +def node12686 : Tree Nat := .leaf 18587711355972288284975781226873758791790744922364113079224192679605018060110592370686034932591098838776080193992204396150718447145530891560536922309450727590810952854797183657330583460885870068621033223307398200704103919199799217084279919881617118706912779360218149470577196798076416 +def node12687 : Tree Nat := .node node12333 node12686 +def node12688 : Tree Nat := .node node6987 node12687 +def node12689 : Tree Nat := .node node10276 node12688 +def node12690 : Tree Nat := .node node12689 node11298 +def node12691 : Tree Nat := .node node12685 node12690 +def node12692 : Tree Nat := .node node12680 node12691 +def node12693 : Tree Nat := .leaf 7164969939549262169300731971661745495056132331054256368853217872995873398203829424322434769533772646599349548939153119135572620513456681170022102694293505237459856520692605536399259381479494104369048499715589065563829710533057903998539005020193465600 +def node12694 : Tree Nat := .node node12693 node11674 +def node12695 : Tree Nat := .node node9077 node12694 +def node12696 : Tree Nat := .node node12342 node12695 +def node12697 : Tree Nat := .node node11999 node12696 +def node12698 : Tree Nat := .leaf 33018408195979077911344184489810038954857014747128397945669039857690094711259940778939113224190845690713234878736626635101426489704623855928127645312468794295826211108275643472268064973423738219776928440975063934678245832023535234268021693035945830131129799912896593920 +def node12699 : Tree Nat := .node node3522 node12698 +def node12700 : Tree Nat := .node node12699 node12349 +def node12701 : Tree Nat := .node node12347 node12700 +def node12702 : Tree Nat := .node node10954 node12701 +def node12703 : Tree Nat := .node node12697 node12702 +def node12704 : Tree Nat := .leaf 1311064997792836947369580459091613708074602387457451439602639160023902085483338671383517729119449281150860415792716314677478680673841033421851036932982797824967870054494347251155099227233088594675195278687449096148327938658436104229818353661771776 +def node12705 : Tree Nat := .node node12704 node57 +def node12706 : Tree Nat := .node node9377 node12705 +def node12707 : Tree Nat := .node node12356 node12706 +def node12708 : Tree Nat := .node node12005 node12707 +def node12709 : Tree Nat := .leaf 3580081487306306757617201040292833165515714235962037214789533165509569190735201290063258866659334854606433284269321377037037334486917419431836307540677293233932232466964807902954104468969295290285682913874423221164781029548110770355760870224929252864 +def node12710 : Tree Nat := .node node7817 node12709 +def node12711 : Tree Nat := .node node12008 node12710 +def node12712 : Tree Nat := .node node12711 node12362 +def node12713 : Tree Nat := .node node12712 node12014 +def node12714 : Tree Nat := .node node12708 node12713 +def node12715 : Tree Nat := .node node12703 node12714 +def node12716 : Tree Nat := .node node12692 node12715 +def node12717 : Tree Nat := .node node12665 node12716 +def node12718 : Tree Nat := .leaf 18587711355972288284975781226873758791790744922364113079224192679605018060110592370686034932591098838776080193992204396150718447145530891560536922309450727590810952855112399706901739294584102389422182133748036114867827492543385564318245694053594803598226909399297474741145408796386816 +def node12719 : Tree Nat := .node node12718 node9105 +def node12720 : Tree Nat := .node node8686 node12719 +def node12721 : Tree Nat := .node node12371 node12720 +def node12722 : Tree Nat := .leaf 38067632857031246407630399952637454346519987155435267318692164130066494027429302350088871353352604648043354633952667899839667920216928895906308403919393755537939248961600008260722961642461572081053982783962710986067117892577280982441431352429821151691937574270374506125058735094406076928 +def node12723 : Tree Nat := .node node12722 node11689 +def node12724 : Tree Nat := .node node9110 node12723 +def node12725 : Tree Nat := .node node11328 node12724 +def node12726 : Tree Nat := .node node12721 node12725 +def node12727 : Tree Nat := .node node12726 node12382 +def node12728 : Tree Nat := .leaf 2436402853695423659241485500093704572832981300202585470158613707181367169647452806765401406730166475577266461747966244666927133055962222523086953015810805027478524365776822430254591676268033873870417079679051609371264905014842868962423942354190077998610359317627499362096884008723679281152 +def node12729 : Tree Nat := .node node12728 node12026 +def node12730 : Tree Nat := .node node9125 node12729 +def node12731 : Tree Nat := .node node10996 node12730 +def node12732 : Tree Nat := .node node11335 node12731 +def node12733 : Tree Nat := .leaf 3495959954241579459953393680419219440137595374617564693200683205906994044878671664833882304724191364341086472425285426571667584554025172963089288037821525663090179556811371531173243113951848008311863944194318276995672144244774796421360749322567680 +def node12734 : Tree Nat := .node node7858 node12733 +def node12735 : Tree Nat := .node node10626 node12734 +def node12736 : Tree Nat := .node node12735 node12387 +def node12737 : Tree Nat := .node node12736 node9961 +def node12738 : Tree Nat := .node node12732 node12737 +def node12739 : Tree Nat := .node node12727 node12738 +def node12740 : Tree Nat := .leaf 1081947199765842424529591879509026010150599323721976877786893974559455166488175871777491082812739205141997164858466744808761614551484843010378492537955101602093719408597215836669307845077287558711085676978679504056370751409971451867729806414449444049432950377866295097950208 +def node12741 : Tree Nat := .node node7429 node12740 +def node12742 : Tree Nat := .node node9402 node12741 +def node12743 : Tree Nat := .node node10319 node12742 +def node12744 : Tree Nat := .leaf 14319451972573509467969100514997122826803385180375608359870009604759873118685487105323799767044618627764764454710451637341099954040595814901701574731452698117813464486560305807146166020242810670567060736155638392860735662896017680241471419032975464960 +def node12745 : Tree Nat := .node node12744 node11704 +def node12746 : Tree Nat := .node node9663 node12745 +def node12747 : Tree Nat := .node node12394 node12746 +def node12748 : Tree Nat := .node node12743 node12747 +def node12749 : Tree Nat := .leaf 135243399970730303066198984938628251268824915465247109664758362321700642924402143304641447917533484128220988908508361161231588449458139225680023134095705253975688756400198735461320694541338408824940872581758593780724415222615975422268763630403263049147183378082292840792064 +def node12750 : Tree Nat := .node node1664 node12749 +def node12751 : Tree Nat := .node node12750 node8290 +def node12752 : Tree Nat := .node node12751 node12399 +def node12753 : Tree Nat := .node node12752 node12409 +def node12754 : Tree Nat := .node node12748 node12753 +def node12755 : Tree Nat := .leaf 33018408195979077911344184489810038954857014747128397945669039857690094711259940778939113224190845690713236678302144452379979613920026930320871193191316115062479451410504688207300333568571865836051369997317923903042499240381584517574443890770676714008626709277228138496 +def node12756 : Tree Nat := .node node1695 node12755 +def node12757 : Tree Nat := .node node12756 node8296 +def node12758 : Tree Nat := .node node12757 node9675 +def node12759 : Tree Nat := .leaf 874043331861891298246386972727742472049734933136564395875795372115744168700406918896976792458411889439871443727997930759948839923015574859797069172044377982190240211685194323517086996890291314360750650481640734436921893220022542682888317813391360 +def node12760 : Tree Nat := .node node12759 node57 +def node12761 : Tree Nat := .node node11358 node12760 +def node12762 : Tree Nat := .node node11713 node12761 +def node12763 : Tree Nat := .node node12758 node12762 +def node12764 : Tree Nat := .leaf 3580081700695792870399535724574524629625881882469897527952195336442751980830001445696019465585799492401964265373801261192732194151282201414060629507921780394268157437629050210835744322501501423850386965055035595032546433645351271776703434611656491008 +def node12765 : Tree Nat := .node node9682 node12764 +def node12766 : Tree Nat := .node node12765 node12040 +def node12767 : Tree Nat := .node node11364 node12766 +def node12768 : Tree Nat := .node node12416 node12767 +def node12769 : Tree Nat := .node node12763 node12768 +def node12770 : Tree Nat := .node node12754 node12769 +def node12771 : Tree Nat := .node node12739 node12770 +def node12772 : Tree Nat := .leaf 3580081487306306757617201040292833165515714235962037214789533165509569190735201290063258866659334854606433284269321377037037334486922462888629446034016464951065050849531858109580724046142792671841426366261174864123042055628736039558360579359991948800 +def node12773 : Tree Nat := .node node12772 node9159 +def node12774 : Tree Nat := .node node9428 node12773 +def node12775 : Tree Nat := .node node10333 node12774 +def node12776 : Tree Nat := .node node12775 node12050 +def node12777 : Tree Nat := .node node12776 node12425 +def node12778 : Tree Nat := .leaf 8254602048994769481416783112254089866662524486502034756622440757077076381466184083838419667145204651066231444997156280311615732834646435534133318012862218527991745071896628494630418480111158402671767436164934691254159974908719924436118164865405781539695897873355898880 +def node12779 : Tree Nat := .node node1820 node12778 +def node12780 : Tree Nat := .node node12779 node10647 +def node12781 : Tree Nat := .node node12780 node11383 +def node12782 : Tree Nat := .node node12781 node12068 +def node12783 : Tree Nat := .node node12782 node12435 +def node12784 : Tree Nat := .node node12777 node12783 +def node12785 : Tree Nat := .leaf 1790150099102876869021435248250019995303749140817283874750189257324506477915690797543620059648397179803965615579109533986997860639735672558654725117645501912590437221810686424928857707466166088325061871354818782352834158388300572887289084777401942016 +def node12786 : Tree Nat := .node node1883 node12785 +def node12787 : Tree Nat := .node node12786 node10654 +def node12788 : Tree Nat := .node node12787 node12079 +def node12789 : Tree Nat := .node node12788 node12441 +def node12790 : Tree Nat := .leaf 540973599882921212264795939754513005075299661860988438659038499017268058136175524568853356593652864839096081116847871072600390363668552701143415501715303665976574006613488981995184332639846109273413715067042251569150154347025598965125540316067394771035672938013210099843072 +def node12791 : Tree Nat := .node node1914 node12790 +def node12792 : Tree Nat := .node node12791 node11045 +def node12793 : Tree Nat := .leaf 2436402853695423659241485500093704572832981300202585470158613707181367169647452806765401406730166475577266461747966244666927133055962222523086953015429732206395029220344498549664605554960831952158384468490189675823245893928445698537581888757572405737889298389562961140651366114873470615552 +def node12794 : Tree Nat := .node node12086 node12793 +def node12795 : Tree Nat := .node node11751 node12794 +def node12796 : Tree Nat := .node node12792 node12795 +def node12797 : Tree Nat := .node node12796 node12093 +def node12798 : Tree Nat := .node node12789 node12797 +def node12799 : Tree Nat := .leaf 14319451972573509467969100514997122826803385180375608359870009604759873118685487105323799767044618627764764454708963071633742551128750799743146941445096440611125837099103813879224216758186571723595021464293850610592294018636481027519309512698379655680 +def node12800 : Tree Nat := .node node11761 node12799 +def node12801 : Tree Nat := .node node12450 node12800 +def node12802 : Tree Nat := .node node12801 node11766 +def node12803 : Tree Nat := .node node12802 node12456 +def node12804 : Tree Nat := .node node12448 node12803 +def node12805 : Tree Nat := .node node12798 node12804 +def node12806 : Tree Nat := .node node12784 node12805 +def node12807 : Tree Nat := .node node12771 node12806 +def node12808 : Tree Nat := .node node12717 node12807 +def node12809 : Tree Nat := .node node12644 node12808 +def node12810 : Tree Nat := .leaf 549146240018868976728371828568883201 +def node12811 : Tree Nat := .leaf 12265838570582234292139772940818853064869839144174091603236253430275416702659094472194084019621807348277731162104884076409766330896268738711128278938477381700370300930 +def node12812 : Tree Nat := .node node12810 node12811 +def node12813 : Tree Nat := .node node12812 node10045 +def node12814 : Tree Nat := .leaf 4173848581067863208777455135578696529537466241409754222086997643224336316123139198476216438958170231612533775426990177126720631098584007447773310844156922587488532671560991855707788103899350725811993837568 +def node12815 : Tree Nat := .node node2066 node12814 +def node12816 : Tree Nat := .node node12815 node8784 +def node12817 : Tree Nat := .node node12813 node12816 +def node12818 : Tree Nat := .leaf 1329217854580114065515339160364253184 +def node12819 : Tree Nat := .node node12818 node12464 +def node12820 : Tree Nat := .node node12819 node12467 +def node12821 : Tree Nat := .node node12820 node12473 +def node12822 : Tree Nat := .node node12817 node12821 +def node12823 : Tree Nat := .leaf 1329217854580114047068595090949668864 +def node12824 : Tree Nat := .leaf 1174833932040723294629219108182784638464528092235128936061936589857048027519223866049752842864261693921081479140056616265625112443297742891187469230735829767922074924516473217648192357910895427666968280407921779758072000 +def node12825 : Tree Nat := .node node12823 node12824 +def node12826 : Tree Nat := .node node12825 node10350 +def node12827 : Tree Nat := .node node12826 node9490 +def node12828 : Tree Nat := .node node12827 node12120 +def node12829 : Tree Nat := .node node12822 node12828 +def node12830 : Tree Nat := .leaf 1324035698926381045275276563951190016 +def node12831 : Tree Nat := .leaf 2739226044434248215562751811568192002836639355327669865343716333886630078548387705159876430977573412304249395495401792806971706583208922950856126338888343865936907107271814084481121865277660115670727912081850416 +def node12832 : Tree Nat := .node node12830 node12831 +def node12833 : Tree Nat := .node node12832 node10356 +def node12834 : Tree Nat := .node node12833 node11445 +def node12835 : Tree Nat := .leaf 22158278651204452854366041692344859515931053418796863105242174835702128838125335101419818186154240184527975782220030826241098091985856624359405022012869001694805927863093768391040699856038639872992477836189338998421752733847199156623971063858418944331373730611934917756930949136 +def node12836 : Tree Nat := .node node78 node12835 +def node12837 : Tree Nat := .node node12836 node11448 +def node12838 : Tree Nat := .node node12837 node12479 +def node12839 : Tree Nat := .node node12834 node12838 +def node12840 : Tree Nat := .leaf 1377768841550803999365903938431737990306104143777184930687080534160827101810320211787610383523038828366996974624686223064266238984212420124177537357936108312146657143528376795856912 +def node12841 : Tree Nat := .node node94 node12840 +def node12842 : Tree Nat := .node node12841 node12483 +def node12843 : Tree Nat := .node node12842 node12487 +def node12844 : Tree Nat := .node node12843 node12492 +def node12845 : Tree Nat := .node node12839 node12844 +def node12846 : Tree Nat := .node node12829 node12845 +def node12847 : Tree Nat := .leaf 780974181788607569674088910768046336 +def node12848 : Tree Nat := .node node12847 node12131 +def node12849 : Tree Nat := .node node12848 node10056 +def node12850 : Tree Nat := .node node12849 node12498 +def node12851 : Tree Nat := .node node12850 node12503 +def node12852 : Tree Nat := .node node12851 node12149 +def node12853 : Tree Nat := .node node12852 node12516 +def node12854 : Tree Nat := .node node12846 node12853 +def node12855 : Tree Nat := .leaf 78188689022077189484316653707591696 +def node12856 : Tree Nat := .node node12855 node7161 +def node12857 : Tree Nat := .node node12856 node10080 +def node12858 : Tree Nat := .node node12857 node8848 +def node12859 : Tree Nat := .node node12858 node11474 +def node12860 : Tree Nat := .node node12859 node12523 +def node12861 : Tree Nat := .node node12860 node12535 +def node12862 : Tree Nat := .node node12861 node12557 +def node12863 : Tree Nat := .node node12854 node12862 +def node12864 : Tree Nat := .leaf 265851683879864270081888596231454724 +def node12865 : Tree Nat := .node node12864 node5191 +def node12866 : Tree Nat := .node node12865 node10106 +def node12867 : Tree Nat := .node node12866 node10425 +def node12868 : Tree Nat := .node node12867 node11530 +def node12869 : Tree Nat := .node node12868 node11860 +def node12870 : Tree Nat := .node node12869 node12565 +def node12871 : Tree Nat := .node node12870 node12586 +def node12872 : Tree Nat := .node node12871 node12642 +def node12873 : Tree Nat := .node node12863 node12872 +def node12874 : Tree Nat := .leaf 446517247424391524383198737061642242 +def node12875 : Tree Nat := .node node12874 node12645 +def node12876 : Tree Nat := .node node12875 node10222 +def node12877 : Tree Nat := .node node12876 node12650 +def node12878 : Tree Nat := .node node12877 node12655 +def node12879 : Tree Nat := .node node12878 node11941 +def node12880 : Tree Nat := .node node12879 node12663 +def node12881 : Tree Nat := .leaf 781886890220771894843166537075917312 +def node12882 : Tree Nat := .node node12881 node12293 +def node12883 : Tree Nat := .node node12882 node10240 +def node12884 : Tree Nat := .node node12883 node9024 +def node12885 : Tree Nat := .node node12884 node11947 +def node12886 : Tree Nat := .node node12885 node12305 +def node12887 : Tree Nat := .node node12886 node12324 +def node12888 : Tree Nat := .node node12880 node12887 +def node12889 : Tree Nat := .node node12888 node12716 +def node12890 : Tree Nat := .leaf 637785494724906688558036426694089724129472193077477744339396095917189711218946406712841270883348912588415715263705092681206651832945760176835136790254383924427919589618579343351905052297694236278521856 +def node12891 : Tree Nat := .node node2258 node12890 +def node12892 : Tree Nat := .node node12891 node12741 +def node12893 : Tree Nat := .node node10319 node12892 +def node12894 : Tree Nat := .node node12893 node12747 +def node12895 : Tree Nat := .node node12894 node12753 +def node12896 : Tree Nat := .leaf 273537340583448134043537804002705584252195533615587765538375434598484549286925806062808292376662338686339624410814248666831029629157703981954575446768476969626262953101687115599427638074593795811563229142843416 +def node12897 : Tree Nat := .node node1710 node12896 +def node12898 : Tree Nat := .node node12897 node11712 +def node12899 : Tree Nat := .node node12898 node12761 +def node12900 : Tree Nat := .node node12758 node12899 +def node12901 : Tree Nat := .leaf 226264784939950833903616720339055966478327916129259925075926351140805642948761479323221608418489175403373075113056283451514049786297694426310621567979334221244495083970495409857041989696 +def node12902 : Tree Nat := .node node1725 node12901 +def node12903 : Tree Nat := .node node12902 node8301 +def node12904 : Tree Nat := .node node12903 node12415 +def node12905 : Tree Nat := .leaf 41797272406528594165780474849099630194941319489272936608910828766346176160970068035211245660863849948935268000582299529131815499301645251479689032091361101608208660324390168422080140390170658723118371110656 +def node12906 : Tree Nat := .node node2055 node12905 +def node12907 : Tree Nat := .node node12906 node11363 +def node12908 : Tree Nat := .node node12907 node12766 +def node12909 : Tree Nat := .node node12904 node12908 +def node12910 : Tree Nat := .node node12900 node12909 +def node12911 : Tree Nat := .node node12895 node12910 +def node12912 : Tree Nat := .node node12739 node12911 +def node12913 : Tree Nat := .leaf 74691854405310111472185289961330176049116609170478949034001217554526222571104903512599620767834280925180175175765153003757732037983356068918227720711343997714434 +def node12914 : Tree Nat := .node node1758 node12913 +def node12915 : Tree Nat := .node node12914 node10332 +def node12916 : Tree Nat := .node node12915 node12774 +def node12917 : Tree Nat := .node node12916 node12050 +def node12918 : Tree Nat := .leaf 22158278651204452854366041692344852687884274149826086447473941316652062609935704105050364663319272036055840726939526793990282689529909133634450204430464105496728548005398291322311600885032989764328806283930518339188674878155844212566485236708731030809863597637165469614762623168 +def node12919 : Tree Nat := .node node1789 node12918 +def node12920 : Tree Nat := .node node12919 node12053 +def node12921 : Tree Nat := .node node12920 node12423 +def node12922 : Tree Nat := .node node12921 node12062 +def node12923 : Tree Nat := .node node12917 node12922 +def node12924 : Tree Nat := .leaf 1665684013498567840545854945322718265661811933250229498685190310495210623536764377527596051964946482781163785737353379000967970663092113431844616461225353432277393678537197825258306383072166570352325951488 +def node12925 : Tree Nat := .node node2414 node12924 +def node12926 : Tree Nat := .node node12925 node11382 +def node12927 : Tree Nat := .node node12780 node12926 +def node12928 : Tree Nat := .leaf 90296911305476077290902507390775003432457258337999597408982453005831199352316877161888809516344547833665027364809749731468667902116503444403292536642970706913227901414667616971095277576 +def node12929 : Tree Nat := .node node1835 node12928 +def node12930 : Tree Nat := .node node12929 node11731 +def node12931 : Tree Nat := .node node12930 node12067 +def node12932 : Tree Nat := .node node12927 node12931 +def node12933 : Tree Nat := .leaf 52682179367767752743195064428310601978756742662778070603506675079729061265637877234982887771037231424101790346505319231980804403441864181703918066622198799930494820164359356420 +def node12934 : Tree Nat := .node node1851 node12933 +def node12935 : Tree Nat := .node node12934 node11736 +def node12936 : Tree Nat := .node node12935 node12429 +def node12937 : Tree Nat := .leaf 971814680042473405660864513097414221423024918407347256046882614589009119917368074711918574309696949585165155976223020494370864892611367539359836328521197540548939783773282923876305028448126041856 +def node12938 : Tree Nat := .node node1866 node12937 +def node12939 : Tree Nat := .node node12938 node12432 +def node12940 : Tree Nat := .node node12939 node10002 +def node12941 : Tree Nat := .node node12936 node12940 +def node12942 : Tree Nat := .node node12932 node12941 +def node12943 : Tree Nat := .node node12923 node12942 +def node12944 : Tree Nat := .node node12943 node12805 +def node12945 : Tree Nat := .node node12912 node12944 +def node12946 : Tree Nat := .node node12889 node12945 +def node12947 : Tree Nat := .node node12873 node12946 +def node12948 : Tree Nat := .leaf 549159373215869825177717486859059201 +def node12949 : Tree Nat := .node node12948 node12811 +def node12950 : Tree Nat := .node node12949 node10045 +def node12951 : Tree Nat := .node node12950 node12816 +def node12952 : Tree Nat := .leaf 1329227995784915301054740775284244480 +def node12953 : Tree Nat := .node node12952 node12464 +def node12954 : Tree Nat := .node node12953 node12467 +def node12955 : Tree Nat := .node node12954 node12473 +def node12956 : Tree Nat := .node node12951 node12955 +def node12957 : Tree Nat := .leaf 1329227916556753358639469471031361536 +def node12958 : Tree Nat := .node node12957 node12824 +def node12959 : Tree Nat := .node node12958 node10350 +def node12960 : Tree Nat := .node node12959 node9490 +def node12961 : Tree Nat := .node node12960 node12120 +def node12962 : Tree Nat := .node node12956 node12961 +def node12963 : Tree Nat := .leaf 1324035778153334633719999528320434176 +def node12964 : Tree Nat := .node node12963 node12831 +def node12965 : Tree Nat := .node node12964 node10356 +def node12966 : Tree Nat := .node node12965 node11445 +def node12967 : Tree Nat := .node node12966 node12838 +def node12968 : Tree Nat := .node node12967 node12844 +def node12969 : Tree Nat := .node node12962 node12968 +def node12970 : Tree Nat := .leaf 780982533369245525885976393933652224 +def node12971 : Tree Nat := .node node12970 node12131 +def node12972 : Tree Nat := .node node12971 node10056 +def node12973 : Tree Nat := .node node12972 node12498 +def node12974 : Tree Nat := .node node12973 node12503 +def node12975 : Tree Nat := .node node12974 node12149 +def node12976 : Tree Nat := .node node12975 node12516 +def node12977 : Tree Nat := .node node12969 node12976 +def node12978 : Tree Nat := .leaf 78189882104997134744260504859967504 +def node12979 : Tree Nat := .node node12978 node7161 +def node12980 : Tree Nat := .node node12979 node10080 +def node12981 : Tree Nat := .node node12980 node8848 +def node12982 : Tree Nat := .node node12981 node11474 +def node12983 : Tree Nat := .node node12982 node12523 +def node12984 : Tree Nat := .node node12983 node12535 +def node12985 : Tree Nat := .node node12984 node12557 +def node12986 : Tree Nat := .node node12977 node12985 +def node12987 : Tree Nat := .leaf 265853743750192993167883229852598276 +def node12988 : Tree Nat := .node node12987 node5191 +def node12989 : Tree Nat := .node node12988 node10106 +def node12990 : Tree Nat := .node node12989 node10425 +def node12991 : Tree Nat := .node node12990 node11530 +def node12992 : Tree Nat := .node node12991 node11860 +def node12993 : Tree Nat := .node node12992 node12565 +def node12994 : Tree Nat := .node node12993 node12586 +def node12995 : Tree Nat := .node node12994 node12642 +def node12996 : Tree Nat := .node node12986 node12995 +def node12997 : Tree Nat := .leaf 446533425939212490135072148578893826 +def node12998 : Tree Nat := .node node12997 node12645 +def node12999 : Tree Nat := .node node12998 node10222 +def node13000 : Tree Nat := .node node12999 node12650 +def node13001 : Tree Nat := .node node13000 node12655 +def node13002 : Tree Nat := .node node13001 node11941 +def node13003 : Tree Nat := .node node13002 node12663 +def node13004 : Tree Nat := .leaf 781895255728022786523852978822054400 +def node13005 : Tree Nat := .node node13004 node12293 +def node13006 : Tree Nat := .node node13005 node10240 +def node13007 : Tree Nat := .node node13006 node9024 +def node13008 : Tree Nat := .node node13007 node11947 +def node13009 : Tree Nat := .node node13008 node12305 +def node13010 : Tree Nat := .node node13009 node12324 +def node13011 : Tree Nat := .node node13003 node13010 +def node13012 : Tree Nat := .node node13011 node12716 +def node13013 : Tree Nat := .node node13012 node12945 +def node13014 : Tree Nat := .node node12996 node13013 +def node13015 : Tree Nat := .leaf 549159373215870023739679754713825281 +def node13016 : Tree Nat := .node node13015 node12811 +def node13017 : Tree Nat := .node node13016 node10045 +def node13018 : Tree Nat := .node node13017 node12816 +def node13019 : Tree Nat := .leaf 1329227995784915854457062986570792960 +def node13020 : Tree Nat := .node node13019 node12464 +def node13021 : Tree Nat := .node node13020 node12467 +def node13022 : Tree Nat := .node node13021 node12473 +def node13023 : Tree Nat := .node node13018 node13022 +def node13024 : Tree Nat := .leaf 79228162514264337580659048448 +def node13025 : Tree Nat := .node node13024 node12824 +def node13026 : Tree Nat := .node node13025 node10350 +def node13027 : Tree Nat := .node node13026 node9490 +def node13028 : Tree Nat := .node node13027 node12120 +def node13029 : Tree Nat := .node node13023 node13028 +def node13030 : Tree Nat := .leaf 5192217631581239183526056983330816 +def node13031 : Tree Nat := .node node13030 node12831 +def node13032 : Tree Nat := .node node13031 node10356 +def node13033 : Tree Nat := .node node13032 node11445 +def node13034 : Tree Nat := .node node13033 node12838 +def node13035 : Tree Nat := .node node13034 node12844 +def node13036 : Tree Nat := .node node13029 node13035 +def node13037 : Tree Nat := .leaf 780982533369245939310113824480166144 +def node13038 : Tree Nat := .node node13037 node12131 +def node13039 : Tree Nat := .node node13038 node10056 +def node13040 : Tree Nat := .node node13039 node12498 +def node13041 : Tree Nat := .node node13040 node12503 +def node13042 : Tree Nat := .node node13041 node12149 +def node13043 : Tree Nat := .node node13042 node12516 +def node13044 : Tree Nat := .node node13036 node13043 +def node13045 : Tree Nat := .leaf 1251038113679918332326938247765688336 +def node13046 : Tree Nat := .node node13045 node7161 +def node13047 : Tree Nat := .node node13046 node10080 +def node13048 : Tree Nat := .node node13047 node8848 +def node13049 : Tree Nat := .node node13048 node11474 +def node13050 : Tree Nat := .node node13049 node12523 +def node13051 : Tree Nat := .node node13050 node12535 +def node13052 : Tree Nat := .node node13051 node12557 +def node13053 : Tree Nat := .node node13044 node13052 +def node13054 : Tree Nat := .leaf 1063374252034722567236550422494707716 +def node13055 : Tree Nat := .node node13054 node5191 +def node13056 : Tree Nat := .node node13055 node10106 +def node13057 : Tree Nat := .node node13056 node10425 +def node13058 : Tree Nat := .node node13057 node11530 +def node13059 : Tree Nat := .node node13058 node11860 +def node13060 : Tree Nat := .node node13059 node12565 +def node13061 : Tree Nat := .node node13060 node12586 +def node13062 : Tree Nat := .node node13061 node12642 +def node13063 : Tree Nat := .node node13053 node13062 +def node13064 : Tree Nat := .leaf 882694569845703146682707379532857346 +def node13065 : Tree Nat := .node node13064 node12645 +def node13066 : Tree Nat := .node node13065 node10222 +def node13067 : Tree Nat := .node node13066 node12650 +def node13068 : Tree Nat := .node node13067 node12655 +def node13069 : Tree Nat := .node node13068 node11941 +def node13070 : Tree Nat := .node node13069 node12663 +def node13071 : Tree Nat := .leaf 781895255728023203190532663052075520 +def node13072 : Tree Nat := .node node13071 node12293 +def node13073 : Tree Nat := .node node13072 node10240 +def node13074 : Tree Nat := .node node13073 node9024 +def node13075 : Tree Nat := .node node13074 node11947 +def node13076 : Tree Nat := .node node13075 node12305 +def node13077 : Tree Nat := .node node13076 node12324 +def node13078 : Tree Nat := .node node13070 node13077 +def node13079 : Tree Nat := .node node13078 node12716 +def node13080 : Tree Nat := .node node13079 node12945 +def node13081 : Tree Nat := .node node13063 node13080 +def node13082 : Tree Nat := .leaf 1329227995784915872903807060280344575 +def node13083 : Tree Nat := .node node13082 node12811 +def node13084 : Tree Nat := .node node13083 node10045 +def node13085 : Tree Nat := .leaf 7507516828804700229971157695509256861311759593549503536677899755757881062691615256630906892622143669048765587635950989016785553242771871920041144482488516403958696424541355426923166035466523350467695506195964986883515036982379190362690015999085553756667903 +def node13086 : Tree Nat := .node node13085 node12814 +def node13087 : Tree Nat := .node node13086 node8784 +def node13088 : Tree Nat := .node node13084 node13087 +def node13089 : Tree Nat := .leaf 78189882104997540576868808472334095 +def node13090 : Tree Nat := .node node13089 node12464 +def node13091 : Tree Nat := .node node13090 node12467 +def node13092 : Tree Nat := .node node13091 node12473 +def node13093 : Tree Nat := .node node13088 node13092 +def node13094 : Tree Nat := .leaf 265853664645823461977737834263687987 +def node13095 : Tree Nat := .node node13094 node12824 +def node13096 : Tree Nat := .node node13095 node10350 +def node13097 : Tree Nat := .leaf 1134503866941667986143541334648056457619674842830209732174383704661281727402804754416548424845268597132444970383912631563207990827489845178429108122191373230708943107068998149163237322978318337638638205048320699552232994768557237690514401021486228613816024412910109967461524701183 +def node13098 : Tree Nat := .node node13097 node9488 +def node13099 : Tree Nat := .node node13098 node9224 +def node13100 : Tree Nat := .node node13096 node13099 +def node13101 : Tree Nat := .node node13100 node12120 +def node13102 : Tree Nat := .node node13093 node13101 +def node13103 : Tree Nat := .leaf 441349289580691512391917718186935125 +def node13104 : Tree Nat := .node node13103 node12831 +def node13105 : Tree Nat := .node node13104 node10356 +def node13106 : Tree Nat := .leaf 1125210230865546156491849650849141005172147100623948788746598902420821053428050286487299832733803496144141082012950154579985768502758488851419781728238585222574812589266531793180956535522916236801065068872748755031425023 +def node13107 : Tree Nat := .node node13106 node9498 +def node13108 : Tree Nat := .node node13107 node11444 +def node13109 : Tree Nat := .node node13105 node13108 +def node13110 : Tree Nat := .node node13109 node12838 +def node13111 : Tree Nat := .node node13110 node12844 +def node13112 : Tree Nat := .node node13102 node13111 +def node13113 : Tree Nat := .leaf 20203490921443235636127691964160 +def node13114 : Tree Nat := .node node13113 node12131 +def node13115 : Tree Nat := .node node13114 node10056 +def node13116 : Tree Nat := .leaf 17311155196269223196464683982066137460447416991840732818070830393671261811490375849033411404231964381810464754670324811932353562430335537915041855151722693554378390873491324469124433380221578326735867175047542352811765745130236894818601835615721695860309386104779270267076607 +def node13117 : Tree Nat := .node node13116 node8379 +def node13118 : Tree Nat := .node node13117 node12497 +def node13119 : Tree Nat := .node node13115 node13118 +def node13120 : Tree Nat := .node node13119 node12503 +def node13121 : Tree Nat := .node node13120 node12149 +def node13122 : Tree Nat := .leaf 388129523075618493122339836630096054427223634588105293390099477028266276159473090555861521249404160932011661038651793952929479422758812987550487914612078970202667472208588016059109786710000848624003605420488586967828307001594609663 +def node13123 : Tree Nat := .node node13122 node8394 +def node13124 : Tree Nat := .node node13123 node11087 +def node13125 : Tree Nat := .node node10068 node13124 +def node13126 : Tree Nat := .node node13125 node12509 +def node13127 : Tree Nat := .leaf 468837596257654785485714567836825287797216999011290225314876832561941490196892712413000809714458310517483176007983386841105428133203049499878352226978873295886886612109912281310141679716984610495621541891484513543913471 +def node13128 : Tree Nat := .node node13127 node8403 +def node13129 : Tree Nat := .node node13128 node11808 +def node13130 : Tree Nat := .node node13129 node10073 +def node13131 : Tree Nat := .node node12514 node13130 +def node13132 : Tree Nat := .node node13126 node13131 +def node13133 : Tree Nat := .node node13121 node13132 +def node13134 : Tree Nat := .node node13112 node13133 +def node13135 : Tree Nat := .leaf 20282100123345840874169005244160 +def node13136 : Tree Nat := .node node13135 node7161 +def node13137 : Tree Nat := .node node13136 node10080 +def node13138 : Tree Nat := .leaf 1198036083490401393367579651265226826447551684806266405050177285577599119244146985902642702006115315422144908141997955354442654161558858392652635956895807234053333644930642165096742786396124080735141558700451638583991144045229014311750217410052339812359073156764277461583242563944447 +def node13139 : Tree Nat := .node node13138 node8411 +def node13140 : Tree Nat := .node node13139 node8847 +def node13141 : Tree Nat := .node node13137 node13140 +def node13142 : Tree Nat := .node node13141 node11474 +def node13143 : Tree Nat := .node node13142 node12523 +def node13144 : Tree Nat := .leaf 20036365607438398109206554221717894591659180118237426039412854667412122224214503810828260586009694292471602677085437682769966064655111192062970664211417467949647261595047783935418163656787200077547300458755866726888308095984177535042959544840056549823002391281592323482449117576528342986784767 +def node13145 : Tree Nat := .node node13144 node8432 +def node13146 : Tree Nat := .node node13145 node11483 +def node13147 : Tree Nat := .node node12527 node13146 +def node13148 : Tree Nat := .node node13147 node11824 +def node13149 : Tree Nat := .node node13148 node12534 +def node13150 : Tree Nat := .node node13143 node13149 +def node13151 : Tree Nat := .leaf 80145462429753592445482322650559168134091064725027669358396684983451368644923776130938100240910653658101242071565417656836259861823657472707729412812233908292102307548806815514861582499591286511208356178336207009271225452082097782481502387044477048311498078250559512591037307049843510587949055 +def node13152 : Tree Nat := .node node13151 node8448 +def node13153 : Tree Nat := .node node13152 node12538 +def node13154 : Tree Nat := .node node11835 node13153 +def node13155 : Tree Nat := .node node13154 node12183 +def node13156 : Tree Nat := .node node13155 node12546 +def node13157 : Tree Nat := .leaf 4989600774417665509015065799559216404602780166926639091188048129501138449035341986869698100080542248342583753843428313671635575063230559098187536994539972933005997472758539794579254625311002825115066060503208231882468157064164019707657553381209589556765297911771193333506945964337182835474431 +def node13158 : Tree Nat := .node node13157 node8463 +def node13159 : Tree Nat := .node node13158 node11132 +def node13160 : Tree Nat := .node node10407 node13159 +def node13161 : Tree Nat := .node node13160 node12198 +def node13162 : Tree Nat := .leaf 17926543156650705493745156729723227086574128068473552473659540154970077439176188202568893103141175937287205588304377392190185369369475267917001639732154358328899734084597219304627307786412468836111251967491421765631 +def node13163 : Tree Nat := .node node13162 node8472 +def node13164 : Tree Nat := .node node13163 node12201 +def node13165 : Tree Nat := .node node13164 node10766 +def node13166 : Tree Nat := .node node12554 node13165 +def node13167 : Tree Nat := .node node13161 node13166 +def node13168 : Tree Nat := .node node13156 node13167 +def node13169 : Tree Nat := .node node13150 node13168 +def node13170 : Tree Nat := .node node13134 node13169 +def node13171 : Tree Nat := .leaf 5172014757211963951353003119804160 +def node13172 : Tree Nat := .node node13171 node5191 +def node13173 : Tree Nat := .node node13172 node10106 +def node13174 : Tree Nat := .leaf 36304123742133375556593330216254635448529824738232755544798166470840175999708721578904841561045755026793346261350008872879909556370672936013382894168378543194507926213841472487214390311393061541483299565880754275502469841512321511300826214601287225876698518922094653410844101050367 +def node13175 : Tree Nat := .node node13174 node6448 +def node13176 : Tree Nat := .node node13175 node10424 +def node13177 : Tree Nat := .node node13173 node13176 +def node13178 : Tree Nat := .node node13177 node11530 +def node13179 : Tree Nat := .node node13178 node11860 +def node13180 : Tree Nat := .leaf 20114328119529598101849381248576356844260372121771258500328082453509786552587602388615402985422003286694629844743189464679972790247107178046857054806744177249097321093177889564539159850498167825446728415712806013666883199524892261241736205001162508566973354993725778404052902189885531837431807 +def node13181 : Tree Nat := .node node13180 node6836 +def node13182 : Tree Nat := .node node13181 node10438 +def node13183 : Tree Nat := .node node10436 node13182 +def node13184 : Tree Nat := .node node13183 node11536 +def node13185 : Tree Nat := .node node13184 node12564 +def node13186 : Tree Nat := .node node13179 node13185 +def node13187 : Tree Nat := .leaf 159979074811142526733376176478649845913726400468227039400546995978457108606195822085848242502208871814147841939303516298562461715320792416588692211721032574627857094924207395842199566855284999841253009260713314861888938826657348399093729138641345229856783628766996861844499652290404577305427967 +def node13188 : Tree Nat := .node node13187 node10117 +def node13189 : Tree Nat := .node node13188 node12571 +def node13190 : Tree Nat := .node node12569 node13189 +def node13191 : Tree Nat := .node node13190 node11552 +def node13192 : Tree Nat := .node node13191 node12224 +def node13193 : Tree Nat := .leaf 9979201548254465038155997574090178006299953753319660660381375882742818927998918350738505463023658415398099156132278510137744736367289781369040026320175171618009363958374242511544740415411849804989814965072301583613655066486254536116781414466088205360887915479527721544144635813554987059904511 +def node13194 : Tree Nat := .node node13193 node9824 +def node13195 : Tree Nat := .node node13194 node11169 +def node13196 : Tree Nat := .node node10464 node13195 +def node13197 : Tree Nat := .node node13196 node11887 +def node13198 : Tree Nat := .leaf 1174833932040724960313232606750625274616384720429471888776451919860092366200491702340667794169296118804398355566270771080656304851059944022032590696334448917359572673155626758359554959412250078440952688030423024364683263 +def node13199 : Tree Nat := .node node13198 node9833 +def node13200 : Tree Nat := .node node13199 node12227 +def node13201 : Tree Nat := .node node13200 node12582 +def node13202 : Tree Nat := .node node12579 node13201 +def node13203 : Tree Nat := .node node13197 node13202 +def node13204 : Tree Nat := .node node13192 node13203 +def node13205 : Tree Nat := .node node13186 node13204 +def node13206 : Tree Nat := .leaf 1876879207201175057492789423877314215327939898387375884169474870502861069060069777085350899625385307944621763169733298966004217108175076334941498697493526348261090679838701955844679066557945412331335633104200459721278358731244457002901161118180813081411583 +def node13207 : Tree Nat := .node node13206 node11892 +def node13208 : Tree Nat := .node node13207 node8954 +def node13209 : Tree Nat := .node node12590 node13208 +def node13210 : Tree Nat := .node node13209 node12595 +def node13211 : Tree Nat := .node node13210 node12242 +def node13212 : Tree Nat := .leaf 32244539253885818706292675051642253103647037187929130507437185080316792066156221825285406495653496851657776485678441071675117668035146022414305557196886535259051522490754145579969797895179315256401775808449739259697302398814583692636500478678799587330732336391127039 +def node13213 : Tree Nat := .node node13212 node11903 +def node13214 : Tree Nat := .node node13213 node12599 +def node13215 : Tree Nat := .node node10491 node13214 +def node13216 : Tree Nat := .node node13215 node12605 +def node13217 : Tree Nat := .node node13216 node12611 +def node13218 : Tree Nat := .node node13211 node13217 +def node13219 : Tree Nat := .leaf 141821638945306632879540928499235702789523804660839184782518748770858768217330637056927231610528714797648669947982388910771338890716884623321751781272675432160266887218119868172972824147326488661501869817027060846856350006731859710772130540814226045834298811153560774974304681983 +def node13220 : Tree Nat := .node node13219 node9868 +def node13221 : Tree Nat := .node node13220 node12618 +def node13222 : Tree Nat := .node node12616 node13221 +def node13223 : Tree Nat := .node node13222 node12624 +def node13224 : Tree Nat := .node node13223 node12270 +def node13225 : Tree Nat := .leaf 8061134813471454564709278378172451595382697492350202586319113003583328947243921783642977354659505911468918994647359185488933685101789674268739788968642849918860900085764455761008810428089234894369044556895150358232326421657180741883978432124687995715360011751260159 +def node13226 : Tree Nat := .node node13225 node10198 +def node13227 : Tree Nat := .node node13226 node11214 +def node13228 : Tree Nat := .node node10515 node13227 +def node13229 : Tree Nat := .node node13228 node12630 +def node13230 : Tree Nat := .leaf 273579137855854662637703584477554704905474600149037125472103942208734233739212779909899012926853449381586694951578066665825364326401150344902364034516509246267139574666783594129778154880340594286607825243209727 +def node13231 : Tree Nat := .node node13230 node10211 +def node13232 : Tree Nat := .node node13231 node11219 +def node13233 : Tree Nat := .node node13232 node8128 +def node13234 : Tree Nat := .node node12638 node13233 +def node13235 : Tree Nat := .node node13229 node13234 +def node13236 : Tree Nat := .node node13224 node13235 +def node13237 : Tree Nat := .node node13218 node13236 +def node13238 : Tree Nat := .node node13205 node13237 +def node13239 : Tree Nat := .node node13170 node13238 +def node13240 : Tree Nat := .leaf 1324035698927589952648428594392924160 +def node13241 : Tree Nat := .node node13240 node12645 +def node13242 : Tree Nat := .node node13241 node10222 +def node13243 : Tree Nat := .leaf 1234340207232534768924172979604602254694906452051709736717661236720499396856479823312072673064313071630115411980215128677346294207804374260756924346473570570601804001752727042444247368600918518930609367174255504442510088617885444184082760394641159356268289413947259495678075933294591 +def node13244 : Tree Nat := .node node13243 node8565 +def node13245 : Tree Nat := .node node13244 node12649 +def node13246 : Tree Nat := .node node13242 node13245 +def node13247 : Tree Nat := .node node13246 node12655 +def node13248 : Tree Nat := .node node13247 node11941 +def node13249 : Tree Nat := .leaf 39994768702785596225770281352084312081721853282407026069857556488069756134593827504028143467174470452474990943962669938400409793704882481838592406687053585316228198534298970086021145454035509544876989239109957934797546575222738120312819642958921720009038195055315048155847105764676003310862335 +def node13250 : Tree Nat := .node node13249 node8579 +def node13251 : Tree Nat := .node node13250 node11235 +def node13252 : Tree Nat := .node node10536 node13251 +def node13253 : Tree Nat := .node node13252 node11241 +def node13254 : Tree Nat := .node node13253 node12662 +def node13255 : Tree Nat := .node node13248 node13254 +def node13256 : Tree Nat := .leaf 1728071821205796398203023290242710 +def node13257 : Tree Nat := .node node13256 node12293 +def node13258 : Tree Nat := .node node13257 node10240 +def node13259 : Tree Nat := .leaf 80457312478118534229036470300930434235522628172007171743766890685245679184089647933239416792566688702726199162643349219304756178487690587881148635952103739212572069218136512981418747960205101428061079815665262519843036191502184975837112522252962909937375155106337792552030983989083779467575295 +def node13260 : Tree Nat := .node node13259 node8601 +def node13261 : Tree Nat := .node node13260 node9023 +def node13262 : Tree Nat := .node node13258 node13261 +def node13263 : Tree Nat := .node node13262 node11947 +def node13264 : Tree Nat := .node node13263 node12305 +def node13265 : Tree Nat := .leaf 5028582029882399525462345320204731981883587735092193063525305450952575249177172116263568223105123230548636787193461383948712621880603312140714785232842096368941520430405193310267830029669133521379494745372248628101557109290324128865943274367303488588767249365288852681829088484564451467460607 +def node13266 : Tree Nat := .node node13265 node8616 +def node13267 : Tree Nat := .node node13266 node9038 +def node13268 : Tree Nat := .node node10252 node13267 +def node13269 : Tree Nat := .node node13268 node12310 +def node13270 : Tree Nat := .leaf 1081947199765842424529591879509026010150599323721976877786911901102607643345088549071012028586067969415086892678226327950891943481813958187189058352707702921661272309510797616656978764698096947630881447428301830436959628321604570912209495215537416191501181007672682454450175 +def node13271 : Tree Nat := .node node13270 node8625 +def node13272 : Tree Nat := .node node13271 node12320 +def node13273 : Tree Nat := .node node13272 node11970 +def node13274 : Tree Nat := .node node12318 node13273 +def node13275 : Tree Nat := .node node13269 node13274 +def node13276 : Tree Nat := .node node13264 node13275 +def node13277 : Tree Nat := .node node13255 node13276 +def node13278 : Tree Nat := .leaf 1876879207201175057492789423877314215327939898387375884169474870502861069060070093590973961046635783876384798228441414893615363744802625114903901272193891965773159178991235475926452926225260928752525353097635840536846071211816353736858610533539366928646143 +def node13279 : Tree Nat := .node node13278 node6587 +def node13280 : Tree Nat := .node node13279 node12667 +def node13281 : Tree Nat := .node node10265 node13280 +def node13282 : Tree Nat := .node node13281 node12673 +def node13283 : Tree Nat := .node node13282 node12679 +def node13284 : Tree Nat := .leaf 1968170611839440239603092822138809854884193543195732940825840228588103579073369240675251808050747348422514460808850067699488827088718515501890242824204507273016030536139841159468466415661238827549579507217206306017314388508107284022186547572678776707298216640511 +def node13285 : Tree Nat := .node node13284 node6981 +def node13286 : Tree Nat := .node node13285 node11284 +def node13287 : Tree Nat := .node node10581 node13286 +def node13288 : Tree Nat := .node node13287 node12684 +def node13289 : Tree Nat := .node node13288 node12690 +def node13290 : Tree Nat := .node node13283 node13289 +def node13291 : Tree Nat := .leaf 141830295051199290754602382260373947395761342649441538550624200908015257966475838851543722998600295523153339307542856779229583930645813040756871935928954994184077134748546386712448692686860792090461209352870009684666016952950219644231626722393336860513790139290787151445707718655 +def node13292 : Tree Nat := .node node13291 node8646 +def node13293 : Tree Nat := .node node13292 node11303 +def node13294 : Tree Nat := .node node11998 node13293 +def node13295 : Tree Nat := .node node13294 node12696 +def node13296 : Tree Nat := .node node13295 node12702 +def node13297 : Tree Nat := .leaf 492012622892656704990238084452251441810928680478211353074222523471479393502725184660276873998006663998813145330047983509730321495612895498074327544186461058746881903333247832437633860389101362010104528074175179849629936774734206299697790850311135402774845456383 +def node13298 : Tree Nat := .node node13297 node8665 +def node13299 : Tree Nat := .node node13298 node12003 +def node13300 : Tree Nat := .node node10602 node13299 +def node13301 : Tree Nat := .node node13300 node12707 +def node13302 : Tree Nat := .leaf 6828046779268970776657768233878085902324275438521959671787668942028781287039163393246395227370680568936631177633751398183847755896434749212611613699815207199423526999689055146138073928553989707314316414176702792404671142025050694560009926213631 +def node13303 : Tree Nat := .node node13302 node8674 +def node13304 : Tree Nat := .node node13303 node11318 +def node13305 : Tree Nat := .node node13304 node12013 +def node13306 : Tree Nat := .node node12712 node13305 +def node13307 : Tree Nat := .node node13301 node13306 +def node13308 : Tree Nat := .node node13296 node13307 +def node13309 : Tree Nat := .node node13290 node13308 +def node13310 : Tree Nat := .node node13277 node13309 +def node13311 : Tree Nat := .leaf 7507516828804700229971157695509256861311759593549503536677899755757881062691614939970702182859795639737729241335368268839526962869220176380869024994616278906372529249382147856492585955442967754510945820115799159267379990268484825305227933581853500618309631 +def node13312 : Tree Nat := .node node13311 node8685 +def node13313 : Tree Nat := .node node13312 node12719 +def node13314 : Tree Nat := .node node12371 node13313 +def node13315 : Tree Nat := .node node13314 node12725 +def node13316 : Tree Nat := .node node13315 node12382 +def node13317 : Tree Nat := .leaf 32246507424497658146532278144464391913490075163096718785559364785344191354011248318908866205655535483151498720787432408330540408855682523067846012624874617360028222110378708653747845669032547654340269655198609248879860651614387510145366648253006329086391402266361855 +def node13318 : Tree Nat := .node node13317 node8696 +def node13319 : Tree Nat := .node node13318 node11333 +def node13320 : Tree Nat := .node node10622 node13319 +def node13321 : Tree Nat := .node node13320 node12731 +def node13322 : Tree Nat := .node node13321 node12737 +def node13323 : Tree Nat := .node node13316 node13322 +def node13324 : Tree Nat := .leaf 8656105892673619465444975048166327535575816414642870886433951036774960517713398590419113722066179432147823147253351950962798170215546662598092199921108283620759921794391459779472859766165906862099710146520716755861149392119382741038929865458471768304223416097881119803834367 +def node13325 : Tree Nat := .node node13324 node12890 +def node13326 : Tree Nat := .node node13325 node12741 +def node13327 : Tree Nat := .node node10319 node13326 +def node13328 : Tree Nat := .node node13327 node12747 +def node13329 : Tree Nat := .node node13328 node12753 +def node13330 : Tree Nat := .leaf 8061626826094347221414268616256904040889269236057812766754246782462871110468075123339448563158751726354989189573569737571599367519269569620284662933113569979541605607989935830180299252965061165383688056254087483958299437229146070822309947079933283080696883983679487 +def node13331 : Tree Nat := .node node13330 node9673 +def node13332 : Tree Nat := .node node13331 node9147 +def node13333 : Tree Nat := .node node12757 node13332 +def node13334 : Tree Nat := .node node12759 node13082 +def node13335 : Tree Nat := .node node11358 node13334 +def node13336 : Tree Nat := .node node12898 node13335 +def node13337 : Tree Nat := .node node13333 node13336 +def node13338 : Tree Nat := .leaf 1174833932040723294629220079997464680937933805781821401243985445075573084210780894769804100209656106251896829950546403362887871301176856649286481267126524720761980671939482040735062038747687999212848008227501372115779583 +def node13339 : Tree Nat := .node node13338 node12905 +def node13340 : Tree Nat := .node node13339 node11363 +def node13341 : Tree Nat := .node node13340 node12766 +def node13342 : Tree Nat := .node node12904 node13341 +def node13343 : Tree Nat := .node node13337 node13342 +def node13344 : Tree Nat := .node node13329 node13343 +def node13345 : Tree Nat := .node node13323 node13344 +def node13346 : Tree Nat := .leaf 72608247484266751113186647294354820488834247026939543948396825646101063287786253971485042109138266243244020558325693611899195180836380228795842510795805830184899484320891698888933334758724964010824766196053363935991772905653606246796970257905615962679339206000441594856484294885375 +def node13347 : Tree Nat := .node node13346 node9427 +def node13348 : Tree Nat := .node node13347 node12773 +def node13349 : Tree Nat := .node node12915 node13348 +def node13350 : Tree Nat := .node node13349 node12050 +def node13351 : Tree Nat := .node node13350 node12922 +def node13352 : Tree Nat := .leaf 40072731214876796218413108378942774334323045285940858530772784274179266683592954082168903349767324293130424338184606348085645673785155640043888534828777831355789397249513415866641676312060666906692242301348507838518265495255970418332236727578522906659536279200944446374943001755283244198133759 +def node13353 : Tree Nat := .node node13352 node12924 +def node13354 : Tree Nat := .node node13353 node11382 +def node13355 : Tree Nat := .node node12780 node13354 +def node13356 : Tree Nat := .node node13355 node12931 +def node13357 : Tree Nat := .node node13356 node12941 +def node13358 : Tree Nat := .node node13351 node13357 +def node13359 : Tree Nat := .leaf 160290924859507184890963588712040320533756863335788821184229948264768520609423743754511922078006017603983437319396672369196710285824121217747960377139064043842851939963770279939992922224534680114065829533015236208406364399917226924053716704235227880827350300527579576103837140806769977111609343 +def node13360 : Tree Nat := .node node13359 node12077 +def node13361 : Tree Nat := .node node13360 node9463 +def node13362 : Tree Nat := .node node12787 node13361 +def node13363 : Tree Nat := .node node13362 node12441 +def node13364 : Tree Nat := .node node13363 node12797 +def node13365 : Tree Nat := .leaf 10018182803719199054603277094735693583580761321485214632718632621999971839155334720690115850865904002970821504265768528967295833113652456910114441206157042932473873922526613546371820348768222940859757187900010682191860799649298422014767388486092887903545083290627190388155027503721618251710463 +def node13366 : Tree Nat := .node node13365 node12096 +def node13367 : Tree Nat := .node node13366 node12099 +def node13368 : Tree Nat := .node node10663 node13367 +def node13369 : Tree Nat := .node node13368 node12447 +def node13370 : Tree Nat := .leaf 2739226045072033710287658726391013369481562983073862426076014871121501917116897813478243768409544927272652705989782486018374878784366859763845742616822186473850268648721702203950014209636142468478077687130226687 +def node13371 : Tree Nat := .node node13370 node12103 +def node13372 : Tree Nat := .node node13371 node12454 +def node13373 : Tree Nat := .node node13372 node12108 +def node13374 : Tree Nat := .node node12802 node13373 +def node13375 : Tree Nat := .node node13369 node13374 +def node13376 : Tree Nat := .node node13364 node13375 +def node13377 : Tree Nat := .node node13358 node13376 +def node13378 : Tree Nat := .node node13345 node13377 +def node13379 : Tree Nat := .node node13310 node13378 +def node13380 : Tree Nat := .node node13239 node13379 +def node13381 : Tree Nat := .leaf 276978483140055660679575521154310658598553426872826080593424479721944743637335064583130340808000721892441268569379212308399932662694284205702097585169193435032414605838253575203503260866196031433458804951352921717574925866750570369867543299119527881831253598167422370116993279 +def node13382 : Tree Nat := .node node13381 node12469 +def node13383 : Tree Nat := .node node13382 node12472 +def node13384 : Tree Nat := .node node13091 node13383 +def node13385 : Tree Nat := .node node13088 node13384 +def node13386 : Tree Nat := .leaf 1134503866941667986143541334648056457619674842830209732174383704661281727402804754416548424845268597132444970383912631563207990827489845178429108122191373230708943107068998149163237322978318337638638205048320699552232994768557237690514401021486223441801267200946158614458404897023 +def node13387 : Tree Nat := .node node13386 node9488 +def node13388 : Tree Nat := .node node13387 node9224 +def node13389 : Tree Nat := .node node13096 node13388 +def node13390 : Tree Nat := .leaf 123003155723136208567847447683223664415745989465967061144775319672827615245282853070109007218536306674745708410782905388586055064621515797122191070561722069598184336831924337253385042086151271460696227772647207623375333095605399263720511828060168641693695869183 +def node13391 : Tree Nat := .node node13390 node11437 +def node13392 : Tree Nat := .node node13391 node12118 +def node13393 : Tree Nat := .node node9229 node13392 +def node13394 : Tree Nat := .node node13389 node13393 +def node13395 : Tree Nat := .node node13385 node13394 +def node13396 : Tree Nat := .leaf 33018408195979077897021236557282287907427960838451981092487189987679470573908052333928986881956429041035710718910443876958184790166011882350154566339868106858294749432546375864417740428279671221168030005380294700000841809675947608112270092401811134385875487573619507455 +def node13397 : Tree Nat := .node node13396 node9504 +def node13398 : Tree Nat := .node node13397 node12478 +def node13399 : Tree Nat := .node node12837 node13398 +def node13400 : Tree Nat := .node node13109 node13399 +def node13401 : Tree Nat := .leaf 48516190384397171392751175090678259260270162528013642586385209916290288086478333150780021580175739629118289543847768199510899830187141888180207452226534790820321120216919046882785569607977848325115592332233136063717435619732881663 +def node13402 : Tree Nat := .node node13401 node12485 +def node13403 : Tree Nat := .node node13402 node12125 +def node13404 : Tree Nat := .node node12842 node13403 +def node13405 : Tree Nat := .node node13404 node12492 +def node13406 : Tree Nat := .node node13400 node13405 +def node13407 : Tree Nat := .node node13395 node13406 +def node13408 : Tree Nat := .leaf 2015283703367863641175612582842135243135427334428804184044917736999987313807108150565911656580400360071894370193173689646129889958808112504284773750881602853973553365132356026392074963350514880265968068991716688117422993563050756776667194658290193433748078187315199 +def node13409 : Tree Nat := .node node13408 node8813 +def node13410 : Tree Nat := .node node13409 node12501 +def node13411 : Tree Nat := .node node11789 node13410 +def node13412 : Tree Nat := .node node13119 node13411 +def node13413 : Tree Nat := .leaf 225921116696657399755928707376375798670333560260644071634548162212369334107823776038057071519881333252061364655668791715358213179274623608611407031717239351202907673747076056987966624041453848789327434685209362819394371583 +def node13414 : Tree Nat := .node node13413 node8818 +def node13415 : Tree Nat := .node node13414 node10368 +def node13416 : Tree Nat := .node node12138 node13415 +def node13417 : Tree Nat := .leaf 225924563982610226070265215820544374824657167771312989075437813652077668501960498285146510074899144885499114984200464467326910359101686978775252846219264264892966590051920900182865697594634952735359432412393566175882117375 +def node13418 : Tree Nat := .node node13417 node12143 +def node13419 : Tree Nat := .node node13418 node12146 +def node13420 : Tree Nat := .node node12142 node13419 +def node13421 : Tree Nat := .node node13416 node13420 +def node13422 : Tree Nat := .node node13412 node13421 +def node13423 : Tree Nat := .leaf 8863852434081664062958681472877695588158784959592295567428676745533724054444448707009155594945536400548669592693422271275626349022051805379194444516422601761535311722779303668492240133077151516401604992088085099140856217169796100269094434467468032314614656786235633007778070783 +def node13424 : Tree Nat := .node node13423 node8828 +def node13425 : Tree Nat := .node node13424 node12507 +def node13426 : Tree Nat := .node node12153 node13425 +def node13427 : Tree Nat := .node node13125 node13426 +def node13428 : Tree Nat := .leaf 1081947199765842424529591879509026010150599323721976877786900707526989651739900452381302641357895255978501721913515669361826438869198939157555349872519364529282686887865300640437034619865895573149131335640835183649031013298945249799126032019919233203469636869194331694563327 +def node13429 : Tree Nat := .node node13428 node8833 +def node13430 : Tree Nat := .node node13429 node12512 +def node13431 : Tree Nat := .node node12158 node13430 +def node13432 : Tree Nat := .leaf 468837596257654785485714567836825287797216999011290225314876832561941490196892712413000809714458310517483176007983386841105428133203049499878352226978873295886886612109912281310141678392948911568031589243055919150989311 +def node13433 : Tree Nat := .node node13432 node8403 +def node13434 : Tree Nat := .node node13433 node11808 +def node13435 : Tree Nat := .node node13434 node10073 +def node13436 : Tree Nat := .node node13431 node13435 +def node13437 : Tree Nat := .node node13427 node13436 +def node13438 : Tree Nat := .node node13422 node13437 +def node13439 : Tree Nat := .node node13407 node13438 +def node13440 : Tree Nat := .leaf 86858970270951006203423838165645771885047073375041211488604415337194479134408200026866468221203321374509304249163184904583451743670206537702115563266644027668708487191084016195953265499820484379492289712844829686163969286747579215443403244899357270621071917752462597415428666947308775636096581631 +def node13441 : Tree Nat := .node node13440 node8850 +def node13442 : Tree Nat := .node node13441 node11472 +def node13443 : Tree Nat := .node node11470 node13442 +def node13444 : Tree Nat := .node node13141 node13443 +def node13445 : Tree Nat := .leaf 320581849719015504285796232270159840383892969391784817983639634828399285715423821179807476921894270412460028816508423648153232402599709517290130818817670178154070101218375702613277248737488700294725089103305924473206939663798042759485596102028104174913448813398890499185713067584077834208870655 +def node13446 : Tree Nat := .node node13445 node8419 +def node13447 : Tree Nat := .node node13446 node12168 +def node13448 : Tree Nat := .node node12521 node13447 +def node13449 : Tree Nat := .leaf 305135869619641084486162424651110383869718645522469604919050302005727267917819995841479478538868055680940285189690738651919013376267824941051617314061007409483742210675248527715269648201148996333276918982055879758765585967492508679507501528971337673079419271430840490144633441190091423743 +def node13450 : Tree Nat := .node node13449 node11476 +def node13451 : Tree Nat := .node node13450 node8427 +def node13452 : Tree Nat := .node node8425 node13451 +def node13453 : Tree Nat := .node node13448 node13452 +def node13454 : Tree Nat := .node node13444 node13453 +def node13455 : Tree Nat := .leaf 20036365607438398109206554221717894591659180118237426039412854667412122224214503810828260586009694292471602677085437682769966064655111192062970664211417467949647261595047783935418163656787200077547300458755866726888308095984177535042959544840056549823002391276420308725237153625175339866980607 +def node13456 : Tree Nat := .node node13455 node8432 +def node13457 : Tree Nat := .node node13456 node11483 +def node13458 : Tree Nat := .node node12527 node13457 +def node13459 : Tree Nat := .leaf 38067632857031246415885002001632223813615570301801070128684750548400235182831352333308404133180821172702099111877852160800355136763992239695518951053977240173283467367941175228282463341185918534820004623241488810812315249396333941409644421671105928804343599933002480967008840944279617535 +def node13460 : Tree Nat := .node node13459 node8862 +def node13461 : Tree Nat := .node node13460 node11822 +def node13462 : Tree Nat := .node node11489 node13461 +def node13463 : Tree Nat := .node node13458 node13462 +def node13464 : Tree Nat := .leaf 18587711355972288284975781226873757001640752520742430762455243433647852495356937686061563313740224455898572328929311704065567065391092933311837846148791088729398392233347632277708175404638606175464530453434801214177405834470295458207525426731480015566053688823400502339576875815272447 +def node13465 : Tree Nat := .node node13464 node8869 +def node13466 : Tree Nat := .node node13465 node12531 +def node13467 : Tree Nat := .node node11494 node13466 +def node13468 : Tree Nat := .node node13467 node12176 +def node13469 : Tree Nat := .node node13463 node13468 +def node13470 : Tree Nat := .node node13454 node13469 +def node13471 : Tree Nat := .leaf 19070991851227567780385655359698316649593705989427444620245069009852873381868266799619284790372586035931953043278025883202425015142334914992320745639743023782957160290155831262614110372560209147570684874137322521731381072630438671218798334986687041177574456521502308787992078865009672447 +def node13472 : Tree Nat := .node node13471 node8884 +def node13473 : Tree Nat := .node node13472 node11504 +def node13474 : Tree Nat := .node node12182 node13473 +def node13475 : Tree Nat := .node node13154 node13474 +def node13476 : Tree Nat := .leaf 4792144333961605573470318597553505032601180409098725599827279743563115417912112873870037829428216777831309210655101407571163493262736114679447454578921403231388587583565533846240720862956847408963542982250236474540534393570768670284273869653759790302298505007449367116913717115158527 +def node13477 : Tree Nat := .node node13476 node8889 +def node13478 : Tree Nat := .node node13477 node12186 +def node13479 : Tree Nat := .node node11840 node13478 +def node13480 : Tree Nat := .leaf 347435881083804024813695352662582961584956833008659305225776271727755038173984289085997064519319836027896598150277906664489114558658205249325521407903002537796268903234728220188901475585127554123903957158063485043643369761486045258142528445235487148116499512003530308197039784633442380816530276351 +def node13481 : Tree Nat := .node node13480 node12542 +def node13482 : Tree Nat := .node node13481 node10091 +def node13483 : Tree Nat := .node node12191 node13482 +def node13484 : Tree Nat := .node node13479 node13483 +def node13485 : Tree Nat := .node node13475 node13484 +def node13486 : Tree Nat := .leaf 4989600774417665509015065799559216404602780166926639091188048129501138449035341986869698100080542248342583753843428313671635575063230559098187536994539972933005997472758539794579254625311002825115066060503208231882468157064164019707657553381209589556765297906599178576294982012984179715670271 +def node13487 : Tree Nat := .node node13486 node8463 +def node13488 : Tree Nat := .node node13487 node11132 +def node13489 : Tree Nat := .node node10407 node13488 +def node13490 : Tree Nat := .leaf 609156476566787278379108054239156247333694058308169791851172548092041729379507673387366203849147725996730025406920568452273150403897892308531071537704644186156703520144043236917508273800981481956093727732268419714023411839396981673670438107794104211235677843750571193599808207008311541759 +def node13491 : Tree Nat := .node node13490 node9275 +def node13492 : Tree Nat := .node node13491 node10410 +def node13493 : Tree Nat := .node node12197 node13492 +def node13494 : Tree Nat := .node node13489 node13493 +def node13495 : Tree Nat := .leaf 1277342670759226379460700660234536462305607824197264347990219482828857053616974461436967345783191853911950530066003400769902543076803619525702886840821972807467189310119954914441588863863238364207919223494656759721532371568606469678750184742073157127139805894409945156215332016459260960272482559 +def node13496 : Tree Nat := .node node13495 node8900 +def node13497 : Tree Nat := .node node13496 node12552 +def node13498 : Tree Nat := .node node12550 node13497 +def node13499 : Tree Nat := .node node13498 node13165 +def node13500 : Tree Nat := .node node13494 node13499 +def node13501 : Tree Nat := .node node13485 node13500 +def node13502 : Tree Nat := .node node13470 node13501 +def node13503 : Tree Nat := .node node13439 node13502 +def node13504 : Tree Nat := .leaf 168608589349493131958015087616540679668592803278962431331060101814331015260871777495148119299778999483168145679854451622674939147754434619637275616256377777392408477111434973918618393799252678538302702349285742709182101189207206478668919921086858129216098575737707761332874045797949568052889583871 +def node13505 : Tree Nat := .node node13504 node7222 +def node13506 : Tree Nat := .node node13505 node11528 +def node13507 : Tree Nat := .node node11525 node13506 +def node13508 : Tree Nat := .node node13177 node13507 +def node13509 : Tree Nat := .leaf 321829249912474136881525683989307835131953557306589263343752782944593437589520939150189555629080100264798835086290555977713254120225443146180701228171476451892310277561050909123407951909422647174765070431906078761372756650335197093869944677908587267228944404948743990980526961672479642214268927 +def node13510 : Tree Nat := .node node13509 node6826 +def node13511 : Tree Nat := .node node13510 node11857 +def node13512 : Tree Nat := .node node10430 node13511 +def node13513 : Tree Nat := .leaf 305730676383032197711281649742622710886123306029018948465096423214894378187525711710577125145017308736797642166709708925119651563701120884476865237687147190834701536676069687533883080766034579488107378925052481974792132810804528819213223678255519999185260752421176859522527806119166869503 +def node13514 : Tree Nat := .node node13513 node11144 +def node13515 : Tree Nat := .node node13514 node9798 +def node13516 : Tree Nat := .node node10112 node13515 +def node13517 : Tree Nat := .node node13512 node13516 +def node13518 : Tree Nat := .node node13508 node13517 +def node13519 : Tree Nat := .leaf 20114328119529598101849381248576356844260372121771258500328082453509786552587602388615402985422003286694629844743189464679972790247107178046857054806744177249097321093177889564539159850498167825446728415712806013666883199524892261241736205001162508566973353669690079476462949541456937444507647 +def node13520 : Tree Nat := .node node13519 node6836 +def node13521 : Tree Nat := .node node13520 node10438 +def node13522 : Tree Nat := .node node10436 node13521 +def node13523 : Tree Nat := .leaf 40446859910595699341125708145656373132591514042419445126956107720017105848770028401130341546201483200632496178089575328505341280298665416420738783615214685575516665677543978420028481860981334107678969827397592415521936031525211183633406223766682073247883336148641733606944663089081942271 +def node13524 : Tree Nat := .node node13523 node7235 +def node13525 : Tree Nat := .node node13524 node11151 +def node13526 : Tree Nat := .node node11535 node13525 +def node13527 : Tree Nat := .node node13522 node13526 +def node13528 : Tree Nat := .leaf 18587711355972288284975781226873757001640752527254561075954200296864920133568817487707092950860057205891604452303042089454261995933702318684836888461722869150513792971597610852869053192966382049615296070527169379437005615326909340540045362780284771742652111347243401418194281174073599 +def node13529 : Tree Nat := .node node13528 node6845 +def node13530 : Tree Nat := .node node13529 node12210 +def node13531 : Tree Nat := .node node12562 node13530 +def node13532 : Tree Nat := .node node13531 node12216 +def node13533 : Tree Nat := .node node13527 node13532 +def node13534 : Tree Nat := .node node13518 node13533 +def node13535 : Tree Nat := .leaf 37175422711944576571966846157115377644457117624326996718013592867814909517272922286185664988388014749487763295594273489954555800867105990784175189628038510374413617503462222491871385824278346527407119254668977871877140251560080523816850153173163401478314836443073507739286455483170815 +def node13536 : Tree Nat := .node node13535 node7242 +def node13537 : Tree Nat := .node node13536 node11550 +def node13538 : Tree Nat := .node node11548 node13537 +def node13539 : Tree Nat := .node node13190 node13538 +def node13540 : Tree Nat := .leaf 4937360828930139075696691888388341703560824888322208164833617614595517561556605024501045357416203106568280468781367495212908167983181339073273592438566943336108922629372796776202083052275359055708099265239702556857507176525057421565370904417591514793333582038634652306645390957936895 +def node13541 : Tree Nat := .node node13540 node9814 +def node13542 : Tree Nat := .node node13541 node11874 +def node13543 : Tree Nat := .node node11871 node13542 +def node13544 : Tree Nat := .leaf 367873285853439564760533587811143966328459060057661429664211016701021150139241504673514450146755572907776759555882616850812232166675443291171532706989528100542462706662124705638869494300965106051153893667243031562928615940775818537943818489297006017639786694339326313511400657065761419907894870015 +def node13545 : Tree Nat := .node node13544 node12220 +def node13546 : Tree Nat := .node node13545 node8508 +def node13547 : Tree Nat := .node node11880 node13546 +def node13548 : Tree Nat := .node node13543 node13547 +def node13549 : Tree Nat := .node node13539 node13548 +def node13550 : Tree Nat := .leaf 74350847640257991860231331556363993181239786870752635029752400361930165761785448651591505484970839553341940157553410627684958321052340855584422428792356060817975930476681643200448303206502130554636552985996031068956834435954675543855893812783291068692475976382214849444775071884247295 +def node13551 : Tree Nat := .node node13550 node10800 +def node13552 : Tree Nat := .node node13551 node11885 +def node13553 : Tree Nat := .node node11557 node13552 +def node13554 : Tree Nat := .node node13196 node13553 +def node13555 : Tree Nat := .leaf 4872657005699999810663491135398204041823608939751973073340296112092162650589745671020362028981173928417388251915025194266042170442037274997643866993603969714391782314214918113366669399820314066283330081797497310614275602110739527794279828745667685699622277864901638295349880606230640066559 +def node13556 : Tree Nat := .node node13555 node10467 +def node13557 : Tree Nat := .node node13556 node12577 +def node13558 : Tree Nat := .node node11562 node13557 +def node13559 : Tree Nat := .leaf 1174833932040724960313232606750625274616384720429471888776451919860092366200491702340667794169296118804398355566270771080656304851059944022032590696334448917359572673155626758359554959412229796340829342189548855359439103 +def node13560 : Tree Nat := .node node13559 node9833 +def node13561 : Tree Nat := .node node13560 node12227 +def node13562 : Tree Nat := .node node13561 node12582 +def node13563 : Tree Nat := .node node13558 node13562 +def node13564 : Tree Nat := .node node13554 node13563 +def node13565 : Tree Nat := .node node13549 node13564 +def node13566 : Tree Nat := .node node13534 node13565 +def node13567 : Tree Nat := .leaf 2269146223124906000117422926276498862782315294279058932144853424001014171895230212411404973000048044792172692986741420723191826847732454366742485245184723751556231813275184199818286288664587407927686291209969248876865125372494088416703025341267716201733360361431055397653445672959 +def node13568 : Tree Nat := .node node13567 node10475 +def node13569 : Tree Nat := .node node13568 node12593 +def node13570 : Tree Nat := .node node11570 node13569 +def node13571 : Tree Nat := .node node13209 node13570 +def node13572 : Tree Nat := .leaf 567286555781226500029355731569122967715603332303024435169262119354790718260422894252365794277193656171034240881504545882039792440605577976305040582381114750828792298657564703515972443248396882185269925306943303416431680051002886638100427216309148444832342603246313994698157522943 +def node13573 : Tree Nat := .node node13572 node11576 +def node13574 : Tree Nat := .node node13573 node12235 +def node13575 : Tree Nat := .node node10482 node13574 +def node13576 : Tree Nat := .leaf 30750788930784052141961861920811980997887234677887817339864608149478746012353383005245511535615183867402719086846186378172349218606166225793694462505817694549368294893849779989912882483817193565211203275397663375979504164983291130147207674082427951500639600895 +def node13577 : Tree Nat := .node node13576 node11897 +def node13578 : Tree Nat := .node node13577 node12239 +def node13579 : Tree Nat := .node node11185 node13578 +def node13580 : Tree Nat := .node node13575 node13579 +def node13581 : Tree Nat := .node node13571 node13580 +def node13582 : Tree Nat := .leaf 32244539253885818706292675051642253103647037187929130507437185080316792066156221825285406495653496851657776485678441071675117668035146022414305557196886535259051522490754145579969797895179315256401775808449739259697302398814583691307292764994007078570430529739423999 +def node13583 : Tree Nat := .node node13582 node11903 +def node13584 : Tree Nat := .node node13583 node12599 +def node13585 : Tree Nat := .node node10491 node13584 +def node13586 : Tree Nat := .leaf 8254602048994769474255309139322199910068143258083693241044839823575153550594486940739435416735876022684849312314722302358075980517169046263441500479711629410651914192877422095937077620632807849196598684646854079044997768909947805864297187601219851308554327151236677631 +def node13587 : Tree Nat := .node node13586 node10165 +def node13588 : Tree Nat := .node node13587 node12603 +def node13589 : Tree Nat := .node node12246 node13588 +def node13590 : Tree Nat := .node node13585 node13589 +def node13591 : Tree Nat := .leaf 6512130313498956863217084807164470744461190538033039686479754608152295293285303498932704226690161011840344628306615244958143754424581746160005740030721115414831250524732072120471607767215869506335382602391011073857551276986966272485949439 +def node13592 : Tree Nat := .node node13591 node11588 +def node13593 : Tree Nat := .node node13592 node12608 +def node13594 : Tree Nat := .node node12251 node13593 +def node13595 : Tree Nat := .node node13594 node11920 +def node13596 : Tree Nat := .node node13590 node13595 +def node13597 : Tree Nat := .node node13581 node13596 +def node13598 : Tree Nat := .leaf 503820925841965910293903145710682853278783176422042742899963128541361843967736281426486644995877983155568212169833255435184329347739794588698106462461282403652790728932768240966668038923127871765125284449793408086921060505933786214231811640066844018184064851706111 +def node13599 : Tree Nat := .node node13598 node10500 +def node13600 : Tree Nat := .node node13599 node12622 +def node13601 : Tree Nat := .node node11206 node13600 +def node13602 : Tree Nat := .node node13222 node13601 +def node13603 : Tree Nat := .leaf 114555615673899844817675135827349603920186156328588973012815230098216247597001467415855239037616505603637170860454974156046109455801580026176644352441657784801933346009161319638632059810916765995044128687677992717902277133203904890087671875514075644159 +def node13604 : Tree Nat := .node node13603 node10188 +def node13605 : Tree Nat := .node node13604 node12263 +def node13606 : Tree Nat := .node node12261 node13605 +def node13607 : Tree Nat := .leaf 9076584892499624000469689828226760282701348722326821713643608315639232502580756490540189131484592466369882212749188672534231992940101449934755636487247161484782176778148646014730649729773003381487614761759138543577896610204126782187795157983712958837860655749919832261291461837055 +def node13608 : Tree Nat := .node node13607 node7290 +def node13609 : Tree Nat := .node node13608 node12267 +def node13610 : Tree Nat := .node node11926 node13609 +def node13611 : Tree Nat := .node node13606 node13610 +def node13612 : Tree Nat := .node node13602 node13611 +def node13613 : Tree Nat := .leaf 8061134813471454564709278378172451595382697492350202586319113003583328947243921783642977354659505911468918994647359185488933685101789674268739788968642849918860900085764455761008810428089234894369044556895150358232326421657180741878806417367476031764007008631455999 +def node13614 : Tree Nat := .node node13613 node10198 +def node13615 : Tree Nat := .node node13614 node11214 +def node13616 : Tree Nat := .node node10515 node13615 +def node13617 : Tree Nat := .leaf 2215963108520416015739670368219423897040103223200861968900182144416075582367312816110528302486423822293081034527335103821046647224874906191755096497613522479383626210196778033937866111658809070779601974003567415185610612313815382293752246014064172520993674680108790763480940543 +def node13618 : Tree Nat := .node node13617 node10848 +def node13619 : Tree Nat := .node node13618 node12628 +def node13620 : Tree Nat := .node node10204 node13619 +def node13621 : Tree Nat := .node node13616 node13620 +def node13622 : Tree Nat := .leaf 270486799941460606132397969877256554634692338922149125534990864827253047922381898296765922036845598671568204247815885628137567517818175826095693888262472651812408910495712160756593870939223671596717691837567818862928306520659828178036691853662185992718945450163999151685887 +def node13623 : Tree Nat := .node node13622 node10518 +def node13624 : Tree Nat := .node node13623 node12636 +def node13625 : Tree Nat := .node node12634 node13624 +def node13626 : Tree Nat := .leaf 273579137855854662637703584477554704905474600149037125472103942208734233739212779909899012926853449381586694951578066665825364326401150344902364034516509246267139574666783592805722173852636703637343404679954687 +def node13627 : Tree Nat := .node node13626 node10211 +def node13628 : Tree Nat := .node node13627 node11219 +def node13629 : Tree Nat := .node node13628 node8128 +def node13630 : Tree Nat := .node node13625 node13629 +def node13631 : Tree Nat := .node node13621 node13630 +def node13632 : Tree Nat := .node node13612 node13631 +def node13633 : Tree Nat := .node node13597 node13632 +def node13634 : Tree Nat := .node node13566 node13633 +def node13635 : Tree Nat := .node node13503 node13634 +def node13636 : Tree Nat := .leaf 1234340207232534768924172979604602254694906452051709736717661236720499396856479823312072673064313071630115411980215128677346294207804374260756924346473570570601804001752727042444247368600918518930609367174255504442510088617885444184082760394641159351096274656735295544325072813490431 +def node13637 : Tree Nat := .node node13636 node8565 +def node13638 : Tree Nat := .node node13637 node12649 +def node13639 : Tree Nat := .node node13242 node13638 +def node13640 : Tree Nat := .leaf 91968321463359891190271877741643521241811080357357754374850699790700430936706816559365054036878295092464935961604259661610452401777491444353936885094292892669342129114234833723624367198344907828786407901963416781473772858743134249540649602208935560444346072948195160674204135057424942184016117759 +def node13641 : Tree Nat := .node node13640 node8991 +def node13642 : Tree Nat := .node node13641 node11609 +def node13643 : Tree Nat := .node node12654 node13642 +def node13644 : Tree Nat := .node node13639 node13643 +def node13645 : Tree Nat := .leaf 639916299244570106898880282343936394601108129500086289847591281966445774086874148613579531170258849978937705569952856868184947918664318708362504720753564462941279276757510887279018182132657416178492560489528341474355086250189390618367775718725920126516888685502715705900587789634404765776478207 +def node13646 : Tree Nat := .node node13645 node8998 +def node13647 : Tree Nat := .node node13646 node11938 +def node13648 : Tree Nat := .node node11936 node13647 +def node13649 : Tree Nat := .leaf 1218759058188390998269292023606661654806717069847887146350174569787895234894393803710342248917586552091505598663909792279820342266659040293446632428157702443356617321741665090067496469685042973419493452164641674827539035806476143598059428512651241732077564209925102977142514243082286858239 +def node13650 : Tree Nat := .node node13649 node11616 +def node13651 : Tree Nat := .node node13650 node8574 +def node13652 : Tree Nat := .node node11615 node13651 +def node13653 : Tree Nat := .node node13648 node13652 +def node13654 : Tree Nat := .node node13644 node13653 +def node13655 : Tree Nat := .leaf 39994768702785596225770281352084312081721853282407026069857556488069756134593827504028143467174470452474990943962669938400409793704882481838592406687053585316228198534298970086021145454035509544876989239109957934797546575222738120312819642958921720009038195050143033398635141813323000191058175 +def node13656 : Tree Nat := .node node13655 node8579 +def node13657 : Tree Nat := .node node13656 node11235 +def node13658 : Tree Nat := .node node10536 node13657 +def node13659 : Tree Nat := .leaf 152270531428124985663540008006528895254462281213872294947618853506483312281637601006710476254648951477568578231959350517633987616622943568599590373193859195360868939825216653169583071331114913603895493890080653363050630102702956458529979846094068988950635429145567954623525049657762840575 +def node13660 : Tree Nat := .node node13659 node9008 +def node13661 : Tree Nat := .node node13660 node11239 +def node13662 : Tree Nat := .node node10884 node13661 +def node13663 : Tree Nat := .node node13658 node13662 +def node13664 : Tree Nat := .leaf 9516908214257811601907599988159363584840065290620124935450087718987904762481275522191874685950243732024609872161685536783436920631949828444073824651566436158632700981972424500129421206791459829592797996473299888060732951885525870173416992842012546755811918398235268209662125336600575999 +def node13665 : Tree Nat := .node node13664 node9015 +def node13666 : Tree Nat := .node node13665 node12659 +def node13667 : Tree Nat := .node node12284 node13666 +def node13668 : Tree Nat := .node node13667 node12289 +def node13669 : Tree Nat := .node node13663 node13668 +def node13670 : Tree Nat := .node node13654 node13669 +def node13671 : Tree Nat := .leaf 80457312478118534229036470300930434235522628172007171743766890685245679184089647933239416792566688702726199162643349219304756178487690587881148635952103739212572069218136512981418747960205101428061079815665262519843036191502184975837112522252962909937375153782302093624441031340655185074651135 +def node13672 : Tree Nat := .node node13671 node8601 +def node13673 : Tree Nat := .node node13672 node9023 +def node13674 : Tree Nat := .node node13258 node13673 +def node13675 : Tree Nat := .leaf 19182518119363401510097021509837085089334432213989030557701434505264689708377241855498476855145954111770111954865225270101930396867267044285639372698380683619098369523605745502539474917124134063916692376392100250429637189441522266501064957788075144989267943834236902727659888418620440575 +def node13676 : Tree Nat := .node node13675 node9026 +def node13677 : Tree Nat := .node node13676 node11634 +def node13678 : Tree Nat := .node node11946 node13677 +def node13679 : Tree Nat := .node node13674 node13678 +def node13680 : Tree Nat := .leaf 9439072172954677644714263904271829727395694639439515609240739454321509785382047952225675997004176433832325951903502590804545085859770249562327929855799949684973133695024869043544004569598801240538962845537402306902327473008038635379576778779074563796933106577631968292120603454865407 +def node13681 : Tree Nat := .node node13680 node9031 +def node13682 : Tree Nat := .node node13681 node11951 +def node13683 : Tree Nat := .node node10904 node13682 +def node13684 : Tree Nat := .leaf 674434357397972527831506359689032488715202958153110094699136562788445821639287146625768890659898391528336492751750116100773007205770255670840498810443826188440795773504687095619308580575390114318856694211300531962836965496574777555039307766611604994364863540197082896066884626629391706598991134975 +def node13685 : Tree Nat := .node node13684 node12301 +def node13686 : Tree Nat := .node node13685 node6951 +def node13687 : Tree Nat := .node node12300 node13686 +def node13688 : Tree Nat := .node node13683 node13687 +def node13689 : Tree Nat := .node node13679 node13688 +def node13690 : Tree Nat := .leaf 5028582029882399525462345320204731981883587735092193063525305450952575249177172116263568223105123230548636787193461383948712621880603312140714785232842096368941520430405193310267830029669133521379494745372248628101557109290324128865943274367303488588767248036081138997036579724262644815757567 +def node13691 : Tree Nat := .node node13690 node8616 +def node13692 : Tree Nat := .node node13691 node9038 +def node13693 : Tree Nat := .node node10252 node13692 +def node13694 : Tree Nat := .leaf 609379529096411867973366339948478118506964670448485409767219194677177969197692491102901687804714868502153666615462946466893632205431910779071873488141615126635493261638544082572070444531516089408435267139195634070617346717681514684276536853985436580047270496982489050002174846609962041343 +def node13695 : Tree Nat := .node node13694 node9350 +def node13696 : Tree Nat := .node node13695 node11961 +def node13697 : Tree Nat := .node node12309 node13696 +def node13698 : Tree Nat := .node node13693 node13697 +def node13699 : Tree Nat := .leaf 1277347543416232079459429376525906018077612080889412371381485013669145509714721103929373520155488338893598791020415041613409168073371303333206532275245895985772137920110930531605961111337859276429609669873223001089364622090072996023559092105177471052211626349662756771325511458853176020616347903 +def node13700 : Tree Nat := .node node13699 node9042 +def node13701 : Tree Nat := .node node13700 node12316 +def node13702 : Tree Nat := .node node12314 node13701 +def node13703 : Tree Nat := .leaf 1081947199765842424529591879509026010150599323721976877786911901102607643345088549071012028586067969415086892678226327950891943481813958187189058352707702921661272309510797616656978764698096947630881447428301830436959628321604570912209495210365401434289217056319679334646015 +def node13704 : Tree Nat := .node node13703 node8625 +def node13705 : Tree Nat := .node node13704 node12320 +def node13706 : Tree Nat := .node node13705 node11970 +def node13707 : Tree Nat := .node node13702 node13706 +def node13708 : Tree Nat := .node node13698 node13707 +def node13709 : Tree Nat := .node node13689 node13708 +def node13710 : Tree Nat := .node node13670 node13709 +def node13711 : Tree Nat := .leaf 1876879207201175057492789423877314215327939898387375884169474870502861069060070093590973961046635783876384798228441414893615363744802625114903901272193891965773159178991235475926452926225260928752525353097635840536846071206644338979646646582186363808841983 +def node13712 : Tree Nat := .node node13711 node6587 +def node13713 : Tree Nat := .node node13712 node12667 +def node13714 : Tree Nat := .node node10265 node13713 +def node13715 : Tree Nat := .leaf 2269284720819188557607214520797381970144826882205520724559655836291846687190913726402047483367509812685079604712967947551928284951134268102634086871681161675151596075755869694094988418475794112983556045632761878673528386101109976751347744536084823962835436097654693442225025581311 +def node13716 : Tree Nat := .node node13715 node10568 +def node13717 : Tree Nat := .node node13716 node12671 +def node13718 : Tree Nat := .node node11279 node13717 +def node13719 : Tree Nat := .node node13714 node13718 +def node13720 : Tree Nat := .leaf 567251935584012117616353577041561371734776462270766013478031382293311805960637328517293275040758938467665397012245017271704235428691565005120448078904513563400770836461779074694694144052535420247984686086107917111790830968012852440975383044206912735420256198194240400750989541375 +def node13721 : Tree Nat := .node node13720 node6975 +def node13722 : Tree Nat := .node node13721 node11980 +def node13723 : Tree Nat := .node node12677 node13722 +def node13724 : Tree Nat := .leaf 30750788930784052141961861945646205950900528103719502925379297944556910045507410279399120945204228792313382002610787910988188490091825741111533237413584381112438465983917439245016505154253351048330085848699459150767942317837394191048614647170584003710438801663 +def node13725 : Tree Nat := .node node13724 node11658 +def node13726 : Tree Nat := .node node13725 node12328 +def node13727 : Tree Nat := .node node11985 node13726 +def node13728 : Tree Nat := .node node13723 node13727 +def node13729 : Tree Nat := .node node13719 node13728 +def node13730 : Tree Nat := .leaf 8254602048994769474255309145988586409736845223991162255450003588722430659544893995193483422244551447177666524461011845455872219001318037887812636521618309039280170203022832835315547568235962024216265884681913660902540744509496526226683770012137745980798173998433108223 +def node13731 : Tree Nat := .node node13730 node7369 +def node13732 : Tree Nat := .node node13731 node12682 +def node13733 : Tree Nat := .node node11666 node13732 +def node13734 : Tree Nat := .node node13287 node13733 +def node13735 : Tree Nat := .leaf 397468889724173685979542788245425099345541698338619579376990907177671153860196467700470072948073273624394463306874264394576519767311383244340052479607909691946642178912766603519238872485298262736059377621684258989886452059731390300415 +def node13736 : Tree Nat := .node node13735 node6986 +def node13737 : Tree Nat := .node node13736 node12687 +def node13738 : Tree Nat := .node node10276 node13737 +def node13739 : Tree Nat := .node node13738 node11298 +def node13740 : Tree Nat := .node node13734 node13739 +def node13741 : Tree Nat := .node node13729 node13740 +def node13742 : Tree Nat := .leaf 141830295051199290754602382260373947395761342649441538550624200908015257966475838851543722998600295523153339307542856779229583930645813040756871935928954994184077134748546386712448692686860792090461209352870009684666016952950219644231626722392012824814862549338138722851314794495 +def node13743 : Tree Nat := .node node13742 node8646 +def node13744 : Tree Nat := .node node13743 node11303 +def node13745 : Tree Nat := .node node11998 node13744 +def node13746 : Tree Nat := .leaf 503820925841965910293903145710583493637006880564327892725666673368473246240567669475682352989106934593376810395043683004339709682878398364814850018495420126823091912531784710277140623037246438902106649274332563816113930590028247814106883934654194190836822823665919 +def node13747 : Tree Nat := .node node13746 node9076 +def node13748 : Tree Nat := .node node13747 node12694 +def node13749 : Tree Nat := .node node12342 node13748 +def node13750 : Tree Nat := .node node13745 node13749 +def node13751 : Tree Nat := .leaf 114555615673899844817675135827349603920186156328588973012815230098216247591936145623178599818602061805628440424236441183793286810769621760146212077663227459888103895663369975594942529988997020774105405362937139803084931237550249716565903149973406482431 +def node13752 : Tree Nat := .node node13751 node9081 +def node13753 : Tree Nat := .node node13752 node10952 +def node13754 : Tree Nat := .node node10288 node13753 +def node13755 : Tree Nat := .leaf 9076030969344193881830906443734197896041214432680857066853762215856310823831566669886141577485648253891936520286387185970107498991864168418146640176962795664917808271276761143081364339715242438384420450311516277979483685930617190356347810880755687516074941531251201392233026748415 +def node13756 : Tree Nat := .node node13755 node12698 +def node13757 : Tree Nat := .node node13756 node12349 +def node13758 : Tree Nat := .node node12347 node13757 +def node13759 : Tree Nat := .node node13754 node13758 +def node13760 : Tree Nat := .node node13750 node13759 +def node13761 : Tree Nat := .leaf 492012622892656704990238084452251441810928680478211353074222523471479393502725184660276873998006663998813145330047983509730321495612895498074327544186461058746881903333247832437633860389101362010104528074175179849629936774732882263998863260358486974180452532223 +def node13762 : Tree Nat := .node node13761 node8665 +def node13763 : Tree Nat := .node node13762 node12003 +def node13764 : Tree Nat := .node node10602 node13763 +def node13765 : Tree Nat := .leaf 2215963108520416015739670368219860918705627185547197085343450321573077336868309251077102326174225549155407086842882886153507097866022858011143218203355784684139059833755154934588180336648220194811903249793435037512778837937724462381679612300118288499687998220258668816237592831 +def node13766 : Tree Nat := .node node13765 node9376 +def node13767 : Tree Nat := .node node13766 node12705 +def node13768 : Tree Nat := .node node12356 node13767 +def node13769 : Tree Nat := .node node13764 node13768 +def node13770 : Tree Nat := .leaf 270486799941460609886385509495647727003124994963545150394648763308944639969102659393676275592250940467361807953988974708791626313912197649469725030384215454103215939714398451354197695534910753912172065410386729530974690402527933667380203919452578728041559626094425923452927 +def node13771 : Tree Nat := .node node13770 node9092 +def node13772 : Tree Nat := .node node13771 node12361 +def node13773 : Tree Nat := .node node12711 node13772 +def node13774 : Tree Nat := .leaf 6828046779268970776657768233878085902324275438521959671787668942028781287039163393246395227370680568936631177633751398183847755896434749212611613699815207199423526999689055146138073928553989707314316414176701463196957457232541934258203274510591 +def node13775 : Tree Nat := .node node13774 node8674 +def node13776 : Tree Nat := .node node13775 node11318 +def node13777 : Tree Nat := .node node13776 node12013 +def node13778 : Tree Nat := .node node13773 node13777 +def node13779 : Tree Nat := .node node13769 node13778 +def node13780 : Tree Nat := .node node13760 node13779 +def node13781 : Tree Nat := .node node13741 node13780 +def node13782 : Tree Nat := .node node13710 node13781 +def node13783 : Tree Nat := .leaf 7507516828804700229971157695509256861311759593549503536677899755757881062691614939970702182859795639737729241335368268839526962869220176380869024994616278906372529249382147856492585955442967754510945820115799159267379990263312810548015969630500497498505471 +def node13784 : Tree Nat := .node node13783 node8685 +def node13785 : Tree Nat := .node node13784 node12719 +def node13786 : Tree Nat := .node node12371 node13785 +def node13787 : Tree Nat := .leaf 138497694282557489791594520883107362511587926461792414802412290885116654711244934379385276898882351777722071648826508466570935182983877595422721801033778925029865199276330556817049578766433639737180896404553634105254771648607715184818862880118210833380403722603202138047774719 +def node13788 : Tree Nat := .node node13787 node9109 +def node13789 : Tree Nat := .node node13788 node12723 +def node13790 : Tree Nat := .node node11328 node13789 +def node13791 : Tree Nat := .node node13786 node13790 +def node13792 : Tree Nat := .leaf 1134538491365238617645709308610684339450379797753347501667578239658343657726760624906612719539297292415998002462756517118968397271384190568611747957444814147151601701445989250704496154691965982943906131784209193584487661492056650093046168263805178581973366522379457431944313176319 +def node13793 : Tree Nat := .node node13792 node9114 +def node13794 : Tree Nat := .node node13793 node9386 +def node13795 : Tree Nat := .node node12376 node13794 +def node13796 : Tree Nat := .leaf 123003155723136208567847447708070018416355381964899431605122243912527778097675492900439533338605641464139113673047619645997955107023597622533631865752384565045090165295010437231576649888568431557609663563836632543763696941310066172361354793569802420766507991295 +def node13797 : Tree Nat := .node node13796 node11694 +def node13798 : Tree Nat := .node node13797 node12379 +def node13799 : Tree Nat := .node node12022 node13798 +def node13800 : Tree Nat := .node node13795 node13799 +def node13801 : Tree Nat := .node node13791 node13800 +def node13802 : Tree Nat := .leaf 32246507424497658146532278144464391913490075163096718785559364785344191354011248318908866205655535483151498720787432408330540408855682523067846012624874617360028222110378708653747845669032547654340269655198609248879860651614387508816158934568213820326089595614658815 +def node13803 : Tree Nat := .node node13802 node8696 +def node13804 : Tree Nat := .node node13803 node11333 +def node13805 : Tree Nat := .node node10622 node13804 +def node13806 : Tree Nat := .leaf 33018408195979077897021236563951930273518967420704215659524541816820944659071993167455629007494867542162264158717584922876283407033358596609923679208455290439931457594477923970132687088832368158479239626062853660846677676937234292924930366614471562916644153865736814591 +def node13807 : Tree Nat := .node node13806 node9124 +def node13808 : Tree Nat := .node node13807 node12729 +def node13809 : Tree Nat := .node node10996 node13808 +def node13810 : Tree Nat := .node node13805 node13809 +def node13811 : Tree Nat := .leaf 6511732893125423073928276657127400410040102860476731377848561062811134572353652677596114027250812584288330251989403902611627946281703492177380333199712947485677694181111595751837530378006434692568839244439024238756701916665726937281331199 +def node13812 : Tree Nat := .node node13811 node9129 +def node13813 : Tree Nat := .node node13812 node12386 +def node13814 : Tree Nat := .node node12735 node13813 +def node13815 : Tree Nat := .node node13814 node9961 +def node13816 : Tree Nat := .node node13810 node13815 +def node13817 : Tree Nat := .node node13801 node13816 +def node13818 : Tree Nat := .leaf 8656105892673619465444975048166327535575816414642870886433951036774960517713398590419113722066179432147823147253351950962798170215546662598092199921108283620759921794391459779472859766165906862099710146520716755861149392119382741038929864134436069376633463449452525410910207 +def node13819 : Tree Nat := .node node13818 node12890 +def node13820 : Tree Nat := .node node13819 node12741 +def node13821 : Tree Nat := .node node10319 node13820 +def node13822 : Tree Nat := .leaf 2015283703367863641175612582842035880461389139542819912243331976362067957714186995885281003401944813791902549089772943823362393928515275778861986212803546325673972774730408460574291099939738563564768712940745341811620167108343011821467279680091606666074499194028031 +def node13823 : Tree Nat := .node node13822 node9662 +def node13824 : Tree Nat := .node node13823 node12745 +def node13825 : Tree Nat := .node node12394 node13824 +def node13826 : Tree Nat := .node node13821 node13825 +def node13827 : Tree Nat := .leaf 225921116696657399755928707376375798670333555195312617614099150595166526000831197939208375616448768444844308775376678197259415801619655891592005693734934921697417155233432635558002928230857957892571846948919886649497747711 +def node13828 : Tree Nat := .node node13827 node9667 +def node13829 : Tree Nat := .node node13828 node12398 +def node13830 : Tree Nat := .node node12751 node13829 +def node13831 : Tree Nat := .leaf 553990777130104003934917592054855974259924061527415598228274596169714978873108889622872645198406642054558278952365671633092016626097594910422476814009311811588144432308231332280759118191506643479319278552639471085147961488712709541928083778736132635259346854376261788282978303 +def node13832 : Tree Nat := .node node13831 node12404 +def node13833 : Tree Nat := .node node13832 node12407 +def node13834 : Tree Nat := .node node12403 node13833 +def node13835 : Tree Nat := .node node13830 node13834 +def node13836 : Tree Nat := .node node13826 node13835 +def node13837 : Tree Nat := .leaf 8061626826094347221414268616256904040889269236057812766754246782462871110468075123339448563158751726354989189573569737571599367519269569620284662933113569979541605607989935830180299252965061165383688056254087483958299437229146069493102233395140774320395077331976447 +def node13838 : Tree Nat := .node node13837 node9673 +def node13839 : Tree Nat := .node node13838 node9147 +def node13840 : Tree Nat := .node node12757 node13839 +def node13841 : Tree Nat := .leaf 8863852434081664062958681472878132609825122888544206837958136310848772034852094046130035258833550989519909403882847570816487973164325535839060701421719436933990676260863165478072794424471089493802230452903266840236962920064251966253162705859928476252198306900701577640077688831 +def node13842 : Tree Nat := .node node13841 node11357 +def node13843 : Tree Nat := .node node12759 node13135 +def node13844 : Tree Nat := .node node13842 node13843 +def node13845 : Tree Nat := .node node12898 node13844 +def node13846 : Tree Nat := .node node13840 node13845 +def node13847 : Tree Nat := .leaf 1081947199765842428283579419127417286713116607617159638942613056013073795264965194137452593836483412298566698713689968775822544520768080289377703883248676138220521111569333297870668621177238560967042745988186232887228049401282685593731614212255271912741300323402883539140863 +def node13848 : Tree Nat := .node node13847 node9678 +def node13849 : Tree Nat := .node node13848 node12414 +def node13850 : Tree Nat := .node node12903 node13849 +def node13851 : Tree Nat := .leaf 1174833932040723294629220079997464680937933805781821401243985445075573084210780894769804100209656106251896829950546403362887871301176856649286481267126524720761980671939482040735062037418460003427932153770438385544986623 +def node13852 : Tree Nat := .node node13851 node12905 +def node13853 : Tree Nat := .node node13852 node11363 +def node13854 : Tree Nat := .node node13853 node12766 +def node13855 : Tree Nat := .node node13850 node13854 +def node13856 : Tree Nat := .node node13846 node13855 +def node13857 : Tree Nat := .node node13836 node13856 +def node13858 : Tree Nat := .node node13817 node13857 +def node13859 : Tree Nat := .leaf 72608247484266751113186647294354820488834247026939543948396825646101063287786253971485042109138266243244020558325693611899195180836380228795842510795805830184899484320891698888933334758724964010824766196053363935991772905653606246796970257905615957507324448788477643503481175081215 +def node13860 : Tree Nat := .node node13859 node9427 +def node13861 : Tree Nat := .node node13860 node12773 +def node13862 : Tree Nat := .node node12915 node13861 +def node13863 : Tree Nat := .leaf 173717940541902012406847659425866484451190533229463526990882236840893119072742199839856502876068937588389229049516035492492906865262399953583505161180764870181157579673159550819488672200170647667420217060905152992175436413411303170551637600442427329845432512562951413717093326263693643802531070207 +def node13864 : Tree Nat := .node node13863 node9690 +def node13865 : Tree Nat := .node node13864 node12048 +def node13866 : Tree Nat := .node node11721 node13865 +def node13867 : Tree Nat := .node node13862 node13866 +def node13868 : Tree Nat := .leaf 641163699438029873998476675731070532890503365471348354882531362507106952652341177184586026177890229202314479090694496935628738694544632002740895571643276383782576266711859013453263643358330239817921192358353938733289475637851398127272992259463923911283983766309110940448196910540540039865041151 +def node13869 : Tree Nat := .node node13868 node9695 +def node13870 : Tree Nat := .node node13869 node12422 +def node13871 : Tree Nat := .node node12920 node13870 +def node13872 : Tree Nat := .leaf 1219353864951782111494411248513669248238417417502665318371385195113776976654427429269755729120838114140898916494294983697473193877894337772409732609568290886049967825033721765654481278587565869435907257226035585937681628243558338676960072350451946772779066999928176578960275731128835440639 +def node13873 : Tree Nat := .node node13872 node12059 +def node13874 : Tree Nat := .node node13873 node7055 +def node13875 : Tree Nat := .node node11726 node13874 +def node13876 : Tree Nat := .node node13871 node13875 +def node13877 : Tree Nat := .node node13867 node13876 +def node13878 : Tree Nat := .leaf 40072731214876796218413108378942774334323045285940858530772784274179266683592954082168903349767324293130424338184606348085645673785155640043888534828777831355789397249513415866641676312060666906692242301348507838518265495255970418332236727578522906659536277876908747447353049106854649805209599 +def node13879 : Tree Nat := .node node13878 node12924 +def node13880 : Tree Nat := .node node13879 node11382 +def node13881 : Tree Nat := .node node12780 node13880 +def node13882 : Tree Nat := .leaf 154649758481689438539253101856584427727906370118567238084748270901022217271244407098556404626491896659290190412922964660798727172120946886784235702852196485941661076272352594379896806449531432218916554131709942067149968839391080282890680995224406801313306755931448117504757363020232917247 +def node13883 : Tree Nat := .node node13882 node9709 +def node13884 : Tree Nat := .node node13883 node12066 +def node13885 : Tree Nat := .node node12930 node13884 +def node13886 : Tree Nat := .node node13881 node13885 +def node13887 : Tree Nat := .leaf 9516908214257811601907599988159363584840065290626636270825807227503749905371816105021419189398839454839689918914562806248206411829822979351300064714670728090477351428117358393598991669469351841968509351516504407542994913425616382779636326741406417431494099721348292879982805681015095551 +def node13888 : Tree Nat := .node node13887 node9714 +def node13889 : Tree Nat := .node node13888 node12428 +def node13890 : Tree Nat := .node node12935 node13889 +def node13891 : Tree Nat := .node node13890 node12940 +def node13892 : Tree Nat := .node node13886 node13891 +def node13893 : Tree Nat := .node node13877 node13892 +def node13894 : Tree Nat := .leaf 160290924859507184890963588712040320533756863335788821184229948264768520609423743754511922078006017603983437319396672369196710285824121217747960377139064043842851939963770279939992922224534680114065829533015236208406364399917226924053716704235227880827350299203543877176247188158341382718685183 +def node13895 : Tree Nat := .node node13894 node12077 +def node13896 : Tree Nat := .node node13895 node9463 +def node13897 : Tree Nat := .node node12787 node13896 +def node13898 : Tree Nat := .leaf 148701690847778306280310070740832021923419923311650029397698061862645982565585358253925509580443099392097636026797386502591340007597866141510220585781267578938273216270938198148028688929417347711928562238815532716661821702988252074193821279163473319304164247152128373177726233554714879 +def node13899 : Tree Nat := .node node13898 node11745 +def node13900 : Tree Nat := .node node13899 node12082 +def node13901 : Tree Nat := .node node12440 node13900 +def node13902 : Tree Nat := .node node13897 node13901 +def node13903 : Tree Nat := .leaf 9584288667923211146940637195106895509586686918352633524518732024561752301339197280802709155441220641788786764210402813327422804732093548427479683312030666151796693172219442849825974286000413401897406023848754974361654848085862909785912343346992327217039512075495977991047815528186111 +def node13904 : Tree Nat := .node node13903 node11750 +def node13905 : Tree Nat := .node node13904 node12794 +def node13906 : Tree Nat := .node node12792 node13905 +def node13907 : Tree Nat := .leaf 694871762167608049626282723770905715162043830833208898076279771632803262962607377701488142089040871141567657864678296095251240318970110686340489458480483915643121487203692938742159498012962646179451956129936101160535614917185381276544808818351698618788122820826897040247302899966553447827029033215 +def node13908 : Tree Nat := .node node13907 node11408 +def node13909 : Tree Nat := .node node13908 node9187 +def node13910 : Tree Nat := .node node12092 node13909 +def node13911 : Tree Nat := .node node13906 node13910 +def node13912 : Tree Nat := .node node13902 node13911 +def node13913 : Tree Nat := .leaf 10018182803719199054603277094735693583580761321485214632718632621999971839155334720690115850865904002970821504265768528967295833113652456910114441206157042932473873922526613546371820348768222940859757187900010682191860799649298422014767388486092887903545081966591491460565074855293023858786303 +def node13914 : Tree Nat := .node node13913 node12096 +def node13915 : Tree Nat := .node node13914 node12099 +def node13916 : Tree Nat := .node node10663 node13915 +def node13917 : Tree Nat := .leaf 297403390559003316441364371679462987949131770409322091479259371325373453793164064587149053478616722460716689797178803623935715975742154320267602450005467807086740497647693172174975943133796607630875584672064863927162867892548431439440543355712961411972630973768639437144943576804753663 +def node13918 : Tree Nat := .node node13917 node11417 +def node13919 : Tree Nat := .node node13918 node9193 +def node13920 : Tree Nat := .node node12446 node13919 +def node13921 : Tree Nat := .node node13916 node13920 +def node13922 : Tree Nat := .leaf 9745314011400000162300582153717612840468120351314379564770510113036312714024121089520989186893633952103646779539050048426379727856838138252855638408405920573308883103035584518742055194901059732900103093998568260455003750990349021753782911846133295858913418827011750602395175160529415110655 +def node13923 : Tree Nat := .node node13922 node11764 +def node13924 : Tree Nat := .node node13923 node11423 +def node13925 : Tree Nat := .node node12801 node13924 +def node13926 : Tree Nat := .leaf 2739226045072033710287658726391013369481562983073862426076014871121501917116897813478243768409544927272652705989782486018374878784366859763845742616822186473850268648721702203944842194878930504526724684010422527 +def node13927 : Tree Nat := .node node13926 node12103 +def node13928 : Tree Nat := .node node13927 node12454 +def node13929 : Tree Nat := .node node13928 node12108 +def node13930 : Tree Nat := .node node13925 node13929 +def node13931 : Tree Nat := .node node13921 node13930 +def node13932 : Tree Nat := .node node13912 node13931 +def node13933 : Tree Nat := .node node13893 node13932 +def node13934 : Tree Nat := .node node13858 node13933 +def node13935 : Tree Nat := .node node13782 node13934 +def node13936 : Tree Nat := .node node13635 node13935 +def node13937 : Tree Nat := .leaf 7507516828804700229971157695509256861311759593549503536677899755757881062691615256630906892622143669048765587635950989016785553242771871920041144482488516403958696424541355426923166035466523350467695506195964986883515036980651118541484219600882530466425193 +def node13938 : Tree Nat := .node node13937 node12814 +def node13939 : Tree Nat := .node node13938 node8784 +def node13940 : Tree Nat := .node node13084 node13939 +def node13941 : Tree Nat := .leaf 276978483140055660679575521154310658598553426872826080593424479721944743637335064583130340808000721892441268569379212308399932662694284205702097585169193435032414605838253575203503260866196031433458804951352921717574925866750570369867543299121235671550893206075598960486213993 +def node13942 : Tree Nat := .node node13941 node12469 +def node13943 : Tree Nat := .node node13942 node12472 +def node13944 : Tree Nat := .node node13091 node13943 +def node13945 : Tree Nat := .node node13940 node13944 +def node13946 : Tree Nat := .leaf 1134503866941667986143541334648056457619674842830209732174383704661281727402804754416548424845268597132444970383912631563207990827489845178429108122191373230708943107068998149163237322978318337638638205048320699552232994768557237690514401021486225149617478275364094926050629478761 +def node13947 : Tree Nat := .node node13946 node9488 +def node13948 : Tree Nat := .node node13947 node9224 +def node13949 : Tree Nat := .node node13096 node13948 +def node13950 : Tree Nat := .leaf 123003155723136208567847447683223664415745989465967061144775319672827615245282853070109007218536306674745708410782905388586055064621515797122191070561722069598184336831924337253385042086151271460696227772647207623375333095605400983632326499984640652592535541353 +def node13951 : Tree Nat := .node node13950 node11437 +def node13952 : Tree Nat := .node node13951 node12118 +def node13953 : Tree Nat := .node node9229 node13952 +def node13954 : Tree Nat := .node node13949 node13953 +def node13955 : Tree Nat := .node node13945 node13954 +def node13956 : Tree Nat := .leaf 1125210230865546156491849650849141005172147100623948788746598902420821053428050286487299832733803496144141082012950154579985768502758488851419781728238585222574812589266531793180956535079846951554927442227546244202015292 +def node13957 : Tree Nat := .node node13956 node9498 +def node13958 : Tree Nat := .node node13957 node11444 +def node13959 : Tree Nat := .node node13105 node13958 +def node13960 : Tree Nat := .leaf 33018408195979077897021236557282287907427960838451981092487189987679470573908052333928986881956429041035710718910443876958184790166011882350154566339868106858294749432546375864417740428279671221168030005380294700000841809675947608112271812313625806310347498472459179625 +def node13961 : Tree Nat := .node node13960 node9504 +def node13962 : Tree Nat := .node node13961 node12478 +def node13963 : Tree Nat := .node node12837 node13962 +def node13964 : Tree Nat := .node node13959 node13963 +def node13965 : Tree Nat := .leaf 48516190384397171392751175090678259260270162528013642586385209916290288086478333150780021580175739629118289543847768199510899830187141888180207452226534790820321120216919046882785569607977848325558661522776860109579100980004607292 +def node13966 : Tree Nat := .node node13965 node12485 +def node13967 : Tree Nat := .node node13966 node12125 +def node13968 : Tree Nat := .node node12842 node13967 +def node13969 : Tree Nat := .node node13968 node12492 +def node13970 : Tree Nat := .node node13964 node13969 +def node13971 : Tree Nat := .node node13955 node13970 +def node13972 : Tree Nat := .leaf 17311155196269223196464683982066137460447416991840732818070830393671261811490375849033411404231964381810464754670324811932353562430335537915041855151722693554378390873491324469124433380221578326735867175047542352811765745130236894818601835174372406279617873712861552080141482 +def node13973 : Tree Nat := .node node13972 node8379 +def node13974 : Tree Nat := .node node13973 node12497 +def node13975 : Tree Nat := .node node13115 node13974 +def node13976 : Tree Nat := .leaf 2015283703367863641175612582842135243135427334428804184044917736999987313807108150565911656580400360071894370193173689646129889958808112504284773750881602853973553365132356026392074963350514880265968068991716688117422993563050756776646912558176255432912252016984319 +def node13977 : Tree Nat := .node node13976 node8813 +def node13978 : Tree Nat := .node node13977 node12501 +def node13979 : Tree Nat := .node node11789 node13978 +def node13980 : Tree Nat := .node node13975 node13979 +def node13981 : Tree Nat := .leaf 225921116696657399755928707376375798670333560260644071634548162212369334107823776038057071519881333252061364655668791715358213179274623608611407031717239351202907673747076056987966624041895177843851660478020573225254765482 +def node13982 : Tree Nat := .node node13981 node8818 +def node13983 : Tree Nat := .node node13982 node10368 +def node13984 : Tree Nat := .node node12138 node13983 +def node13985 : Tree Nat := .leaf 225924563982610226070265215820544374824657167771312989075437813652077668501960498285146510074899144885499114984200464467326910359101686978775252846219264264892966590051920900182865697594634952656750230473183065973844869375 +def node13986 : Tree Nat := .node node13985 node12143 +def node13987 : Tree Nat := .node node13986 node12146 +def node13988 : Tree Nat := .node node12142 node13987 +def node13989 : Tree Nat := .node node13984 node13988 +def node13990 : Tree Nat := .node node13980 node13989 +def node13991 : Tree Nat := .node node13990 node13437 +def node13992 : Tree Nat := .node node13971 node13991 +def node13993 : Tree Nat := .leaf 1198036083490401393367579651265226826447551684806266405050177285577599119244146985902642702006115315422144908141997955354442654161558858392652635956895807234053333644930642165096742786396124080735141558700451638583991144045229014311750217410052339810618853120470454052598109853423209 +def node13994 : Tree Nat := .node node13993 node8411 +def node13995 : Tree Nat := .node node13994 node8847 +def node13996 : Tree Nat := .node node13137 node13995 +def node13997 : Tree Nat := .leaf 86858970270951006203423838165645771885047073375041211488604415337194479134408200026866468221203321374509304249163184904583451743670206537702115563266644027668708487191084016195953265499820484379492289712844829686163969286747579215443403244899357270621071917752460869343608913389284883990403311977 +def node13998 : Tree Nat := .node node13997 node8850 +def node13999 : Tree Nat := .node node13998 node11472 +def node14000 : Tree Nat := .node node11470 node13999 +def node14001 : Tree Nat := .node node13996 node14000 +def node14002 : Tree Nat := .leaf 320581849719015504285796232270159840383892969391784817983639634828399285715423821179807476921894270412460028816508423648153232402599709517290130818817670178154070101218375702613277248737488700294725089103305924473206939663798042759485596102028104174913448813400610410999423842902674779385140841 +def node14003 : Tree Nat := .node node14002 node8419 +def node14004 : Tree Nat := .node node14003 node12168 +def node14005 : Tree Nat := .node node12521 node14004 +def node14006 : Tree Nat := .leaf 305135869619641084486162424651110383869718645522469604919050302005727267917819995841479478538868055680940285189690738651919013376267824941051617314061007409483742210675248527715269648201148996333276918982055879758765585967492508679507501528971337673079417531236925694849956279529358202473 +def node14007 : Tree Nat := .node node14006 node11476 +def node14008 : Tree Nat := .node node14007 node8427 +def node14009 : Tree Nat := .node node8425 node14008 +def node14010 : Tree Nat := .node node14005 node14009 +def node14011 : Tree Nat := .node node14001 node14010 +def node14012 : Tree Nat := .leaf 20036365607438398109206554221717894591659180118237426039412854667412122224214503810828260586009694292471602677085437682769966064655111192062970664211417467949647261595047783935418163656787200077547300458755866726888308095984177535042959544840056549823002390836799033317238253736703912665830716 +def node14013 : Tree Nat := .node node14012 node8432 +def node14014 : Tree Nat := .node node14013 node11483 +def node14015 : Tree Nat := .node node12527 node14014 +def node14016 : Tree Nat := .leaf 38067632857031246415885002001632223813615570301801070128684750548400235182831352333308404133180821172702099111877852160800355136763992239695518951053977240173283467367941175228282463341185918534820004623241488810812315249396333941409644421671105928804341859739087685672331679283546396265 +def node14017 : Tree Nat := .node node14016 node8862 +def node14018 : Tree Nat := .node node14017 node11822 +def node14019 : Tree Nat := .node node11489 node14018 +def node14020 : Tree Nat := .node node14015 node14019 +def node14021 : Tree Nat := .leaf 18587711355972288284975781226873757001640752520742430762455243433647852495356937686061563313740224455898572328929311704065567065391092933311837846148791088729398392233347632277708175404638606175464530453434801214177405834470295458207525426731480015122964200292661646144936941146428732 +def node14022 : Tree Nat := .node node14021 node8869 +def node14023 : Tree Nat := .node node14022 node12531 +def node14024 : Tree Nat := .node node11494 node14023 +def node14025 : Tree Nat := .node node14024 node12176 +def node14026 : Tree Nat := .node node14020 node14025 +def node14027 : Tree Nat := .node node14011 node14026 +def node14028 : Tree Nat := .leaf 80145462429753592445482322650559168134091064725027669358396684983451368644923776130938100240910653658101242071565417656836259861823657472707729412812233908292102307548806815514861582499591286511208356178336207009271225452082097782481502387044477048311498077809198053750271787217498420863746986 +def node14029 : Tree Nat := .node node14028 node8448 +def node14030 : Tree Nat := .node node14029 node12538 +def node14031 : Tree Nat := .node node11835 node14030 +def node14032 : Tree Nat := .node node14031 node13474 +def node14033 : Tree Nat := .leaf 4792144333961605573470318597553505032601180409098725599827279743563115417912112873870037829428216777831309210655101407571163493262736114679447454578921403231388587583565533846240720862956847408963542982250236474540534393570768670284273869653759790743639634089336162079181711242312874 +def node14034 : Tree Nat := .node node14033 node8889 +def node14035 : Tree Nat := .node node14034 node12186 +def node14036 : Tree Nat := .node node11840 node14035 +def node14037 : Tree Nat := .leaf 347435881083804024813695352662582961584956833008659305225776271727755038173984289085997064519319836027896598150277906664489114558658205249325521407903002537796268903234728220188901475585127554123903957158063485043643369761486045258142528445235487148116499512003530287993548863190206744688838312191 +def node14038 : Tree Nat := .node node14037 node12542 +def node14039 : Tree Nat := .node node14038 node10091 +def node14040 : Tree Nat := .node node12191 node14039 +def node14041 : Tree Nat := .node node14036 node14040 +def node14042 : Tree Nat := .node node14032 node14041 +def node14043 : Tree Nat := .leaf 609156476566787278379108054239156247333694058308169791851172548092041729379507673387366203849147725996730025406920568452273150403897892308531071537704644186156703520144043236917508273800981481956093727732268419714023411839396981673670438107794104211235677823468471070253967332839306297599 +def node14044 : Tree Nat := .node node14043 node9275 +def node14045 : Tree Nat := .node node14044 node10410 +def node14046 : Tree Nat := .node node12197 node14045 +def node14047 : Tree Nat := .node node13489 node14046 +def node14048 : Tree Nat := .leaf 17926543156650705493745156729723227086574128068473552473659540154970077439176188202568893103141175937287205588304377392190185369369475267917001639732154358328899734084597219304627307766208977914668016331363729801471 +def node14049 : Tree Nat := .node node14048 node8472 +def node14050 : Tree Nat := .node node14049 node12201 +def node14051 : Tree Nat := .node node14050 node10766 +def node14052 : Tree Nat := .node node13498 node14051 +def node14053 : Tree Nat := .node node14047 node14052 +def node14054 : Tree Nat := .node node14042 node14053 +def node14055 : Tree Nat := .node node14027 node14054 +def node14056 : Tree Nat := .node node13992 node14055 +def node14057 : Tree Nat := .leaf 36304123742133375556593330216254635448529824738232755544798166470840175999708721578904841561045755026793346261350008872879909556370672936013382894168378543194507926213841472487214390311393061541483299565880754275502469841512321511300826214601287224136504604126799976249183367829097 +def node14058 : Tree Nat := .node node14057 node6448 +def node14059 : Tree Nat := .node node14058 node10424 +def node14060 : Tree Nat := .node node13173 node14059 +def node14061 : Tree Nat := .leaf 168608589349493131958015087616540679668592803278962431331060101814331015260871777495148119299778999483168145679854451622674939147754434619637275616256377777392408477111434973918618393799252678538302702349285742709182101189207206478668919921086858129216098575737709481244687756573268164998065854057 +def node14062 : Tree Nat := .node node14061 node7222 +def node14063 : Tree Nat := .node node14062 node11528 +def node14064 : Tree Nat := .node node11525 node14063 +def node14065 : Tree Nat := .node node14060 node14064 +def node14066 : Tree Nat := .leaf 321829249912474136881525683989307835131953557306589263343752782944593437589520939150189555629080100264798835086290555977713254120225443146180701228171476451892310277561050909123407951909422647174765070431906078761372756650335197093869944677908587267228944404947015919160773403648587996520999273 +def node14067 : Tree Nat := .node node14066 node6826 +def node14068 : Tree Nat := .node node14067 node11857 +def node14069 : Tree Nat := .node node10430 node14068 +def node14070 : Tree Nat := .leaf 305730676383032197711281649742622710886123306029018948465096423214894378187525711710577125145017308736797642166709708925119651563701120884476865237687147190834701536676069687533883080766034579488107378925052481974792132810804528819213223678255519999185259012201140565699118820986456348265 +def node14071 : Tree Nat := .node node14070 node11144 +def node14072 : Tree Nat := .node node14071 node9798 +def node14073 : Tree Nat := .node node10112 node14072 +def node14074 : Tree Nat := .node node14069 node14073 +def node14075 : Tree Nat := .node node14065 node14074 +def node14076 : Tree Nat := .leaf 20114328119529598101849381248576356844260372121771258500328082453509786552587602388615402985422003286694629844743189464679972790247107178046857054806744177249097321093177889564539159850498167825446728415712806013666883199524892261241736205001162508566973354109311275863431736991957781801445948 +def node14077 : Tree Nat := .node node14076 node6836 +def node14078 : Tree Nat := .node node14077 node10438 +def node14079 : Tree Nat := .node node10436 node14078 +def node14080 : Tree Nat := .leaf 40446859910595699341125708145656373132591514042419445126956107720017105848770028401130341546201483200632496178089575328505341280298665416420738783615214685575516665677543978420028481860981334107678969827397592415521936031525211183633406223766682073247885056086576466222357857950930605673 +def node14081 : Tree Nat := .node node14080 node7235 +def node14082 : Tree Nat := .node node14081 node11151 +def node14083 : Tree Nat := .node node11535 node14082 +def node14084 : Tree Nat := .node node14079 node14083 +def node14085 : Tree Nat := .leaf 18587711355972288284975781226873757001640752527254561075954200296864920133568817487707092950860057205891604452303042089454261995933702318684836888461722869150513792971597610852869053192966382049615296070527169379437005615326909340540045362780284771303030851825341450150707680426743100 +def node14086 : Tree Nat := .node node14085 node6845 +def node14087 : Tree Nat := .node node14086 node12210 +def node14088 : Tree Nat := .node node12562 node14087 +def node14089 : Tree Nat := .node node14088 node12216 +def node14090 : Tree Nat := .node node14084 node14089 +def node14091 : Tree Nat := .node node14075 node14090 +def node14092 : Tree Nat := .leaf 159979074811142526733376176478649845913726400468227039400546995978457108606195822085848242502208871814147841939303516298562461715320792416588692211721032574627857094924207395842199566855284999841253009260713314861888938826657348399093729138641345229856783628325635450415876141158489534156424106 +def node14093 : Tree Nat := .node node14092 node10117 +def node14094 : Tree Nat := .node node14093 node12571 +def node14095 : Tree Nat := .node node12569 node14094 +def node14096 : Tree Nat := .leaf 37175422711944576571966846157115377644457117624326996718013592867814909517272922286185664988388014749487763295594273489954555800867105990784175189628038510374413617503462222491871385824278346527407119254668977871877140251560080523816850153173163401478314757217328808221252918527983615 +def node14097 : Tree Nat := .node node14096 node7242 +def node14098 : Tree Nat := .node node14097 node11550 +def node14099 : Tree Nat := .node node11548 node14098 +def node14100 : Tree Nat := .node node14095 node14099 +def node14101 : Tree Nat := .leaf 4937360828930139075696691888388341703560824888322208164833617614595517561556605024501045357416203106568280468781367495212908167983181339073273592438566943336108922629372796776202083052275359055708099265239702556857507176525057421565370904417591514351984292827876322377586900717913002 +def node14102 : Tree Nat := .node node14101 node9814 +def node14103 : Tree Nat := .node node14102 node11874 +def node14104 : Tree Nat := .node node11871 node14103 +def node14105 : Tree Nat := .leaf 367873285853439564760533587811143966328459060057661429664211016701021150139241504673514450146755572907776759555882616850812232166675443291171532706989528100542462706662124705638869494300965106051153893667243031562928615940775818537943818489297006017639786694339326293229300533719920545738889625855 +def node14106 : Tree Nat := .node node14105 node12220 +def node14107 : Tree Nat := .node node14106 node8508 +def node14108 : Tree Nat := .node node11880 node14107 +def node14109 : Tree Nat := .node node14104 node14108 +def node14110 : Tree Nat := .node node14100 node14109 +def node14111 : Tree Nat := .leaf 9979201548254465038155997574090178006299953753319660660381375882742818927998918350738505463023658415398099156132278510137744736367289781369040026320175171618009363958374242511544740415411849804989814965072301583613655066486254536116781414466088205360887915479507518053223192577918859367940351 +def node14112 : Tree Nat := .node node14111 node9824 +def node14113 : Tree Nat := .node node14112 node11169 +def node14114 : Tree Nat := .node node10464 node14113 +def node14115 : Tree Nat := .leaf 74350847640257991860231331556363993181239786870752635029752400361930165761785448651591505484970839553341940157553410627684958321052340855584422428792356060817975930476681643200448303206502130554636552985996031068956834435954675543855893812783291068692455773510253981118863342384971775 +def node14116 : Tree Nat := .node node14115 node10800 +def node14117 : Tree Nat := .node node14116 node11885 +def node14118 : Tree Nat := .node node11557 node14117 +def node14119 : Tree Nat := .node node14114 node14118 +def node14120 : Tree Nat := .leaf 4872657005699999810663491135398204041823608939751973073340296112092162650589745671020362028981173928417388251915025194266042170442037274997643866993603969714391782314214918113366669399820314066283330081797497310614275602110739527794279828745667685699622277844619538172004039732061634822399 +def node14121 : Tree Nat := .node node14120 node10467 +def node14122 : Tree Nat := .node node14121 node12577 +def node14123 : Tree Nat := .node node11562 node14122 +def node14124 : Tree Nat := .node node14123 node13562 +def node14125 : Tree Nat := .node node14119 node14124 +def node14126 : Tree Nat := .node node14110 node14125 +def node14127 : Tree Nat := .node node14091 node14126 +def node14128 : Tree Nat := .leaf 1876879207201175057492789423877314215327939898387375884169474870502861069060069777085350899625385307944621763169733298966004217108175076334941498697493526348261090679838701955844679066557945412331335633104200459721278358729516358690747204317540667358996841 +def node14129 : Tree Nat := .node node14128 node11892 +def node14130 : Tree Nat := .node node14129 node8954 +def node14131 : Tree Nat := .node node12590 node14130 +def node14132 : Tree Nat := .leaf 2269146223124906000117422926276498862782315294279058932144853424001014171895230212411404973000048044792172692986741420723191826847732454366742485245184723751556231813275184199818286288664587407927686291209969248876865125372494088416703025341267714461539446536693371293506838763113 +def node14133 : Tree Nat := .node node14132 node10475 +def node14134 : Tree Nat := .node node14133 node12593 +def node14135 : Tree Nat := .node node11570 node14134 +def node14136 : Tree Nat := .node node14131 node14135 +def node14137 : Tree Nat := .leaf 567286555781226500029355731569122967715603332303024435169262119354790718260422894252365794277193656171034240881504545882039792440605577976305040582381114750828792298657564703515972443248396882185269925306943303416431680051002886638100427216309146704612307756680658256114703177321 +def node14138 : Tree Nat := .node node14137 node11576 +def node14139 : Tree Nat := .node node14138 node12235 +def node14140 : Tree Nat := .node node10482 node14139 +def node14141 : Tree Nat := .leaf 30750788930784052141961861920811980997887234677887817339864608149478746012353383005245511535615183867402719086846186378172349218606166225793694462505817694549368294893849779989912882483817193565211203275397663375979504164983292850085143844547755076885487523433 +def node14142 : Tree Nat := .node node14141 node11897 +def node14143 : Tree Nat := .node node14142 node12239 +def node14144 : Tree Nat := .node node11185 node14143 +def node14145 : Tree Nat := .node node14140 node14144 +def node14146 : Tree Nat := .node node14136 node14145 +def node14147 : Tree Nat := .leaf 32244539253885818706292675051642253103647037187929130507437185080316792066156221825285406495653496851657776485678441071675117668035146022414305557196886535259051522490754145579969797895179315256401775808449739259697302398814583691750361971424622574320520371094508860 +def node14148 : Tree Nat := .node node14147 node11903 +def node14149 : Tree Nat := .node node14148 node12599 +def node14150 : Tree Nat := .node node10491 node14149 +def node14151 : Tree Nat := .leaf 8254602048994769474255309139322199910068143258083693241044839823575153550594486940739435416735876022684849312314722302358075980517169046263441500479711629410651914192877422095937077620632807849196598684646854079044997768909947805864295447381185004742898588567782332009 +def node14152 : Tree Nat := .node node14151 node10165 +def node14153 : Tree Nat := .node node14152 node12603 +def node14154 : Tree Nat := .node node12246 node14153 +def node14155 : Tree Nat := .node node14150 node14154 +def node14156 : Tree Nat := .leaf 6512130313498956863217084807164470744461190538033039686479754608152295293285303498932704226690161011840344628306615244958143754424581746160005740030721115414831250524732072120471607767215869506335382602389270879943726539302862125879039593 +def node14157 : Tree Nat := .node node14156 node11588 +def node14158 : Tree Nat := .node node14157 node12608 +def node14159 : Tree Nat := .node node12251 node14158 +def node14160 : Tree Nat := .node node14159 node11920 +def node14161 : Tree Nat := .node node14155 node14160 +def node14162 : Tree Nat := .node node14146 node14161 +def node14163 : Tree Nat := .leaf 141821638945306632879540928499235702789523804660839184782518748770858768217330637056927231610528714797648669947982388910771338890716884623321751781272675432160266887218119868172972824147326488661501869817027060846856350006731859710772130540813784696497427842999875736184061246634 +def node14164 : Tree Nat := .node node14163 node9868 +def node14165 : Tree Nat := .node node14164 node12618 +def node14166 : Tree Nat := .node node12616 node14165 +def node14167 : Tree Nat := .leaf 503820925841965910293903145710682853278783176422042742899963128541361843967736281426486644995877983155568212169833255435184329347739794588698106462461282403652790728932768240966668038923127871765125284449793408086921060505933786214211608765697568786011006693343231 +def node14168 : Tree Nat := .node node14167 node10500 +def node14169 : Tree Nat := .node node14168 node12622 +def node14170 : Tree Nat := .node node11206 node14169 +def node14171 : Tree Nat := .node node14166 node14170 +def node14172 : Tree Nat := .leaf 114555615673899844817675135827349603920186156328588973012815230098216247597001467415855239037616505603637170860454974156046109455801580026176644352441657784801933346009161319638632059810916765995044128687677992717901835771745434063394963854960914480298 +def node14173 : Tree Nat := .node node14172 node10188 +def node14174 : Tree Nat := .node node14173 node12263 +def node14175 : Tree Nat := .node node12261 node14174 +def node14176 : Tree Nat := .node node14175 node13610 +def node14177 : Tree Nat := .node node14171 node14176 +def node14178 : Tree Nat := .leaf 8061134813471454564709278378172451595382697492350202586319113003583328947243921783642977354659505911468918994647359185488933685101789674268739788968642849918860900085764455761008810428089234894369044556895150358232326421657180741878786214493106756531833950473093119 +def node14179 : Tree Nat := .node node14178 node10198 +def node14180 : Tree Nat := .node node14179 node11214 +def node14181 : Tree Nat := .node node10515 node14180 +def node14182 : Tree Nat := .leaf 2215963108520416015739670368219423897040103223200861968900182144416075582367312816110528302486423822293081034527335103821046647224874906191755096497613522479383626210196778033937866111658809070779601974003567415185610612313815382293752246014064172441765512165844453174231957503 +def node14183 : Tree Nat := .node node14182 node10848 +def node14184 : Tree Nat := .node node14183 node12628 +def node14185 : Tree Nat := .node node10204 node14184 +def node14186 : Tree Nat := .node node14181 node14185 +def node14187 : Tree Nat := .leaf 270486799941460606132397969877256554634692338922149125534990864827253047922381898296765922036845598671568204247815885628137567517818175826095693888262472651812408910495712160756593870939223671596717691837567818862928306520659828178036691853641903892605007592319660140331007 +def node14188 : Tree Nat := .node node14187 node10518 +def node14189 : Tree Nat := .node node14188 node12636 +def node14190 : Tree Nat := .node node12634 node14189 +def node14191 : Tree Nat := .leaf 273579137855854662637703584477554704905474600149037125472103942208734233739212779909899012926853449381586694951578066665825364326401150344902364034516509246267139574666783592805742376727005942120145693895098367 +def node14192 : Tree Nat := .node node14191 node10211 +def node14193 : Tree Nat := .node node14192 node11219 +def node14194 : Tree Nat := .node node14193 node8128 +def node14195 : Tree Nat := .node node14190 node14194 +def node14196 : Tree Nat := .node node14186 node14195 +def node14197 : Tree Nat := .node node14177 node14196 +def node14198 : Tree Nat := .node node14162 node14197 +def node14199 : Tree Nat := .node node14127 node14198 +def node14200 : Tree Nat := .node node14056 node14199 +def node14201 : Tree Nat := .leaf 1234340207232534768924172979604602254694906452051709736717661236720499396856479823312072673064313071630115411980215128677346294207804374260756924346473570570601804001752727042444247368600918518930609367174255504442510088617885444184082760394641159352816186470446070862922017989760617 +def node14202 : Tree Nat := .node node14201 node8565 +def node14203 : Tree Nat := .node node14202 node12649 +def node14204 : Tree Nat := .node node13242 node14203 +def node14205 : Tree Nat := .leaf 91968321463359891190271877741643521241811080357357754374850699790700430936706816559365054036878295092464935961604259661610452401777491444353936885094292892669342129114234833723624367198344907828786407901963416781473772858743134249540649602208935560444346072948193420480289339762747780523282896489 +def node14206 : Tree Nat := .node node14205 node8991 +def node14207 : Tree Nat := .node node14206 node11609 +def node14208 : Tree Nat := .node node12654 node14207 +def node14209 : Tree Nat := .node node14204 node14208 +def node14210 : Tree Nat := .leaf 639916299244570106898880282343936394601108129500086289847591281966445774086874148613579531170258849978937705569952856868184947918664318708362504720753564462941279276757510887279018182132657416178492560489528341474355086250189390618367775718725920126516888685500975485864293966225419633065956969 +def node14211 : Tree Nat := .node node14210 node8998 +def node14212 : Tree Nat := .node node14211 node11938 +def node14213 : Tree Nat := .node node11936 node14212 +def node14214 : Tree Nat := .leaf 1218759058188390998269292023606661654806717069847887146350174569787895234894393803710342248917586552091505598663909792279820342266659040293446632428157702443356617321741665090067496469685042973419493452164641674827539035806476143598059428512651241732077562481853283223584490351436593588585 +def node14215 : Tree Nat := .node node14214 node11616 +def node14216 : Tree Nat := .node node14215 node8574 +def node14217 : Tree Nat := .node node11615 node14216 +def node14218 : Tree Nat := .node node14213 node14217 +def node14219 : Tree Nat := .node node14209 node14218 +def node14220 : Tree Nat := .leaf 39994768702785596225770281352084312081721853282407026069857556488069756134593827504028143467174470452474990943962669938400409793704882481838592406687053585316228198534298970086021145454035509544876989239109957934797546575222738120312819642958921720009038194610521773876733190545836399443727676 +def node14221 : Tree Nat := .node node14220 node8579 +def node14222 : Tree Nat := .node node14221 node11235 +def node14223 : Tree Nat := .node node10536 node14222 +def node14224 : Tree Nat := .leaf 152270531428124985663540008006528895254462281213872294947618853506483312281637601006710476254648951477568578231959350517633987616622943568599590373193859195360868939825216653169583071331114913603895493890080653363050630102702956458529979846094068988950633701073748201065501158012069570921 +def node14225 : Tree Nat := .node node14224 node9008 +def node14226 : Tree Nat := .node node14225 node11239 +def node14227 : Tree Nat := .node node10884 node14226 +def node14228 : Tree Nat := .node node14223 node14227 +def node14229 : Tree Nat := .leaf 9516908214257811601907599988159363584840065290620124935450087718987904762481275522191874685950243732024609872161685536783436920631949828444073824651566436158632700981972424500129421206791459829592797996473299888060732951885525870173416992842012546756251539594622236997112626180957514300 +def node14230 : Tree Nat := .node node14229 node9015 +def node14231 : Tree Nat := .node node14230 node12659 +def node14232 : Tree Nat := .node node12284 node14231 +def node14233 : Tree Nat := .node node14232 node12289 +def node14234 : Tree Nat := .node node14228 node14233 +def node14235 : Tree Nat := .node node14219 node14234 +def node14236 : Tree Nat := .leaf 80457312478118534229036470300930434235522628172007171743766890685245679184089647933239416792566688702726199162643349219304756178487690587881148635952103739212572069218136512981418747960205101428061079815665262519843036191502184975837112522252962909937375154223643222706327826302923179201805482 +def node14237 : Tree Nat := .node node14236 node8601 +def node14238 : Tree Nat := .node node14237 node9023 +def node14239 : Tree Nat := .node node13258 node14238 +def node14240 : Tree Nat := .leaf 19182518119363401510097021509837085089334432213989030557701434505264689708377241855498476855145954111770111954865225270101930396867267044285639372698380683619098369523605745502539474917124134063916692376392100250429637189441522266501064957788075144989267923630745981284424252290928476415 +def node14241 : Tree Nat := .node node14240 node9026 +def node14242 : Tree Nat := .node node14241 node11634 +def node14243 : Tree Nat := .node node11946 node14242 +def node14244 : Tree Nat := .node node14239 node14243 +def node14245 : Tree Nat := .leaf 9439072172954677644714263904271829727395694639439515609240739454321509785382047952225675997004176433832325951903502590804545085859770249562327929855799949684973133695024869043544004569598801240538962845537402306902327473008038635379576778779074563355571647736866448459775513730663338 +def node14246 : Tree Nat := .node node14245 node9031 +def node14247 : Tree Nat := .node node14246 node11951 +def node14248 : Tree Nat := .node node10904 node14247 +def node14249 : Tree Nat := .node node14248 node13687 +def node14250 : Tree Nat := .node node14244 node14249 +def node14251 : Tree Nat := .leaf 5028582029882399525462345320204731981883587735092193063525305450952575249177172116263568223105123230548636787193461383948712621880603312140714785232842096368941520430405193310267830029669133521379494745372248628101557109290324128865943274367303488588767248036060936125075711398350915316482047 +def node14252 : Tree Nat := .node node14251 node8616 +def node14253 : Tree Nat := .node node14252 node9038 +def node14254 : Tree Nat := .node node10252 node14253 +def node14255 : Tree Nat := .leaf 609379529096411867973366339948478118506964670448485409767219194677177969197692491102901687804714868502153666615462946466893632205431910779071873488141615126635493261638544082572070444531516089408435267139195634070617346717681514684276536853985436580047270476778998128558939210482270077183 +def node14256 : Tree Nat := .node node14255 node9350 +def node14257 : Tree Nat := .node node14256 node11961 +def node14258 : Tree Nat := .node node12309 node14257 +def node14259 : Tree Nat := .node node14254 node14258 +def node14260 : Tree Nat := .leaf 1277347543416232079459429376525906018077612080889412371381485013669145509714721103929373520155488338893598791020415041613409168073371303333206532275245895985772137920110930531605961111337859276429609669873223001089364622090072996023559092105177471052211626349662736489225388113156414840697257983 +def node14261 : Tree Nat := .node node14260 node9042 +def node14262 : Tree Nat := .node node14261 node12316 +def node14263 : Tree Nat := .node node12314 node14262 +def node14264 : Tree Nat := .node node14263 node13706 +def node14265 : Tree Nat := .node node14259 node14264 +def node14266 : Tree Nat := .node node14250 node14265 +def node14267 : Tree Nat := .node node14235 node14266 +def node14268 : Tree Nat := .leaf 1876879207201175057492789423877314215327939898387375884169474870502861069060070093590973961046635783876384798228441414893615363744802625114903901272193891965773159178991235475926452926225260928752525353097635840536846071208352155190721064518497956033423721 +def node14269 : Tree Nat := .node node14268 node6587 +def node14270 : Tree Nat := .node node14269 node12667 +def node14271 : Tree Nat := .node node10265 node14270 +def node14272 : Tree Nat := .leaf 2269284720819188557607214520797381970144826882205520724559655836291846687190913726402047483367509812685079604712967947551928284951134268102634086871681161675151596075755869694094988418475794112983556045632761878673528386101109976751347744536084825682747250769579165453123865253481 +def node14273 : Tree Nat := .node node14272 node10568 +def node14274 : Tree Nat := .node node14273 node12671 +def node14275 : Tree Nat := .node node11279 node14274 +def node14276 : Tree Nat := .node node14271 node14275 +def node14277 : Tree Nat := .leaf 567251935584012117616353577041561371734776462270766013478031382293311805960637328517293275040758938467665397012245017271704235428691565005120448078904513563400770836461779074694694144052535420247984686086107917111790830968012852440975383044206911007348434992397842197727699298665 +def node14278 : Tree Nat := .node node14277 node6975 +def node14279 : Tree Nat := .node node14278 node11980 +def node14280 : Tree Nat := .node node12677 node14279 +def node14281 : Tree Nat := .leaf 30750788930784052141961861945646205950900528103719502925379297944556910045507410279399120945204228792313382002610787910988188490091825741111533237413584381112438465983917439245016505154253351048330085848699459150767942317837395898838334286778492180300808022377 +def node14282 : Tree Nat := .node node14281 node11658 +def node14283 : Tree Nat := .node node14282 node12328 +def node14284 : Tree Nat := .node node11985 node14283 +def node14285 : Tree Nat := .node node14280 node14284 +def node14286 : Tree Nat := .node node14276 node14285 +def node14287 : Tree Nat := .leaf 1968170611839440239603092822138809854884193543195732940825840228588103579073369240675251808050747348422514460808850067699488827088718515501890242824204507273016030536139841159468466415661238827549579507217206306017314388508106840952916982006310335316806066678332 +def node14288 : Tree Nat := .node node14287 node6981 +def node14289 : Tree Nat := .node node14288 node11284 +def node14290 : Tree Nat := .node node10581 node14289 +def node14291 : Tree Nat := .leaf 8254602048994769474255309145988586409736845223991162255450003588722430659544893995193483422244551447177666524461011845455872219001318037887812636521618309039280170203022832835315547568235962024216265884681913660902540744509496526226685477801857385588706350588802328937 +def node14292 : Tree Nat := .node node14291 node7369 +def node14293 : Tree Nat := .node node14292 node12682 +def node14294 : Tree Nat := .node node11666 node14293 +def node14295 : Tree Nat := .node node14290 node14294 +def node14296 : Tree Nat := .leaf 397468889724173685979542788245425099345541698338619579376990907177671153860196467700470072948073273624394463306874264394576519767311383244340052479607909691946642178912766603519238872485298262736059379329500470064304388371323614882153 +def node14297 : Tree Nat := .node node14296 node6986 +def node14298 : Tree Nat := .node node14297 node12687 +def node14299 : Tree Nat := .node node10276 node14298 +def node14300 : Tree Nat := .node node14299 node11298 +def node14301 : Tree Nat := .node node14295 node14300 +def node14302 : Tree Nat := .node node14286 node14301 +def node14303 : Tree Nat := .leaf 141830295051199290754602382260373947395761342649441538550624200908015257966475838851543722998600295523153339307542856779229583930645813040756871935928954994184077134748546386712448692686860792090461209352870009684666016952950219644231626722392454153869386775130949933257175188394 +def node14304 : Tree Nat := .node node14303 node8646 +def node14305 : Tree Nat := .node node14304 node11303 +def node14306 : Tree Nat := .node node11998 node14305 +def node14307 : Tree Nat := .leaf 503820925841965910293903145710583493637006880564327892725666673368473246240567669475682352989106934593376810395043683004339709682878398364814850018495420126823091912531784710277140623037246438902106649274332563816113930590028247814106805325452254980336620786417919 +def node14308 : Tree Nat := .node node14307 node9076 +def node14309 : Tree Nat := .node node14308 node12694 +def node14310 : Tree Nat := .node node12342 node14309 +def node14311 : Tree Nat := .node node14306 node14310 +def node14312 : Tree Nat := .leaf 114555615673899844817675135827349603920186156328588973012815230098216247591936145623178599818602061805628440424236441183793286810769621760146212077663227459888103895663369975594942529988997020774105405362937139803084489888260669025053511232255219547306 +def node14313 : Tree Nat := .node node14312 node9081 +def node14314 : Tree Nat := .node node14313 node10952 +def node14315 : Tree Nat := .node node10288 node14314 +def node14316 : Tree Nat := .leaf 9076030969344193881830906443734197896041214432680857066853762215856310823831566669886141577485648253891936520286387185970107498991864168418146640176962795664917808271276761143081364339715242438384420450311516277979483685930617190356347810880755687495792841417313200556406856417535 +def node14317 : Tree Nat := .node node14316 node12698 +def node14318 : Tree Nat := .node node14317 node12349 +def node14319 : Tree Nat := .node node12347 node14318 +def node14320 : Tree Nat := .node node14315 node14319 +def node14321 : Tree Nat := .node node14311 node14320 +def node14322 : Tree Nat := .leaf 492012622892656704990238084452251441810928680478211353074222523471479393502725184660276873998006663998813145330047983509730321495612895498074327544186461058746881903333247832437633860389101362010104528074175179849629936774732882243795374747322157603762286297343 +def node14323 : Tree Nat := .node node14322 node8665 +def node14324 : Tree Nat := .node node14323 node12003 +def node14325 : Tree Nat := .node node10602 node14324 +def node14326 : Tree Nat := .leaf 2215963108520416015739670368219860918705627185547197085343450321573077336868309251077102326174225549155407086842882886153507097866022858011143218203355784684139059833755154934588180336648220194811903249793435037512778837937724462381679612300118288421078796281048168614200344831 +def node14327 : Tree Nat := .node node14326 node9376 +def node14328 : Tree Nat := .node node14327 node12705 +def node14329 : Tree Nat := .node node12356 node14328 +def node14330 : Tree Nat := .node node14325 node14329 +def node14331 : Tree Nat := .leaf 270486799941460609886385509495647727003124994963545150394648763308944639969102659393676275592250940467361807953988974708791626313912197649469725030384215454103215939714398451354197695534910753912172065410386729530974690402527933667380203919432296627927621625258599753122047 +def node14332 : Tree Nat := .node node14331 node9092 +def node14333 : Tree Nat := .node node14332 node12361 +def node14334 : Tree Nat := .node node12711 node14333 +def node14335 : Tree Nat := .leaf 6828046779268970776657768233878085902324275438521959671787668942028781287039163393246395227370680568936631177633751398183847755896434749212611613699815207199423526999689055146138073928553989707314316414176701463176754585271673608346473775235071 +def node14336 : Tree Nat := .node node14335 node8674 +def node14337 : Tree Nat := .node node14336 node11318 +def node14338 : Tree Nat := .node node14337 node12013 +def node14339 : Tree Nat := .node node14334 node14338 +def node14340 : Tree Nat := .node node14330 node14339 +def node14341 : Tree Nat := .node node14321 node14340 +def node14342 : Tree Nat := .node node14302 node14341 +def node14343 : Tree Nat := .node node14267 node14342 +def node14344 : Tree Nat := .leaf 7507516828804700229971157695509256861311759593549503536677899755757881062691614939970702182859795639737729241335368268839526962869220176380869024994616278906372529249382147856492585955442967754510945820115799159267379990265020600267655577538677087867726185 +def node14345 : Tree Nat := .node node14344 node8685 +def node14346 : Tree Nat := .node node14345 node12719 +def node14347 : Tree Nat := .node node12371 node14346 +def node14348 : Tree Nat := .leaf 138497694282557489791594520883107362511587926461792414802412290885116654711244934379385276898882351777722071648826508466570935182983877595422721801033778925029865199276330556817049578766433639737180896404553634105254771648607715184818862880116482761559197926204999114757532009 +def node14349 : Tree Nat := .node node14348 node9109 +def node14350 : Tree Nat := .node node14349 node12723 +def node14351 : Tree Nat := .node node11328 node14350 +def node14352 : Tree Nat := .node node14347 node14351 +def node14353 : Tree Nat := .leaf 1134538491365238617645709308610684339450379797753347501667578239658343657726760624906612719539297292415998002462756517118968397271384190568611747957444814147151601701445989250704496154691965982943906131784209193584487661492056650093046168263805180301885181194303929442843152848489 +def node14354 : Tree Nat := .node node14353 node9114 +def node14355 : Tree Nat := .node node14354 node9386 +def node14356 : Tree Nat := .node node12376 node14355 +def node14357 : Tree Nat := .leaf 123003155723136208567847447708070018416355381964899431605122243912527778097675492900439533338605641464139113673047619645997955107023597622533631865752384565045090165295010437231576649888568431557609663563836632543763696941310067880177565867987738732358732573033 +def node14358 : Tree Nat := .node node14357 node11694 +def node14359 : Tree Nat := .node node14358 node12379 +def node14360 : Tree Nat := .node node12022 node14359 +def node14361 : Tree Nat := .node node14356 node14360 +def node14362 : Tree Nat := .node node14352 node14361 +def node14363 : Tree Nat := .leaf 32246507424497658146532278144464391913490075163096718785559364785344191354011248318908866205655535483151498720787432408330540408855682523067846012624874617360028222110378708653747845669032547654340269655198609248879860651614387509259228125111937866187754955886384444 +def node14364 : Tree Nat := .node node14363 node8696 +def node14365 : Tree Nat := .node node14364 node11333 +def node14366 : Tree Nat := .node node10622 node14365 +def node14367 : Tree Nat := .leaf 33018408195979077897021236563951930273518967420704215659524541816820944659071993167455629007494867542162264158717584922876283407033358596609923679208455290439931457594477923970132687088832368158479239626062853660846677676937234292924928638516159408959843513720014399849 +def node14368 : Tree Nat := .node node14367 node9124 +def node14369 : Tree Nat := .node node14368 node12729 +def node14370 : Tree Nat := .node node10996 node14369 +def node14371 : Tree Nat := .node node14366 node14370 +def node14372 : Tree Nat := .leaf 6511732893125423073928276657127400410040102860476731377848561062811134572353652677596114027250812584288330251989403902611627946281703492177380333199712947485677694181111595751837530378006434692568839243995954953510564290020524426451921468 +def node14373 : Tree Nat := .node node14372 node9129 +def node14374 : Tree Nat := .node node14373 node12386 +def node14375 : Tree Nat := .node node12735 node14374 +def node14376 : Tree Nat := .node node14375 node9961 +def node14377 : Tree Nat := .node node14371 node14376 +def node14378 : Tree Nat := .node node14362 node14377 +def node14379 : Tree Nat := .leaf 8656105892673619465444975048166327535575816414642870886433951036774960517713398590419113722066179432147823147253351950962798170215546662598092199921108283620759921794391459779472859766165906862099710146520716755861149392119382741038929864575765076487277848120654794356016042 +def node14380 : Tree Nat := .node node14379 node12890 +def node14381 : Tree Nat := .node node14380 node12741 +def node14382 : Tree Nat := .node node10319 node14381 +def node14383 : Tree Nat := .node node14382 node13825 +def node14384 : Tree Nat := .leaf 225921116696657399755928707376375798670333555195312617614099150595166526000831197939208375616448768444844308775376678197259415801619655891592005693734934921697417155233432635558002928231299299021900347084862620663517987754 +def node14385 : Tree Nat := .node node14384 node9667 +def node14386 : Tree Nat := .node node14385 node12398 +def node14387 : Tree Nat := .node node12751 node14386 +def node14388 : Tree Nat := .leaf 553990777130104003934917592054855974259924061527415598228274596169714978873108889622872645198406642054558278952365671633092016626097594910422476814009311811588144432308231332280759118191506643479319278552639471085147961488712709541928083778736112431770833818046891370116743423 +def node14389 : Tree Nat := .node node14388 node12404 +def node14390 : Tree Nat := .node node14389 node12407 +def node14391 : Tree Nat := .node node12403 node14390 +def node14392 : Tree Nat := .node node14387 node14391 +def node14393 : Tree Nat := .node node14383 node14392 +def node14394 : Tree Nat := .node node12759 node13103 +def node14395 : Tree Nat := .node node13842 node14394 +def node14396 : Tree Nat := .node node12898 node14395 +def node14397 : Tree Nat := .node node13840 node14396 +def node14398 : Tree Nat := .node node14397 node13855 +def node14399 : Tree Nat := .node node14393 node14398 +def node14400 : Tree Nat := .node node14378 node14399 +def node14401 : Tree Nat := .leaf 72608247484266751113186647294354820488834247026939543948396825646101063287786253971485042109138266243244020558325693611899195180836380228795842510795805830184899484320891698888933334758724964010824766196053363935991772905653606246796970257905615959227262383521093056698343023744617 +def node14402 : Tree Nat := .node node14401 node9427 +def node14403 : Tree Nat := .node node14402 node12773 +def node14404 : Tree Nat := .node node12915 node14403 +def node14405 : Tree Nat := .leaf 173717940541902012406847659425866484451190533229463526990882236840893119072742199839856502876068937588389229049516035492492906865262399953583505161180764870181157579673159550819488672200170647667420217060905152992175436413411303170551637600442427329845432512562953121506814408702136485890716625257 +def node14406 : Tree Nat := .node node14405 node9690 +def node14407 : Tree Nat := .node node14406 node12048 +def node14408 : Tree Nat := .node node11721 node14407 +def node14409 : Tree Nat := .node node14404 node14408 +def node14410 : Tree Nat := .leaf 641163699438029873998476675731070532890503365471348354882531362507106952652341177184586026177890229202314479090694496935628738694544632002740895571643276383782576266711859013453263643358330239817921192358353938733289475637851398127272992259463923911283983766310818756660227497009530610900560233 +def node14411 : Tree Nat := .node node14410 node9695 +def node14412 : Tree Nat := .node node14411 node12422 +def node14413 : Tree Nat := .node node12920 node14412 +def node14414 : Tree Nat := .leaf 1219353864951782111494411248513669248238417417502665318371385195113776976654427429269755729120838114140898916494294983697473193877894337772409732609568290886049967825033721765654481278587565869435907257226035585937681628243558338676960072350451946772779065271829865390579847083668933929321 +def node14415 : Tree Nat := .node node14414 node12059 +def node14416 : Tree Nat := .node node14415 node7055 +def node14417 : Tree Nat := .node node11726 node14416 +def node14418 : Tree Nat := .node node14413 node14417 +def node14419 : Tree Nat := .node node14409 node14418 +def node14420 : Tree Nat := .leaf 40072731214876796218413108378942774334323045285940858530772784274179266683592954082168903349767324293130424338184606348085645673785155640043888534828777831355789397249513415866641676312060666906692242301348507838518265495255970418332236727578522906659536278316529928152939475016433616786139708 +def node14421 : Tree Nat := .node node14420 node12924 +def node14422 : Tree Nat := .node node14421 node11382 +def node14423 : Tree Nat := .node node12780 node14422 +def node14424 : Tree Nat := .leaf 154649758481689438539253101856584427727906370118567238084748270901022217271244407098556404626491896659290190412922964660798727172120946886784235702852196485941661076272352594379896806449531432218916554131709942067149968839391080282890680995224406801313308463747660148091226353591268436329 +def node14425 : Tree Nat := .node node14424 node9709 +def node14426 : Tree Nat := .node node14425 node12066 +def node14427 : Tree Nat := .node node12930 node14426 +def node14428 : Tree Nat := .node node14423 node14427 +def node14429 : Tree Nat := .leaf 9516908214257811601907599988159363584840065290626636270825807227503749905371816105021419189398839454839689918914562806248206411829822979351300064714670728090477351428117358393598991669469351841968509351516504407542994913425616382779636326741406417431495807511069375318425647769200650601 +def node14430 : Tree Nat := .node node14429 node9714 +def node14431 : Tree Nat := .node node14430 node12428 +def node14432 : Tree Nat := .node node12935 node14431 +def node14433 : Tree Nat := .node node14432 node12940 +def node14434 : Tree Nat := .node node14428 node14433 +def node14435 : Tree Nat := .node node14419 node14434 +def node14436 : Tree Nat := .leaf 160290924859507184890963588712040320533756863335788821184229948264768520609423743754511922078006017603983437319396672369196710285824121217747960377139064043842851939963770279939992922224534680114065829533015236208406364399917226924053716704235227880827350299644885053546959935565789687851662506 +def node14437 : Tree Nat := .node node14436 node12077 +def node14438 : Tree Nat := .node node14437 node9463 +def node14439 : Tree Nat := .node node12787 node14438 +def node14440 : Tree Nat := .leaf 148701690847778306280310070740832021923419923311650029397698061862645982565585358253925509580443099392097636026797386502591340007597866141510220585781267578938273216270938198148028688929417347711928562238815532716661821702988252074193821279163473319304143965052005027480965053635624959 +def node14441 : Tree Nat := .node node14440 node11745 +def node14442 : Tree Nat := .node node14441 node12082 +def node14443 : Tree Nat := .node node12440 node14442 +def node14444 : Tree Nat := .node node14439 node14443 +def node14445 : Tree Nat := .leaf 9584288667923211146940637195106895509586686918352633524518732024561752301339197280802709155441220641788786764210402813327422804732093548427479683312030666151796693172219442849825974286000413401897406023848754974361654848085862909785912343346992327658368566846340756528632042910989482 +def node14446 : Tree Nat := .node node14445 node11750 +def node14447 : Tree Nat := .node node14446 node12794 +def node14448 : Tree Nat := .node node12792 node14447 +def node14449 : Tree Nat := .leaf 694871762167608049626282723770905715162043830833208898076279771632803262962607377701488142089040871141567657864678296095251240318970110686340489458480483915643121487203692938742159498012962646179451956129936101160535614917185381276544808818351698618788122820826897040168691299028275603137307279615 +def node14450 : Tree Nat := .node node14449 node11408 +def node14451 : Tree Nat := .node node14450 node9187 +def node14452 : Tree Nat := .node node12092 node14451 +def node14453 : Tree Nat := .node node14448 node14452 +def node14454 : Tree Nat := .node node14444 node14453 +def node14455 : Tree Nat := .leaf 297403390559003316441364371679462987949131770409322091479259371325373453793164064587149053478616722460716689797178803623935715975742154320267602450005467807086740497647693172174975943133796607630875584672064863927162867892548431439440543355712961411972610691668516091448182396885663743 +def node14456 : Tree Nat := .node node14455 node11417 +def node14457 : Tree Nat := .node node14456 node9193 +def node14458 : Tree Nat := .node node12446 node14457 +def node14459 : Tree Nat := .node node13916 node14458 +def node14460 : Tree Nat := .leaf 2739226045072033710287658726391013369481562983073862426076014871121501917116897813478243768409544927272652705989782486018374878784366859763845742616822186473850268648721702203944842116267329566248879994288668927 +def node14461 : Tree Nat := .node node14460 node12103 +def node14462 : Tree Nat := .node node14461 node12454 +def node14463 : Tree Nat := .node node14462 node12108 +def node14464 : Tree Nat := .node node13925 node14463 +def node14465 : Tree Nat := .node node14459 node14464 +def node14466 : Tree Nat := .node node14454 node14465 +def node14467 : Tree Nat := .node node14435 node14466 +def node14468 : Tree Nat := .node node14400 node14467 +def node14469 : Tree Nat := .node node14343 node14468 +def node14470 : Tree Nat := .node node14200 node14469 +def node14471 : Tree Nat := .leaf 546415263936042716054277313145405441 +def node14472 : Tree Nat := .node node14471 node12811 +def node14473 : Tree Nat := .node node14472 node10045 +def node14474 : Tree Nat := .node node14473 node13939 +def node14475 : Tree Nat := .node node13240 node12464 +def node14476 : Tree Nat := .node node14475 node12467 +def node14477 : Tree Nat := .leaf 276978483140055660679575521154310658598553426872826080593424479721944743637335064583130340808000721892441268569379212308399932662694284205702097585169193435032414605838253575203503260866196031433458804951352921717574925866750570369867543299043453345332673256107580977830454886 +def node14478 : Tree Nat := .node node14477 node12469 +def node14479 : Tree Nat := .node node14478 node12472 +def node14480 : Tree Nat := .node node14476 node14479 +def node14481 : Tree Nat := .node node14474 node14480 +def node14482 : Tree Nat := .leaf 79228162514264337589248983040 +def node14483 : Tree Nat := .node node14482 node12824 +def node14484 : Tree Nat := .node node14483 node10350 +def node14485 : Tree Nat := .leaf 1134503866941667986143541334648056457619674842830209732174383704661281727402804754416548424845268597132444970383912631563207990827489845178429108122191373230708943107068998149163237322978318337638638205048320699552232994768557237690514401021485960696706869336094317474317455088218 +def node14486 : Tree Nat := .node node14485 node9488 +def node14487 : Tree Nat := .node node14486 node9224 +def node14488 : Tree Nat := .node node14484 node14487 +def node14489 : Tree Nat := .leaf 123003155723136208567847447683223664415745989465967061144775319672827615245282853070109007218536306674745708410782905388586055064621515797122191070561722069598184336831924337253385042086151271460696227772647207623375333095605712918061611023823283573086171933269 +def node14490 : Tree Nat := .node node14489 node11437 +def node14491 : Tree Nat := .node node14490 node12118 +def node14492 : Tree Nat := .node node9229 node14491 +def node14493 : Tree Nat := .node node14488 node14492 +def node14494 : Tree Nat := .node node14481 node14493 +def node14495 : Tree Nat := .leaf 5192217631581239183526061278167040 +def node14496 : Tree Nat := .node node14495 node12831 +def node14497 : Tree Nat := .node node14496 node10356 +def node14498 : Tree Nat := .node node14497 node13958 +def node14499 : Tree Nat := .leaf 33018408195979077897021236557282287907427960838451981092487189987679470573908052333928986881956429041035710718910443876958184790166011882350154566339868106858294749432546375864417740428279671221168030005380294700000841809675947608112739223301207633839012114713806527027 +def node14500 : Tree Nat := .node node14499 node9504 +def node14501 : Tree Nat := .node node14500 node12478 +def node14502 : Tree Nat := .node node12837 node14501 +def node14503 : Tree Nat := .node node14498 node14502 +def node14504 : Tree Nat := .leaf 48516190384397171392751175090678259260270162528013642586385209916290288086478333150780021580175739629118289543847768199510899830187141888180207452226534790820321120216919046882785569607977848325647263248446981871303469249891558927 +def node14505 : Tree Nat := .node node14504 node12485 +def node14506 : Tree Nat := .node node14505 node12125 +def node14507 : Tree Nat := .node node12842 node14506 +def node14508 : Tree Nat := .node node14507 node12492 +def node14509 : Tree Nat := .node node14503 node14508 +def node14510 : Tree Nat := .node node14494 node14509 +def node14511 : Tree Nat := .leaf 781898821049950510217519904804372736 +def node14512 : Tree Nat := .node node14511 node12131 +def node14513 : Tree Nat := .node node14512 node10056 +def node14514 : Tree Nat := .node node14513 node13974 +def node14515 : Tree Nat := .leaf 2015283703367863641175612582842135243135427334428804184044917736999987313807108150565911656580400360071894370193173689646129889958808112504284773750881602853973553365132356026392074963350514880265968068991716688117422993563050757243654165760048833792176798233447589 +def node14516 : Tree Nat := .node node14515 node8813 +def node14517 : Tree Nat := .node node14516 node12501 +def node14518 : Tree Nat := .node node11789 node14517 +def node14519 : Tree Nat := .node node14514 node14518 +def node14520 : Tree Nat := .leaf 225921116696657399755928707376375798670333560260644071634548162212369334107823776038057071519881333252061364655668791715358213179274623608611407031717239351202907673747076056987966624041982421915729098256267705155566891161 +def node14521 : Tree Nat := .node node14520 node8818 +def node14522 : Tree Nat := .node node14521 node10368 +def node14523 : Tree Nat := .node node12138 node14522 +def node14524 : Tree Nat := .leaf 225924563982610226070265215820544374824657167771312989075437813652077668501960498285146510074899144885499114984200464467326910359101686978775252846219264264892966590051920900182865697595181347717195351754562376409390186390 +def node14525 : Tree Nat := .node node14524 node12143 +def node14526 : Tree Nat := .node node14525 node12146 +def node14527 : Tree Nat := .node node12142 node14526 +def node14528 : Tree Nat := .node node14523 node14527 +def node14529 : Tree Nat := .node node14519 node14528 +def node14530 : Tree Nat := .leaf 388129523075618493122339836630096054427223634588105293390099477028266276159473090555861521249404160932011661038651793952929479422758812987550487914612078970202667472208588016059109786710000848623737751755842763505850569167330921676 +def node14531 : Tree Nat := .node node14530 node8394 +def node14532 : Tree Nat := .node node14531 node11087 +def node14533 : Tree Nat := .node node10068 node14532 +def node14534 : Tree Nat := .leaf 8863852434081664062958681472877695588158784959592295567428676745533724054444448707009155594945536400548669592693422271275626349022051805379194444516422601761535311722779303668492240133077151516401604992088085099140856217169796100269094434467780775181909129324952181113383304387 +def node14535 : Tree Nat := .node node14534 node8828 +def node14536 : Tree Nat := .node node14535 node12507 +def node14537 : Tree Nat := .node node12153 node14536 +def node14538 : Tree Nat := .node node14533 node14537 +def node14539 : Tree Nat := .leaf 1081947199765842424529591879509026010150599323721976877786900707526989651739900452381302641357895255978501721913515669361826438869198939157555349872519364529282686887865300640437034619865895573149131335640835183649031013298945249799126031941729351098472096292325523222229232 +def node14540 : Tree Nat := .node node14539 node8833 +def node14541 : Tree Nat := .node node14540 node12512 +def node14542 : Tree Nat := .node node12158 node14541 +def node14543 : Tree Nat := .node node14542 node13435 +def node14544 : Tree Nat := .node node14538 node14543 +def node14545 : Tree Nat := .node node14529 node14544 +def node14546 : Tree Nat := .node node14510 node14545 +def node14547 : Tree Nat := .leaf 1251038113679918332326938251807948816 +def node14548 : Tree Nat := .node node14547 node7161 +def node14549 : Tree Nat := .node node14548 node10080 +def node14550 : Tree Nat := .node node14549 node13995 +def node14551 : Tree Nat := .leaf 86858970270951006203423838165645771885047073375041211488604415337194479134408200026866468221203321374509304249163184904583451743670206537702115563266644027668708487191084016195953265499820484379492289712844829686163969286747579215443403244899357270621071917752538651669827133339261357294955030118 +def node14552 : Tree Nat := .node node14551 node8850 +def node14553 : Tree Nat := .node node14552 node11472 +def node14554 : Tree Nat := .node node11470 node14553 +def node14555 : Tree Nat := .node node14550 node14554 +def node14556 : Tree Nat := .leaf 320581849719015504285796232270159840383892969391784817983639634828399285715423821179807476921894270412460028816508423648153232402599709517290130818817670178154070101218375702613277248737488700294725089103305924473206939663798042759485596102028104174913448813136138644087805846146116722719958362 +def node14557 : Tree Nat := .node node14556 node8419 +def node14558 : Tree Nat := .node node14557 node12168 +def node14559 : Tree Nat := .node node12521 node14558 +def node14560 : Tree Nat := .leaf 305135869619641084486162424651110383869718645522469604919050302005727267917819995841479478538868055680940285189690738651919013376267824941051617314061007409483742210675248527715269648201148996333276918982055879758765585967492508679507501528971337673079105596807641171012013694264121731669 +def node14561 : Tree Nat := .node node14560 node11476 +def node14562 : Tree Nat := .node node14561 node8427 +def node14563 : Tree Nat := .node node8425 node14562 +def node14564 : Tree Nat := .node node14559 node14563 +def node14565 : Tree Nat := .node node14555 node14564 +def node14566 : Tree Nat := .leaf 38067632857031246415885002001632223813615570301801070128684750548400235182831352333308404133180821172702099111877852160800355136763992239695518951053977240173283467367941175228282463341185918534820004623241488810812315249396333941409644421671105928803874448751505858146032579262260337203 +def node14567 : Tree Nat := .node node14566 node8862 +def node14568 : Tree Nat := .node node14567 node11822 +def node14569 : Tree Nat := .node node11489 node14568 +def node14570 : Tree Nat := .node node14015 node14569 +def node14571 : Tree Nat := .leaf 18587711355972288284975781226873757001640752520742430762455243433647852495356937686061563313740224455898572328929311704065567065391092933311837846148791088729398392233347632277708175404638606175464530453434801214177405834470295458207525426731480015034362474663804476150205842324874767 +def node14572 : Tree Nat := .node node14571 node8869 +def node14573 : Tree Nat := .node node14572 node12531 +def node14574 : Tree Nat := .node node11494 node14573 +def node14575 : Tree Nat := .node node14574 node12176 +def node14576 : Tree Nat := .node node14570 node14575 +def node14577 : Tree Nat := .node node14565 node14576 +def node14578 : Tree Nat := .leaf 19070991851227567780385655359698316649593705989427444620245069009852873381868266799619284790372586035931953043278025883202425015142334914992320745639743023782957160290155831262614110372560209147570684874137322521731381072630438671218798334986687041177107449268300436202378641736395574437 +def node14579 : Tree Nat := .node node14578 node8884 +def node14580 : Tree Nat := .node node14579 node11504 +def node14581 : Tree Nat := .node node12182 node14580 +def node14582 : Tree Nat := .node node14031 node14581 +def node14583 : Tree Nat := .leaf 4792144333961605573470318597553505032601180409098725599827279743563115417912112873870037829428216777831309210655101407571163493262736114679447454578921403231388587583565533846240720862956847408963542982250236474540534393570768670284273869653759790830864849664095213364029845976453017 +def node14584 : Tree Nat := .node node14583 node8889 +def node14585 : Tree Nat := .node node14584 node12186 +def node14586 : Tree Nat := .node node11840 node14585 +def node14587 : Tree Nat := .leaf 347435881083804024813695352662582961584956833008659305225776271727755038173984289085997064519319836027896598150277906664489114558658205249325521407903002537796268903234728220188901475585127554123903957158063485043643369761486045258142528445235487148116499512002983892933103741917388103503384870806 +def node14588 : Tree Nat := .node node14587 node12542 +def node14589 : Tree Nat := .node node14588 node10091 +def node14590 : Tree Nat := .node node12191 node14589 +def node14591 : Tree Nat := .node node14586 node14590 +def node14592 : Tree Nat := .node node14582 node14591 +def node14593 : Tree Nat := .leaf 4989600774417665509015065799559216404602780166926639091188048129501138449035341986869698100080542248342583753843428313671635575063230559098187536994539972933005997472758539794579254625311002825115066060503208231882468157064164019707657553381209589556765297642814319833354977450215088807752652 +def node14594 : Tree Nat := .node node14593 node8463 +def node14595 : Tree Nat := .node node14594 node11132 +def node14596 : Tree Nat := .node node10407 node14595 +def node14597 : Tree Nat := .leaf 609156476566787278379108054239156247333694058308169791851172548092041729379507673387366203849147725996730025406920568452273150403897892308531071537704644186156703520144043236917508273800981481956093727732268419714023411839396981673670438107794104211235365080601176597713122964536911740099 +def node14598 : Tree Nat := .node node14597 node9275 +def node14599 : Tree Nat := .node node14598 node10410 +def node14600 : Tree Nat := .node node12197 node14599 +def node14601 : Tree Nat := .node node14596 node14600 +def node14602 : Tree Nat := .leaf 1277342670759226379460700660234536462305607824197264347990219482828857053616974461436967345783191853911950530066003400769902543076803619525702886840821972807467189310119954914441588863863238364207919223494656759721532371568606469678750184742073157127139805894332363746434717334615215936099061744 +def node14603 : Tree Nat := .node node14602 node8900 +def node14604 : Tree Nat := .node node14603 node12552 +def node14605 : Tree Nat := .node node12550 node14604 +def node14606 : Tree Nat := .node node14605 node14051 +def node14607 : Tree Nat := .node node14601 node14606 +def node14608 : Tree Nat := .node node14592 node14607 +def node14609 : Tree Nat := .node node14577 node14608 +def node14610 : Tree Nat := .node node14546 node14609 +def node14611 : Tree Nat := .leaf 1063374331139092410926069226016604164 +def node14612 : Tree Nat := .node node14611 node5191 +def node14613 : Tree Nat := .node node14612 node10106 +def node14614 : Tree Nat := .node node14613 node14059 +def node14615 : Tree Nat := .leaf 168608589349493131958015087616540679668592803278962431331060101814331015260871777495148119299778999483168145679854451622674939147754434619637275616256377777392408477111434973918618393799252678538302702349285742709182101189207206478668919921086858129216098575737631697492340822367590109711292406118 +def node14616 : Tree Nat := .node node14615 node7222 +def node14617 : Tree Nat := .node node14616 node11528 +def node14618 : Tree Nat := .node node11525 node14617 +def node14619 : Tree Nat := .node node14614 node14618 +def node14620 : Tree Nat := .leaf 321829249912474136881525683989307835131953557306589263343752782944593437589520939150189555629080100264798835086290555977713254120225443146180701228171476451892310277561050909123407951909422647174765070431906078761372756650335197093869944677908587267228944405211468829893183999528542800398277210 +def node14621 : Tree Nat := .node node14620 node6826 +def node14622 : Tree Nat := .node node14621 node11857 +def node14623 : Tree Nat := .node node10430 node14622 +def node14624 : Tree Nat := .leaf 305730676383032197711281649742622710886123306029018948465096423214894378187525711710577125145017308736797642166709708925119651563701120884476865237687147190834701536676069687533883080766034579488107378925052481974792132810804528819213223678255519999184947077775037817407089760130163518037 +def node14625 : Tree Nat := .node node14624 node11144 +def node14626 : Tree Nat := .node node14625 node9798 +def node14627 : Tree Nat := .node node10112 node14626 +def node14628 : Tree Nat := .node node14623 node14627 +def node14629 : Tree Nat := .node node14619 node14628 +def node14630 : Tree Nat := .leaf 40446859910595699341125708145656373132591514042419445126956107720017105848770028401130341546201483200632496178089575328505341280298665416420738783615214685575516665677543978420028481860981334107678969827397592415521936031525211183633406223766682073247417853627518259469539801851194858035 +def node14631 : Tree Nat := .node node14630 node7235 +def node14632 : Tree Nat := .node node14631 node11151 +def node14633 : Tree Nat := .node node11535 node14632 +def node14634 : Tree Nat := .node node14079 node14633 +def node14635 : Tree Nat := .leaf 18587711355972288284975781226873757001640752527254561075954200296864920133568817487707092950860057205891604452303042089454261995933702318684836888461722869150513792971597610852869053192966382049615296070527169379437005615326909340540045362780284771215094484264175594196225969842906639 +def node14636 : Tree Nat := .node node14635 node6845 +def node14637 : Tree Nat := .node node14636 node12210 +def node14638 : Tree Nat := .node node12562 node14637 +def node14639 : Tree Nat := .node node14638 node12216 +def node14640 : Tree Nat := .node node14634 node14639 +def node14641 : Tree Nat := .node node14629 node14640 +def node14642 : Tree Nat := .leaf 37175422711944576571966846157115377644457117624326996718013592867814909517272922286185664988388014749487763295594273489954555800867105990784175189628038510374413617503462222491871385824278346527407119254668977871877140251560080523816850153173163401945312503401810744116324710949139365 +def node14643 : Tree Nat := .node node14642 node7242 +def node14644 : Tree Nat := .node node14643 node11550 +def node14645 : Tree Nat := .node node11548 node14644 +def node14646 : Tree Nat := .node node14095 node14645 +def node14647 : Tree Nat := .leaf 4937360828930139075696691888388341703560824888322208164833617614595517561556605024501045357416203106568280468781367495212908167983181339073273592438566943336108922629372796776202083052275359055708099265239702556857507176525057421565370904417591514264740220992024035419998393229570201 +def node14648 : Tree Nat := .node node14647 node9814 +def node14649 : Tree Nat := .node node14648 node11874 +def node14650 : Tree Nat := .node node11871 node14649 +def node14651 : Tree Nat := .leaf 367873285853439564760533587811143966328459060057661429664211016701021150139241504673514450146755572907776759555882616850812232166675443291171532706989528100542462706662124705638869494300965106051153893667243031562928615940775818537943818489297006017639786694338779898205594532697528314892867272598 +def node14652 : Tree Nat := .node node14651 node12220 +def node14653 : Tree Nat := .node node14652 node8508 +def node14654 : Tree Nat := .node node11880 node14653 +def node14655 : Tree Nat := .node node14650 node14654 +def node14656 : Tree Nat := .node node14646 node14655 +def node14657 : Tree Nat := .leaf 9979201548254465038155997574090178006299953753319660660381375882742818927998918350738505463023658415398099156132278510137744736367289781369040026320175171618009363958374242511544740415411849804989814965072301583613655066486254536116781414466088205360887915213678097348921212631158638819619788 +def node14658 : Tree Nat := .node node14657 node9824 +def node14659 : Tree Nat := .node node14658 node11169 +def node14660 : Tree Nat := .node node10464 node14659 +def node14661 : Tree Nat := .leaf 74350847640257991860231331556363993181239786870752635029752400361930165761785448651591505484970839553341940157553410627684958321052340855584422428792356060817975930476681643200448303206502130554636552985996031068956834435954675543855893812783291069005222409107843018966718788174857155 +def node14662 : Tree Nat := .node node14661 node10800 +def node14663 : Tree Nat := .node node14662 node11885 +def node14664 : Tree Nat := .node node11557 node14663 +def node14665 : Tree Nat := .node node14660 node14664 +def node14666 : Tree Nat := .leaf 4872657005699999810663491135398204041823608939751973073340296112092162650589745671020362028981173928417388251915025194266042170442037274997643866993603969714391782314214918113366669399820314066283330081797497310614275602110739527794279828745667685699622199657123562605720065042468742041584 +def node14667 : Tree Nat := .node node14666 node10467 +def node14668 : Tree Nat := .node node14667 node12577 +def node14669 : Tree Nat := .node node11562 node14668 +def node14670 : Tree Nat := .node node14669 node13562 +def node14671 : Tree Nat := .node node14665 node14670 +def node14672 : Tree Nat := .node node14656 node14671 +def node14673 : Tree Nat := .node node14641 node14672 +def node14674 : Tree Nat := .leaf 2269146223124906000117422926276498862782315294279058932144853424001014171895230212411404973000048044792172692986741420723191826847732454366742485245184723751556231813275184199818286288664587407927686291209969248876865125372494088416703025341267792245291793470899057803960886991206 +def node14675 : Tree Nat := .node node14674 node10475 +def node14676 : Tree Nat := .node node14675 node12593 +def node14677 : Tree Nat := .node node11570 node14676 +def node14678 : Tree Nat := .node node14131 node14677 +def node14679 : Tree Nat := .leaf 567286555781226500029355731569122967715603332303024435169262119354790718260422894252365794277193656171034240881504545882039792440605577976305040582381114750828792298657564703515972443248396882185269925306943303416431680051002886638100427216309411176379342845339434530588515607898 +def node14680 : Tree Nat := .node node14679 node11576 +def node14681 : Tree Nat := .node node14680 node12235 +def node14682 : Tree Nat := .node node10482 node14681 +def node14683 : Tree Nat := .leaf 30750788930784052141961861920811980997887234677887817339864608149478746012353383005245511535615183867402719086846186378172349218606166225793694462505817694549368294893849779989912882483817193565211203275397663375979504164983604784511246592839083802513396181589 +def node14684 : Tree Nat := .node node14683 node11897 +def node14685 : Tree Nat := .node node14684 node12239 +def node14686 : Tree Nat := .node node11185 node14685 +def node14687 : Tree Nat := .node node14682 node14686 +def node14688 : Tree Nat := .node node14678 node14687 +def node14689 : Tree Nat := .leaf 8254602048994769474255309139322199910068143258083693241044839823575153550594486940739435416735876022684849312314722302358075980517169046263441500479711629410651914192877422095937077620632807849196598684646854079044997768909947805864762649840243211493351129478248880691 +def node14690 : Tree Nat := .node node14689 node10165 +def node14691 : Tree Nat := .node node14690 node12603 +def node14692 : Tree Nat := .node node12246 node14691 +def node14693 : Tree Nat := .node node14150 node14692 +def node14694 : Tree Nat := .leaf 6512130313498956863217084807164470744461190538033039686479754608152295293285303498932704226690161011840344628306615244958143754424581746160005740030721115414831250524732072120471607767215869506335382602918548434685659708822966158812079631 +def node14695 : Tree Nat := .node node14694 node11588 +def node14696 : Tree Nat := .node node14695 node12608 +def node14697 : Tree Nat := .node node12251 node14696 +def node14698 : Tree Nat := .node node14697 node11920 +def node14699 : Tree Nat := .node node14693 node14698 +def node14700 : Tree Nat := .node node14688 node14699 +def node14701 : Tree Nat := .leaf 503820925841965910293903145710682853278783176422042742899963128541361843967736281426486644995877983155568212169833255435184329347739794588698106462461282403652790728932768240966668038923127871765125284449793408086921060505933785747213862581215640336514784859599781 +def node14702 : Tree Nat := .node node14701 node10500 +def node14703 : Tree Nat := .node node14702 node12622 +def node14704 : Tree Nat := .node node11206 node14703 +def node14705 : Tree Nat := .node node14166 node14704 +def node14706 : Tree Nat := .leaf 114555615673899844817675135827349603920186156328588973012815230098216247597001467415855239037616505603637170860454974156046109455801580026176644352441657784801933346009161319638632059810916765995044128687677992717901748546529900889170885763595464150937 +def node14707 : Tree Nat := .node node14706 node10188 +def node14708 : Tree Nat := .node node14707 node12263 +def node14709 : Tree Nat := .node node12261 node14708 +def node14710 : Tree Nat := .leaf 9076584892499624000469689828226760282701348722326821713643608315639232502580756490540189131484592466369882212749188672534231992940101449934755636487247161484782176778148646014730649729773003381487614761759138543577896610204126782187795157983713505232884361750933663822884014587798 +def node14711 : Tree Nat := .node node14710 node7290 +def node14712 : Tree Nat := .node node14711 node12267 +def node14713 : Tree Nat := .node node11926 node14712 +def node14714 : Tree Nat := .node node14709 node14713 +def node14715 : Tree Nat := .node node14705 node14714 +def node14716 : Tree Nat := .leaf 8061134813471454564709278378172451595382697492350202586319113003583328947243921783642977354659505911468918994647359185488933685101789674268739788968642849918860900085764455761008810428089234894369044556895150358232326421657180741615025599445067366798655544660053196 +def node14717 : Tree Nat := .node node14716 node10198 +def node14718 : Tree Nat := .node node14717 node11214 +def node14719 : Tree Nat := .node node10515 node14718 +def node14720 : Tree Nat := .leaf 2215963108520416015739670368219423897040103223200861968900182144416075582367312816110528302486423822293081034527335103821046647224874906191755096497613522479383626210196778033937866111658809070779601974003567415185610612313815382293752246013751405806167923130192235802432619459 +def node14721 : Tree Nat := .node node14720 node10848 +def node14722 : Tree Nat := .node node14721 node12628 +def node14723 : Tree Nat := .node node10204 node14722 +def node14724 : Tree Nat := .node node14719 node14723 +def node14725 : Tree Nat := .leaf 270486799941460606132397969877256554634692338922149125534990864827253047922381898296765922036845598671568204247815885628137567517818175826095693888262472651812408910495712160756593870939223671596717691837567818862928306520659828178036691776062880241410514287121127212839152 +def node14726 : Tree Nat := .node node14725 node10518 +def node14727 : Tree Nat := .node node14726 node12636 +def node14728 : Tree Nat := .node node12634 node14727 +def node14729 : Tree Nat := .node node14728 node14194 +def node14730 : Tree Nat := .node node14724 node14729 +def node14731 : Tree Nat := .node node14715 node14730 +def node14732 : Tree Nat := .node node14700 node14731 +def node14733 : Tree Nat := .node node14673 node14732 +def node14734 : Tree Nat := .node node14610 node14733 +def node14735 : Tree Nat := .leaf 887878706204224360511889342093393922 +def node14736 : Tree Nat := .node node14735 node12645 +def node14737 : Tree Nat := .node node14736 node10222 +def node14738 : Tree Nat := .node node14737 node14203 +def node14739 : Tree Nat := .leaf 91968321463359891190271877741643521241811080357357754374850699790700430936706816559365054036878295092464935961604259661610452401777491444353936885094292892669342129114234833723624367198344907828786407901963416781473772858743134249540649602208935560444346072948115435326880204863663164167711136102 +def node14740 : Tree Nat := .node node14739 node8991 +def node14741 : Tree Nat := .node node14740 node11609 +def node14742 : Tree Nat := .node node12654 node14741 +def node14743 : Tree Nat := .node node14738 node14742 +def node14744 : Tree Nat := .leaf 639916299244570106898880282343936394601108129500086289847591281966445774086874148613579531170258849978937705569952856868184947918664318708362504720753564462941279276757510887279018182132657416178492560489528341474355086250189390618367775718725920126516888685235832973328669978472527199514699098 +def node14745 : Tree Nat := .node node14744 node8998 +def node14746 : Tree Nat := .node node14745 node11938 +def node14747 : Tree Nat := .node node11936 node14746 +def node14748 : Tree Nat := .leaf 1218759058188390998269292023606661654806717069847887146350174569787895234894393803710342248917586552091505598663909792279820342266659040293446632428157702443356617321741665090067496469685042973419493452164641674827539035806476143598059428512651241732077873604983088864594177849895757501781 +def node14749 : Tree Nat := .node node14748 node11616 +def node14750 : Tree Nat := .node node14749 node8574 +def node14751 : Tree Nat := .node node11615 node14750 +def node14752 : Tree Nat := .node node14747 node14751 +def node14753 : Tree Nat := .node node14743 node14752 +def node14754 : Tree Nat := .leaf 152270531428124985663540008006528895254462281213872294947618853506483312281637601006710476254648951477568578231959350517633987616622943568599590373193859195360868939825216653169583071331114913603895493890080653363050630102702956458529979846094068988951100909224854705018953362705705772339 +def node14755 : Tree Nat := .node node14754 node9008 +def node14756 : Tree Nat := .node node14755 node11239 +def node14757 : Tree Nat := .node node10884 node14756 +def node14758 : Tree Nat := .node node14223 node14757 +def node14759 : Tree Nat := .leaf 9516908214257811601907599988159363584840065290620124935450087718987904762481275522191874685950243732024609872161685536783436920631949828444073824651566436158632700981972424500129421206791459829592797996473299888060732951885525870173416992842012546756339451718365674041149779728841218319 +def node14760 : Tree Nat := .node node14759 node9015 +def node14761 : Tree Nat := .node node14760 node12659 +def node14762 : Tree Nat := .node node12284 node14761 +def node14763 : Tree Nat := .node node14762 node12289 +def node14764 : Tree Nat := .node node14758 node14763 +def node14765 : Tree Nat := .node node14753 node14764 +def node14766 : Tree Nat := .leaf 781895255728023203190532673413480960 +def node14767 : Tree Nat := .node node14766 node12293 +def node14768 : Tree Nat := .node node14767 node10240 +def node14769 : Tree Nat := .node node14768 node14238 +def node14770 : Tree Nat := .leaf 19182518119363401510097021509837085089334432213989030557701434505264689708377241855498476855145954111770111954865225270101930396867267044285639372698380683619098369523605745502539474917124134063916692376392100250429637189441522266501064957788075144988800317412636061464225181101117263013 +def node14771 : Tree Nat := .node node14770 node9026 +def node14772 : Tree Nat := .node node14771 node11634 +def node14773 : Tree Nat := .node node11946 node14772 +def node14774 : Tree Nat := .node node14769 node14773 +def node14775 : Tree Nat := .leaf 9439072172954677644714263904271829727395694639439515609240739454321509785382047952225675997004176433832325951903502590804545085859770249562327929855799949684973133695024869043544004569598801240538962845537402306902327473008038635379576778779074563266277626383016608164492234625249433 +def node14776 : Tree Nat := .node node14775 node9031 +def node14777 : Tree Nat := .node node14776 node11951 +def node14778 : Tree Nat := .node node10904 node14777 +def node14779 : Tree Nat := .leaf 674434357397972527831506359689032488715202958153110094699136562788445821639287146625768890659898391528336492751750116100773007205770255670840498810443826188440795773504687095619308580575390114318856694211300531962836965496574777555039307766611604994364863540196538908750298178442130252246090645398 +def node14780 : Tree Nat := .node node14779 node12301 +def node14781 : Tree Nat := .node node14780 node6951 +def node14782 : Tree Nat := .node node12300 node14781 +def node14783 : Tree Nat := .node node14778 node14782 +def node14784 : Tree Nat := .node node14774 node14783 +def node14785 : Tree Nat := .leaf 5028582029882399525462345320204731981883587735092193063525305450952575249177172116263568223105123230548636787193461383948712621880603312140714785232842096368941520430405193310267830029669133521379494745372248628101557109290324128865943274367303488588767248301914600647106504991821658151767244 +def node14786 : Tree Nat := .node node14785 node8616 +def node14787 : Tree Nat := .node node14786 node9038 +def node14788 : Tree Nat := .node node10252 node14787 +def node14789 : Tree Nat := .leaf 609379529096411867973366339948478118506964670448485409767219194677177969197692491102901687804714868502153666615462946466893632205431910779071873488141615126635493261638544082572070444531516089408435267139195634070617346717681514684276536853985436580046957733902564737863210323618196896963 +def node14790 : Tree Nat := .node node14789 node9350 +def node14791 : Tree Nat := .node node14790 node11961 +def node14792 : Tree Nat := .node node12309 node14791 +def node14793 : Tree Nat := .node node14788 node14792 +def node14794 : Tree Nat := .leaf 1277347543416232079459429376525906018077612080889412371381485013669145509714721103929373520155488338893598791020415041613409168073371303333206532275245895985772137920110930531605961111337859276429609669873223001089364622090072996023559092105177471052211626349740926371330385653724806285165129968 +def node14795 : Tree Nat := .node node14794 node9042 +def node14796 : Tree Nat := .node node14795 node12316 +def node14797 : Tree Nat := .node node12314 node14796 +def node14798 : Tree Nat := .node node14797 node13706 +def node14799 : Tree Nat := .node node14793 node14798 +def node14800 : Tree Nat := .node node14784 node14799 +def node14801 : Tree Nat := .node node14765 node14800 +def node14802 : Tree Nat := .leaf 2269284720819188557607214520797381970144826882205520724559655836291846687190913726402047483367509812685079604712967947551928284951134268102634086871681161675151596075755869694094988418475794112983556045632761878673528386101109976751347744536084903667900659904478258502810764876134 +def node14803 : Tree Nat := .node node14802 node10568 +def node14804 : Tree Nat := .node node14803 node12671 +def node14805 : Tree Nat := .node node11279 node14804 +def node14806 : Tree Nat := .node node14271 node14805 +def node14807 : Tree Nat := .leaf 567251935584012117616353577041561371734776462270766013478031382293311805960637328517293275040758938467665397012245017271704235428691565005120448078904513563400770836461779074694694144052535420247984686086107917111790830968012852440975383044206645845979596689683110264941354900058 +def node14808 : Tree Nat := .node node14807 node6975 +def node14809 : Tree Nat := .node node14808 node11980 +def node14810 : Tree Nat := .node node12677 node14809 +def node14811 : Tree Nat := .leaf 30750788930784052141961861945646205950900528103719502925379297944556910045507410279399120945204228792313382002610787910988188490091825741111533237413584381112438465983917439245016505154253351048330085848699459150767942317837084775708528645768063812412727317845 +def node14812 : Tree Nat := .node node14811 node11658 +def node14813 : Tree Nat := .node node14812 node12328 +def node14814 : Tree Nat := .node node11985 node14813 +def node14815 : Tree Nat := .node node14810 node14814 +def node14816 : Tree Nat := .node node14806 node14815 +def node14817 : Tree Nat := .leaf 8254602048994769474255309145988586409736845223991162255450003588722430659544893995193483422244551447177666524461011845455872219001318037887812636521618309039280170203022832835315547568235962024216265884681913660902540744509496526226218269650750881632719745719843071283 +def node14818 : Tree Nat := .node node14817 node7369 +def node14819 : Tree Nat := .node node14818 node12682 +def node14820 : Tree Nat := .node node11666 node14819 +def node14821 : Tree Nat := .node node14290 node14820 +def node14822 : Tree Nat := .leaf 397468889724173685979542788245425099345541698338619579376990907177671153860196467700470072948073273624394463306874264394576519767311383244340052479607909691946642178912766603519238872485298262736058850068097750795927358997442129729807 +def node14823 : Tree Nat := .node node14822 node6986 +def node14824 : Tree Nat := .node node14823 node12687 +def node14825 : Tree Nat := .node node10276 node14824 +def node14826 : Tree Nat := .node node14825 node11298 +def node14827 : Tree Nat := .node node14821 node14826 +def node14828 : Tree Nat := .node node14816 node14827 +def node14829 : Tree Nat := .leaf 503820925841965910293903145710583493637006880564327892725666673368473246240567669475682352989106934593376810395043683004339709682878398364814850018495420126823091912531784710277140623037246438902106649274332563816113930590028248281713023435372082433581423787625637 +def node14830 : Tree Nat := .node node14829 node9076 +def node14831 : Tree Nat := .node node14830 node12694 +def node14832 : Tree Nat := .node node12342 node14831 +def node14833 : Tree Nat := .node node14306 node14832 +def node14834 : Tree Nat := .leaf 114555615673899844817675135827349603920186156328588973012815230098216247591936145623178599818602061805628440424236441183793286810769621760146212077663227459888103895663369975594942529988997020774105405362937139803084400575383012496486270553679134855065 +def node14835 : Tree Nat := .node node14834 node9081 +def node14836 : Tree Nat := .node node14835 node10952 +def node14837 : Tree Nat := .node node10288 node14836 +def node14838 : Tree Nat := .leaf 9076030969344193881830906443734197896041214432680857066853762215856310823831566669886141577485648253891936520286387185970107498991864168418146640176962795664917808271276761143081364339715242438384420450311516277979483685930617190356347810880756231483109427865491901120129870987158 +def node14839 : Tree Nat := .node node14838 node12698 +def node14840 : Tree Nat := .node node14839 node12349 +def node14841 : Tree Nat := .node node12347 node14840 +def node14842 : Tree Nat := .node node14837 node14841 +def node14843 : Tree Nat := .node node14833 node14842 +def node14844 : Tree Nat := .leaf 492012622892656704990238084452251441810928680478211353074222523471479393502725184660276873998006663998813145330047983509730321495612895498074327544186461058746881903333247832437633860389101362010104528074175179849629936774733146028654240516632342134536985654220 +def node14845 : Tree Nat := .node node14844 node8665 +def node14846 : Tree Nat := .node node14845 node12003 +def node14847 : Tree Nat := .node node10602 node14846 +def node14848 : Tree Nat := .leaf 2215963108520416015739670368219860918705627185547197085343450321573077336868309251077102326174225549155407086842882886153507097866022858011143218203355784684139059833755154934588180336648220194811903249793435037512778837937724462381679612300431031297512186978904875675078638787 +def node14849 : Tree Nat := .node node14848 node9376 +def node14850 : Tree Nat := .node node14849 node12705 +def node14851 : Tree Nat := .node node12356 node14850 +def node14852 : Tree Nat := .node node14847 node14851 +def node14853 : Tree Nat := .leaf 270486799941460609886385509495647727003124994963545150394648763308944639969102659393676275592250940467361807953988974708791626313912197649469725030384215454103215939714398451354197695534910753912172065410386729530974690402527933667380203997013706408542303477715017229406192 +def node14854 : Tree Nat := .node node14853 node9092 +def node14855 : Tree Nat := .node node14854 node12361 +def node14856 : Tree Nat := .node node12711 node14855 +def node14857 : Tree Nat := .node node14856 node14338 +def node14858 : Tree Nat := .node node14852 node14857 +def node14859 : Tree Nat := .node node14843 node14858 +def node14860 : Tree Nat := .node node14828 node14859 +def node14861 : Tree Nat := .node node14801 node14860 +def node14862 : Tree Nat := .leaf 138497694282557489791594520883107362511587926461792414802412290885116654711244934379385276898882351777722071648826508466570935182983877595422721801033778925029865199276330556817049578766433639737180896404553634105254771648607715184818862880038496182021405439808139890810644070 +def node14863 : Tree Nat := .node node14862 node9109 +def node14864 : Tree Nat := .node node14863 node12723 +def node14865 : Tree Nat := .node node11328 node14864 +def node14866 : Tree Nat := .node node14347 node14865 +def node14867 : Tree Nat := .leaf 1134538491365238617645709308610684339450379797753347501667578239658343657726760624906612719539297292415998002462756517118968397271384190568611747957444814147151601701445989250704496154691965982943906131784209193584487661492056650093046168263805445444397839968496864003211196933466 +def node14868 : Tree Nat := .node node14867 node9114 +def node14869 : Tree Nat := .node node14868 node9386 +def node14870 : Tree Nat := .node node12376 node14869 +def node14871 : Tree Nat := .leaf 123003155723136208567847447708070018416355381964899431605122243912527778097675492900439533338605641464139113673047619645997955107023597622533631865752384565045090165295010437231576649888568431557609663563836632543763696941309756757044752529001829369905386837333 +def node14872 : Tree Nat := .node node14871 node11694 +def node14873 : Tree Nat := .node node14872 node12379 +def node14874 : Tree Nat := .node node12022 node14873 +def node14875 : Tree Nat := .node node14870 node14874 +def node14876 : Tree Nat := .node node14866 node14875 +def node14877 : Tree Nat := .leaf 33018408195979077897021236563951930273518967420704215659524541816820944659071993167455629007494867542162264158717584922876283407033358596609923679208455290439931457594477923970132687088832368158479239626062853660846677676937234292924461233245384679422420567965934396723 +def node14878 : Tree Nat := .node node14877 node9124 +def node14879 : Tree Nat := .node node14878 node12729 +def node14880 : Tree Nat := .node node10996 node14879 +def node14881 : Tree Nat := .node node14366 node14880 +def node14882 : Tree Nat := .leaf 6511732893125423073928276657127400410040102860476731377848561062811134572353652677596114027250812584288330251989403902611627946281703492177380333199712947485677694181111595751837530378006434692568839243907328984022713717243519122118646031 +def node14883 : Tree Nat := .node node14882 node9129 +def node14884 : Tree Nat := .node node14883 node12386 +def node14885 : Tree Nat := .node node12735 node14884 +def node14886 : Tree Nat := .node node14885 node9961 +def node14887 : Tree Nat := .node node14881 node14886 +def node14888 : Tree Nat := .node node14876 node14887 +def node14889 : Tree Nat := .leaf 2015283703367863641175612582842035880461389139542819912243331976362067957714186995885281003401944813791902549089772943823362393928515275778861986212803546325673972774730408460574291099939738563564768712940745341811620167108343011353851553827425637534283866986394533 +def node14890 : Tree Nat := .node node14889 node9662 +def node14891 : Tree Nat := .node node14890 node12745 +def node14892 : Tree Nat := .node node12394 node14891 +def node14893 : Tree Nat := .node node14382 node14892 +def node14894 : Tree Nat := .leaf 225921116696657399755928707376375798670333555195312617614099150595166526000831197939208375616448768444844308775376678197259415801619655891592005693734934921697417155233432635558002928231388593043213575460713652580967116953 +def node14895 : Tree Nat := .node node14894 node9667 +def node14896 : Tree Nat := .node node14895 node12398 +def node14897 : Tree Nat := .node node12751 node14896 +def node14898 : Tree Nat := .leaf 553990777130104003934917592054855974259924061527415598228274596169714978873108889622872645198406642054558278952365671633092016626097594910422476814009311811588144432308231332280759118191506643479319278552639471085147961488712709541928083779280099711617890948118264077276807062 +def node14899 : Tree Nat := .node node14898 node12404 +def node14900 : Tree Nat := .node node14899 node12407 +def node14901 : Tree Nat := .node node12403 node14900 +def node14902 : Tree Nat := .node node14897 node14901 +def node14903 : Tree Nat := .node node14893 node14902 +def node14904 : Tree Nat := .leaf 8061626826094347221414268616256904040889269236057812766754246782462871110468075123339448563158751726354989189573569737571599367519269569620284662933113569979541605607989935830180299252965061165383688056254087483958299437229146069758931654223234315846777965728969676 +def node14905 : Tree Nat := .node node14904 node9673 +def node14906 : Tree Nat := .node node14905 node9147 +def node14907 : Tree Nat := .node node12757 node14906 +def node14908 : Tree Nat := .leaf 8863852434081664062958681472878132609825122888544206837958136310848772034852094046130035258833550989519909403882847570816487973164325535839060701421719436933990676260863165478072794424471089493802230452903266840236962920064251966253162705859615709607170524141177983719023297475 +def node14909 : Tree Nat := .node node14908 node11357 +def node14910 : Tree Nat := .node node14909 node12760 +def node14911 : Tree Nat := .node node12898 node14910 +def node14912 : Tree Nat := .node node14907 node14911 +def node14913 : Tree Nat := .leaf 1081947199765842428283579419127417286713116607617159638942613056013073795264965194137452593836483412298566698713689968775822544520768080289377703883248676138220521111569333297870668621177238560967042745988186232887228049401282685593731614290442767888307584306569581731713008 +def node14914 : Tree Nat := .node node14913 node9678 +def node14915 : Tree Nat := .node node14914 node12414 +def node14916 : Tree Nat := .node node12903 node14915 +def node14917 : Tree Nat := .node node14916 node13854 +def node14918 : Tree Nat := .node node14912 node14917 +def node14919 : Tree Nat := .node node14903 node14918 +def node14920 : Tree Nat := .node node14888 node14919 +def node14921 : Tree Nat := .leaf 173717940541902012406847659425866484451190533229463526990882236840893119072742199839856502876068937588389229049516035492492906865262399953583505161180764870181157579673159550819488672200170647667420217060905152992175436413411303170551637600442427329845432512563031108086352201188541778291370190438 +def node14922 : Tree Nat := .node node14921 node9690 +def node14923 : Tree Nat := .node node14922 node12048 +def node14924 : Tree Nat := .node node11721 node14923 +def node14925 : Tree Nat := .node node14404 node14924 +def node14926 : Tree Nat := .leaf 641163699438029873998476675731070532890503365471348354882531362507106952652341177184586026177890229202314479090694496935628738694544632002740895571643276383782576266711859013453263643358330239817921192358353938733289475637851398127272992259463923911283983766575980125621679752840344678182115930 +def node14927 : Tree Nat := .node node14926 node9695 +def node14928 : Tree Nat := .node node14927 node12422 +def node14929 : Tree Nat := .node node12920 node14928 +def node14930 : Tree Nat := .leaf 1219353864951782111494411248513669248238417417502665318371385195113776976654427429269755729120838114140898916494294983697473193877894337772409732609568290886049967825033721765654481278587565869435907257226035585937681628243558338676960072350451946772779376394962678729566497315551212164437 +def node14931 : Tree Nat := .node node14930 node12059 +def node14932 : Tree Nat := .node node14931 node7055 +def node14933 : Tree Nat := .node node11726 node14932 +def node14934 : Tree Nat := .node node14929 node14933 +def node14935 : Tree Nat := .node node14925 node14934 +def node14936 : Tree Nat := .leaf 154649758481689438539253101856584427727906370118567238084748270901022217271244407098556404626491896659290190412922964660798727172120946886784235702852196485941661076272352594379896806449531432218916554131709942067149968839391080282890680995224406801313775869018434877631183700551463707955 +def node14937 : Tree Nat := .node node14936 node9709 +def node14938 : Tree Nat := .node node14937 node12066 +def node14939 : Tree Nat := .node node12930 node14938 +def node14940 : Tree Nat := .node node14423 node14939 +def node14941 : Tree Nat := .leaf 9516908214257811601907599988159363584840065290626636270825807227503749905371816105021419189398839454839689918914562806248206411829822979351300064714670728090477351428117358393598991669469351841968509351516504407542994913425616382779636326741406417432025774678260322975783620972484598031 +def node14942 : Tree Nat := .node node14941 node9714 +def node14943 : Tree Nat := .node node14942 node12428 +def node14944 : Tree Nat := .node node12935 node14943 +def node14945 : Tree Nat := .node node14944 node12940 +def node14946 : Tree Nat := .node node14940 node14945 +def node14947 : Tree Nat := .node node14935 node14946 +def node14948 : Tree Nat := .leaf 148701690847778306280310070740832021923419923311650029397698061862645982565585358253925509580443099392097636026797386502591340007597866141510220585781267578938273216270938198148028688929417347711928562238815532716661821702988252074193821279163473319771759690904670989167179084463485861 +def node14949 : Tree Nat := .node node14948 node11745 +def node14950 : Tree Nat := .node node14949 node12082 +def node14951 : Tree Nat := .node node12440 node14950 +def node14952 : Tree Nat := .node node14439 node14951 +def node14953 : Tree Nat := .leaf 9584288667923211146940637195106895509586686918352633524518732024561752301339197280802709155441220641788786764210402813327422804732093548427479683312030666151796693172219442849825974286000413401897406023848754974361654848085862909785912343346992327747681444462247195242272603791560601 +def node14954 : Tree Nat := .node node14953 node11750 +def node14955 : Tree Nat := .node node14954 node12794 +def node14956 : Tree Nat := .node node12792 node14955 +def node14957 : Tree Nat := .leaf 694871762167608049626282723770905715162043830833208898076279771632803262962607377701488142089040871141567657864678296095251240318970110686340489458480483915643121487203692938742159498012962646179451956129936101160535614917185381276544808818351698618788122820826353052888844241906765121063411384214 +def node14958 : Tree Nat := .node node14957 node11408 +def node14959 : Tree Nat := .node node14958 node9187 +def node14960 : Tree Nat := .node node12092 node14959 +def node14961 : Tree Nat := .node node14956 node14960 +def node14962 : Tree Nat := .node node14952 node14961 +def node14963 : Tree Nat := .leaf 10018182803719199054603277094735693583580761321485214632718632621999971839155334720690115850865904002970821504265768528967295833113652456910114441206157042932473873922526613546371820348768222940859757187900010682191860799649298422014767388486092887903545082230352106385776265771354169460116684 +def node14964 : Tree Nat := .node node14963 node12096 +def node14965 : Tree Nat := .node node14964 node12099 +def node14966 : Tree Nat := .node node10663 node14965 +def node14967 : Tree Nat := .leaf 297403390559003316441364371679462987949131770409322091479259371325373453793164064587149053478616722460716689797178803623935715975742154320267602450005467807086740497647693172174975943133796607630875584672064863927162867892548431439440543355712961412285377336696298848776138243933717443 +def node14968 : Tree Nat := .node node14967 node11417 +def node14969 : Tree Nat := .node node14968 node9193 +def node14970 : Tree Nat := .node node12446 node14969 +def node14971 : Tree Nat := .node node14966 node14970 +def node14972 : Tree Nat := .leaf 9745314011400000162300582153717612840468120351314379564770510113036312714024121089520989186893633952103646779539050048426379727856838138252855638408405920573308883103035584518742055194901059732900103093998568260455003750990349021753782911846133295858913496406035401796888471947927744409840 +def node14973 : Tree Nat := .node node14972 node11764 +def node14974 : Tree Nat := .node node14973 node11423 +def node14975 : Tree Nat := .node node12801 node14974 +def node14976 : Tree Nat := .node node14975 node14463 +def node14977 : Tree Nat := .node node14971 node14976 +def node14978 : Tree Nat := .node node14962 node14977 +def node14979 : Tree Nat := .node node14947 node14978 +def node14980 : Tree Nat := .node node14920 node14979 +def node14981 : Tree Nat := .node node14861 node14980 +def node14982 : Tree Nat := .node node14734 node14981 +def node14983 : Tree Nat := .leaf 549159373215870023480216279236739073 +def node14984 : Tree Nat := .node node14983 node12811 +def node14985 : Tree Nat := .node node14984 node10045 +def node14986 : Tree Nat := .node node14985 node13939 +def node14987 : Tree Nat := .node node13021 node14479 +def node14988 : Tree Nat := .node node14986 node14987 +def node14989 : Tree Nat := .leaf 79228162513111416093232070656 +def node14990 : Tree Nat := .node node14989 node12824 +def node14991 : Tree Nat := .node node14990 node10350 +def node14992 : Tree Nat := .node node14991 node14487 +def node14993 : Tree Nat := .node node14992 node14492 +def node14994 : Tree Nat := .node node14988 node14993 +def node14995 : Tree Nat := .leaf 5192217631581238030886027353194496 +def node14996 : Tree Nat := .node node14995 node12831 +def node14997 : Tree Nat := .node node14996 node10356 +def node14998 : Tree Nat := .node node14997 node13958 +def node14999 : Tree Nat := .node node14998 node14502 +def node15000 : Tree Nat := .node node14999 node14508 +def node15001 : Tree Nat := .node node14994 node15000 +def node15002 : Tree Nat := .leaf 780982533369245938631875043184869632 +def node15003 : Tree Nat := .node node15002 node12131 +def node15004 : Tree Nat := .node node15003 node10056 +def node15005 : Tree Nat := .node node15004 node13974 +def node15006 : Tree Nat := .node node15005 node14518 +def node15007 : Tree Nat := .node node15006 node14528 +def node15008 : Tree Nat := .node node15007 node14544 +def node15009 : Tree Nat := .node node15001 node15008 +def node15010 : Tree Nat := .leaf 1251038113679918331178255429203394576 +def node15011 : Tree Nat := .node node15010 node7161 +def node15012 : Tree Nat := .node node15011 node10080 +def node15013 : Tree Nat := .node node15012 node13995 +def node15014 : Tree Nat := .node node15013 node14554 +def node15015 : Tree Nat := .node node15014 node14564 +def node15016 : Tree Nat := .node node15015 node14576 +def node15017 : Tree Nat := .node node15016 node14608 +def node15018 : Tree Nat := .node node15009 node15017 +def node15019 : Tree Nat := .leaf 1063374252034722566141274577365368836 +def node15020 : Tree Nat := .node node15019 node5191 +def node15021 : Tree Nat := .node node15020 node10106 +def node15022 : Tree Nat := .node node15021 node14059 +def node15023 : Tree Nat := .node node15022 node14618 +def node15024 : Tree Nat := .node node15023 node14628 +def node15025 : Tree Nat := .node node15024 node14640 +def node15026 : Tree Nat := .node node15025 node14672 +def node15027 : Tree Nat := .node node15026 node14732 +def node15028 : Tree Nat := .node node15018 node15027 +def node15029 : Tree Nat := .leaf 882694569845703145266904962690973698 +def node15030 : Tree Nat := .node node15029 node12645 +def node15031 : Tree Nat := .node node15030 node10222 +def node15032 : Tree Nat := .node node15031 node14203 +def node15033 : Tree Nat := .node node15032 node14742 +def node15034 : Tree Nat := .node node15033 node14752 +def node15035 : Tree Nat := .node node15034 node14764 +def node15036 : Tree Nat := .leaf 781895255728023202728516141893812736 +def node15037 : Tree Nat := .node node15036 node12293 +def node15038 : Tree Nat := .node node15037 node10240 +def node15039 : Tree Nat := .node node15038 node14238 +def node15040 : Tree Nat := .node node15039 node14773 +def node15041 : Tree Nat := .node node15040 node14783 +def node15042 : Tree Nat := .node node15041 node14799 +def node15043 : Tree Nat := .node node15035 node15042 +def node15044 : Tree Nat := .node node15043 node14860 +def node15045 : Tree Nat := .node node15044 node14980 +def node15046 : Tree Nat := .node node15028 node15045 +def node15047 : Tree Nat := .leaf 549156381223670802563583802194526209 +def node15048 : Tree Nat := .node node15047 node12811 +def node15049 : Tree Nat := .node node15048 node10045 +def node15050 : Tree Nat := .node node15049 node13939 +def node15051 : Tree Nat := .leaf 1329225460483715434891748140583485440 +def node15052 : Tree Nat := .node node15051 node12464 +def node15053 : Tree Nat := .node node15052 node12467 +def node15054 : Tree Nat := .node node15053 node14479 +def node15055 : Tree Nat := .node node15050 node15054 +def node15056 : Tree Nat := .leaf 1329222925182514959986201077762490368 +def node15057 : Tree Nat := .node node15056 node12824 +def node15058 : Tree Nat := .node node15057 node10350 +def node15059 : Tree Nat := .node node15058 node14487 +def node15060 : Tree Nat := .node node15059 node14492 +def node15061 : Tree Nat := .node node15055 node15060 +def node15062 : Tree Nat := .node node12833 node13958 +def node15063 : Tree Nat := .node node15062 node14502 +def node15064 : Tree Nat := .node node15063 node14508 +def node15065 : Tree Nat := .node node15061 node15064 +def node15066 : Tree Nat := .leaf 780979252391008482591694897580867840 +def node15067 : Tree Nat := .node node15066 node12131 +def node15068 : Tree Nat := .node node15067 node10056 +def node15069 : Tree Nat := .node node15068 node13974 +def node15070 : Tree Nat := .node node15069 node14518 +def node15071 : Tree Nat := .node node15070 node14528 +def node15072 : Tree Nat := .node node15071 node14544 +def node15073 : Tree Nat := .node node15065 node15072 +def node15074 : Tree Nat := .node node12857 node13995 +def node15075 : Tree Nat := .node node15074 node14554 +def node15076 : Tree Nat := .node node15075 node14564 +def node15077 : Tree Nat := .node node15076 node14576 +def node15078 : Tree Nat := .node node15077 node14608 +def node15079 : Tree Nat := .node node15073 node15078 +def node15080 : Tree Nat := .node node12866 node14059 +def node15081 : Tree Nat := .node node15080 node14618 +def node15082 : Tree Nat := .node node15081 node14628 +def node15083 : Tree Nat := .node node15082 node14640 +def node15084 : Tree Nat := .node node15083 node14672 +def node15085 : Tree Nat := .node node15084 node14732 +def node15086 : Tree Nat := .node node15079 node15085 +def node15087 : Tree Nat := .leaf 446532459231594263136016697500106754 +def node15088 : Tree Nat := .node node15087 node12645 +def node15089 : Tree Nat := .node node15088 node10222 +def node15090 : Tree Nat := .node node15089 node14203 +def node15091 : Tree Nat := .node node15090 node14742 +def node15092 : Tree Nat := .node node15091 node14752 +def node15093 : Tree Nat := .node node15092 node14764 +def node15094 : Tree Nat := .leaf 781891960823172807760772523888738816 +def node15095 : Tree Nat := .node node15094 node12293 +def node15096 : Tree Nat := .node node15095 node10240 +def node15097 : Tree Nat := .node node15096 node14238 +def node15098 : Tree Nat := .node node15097 node14773 +def node15099 : Tree Nat := .node node15098 node14783 +def node15100 : Tree Nat := .node node15099 node14799 +def node15101 : Tree Nat := .node node15093 node15100 +def node15102 : Tree Nat := .node node15101 node14860 +def node15103 : Tree Nat := .node node15102 node14980 +def node15104 : Tree Nat := .node node15086 node15103 +def node15105 : Tree Nat := .node node0 node12811 +def node15106 : Tree Nat := .node node15105 node10045 +def node15107 : Tree Nat := .node node15106 node13939 +def node15108 : Tree Nat := .node node12468 node14479 +def node15109 : Tree Nat := .node node15107 node15108 +def node15110 : Tree Nat := .node node31 node12824 +def node15111 : Tree Nat := .node node15110 node10350 +def node15112 : Tree Nat := .node node15111 node14487 +def node15113 : Tree Nat := .leaf 123003155723136208567847447732916373157263089870897223698056203073150878825403188687253134589235925338016627618469354633994273577081379955368070390873260324576452774621747177802761144047124604389108712290194161096250316122164083003686341952621732472379240655360 +def node15114 : Tree Nat := .node node15113 node11437 +def node15115 : Tree Nat := .node node15114 node12118 +def node15116 : Tree Nat := .node node9229 node15115 +def node15117 : Tree Nat := .node node15112 node15116 +def node15118 : Tree Nat := .node node15109 node15117 +def node15119 : Tree Nat := .node node63 node12831 +def node15120 : Tree Nat := .node node15119 node10356 +def node15121 : Tree Nat := .node node15120 node13958 +def node15122 : Tree Nat := .leaf 33018408195979077897021236557282287907427960838451981092487189987679470573908052333928986881956429041035710644221445334737151091162931188344596362448412041299131895220783939925707905061781824127604294549544141565594059532815922460696723333087207720755679903202747767296 +def node15123 : Tree Nat := .node node15122 node9504 +def node15124 : Tree Nat := .node node15123 node12478 +def node15125 : Tree Nat := .node node12837 node15124 +def node15126 : Tree Nat := .node node15121 node15125 +def node15127 : Tree Nat := .leaf 48516190384397171392751175090678259260270162528013642586385209916290288057879478836212461966784344307945219753934280904187324755502785328721684776079658618896560715629870127362821018301577447945277527045773533175205724976889357824 +def node15128 : Tree Nat := .node node15127 node12485 +def node15129 : Tree Nat := .node node15128 node12125 +def node15130 : Tree Nat := .node node12842 node15129 +def node15131 : Tree Nat := .node node15130 node12492 +def node15132 : Tree Nat := .node node15126 node15131 +def node15133 : Tree Nat := .node node15118 node15132 +def node15134 : Tree Nat := .node node12133 node13974 +def node15135 : Tree Nat := .leaf 2015283703367863641175612582842135243135427334428804184044917736999987313807108150565911635557316234858008975050459402976118736972643438901278381055521834957709419309923646549497976985118969783337493451200955947753919733662036487314336593551560951706680653792070656 +def node15136 : Tree Nat := .node node15135 node8813 +def node15137 : Tree Nat := .node node15136 node12501 +def node15138 : Tree Nat := .node node11789 node15137 +def node15139 : Tree Nat := .node node15134 node15138 +def node15140 : Tree Nat := .node node15139 node14528 +def node15141 : Tree Nat := .leaf 8863852434081664062958681530156377468441383226333685975837272857607299162246333457389861819674491312570523648792913049214290989131911494578143828943275477371199519078588636585138721154021620273485546852229755610755508314113211399961710568396800212983133788006516990154014211072 +def node15142 : Tree Nat := .node node15141 node8828 +def node15143 : Tree Nat := .node node15142 node12507 +def node15144 : Tree Nat := .node node12153 node15143 +def node15145 : Tree Nat := .node node14533 node15144 +def node15146 : Tree Nat := .node node15145 node14543 +def node15147 : Tree Nat := .node node15140 node15146 +def node15148 : Tree Nat := .node node15133 node15147 +def node15149 : Tree Nat := .node node10081 node13995 +def node15150 : Tree Nat := .node node15149 node14554 +def node15151 : Tree Nat := .leaf 305135869619641084486162424651110383869718645522469604968743010747244368322750158394760361939191319261060620806834866626452620010985360507386799517592248468651001635551596388219815942479283416866916093311708010145141725530844998119269638965139861487604296892261852329041829577460442769920 +def node15152 : Tree Nat := .node node15151 node11476 +def node15153 : Tree Nat := .node node15152 node8427 +def node15154 : Tree Nat := .node node8425 node15153 +def node15155 : Tree Nat := .node node14559 node15154 +def node15156 : Tree Nat := .node node15150 node15155 +def node15157 : Tree Nat := .leaf 38067632857031246415885002001632223813615570301801070128684750548400235182831352333308404133180821172702099111877852160800355090193204913369462644616762219205111881412092099056098566009145811420095048453542831211252867942878037994008553604316675301439521405376879001365920248158475672064 +def node15158 : Tree Nat := .node node15157 node8862 +def node15159 : Tree Nat := .node node15158 node11822 +def node15160 : Tree Nat := .node node11489 node15159 +def node15161 : Tree Nat := .node node14015 node15160 +def node15162 : Tree Nat := .leaf 18587711355972288284975781226873757001640752520742430762455243433647852495356937686061563313740224455898572328929311704065567036899501082183819009553987967541975371339695263518872247742070538266715966547147005104831995632756603359763228985822968041494657334485928339623930761371346432 +def node15163 : Tree Nat := .node node15162 node8869 +def node15164 : Tree Nat := .node node15163 node12531 +def node15165 : Tree Nat := .node node11494 node15164 +def node15166 : Tree Nat := .node node15165 node12176 +def node15167 : Tree Nat := .node node15161 node15166 +def node15168 : Tree Nat := .node node15156 node15167 +def node15169 : Tree Nat := .leaf 19070991851227567780385655359698316649593705989427444620245069009852873381868266799619284790372586035931953043264917371924350474837128281378279444567881062280592932774710489289690557441914020187543915610118868416301578083645164369337678512824602065626139608659352529693624562300712569856 +def node15170 : Tree Nat := .node node15169 node8884 +def node15171 : Tree Nat := .node node15170 node11504 +def node15172 : Tree Nat := .node node12182 node15171 +def node15173 : Tree Nat := .node node14031 node15172 +def node15174 : Tree Nat := .node node15173 node14591 +def node15175 : Tree Nat := .leaf 609156476566787278379108054239156247390972740188452390117913938500450325491581248495168088599528432221458980318942422508374483936926801841879330423476341748752949423693363909326235676200169771650081237921035040639193236046100241375609343566129186450940714983555019144212770144692605828096 +def node15176 : Tree Nat := .node node15175 node9275 +def node15177 : Tree Nat := .node node15176 node10410 +def node15178 : Tree Nat := .node node12197 node15177 +def node15179 : Tree Nat := .node node14596 node15178 +def node15180 : Tree Nat := .node node15179 node14606 +def node15181 : Tree Nat := .node node15174 node15180 +def node15182 : Tree Nat := .node node15168 node15181 +def node15183 : Tree Nat := .node node15148 node15182 +def node15184 : Tree Nat := .node node10107 node14059 +def node15185 : Tree Nat := .node node15184 node14618 +def node15186 : Tree Nat := .leaf 305730676383032197711281649742622710886123306029018948514789131956411478592455874263858008545340572316917977783853836809078160002701663997014737497499934867995851671557847267009478169149189102610174103187663208097357851378916017520643083519930012695515115191754826941052200595740996708864 +def node15187 : Tree Nat := .node node15186 node11144 +def node15188 : Tree Nat := .node node15187 node9798 +def node15189 : Tree Nat := .node node10112 node15188 +def node15190 : Tree Nat := .node node14623 node15189 +def node15191 : Tree Nat := .node node15185 node15190 +def node15192 : Tree Nat := .leaf 40446859910595699341125708145656373132591514042419445126956107720017105848770028401130341546201483200632496178089575328505341240757430894068426825319466082866691734205596649594589323748871809198950233456898732189463560762336379532983738271288650075895980521962734666765232440849228716544 +def node15193 : Tree Nat := .node node15192 node7235 +def node15194 : Tree Nat := .node node15193 node11151 +def node15195 : Tree Nat := .node node11535 node15194 +def node15196 : Tree Nat := .node node14079 node15195 +def node15197 : Tree Nat := .leaf 18587711355972288284975781226873757001640752527254561075954200296864920133568817487707092950860057205891604452303042089454261969158309882589470480612394947733439076395304067129859477879014178937252528013653386300731505578976855986419826769741987306955886344015460410813457961668142592 +def node15198 : Tree Nat := .node node15197 node6845 +def node15199 : Tree Nat := .node node15198 node12210 +def node15200 : Tree Nat := .node node12562 node15199 +def node15201 : Tree Nat := .node node15200 node12216 +def node15202 : Tree Nat := .node node15196 node15201 +def node15203 : Tree Nat := .node node15191 node15202 +def node15204 : Tree Nat := .leaf 37175422711944576571966846157115377644457117624326996718013592867814909517272922286185664988388014749487763284464405423664851768144492544900051638047127800819880821370624698311496256030344323863169063726159232358855522674414893357507948265542197530717841135269049578695099452455727872 +def node15205 : Tree Nat := .node node15204 node7242 +def node15206 : Tree Nat := .node node15205 node11550 +def node15207 : Tree Nat := .node node11548 node15206 +def node15208 : Tree Nat := .node node14095 node15207 +def node15209 : Tree Nat := .node node15208 node14655 +def node15210 : Tree Nat := .leaf 74350847640257991860231331556364050459921667153350901771142808770526277835360556453476255865677064282296852179407466729479180122523097513443107343676963199412136464711470315157368073030243992802907099673286722495819464911366278731633891808482057218437741651104861473134491722634740480 +def node15211 : Tree Nat := .node node15210 node10800 +def node15212 : Tree Nat := .node node15211 node11885 +def node15213 : Tree Nat := .node node11557 node15212 +def node15214 : Tree Nat := .node node14660 node15213 +def node15215 : Tree Nat := .leaf 1174833932040724960313232606750625274616384720429471888776377230861550145166792699259973788611092227348332796403416559318220366141224577524185497132598993081206438266373349898334407543396339582340916258857337344300679372 +def node15216 : Tree Nat := .node node15215 node9833 +def node15217 : Tree Nat := .node node15216 node12227 +def node15218 : Tree Nat := .node node15217 node12582 +def node15219 : Tree Nat := .node node14669 node15218 +def node15220 : Tree Nat := .node node15214 node15219 +def node15221 : Tree Nat := .node node15209 node15220 +def node15222 : Tree Nat := .node node15203 node15221 +def node15223 : Tree Nat := .leaf 30750788930784052141961861970504689739404335082817979893145491549802009592473718622389638906314802530673638294532635623580567731066030384039573782817355949527636732683672620539288984444790526493623687792944616848854487191541974870135977521637532701806464903680 +def node15224 : Tree Nat := .node node15223 node11897 +def node15225 : Tree Nat := .node node15224 node12239 +def node15226 : Tree Nat := .node node11185 node15225 +def node15227 : Tree Nat := .node node14682 node15226 +def node15228 : Tree Nat := .node node14678 node15227 +def node15229 : Tree Nat := .leaf 8254602048994769474255309139322199910068143258083693241044839823575153550594486940739435416735876022684849237625723760137042281514088352257883296588255563851489059981114986157227242254134960755632863228810700944638215492049922658448746759626243298410018917967190120960 +def node15230 : Tree Nat := .node node15229 node10165 +def node15231 : Tree Nat := .node node15230 node12603 +def node15232 : Tree Nat := .node node12246 node15231 +def node15233 : Tree Nat := .node node14150 node15232 +def node15234 : Tree Nat := .leaf 6512130313498956863217084807164470744461190538033039686479754608152295293285303470333849912122601398448949307133545455044656459101006671475649180572198439267955078600971667533422688247251318199934982222548812232012211012725221885809878528 +def node15235 : Tree Nat := .node node15234 node11588 +def node15236 : Tree Nat := .node node15235 node12608 +def node15237 : Tree Nat := .node node12251 node15236 +def node15238 : Tree Nat := .node node15237 node11920 +def node15239 : Tree Nat := .node node15233 node15238 +def node15240 : Tree Nat := .node node15228 node15239 +def node15241 : Tree Nat := .leaf 503820925841965910293903145710682853278783176422042742899963128541361843967736281426486623972793857941682817027118968765173176361575120985691713767101514507388656673724058764072570060691582774836650666659032667723417800604919515817896290372727758251018640418222848 +def node15242 : Tree Nat := .node node15241 node10500 +def node15243 : Tree Nat := .node node15242 node12622 +def node15244 : Tree Nat := .node node11206 node15243 +def node15245 : Tree Nat := .node node14166 node15244 +def node15246 : Tree Nat := .node node15245 node14714 +def node15247 : Tree Nat := .leaf 2215963108520416015739670425498105777322701489942252377308778256489650690169197566491234527215378734314935090626825881759711287334734595390704480924466398089047833566006110950584347132603277827863543834145237926800262709257230681986368379942770843607392581811757044843063526144 +def node15248 : Tree Nat := .node node15247 node10848 +def node15249 : Tree Nat := .node node15248 node12628 +def node15250 : Tree Nat := .node node10204 node15249 +def node15251 : Tree Nat := .node node14719 node15250 +def node15252 : Tree Nat := .leaf 273579137855854662637703584477554683882390474935151730329389655538723080753048106306892620231493681485322560896369357188931266348169605247973889416725748505903636314765769322876424804518518060034649549453721434 +def node15253 : Tree Nat := .node node15252 node10211 +def node15254 : Tree Nat := .node node15253 node11219 +def node15255 : Tree Nat := .node node15254 node8128 +def node15256 : Tree Nat := .node node14728 node15255 +def node15257 : Tree Nat := .node node15251 node15256 +def node15258 : Tree Nat := .node node15246 node15257 +def node15259 : Tree Nat := .node node15240 node15258 +def node15260 : Tree Nat := .node node15222 node15259 +def node15261 : Tree Nat := .node node15183 node15260 +def node15262 : Tree Nat := .node node12647 node14203 +def node15263 : Tree Nat := .node node15262 node14742 +def node15264 : Tree Nat := .leaf 1218759058188390998269292023606661654806717069847887146399867278529412335299323966263623132317909815671625934281053919680711660328502290319065518321472072083151851243319067837388685126628304710346507109403031578209782509066635628361717141183690901798034584751099293804854195098383988839680 +def node15265 : Tree Nat := .node node15264 node11616 +def node15266 : Tree Nat := .node node15265 node8574 +def node15267 : Tree Nat := .node node11615 node15266 +def node15268 : Tree Nat := .node node14747 node15267 +def node15269 : Tree Nat := .node node15263 node15268 +def node15270 : Tree Nat := .leaf 152270531428124985663540008006528895254462281213872294947618853506483312281637601006710476254648951477568578231959350517633987577081709046247278414898110592652044008353269324344143913219005388695166757519581793136992254833514124807880311893616036991599663577560071112314646001703739630848 +def node15271 : Tree Nat := .node node15270 node9008 +def node15272 : Tree Nat := .node node15271 node11239 +def node15273 : Tree Nat := .node node10884 node15272 +def node15274 : Tree Nat := .node node14223 node15273 +def node15275 : Tree Nat := .leaf 9516908214257811601907599988159363584840065290620124935450087718987904762481275522191874685950243732024609872161685536783436920658376617873990683534826839430096423699234254532517028554284599435168394899748260508931864666975448617893343187532950899079775650575920948405215730976808147200 +def node15276 : Tree Nat := .node node15275 node9015 +def node15277 : Tree Nat := .node node15276 node12659 +def node15278 : Tree Nat := .node node12284 node15277 +def node15279 : Tree Nat := .node node15278 node12289 +def node15280 : Tree Nat := .node node15274 node15279 +def node15281 : Tree Nat := .node node15269 node15280 +def node15282 : Tree Nat := .node node12295 node14238 +def node15283 : Tree Nat := .leaf 19182518119363401510097021509837085089334432213989030557701434505264689708377241855498476855145954111770111954854095402035640692834544430839755249146799772909543836727472907978359099787330200041252454320863590504916615571864377079334756055900444179117572846044503300298803955842623851520 +def node15284 : Tree Nat := .node node15283 node9026 +def node15285 : Tree Nat := .node node15284 node11634 +def node15286 : Tree Nat := .node node11946 node15285 +def node15287 : Tree Nat := .node node15282 node15286 +def node15288 : Tree Nat := .node node15287 node14783 +def node15289 : Tree Nat := .leaf 609379529096411867973366339948478118564243352328768008033960585085586565309766066210703572555095574726882621527484800522995426427233381535729732173056499733774087422172778871244027364301339831270683537685882924762044209348156926287464314851981135346196390253144561756317378096552656780288 +def node15290 : Tree Nat := .node node15289 node9350 +def node15291 : Tree Nat := .node node15290 node11961 +def node15292 : Tree Nat := .node node12309 node15291 +def node15293 : Tree Nat := .node node14788 node15292 +def node15294 : Tree Nat := .node node15293 node14798 +def node15295 : Tree Nat := .node node15288 node15294 +def node15296 : Tree Nat := .node node15281 node15295 +def node15297 : Tree Nat := .leaf 30750788930784052141961861995338914692417628508649665478660181344880173625627745896543248315903847455584301210297237156396407002551689899357412557725122636090706903773740279794392607115226683976742570366246412623642925344395454861333259574566512711705796039936 +def node15298 : Tree Nat := .node node15297 node11658 +def node15299 : Tree Nat := .node node15298 node12328 +def node15300 : Tree Nat := .node node11985 node15299 +def node15301 : Tree Nat := .node node14810 node15300 +def node15302 : Tree Nat := .node node14806 node15301 +def node15303 : Tree Nat := .leaf 8254602048994769474255309145988586409736845223991162255450003588722430659544893995193483422244551447177666449772013303234838519998237343882254432630162243480117315991260396896605712201738114930652530428845760526495758467649471378810202379436750968549387534208784311552 +def node15304 : Tree Nat := .node node15303 node7369 +def node15305 : Tree Nat := .node node15304 node12682 +def node15306 : Tree Nat := .node node11666 node15305 +def node15307 : Tree Nat := .node node14290 node15306 +def node15308 : Tree Nat := .leaf 397468889724173685979542788245425099345541698338619579376990907177671153860167868846155505388459882229073290237084350907281196192236698887780593956931762815774718418508179554599718907933991862335678480331895077347231261253169127528704 +def node15309 : Tree Nat := .node node15308 node6986 +def node15310 : Tree Nat := .node node15309 node12687 +def node15311 : Tree Nat := .node node10276 node15310 +def node15312 : Tree Nat := .node node15311 node11298 +def node15313 : Tree Nat := .node node15307 node15312 +def node15314 : Tree Nat := .node node15302 node15313 +def node15315 : Tree Nat := .leaf 503820925841965910293903145710583493637006880564327892725666673368473246240567669475682331966022809379491415252329396334328556696713724761808457323135652230558957857323075233383042644805701341973632031483571823452610670689013978352395451226884200348085279346248704 +def node15316 : Tree Nat := .node node15315 node9076 +def node15317 : Tree Nat := .node node15316 node12694 +def node15318 : Tree Nat := .node node12342 node15317 +def node15319 : Tree Nat := .node node14306 node15318 +def node15320 : Tree Nat := .node node15319 node14842 +def node15321 : Tree Nat := .leaf 2215963108520416015739670425498542798988225452288587493752046433646652444670194001457808550903180461177261142942373664092171737975882547210092602630208660293803267189564487851234661357592688951895845109935105549127430934881139762074295746229450469098736845660469684715709545472 +def node15322 : Tree Nat := .node node15321 node9376 +def node15323 : Tree Nat := .node node15322 node12705 +def node15324 : Tree Nat := .node node12356 node15323 +def node15325 : Tree Nat := .node node14847 node15324 +def node15326 : Tree Nat := .leaf 6828046779268970776657768233878085902324275438521959671787668942028781287039163393246366628516366001377017786238430225114057842409139425637536929343255748676747380123517131385733486879634469742763010013776321093440551911822977510602200773033968 +def node15327 : Tree Nat := .node node15326 node8674 +def node15328 : Tree Nat := .node node15327 node11318 +def node15329 : Tree Nat := .node node15328 node12013 +def node15330 : Tree Nat := .node node14856 node15329 +def node15331 : Tree Nat := .node node15325 node15330 +def node15332 : Tree Nat := .node node15320 node15331 +def node15333 : Tree Nat := .node node15314 node15332 +def node15334 : Tree Nat := .node node15296 node15333 +def node15335 : Tree Nat := .leaf 123003155723136208567847447757762727157872482369829594158403127312851041677795828517583660709305260127410032880734068891406173619483461780779511186063922820023358603084833277780952751849541764486022148081383586016638679967868126842669483457800278269198455559424 +def node15336 : Tree Nat := .node node15335 node11694 +def node15337 : Tree Nat := .node node15336 node12379 +def node15338 : Tree Nat := .node node12022 node15337 +def node15339 : Tree Nat := .node node14870 node15338 +def node15340 : Tree Nat := .node node14866 node15339 +def node15341 : Tree Nat := .leaf 33018408195979077897021236563951930273518967420704215659524541816820944659071993167455629007494867542162264084028586380655249708030277902604365475316999224880768603382715488031422851722334521064915504170226700526439895400077209145508445343031384766339088356454875636992 +def node15342 : Tree Nat := .node node15341 node9124 +def node15343 : Tree Nat := .node node15342 node12729 +def node15344 : Tree Nat := .node node10996 node15343 +def node15345 : Tree Nat := .node node14366 node15344 +def node15346 : Tree Nat := .leaf 6511732893125423073928276657127400410040102860476731377848561062811134572353652648997259712683252970896934930816334112698140650958128417493023773741190271338801522257351191164788610858041883386168438863537592781349265021145774849116444928 +def node15347 : Tree Nat := .node node15346 node9129 +def node15348 : Tree Nat := .node node15347 node12386 +def node15349 : Tree Nat := .node node12735 node15348 +def node15350 : Tree Nat := .node node15349 node9961 +def node15351 : Tree Nat := .node node15345 node15350 +def node15352 : Tree Nat := .node node15340 node15351 +def node15353 : Tree Nat := .leaf 2015283703367863641175612582842035880461389139542819912243331976362067957714186995885280982378860688578017153947058657153351240942350602175855593517443778429409838719521698983680193121708193466636294095149984601448116907207328741424533981618937755448787722545017600 +def node15354 : Tree Nat := .node node15353 node9662 +def node15355 : Tree Nat := .node node15354 node12745 +def node15356 : Tree Nat := .node node12394 node15355 +def node15357 : Tree Nat := .node node14382 node15356 +def node15358 : Tree Nat := .node node15357 node14902 +def node15359 : Tree Nat := .leaf 8863852434081664062958681530156814490107721155285597246366732422922347142653978796510741483562505901541763459982338348755152613274185225038010085848572312543654883616672498394719275445415558250886172313044937351851615017007667265945778839788635147408395182822742792759654204160 +def node15360 : Tree Nat := .node node15359 node11357 +def node15361 : Tree Nat := .node node15360 node12760 +def node15362 : Tree Nat := .node node12898 node15361 +def node15363 : Tree Nat := .node node14907 node15362 +def node15364 : Tree Nat := .leaf 1174833932040723294629220079997464680937933805781821401243910756077030863177081891689110094651452214795831270787692191600451932591341490151439387703391068884608846265157205180709914621402569789428019070438226874486226892 +def node15365 : Tree Nat := .node node15364 node12905 +def node15366 : Tree Nat := .node node15365 node11363 +def node15367 : Tree Nat := .node node15366 node12766 +def node15368 : Tree Nat := .node node14916 node15367 +def node15369 : Tree Nat := .node node15363 node15368 +def node15370 : Tree Nat := .node node15358 node15369 +def node15371 : Tree Nat := .node node15352 node15370 +def node15372 : Tree Nat := .leaf 1219353864951782111494411248513669248238417417502665318421077903855294077059357591823036612521161377721019252111439111188939610135454580251825928446601113907851311036605694794004621141425807503774493364531466893583735522498958824178950062615985637956931110722553305704211219611624931349760 +def node15373 : Tree Nat := .node node15372 node12059 +def node15374 : Tree Nat := .node node15373 node7055 +def node15375 : Tree Nat := .node node11726 node15374 +def node15376 : Tree Nat := .node node14929 node15375 +def node15377 : Tree Nat := .node node14925 node15376 +def node15378 : Tree Nat := .leaf 154649758481689438539253101856584427727906370118567238084748270901022217271244407098556404626491896659290190412922964660798727125550159560458179396414981464973489490316503518207712909117491325104191597962011284467590521532872784335489590177869976173949422825643808020851071369447679042816 +def node15379 : Tree Nat := .node node15378 node9709 +def node15380 : Tree Nat := .node node15379 node12066 +def node15381 : Tree Nat := .node node12930 node15380 +def node15382 : Tree Nat := .node node14423 node15381 +def node15383 : Tree Nat := .leaf 9516908214257811601907599988159363584840065290626636270825807227503749905371816105021419189398839454839689918914562806248206411857965968196249576026676606561711422449696547251022425369311107312340492050640879041444766538680902769243886599280214984264742470535744758292993079293230291200 +def node15384 : Tree Nat := .node node15383 node9714 +def node15385 : Tree Nat := .node node15384 node12428 +def node15386 : Tree Nat := .node node12935 node15385 +def node15387 : Tree Nat := .node node15386 node12940 +def node15388 : Tree Nat := .node node15382 node15387 +def node15389 : Tree Nat := .node node15377 node15388 +def node15390 : Tree Nat := .leaf 297403390559003316441364371679463045227813650691920358220649779733969565866739172389033803859322947189671601819032859725269249004651687668526488221703030403332644046968365580902378342322086301618385773438685789096987074595808133378346001690795201117635280290538845348423318399627805440 +def node15391 : Tree Nat := .node node15390 node11417 +def node15392 : Tree Nat := .node node15391 node9193 +def node15393 : Tree Nat := .node node12446 node15392 +def node15394 : Tree Nat := .node node14966 node15393 +def node15395 : Tree Nat := .leaf 2739226045072033710287658726391013369481562983073862397477160556553942303725502492305173978496057631949077631305425926559852202637490687840085338029773266953885717342321301823575105913593880870151135721286467824 +def node15396 : Tree Nat := .node node15395 node12103 +def node15397 : Tree Nat := .node node15396 node12454 +def node15398 : Tree Nat := .node node15397 node12108 +def node15399 : Tree Nat := .node node14975 node15398 +def node15400 : Tree Nat := .node node15394 node15399 +def node15401 : Tree Nat := .node node14962 node15400 +def node15402 : Tree Nat := .node node15389 node15401 +def node15403 : Tree Nat := .node node15371 node15402 +def node15404 : Tree Nat := .node node15334 node15403 +def node15405 : Tree Nat := .node node15261 node15404 +def node15406 : Tree Nat := .leaf 7507516828804700229971157695509256861311759593549503536677899755757880972398156477780500115392148555129098941605120975421358609337268377851435968137607250746333311335562791469108340271963835182505208600985596065392094239938805605710167481610963902028081408 +def node15407 : Tree Nat := .node node15406 node12814 +def node15408 : Tree Nat := .node node15407 node8784 +def node15409 : Tree Nat := .node node15106 node15408 +def node15410 : Tree Nat := .leaf 4538292463156268884809873812257905527113274225333426531348093851670545687159400945307666050330311176768482470589594336982197970400033561643586429451371282206166754971538726692587479032961312177788215602012104989433491599359793912379717036342023729570918050702889058488546872813056 +def node15411 : Tree Nat := .node node15410 node12469 +def node15412 : Tree Nat := .node node15411 node12472 +def node15413 : Tree Nat := .node node12468 node15412 +def node15414 : Tree Nat := .node node15409 node15413 +def node15415 : Tree Nat := .leaf 1134573115789067205461908369119382699691688520550762052093256010792250990233174450602358484788549320991999708484415251003506231823727811199013134802003572459682281146343978038761761413981676371176643972925297163146796182113935578060879303844387614228281246212416763026838484179456 +def node15416 : Tree Nat := .node node15415 node9488 +def node15417 : Tree Nat := .node node15416 node9224 +def node15418 : Tree Nat := .node node15111 node15417 +def node15419 : Tree Nat := .node node15418 node15116 +def node15420 : Tree Nat := .node node15414 node15419 +def node15421 : Tree Nat := .leaf 70910819472717805518518461762433435520739548614634136462227683642007896408642214668902357301227728301105868721131694922218675190891622501715742916174558649306427330646600664173238113964288680993568132932251351093584071162497909603553588880856220449053599014081045674487307741696 +def node15422 : Tree Nat := .node node15421 node9498 +def node15423 : Tree Nat := .node node15422 node11444 +def node15424 : Tree Nat := .node node15120 node15423 +def node15425 : Tree Nat := .node node15424 node15125 +def node15426 : Tree Nat := .node node15425 node15131 +def node15427 : Tree Nat := .node node15420 node15426 +def node15428 : Tree Nat := .leaf 17311155196269223196464683982066137460447416991840732818070830393671260145870050225536982841962827905252999217111518720497926743069048328366117307524639184654363395853540031993243926838088327873690174998640022864562521367808595168899638365215206012150444368560386516571470848 +def node15429 : Tree Nat := .node node15428 node8379 +def node15430 : Tree Nat := .node node15429 node12497 +def node15431 : Tree Nat := .node node12133 node15430 +def node15432 : Tree Nat := .node node15431 node15138 +def node15433 : Tree Nat := .leaf 458222462695599379270700543124097915766146226034543166261162062688241686235243254048793332100351002716323229891272117829806997235166900156308762918682121886231955745946334476198478229031165856255733185897367923606822275187792388689646242256106244730880 +def node15434 : Tree Nat := .node node15433 node8818 +def node15435 : Tree Nat := .node node15434 node10368 +def node15436 : Tree Nat := .node node12138 node15435 +def node15437 : Tree Nat := .leaf 18153169852625075539254866889738487863162542998668723719383085675883720560700123307359189830245029013542086492768043232281531708838641156604113288164306628409988739323062651983354225984272860676366106387409048305008884353248518623373335219074500665789844791663786548307090083545088 +def node15438 : Tree Nat := .node node15437 node12143 +def node15439 : Tree Nat := .node node15438 node12146 +def node15440 : Tree Nat := .node node12142 node15439 +def node15441 : Tree Nat := .node node15436 node15440 +def node15442 : Tree Nat := .node node15432 node15441 +def node15443 : Tree Nat := .leaf 22158278915351719406283974454238294293253600614027963924553193280101997820984000720568604387210368574479850403557762687581222216155512597455705723208398720352044603987879154884857297842798076599972210835549307559617605486445468791320671346669543629560683511814595283734315715584 +def node15444 : Tree Nat := .node node15443 node8394 +def node15445 : Tree Nat := .node node15444 node11087 +def node15446 : Tree Nat := .node node10068 node15445 +def node15447 : Tree Nat := .leaf 540973599882921212264853218436393287673566403251396847255150572593178505309939161322570416346288260259265333487697023593408297587271866611531971688198067937643336138627520246554017917497385647292170296975292051952168421029985589878655441777874809979806456723037345592130560 +def node15448 : Tree Nat := .node node15447 node8828 +def node15449 : Tree Nat := .node node15448 node12507 +def node15450 : Tree Nat := .node node12153 node15449 +def node15451 : Tree Nat := .node node15446 node15450 +def node15452 : Tree Nat := .leaf 1082013240613047810748509635224066541555723574428421032709948785622709447310381981201139324611788339810688580352524416604147849611158360708814145953111360132662640637380547444356357950306988658895305743477866935347354022375922969990957542963754545296467959031497302442307584 +def node15453 : Tree Nat := .node node15452 node8833 +def node15454 : Tree Nat := .node node15453 node12512 +def node15455 : Tree Nat := .node node12158 node15454 +def node15456 : Tree Nat := .leaf 468837596257653119865388944340396725528080522453824687756070741127514670835605502864076262087374801617468180988032094365224921591069799046832660050571353807637642234788270555391178208433782517438858084090580883642318677 +def node15457 : Tree Nat := .node node15456 node8403 +def node15458 : Tree Nat := .node node15457 node11808 +def node15459 : Tree Nat := .node node15458 node10073 +def node15460 : Tree Nat := .node node15455 node15459 +def node15461 : Tree Nat := .node node15451 node15460 +def node15462 : Tree Nat := .node node15442 node15461 +def node15463 : Tree Nat := .node node15427 node15462 +def node15464 : Tree Nat := .leaf 1198036083490401393367579651265226826447551684806266405050177285577599119244146985902642702006115259121517669564685494258092759599884361455782156891511948092974684402153296914759012435170883966430860409802712994857367958263819718874644618127910183830363864694355049527845499445679616 +def node15465 : Tree Nat := .node node15464 node8411 +def node15466 : Tree Nat := .node node15465 node8847 +def node15467 : Tree Nat := .node node10081 node15466 +def node15468 : Tree Nat := .leaf 86858970270951010741439322838774601034241310111792427943280087243748184401908627217690210636966931618322214737485912186156068521607210919574602591797280975942106643841081055681064204273654973202547243377873580974721217663611408482637497758546944891123794986597543917140187554985472135623453992448 +def node15469 : Tree Nat := .node node15468 node8850 +def node15470 : Tree Nat := .node node15469 node11472 +def node15471 : Tree Nat := .node node11470 node15470 +def node15472 : Tree Nat := .node node15467 node15471 +def node15473 : Tree Nat := .leaf 320581849719015504355045079669379158750927440718026889997317355380719204587729952149070307291638296879850610206968102054467520791982062235283293716561360835917237416994914736943644764037777539147758988845373875771376943832680847035417499306328364944462876950466290110267663167481760991759279360 +def node15474 : Tree Nat := .node node15473 node8419 +def node15475 : Tree Nat := .node node15474 node12168 +def node15476 : Tree Nat := .node node12521 node15475 +def node15477 : Tree Nat := .node node15476 node15154 +def node15478 : Tree Nat := .node node15472 node15477 +def node15479 : Tree Nat := .leaf 20036365607438469020026026939523413110120942551672946778961469301548584450772935588064597130386746884106364066941596714012798556151214737203992100181991246982493323033708693291951027120555240956619957874093193015874263457500116161017898549184504234884381579094263000903681248698242048417486080 +def node15480 : Tree Nat := .node node15479 node8432 +def node15481 : Tree Nat := .node node15480 node11483 +def node15482 : Tree Nat := .node node12527 node15481 +def node15483 : Tree Nat := .node node15482 node15160 +def node15484 : Tree Nat := .node node15483 node15166 +def node15485 : Tree Nat := .node node15478 node15484 +def node15486 : Tree Nat := .leaf 80145462429753592445482322650559168134091064725027669358396684983451368644923776130938101710575646855303973155920538077328141218493192259267517782836899093188212202513880499838404225164254191636985273715512487422033215661002312721573940117100394242313259910811260859783841543117820983772627712 +def node15487 : Tree Nat := .node node15486 node8448 +def node15488 : Tree Nat := .node node15487 node12538 +def node15489 : Tree Nat := .node node11835 node15488 +def node15490 : Tree Nat := .node node15489 node15172 +def node15491 : Tree Nat := .leaf 4792144333961605573470318597553963255063876008477996300370403615557764867480747661107591615115106349186577640495629186954171886810925305804945467534831213409787788253413844947500755218129716995677820576749526914662277349758347625816246609178171867894951953628099841965706740106596096 +def node15492 : Tree Nat := .node node15491 node8889 +def node15493 : Tree Nat := .node node15492 node12186 +def node15494 : Tree Nat := .node node11840 node15493 +def node15495 : Tree Nat := .leaf 347435881083804042966865205287658500839823722747147168388319270396478757556844040405735014993372878171265895159253302155491839848298865196432019993150858918428928573073190637819405376723604722212002536373091465256925611732536059363229426274205115042805277991970451372157073003814974822451149144064 +def node15496 : Tree Nat := .node node15495 node12542 +def node15497 : Tree Nat := .node node15496 node10091 +def node15498 : Tree Nat := .node node12191 node15497 +def node15499 : Tree Nat := .node node15494 node15498 +def node15500 : Tree Nat := .node node15490 node15499 +def node15501 : Tree Nat := .leaf 4989600774417687667293981151278622688577234405220932344788661769335539926610129639825077852177017316570041384763178593866056865925895996627268729443331929260913504409134496718711046628806478514411788574579221615541227984064542072165876734008844104668171911981653133867411096920465877972562688 +def node15502 : Tree Nat := .node node15501 node8463 +def node15503 : Tree Nat := .node node15502 node11132 +def node15504 : Tree Nat := .node node10407 node15503 +def node15505 : Tree Nat := .leaf 609156476557923966918626273097409830714034799113298680457983503921460307784546542511427065081299892972200835294632158124915058584736104261045006200764809451781362144390102033583785667135277604513977115033196785957260455727396685229917162151757354537985692645381865162662976191884183747584 +def node15506 : Tree Nat := .node node15505 node9275 +def node15507 : Tree Nat := .node node15506 node10410 +def node15508 : Tree Nat := .node node12197 node15507 +def node15509 : Tree Nat := .node node15504 node15508 +def node15510 : Tree Nat := .leaf 1277342670759226379460700726275383667691826741952979388521624607079563497772074010387482329172321654743408155990716753473225453530535340893624126615961507135262565226262748784855649934206396360797971252879215252241505205544473935562100432506867804604867426909885182911115448032321814873466998528 +def node15511 : Tree Nat := .node node15510 node8900 +def node15512 : Tree Nat := .node node15511 node12552 +def node15513 : Tree Nat := .node node12550 node15512 +def node15514 : Tree Nat := .leaf 17926543156650705493745156729632933627795277661696322478545620488324046609162592775624987599647107332110860707038719766805096390805517453091238137043986395841994523715675727883830265920696146597930026412735291457686 +def node15515 : Tree Nat := .node node15514 node8472 +def node15516 : Tree Nat := .node node15515 node12201 +def node15517 : Tree Nat := .node node15516 node10766 +def node15518 : Tree Nat := .node node15513 node15517 +def node15519 : Tree Nat := .node node15509 node15518 +def node15520 : Tree Nat := .node node15500 node15519 +def node15521 : Tree Nat := .node node15485 node15520 +def node15522 : Tree Nat := .node node15463 node15521 +def node15523 : Tree Nat := .leaf 36304123742133375556593330216254635448529824738232755544798166470840175999708721578904841561045707224373992752311126809941319834194213272632787461295290593222069889893453995785367865686189190905772852897413890492895529605372428517511057484778791509279147279311728817788077467735552 +def node15524 : Tree Nat := .node node15523 node6448 +def node15525 : Tree Nat := .node node15524 node10424 +def node15526 : Tree Nat := .node node10107 node15525 +def node15527 : Tree Nat := .leaf 168608589349493136496030572289669508817787040015713647785735773720884720528372204685971861715542609726871557593354246219000167807154632009712325160613049287331906013331849409390721075296945259889740742419627078567973083790614506832550003922776381878045488504064589090778054885211811907425872877824 +def node15528 : Tree Nat := .node node15527 node7222 +def node15529 : Tree Nat := .node node15528 node11528 +def node15530 : Tree Nat := .node node11525 node15529 +def node15531 : Tree Nat := .node node15526 node15530 +def node15532 : Tree Nat := .leaf 321829249912474136950774531388527153498988028632831335357430503496913356461827070119452385998816950633589820760289861556291114326593359001211039126948516598595004467800993434304926231161651599978457535716368868065682441740355119912890164208314864476081381757190127312302594171030673307236063744 +def node15533 : Tree Nat := .node node15532 node6826 +def node15534 : Tree Nat := .node node15533 node11857 +def node15535 : Tree Nat := .node node10430 node15534 +def node15536 : Tree Nat := .node node15535 node15189 +def node15537 : Tree Nat := .node node15531 node15536 +def node15538 : Tree Nat := .leaf 20114328119529669012668853966381875362722134555206779239876697087646248779146034165820918421000920877310401059504347742023096259461043688854880751110899603815358924589766534060070528482858105371377716586637909066811917835280316347544886844990403804930334312299245963618521278531984433656211968 +def node15539 : Tree Nat := .node node15538 node6836 +def node15540 : Tree Nat := .node node15539 node10438 +def node15541 : Tree Nat := .node node10436 node15540 +def node15542 : Tree Nat := .leaf 40446859910595699341125708145656373132591514042419445126956107720016824550504610199778106381062904224028920164321011987772406589093146069326469470774822112249122461688789635386930032378599152626014136569806163690888392306391590907442750794776147055292107890235293049400909512960928733696 +def node15543 : Tree Nat := .node node15542 node7235 +def node15544 : Tree Nat := .node node15543 node11151 +def node15545 : Tree Nat := .node node11535 node15544 +def node15546 : Tree Nat := .node node15541 node15545 +def node15547 : Tree Nat := .node node15546 node15201 +def node15548 : Tree Nat := .node node15537 node15547 +def node15549 : Tree Nat := .leaf 159979074811142526733376176478649845913726400468227039400546995978457108606195822085848243501581067188245699076664998184496941037856076071449348303337804900357211823500457501182208563867255775326781313185993165644779776677778403174084914552590628585870436665883513876425034407900892457302672128 +def node15550 : Tree Nat := .node node15549 node10117 +def node15551 : Tree Nat := .node node15550 node12571 +def node15552 : Tree Nat := .node node12569 node15551 +def node15553 : Tree Nat := .node node15552 node15207 +def node15554 : Tree Nat := .leaf 4937360828930139075696691888388799926023520487701478865376741486590167011125239811738599143103092677923159881537312681506056023294149483840864188560204025055133530424562609176392157268723256106583585879024474445109440683726786831684023790006889196813129140860366678227606395841867776 +def node15555 : Tree Nat := .node node15554 node9814 +def node15556 : Tree Nat := .node node15555 node11874 +def node15557 : Tree Nat := .node node11871 node15556 +def node15558 : Tree Nat := .leaf 367873285853439582913703440436219505583325949796149292826754015369744869522101255993252400620808615051146054894042356474311825629715173416394001179971085439954444674159577150390283841480438426759072547087080663152318191800592686638866389642691195099098101408846949921865107852115274915600570908672 +def node15559 : Tree Nat := .node node15558 node12220 +def node15560 : Tree Nat := .node node15559 node8508 +def node15561 : Tree Nat := .node node11880 node15560 +def node15562 : Tree Nat := .node node15557 node15561 +def node15563 : Tree Nat := .node node15553 node15562 +def node15564 : Tree Nat := .leaf 9979201548254487196434912925809584290274407991613953913981989522577220405573708696883466807887369191012376821677905552106145072694971282017943589959830128051297793092016773560963560634187379857534006545097627061379992814927795162337995772168242338235928803684360948156208575003554316704494336 +def node15565 : Tree Nat := .node node15564 node9824 +def node15566 : Tree Nat := .node node15565 node11169 +def node15567 : Tree Nat := .node node10464 node15566 +def node15568 : Tree Nat := .leaf 74350845424430126739786046119759881225436398364923486788534164023104585860630590327701307231653715674694717798477647549916301115791945288173414903095818856544473767713508152948135845769451914739743908698516798685138651234689082037831195914368980309930966781480148042819576185009455872 +def node15569 : Tree Nat := .node node15568 node10800 +def node15570 : Tree Nat := .node node15569 node11885 +def node15571 : Tree Nat := .node node11557 node15570 +def node15572 : Tree Nat := .node node15567 node15571 +def node15573 : Tree Nat := .leaf 4872657005699999810729531982603590260741364654792504478464546818536317794263914290819649548611831045490623330132633389857394725341560365967010105921658326119587940658554034844716160968504350651489228169639875840113143477185155791023233552810584797268013885174780864020126513498195646942976 +def node15574 : Tree Nat := .node node15573 node10467 +def node15575 : Tree Nat := .node node15574 node12577 +def node15576 : Tree Nat := .node node11562 node15575 +def node15577 : Tree Nat := .node node15576 node15218 +def node15578 : Tree Nat := .node node15572 node15577 +def node15579 : Tree Nat := .node node15563 node15578 +def node15580 : Tree Nat := .node node15548 node15579 +def node15581 : Tree Nat := .leaf 1876879207201175057492789423877314215327939898387375884169474870502860978766610998234944122395390194024955117138903285370577273202671582266336322352612260690635705590860137998029853303055257244368848727893831538229857561687670845859430466327622038920653056 +def node15582 : Tree Nat := .node node15581 node11892 +def node15583 : Tree Nat := .node node15582 node8954 +def node15584 : Tree Nat := .node node12590 node15583 +def node15585 : Tree Nat := .leaf 6807161707798034829266617163013250079236990966185612637412353851191837914310993822654487892989551220838762722307766378493081397315103321726123212598970836764287954370208072638830561818365033389684468434417122885388639149806421250226050194139992478362864511500532008711529929349376 +def node15586 : Tree Nat := .node node15585 node10475 +def node15587 : Tree Nat := .node node15586 node12593 +def node15588 : Tree Nat := .node node11570 node15587 +def node15589 : Tree Nat := .node node15584 node15588 +def node15590 : Tree Nat := .leaf 567355804628625719347722766040449209787617010023576755088134425485759981090792590438175854220474380030588978982007165322338033436843543996889067262193313979802130337932544593114496534251754915723275693183919767010994867396381227008465330039211064707953719721661880083109544699136 +def node15591 : Tree Nat := .node node15590 node11576 +def node15592 : Tree Nat := .node node15591 node12235 +def node15593 : Tree Nat := .node node10482 node15592 +def node15594 : Tree Nat := .node node15593 node15226 +def node15595 : Tree Nat := .node node15589 node15594 +def node15596 : Tree Nat := .leaf 70910819472750050057772347581139728195791190867737783499414487562284468047566039611317664382047841560500898269194606099801932810909869569097290762364239151367480076099846765541148882341365892302611892465779514284169946089168340374159222508012890964073468709213138648614200235264 +def node15597 : Tree Nat := .node node15596 node11903 +def node15598 : Tree Nat := .node node15597 node12599 +def node15599 : Tree Nat := .node node10491 node15598 +def node15600 : Tree Nat := .leaf 8254602048994769474255309139322199910068143258083411942779421622222918385455907964135859402967312681951914585961438935395084926969444381640314024071448549643829768610842329584291145367042392257057694772865912319097228015537419637844874127898801681045695990078890138112 +def node15601 : Tree Nat := .node node15600 node10165 +def node15602 : Tree Nat := .node node15601 node12603 +def node15603 : Tree Nat := .node node12246 node15602 +def node15604 : Tree Nat := .node node15599 node15603 +def node15605 : Tree Nat := .node node15604 node15238 +def node15606 : Tree Nat := .node node15595 node15605 +def node15607 : Tree Nat := .leaf 141821638945306632879540928499235702789523804660839184782518748770858768215665016731303735181966445661172112482444830104679904463897523336112202856725048348651366872223099916880496943640784355411048824124850653327368100762354538069046211577343825530103298669494723261148552576000 +def node15608 : Tree Nat := .node node15607 node9868 +def node15609 : Tree Nat := .node node15608 node12618 +def node15610 : Tree Nat := .node node12616 node15609 +def node15611 : Tree Nat := .node node15610 node15244 +def node15612 : Tree Nat := .leaf 572778078369499224088375678951221598569635724963376210566600916987787600271984077393014022975755138985852576975689034914333225357716418817829738479408421457854614468346884388805393049490879714577030238528057949700682041312406560480560860314546141990656 +def node15613 : Tree Nat := .node node15612 node10188 +def node15614 : Tree Nat := .node node15613 node12263 +def node15615 : Tree Nat := .node node12261 node15614 +def node15616 : Tree Nat := .leaf 27229754745124699539724556717965248145863891720995545433026468066958970453054809532683558417354796822744197392528156467002111624110240646040583778141478890749885416986227097533617548803686762370874945896321967584321887996862593484660947511360618989675011958062965649753564707946496 +def node15617 : Tree Nat := .node node15616 node7290 +def node15618 : Tree Nat := .node node15617 node12267 +def node15619 : Tree Nat := .node node11926 node15618 +def node15620 : Tree Nat := .node node15615 node15619 +def node15621 : Tree Nat := .node node15611 node15620 +def node15622 : Tree Nat := .leaf 22158278915359780541097445908803003571631773065235217098969924989565977097357487995088624674405906258444410432440965330416396484785140009891403351950655799102361452884868536362184249311008597495788221100241009131965912620744591331032327678787420903404285815675543370111644847104 +def node15623 : Tree Nat := .node node15622 node10198 +def node15624 : Tree Nat := .node node15623 node11214 +def node15625 : Tree Nat := .node node10515 node15624 +def node15626 : Tree Nat := .leaf 135243399970730303066256263620508534274074959643732561356564514920724043422617857211178607776599934005271447263002752980135109464902950123336581598735392049871403796878723323555054540114636888773910334557113123585512563427986092255303034264068737767868381442129305438241536 +def node15627 : Tree Nat := .node node15626 node10848 +def node15628 : Tree Nat := .node node15627 node12628 +def node15629 : Tree Nat := .node node10204 node15628 +def node15630 : Tree Nat := .node node15625 node15629 +def node15631 : Tree Nat := .leaf 270552840788665992351315725592297086039816589628593280458038942922972843492863427116602605290738682503755062686824632870458978259777597377354489968854468255192362660010958964675917201380316757342892099674599570561251315597637548369868202798088074439406377026292906432917504 +def node15632 : Tree Nat := .node node15631 node10518 +def node15633 : Tree Nat := .node node15632 node12636 +def node15634 : Tree Nat := .node node12634 node15633 +def node15635 : Tree Nat := .node node15634 node15255 +def node15636 : Tree Nat := .node node15630 node15635 +def node15637 : Tree Nat := .node node15621 node15636 +def node15638 : Tree Nat := .node node15606 node15637 +def node15639 : Tree Nat := .node node15580 node15638 +def node15640 : Tree Nat := .node node15522 node15639 +def node15641 : Tree Nat := .leaf 1234340207232534768924172979604602254694906452051709736717661236720499396856479823312072673064313023827696058471176246614407704485627914597376328913600482620629365965432339565742400843975714648294898920505788640659903148381745551190292991664818663637958829145630999704460912089667072 +def node15642 : Tree Nat := .node node15641 node8565 +def node15643 : Tree Nat := .node node15642 node12649 +def node15644 : Tree Nat := .node node12647 node15643 +def node15645 : Tree Nat := .leaf 91968321463359895728287362414772350391005317094108970829526371697254136204207243750188796452641905335584355476048413269949611095648051544842653180523148731494703023043542047793016343223280649331600908800638537014844671324382280399085677540122118660349292585178817510294480354097277065274726324480 +def node15646 : Tree Nat := .node node15645 node8991 +def node15647 : Tree Nat := .node node15646 node11609 +def node15648 : Tree Nat := .node node12654 node15647 +def node15649 : Tree Nat := .node node15644 node15648 +def node15650 : Tree Nat := .leaf 639916299244570106968129129743155712968142600826328361861269002518765692959180279582842361539957427821864180756163507365501857815621904627591109291708468550654783464135605363666673869128566976719030708666763600144743069586273945667192348988364285011652041848673195542295695350862584307944301824 +def node15651 : Tree Nat := .node node15650 node8998 +def node15652 : Tree Nat := .node node15651 node11938 +def node15653 : Tree Nat := .node node11936 node15652 +def node15654 : Tree Nat := .node node15653 node15267 +def node15655 : Tree Nat := .node node15649 node15654 +def node15656 : Tree Nat := .leaf 39994768702785667136589754069889830600183615715842546809406171122206218361152259281069279655830001370989481224883824194945085144080594809537294824770311132060706026339835535322877874985552229314052408106503203730124337340255417995033099006387062276649635259106966969197937647171135137181750528 +def node15657 : Tree Nat := .node node15656 node8579 +def node15658 : Tree Nat := .node node15657 node11235 +def node15659 : Tree Nat := .node node10536 node15658 +def node15660 : Tree Nat := .leaf 152270531428124985663540008006528895254462281213872294947618853506483030983372182805358241089510372500965002218190787176901052925417424221505321060353466622034474735836462310136484621848732732122230660632489224638417086377569336182339324417103533970995790945832629494950323073815439648000 +def node15661 : Tree Nat := .node node15660 node9008 +def node15662 : Tree Nat := .node node15661 node11239 +def node15663 : Tree Nat := .node node10884 node15662 +def node15664 : Tree Nat := .node node15659 node15663 +def node15665 : Tree Nat := .leaf 9516908214257811601907599988159363584840393356930223021725004076677495642211373195038513992485907865353096123302030619843752902559467383547183738375691031868163388012490710605897197900352425095258001194149290522587698107365288155986248018323705511762496638034197089969570182917997893888 +def node15666 : Tree Nat := .node node15665 node9015 +def node15667 : Tree Nat := .node node15666 node12659 +def node15668 : Tree Nat := .node node12284 node15667 +def node15669 : Tree Nat := .node node15668 node12289 +def node15670 : Tree Nat := .node node15664 node15669 +def node15671 : Tree Nat := .node node15655 node15670 +def node15672 : Tree Nat := .leaf 80457312478118534229036470300930434235522628172007171743766890685245679184089647933239415283710629020264728582705425587599757985640301540346432576060114149385899243720660863742581634824484518832263444477497488610087728134361052208954952250300199130014447949412538288585291484203088023614012416 +def node15673 : Tree Nat := .node node15672 node8601 +def node15674 : Tree Nat := .node node15673 node9023 +def node15675 : Tree Nat := .node node12295 node15674 +def node15676 : Tree Nat := .node node15675 node15286 +def node15677 : Tree Nat := .leaf 9439072172954677644714263904272287949858390238818786309783863326316159234950682739463229782691066005185130606875007280618436737238892813754412302861315812953999912825369355038027624712846844766940897562178075251848610585618570469960523776714428808397609564407828660070399482475704320 +def node15678 : Tree Nat := .node node15677 node9031 +def node15679 : Tree Nat := .node node15678 node11951 +def node15680 : Tree Nat := .node node10904 node15679 +def node15681 : Tree Nat := .leaf 674434357397972545984676212314108027970069847891597957861679561457169541022146897945506841133951433671705779178893024430922564260271693412681473351338455308009163328516753018348911973306842915665815743390122970891465655429814866967085469983603453738594038172255122502732713137967396222340137549824 +def node15682 : Tree Nat := .node node15681 node12301 +def node15683 : Tree Nat := .node node15682 node6951 +def node15684 : Tree Nat := .node node12300 node15683 +def node15685 : Tree Nat := .node node15680 node15684 +def node15686 : Tree Nat := .node node15676 node15685 +def node15687 : Tree Nat := .leaf 5028582029882421683741260671924138265858041973386486317125919090786976726751969868679878948078732201476669547960249520795555333237078986369129869647370303092027485606530803204225977840464813072854226256758182364663734141695061832935394369024386570313802390635168552580779785345115780016819200 +def node15688 : Tree Nat := .node node15687 node8616 +def node15689 : Tree Nat := .node node15688 node9038 +def node15690 : Tree Nat := .node node10252 node15689 +def node15691 : Tree Nat := .leaf 609379529094196040108245894663041514395008867059979580618977976440839143617791336244577797606461551378275019393103870703815863548226650383504462480615918589431219759475780909081818132074079039192620374494908154838233528534480249090770512156087022269287883478274937042887063181015031495680 +def node15692 : Tree Nat := .node node15691 node9350 +def node15693 : Tree Nat := .node node15692 node11961 +def node15694 : Tree Nat := .node node12309 node15693 +def node15695 : Tree Nat := .node node15690 node15694 +def node15696 : Tree Nat := .leaf 1277347543416232079459429442566753223463830998645127411912890137919851953869864778097993319443007969550715864255493259221604759425926202856297501641484824040128543116269274870722692460829427960466194875771310843467894120957948070439822321058901535969323194741426444028631800060173262012070031360 +def node15697 : Tree Nat := .node node15696 node9042 +def node15698 : Tree Nat := .node node15697 node12316 +def node15699 : Tree Nat := .node node12314 node15698 +def node15700 : Tree Nat := .leaf 1081947199765842424529591879509026010150599323721976877786911901102607643345088549071011938292609190564680115448231214031225297450983944591762114447204208853056095964629531959031593675719532989816055683925613662474472723111235649420788698168519888602972479066401050896302230 +def node15701 : Tree Nat := .node node15700 node8625 +def node15702 : Tree Nat := .node node15701 node12320 +def node15703 : Tree Nat := .node node15702 node11970 +def node15704 : Tree Nat := .node node15699 node15703 +def node15705 : Tree Nat := .node node15695 node15704 +def node15706 : Tree Nat := .node node15686 node15705 +def node15707 : Tree Nat := .node node15671 node15706 +def node15708 : Tree Nat := .leaf 1876879207201175057492789423877314215327939898387375884169474870502860978766611314740567183816640669956718152197611401298188419839299131046298724927312626308147774090012671518111627162722572760790038447887266919045425274166506642359404326528579327595079936 +def node15709 : Tree Nat := .node node15708 node6587 +def node15710 : Tree Nat := .node node15709 node12667 +def node15711 : Tree Nat := .node node10265 node15710 +def node15712 : Tree Nat := .leaf 6807300205492317386756408757534133186599502554112074429827156263482670429606677336645130403357012988731669634033992905321817855418505135462014814225467274687883318632688758133107263948176240094740338188839915515185302410535037138560694913334809589785473377934111209410379807234304 +def node15713 : Tree Nat := .node node15712 node10568 +def node15714 : Tree Nat := .node node15713 node12671 +def node15715 : Tree Nat := .node node11279 node15714 +def node15716 : Tree Nat := .node node15711 node15715 +def node15717 : Tree Nat := .leaf 567321184431411336934720611512887613806790139991318333396903688424281068791007024703103334984039662327220135112747636712002476424929531025704474758716712792374108875736758964293218235055893453785990453963084380706354018313391192811340285867108299377553973566005555817462383991296 +def node15718 : Tree Nat := .node node15717 node6975 +def node15719 : Tree Nat := .node node15718 node11980 +def node15720 : Tree Nat := .node node12677 node15719 +def node15721 : Tree Nat := .node node15720 node15300 +def node15722 : Tree Nat := .node node15716 node15721 +def node15723 : Tree Nat := .leaf 70910819472717807486689073601873675123832370753443991346420101627509971688325951407355087233591796829257052823090296745830715178688262150918082705060340347700526013769094987034688664335627081973183128811761940057941003567114949089074796432427981555019026092949153445049172404736 +def node15724 : Tree Nat := .node node15723 node6981 +def node15725 : Tree Nat := .node node15724 node11284 +def node15726 : Tree Nat := .node node10581 node15725 +def node15727 : Tree Nat := .leaf 8254602048994769474255309145988586409736845223990880957184585387370195494406315018589907408475988106444731798107728478492881165453593373264685160113355229272458024620987740323669615314645546432077361972900971900954770991136968358206329747709309351185064606320484328704 +def node15728 : Tree Nat := .node node15727 node7369 +def node15729 : Tree Nat := .node node15728 node12682 +def node15730 : Tree Nat := .node node11666 node15729 +def node15731 : Tree Nat := .node node15726 node15730 +def node15732 : Tree Nat := .node node15731 node15312 +def node15733 : Tree Nat := .node node15722 node15732 +def node15734 : Tree Nat := .leaf 141830295051199290754602382260373947395761342649441538550624200908015257964810218525920226570038026386676781842005297973138149503826451753547323011381327910675177119753526435419972812180318658840008163660693602165177767708572898002505707758922494987475257601625797458221666517760 +def node15735 : Tree Nat := .node node15734 node8646 +def node15736 : Tree Nat := .node node15735 node11303 +def node15737 : Tree Nat := .node node11998 node15736 +def node15738 : Tree Nat := .node node15737 node15318 +def node15739 : Tree Nat := .leaf 572778078369499224088375678951221598569635724963376210566600916987787600266918755600337383756740695187843846539470501942080402712684460551799306204629991132940785018001093044761703519668959969356091515203317096785864693341259672087876245104629812694784 +def node15740 : Tree Nat := .node node15739 node9081 +def node15741 : Tree Nat := .node node15740 node10952 +def node15742 : Tree Nat := .node node10288 node15741 +def node15743 : Tree Nat := .leaf 27229200821969269421085773333472685759203757431349580786236621967176048774305619712029510863355852610266251700065354980437987130162003364523974781831194524930021048479355212661968263413629001427771751584874345318723475072589083892829500164257661715925237024177523887050810564345856 +def node15744 : Tree Nat := .node node15743 node12698 +def node15745 : Tree Nat := .node node15744 node12349 +def node15746 : Tree Nat := .node node12347 node15745 +def node15747 : Tree Nat := .node node15742 node15746 +def node15748 : Tree Nat := .node node15738 node15747 +def node15749 : Tree Nat := .leaf 22158278915351719898296597346894999283491685065891276212406255265191011058576428137620774255347447941366624924536160410234894455647634585936623057889282557387720354221410734208980388188495421122993992254448002097513545544561538854240607272778951906459081264941086849103970448128 +def node15750 : Tree Nat := .node node15749 node8665 +def node15751 : Tree Nat := .node node15750 node12003 +def node15752 : Tree Nat := .node node10602 node15751 +def node15753 : Tree Nat := .leaf 135243399970730303066256264057530199798037305978849004624741671922478544419052823785202295578326796331323762810785085440585750612854769511458287340997596805305027355255623973869279529525760921075186124424735450753738187337066180182669320943694229112132230154769178084260864 +def node15754 : Tree Nat := .node node15753 node9376 +def node15755 : Tree Nat := .node node15754 node12705 +def node15756 : Tree Nat := .node node12356 node15755 +def node15757 : Tree Nat := .node node15752 node15756 +def node15758 : Tree Nat := .leaf 270552840788665996105303265210688258408249245669989305317696841404664435539584188213512958846144024299548666392997721951113037055871619200728521110976211057483169689229645255273521025976003839658346473247418481229297699479505653859211715019038900606538166216886796449484544 +def node15759 : Tree Nat := .node node15758 node9092 +def node15760 : Tree Nat := .node node15759 node12361 +def node15761 : Tree Nat := .node node12711 node15760 +def node15762 : Tree Nat := .node node15761 node15329 +def node15763 : Tree Nat := .node node15757 node15762 +def node15764 : Tree Nat := .node node15748 node15763 +def node15765 : Tree Nat := .node node15733 node15764 +def node15766 : Tree Nat := .node node15707 node15765 +def node15767 : Tree Nat := .leaf 7507516828804700229971157695509256861311759593549503536677899755757880972398156161120295405629800525818062595304538255244100018963716682312263848649735013248747144160403583898677760191940279586548458914905430237775959193223175087436338839548758459429382400 +def node15768 : Tree Nat := .node node15767 node8685 +def node15769 : Tree Nat := .node node15768 node12719 +def node15770 : Tree Nat := .node node12371 node15769 +def node15771 : Tree Nat := .leaf 4538153982367411386638985831257634323817187259833015497682302839481708859070474855177462305266402058398367751392673784278356141402553851236976150075587146791656752422132164769569092579279212415396519324103558190145879279205575769524531987661604724613754739435072759047459853002240 +def node15772 : Tree Nat := .node node15771 node9109 +def node15773 : Tree Nat := .node node15772 node12723 +def node15774 : Tree Nat := .node node11328 node15773 +def node15775 : Tree Nat := .node node15770 node15774 +def node15776 : Tree Nat := .leaf 1134607740212637836964076343082010581522393475473899821586450545789312920557130321092422779482578016275552740563259136559266638267622156589195774637257013376124939740720969140303020245695324016481911899661185657179050848837434990463411071086707098975972216844819309555732226024704 +def node15777 : Tree Nat := .node node15776 node9114 +def node15778 : Tree Nat := .node node15777 node9386 +def node15779 : Tree Nat := .node node12376 node15778 +def node15780 : Tree Nat := .node node15779 node15338 +def node15781 : Tree Nat := .node node15775 node15780 +def node15782 : Tree Nat := .leaf 70910819472750052025942959420579967798884013006547626537389655150562590227271067010605519408541465020210900307826099822037041802246524991838111298864892691822908064181947742240768506904439670350385745698177452778016694959157522932412022311830399830227156024505005883198992110848 +def node15783 : Tree Nat := .node node15782 node8696 +def node15784 : Tree Nat := .node node15783 node11333 +def node15785 : Tree Nat := .node node10622 node15784 +def node15786 : Tree Nat := .node node15785 node15344 +def node15787 : Tree Nat := .node node15786 node15350 +def node15788 : Tree Nat := .node node15781 node15787 +def node15789 : Tree Nat := .leaf 8656105892673619465444975048166327535575816414642870886433951036774958852093072966922685159797042955590357609694545859528371350854259453049167652294024774720744926774440167303592353224032656409054017970113197267611905014797741015119966394616598682358104342968179758847345408 +def node15790 : Tree Nat := .node node15789 node12890 +def node15791 : Tree Nat := .node node15790 node12741 +def node15792 : Tree Nat := .node node10319 node15791 +def node15793 : Tree Nat := .node node15792 node15356 +def node15794 : Tree Nat := .leaf 458222462695599379270700543124097915766146226034543166261162062688241686230177922594772883088733799908216237313173269133903564670359683100428470805164023088854300778229315074860495924601660365737219542475937959911011681358919873166850688203531644956672 +def node15795 : Tree Nat := .node node15794 node9667 +def node15796 : Tree Nat := .node node15795 node12398 +def node15797 : Tree Nat := .node node12751 node15796 +def node15798 : Tree Nat := .leaf 18153723843402205643258801807330542719136802922730251134981088025915907665452926151032992158515402763016369738057920160139512723186765293700738564131045738576914828352510759750219179833031950496030810453841381680215076534619955415182694281460684764541839214202980104194757970165760 +def node15799 : Tree Nat := .node node15798 node12404 +def node15800 : Tree Nat := .node node15799 node12407 +def node15801 : Tree Nat := .node node12403 node15800 +def node15802 : Tree Nat := .node node15797 node15801 +def node15803 : Tree Nat := .node node15793 node15802 +def node15804 : Tree Nat := .leaf 22158278915359781033110068801459708561869857517680723670713632599746412231136367537251848827745602729652909678255851400611322695337222675573820831846007343976325923604929217067706474791077768984613096926512023775465271557870317304047899644115564809459063982624591492532713763584 +def node15805 : Tree Nat := .node node15804 node9673 +def node15806 : Tree Nat := .node node15805 node9147 +def node15807 : Tree Nat := .node node12757 node15806 +def node15808 : Tree Nat := .leaf 540973599882921212264853218873414954011495355162667376714715887641158912955278282202234304360877231499076522912996564455032439861002326477788876985033240393007874222489329827108309311435363047917631112157033148058871315485851573946926833612809235241201272948839951232123648 +def node15809 : Tree Nat := .node node15808 node11357 +def node15810 : Tree Nat := .node node15809 node12760 +def node15811 : Tree Nat := .node node12898 node15810 +def node15812 : Tree Nat := .node node15807 node15811 +def node15813 : Tree Nat := .leaf 1082013240613047814502497174842457818118240858323603793865661134108793590835446722957289277090376496130753557152698716018143955262727501840636499963840671741600474861084580101789991951618331646713217153825217984585551058478260405785563125312467962086303447045741360951791360 +def node15814 : Tree Nat := .node node15813 node9678 +def node15815 : Tree Nat := .node node15814 node12414 +def node15816 : Tree Nat := .node node12903 node15815 +def node15817 : Tree Nat := .node node15816 node15367 +def node15818 : Tree Nat := .node node15812 node15817 +def node15819 : Tree Nat := .node node15803 node15818 +def node15820 : Tree Nat := .node node15788 node15819 +def node15821 : Tree Nat := .leaf 72608247484266751113186647294354820488834247026939543948396825646101063287786253971485042109138209942616781981013232515549300619161883291925363445411946689106250241543546448551202983533484849706543617298314720209368587124244310809691370975763459978972273957405688531945732616001024 +def node15822 : Tree Nat := .node node15821 node9427 +def node15823 : Tree Nat := .node node15822 node12773 +def node15824 : Tree Nat := .node node12915 node15823 +def node15825 : Tree Nat := .leaf 173717940541902016944863144098995313600384769966214743445557908747446824340242627030680245291832547831618147138783121786079453677669767045869658940783586147340419094032049368901888905501248296641851631554267688655312600654506978233409676050313674301423712165311781055238598709224144660012303869440 +def node15826 : Tree Nat := .node node15825 node9690 +def node15827 : Tree Nat := .node node15826 node12048 +def node15828 : Tree Nat := .node node11721 node15827 +def node15829 : Tree Nat := .node node15824 node15828 +def node15830 : Tree Nat := .leaf 641163699438029874067725523130289851257537836797590426896209083059426871524647308153848856547595983143840549993365520260682076774516654784932325141564830982556553579626549998989768566402299686407800774993194359397537778052798834633009249202996272357116127715364835678359152275063915548813253120 +def node15831 : Tree Nat := .node node15830 node9695 +def node15832 : Tree Nat := .node node15831 node12422 +def node15833 : Tree Nat := .node node12920 node15832 +def node15834 : Tree Nat := .node node15833 node15375 +def node15835 : Tree Nat := .node node15829 node15834 +def node15836 : Tree Nat := .leaf 40072731214876867129232581096748292852784807719376379270321398908315728910151385859240860647220990212663904794200761358530030046443035002075588692578453730566851682997122245964499900674985490009009330413153976869685976986049164832724304455361869851998151572880504403305497385063243838421051904 +def node15837 : Tree Nat := .node node15836 node12924 +def node15838 : Tree Nat := .node node15837 node11382 +def node15839 : Tree Nat := .node node12780 node15838 +def node15840 : Tree Nat := .node node15839 node15381 +def node15841 : Tree Nat := .node node15840 node15387 +def node15842 : Tree Nat := .node node15835 node15841 +def node15843 : Tree Nat := .leaf 160290924859507184890963588712040320533756863335788821184229948264768520609423743754511921039442755744626840686452387272049114127110983301912376595654967313182934280855118209684689454741506227158516807806743891928522208700575254321272808748389097938892531890277964499450335082623874172026502144 +def node15844 : Tree Nat := .node node15843 node12077 +def node15845 : Tree Nat := .node node15844 node9463 +def node15846 : Tree Nat := .node node12787 node15845 +def node15847 : Tree Nat := .leaf 148701690847778306280310070740832021923419923311650029397698061862645982565585358253925509580443099392097636013688875224516799702391232527468919513919306076574045700825596225224475758283228387685159298220361427286858832717713950193073999117078497768803919081956764480413099648780481280 +def node15848 : Tree Nat := .node node15847 node11745 +def node15849 : Tree Nat := .node node15848 node12082 +def node15850 : Tree Nat := .node node12440 node15849 +def node15851 : Tree Nat := .node node15846 node15850 +def node15852 : Tree Nat := .leaf 9584288667923211146940637195107353732049382517731904225061855896556401750907832068040262941128110213141980436266490096231174994348437158977471473151819257880198065177222427545379554567973429464138131721203946471177747409682244289780179195217460967394711566582721232942248743159860992 +def node15853 : Tree Nat := .node node15852 node11750 +def node15854 : Tree Nat := .node node15853 node12794 +def node15855 : Tree Nat := .node node12792 node15854 +def node15856 : Tree Nat := .leaf 694871762167608067779452576395981254416910720571696761238822770301526982345467129021226092563093913284936945962636860292903929200072478250065494111641412076432166744556768834350852444703419294906590931103948888713056970961658616692755297710918986176247761218344234102435715143911871209397518925824 +def node15857 : Tree Nat := .node node15856 node11408 +def node15858 : Tree Nat := .node node15857 node9187 +def node15859 : Tree Nat := .node node12092 node15858 +def node15860 : Tree Nat := .node node15855 node15859 +def node15861 : Tree Nat := .node node15851 node15860 +def node15862 : Tree Nat := .leaf 10018182803719221212882192446455099867555215559779507886319246261834373316730135166296008168606748681285674299658433427588117589935144194258351896811548249760940761295918797565616996374843956855581957765235256512861615753495198699847213660217695587392214498695450095092680789026793180045233152 +def node15863 : Tree Nat := .node node15862 node12096 +def node15864 : Tree Nat := .node node15863 node12099 +def node15865 : Tree Nat := .node node10663 node15864 +def node15866 : Tree Nat := .leaf 297403381695691855959583229933046368289872575538210698290215200743951858832033188648010285630783697931526577508768476265843896813954106834202265510170733431745364743706489838452369277429919165514262885600431107164206755892251987686164587318963288162612942117384863798629365591205724928 +def node15867 : Tree Nat := .node node15866 node11417 +def node15868 : Tree Nat := .node node15867 node9193 +def node15869 : Tree Nat := .node node12446 node15868 +def node15870 : Tree Nat := .node node15865 node15869 +def node15871 : Tree Nat := .leaf 9745314011400000162366623000922999059385876066354910969894760819480467813573071604504378316694465409729571492891753371336833459578206059492630777942733715949225025896905998579812398352897649784929487652491088233288979618456232372001547706493611023479929049225200082527586178546865112346624 +def node15872 : Tree Nat := .node node15871 node11764 +def node15873 : Tree Nat := .node node15872 node11423 +def node15874 : Tree Nat := .node node12801 node15873 +def node15875 : Tree Nat := .node node15874 node15398 +def node15876 : Tree Nat := .node node15870 node15875 +def node15877 : Tree Nat := .node node15861 node15876 +def node15878 : Tree Nat := .node node15842 node15877 +def node15879 : Tree Nat := .node node15820 node15878 +def node15880 : Tree Nat := .node node15766 node15879 +def node15881 : Tree Nat := .node node15640 node15880 +def node15882 : Tree Nat := .leaf 7507516828804700229971157695509256861311759593549503536677899755757880972394849832561548074128333980112720047562907932330040417432584337039659808602132752139594035200713478417887885599762162927996736399775909949573116596403936900158987431257073116663015680 +def node15883 : Tree Nat := .node node15882 node12814 +def node15884 : Tree Nat := .node node15883 node8784 +def node15885 : Tree Nat := .node node15106 node15884 +def node15886 : Tree Nat := .leaf 276995389596940235707535226076096047046133054332088248323042815523687195810747944606465408330630356835118507960594565434371176978724891701332241893216487221513671988777613945518653277353722087768861468590155848759729348365153219600839120492680400179015530071888479593752690688 +def node15887 : Tree Nat := .node node15886 node12469 +def node15888 : Tree Nat := .node node15887 node12472 +def node15889 : Tree Nat := .node node12468 node15888 +def node15890 : Tree Nat := .node node15885 node15889 +def node15891 : Tree Nat := .leaf 69248847141263004335947925255763661409916205389645061660029539212704257825757503759363062617339460693508035912242279970490097962078392609772257376018779117516058996956707372049414610800224124462599200940544263317017407481193337365800135220007637093502390779739396323457128960 +def node15892 : Tree Nat := .node node15891 node9488 +def node15893 : Tree Nat := .node node15892 node9224 +def node15894 : Tree Nat := .node node15111 node15893 +def node15895 : Tree Nat := .leaf 123003155723136208567847447732916373157248969801103682610571457528939855686086431917643421299711995003413971635029540614727577412259756590040572881235429807073711383877430605258510977656228787413396934427662302958418858044065789013560345632430499926878321682944 +def node15896 : Tree Nat := .node node15895 node11437 +def node15897 : Tree Nat := .node node15896 node12118 +def node15898 : Tree Nat := .node node9229 node15897 +def node15899 : Tree Nat := .node node15894 node15898 +def node15900 : Tree Nat := .node node15890 node15899 +def node15901 : Tree Nat := .leaf 33018408195979077897021236557282287907427960838450855899425517182270529913353736427514682826882175678103972037564306035769321672984355305874319272381183984468494729739693313633963517513411550133303620725764987063430109626765910378281232806177441251335137564617447463424 +def node15902 : Tree Nat := .node node15901 node9504 +def node15903 : Tree Nat := .node node15902 node12478 +def node15904 : Tree Nat := .node node12837 node15903 +def node15905 : Tree Nat := .node node15424 node15904 +def node15906 : Tree Nat := .leaf 794937779448347371950501165685238095423151319948555938581424719562827791022380145218234821152456839615748775209159685092946811204044518020842251953605587387042773841220707409192998547437771016605658235893114669678616789827594953844224 +def node15907 : Tree Nat := .node node15906 node12485 +def node15908 : Tree Nat := .node node15907 node12125 +def node15909 : Tree Nat := .node node12842 node15908 +def node15910 : Tree Nat := .node node15909 node12492 +def node15911 : Tree Nat := .node node15905 node15910 +def node15912 : Tree Nat := .node node15900 node15911 +def node15913 : Tree Nat := .leaf 283643277890613250014677865784561483857905853082136702046805262254182280701243752955855366446148918881911502969600561320411476547979603227073040833382328236822207475847558440950639641282220154193479981076238209216456362581714423390629289341939646589219726061105148459997565893632 +def node15914 : Tree Nat := .node node15913 node8379 +def node15915 : Tree Nat := .node node15914 node12497 +def node15916 : Tree Nat := .node node12133 node15915 +def node15917 : Tree Nat := .leaf 2015283703367863641175612582842135243135427334428804184044917736999987313807108150565911635556546346523345380614602125841597130118896386972313426398027841474588819376338583724719707300743287993989450409677767732102326912414881658939979860530403092029755512693246976 +def node15918 : Tree Nat := .node node15917 node8813 +def node15919 : Tree Nat := .node node15918 node12501 +def node15920 : Tree Nat := .node node11789 node15919 +def node15921 : Tree Nat := .node node15916 node15920 +def node15922 : Tree Nat := .leaf 458222462695599379270700543123871994649449568634787237553785692458956873621225886870553307957608580009943860019247018891462005627023356501188818290934836322569399535488067688630195034913453168840592715690824556476822514847488547419421667465910550196224 +def node15923 : Tree Nat := .node node15922 node8818 +def node15924 : Tree Nat := .node node15923 node10368 +def node15925 : Tree Nat := .node node12138 node15924 +def node15926 : Tree Nat := .leaf 1107981558387760942830140904192515176764684170790743560240691579143294954658590196057951125313214331030318954809116471499687287287690457532539459518380235155521894401023667028579881444629019050060714429168025280959464204795678062997074192893326579090727396734642133361882693632 +def node15927 : Tree Nat := .node node15926 node12143 +def node15928 : Tree Nat := .node node15927 node12146 +def node15929 : Tree Nat := .node node12142 node15928 +def node15930 : Tree Nat := .node node15925 node15929 +def node15931 : Tree Nat := .node node15921 node15930 +def node15932 : Tree Nat := .leaf 4431655730240891554958517924192519684687878034743431748512838054233017519724116556497029208100791724671306971600548206838322532830481508765730016774281941628748368818184632968163741568589071346353065816477416083649497738101932844987463100804754778999231534631958672047386446848 +def node15933 : Tree Nat := .node node15932 node8394 +def node15934 : Tree Nat := .node node15933 node11087 +def node15935 : Tree Nat := .node node10068 node15934 +def node15936 : Tree Nat := .node node15935 node15450 +def node15937 : Tree Nat := .leaf 4030813428063123713241925966829309394790689640201612525370761949391183939859747812182186044419930897170529387685830214650633247740765720507772967161817931183987938137752371231085266732908233263648115328450325851391844170868786032427407194973395756934590010185805824 +def node15938 : Tree Nat := .node node15937 node8833 +def node15939 : Tree Nat := .node node15938 node12512 +def node15940 : Tree Nat := .node node12158 node15939 +def node15941 : Tree Nat := .node node15940 node15459 +def node15942 : Tree Nat := .node node15936 node15941 +def node15943 : Tree Nat := .node node15931 node15942 +def node15944 : Tree Nat := .node node15912 node15943 +def node15945 : Tree Nat := .leaf 1198036083490401393367579651265226826447551684806266405050177285577599119244146985902642702006115259118211024345733452994278184583505467413569113800193756188290643590377137379284513828431607831581547358582258322655695703755347517664958502308932540295495159143174999173954714080613888 +def node15946 : Tree Nat := .node node15945 node8411 +def node15947 : Tree Nat := .node node15946 node8847 +def node15948 : Tree Nat := .node node10081 node15947 +def node15949 : Tree Nat := .leaf 86858970270951006203423855072102656460075033079962996877051994964653741302137818362668210673376734255262629815505365774508716439973468502811003368742444224057009434363015336735822904723705894560586863693915125274274477120096574897905627747118185731007597765066494746401152382168302126670333870080 +def node15950 : Tree Nat := .node node15949 node8850 +def node15951 : Tree Nat := .node node15950 node11472 +def node15952 : Tree Nat := .node node11470 node15951 +def node15953 : Tree Nat := .node node15948 node15952 +def node15954 : Tree Nat := .leaf 320581849719014369851178137743436701178506246591090859718713010008312172991748699110784331942945198280728884274986570748267072288973338699541567950828554432554692789441234172178557417016446149435759617969226823590003219476061963556252792851943641430959167782859698922523841530458130476732228864 +def node15955 : Tree Nat := .node node15954 node8419 +def node15956 : Tree Nat := .node node15955 node12168 +def node15957 : Tree Nat := .node node12521 node15956 +def node15958 : Tree Nat := .leaf 305135869619641084486162424651110383869718645522469604968743010747230248252956617307275616394980296121743864037225153336928689676382704523946985498325552303829378270224098878581985424976542026122599520767457843754245908555133220256737780827308403409506002902135856008850597031959523797504 +def node15959 : Tree Nat := .node node15958 node11476 +def node15960 : Tree Nat := .node node15959 node8427 +def node15961 : Tree Nat := .node node8425 node15960 +def node15962 : Tree Nat := .node node15957 node15961 +def node15963 : Tree Nat := .node node15953 node15962 +def node15964 : Tree Nat := .leaf 38067632857031246415885002001632223813615570301801070128684750548399109989769679527899463472626505266287795056803598797868616483536065614401633226438186336734834791344864042225461400528055185128350660905172557216952194119098883491844603698266663219024030878467112531945377909573175368192 +def node15965 : Tree Nat := .node node15964 node8862 +def node15966 : Tree Nat := .node node15965 node11822 +def node15967 : Tree Nat := .node node11489 node15966 +def node15968 : Tree Nat := .node node15482 node15967 +def node15969 : Tree Nat := .leaf 18587711355972288284975781226873757001640752520743225651718501396622631603771447833478727204790010483823511167263664615566301359165240480792509499609259408371964777090507306142751536757306051796984796054875428982112500710295668995489648455262125754453023403382073781208033379435832832 +def node15970 : Tree Nat := .node node15969 node8869 +def node15971 : Tree Nat := .node node15970 node12531 +def node15972 : Tree Nat := .node node11494 node15971 +def node15973 : Tree Nat := .node node15972 node12176 +def node15974 : Tree Nat := .node node15968 node15973 +def node15975 : Tree Nat := .node node15963 node15974 +def node15976 : Tree Nat := .leaf 80145462429753876071449058067539959615492165304445389803802350128312682632115199919547542808458552485133436462876592083578111601942993950246139019371077837862928277317478137391516676869155110283382629097578353028324116900571506313374000463715189702702963485242644067359458279705894464767050496 +def node15977 : Tree Nat := .node node15976 node8448 +def node15978 : Tree Nat := .node node15977 node12538 +def node15979 : Tree Nat := .node node11835 node15978 +def node15980 : Tree Nat := .leaf 19070991851227567780385655359698316649593705989427444620245069009852873381868266799619284790372586035931953043264916602036015811242692424101144922961027315228663967820052995296207436841980435124719137340434492734512230040603641181122026920003354910797765251926331371833947637159613746176 +def node15981 : Tree Nat := .node node15980 node8884 +def node15982 : Tree Nat := .node node15981 node11504 +def node15983 : Tree Nat := .node node12182 node15982 +def node15984 : Tree Nat := .node node15979 node15983 +def node15985 : Tree Nat := .leaf 4792144333961605573470318597553963255063876008477996300370403389636648170823347905178884238744877064373963623128450946930029144388218926435073442435892868418179644709758725002873007932566054439467362309961958631468159637070932485346040065811041868134611649786829617390916544412061440 +def node15986 : Tree Nat := .node node15985 node8889 +def node15987 : Tree Nat := .node node15986 node12186 +def node15988 : Tree Nat := .node node11840 node15987 +def node15989 : Tree Nat := .leaf 347435881083804024814803334220970722527786973912851820402540955898545781733999056101157749247908161008134016039537502944435666035064749386399998441797392771848179868284942462986187948061976405886356433544859807940879938752655779635304537230482169732467133110363112161403008736763068648722948292608 +def node15990 : Tree Nat := .node node15989 node12542 +def node15991 : Tree Nat := .node node15990 node10091 +def node15992 : Tree Nat := .node node12191 node15991 +def node15993 : Tree Nat := .node node15988 node15992 +def node15994 : Tree Nat := .node node15984 node15993 +def node15995 : Tree Nat := .leaf 1277342670759226379459618713038801433309141356030997247946898192899925766379565674127230381674402456702066764478287151177834695847353345864705808981000982022294516800817410391884805224753003751491367266159993530315518133064644183955203404335883725805745255399348835560792375830224907581210496768 +def node15996 : Tree Nat := .node node15995 node8900 +def node15997 : Tree Nat := .node node15996 node12552 +def node15998 : Tree Nat := .node node12550 node15997 +def node15999 : Tree Nat := .node node15998 node15517 +def node16000 : Tree Nat := .node node15509 node15999 +def node16001 : Tree Nat := .node node15994 node16000 +def node16002 : Tree Nat := .node node15975 node16001 +def node16003 : Tree Nat := .node node15944 node16002 +def node16004 : Tree Nat := .leaf 36304123742133375556593330216254635448529824738232755544798166470840175999708721578904841561045707223547331447573116493987676080099489762079526688465742617051059686949414111916743214001370157193444590092300222442477465978254378215089528530034380625561970890914611440301754749785600 +def node16005 : Tree Nat := .node node16004 node6448 +def node16006 : Tree Nat := .node node16005 node10424 +def node16007 : Tree Nat := .node node10107 node16006 +def node16008 : Tree Nat := .leaf 168608589349493129689007370639145679328475451375828544365186099553689494036883841479485775140248452449316646342219284592297125119785504778224143604134750429935383945143010563343751896006583398766903577327053596760575599019580224137171405783777850303761943114375155720746316295134377703159381557248 +def node16009 : Tree Nat := .node node16008 node7222 +def node16010 : Tree Nat := .node node16009 node11528 +def node16011 : Tree Nat := .node node11525 node16010 +def node16012 : Tree Nat := .node node16007 node16011 +def node16013 : Tree Nat := .leaf 321829249912473569698841060683512238743863977639841730821896205087490761579911405576852714278273213190902625221903378515520480674320762818502164698434406991931507555086017992240497245672112864939549760334153607259626143492659111193902182345213347311544297416327779637855085842612346017721375232 +def node16014 : Tree Nat := .node node16013 node6826 +def node16015 : Tree Nat := .node node16014 node11857 +def node16016 : Tree Nat := .node node10430 node16015 +def node16017 : Tree Nat := .leaf 305730676383032197711281649742622710886123306029018948514789131956404418557559103720115635773235060747259599399061594014791323166637421633866832494558378484389201792729116226527022526877036706868578268285617231963379292362734118411538475411010597908721644989533951341036811400062865287680 +def node16018 : Tree Nat := .node node16017 node11144 +def node16019 : Tree Nat := .node node16018 node9798 +def node16020 : Tree Nat := .node node10112 node16019 +def node16021 : Tree Nat := .node node16016 node16020 +def node16022 : Tree Nat := .node node16012 node16021 +def node16023 : Tree Nat := .leaf 18587711355972288284975781226873757001968818837352647350870557986455799863666490334346399486524190534377855592648125149770243870249075555782525321476587385800403389651760140510028823946839839026858822414683399956564945968816394079324657560496599989676873802291601975167909902857889280 +def node16024 : Tree Nat := .node node16023 node6845 +def node16025 : Tree Nat := .node node16024 node12210 +def node16026 : Tree Nat := .node node12562 node16025 +def node16027 : Tree Nat := .node node16026 node12216 +def node16028 : Tree Nat := .node node15546 node16027 +def node16029 : Tree Nat := .node node16022 node16028 +def node16030 : Tree Nat := .leaf 159979074811142668546359544187140243095870181888438343777712106088665082971649375941657643092694452239109831650513805372464594245910280373657033727872475431581151860597554608512690956133263623746908073937682168710203303256699235009553287144350312938795228418221899520190354595071012587288576768 +def node16031 : Tree Nat := .node node16030 node10117 +def node16032 : Tree Nat := .node node16031 node12571 +def node16033 : Tree Nat := .node node12569 node16032 +def node16034 : Tree Nat := .leaf 37175422711944576571966846157115377644457117624326996718013592867814909517272922286185664988388014749487763284464212951581185869535528225616421236333691037837639582858145933827816823410283757743028127523647706799162808818974767376962307489352155730626248364595109909085419069805441792 +def node16035 : Tree Nat := .node node16034 node7242 +def node16036 : Tree Nat := .node node16035 node11550 +def node16037 : Tree Nat := .node node11548 node16036 +def node16038 : Tree Nat := .node node16033 node16037 +def node16039 : Tree Nat := .leaf 4937360828930139075696691888388799926023520487701478865376741373629608662796539933774245454917978089692928140163967627831981720434596281774426184167991018902631553533184689571821721422143877515176952153133825397519142875302269959852019569089849712476168251648460228800171301339328512 +def node16040 : Tree Nat := .node node16039 node9814 +def node16041 : Tree Nat := .node node16040 node11874 +def node16042 : Tree Nat := .node node11871 node16041 +def node16043 : Tree Nat := .leaf 367873285853439555685610633836187838146021615475490322990048405543651321891992667948261925888600143919551767681518798827181782044677283479618434891298718457261657923690312443935063665151878498080164711223195276438827818581535311720726281039688927540343464239511571939491582923052066174564253171712 +def node16044 : Tree Nat := .node node16043 node12220 +def node16045 : Tree Nat := .node node16044 node8508 +def node16046 : Tree Nat := .node node11880 node16045 +def node16047 : Tree Nat := .node node16042 node16046 +def node16048 : Tree Nat := .node node16038 node16047 +def node16049 : Tree Nat := .leaf 9979201548254482764779314758551797333377657607589645466278789269191439941138434998850806305110717868052348657688772668052024271582932608659520322893756006366377553544096145156752882258833439273301207230032973301302879603556532748718549971037523235614420732134784917504954351351899266858824448 +def node16050 : Tree Nat := .node node16049 node9824 +def node16051 : Tree Nat := .node node16050 node11169 +def node16052 : Tree Nat := .node node10464 node16051 +def node16053 : Tree Nat := .node node16052 node15571 +def node16054 : Tree Nat := .leaf 4872657005699999540259241245240973667291905395814643084768429866980727262314109224026506796198229488300646966480241385282207567610557752470355299741350592966153231773981885211324317330692027804047496505443737509413441810170561012313167034244245752298773442405387549218493939977574807441152 +def node16055 : Tree Nat := .node node16054 node10467 +def node16056 : Tree Nat := .node node16055 node12577 +def node16057 : Tree Nat := .node node11562 node16056 +def node16058 : Tree Nat := .node node16057 node15218 +def node16059 : Tree Nat := .node node16053 node16058 +def node16060 : Tree Nat := .node node16048 node16059 +def node16061 : Tree Nat := .node node16029 node16060 +def node16062 : Tree Nat := .leaf 1876879207201175057492789423877314215327939898387375884169474870502860978765784336930206112079436550270860393628350024597747725226500572063392282468743636038950886557147809735224739635004839180741730677591410009275113150803953669471033348950135716202703104 +def node16063 : Tree Nat := .node node16062 node11892 +def node16064 : Tree Nat := .node node16063 node8954 +def node16065 : Tree Nat := .node node12590 node16064 +def node16066 : Tree Nat := .leaf 138506147510999777305574373364975816441292018417410920865487985351827735699665376932981738416259212059679620397251261593215758625022868726690530781997918240985190917710777707724653272459907877070949646088602693260551667422718651766648750303044992832772910454574507263438028800 +def node16067 : Tree Nat := .node node16066 node10475 +def node16068 : Tree Nat := .node node16067 node12593 +def node16069 : Tree Nat := .node node11570 node16068 +def node16070 : Tree Nat := .node node16065 node16069 +def node16071 : Tree Nat := .leaf 103871157920704432967641989456220183081475725167332493252509821217381419072046700733167024935993547548208348354892726155324562415029887282403765280599004360065908947055054379457626476372700462469636885672071002275879414518125491300792954870202360279272213333461755820030010624 +def node16072 : Tree Nat := .node node16071 node11576 +def node16073 : Tree Nat := .node node16072 node12235 +def node16074 : Tree Nat := .node node10482 node16073 +def node16075 : Tree Nat := .leaf 30750788930784052141961861970504689739397275047921209349403118777696498022815340237597396112027965694609395931384730620639011347459380505210842742334900307255484336942076785637243008310811967477441788683840008739935072404748504667915101921622143506128333482496 +def node16076 : Tree Nat := .node node16075 node11897 +def node16077 : Tree Nat := .node node16076 node12239 +def node16078 : Tree Nat := .node node11185 node16077 +def node16079 : Tree Nat := .node node16074 node16078 +def node16080 : Tree Nat := .node node16070 node16079 +def node16081 : Tree Nat := .leaf 328066316610216588415314552807964537262143591100497073697173014966005748497378353601285371424615585315656239313141745200509768301112532481176017543474840661804733668985092256805107923262226340156148990689594905269799690288352577079673826999625216 +def node16082 : Tree Nat := .node node16081 node11588 +def node16083 : Tree Nat := .node node16082 node12608 +def node16084 : Tree Nat := .node node12251 node16083 +def node16085 : Tree Nat := .node node16084 node11920 +def node16086 : Tree Nat := .node node15604 node16085 +def node16087 : Tree Nat := .node node16080 node16086 +def node16088 : Tree Nat := .leaf 283634622313015123276723072280655914093900969770949392756884202324714577615256130116354599314540294468360080135652884308982112149322058006643426796762145445758697354615365924728917070401536044414114247651429574159203569134946297753399136369096163915747063989681893381278538480640 +def node16089 : Tree Nat := .node node16088 node9868 +def node16090 : Tree Nat := .node node16089 node12618 +def node16091 : Tree Nat := .node node12616 node16090 +def node16092 : Tree Nat := .leaf 503820925841965910293903145710682853278783176422042742899963128541361843967736281426486623972601385858016918418154649481542774648138358003450475254622750023709224053663492643931633858180057215143936811218906687177777024414877715726303519698788088641338257767936768 +def node16093 : Tree Nat := .node node16092 node10500 +def node16094 : Tree Nat := .node node16093 node12622 +def node16095 : Tree Nat := .node node11206 node16094 +def node16096 : Tree Nat := .node node16091 node16095 +def node16097 : Tree Nat := .leaf 572778078369499224088375678951108638011287396263498246212912731873199370040242704047960348901452279432650510537684642701327072855739527439910133908972574878476023061713158498156345459193071290060158406523837032661197704351517348574111432879451639451392 +def node16098 : Tree Nat := .node node16097 node10188 +def node16099 : Tree Nat := .node node16098 node12263 +def node16100 : Tree Nat := .node node12261 node16099 +def node16101 : Tree Nat := .leaf 1661938524667872287252383644589176027186111169451885396359478913979978322601061551964130142273265097067348943118577065336057821568279057890991391009626043430196809898537604938640967822876984161455523102910209403747888259591217102192874191283611692638433133902441012528390209536 +def node16102 : Tree Nat := .node node16101 node7290 +def node16103 : Tree Nat := .node node16102 node12267 +def node16104 : Tree Nat := .node node11926 node16103 +def node16105 : Tree Nat := .node node16100 node16104 +def node16106 : Tree Nat := .node node16096 node16105 +def node16107 : Tree Nat := .leaf 17726623317192522754140549158418979263184069864981831318505489715867944436854711343765664646241917125560356311639853291743038061518073935769718431711107878473957242206493182421600016511693532842028143987029637869552293174943460611929706170715871327373634561451891715061799177216 +def node16108 : Tree Nat := .node node16107 node10198 +def node16109 : Tree Nat := .node node16108 node11214 +def node16110 : Tree Nat := .node node10515 node16109 +def node16111 : Tree Nat := .node node16110 node15629 +def node16112 : Tree Nat := .leaf 82550051303375757866266333319224646120472677037689926089137856179700740449825559412628927086290499179875529093630256962323453597289644201055259969896105558970816373146641828475469716120619012192398007584975782541249079071209324898962355318681124604744452772285593415680 +def node16113 : Tree Nat := .node node16112 node10518 +def node16114 : Tree Nat := .node node16113 node12636 +def node16115 : Tree Nat := .node node12634 node16114 +def node16116 : Tree Nat := .node node16115 node15255 +def node16117 : Tree Nat := .node node16111 node16116 +def node16118 : Tree Nat := .node node16106 node16117 +def node16119 : Tree Nat := .node node16087 node16118 +def node16120 : Tree Nat := .node node16061 node16119 +def node16121 : Tree Nat := .node node16003 node16120 +def node16122 : Tree Nat := .leaf 1234340207232534768924172979604602254694906452051709736717661236720499396856479823312072673064313023826869397166438236298454060731533191086823068140770934644458355762488299681873776192290895614582570657700674972609485084754627500887871462710074252754241652757233882326974589371717120 +def node16123 : Tree Nat := .node node16122 node8565 +def node16124 : Tree Nat := .node node16123 node12649 +def node16125 : Tree Nat := .node node12647 node16124 +def node16126 : Tree Nat := .leaf 91968321463359888921264160764248520901693728454223867408976697530058909712718880543702709877347748058029444224913451643246568408278924313354471624044849874098180954854703201746047163932918788208763743708065055207447186553347997703707079401123587086065747195489384140262741764019842861008235003904 +def node16127 : Tree Nat := .node node16126 node8991 +def node16128 : Tree Nat := .node node16127 node11609 +def node16129 : Tree Nat := .node node12654 node16128 +def node16130 : Tree Nat := .node node16125 node16129 +def node16131 : Tree Nat := .leaf 639916299244569539716195659038140798213018549833338757325734704109343098077264615040242689819413690379176985217777024324731224163349308444882234863194358943991286551420629921602244883639028241680122933284548339338686771338577936948204367125262767847114957507810847867848187022444257018429613312 +def node16132 : Tree Nat := .node node16131 node8998 +def node16133 : Tree Nat := .node node16132 node11938 +def node16134 : Tree Nat := .node node11936 node16133 +def node16135 : Tree Nat := .leaf 1218759058188390998269292023606661654806717069847887146399867278529405275264427195719880759545804304101967555896261676886424823492438047955917613318530515699545201364490336796906229484356152314604911274500985602075803950050453729252612533074771487011241114548878418204838805902705857418496 +def node16136 : Tree Nat := .node node16135 node11616 +def node16137 : Tree Nat := .node node16136 node8574 +def node16138 : Tree Nat := .node node11615 node16137 +def node16139 : Tree Nat := .node node16134 node16138 +def node16140 : Tree Nat := .node node16130 node16139 +def node16141 : Tree Nat := .node node16140 node15670 +def node16142 : Tree Nat := .leaf 80457312478118676042019838009420831417666409592218476120932000795453653549543201789048814874824014071128861156554232775567411193694505842554118000594784680609839280817757971073064027090492367252390205229186491675511254713281884044423324842059883482939239701750923932350611671373208153599917056 +def node16143 : Tree Nat := .node node16142 node8601 +def node16144 : Tree Nat := .node node16143 node9023 +def node16145 : Tree Nat := .node node12295 node16144 +def node16146 : Tree Nat := .leaf 19182518119363401510097021509837085089334432213989030557701434505264689708377241855498476855145954111770111954854095209563557026935935466520471618745086336146561595488960429213875420354710139475132313384661078979356922858008936953354210415124254137317481253273829360629194275459973565440 +def node16147 : Tree Nat := .node node16146 node9026 +def node16148 : Tree Nat := .node node16147 node11634 +def node16149 : Tree Nat := .node node11946 node16148 +def node16150 : Tree Nat := .node node16145 node16149 +def node16151 : Tree Nat := .leaf 9439072172954677644714263904272287949858390238818786309783863213355600886621982861498876094505951416954898865501662226944362434379339611687974298469102806801497935933991435433457188866267466175534263836287426204258312777194053598128519555797389324060648675195922210642964387973165056 +def node16152 : Tree Nat := .node node16151 node9031 +def node16153 : Tree Nat := .node node16152 node11951 +def node16154 : Tree Nat := .node node10904 node16153 +def node16155 : Tree Nat := .leaf 674434357397972518756583405714076360532765513570938988024973951631075993392038309900516366401742962540111491966369466783792520675233803475905907062666088325316376578047488311893691796978282986986907907526237584177975282210757492048945361380601186179839401002919744520359188208904187481303819812864 +def node16156 : Tree Nat := .node node16155 node12301 +def node16157 : Tree Nat := .node node16156 node6951 +def node16158 : Tree Nat := .node node12300 node16157 +def node16159 : Tree Nat := .node node16154 node16158 +def node16160 : Tree Nat := .node node16150 node16159 +def node16161 : Tree Nat := .leaf 5028582029882417252085662504666351308961291589362177869422718837401196262316696170647218445302080878516641383971116636741434532125040313010706602581296181407107246058610174800015299465110872488621426941693528604586620930323799419315948567893667467692294319085592521929525561693460730171149312 +def node16162 : Tree Nat := .node node16161 node8616 +def node16163 : Tree Nat := .node node16162 node9038 +def node16164 : Tree Nat := .node node10252 node16163 +def node16165 : Tree Nat := .node node16164 node15694 +def node16166 : Tree Nat := .leaf 1277347543416232079459158972276015860847237549185868434051496441802900398279332828292926526300255555949158674279129606829600184238768471853684004986678643732395389681560390298573059068985790148143347434039646647329563421256281055845043610992382969630278225500983674635316998427599741391230529536 +def node16167 : Tree Nat := .node node16166 node9042 +def node16168 : Tree Nat := .node node16167 node12316 +def node16169 : Tree Nat := .node node12314 node16168 +def node16170 : Tree Nat := .node node16169 node15703 +def node16171 : Tree Nat := .node node16165 node16170 +def node16172 : Tree Nat := .node node16160 node16171 +def node16173 : Tree Nat := .node node16141 node16172 +def node16174 : Tree Nat := .leaf 1876879207201175057492789423877314215327939898387375884169474870502860978765784653435829173500687026202623428687058140525358871863128120843354685043444001656462955056300343255306513494672154697162920397584845390090680863282789465971007209151093004877129984 +def node16175 : Tree Nat := .node node16174 node6587 +def node16176 : Tree Nat := .node node16175 node12667 +def node16177 : Tree Nat := .node node10265 node16176 +def node16178 : Tree Nat := .leaf 277003841793557267097168894248083178952879944879203335667900276184343031383179367575492105878027104966591346623778090329673862026836604618292157278435841836349453398396271984426783083666612932940704068881232489923812396038606986411367945120156415441639344033775206113315913728 +def node16179 : Tree Nat := .node node16178 node10568 +def node16180 : Tree Nat := .node node16179 node12671 +def node16181 : Tree Nat := .node node11279 node16180 +def node16182 : Tree Nat := .node node16177 node16181 +def node16183 : Tree Nat := .leaf 69250960706322019965487461894624202254605692908910802021772759738469119286480965660647788501275844179364479095364115819767550501016916097811261803997816932044446751269425558179327280511238525184397664836684697635030331528091294175748782767437029879526057677137490172869302784 +def node16184 : Tree Nat := .node node16183 node6975 +def node16185 : Tree Nat := .node node16184 node11980 +def node16186 : Tree Nat := .node node12677 node16185 +def node16187 : Tree Nat := .leaf 30750788930784052141961861995338914692410568473752894934917808572774662055969367511751005521617010619520058847149332153454850618945040020528681517242666993818554508032144444892346630981248124960560671257141804514723510557601984659112383974551123516027664618752 +def node16188 : Tree Nat := .node node16187 node11658 +def node16189 : Tree Nat := .node node16188 node12328 +def node16190 : Tree Nat := .node node11985 node16189 +def node16191 : Tree Nat := .node node16186 node16190 +def node16192 : Tree Nat := .node node16182 node16191 +def node16193 : Tree Nat := .leaf 328066310098483743806081863276859272885918271738652077362471948065628131252260731469842068959611828698443300746421511357201397607363354576361582766713440683563226163845788374251948569394137811812764782616948361201319353353488795615705110317275392 +def node16194 : Tree Nat := .node node16193 node6986 +def node16195 : Tree Nat := .node node16194 node12687 +def node16196 : Tree Nat := .node node10276 node16195 +def node16197 : Tree Nat := .node node16196 node11298 +def node16198 : Tree Nat := .node node15731 node16197 +def node16199 : Tree Nat := .node node16192 node16198 +def node16200 : Tree Nat := .leaf 283643278418907781151784526041794158700138507759551746524989654461871067364401331910971090702611875193864749495213352177440357189250986424078546951418425007782507602145792443268392938941070347843073587187272522997013236081164657686858632550674833373119022921812967578351652422400 +def node16201 : Tree Nat := .node node16200 node8646 +def node16202 : Tree Nat := .node node16201 node11303 +def node16203 : Tree Nat := .node node11998 node16202 +def node16204 : Tree Nat := .leaf 503820925841965910293903145710583493637006880564327892725666673368473246240567669475682331965830337295825516643365077050698154983276961779567218810656887746879525237262509113242106442294175782280918176043445842906969894498972178260802680552944530738404896695962624 +def node16205 : Tree Nat := .node node16204 node9076 +def node16206 : Tree Nat := .node node16205 node12694 +def node16207 : Tree Nat := .node node12342 node16206 +def node16208 : Tree Nat := .node node16203 node16207 +def node16209 : Tree Nat := .leaf 572778078369499224088375678951108638011287396263498246212912731873199370035177382255283709682437835634641780101466109729074250210707569173879701634194144553562193611367367154112655929371151544839219683199096179746380356380370460181426817669535310155520 +def node16210 : Tree Nat := .node node16209 node9081 +def node16211 : Tree Nat := .node node16210 node10952 +def node16212 : Tree Nat := .node node10288 node16211 +def node16213 : Tree Nat := .leaf 1108015369237753648468999152026789367051821523487238606513379131058299573411240897916576143329052619121656480317090501211563873330997541281995080725260223565828303026652733289355577765116041058261211655287943805334963986081625270745527088326337942863499248460678309774246608896 +def node16214 : Tree Nat := .node node16213 node12698 +def node16215 : Tree Nat := .node node16214 node12349 +def node16216 : Tree Nat := .node node12347 node16215 +def node16217 : Tree Nat := .node node16212 node16216 +def node16218 : Tree Nat := .node node16208 node16217 +def node16219 : Tree Nat := .leaf 17726623317184462111339700596510974975043981865637890431941819991492978398073651486297814227183458808482570803735048371561536032380568511814938137649734636759316143543035380268396155389180356469233915141236630835099926098760408135137985764707402330428430010717435194054124778240 +def node16220 : Tree Nat := .node node16219 node8665 +def node16221 : Tree Nat := .node node16220 node12003 +def node16222 : Tree Nat := .node node10602 node16221 +def node16223 : Tree Nat := .node node16222 node15756 +def node16224 : Tree Nat := .leaf 82550051303379511853805951710397014553128718433714785747036337871292787170586656322982482491632294973479235266719337616382249691311467575086402091638907849777845591832932426079294311807701327646771580403886450587632960939314814242474576269507291736533643366175609982720 +def node16225 : Tree Nat := .node node16224 node9092 +def node16226 : Tree Nat := .node node16225 node12361 +def node16227 : Tree Nat := .node node12711 node16226 +def node16228 : Tree Nat := .node node16227 node15329 +def node16229 : Tree Nat := .node node16223 node16228 +def node16230 : Tree Nat := .node node16218 node16229 +def node16231 : Tree Nat := .node node16199 node16230 +def node16232 : Tree Nat := .node node16173 node16231 +def node16233 : Tree Nat := .leaf 7507516828804700229971157695509256861311759593549503536677899755757880972394849515901343364365985950801683701262325212152781827059032641500487689114260514642007868025554270847457305519738607332039986713695744121956981549688306381885158789194867674064316672 +def node16234 : Tree Nat := .node node16233 node8685 +def node16235 : Tree Nat := .node node16234 node12719 +def node16236 : Tree Nat := .node node12371 node16235 +def node16237 : Tree Nat := .leaf 138514600739442064819554225804892750959167553921054582532030626686859106884657814402720344421511986720399311040041861592542179499014485091052866109081072711511122582215690927132199595253959696072583560043356561147409194147010364415790440073675443015704262255589038506732879872 +def node16238 : Tree Nat := .node node16237 node9109 +def node16239 : Tree Nat := .node node16238 node12723 +def node16240 : Tree Nat := .node node11328 node16239 +def node16241 : Tree Nat := .node node16236 node16240 +def node16242 : Tree Nat := .leaf 103873270711894506503921887883645492114871128527414554854564536274634581781627993823657756646034744246540114756127835730896541856423782792412092629459695560174653373947808913308246324447869429730525936829038295571684130980605739897567377539492384784473023182285925217198974208 +def node16243 : Tree Nat := .node node16242 node9114 +def node16244 : Tree Nat := .node node16243 node9386 +def node16245 : Tree Nat := .node node12376 node16244 +def node16246 : Tree Nat := .leaf 123003155723136208567847447757762727157858362300036053070918381768640018538479071747973947419781329792807376897294254872139477454661838415452013676426092302520617212340516705236702585458645947510310370218851727878807221889769832852543487137609045723697536587008 +def node16247 : Tree Nat := .node node16246 node11694 +def node16248 : Tree Nat := .node node16247 node12379 +def node16249 : Tree Nat := .node node12022 node16248 +def node16250 : Tree Nat := .node node16245 node16249 +def node16251 : Tree Nat := .node node16241 node16250 +def node16252 : Tree Nat := .leaf 33018408195979077897021236563951930273518967420703090466462869011412003998517677261041324952420614179230525477371447081687420289851702020134088385249771168050131437901624861739678464173964247070614830346447546024275945494027197063092954816121618296918546017869575333120 +def node16253 : Tree Nat := .node node16252 node9124 +def node16254 : Tree Nat := .node node16253 node12729 +def node16255 : Tree Nat := .node node10996 node16254 +def node16256 : Tree Nat := .node node15785 node16255 +def node16257 : Tree Nat := .leaf 6512527782388681036903055765541910557457266751526517405773499901145487483854386971262999111291943460952206371646323518448952693582007706508259287271459100846529946134631696242327676493768302855607596576495958850245410462729877467180931328 +def node16258 : Tree Nat := .node node16257 node9129 +def node16259 : Tree Nat := .node node16258 node12386 +def node16260 : Tree Nat := .node node12735 node16259 +def node16261 : Tree Nat := .node node16260 node9961 +def node16262 : Tree Nat := .node node16256 node16261 +def node16263 : Tree Nat := .node node16251 node16262 +def node16264 : Tree Nat := .leaf 283634622841309654410946846075627584047980981481559504184873625374825384399949975978596752148466753096961840327993144347550506992587388438197723883727097622412273857378479341085949989708606098522015344919209682390859411965361412536475509669969047981889933721079556253239841768192 +def node16265 : Tree Nat := .node node16264 node12890 +def node16266 : Tree Nat := .node node16265 node12741 +def node16267 : Tree Nat := .node node10319 node16266 +def node16268 : Tree Nat := .leaf 2015283703367863641175612582842035880461389139542819912243331976362067957714186995885280982378090800243353559511201380018829634088603550246890638859949784946289238785936636158901923437332511677288251053626796385796524085960173913050177248597779895771862581446193920 +def node16269 : Tree Nat := .node node16268 node9662 +def node16270 : Tree Nat := .node node16269 node12745 +def node16271 : Tree Nat := .node node12394 node16270 +def node16272 : Tree Nat := .node node16267 node16271 +def node16273 : Tree Nat := .leaf 458222462695599379270700543123871994649449568634787237553785692458956873616160555416532858945991377201836867441148170195558573062216139445308526177416737525191744567771048287292212730483947678322079072269394592781011921018616031896626113413335950422016 +def node16274 : Tree Nat := .node node16273 node9667 +def node16275 : Tree Nat := .node node16274 node12398 +def node16276 : Tree Nat := .node node12751 node16275 +def node16277 : Tree Nat := .leaf 1661972335517864946765058496247371151024608232318159158243041611330399707461433869860279395686963805313564244686044329480701635411827554157815426257490402081610923849131433893533730203718838714764780861501400487151645576232469872356136579077425331085149935928198021029769314304 +def node16278 : Tree Nat := .node node16277 node12404 +def node16279 : Tree Nat := .node node16278 node12407 +def node16280 : Tree Nat := .node node12403 node16279 +def node16281 : Tree Nat := .node node16276 node16280 +def node16282 : Tree Nat := .node node16272 node16281 +def node16283 : Tree Nat := .leaf 4431655730248953181784612271413933953304134938396191494673277373877431929876483373180273648636025879844366246298636919868423012012191586883845125411890565253029688435234695151012918516868763730993951907440132299497163809526781357714691398250775958897612005441954880845784494848 +def node16284 : Tree Nat := .node node16283 node9673 +def node16285 : Tree Nat := .node node16284 node9147 +def node16286 : Tree Nat := .node node12757 node16285 +def node16287 : Tree Nat := .node node16286 node15811 +def node16288 : Tree Nat := .leaf 4030813431817111252860317243391826678685872401357324873856846092916248681615897764660774200739995873970703687099826320302202388872588074518502278770755765407691970795186005232396609720726144673995466377688522887494181606663391614776120611763231244948834068695289600 +def node16289 : Tree Nat := .node node16288 node9678 +def node16290 : Tree Nat := .node node16289 node12414 +def node16291 : Tree Nat := .node node12903 node16290 +def node16292 : Tree Nat := .node node16291 node15367 +def node16293 : Tree Nat := .node node16287 node16292 +def node16294 : Tree Nat := .node node16282 node16293 +def node16295 : Tree Nat := .node node16263 node16294 +def node16296 : Tree Nat := .leaf 72608247484266751113186647294354820488834247026939543948396825646101063287786253971485042109138209939310136762061191251734725602782989249712320354093754784422209429767386913076704376794208714857230566077860048007696332615772109600005255156785816444103568406225638178054947250935296 +def node16297 : Tree Nat := .node node16296 node9427 +def node16298 : Tree Nat := .node node16297 node12773 +def node16299 : Tree Nat := .node node12915 node16298 +def node16300 : Tree Nat := .leaf 173717940541902012406847676332323369026218492934385312379329816468352381240471818175658245328242350468558562216802575374432101596036024629106059717728749395455321884553983649956647605951299217999891251870309232954865860110992144648677806038884915141307514943780731884499563536406974651059183747072 +def node16301 : Tree Nat := .node node16300 node9690 +def node16302 : Tree Nat := .node node16301 node12048 +def node16303 : Tree Nat := .node node11721 node16302 +def node16304 : Tree Nat := .node node16299 node16303 +def node16305 : Tree Nat := .leaf 641163699438028739563858581204347393685116642670654396617604737687019839928666055115562881198902884544718824061383988954481628271507931249190599375832024579194008952072869434224681219380968296695801404117047307216164053696179951153844542748611548843612418547758244490615330638040285033786202624 +def node16306 : Tree Nat := .node node16305 node9695 +def node16307 : Tree Nat := .node node16306 node12422 +def node16308 : Tree Nat := .node node12920 node16307 +def node16309 : Tree Nat := .leaf 1219353864951782111494411248513669248238417417502665318421077903855279956989564050735551866976950354581702495341829397899415679800851924268386114427334417743029687671278197284366790623923066113030176791987216727192839705523247046316418204478154179878832816732427309384019987066124012377344 +def node16310 : Tree Nat := .node node16309 node12059 +def node16311 : Tree Nat := .node node16310 node7055 +def node16312 : Tree Nat := .node node11726 node16311 +def node16313 : Tree Nat := .node node16308 node16312 +def node16314 : Tree Nat := .node node16304 node16313 +def node16315 : Tree Nat := .leaf 154649758481689438539253101856584427727906370118567238084748270901021092078182734293147463965937580752875886357848711297866988518893020261490349978236405582503212400249275461377075743636400698812447210413641010473289847709093629833325640271819964091533932298734041551430529030862378738944 +def node16316 : Tree Nat := .node node16315 node9709 +def node16317 : Tree Nat := .node node16316 node12066 +def node16318 : Tree Nat := .node node12930 node16317 +def node16319 : Tree Nat := .node node15839 node16318 +def node16320 : Tree Nat := .leaf 9516908214257811601907599988159363584840065290626637065715070485466724684480230615168836353289889240867614857752897159159707146180231707594858266516731878002541411855447359293646304658326342825870760880148607465322047043758441834879613018749654141977700836604640903734577181911294777600 +def node16321 : Tree Nat := .node node16320 node9714 +def node16322 : Tree Nat := .node node16321 node12428 +def node16323 : Tree Nat := .node node12935 node16322 +def node16324 : Tree Nat := .node node16323 node12940 +def node16325 : Tree Nat := .node node16319 node16324 +def node16326 : Tree Nat := .node node16314 node16325 +def node16327 : Tree Nat := .leaf 160290924859507468516930324129021112015157963915206541629635613409629834596615167543121362137325661374456303993408441278299084510560784992890997832189146057857650355658715847237801906446407145804914163188809757534813109940144447913072869095003893399282235464709347707025951819211947653020924928 +def node16328 : Tree Nat := .node node16327 node12077 +def node16329 : Tree Nat := .node node16328 node9463 +def node16330 : Tree Nat := .node node12787 node16329 +def node16331 : Tree Nat := .leaf 148701690847778306280310070740832021923419923311650029397698061862645982565585358253925509580443099392097636013688105336182136107955375250334397907065559024645080746168102231741355158349643324860381028535985745497510789676190761977422406295831342940429562348935606620736174507681657600 +def node16332 : Tree Nat := .node node16331 node11745 +def node16333 : Tree Nat := .node node16332 node12082 +def node16334 : Tree Nat := .node node12440 node16333 +def node16335 : Tree Nat := .node node16330 node16334 +def node16336 : Tree Nat := .leaf 9584288667923211146940637195107353732049382517731904225061855670635285054250432312111555564757880928329366418899311856207032251925730779607599448052880912888589921633567307600751807282409766907927673454416378187983629696994829149309972651850330967634371262741451008367458547465326336 +def node16337 : Tree Nat := .node node16336 node11750 +def node16338 : Tree Nat := .node node16337 node12794 +def node16339 : Tree Nat := .node node12792 node16338 +def node16340 : Tree Nat := .leaf 694871762167608049627390705329293476104873971737401413253044455803594006522622144716648826817629196121805066842921061081847755386838362440033472560287945929851418039768520659517635016041790978580944828275717231397011297981778336964830408667196040865909616336736894891681650876859965035669318074368 +def node16341 : Tree Nat := .node node16340 node11408 +def node16342 : Tree Nat := .node node16341 node9187 +def node16343 : Tree Nat := .node node12092 node16342 +def node16344 : Tree Nat := .node node16339 node16343 +def node16345 : Tree Nat := .node node16335 node16344 +def node16346 : Tree Nat := .leaf 9745314011399999080353386418688616373999954084214336243480581181749075305236811352556880397496424068338059063289457980579150277583177141174995817417620747900799580558513027735102944960288343180942768430769162246216499788704625474973376722414811901308418512877849759455384081639572855844864 +def node16347 : Tree Nat := .node node16346 node11764 +def node16348 : Tree Nat := .node node16347 node11423 +def node16349 : Tree Nat := .node node12801 node16348 +def node16350 : Tree Nat := .node node16349 node15398 +def node16351 : Tree Nat := .node node15870 node16350 +def node16352 : Tree Nat := .node node16345 node16351 +def node16353 : Tree Nat := .node node16326 node16352 +def node16354 : Tree Nat := .node node16295 node16353 +def node16355 : Tree Nat := .node node16232 node16354 +def node16356 : Tree Nat := .node node16121 node16355 +def node16357 : Tree Nat := .leaf 633320409419524696058622072638044630824823392368312804311809215019366671325932617742950984961340758007102050487495827528026408304619123615592079716381985515041317670559898405120 +def node16358 : Tree Nat := .node node16357 node12814 +def node16359 : Tree Nat := .node node16358 node8784 +def node16360 : Tree Nat := .node node15106 node16359 +def node16361 : Tree Nat := .leaf 276995389596940235707535226048128367438247350030898029637813481060091747400425041745682742520735129541708326702149823220131832958109758969285454767170181670318284047978201107822037655860347705053311834451875305991533780413858531778842414806154211813212784265083232127176933376 +def node16362 : Tree Nat := .node node16361 node12469 +def node16363 : Tree Nat := .node node16362 node12472 +def node16364 : Tree Nat := .node node12468 node16363 +def node16365 : Tree Nat := .node node16360 node16364 +def node16366 : Tree Nat := .leaf 69248847141263004335947925255763661409909846275538986389069994123860647911741353884081224340874612192298438187331782033861578200280295797827718428114089669550785873848973718145475538529353125417176787513604114148890546058677512571337182520775245525781802149297298484863457792 +def node16367 : Tree Nat := .node node16366 node9488 +def node16368 : Tree Nat := .node node16367 node9224 +def node16369 : Tree Nat := .node node15111 node16368 +def node16370 : Tree Nat := .leaf 49692708001218785428781649145413541659466268234700751836787325881622748439277051046870764872237697315262292677970435250793868909009767435371444123195878440313946094334073774340988300803516439901794490979796353204610756747076728564224 +def node16371 : Tree Nat := .node node16370 node11437 +def node16372 : Tree Nat := .node node16371 node12118 +def node16373 : Tree Nat := .node node9229 node16372 +def node16374 : Tree Nat := .node node16369 node16373 +def node16375 : Tree Nat := .node node16365 node16374 +def node16376 : Tree Nat := .leaf 64493014849009979411870815469268937895748230362798113679355545766722387992607317550459396725720908724824410637724480513911449855151349628353327852504636515470481406325353706266912512449357361787540242386280314093708421022406703902353663150116383014525139338431998464 +def node16377 : Tree Nat := .node node16376 node9498 +def node16378 : Tree Nat := .node node16377 node11444 +def node16379 : Tree Nat := .node node15120 node16378 +def node16380 : Tree Nat := .leaf 14322947932527751047429053908677542046243522775750225924563210287965780112730365776988633649349342819129105541181434874738669137554299981639814863023332895183872915634518640623502950915740192414835539856994264539360817829792557886758277588536293743104 +def node16381 : Tree Nat := .node node16380 node9504 +def node16382 : Tree Nat := .node node16381 node12478 +def node16383 : Tree Nat := .node node12837 node16382 +def node16384 : Tree Nat := .node node16379 node16383 +def node16385 : Tree Nat := .leaf 3580081700695792075461756276227152679124716205226901663331355548454952204852948264092209554482260588186324009538137783758471079098551499069672506652989587615142455892157915186154809010880204677763785718413073356250042903823065040684308182537190401536 +def node16386 : Tree Nat := .node node16385 node12485 +def node16387 : Tree Nat := .node node16386 node12125 +def node16388 : Tree Nat := .node node12842 node16387 +def node16389 : Tree Nat := .node node16388 node12492 +def node16390 : Tree Nat := .node node16384 node16389 +def node16391 : Tree Nat := .node node16375 node16390 +def node16392 : Tree Nat := .leaf 17312211785315751083986981313940915352477461568884746597267498530965161977935303434283333048616779145345367330696335499065165408569783465091670648626757363742846693062053765229839693820523244059810326357588648603273046692047608989799378672139108876930050972271986303016975360 +def node16393 : Tree Nat := .node node16392 node8379 +def node16394 : Tree Nat := .node node16393 node12497 +def node16395 : Tree Nat := .node node12133 node16394 +def node16396 : Tree Nat := .leaf 198725348076389771968543603171521275838712185842309361261306356911092559983642213027071411701098070559383765463464772911321410356377365871156810065554483349860722394246587466425767427340866033871269810464071216445672840628061624912896 +def node16397 : Tree Nat := .node node16396 node8813 +def node16398 : Tree Nat := .node node16397 node12501 +def node16399 : Tree Nat := .node node11789 node16398 +def node16400 : Tree Nat := .node node16395 node16399 +def node16401 : Tree Nat := .leaf 10130662908040898023234405616157824067310859012198384732756513621748289253309657688005317069155158717417442501865883285995264092373373886427189696116376164284068845000841898885120 +def node16402 : Tree Nat := .node node16401 node8818 +def node16403 : Tree Nat := .node node16402 node10368 +def node16404 : Tree Nat := .node node12138 node16403 +def node16405 : Tree Nat := .leaf 1107981558387760942830140904192513469752989353548049349529988455025863415586260412504839150722630730936924633772149391631210744044056113495196450252091071739084775399948614332105986439661142421974342242950386817946810541318071014106807776372629905062298287176221433976534466560 +def node16406 : Tree Nat := .node node16405 node12143 +def node16407 : Tree Nat := .node node16406 node12146 +def node16408 : Tree Nat := .node node12142 node16407 +def node16409 : Tree Nat := .node node16404 node16408 +def node16410 : Tree Nat := .node node16400 node16409 +def node16411 : Tree Nat := .leaf 16123253712252494852967703867317234473937057590699528419838886441680596998151829387614849181430227181206102659433538791868583087447834678023954428895461766505381212214853316878632273622029432376235217519927071141731158218219835493217617303526106070544289340158954496 +def node16412 : Tree Nat := .node node16411 node8394 +def node16413 : Tree Nat := .node node16412 node11087 +def node16414 : Tree Nat := .node node10068 node16413 +def node16415 : Tree Nat := .leaf 57278681880282598266741390408408596112073575910447173763636753717059752635395420171139352061563291484028000893808044834014647092972491880950235164154076640029659283582601381345411292020534570533648605409876205844863858127498877697184821250450299567104 +def node16416 : Tree Nat := .node node16415 node8828 +def node16417 : Tree Nat := .node node16416 node12507 +def node16418 : Tree Nat := .node node12153 node16417 +def node16419 : Tree Nat := .node node16414 node16418 +def node16420 : Tree Nat := .leaf 4030813428063123713241925966829308618484264397674882104959723178086729353553675105362301598821553113729194542623277030518159160441594819685932831234241570115697574993850468144479282639145253472308067846784631784683626892949261304304044152586233253000901172881584128 +def node16421 : Tree Nat := .node node16420 node8833 +def node16422 : Tree Nat := .node node16421 node12512 +def node16423 : Tree Nat := .node node12158 node16422 +def node16424 : Tree Nat := .node node16423 node15459 +def node16425 : Tree Nat := .node node16419 node16424 +def node16426 : Tree Nat := .node node16410 node16425 +def node16427 : Tree Nat := .node node16391 node16426 +def node16428 : Tree Nat := .leaf 1198036083490401393367579649388347619246376627313476981172863070249659220856771101733167831503252104811208426674986642294444401401820479136794286050646105846314692323651423195139642554940068010349550123008190826365428312189526134006837982787147931329149835509463700480977092053536768 +def node16429 : Tree Nat := .node node16428 node8411 +def node16430 : Tree Nat := .node node16429 node8847 +def node16431 : Tree Nat := .node node10081 node16430 +def node16432 : Tree Nat := .leaf 86858970270951006203423855072102656460075033079928037277542137834277158770596937168896873773783724123268871196802876876841083569032670399225393828017982601638223981522645532017355676722666710169115539570572481486567342864967287662626553320728317296509893378157477603427129189207747237890933653504 +def node16433 : Tree Nat := .node node16432 node8850 +def node16434 : Tree Nat := .node node16433 node11472 +def node16435 : Tree Nat := .node node11470 node16434 +def node16436 : Tree Nat := .node node16431 node16435 +def node16437 : Tree Nat := .leaf 320581849719014369851178137743436701178506246591090859718711420229785639715057344252499845075206122102899079473042629140084523879119736956268578261894594434294805578072693029141049835534802644531833670997456412613449175596863796385904572002478964510417212333564168596559462165692650025755124992 +def node16438 : Tree Nat := .node node16437 node8419 +def node16439 : Tree Nat := .node node16438 node12168 +def node16440 : Tree Nat := .node node12521 node16439 +def node16441 : Tree Nat := .leaf 305135869619641084486162424620359594938934593380507743047937093532849808170367399540702156499061065743248581914503417796562880801024700561438448184376983701893104868017108099234851475610997728034886881519200725522121296648069211773548558252463356174806379687445724356813655097737199266304 +def node16442 : Tree Nat := .node node16441 node11476 +def node16443 : Tree Nat := .node node16442 node8427 +def node16444 : Tree Nat := .node node8425 node16443 +def node16445 : Tree Nat := .node node16440 node16444 +def node16446 : Tree Nat := .node node16436 node16445 +def node16447 : Tree Nat := .leaf 20036365607438504475435763266179664944839502503052169823931230636317198595816592083828517751639789635728246922937169621421161514008906043953626163465459004235611603358947387948466662287340496774870624942883596612267027828650508043263407640940560897920265567581451862779801817083283654681711872 +def node16448 : Tree Nat := .node node16447 node8432 +def node16449 : Tree Nat := .node node16448 node11483 +def node16450 : Tree Nat := .node node12527 node16449 +def node16451 : Tree Nat := .leaf 38067632857031246407630399952637454346521735135414016041633293135079086413465465204855561186051413137468439753465636926044125567502528019380563067658778256029213659291008291880714233284073527419418061227625573229458457192756364565400202681883580214482774376770493351693335020251383486976 +def node16452 : Tree Nat := .node node16451 node8862 +def node16453 : Tree Nat := .node node16452 node11822 +def node16454 : Tree Nat := .node node11489 node16453 +def node16455 : Tree Nat := .node node16450 node16454 +def node16456 : Tree Nat := .node node16455 node15973 +def node16457 : Tree Nat := .node node16446 node16456 +def node16458 : Tree Nat := .leaf 80145462429753592445483379239605696021613362056902447328567523695806174698493707440746101246497742174501976488570323051873856885272013117298958342531649944849272773099939059638672051078349066421579063821215181565802799892795953758004939947711164052773844115868280937549484186518023181830243072 +def node16459 : Tree Nat := .node node16458 node8448 +def node16460 : Tree Nat := .node node16459 node12538 +def node16461 : Tree Nat := .node node11835 node16460 +def node16462 : Tree Nat := .leaf 19070991851227567780385151538772474683683412086281734136115622172116709172958156363359286751861621265688522904260182407276940792000913827888141674654318073998721638258605481312943479347981743273554201657277448671140995687082081324246017525292628319825533858427240015422440365556018236416 +def node16463 : Tree Nat := .node node16462 node8884 +def node16464 : Tree Nat := .node node16463 node11504 +def node16465 : Tree Nat := .node node12182 node16464 +def node16466 : Tree Nat := .node node16461 node16465 +def node16467 : Tree Nat := .leaf 4792144333961605573470318597553390476985506509253907924691452280998636883427084406932671326013003864472795518265713256884666418582428757287939010767309991225652635866143578428564201744736167124533614312609368491834666362915457626824746353481735522338985661966520095696445156714938368 +def node16468 : Tree Nat := .node node16467 node8889 +def node16469 : Tree Nat := .node node16468 node12186 +def node16470 : Tree Nat := .node node11840 node16469 +def node16471 : Tree Nat := .leaf 347435881083804024814803334218906946060306821052810417508159766761745804882280875273102226827888248936083528160005257575196131070966956850155739697122262977638668791146946346556308518344907669553243433058795196041440268869608547260686175161362779290582871576248128638085855655484195655433316859904 +def node16472 : Tree Nat := .node node16471 node12542 +def node16473 : Tree Nat := .node node16472 node10091 +def node16474 : Tree Nat := .node node12191 node16473 +def node16475 : Tree Nat := .node node16470 node16474 +def node16476 : Tree Nat := .node node16466 node16475 +def node16477 : Tree Nat := .leaf 4989600774417687667293717020135324452865067159677447525377718748283479748053451325955935617780394804517996033186631846649769193390066326077608715781818600220938702906670021951978129835635611934153999058911744600734246813204613427185006821560975455404631222751769248623646410330919852810449664 +def node16478 : Tree Nat := .node node16477 node8463 +def node16479 : Tree Nat := .node node16478 node11132 +def node16480 : Tree Nat := .node node10407 node16479 +def node16481 : Tree Nat := .leaf 609156476557923831675226302367106764515049860485047411633068038674350643026184220810784140679156588330752917761148029903926150076374943029456556742625583771758228048684848057895029266936542143193282573694787961016387873968802904505501939535781932269222062242118816015479598109591342955520 +def node16482 : Tree Nat := .node node16481 node9275 +def node16483 : Tree Nat := .node node16482 node10410 +def node16484 : Tree Nat := .node node12197 node16483 +def node16485 : Tree Nat := .node node16480 node16484 +def node16486 : Tree Nat := .leaf 1277342670759226379459618713038801433309141356030997247946898191929613803453369599535765655032555218537160258364064248287538951673502182956131671946980039658468884123879554075085229167228703477359881341331853015266106999511094988441708595573007812241063410744341837821463859806953649992218185472 +def node16487 : Tree Nat := .node node16486 node8900 +def node16488 : Tree Nat := .node node16487 node12552 +def node16489 : Tree Nat := .node node12550 node16488 +def node16490 : Tree Nat := .node node16489 node15517 +def node16491 : Tree Nat := .node node16485 node16490 +def node16492 : Tree Nat := .node node16476 node16491 +def node16493 : Tree Nat := .node node16457 node16492 +def node16494 : Tree Nat := .node node16427 node16493 +def node16495 : Tree Nat := .leaf 36304123742133375556593322708737806643829594767075060035541305159080582450205184901005085803129926169200892557854741037645132005491408029239060417698894726229932808805584063875163253276623840999331181865211074040260280385573597025842255779204929232644461791276753170896734650566144 +def node16496 : Tree Nat := .node node16495 node6448 +def node16497 : Tree Nat := .node node16496 node10424 +def node16498 : Tree Nat := .node node10107 node16497 +def node16499 : Tree Nat := .leaf 168608589349493129689007370639145679328475451375800576685578213849388303818198612145022179691838129546309865576645479118007197447144650713613320947882181379424802997444187452441878831697594775967051076912643668471505028351499905043319196199882470453708835554664565702800984844251329303797944221696 +def node16500 : Tree Nat := .node node16499 node7222 +def node16501 : Tree Nat := .node node16500 node11528 +def node16502 : Tree Nat := .node node11525 node16501 +def node16503 : Tree Nat := .node node16498 node16502 +def node16504 : Tree Nat := .leaf 321829249912473569698841060683512238743863977639841730821889845973384686308951860488009104364247495184154659323491366243995645372057682397923211604680776165239671106465866532076758474500299362969822108786475725555723304627235120083226409357505544436152023669960064091773901012392177052967524864 +def node16505 : Tree Nat := .node node16504 node6826 +def node16506 : Tree Nat := .node node16505 node11857 +def node16507 : Tree Nat := .node node10430 node16506 +def node16508 : Tree Nat := .leaf 305730676383032197711281649619619555162987097461171500831565466800374234185237070254957719903761473295873919318205498475935279008211177773978310160443893878050258827332884888046860020953119561813828519466929488936016037956422957340421436463449471608856981740248401892090614474012559976960 +def node16509 : Tree Nat := .node node16508 node11144 +def node16510 : Tree Nat := .node node16509 node9798 +def node16511 : Tree Nat := .node node10112 node16510 +def node16512 : Tree Nat := .node node16507 node16511 +def node16513 : Tree Nat := .node node16503 node16512 +def node16514 : Tree Nat := .leaf 20114328119529704468078590293038127197448026065989131875016535456804826053930252946719917781021309177774213344362491592898183944001706553591078596880905075223681269087141504206242993218731452191787318203707472130349525998708327604774777221223160288043168919968330738986300840773085972047178240 +def node16515 : Tree Nat := .node node16514 node6836 +def node16516 : Tree Nat := .node node16515 node10438 +def node16517 : Tree Nat := .node node10436 node16516 +def node16518 : Tree Nat := .leaf 40446859910595699308107299949677295249893225417664908266957200790243510697322615793257802392272378084480017450169202086657066401312665035407700214756498606720728778983058311791596925360009689440891266095765126564813280940023936290483927616646451933065270716115678800946552627515443468800 +def node16519 : Tree Nat := .node node16518 node7235 +def node16520 : Tree Nat := .node node16519 node11151 +def node16521 : Tree Nat := .node node11535 node16520 +def node16522 : Tree Nat := .node node16517 node16521 +def node16523 : Tree Nat := .node node16522 node16027 +def node16524 : Tree Nat := .node node16513 node16523 +def node16525 : Tree Nat := .leaf 159979074811142384920393865359205977580067070466892142351720115470478026267844164341669197810277492018653206590363533992360111760634793788416979207677242914232213427804269436392416282000137877846604908538918253318694159327391894717080595113515947219812553294682911354830054654850642370537898752 +def node16526 : Tree Nat := .node node16525 node10117 +def node16527 : Tree Nat := .node node16526 node12571 +def node16528 : Tree Nat := .node node12569 node16527 +def node16529 : Tree Nat := .leaf 37175422711944576569951562453747514003281505041485060200226241923158073876831176070461516386766748908283104850741982226928452036587344399387402133101306686121219317214807361707312090563592893900543999894156060391070317299909553546757877279347497124944322196387797759184079649777922816 +def node16530 : Tree Nat := .node node16529 node7242 +def node16531 : Tree Nat := .node node16530 node11550 +def node16532 : Tree Nat := .node node11548 node16531 +def node16533 : Tree Nat := .node node16528 node16532 +def node16534 : Tree Nat := .leaf 4937360828930139075696691888388341703560824888322208164833617501634959213227905146536691669225519132818798355493894991302233295277241100594597692229081450669237829524093917441357482725209350051592231269876587909159682706771625237344275646506314220303172893804442228238770245115445248 +def node16535 : Tree Nat := .node node16534 node9814 +def node16536 : Tree Nat := .node node16535 node11874 +def node16537 : Tree Nat := .node node11871 node16536 +def node16538 : Tree Nat := .leaf 367873285853439555685610633836187838146021615475490321283036710726408627681281964824144494349527814135998653479174007403750878621505743303904584865033352058263411311302676650013173807538798315543450915157973601645551224913673478585494525142110735407145912802378229427794669551794355853701688197120 +def node16539 : Tree Nat := .node node16538 node12220 +def node16540 : Tree Nat := .node node16539 node8508 +def node16541 : Tree Nat := .node node11880 node16540 +def node16542 : Tree Nat := .node node16537 node16541 +def node16543 : Tree Nat := .node node16533 node16542 +def node16544 : Tree Nat := .leaf 9979201548254487196435045015564637833528905205978739799427648930131328008576363702681300080704073877696393594680037844491106942751092807284332080731380291805783597803488257194808522467917046482430286386773075336301273564864360594719285479943965546686927619932403499326376929753399414400168704 +def node16545 : Tree Nat := .node node16544 node9824 +def node16546 : Tree Nat := .node node16545 node11169 +def node16547 : Tree Nat := .node node10464 node16546 +def node16548 : Tree Nat := .leaf 74350845423889153139903124907495085285681885359848187126673175584445547361613322269565131707084862318101064933638551468799453244719344897809746350394675441042758464047531578941522356787456730407104062589243384970071608983119931883484170315403854769614899386709112369881562974909612800 +def node16549 : Tree Nat := .node node16548 node10800 +def node16550 : Tree Nat := .node node16549 node11885 +def node16551 : Tree Nat := .node node11557 node16550 +def node16552 : Tree Nat := .node node16547 node16551 +def node16553 : Tree Nat := .leaf 4872657005699999540259241245240973667291905395814643084767653560555303998690331487067930748777742086044685659945437285942844388552137477512028050563269317864308715214039820171571358864547884011144993682438995647035987305572267775669245432195251184321405786016570841584097917163256037707520 +def node16554 : Tree Nat := .node node16553 node10467 +def node16555 : Tree Nat := .node node16554 node12577 +def node16556 : Tree Nat := .node node11562 node16555 +def node16557 : Tree Nat := .node node16556 node15218 +def node16558 : Tree Nat := .node node16552 node16557 +def node16559 : Tree Nat := .node node16543 node16558 +def node16560 : Tree Nat := .node node16524 node16559 +def node16561 : Tree Nat := .leaf 316737495533932896806000672947364985406770957499807714689649647758335385024375068625115069912270344247804382730648764876319422142111147161569779401907770207392027783248134037504 +def node16562 : Tree Nat := .node node16561 node11892 +def node16563 : Tree Nat := .node node16562 node8954 +def node16564 : Tree Nat := .node node12590 node16563 +def node16565 : Tree Nat := .leaf 138506147510999777305574373330016216931434888040828389324606791580490836106655394441277277957863238825957925043599292108917943421373051526885504465076792616458563942422594563879357095668464196905354147606791768011829567776056341926458884035389339295911587642541701411814703104 +def node16566 : Tree Nat := .node node16565 node10475 +def node16567 : Tree Nat := .node node16566 node12593 +def node16568 : Tree Nat := .node node11570 node16567 +def node16569 : Tree Nat := .node node16564 node16568 +def node16570 : Tree Nat := .leaf 103871157920704432967641989456220183081474135388805959975818466359096932214105391176651905007945306742829079154083587977295304648562758385376518801863563708257224983191175293921205708851177893777038490800326984275616636425246369251875751687478583794558342541387062063013078272 +def node16571 : Tree Nat := .node node16570 node11576 +def node16572 : Tree Nat := .node node16571 node12235 +def node16573 : Tree Nat := .node node10482 node16572 +def node16574 : Tree Nat := .leaf 49698772525016834965331991582829658881777267644320058114875784236862893371518422220136703130285460311197657708923808994515812806502493304787949304589516511601182154406090788270320461847607178545653865165455292405214148603450329442816 +def node16575 : Tree Nat := .node node16574 node11897 +def node16576 : Tree Nat := .node node16575 node12239 +def node16577 : Tree Nat := .node node11185 node16576 +def node16578 : Tree Nat := .node node16573 node16577 +def node16579 : Tree Nat := .node node16569 node16578 +def node16580 : Tree Nat := .leaf 96737554102888466558760360930741113965005304421549287058966680446683808532335393973857142642330557456174232032029911938731049766432267415954429951423959473923471944317647922759755084702684067453839789205020360317489316893360986135413695859278234230204428664077374720 +def node16581 : Tree Nat := .node node16580 node11903 +def node16582 : Tree Nat := .node node16581 node12599 +def node16583 : Tree Nat := .node node10491 node16582 +def node16584 : Tree Nat := .leaf 7161473972935145823016685844763388366475207299179016098880815835316504099629350810127423782400746203953924338453498993084239363760020756846998428885749987171298062476692166245581110443794822140675592837176714713510269013558746270977068587180020292096 +def node16585 : Tree Nat := .node node16584 node10165 +def node16586 : Tree Nat := .node node16585 node12603 +def node16587 : Tree Nat := .node node12246 node16586 +def node16588 : Tree Nat := .node node16583 node16587 +def node16589 : Tree Nat := .leaf 1790040957049150429497764988770267201631235312565244900700235644730890410579122871188366884669833627493033510019634793871967021223935224402015029126184376128089657842673246725250091179844056403147031231253711402457014999523686161130753467714075452928 +def node16590 : Tree Nat := .node node16589 node11588 +def node16591 : Tree Nat := .node node16590 node12608 +def node16592 : Tree Nat := .node node12251 node16591 +def node16593 : Tree Nat := .node node16592 node11920 +def node16594 : Tree Nat := .node node16588 node16593 +def node16595 : Tree Nat := .node node16579 node16594 +def node16596 : Tree Nat := .leaf 8656634187189011207269169234367892553118574466516492454770376287103910411060356487922070164112694609545114037612706465150410520177030702245426290228325578118180195284290632904537195519002104170962829365297391813861749434234722253463224977810030828052094297185121149000891392 +def node16597 : Tree Nat := .node node16596 node9868 +def node16598 : Tree Nat := .node node16597 node12618 +def node16599 : Tree Nat := .node node12616 node16598 +def node16600 : Tree Nat := .leaf 198723831945440257833832789526868543323333002966037996348125771068843701083432548721484715739659887900087342969057808247645013268748232235606286985324126892132539940663770712416802763972573914764757029435669281012792885892127184139008 +def node16601 : Tree Nat := .node node16600 node10500 +def node16602 : Tree Nat := .node node16601 node12622 +def node16603 : Tree Nat := .node node11206 node16602 +def node16604 : Tree Nat := .node node16599 node16603 +def node16605 : Tree Nat := .leaf 10130658077368993126933026111108692996370701150373079772868884228323420452409126211090973357250830034895692072200812481164637537937364112874830675312881472095860572956858043924480 +def node16606 : Tree Nat := .node node16605 node10188 +def node16607 : Tree Nat := .node node16606 node12263 +def node16608 : Tree Nat := .node node12261 node16607 +def node16609 : Tree Nat := .leaf 1661938522604095819772230784547773132804922032651908544641298085924455902581149479915923483049830825437134564823634674754245691146773543646769910130579564583921718874721825011186653036701693416802650423518321381490213909470952990968473764262738589767884580615723864845894418432 +def node16610 : Tree Nat := .node node16609 node7290 +def node16611 : Tree Nat := .node node16610 node12267 +def node16612 : Tree Nat := .node node11926 node16611 +def node16613 : Tree Nat := .node node16608 node16612 +def node16614 : Tree Nat := .node node16604 node16613 +def node16615 : Tree Nat := .leaf 396245082740244626813467446086315542861523573118408985201834555847845347369801512390838829731632087700595934825908471058557489591884450873441354823519818198915941100810890766847658068164367221781544950766516380048132440035684302877145059769121855924631515849522064641024 +def node16616 : Tree Nat := .node node16615 node10198 +def node16617 : Tree Nat := .node node16616 node11214 +def node16618 : Tree Nat := .node node10515 node16617 +def node16619 : Tree Nat := .leaf 57278681880283005250044178485451691806152599023400498215713906537159859066449877050576290820167492070778564025466781059399618427824809659101796925407263848808600224926171409131263811840200691507859575523234663803955783435004579054012542785596009202432 +def node16620 : Tree Nat := .node node16619 node10848 +def node16621 : Tree Nat := .node node16620 node12628 +def node16622 : Tree Nat := .node node10204 node16621 +def node16623 : Tree Nat := .node node16618 node16622 +def node16624 : Tree Nat := .leaf 82550051303375757866266333319224646119502365074775026070381224323046689647029471417968109599047609745800411538445133600610877448925442064062303033567189574375285208858822835738105089169360107271198406173888010916852134022126933582597319135052691118103756620596935389184 +def node16625 : Tree Nat := .node node16624 node10518 +def node16626 : Tree Nat := .node node16625 node12636 +def node16627 : Tree Nat := .node node12634 node16626 +def node16628 : Tree Nat := .node node16627 node15255 +def node16629 : Tree Nat := .node node16623 node16628 +def node16630 : Tree Nat := .node node16614 node16629 +def node16631 : Tree Nat := .node node16595 node16630 +def node16632 : Tree Nat := .node node16560 node16631 +def node16633 : Tree Nat := .node node16494 node16632 +def node16634 : Tree Nat := .leaf 1234340207232534768924172972097085425890206222080552041208404375408739803306976286634172917306397242772522958276719860842111516656925109353982601870004086753637228884344469633832196231566149298388457249473585824207267899161946719698624189959244801361324143657596024057569569272497664 +def node16635 : Tree Nat := .node node16634 node8565 +def node16636 : Tree Nat := .node node16635 node12649 +def node16637 : Tree Nat := .node node12647 node16636 +def node16638 : Tree Nat := .leaf 91968321463359888921264160764248520901693728454195899729368811825757719494033651209239114428937425155022663459339646168956640735638070248743648967792280823587600007155880090844174099623930165408911243293655126918376615885267678609854869817228207236012639635778794122317410313136794461646797668352 +def node16639 : Tree Nat := .node node16638 node8991 +def node16640 : Tree Nat := .node node16639 node11609 +def node16641 : Tree Nat := .node node12654 node16640 +def node16642 : Tree Nat := .node node16637 node16641 +def node16643 : Tree Nat := .leaf 639916299244569539716195659038140798213018549833338757325728344995237022806305069951399079905387972372429019319365012053206388861086228024303281769440728117299450102800478461438506112467214739710395281736870457634783932473153945837528594137554964971722683761443132321767002192224088053675762944 +def node16644 : Tree Nat := .node node16643 node8998 +def node16645 : Tree Nat := .node node16644 node11938 +def node16646 : Tree Nat := .node node11936 node16645 +def node16647 : Tree Nat := .leaf 1218759058188390998269292023483658499083580861280039698716643613373375090892105162254722843676330716650581875815405581347568779334011804096029090984416031093206258399094105458426066978432235169550161525682297859048440695644142568181495494127210360711376451299592868755892608976655552107776 +def node16648 : Tree Nat := .node node16647 node11616 +def node16649 : Tree Nat := .node node16648 node8574 +def node16650 : Tree Nat := .node node11615 node16649 +def node16651 : Tree Nat := .node node16646 node16650 +def node16652 : Tree Nat := .node node16642 node16651 +def node16653 : Tree Nat := .leaf 39994768702785702591999490396546082434909507226624899444546009491364795635936478061968279015850389671453293509741968045820172828621257674273492670540316603469028370837210505469050339721425576134462009723572766793661945503683429252262989382619818759762469866776051744565717209412236675572716800 +def node16654 : Tree Nat := .node node16653 node8579 +def node16655 : Tree Nat := .node node16654 node11235 +def node16656 : Tree Nat := .node node10536 node16655 +def node16657 : Tree Nat := .leaf 152270531428124985630521599810549817371763992589117758087619946576709717130190188398837937100719846361416099504038977275785712737636943187586551804335143116506081053130730986541151514830143268937107790158448187512341975011201681565380501238973838848768953771713015246495966188369954383104 +def node16658 : Tree Nat := .node node16657 node9008 +def node16659 : Tree Nat := .node node16658 node11239 +def node16660 : Tree Nat := .node node10884 node16659 +def node16661 : Tree Nat := .node node16656 node16660 +def node16662 : Tree Nat := .leaf 9516908214257811601907599988159363588420037635879217383808601266279805056323431018881376309090621470739658025887458484444279628708776529683455696147667901857343420569889266792150272084579804999498383189420249043355970742061186916065383059398736194565893525579538903339483196227863353600 +def node16663 : Tree Nat := .node node16662 node9015 +def node16664 : Tree Nat := .node node16663 node12659 +def node16665 : Tree Nat := .node node12284 node16664 +def node16666 : Tree Nat := .node node16665 node12289 +def node16667 : Tree Nat := .node node16661 node16666 +def node16668 : Tree Nat := .node node16652 node16667 +def node16669 : Tree Nat := .leaf 80457312478118392416054159181486565901863298170672274694940010177266596845737990189060369592407053850672236096403961395462928708419019257314063480399552163260900848024472798952789352957366621352087039830422576284002110783974543751950632811225517763956564578211935766990311731152837936849239040 +def node16670 : Tree Nat := .node node16669 node8601 +def node16671 : Tree Nat := .node node16670 node9023 +def node16672 : Tree Nat := .node node12295 node16671 +def node16673 : Tree Nat := .leaf 19182518119363401510095006226133717225693256601406188621183647154320032872736800109282752706544332845928907296420372978838904293102987282694242599641853951794845175223317090641754915621863448611289829257031587332948830366489871739524005984914249478711799327105622048479292936039946046464 +def node16674 : Tree Nat := .node node16673 node9026 +def node16675 : Tree Nat := .node node16674 node11634 +def node16676 : Tree Nat := .node node11946 node16675 +def node16677 : Tree Nat := .node node16672 node16676 +def node16678 : Tree Nat := .leaf 9439072172954677644714263904271829727395694639439515609240739341360951437053348074261322308813492460080769080831589590414614009221984430508145806530193238568104211924900663302992950169332938711949542953030188715898852608663408875620775633213853831887653317351904210081563331749281792 +def node16679 : Tree Nat := .node node16678 node9031 +def node16680 : Tree Nat := .node node16679 node11951 +def node16681 : Tree Nat := .node node10904 node16680 +def node16682 : Tree Nat := .leaf 674434357397972518756583405714076360532765513570938986317962256813833299181327606776398934862670632756558377764024675360361617252062263300192057036400721926318129965659852517971801939365202804450194111461015909384698688542895658913713605483022994046641849565786402008662274837646477160441254838272 +def node16683 : Tree Nat := .node node16682 node12301 +def node16684 : Tree Nat := .node node16683 node6951 +def node16685 : Tree Nat := .node node12300 node16684 +def node16686 : Tree Nat := .node node16681 node16685 +def node16687 : Tree Nat := .node node16677 node16686 +def node16688 : Tree Nat := .leaf 5028582029882421683741392761679191809112539187751272202571578498341084329754625547775107619087245815007391329618851003624011964659454527415473953216636216082057988833698633451728393745865559911800572937118909076850572663456372441380492292172876506630950445306548605326654359134850527959763968 +def node16689 : Tree Nat := .node node16688 node8616 +def node16690 : Tree Nat := .node node16689 node9038 +def node16691 : Tree Nat := .node node10252 node16690 +def node16692 : Tree Nat := .leaf 609379529094195499134646011741829249599069112546974505319316115452400484579292318976519661430936982524918425740239031607734746700355577783114098812063217446015718044172114932507811518585097044008287734648798881424518461492228679940616165130488057143747567410880166007214125167804931652608 +def node16693 : Tree Nat := .node node16692 node9350 +def node16694 : Tree Nat := .node node16693 node11961 +def node16695 : Tree Nat := .node node12309 node16694 +def node16696 : Tree Nat := .node node16691 node16695 +def node16697 : Tree Nat := .leaf 1277347543416232079459158972276015860847237549185868434051496441026593972856069204515189567724208135461756418317823072025500844875589413433409046659429465651120287837043830356508019316027324003999554531536823642587701043801776457551806967070780920635710248133327285818609364031576927072460795904 +def node16698 : Tree Nat := .node node16697 node9042 +def node16699 : Tree Nat := .node node16698 node12316 +def node16700 : Tree Nat := .node node12314 node16699 +def node16701 : Tree Nat := .node node16700 node15703 +def node16702 : Tree Nat := .node node16696 node16701 +def node16703 : Tree Nat := .node node16687 node16702 +def node16704 : Tree Nat := .node node16668 node16703 +def node16705 : Tree Nat := .leaf 633243118595354147281932435982423693522698568646444342238429610160910085389992580693614222445790426021664050046165186066039415577491962729282258237704270181252228740536808464384 +def node16706 : Tree Nat := .node node16705 node6587 +def node16707 : Tree Nat := .node node16706 node12667 +def node16708 : Tree Nat := .node node10265 node16707 +def node16709 : Tree Nat := .leaf 277003841793557267097168894213123579443022814502620804127019082413006131790169385083787645419631131732869651270126120845376046823186787418487130961514716211822826423108088840581486906875169252775108570399421564675090296391944676571178078852500761904778021221742400261692588032 +def node16710 : Tree Nat := .node node16709 node10568 +def node16711 : Tree Nat := .node node16710 node12671 +def node16712 : Tree Nat := .node node11279 node16711 +def node16713 : Tree Nat := .node node16708 node16712 +def node16714 : Tree Nat := .leaf 69250960706322019965487461894624202254604103130384268745081404880184632428539656104132668573227603373985209894554977641738292734549787200784015325262376280235762787405546472642906512989715956491799269964940679634767553435212172126831579584713253394812186885062796415852370432 +def node16715 : Tree Nat := .node node16714 node6975 +def node16716 : Tree Nat := .node node16715 node11980 +def node16717 : Tree Nat := .node node12677 node16716 +def node16718 : Tree Nat := .leaf 74532997478030128391163677168344348676855431677474085389029393646451938296429085135901304663101299582683317224241647769423579493065563475878016963844620134271618311889209670843622257622395616698507345156652574458143128613349660579072 +def node16719 : Tree Nat := .node node16718 node11658 +def node16720 : Tree Nat := .node node16719 node12328 +def node16721 : Tree Nat := .node node11985 node16720 +def node16722 : Tree Nat := .node node16717 node16721 +def node16723 : Tree Nat := .node node16713 node16722 +def node16724 : Tree Nat := .leaf 64494983019614487292707288971920999671213151427163352284470321206595604569758245517812411398485111351864878060812279717123631587224210112055626284469897143171693437857429917020944755273920413436265562976077838264098031808934910550504286804835617966219225099049544192 +def node16725 : Tree Nat := .node node16724 node6981 +def node16726 : Tree Nat := .node node16725 node11284 +def node16727 : Tree Nat := .node node10581 node16726 +def node16728 : Tree Nat := .leaf 7161473979601532322685387810670857380880371064326293207831222889770552105138026234620240994547035747051720576937647984708610499801927436475626684895895397910676532424295320420600777643829881722533135812776263433871724633369253941116437203421614482688 +def node16729 : Tree Nat := .node node16728 node7369 +def node16730 : Tree Nat := .node node16729 node12682 +def node16731 : Tree Nat := .node node11666 node16730 +def node16732 : Tree Nat := .node node16727 node16731 +def node16733 : Tree Nat := .leaf 1790040957042638696653155756080736096366859087245883055703900943663990032961877753566235441367368623736416297081068073638123712853241475224110214691407614728111416335168107421367538020490188314618687847045638755912946519186751297349289498997393103104 +def node16734 : Tree Nat := .node node16733 node6986 +def node16735 : Tree Nat := .node node16734 node12687 +def node16736 : Tree Nat := .node node10276 node16735 +def node16737 : Tree Nat := .node node16736 node11298 +def node16738 : Tree Nat := .node node16732 node16737 +def node16739 : Tree Nat := .node node16723 node16738 +def node16740 : Tree Nat := .leaf 17312740079846886268722930372612498790656563068870260560222513443593659556262151104413458235693420114214473598080574923395450449105448137365580946507887601928427725710809172380405735053305533130302365208246229623528695652594655712959406556479488200011026428259318222114833152 +def node16741 : Tree Nat := .node node16740 node8646 +def node16742 : Tree Nat := .node node16741 node11303 +def node16743 : Tree Nat := .node node11998 node16742 +def node16744 : Tree Nat := .leaf 99364190169144400118982615230413370434735275797426045543833764297795138892030773931912284895040223038691119085801364281782736439049415834622756295796711006251107077645135536955958493165443998859219563934830135169234982958766112164864 +def node16745 : Tree Nat := .node node16744 node9076 +def node16746 : Tree Nat := .node node16745 node12694 +def node16747 : Tree Nat := .node node12342 node16746 +def node16748 : Tree Nat := .node node16743 node16747 +def node16749 : Tree Nat := .leaf 5065336284692353907918582313099962560152168178120257127836925962292988177630695886177143906905038690852002542378892735943698814612623259960013327341734583703175957746941714628608 +def node16750 : Tree Nat := .node node16749 node9081 +def node16751 : Tree Nat := .node node16750 node10952 +def node16752 : Tree Nat := .node node10288 node16751 +def node16753 : Tree Nat := .leaf 1108015367173977180988846291985386472670632386687261754795198303002777153391328825868369484105618347491442102022148110629751742909492027037773599846213744719553212002836953361901262978940750313608338975896055783077289635961361159521126661305464839992950695173961162091750817792 +def node16754 : Tree Nat := .node node16753 node12698 +def node16755 : Tree Nat := .node node16754 node12349 +def node16756 : Tree Nat := .node node12347 node16755 +def node16757 : Tree Nat := .node node16752 node16756 +def node16758 : Tree Nat := .node node16748 node16757 +def node16759 : Tree Nat := .leaf 396237022097443778251559441798175454862179632231845315477459589809064287512333661971780371414554302192691129905726969029419984167929670579379981581805177100252483298657686905725144891791572992935751943732064012971949387558892582471136590772176651373897059328514390242048 +def node16760 : Tree Nat := .node node16759 node8665 +def node16761 : Tree Nat := .node node16760 node12003 +def node16762 : Tree Nat := .node node10602 node16761 +def node16763 : Tree Nat := .leaf 57279118901948529212390513601894959983309600777901494650680480560847660793312203102891838602499952521419711977286169181105360690029565092725355302307914163033589636050203710407053679462527859733483484603322591170242463060495923317861255425468655221760 +def node16764 : Tree Nat := .node node16763 node9376 +def node16765 : Tree Nat := .node node16764 node12705 +def node16766 : Tree Nat := .node node12356 node16765 +def node16767 : Tree Nat := .node node16762 node16766 +def node16768 : Tree Nat := .leaf 82550051303379511853805951710397014552158406470799885728279706014638736367790568328321665004389405539404117711534214254669673542947265438093445155309991865182314427545113433341929684856442422725571978992798678963236015890232422926109540085878858249892947214486951956224 +def node16769 : Tree Nat := .node node16768 node9092 +def node16770 : Tree Nat := .node node16769 node12361 +def node16771 : Tree Nat := .node node12711 node16770 +def node16772 : Tree Nat := .node node16771 node15329 +def node16773 : Tree Nat := .node node16767 node16772 +def node16774 : Tree Nat := .node node16758 node16773 +def node16775 : Tree Nat := .node node16739 node16774 +def node16776 : Tree Nat := .node node16704 node16775 +def node16777 : Tree Nat := .leaf 316660204709762348029311036291744048104646133777939252616270042899878799088435031575775825753770327427022026931899870778340328138791507480545364085863711686399255465117299706112 +def node16778 : Tree Nat := .node node16777 node8685 +def node16779 : Tree Nat := .node node16778 node12719 +def node16780 : Tree Nat := .node node12371 node16779 +def node16781 : Tree Nat := .leaf 138514600739442064819554225776925071351281849619864363846801292223263658474334911541937678611616759426989129781597119378302835478399352359006078983034767160315734641416278089435583973760585313357033925905076018379213626195715676593793734387149254649901516448783791040157122560 +def node16782 : Tree Nat := .node node16781 node9109 +def node16783 : Tree Nat := .node node16782 node12723 +def node16784 : Tree Nat := .node node11328 node16783 +def node16785 : Tree Nat := .node node16780 node16784 +def node16786 : Tree Nat := .leaf 103873270711894506503921887883645492114864769413308479583604991185790971867611843948375918369569895745330517031217337794268022094625685980467553681555006112209380250840075259404307252176998430685103523402098146403557269558089915103104424840259993216752434551843827378605303040 +def node16787 : Tree Nat := .node node16786 node9114 +def node16788 : Tree Nat := .node node16787 node9386 +def node16789 : Tree Nat := .node node12376 node16788 +def node16790 : Tree Nat := .leaf 74539062001828177927714019605760465899166431087093391667117852001692083228670456309135479129649597357664374503381876045984531404456673263834530223174070048116363254430987210132177725723904803747498534818779494709789302543895943468288 +def node16791 : Tree Nat := .node node16790 node11694 +def node16792 : Tree Nat := .node node16791 node12379 +def node16793 : Tree Nat := .node node12022 node16792 +def node16794 : Tree Nat := .node node16789 node16793 +def node16795 : Tree Nat := .node node16785 node16794 +def node16796 : Tree Nat := .leaf 96739522273507637558403093613733329809238305524769622234049364395574729695769424864196115830752495419229310456091091868813939977519732318687370368985370050817559473855746646417901869266970127713641926818904110753321749880840134876533044323673393438485348050116367616 +def node16797 : Tree Nat := .node node16796 node8696 +def node16798 : Tree Nat := .node node16797 node11333 +def node16799 : Tree Nat := .node node10622 node16798 +def node16800 : Tree Nat := .leaf 14322947939197393413520060490929776613280874604891700009727151121492422238268804278115187089156483865047204158048781588998438250422887165221451571185264443289587862295071337560814160536422751375681375724255551224172539839736734932341686041788421612800 +def node16801 : Tree Nat := .node node16800 node9124 +def node16802 : Tree Nat := .node node16801 node12729 +def node16803 : Tree Nat := .node node10996 node16802 +def node16804 : Tree Nat := .node node16799 node16803 +def node16805 : Tree Nat := .leaf 3580081700702303808306365508916683784389092430546263506931562117304787123329374188748272919073378369062794800542250374381342193457315358816443310314979826060161961387417058089515599486415123161259006583497664347168302969558640772530248232409417488640 +def node16806 : Tree Nat := .node node16805 node9129 +def node16807 : Tree Nat := .node node16806 node12386 +def node16808 : Tree Nat := .node node12735 node16807 +def node16809 : Tree Nat := .node node16808 node9961 +def node16810 : Tree Nat := .node node16804 node16809 +def node16811 : Tree Nat := .node node16795 node16810 +def node16812 : Tree Nat := .leaf 8657162481720147352967272380041105427605860991686884665630619174068860684158326175669035366450994195682725723279362638095610016354994589774720993396142953809228223982953900540188120206467572595174169329061823006322430339036754836019706701540501547137710946679779545292849920 +def node16813 : Tree Nat := .node node16812 node12890 +def node16814 : Tree Nat := .node node16813 node12741 +def node16815 : Tree Nat := .node node10319 node16814 +def node16816 : Tree Nat := .leaf 99362674038194885984271801585760637919356092921154680630653178455546279991821109626325588933602040266547040040677234833264882056796775469209244247770619939084405693047231415454421121538039579163523920661459283822476582735130377859840 +def node16817 : Tree Nat := .node node16816 node9662 +def node16818 : Tree Nat := .node node16817 node12745 +def node16819 : Tree Nat := .node node12394 node16818 +def node16820 : Tree Nat := .node node16815 node16819 +def node16821 : Tree Nat := .leaf 5065331454020449011617202808050831489212010316294952167949296565867997139791558890627662101438139316079460197436377795476750448951943922731379102287503648761273290948267299110912 +def node16822 : Tree Nat := .node node16821 node9667 +def node16823 : Tree Nat := .node node16822 node12398 +def node16824 : Tree Nat := .node node12751 node16823 +def node16825 : Tree Nat := .leaf 1661972335517864946765058496247369444012913415075464947532338487212968168389104086307167421096380205220169923649077249612225092168193210120472416991201238665173804848056381197059835198750962086678408675283762024138991912754862823465870162556728657056720826369777321644421087232 +def node16826 : Tree Nat := .node node16825 node12404 +def node16827 : Tree Nat := .node node16826 node12407 +def node16828 : Tree Nat := .node node12403 node16827 +def node16829 : Tree Nat := .node node16824 node16828 +def node16830 : Tree Nat := .node node16820 node16829 +def node16831 : Tree Nat := .leaf 24184880538346842074381972483574138126696803751138848064253296594047413681396269922849004354489501879294815689534017973578661205562943315632578053176781383555443395064030265158324658262915523338951433367593142566579670945448132939238797201906576880540498138557002496 +def node16832 : Tree Nat := .node node16831 node9673 +def node16833 : Tree Nat := .node node16832 node9147 +def node16834 : Tree Nat := .node node12757 node16833 +def node16835 : Tree Nat := .leaf 57279118901948936195693301678938055677388623890854819102757633380947767224366659982328777361104153108170274624267911090919943928144947245488319025963657194321053221560002006806226473761630677236543061275860274116255693061924139092001047053055939560192 +def node16836 : Tree Nat := .node node16835 node11357 +def node16837 : Tree Nat := .node node16836 node12760 +def node16838 : Tree Nat := .node node12898 node16837 +def node16839 : Tree Nat := .node node16834 node16838 +def node16840 : Tree Nat := .leaf 4030813431817111252860317243391825902379447158830594453445807321611794095309825057840889755141618090529368842037273136169728301573417173696662142843179404339401607651284102145790625626963164882655418896022828820785964328743866886652757569376068741015145231391067904 +def node16841 : Tree Nat := .node node16840 node9678 +def node16842 : Tree Nat := .node node16841 node12414 +def node16843 : Tree Nat := .node node12903 node16842 +def node16844 : Tree Nat := .node node16843 node15367 +def node16845 : Tree Nat := .node node16839 node16844 +def node16846 : Tree Nat := .node node16830 node16845 +def node16847 : Tree Nat := .node node16811 node16846 +def node16848 : Tree Nat := .leaf 72608247484266751113186645417475613287659189534150120071082610318161164900410369802010171606275055632307539091314380551900942421098000972937492604546104442446258163041672728931833103302668893625233330503792551717428941049950725941884735635001207477758244772514339485077325223858176 +def node16849 : Tree Nat := .node node16848 node9427 +def node16850 : Tree Nat := .node node16849 node12773 +def node16851 : Tree Nat := .node node12915 node16850 +def node16852 : Tree Nat := .leaf 173717940541902012406847676332323369026218492934350352779819959337975798708930936981886908428649340336564803598100086476764468725095226525520450177004287773036536431713613845238180377950260033608419927746966589167158725855862857413398731612495046706809810556871714741525540343446419762279783530496 +def node16853 : Tree Nat := .node node16852 node9690 +def node16854 : Tree Nat := .node node16853 node12048 +def node16855 : Tree Nat := .node node11721 node16854 +def node16856 : Tree Nat := .node node16851 node16855 +def node16857 : Tree Nat := .leaf 641163699438028739563858581204347393685116642670654396617603147908493306651974700257278394331163808366889019259440047346299079861654329505917609686898064580934121740704328291187173637899324791791875457145276896239610009816981783983496321899146871923070463098462714164650951273274804582809098752 +def node16858 : Tree Nat := .node node16857 node9695 +def node16859 : Tree Nat := .node node16858 node12422 +def node16860 : Tree Nat := .node node12920 node16859 +def node16861 : Tree Nat := .leaf 1219353864951782111494411248482918459307633365360703456500271986640899516906974832968978407081031124203207213219107662359049870925493920305877577113385849141093414269071206505019656674557521814942464152738959608960715093616183037833228981903309132644133193517737177731983045131901687846144 +def node16862 : Tree Nat := .node node16861 node12059 +def node16863 : Tree Nat := .node node16862 node7055 +def node16864 : Tree Nat := .node node11726 node16863 +def node16865 : Tree Nat := .node node16860 node16864 +def node16866 : Tree Nat := .node node16856 node16865 +def node16867 : Tree Nat := .leaf 40072731214876902584642317423404544687503367670755602315291160243084343055195042355004781268474032964285787650196334265938393004300726308825222755861921487819969963322360940621015535841770745827259997481944380466078741357199556714969813547117926515034035561367693265181617953448285444685277696 +def node16868 : Tree Nat := .node node16867 node12924 +def node16869 : Tree Nat := .node node16868 node11382 +def node16870 : Tree Nat := .node node12780 node16869 +def node16871 : Tree Nat := .leaf 154649758481689438530998499807589658260812534952180183997696813487701068501878519970103561679362488624056531054510749426042497602859482666469279819456997501797591268195419711032328576392419041103514610736094026485796110782751110906881239255436881086992675797037422371178486141540586857728 +def node16872 : Tree Nat := .node node16871 node9709 +def node16873 : Tree Nat := .node node16872 node12066 +def node16874 : Tree Nat := .node node12930 node16873 +def node16875 : Tree Nat := .node node16870 node16874 +def node16876 : Tree Nat := .node node16875 node16324 +def node16877 : Tree Nat := .node node16866 node16876 +def node16878 : Tree Nat := .leaf 160290924859507184890964645301086848421279160667663599154400786977123326662993675064319920575364851063824844019102172246594829793889804159943817155349718164843994851441176769484957280655601101943110597912446586072291792932368895357703808578999867749353116095334984577215977726024076370084117504 +def node16879 : Tree Nat := .node node16878 node12077 +def node16880 : Tree Nat := .node node16879 node9463 +def node16881 : Tree Nat := .node node12787 node16880 +def node16882 : Tree Nat := .leaf 148701690847778306279806249814990056013126020165939545268251224126481773655474921993927471069478329148667497008953910577107116866176779037331149600356317794702751184720588248477397664350951473695445345378941682126276436154630905101413011585104751968198168849844250209228902904086147840 +def node16883 : Tree Nat := .node node16882 node11745 +def node16884 : Tree Nat := .node node16883 node12082 +def node16885 : Tree Nat := .node node12440 node16884 +def node16886 : Tree Nat := .node node16881 node16885 +def node16887 : Tree Nat := .leaf 9584288667923211146940637195106780953971013018507815849382904561997273766854168813865342652026007728428198314036574166161669526119940610460465016384298035696062912789952161026443001094579879592993925457063788048350136422839354290788678939521024621838745274921141486672987159768203264 +def node16888 : Tree Nat := .node node16887 node11750 +def node16889 : Tree Nat := .node node16888 node12794 +def node16890 : Tree Nat := .node node12792 node16889 +def node16891 : Tree Nat := .leaf 694871762167608049627390705327229699637393818877360010358663266666794029670903963888593304397609284049754578963388815712608220422740569903789213815612816135641906962630524543087755586324722242247831827789652619497571628098731104590212046598076650424025354802621911368364497795581092042379686641664 +def node16892 : Tree Nat := .node node16891 node11408 +def node16893 : Tree Nat := .node node16892 node9187 +def node16894 : Tree Nat := .node node12092 node16893 +def node16895 : Tree Nat := .node node16890 node16894 +def node16896 : Tree Nat := .node node16886 node16895 +def node16897 : Tree Nat := .leaf 10018182803719221212881928315311801631843048314236023066908303240782313138173456852426865934210126169233628948081886680371829917399314523708691883150034920720965959793454322798884079581673090275324168249567779498054634582635270054866343747769826938128673809465566209848916102437247154883120128 +def node16898 : Tree Nat := .node node16897 node12096 +def node16899 : Tree Nat := .node node16898 node12099 +def node16900 : Tree Nat := .node node10663 node16899 +def node16901 : Tree Nat := .leaf 297403381695556612559612499629980169304933947286941873374749953634287100469711488005085883487479056483609044024640255276935388452792875245752807370945053408611269038452514149695969078694457844819721547191606166291624997298471263270941971343541019398982538854335716615251283298364932864 +def node16902 : Tree Nat := .node node16901 node11417 +def node16903 : Tree Nat := .node node16902 node9193 +def node16904 : Tree Nat := .node node12446 node16903 +def node16905 : Tree Nat := .node node16900 node16904 +def node16906 : Tree Nat := .leaf 9745314011399999080353386418688616373999954084214336243479610869786149109162219887830238550258259161831944840386567684834976426420268567037961796475256922268122642702196228159045420660014211695017940290254112835082946239509111980164613846501247219463763505880110430939360810381983863533568 +def node16907 : Tree Nat := .node node16906 node11764 +def node16908 : Tree Nat := .node node16907 node11423 +def node16909 : Tree Nat := .node node12801 node16908 +def node16910 : Tree Nat := .node node16909 node15398 +def node16911 : Tree Nat := .node node16905 node16910 +def node16912 : Tree Nat := .node node16896 node16911 +def node16913 : Tree Nat := .node node16877 node16912 +def node16914 : Tree Nat := .node node16847 node16913 +def node16915 : Tree Nat := .node node16776 node16914 +def node16916 : Tree Nat := .node node16633 node16915 +def node16917 : Tree Nat := .leaf 340282366920938463463374607431768211712 +def node16918 : Tree Nat := .node node16917 node12814 +def node16919 : Tree Nat := .node node16918 node8784 +def node16920 : Tree Nat := .node node15106 node16919 +def node16921 : Tree Nat := .node node16920 node16364 +def node16922 : Tree Nat := .node node16921 node16374 +def node16923 : Tree Nat := .leaf 22300745198530623141535718272648361522757632 +def node16924 : Tree Nat := .node node16923 node9498 +def node16925 : Tree Nat := .node node16924 node11444 +def node16926 : Tree Nat := .node node15120 node16925 +def node16927 : Tree Nat := .node node16926 node16383 +def node16928 : Tree Nat := .node node16927 node16389 +def node16929 : Tree Nat := .node node16922 node16928 +def node16930 : Tree Nat := .leaf 87112285931760246646623899502532662198272 +def node16931 : Tree Nat := .node node16930 node8379 +def node16932 : Tree Nat := .node node16931 node12497 +def node16933 : Tree Nat := .node node12133 node16932 +def node16934 : Tree Nat := .node node16933 node16399 +def node16935 : Tree Nat := .node node16934 node16409 +def node16936 : Tree Nat := .leaf 5708990770823839524233143877797980549825953792 +def node16937 : Tree Nat := .node node16936 node8394 +def node16938 : Tree Nat := .node node16937 node11087 +def node16939 : Tree Nat := .node node10068 node16938 +def node16940 : Tree Nat := .node node16939 node16418 +def node16941 : Tree Nat := .leaf 1329227995784915872903807060280344577 +def node16942 : Tree Nat := .node node16941 node8403 +def node16943 : Tree Nat := .node node16942 node11808 +def node16944 : Tree Nat := .node node16943 node10073 +def node16945 : Tree Nat := .node node16423 node16944 +def node16946 : Tree Nat := .node node16940 node16945 +def node16947 : Tree Nat := .node node16935 node16946 +def node16948 : Tree Nat := .node node16929 node16947 +def node16949 : Tree Nat := .leaf 5444517870735015415413993718908291387392 +def node16950 : Tree Nat := .node node16949 node8411 +def node16951 : Tree Nat := .node node16950 node8847 +def node16952 : Tree Nat := .node node10081 node16951 +def node16953 : Tree Nat := .node node16952 node16435 +def node16954 : Tree Nat := .node node16953 node16445 +def node16955 : Tree Nat := .leaf 356811923176489970264571492362373784364122112 +def node16956 : Tree Nat := .node node16955 node8432 +def node16957 : Tree Nat := .node node16956 node11483 +def node16958 : Tree Nat := .node node12527 node16957 +def node16959 : Tree Nat := .node node16958 node16454 +def node16960 : Tree Nat := .leaf 18587711355972288284975781226873758791790851623618504846111043336295880128987804321300740297589344031949660391498383949997417484773948211886773949467050624638866364427617265034647708682185179214536534901323301038150877415048993077374230441687016743109726753881999586974128450373576192 +def node16961 : Tree Nat := .node node16960 node8869 +def node16962 : Tree Nat := .node node16961 node12531 +def node16963 : Tree Nat := .node node11494 node16962 +def node16964 : Tree Nat := .node node16963 node12176 +def node16965 : Tree Nat := .node node16959 node16964 +def node16966 : Tree Nat := .node node16954 node16965 +def node16967 : Tree Nat := .leaf 1393796574908163946345982392040522595172352 +def node16968 : Tree Nat := .node node16967 node8448 +def node16969 : Tree Nat := .node node16968 node12538 +def node16970 : Tree Nat := .node node11835 node16969 +def node16971 : Tree Nat := .node node16970 node16465 +def node16972 : Tree Nat := .node node16971 node16475 +def node16973 : Tree Nat := .leaf 91343852333181432387730302044767688797215260672 +def node16974 : Tree Nat := .node node16973 node8463 +def node16975 : Tree Nat := .node node16974 node11132 +def node16976 : Tree Nat := .node node10407 node16975 +def node16977 : Tree Nat := .node node16976 node16484 +def node16978 : Tree Nat := .leaf 21267647932558653966460912964485513232 +def node16979 : Tree Nat := .node node16978 node8472 +def node16980 : Tree Nat := .node node16979 node12201 +def node16981 : Tree Nat := .node node16980 node10766 +def node16982 : Tree Nat := .node node16489 node16981 +def node16983 : Tree Nat := .node node16977 node16982 +def node16984 : Tree Nat := .node node16972 node16983 +def node16985 : Tree Nat := .node node16966 node16984 +def node16986 : Tree Nat := .node node16948 node16985 +def node16987 : Tree Nat := .leaf 1361129467683753853853498429727072846848 +def node16988 : Tree Nat := .node node16987 node6448 +def node16989 : Tree Nat := .node node16988 node10424 +def node16990 : Tree Nat := .node node10107 node16989 +def node16991 : Tree Nat := .node node16990 node16502 +def node16992 : Tree Nat := .node node16991 node16512 +def node16993 : Tree Nat := .leaf 89202980794122492566142873090593446091030528 +def node16994 : Tree Nat := .node node16993 node6836 +def node16995 : Tree Nat := .node node16994 node10438 +def node16996 : Tree Nat := .node node10436 node16995 +def node16997 : Tree Nat := .node node16996 node16521 +def node16998 : Tree Nat := .leaf 18587711355972288284975781226873760581613097786347009434467747588765213975724314177208716091237795920939758178075989750296970019558221692054483093453457374980435947050316326763103008174219743267240817685641920724837580664715154158459698635527282793073761347633415345080923212723348992 +def node16999 : Tree Nat := .node node16998 node6845 +def node17000 : Tree Nat := .node node16999 node12210 +def node17001 : Tree Nat := .node node12562 node17000 +def node17002 : Tree Nat := .node node17001 node12216 +def node17003 : Tree Nat := .node node16997 node17002 +def node17004 : Tree Nat := .node node16992 node17003 +def node17005 : Tree Nat := .leaf 348449143727040986586495598010130648793088 +def node17006 : Tree Nat := .node node17005 node10117 +def node17007 : Tree Nat := .node node17006 node12571 +def node17008 : Tree Nat := .node node12569 node17007 +def node17009 : Tree Nat := .node node17008 node16532 +def node17010 : Tree Nat := .node node17009 node16542 +def node17011 : Tree Nat := .leaf 22835963083295358096932575511191922199303815168 +def node17012 : Tree Nat := .node node17011 node9824 +def node17013 : Tree Nat := .node node17012 node11169 +def node17014 : Tree Nat := .node node10464 node17013 +def node17015 : Tree Nat := .node node17014 node16551 +def node17016 : Tree Nat := .leaf 5316911983139663491615228241121378308 +def node17017 : Tree Nat := .node node17016 node9833 +def node17018 : Tree Nat := .node node17017 node12227 +def node17019 : Tree Nat := .node node17018 node12582 +def node17020 : Tree Nat := .node node16556 node17019 +def node17021 : Tree Nat := .node node17015 node17020 +def node17022 : Tree Nat := .node node17010 node17021 +def node17023 : Tree Nat := .node node17004 node17022 +def node17024 : Tree Nat := .leaf 21778071482940061661655974875633165549568 +def node17025 : Tree Nat := .node node17024 node11892 +def node17026 : Tree Nat := .node node17025 node8954 +def node17027 : Tree Nat := .node node12590 node17026 +def node17028 : Tree Nat := .node node17027 node16568 +def node17029 : Tree Nat := .node node17028 node16578 +def node17030 : Tree Nat := .leaf 1427247692705959881058285969449495137456488448 +def node17031 : Tree Nat := .node node17030 node11903 +def node17032 : Tree Nat := .node node17031 node12599 +def node17033 : Tree Nat := .node node10491 node17032 +def node17034 : Tree Nat := .node node17033 node16587 +def node17035 : Tree Nat := .node node17034 node16593 +def node17036 : Tree Nat := .node node17029 node17035 +def node17037 : Tree Nat := .leaf 5575186299632655785383929568162090380689408 +def node17038 : Tree Nat := .node node17037 node9868 +def node17039 : Tree Nat := .node node17038 node12618 +def node17040 : Tree Nat := .node node12616 node17039 +def node17041 : Tree Nat := .node node17040 node16603 +def node17042 : Tree Nat := .node node17041 node16613 +def node17043 : Tree Nat := .leaf 365375409332725729550921208179070755188861042688 +def node17044 : Tree Nat := .node node17043 node10198 +def node17045 : Tree Nat := .node node17044 node11214 +def node17046 : Tree Nat := .node node10515 node17045 +def node17047 : Tree Nat := .node node17046 node16622 +def node17048 : Tree Nat := .leaf 85070591730234615865843651857942052928 +def node17049 : Tree Nat := .node node17048 node10211 +def node17050 : Tree Nat := .node node17049 node11219 +def node17051 : Tree Nat := .node node17050 node8128 +def node17052 : Tree Nat := .node node16627 node17051 +def node17053 : Tree Nat := .node node17047 node17052 +def node17054 : Tree Nat := .node node17042 node17053 +def node17055 : Tree Nat := .node node17036 node17054 +def node17056 : Tree Nat := .node node17023 node17055 +def node17057 : Tree Nat := .node node16986 node17056 +def node17058 : Tree Nat := .leaf 680564733841876926926749214863536423424 +def node17059 : Tree Nat := .node node17058 node8565 +def node17060 : Tree Nat := .node node17059 node12649 +def node17061 : Tree Nat := .node node12647 node17060 +def node17062 : Tree Nat := .node node17061 node16641 +def node17063 : Tree Nat := .node node17062 node16651 +def node17064 : Tree Nat := .leaf 44601490397061246283071436545296723045515264 +def node17065 : Tree Nat := .node node17064 node8579 +def node17066 : Tree Nat := .node node17065 node11235 +def node17067 : Tree Nat := .node node10536 node17066 +def node17068 : Tree Nat := .node node17067 node16660 +def node17069 : Tree Nat := .node node17068 node16666 +def node17070 : Tree Nat := .node node17063 node17069 +def node17071 : Tree Nat := .leaf 174224571863520493293247799005065324396544 +def node17072 : Tree Nat := .node node17071 node8601 +def node17073 : Tree Nat := .node node17072 node9023 +def node17074 : Tree Nat := .node node12295 node17073 +def node17075 : Tree Nat := .node node17074 node16676 +def node17076 : Tree Nat := .node node17075 node16686 +def node17077 : Tree Nat := .leaf 11417981541647679048466287755595961099651907584 +def node17078 : Tree Nat := .node node17077 node8616 +def node17079 : Tree Nat := .node node17078 node9038 +def node17080 : Tree Nat := .node node10252 node17079 +def node17081 : Tree Nat := .node node17080 node16695 +def node17082 : Tree Nat := .leaf 2658455991569831745807614120560689154 +def node17083 : Tree Nat := .node node17082 node8625 +def node17084 : Tree Nat := .node node17083 node12320 +def node17085 : Tree Nat := .node node17084 node11970 +def node17086 : Tree Nat := .node node16700 node17085 +def node17087 : Tree Nat := .node node17081 node17086 +def node17088 : Tree Nat := .node node17076 node17087 +def node17089 : Tree Nat := .node node17070 node17088 +def node17090 : Tree Nat := .leaf 10889035741470030830827987437816582774784 +def node17091 : Tree Nat := .node node17090 node6587 +def node17092 : Tree Nat := .node node17091 node12667 +def node17093 : Tree Nat := .node node10265 node17092 +def node17094 : Tree Nat := .node node17093 node16712 +def node17095 : Tree Nat := .node node17094 node16722 +def node17096 : Tree Nat := .leaf 713623846352979940529142984724747568728244224 +def node17097 : Tree Nat := .node node17096 node6981 +def node17098 : Tree Nat := .node node17097 node11284 +def node17099 : Tree Nat := .node node10581 node17098 +def node17100 : Tree Nat := .node node17099 node16731 +def node17101 : Tree Nat := .node node17100 node16737 +def node17102 : Tree Nat := .node node17095 node17101 +def node17103 : Tree Nat := .leaf 2787593149816327892691964784081045190344704 +def node17104 : Tree Nat := .node node17103 node8646 +def node17105 : Tree Nat := .node node17104 node11303 +def node17106 : Tree Nat := .node node11998 node17105 +def node17107 : Tree Nat := .node node17106 node16747 +def node17108 : Tree Nat := .node node17107 node16757 +def node17109 : Tree Nat := .leaf 182687704666362864775460604089535377594430521344 +def node17110 : Tree Nat := .node node17109 node8665 +def node17111 : Tree Nat := .node node17110 node12003 +def node17112 : Tree Nat := .node node10602 node17111 +def node17113 : Tree Nat := .node node17112 node16766 +def node17114 : Tree Nat := .leaf 42535295865117307932921825928971026464 +def node17115 : Tree Nat := .node node17114 node8674 +def node17116 : Tree Nat := .node node17115 node11318 +def node17117 : Tree Nat := .node node17116 node12013 +def node17118 : Tree Nat := .node node16771 node17117 +def node17119 : Tree Nat := .node node17113 node17118 +def node17120 : Tree Nat := .node node17108 node17119 +def node17121 : Tree Nat := .node node17102 node17120 +def node17122 : Tree Nat := .node node17089 node17121 +def node17123 : Tree Nat := .leaf 2722258935367507707706996859454145693696 +def node17124 : Tree Nat := .node node17123 node8685 +def node17125 : Tree Nat := .node node17124 node12719 +def node17126 : Tree Nat := .node node12371 node17125 +def node17127 : Tree Nat := .node node17126 node16784 +def node17128 : Tree Nat := .node node17127 node16794 +def node17129 : Tree Nat := .leaf 178405961588244985132285746181186892182061056 +def node17130 : Tree Nat := .node node17129 node8696 +def node17131 : Tree Nat := .node node17130 node11333 +def node17132 : Tree Nat := .node node10622 node17131 +def node17133 : Tree Nat := .node node17132 node16803 +def node17134 : Tree Nat := .node node17133 node16809 +def node17135 : Tree Nat := .node node17128 node17134 +def node17136 : Tree Nat := .leaf 696898287454081973172991196020261297586176 +def node17137 : Tree Nat := .node node17136 node12890 +def node17138 : Tree Nat := .node node17137 node12741 +def node17139 : Tree Nat := .node node10319 node17138 +def node17140 : Tree Nat := .node node17139 node16819 +def node17141 : Tree Nat := .node node17140 node16829 +def node17142 : Tree Nat := .leaf 45671926166590716193865151022383844398607630336 +def node17143 : Tree Nat := .node node17142 node9673 +def node17144 : Tree Nat := .node node17143 node9147 +def node17145 : Tree Nat := .node node12757 node17144 +def node17146 : Tree Nat := .node node17145 node16838 +def node17147 : Tree Nat := .leaf 10633823966279326983230456482242756616 +def node17148 : Tree Nat := .node node17147 node12905 +def node17149 : Tree Nat := .node node17148 node11363 +def node17150 : Tree Nat := .node node17149 node12766 +def node17151 : Tree Nat := .node node16843 node17150 +def node17152 : Tree Nat := .node node17146 node17151 +def node17153 : Tree Nat := .node node17141 node17152 +def node17154 : Tree Nat := .node node17135 node17153 +def node17155 : Tree Nat := .leaf 43556142965880123323311949751266331099136 +def node17156 : Tree Nat := .node node17155 node9427 +def node17157 : Tree Nat := .node node17156 node12773 +def node17158 : Tree Nat := .node node12915 node17157 +def node17159 : Tree Nat := .node node17158 node16855 +def node17160 : Tree Nat := .node node17159 node16865 +def node17161 : Tree Nat := .leaf 2854495385411919762116571938898990274912976896 +def node17162 : Tree Nat := .node node17161 node12924 +def node17163 : Tree Nat := .node node17162 node11382 +def node17164 : Tree Nat := .node node12780 node17163 +def node17165 : Tree Nat := .node node17164 node16874 +def node17166 : Tree Nat := .leaf 9516908214257811601907599988159363586630215389729512344909463027406397933005446971656658366382688574415741006977131878494138262305840415325952530966589669218808313442784469252538200830251221953288312618995055337378085420463195158961497600736079032966357539955140829540343276982232520960 +def node17167 : Tree Nat := .node node17166 node9714 +def node17168 : Tree Nat := .node node17167 node12428 +def node17169 : Tree Nat := .node node12935 node17168 +def node17170 : Tree Nat := .node node17169 node12940 +def node17171 : Tree Nat := .node node17165 node17170 +def node17172 : Tree Nat := .node node17160 node17171 +def node17173 : Tree Nat := .leaf 11150372599265311570767859136324180761378816 +def node17174 : Tree Nat := .node node17173 node12077 +def node17175 : Tree Nat := .node node17174 node9463 +def node17176 : Tree Nat := .node node12787 node17175 +def node17177 : Tree Nat := .node node17176 node16885 +def node17178 : Tree Nat := .node node17177 node16895 +def node17179 : Tree Nat := .leaf 170141183460469231731687303715884105856 +def node17180 : Tree Nat := .node node17179 node12103 +def node17181 : Tree Nat := .node node17180 node12454 +def node17182 : Tree Nat := .node node17181 node12108 +def node17183 : Tree Nat := .node node16909 node17182 +def node17184 : Tree Nat := .node node16905 node17183 +def node17185 : Tree Nat := .node node17178 node17184 +def node17186 : Tree Nat := .node node17172 node17185 +def node17187 : Tree Nat := .node node17154 node17186 +def node17188 : Tree Nat := .node node17122 node17187 +def node17189 : Tree Nat := .node node17057 node17188 +def node17190 : Tree Nat := .leaf 6277101735386680763835789423207666420824721927333679726592 +def node17191 : Tree Nat := .node node17190 node12469 +def node17192 : Tree Nat := .node node17191 node12472 +def node17193 : Tree Nat := .node node12468 node17192 +def node17194 : Tree Nat := .node node16920 node17193 +def node17195 : Tree Nat := .leaf 1461501637330902918203684832716283020755444170752 +def node17196 : Tree Nat := .node node17195 node9488 +def node17197 : Tree Nat := .node node17196 node9224 +def node17198 : Tree Nat := .node node15111 node17197 +def node17199 : Tree Nat := .node node17198 node16373 +def node17200 : Tree Nat := .node node17194 node17199 +def node17201 : Tree Nat := .leaf 95780971304118053647396689196894324048228789174403072 +def node17202 : Tree Nat := .node node17201 node12485 +def node17203 : Tree Nat := .node node17202 node12125 +def node17204 : Tree Nat := .node node12842 node17203 +def node17205 : Tree Nat := .node node17204 node12492 +def node17206 : Tree Nat := .node node16927 node17205 +def node17207 : Tree Nat := .node node17200 node17206 +def node17208 : Tree Nat := .leaf 374144419156711147060143317175368453313393707712512 +def node17209 : Tree Nat := .node node17208 node8818 +def node17210 : Tree Nat := .node node17209 node10368 +def node17211 : Tree Nat := .node node12138 node17210 +def node17212 : Tree Nat := .node node17211 node16408 +def node17213 : Tree Nat := .node node16934 node17212 +def node17214 : Tree Nat := .leaf 24519928653854221733733552434404946956346570028647186432 +def node17215 : Tree Nat := .node node17214 node8833 +def node17216 : Tree Nat := .node node17215 node12512 +def node17217 : Tree Nat := .node node12158 node17216 +def node17218 : Tree Nat := .node node17217 node16944 +def node17219 : Tree Nat := .node node16940 node17218 +def node17220 : Tree Nat := .node node17213 node17219 +def node17221 : Tree Nat := .node node17207 node17220 +def node17222 : Tree Nat := .leaf 100433627766186892221372630771322662733195550837338875625472 +def node17223 : Tree Nat := .node node17222 node8850 +def node17224 : Tree Nat := .node node17223 node11472 +def node17225 : Tree Nat := .node node11470 node17224 +def node17226 : Tree Nat := .node node16952 node17225 +def node17227 : Tree Nat := .leaf 23384026197294446691258957323460528332087106732032 +def node17228 : Tree Nat := .node node17227 node8419 +def node17229 : Tree Nat := .node node17228 node12168 +def node17230 : Tree Nat := .node node12521 node17229 +def node17231 : Tree Nat := .node node17230 node16444 +def node17232 : Tree Nat := .node node17226 node17231 +def node17233 : Tree Nat := .leaf 1532495540865888858358347027150309184771660626790449152 +def node17234 : Tree Nat := .node node17233 node8869 +def node17235 : Tree Nat := .node node17234 node12531 +def node17236 : Tree Nat := .node node11494 node17235 +def node17237 : Tree Nat := .node node17236 node12176 +def node17238 : Tree Nat := .node node16959 node17237 +def node17239 : Tree Nat := .node node17232 node17238 +def node17240 : Tree Nat := .leaf 5986310706507378352962293074805895253014299323400192 +def node17241 : Tree Nat := .node node17240 node8889 +def node17242 : Tree Nat := .node node17241 node12186 +def node17243 : Tree Nat := .node node11840 node17242 +def node17244 : Tree Nat := .node node17243 node16474 +def node17245 : Tree Nat := .node node16971 node17244 +def node17246 : Tree Nat := .leaf 392318858461667547739736838950479151301545120458354982912 +def node17247 : Tree Nat := .node node17246 node8900 +def node17248 : Tree Nat := .node node17247 node12552 +def node17249 : Tree Nat := .node node12550 node17248 +def node17250 : Tree Nat := .node node17249 node16981 +def node17251 : Tree Nat := .node node16977 node17250 +def node17252 : Tree Nat := .node node17245 node17251 +def node17253 : Tree Nat := .node node17239 node17252 +def node17254 : Tree Nat := .node node17221 node17253 +def node17255 : Tree Nat := .leaf 25108406941546723055343157692830665683298887709334718906368 +def node17256 : Tree Nat := .node node17255 node7222 +def node17257 : Tree Nat := .node node17256 node11528 +def node17258 : Tree Nat := .node node11525 node17257 +def node17259 : Tree Nat := .node node16990 node17258 +def node17260 : Tree Nat := .leaf 5846006549323611672814739330865132083021776683008 +def node17261 : Tree Nat := .node node17260 node6826 +def node17262 : Tree Nat := .node node17261 node11857 +def node17263 : Tree Nat := .node node10430 node17262 +def node17264 : Tree Nat := .node node17263 node16511 +def node17265 : Tree Nat := .node node17259 node17264 +def node17266 : Tree Nat := .leaf 383123885216472214589586756787577296192915156697612288 +def node17267 : Tree Nat := .node node17266 node6845 +def node17268 : Tree Nat := .node node17267 node12210 +def node17269 : Tree Nat := .node node12562 node17268 +def node17270 : Tree Nat := .node node17269 node12216 +def node17271 : Tree Nat := .node node16997 node17270 +def node17272 : Tree Nat := .node node17265 node17271 +def node17273 : Tree Nat := .leaf 1496577676626844588240573268701473813253574830850048 +def node17274 : Tree Nat := .node node17273 node9814 +def node17275 : Tree Nat := .node node17274 node11874 +def node17276 : Tree Nat := .node node11871 node17275 +def node17277 : Tree Nat := .node node17276 node16541 +def node17278 : Tree Nat := .node node17009 node17277 +def node17279 : Tree Nat := .leaf 98079714615416886934934209737619787825386280114588745728 +def node17280 : Tree Nat := .node node17279 node10467 +def node17281 : Tree Nat := .node node17280 node12577 +def node17282 : Tree Nat := .node node11562 node17281 +def node17283 : Tree Nat := .node node17282 node17019 +def node17284 : Tree Nat := .node node17015 node17283 +def node17285 : Tree Nat := .node node17278 node17284 +def node17286 : Tree Nat := .node node17272 node17285 +def node17287 : Tree Nat := .leaf 401734511064747568885490523085290650932782203349355502501888 +def node17288 : Tree Nat := .node node17287 node10475 +def node17289 : Tree Nat := .node node17288 node12593 +def node17290 : Tree Nat := .node node11570 node17289 +def node17291 : Tree Nat := .node node17027 node17290 +def node17292 : Tree Nat := .leaf 93536104789177786765035829293842113328348426928128 +def node17293 : Tree Nat := .node node17292 node11576 +def node17294 : Tree Nat := .node node17293 node12235 +def node17295 : Tree Nat := .node node10482 node17294 +def node17296 : Tree Nat := .node node17295 node16577 +def node17297 : Tree Nat := .node node17291 node17296 +def node17298 : Tree Nat := .leaf 6129982163463555433433388108601236739086642507161796608 +def node17299 : Tree Nat := .node node17298 node11588 +def node17300 : Tree Nat := .node node17299 node12608 +def node17301 : Tree Nat := .node node12251 node17300 +def node17302 : Tree Nat := .node node17301 node11920 +def node17303 : Tree Nat := .node node17034 node17302 +def node17304 : Tree Nat := .node node17297 node17303 +def node17305 : Tree Nat := .leaf 23945242826029513411849172299223581012057197293600768 +def node17306 : Tree Nat := .node node17305 node10188 +def node17307 : Tree Nat := .node node17306 node12263 +def node17308 : Tree Nat := .node node12261 node17307 +def node17309 : Tree Nat := .node node17308 node16612 +def node17310 : Tree Nat := .node node17041 node17309 +def node17311 : Tree Nat := .leaf 1569275433846670190958947355801916605206180481833419931648 +def node17312 : Tree Nat := .node node17311 node10518 +def node17313 : Tree Nat := .node node17312 node12636 +def node17314 : Tree Nat := .node node12634 node17313 +def node17315 : Tree Nat := .node node17314 node17051 +def node17316 : Tree Nat := .node node17047 node17315 +def node17317 : Tree Nat := .node node17310 node17316 +def node17318 : Tree Nat := .node node17304 node17317 +def node17319 : Tree Nat := .node node17286 node17318 +def node17320 : Tree Nat := .node node17254 node17319 +def node17321 : Tree Nat := .leaf 12554203470773361527671578846415332841649443854667359453184 +def node17322 : Tree Nat := .node node17321 node8991 +def node17323 : Tree Nat := .node node17322 node11609 +def node17324 : Tree Nat := .node node12654 node17323 +def node17325 : Tree Nat := .node node17061 node17324 +def node17326 : Tree Nat := .leaf 2923003274661805836407369665432566041510888341504 +def node17327 : Tree Nat := .node node17326 node8998 +def node17328 : Tree Nat := .node node17327 node11938 +def node17329 : Tree Nat := .node node11936 node17328 +def node17330 : Tree Nat := .node node17329 node16650 +def node17331 : Tree Nat := .node node17325 node17330 +def node17332 : Tree Nat := .leaf 191561942608236107294793378393788648096457578348806144 +def node17333 : Tree Nat := .node node17332 node9015 +def node17334 : Tree Nat := .node node17333 node12659 +def node17335 : Tree Nat := .node node12284 node17334 +def node17336 : Tree Nat := .node node17335 node12289 +def node17337 : Tree Nat := .node node17068 node17336 +def node17338 : Tree Nat := .node node17331 node17337 +def node17339 : Tree Nat := .leaf 748288838313422294120286634350736906626787415425024 +def node17340 : Tree Nat := .node node17339 node9031 +def node17341 : Tree Nat := .node node17340 node11951 +def node17342 : Tree Nat := .node node10904 node17341 +def node17343 : Tree Nat := .node node17342 node16685 +def node17344 : Tree Nat := .node node17075 node17343 +def node17345 : Tree Nat := .leaf 49039857307708443467467104868809893912693140057294372864 +def node17346 : Tree Nat := .node node17345 node9042 +def node17347 : Tree Nat := .node node17346 node12316 +def node17348 : Tree Nat := .node node12314 node17347 +def node17349 : Tree Nat := .node node17348 node17085 +def node17350 : Tree Nat := .node node17081 node17349 +def node17351 : Tree Nat := .node node17344 node17350 +def node17352 : Tree Nat := .node node17338 node17351 +def node17353 : Tree Nat := .leaf 200867255532373784442745261542645325466391101674677751250944 +def node17354 : Tree Nat := .node node17353 node10568 +def node17355 : Tree Nat := .node node17354 node12671 +def node17356 : Tree Nat := .node node11279 node17355 +def node17357 : Tree Nat := .node node17093 node17356 +def node17358 : Tree Nat := .leaf 46768052394588893382517914646921056664174213464064 +def node17359 : Tree Nat := .node node17358 node6975 +def node17360 : Tree Nat := .node node17359 node11980 +def node17361 : Tree Nat := .node node12677 node17360 +def node17362 : Tree Nat := .node node17361 node16721 +def node17363 : Tree Nat := .node node17357 node17362 +def node17364 : Tree Nat := .leaf 3064991081731777716716694054300618369543321253580898304 +def node17365 : Tree Nat := .node node17364 node6986 +def node17366 : Tree Nat := .node node17365 node12687 +def node17367 : Tree Nat := .node node10276 node17366 +def node17368 : Tree Nat := .node node17367 node11298 +def node17369 : Tree Nat := .node node17100 node17368 +def node17370 : Tree Nat := .node node17363 node17369 +def node17371 : Tree Nat := .leaf 11972621413014756705924586149611790506028598646800384 +def node17372 : Tree Nat := .node node17371 node9081 +def node17373 : Tree Nat := .node node17372 node10952 +def node17374 : Tree Nat := .node node10288 node17373 +def node17375 : Tree Nat := .node node17374 node16756 +def node17376 : Tree Nat := .node node17107 node17375 +def node17377 : Tree Nat := .leaf 784637716923335095479473677900958302603090240916709965824 +def node17378 : Tree Nat := .node node17377 node9092 +def node17379 : Tree Nat := .node node17378 node12361 +def node17380 : Tree Nat := .node node12711 node17379 +def node17381 : Tree Nat := .node node17380 node17117 +def node17382 : Tree Nat := .node node17113 node17381 +def node17383 : Tree Nat := .node node17376 node17382 +def node17384 : Tree Nat := .node node17370 node17383 +def node17385 : Tree Nat := .node node17352 node17384 +def node17386 : Tree Nat := .leaf 50216813883093446110686315385661331366597775418669437812736 +def node17387 : Tree Nat := .node node17386 node9109 +def node17388 : Tree Nat := .node node17387 node12723 +def node17389 : Tree Nat := .node node11328 node17388 +def node17390 : Tree Nat := .node node17126 node17389 +def node17391 : Tree Nat := .leaf 11692013098647223345629478661730264166043553366016 +def node17392 : Tree Nat := .node node17391 node9114 +def node17393 : Tree Nat := .node node17392 node9386 +def node17394 : Tree Nat := .node node12376 node17393 +def node17395 : Tree Nat := .node node17394 node16793 +def node17396 : Tree Nat := .node node17390 node17395 +def node17397 : Tree Nat := .leaf 766247770432944429179173513575154592385830313395224576 +def node17398 : Tree Nat := .node node17397 node9129 +def node17399 : Tree Nat := .node node17398 node12386 +def node17400 : Tree Nat := .node node12735 node17399 +def node17401 : Tree Nat := .node node17400 node9961 +def node17402 : Tree Nat := .node node17133 node17401 +def node17403 : Tree Nat := .node node17396 node17402 +def node17404 : Tree Nat := .leaf 2993155353253689176481146537402947626507149661700096 +def node17405 : Tree Nat := .node node17404 node9667 +def node17406 : Tree Nat := .node node17405 node12398 +def node17407 : Tree Nat := .node node12751 node17406 +def node17408 : Tree Nat := .node node17407 node16828 +def node17409 : Tree Nat := .node node17140 node17408 +def node17410 : Tree Nat := .leaf 196159429230833773869868419475239575650772560229177491456 +def node17411 : Tree Nat := .node node17410 node9678 +def node17412 : Tree Nat := .node node17411 node12414 +def node17413 : Tree Nat := .node node12903 node17412 +def node17414 : Tree Nat := .node node17413 node17150 +def node17415 : Tree Nat := .node node17146 node17414 +def node17416 : Tree Nat := .node node17409 node17415 +def node17417 : Tree Nat := .node node17403 node17416 +def node17418 : Tree Nat := .leaf 803469022129495137770981046170581301865564406698711005003776 +def node17419 : Tree Nat := .node node17418 node9690 +def node17420 : Tree Nat := .node node17419 node12048 +def node17421 : Tree Nat := .node node11721 node17420 +def node17422 : Tree Nat := .node node17158 node17421 +def node17423 : Tree Nat := .leaf 187072209578355573530071658587684226656696853856256 +def node17424 : Tree Nat := .node node17423 node9695 +def node17425 : Tree Nat := .node node17424 node12422 +def node17426 : Tree Nat := .node node12920 node17425 +def node17427 : Tree Nat := .node node17426 node16864 +def node17428 : Tree Nat := .node node17422 node17427 +def node17429 : Tree Nat := .leaf 12259964326927110866866776217202473478173285014323593216 +def node17430 : Tree Nat := .node node17429 node9714 +def node17431 : Tree Nat := .node node17430 node12428 +def node17432 : Tree Nat := .node node12935 node17431 +def node17433 : Tree Nat := .node node17432 node12940 +def node17434 : Tree Nat := .node node17165 node17433 +def node17435 : Tree Nat := .node node17428 node17434 +def node17436 : Tree Nat := .leaf 47890485652059026823698344598447162024114394587201536 +def node17437 : Tree Nat := .node node17436 node11750 +def node17438 : Tree Nat := .node node17437 node12794 +def node17439 : Tree Nat := .node node12792 node17438 +def node17440 : Tree Nat := .node node17439 node16894 +def node17441 : Tree Nat := .node node17177 node17440 +def node17442 : Tree Nat := .leaf 730750818665451459101842416358141510377722085376 +def node17443 : Tree Nat := .node node17442 node12096 +def node17444 : Tree Nat := .node node17443 node12099 +def node17445 : Tree Nat := .node node10663 node17444 +def node17446 : Tree Nat := .node node17445 node16904 +def node17447 : Tree Nat := .leaf 3138550867693340381917894711603833210412360963666839863296 +def node17448 : Tree Nat := .node node17447 node11764 +def node17449 : Tree Nat := .node node17448 node11423 +def node17450 : Tree Nat := .node node12801 node17449 +def node17451 : Tree Nat := .node node17450 node17182 +def node17452 : Tree Nat := .node node17446 node17451 +def node17453 : Tree Nat := .node node17441 node17452 +def node17454 : Tree Nat := .node node17435 node17453 +def node17455 : Tree Nat := .node node17417 node17454 +def node17456 : Tree Nat := .node node17385 node17455 +def node17457 : Tree Nat := .node node17320 node17456 +def node17458 : Tree Nat := .leaf 26959946667150639794667015087019630693919554026192242905050861535232 +def node17459 : Tree Nat := .node node17458 node11437 +def node17460 : Tree Nat := .node node17459 node12118 +def node17461 : Tree Nat := .node node9229 node17460 +def node17462 : Tree Nat := .node node17198 node17461 +def node17463 : Tree Nat := .node node17194 node17462 +def node17464 : Tree Nat := .leaf 411376139330301510538742295639337626555168976229740034561933312 +def node17465 : Tree Nat := .node node17464 node9504 +def node17466 : Tree Nat := .node node17465 node12478 +def node17467 : Tree Nat := .node node12837 node17466 +def node17468 : Tree Nat := .node node16926 node17467 +def node17469 : Tree Nat := .node node17468 node17205 +def node17470 : Tree Nat := .node node17463 node17469 +def node17471 : Tree Nat := .leaf 1606938044258990275541962092341162603731128813397422010007552 +def node17472 : Tree Nat := .node node17471 node8813 +def node17473 : Tree Nat := .node node17472 node12501 +def node17474 : Tree Nat := .node node11789 node17473 +def node17475 : Tree Nat := .node node16933 node17474 +def node17476 : Tree Nat := .leaf 6901746346790563787434755862277025457643405830705214183693020553019392 +def node17477 : Tree Nat := .node node17476 node12143 +def node17478 : Tree Nat := .node node17477 node12146 +def node17479 : Tree Nat := .node node12142 node17478 +def node17480 : Tree Nat := .node node17211 node17479 +def node17481 : Tree Nat := .node node17475 node17480 +def node17482 : Tree Nat := .leaf 105312291668557186697918027683670432398123257914813448847854927872 +def node17483 : Tree Nat := .node node17482 node8828 +def node17484 : Tree Nat := .node node17483 node12507 +def node17485 : Tree Nat := .node node12153 node17484 +def node17486 : Tree Nat := .node node16939 node17485 +def node17487 : Tree Nat := .node node17486 node17218 +def node17488 : Tree Nat := .node node17481 node17487 +def node17489 : Tree Nat := .node node17470 node17488 +def node17490 : Tree Nat := .leaf 431359146674410236714672241392314091102712864419075886480813784563712 +def node17491 : Tree Nat := .node node17490 node11476 +def node17492 : Tree Nat := .node node17491 node8427 +def node17493 : Tree Nat := .node node8425 node17492 +def node17494 : Tree Nat := .node node17230 node17493 +def node17495 : Tree Nat := .node node17226 node17494 +def node17496 : Tree Nat := .leaf 6582018229284824168619876730229402024882703619675840552990932992 +def node17497 : Tree Nat := .node node17496 node8862 +def node17498 : Tree Nat := .node node17497 node11822 +def node17499 : Tree Nat := .node node11489 node17498 +def node17500 : Tree Nat := .node node16958 node17499 +def node17501 : Tree Nat := .node node17500 node17237 +def node17502 : Tree Nat := .node node17495 node17501 +def node17503 : Tree Nat := .leaf 25711008708143844408671393477458601659698061014358752160120832 +def node17504 : Tree Nat := .node node17503 node8884 +def node17505 : Tree Nat := .node node17504 node11504 +def node17506 : Tree Nat := .node node12182 node17505 +def node17507 : Tree Nat := .node node16970 node17506 +def node17508 : Tree Nat := .leaf 110427941548649020598956093796432407322294493291283426939088328848310272 +def node17509 : Tree Nat := .node node17508 node12542 +def node17510 : Tree Nat := .node node17509 node10091 +def node17511 : Tree Nat := .node node12191 node17510 +def node17512 : Tree Nat := .node node17243 node17511 +def node17513 : Tree Nat := .node node17507 node17512 +def node17514 : Tree Nat := .leaf 1684996666696914987166688442938726918369972126637015181565678845952 +def node17515 : Tree Nat := .node node17514 node9275 +def node17516 : Tree Nat := .node node17515 node10410 +def node17517 : Tree Nat := .node node12197 node17516 +def node17518 : Tree Nat := .node node16976 node17517 +def node17519 : Tree Nat := .node node17518 node17250 +def node17520 : Tree Nat := .node node17513 node17519 +def node17521 : Tree Nat := .node node17502 node17520 +def node17522 : Tree Nat := .node node17489 node17521 +def node17523 : Tree Nat := .leaf 107839786668602559178668060348078522775678216104768971620203446140928 +def node17524 : Tree Nat := .node node17523 node11144 +def node17525 : Tree Nat := .node node17524 node9798 +def node17526 : Tree Nat := .node node10112 node17525 +def node17527 : Tree Nat := .node node17263 node17526 +def node17528 : Tree Nat := .node node17259 node17527 +def node17529 : Tree Nat := .leaf 1645504557321206042154969182557350506220675904918960138247733248 +def node17530 : Tree Nat := .node node17529 node7235 +def node17531 : Tree Nat := .node node17530 node11151 +def node17532 : Tree Nat := .node node11535 node17531 +def node17533 : Tree Nat := .node node16996 node17532 +def node17534 : Tree Nat := .node node17533 node17270 +def node17535 : Tree Nat := .node node17528 node17534 +def node17536 : Tree Nat := .leaf 6427752177035961102167848369364650414924515253589688040030208 +def node17537 : Tree Nat := .node node17536 node7242 +def node17538 : Tree Nat := .node node17537 node11550 +def node17539 : Tree Nat := .node node11548 node17538 +def node17540 : Tree Nat := .node node17008 node17539 +def node17541 : Tree Nat := .leaf 27606985387162255149739023449108101830573623322820856734772082212077568 +def node17542 : Tree Nat := .node node17541 node12220 +def node17543 : Tree Nat := .node node17542 node8508 +def node17544 : Tree Nat := .node node11880 node17543 +def node17545 : Tree Nat := .node node17276 node17544 +def node17546 : Tree Nat := .node node17540 node17545 +def node17547 : Tree Nat := .leaf 421249166674228746791672110734681729592493031659253795391419711488 +def node17548 : Tree Nat := .node node17547 node10800 +def node17549 : Tree Nat := .node node17548 node11885 +def node17550 : Tree Nat := .node node11557 node17549 +def node17551 : Tree Nat := .node node17014 node17550 +def node17552 : Tree Nat := .node node17551 node17283 +def node17553 : Tree Nat := .node node17546 node17552 +def node17554 : Tree Nat := .node node17535 node17553 +def node17555 : Tree Nat := .leaf 1725436586697640946858688965569256364410851457676303545923255138254848 +def node17556 : Tree Nat := .node node17555 node11897 +def node17557 : Tree Nat := .node node17556 node12239 +def node17558 : Tree Nat := .node node11185 node17557 +def node17559 : Tree Nat := .node node17295 node17558 +def node17560 : Tree Nat := .node node17291 node17559 +def node17561 : Tree Nat := .leaf 26328072917139296674479506920917608099530814478703362211963731968 +def node17562 : Tree Nat := .node node17561 node10165 +def node17563 : Tree Nat := .node node17562 node12603 +def node17564 : Tree Nat := .node node12246 node17563 +def node17565 : Tree Nat := .node node17033 node17564 +def node17566 : Tree Nat := .node node17565 node17302 +def node17567 : Tree Nat := .node node17560 node17566 +def node17568 : Tree Nat := .leaf 102844034832575377634685573909834406638792244057435008640483328 +def node17569 : Tree Nat := .node node17568 node10500 +def node17570 : Tree Nat := .node node17569 node12622 +def node17571 : Tree Nat := .node node11206 node17570 +def node17572 : Tree Nat := .node node17040 node17571 +def node17573 : Tree Nat := .leaf 441711766194596082395824375185729629289177973165133707756353315393241088 +def node17574 : Tree Nat := .node node17573 node7290 +def node17575 : Tree Nat := .node node17574 node12267 +def node17576 : Tree Nat := .node node11926 node17575 +def node17577 : Tree Nat := .node node17308 node17576 +def node17578 : Tree Nat := .node node17572 node17577 +def node17579 : Tree Nat := .leaf 6739986666787659948666753771754907673479888506548060726262715383808 +def node17580 : Tree Nat := .node node17579 node10848 +def node17581 : Tree Nat := .node node17580 node12628 +def node17582 : Tree Nat := .node node10204 node17581 +def node17583 : Tree Nat := .node node17046 node17582 +def node17584 : Tree Nat := .node node17583 node17315 +def node17585 : Tree Nat := .node node17578 node17584 +def node17586 : Tree Nat := .node node17567 node17585 +def node17587 : Tree Nat := .node node17554 node17586 +def node17588 : Tree Nat := .node node17522 node17587 +def node17589 : Tree Nat := .leaf 53919893334301279589334030174039261387839108052384485810101723070464 +def node17590 : Tree Nat := .node node17589 node11616 +def node17591 : Tree Nat := .node node17590 node8574 +def node17592 : Tree Nat := .node node11615 node17591 +def node17593 : Tree Nat := .node node17329 node17592 +def node17594 : Tree Nat := .node node17325 node17593 +def node17595 : Tree Nat := .leaf 822752278660603021077484591278675253110337952459480069123866624 +def node17596 : Tree Nat := .node node17595 node9008 +def node17597 : Tree Nat := .node node17596 node11239 +def node17598 : Tree Nat := .node node10884 node17597 +def node17599 : Tree Nat := .node node17067 node17598 +def node17600 : Tree Nat := .node node17599 node17336 +def node17601 : Tree Nat := .node node17594 node17600 +def node17602 : Tree Nat := .leaf 3213876088517980551083924184682325207462257626794844020015104 +def node17603 : Tree Nat := .node node17602 node9026 +def node17604 : Tree Nat := .node node17603 node11634 +def node17605 : Tree Nat := .node node11946 node17604 +def node17606 : Tree Nat := .node node17074 node17605 +def node17607 : Tree Nat := .leaf 13803492693581127574869511724554050915286811661410428367386041106038784 +def node17608 : Tree Nat := .node node17607 node12301 +def node17609 : Tree Nat := .node node17608 node6951 +def node17610 : Tree Nat := .node node12300 node17609 +def node17611 : Tree Nat := .node node17342 node17610 +def node17612 : Tree Nat := .node node17606 node17611 +def node17613 : Tree Nat := .leaf 210624583337114373395836055367340864796246515829626897695709855744 +def node17614 : Tree Nat := .node node17613 node9350 +def node17615 : Tree Nat := .node node17614 node11961 +def node17616 : Tree Nat := .node node12309 node17615 +def node17617 : Tree Nat := .node node17080 node17616 +def node17618 : Tree Nat := .node node17617 node17349 +def node17619 : Tree Nat := .node node17612 node17618 +def node17620 : Tree Nat := .node node17601 node17619 +def node17621 : Tree Nat := .leaf 862718293348820473429344482784628182205425728838151772961627569127424 +def node17622 : Tree Nat := .node node17621 node11658 +def node17623 : Tree Nat := .node node17622 node12328 +def node17624 : Tree Nat := .node node11985 node17623 +def node17625 : Tree Nat := .node node17361 node17624 +def node17626 : Tree Nat := .node node17357 node17625 +def node17627 : Tree Nat := .leaf 13164036458569648337239753460458804049765407239351681105981865984 +def node17628 : Tree Nat := .node node17627 node7369 +def node17629 : Tree Nat := .node node17628 node12682 +def node17630 : Tree Nat := .node node11666 node17629 +def node17631 : Tree Nat := .node node17099 node17630 +def node17632 : Tree Nat := .node node17631 node17368 +def node17633 : Tree Nat := .node node17626 node17632 +def node17634 : Tree Nat := .leaf 51422017416287688817342786954917203319396122028717504320241664 +def node17635 : Tree Nat := .node node17634 node9076 +def node17636 : Tree Nat := .node node17635 node12694 +def node17637 : Tree Nat := .node node12342 node17636 +def node17638 : Tree Nat := .node node17106 node17637 +def node17639 : Tree Nat := .leaf 220855883097298041197912187592864814644588986582566853878176657696620544 +def node17640 : Tree Nat := .node node17639 node12698 +def node17641 : Tree Nat := .node node17640 node12349 +def node17642 : Tree Nat := .node node12347 node17641 +def node17643 : Tree Nat := .node node17374 node17642 +def node17644 : Tree Nat := .node node17638 node17643 +def node17645 : Tree Nat := .leaf 3369993333393829974333376885877453836739944253274030363131357691904 +def node17646 : Tree Nat := .node node17645 node9376 +def node17647 : Tree Nat := .node node17646 node12705 +def node17648 : Tree Nat := .node node12356 node17647 +def node17649 : Tree Nat := .node node17112 node17648 +def node17650 : Tree Nat := .node node17649 node17381 +def node17651 : Tree Nat := .node node17644 node17650 +def node17652 : Tree Nat := .node node17633 node17651 +def node17653 : Tree Nat := .node node17620 node17652 +def node17654 : Tree Nat := .leaf 215679573337205118357336120696157045551356432209537943240406892281856 +def node17655 : Tree Nat := .node node17654 node11694 +def node17656 : Tree Nat := .node node17655 node12379 +def node17657 : Tree Nat := .node node12022 node17656 +def node17658 : Tree Nat := .node node17394 node17657 +def node17659 : Tree Nat := .node node17390 node17658 +def node17660 : Tree Nat := .leaf 3291009114642412084309938365114701012441351809837920276495466496 +def node17661 : Tree Nat := .node node17660 node9124 +def node17662 : Tree Nat := .node node17661 node12729 +def node17663 : Tree Nat := .node node10996 node17662 +def node17664 : Tree Nat := .node node17132 node17663 +def node17665 : Tree Nat := .node node17664 node17401 +def node17666 : Tree Nat := .node node17659 node17665 +def node17667 : Tree Nat := .node node17136 node9401 +def node17668 : Tree Nat := .node node17667 node12741 +def node17669 : Tree Nat := .node node10319 node17668 +def node17670 : Tree Nat := .leaf 12855504354071922204335696738729300829849030507179376080060416 +def node17671 : Tree Nat := .node node17670 node9662 +def node17672 : Tree Nat := .node node17671 node12745 +def node17673 : Tree Nat := .node node12394 node17672 +def node17674 : Tree Nat := .node node17669 node17673 +def node17675 : Tree Nat := .leaf 55213970774324510299478046898216203661147246645641713469544164424155136 +def node17676 : Tree Nat := .node node17675 node12404 +def node17677 : Tree Nat := .node node17676 node12407 +def node17678 : Tree Nat := .node node12403 node17677 +def node17679 : Tree Nat := .node node17407 node17678 +def node17680 : Tree Nat := .node node17674 node17679 +def node17681 : Tree Nat := .leaf 842498333348457493583344221469363459184986063318507590782839422976 +def node17682 : Tree Nat := .node node17681 node11357 +def node17683 : Tree Nat := .node node17682 node12760 +def node17684 : Tree Nat := .node node12898 node17683 +def node17685 : Tree Nat := .node node17145 node17684 +def node17686 : Tree Nat := .leaf 226264784939950833903616720339055966478327916129259925075926351140805642948761479323221608418489175403251658307292175384581583417121224494645471140538575501166256808361813892031716458496 +def node17687 : Tree Nat := .node node1725 node17686 +def node17688 : Tree Nat := .node node17687 node8301 +def node17689 : Tree Nat := .node node17688 node17412 +def node17690 : Tree Nat := .node node17689 node17150 +def node17691 : Tree Nat := .node node17685 node17690 +def node17692 : Tree Nat := .node node17680 node17691 +def node17693 : Tree Nat := .node node17666 node17692 +def node17694 : Tree Nat := .leaf 3450873173395281893717377931138512728821702915352607091846510276509696 +def node17695 : Tree Nat := .node node17694 node12059 +def node17696 : Tree Nat := .node node17695 node7055 +def node17697 : Tree Nat := .node node11726 node17696 +def node17698 : Tree Nat := .node node17426 node17697 +def node17699 : Tree Nat := .node node17422 node17698 +def node17700 : Tree Nat := .leaf 52656145834278593348959013841835216199061628957406724423927463936 +def node17701 : Tree Nat := .node node17700 node9709 +def node17702 : Tree Nat := .node node17701 node12066 +def node17703 : Tree Nat := .node node12930 node17702 +def node17704 : Tree Nat := .node node17164 node17703 +def node17705 : Tree Nat := .node node17704 node17433 +def node17706 : Tree Nat := .node node17699 node17705 +def node17707 : Tree Nat := .leaf 205688069665150755269371147819668813277584488114870017280966656 +def node17708 : Tree Nat := .node node17707 node11745 +def node17709 : Tree Nat := .node node17708 node12082 +def node17710 : Tree Nat := .node node12440 node17709 +def node17711 : Tree Nat := .node node17176 node17710 +def node17712 : Tree Nat := .leaf 883423532389192164791648750371459258578355946330267415512706630786482176 +def node17713 : Tree Nat := .node node17712 node11408 +def node17714 : Tree Nat := .node node17713 node9187 +def node17715 : Tree Nat := .node node12092 node17714 +def node17716 : Tree Nat := .node node17439 node17715 +def node17717 : Tree Nat := .node node17711 node17716 +def node17718 : Tree Nat := .leaf 13479973333575319897333507543509815346959777013096121452525430767616 +def node17719 : Tree Nat := .node node17718 node11417 +def node17720 : Tree Nat := .node node17719 node9193 +def node17721 : Tree Nat := .node node12446 node17720 +def node17722 : Tree Nat := .node node17445 node17721 +def node17723 : Tree Nat := .node node17722 node17451 +def node17724 : Tree Nat := .node node17717 node17723 +def node17725 : Tree Nat := .node node17706 node17724 +def node17726 : Tree Nat := .node node17693 node17725 +def node17727 : Tree Nat := .node node17653 node17726 +def node17728 : Tree Nat := .node node17588 node17727 +def node17729 : Tree Nat := .node node16917 node9211 +def node17730 : Tree Nat := .node node17729 node8784 +def node17731 : Tree Nat := .node node10046 node17730 +def node17732 : Tree Nat := .node node9216 node12467 +def node17733 : Tree Nat := .node node17190 node9483 +def node17734 : Tree Nat := .node node17733 node11068 +def node17735 : Tree Nat := .node node17732 node17734 +def node17736 : Tree Nat := .node node17731 node17735 +def node17737 : Tree Nat := .node node10351 node17197 +def node17738 : Tree Nat := .node node17737 node17461 +def node17739 : Tree Nat := .node node17736 node17738 +def node17740 : Tree Nat := .node node10357 node16925 +def node17741 : Tree Nat := .node node11449 node17466 +def node17742 : Tree Nat := .node node17740 node17741 +def node17743 : Tree Nat := .node node17201 node9509 +def node17744 : Tree Nat := .node node17743 node12125 +def node17745 : Tree Nat := .node node12484 node17744 +def node17746 : Tree Nat := .node node17745 node11783 +def node17747 : Tree Nat := .node node17742 node17746 +def node17748 : Tree Nat := .node node17739 node17747 +def node17749 : Tree Nat := .node node16931 node8810 +def node17750 : Tree Nat := .node node12133 node17749 +def node17751 : Tree Nat := .node node17472 node11791 +def node17752 : Tree Nat := .node node11789 node17751 +def node17753 : Tree Nat := .node node17750 node17752 +def node17754 : Tree Nat := .node node17753 node17480 +def node17755 : Tree Nat := .node node17483 node11803 +def node17756 : Tree Nat := .node node12153 node17755 +def node17757 : Tree Nat := .node node16939 node17756 +def node17758 : Tree Nat := .node node17215 node12160 +def node17759 : Tree Nat := .node node12158 node17758 +def node17760 : Tree Nat := .node node17759 node16944 +def node17761 : Tree Nat := .node node17757 node17760 +def node17762 : Tree Nat := .node node17754 node17761 +def node17763 : Tree Nat := .node node17748 node17762 +def node17764 : Tree Nat := .node node10725 node17229 +def node17765 : Tree Nat := .node node17764 node17493 +def node17766 : Tree Nat := .node node17226 node17765 +def node17767 : Tree Nat := .node node10731 node16957 +def node17768 : Tree Nat := .node node17767 node17499 +def node17769 : Tree Nat := .node node17234 node10735 +def node17770 : Tree Nat := .node node11494 node17769 +def node17771 : Tree Nat := .node node17770 node12176 +def node17772 : Tree Nat := .node node17768 node17771 +def node17773 : Tree Nat := .node node17766 node17772 +def node17774 : Tree Nat := .node node16968 node11122 +def node17775 : Tree Nat := .node node11835 node17774 +def node17776 : Tree Nat := .node node17775 node17506 +def node17777 : Tree Nat := .node node17508 node9778 +def node17778 : Tree Nat := .node node17777 node10091 +def node17779 : Tree Nat := .node node12191 node17778 +def node17780 : Tree Nat := .node node17243 node17779 +def node17781 : Tree Nat := .node node17776 node17780 +def node17782 : Tree Nat := .node node11849 node17248 +def node17783 : Tree Nat := .node node17782 node16981 +def node17784 : Tree Nat := .node node17518 node17783 +def node17785 : Tree Nat := .node node17781 node17784 +def node17786 : Tree Nat := .node node17773 node17785 +def node17787 : Tree Nat := .node node17763 node17786 +def node17788 : Tree Nat := .node node11540 node17268 +def node17789 : Tree Nat := .node node17788 node12216 +def node17790 : Tree Nat := .node node17533 node17789 +def node17791 : Tree Nat := .node node17528 node17790 +def node17792 : Tree Nat := .node node17006 node8927 +def node17793 : Tree Nat := .node node10450 node17792 +def node17794 : Tree Nat := .node node17793 node17539 +def node17795 : Tree Nat := .node node17794 node17545 +def node17796 : Tree Nat := .node node17280 node10806 +def node17797 : Tree Nat := .node node11562 node17796 +def node17798 : Tree Nat := .node node17018 node10143 +def node17799 : Tree Nat := .node node17797 node17798 +def node17800 : Tree Nat := .node node17551 node17799 +def node17801 : Tree Nat := .node node17795 node17800 +def node17802 : Tree Nat := .node node17791 node17801 +def node17803 : Tree Nat := .node node10153 node17026 +def node17804 : Tree Nat := .node node17288 node11572 +def node17805 : Tree Nat := .node node11570 node17804 +def node17806 : Tree Nat := .node node17803 node17805 +def node17807 : Tree Nat := .node node17806 node17559 +def node17808 : Tree Nat := .node node17031 node10823 +def node17809 : Tree Nat := .node node10491 node17808 +def node17810 : Tree Nat := .node node17809 node17564 +def node17811 : Tree Nat := .node node17299 node12253 +def node17812 : Tree Nat := .node node12251 node17811 +def node17813 : Tree Nat := .node node17812 node11920 +def node17814 : Tree Nat := .node node17810 node17813 +def node17815 : Tree Nat := .node node17807 node17814 +def node17816 : Tree Nat := .node node17038 node8972 +def node17817 : Tree Nat := .node node10836 node17816 +def node17818 : Tree Nat := .node node17569 node11596 +def node17819 : Tree Nat := .node node11206 node17818 +def node17820 : Tree Nat := .node node17817 node17819 +def node17821 : Tree Nat := .node node17820 node17577 +def node17822 : Tree Nat := .node node17580 node5301 +def node17823 : Tree Nat := .node node10204 node17822 +def node17824 : Tree Nat := .node node17046 node17823 +def node17825 : Tree Nat := .node node10855 node17313 +def node17826 : Tree Nat := .node node17825 node17051 +def node17827 : Tree Nat := .node node17824 node17826 +def node17828 : Tree Nat := .node node17821 node17827 +def node17829 : Tree Nat := .node node17815 node17828 +def node17830 : Tree Nat := .node node17802 node17829 +def node17831 : Tree Nat := .node node17787 node17830 +def node17832 : Tree Nat := .node node17059 node8988 +def node17833 : Tree Nat := .node node12647 node17832 +def node17834 : Tree Nat := .node node17833 node17324 +def node17835 : Tree Nat := .node node17834 node17593 +def node17836 : Tree Nat := .node node17835 node17600 +def node17837 : Tree Nat := .node node17836 node17619 +def node17838 : Tree Nat := .node node17091 node9055 +def node17839 : Tree Nat := .node node10265 node17838 +def node17840 : Tree Nat := .node node17354 node11654 +def node17841 : Tree Nat := .node node11279 node17840 +def node17842 : Tree Nat := .node node17839 node17841 +def node17843 : Tree Nat := .node node11978 node17360 +def node17844 : Tree Nat := .node node17843 node17624 +def node17845 : Tree Nat := .node node17842 node17844 +def node17846 : Tree Nat := .node node17365 node12334 +def node17847 : Tree Nat := .node node10276 node17846 +def node17848 : Tree Nat := .node node17847 node11298 +def node17849 : Tree Nat := .node node17631 node17848 +def node17850 : Tree Nat := .node node17845 node17849 +def node17851 : Tree Nat := .node node17635 node11675 +def node17852 : Tree Nat := .node node12342 node17851 +def node17853 : Tree Nat := .node node17106 node17852 +def node17854 : Tree Nat := .node node17639 node9932 +def node17855 : Tree Nat := .node node17854 node12349 +def node17856 : Tree Nat := .node node12347 node17855 +def node17857 : Tree Nat := .node node17374 node17856 +def node17858 : Tree Nat := .node node17853 node17857 +def node17859 : Tree Nat := .node node12009 node17379 +def node17860 : Tree Nat := .node node17859 node17117 +def node17861 : Tree Nat := .node node17649 node17860 +def node17862 : Tree Nat := .node node17858 node17861 +def node17863 : Tree Nat := .node node17850 node17862 +def node17864 : Tree Nat := .node node17837 node17863 +def node17865 : Tree Nat := .node node17124 node9106 +def node17866 : Tree Nat := .node node12371 node17865 +def node17867 : Tree Nat := .node node17387 node11690 +def node17868 : Tree Nat := .node node11328 node17867 +def node17869 : Tree Nat := .node node17866 node17868 +def node17870 : Tree Nat := .node node17869 node17658 +def node17871 : Tree Nat := .node node11001 node17399 +def node17872 : Tree Nat := .node node17871 node9961 +def node17873 : Tree Nat := .node node17664 node17872 +def node17874 : Tree Nat := .node node17870 node17873 +def node17875 : Tree Nat := .node node17667 node9141 +def node17876 : Tree Nat := .node node10319 node17875 +def node17877 : Tree Nat := .node node17671 node11705 +def node17878 : Tree Nat := .node node12394 node17877 +def node17879 : Tree Nat := .node node17876 node17878 +def node17880 : Tree Nat := .node node9972 node17406 +def node17881 : Tree Nat := .node node17880 node17678 +def node17882 : Tree Nat := .node node17879 node17881 +def node17883 : Tree Nat := .node node9985 node17144 +def node17884 : Tree Nat := .node node11713 node17683 +def node17885 : Tree Nat := .node node17883 node17884 +def node17886 : Tree Nat := .node node9414 node17412 +def node17887 : Tree Nat := .node node17147 node9416 +def node17888 : Tree Nat := .node node17887 node11363 +def node17889 : Tree Nat := .node node17888 node12041 +def node17890 : Tree Nat := .node node17886 node17889 +def node17891 : Tree Nat := .node node17885 node17890 +def node17892 : Tree Nat := .node node17882 node17891 +def node17893 : Tree Nat := .node node17874 node17892 +def node17894 : Tree Nat := .node node17156 node9160 +def node17895 : Tree Nat := .node node10333 node17894 +def node17896 : Tree Nat := .node node17895 node17421 +def node17897 : Tree Nat := .node node12054 node17425 +def node17898 : Tree Nat := .node node17897 node17697 +def node17899 : Tree Nat := .node node17896 node17898 +def node17900 : Tree Nat := .node node17161 node9705 +def node17901 : Tree Nat := .node node17900 node11382 +def node17902 : Tree Nat := .node node10648 node17901 +def node17903 : Tree Nat := .node node11732 node17702 +def node17904 : Tree Nat := .node node17902 node17903 +def node17905 : Tree Nat := .node node11737 node17431 +def node17906 : Tree Nat := .node node17905 node12434 +def node17907 : Tree Nat := .node node17904 node17906 +def node17908 : Tree Nat := .node node17899 node17907 +def node17909 : Tree Nat := .node node10655 node17175 +def node17910 : Tree Nat := .node node17909 node17710 +def node17911 : Tree Nat := .node node17910 node17716 +def node17912 : Tree Nat := .node node12451 node17449 +def node17913 : Tree Nat := .node node17912 node17182 +def node17914 : Tree Nat := .node node17722 node17913 +def node17915 : Tree Nat := .node node17911 node17914 +def node17916 : Tree Nat := .node node17908 node17915 +def node17917 : Tree Nat := .node node17893 node17916 +def node17918 : Tree Nat := .node node17864 node17917 +def node17919 : Tree Nat := .node node17831 node17918 +def node17920 : Tree Nat := .node node10674 node17734 +def node17921 : Tree Nat := .node node17731 node17920 +def node17922 : Tree Nat := .node node17459 node5074 +def node17923 : Tree Nat := .node node9229 node17922 +def node17924 : Tree Nat := .node node17737 node17923 +def node17925 : Tree Nat := .node node17921 node17924 +def node17926 : Tree Nat := .node node17465 node11776 +def node17927 : Tree Nat := .node node11449 node17926 +def node17928 : Tree Nat := .node node17740 node17927 +def node17929 : Tree Nat := .node node17743 node10685 +def node17930 : Tree Nat := .node node10683 node17929 +def node17931 : Tree Nat := .node node17930 node11783 +def node17932 : Tree Nat := .node node17928 node17931 +def node17933 : Tree Nat := .node node17925 node17932 +def node17934 : Tree Nat := .node node10057 node17749 +def node17935 : Tree Nat := .node node17934 node17752 +def node17936 : Tree Nat := .node node17476 node9763 +def node17937 : Tree Nat := .node node17936 node5105 +def node17938 : Tree Nat := .node node11798 node17937 +def node17939 : Tree Nat := .node node17211 node17938 +def node17940 : Tree Nat := .node node17935 node17939 +def node17941 : Tree Nat := .node node11462 node17755 +def node17942 : Tree Nat := .node node16939 node17941 +def node17943 : Tree Nat := .node node17215 node10711 +def node17944 : Tree Nat := .node node10375 node17943 +def node17945 : Tree Nat := .node node17944 node16944 +def node17946 : Tree Nat := .node node17942 node17945 +def node17947 : Tree Nat := .node node17940 node17946 +def node17948 : Tree Nat := .node node17933 node17947 +def node17949 : Tree Nat := .node node17770 node11829 +def node17950 : Tree Nat := .node node17768 node17949 +def node17951 : Tree Nat := .node node17766 node17950 +def node17952 : Tree Nat := .node node11502 node17505 +def node17953 : Tree Nat := .node node17775 node17952 +def node17954 : Tree Nat := .node node17241 node11842 +def node17955 : Tree Nat := .node node11840 node17954 +def node17956 : Tree Nat := .node node11510 node17778 +def node17957 : Tree Nat := .node node17955 node17956 +def node17958 : Tree Nat := .node node17953 node17957 +def node17959 : Tree Nat := .node node11137 node17516 +def node17960 : Tree Nat := .node node16976 node17959 +def node17961 : Tree Nat := .node node17247 node10761 +def node17962 : Tree Nat := .node node11849 node17961 +def node17963 : Tree Nat := .node node16979 node8905 +def node17964 : Tree Nat := .node node17963 node10766 +def node17965 : Tree Nat := .node node17962 node17964 +def node17966 : Tree Nat := .node node17960 node17965 +def node17967 : Tree Nat := .node node17958 node17966 +def node17968 : Tree Nat := .node node17951 node17967 +def node17969 : Tree Nat := .node node17948 node17968 +def node17970 : Tree Nat := .node node17267 node10783 +def node17971 : Tree Nat := .node node11540 node17970 +def node17972 : Tree Nat := .node node17971 node11865 +def node17973 : Tree Nat := .node node17533 node17972 +def node17974 : Tree Nat := .node node17528 node17973 +def node17975 : Tree Nat := .node node17541 node9818 +def node17976 : Tree Nat := .node node17975 node8508 +def node17977 : Tree Nat := .node node11880 node17976 +def node17978 : Tree Nat := .node node17276 node17977 +def node17979 : Tree Nat := .node node17794 node17978 +def node17980 : Tree Nat := .node node17017 node8946 +def node17981 : Tree Nat := .node node17980 node10143 +def node17982 : Tree Nat := .node node17797 node17981 +def node17983 : Tree Nat := .node node17551 node17982 +def node17984 : Tree Nat := .node node17979 node17983 +def node17985 : Tree Nat := .node node17974 node17984 +def node17986 : Tree Nat := .node node17293 node10484 +def node17987 : Tree Nat := .node node10482 node17986 +def node17988 : Tree Nat := .node node17556 node5264 +def node17989 : Tree Nat := .node node11185 node17988 +def node17990 : Tree Nat := .node node17987 node17989 +def node17991 : Tree Nat := .node node17806 node17990 +def node17992 : Tree Nat := .node node17562 node11908 +def node17993 : Tree Nat := .node node11585 node17992 +def node17994 : Tree Nat := .node node17809 node17993 +def node17995 : Tree Nat := .node node17299 node10828 +def node17996 : Tree Nat := .node node10172 node17995 +def node17997 : Tree Nat := .node node17996 node11920 +def node17998 : Tree Nat := .node node17994 node17997 +def node17999 : Tree Nat := .node node17991 node17998 +def node18000 : Tree Nat := .node node17306 node10843 +def node18001 : Tree Nat := .node node12261 node18000 +def node18002 : Tree Nat := .node node17574 node5295 +def node18003 : Tree Nat := .node node11926 node18002 +def node18004 : Tree Nat := .node node18001 node18003 +def node18005 : Tree Nat := .node node17820 node18004 +def node18006 : Tree Nat := .node node17312 node10857 +def node18007 : Tree Nat := .node node10855 node18006 +def node18008 : Tree Nat := .node node18007 node17051 +def node18009 : Tree Nat := .node node17824 node18008 +def node18010 : Tree Nat := .node node18005 node18009 +def node18011 : Tree Nat := .node node17999 node18010 +def node18012 : Tree Nat := .node node17985 node18011 +def node18013 : Tree Nat := .node node17969 node18012 +def node18014 : Tree Nat := .node node10223 node17832 +def node18015 : Tree Nat := .node node11607 node17323 +def node18016 : Tree Nat := .node node18014 node18015 +def node18017 : Tree Nat := .node node18016 node17593 +def node18018 : Tree Nat := .node node17333 node10891 +def node18019 : Tree Nat := .node node11624 node18018 +def node18020 : Tree Nat := .node node18019 node11246 +def node18021 : Tree Nat := .node node17599 node18020 +def node18022 : Tree Nat := .node node18017 node18021 +def node18023 : Tree Nat := .node node10241 node17073 +def node18024 : Tree Nat := .node node18023 node17605 +def node18025 : Tree Nat := .node node17607 node9907 +def node18026 : Tree Nat := .node node18025 node6951 +def node18027 : Tree Nat := .node node11956 node18026 +def node18028 : Tree Nat := .node node17342 node18027 +def node18029 : Tree Nat := .node node18024 node18028 +def node18030 : Tree Nat := .node node11642 node17615 +def node18031 : Tree Nat := .node node17080 node18030 +def node18032 : Tree Nat := .node node17346 node10918 +def node18033 : Tree Nat := .node node11647 node18032 +def node18034 : Tree Nat := .node node17083 node11966 +def node18035 : Tree Nat := .node node18034 node11970 +def node18036 : Tree Nat := .node node18033 node18035 +def node18037 : Tree Nat := .node node18031 node18036 +def node18038 : Tree Nat := .node node18029 node18037 +def node18039 : Tree Nat := .node node18022 node18038 +def node18040 : Tree Nat := .node node17622 node5392 +def node18041 : Tree Nat := .node node11985 node18040 +def node18042 : Tree Nat := .node node17843 node18041 +def node18043 : Tree Nat := .node node17842 node18042 +def node18044 : Tree Nat := .node node17628 node11990 +def node18045 : Tree Nat := .node node11666 node18044 +def node18046 : Tree Nat := .node node17099 node18045 +def node18047 : Tree Nat := .node node17365 node10940 +def node18048 : Tree Nat := .node node10276 node18047 +def node18049 : Tree Nat := .node node18048 node11298 +def node18050 : Tree Nat := .node node18046 node18049 +def node18051 : Tree Nat := .node node18043 node18050 +def node18052 : Tree Nat := .node node11673 node17851 +def node18053 : Tree Nat := .node node17106 node18052 +def node18054 : Tree Nat := .node node17854 node5423 +def node18055 : Tree Nat := .node node10957 node18054 +def node18056 : Tree Nat := .node node17374 node18055 +def node18057 : Tree Nat := .node node18053 node18056 +def node18058 : Tree Nat := .node node17646 node5429 +def node18059 : Tree Nat := .node node11682 node18058 +def node18060 : Tree Nat := .node node17112 node18059 +def node18061 : Tree Nat := .node node17378 node10970 +def node18062 : Tree Nat := .node node12009 node18061 +def node18063 : Tree Nat := .node node18062 node17117 +def node18064 : Tree Nat := .node node18060 node18063 +def node18065 : Tree Nat := .node node18057 node18064 +def node18066 : Tree Nat := .node node18051 node18065 +def node18067 : Tree Nat := .node node18039 node18066 +def node18068 : Tree Nat := .node node10297 node17865 +def node18069 : Tree Nat := .node node18068 node17868 +def node18070 : Tree Nat := .node node17655 node5456 +def node18071 : Tree Nat := .node node12022 node18070 +def node18072 : Tree Nat := .node node17394 node18071 +def node18073 : Tree Nat := .node node18069 node18072 +def node18074 : Tree Nat := .node node17661 node12027 +def node18075 : Tree Nat := .node node10996 node18074 +def node18076 : Tree Nat := .node node17132 node18075 +def node18077 : Tree Nat := .node node17398 node11003 +def node18078 : Tree Nat := .node node11001 node18077 +def node18079 : Tree Nat := .node node18078 node9961 +def node18080 : Tree Nat := .node node18076 node18079 +def node18081 : Tree Nat := .node node18073 node18080 +def node18082 : Tree Nat := .node node11703 node17877 +def node18083 : Tree Nat := .node node17876 node18082 +def node18084 : Tree Nat := .node node17405 node10633 +def node18085 : Tree Nat := .node node9972 node18084 +def node18086 : Tree Nat := .node node17675 node9977 +def node18087 : Tree Nat := .node node18086 node5487 +def node18088 : Tree Nat := .node node12403 node18087 +def node18089 : Tree Nat := .node node18085 node18088 +def node18090 : Tree Nat := .node node18083 node18089 +def node18091 : Tree Nat := .node node17682 node5493 +def node18092 : Tree Nat := .node node11713 node18091 +def node18093 : Tree Nat := .node node17883 node18092 +def node18094 : Tree Nat := .node node17411 node11016 +def node18095 : Tree Nat := .node node9414 node18094 +def node18096 : Tree Nat := .node node18095 node17889 +def node18097 : Tree Nat := .node node18093 node18096 +def node18098 : Tree Nat := .node node18090 node18097 +def node18099 : Tree Nat := .node node18081 node18098 +def node18100 : Tree Nat := .node node17424 node12056 +def node18101 : Tree Nat := .node node12054 node18100 +def node18102 : Tree Nat := .node node18101 node17697 +def node18103 : Tree Nat := .node node17896 node18102 +def node18104 : Tree Nat := .node node17430 node11038 +def node18105 : Tree Nat := .node node11737 node18104 +def node18106 : Tree Nat := .node node18105 node12073 +def node18107 : Tree Nat := .node node17904 node18106 +def node18108 : Tree Nat := .node node18103 node18107 +def node18109 : Tree Nat := .node node11744 node17709 +def node18110 : Tree Nat := .node node17909 node18109 +def node18111 : Tree Nat := .node node17437 node12087 +def node18112 : Tree Nat := .node node11046 node18111 +def node18113 : Tree Nat := .node node18112 node17715 +def node18114 : Tree Nat := .node node18110 node18113 +def node18115 : Tree Nat := .node node11758 node17720 +def node18116 : Tree Nat := .node node17445 node18115 +def node18117 : Tree Nat := .node node11763 node17449 +def node18118 : Tree Nat := .node node17180 node11427 +def node18119 : Tree Nat := .node node18118 node12108 +def node18120 : Tree Nat := .node node18117 node18119 +def node18121 : Tree Nat := .node node18116 node18120 +def node18122 : Tree Nat := .node node18114 node18121 +def node18123 : Tree Nat := .node node18108 node18122 +def node18124 : Tree Nat := .node node18099 node18123 +def node18125 : Tree Nat := .node node18067 node18124 +def node18126 : Tree Nat := .node node18013 node18125 +def node18127 : Tree Nat := .node node17465 node11074 +def node18128 : Tree Nat := .node node11449 node18127 +def node18129 : Tree Nat := .node node17740 node18128 +def node18130 : Tree Nat := .node node17930 node9252 +def node18131 : Tree Nat := .node node18129 node18130 +def node18132 : Tree Nat := .node node17925 node18131 +def node18133 : Tree Nat := .node node17472 node10695 +def node18134 : Tree Nat := .node node11456 node18133 +def node18135 : Tree Nat := .node node17934 node18134 +def node18136 : Tree Nat := .node node10062 node17210 +def node18137 : Tree Nat := .node node11082 node17937 +def node18138 : Tree Nat := .node node18136 node18137 +def node18139 : Tree Nat := .node node18135 node18138 +def node18140 : Tree Nat := .node node17483 node11094 +def node18141 : Tree Nat := .node node11462 node18140 +def node18142 : Tree Nat := .node node16939 node18141 +def node18143 : Tree Nat := .node node16942 node11099 +def node18144 : Tree Nat := .node node18143 node10073 +def node18145 : Tree Nat := .node node17944 node18144 +def node18146 : Tree Nat := .node node18142 node18145 +def node18147 : Tree Nat := .node node18139 node18146 +def node18148 : Tree Nat := .node node18132 node18147 +def node18149 : Tree Nat := .node node17228 node10382 +def node18150 : Tree Nat := .node node10725 node18149 +def node18151 : Tree Nat := .node node17490 node9517 +def node18152 : Tree Nat := .node node18151 node8427 +def node18153 : Tree Nat := .node node8425 node18152 +def node18154 : Tree Nat := .node node18150 node18153 +def node18155 : Tree Nat := .node node17226 node18154 +def node18156 : Tree Nat := .node node17497 node11110 +def node18157 : Tree Nat := .node node11489 node18156 +def node18158 : Tree Nat := .node node17767 node18157 +def node18159 : Tree Nat := .node node17770 node11117 +def node18160 : Tree Nat := .node node18158 node18159 +def node18161 : Tree Nat := .node node18155 node18160 +def node18162 : Tree Nat := .node node9532 node17774 +def node18163 : Tree Nat := .node node11499 node10741 +def node18164 : Tree Nat := .node node10395 node18163 +def node18165 : Tree Nat := .node node18164 node17505 +def node18166 : Tree Nat := .node node18162 node18165 +def node18167 : Tree Nat := .node node17241 node10400 +def node18168 : Tree Nat := .node node10088 node18167 +def node18169 : Tree Nat := .node node10748 node17778 +def node18170 : Tree Nat := .node node18168 node18169 +def node18171 : Tree Nat := .node node18166 node18170 +def node18172 : Tree Nat := .node node11516 node17961 +def node18173 : Tree Nat := .node node18172 node17964 +def node18174 : Tree Nat := .node node17960 node18173 +def node18175 : Tree Nat := .node node18171 node18174 +def node18176 : Tree Nat := .node node18161 node18175 +def node18177 : Tree Nat := .node node18148 node18176 +def node18178 : Tree Nat := .node node17261 node9289 +def node18179 : Tree Nat := .node node10430 node18178 +def node18180 : Tree Nat := .node node18179 node17526 +def node18181 : Tree Nat := .node node17259 node18180 +def node18182 : Tree Nat := .node node17971 node9810 +def node18183 : Tree Nat := .node node17533 node18182 +def node18184 : Tree Nat := .node node18181 node18183 +def node18185 : Tree Nat := .node node17274 node10457 +def node18186 : Tree Nat := .node node10796 node18185 +def node18187 : Tree Nat := .node node11164 node17976 +def node18188 : Tree Nat := .node node18186 node18187 +def node18189 : Tree Nat := .node node17794 node18188 +def node18190 : Tree Nat := .node node17548 node11176 +def node18191 : Tree Nat := .node node11174 node18190 +def node18192 : Tree Nat := .node node17014 node18191 +def node18193 : Tree Nat := .node node18192 node17982 +def node18194 : Tree Nat := .node node18189 node18193 +def node18195 : Tree Nat := .node node18184 node18194 +def node18196 : Tree Nat := .node node17024 node9575 +def node18197 : Tree Nat := .node node18196 node8954 +def node18198 : Tree Nat := .node node10153 node18197 +def node18199 : Tree Nat := .node node18198 node17805 +def node18200 : Tree Nat := .node node17555 node9588 +def node18201 : Tree Nat := .node node18200 node5264 +def node18202 : Tree Nat := .node node11185 node18201 +def node18203 : Tree Nat := .node node17987 node18202 +def node18204 : Tree Nat := .node node18199 node18203 +def node18205 : Tree Nat := .node node17030 node9594 +def node18206 : Tree Nat := .node node18205 node10823 +def node18207 : Tree Nat := .node node10491 node18206 +def node18208 : Tree Nat := .node node17562 node11193 +def node18209 : Tree Nat := .node node11585 node18208 +def node18210 : Tree Nat := .node node18207 node18209 +def node18211 : Tree Nat := .node node17996 node11200 +def node18212 : Tree Nat := .node node18210 node18211 +def node18213 : Tree Nat := .node node18204 node18212 +def node18214 : Tree Nat := .node node10841 node18000 +def node18215 : Tree Nat := .node node10194 node18002 +def node18216 : Tree Nat := .node node18214 node18215 +def node18217 : Tree Nat := .node node17820 node18216 +def node18218 : Tree Nat := .node node18217 node18009 +def node18219 : Tree Nat := .node node18213 node18218 +def node18220 : Tree Nat := .node node18195 node18219 +def node18221 : Tree Nat := .node node18177 node18220 +def node18222 : Tree Nat := .node node17327 node9338 +def node18223 : Tree Nat := .node node10530 node18222 +def node18224 : Tree Nat := .node node11230 node17591 +def node18225 : Tree Nat := .node node18223 node18224 +def node18226 : Tree Nat := .node node18016 node18225 +def node18227 : Tree Nat := .node node18226 node18021 +def node18228 : Tree Nat := .node node11632 node17604 +def node18229 : Tree Nat := .node node18023 node18228 +def node18230 : Tree Nat := .node node17340 node10552 +def node18231 : Tree Nat := .node node10904 node18230 +def node18232 : Tree Nat := .node node11257 node18026 +def node18233 : Tree Nat := .node node18231 node18232 +def node18234 : Tree Nat := .node node18229 node18233 +def node18235 : Tree Nat := .node node17614 node11265 +def node18236 : Tree Nat := .node node11642 node18235 +def node18237 : Tree Nat := .node node17080 node18236 +def node18238 : Tree Nat := .node node17083 node11270 +def node18239 : Tree Nat := .node node18238 node10257 +def node18240 : Tree Nat := .node node18033 node18239 +def node18241 : Tree Nat := .node node18237 node18240 +def node18242 : Tree Nat := .node node18234 node18241 +def node18243 : Tree Nat := .node node18227 node18242 +def node18244 : Tree Nat := .node node17359 node10574 +def node18245 : Tree Nat := .node node10935 node18244 +def node18246 : Tree Nat := .node node8635 node18040 +def node18247 : Tree Nat := .node node18245 node18246 +def node18248 : Tree Nat := .node node17842 node18247 +def node18249 : Tree Nat := .node node17628 node11291 +def node18250 : Tree Nat := .node node11666 node18249 +def node18251 : Tree Nat := .node node17099 node18250 +def node18252 : Tree Nat := .node node18251 node18049 +def node18253 : Tree Nat := .node node18248 node18252 +def node18254 : Tree Nat := .node node10592 node17105 +def node18255 : Tree Nat := .node node10948 node17851 +def node18256 : Tree Nat := .node node18254 node18255 +def node18257 : Tree Nat := .node node18256 node18056 +def node18258 : Tree Nat := .node node17110 node9647 +def node18259 : Tree Nat := .node node10602 node18258 +def node18260 : Tree Nat := .node node18259 node18059 +def node18261 : Tree Nat := .node node10968 node18061 +def node18262 : Tree Nat := .node node17116 node7823 +def node18263 : Tree Nat := .node node18261 node18262 +def node18264 : Tree Nat := .node node18260 node18263 +def node18265 : Tree Nat := .node node18257 node18264 +def node18266 : Tree Nat := .node node18253 node18265 +def node18267 : Tree Nat := .node node18243 node18266 +def node18268 : Tree Nat := .node node10616 node17393 +def node18269 : Tree Nat := .node node10990 node18070 +def node18270 : Tree Nat := .node node18268 node18269 +def node18271 : Tree Nat := .node node18069 node18270 +def node18272 : Tree Nat := .node node17661 node11337 +def node18273 : Tree Nat := .node node10996 node18272 +def node18274 : Tree Nat := .node node17132 node18273 +def node18275 : Tree Nat := .node node18274 node18079 +def node18276 : Tree Nat := .node node18271 node18275 +def node18277 : Tree Nat := .node node11350 node18087 +def node18278 : Tree Nat := .node node18085 node18277 +def node18279 : Tree Nat := .node node18083 node18278 +def node18280 : Tree Nat := .node node17888 node10325 +def node18281 : Tree Nat := .node node18095 node18280 +def node18282 : Tree Nat := .node node18093 node18281 +def node18283 : Tree Nat := .node node18279 node18282 +def node18284 : Tree Nat := .node node18276 node18283 +def node18285 : Tree Nat := .node node17419 node11027 +def node18286 : Tree Nat := .node node11721 node18285 +def node18287 : Tree Nat := .node node17895 node18286 +def node18288 : Tree Nat := .node node17424 node10641 +def node18289 : Tree Nat := .node node11033 node18288 +def node18290 : Tree Nat := .node node17694 node9699 +def node18291 : Tree Nat := .node node18290 node7055 +def node18292 : Tree Nat := .node node11726 node18291 +def node18293 : Tree Nat := .node node18289 node18292 +def node18294 : Tree Nat := .node node18287 node18293 +def node18295 : Tree Nat := .node node17701 node11389 +def node18296 : Tree Nat := .node node11732 node18295 +def node18297 : Tree Nat := .node node17902 node18296 +def node18298 : Tree Nat := .node node18105 node11396 +def node18299 : Tree Nat := .node node18297 node18298 +def node18300 : Tree Nat := .node node18294 node18299 +def node18301 : Tree Nat := .node node17173 node9721 +def node18302 : Tree Nat := .node node18301 node9463 +def node18303 : Tree Nat := .node node10655 node18302 +def node18304 : Tree Nat := .node node17708 node11404 +def node18305 : Tree Nat := .node node11744 node18304 +def node18306 : Tree Nat := .node node18303 node18305 +def node18307 : Tree Nat := .node node17437 node11048 +def node18308 : Tree Nat := .node node11046 node18307 +def node18309 : Tree Nat := .node node10018 node17714 +def node18310 : Tree Nat := .node node18308 node18309 +def node18311 : Tree Nat := .node node18306 node18310 +def node18312 : Tree Nat := .node node17442 node9736 +def node18313 : Tree Nat := .node node18312 node9739 +def node18314 : Tree Nat := .node node10663 node18313 +def node18315 : Tree Nat := .node node18314 node18115 +def node18316 : Tree Nat := .node node17179 node9747 +def node18317 : Tree Nat := .node node18316 node11427 +def node18318 : Tree Nat := .node node18317 node7914 +def node18319 : Tree Nat := .node node18117 node18318 +def node18320 : Tree Nat := .node node18315 node18319 +def node18321 : Tree Nat := .node node18311 node18320 +def node18322 : Tree Nat := .node node18300 node18321 +def node18323 : Tree Nat := .node node18284 node18322 +def node18324 : Tree Nat := .node node18267 node18323 +def node18325 : Tree Nat := .node node18221 node18324 +def node18326 : Tree Nat := .node node17733 node10676 +def node18327 : Tree Nat := .node node10674 node18326 +def node18328 : Tree Nat := .node node17731 node18327 +def node18329 : Tree Nat := .node node17458 node9492 +def node18330 : Tree Nat := .node node18329 node5074 +def node18331 : Tree Nat := .node node9229 node18330 +def node18332 : Tree Nat := .node node17737 node18331 +def node18333 : Tree Nat := .node node18328 node18332 +def node18334 : Tree Nat := .node node16924 node9501 +def node18335 : Tree Nat := .node node10357 node18334 +def node18336 : Tree Nat := .node node9239 node18127 +def node18337 : Tree Nat := .node node18335 node18336 +def node18338 : Tree Nat := .node node18337 node18130 +def node18339 : Tree Nat := .node node18333 node18338 +def node18340 : Tree Nat := .node node10693 node18133 +def node18341 : Tree Nat := .node node17934 node18340 +def node18342 : Tree Nat := .node node18341 node18138 +def node18343 : Tree Nat := .node node16937 node8825 +def node18344 : Tree Nat := .node node10068 node18343 +def node18345 : Tree Nat := .node node11092 node18140 +def node18346 : Tree Nat := .node node18344 node18345 +def node18347 : Tree Nat := .node node18346 node18145 +def node18348 : Tree Nat := .node node18342 node18347 +def node18349 : Tree Nat := .node node18339 node18348 +def node18350 : Tree Nat := .node node17223 node10719 +def node18351 : Tree Nat := .node node7990 node18350 +def node18352 : Tree Nat := .node node16952 node18351 +def node18353 : Tree Nat := .node node18352 node18154 +def node18354 : Tree Nat := .node node16956 node9524 +def node18355 : Tree Nat := .node node10731 node18354 +def node18356 : Tree Nat := .node node11108 node18156 +def node18357 : Tree Nat := .node node18355 node18356 +def node18358 : Tree Nat := .node node8012 node17769 +def node18359 : Tree Nat := .node node18358 node11117 +def node18360 : Tree Nat := .node node18357 node18359 +def node18361 : Tree Nat := .node node18353 node18360 +def node18362 : Tree Nat := .node node17504 node11126 +def node18363 : Tree Nat := .node node10743 node18362 +def node18364 : Tree Nat := .node node18162 node18363 +def node18365 : Tree Nat := .node node18364 node18170 +def node18366 : Tree Nat := .node node16974 node8896 +def node18367 : Tree Nat := .node node10407 node18366 +def node18368 : Tree Nat := .node node18367 node17959 +def node18369 : Tree Nat := .node node10759 node17961 +def node18370 : Tree Nat := .node node18369 node17964 +def node18371 : Tree Nat := .node node18368 node18370 +def node18372 : Tree Nat := .node node18365 node18371 +def node18373 : Tree Nat := .node node18361 node18372 +def node18374 : Tree Nat := .node node18349 node18373 +def node18375 : Tree Nat := .node node17256 node10774 +def node18376 : Tree Nat := .node node8056 node18375 +def node18377 : Tree Nat := .node node16990 node18376 +def node18378 : Tree Nat := .node node17523 node9560 +def node18379 : Tree Nat := .node node18378 node9798 +def node18380 : Tree Nat := .node node10112 node18379 +def node18381 : Tree Nat := .node node18179 node18380 +def node18382 : Tree Nat := .node node18377 node18381 +def node18383 : Tree Nat := .leaf 2554675596204441358920157072691184177979384786912154013983839709802534754945326036915761576555810492025827646781516081568684798709636496710198389788982737077311407560861618224693342323966567660890030587592981715150416151935357900642741522568146145390861518885495484227969937646504178224939925504 +def node18384 : Tree Nat := .node node10441 node18383 +def node18385 : Tree Nat := .node node17530 node18384 +def node18386 : Tree Nat := .node node8489 node18385 +def node18387 : Tree Nat := .node node16996 node18386 +def node18388 : Tree Nat := .node node10781 node17970 +def node18389 : Tree Nat := .node node18388 node9810 +def node18390 : Tree Nat := .node node18387 node18389 +def node18391 : Tree Nat := .node node18382 node18390 +def node18392 : Tree Nat := .node node17537 node11158 +def node18393 : Tree Nat := .node node10791 node18392 +def node18394 : Tree Nat := .node node17793 node18393 +def node18395 : Tree Nat := .node node18394 node18188 +def node18396 : Tree Nat := .node node17012 node8937 +def node18397 : Tree Nat := .node node10464 node18396 +def node18398 : Tree Nat := .node node18397 node18191 +def node18399 : Tree Nat := .node node10139 node17796 +def node18400 : Tree Nat := .node node18399 node17981 +def node18401 : Tree Nat := .node node18398 node18400 +def node18402 : Tree Nat := .node node18395 node18401 +def node18403 : Tree Nat := .node node18391 node18402 +def node18404 : Tree Nat := .node node17288 node10817 +def node18405 : Tree Nat := .node node10815 node18404 +def node18406 : Tree Nat := .node node18198 node18405 +def node18407 : Tree Nat := .node node17292 node9584 +def node18408 : Tree Nat := .node node18407 node10484 +def node18409 : Tree Nat := .node node10482 node18408 +def node18410 : Tree Nat := .node node18409 node18202 +def node18411 : Tree Nat := .node node18406 node18410 +def node18412 : Tree Nat := .node node11191 node18208 +def node18413 : Tree Nat := .node node18207 node18412 +def node18414 : Tree Nat := .node node17298 node9599 +def node18415 : Tree Nat := .node node18414 node10828 +def node18416 : Tree Nat := .node node10172 node18415 +def node18417 : Tree Nat := .node node18416 node11200 +def node18418 : Tree Nat := .node node18413 node18417 +def node18419 : Tree Nat := .node node18411 node18418 +def node18420 : Tree Nat := .node node17569 node11208 +def node18421 : Tree Nat := .node node11206 node18420 +def node18422 : Tree Nat := .node node17817 node18421 +def node18423 : Tree Nat := .node node18422 node18216 +def node18424 : Tree Nat := .node node17044 node9328 +def node18425 : Tree Nat := .node node10515 node18424 +def node18426 : Tree Nat := .node node18425 node17823 +def node18427 : Tree Nat := .node node18426 node18008 +def node18428 : Tree Nat := .node node18423 node18427 +def node18429 : Tree Nat := .node node18419 node18428 +def node18430 : Tree Nat := .node node18403 node18429 +def node18431 : Tree Nat := .node node18374 node18430 +def node18432 : Tree Nat := .node node17322 node10872 +def node18433 : Tree Nat := .node node10870 node18432 +def node18434 : Tree Nat := .node node18014 node18433 +def node18435 : Tree Nat := .node node17589 node9618 +def node18436 : Tree Nat := .node node18435 node8574 +def node18437 : Tree Nat := .node node11230 node18436 +def node18438 : Tree Nat := .node node18223 node18437 +def node18439 : Tree Nat := .node node18434 node18438 +def node18440 : Tree Nat := .leaf 3832013394306662038380235609031737750202768213424770569900035515350172715726674014484873138633232261048339533106428255681093456573120944038068549026142324935447843284483754083518656634239652684908759237646077212412101165064119091769774464077803021125548585934376869662761905367573213156722343936 +def node18441 : Tree Nat := .node node9010 node18440 +def node18442 : Tree Nat := .node node17596 node18441 +def node18443 : Tree Nat := .node node10884 node18442 +def node18444 : Tree Nat := .node node17067 node18443 +def node18445 : Tree Nat := .node node10889 node18018 +def node18446 : Tree Nat := .node node18445 node11246 +def node18447 : Tree Nat := .node node18444 node18446 +def node18448 : Tree Nat := .node node18439 node18447 +def node18449 : Tree Nat := .node node17603 node11251 +def node18450 : Tree Nat := .node node10899 node18449 +def node18451 : Tree Nat := .node node18023 node18450 +def node18452 : Tree Nat := .node node18451 node18233 +def node18453 : Tree Nat := .node node11263 node18235 +def node18454 : Tree Nat := .node node17080 node18453 +def node18455 : Tree Nat := .node node10559 node18032 +def node18456 : Tree Nat := .node node18455 node18239 +def node18457 : Tree Nat := .node node18454 node18456 +def node18458 : Tree Nat := .node node18452 node18457 +def node18459 : Tree Nat := .node node18448 node18458 +def node18460 : Tree Nat := .node node17354 node10929 +def node18461 : Tree Nat := .node node11279 node18460 +def node18462 : Tree Nat := .node node17839 node18461 +def node18463 : Tree Nat := .node node17621 node9633 +def node18464 : Tree Nat := .node node18463 node5392 +def node18465 : Tree Nat := .node node8635 node18464 +def node18466 : Tree Nat := .node node18245 node18465 +def node18467 : Tree Nat := .node node18462 node18466 +def node18468 : Tree Nat := .node node17097 node9061 +def node18469 : Tree Nat := .node node10581 node18468 +def node18470 : Tree Nat := .node node11289 node18249 +def node18471 : Tree Nat := .node node18469 node18470 +def node18472 : Tree Nat := .node node18471 node18049 +def node18473 : Tree Nat := .node node18467 node18472 +def node18474 : Tree Nat := .node node17635 node11307 +def node18475 : Tree Nat := .node node10948 node18474 +def node18476 : Tree Nat := .node node18254 node18475 +def node18477 : Tree Nat := .node node18476 node18056 +def node18478 : Tree Nat := .node node11314 node18058 +def node18479 : Tree Nat := .node node18259 node18478 +def node18480 : Tree Nat := .node node18479 node18263 +def node18481 : Tree Nat := .node node18477 node18480 +def node18482 : Tree Nat := .node node18473 node18481 +def node18483 : Tree Nat := .node node18459 node18482 +def node18484 : Tree Nat := .node node17387 node10984 +def node18485 : Tree Nat := .node node11328 node18484 +def node18486 : Tree Nat := .node node18068 node18485 +def node18487 : Tree Nat := .node node17654 node9655 +def node18488 : Tree Nat := .node node18487 node5456 +def node18489 : Tree Nat := .node node10990 node18488 +def node18490 : Tree Nat := .node node18268 node18489 +def node18491 : Tree Nat := .node node18486 node18490 +def node18492 : Tree Nat := .node node17130 node9121 +def node18493 : Tree Nat := .node node10622 node18492 +def node18494 : Tree Nat := .node node18493 node18273 +def node18495 : Tree Nat := .node node18494 node18079 +def node18496 : Tree Nat := .node node18491 node18495 +def node18497 : Tree Nat := .node node17671 node11344 +def node18498 : Tree Nat := .node node11011 node18497 +def node18499 : Tree Nat := .node node17876 node18498 +def node18500 : Tree Nat := .node node18499 node18278 +def node18501 : Tree Nat := .node node17681 node9987 +def node18502 : Tree Nat := .node node18501 node5493 +def node18503 : Tree Nat := .node node11356 node18502 +def node18504 : Tree Nat := .node node17883 node18503 +def node18505 : Tree Nat := .node node18504 node18281 +def node18506 : Tree Nat := .node node18500 node18505 +def node18507 : Tree Nat := .node node18496 node18506 +def node18508 : Tree Nat := .node node11025 node18285 +def node18509 : Tree Nat := .node node17895 node18508 +def node18510 : Tree Nat := .node node11377 node18291 +def node18511 : Tree Nat := .node node18289 node18510 +def node18512 : Tree Nat := .node node18509 node18511 +def node18513 : Tree Nat := .node node11387 node18295 +def node18514 : Tree Nat := .node node17902 node18513 +def node18515 : Tree Nat := .node node9453 node18104 +def node18516 : Tree Nat := .node node18515 node11396 +def node18517 : Tree Nat := .node node18514 node18516 +def node18518 : Tree Nat := .node node18512 node18517 +def node18519 : Tree Nat := .node node17707 node9725 +def node18520 : Tree Nat := .node node18519 node11404 +def node18521 : Tree Nat := .node node11402 node18520 +def node18522 : Tree Nat := .node node18303 node18521 +def node18523 : Tree Nat := .node node17436 node9730 +def node18524 : Tree Nat := .node node18523 node11048 +def node18525 : Tree Nat := .node node11046 node18524 +def node18526 : Tree Nat := .node node17712 node10019 +def node18527 : Tree Nat := .node node18526 node9187 +def node18528 : Tree Nat := .node node10018 node18527 +def node18529 : Tree Nat := .node node18525 node18528 +def node18530 : Tree Nat := .node node18522 node18529 +def node18531 : Tree Nat := .node node17718 node10028 +def node18532 : Tree Nat := .node node18531 node9193 +def node18533 : Tree Nat := .node node11416 node18532 +def node18534 : Tree Nat := .node node18314 node18533 +def node18535 : Tree Nat := .node node17447 node9743 +def node18536 : Tree Nat := .node node18535 node11057 +def node18537 : Tree Nat := .node node11055 node18536 +def node18538 : Tree Nat := .node node18537 node18318 +def node18539 : Tree Nat := .node node18534 node18538 +def node18540 : Tree Nat := .node node18530 node18539 +def node18541 : Tree Nat := .node node18518 node18540 +def node18542 : Tree Nat := .node node18507 node18541 +def node18543 : Tree Nat := .node node18483 node18542 +def node18544 : Tree Nat := .node node18431 node18543 +def node18545 : Tree Nat := .node node17733 node5069 +def node18546 : Tree Nat := .node node10050 node18545 +def node18547 : Tree Nat := .node node17731 node18546 +def node18548 : Tree Nat := .node node18547 node18332 +def node18549 : Tree Nat := .node node17465 node5080 +def node18550 : Tree Nat := .node node9239 node18549 +def node18551 : Tree Nat := .node node18335 node18550 +def node18552 : Tree Nat := .node node17743 node5085 +def node18553 : Tree Nat := .node node9244 node18552 +def node18554 : Tree Nat := .node node18553 node9252 +def node18555 : Tree Nat := .node node18551 node18554 +def node18556 : Tree Nat := .node node18548 node18555 +def node18557 : Tree Nat := .node node17472 node5096 +def node18558 : Tree Nat := .node node10364 node18557 +def node18559 : Tree Nat := .node node17934 node18558 +def node18560 : Tree Nat := .node node8390 node17937 +def node18561 : Tree Nat := .node node18136 node18560 +def node18562 : Tree Nat := .node node18559 node18561 +def node18563 : Tree Nat := .node node17483 node5111 +def node18564 : Tree Nat := .node node8400 node18563 +def node18565 : Tree Nat := .node node18344 node18564 +def node18566 : Tree Nat := .node node17215 node5116 +def node18567 : Tree Nat := .node node10375 node18566 +def node18568 : Tree Nat := .node node16942 node8838 +def node18569 : Tree Nat := .node node18568 node10073 +def node18570 : Tree Nat := .node node18567 node18569 +def node18571 : Tree Nat := .node node18565 node18570 +def node18572 : Tree Nat := .node node18562 node18571 +def node18573 : Tree Nat := .node node18556 node18572 +def node18574 : Tree Nat := .node node17223 node8853 +def node18575 : Tree Nat := .node node7990 node18574 +def node18576 : Tree Nat := .node node16952 node18575 +def node18577 : Tree Nat := .node node18576 node18154 +def node18578 : Tree Nat := .node node10389 node18354 +def node18579 : Tree Nat := .node node17497 node8865 +def node18580 : Tree Nat := .node node8438 node18579 +def node18581 : Tree Nat := .node node18578 node18580 +def node18582 : Tree Nat := .node node17234 node8442 +def node18583 : Tree Nat := .node node8012 node18582 +def node18584 : Tree Nat := .node node18583 node9774 +def node18585 : Tree Nat := .node node18581 node18584 +def node18586 : Tree Nat := .node node18577 node18585 +def node18587 : Tree Nat := .node node16968 node8881 +def node18588 : Tree Nat := .node node9532 node18587 +def node18589 : Tree Nat := .node node17504 node7199 +def node18590 : Tree Nat := .node node10396 node18589 +def node18591 : Tree Nat := .node node18588 node18590 +def node18592 : Tree Nat := .node node8459 node17778 +def node18593 : Tree Nat := .node node18168 node18592 +def node18594 : Tree Nat := .node node18591 node18593 +def node18595 : Tree Nat := .node node8469 node17516 +def node18596 : Tree Nat := .node node18367 node18595 +def node18597 : Tree Nat := .node node17247 node10097 +def node18598 : Tree Nat := .node node10416 node18597 +def node18599 : Tree Nat := .node node18598 node17964 +def node18600 : Tree Nat := .node node18596 node18599 +def node18601 : Tree Nat := .node node18594 node18600 +def node18602 : Tree Nat := .node node18586 node18601 +def node18603 : Tree Nat := .node node18573 node18602 +def node18604 : Tree Nat := .node node17256 node9556 +def node18605 : Tree Nat := .node node8056 node18604 +def node18606 : Tree Nat := .node node16990 node18605 +def node18607 : Tree Nat := .node node18606 node18381 +def node18608 : Tree Nat := .node node17530 node10442 +def node18609 : Tree Nat := .node node8489 node18608 +def node18610 : Tree Nat := .node node16996 node18609 +def node18611 : Tree Nat := .node node17267 node9804 +def node18612 : Tree Nat := .node node8067 node18611 +def node18613 : Tree Nat := .node node18612 node9810 +def node18614 : Tree Nat := .node node18610 node18613 +def node18615 : Tree Nat := .node node18607 node18614 +def node18616 : Tree Nat := .node node17537 node8931 +def node18617 : Tree Nat := .node node10123 node18616 +def node18618 : Tree Nat := .node node17793 node18617 +def node18619 : Tree Nat := .node node10128 node17976 +def node18620 : Tree Nat := .node node18186 node18619 +def node18621 : Tree Nat := .node node18618 node18620 +def node18622 : Tree Nat := .node node17548 node8941 +def node18623 : Tree Nat := .node node10134 node18622 +def node18624 : Tree Nat := .node node18397 node18623 +def node18625 : Tree Nat := .node node17280 node8519 +def node18626 : Tree Nat := .node node10139 node18625 +def node18627 : Tree Nat := .node node18626 node17981 +def node18628 : Tree Nat := .node node18624 node18627 +def node18629 : Tree Nat := .node node18621 node18628 +def node18630 : Tree Nat := .node node18615 node18629 +def node18631 : Tree Nat := .node node17288 node5255 +def node18632 : Tree Nat := .node node9843 node18631 +def node18633 : Tree Nat := .node node18198 node18632 +def node18634 : Tree Nat := .node node9848 node18201 +def node18635 : Tree Nat := .node node18409 node18634 +def node18636 : Tree Nat := .node node18633 node18635 +def node18637 : Tree Nat := .node node17562 node5270 +def node18638 : Tree Nat := .node node9854 node18637 +def node18639 : Tree Nat := .node node18207 node18638 +def node18640 : Tree Nat := .node node18414 node5275 +def node18641 : Tree Nat := .node node10172 node18640 +def node18642 : Tree Nat := .node node18641 node10177 +def node18643 : Tree Nat := .node node18639 node18642 +def node18644 : Tree Nat := .node node18636 node18643 +def node18645 : Tree Nat := .node node17569 node5286 +def node18646 : Tree Nat := .node node10185 node18645 +def node18647 : Tree Nat := .node node17817 node18646 +def node18648 : Tree Nat := .node node17306 node8112 +def node18649 : Tree Nat := .node node10841 node18648 +def node18650 : Tree Nat := .node node18649 node18215 +def node18651 : Tree Nat := .node node18647 node18650 +def node18652 : Tree Nat := .node node17312 node5306 +def node18653 : Tree Nat := .node node10209 node18652 +def node18654 : Tree Nat := .node node17049 node8978 +def node18655 : Tree Nat := .node node18654 node8128 +def node18656 : Tree Nat := .node node18653 node18655 +def node18657 : Tree Nat := .node node18426 node18656 +def node18658 : Tree Nat := .node node18651 node18657 +def node18659 : Tree Nat := .node node18644 node18658 +def node18660 : Tree Nat := .node node18630 node18659 +def node18661 : Tree Nat := .node node18603 node18660 +def node18662 : Tree Nat := .node node10867 node8139 +def node18663 : Tree Nat := .node node17322 node8994 +def node18664 : Tree Nat := .node node18662 node18663 +def node18665 : Tree Nat := .node node18014 node18664 +def node18666 : Tree Nat := .node node8572 node18436 +def node18667 : Tree Nat := .node node18223 node18666 +def node18668 : Tree Nat := .node node18665 node18667 +def node18669 : Tree Nat := .node node17065 node9005 +def node18670 : Tree Nat := .node node10536 node18669 +def node18671 : Tree Nat := .node node17596 node9011 +def node18672 : Tree Nat := .node node10884 node18671 +def node18673 : Tree Nat := .node node18670 node18672 +def node18674 : Tree Nat := .node node17333 node8589 +def node18675 : Tree Nat := .node node10541 node18674 +def node18676 : Tree Nat := .node node18675 node9898 +def node18677 : Tree Nat := .node node18673 node18676 +def node18678 : Tree Nat := .node node18668 node18677 +def node18679 : Tree Nat := .node node17603 node7340 +def node18680 : Tree Nat := .node node10548 node18679 +def node18681 : Tree Nat := .node node18023 node18680 +def node18682 : Tree Nat := .node node8612 node18026 +def node18683 : Tree Nat := .node node18231 node18682 +def node18684 : Tree Nat := .node node18681 node18683 +def node18685 : Tree Nat := .node node17614 node6961 +def node18686 : Tree Nat := .node node8622 node18685 +def node18687 : Tree Nat := .node node17080 node18686 +def node18688 : Tree Nat := .node node17346 node6968 +def node18689 : Tree Nat := .node node10559 node18688 +def node18690 : Tree Nat := .node node17083 node9047 +def node18691 : Tree Nat := .node node18690 node10257 +def node18692 : Tree Nat := .node node18689 node18691 +def node18693 : Tree Nat := .node node18687 node18692 +def node18694 : Tree Nat := .node node18684 node18693 +def node18695 : Tree Nat := .node node18678 node18694 +def node18696 : Tree Nat := .node node17354 node5387 +def node18697 : Tree Nat := .node node10567 node18696 +def node18698 : Tree Nat := .node node17839 node18697 +def node18699 : Tree Nat := .node node18698 node18466 +def node18700 : Tree Nat := .node node17628 node5398 +def node18701 : Tree Nat := .node node10585 node18700 +def node18702 : Tree Nat := .node node18469 node18701 +def node18703 : Tree Nat := .node node17365 node5403 +def node18704 : Tree Nat := .node node10276 node18703 +def node18705 : Tree Nat := .node node18704 node9923 +def node18706 : Tree Nat := .node node18702 node18705 +def node18707 : Tree Nat := .node node18699 node18706 +def node18708 : Tree Nat := .node node17104 node9371 +def node18709 : Tree Nat := .node node10592 node18708 +def node18710 : Tree Nat := .node node17635 node5414 +def node18711 : Tree Nat := .node node10596 node18710 +def node18712 : Tree Nat := .node node18709 node18711 +def node18713 : Tree Nat := .node node8661 node18054 +def node18714 : Tree Nat := .node node17374 node18713 +def node18715 : Tree Nat := .node node18712 node18714 +def node18716 : Tree Nat := .node node8671 node18058 +def node18717 : Tree Nat := .node node18259 node18716 +def node18718 : Tree Nat := .node node17378 node5434 +def node18719 : Tree Nat := .node node10607 node18718 +def node18720 : Tree Nat := .node node17115 node9097 +def node18721 : Tree Nat := .node node18720 node7823 +def node18722 : Tree Nat := .node node18719 node18721 +def node18723 : Tree Nat := .node node18717 node18722 +def node18724 : Tree Nat := .node node18715 node18723 +def node18725 : Tree Nat := .node node18707 node18724 +def node18726 : Tree Nat := .node node18695 node18725 +def node18727 : Tree Nat := .node node10979 node10300 +def node18728 : Tree Nat := .node node17387 node5451 +def node18729 : Tree Nat := .node node18727 node18728 +def node18730 : Tree Nat := .node node18068 node18729 +def node18731 : Tree Nat := .node node8692 node18488 +def node18732 : Tree Nat := .node node18268 node18731 +def node18733 : Tree Nat := .node node18730 node18732 +def node18734 : Tree Nat := .node node17661 node5462 +def node18735 : Tree Nat := .node node10996 node18734 +def node18736 : Tree Nat := .node node18493 node18735 +def node18737 : Tree Nat := .node node17398 node5467 +def node18738 : Tree Nat := .node node10627 node18737 +def node18739 : Tree Nat := .node node18738 node9961 +def node18740 : Tree Nat := .node node18736 node18739 +def node18741 : Tree Nat := .node node18733 node18740 +def node18742 : Tree Nat := .node node17671 node5478 +def node18743 : Tree Nat := .node node9967 node18742 +def node18744 : Tree Nat := .node node17876 node18743 +def node18745 : Tree Nat := .node node9976 node18087 +def node18746 : Tree Nat := .node node18085 node18745 +def node18747 : Tree Nat := .node node18744 node18746 +def node18748 : Tree Nat := .node node9409 node18502 +def node18749 : Tree Nat := .node node17883 node18748 +def node18750 : Tree Nat := .node node17411 node5498 +def node18751 : Tree Nat := .node node9414 node18750 +def node18752 : Tree Nat := .node node17887 node9152 +def node18753 : Tree Nat := .node node18752 node10325 +def node18754 : Tree Nat := .node node18751 node18753 +def node18755 : Tree Nat := .node node18749 node18754 +def node18756 : Tree Nat := .node node18747 node18755 +def node18757 : Tree Nat := .node node18741 node18756 +def node18758 : Tree Nat := .node node17419 node7455 +def node18759 : Tree Nat := .node node9433 node18758 +def node18760 : Tree Nat := .node node17895 node18759 +def node18761 : Tree Nat := .node node9442 node18291 +def node18762 : Tree Nat := .node node18289 node18761 +def node18763 : Tree Nat := .node node18760 node18762 +def node18764 : Tree Nat := .node node17900 node9166 +def node18765 : Tree Nat := .node node10648 node18764 +def node18766 : Tree Nat := .node node17701 node7065 +def node18767 : Tree Nat := .node node9448 node18766 +def node18768 : Tree Nat := .node node18765 node18767 +def node18769 : Tree Nat := .node node17430 node7072 +def node18770 : Tree Nat := .node node9453 node18769 +def node18771 : Tree Nat := .node node18770 node10003 +def node18772 : Tree Nat := .node node18768 node18771 +def node18773 : Tree Nat := .node node18763 node18772 +def node18774 : Tree Nat := .node node18519 node9182 +def node18775 : Tree Nat := .node node10009 node18774 +def node18776 : Tree Nat := .node node18303 node18775 +def node18777 : Tree Nat := .node node18523 node5546 +def node18778 : Tree Nat := .node node11046 node18777 +def node18779 : Tree Nat := .node node18778 node18528 +def node18780 : Tree Nat := .node node18776 node18779 +def node18781 : Tree Nat := .node node10027 node18532 +def node18782 : Tree Nat := .node node18314 node18781 +def node18783 : Tree Nat := .node node18535 node8772 +def node18784 : Tree Nat := .node node10035 node18783 +def node18785 : Tree Nat := .node node18316 node9198 +def node18786 : Tree Nat := .node node18785 node7914 +def node18787 : Tree Nat := .node node18784 node18786 +def node18788 : Tree Nat := .node node18782 node18787 +def node18789 : Tree Nat := .node node18780 node18788 +def node18790 : Tree Nat := .node node18773 node18789 +def node18791 : Tree Nat := .node node18757 node18790 +def node18792 : Tree Nat := .node node18726 node18791 +def node18793 : Tree Nat := .node node18661 node18792 +def node18794 : Tree Nat := .node node9222 node17197 +def node18795 : Tree Nat := .node node18794 node18331 +def node18796 : Tree Nat := .node node18547 node18795 +def node18797 : Tree Nat := .node node9235 node18334 +def node18798 : Tree Nat := .node node18797 node18550 +def node18799 : Tree Nat := .node node18798 node18554 +def node18800 : Tree Nat := .node node18796 node18799 +def node18801 : Tree Nat := .node node9760 node17749 +def node18802 : Tree Nat := .node node8385 node18557 +def node18803 : Tree Nat := .node node18801 node18802 +def node18804 : Tree Nat := .node node17209 node5999 +def node18805 : Tree Nat := .node node10062 node18804 +def node18806 : Tree Nat := .node node18805 node18560 +def node18807 : Tree Nat := .node node18803 node18806 +def node18808 : Tree Nat := .node node7982 node18566 +def node18809 : Tree Nat := .node node18808 node18569 +def node18810 : Tree Nat := .node node18565 node18809 +def node18811 : Tree Nat := .node node18807 node18810 +def node18812 : Tree Nat := .node node18800 node18811 +def node18813 : Tree Nat := .node node17228 node4610 +def node18814 : Tree Nat := .node node8418 node18813 +def node18815 : Tree Nat := .node node18814 node18153 +def node18816 : Tree Nat := .node node18576 node18815 +def node18817 : Tree Nat := .node node9265 node18354 +def node18818 : Tree Nat := .node node18817 node18580 +def node18819 : Tree Nat := .node node18818 node18584 +def node18820 : Tree Nat := .node node18816 node18819 +def node18821 : Tree Nat := .node node8454 node18589 +def node18822 : Tree Nat := .node node18588 node18821 +def node18823 : Tree Nat := .node node17241 node5164 +def node18824 : Tree Nat := .node node10088 node18823 +def node18825 : Tree Nat := .node node18824 node18592 +def node18826 : Tree Nat := .node node18822 node18825 +def node18827 : Tree Nat := .node node9786 node18366 +def node18828 : Tree Nat := .node node17515 node9542 +def node18829 : Tree Nat := .node node8469 node18828 +def node18830 : Tree Nat := .node node18827 node18829 +def node18831 : Tree Nat := .node node8047 node18597 +def node18832 : Tree Nat := .node node17963 node9281 +def node18833 : Tree Nat := .node node18831 node18832 +def node18834 : Tree Nat := .node node18830 node18833 +def node18835 : Tree Nat := .node node18826 node18834 +def node18836 : Tree Nat := .node node18820 node18835 +def node18837 : Tree Nat := .node node18812 node18836 +def node18838 : Tree Nat := .node node16988 node8914 +def node18839 : Tree Nat := .node node10107 node18838 +def node18840 : Tree Nat := .node node18839 node18605 +def node18841 : Tree Nat := .node node9795 node18178 +def node18842 : Tree Nat := .node node18841 node18380 +def node18843 : Tree Nat := .node node18840 node18842 +def node18844 : Tree Nat := .node node16994 node8920 +def node18845 : Tree Nat := .node node7634 node18844 +def node18846 : Tree Nat := .node node17530 node6841 +def node18847 : Tree Nat := .node node8489 node18846 +def node18848 : Tree Nat := .node node18845 node18847 +def node18849 : Tree Nat := .node node18848 node18613 +def node18850 : Tree Nat := .node node18843 node18849 +def node18851 : Tree Nat := .node node7646 node17792 +def node18852 : Tree Nat := .node node18851 node18617 +def node18853 : Tree Nat := .node node17274 node5228 +def node18854 : Tree Nat := .node node8074 node18853 +def node18855 : Tree Nat := .node node18854 node18619 +def node18856 : Tree Nat := .node node18852 node18855 +def node18857 : Tree Nat := .node node7652 node18396 +def node18858 : Tree Nat := .node node17547 node7255 +def node18859 : Tree Nat := .node node18858 node8941 +def node18860 : Tree Nat := .node node10134 node18859 +def node18861 : Tree Nat := .node node18857 node18860 +def node18862 : Tree Nat := .node node17279 node6873 +def node18863 : Tree Nat := .node node18862 node8519 +def node18864 : Tree Nat := .node node10139 node18863 +def node18865 : Tree Nat := .node node18864 node17981 +def node18866 : Tree Nat := .node node18861 node18865 +def node18867 : Tree Nat := .node node18856 node18866 +def node18868 : Tree Nat := .node node18850 node18867 +def node18869 : Tree Nat := .node node17287 node9579 +def node18870 : Tree Nat := .node node18869 node5255 +def node18871 : Tree Nat := .node node9843 node18870 +def node18872 : Tree Nat := .node node18198 node18871 +def node18873 : Tree Nat := .node node18407 node10160 +def node18874 : Tree Nat := .node node10158 node18873 +def node18875 : Tree Nat := .node node18874 node18634 +def node18876 : Tree Nat := .node node18872 node18875 +def node18877 : Tree Nat := .node node18205 node9312 +def node18878 : Tree Nat := .node node7675 node18877 +def node18879 : Tree Nat := .node node17561 node7278 +def node18880 : Tree Nat := .node node18879 node5270 +def node18881 : Tree Nat := .node node9854 node18880 +def node18882 : Tree Nat := .node node18878 node18881 +def node18883 : Tree Nat := .node node18882 node18642 +def node18884 : Tree Nat := .node node18876 node18883 +def node18885 : Tree Nat := .node node7687 node17816 +def node18886 : Tree Nat := .leaf 4065122478611946121818419435478921215417418853827517800827540389943159478693508531146778592905248372255313520414341184510025528551064746023773293317531927820264298847036308979712 +def node18887 : Tree Nat := .node node894 node18886 +def node18888 : Tree Nat := .node node18887 node10184 +def node18889 : Tree Nat := .node node17568 node7285 +def node18890 : Tree Nat := .node node18889 node5286 +def node18891 : Tree Nat := .node node18888 node18890 +def node18892 : Tree Nat := .node node18885 node18891 +def node18893 : Tree Nat := .node node8110 node18648 +def node18894 : Tree Nat := .node node18893 node18215 +def node18895 : Tree Nat := .node node18892 node18894 +def node18896 : Tree Nat := .node node8119 node18424 +def node18897 : Tree Nat := .node node17579 node7296 +def node18898 : Tree Nat := .node node18897 node5301 +def node18899 : Tree Nat := .node node10204 node18898 +def node18900 : Tree Nat := .node node18896 node18899 +def node18901 : Tree Nat := .node node17311 node6912 +def node18902 : Tree Nat := .node node18901 node5306 +def node18903 : Tree Nat := .node node10209 node18902 +def node18904 : Tree Nat := .node node18903 node18655 +def node18905 : Tree Nat := .node node18900 node18904 +def node18906 : Tree Nat := .node node18895 node18905 +def node18907 : Tree Nat := .node node18884 node18906 +def node18908 : Tree Nat := .node node18868 node18907 +def node18909 : Tree Nat := .node node18837 node18908 +def node18910 : Tree Nat := .node node8140 node18663 +def node18911 : Tree Nat := .node node18014 node18910 +def node18912 : Tree Nat := .node node8145 node18222 +def node18913 : Tree Nat := .node node18912 node18666 +def node18914 : Tree Nat := .node node18911 node18913 +def node18915 : Tree Nat := .node node10234 node18669 +def node18916 : Tree Nat := .node node9892 node18671 +def node18917 : Tree Nat := .node node18915 node18916 +def node18918 : Tree Nat := .node node8160 node18674 +def node18919 : Tree Nat := .node node18918 node9898 +def node18920 : Tree Nat := .node node18917 node18919 +def node18921 : Tree Nat := .node node18914 node18920 +def node18922 : Tree Nat := .node node9904 node17073 +def node18923 : Tree Nat := .node node8607 node18679 +def node18924 : Tree Nat := .node node18922 node18923 +def node18925 : Tree Nat := .node node17340 node5356 +def node18926 : Tree Nat := .node node10246 node18925 +def node18927 : Tree Nat := .node node18926 node18682 +def node18928 : Tree Nat := .node node18924 node18927 +def node18929 : Tree Nat := .node node8191 node18688 +def node18930 : Tree Nat := .node node18929 node18691 +def node18931 : Tree Nat := .node node18687 node18930 +def node18932 : Tree Nat := .node node18928 node18931 +def node18933 : Tree Nat := .node node18921 node18932 +def node18934 : Tree Nat := .node node17353 node7358 +def node18935 : Tree Nat := .node node18934 node5387 +def node18936 : Tree Nat := .node node8199 node18935 +def node18937 : Tree Nat := .node node17839 node18936 +def node18938 : Tree Nat := .node node17359 node10269 +def node18939 : Tree Nat := .node node8204 node18938 +def node18940 : Tree Nat := .node node18939 node18465 +def node18941 : Tree Nat := .node node18937 node18940 +def node18942 : Tree Nat := .node node7785 node18468 +def node18943 : Tree Nat := .node node8641 node18700 +def node18944 : Tree Nat := .node node18942 node18943 +def node18945 : Tree Nat := .node node18944 node18705 +def node18946 : Tree Nat := .node node18941 node18945 +def node18947 : Tree Nat := .node node9929 node18708 +def node18948 : Tree Nat := .node node10283 node18710 +def node18949 : Tree Nat := .node node18947 node18948 +def node18950 : Tree Nat := .node node17372 node8224 +def node18951 : Tree Nat := .node node10288 node18950 +def node18952 : Tree Nat := .node node18951 node18713 +def node18953 : Tree Nat := .node node18949 node18952 +def node18954 : Tree Nat := .node node9940 node18258 +def node18955 : Tree Nat := .node node18954 node18716 +def node18956 : Tree Nat := .node node8246 node18718 +def node18957 : Tree Nat := .node node18956 node18721 +def node18958 : Tree Nat := .node node18955 node18957 +def node18959 : Tree Nat := .node node18953 node18958 +def node18960 : Tree Nat := .node node18946 node18959 +def node18961 : Tree Nat := .node node18933 node18960 +def node18962 : Tree Nat := .node node10301 node18728 +def node18963 : Tree Nat := .node node18068 node18962 +def node18964 : Tree Nat := .node node8262 node17393 +def node18965 : Tree Nat := .node node18964 node18731 +def node18966 : Tree Nat := .node node18963 node18965 +def node18967 : Tree Nat := .node node10312 node18492 +def node18968 : Tree Nat := .node node9955 node18734 +def node18969 : Tree Nat := .node node18967 node18968 +def node18970 : Tree Nat := .node node8280 node18737 +def node18971 : Tree Nat := .node node18970 node9961 +def node18972 : Tree Nat := .node node18969 node18971 +def node18973 : Tree Nat := .node node18966 node18972 +def node18974 : Tree Nat := .node node9400 node17875 +def node18975 : Tree Nat := .node node18974 node18743 +def node18976 : Tree Nat := .node node17405 node6285 +def node18977 : Tree Nat := .node node9972 node18976 +def node18978 : Tree Nat := .node node18977 node18745 +def node18979 : Tree Nat := .node node18975 node18978 +def node18980 : Tree Nat := .node node18979 node18755 +def node18981 : Tree Nat := .node node18973 node18980 +def node18982 : Tree Nat := .node node17424 node5515 +def node18983 : Tree Nat := .node node9438 node18982 +def node18984 : Tree Nat := .node node18983 node18761 +def node18985 : Tree Nat := .node node18760 node18984 +def node18986 : Tree Nat := .node node9997 node18764 +def node18987 : Tree Nat := .node node18986 node18767 +def node18988 : Tree Nat := .node node18987 node18771 +def node18989 : Tree Nat := .node node18985 node18988 +def node18990 : Tree Nat := .node node10340 node18302 +def node18991 : Tree Nat := .node node18990 node18775 +def node18992 : Tree Nat := .node node10014 node18777 +def node18993 : Tree Nat := .node node18992 node18528 +def node18994 : Tree Nat := .node node18991 node18993 +def node18995 : Tree Nat := .node node8333 node18313 +def node18996 : Tree Nat := .node node18995 node18781 +def node18997 : Tree Nat := .node node18996 node18787 +def node18998 : Tree Nat := .node node18994 node18997 +def node18999 : Tree Nat := .node node18989 node18998 +def node19000 : Tree Nat := .node node18981 node18999 +def node19001 : Tree Nat := .node node18961 node19000 +def node19002 : Tree Nat := .node node18909 node19001 +def node19003 : Tree Nat := .node node9481 node17730 +def node19004 : Tree Nat := .node node9217 node18545 +def node19005 : Tree Nat := .node node19003 node19004 +def node19006 : Tree Nat := .node node19005 node18795 +def node19007 : Tree Nat := .node node19006 node18799 +def node19008 : Tree Nat := .node node7967 node18804 +def node19009 : Tree Nat := .node node19008 node18560 +def node19010 : Tree Nat := .node node18803 node19009 +def node19011 : Tree Nat := .node node7549 node18343 +def node19012 : Tree Nat := .node node19011 node18564 +def node19013 : Tree Nat := .node node18568 node9258 +def node19014 : Tree Nat := .node node18808 node19013 +def node19015 : Tree Nat := .node node19012 node19014 +def node19016 : Tree Nat := .node node19010 node19015 +def node19017 : Tree Nat := .node node19007 node19016 +def node19018 : Tree Nat := .node node7566 node16951 +def node19019 : Tree Nat := .node node19018 node18575 +def node19020 : Tree Nat := .node node19019 node18815 +def node19021 : Tree Nat := .node node18583 node9271 +def node19022 : Tree Nat := .node node18818 node19021 +def node19023 : Tree Nat := .node node19020 node19022 +def node19024 : Tree Nat := .node node8028 node18823 +def node19025 : Tree Nat := .node node17777 node9536 +def node19026 : Tree Nat := .node node8459 node19025 +def node19027 : Tree Nat := .node node19024 node19026 +def node19028 : Tree Nat := .node node18822 node19027 +def node19029 : Tree Nat := .node node8038 node18366 +def node19030 : Tree Nat := .node node19029 node18829 +def node19031 : Tree Nat := .node node17247 node9547 +def node19032 : Tree Nat := .node node8047 node19031 +def node19033 : Tree Nat := .node node19032 node18832 +def node19034 : Tree Nat := .node node19030 node19033 +def node19035 : Tree Nat := .node node19028 node19034 +def node19036 : Tree Nat := .node node19023 node19035 +def node19037 : Tree Nat := .node node19017 node19036 +def node19038 : Tree Nat := .node node7628 node18838 +def node19039 : Tree Nat := .node node19038 node18605 +def node19040 : Tree Nat := .node node8061 node18178 +def node19041 : Tree Nat := .node node18378 node6831 +def node19042 : Tree Nat := .node node8483 node19041 +def node19043 : Tree Nat := .node node19040 node19042 +def node19044 : Tree Nat := .node node19039 node19043 +def node19045 : Tree Nat := .node node17267 node6848 +def node19046 : Tree Nat := .node node8067 node19045 +def node19047 : Tree Nat := .node node19046 node9297 +def node19048 : Tree Nat := .node node18848 node19047 +def node19049 : Tree Nat := .node node19044 node19048 +def node19050 : Tree Nat := .node node17005 node6471 +def node19051 : Tree Nat := .node node19050 node8927 +def node19052 : Tree Nat := .node node7646 node19051 +def node19053 : Tree Nat := .node node8501 node18616 +def node19054 : Tree Nat := .node node19052 node19053 +def node19055 : Tree Nat := .node node17273 node6854 +def node19056 : Tree Nat := .node node19055 node5228 +def node19057 : Tree Nat := .node node8074 node19056 +def node19058 : Tree Nat := .node node8506 node17976 +def node19059 : Tree Nat := .node node19057 node19058 +def node19060 : Tree Nat := .node node19054 node19059 +def node19061 : Tree Nat := .node node17011 node6864 +def node19062 : Tree Nat := .node node19061 node8937 +def node19063 : Tree Nat := .node node7652 node19062 +def node19064 : Tree Nat := .node node8515 node18859 +def node19065 : Tree Nat := .node node19063 node19064 +def node19066 : Tree Nat := .node node8080 node18863 +def node19067 : Tree Nat := .node node17016 node6482 +def node19068 : Tree Nat := .node node19067 node8946 +def node19069 : Tree Nat := .node node19068 node9569 +def node19070 : Tree Nat := .node node19066 node19069 +def node19071 : Tree Nat := .node node19065 node19070 +def node19072 : Tree Nat := .node node19060 node19071 +def node19073 : Tree Nat := .node node19049 node19072 +def node19074 : Tree Nat := .node node7669 node18197 +def node19075 : Tree Nat := .node node8092 node18870 +def node19076 : Tree Nat := .node node19074 node19075 +def node19077 : Tree Nat := .node node18407 node9306 +def node19078 : Tree Nat := .node node9304 node19077 +def node19079 : Tree Nat := .node node8528 node18201 +def node19080 : Tree Nat := .node node19078 node19079 +def node19081 : Tree Nat := .node node19076 node19080 +def node19082 : Tree Nat := .node node9859 node18640 +def node19083 : Tree Nat := .node node19082 node9606 +def node19084 : Tree Nat := .node node18882 node19083 +def node19085 : Tree Nat := .node node19081 node19084 +def node19086 : Tree Nat := .node node17037 node6517 +def node19087 : Tree Nat := .node node19086 node8972 +def node19088 : Tree Nat := .node node7687 node19087 +def node19089 : Tree Nat := .node node8541 node18890 +def node19090 : Tree Nat := .node node19088 node19089 +def node19091 : Tree Nat := .node node17305 node6901 +def node19092 : Tree Nat := .node node19091 node8112 +def node19093 : Tree Nat := .node node8110 node19092 +def node19094 : Tree Nat := .node node8546 node18002 +def node19095 : Tree Nat := .node node19093 node19094 +def node19096 : Tree Nat := .node node19090 node19095 +def node19097 : Tree Nat := .node node17043 node6907 +def node19098 : Tree Nat := .node node19097 node9328 +def node19099 : Tree Nat := .node node8119 node19098 +def node19100 : Tree Nat := .node node8552 node18898 +def node19101 : Tree Nat := .node node19099 node19100 +def node19102 : Tree Nat := .node node8124 node18902 +def node19103 : Tree Nat := .node node17048 node6528 +def node19104 : Tree Nat := .node node19103 node8978 +def node19105 : Tree Nat := .node node19104 node8128 +def node19106 : Tree Nat := .node node19102 node19105 +def node19107 : Tree Nat := .node node19101 node19106 +def node19108 : Tree Nat := .node node19096 node19107 +def node19109 : Tree Nat := .node node19085 node19108 +def node19110 : Tree Nat := .node node19073 node19109 +def node19111 : Tree Nat := .node node19037 node19110 +def node19112 : Tree Nat := .node node9886 node17832 +def node19113 : Tree Nat := .node node19112 node18910 +def node19114 : Tree Nat := .node node19113 node18913 +def node19115 : Tree Nat := .node node7729 node18669 +def node19116 : Tree Nat := .node node8585 node18671 +def node19117 : Tree Nat := .node node19115 node19116 +def node19118 : Tree Nat := .node node18918 node9346 +def node19119 : Tree Nat := .node node19117 node19118 +def node19120 : Tree Nat := .node node19114 node19119 +def node19121 : Tree Nat := .node node8176 node18925 +def node19122 : Tree Nat := .node node19121 node18682 +def node19123 : Tree Nat := .node node18924 node19122 +def node19124 : Tree Nat := .node node7762 node17079 +def node19125 : Tree Nat := .node node19124 node18686 +def node19126 : Tree Nat := .node node18690 node9627 +def node19127 : Tree Nat := .node node18929 node19126 +def node19128 : Tree Nat := .node node19125 node19127 +def node19129 : Tree Nat := .node node19123 node19128 +def node19130 : Tree Nat := .node node19120 node19129 +def node19131 : Tree Nat := .node node7779 node17838 +def node19132 : Tree Nat := .node node19131 node18936 +def node19133 : Tree Nat := .node node17359 node6206 +def node19134 : Tree Nat := .node node8204 node19133 +def node19135 : Tree Nat := .node node19134 node18465 +def node19136 : Tree Nat := .node node19132 node19135 +def node19137 : Tree Nat := .node node8210 node18703 +def node19138 : Tree Nat := .node node19137 node9366 +def node19139 : Tree Nat := .node node18944 node19138 +def node19140 : Tree Nat := .node node19136 node19139 +def node19141 : Tree Nat := .node node8652 node18710 +def node19142 : Tree Nat := .node node18947 node19141 +def node19143 : Tree Nat := .node node8657 node18950 +def node19144 : Tree Nat := .node node19143 node18713 +def node19145 : Tree Nat := .node node19142 node19144 +def node19146 : Tree Nat := .node node8237 node18258 +def node19147 : Tree Nat := .node node19146 node18716 +def node19148 : Tree Nat := .node node19147 node18957 +def node19149 : Tree Nat := .node node19145 node19148 +def node19150 : Tree Nat := .node node19140 node19149 +def node19151 : Tree Nat := .node node19130 node19150 +def node19152 : Tree Nat := .node node9949 node17865 +def node19153 : Tree Nat := .node node8257 node18728 +def node19154 : Tree Nat := .node node19152 node19153 +def node19155 : Tree Nat := .node node19154 node18965 +def node19156 : Tree Nat := .node node7849 node18492 +def node19157 : Tree Nat := .node node8702 node18734 +def node19158 : Tree Nat := .node node19156 node19157 +def node19159 : Tree Nat := .node node18970 node9394 +def node19160 : Tree Nat := .node node19158 node19159 +def node19161 : Tree Nat := .node node19155 node19160 +def node19162 : Tree Nat := .node node17681 node1718 +def node19163 : Tree Nat := .node node19162 node5493 +def node19164 : Tree Nat := .node node9409 node19163 +def node19165 : Tree Nat := .node node17883 node19164 +def node19166 : Tree Nat := .node node18752 node9684 +def node19167 : Tree Nat := .node node18751 node19166 +def node19168 : Tree Nat := .node node19165 node19167 +def node19169 : Tree Nat := .node node18979 node19168 +def node19170 : Tree Nat := .node node19161 node19169 +def node19171 : Tree Nat := .node node9426 node17894 +def node19172 : Tree Nat := .node node19171 node18759 +def node19173 : Tree Nat := .node node19172 node18984 +def node19174 : Tree Nat := .node node18770 node9458 +def node19175 : Tree Nat := .node node18987 node19174 +def node19176 : Tree Nat := .node node19173 node19175 +def node19177 : Tree Nat := .node node7903 node18302 +def node19178 : Tree Nat := .node node19177 node18775 +def node19179 : Tree Nat := .node node19178 node18993 +def node19180 : Tree Nat := .node node17718 node7488 +def node19181 : Tree Nat := .node node19180 node9193 +def node19182 : Tree Nat := .node node10027 node19181 +def node19183 : Tree Nat := .node node18995 node19182 +def node19184 : Tree Nat := .node node19183 node18787 +def node19185 : Tree Nat := .node node19179 node19184 +def node19186 : Tree Nat := .node node19176 node19185 +def node19187 : Tree Nat := .node node19170 node19186 +def node19188 : Tree Nat := .node node19151 node19187 +def node19189 : Tree Nat := .node node19111 node19188 +def node19190 : Tree Nat := .node node9210 node17730 +def node19191 : Tree Nat := .node node17190 node8787 +def node19192 : Tree Nat := .node node19191 node5069 +def node19193 : Tree Nat := .node node9217 node19192 +def node19194 : Tree Nat := .node node19190 node19193 +def node19195 : Tree Nat := .node node17195 node8352 +def node19196 : Tree Nat := .node node19195 node9224 +def node19197 : Tree Nat := .node node9222 node19196 +def node19198 : Tree Nat := .node node17458 node7118 +def node19199 : Tree Nat := .node node19198 node5074 +def node19200 : Tree Nat := .node node9229 node19199 +def node19201 : Tree Nat := .node node19197 node19200 +def node19202 : Tree Nat := .node node19194 node19201 +def node19203 : Tree Nat := .node node16923 node8362 +def node19204 : Tree Nat := .node node19203 node8794 +def node19205 : Tree Nat := .node node9235 node19204 +def node19206 : Tree Nat := .node node17464 node8797 +def node19207 : Tree Nat := .node node19206 node5080 +def node19208 : Tree Nat := .node node9239 node19207 +def node19209 : Tree Nat := .node node19205 node19208 +def node19210 : Tree Nat := .node node17201 node8802 +def node19211 : Tree Nat := .node node19210 node5085 +def node19212 : Tree Nat := .node node9244 node19211 +def node19213 : Tree Nat := .node node19212 node9252 +def node19214 : Tree Nat := .node node19209 node19213 +def node19215 : Tree Nat := .node node19202 node19214 +def node19216 : Tree Nat := .node node7536 node17749 +def node19217 : Tree Nat := .node node19216 node18802 +def node19218 : Tree Nat := .node node17476 node7147 +def node19219 : Tree Nat := .node node19218 node5105 +def node19220 : Tree Nat := .node node8390 node19219 +def node19221 : Tree Nat := .node node19008 node19220 +def node19222 : Tree Nat := .node node19217 node19221 +def node19223 : Tree Nat := .node node19222 node19015 +def node19224 : Tree Nat := .node node19215 node19223 +def node19225 : Tree Nat := .node node17490 node7175 +def node19226 : Tree Nat := .node node19225 node8427 +def node19227 : Tree Nat := .node node8425 node19226 +def node19228 : Tree Nat := .node node18814 node19227 +def node19229 : Tree Nat := .node node19019 node19228 +def node19230 : Tree Nat := .node node16956 node8859 +def node19231 : Tree Nat := .node node9265 node19230 +def node19232 : Tree Nat := .node node19231 node18580 +def node19233 : Tree Nat := .node node19232 node19021 +def node19234 : Tree Nat := .node node19229 node19233 +def node19235 : Tree Nat := .node node7599 node18587 +def node19236 : Tree Nat := .node node19235 node18821 +def node19237 : Tree Nat := .node node17508 node7203 +def node19238 : Tree Nat := .node node19237 node6801 +def node19239 : Tree Nat := .node node8459 node19238 +def node19240 : Tree Nat := .node node19024 node19239 +def node19241 : Tree Nat := .node node19236 node19240 +def node19242 : Tree Nat := .node node17515 node6811 +def node19243 : Tree Nat := .node node8469 node19242 +def node19244 : Tree Nat := .node node19029 node19243 +def node19245 : Tree Nat := .node node17247 node6818 +def node19246 : Tree Nat := .node node8047 node19245 +def node19247 : Tree Nat := .node node19246 node18832 +def node19248 : Tree Nat := .node node19244 node19247 +def node19249 : Tree Nat := .node node19241 node19248 +def node19250 : Tree Nat := .node node19234 node19249 +def node19251 : Tree Nat := .node node19224 node19250 +def node19252 : Tree Nat := .node node17256 node7225 +def node19253 : Tree Nat := .node node8056 node19252 +def node19254 : Tree Nat := .node node19038 node19253 +def node19255 : Tree Nat := .node node17523 node7229 +def node19256 : Tree Nat := .node node19255 node6831 +def node19257 : Tree Nat := .node node8483 node19256 +def node19258 : Tree Nat := .node node19040 node19257 +def node19259 : Tree Nat := .node node19254 node19258 +def node19260 : Tree Nat := .node node19259 node19048 +def node19261 : Tree Nat := .node node17541 node7249 +def node19262 : Tree Nat := .node node19261 node8508 +def node19263 : Tree Nat := .node node8506 node19262 +def node19264 : Tree Nat := .node node19057 node19263 +def node19265 : Tree Nat := .node node19054 node19264 +def node19266 : Tree Nat := .node node19068 node8084 +def node19267 : Tree Nat := .node node19066 node19266 +def node19268 : Tree Nat := .node node19065 node19267 +def node19269 : Tree Nat := .node node19265 node19268 +def node19270 : Tree Nat := .node node19260 node19269 +def node19271 : Tree Nat := .node node17024 node6493 +def node19272 : Tree Nat := .node node19271 node8954 +def node19273 : Tree Nat := .node node7669 node19272 +def node19274 : Tree Nat := .node node17287 node7267 +def node19275 : Tree Nat := .node node19274 node5255 +def node19276 : Tree Nat := .node node8092 node19275 +def node19277 : Tree Nat := .node node19273 node19276 +def node19278 : Tree Nat := .node node17292 node6883 +def node19279 : Tree Nat := .node node19278 node9306 +def node19280 : Tree Nat := .node node9304 node19279 +def node19281 : Tree Nat := .node node17555 node7272 +def node19282 : Tree Nat := .node node19281 node5264 +def node19283 : Tree Nat := .node node8528 node19282 +def node19284 : Tree Nat := .node node19280 node19283 +def node19285 : Tree Nat := .node node19277 node19284 +def node19286 : Tree Nat := .node node17030 node6889 +def node19287 : Tree Nat := .node node19286 node9312 +def node19288 : Tree Nat := .node node7675 node19287 +def node19289 : Tree Nat := .node node8534 node18880 +def node19290 : Tree Nat := .node node19288 node19289 +def node19291 : Tree Nat := .node node17298 node6894 +def node19292 : Tree Nat := .node node19291 node5275 +def node19293 : Tree Nat := .node node9318 node19292 +def node19294 : Tree Nat := .node node19293 node9323 +def node19295 : Tree Nat := .node node19290 node19294 +def node19296 : Tree Nat := .node node19285 node19295 +def node19297 : Tree Nat := .node node19296 node19108 +def node19298 : Tree Nat := .node node19270 node19297 +def node19299 : Tree Nat := .node node19251 node19298 +def node19300 : Tree Nat := .node node7716 node17832 +def node19301 : Tree Nat := .node node19300 node18910 +def node19302 : Tree Nat := .node node17589 node7317 +def node19303 : Tree Nat := .node node19302 node8574 +def node19304 : Tree Nat := .node node8572 node19303 +def node19305 : Tree Nat := .node node18912 node19304 +def node19306 : Tree Nat := .node node19301 node19305 +def node19307 : Tree Nat := .node node19306 node19119 +def node19308 : Tree Nat := .node node7749 node17073 +def node19309 : Tree Nat := .node node19308 node18923 +def node19310 : Tree Nat := .node node17607 node7344 +def node19311 : Tree Nat := .node node19310 node6951 +def node19312 : Tree Nat := .node node8612 node19311 +def node19313 : Tree Nat := .node node19121 node19312 +def node19314 : Tree Nat := .node node19309 node19313 +def node19315 : Tree Nat := .node node19314 node19128 +def node19316 : Tree Nat := .node node19307 node19315 +def node19317 : Tree Nat := .node node17621 node7363 +def node19318 : Tree Nat := .node node19317 node5392 +def node19319 : Tree Nat := .node node8635 node19318 +def node19320 : Tree Nat := .node node19134 node19319 +def node19321 : Tree Nat := .node node19132 node19320 +def node19322 : Tree Nat := .node node19321 node19139 +def node19323 : Tree Nat := .node node7797 node18708 +def node19324 : Tree Nat := .node node19323 node19141 +def node19325 : Tree Nat := .node node17639 node7388 +def node19326 : Tree Nat := .node node19325 node5423 +def node19327 : Tree Nat := .node node8661 node19326 +def node19328 : Tree Nat := .node node19143 node19327 +def node19329 : Tree Nat := .node node19324 node19328 +def node19330 : Tree Nat := .node node17110 node9088 +def node19331 : Tree Nat := .node node8237 node19330 +def node19332 : Tree Nat := .node node19331 node18716 +def node19333 : Tree Nat := .node node19332 node18957 +def node19334 : Tree Nat := .node node19329 node19333 +def node19335 : Tree Nat := .node node19322 node19334 +def node19336 : Tree Nat := .node node19316 node19335 +def node19337 : Tree Nat := .node node7832 node17865 +def node19338 : Tree Nat := .node node19337 node19153 +def node19339 : Tree Nat := .node node17654 node7416 +def node19340 : Tree Nat := .node node19339 node5456 +def node19341 : Tree Nat := .node node8692 node19340 +def node19342 : Tree Nat := .node node18964 node19341 +def node19343 : Tree Nat := .node node19338 node19342 +def node19344 : Tree Nat := .node node19343 node19160 +def node19345 : Tree Nat := .node node17670 node7433 +def node19346 : Tree Nat := .node node19345 node5478 +def node19347 : Tree Nat := .node node8716 node19346 +def node19348 : Tree Nat := .node node18974 node19347 +def node19349 : Tree Nat := .node node17404 node7031 +def node19350 : Tree Nat := .node node19349 node6285 +def node19351 : Tree Nat := .node node8291 node19350 +def node19352 : Tree Nat := .node node17675 node7438 +def node19353 : Tree Nat := .node node19352 node5487 +def node19354 : Tree Nat := .node node8721 node19353 +def node19355 : Tree Nat := .node node19351 node19354 +def node19356 : Tree Nat := .node node19348 node19355 +def node19357 : Tree Nat := .node node17142 node7037 +def node19358 : Tree Nat := .node node19357 node9147 +def node19359 : Tree Nat := .node node8297 node19358 +def node19360 : Tree Nat := .node node17681 node7444 +def node19361 : Tree Nat := .node node19360 node5493 +def node19362 : Tree Nat := .node node9409 node19361 +def node19363 : Tree Nat := .node node19359 node19362 +def node19364 : Tree Nat := .node node17410 node7042 +def node19365 : Tree Nat := .node node19364 node5498 +def node19366 : Tree Nat := .node node9414 node19365 +def node19367 : Tree Nat := .node node18752 node7877 +def node19368 : Tree Nat := .node node19366 node19367 +def node19369 : Tree Nat := .node node19363 node19368 +def node19370 : Tree Nat := .node node19356 node19369 +def node19371 : Tree Nat := .node node19344 node19370 +def node19372 : Tree Nat := .node node17418 node7452 +def node19373 : Tree Nat := .node node19372 node7455 +def node19374 : Tree Nat := .node node9433 node19373 +def node19375 : Tree Nat := .node node19171 node19374 +def node19376 : Tree Nat := .node node17423 node7050 +def node19377 : Tree Nat := .node node19376 node5515 +def node19378 : Tree Nat := .node node9438 node19377 +def node19379 : Tree Nat := .node node17694 node7459 +def node19380 : Tree Nat := .node node19379 node7055 +def node19381 : Tree Nat := .node node9442 node19380 +def node19382 : Tree Nat := .node node19378 node19381 +def node19383 : Tree Nat := .node node19375 node19382 +def node19384 : Tree Nat := .node node17161 node7060 +def node19385 : Tree Nat := .node node19384 node9166 +def node19386 : Tree Nat := .node node7891 node19385 +def node19387 : Tree Nat := .node node17700 node7465 +def node19388 : Tree Nat := .node node19387 node7065 +def node19389 : Tree Nat := .node node9448 node19388 +def node19390 : Tree Nat := .node node19386 node19389 +def node19391 : Tree Nat := .node node17429 node7069 +def node19392 : Tree Nat := .node node19391 node7072 +def node19393 : Tree Nat := .node node9453 node19392 +def node19394 : Tree Nat := .node node19393 node9458 +def node19395 : Tree Nat := .node node19390 node19394 +def node19396 : Tree Nat := .node node19383 node19395 +def node19397 : Tree Nat := .node node17173 node6705 +def node19398 : Tree Nat := .node node19397 node9463 +def node19399 : Tree Nat := .node node7903 node19398 +def node19400 : Tree Nat := .node node17707 node7476 +def node19401 : Tree Nat := .node node19400 node9182 +def node19402 : Tree Nat := .node node8753 node19401 +def node19403 : Tree Nat := .node node19399 node19402 +def node19404 : Tree Nat := .node node17436 node7078 +def node19405 : Tree Nat := .node node19404 node5546 +def node19406 : Tree Nat := .node node8758 node19405 +def node19407 : Tree Nat := .node node17712 node7906 +def node19408 : Tree Nat := .node node19407 node9187 +def node19409 : Tree Nat := .node node8762 node19408 +def node19410 : Tree Nat := .node node19406 node19409 +def node19411 : Tree Nat := .node node19403 node19410 +def node19412 : Tree Nat := .node node17442 node7088 +def node19413 : Tree Nat := .node node19412 node9469 +def node19414 : Tree Nat := .node node8333 node19413 +def node19415 : Tree Nat := .node node8768 node19181 +def node19416 : Tree Nat := .node node19414 node19415 +def node19417 : Tree Nat := .node node17447 node7097 +def node19418 : Tree Nat := .node node19417 node8772 +def node19419 : Tree Nat := .node node8338 node19418 +def node19420 : Tree Nat := .node node17179 node6720 +def node19421 : Tree Nat := .node node19420 node9198 +def node19422 : Tree Nat := .node node19421 node7914 +def node19423 : Tree Nat := .node node19419 node19422 +def node19424 : Tree Nat := .node node19416 node19423 +def node19425 : Tree Nat := .node node19411 node19424 +def node19426 : Tree Nat := .node node19396 node19425 +def node19427 : Tree Nat := .node node19371 node19426 +def node19428 : Tree Nat := .node node19336 node19427 +def node19429 : Tree Nat := .node node19299 node19428 +def node19430 : Tree Nat := .node node16917 node8347 +def node19431 : Tree Nat := .node node19430 node7114 +def node19432 : Tree Nat := .node node7501 node19431 +def node19433 : Tree Nat := .node node17190 node6731 +def node19434 : Tree Nat := .node node19433 node5069 +def node19435 : Tree Nat := .node node7925 node19434 +def node19436 : Tree Nat := .node node19432 node19435 +def node19437 : Tree Nat := .node node19195 node7933 +def node19438 : Tree Nat := .node node7931 node19437 +def node19439 : Tree Nat := .node node8358 node19199 +def node19440 : Tree Nat := .node node19438 node19439 +def node19441 : Tree Nat := .node node19436 node19440 +def node19442 : Tree Nat := .node node19203 node7128 +def node19443 : Tree Nat := .node node7518 node19442 +def node19444 : Tree Nat := .node node17464 node7131 +def node19445 : Tree Nat := .node node19444 node5080 +def node19446 : Tree Nat := .node node8368 node19445 +def node19447 : Tree Nat := .node node19443 node19446 +def node19448 : Tree Nat := .node node17201 node6742 +def node19449 : Tree Nat := .node node19448 node5085 +def node19450 : Tree Nat := .node node7951 node19449 +def node19451 : Tree Nat := .node node19450 node8375 +def node19452 : Tree Nat := .node node19447 node19451 +def node19453 : Tree Nat := .node node19441 node19452 +def node19454 : Tree Nat := .node node16931 node4569 +def node19455 : Tree Nat := .node node7536 node19454 +def node19456 : Tree Nat := .node node17471 node7142 +def node19457 : Tree Nat := .node node19456 node5096 +def node19458 : Tree Nat := .node node8385 node19457 +def node19459 : Tree Nat := .node node19455 node19458 +def node19460 : Tree Nat := .node node17208 node6749 +def node19461 : Tree Nat := .node node19460 node5999 +def node19462 : Tree Nat := .node node7967 node19461 +def node19463 : Tree Nat := .node node19462 node19220 +def node19464 : Tree Nat := .node node19459 node19463 +def node19465 : Tree Nat := .node node16937 node4584 +def node19466 : Tree Nat := .node node7549 node19465 +def node19467 : Tree Nat := .node node17482 node7153 +def node19468 : Tree Nat := .node node19467 node5111 +def node19469 : Tree Nat := .node node8400 node19468 +def node19470 : Tree Nat := .node node19466 node19469 +def node19471 : Tree Nat := .node node17214 node6760 +def node19472 : Tree Nat := .node node19471 node5116 +def node19473 : Tree Nat := .node node7982 node19472 +def node19474 : Tree Nat := .node node16942 node6393 +def node19475 : Tree Nat := .node node19474 node7558 +def node19476 : Tree Nat := .node node19473 node19475 +def node19477 : Tree Nat := .node node19470 node19476 +def node19478 : Tree Nat := .node node19464 node19477 +def node19479 : Tree Nat := .node node19453 node19478 +def node19480 : Tree Nat := .node node16950 node7165 +def node19481 : Tree Nat := .node node7566 node19480 +def node19482 : Tree Nat := .node node17222 node7168 +def node19483 : Tree Nat := .node node19482 node7171 +def node19484 : Tree Nat := .node node7990 node19483 +def node19485 : Tree Nat := .node node19481 node19484 +def node19486 : Tree Nat := .node node19485 node19228 +def node19487 : Tree Nat := .node node16956 node7182 +def node19488 : Tree Nat := .node node7583 node19487 +def node19489 : Tree Nat := .node node17496 node7185 +def node19490 : Tree Nat := .node node19489 node6783 +def node19491 : Tree Nat := .node node8438 node19490 +def node19492 : Tree Nat := .node node19488 node19491 +def node19493 : Tree Nat := .node node17233 node6787 +def node19494 : Tree Nat := .node node19493 node8442 +def node19495 : Tree Nat := .node node8012 node19494 +def node19496 : Tree Nat := .node node19495 node8017 +def node19497 : Tree Nat := .node node19492 node19496 +def node19498 : Tree Nat := .node node19486 node19497 +def node19499 : Tree Nat := .node node16968 node4636 +def node19500 : Tree Nat := .node node7599 node19499 +def node19501 : Tree Nat := .node node17503 node7196 +def node19502 : Tree Nat := .node node19501 node7199 +def node19503 : Tree Nat := .node node8454 node19502 +def node19504 : Tree Nat := .node node19500 node19503 +def node19505 : Tree Nat := .node node17240 node6796 +def node19506 : Tree Nat := .node node19505 node5164 +def node19507 : Tree Nat := .node node8028 node19506 +def node19508 : Tree Nat := .node node19507 node19239 +def node19509 : Tree Nat := .node node19504 node19508 +def node19510 : Tree Nat := .node node16974 node4651 +def node19511 : Tree Nat := .node node8038 node19510 +def node19512 : Tree Nat := .node node17514 node7209 +def node19513 : Tree Nat := .node node19512 node6811 +def node19514 : Tree Nat := .node node8469 node19513 +def node19515 : Tree Nat := .node node19511 node19514 +def node19516 : Tree Nat := .node node17246 node6815 +def node19517 : Tree Nat := .node node19516 node6818 +def node19518 : Tree Nat := .node node8047 node19517 +def node19519 : Tree Nat := .node node16979 node4660 +def node19520 : Tree Nat := .node node19519 node7619 +def node19521 : Tree Nat := .node node19518 node19520 +def node19522 : Tree Nat := .node node19515 node19521 +def node19523 : Tree Nat := .node node19509 node19522 +def node19524 : Tree Nat := .node node19498 node19523 +def node19525 : Tree Nat := .node node19479 node19524 +def node19526 : Tree Nat := .node node16988 node7219 +def node19527 : Tree Nat := .node node7628 node19526 +def node19528 : Tree Nat := .node node19527 node19253 +def node19529 : Tree Nat := .node node17261 node4678 +def node19530 : Tree Nat := .node node8061 node19529 +def node19531 : Tree Nat := .node node19530 node19257 +def node19532 : Tree Nat := .node node19528 node19531 +def node19533 : Tree Nat := .node node16994 node5683 +def node19534 : Tree Nat := .node node7634 node19533 +def node19535 : Tree Nat := .node node19534 node18847 +def node19536 : Tree Nat := .node node19046 node7640 +def node19537 : Tree Nat := .node node19535 node19536 +def node19538 : Tree Nat := .node node19532 node19537 +def node19539 : Tree Nat := .node node19050 node4704 +def node19540 : Tree Nat := .node node7646 node19539 +def node19541 : Tree Nat := .node node17537 node7245 +def node19542 : Tree Nat := .node node8501 node19541 +def node19543 : Tree Nat := .node node19540 node19542 +def node19544 : Tree Nat := .node node19543 node19264 +def node19545 : Tree Nat := .node node19061 node4719 +def node19546 : Tree Nat := .node node7652 node19545 +def node19547 : Tree Nat := .node node18858 node6869 +def node19548 : Tree Nat := .node node8515 node19547 +def node19549 : Tree Nat := .node node19546 node19548 +def node19550 : Tree Nat := .node node19067 node4728 +def node19551 : Tree Nat := .node node19550 node8084 +def node19552 : Tree Nat := .node node19066 node19551 +def node19553 : Tree Nat := .node node19549 node19552 +def node19554 : Tree Nat := .node node19544 node19553 +def node19555 : Tree Nat := .node node19538 node19554 +def node19556 : Tree Nat := .node node19271 node7264 +def node19557 : Tree Nat := .node node7669 node19556 +def node19558 : Tree Nat := .node node19557 node19276 +def node19559 : Tree Nat := .node node19278 node6107 +def node19560 : Tree Nat := .node node8097 node19559 +def node19561 : Tree Nat := .node node19560 node19283 +def node19562 : Tree Nat := .node node19558 node19561 +def node19563 : Tree Nat := .node node19286 node5736 +def node19564 : Tree Nat := .node node7675 node19563 +def node19565 : Tree Nat := .node node19564 node19289 +def node19566 : Tree Nat := .node node8103 node19292 +def node19567 : Tree Nat := .node node19566 node7681 +def node19568 : Tree Nat := .node node19565 node19567 +def node19569 : Tree Nat := .node node19562 node19568 +def node19570 : Tree Nat := .node node19086 node4767 +def node19571 : Tree Nat := .node node7687 node19570 +def node19572 : Tree Nat := .node node19571 node19089 +def node19573 : Tree Nat := .node node19572 node19095 +def node19574 : Tree Nat := .node node19097 node4782 +def node19575 : Tree Nat := .node node8119 node19574 +def node19576 : Tree Nat := .node node19575 node19100 +def node19577 : Tree Nat := .node node19103 node8556 +def node19578 : Tree Nat := .node node19577 node8128 +def node19579 : Tree Nat := .node node19102 node19578 +def node19580 : Tree Nat := .node node19576 node19579 +def node19581 : Tree Nat := .node node19573 node19580 +def node19582 : Tree Nat := .node node19569 node19581 +def node19583 : Tree Nat := .node node19555 node19582 +def node19584 : Tree Nat := .node node19525 node19583 +def node19585 : Tree Nat := .node node17059 node4801 +def node19586 : Tree Nat := .node node7716 node19585 +def node19587 : Tree Nat := .node node17321 node7310 +def node19588 : Tree Nat := .node node19587 node7313 +def node19589 : Tree Nat := .node node8140 node19588 +def node19590 : Tree Nat := .node node19586 node19589 +def node19591 : Tree Nat := .node node17326 node6922 +def node19592 : Tree Nat := .node node19591 node4806 +def node19593 : Tree Nat := .node node8145 node19592 +def node19594 : Tree Nat := .node node19302 node6927 +def node19595 : Tree Nat := .node node8572 node19594 +def node19596 : Tree Nat := .node node19593 node19595 +def node19597 : Tree Nat := .node node19590 node19596 +def node19598 : Tree Nat := .node node17065 node4816 +def node19599 : Tree Nat := .node node7729 node19598 +def node19600 : Tree Nat := .node node17595 node7323 +def node19601 : Tree Nat := .node node19600 node6933 +def node19602 : Tree Nat := .node node8585 node19601 +def node19603 : Tree Nat := .node node19599 node19602 +def node19604 : Tree Nat := .node node17332 node6937 +def node19605 : Tree Nat := .node node19604 node8589 +def node19606 : Tree Nat := .node node8160 node19605 +def node19607 : Tree Nat := .node node19606 node8597 +def node19608 : Tree Nat := .node node19603 node19607 +def node19609 : Tree Nat := .node node19597 node19608 +def node19610 : Tree Nat := .node node17072 node7334 +def node19611 : Tree Nat := .node node7749 node19610 +def node19612 : Tree Nat := .node node17602 node7337 +def node19613 : Tree Nat := .node node19612 node7340 +def node19614 : Tree Nat := .node node8607 node19613 +def node19615 : Tree Nat := .node node19611 node19614 +def node19616 : Tree Nat := .node node17339 node6946 +def node19617 : Tree Nat := .node node19616 node5356 +def node19618 : Tree Nat := .node node8176 node19617 +def node19619 : Tree Nat := .node node19618 node19312 +def node19620 : Tree Nat := .node node19615 node19619 +def node19621 : Tree Nat := .node node17078 node5808 +def node19622 : Tree Nat := .node node7762 node19621 +def node19623 : Tree Nat := .node node17613 node7350 +def node19624 : Tree Nat := .node node19623 node6961 +def node19625 : Tree Nat := .node node8622 node19624 +def node19626 : Tree Nat := .node node19622 node19625 +def node19627 : Tree Nat := .node node17345 node6965 +def node19628 : Tree Nat := .node node19627 node6968 +def node19629 : Tree Nat := .node node8191 node19628 +def node19630 : Tree Nat := .node node17083 node4856 +def node19631 : Tree Nat := .node node19630 node7771 +def node19632 : Tree Nat := .node node19629 node19631 +def node19633 : Tree Nat := .node node19626 node19632 +def node19634 : Tree Nat := .node node19620 node19633 +def node19635 : Tree Nat := .node node19609 node19634 +def node19636 : Tree Nat := .node node17091 node4864 +def node19637 : Tree Nat := .node node7779 node19636 +def node19638 : Tree Nat := .node node19637 node18936 +def node19639 : Tree Nat := .node node19638 node19320 +def node19640 : Tree Nat := .node node17097 node4883 +def node19641 : Tree Nat := .node node7785 node19640 +def node19642 : Tree Nat := .node node19641 node18943 +def node19643 : Tree Nat := .node node19137 node7791 +def node19644 : Tree Nat := .node node19642 node19643 +def node19645 : Tree Nat := .node node19639 node19644 +def node19646 : Tree Nat := .node node17104 node7380 +def node19647 : Tree Nat := .node node7797 node19646 +def node19648 : Tree Nat := .node node17634 node7383 +def node19649 : Tree Nat := .node node19648 node5414 +def node19650 : Tree Nat := .node node8652 node19649 +def node19651 : Tree Nat := .node node19647 node19650 +def node19652 : Tree Nat := .node node17371 node6993 +def node19653 : Tree Nat := .node node19652 node8224 +def node19654 : Tree Nat := .node node8657 node19653 +def node19655 : Tree Nat := .node node19654 node19327 +def node19656 : Tree Nat := .node node19651 node19655 +def node19657 : Tree Nat := .node node17110 node7395 +def node19658 : Tree Nat := .node node8237 node19657 +def node19659 : Tree Nat := .node node17645 node7398 +def node19660 : Tree Nat := .node node19659 node5429 +def node19661 : Tree Nat := .node node8671 node19660 +def node19662 : Tree Nat := .node node19658 node19661 +def node19663 : Tree Nat := .node node17377 node7004 +def node19664 : Tree Nat := .node node19663 node5434 +def node19665 : Tree Nat := .node node8246 node19664 +def node19666 : Tree Nat := .node node17115 node8677 +def node19667 : Tree Nat := .node node19666 node7823 +def node19668 : Tree Nat := .node node19665 node19667 +def node19669 : Tree Nat := .node node19662 node19668 +def node19670 : Tree Nat := .node node19656 node19669 +def node19671 : Tree Nat := .node node19645 node19670 +def node19672 : Tree Nat := .node node19635 node19671 +def node19673 : Tree Nat := .node node17124 node4932 +def node19674 : Tree Nat := .node node7832 node19673 +def node19675 : Tree Nat := .node node17386 node7411 +def node19676 : Tree Nat := .node node19675 node5451 +def node19677 : Tree Nat := .node node8257 node19676 +def node19678 : Tree Nat := .node node19674 node19677 +def node19679 : Tree Nat := .node node17391 node7013 +def node19680 : Tree Nat := .node node19679 node8264 +def node19681 : Tree Nat := .node node8262 node19680 +def node19682 : Tree Nat := .node node19681 node19341 +def node19683 : Tree Nat := .node node19678 node19682 +def node19684 : Tree Nat := .node node17130 node4951 +def node19685 : Tree Nat := .node node7849 node19684 +def node19686 : Tree Nat := .node node17660 node7422 +def node19687 : Tree Nat := .node node19686 node5462 +def node19688 : Tree Nat := .node node8702 node19687 +def node19689 : Tree Nat := .node node19685 node19688 +def node19690 : Tree Nat := .node node17397 node7024 +def node19691 : Tree Nat := .node node19690 node5467 +def node19692 : Tree Nat := .node node8280 node19691 +def node19693 : Tree Nat := .node node19692 node8710 +def node19694 : Tree Nat := .node node19689 node19693 +def node19695 : Tree Nat := .node node19683 node19694 +def node19696 : Tree Nat := .node node17136 node6659 +def node19697 : Tree Nat := .node node19696 node7430 +def node19698 : Tree Nat := .node node7871 node19697 +def node19699 : Tree Nat := .node node19698 node19347 +def node19700 : Tree Nat := .node node19699 node19355 +def node19701 : Tree Nat := .node node19357 node5910 +def node19702 : Tree Nat := .node node8297 node19701 +def node19703 : Tree Nat := .node node8727 node19361 +def node19704 : Tree Nat := .node node19702 node19703 +def node19705 : Tree Nat := .node node8302 node19365 +def node19706 : Tree Nat := .node node17147 node6674 +def node19707 : Tree Nat := .node node19706 node6677 +def node19708 : Tree Nat := .node node19707 node7877 +def node19709 : Tree Nat := .node node19705 node19708 +def node19710 : Tree Nat := .node node19704 node19709 +def node19711 : Tree Nat := .node node19700 node19710 +def node19712 : Tree Nat := .node node19695 node19711 +def node19713 : Tree Nat := .node node17155 node6684 +def node19714 : Tree Nat := .node node19713 node4999 +def node19715 : Tree Nat := .node node7885 node19714 +def node19716 : Tree Nat := .node node8735 node19373 +def node19717 : Tree Nat := .node node19715 node19716 +def node19718 : Tree Nat := .node node8310 node19377 +def node19719 : Tree Nat := .node node8740 node19380 +def node19720 : Tree Nat := .node node19718 node19719 +def node19721 : Tree Nat := .node node19717 node19720 +def node19722 : Tree Nat := .node node19384 node5014 +def node19723 : Tree Nat := .node node7891 node19722 +def node19724 : Tree Nat := .node node8746 node19388 +def node19725 : Tree Nat := .node node19723 node19724 +def node19726 : Tree Nat := .node node8316 node19392 +def node19727 : Tree Nat := .node node19726 node7897 +def node19728 : Tree Nat := .node node19725 node19727 +def node19729 : Tree Nat := .node node19721 node19728 +def node19730 : Tree Nat := .node node19397 node7473 +def node19731 : Tree Nat := .node node7903 node19730 +def node19732 : Tree Nat := .node node19400 node7479 +def node19733 : Tree Nat := .node node8753 node19732 +def node19734 : Tree Nat := .node node19731 node19733 +def node19735 : Tree Nat := .node node19407 node7083 +def node19736 : Tree Nat := .node node8762 node19735 +def node19737 : Tree Nat := .node node19406 node19736 +def node19738 : Tree Nat := .node node19734 node19737 +def node19739 : Tree Nat := .node node19412 node7485 +def node19740 : Tree Nat := .node node8333 node19739 +def node19741 : Tree Nat := .node node19180 node7093 +def node19742 : Tree Nat := .node node8768 node19741 +def node19743 : Tree Nat := .node node19740 node19742 +def node19744 : Tree Nat := .node node19420 node5054 +def node19745 : Tree Nat := .node node19744 node7914 +def node19746 : Tree Nat := .node node19419 node19745 +def node19747 : Tree Nat := .node node19743 node19746 +def node19748 : Tree Nat := .node node19738 node19747 +def node19749 : Tree Nat := .node node19729 node19748 +def node19750 : Tree Nat := .node node19712 node19749 +def node19751 : Tree Nat := .node node19672 node19750 +def node19752 : Tree Nat := .node node19584 node19751 +def node19753 : Tree Nat := .node node16917 node6354 +def node19754 : Tree Nat := .node node19753 node7114 +def node19755 : Tree Nat := .node node7501 node19754 +def node19756 : Tree Nat := .node node5965 node7506 +def node19757 : Tree Nat := .node node19756 node19434 +def node19758 : Tree Nat := .node node19755 node19757 +def node19759 : Tree Nat := .node node17195 node6736 +def node19760 : Tree Nat := .node node19759 node5970 +def node19761 : Tree Nat := .node node7512 node19760 +def node19762 : Tree Nat := .node node5977 node19199 +def node19763 : Tree Nat := .node node19761 node19762 +def node19764 : Tree Nat := .node node19758 node19763 +def node19765 : Tree Nat := .node node16923 node6365 +def node19766 : Tree Nat := .node node19765 node7128 +def node19767 : Tree Nat := .node node7126 node19766 +def node19768 : Tree Nat := .node node5983 node19445 +def node19769 : Tree Nat := .node node19767 node19768 +def node19770 : Tree Nat := .node node5988 node19449 +def node19771 : Tree Nat := .node node19770 node7530 +def node19772 : Tree Nat := .node node19769 node19771 +def node19773 : Tree Nat := .node node19764 node19772 +def node19774 : Tree Nat := .node node16930 node6379 +def node19775 : Tree Nat := .node node19774 node4569 +def node19776 : Tree Nat := .node node7140 node19775 +def node19777 : Tree Nat := .node node5995 node19457 +def node19778 : Tree Nat := .node node19776 node19777 +def node19779 : Tree Nat := .node node7541 node19461 +def node19780 : Tree Nat := .node node6386 node19219 +def node19781 : Tree Nat := .node node19779 node19780 +def node19782 : Tree Nat := .node node19778 node19781 +def node19783 : Tree Nat := .node node7546 node4073 +def node19784 : Tree Nat := .node node16936 node6755 +def node19785 : Tree Nat := .node node19784 node4584 +def node19786 : Tree Nat := .node node19783 node19785 +def node19787 : Tree Nat := .node node6006 node19468 +def node19788 : Tree Nat := .node node19786 node19787 +def node19789 : Tree Nat := .node node6013 node19472 +def node19790 : Tree Nat := .node node16941 node6390 +def node19791 : Tree Nat := .node node19790 node6393 +def node19792 : Tree Nat := .node node19791 node7558 +def node19793 : Tree Nat := .node node19789 node19792 +def node19794 : Tree Nat := .node node19788 node19793 +def node19795 : Tree Nat := .node node19782 node19794 +def node19796 : Tree Nat := .node node19773 node19795 +def node19797 : Tree Nat := .node node16949 node6403 +def node19798 : Tree Nat := .node node19797 node7165 +def node19799 : Tree Nat := .node node7566 node19798 +def node19800 : Tree Nat := .node node6021 node19483 +def node19801 : Tree Nat := .node node19799 node19800 +def node19802 : Tree Nat := .node node17227 node6768 +def node19803 : Tree Nat := .node node19802 node4610 +def node19804 : Tree Nat := .node node7575 node19803 +def node19805 : Tree Nat := .node node19225 node6773 +def node19806 : Tree Nat := .node node6414 node19805 +def node19807 : Tree Nat := .node node19804 node19806 +def node19808 : Tree Nat := .node node19801 node19807 +def node19809 : Tree Nat := .node node7580 node4107 +def node19810 : Tree Nat := .node node16955 node6778 +def node19811 : Tree Nat := .node node19810 node7182 +def node19812 : Tree Nat := .node node19809 node19811 +def node19813 : Tree Nat := .node node6032 node19490 +def node19814 : Tree Nat := .node node19812 node19813 +def node19815 : Tree Nat := .node node19493 node6790 +def node19816 : Tree Nat := .node node6037 node19815 +def node19817 : Tree Nat := .node node19816 node7593 +def node19818 : Tree Nat := .node node19814 node19817 +def node19819 : Tree Nat := .node node19808 node19818 +def node19820 : Tree Nat := .node node16967 node6425 +def node19821 : Tree Nat := .node node19820 node4636 +def node19822 : Tree Nat := .node node7194 node19821 +def node19823 : Tree Nat := .node node6044 node19502 +def node19824 : Tree Nat := .node node19822 node19823 +def node19825 : Tree Nat := .node node5656 node19506 +def node19826 : Tree Nat := .node node6432 node19238 +def node19827 : Tree Nat := .node node19825 node19826 +def node19828 : Tree Nat := .node node19824 node19827 +def node19829 : Tree Nat := .node node16973 node6806 +def node19830 : Tree Nat := .node node19829 node4651 +def node19831 : Tree Nat := .node node7610 node19830 +def node19832 : Tree Nat := .node node6050 node19513 +def node19833 : Tree Nat := .node node19831 node19832 +def node19834 : Tree Nat := .node node6055 node19517 +def node19835 : Tree Nat := .node node16978 node6436 +def node19836 : Tree Nat := .node node19835 node4660 +def node19837 : Tree Nat := .node node19836 node7619 +def node19838 : Tree Nat := .node node19834 node19837 +def node19839 : Tree Nat := .node node19833 node19838 +def node19840 : Tree Nat := .node node19828 node19839 +def node19841 : Tree Nat := .node node19819 node19840 +def node19842 : Tree Nat := .node node19796 node19841 +def node19843 : Tree Nat := .node node6064 node19252 +def node19844 : Tree Nat := .node node19527 node19843 +def node19845 : Tree Nat := .node node6455 node19529 +def node19846 : Tree Nat := .node node6071 node19256 +def node19847 : Tree Nat := .node node19845 node19846 +def node19848 : Tree Nat := .node node19844 node19847 +def node19849 : Tree Nat := .node node5681 node19533 +def node19850 : Tree Nat := .node node6077 node18846 +def node19851 : Tree Nat := .node node19849 node19850 +def node19852 : Tree Nat := .node node5689 node19045 +def node19853 : Tree Nat := .node node19852 node7640 +def node19854 : Tree Nat := .node node19851 node19853 +def node19855 : Tree Nat := .node node19848 node19854 +def node19856 : Tree Nat := .node node5696 node19539 +def node19857 : Tree Nat := .node node6084 node19541 +def node19858 : Tree Nat := .node node19856 node19857 +def node19859 : Tree Nat := .node node5701 node19056 +def node19860 : Tree Nat := .node node19261 node6859 +def node19861 : Tree Nat := .node node6478 node19860 +def node19862 : Tree Nat := .node node19859 node19861 +def node19863 : Tree Nat := .node node19858 node19862 +def node19864 : Tree Nat := .node node5707 node19545 +def node19865 : Tree Nat := .node node7656 node19547 +def node19866 : Tree Nat := .node node19864 node19865 +def node19867 : Tree Nat := .node node18862 node6876 +def node19868 : Tree Nat := .node node6095 node19867 +def node19869 : Tree Nat := .node node19550 node7661 +def node19870 : Tree Nat := .node node19868 node19869 +def node19871 : Tree Nat := .node node19866 node19870 +def node19872 : Tree Nat := .node node19863 node19871 +def node19873 : Tree Nat := .node node19855 node19872 +def node19874 : Tree Nat := .node node5719 node19556 +def node19875 : Tree Nat := .node node6103 node19275 +def node19876 : Tree Nat := .node node19874 node19875 +def node19877 : Tree Nat := .node node6500 node19559 +def node19878 : Tree Nat := .node node6504 node19282 +def node19879 : Tree Nat := .node node19877 node19878 +def node19880 : Tree Nat := .node node19876 node19879 +def node19881 : Tree Nat := .node node5734 node19563 +def node19882 : Tree Nat := .node node6118 node18880 +def node19883 : Tree Nat := .node node19881 node19882 +def node19884 : Tree Nat := .node node6125 node19292 +def node19885 : Tree Nat := .node node19884 node7681 +def node19886 : Tree Nat := .node node19883 node19885 +def node19887 : Tree Nat := .node node19880 node19886 +def node19888 : Tree Nat := .node node5744 node19570 +def node19889 : Tree Nat := .node node7691 node18890 +def node19890 : Tree Nat := .node node19888 node19889 +def node19891 : Tree Nat := .node node19091 node6136 +def node19892 : Tree Nat := .node node5753 node19891 +def node19893 : Tree Nat := .node node6524 node18002 +def node19894 : Tree Nat := .node node19892 node19893 +def node19895 : Tree Nat := .node node19890 node19894 +def node19896 : Tree Nat := .node node5759 node19574 +def node19897 : Tree Nat := .node node7697 node18898 +def node19898 : Tree Nat := .node node19896 node19897 +def node19899 : Tree Nat := .node node6150 node18902 +def node19900 : Tree Nat := .node node19103 node6531 +def node19901 : Tree Nat := .node node19900 node7706 +def node19902 : Tree Nat := .node node19899 node19901 +def node19903 : Tree Nat := .node node19898 node19902 +def node19904 : Tree Nat := .node node19895 node19903 +def node19905 : Tree Nat := .node node19887 node19904 +def node19906 : Tree Nat := .node node19873 node19905 +def node19907 : Tree Nat := .node node19842 node19906 +def node19908 : Tree Nat := .node node17058 node6543 +def node19909 : Tree Nat := .node node19908 node4801 +def node19910 : Tree Nat := .node node7716 node19909 +def node19911 : Tree Nat := .node node6160 node19588 +def node19912 : Tree Nat := .node node19910 node19911 +def node19913 : Tree Nat := .node node5773 node19592 +def node19914 : Tree Nat := .node node6165 node19594 +def node19915 : Tree Nat := .node node19913 node19914 +def node19916 : Tree Nat := .node node19912 node19915 +def node19917 : Tree Nat := .node node7726 node4300 +def node19918 : Tree Nat := .node node17064 node6549 +def node19919 : Tree Nat := .node node19918 node4816 +def node19920 : Tree Nat := .node node19917 node19919 +def node19921 : Tree Nat := .node node7733 node19601 +def node19922 : Tree Nat := .node node19920 node19921 +def node19923 : Tree Nat := .node node19604 node6940 +def node19924 : Tree Nat := .node node5788 node19923 +def node19925 : Tree Nat := .node node19924 node7743 +def node19926 : Tree Nat := .node node19922 node19925 +def node19927 : Tree Nat := .node node19916 node19926 +def node19928 : Tree Nat := .node node17071 node6564 +def node19929 : Tree Nat := .node node19928 node7334 +def node19930 : Tree Nat := .node node7332 node19929 +def node19931 : Tree Nat := .node node6178 node19613 +def node19932 : Tree Nat := .node node19930 node19931 +def node19933 : Tree Nat := .node node7754 node19617 +def node19934 : Tree Nat := .node node6575 node19311 +def node19935 : Tree Nat := .node node19933 node19934 +def node19936 : Tree Nat := .node node19932 node19935 +def node19937 : Tree Nat := .node node7759 node4337 +def node19938 : Tree Nat := .node node17077 node6956 +def node19939 : Tree Nat := .node node19938 node5808 +def node19940 : Tree Nat := .node node19937 node19939 +def node19941 : Tree Nat := .node node6189 node19624 +def node19942 : Tree Nat := .node node19940 node19941 +def node19943 : Tree Nat := .node node6194 node19628 +def node19944 : Tree Nat := .node node17082 node6579 +def node19945 : Tree Nat := .node node19944 node4856 +def node19946 : Tree Nat := .node node19945 node7771 +def node19947 : Tree Nat := .node node19943 node19946 +def node19948 : Tree Nat := .node node19942 node19947 +def node19949 : Tree Nat := .node node19936 node19948 +def node19950 : Tree Nat := .node node19927 node19949 +def node19951 : Tree Nat := .node node6202 node18935 +def node19952 : Tree Nat := .node node19637 node19951 +def node19953 : Tree Nat := .node node5822 node19133 +def node19954 : Tree Nat := .node node6594 node19318 +def node19955 : Tree Nat := .node node19953 node19954 +def node19956 : Tree Nat := .node node19952 node19955 +def node19957 : Tree Nat := .node node5828 node19640 +def node19958 : Tree Nat := .node node6213 node18700 +def node19959 : Tree Nat := .node node19957 node19958 +def node19960 : Tree Nat := .node node6220 node18703 +def node19961 : Tree Nat := .node node19960 node7791 +def node19962 : Tree Nat := .node node19959 node19961 +def node19963 : Tree Nat := .node node19956 node19962 +def node19964 : Tree Nat := .node node17103 node6610 +def node19965 : Tree Nat := .node node19964 node7380 +def node19966 : Tree Nat := .node node7378 node19965 +def node19967 : Tree Nat := .node node7801 node19649 +def node19968 : Tree Nat := .node node19966 node19967 +def node19969 : Tree Nat := .node node19652 node6231 +def node19970 : Tree Nat := .node node6617 node19969 +def node19971 : Tree Nat := .node node6621 node19326 +def node19972 : Tree Nat := .node node19970 node19971 +def node19973 : Tree Nat := .node node19968 node19972 +def node19974 : Tree Nat := .node node17109 node6999 +def node19975 : Tree Nat := .node node19974 node7395 +def node19976 : Tree Nat := .node node7812 node19975 +def node19977 : Tree Nat := .node node6242 node19660 +def node19978 : Tree Nat := .node node19976 node19977 +def node19979 : Tree Nat := .node node6249 node19664 +def node19980 : Tree Nat := .node node17114 node6625 +def node19981 : Tree Nat := .node node19980 node6628 +def node19982 : Tree Nat := .node node19981 node7823 +def node19983 : Tree Nat := .node node19979 node19982 +def node19984 : Tree Nat := .node node19978 node19983 +def node19985 : Tree Nat := .node node19973 node19984 +def node19986 : Tree Nat := .node node19963 node19985 +def node19987 : Tree Nat := .node node19950 node19986 +def node19988 : Tree Nat := .node node17123 node6636 +def node19989 : Tree Nat := .node node19988 node4932 +def node19990 : Tree Nat := .node node7832 node19989 +def node19991 : Tree Nat := .node node7836 node19676 +def node19992 : Tree Nat := .node node19990 node19991 +def node19993 : Tree Nat := .node node19679 node6262 +def node19994 : Tree Nat := .node node5871 node19993 +def node19995 : Tree Nat := .node node6643 node19340 +def node19996 : Tree Nat := .node node19994 node19995 +def node19997 : Tree Nat := .node node19992 node19996 +def node19998 : Tree Nat := .node node7846 node4427 +def node19999 : Tree Nat := .node node17129 node7019 +def node20000 : Tree Nat := .node node19999 node4951 +def node20001 : Tree Nat := .node node19998 node20000 +def node20002 : Tree Nat := .node node7853 node19687 +def node20003 : Tree Nat := .node node20001 node20002 +def node20004 : Tree Nat := .node node6274 node19691 +def node20005 : Tree Nat := .node node20004 node7865 +def node20006 : Tree Nat := .node node20003 node20005 +def node20007 : Tree Nat := .node node19997 node20006 +def node20008 : Tree Nat := .node node5893 node19697 +def node20009 : Tree Nat := .node node6281 node19346 +def node20010 : Tree Nat := .node node20008 node20009 +def node20011 : Tree Nat := .node node6666 node19350 +def node20012 : Tree Nat := .node node6670 node19353 +def node20013 : Tree Nat := .node node20011 node20012 +def node20014 : Tree Nat := .node node20010 node20013 +def node20015 : Tree Nat := .node node5908 node19701 +def node20016 : Tree Nat := .node node6296 node19361 +def node20017 : Tree Nat := .node node20015 node20016 +def node20018 : Tree Nat := .node node6303 node19365 +def node20019 : Tree Nat := .node node20018 node19708 +def node20020 : Tree Nat := .node node20017 node20019 +def node20021 : Tree Nat := .node node20014 node20020 +def node20022 : Tree Nat := .node node20007 node20021 +def node20023 : Tree Nat := .node node5919 node19714 +def node20024 : Tree Nat := .node node6311 node19373 +def node20025 : Tree Nat := .node node20023 node20024 +def node20026 : Tree Nat := .node node5924 node19377 +def node20027 : Tree Nat := .node node6691 node19380 +def node20028 : Tree Nat := .node node20026 node20027 +def node20029 : Tree Nat := .node node20025 node20028 +def node20030 : Tree Nat := .node node5930 node19722 +def node20031 : Tree Nat := .node node6317 node19388 +def node20032 : Tree Nat := .node node20030 node20031 +def node20033 : Tree Nat := .node node6322 node19392 +def node20034 : Tree Nat := .node node20033 node7897 +def node20035 : Tree Nat := .node node20032 node20034 +def node20036 : Tree Nat := .node node20029 node20035 +def node20037 : Tree Nat := .node node5941 node19730 +def node20038 : Tree Nat := .node node6329 node19732 +def node20039 : Tree Nat := .node node20037 node20038 +def node20040 : Tree Nat := .node node6712 node19405 +def node20041 : Tree Nat := .node node6716 node19735 +def node20042 : Tree Nat := .node node20040 node20041 +def node20043 : Tree Nat := .node node20039 node20042 +def node20044 : Tree Nat := .node node5952 node19739 +def node20045 : Tree Nat := .node node6340 node19741 +def node20046 : Tree Nat := .node node20044 node20045 +def node20047 : Tree Nat := .node node19417 node7100 +def node20048 : Tree Nat := .node node6345 node20047 +def node20049 : Tree Nat := .node node20048 node19745 +def node20050 : Tree Nat := .node node20046 node20049 +def node20051 : Tree Nat := .node node20043 node20050 +def node20052 : Tree Nat := .node node20036 node20051 +def node20053 : Tree Nat := .node node20022 node20052 +def node20054 : Tree Nat := .node node19987 node20053 +def node20055 : Tree Nat := .node node19907 node20054 +def node20056 : Tree Nat := .node node19753 node4538 +def node20057 : Tree Nat := .node node5066 node20056 +def node20058 : Tree Nat := .node node17190 node23 +def node20059 : Tree Nat := .node node20058 node5069 +def node20060 : Tree Nat := .node node5966 node20059 +def node20061 : Tree Nat := .node node20057 node20060 +def node20062 : Tree Nat := .node node17195 node39 +def node20063 : Tree Nat := .node node20062 node5970 +def node20064 : Tree Nat := .node node6361 node20063 +def node20065 : Tree Nat := .node node17458 node3538 +def node20066 : Tree Nat := .node node20065 node5074 +def node20067 : Tree Nat := .node node5977 node20066 +def node20068 : Tree Nat := .node node20064 node20067 +def node20069 : Tree Nat := .node node20061 node20068 +def node20070 : Tree Nat := .node node19765 node5590 +def node20071 : Tree Nat := .node node5588 node20070 +def node20072 : Tree Nat := .node node17464 node86 +def node20073 : Tree Nat := .node node20072 node5080 +def node20074 : Tree Nat := .node node5983 node20073 +def node20075 : Tree Nat := .node node20071 node20074 +def node20076 : Tree Nat := .node node17201 node102 +def node20077 : Tree Nat := .node node20076 node5085 +def node20078 : Tree Nat := .node node5988 node20077 +def node20079 : Tree Nat := .node node20078 node6375 +def node20080 : Tree Nat := .node node20075 node20079 +def node20081 : Tree Nat := .node node20069 node20080 +def node20082 : Tree Nat := .node node5603 node19775 +def node20083 : Tree Nat := .node node17471 node149 +def node20084 : Tree Nat := .node node20083 node5096 +def node20085 : Tree Nat := .node node5995 node20084 +def node20086 : Tree Nat := .node node20082 node20085 +def node20087 : Tree Nat := .node node17208 node165 +def node20088 : Tree Nat := .node node20087 node5999 +def node20089 : Tree Nat := .node node5612 node20088 +def node20090 : Tree Nat := .node node17476 node3551 +def node20091 : Tree Nat := .node node20090 node5105 +def node20092 : Tree Nat := .node node6386 node20091 +def node20093 : Tree Nat := .node node20089 node20092 +def node20094 : Tree Nat := .node node20086 node20093 +def node20095 : Tree Nat := .node node16936 node196 +def node20096 : Tree Nat := .node node20095 node4584 +def node20097 : Tree Nat := .node node5618 node20096 +def node20098 : Tree Nat := .node node17482 node211 +def node20099 : Tree Nat := .node node20098 node5111 +def node20100 : Tree Nat := .node node6006 node20099 +def node20101 : Tree Nat := .node node20097 node20100 +def node20102 : Tree Nat := .node node17214 node227 +def node20103 : Tree Nat := .node node20102 node5116 +def node20104 : Tree Nat := .node node6013 node20103 +def node20105 : Tree Nat := .node node19791 node6397 +def node20106 : Tree Nat := .node node20104 node20105 +def node20107 : Tree Nat := .node node20101 node20106 +def node20108 : Tree Nat := .node node20094 node20107 +def node20109 : Tree Nat := .node node20081 node20108 +def node20110 : Tree Nat := .node node19797 node4601 +def node20111 : Tree Nat := .node node5129 node20110 +def node20112 : Tree Nat := .node node17222 node275 +def node20113 : Tree Nat := .node node20112 node5132 +def node20114 : Tree Nat := .node node6021 node20113 +def node20115 : Tree Nat := .node node20111 node20114 +def node20116 : Tree Nat := .node node17227 node291 +def node20117 : Tree Nat := .node node20116 node4610 +def node20118 : Tree Nat := .node node6410 node20117 +def node20119 : Tree Nat := .node node17490 node3570 +def node20120 : Tree Nat := .node node20119 node5137 +def node20121 : Tree Nat := .node node6414 node20120 +def node20122 : Tree Nat := .node node20118 node20121 +def node20123 : Tree Nat := .node node20115 node20122 +def node20124 : Tree Nat := .node node19810 node5638 +def node20125 : Tree Nat := .node node5636 node20124 +def node20126 : Tree Nat := .node node17496 node337 +def node20127 : Tree Nat := .node node20126 node5143 +def node20128 : Tree Nat := .node node6032 node20127 +def node20129 : Tree Nat := .node node20125 node20128 +def node20130 : Tree Nat := .node node17233 node353 +def node20131 : Tree Nat := .node node20130 node5148 +def node20132 : Tree Nat := .node node6037 node20131 +def node20133 : Tree Nat := .node node20132 node6421 +def node20134 : Tree Nat := .node node20129 node20133 +def node20135 : Tree Nat := .node node20123 node20134 +def node20136 : Tree Nat := .node node5651 node19821 +def node20137 : Tree Nat := .node node17503 node400 +def node20138 : Tree Nat := .node node20137 node5159 +def node20139 : Tree Nat := .node node6044 node20138 +def node20140 : Tree Nat := .node node20136 node20139 +def node20141 : Tree Nat := .node node17240 node416 +def node20142 : Tree Nat := .node node20141 node5164 +def node20143 : Tree Nat := .node node5656 node20142 +def node20144 : Tree Nat := .node node17508 node3818 +def node20145 : Tree Nat := .node node20144 node5168 +def node20146 : Tree Nat := .node node6432 node20145 +def node20147 : Tree Nat := .node node20143 node20146 +def node20148 : Tree Nat := .node node20140 node20147 +def node20149 : Tree Nat := .node node16973 node447 +def node20150 : Tree Nat := .node node20149 node4651 +def node20151 : Tree Nat := .node node5662 node20150 +def node20152 : Tree Nat := .node node17514 node462 +def node20153 : Tree Nat := .node node20152 node5174 +def node20154 : Tree Nat := .node node6050 node20153 +def node20155 : Tree Nat := .node node20151 node20154 +def node20156 : Tree Nat := .node node17246 node477 +def node20157 : Tree Nat := .node node20156 node5179 +def node20158 : Tree Nat := .node node6055 node20157 +def node20159 : Tree Nat := .node node19836 node6441 +def node20160 : Tree Nat := .node node20158 node20159 +def node20161 : Tree Nat := .node node20155 node20160 +def node20162 : Tree Nat := .node node20148 node20161 +def node20163 : Tree Nat := .node node20135 node20162 +def node20164 : Tree Nat := .node node20109 node20163 +def node20165 : Tree Nat := .node node16988 node4669 +def node20166 : Tree Nat := .node node5193 node20165 +def node20167 : Tree Nat := .node node17255 node526 +def node20168 : Tree Nat := .node node20167 node5196 +def node20169 : Tree Nat := .node node6064 node20168 +def node20170 : Tree Nat := .node node20166 node20169 +def node20171 : Tree Nat := .node node17260 node542 +def node20172 : Tree Nat := .node node20171 node4678 +def node20173 : Tree Nat := .node node6455 node20172 +def node20174 : Tree Nat := .node node17523 node557 +def node20175 : Tree Nat := .node node20174 node5201 +def node20176 : Tree Nat := .node node6071 node20175 +def node20177 : Tree Nat := .node node20173 node20176 +def node20178 : Tree Nat := .node node20170 node20177 +def node20179 : Tree Nat := .node node17529 node588 +def node20180 : Tree Nat := .node node20179 node5207 +def node20181 : Tree Nat := .node node6077 node20180 +def node20182 : Tree Nat := .node node19849 node20181 +def node20183 : Tree Nat := .node node17266 node604 +def node20184 : Tree Nat := .node node20183 node5212 +def node20185 : Tree Nat := .node node5689 node20184 +def node20186 : Tree Nat := .node node20185 node6467 +def node20187 : Tree Nat := .node node20182 node20186 +def node20188 : Tree Nat := .node node20178 node20187 +def node20189 : Tree Nat := .node node17536 node651 +def node20190 : Tree Nat := .node node20189 node5223 +def node20191 : Tree Nat := .node node6084 node20190 +def node20192 : Tree Nat := .node node19856 node20191 +def node20193 : Tree Nat := .node node17273 node667 +def node20194 : Tree Nat := .node node20193 node5228 +def node20195 : Tree Nat := .node node5701 node20194 +def node20196 : Tree Nat := .node node17541 node3610 +def node20197 : Tree Nat := .node node20196 node5232 +def node20198 : Tree Nat := .node node6478 node20197 +def node20199 : Tree Nat := .node node20195 node20198 +def node20200 : Tree Nat := .node node20192 node20199 +def node20201 : Tree Nat := .node node17011 node698 +def node20202 : Tree Nat := .node node20201 node4719 +def node20203 : Tree Nat := .node node5707 node20202 +def node20204 : Tree Nat := .node node17547 node713 +def node20205 : Tree Nat := .node node20204 node5238 +def node20206 : Tree Nat := .node node6090 node20205 +def node20207 : Tree Nat := .node node20203 node20206 +def node20208 : Tree Nat := .node node17279 node729 +def node20209 : Tree Nat := .node node20208 node5243 +def node20210 : Tree Nat := .node node6095 node20209 +def node20211 : Tree Nat := .node node19550 node6487 +def node20212 : Tree Nat := .node node20210 node20211 +def node20213 : Tree Nat := .node node20207 node20212 +def node20214 : Tree Nat := .node node20200 node20213 +def node20215 : Tree Nat := .node node20188 node20214 +def node20216 : Tree Nat := .node node19271 node4736 +def node20217 : Tree Nat := .node node5719 node20216 +def node20218 : Tree Nat := .node node17287 node777 +def node20219 : Tree Nat := .node node20218 node5255 +def node20220 : Tree Nat := .node node6103 node20219 +def node20221 : Tree Nat := .node node20217 node20220 +def node20222 : Tree Nat := .node node17292 node793 +def node20223 : Tree Nat := .node node20222 node6107 +def node20224 : Tree Nat := .node node6500 node20223 +def node20225 : Tree Nat := .node node17555 node3624 +def node20226 : Tree Nat := .node node20225 node5264 +def node20227 : Tree Nat := .node node6504 node20226 +def node20228 : Tree Nat := .node node20224 node20227 +def node20229 : Tree Nat := .node node20221 node20228 +def node20230 : Tree Nat := .leaf 19136262932255243894327540630475154705164967900866663911068029494595001430924024396931296128159696131577158553613765316960850876967683885097823130383956161858642094270647956759878025783704832794689536 +def node20231 : Tree Nat := .node node17030 node20230 +def node20232 : Tree Nat := .node node20231 node5736 +def node20233 : Tree Nat := .node node5734 node20232 +def node20234 : Tree Nat := .node node17561 node839 +def node20235 : Tree Nat := .node node20234 node5270 +def node20236 : Tree Nat := .node node6118 node20235 +def node20237 : Tree Nat := .node node20233 node20236 +def node20238 : Tree Nat := .node node17298 node855 +def node20239 : Tree Nat := .node node20238 node5275 +def node20240 : Tree Nat := .node node6125 node20239 +def node20241 : Tree Nat := .node node20240 node6513 +def node20242 : Tree Nat := .node node20237 node20241 +def node20243 : Tree Nat := .node node20229 node20242 +def node20244 : Tree Nat := .node node17568 node902 +def node20245 : Tree Nat := .node node20244 node5286 +def node20246 : Tree Nat := .node node6132 node20245 +def node20247 : Tree Nat := .node node19888 node20246 +def node20248 : Tree Nat := .node node17305 node918 +def node20249 : Tree Nat := .node node20248 node6136 +def node20250 : Tree Nat := .node node5753 node20249 +def node20251 : Tree Nat := .node node17573 node3922 +def node20252 : Tree Nat := .node node20251 node5295 +def node20253 : Tree Nat := .node node6524 node20252 +def node20254 : Tree Nat := .node node20250 node20253 +def node20255 : Tree Nat := .node node20247 node20254 +def node20256 : Tree Nat := .node node17043 node949 +def node20257 : Tree Nat := .node node20256 node4782 +def node20258 : Tree Nat := .node node5759 node20257 +def node20259 : Tree Nat := .node node17579 node964 +def node20260 : Tree Nat := .node node20259 node5301 +def node20261 : Tree Nat := .node node6143 node20260 +def node20262 : Tree Nat := .node node20258 node20261 +def node20263 : Tree Nat := .node node17311 node979 +def node20264 : Tree Nat := .node node20263 node5306 +def node20265 : Tree Nat := .node node6150 node20264 +def node20266 : Tree Nat := .node node19900 node6535 +def node20267 : Tree Nat := .node node20265 node20266 +def node20268 : Tree Nat := .node node20262 node20267 +def node20269 : Tree Nat := .node node20255 node20268 +def node20270 : Tree Nat := .node node20243 node20269 +def node20271 : Tree Nat := .node node20215 node20270 +def node20272 : Tree Nat := .node node20164 node20271 +def node20273 : Tree Nat := .node node5321 node19909 +def node20274 : Tree Nat := .node node17321 node1029 +def node20275 : Tree Nat := .node node20274 node5324 +def node20276 : Tree Nat := .node node6160 node20275 +def node20277 : Tree Nat := .node node20273 node20276 +def node20278 : Tree Nat := .node node17326 node1045 +def node20279 : Tree Nat := .node node20278 node4806 +def node20280 : Tree Nat := .node node5773 node20279 +def node20281 : Tree Nat := .node node17589 node3657 +def node20282 : Tree Nat := .node node20281 node5329 +def node20283 : Tree Nat := .node node6165 node20282 +def node20284 : Tree Nat := .node node20280 node20283 +def node20285 : Tree Nat := .node node20277 node20284 +def node20286 : Tree Nat := .node node5779 node19919 +def node20287 : Tree Nat := .node node17595 node1091 +def node20288 : Tree Nat := .node node20287 node5335 +def node20289 : Tree Nat := .node node6171 node20288 +def node20290 : Tree Nat := .node node20286 node20289 +def node20291 : Tree Nat := .node node17332 node1107 +def node20292 : Tree Nat := .node node20291 node5340 +def node20293 : Tree Nat := .node node5788 node20292 +def node20294 : Tree Nat := .node node20293 node6560 +def node20295 : Tree Nat := .node node20290 node20294 +def node20296 : Tree Nat := .node node20285 node20295 +def node20297 : Tree Nat := .node node19928 node4832 +def node20298 : Tree Nat := .node node5795 node20297 +def node20299 : Tree Nat := .node node17602 node1154 +def node20300 : Tree Nat := .node node20299 node5351 +def node20301 : Tree Nat := .node node6178 node20300 +def node20302 : Tree Nat := .node node20298 node20301 +def node20303 : Tree Nat := .node node17339 node1170 +def node20304 : Tree Nat := .node node20303 node5356 +def node20305 : Tree Nat := .node node6571 node20304 +def node20306 : Tree Nat := .node node17607 node1185 +def node20307 : Tree Nat := .node node20306 node5360 +def node20308 : Tree Nat := .node node6575 node20307 +def node20309 : Tree Nat := .node node20305 node20308 +def node20310 : Tree Nat := .node node20302 node20309 +def node20311 : Tree Nat := .node node17077 node1201 +def node20312 : Tree Nat := .node node20311 node5808 +def node20313 : Tree Nat := .node node5806 node20312 +def node20314 : Tree Nat := .node node17613 node1216 +def node20315 : Tree Nat := .node node20314 node5366 +def node20316 : Tree Nat := .node node6189 node20315 +def node20317 : Tree Nat := .node node20313 node20316 +def node20318 : Tree Nat := .node node17345 node1232 +def node20319 : Tree Nat := .node node20318 node5371 +def node20320 : Tree Nat := .node node6194 node20319 +def node20321 : Tree Nat := .node node19945 node5376 +def node20322 : Tree Nat := .node node20320 node20321 +def node20323 : Tree Nat := .node node20317 node20322 +def node20324 : Tree Nat := .node node20310 node20323 +def node20325 : Tree Nat := .node node20296 node20324 +def node20326 : Tree Nat := .node node5384 node19636 +def node20327 : Tree Nat := .node node17353 node1280 +def node20328 : Tree Nat := .node node20327 node5387 +def node20329 : Tree Nat := .node node6202 node20328 +def node20330 : Tree Nat := .node node20326 node20329 +def node20331 : Tree Nat := .node node17358 node1296 +def node20332 : Tree Nat := .node node20331 node6206 +def node20333 : Tree Nat := .node node5822 node20332 +def node20334 : Tree Nat := .node node17621 node1311 +def node20335 : Tree Nat := .node node20334 node5392 +def node20336 : Tree Nat := .node node6594 node20335 +def node20337 : Tree Nat := .node node20333 node20336 +def node20338 : Tree Nat := .node node20330 node20337 +def node20339 : Tree Nat := .node node17627 node1342 +def node20340 : Tree Nat := .node node20339 node5398 +def node20341 : Tree Nat := .node node6213 node20340 +def node20342 : Tree Nat := .node node19957 node20341 +def node20343 : Tree Nat := .node node17364 node1358 +def node20344 : Tree Nat := .node node20343 node5403 +def node20345 : Tree Nat := .node node6220 node20344 +def node20346 : Tree Nat := .node node20345 node6606 +def node20347 : Tree Nat := .node node20342 node20346 +def node20348 : Tree Nat := .node node20338 node20347 +def node20349 : Tree Nat := .node node19964 node4899 +def node20350 : Tree Nat := .node node5839 node20349 +def node20351 : Tree Nat := .node node17634 node1405 +def node20352 : Tree Nat := .node node20351 node5414 +def node20353 : Tree Nat := .node node6227 node20352 +def node20354 : Tree Nat := .node node20350 node20353 +def node20355 : Tree Nat := .node node17371 node1421 +def node20356 : Tree Nat := .node node20355 node6231 +def node20357 : Tree Nat := .node node6617 node20356 +def node20358 : Tree Nat := .node node17639 node3965 +def node20359 : Tree Nat := .node node20358 node5423 +def node20360 : Tree Nat := .node node6621 node20359 +def node20361 : Tree Nat := .node node20357 node20360 +def node20362 : Tree Nat := .node node20354 node20361 +def node20363 : Tree Nat := .node node17109 node1452 +def node20364 : Tree Nat := .node node20363 node5856 +def node20365 : Tree Nat := .node node5854 node20364 +def node20366 : Tree Nat := .node node17645 node1467 +def node20367 : Tree Nat := .node node20366 node5429 +def node20368 : Tree Nat := .node node6242 node20367 +def node20369 : Tree Nat := .node node20365 node20368 +def node20370 : Tree Nat := .node node17377 node1482 +def node20371 : Tree Nat := .node node20370 node5434 +def node20372 : Tree Nat := .node node6249 node20371 +def node20373 : Tree Nat := .node node19981 node5439 +def node20374 : Tree Nat := .node node20372 node20373 +def node20375 : Tree Nat := .node node20369 node20374 +def node20376 : Tree Nat := .node node20362 node20375 +def node20377 : Tree Nat := .node node20348 node20376 +def node20378 : Tree Nat := .node node20325 node20377 +def node20379 : Tree Nat := .node node5448 node19989 +def node20380 : Tree Nat := .node node17386 node1531 +def node20381 : Tree Nat := .node node20380 node5451 +def node20382 : Tree Nat := .node node6258 node20381 +def node20383 : Tree Nat := .node node20379 node20382 +def node20384 : Tree Nat := .node node17391 node1547 +def node20385 : Tree Nat := .node node20384 node6262 +def node20386 : Tree Nat := .node node5871 node20385 +def node20387 : Tree Nat := .node node17654 node1562 +def node20388 : Tree Nat := .node node20387 node5456 +def node20389 : Tree Nat := .node node6643 node20388 +def node20390 : Tree Nat := .node node20386 node20389 +def node20391 : Tree Nat := .node node20383 node20390 +def node20392 : Tree Nat := .node node5877 node20000 +def node20393 : Tree Nat := .node node17660 node1593 +def node20394 : Tree Nat := .node node20393 node5462 +def node20395 : Tree Nat := .node node6269 node20394 +def node20396 : Tree Nat := .node node20392 node20395 +def node20397 : Tree Nat := .node node17397 node1609 +def node20398 : Tree Nat := .node node20397 node5467 +def node20399 : Tree Nat := .node node6274 node20398 +def node20400 : Tree Nat := .node node20399 node6655 +def node20401 : Tree Nat := .node node20396 node20400 +def node20402 : Tree Nat := .node node20391 node20401 +def node20403 : Tree Nat := .node node19696 node4967 +def node20404 : Tree Nat := .node node5893 node20403 +def node20405 : Tree Nat := .node node17670 node1656 +def node20406 : Tree Nat := .node node20405 node5478 +def node20407 : Tree Nat := .node node6281 node20406 +def node20408 : Tree Nat := .node node20404 node20407 +def node20409 : Tree Nat := .node node17404 node1672 +def node20410 : Tree Nat := .node node20409 node6285 +def node20411 : Tree Nat := .node node6666 node20410 +def node20412 : Tree Nat := .node node17675 node1687 +def node20413 : Tree Nat := .node node20412 node5487 +def node20414 : Tree Nat := .node node6670 node20413 +def node20415 : Tree Nat := .node node20411 node20414 +def node20416 : Tree Nat := .node node20408 node20415 +def node20417 : Tree Nat := .node node17142 node1703 +def node20418 : Tree Nat := .node node20417 node5910 +def node20419 : Tree Nat := .node node5908 node20418 +def node20420 : Tree Nat := .node node6296 node19163 +def node20421 : Tree Nat := .node node20419 node20420 +def node20422 : Tree Nat := .node node17410 node1733 +def node20423 : Tree Nat := .node node20422 node5498 +def node20424 : Tree Nat := .node node6303 node20423 +def node20425 : Tree Nat := .node node19707 node5503 +def node20426 : Tree Nat := .node node20424 node20425 +def node20427 : Tree Nat := .node node20421 node20426 +def node20428 : Tree Nat := .node node20416 node20427 +def node20429 : Tree Nat := .node node20402 node20428 +def node20430 : Tree Nat := .node node17418 node1781 +def node20431 : Tree Nat := .node node20430 node5510 +def node20432 : Tree Nat := .node node6311 node20431 +def node20433 : Tree Nat := .node node20023 node20432 +def node20434 : Tree Nat := .node node17423 node1797 +def node20435 : Tree Nat := .node node20434 node5515 +def node20436 : Tree Nat := .node node5924 node20435 +def node20437 : Tree Nat := .node node17694 node1812 +def node20438 : Tree Nat := .node node20437 node5519 +def node20439 : Tree Nat := .node node6691 node20438 +def node20440 : Tree Nat := .node node20436 node20439 +def node20441 : Tree Nat := .node node20433 node20440 +def node20442 : Tree Nat := .node node17161 node1828 +def node20443 : Tree Nat := .node node20442 node5014 +def node20444 : Tree Nat := .node node5930 node20443 +def node20445 : Tree Nat := .node node17700 node1843 +def node20446 : Tree Nat := .node node20445 node5525 +def node20447 : Tree Nat := .node node6317 node20446 +def node20448 : Tree Nat := .node node20444 node20447 +def node20449 : Tree Nat := .node node17429 node1859 +def node20450 : Tree Nat := .node node20449 node5530 +def node20451 : Tree Nat := .node node6322 node20450 +def node20452 : Tree Nat := .node node20451 node6701 +def node20453 : Tree Nat := .node node20448 node20452 +def node20454 : Tree Nat := .node node20441 node20453 +def node20455 : Tree Nat := .node node19397 node5030 +def node20456 : Tree Nat := .node node5941 node20455 +def node20457 : Tree Nat := .node node17707 node1906 +def node20458 : Tree Nat := .node node20457 node5541 +def node20459 : Tree Nat := .node node6329 node20458 +def node20460 : Tree Nat := .node node20456 node20459 +def node20461 : Tree Nat := .node node17436 node1922 +def node20462 : Tree Nat := .node node20461 node5546 +def node20463 : Tree Nat := .node node6712 node20462 +def node20464 : Tree Nat := .node node17712 node1937 +def node20465 : Tree Nat := .node node20464 node5550 +def node20466 : Tree Nat := .node node6716 node20465 +def node20467 : Tree Nat := .node node20463 node20466 +def node20468 : Tree Nat := .node node20460 node20467 +def node20469 : Tree Nat := .node node17442 node1953 +def node20470 : Tree Nat := .node node20469 node5954 +def node20471 : Tree Nat := .node node5952 node20470 +def node20472 : Tree Nat := .node node17718 node1968 +def node20473 : Tree Nat := .node node20472 node5556 +def node20474 : Tree Nat := .node node6340 node20473 +def node20475 : Tree Nat := .node node20471 node20474 +def node20476 : Tree Nat := .node node17447 node1983 +def node20477 : Tree Nat := .node node20476 node5561 +def node20478 : Tree Nat := .node node6345 node20477 +def node20479 : Tree Nat := .node node19744 node5566 +def node20480 : Tree Nat := .node node20478 node20479 +def node20481 : Tree Nat := .node node20475 node20480 +def node20482 : Tree Nat := .node node20468 node20481 +def node20483 : Tree Nat := .node node20454 node20482 +def node20484 : Tree Nat := .node node20429 node20483 +def node20485 : Tree Nat := .node node20378 node20484 +def node20486 : Tree Nat := .node node20272 node20485 +def node20487 : Tree Nat := .node node16917 node8 +def node20488 : Tree Nat := .node node20487 node4538 +def node20489 : Tree Nat := .node node5066 node20488 +def node20490 : Tree Nat := .node node4021 node20059 +def node20491 : Tree Nat := .node node20489 node20490 +def node20492 : Tree Nat := .node node20062 node4543 +def node20493 : Tree Nat := .node node5582 node20492 +def node20494 : Tree Nat := .node node4548 node20066 +def node20495 : Tree Nat := .node node20493 node20494 +def node20496 : Tree Nat := .node node20491 node20495 +def node20497 : Tree Nat := .node node16923 node71 +def node20498 : Tree Nat := .node node20497 node5590 +def node20499 : Tree Nat := .node node5588 node20498 +def node20500 : Tree Nat := .node node4558 node20073 +def node20501 : Tree Nat := .node node20499 node20500 +def node20502 : Tree Nat := .node node4046 node20077 +def node20503 : Tree Nat := .node node20502 node5091 +def node20504 : Tree Nat := .node node20501 node20503 +def node20505 : Tree Nat := .node node20496 node20504 +def node20506 : Tree Nat := .node node16930 node134 +def node20507 : Tree Nat := .node node20506 node4569 +def node20508 : Tree Nat := .node node5603 node20507 +def node20509 : Tree Nat := .node node4574 node20084 +def node20510 : Tree Nat := .node node20508 node20509 +def node20511 : Tree Nat := .node node20087 node5101 +def node20512 : Tree Nat := .node node4065 node20511 +def node20513 : Tree Nat := .node node4579 node20091 +def node20514 : Tree Nat := .node node20512 node20513 +def node20515 : Tree Nat := .node node20510 node20514 +def node20516 : Tree Nat := .node node5622 node20099 +def node20517 : Tree Nat := .node node20097 node20516 +def node20518 : Tree Nat := .node node4079 node20103 +def node20519 : Tree Nat := .node node16941 node235 +def node20520 : Tree Nat := .node node20519 node4593 +def node20521 : Tree Nat := .node node20520 node5121 +def node20522 : Tree Nat := .node node20518 node20521 +def node20523 : Tree Nat := .node node20517 node20522 +def node20524 : Tree Nat := .node node20515 node20523 +def node20525 : Tree Nat := .node node20505 node20524 +def node20526 : Tree Nat := .node node16949 node260 +def node20527 : Tree Nat := .node node20526 node4601 +def node20528 : Tree Nat := .node node5129 node20527 +def node20529 : Tree Nat := .node node4606 node20113 +def node20530 : Tree Nat := .node node20528 node20529 +def node20531 : Tree Nat := .node node4099 node20117 +def node20532 : Tree Nat := .node node4615 node20120 +def node20533 : Tree Nat := .node node20531 node20532 +def node20534 : Tree Nat := .node node20530 node20533 +def node20535 : Tree Nat := .node node16955 node322 +def node20536 : Tree Nat := .node node20535 node5638 +def node20537 : Tree Nat := .node node5636 node20536 +def node20538 : Tree Nat := .node node4625 node20127 +def node20539 : Tree Nat := .node node20537 node20538 +def node20540 : Tree Nat := .node node4116 node20131 +def node20541 : Tree Nat := .node node20540 node5154 +def node20542 : Tree Nat := .node node20539 node20541 +def node20543 : Tree Nat := .node node20534 node20542 +def node20544 : Tree Nat := .node node16967 node385 +def node20545 : Tree Nat := .node node20544 node4636 +def node20546 : Tree Nat := .node node5651 node20545 +def node20547 : Tree Nat := .node node4641 node20138 +def node20548 : Tree Nat := .node node20546 node20547 +def node20549 : Tree Nat := .node node4132 node20142 +def node20550 : Tree Nat := .node node4646 node20145 +def node20551 : Tree Nat := .node node20549 node20550 +def node20552 : Tree Nat := .node node20548 node20551 +def node20553 : Tree Nat := .node node5666 node20153 +def node20554 : Tree Nat := .node node20151 node20553 +def node20555 : Tree Nat := .node node4146 node20157 +def node20556 : Tree Nat := .node node16978 node485 +def node20557 : Tree Nat := .node node20556 node4660 +def node20558 : Tree Nat := .node node20557 node5184 +def node20559 : Tree Nat := .node node20555 node20558 +def node20560 : Tree Nat := .node node20554 node20559 +def node20561 : Tree Nat := .node node20552 node20560 +def node20562 : Tree Nat := .node node20543 node20561 +def node20563 : Tree Nat := .node node20525 node20562 +def node20564 : Tree Nat := .node node16987 node511 +def node20565 : Tree Nat := .node node20564 node4669 +def node20566 : Tree Nat := .node node5193 node20565 +def node20567 : Tree Nat := .node node4674 node20168 +def node20568 : Tree Nat := .node node20566 node20567 +def node20569 : Tree Nat := .node node5675 node20172 +def node20570 : Tree Nat := .node node4683 node20175 +def node20571 : Tree Nat := .node node20569 node20570 +def node20572 : Tree Nat := .node node20568 node20571 +def node20573 : Tree Nat := .node node16993 node573 +def node20574 : Tree Nat := .node node20573 node5683 +def node20575 : Tree Nat := .node node5681 node20574 +def node20576 : Tree Nat := .node node4693 node20180 +def node20577 : Tree Nat := .node node20575 node20576 +def node20578 : Tree Nat := .node node4184 node20184 +def node20579 : Tree Nat := .node node20578 node5218 +def node20580 : Tree Nat := .node node20577 node20579 +def node20581 : Tree Nat := .node node20572 node20580 +def node20582 : Tree Nat := .node node17005 node636 +def node20583 : Tree Nat := .node node20582 node4704 +def node20584 : Tree Nat := .node node5696 node20583 +def node20585 : Tree Nat := .node node4709 node20190 +def node20586 : Tree Nat := .node node20584 node20585 +def node20587 : Tree Nat := .node node4200 node20194 +def node20588 : Tree Nat := .node node4714 node20197 +def node20589 : Tree Nat := .node node20587 node20588 +def node20590 : Tree Nat := .node node20586 node20589 +def node20591 : Tree Nat := .node node5711 node20205 +def node20592 : Tree Nat := .node node20203 node20591 +def node20593 : Tree Nat := .node node4211 node20209 +def node20594 : Tree Nat := .node node17016 node737 +def node20595 : Tree Nat := .node node20594 node4728 +def node20596 : Tree Nat := .node node20595 node5248 +def node20597 : Tree Nat := .node node20593 node20596 +def node20598 : Tree Nat := .node node20592 node20597 +def node20599 : Tree Nat := .node node20590 node20598 +def node20600 : Tree Nat := .node node20581 node20599 +def node20601 : Tree Nat := .node node17024 node762 +def node20602 : Tree Nat := .node node20601 node4736 +def node20603 : Tree Nat := .node node5719 node20602 +def node20604 : Tree Nat := .node node4741 node20219 +def node20605 : Tree Nat := .node node20603 node20604 +def node20606 : Tree Nat := .node node20222 node5260 +def node20607 : Tree Nat := .node node4231 node20606 +def node20608 : Tree Nat := .node node4746 node20226 +def node20609 : Tree Nat := .node node20607 node20608 +def node20610 : Tree Nat := .node node20605 node20609 +def node20611 : Tree Nat := .node node17030 node824 +def node20612 : Tree Nat := .node node20611 node5736 +def node20613 : Tree Nat := .node node5734 node20612 +def node20614 : Tree Nat := .node node4756 node20235 +def node20615 : Tree Nat := .node node20613 node20614 +def node20616 : Tree Nat := .node node4242 node20239 +def node20617 : Tree Nat := .node node20616 node5281 +def node20618 : Tree Nat := .node node20615 node20617 +def node20619 : Tree Nat := .node node20610 node20618 +def node20620 : Tree Nat := .node node17037 node887 +def node20621 : Tree Nat := .node node20620 node4767 +def node20622 : Tree Nat := .node node5744 node20621 +def node20623 : Tree Nat := .node node4772 node20245 +def node20624 : Tree Nat := .node node20622 node20623 +def node20625 : Tree Nat := .node node20248 node5291 +def node20626 : Tree Nat := .node node4258 node20625 +def node20627 : Tree Nat := .node node4777 node20252 +def node20628 : Tree Nat := .node node20626 node20627 +def node20629 : Tree Nat := .node node20624 node20628 +def node20630 : Tree Nat := .node node5763 node20260 +def node20631 : Tree Nat := .node node20258 node20630 +def node20632 : Tree Nat := .node node4272 node20264 +def node20633 : Tree Nat := .node node17048 node987 +def node20634 : Tree Nat := .node node20633 node4791 +def node20635 : Tree Nat := .node node20634 node5311 +def node20636 : Tree Nat := .node node20632 node20635 +def node20637 : Tree Nat := .node node20631 node20636 +def node20638 : Tree Nat := .node node20629 node20637 +def node20639 : Tree Nat := .node node20619 node20638 +def node20640 : Tree Nat := .node node20600 node20639 +def node20641 : Tree Nat := .node node20563 node20640 +def node20642 : Tree Nat := .node node17058 node1014 +def node20643 : Tree Nat := .node node20642 node4801 +def node20644 : Tree Nat := .node node5321 node20643 +def node20645 : Tree Nat := .node node4290 node20275 +def node20646 : Tree Nat := .node node20644 node20645 +def node20647 : Tree Nat := .node node4811 node20282 +def node20648 : Tree Nat := .node node20280 node20647 +def node20649 : Tree Nat := .node node20646 node20648 +def node20650 : Tree Nat := .node node17064 node1076 +def node20651 : Tree Nat := .node node20650 node4816 +def node20652 : Tree Nat := .node node5779 node20651 +def node20653 : Tree Nat := .node node5783 node20288 +def node20654 : Tree Nat := .node node20652 node20653 +def node20655 : Tree Nat := .node node4310 node20292 +def node20656 : Tree Nat := .node node20655 node5346 +def node20657 : Tree Nat := .node node20654 node20656 +def node20658 : Tree Nat := .node node20649 node20657 +def node20659 : Tree Nat := .node node17071 node1139 +def node20660 : Tree Nat := .node node20659 node4832 +def node20661 : Tree Nat := .node node5795 node20660 +def node20662 : Tree Nat := .node node4837 node20300 +def node20663 : Tree Nat := .node node20661 node20662 +def node20664 : Tree Nat := .node node4329 node20304 +def node20665 : Tree Nat := .node node4842 node20307 +def node20666 : Tree Nat := .node node20664 node20665 +def node20667 : Tree Nat := .node node20663 node20666 +def node20668 : Tree Nat := .node node4852 node20315 +def node20669 : Tree Nat := .node node20313 node20668 +def node20670 : Tree Nat := .node node4343 node20319 +def node20671 : Tree Nat := .node node17082 node1240 +def node20672 : Tree Nat := .node node20671 node4856 +def node20673 : Tree Nat := .node node20672 node5376 +def node20674 : Tree Nat := .node node20670 node20673 +def node20675 : Tree Nat := .node node20669 node20674 +def node20676 : Tree Nat := .node node20667 node20675 +def node20677 : Tree Nat := .node node20658 node20676 +def node20678 : Tree Nat := .node node17090 node1265 +def node20679 : Tree Nat := .node node20678 node4864 +def node20680 : Tree Nat := .node node5384 node20679 +def node20681 : Tree Nat := .node node4869 node20328 +def node20682 : Tree Nat := .node node20680 node20681 +def node20683 : Tree Nat := .node node20331 node4873 +def node20684 : Tree Nat := .node node4360 node20683 +def node20685 : Tree Nat := .node node4878 node20335 +def node20686 : Tree Nat := .node node20684 node20685 +def node20687 : Tree Nat := .node node20682 node20686 +def node20688 : Tree Nat := .node node17096 node1327 +def node20689 : Tree Nat := .node node20688 node4883 +def node20690 : Tree Nat := .node node5828 node20689 +def node20691 : Tree Nat := .node node5832 node20340 +def node20692 : Tree Nat := .node node20690 node20691 +def node20693 : Tree Nat := .node node4374 node20344 +def node20694 : Tree Nat := .node node20693 node5409 +def node20695 : Tree Nat := .node node20692 node20694 +def node20696 : Tree Nat := .node node20687 node20695 +def node20697 : Tree Nat := .node node17103 node1390 +def node20698 : Tree Nat := .node node20697 node4899 +def node20699 : Tree Nat := .node node5839 node20698 +def node20700 : Tree Nat := .node node4904 node20352 +def node20701 : Tree Nat := .node node20699 node20700 +def node20702 : Tree Nat := .node node20355 node5419 +def node20703 : Tree Nat := .node node4390 node20702 +def node20704 : Tree Nat := .node node4909 node20359 +def node20705 : Tree Nat := .node node20703 node20704 +def node20706 : Tree Nat := .node node20701 node20705 +def node20707 : Tree Nat := .node node4919 node20367 +def node20708 : Tree Nat := .node node20365 node20707 +def node20709 : Tree Nat := .node node4404 node20371 +def node20710 : Tree Nat := .node node17114 node1490 +def node20711 : Tree Nat := .node node20710 node4923 +def node20712 : Tree Nat := .node node20711 node5439 +def node20713 : Tree Nat := .node node20709 node20712 +def node20714 : Tree Nat := .node node20708 node20713 +def node20715 : Tree Nat := .node node20706 node20714 +def node20716 : Tree Nat := .node node20696 node20715 +def node20717 : Tree Nat := .node node20677 node20716 +def node20718 : Tree Nat := .node node17123 node1516 +def node20719 : Tree Nat := .node node20718 node4932 +def node20720 : Tree Nat := .node node5448 node20719 +def node20721 : Tree Nat := .node node4937 node20381 +def node20722 : Tree Nat := .node node20720 node20721 +def node20723 : Tree Nat := .node node20384 node4941 +def node20724 : Tree Nat := .node node5871 node20723 +def node20725 : Tree Nat := .node node4946 node20388 +def node20726 : Tree Nat := .node node20724 node20725 +def node20727 : Tree Nat := .node node20722 node20726 +def node20728 : Tree Nat := .node node17129 node1578 +def node20729 : Tree Nat := .node node20728 node4951 +def node20730 : Tree Nat := .node node5877 node20729 +def node20731 : Tree Nat := .node node5881 node20394 +def node20732 : Tree Nat := .node node20730 node20731 +def node20733 : Tree Nat := .node node4433 node20398 +def node20734 : Tree Nat := .node node20733 node5473 +def node20735 : Tree Nat := .node node20732 node20734 +def node20736 : Tree Nat := .node node20727 node20735 +def node20737 : Tree Nat := .node node17136 node1641 +def node20738 : Tree Nat := .node node20737 node4967 +def node20739 : Tree Nat := .node node5893 node20738 +def node20740 : Tree Nat := .node node4972 node20406 +def node20741 : Tree Nat := .node node20739 node20740 +def node20742 : Tree Nat := .node node20409 node5483 +def node20743 : Tree Nat := .node node4449 node20742 +def node20744 : Tree Nat := .node node4977 node20413 +def node20745 : Tree Nat := .node node20743 node20744 +def node20746 : Tree Nat := .node node20741 node20745 +def node20747 : Tree Nat := .node node4987 node19163 +def node20748 : Tree Nat := .node node20419 node20747 +def node20749 : Tree Nat := .node node4460 node20423 +def node20750 : Tree Nat := .node node17147 node1741 +def node20751 : Tree Nat := .node node20750 node4991 +def node20752 : Tree Nat := .node node20751 node5503 +def node20753 : Tree Nat := .node node20749 node20752 +def node20754 : Tree Nat := .node node20748 node20753 +def node20755 : Tree Nat := .node node20746 node20754 +def node20756 : Tree Nat := .node node20736 node20755 +def node20757 : Tree Nat := .node node17155 node1766 +def node20758 : Tree Nat := .node node20757 node4999 +def node20759 : Tree Nat := .node node5919 node20758 +def node20760 : Tree Nat := .node node5004 node20431 +def node20761 : Tree Nat := .node node20759 node20760 +def node20762 : Tree Nat := .node node4477 node20435 +def node20763 : Tree Nat := .node node5009 node20438 +def node20764 : Tree Nat := .node node20762 node20763 +def node20765 : Tree Nat := .node node20761 node20764 +def node20766 : Tree Nat := .node node5934 node20446 +def node20767 : Tree Nat := .node node20444 node20766 +def node20768 : Tree Nat := .node node4488 node20450 +def node20769 : Tree Nat := .node node20768 node5536 +def node20770 : Tree Nat := .node node20767 node20769 +def node20771 : Tree Nat := .node node20765 node20770 +def node20772 : Tree Nat := .node node17173 node1891 +def node20773 : Tree Nat := .node node20772 node5030 +def node20774 : Tree Nat := .node node5941 node20773 +def node20775 : Tree Nat := .node node5035 node20458 +def node20776 : Tree Nat := .node node20774 node20775 +def node20777 : Tree Nat := .node node4507 node20462 +def node20778 : Tree Nat := .node node5040 node20465 +def node20779 : Tree Nat := .node node20777 node20778 +def node20780 : Tree Nat := .node node20776 node20779 +def node20781 : Tree Nat := .node node5050 node20473 +def node20782 : Tree Nat := .node node20471 node20781 +def node20783 : Tree Nat := .node node4521 node20477 +def node20784 : Tree Nat := .node node17179 node1991 +def node20785 : Tree Nat := .node node20784 node5054 +def node20786 : Tree Nat := .node node20785 node5566 +def node20787 : Tree Nat := .node node20783 node20786 +def node20788 : Tree Nat := .node node20782 node20787 +def node20789 : Tree Nat := .node node20780 node20788 +def node20790 : Tree Nat := .node node20771 node20789 +def node20791 : Tree Nat := .node node20756 node20790 +def node20792 : Tree Nat := .node node20717 node20791 +def node20793 : Tree Nat := .node node20641 node20792 +def node20794 : Tree Nat := .node node20487 node4016 +def node20795 : Tree Nat := .node node4014 node20794 +def node20796 : Tree Nat := .node node20058 node4023 +def node20797 : Tree Nat := .node node4021 node20796 +def node20798 : Tree Nat := .node node20795 node20797 +def node20799 : Tree Nat := .node node20062 node4031 +def node20800 : Tree Nat := .node node4029 node20799 +def node20801 : Tree Nat := .node node20065 node58 +def node20802 : Tree Nat := .node node4548 node20801 +def node20803 : Tree Nat := .node node20800 node20802 +def node20804 : Tree Nat := .node node20798 node20803 +def node20805 : Tree Nat := .node node20497 node4040 +def node20806 : Tree Nat := .node node4038 node20805 +def node20807 : Tree Nat := .node node20072 node90 +def node20808 : Tree Nat := .node node4558 node20807 +def node20809 : Tree Nat := .node node20806 node20808 +def node20810 : Tree Nat := .node node20076 node4048 +def node20811 : Tree Nat := .node node4046 node20810 +def node20812 : Tree Nat := .node node20811 node4564 +def node20813 : Tree Nat := .node node20809 node20812 +def node20814 : Tree Nat := .node node20804 node20813 +def node20815 : Tree Nat := .node node20506 node138 +def node20816 : Tree Nat := .node node4060 node20815 +def node20817 : Tree Nat := .node node20083 node153 +def node20818 : Tree Nat := .node node4574 node20817 +def node20819 : Tree Nat := .node node20816 node20818 +def node20820 : Tree Nat := .node node20087 node4067 +def node20821 : Tree Nat := .node node4065 node20820 +def node20822 : Tree Nat := .node node20090 node183 +def node20823 : Tree Nat := .node node4579 node20822 +def node20824 : Tree Nat := .node node20821 node20823 +def node20825 : Tree Nat := .node node20819 node20824 +def node20826 : Tree Nat := .node node20095 node200 +def node20827 : Tree Nat := .node node4074 node20826 +def node20828 : Tree Nat := .node node20098 node215 +def node20829 : Tree Nat := .node node4589 node20828 +def node20830 : Tree Nat := .node node20827 node20829 +def node20831 : Tree Nat := .node node20102 node231 +def node20832 : Tree Nat := .node node4079 node20831 +def node20833 : Tree Nat := .node node20519 node239 +def node20834 : Tree Nat := .node node20833 node4083 +def node20835 : Tree Nat := .node node20832 node20834 +def node20836 : Tree Nat := .node node20830 node20835 +def node20837 : Tree Nat := .node node20825 node20836 +def node20838 : Tree Nat := .node node20814 node20837 +def node20839 : Tree Nat := .node node20526 node4093 +def node20840 : Tree Nat := .node node4091 node20839 +def node20841 : Tree Nat := .node node20112 node279 +def node20842 : Tree Nat := .node node4606 node20841 +def node20843 : Tree Nat := .node node20840 node20842 +def node20844 : Tree Nat := .node node20116 node4101 +def node20845 : Tree Nat := .node node4099 node20844 +def node20846 : Tree Nat := .node node20119 node309 +def node20847 : Tree Nat := .node node4615 node20846 +def node20848 : Tree Nat := .node node20845 node20847 +def node20849 : Tree Nat := .node node20843 node20848 +def node20850 : Tree Nat := .node node20535 node4110 +def node20851 : Tree Nat := .node node4108 node20850 +def node20852 : Tree Nat := .node node20126 node341 +def node20853 : Tree Nat := .node node4625 node20852 +def node20854 : Tree Nat := .node node20851 node20853 +def node20855 : Tree Nat := .node node20130 node357 +def node20856 : Tree Nat := .node node4116 node20855 +def node20857 : Tree Nat := .node node20856 node4631 +def node20858 : Tree Nat := .node node20854 node20857 +def node20859 : Tree Nat := .node node20849 node20858 +def node20860 : Tree Nat := .node node20544 node389 +def node20861 : Tree Nat := .node node4127 node20860 +def node20862 : Tree Nat := .node node20137 node404 +def node20863 : Tree Nat := .node node4641 node20862 +def node20864 : Tree Nat := .node node20861 node20863 +def node20865 : Tree Nat := .node node20141 node420 +def node20866 : Tree Nat := .node node4132 node20865 +def node20867 : Tree Nat := .node node20144 node434 +def node20868 : Tree Nat := .node node4646 node20867 +def node20869 : Tree Nat := .node node20866 node20868 +def node20870 : Tree Nat := .node node20864 node20869 +def node20871 : Tree Nat := .node node20149 node4140 +def node20872 : Tree Nat := .node node4138 node20871 +def node20873 : Tree Nat := .node node20152 node465 +def node20874 : Tree Nat := .node node4656 node20873 +def node20875 : Tree Nat := .node node20872 node20874 +def node20876 : Tree Nat := .node node20156 node4148 +def node20877 : Tree Nat := .node node4146 node20876 +def node20878 : Tree Nat := .node node20556 node489 +def node20879 : Tree Nat := .node node20878 node4153 +def node20880 : Tree Nat := .node node20877 node20879 +def node20881 : Tree Nat := .node node20875 node20880 +def node20882 : Tree Nat := .node node20870 node20881 +def node20883 : Tree Nat := .node node20859 node20882 +def node20884 : Tree Nat := .node node20838 node20883 +def node20885 : Tree Nat := .node node20564 node4164 +def node20886 : Tree Nat := .node node4162 node20885 +def node20887 : Tree Nat := .node node20167 node530 +def node20888 : Tree Nat := .node node4674 node20887 +def node20889 : Tree Nat := .node node20886 node20888 +def node20890 : Tree Nat := .node node20171 node4172 +def node20891 : Tree Nat := .node node4170 node20890 +def node20892 : Tree Nat := .node node20174 node560 +def node20893 : Tree Nat := .node node4683 node20892 +def node20894 : Tree Nat := .node node20891 node20893 +def node20895 : Tree Nat := .node node20889 node20894 +def node20896 : Tree Nat := .node node20573 node577 +def node20897 : Tree Nat := .node node4179 node20896 +def node20898 : Tree Nat := .node node20179 node592 +def node20899 : Tree Nat := .node node4693 node20898 +def node20900 : Tree Nat := .node node20897 node20899 +def node20901 : Tree Nat := .node node20183 node608 +def node20902 : Tree Nat := .node node4184 node20901 +def node20903 : Tree Nat := .node node20902 node4699 +def node20904 : Tree Nat := .node node20900 node20903 +def node20905 : Tree Nat := .node node20895 node20904 +def node20906 : Tree Nat := .node node20582 node640 +def node20907 : Tree Nat := .node node4195 node20906 +def node20908 : Tree Nat := .node node20189 node655 +def node20909 : Tree Nat := .node node4709 node20908 +def node20910 : Tree Nat := .node node20907 node20909 +def node20911 : Tree Nat := .node node20193 node671 +def node20912 : Tree Nat := .node node4200 node20911 +def node20913 : Tree Nat := .node node20196 node685 +def node20914 : Tree Nat := .node node4714 node20913 +def node20915 : Tree Nat := .node node20912 node20914 +def node20916 : Tree Nat := .node node20910 node20915 +def node20917 : Tree Nat := .node node20201 node702 +def node20918 : Tree Nat := .node node4206 node20917 +def node20919 : Tree Nat := .node node20204 node717 +def node20920 : Tree Nat := .node node4724 node20919 +def node20921 : Tree Nat := .node node20918 node20920 +def node20922 : Tree Nat := .node node20208 node733 +def node20923 : Tree Nat := .node node4211 node20922 +def node20924 : Tree Nat := .node node20594 node741 +def node20925 : Tree Nat := .node node20924 node4215 +def node20926 : Tree Nat := .node node20923 node20925 +def node20927 : Tree Nat := .node node20921 node20926 +def node20928 : Tree Nat := .node node20916 node20927 +def node20929 : Tree Nat := .node node20905 node20928 +def node20930 : Tree Nat := .node node20601 node4225 +def node20931 : Tree Nat := .node node4223 node20930 +def node20932 : Tree Nat := .node node20218 node781 +def node20933 : Tree Nat := .node node4741 node20932 +def node20934 : Tree Nat := .node node20931 node20933 +def node20935 : Tree Nat := .node node20222 node797 +def node20936 : Tree Nat := .node node4231 node20935 +def node20937 : Tree Nat := .node node20225 node811 +def node20938 : Tree Nat := .node node4746 node20937 +def node20939 : Tree Nat := .node node20936 node20938 +def node20940 : Tree Nat := .node node20934 node20939 +def node20941 : Tree Nat := .node node20611 node828 +def node20942 : Tree Nat := .node node4237 node20941 +def node20943 : Tree Nat := .node node20234 node843 +def node20944 : Tree Nat := .node node4756 node20943 +def node20945 : Tree Nat := .node node20942 node20944 +def node20946 : Tree Nat := .node node20238 node859 +def node20947 : Tree Nat := .node node4242 node20946 +def node20948 : Tree Nat := .node node20947 node4247 +def node20949 : Tree Nat := .node node20945 node20948 +def node20950 : Tree Nat := .node node20940 node20949 +def node20951 : Tree Nat := .node node20620 node891 +def node20952 : Tree Nat := .node node4253 node20951 +def node20953 : Tree Nat := .node node20244 node906 +def node20954 : Tree Nat := .node node4772 node20953 +def node20955 : Tree Nat := .node node20952 node20954 +def node20956 : Tree Nat := .node node20248 node4260 +def node20957 : Tree Nat := .node node4258 node20956 +def node20958 : Tree Nat := .node node20251 node936 +def node20959 : Tree Nat := .node node4777 node20958 +def node20960 : Tree Nat := .node node20957 node20959 +def node20961 : Tree Nat := .node node20955 node20960 +def node20962 : Tree Nat := .node node20256 node953 +def node20963 : Tree Nat := .node node4267 node20962 +def node20964 : Tree Nat := .node node20259 node967 +def node20965 : Tree Nat := .node node4787 node20964 +def node20966 : Tree Nat := .node node20963 node20965 +def node20967 : Tree Nat := .node node20263 node983 +def node20968 : Tree Nat := .node node4272 node20967 +def node20969 : Tree Nat := .node node20633 node991 +def node20970 : Tree Nat := .node node20969 node4276 +def node20971 : Tree Nat := .node node20968 node20970 +def node20972 : Tree Nat := .node node20966 node20971 +def node20973 : Tree Nat := .node node20961 node20972 +def node20974 : Tree Nat := .node node20950 node20973 +def node20975 : Tree Nat := .node node20929 node20974 +def node20976 : Tree Nat := .node node20884 node20975 +def node20977 : Tree Nat := .node node20642 node1018 +def node20978 : Tree Nat := .node node4286 node20977 +def node20979 : Tree Nat := .node node20274 node1033 +def node20980 : Tree Nat := .node node4290 node20979 +def node20981 : Tree Nat := .node node20978 node20980 +def node20982 : Tree Nat := .node node20278 node1049 +def node20983 : Tree Nat := .node node4295 node20982 +def node20984 : Tree Nat := .node node20281 node1063 +def node20985 : Tree Nat := .node node4811 node20984 +def node20986 : Tree Nat := .node node20983 node20985 +def node20987 : Tree Nat := .node node20981 node20986 +def node20988 : Tree Nat := .node node20650 node1080 +def node20989 : Tree Nat := .node node4301 node20988 +def node20990 : Tree Nat := .node node20287 node4304 +def node20991 : Tree Nat := .node node4821 node20990 +def node20992 : Tree Nat := .node node20989 node20991 +def node20993 : Tree Nat := .node node20291 node4312 +def node20994 : Tree Nat := .node node4310 node20993 +def node20995 : Tree Nat := .node node20994 node4827 +def node20996 : Tree Nat := .node node20992 node20995 +def node20997 : Tree Nat := .node node20987 node20996 +def node20998 : Tree Nat := .node node20659 node1143 +def node20999 : Tree Nat := .node node4324 node20998 +def node21000 : Tree Nat := .node node20299 node1158 +def node21001 : Tree Nat := .node node4837 node21000 +def node21002 : Tree Nat := .node node20999 node21001 +def node21003 : Tree Nat := .node node20303 node4331 +def node21004 : Tree Nat := .node node4329 node21003 +def node21005 : Tree Nat := .node node20306 node1188 +def node21006 : Tree Nat := .node node4842 node21005 +def node21007 : Tree Nat := .node node21004 node21006 +def node21008 : Tree Nat := .node node21002 node21007 +def node21009 : Tree Nat := .node node20311 node1205 +def node21010 : Tree Nat := .node node4338 node21009 +def node21011 : Tree Nat := .node node20314 node1220 +def node21012 : Tree Nat := .node node4852 node21011 +def node21013 : Tree Nat := .node node21010 node21012 +def node21014 : Tree Nat := .node node20318 node1236 +def node21015 : Tree Nat := .node node4343 node21014 +def node21016 : Tree Nat := .node node20671 node1244 +def node21017 : Tree Nat := .node node21016 node4347 +def node21018 : Tree Nat := .node node21015 node21017 +def node21019 : Tree Nat := .node node21013 node21018 +def node21020 : Tree Nat := .node node21008 node21019 +def node21021 : Tree Nat := .node node20997 node21020 +def node21022 : Tree Nat := .node node20678 node1269 +def node21023 : Tree Nat := .node node4355 node21022 +def node21024 : Tree Nat := .node node20327 node1284 +def node21025 : Tree Nat := .node node4869 node21024 +def node21026 : Tree Nat := .node node21023 node21025 +def node21027 : Tree Nat := .node node20331 node4362 +def node21028 : Tree Nat := .node node4360 node21027 +def node21029 : Tree Nat := .node node20334 node1314 +def node21030 : Tree Nat := .node node4878 node21029 +def node21031 : Tree Nat := .node node21028 node21030 +def node21032 : Tree Nat := .node node21026 node21031 +def node21033 : Tree Nat := .node node20688 node1331 +def node21034 : Tree Nat := .node node4369 node21033 +def node21035 : Tree Nat := .node node20339 node1346 +def node21036 : Tree Nat := .node node4888 node21035 +def node21037 : Tree Nat := .node node21034 node21036 +def node21038 : Tree Nat := .node node20343 node1362 +def node21039 : Tree Nat := .node node4374 node21038 +def node21040 : Tree Nat := .node node21039 node4894 +def node21041 : Tree Nat := .node node21037 node21040 +def node21042 : Tree Nat := .node node21032 node21041 +def node21043 : Tree Nat := .node node20697 node1394 +def node21044 : Tree Nat := .node node4385 node21043 +def node21045 : Tree Nat := .node node20351 node1409 +def node21046 : Tree Nat := .node node4904 node21045 +def node21047 : Tree Nat := .node node21044 node21046 +def node21048 : Tree Nat := .node node20355 node4392 +def node21049 : Tree Nat := .node node4390 node21048 +def node21050 : Tree Nat := .node node20358 node1439 +def node21051 : Tree Nat := .node node4909 node21050 +def node21052 : Tree Nat := .node node21049 node21051 +def node21053 : Tree Nat := .node node21047 node21052 +def node21054 : Tree Nat := .node node20363 node1456 +def node21055 : Tree Nat := .node node4399 node21054 +def node21056 : Tree Nat := .node node20366 node1470 +def node21057 : Tree Nat := .node node4919 node21056 +def node21058 : Tree Nat := .node node21055 node21057 +def node21059 : Tree Nat := .node node20370 node1486 +def node21060 : Tree Nat := .node node4404 node21059 +def node21061 : Tree Nat := .node node20710 node1494 +def node21062 : Tree Nat := .node node21061 node4408 +def node21063 : Tree Nat := .node node21060 node21062 +def node21064 : Tree Nat := .node node21058 node21063 +def node21065 : Tree Nat := .node node21053 node21064 +def node21066 : Tree Nat := .node node21042 node21065 +def node21067 : Tree Nat := .node node21021 node21066 +def node21068 : Tree Nat := .node node20718 node1520 +def node21069 : Tree Nat := .node node4417 node21068 +def node21070 : Tree Nat := .node node20380 node1535 +def node21071 : Tree Nat := .node node4937 node21070 +def node21072 : Tree Nat := .node node21069 node21071 +def node21073 : Tree Nat := .node node20384 node1551 +def node21074 : Tree Nat := .node node4422 node21073 +def node21075 : Tree Nat := .node node20387 node1565 +def node21076 : Tree Nat := .node node4946 node21075 +def node21077 : Tree Nat := .node node21074 node21076 +def node21078 : Tree Nat := .node node21072 node21077 +def node21079 : Tree Nat := .node node20728 node1582 +def node21080 : Tree Nat := .node node4428 node21079 +def node21081 : Tree Nat := .node node20393 node1597 +def node21082 : Tree Nat := .node node4956 node21081 +def node21083 : Tree Nat := .node node21080 node21082 +def node21084 : Tree Nat := .node node20397 node1613 +def node21085 : Tree Nat := .node node4433 node21084 +def node21086 : Tree Nat := .node node21085 node4962 +def node21087 : Tree Nat := .node node21083 node21086 +def node21088 : Tree Nat := .node node21078 node21087 +def node21089 : Tree Nat := .node node20737 node1645 +def node21090 : Tree Nat := .node node4444 node21089 +def node21091 : Tree Nat := .node node20405 node1660 +def node21092 : Tree Nat := .node node4972 node21091 +def node21093 : Tree Nat := .node node21090 node21092 +def node21094 : Tree Nat := .node node20409 node1676 +def node21095 : Tree Nat := .node node4449 node21094 +def node21096 : Tree Nat := .node node20412 node1690 +def node21097 : Tree Nat := .node node4977 node21096 +def node21098 : Tree Nat := .node node21095 node21097 +def node21099 : Tree Nat := .node node21093 node21098 +def node21100 : Tree Nat := .node node20417 node1707 +def node21101 : Tree Nat := .node node4455 node21100 +def node21102 : Tree Nat := .node node19162 node1721 +def node21103 : Tree Nat := .node node4987 node21102 +def node21104 : Tree Nat := .node node21101 node21103 +def node21105 : Tree Nat := .node node20422 node1737 +def node21106 : Tree Nat := .node node4460 node21105 +def node21107 : Tree Nat := .node node20750 node1745 +def node21108 : Tree Nat := .node node21107 node4464 +def node21109 : Tree Nat := .node node21106 node21108 +def node21110 : Tree Nat := .node node21104 node21109 +def node21111 : Tree Nat := .node node21099 node21110 +def node21112 : Tree Nat := .node node21088 node21111 +def node21113 : Tree Nat := .node node20757 node1770 +def node21114 : Tree Nat := .node node4472 node21113 +def node21115 : Tree Nat := .node node20430 node1785 +def node21116 : Tree Nat := .node node5004 node21115 +def node21117 : Tree Nat := .node node21114 node21116 +def node21118 : Tree Nat := .node node20434 node1801 +def node21119 : Tree Nat := .node node4477 node21118 +def node21120 : Tree Nat := .node node20437 node1815 +def node21121 : Tree Nat := .node node5009 node21120 +def node21122 : Tree Nat := .node node21119 node21121 +def node21123 : Tree Nat := .node node21117 node21122 +def node21124 : Tree Nat := .node node20442 node1832 +def node21125 : Tree Nat := .node node4483 node21124 +def node21126 : Tree Nat := .node node20445 node1847 +def node21127 : Tree Nat := .node node5019 node21126 +def node21128 : Tree Nat := .node node21125 node21127 +def node21129 : Tree Nat := .node node20449 node4490 +def node21130 : Tree Nat := .node node4488 node21129 +def node21131 : Tree Nat := .node node21130 node4496 +def node21132 : Tree Nat := .node node21128 node21131 +def node21133 : Tree Nat := .node node21123 node21132 +def node21134 : Tree Nat := .node node20772 node1895 +def node21135 : Tree Nat := .node node4502 node21134 +def node21136 : Tree Nat := .node node20457 node1910 +def node21137 : Tree Nat := .node node5035 node21136 +def node21138 : Tree Nat := .node node21135 node21137 +def node21139 : Tree Nat := .node node20461 node4509 +def node21140 : Tree Nat := .node node4507 node21139 +def node21141 : Tree Nat := .node node20464 node1940 +def node21142 : Tree Nat := .node node5040 node21141 +def node21143 : Tree Nat := .node node21140 node21142 +def node21144 : Tree Nat := .node node21138 node21143 +def node21145 : Tree Nat := .node node20469 node1957 +def node21146 : Tree Nat := .node node4516 node21145 +def node21147 : Tree Nat := .node node20472 node1971 +def node21148 : Tree Nat := .node node5050 node21147 +def node21149 : Tree Nat := .node node21146 node21148 +def node21150 : Tree Nat := .node node20476 node4523 +def node21151 : Tree Nat := .node node4521 node21150 +def node21152 : Tree Nat := .node node20784 node1995 +def node21153 : Tree Nat := .node node21152 node4528 +def node21154 : Tree Nat := .node node21151 node21153 +def node21155 : Tree Nat := .node node21149 node21154 +def node21156 : Tree Nat := .node node21144 node21155 +def node21157 : Tree Nat := .node node21133 node21156 +def node21158 : Tree Nat := .node node21112 node21157 +def node21159 : Tree Nat := .node node21067 node21158 +def node21160 : Tree Nat := .node node20976 node21159 +def node21161 : Tree Nat := .node node3 node3732 +def node21162 : Tree Nat := .node node2 node21161 +def node21163 : Tree Nat := .node node21162 node20794 +def node21164 : Tree Nat := .node node21 node20796 +def node21165 : Tree Nat := .node node21163 node21164 +def node21166 : Tree Nat := .node node3739 node20799 +def node21167 : Tree Nat := .node node52 node20801 +def node21168 : Tree Nat := .node node21166 node21167 +def node21169 : Tree Nat := .node node21165 node21168 +def node21170 : Tree Nat := .node node69 node20805 +def node21171 : Tree Nat := .node node84 node20807 +def node21172 : Tree Nat := .node node21170 node21171 +def node21173 : Tree Nat := .node node3745 node20810 +def node21174 : Tree Nat := .node node21173 node3750 +def node21175 : Tree Nat := .node node21172 node21174 +def node21176 : Tree Nat := .node node21169 node21175 +def node21177 : Tree Nat := .node node3756 node20815 +def node21178 : Tree Nat := .node node147 node20817 +def node21179 : Tree Nat := .node node21177 node21178 +def node21180 : Tree Nat := .node node163 node20820 +def node21181 : Tree Nat := .node node3761 node20822 +def node21182 : Tree Nat := .node node21180 node21181 +def node21183 : Tree Nat := .node node21179 node21182 +def node21184 : Tree Nat := .node node3767 node20826 +def node21185 : Tree Nat := .node node209 node20828 +def node21186 : Tree Nat := .node node21184 node21185 +def node21187 : Tree Nat := .node node3772 node20831 +def node21188 : Tree Nat := .node node241 node3774 +def node21189 : Tree Nat := .node node21188 node245 +def node21190 : Tree Nat := .node node20833 node21189 +def node21191 : Tree Nat := .node node21187 node21190 +def node21192 : Tree Nat := .node node21186 node21191 +def node21193 : Tree Nat := .node node21183 node21192 +def node21194 : Tree Nat := .node node21176 node21193 +def node21195 : Tree Nat := .node node255 node3782 +def node21196 : Tree Nat := .node node254 node21195 +def node21197 : Tree Nat := .node node21196 node20839 +def node21198 : Tree Nat := .node node273 node20841 +def node21199 : Tree Nat := .node node21197 node21198 +def node21200 : Tree Nat := .node node289 node20844 +def node21201 : Tree Nat := .node node3789 node20846 +def node21202 : Tree Nat := .node node21200 node21201 +def node21203 : Tree Nat := .node node21199 node21202 +def node21204 : Tree Nat := .node node3795 node20850 +def node21205 : Tree Nat := .node node335 node20852 +def node21206 : Tree Nat := .node node21204 node21205 +def node21207 : Tree Nat := .node node3800 node20855 +def node21208 : Tree Nat := .node node367 node3802 +def node21209 : Tree Nat := .node node21208 node371 +def node21210 : Tree Nat := .node node366 node21209 +def node21211 : Tree Nat := .node node21207 node21210 +def node21212 : Tree Nat := .node node21206 node21211 +def node21213 : Tree Nat := .node node21203 node21212 +def node21214 : Tree Nat := .node node383 node20860 +def node21215 : Tree Nat := .node node3811 node20862 +def node21216 : Tree Nat := .node node21214 node21215 +def node21217 : Tree Nat := .node node3816 node20865 +def node21218 : Tree Nat := .node node429 node20867 +def node21219 : Tree Nat := .node node21217 node21218 +def node21220 : Tree Nat := .node node21216 node21219 +def node21221 : Tree Nat := .node node442 node3824 +def node21222 : Tree Nat := .node node441 node21221 +def node21223 : Tree Nat := .node node21222 node20871 +def node21224 : Tree Nat := .node node460 node20873 +def node21225 : Tree Nat := .node node21223 node21224 +def node21226 : Tree Nat := .node node475 node20876 +def node21227 : Tree Nat := .node node20878 node3831 +def node21228 : Tree Nat := .node node21226 node21227 +def node21229 : Tree Nat := .node node21225 node21228 +def node21230 : Tree Nat := .node node21220 node21229 +def node21231 : Tree Nat := .node node21213 node21230 +def node21232 : Tree Nat := .node node21194 node21231 +def node21233 : Tree Nat := .node node3840 node20885 +def node21234 : Tree Nat := .node node3844 node20887 +def node21235 : Tree Nat := .node node21233 node21234 +def node21236 : Tree Nat := .node node3849 node20890 +def node21237 : Tree Nat := .node node3853 node20892 +def node21238 : Tree Nat := .node node21236 node21237 +def node21239 : Tree Nat := .node node21235 node21238 +def node21240 : Tree Nat := .node node568 node3857 +def node21241 : Tree Nat := .node node567 node21240 +def node21242 : Tree Nat := .node node21241 node20896 +def node21243 : Tree Nat := .node node586 node20898 +def node21244 : Tree Nat := .node node21242 node21243 +def node21245 : Tree Nat := .node node602 node20901 +def node21246 : Tree Nat := .node node3864 node623 +def node21247 : Tree Nat := .node node21245 node21246 +def node21248 : Tree Nat := .node node21244 node21247 +def node21249 : Tree Nat := .node node21239 node21248 +def node21250 : Tree Nat := .node node634 node20906 +def node21251 : Tree Nat := .node node649 node20908 +def node21252 : Tree Nat := .node node21250 node21251 +def node21253 : Tree Nat := .node node3871 node20911 +def node21254 : Tree Nat := .node node680 node20913 +def node21255 : Tree Nat := .node node21253 node21254 +def node21256 : Tree Nat := .node node21252 node21255 +def node21257 : Tree Nat := .node node3877 node20917 +def node21258 : Tree Nat := .node node3881 node20919 +def node21259 : Tree Nat := .node node21257 node21258 +def node21260 : Tree Nat := .node node3886 node20922 +def node21261 : Tree Nat := .node node743 node3888 +def node21262 : Tree Nat := .node node21261 node747 +def node21263 : Tree Nat := .node node20924 node21262 +def node21264 : Tree Nat := .node node21260 node21263 +def node21265 : Tree Nat := .node node21259 node21264 +def node21266 : Tree Nat := .node node21256 node21265 +def node21267 : Tree Nat := .node node21249 node21266 +def node21268 : Tree Nat := .node node760 node20930 +def node21269 : Tree Nat := .node node775 node20932 +def node21270 : Tree Nat := .node node21268 node21269 +def node21271 : Tree Nat := .node node3898 node20935 +def node21272 : Tree Nat := .node node806 node20937 +def node21273 : Tree Nat := .node node21271 node21272 +def node21274 : Tree Nat := .node node21270 node21273 +def node21275 : Tree Nat := .node node3904 node20941 +def node21276 : Tree Nat := .node node3908 node20943 +def node21277 : Tree Nat := .node node21275 node21276 +def node21278 : Tree Nat := .node node853 node20946 +def node21279 : Tree Nat := .node node21278 node875 +def node21280 : Tree Nat := .node node21277 node21279 +def node21281 : Tree Nat := .node node21274 node21280 +def node21282 : Tree Nat := .node node3915 node20951 +def node21283 : Tree Nat := .node node3919 node20953 +def node21284 : Tree Nat := .node node21282 node21283 +def node21285 : Tree Nat := .node node916 node20956 +def node21286 : Tree Nat := .node node931 node20958 +def node21287 : Tree Nat := .node node21285 node21286 +def node21288 : Tree Nat := .node node21284 node21287 +def node21289 : Tree Nat := .node node944 node3928 +def node21290 : Tree Nat := .node node943 node21289 +def node21291 : Tree Nat := .node node21290 node20962 +def node21292 : Tree Nat := .node node962 node20964 +def node21293 : Tree Nat := .node node21291 node21292 +def node21294 : Tree Nat := .node node977 node20967 +def node21295 : Tree Nat := .node node993 node3933 +def node21296 : Tree Nat := .node node21295 node997 +def node21297 : Tree Nat := .node node20969 node21296 +def node21298 : Tree Nat := .node node21294 node21297 +def node21299 : Tree Nat := .node node21293 node21298 +def node21300 : Tree Nat := .node node21288 node21299 +def node21301 : Tree Nat := .node node21281 node21300 +def node21302 : Tree Nat := .node node21267 node21301 +def node21303 : Tree Nat := .node node21232 node21302 +def node21304 : Tree Nat := .node node1012 node20977 +def node21305 : Tree Nat := .node node1027 node20979 +def node21306 : Tree Nat := .node node21304 node21305 +def node21307 : Tree Nat := .node node1043 node20982 +def node21308 : Tree Nat := .node node1058 node20984 +def node21309 : Tree Nat := .node node21307 node21308 +def node21310 : Tree Nat := .node node21306 node21309 +def node21311 : Tree Nat := .node node1074 node20988 +def node21312 : Tree Nat := .node node3945 node20990 +def node21313 : Tree Nat := .node node21311 node21312 +def node21314 : Tree Nat := .node node1105 node20993 +def node21315 : Tree Nat := .node node21314 node1127 +def node21316 : Tree Nat := .node node21313 node21315 +def node21317 : Tree Nat := .node node21310 node21316 +def node21318 : Tree Nat := .node node1137 node20998 +def node21319 : Tree Nat := .node node1152 node21000 +def node21320 : Tree Nat := .node node21318 node21319 +def node21321 : Tree Nat := .node node1168 node21003 +def node21322 : Tree Nat := .node node1183 node21005 +def node21323 : Tree Nat := .node node21321 node21322 +def node21324 : Tree Nat := .node node21320 node21323 +def node21325 : Tree Nat := .node node3952 node21009 +def node21326 : Tree Nat := .node node1214 node21011 +def node21327 : Tree Nat := .node node21325 node21326 +def node21328 : Tree Nat := .node node1230 node21014 +def node21329 : Tree Nat := .node node21016 node1251 +def node21330 : Tree Nat := .node node21328 node21329 +def node21331 : Tree Nat := .node node21327 node21330 +def node21332 : Tree Nat := .node node21324 node21331 +def node21333 : Tree Nat := .node node21317 node21332 +def node21334 : Tree Nat := .node node1263 node21022 +def node21335 : Tree Nat := .node node1278 node21024 +def node21336 : Tree Nat := .node node21334 node21335 +def node21337 : Tree Nat := .node node1294 node21027 +def node21338 : Tree Nat := .node node1309 node21029 +def node21339 : Tree Nat := .node node21337 node21338 +def node21340 : Tree Nat := .node node21336 node21339 +def node21341 : Tree Nat := .node node1325 node21033 +def node21342 : Tree Nat := .node node1340 node21035 +def node21343 : Tree Nat := .node node21341 node21342 +def node21344 : Tree Nat := .node node3960 node21038 +def node21345 : Tree Nat := .node node21344 node1378 +def node21346 : Tree Nat := .node node21343 node21345 +def node21347 : Tree Nat := .node node21340 node21346 +def node21348 : Tree Nat := .node node1388 node21043 +def node21349 : Tree Nat := .node node1403 node21045 +def node21350 : Tree Nat := .node node21348 node21349 +def node21351 : Tree Nat := .node node1419 node21048 +def node21352 : Tree Nat := .node node1434 node21050 +def node21353 : Tree Nat := .node node21351 node21352 +def node21354 : Tree Nat := .node node21350 node21353 +def node21355 : Tree Nat := .node node1450 node21054 +def node21356 : Tree Nat := .node node1465 node21056 +def node21357 : Tree Nat := .node node21355 node21356 +def node21358 : Tree Nat := .node node1480 node21059 +def node21359 : Tree Nat := .node node21061 node3973 +def node21360 : Tree Nat := .node node21358 node21359 +def node21361 : Tree Nat := .node node21357 node21360 +def node21362 : Tree Nat := .node node21354 node21361 +def node21363 : Tree Nat := .node node21347 node21362 +def node21364 : Tree Nat := .node node21333 node21363 +def node21365 : Tree Nat := .node node1514 node21068 +def node21366 : Tree Nat := .node node3982 node21070 +def node21367 : Tree Nat := .node node21365 node21366 +def node21368 : Tree Nat := .node node1545 node21073 +def node21369 : Tree Nat := .node node1560 node21075 +def node21370 : Tree Nat := .node node21368 node21369 +def node21371 : Tree Nat := .node node21367 node21370 +def node21372 : Tree Nat := .node node1576 node21079 +def node21373 : Tree Nat := .node node1591 node21081 +def node21374 : Tree Nat := .node node21372 node21373 +def node21375 : Tree Nat := .node node1607 node21084 +def node21376 : Tree Nat := .node node21375 node1629 +def node21377 : Tree Nat := .node node21374 node21376 +def node21378 : Tree Nat := .node node21371 node21377 +def node21379 : Tree Nat := .node node1636 node3987 +def node21380 : Tree Nat := .node node1635 node21379 +def node21381 : Tree Nat := .node node21380 node21089 +def node21382 : Tree Nat := .node node1654 node21091 +def node21383 : Tree Nat := .node node21381 node21382 +def node21384 : Tree Nat := .node node1670 node21094 +def node21385 : Tree Nat := .node node1685 node21096 +def node21386 : Tree Nat := .node node21384 node21385 +def node21387 : Tree Nat := .node node21383 node21386 +def node21388 : Tree Nat := .node node1701 node21100 +def node21389 : Tree Nat := .node node1716 node21102 +def node21390 : Tree Nat := .node node21388 node21389 +def node21391 : Tree Nat := .node node1731 node21105 +def node21392 : Tree Nat := .node node21107 node3995 +def node21393 : Tree Nat := .node node21391 node21392 +def node21394 : Tree Nat := .node node21390 node21393 +def node21395 : Tree Nat := .node node21387 node21394 +def node21396 : Tree Nat := .node node21378 node21395 +def node21397 : Tree Nat := .node node1764 node21113 +def node21398 : Tree Nat := .node node1779 node21115 +def node21399 : Tree Nat := .node node21397 node21398 +def node21400 : Tree Nat := .node node4003 node21118 +def node21401 : Tree Nat := .node node1810 node21120 +def node21402 : Tree Nat := .node node21400 node21401 +def node21403 : Tree Nat := .node node21399 node21402 +def node21404 : Tree Nat := .node node1826 node21124 +def node21405 : Tree Nat := .node node1841 node21126 +def node21406 : Tree Nat := .node node21404 node21405 +def node21407 : Tree Nat := .node node1857 node21129 +def node21408 : Tree Nat := .node node21407 node1879 +def node21409 : Tree Nat := .node node21406 node21408 +def node21410 : Tree Nat := .node node21403 node21409 +def node21411 : Tree Nat := .node node1889 node21134 +def node21412 : Tree Nat := .node node1904 node21136 +def node21413 : Tree Nat := .node node21411 node21412 +def node21414 : Tree Nat := .node node1920 node21139 +def node21415 : Tree Nat := .node node1935 node21141 +def node21416 : Tree Nat := .node node21414 node21415 +def node21417 : Tree Nat := .node node21413 node21416 +def node21418 : Tree Nat := .node node1951 node21145 +def node21419 : Tree Nat := .node node1966 node21147 +def node21420 : Tree Nat := .node node21418 node21419 +def node21421 : Tree Nat := .node node1981 node21150 +def node21422 : Tree Nat := .node node21152 node2002 +def node21423 : Tree Nat := .node node21421 node21422 +def node21424 : Tree Nat := .node node21420 node21423 +def node21425 : Tree Nat := .node node21417 node21424 +def node21426 : Tree Nat := .node node21410 node21425 +def node21427 : Tree Nat := .node node21396 node21426 +def node21428 : Tree Nat := .node node21364 node21427 +def node21429 : Tree Nat := .node node21303 node21428 +def node21430 : Tree Nat := .node node20487 node12 +def node21431 : Tree Nat := .node node6 node21430 +def node21432 : Tree Nat := .node node21431 node21164 +def node21433 : Tree Nat := .node node20062 node43 +def node21434 : Tree Nat := .node node37 node21433 +def node21435 : Tree Nat := .node node17458 node54 +def node21436 : Tree Nat := .node node21435 node58 +def node21437 : Tree Nat := .node node52 node21436 +def node21438 : Tree Nat := .node node21434 node21437 +def node21439 : Tree Nat := .node node21432 node21438 +def node21440 : Tree Nat := .node node20497 node75 +def node21441 : Tree Nat := .node node69 node21440 +def node21442 : Tree Nat := .node node21441 node21171 +def node21443 : Tree Nat := .node node20076 node106 +def node21444 : Tree Nat := .node node100 node21443 +def node21445 : Tree Nat := .node node21444 node122 +def node21446 : Tree Nat := .node node21442 node21445 +def node21447 : Tree Nat := .node node21439 node21446 +def node21448 : Tree Nat := .node node132 node20815 +def node21449 : Tree Nat := .node node21448 node21178 +def node21450 : Tree Nat := .node node20087 node169 +def node21451 : Tree Nat := .node node163 node21450 +def node21452 : Tree Nat := .node node17476 node180 +def node21453 : Tree Nat := .node node21452 node183 +def node21454 : Tree Nat := .node node178 node21453 +def node21455 : Tree Nat := .node node21451 node21454 +def node21456 : Tree Nat := .node node21449 node21455 +def node21457 : Tree Nat := .node node194 node20826 +def node21458 : Tree Nat := .node node21457 node21185 +def node21459 : Tree Nat := .node node225 node20831 +def node21460 : Tree Nat := .node node20833 node246 +def node21461 : Tree Nat := .node node21459 node21460 +def node21462 : Tree Nat := .node node21458 node21461 +def node21463 : Tree Nat := .node node21456 node21462 +def node21464 : Tree Nat := .node node21447 node21463 +def node21465 : Tree Nat := .node node20526 node264 +def node21466 : Tree Nat := .node node258 node21465 +def node21467 : Tree Nat := .node node21466 node21198 +def node21468 : Tree Nat := .node node20116 node295 +def node21469 : Tree Nat := .node node289 node21468 +def node21470 : Tree Nat := .node node17490 node306 +def node21471 : Tree Nat := .node node21470 node309 +def node21472 : Tree Nat := .node node304 node21471 +def node21473 : Tree Nat := .node node21469 node21472 +def node21474 : Tree Nat := .node node21467 node21473 +def node21475 : Tree Nat := .node node20535 node326 +def node21476 : Tree Nat := .node node320 node21475 +def node21477 : Tree Nat := .node node21476 node21205 +def node21478 : Tree Nat := .node node351 node20855 +def node21479 : Tree Nat := .node node21478 node373 +def node21480 : Tree Nat := .node node21477 node21479 +def node21481 : Tree Nat := .node node21474 node21480 +def node21482 : Tree Nat := .node node398 node20862 +def node21483 : Tree Nat := .node node21214 node21482 +def node21484 : Tree Nat := .node node414 node20865 +def node21485 : Tree Nat := .node node17508 node431 +def node21486 : Tree Nat := .node node21485 node434 +def node21487 : Tree Nat := .node node429 node21486 +def node21488 : Tree Nat := .node node21484 node21487 +def node21489 : Tree Nat := .node node21483 node21488 +def node21490 : Tree Nat := .node node20149 node451 +def node21491 : Tree Nat := .node node445 node21490 +def node21492 : Tree Nat := .node node21491 node21224 +def node21493 : Tree Nat := .node node20156 node481 +def node21494 : Tree Nat := .node node475 node21493 +def node21495 : Tree Nat := .node node20878 node496 +def node21496 : Tree Nat := .node node21494 node21495 +def node21497 : Tree Nat := .node node21492 node21496 +def node21498 : Tree Nat := .node node21489 node21497 +def node21499 : Tree Nat := .node node21481 node21498 +def node21500 : Tree Nat := .node node21464 node21499 +def node21501 : Tree Nat := .node node20564 node515 +def node21502 : Tree Nat := .node node509 node21501 +def node21503 : Tree Nat := .node node524 node20887 +def node21504 : Tree Nat := .node node21502 node21503 +def node21505 : Tree Nat := .node node20171 node546 +def node21506 : Tree Nat := .node node540 node21505 +def node21507 : Tree Nat := .node node555 node20892 +def node21508 : Tree Nat := .node node21506 node21507 +def node21509 : Tree Nat := .node node21504 node21508 +def node21510 : Tree Nat := .node node571 node20896 +def node21511 : Tree Nat := .node node21510 node21243 +def node21512 : Tree Nat := .node node21245 node624 +def node21513 : Tree Nat := .node node21511 node21512 +def node21514 : Tree Nat := .node node21509 node21513 +def node21515 : Tree Nat := .node node665 node20911 +def node21516 : Tree Nat := .node node17541 node682 +def node21517 : Tree Nat := .node node21516 node685 +def node21518 : Tree Nat := .node node680 node21517 +def node21519 : Tree Nat := .node node21515 node21518 +def node21520 : Tree Nat := .node node21252 node21519 +def node21521 : Tree Nat := .node node696 node20917 +def node21522 : Tree Nat := .node node711 node20919 +def node21523 : Tree Nat := .node node21521 node21522 +def node21524 : Tree Nat := .node node727 node20922 +def node21525 : Tree Nat := .node node20924 node748 +def node21526 : Tree Nat := .node node21524 node21525 +def node21527 : Tree Nat := .node node21523 node21526 +def node21528 : Tree Nat := .node node21520 node21527 +def node21529 : Tree Nat := .node node21514 node21528 +def node21530 : Tree Nat := .node node20601 node766 +def node21531 : Tree Nat := .node node760 node21530 +def node21532 : Tree Nat := .node node21531 node21269 +def node21533 : Tree Nat := .node node791 node20935 +def node21534 : Tree Nat := .node node17555 node808 +def node21535 : Tree Nat := .node node21534 node811 +def node21536 : Tree Nat := .node node806 node21535 +def node21537 : Tree Nat := .node node21533 node21536 +def node21538 : Tree Nat := .node node21532 node21537 +def node21539 : Tree Nat := .node node822 node20941 +def node21540 : Tree Nat := .node node837 node20943 +def node21541 : Tree Nat := .node node21539 node21540 +def node21542 : Tree Nat := .node node21541 node21279 +def node21543 : Tree Nat := .node node21538 node21542 +def node21544 : Tree Nat := .node node885 node20951 +def node21545 : Tree Nat := .node node900 node20953 +def node21546 : Tree Nat := .node node21544 node21545 +def node21547 : Tree Nat := .node node20248 node922 +def node21548 : Tree Nat := .node node916 node21547 +def node21549 : Tree Nat := .node node17573 node933 +def node21550 : Tree Nat := .node node21549 node936 +def node21551 : Tree Nat := .node node931 node21550 +def node21552 : Tree Nat := .node node21548 node21551 +def node21553 : Tree Nat := .node node21546 node21552 +def node21554 : Tree Nat := .node node947 node20962 +def node21555 : Tree Nat := .node node21554 node21292 +def node21556 : Tree Nat := .node node20969 node998 +def node21557 : Tree Nat := .node node21294 node21556 +def node21558 : Tree Nat := .node node21555 node21557 +def node21559 : Tree Nat := .node node21553 node21558 +def node21560 : Tree Nat := .node node21543 node21559 +def node21561 : Tree Nat := .node node21529 node21560 +def node21562 : Tree Nat := .node node21500 node21561 +def node21563 : Tree Nat := .node node17589 node1060 +def node21564 : Tree Nat := .node node21563 node1063 +def node21565 : Tree Nat := .node node1058 node21564 +def node21566 : Tree Nat := .node node21307 node21565 +def node21567 : Tree Nat := .node node21306 node21566 +def node21568 : Tree Nat := .node node1089 node20990 +def node21569 : Tree Nat := .node node21311 node21568 +def node21570 : Tree Nat := .node node20291 node1111 +def node21571 : Tree Nat := .node node1105 node21570 +def node21572 : Tree Nat := .node node21571 node1127 +def node21573 : Tree Nat := .node node21569 node21572 +def node21574 : Tree Nat := .node node21567 node21573 +def node21575 : Tree Nat := .node node20303 node1174 +def node21576 : Tree Nat := .node node1168 node21575 +def node21577 : Tree Nat := .node node21576 node21322 +def node21578 : Tree Nat := .node node21320 node21577 +def node21579 : Tree Nat := .node node1199 node21009 +def node21580 : Tree Nat := .node node21579 node21326 +def node21581 : Tree Nat := .node node21580 node21330 +def node21582 : Tree Nat := .node node21578 node21581 +def node21583 : Tree Nat := .node node21574 node21582 +def node21584 : Tree Nat := .node node20331 node1300 +def node21585 : Tree Nat := .node node1294 node21584 +def node21586 : Tree Nat := .node node21585 node21338 +def node21587 : Tree Nat := .node node21336 node21586 +def node21588 : Tree Nat := .node node1356 node21038 +def node21589 : Tree Nat := .node node21588 node1378 +def node21590 : Tree Nat := .node node21343 node21589 +def node21591 : Tree Nat := .node node21587 node21590 +def node21592 : Tree Nat := .node node20355 node1425 +def node21593 : Tree Nat := .node node1419 node21592 +def node21594 : Tree Nat := .node node17639 node1436 +def node21595 : Tree Nat := .node node21594 node1439 +def node21596 : Tree Nat := .node node1434 node21595 +def node21597 : Tree Nat := .node node21593 node21596 +def node21598 : Tree Nat := .node node21350 node21597 +def node21599 : Tree Nat := .node node21061 node1501 +def node21600 : Tree Nat := .node node21358 node21599 +def node21601 : Tree Nat := .node node21357 node21600 +def node21602 : Tree Nat := .node node21598 node21601 +def node21603 : Tree Nat := .node node21591 node21602 +def node21604 : Tree Nat := .node node21583 node21603 +def node21605 : Tree Nat := .node node1529 node21070 +def node21606 : Tree Nat := .node node21365 node21605 +def node21607 : Tree Nat := .node node21606 node21370 +def node21608 : Tree Nat := .node node21607 node21377 +def node21609 : Tree Nat := .node node1639 node21089 +def node21610 : Tree Nat := .node node21609 node21382 +def node21611 : Tree Nat := .node node21610 node21386 +def node21612 : Tree Nat := .node node21107 node1752 +def node21613 : Tree Nat := .node node21391 node21612 +def node21614 : Tree Nat := .node node21390 node21613 +def node21615 : Tree Nat := .node node21611 node21614 +def node21616 : Tree Nat := .node node21608 node21615 +def node21617 : Tree Nat := .node node1795 node21118 +def node21618 : Tree Nat := .node node21617 node21401 +def node21619 : Tree Nat := .node node21399 node21618 +def node21620 : Tree Nat := .node node20449 node1863 +def node21621 : Tree Nat := .node node1857 node21620 +def node21622 : Tree Nat := .node node21621 node1879 +def node21623 : Tree Nat := .node node21406 node21622 +def node21624 : Tree Nat := .node node21619 node21623 +def node21625 : Tree Nat := .node node20461 node1926 +def node21626 : Tree Nat := .node node1920 node21625 +def node21627 : Tree Nat := .node node21626 node21415 +def node21628 : Tree Nat := .node node21413 node21627 +def node21629 : Tree Nat := .node node20476 node1987 +def node21630 : Tree Nat := .node node1981 node21629 +def node21631 : Tree Nat := .node node21630 node21422 +def node21632 : Tree Nat := .node node21420 node21631 +def node21633 : Tree Nat := .node node21628 node21632 +def node21634 : Tree Nat := .node node21624 node21633 +def node21635 : Tree Nat := .node node21616 node21634 +def node21636 : Tree Nat := .node node21604 node21635 +def node21637 : Tree Nat := .node node21562 node21636 +def node21638 : Tree Nat := .node node20058 node27 +def node21639 : Tree Nat := .node node21 node21638 +def node21640 : Tree Nat := .node node21431 node21639 +def node21641 : Tree Nat := .node node21640 node21438 +def node21642 : Tree Nat := .node node21641 node21446 +def node21643 : Tree Nat := .node node21642 node21463 +def node21644 : Tree Nat := .node node21643 node21499 +def node21645 : Tree Nat := .node node21644 node21561 +def node21646 : Tree Nat := .node node20287 node1095 +def node21647 : Tree Nat := .node node1089 node21646 +def node21648 : Tree Nat := .node node21311 node21647 +def node21649 : Tree Nat := .node node21648 node21572 +def node21650 : Tree Nat := .node node21567 node21649 +def node21651 : Tree Nat := .node node21650 node21582 +def node21652 : Tree Nat := .node node21651 node21603 +def node21653 : Tree Nat := .node node21652 node21635 +def node21654 : Tree Nat := .node node21645 node21653 +def state0 : Tree Nat × Bool := (node2010, true) +def state1 : Tree Nat × Bool := (node2065, true) +def state2 : Tree Nat × Bool := (node2112, true) +def state3 : Tree Nat × Bool := (node2151, true) +def state4 : Tree Nat × Bool := (node2190, true) +def state5 : Tree Nat × Bool := (node2229, true) +def state6 : Tree Nat × Bool := (node2268, true) +def state7 : Tree Nat × Bool := (node2307, true) +def state8 : Tree Nat × Bool := (node2346, true) +def state9 : Tree Nat × Bool := (node2385, true) +def state10 : Tree Nat × Bool := (node2424, true) +def state11 : Tree Nat × Bool := (node2471, true) +def state12 : Tree Nat × Bool := (node2510, true) +def state13 : Tree Nat × Bool := (node2549, true) +def state14 : Tree Nat × Bool := (node2588, true) +def state15 : Tree Nat × Bool := (node2627, true) +def state16 : Tree Nat × Bool := (node2657, true) +def state17 : Tree Nat × Bool := (node2696, true) +def state18 : Tree Nat × Bool := (node2735, true) +def state19 : Tree Nat × Bool := (node2774, true) +def state20 : Tree Nat × Bool := (node2821, true) +def state21 : Tree Nat × Bool := (node2868, true) +def state22 : Tree Nat × Bool := (node2923, true) +def state23 : Tree Nat × Bool := (node2953, true) +def state24 : Tree Nat × Bool := (node2992, true) +def state25 : Tree Nat × Bool := (node3031, true) +def state26 : Tree Nat × Bool := (node3070, true) +def state27 : Tree Nat × Bool := (node3100, true) +def state28 : Tree Nat × Bool := (node3139, true) +def state29 : Tree Nat × Bool := (node3178, true) +def state30 : Tree Nat × Bool := (node3208, true) +def state31 : Tree Nat × Bool := (node3247, true) +def state32 : Tree Nat × Bool := (node3286, true) +def state33 : Tree Nat × Bool := (node3316, true) +def state34 : Tree Nat × Bool := (node3355, true) +def state35 : Tree Nat × Bool := (node3394, true) +def state36 : Tree Nat × Bool := (node3424, true) +def state37 : Tree Nat × Bool := (node3463, true) +def state38 : Tree Nat × Bool := (node3502, true) +def state39 : Tree Nat × Bool := (node3532, true) +def state40 : Tree Nat × Bool := (node3731, true) +def state41 : Tree Nat × Bool := (node4011, true) +def state42 : Tree Nat × Bool := (node4536, true) +def state43 : Tree Nat × Bool := (node5063, true) +def state44 : Tree Nat × Bool := (node5574, true) +def state45 : Tree Nat × Bool := (node5963, true) +def state46 : Tree Nat × Bool := (node6353, true) +def state47 : Tree Nat × Bool := (node6730, true) +def state48 : Tree Nat × Bool := (node7109, true) +def state49 : Tree Nat × Bool := (node7498, true) +def state50 : Tree Nat × Bool := (node7922, true) +def state51 : Tree Nat × Bool := (node8346, true) +def state52 : Tree Nat × Bool := (node8781, true) +def state53 : Tree Nat × Bool := (node9207, true) +def state54 : Tree Nat × Bool := (node9478, true) +def state55 : Tree Nat × Bool := (node9757, true) +def state56 : Tree Nat × Bool := (node10043, true) +def state57 : Tree Nat × Bool := (node10348, true) +def state58 : Tree Nat × Bool := (node10671, true) +def state59 : Tree Nat × Bool := (node11066, true) +def state60 : Tree Nat × Bool := (node11436, true) +def state61 : Tree Nat × Bool := (node11774, true) +def state62 : Tree Nat × Bool := (node12116, true) +def state63 : Tree Nat × Bool := (node12463, true) +def state64 : Tree Nat × Bool := (node12809, true) +def state65 : Tree Nat × Bool := (node12947, true) +def state66 : Tree Nat × Bool := (node13014, true) +def state67 : Tree Nat × Bool := (node13081, true) +def state68 : Tree Nat × Bool := (node13380, true) +def state69 : Tree Nat × Bool := (node13936, true) +def state70 : Tree Nat × Bool := (node14470, true) +def state71 : Tree Nat × Bool := (node14982, true) +def state72 : Tree Nat × Bool := (node15046, true) +def state73 : Tree Nat × Bool := (node15104, true) +def state74 : Tree Nat × Bool := (node15405, true) +def state75 : Tree Nat × Bool := (node15881, true) +def state76 : Tree Nat × Bool := (node16356, true) +def state77 : Tree Nat × Bool := (node16916, true) +def state78 : Tree Nat × Bool := (node17189, true) +def state79 : Tree Nat × Bool := (node17457, true) +def state80 : Tree Nat × Bool := (node17728, true) +def state81 : Tree Nat × Bool := (node17919, true) +def state82 : Tree Nat × Bool := (node18126, true) +def state83 : Tree Nat × Bool := (node18325, true) +def state84 : Tree Nat × Bool := (node18544, true) +def state85 : Tree Nat × Bool := (node18793, true) +def state86 : Tree Nat × Bool := (node19002, true) +def state87 : Tree Nat × Bool := (node19189, true) +def state88 : Tree Nat × Bool := (node19429, true) +def state89 : Tree Nat × Bool := (node19752, true) +def state90 : Tree Nat × Bool := (node20055, true) +def state91 : Tree Nat × Bool := (node20486, true) +def state92 : Tree Nat × Bool := (node20793, true) +def state93 : Tree Nat × Bool := (node21160, true) +def state94 : Tree Nat × Bool := (node21429, true) +def state95 : Tree Nat × Bool := (node21637, true) +def state96 : Tree Nat × Bool := (node21654, true) +def initial : Tree Nat := node2010 +def expected : Tree Nat := node21654 +def chunk0 : List Event := [⟨1,120,251,true⟩, +⟨1,120,255,true⟩, +⟨1,120,261,true⟩, +⟨1,120,266,true⟩, +⟨1,120,273,true⟩, +⟨1,120,278,true⟩, +⟨1,120,285,true⟩, +⟨1,120,624,true⟩, +⟨1,120,626,true⟩, +⟨1,120,628,true⟩, +⟨1,120,630,true⟩, +⟨1,120,640,true⟩, +⟨1,120,642,true⟩, +⟨1,120,644,true⟩, +⟨1,120,646,true⟩, +⟨1,120,656,true⟩, +⟨1,120,658,true⟩, +⟨1,120,660,true⟩, +⟨1,120,662,true⟩, +⟨1,120,672,true⟩, +⟨1,120,674,true⟩, +⟨1,120,676,true⟩, +⟨1,120,678,true⟩, +⟨1,120,688,true⟩, +⟨1,120,690,true⟩, +⟨1,120,692,true⟩, +⟨1,120,694,true⟩, +⟨1,120,704,true⟩, +⟨1,120,706,true⟩, +⟨1,120,708,true⟩, +⟨1,120,710,true⟩, +⟨1,120,720,true⟩, +⟨1,120,722,true⟩, +⟨1,120,724,true⟩, +⟨1,120,726,true⟩, +⟨1,121,245,true⟩, +⟨1,121,253,true⟩, +⟨1,121,259,true⟩, +⟨1,121,264,true⟩, +⟨1,121,271,true⟩, +⟨1,121,277,true⟩, +⟨1,121,282,true⟩, +⟨1,121,560,true⟩, +⟨1,121,562,true⟩, +⟨1,121,564,true⟩, +⟨1,121,566,true⟩, +⟨1,121,576,true⟩, +⟨1,121,578,true⟩, +⟨1,121,580,true⟩, +⟨1,121,582,true⟩, +⟨1,121,592,true⟩, +⟨1,121,594,true⟩, +⟨1,121,596,true⟩, +⟨1,121,598,true⟩, +⟨1,121,608,true⟩, +⟨1,121,610,true⟩, +⟨1,121,612,true⟩, +⟨1,121,614,true⟩, +⟨1,121,688,true⟩, +⟨1,121,690,true⟩, +⟨1,121,692,true⟩, +⟨1,121,694,true⟩, +⟨1,121,704,true⟩, +⟨1,121,706,true⟩, +⟨1,121,708,true⟩, +⟨1,121,710,true⟩, +⟨1,121,711,true⟩, +⟨1,121,720,true⟩, +⟨1,121,722,true⟩, +⟨1,121,724,true⟩, +⟨1,121,726,true⟩, +⟨1,121,907,true⟩, +⟨1,122,240,true⟩, +⟨1,122,246,true⟩, +⟨1,122,528,true⟩, +⟨1,122,530,true⟩, +⟨1,122,532,true⟩, +⟨1,122,534,true⟩, +⟨1,122,544,true⟩, +⟨1,122,546,true⟩, +⟨1,122,548,true⟩, +⟨1,122,550,true⟩, +⟨1,122,592,true⟩, +⟨1,122,594,true⟩, +⟨1,122,596,true⟩, +⟨1,122,598,true⟩, +⟨1,122,599,true⟩, +⟨1,122,608,true⟩, +⟨1,122,610,true⟩, +⟨1,122,612,true⟩, +⟨1,122,614,true⟩, +⟨1,122,656,true⟩, +⟨1,122,658,true⟩, +⟨1,122,660,true⟩, +⟨1,122,662,true⟩, +⟨1,122,663,true⟩, +⟨1,122,672,true⟩, +⟨1,122,674,true⟩, +⟨1,122,676,true⟩, +⟨1,122,678,true⟩, +⟨1,122,720,true⟩, +⟨1,122,722,true⟩, +⟨1,122,724,true⟩, +⟨1,122,726,true⟩, +⟨1,122,727,true⟩, +⟨1,123,240,true⟩, +⟨1,123,246,true⟩, +⟨1,123,528,true⟩, +⟨1,123,530,true⟩, +⟨1,123,532,true⟩, +⟨1,123,534,true⟩, +⟨1,123,544,true⟩, +⟨1,123,546,true⟩, +⟨1,123,548,true⟩, +⟨1,123,550,true⟩, +⟨1,123,560,true⟩, +⟨1,123,562,true⟩, +⟨1,123,564,true⟩, +⟨1,123,566,true⟩, +⟨1,123,567,true⟩, +⟨1,123,576,true⟩, +⟨1,123,578,true⟩, +⟨1,123,580,true⟩, +⟨1,123,582,true⟩, +⟨1,123,583,true⟩, +⟨1,123,624,true⟩, +⟨1,123,626,true⟩, +⟨1,123,628,true⟩, +⟨1,123,630,true⟩, +⟨1,123,631,true⟩, +⟨1,123,640,true⟩, +⟨1,123,642,true⟩, +⟨1,123,644,true⟩, +⟨1,123,646,true⟩, +⟨1,123,647,true⟩, +⟨1,123,720,true⟩, +⟨1,123,722,true⟩, +⟨1,123,724,true⟩, +⟨1,123,726,true⟩, +⟨1,123,727,true⟩, +⟨1,124,245,true⟩, +⟨1,124,253,true⟩, +⟨1,124,259,true⟩, +⟨1,124,271,true⟩, +⟨1,124,277,true⟩, +⟨1,124,282,true⟩, +⟨1,124,512,true⟩, +⟨1,124,514,true⟩, +⟨1,124,516,true⟩, +⟨1,124,518,true⟩, +⟨1,124,544,true⟩, +⟨1,124,546,true⟩, +⟨1,124,548,true⟩, +⟨1,124,550,true⟩, +⟨1,124,551,true⟩, +⟨1,124,576,true⟩, +⟨1,124,578,true⟩, +⟨1,124,580,true⟩, +⟨1,124,582,true⟩, +⟨1,124,608,true⟩, +⟨1,124,610,true⟩, +⟨1,124,612,true⟩, +⟨1,124,614,true⟩, +⟨1,124,640,true⟩, +⟨1,124,642,true⟩, +⟨1,124,644,true⟩, +⟨1,124,646,true⟩, +⟨1,124,672,true⟩, +⟨1,124,674,true⟩, +⟨1,124,676,true⟩, +⟨1,124,678,true⟩, +⟨1,124,679,true⟩, +⟨1,124,704,true⟩, +⟨1,124,706,true⟩, +⟨1,124,708,true⟩, +⟨1,124,710,true⟩, +⟨1,124,711,true⟩, +⟨1,125,252,true⟩, +⟨1,125,258,true⟩, +⟨1,125,264,true⟩, +⟨1,125,280,true⟩, +⟨1,125,286,true⟩, +⟨1,125,416,true⟩, +⟨1,125,418,true⟩, +⟨1,125,420,true⟩, +⟨1,125,422,true⟩, +⟨1,125,424,true⟩, +⟨1,125,426,true⟩, +⟨1,125,428,true⟩, +⟨1,125,430,true⟩, +⟨1,125,512,true⟩, +⟨1,125,514,true⟩, +⟨1,125,516,true⟩, +⟨1,125,518,true⟩, +⟨1,125,523,true⟩, +⟨1,125,544,true⟩, +⟨1,125,546,true⟩, +⟨1,125,548,true⟩, +⟨1,125,550,true⟩, +⟨1,125,551,true⟩] +def chunk1 : List Event := [⟨1,125,560,true⟩, +⟨1,125,562,true⟩, +⟨1,125,564,true⟩, +⟨1,125,566,true⟩, +⟨1,125,624,true⟩, +⟨1,125,626,true⟩, +⟨1,125,628,true⟩, +⟨1,125,630,true⟩, +⟨1,125,656,true⟩, +⟨1,125,658,true⟩, +⟨1,125,660,true⟩, +⟨1,125,662,true⟩, +⟨1,125,704,true⟩, +⟨1,125,706,true⟩, +⟨1,125,708,true⟩, +⟨1,125,710,true⟩, +⟨1,125,715,true⟩, +⟨1,125,810,true⟩, +⟨1,126,243,true⟩, +⟨1,126,246,true⟩, +⟨1,126,253,true⟩, +⟨1,126,262,true⟩, +⟨1,126,265,true⟩, +⟨1,126,270,true⟩, +⟨1,126,282,true⟩, +⟨1,126,512,true⟩, +⟨1,126,514,true⟩, +⟨1,126,516,true⟩, +⟨1,126,518,true⟩, +⟨1,126,519,true⟩, +⟨1,126,528,true⟩, +⟨1,126,530,true⟩, +⟨1,126,532,true⟩, +⟨1,126,534,true⟩, +⟨1,126,576,true⟩, +⟨1,126,578,true⟩, +⟨1,126,580,true⟩, +⟨1,126,582,true⟩, +⟨1,126,592,true⟩, +⟨1,126,594,true⟩, +⟨1,126,596,true⟩, +⟨1,126,598,true⟩, +⟨1,126,603,true⟩, +⟨1,126,624,true⟩, +⟨1,126,626,true⟩, +⟨1,126,628,true⟩, +⟨1,126,630,true⟩, +⟨1,126,635,true⟩, +⟨1,126,672,true⟩, +⟨1,126,674,true⟩, +⟨1,126,676,true⟩, +⟨1,126,678,true⟩, +⟨1,126,683,true⟩, +⟨1,126,688,true⟩, +⟨1,126,690,true⟩, +⟨1,126,692,true⟩, +⟨1,126,694,true⟩, +⟨1,126,695,true⟩, +⟨1,127,252,true⟩, +⟨1,127,258,true⟩, +⟨1,127,276,true⟩, +⟨1,127,512,true⟩, +⟨1,127,514,true⟩, +⟨1,127,516,true⟩, +⟨1,127,518,true⟩, +⟨1,127,523,true⟩, +⟨1,127,528,true⟩, +⟨1,127,530,true⟩, +⟨1,127,532,true⟩, +⟨1,127,534,true⟩, +⟨1,127,560,true⟩, +⟨1,127,562,true⟩, +⟨1,127,564,true⟩, +⟨1,127,566,true⟩, +⟨1,127,571,true⟩, +⟨1,127,608,true⟩, +⟨1,127,610,true⟩, +⟨1,127,612,true⟩, +⟨1,127,614,true⟩, +⟨1,127,615,true⟩, +⟨1,127,640,true⟩, +⟨1,127,642,true⟩, +⟨1,127,644,true⟩, +⟨1,127,646,true⟩, +⟨1,127,651,true⟩, +⟨1,127,656,true⟩, +⟨1,127,658,true⟩, +⟨1,127,660,true⟩, +⟨1,127,662,true⟩, +⟨1,127,667,true⟩, +⟨1,127,688,true⟩, +⟨1,127,690,true⟩, +⟨1,127,692,true⟩, +⟨1,127,694,true⟩, +⟨1,127,699,true⟩, +⟨1,128,245,true⟩, +⟨1,128,259,true⟩, +⟨1,128,271,true⟩, +⟨1,128,277,true⟩, +⟨1,128,295,true⟩, +⟨1,128,309,true⟩, +⟨1,128,311,true⟩, +⟨1,128,313,true⟩, +⟨1,128,315,true⟩, +⟨1,128,322,true⟩, +⟨1,128,326,true⟩, +⟨1,128,328,true⟩, +⟨1,128,332,true⟩, +⟨1,128,341,true⟩, +⟨1,128,343,true⟩, +⟨1,128,345,true⟩, +⟨1,128,347,true⟩, +⟨1,128,354,true⟩, +⟨1,128,358,true⟩, +⟨1,128,360,true⟩, +⟨1,128,364,true⟩, +⟨1,128,387,true⟩, +⟨1,128,391,true⟩, +⟨1,128,395,true⟩, +⟨1,128,399,true⟩, +⟨1,128,405,true⟩, +⟨1,128,407,true⟩, +⟨1,128,409,true⟩, +⟨1,128,411,true⟩, +⟨1,128,436,true⟩, +⟨1,128,438,true⟩, +⟨1,128,444,true⟩, +⟨1,128,446,true⟩, +⟨1,128,451,true⟩, +⟨1,128,455,true⟩, +⟨1,128,459,true⟩, +⟨1,128,463,true⟩, +⟨1,128,468,true⟩, +⟨1,128,470,true⟩, +⟨1,128,476,true⟩, +⟨1,128,478,true⟩, +⟨1,128,483,true⟩, +⟨1,128,487,true⟩, +⟨1,128,491,true⟩, +⟨1,128,495,true⟩, +⟨1,128,525,true⟩, +⟨1,128,527,true⟩, +⟨1,128,541,true⟩, +⟨1,128,543,true⟩, +⟨1,128,553,true⟩, +⟨1,128,555,true⟩, +⟨1,128,573,true⟩, +⟨1,128,575,true⟩, +⟨1,128,585,true⟩, +⟨1,128,587,true⟩, +⟨1,128,594,true⟩, +⟨1,128,595,true⟩, +⟨1,128,598,true⟩, +⟨1,128,599,true⟩, +⟨1,128,608,true⟩, +⟨1,128,610,true⟩, +⟨1,128,612,true⟩, +⟨1,128,614,true⟩, +⟨1,128,644,true⟩, +⟨1,128,646,true⟩, +⟨1,128,850,true⟩, +⟨1,129,245,true⟩, +⟨1,129,259,true⟩, +⟨1,129,271,true⟩, +⟨1,129,277,true⟩, +⟨1,129,293,true⟩, +⟨1,129,309,true⟩, +⟨1,129,311,true⟩, +⟨1,129,313,true⟩, +⟨1,129,315,true⟩, +⟨1,129,320,true⟩, +⟨1,129,324,true⟩, +⟨1,129,330,true⟩, +⟨1,129,334,true⟩, +⟨1,129,341,true⟩, +⟨1,129,343,true⟩, +⟨1,129,345,true⟩, +⟨1,129,347,true⟩, +⟨1,129,352,true⟩, +⟨1,129,356,true⟩, +⟨1,129,362,true⟩, +⟨1,129,366,true⟩, +⟨1,129,385,true⟩, +⟨1,129,389,true⟩, +⟨1,129,393,true⟩, +⟨1,129,397,true⟩, +⟨1,129,405,true⟩, +⟨1,129,407,true⟩, +⟨1,129,409,true⟩, +⟨1,129,411,true⟩, +⟨1,129,436,true⟩, +⟨1,129,438,true⟩, +⟨1,129,444,true⟩, +⟨1,129,446,true⟩, +⟨1,129,449,true⟩, +⟨1,129,453,true⟩, +⟨1,129,457,true⟩, +⟨1,129,461,true⟩, +⟨1,129,468,true⟩, +⟨1,129,470,true⟩] +def chunk2 : List Event := [⟨1,129,476,true⟩, +⟨1,129,478,true⟩, +⟨1,129,481,true⟩, +⟨1,129,485,true⟩, +⟨1,129,489,true⟩, +⟨1,129,493,true⟩, +⟨1,129,499,true⟩, +⟨1,129,501,true⟩, +⟨1,129,505,true⟩, +⟨1,129,511,true⟩, +⟨1,129,525,true⟩, +⟨1,129,527,true⟩, +⟨1,129,541,true⟩, +⟨1,129,543,true⟩, +⟨1,129,552,true⟩, +⟨1,129,554,true⟩, +⟨1,129,573,true⟩, +⟨1,129,575,true⟩, +⟨1,129,584,true⟩, +⟨1,129,586,true⟩, +⟨1,129,592,true⟩, +⟨1,129,593,true⟩, +⟨1,129,596,true⟩, +⟨1,129,597,true⟩, +⟨1,129,608,true⟩, +⟨1,129,613,true⟩, +⟨1,129,614,true⟩, +⟨1,129,622,true⟩, +⟨1,129,623,true⟩, +⟨1,129,644,true⟩, +⟨1,129,646,true⟩, +⟨1,129,850,true⟩, +⟨1,129,933,true⟩, +⟨1,129,937,true⟩, +⟨1,130,245,true⟩, +⟨1,130,259,true⟩, +⟨1,130,271,true⟩, +⟨1,130,277,true⟩, +⟨1,130,291,true⟩, +⟨1,130,305,true⟩, +⟨1,130,307,true⟩, +⟨1,130,317,true⟩, +⟨1,130,319,true⟩, +⟨1,130,322,true⟩, +⟨1,130,326,true⟩, +⟨1,130,328,true⟩, +⟨1,130,332,true⟩, +⟨1,130,337,true⟩, +⟨1,130,339,true⟩, +⟨1,130,349,true⟩, +⟨1,130,351,true⟩, +⟨1,130,354,true⟩, +⟨1,130,358,true⟩, +⟨1,130,360,true⟩, +⟨1,130,364,true⟩, +⟨1,130,385,true⟩, +⟨1,130,389,true⟩, +⟨1,130,393,true⟩, +⟨1,130,397,true⟩, +⟨1,130,405,true⟩, +⟨1,130,407,true⟩, +⟨1,130,409,true⟩, +⟨1,130,411,true⟩, +⟨1,130,432,true⟩, +⟨1,130,434,true⟩, +⟨1,130,440,true⟩, +⟨1,130,442,true⟩, +⟨1,130,451,true⟩, +⟨1,130,455,true⟩, +⟨1,130,459,true⟩, +⟨1,130,463,true⟩, +⟨1,130,464,true⟩, +⟨1,130,466,true⟩, +⟨1,130,472,true⟩, +⟨1,130,474,true⟩, +⟨1,130,483,true⟩, +⟨1,130,487,true⟩, +⟨1,130,491,true⟩, +⟨1,130,495,true⟩, +⟨1,130,498,true⟩, +⟨1,130,500,true⟩, +⟨1,130,504,true⟩, +⟨1,130,510,true⟩, +⟨1,130,525,true⟩, +⟨1,130,527,true⟩, +⟨1,130,540,true⟩, +⟨1,130,542,true⟩, +⟨1,130,553,true⟩, +⟨1,130,555,true⟩, +⟨1,130,572,true⟩, +⟨1,130,574,true⟩, +⟨1,130,585,true⟩, +⟨1,130,587,true⟩, +⟨1,130,592,true⟩, +⟨1,130,593,true⟩, +⟨1,130,596,true⟩, +⟨1,130,597,true⟩, +⟨1,130,608,true⟩, +⟨1,130,614,true⟩, +⟨1,130,618,true⟩, +⟨1,130,623,true⟩, +⟨1,130,644,true⟩, +⟨1,130,646,true⟩, +⟨1,130,850,true⟩, +⟨1,130,932,true⟩, +⟨1,131,245,true⟩, +⟨1,131,259,true⟩, +⟨1,131,271,true⟩, +⟨1,131,277,true⟩, +⟨1,131,289,true⟩, +⟨1,131,305,true⟩, +⟨1,131,307,true⟩, +⟨1,131,317,true⟩, +⟨1,131,319,true⟩, +⟨1,131,320,true⟩, +⟨1,131,324,true⟩, +⟨1,131,330,true⟩, +⟨1,131,334,true⟩, +⟨1,131,337,true⟩, +⟨1,131,339,true⟩, +⟨1,131,349,true⟩, +⟨1,131,351,true⟩, +⟨1,131,352,true⟩, +⟨1,131,356,true⟩, +⟨1,131,362,true⟩, +⟨1,131,366,true⟩, +⟨1,131,387,true⟩, +⟨1,131,391,true⟩, +⟨1,131,395,true⟩, +⟨1,131,399,true⟩, +⟨1,131,405,true⟩, +⟨1,131,407,true⟩, +⟨1,131,409,true⟩, +⟨1,131,411,true⟩, +⟨1,131,432,true⟩, +⟨1,131,434,true⟩, +⟨1,131,440,true⟩, +⟨1,131,442,true⟩, +⟨1,131,449,true⟩, +⟨1,131,453,true⟩, +⟨1,131,457,true⟩, +⟨1,131,461,true⟩, +⟨1,131,464,true⟩, +⟨1,131,466,true⟩, +⟨1,131,472,true⟩, +⟨1,131,474,true⟩, +⟨1,131,481,true⟩, +⟨1,131,485,true⟩, +⟨1,131,489,true⟩, +⟨1,131,493,true⟩, +⟨1,131,525,true⟩, +⟨1,131,527,true⟩, +⟨1,131,540,true⟩, +⟨1,131,542,true⟩, +⟨1,131,552,true⟩, +⟨1,131,554,true⟩, +⟨1,131,572,true⟩, +⟨1,131,574,true⟩, +⟨1,131,584,true⟩, +⟨1,131,586,true⟩, +⟨1,131,594,true⟩, +⟨1,131,595,true⟩, +⟨1,131,598,true⟩, +⟨1,131,599,true⟩, +⟨1,131,608,true⟩, +⟨1,131,610,true⟩, +⟨1,131,612,true⟩, +⟨1,131,614,true⟩, +⟨1,131,644,true⟩, +⟨1,131,646,true⟩, +⟨1,131,850,true⟩, +⟨1,132,245,true⟩, +⟨1,132,259,true⟩, +⟨1,132,271,true⟩, +⟨1,132,277,true⟩, +⟨1,132,302,true⟩, +⟨1,132,305,true⟩, +⟨1,132,307,true⟩, +⟨1,132,317,true⟩, +⟨1,132,319,true⟩, +⟨1,132,322,true⟩, +⟨1,132,326,true⟩, +⟨1,132,328,true⟩, +⟨1,132,332,true⟩, +⟨1,132,341,true⟩, +⟨1,132,343,true⟩, +⟨1,132,345,true⟩, +⟨1,132,347,true⟩, +⟨1,132,352,true⟩, +⟨1,132,356,true⟩, +⟨1,132,362,true⟩, +⟨1,132,366,true⟩, +⟨1,132,387,true⟩, +⟨1,132,391,true⟩, +⟨1,132,395,true⟩, +⟨1,132,399,true⟩, +⟨1,132,401,true⟩, +⟨1,132,403,true⟩, +⟨1,132,413,true⟩, +⟨1,132,415,true⟩] +def chunk3 : List Event := [⟨1,132,436,true⟩, +⟨1,132,438,true⟩, +⟨1,132,444,true⟩, +⟨1,132,446,true⟩, +⟨1,132,449,true⟩, +⟨1,132,453,true⟩, +⟨1,132,457,true⟩, +⟨1,132,461,true⟩, +⟨1,132,464,true⟩, +⟨1,132,466,true⟩, +⟨1,132,472,true⟩, +⟨1,132,474,true⟩, +⟨1,132,483,true⟩, +⟨1,132,487,true⟩, +⟨1,132,491,true⟩, +⟨1,132,495,true⟩, +⟨1,132,500,true⟩, +⟨1,132,501,true⟩, +⟨1,132,505,true⟩, +⟨1,132,510,true⟩, +⟨1,132,524,true⟩, +⟨1,132,526,true⟩, +⟨1,132,541,true⟩, +⟨1,132,543,true⟩, +⟨1,132,553,true⟩, +⟨1,132,555,true⟩, +⟨1,132,572,true⟩, +⟨1,132,574,true⟩, +⟨1,132,584,true⟩, +⟨1,132,586,true⟩, +⟨1,132,594,true⟩, +⟨1,132,595,true⟩, +⟨1,132,598,true⟩, +⟨1,132,599,true⟩, +⟨1,132,608,true⟩, +⟨1,132,610,true⟩, +⟨1,132,613,true⟩, +⟨1,132,614,true⟩, +⟨1,132,618,true⟩, +⟨1,132,619,true⟩, +⟨1,132,640,true⟩, +⟨1,132,642,true⟩, +⟨1,132,848,true⟩, +⟨1,132,932,true⟩, +⟨1,132,937,true⟩, +⟨1,133,245,true⟩, +⟨1,133,259,true⟩, +⟨1,133,271,true⟩, +⟨1,133,277,true⟩, +⟨1,133,300,true⟩, +⟨1,133,305,true⟩, +⟨1,133,307,true⟩, +⟨1,133,317,true⟩, +⟨1,133,319,true⟩, +⟨1,133,320,true⟩, +⟨1,133,324,true⟩, +⟨1,133,330,true⟩, +⟨1,133,334,true⟩, +⟨1,133,341,true⟩, +⟨1,133,343,true⟩, +⟨1,133,345,true⟩, +⟨1,133,347,true⟩, +⟨1,133,354,true⟩, +⟨1,133,358,true⟩, +⟨1,133,360,true⟩, +⟨1,133,364,true⟩, +⟨1,133,385,true⟩, +⟨1,133,389,true⟩, +⟨1,133,393,true⟩, +⟨1,133,397,true⟩, +⟨1,133,401,true⟩, +⟨1,133,403,true⟩, +⟨1,133,413,true⟩, +⟨1,133,415,true⟩, +⟨1,133,436,true⟩, +⟨1,133,438,true⟩, +⟨1,133,444,true⟩, +⟨1,133,446,true⟩, +⟨1,133,451,true⟩, +⟨1,133,455,true⟩, +⟨1,133,459,true⟩, +⟨1,133,463,true⟩, +⟨1,133,464,true⟩, +⟨1,133,466,true⟩, +⟨1,133,472,true⟩, +⟨1,133,474,true⟩, +⟨1,133,481,true⟩, +⟨1,133,485,true⟩, +⟨1,133,489,true⟩, +⟨1,133,493,true⟩, +⟨1,133,524,true⟩, +⟨1,133,526,true⟩, +⟨1,133,541,true⟩, +⟨1,133,543,true⟩, +⟨1,133,552,true⟩, +⟨1,133,554,true⟩, +⟨1,133,572,true⟩, +⟨1,133,574,true⟩, +⟨1,133,585,true⟩, +⟨1,133,587,true⟩, +⟨1,133,592,true⟩, +⟨1,133,593,true⟩, +⟨1,133,596,true⟩, +⟨1,133,597,true⟩, +⟨1,133,608,true⟩, +⟨1,133,610,true⟩, +⟨1,133,612,true⟩, +⟨1,133,614,true⟩, +⟨1,133,640,true⟩, +⟨1,133,642,true⟩, +⟨1,133,848,true⟩, +⟨1,134,245,true⟩, +⟨1,134,259,true⟩, +⟨1,134,271,true⟩, +⟨1,134,277,true⟩, +⟨1,134,298,true⟩, +⟨1,134,309,true⟩, +⟨1,134,311,true⟩, +⟨1,134,313,true⟩, +⟨1,134,315,true⟩, +⟨1,134,322,true⟩, +⟨1,134,326,true⟩, +⟨1,134,328,true⟩, +⟨1,134,332,true⟩, +⟨1,134,337,true⟩, +⟨1,134,339,true⟩, +⟨1,134,349,true⟩, +⟨1,134,351,true⟩, +⟨1,134,352,true⟩, +⟨1,134,356,true⟩, +⟨1,134,362,true⟩, +⟨1,134,366,true⟩, +⟨1,134,385,true⟩, +⟨1,134,389,true⟩, +⟨1,134,393,true⟩, +⟨1,134,397,true⟩, +⟨1,134,401,true⟩, +⟨1,134,403,true⟩, +⟨1,134,413,true⟩, +⟨1,134,415,true⟩, +⟨1,134,432,true⟩, +⟨1,134,434,true⟩, +⟨1,134,440,true⟩, +⟨1,134,442,true⟩, +⟨1,134,449,true⟩, +⟨1,134,453,true⟩, +⟨1,134,457,true⟩, +⟨1,134,461,true⟩, +⟨1,134,468,true⟩, +⟨1,134,470,true⟩, +⟨1,134,476,true⟩, +⟨1,134,478,true⟩, +⟨1,134,483,true⟩, +⟨1,134,487,true⟩, +⟨1,134,491,true⟩, +⟨1,134,495,true⟩, +⟨1,134,524,true⟩, +⟨1,134,526,true⟩, +⟨1,134,540,true⟩, +⟨1,134,542,true⟩, +⟨1,134,553,true⟩, +⟨1,134,555,true⟩, +⟨1,134,573,true⟩, +⟨1,134,575,true⟩, +⟨1,134,584,true⟩, +⟨1,134,586,true⟩, +⟨1,134,592,true⟩, +⟨1,134,593,true⟩, +⟨1,134,596,true⟩, +⟨1,134,597,true⟩, +⟨1,134,608,true⟩, +⟨1,134,610,true⟩, +⟨1,134,612,true⟩, +⟨1,134,614,true⟩, +⟨1,134,640,true⟩, +⟨1,134,642,true⟩, +⟨1,134,848,true⟩, +⟨1,135,245,true⟩, +⟨1,135,259,true⟩, +⟨1,135,271,true⟩, +⟨1,135,277,true⟩, +⟨1,135,296,true⟩, +⟨1,135,309,true⟩, +⟨1,135,311,true⟩, +⟨1,135,313,true⟩, +⟨1,135,315,true⟩, +⟨1,135,320,true⟩, +⟨1,135,324,true⟩, +⟨1,135,330,true⟩, +⟨1,135,334,true⟩, +⟨1,135,337,true⟩, +⟨1,135,339,true⟩, +⟨1,135,349,true⟩, +⟨1,135,351,true⟩, +⟨1,135,354,true⟩, +⟨1,135,358,true⟩, +⟨1,135,360,true⟩, +⟨1,135,364,true⟩, +⟨1,135,387,true⟩, +⟨1,135,391,true⟩] +def chunk4 : List Event := [⟨1,135,395,true⟩, +⟨1,135,399,true⟩, +⟨1,135,401,true⟩, +⟨1,135,403,true⟩, +⟨1,135,413,true⟩, +⟨1,135,415,true⟩, +⟨1,135,432,true⟩, +⟨1,135,434,true⟩, +⟨1,135,440,true⟩, +⟨1,135,442,true⟩, +⟨1,135,451,true⟩, +⟨1,135,455,true⟩, +⟨1,135,459,true⟩, +⟨1,135,463,true⟩, +⟨1,135,468,true⟩, +⟨1,135,470,true⟩, +⟨1,135,476,true⟩, +⟨1,135,478,true⟩, +⟨1,135,481,true⟩, +⟨1,135,485,true⟩, +⟨1,135,489,true⟩, +⟨1,135,493,true⟩, +⟨1,135,498,true⟩, +⟨1,135,499,true⟩, +⟨1,135,504,true⟩, +⟨1,135,511,true⟩, +⟨1,135,524,true⟩, +⟨1,135,526,true⟩, +⟨1,135,540,true⟩, +⟨1,135,542,true⟩, +⟨1,135,552,true⟩, +⟨1,135,554,true⟩, +⟨1,135,573,true⟩, +⟨1,135,575,true⟩, +⟨1,135,585,true⟩, +⟨1,135,587,true⟩, +⟨1,135,594,true⟩, +⟨1,135,595,true⟩, +⟨1,135,598,true⟩, +⟨1,135,599,true⟩, +⟨1,135,608,true⟩, +⟨1,135,610,true⟩, +⟨1,135,614,true⟩, +⟨1,135,619,true⟩, +⟨1,135,622,true⟩, +⟨1,135,640,true⟩, +⟨1,135,642,true⟩, +⟨1,135,848,true⟩, +⟨1,135,933,true⟩, +⟨1,136,251,true⟩, +⟨1,136,261,true⟩, +⟨1,136,273,true⟩, +⟨1,136,285,true⟩, +⟨1,136,293,true⟩, +⟨1,136,295,true⟩, +⟨1,136,297,true⟩, +⟨1,136,299,true⟩, +⟨1,136,311,true⟩, +⟨1,136,324,true⟩, +⟨1,136,326,true⟩, +⟨1,136,332,true⟩, +⟨1,136,334,true⟩, +⟨1,136,340,true⟩, +⟨1,136,342,true⟩, +⟨1,136,348,true⟩, +⟨1,136,350,true⟩, +⟨1,136,370,true⟩, +⟨1,136,374,true⟩, +⟨1,136,376,true⟩, +⟨1,136,380,true⟩, +⟨1,136,388,true⟩, +⟨1,136,390,true⟩, +⟨1,136,396,true⟩, +⟨1,136,398,true⟩, +⟨1,136,404,true⟩, +⟨1,136,406,true⟩, +⟨1,136,412,true⟩, +⟨1,136,414,true⟩, +⟨1,136,420,true⟩, +⟨1,136,422,true⟩, +⟨1,136,428,true⟩, +⟨1,136,430,true⟩, +⟨1,136,452,true⟩, +⟨1,136,454,true⟩, +⟨1,136,460,true⟩, +⟨1,136,462,true⟩, +⟨1,136,468,true⟩, +⟨1,136,470,true⟩, +⟨1,136,476,true⟩, +⟨1,136,478,true⟩, +⟨1,136,499,true⟩, +⟨1,136,503,true⟩, +⟨1,136,507,true⟩, +⟨1,136,511,true⟩, +⟨1,136,580,true⟩, +⟨1,136,582,true⟩, +⟨1,136,637,true⟩, +⟨1,136,639,true⟩, +⟨1,136,649,true⟩, +⟨1,136,651,true⟩, +⟨1,136,658,true⟩, +⟨1,136,659,true⟩, +⟨1,136,662,true⟩, +⟨1,136,663,true⟩, +⟨1,136,672,true⟩, +⟨1,136,674,true⟩, +⟨1,136,676,true⟩, +⟨1,136,678,true⟩, +⟨1,136,794,true⟩, +⟨1,136,843,true⟩, +⟨1,136,871,true⟩, +⟨1,136,911,true⟩, +⟨1,137,251,true⟩, +⟨1,137,261,true⟩, +⟨1,137,273,true⟩, +⟨1,137,285,true⟩, +⟨1,137,293,true⟩, +⟨1,137,295,true⟩, +⟨1,137,297,true⟩, +⟨1,137,299,true⟩, +⟨1,137,308,true⟩, +⟨1,137,320,true⟩, +⟨1,137,322,true⟩, +⟨1,137,328,true⟩, +⟨1,137,330,true⟩, +⟨1,137,340,true⟩, +⟨1,137,342,true⟩, +⟨1,137,348,true⟩, +⟨1,137,350,true⟩, +⟨1,137,368,true⟩, +⟨1,137,372,true⟩, +⟨1,137,378,true⟩, +⟨1,137,382,true⟩, +⟨1,137,384,true⟩, +⟨1,137,386,true⟩, +⟨1,137,392,true⟩, +⟨1,137,394,true⟩, +⟨1,137,404,true⟩, +⟨1,137,406,true⟩, +⟨1,137,412,true⟩, +⟨1,137,414,true⟩, +⟨1,137,420,true⟩, +⟨1,137,422,true⟩, +⟨1,137,428,true⟩, +⟨1,137,430,true⟩, +⟨1,137,448,true⟩, +⟨1,137,450,true⟩, +⟨1,137,456,true⟩, +⟨1,137,458,true⟩, +⟨1,137,468,true⟩, +⟨1,137,470,true⟩, +⟨1,137,476,true⟩, +⟨1,137,478,true⟩, +⟨1,137,483,true⟩, +⟨1,137,484,true⟩, +⟨1,137,494,true⟩, +⟨1,137,495,true⟩, +⟨1,137,497,true⟩, +⟨1,137,501,true⟩, +⟨1,137,505,true⟩, +⟨1,137,509,true⟩, +⟨1,137,580,true⟩, +⟨1,137,582,true⟩, +⟨1,137,637,true⟩, +⟨1,137,639,true⟩, +⟨1,137,648,true⟩, +⟨1,137,650,true⟩, +⟨1,137,656,true⟩, +⟨1,137,657,true⟩, +⟨1,137,660,true⟩, +⟨1,137,661,true⟩, +⟨1,137,672,true⟩, +⟨1,137,676,true⟩, +⟨1,137,677,true⟩, +⟨1,137,678,true⟩, +⟨1,137,682,true⟩, +⟨1,137,686,true⟩, +⟨1,137,794,true⟩, +⟨1,137,843,true⟩, +⟨1,137,870,true⟩, +⟨1,137,910,true⟩, +⟨1,137,924,true⟩, +⟨1,137,966,true⟩, +⟨1,137,973,true⟩, +⟨1,138,251,true⟩, +⟨1,138,261,true⟩, +⟨1,138,273,true⟩, +⟨1,138,285,true⟩, +⟨1,138,289,true⟩, +⟨1,138,291,true⟩, +⟨1,138,301,true⟩, +⟨1,138,303,true⟩, +⟨1,138,306,true⟩, +⟨1,138,324,true⟩, +⟨1,138,326,true⟩, +⟨1,138,332,true⟩, +⟨1,138,334,true⟩, +⟨1,138,336,true⟩, +⟨1,138,338,true⟩, +⟨1,138,344,true⟩] +def chunk5 : List Event := [⟨1,138,346,true⟩, +⟨1,138,370,true⟩, +⟨1,138,374,true⟩, +⟨1,138,376,true⟩, +⟨1,138,380,true⟩, +⟨1,138,384,true⟩, +⟨1,138,386,true⟩, +⟨1,138,392,true⟩, +⟨1,138,394,true⟩, +⟨1,138,404,true⟩, +⟨1,138,406,true⟩, +⟨1,138,412,true⟩, +⟨1,138,414,true⟩, +⟨1,138,416,true⟩, +⟨1,138,418,true⟩, +⟨1,138,424,true⟩, +⟨1,138,426,true⟩, +⟨1,138,452,true⟩, +⟨1,138,454,true⟩, +⟨1,138,460,true⟩, +⟨1,138,462,true⟩, +⟨1,138,464,true⟩, +⟨1,138,466,true⟩, +⟨1,138,472,true⟩, +⟨1,138,474,true⟩, +⟨1,138,482,true⟩, +⟨1,138,485,true⟩, +⟨1,138,486,true⟩, +⟨1,138,487,true⟩, +⟨1,138,488,true⟩, +⟨1,138,489,true⟩, +⟨1,138,491,true⟩, +⟨1,138,492,true⟩, +⟨1,138,499,true⟩, +⟨1,138,503,true⟩, +⟨1,138,507,true⟩, +⟨1,138,511,true⟩, +⟨1,138,580,true⟩, +⟨1,138,582,true⟩, +⟨1,138,636,true⟩, +⟨1,138,638,true⟩, +⟨1,138,649,true⟩, +⟨1,138,651,true⟩, +⟨1,138,656,true⟩, +⟨1,138,657,true⟩, +⟨1,138,660,true⟩, +⟨1,138,661,true⟩, +⟨1,138,672,true⟩, +⟨1,138,676,true⟩, +⟨1,138,677,true⟩, +⟨1,138,794,true⟩, +⟨1,138,842,true⟩, +⟨1,138,870,true⟩, +⟨1,138,896,true⟩, +⟨1,138,911,true⟩, +⟨1,138,924,true⟩, +⟨1,138,965,true⟩, +⟨1,138,974,true⟩, +⟨1,139,251,true⟩, +⟨1,139,261,true⟩, +⟨1,139,273,true⟩, +⟨1,139,285,true⟩, +⟨1,139,289,true⟩, +⟨1,139,291,true⟩, +⟨1,139,301,true⟩, +⟨1,139,303,true⟩, +⟨1,139,305,true⟩, +⟨1,139,320,true⟩, +⟨1,139,322,true⟩, +⟨1,139,328,true⟩, +⟨1,139,330,true⟩, +⟨1,139,336,true⟩, +⟨1,139,338,true⟩, +⟨1,139,344,true⟩, +⟨1,139,346,true⟩, +⟨1,139,368,true⟩, +⟨1,139,372,true⟩, +⟨1,139,378,true⟩, +⟨1,139,382,true⟩, +⟨1,139,388,true⟩, +⟨1,139,390,true⟩, +⟨1,139,396,true⟩, +⟨1,139,398,true⟩, +⟨1,139,404,true⟩, +⟨1,139,406,true⟩, +⟨1,139,412,true⟩, +⟨1,139,414,true⟩, +⟨1,139,416,true⟩, +⟨1,139,418,true⟩, +⟨1,139,424,true⟩, +⟨1,139,426,true⟩, +⟨1,139,448,true⟩, +⟨1,139,450,true⟩, +⟨1,139,456,true⟩, +⟨1,139,458,true⟩, +⟨1,139,464,true⟩, +⟨1,139,466,true⟩, +⟨1,139,472,true⟩, +⟨1,139,474,true⟩, +⟨1,139,497,true⟩, +⟨1,139,501,true⟩, +⟨1,139,505,true⟩, +⟨1,139,509,true⟩, +⟨1,139,580,true⟩, +⟨1,139,582,true⟩, +⟨1,139,636,true⟩, +⟨1,139,638,true⟩, +⟨1,139,648,true⟩, +⟨1,139,650,true⟩, +⟨1,139,658,true⟩, +⟨1,139,659,true⟩, +⟨1,139,662,true⟩, +⟨1,139,663,true⟩, +⟨1,139,672,true⟩, +⟨1,139,674,true⟩, +⟨1,139,676,true⟩, +⟨1,139,678,true⟩, +⟨1,139,794,true⟩, +⟨1,139,842,true⟩, +⟨1,139,871,true⟩, +⟨1,139,896,true⟩, +⟨1,139,910,true⟩, +⟨1,140,251,true⟩, +⟨1,140,261,true⟩, +⟨1,140,273,true⟩, +⟨1,140,285,true⟩, +⟨1,140,289,true⟩, +⟨1,140,291,true⟩, +⟨1,140,301,true⟩, +⟨1,140,303,true⟩, +⟨1,140,319,true⟩, +⟨1,140,324,true⟩, +⟨1,140,326,true⟩, +⟨1,140,332,true⟩, +⟨1,140,334,true⟩, +⟨1,140,340,true⟩, +⟨1,140,342,true⟩, +⟨1,140,348,true⟩, +⟨1,140,350,true⟩, +⟨1,140,368,true⟩, +⟨1,140,372,true⟩, +⟨1,140,378,true⟩, +⟨1,140,382,true⟩, +⟨1,140,388,true⟩, +⟨1,140,390,true⟩, +⟨1,140,396,true⟩, +⟨1,140,398,true⟩, +⟨1,140,400,true⟩, +⟨1,140,402,true⟩, +⟨1,140,408,true⟩, +⟨1,140,410,true⟩, +⟨1,140,420,true⟩, +⟨1,140,422,true⟩, +⟨1,140,428,true⟩, +⟨1,140,430,true⟩, +⟨1,140,448,true⟩, +⟨1,140,450,true⟩, +⟨1,140,456,true⟩, +⟨1,140,458,true⟩, +⟨1,140,464,true⟩, +⟨1,140,466,true⟩, +⟨1,140,472,true⟩, +⟨1,140,474,true⟩, +⟨1,140,484,true⟩, +⟨1,140,485,true⟩, +⟨1,140,486,true⟩, +⟨1,140,487,true⟩, +⟨1,140,489,true⟩, +⟨1,140,491,true⟩, +⟨1,140,492,true⟩, +⟨1,140,494,true⟩, +⟨1,140,499,true⟩, +⟨1,140,503,true⟩, +⟨1,140,507,true⟩, +⟨1,140,511,true⟩, +⟨1,140,576,true⟩, +⟨1,140,578,true⟩, +⟨1,140,636,true⟩, +⟨1,140,638,true⟩, +⟨1,140,648,true⟩, +⟨1,140,650,true⟩, +⟨1,140,658,true⟩, +⟨1,140,659,true⟩, +⟨1,140,662,true⟩, +⟨1,140,663,true⟩, +⟨1,140,672,true⟩, +⟨1,140,674,true⟩, +⟨1,140,677,true⟩, +⟨1,140,682,true⟩, +⟨1,140,687,true⟩, +⟨1,140,792,true⟩, +⟨1,140,842,true⟩, +⟨1,140,871,true⟩, +⟨1,140,896,true⟩, +⟨1,140,910,true⟩, +⟨1,140,965,true⟩, +⟨1,140,973,true⟩, +⟨1,141,251,true⟩, +⟨1,141,261,true⟩, +⟨1,141,273,true⟩] +def chunk6 : List Event := [⟨1,141,285,true⟩, +⟨1,141,289,true⟩, +⟨1,141,291,true⟩, +⟨1,141,301,true⟩, +⟨1,141,303,true⟩, +⟨1,141,316,true⟩, +⟨1,141,320,true⟩, +⟨1,141,322,true⟩, +⟨1,141,328,true⟩, +⟨1,141,330,true⟩, +⟨1,141,340,true⟩, +⟨1,141,342,true⟩, +⟨1,141,348,true⟩, +⟨1,141,350,true⟩, +⟨1,141,370,true⟩, +⟨1,141,374,true⟩, +⟨1,141,376,true⟩, +⟨1,141,380,true⟩, +⟨1,141,384,true⟩, +⟨1,141,386,true⟩, +⟨1,141,392,true⟩, +⟨1,141,394,true⟩, +⟨1,141,400,true⟩, +⟨1,141,402,true⟩, +⟨1,141,408,true⟩, +⟨1,141,410,true⟩, +⟨1,141,420,true⟩, +⟨1,141,422,true⟩, +⟨1,141,428,true⟩, +⟨1,141,430,true⟩, +⟨1,141,452,true⟩, +⟨1,141,454,true⟩, +⟨1,141,460,true⟩, +⟨1,141,462,true⟩, +⟨1,141,464,true⟩, +⟨1,141,466,true⟩, +⟨1,141,472,true⟩, +⟨1,141,474,true⟩, +⟨1,141,497,true⟩, +⟨1,141,501,true⟩, +⟨1,141,505,true⟩, +⟨1,141,509,true⟩, +⟨1,141,576,true⟩, +⟨1,141,578,true⟩, +⟨1,141,636,true⟩, +⟨1,141,638,true⟩, +⟨1,141,649,true⟩, +⟨1,141,651,true⟩, +⟨1,141,656,true⟩, +⟨1,141,657,true⟩, +⟨1,141,660,true⟩, +⟨1,141,661,true⟩, +⟨1,141,672,true⟩, +⟨1,141,674,true⟩, +⟨1,141,676,true⟩, +⟨1,141,678,true⟩, +⟨1,141,792,true⟩, +⟨1,141,842,true⟩, +⟨1,141,870,true⟩, +⟨1,141,896,true⟩, +⟨1,141,911,true⟩, +⟨1,141,924,true⟩, +⟨1,142,251,true⟩, +⟨1,142,261,true⟩, +⟨1,142,273,true⟩, +⟨1,142,285,true⟩, +⟨1,142,293,true⟩, +⟨1,142,295,true⟩, +⟨1,142,297,true⟩, +⟨1,142,299,true⟩, +⟨1,142,314,true⟩, +⟨1,142,324,true⟩, +⟨1,142,326,true⟩, +⟨1,142,332,true⟩, +⟨1,142,334,true⟩, +⟨1,142,336,true⟩, +⟨1,142,338,true⟩, +⟨1,142,344,true⟩, +⟨1,142,346,true⟩, +⟨1,142,368,true⟩, +⟨1,142,372,true⟩, +⟨1,142,378,true⟩, +⟨1,142,382,true⟩, +⟨1,142,384,true⟩, +⟨1,142,386,true⟩, +⟨1,142,392,true⟩, +⟨1,142,394,true⟩, +⟨1,142,400,true⟩, +⟨1,142,402,true⟩, +⟨1,142,408,true⟩, +⟨1,142,410,true⟩, +⟨1,142,416,true⟩, +⟨1,142,418,true⟩, +⟨1,142,424,true⟩, +⟨1,142,426,true⟩, +⟨1,142,448,true⟩, +⟨1,142,450,true⟩, +⟨1,142,456,true⟩, +⟨1,142,458,true⟩, +⟨1,142,468,true⟩, +⟨1,142,470,true⟩, +⟨1,142,476,true⟩, +⟨1,142,478,true⟩, +⟨1,142,499,true⟩, +⟨1,142,503,true⟩, +⟨1,142,507,true⟩, +⟨1,142,511,true⟩, +⟨1,142,576,true⟩, +⟨1,142,578,true⟩, +⟨1,142,637,true⟩, +⟨1,142,639,true⟩, +⟨1,142,648,true⟩, +⟨1,142,650,true⟩, +⟨1,142,656,true⟩, +⟨1,142,657,true⟩, +⟨1,142,660,true⟩, +⟨1,142,661,true⟩, +⟨1,142,672,true⟩, +⟨1,142,674,true⟩, +⟨1,142,676,true⟩, +⟨1,142,678,true⟩, +⟨1,142,792,true⟩, +⟨1,142,843,true⟩, +⟨1,142,870,true⟩, +⟨1,142,910,true⟩, +⟨1,142,924,true⟩, +⟨1,143,251,true⟩, +⟨1,143,261,true⟩, +⟨1,143,273,true⟩, +⟨1,143,285,true⟩, +⟨1,143,293,true⟩, +⟨1,143,295,true⟩, +⟨1,143,297,true⟩, +⟨1,143,299,true⟩, +⟨1,143,313,true⟩, +⟨1,143,320,true⟩, +⟨1,143,322,true⟩, +⟨1,143,328,true⟩, +⟨1,143,330,true⟩, +⟨1,143,336,true⟩, +⟨1,143,338,true⟩, +⟨1,143,344,true⟩, +⟨1,143,346,true⟩, +⟨1,143,370,true⟩, +⟨1,143,374,true⟩, +⟨1,143,376,true⟩, +⟨1,143,380,true⟩, +⟨1,143,388,true⟩, +⟨1,143,390,true⟩, +⟨1,143,396,true⟩, +⟨1,143,398,true⟩, +⟨1,143,400,true⟩, +⟨1,143,402,true⟩, +⟨1,143,408,true⟩, +⟨1,143,410,true⟩, +⟨1,143,416,true⟩, +⟨1,143,418,true⟩, +⟨1,143,424,true⟩, +⟨1,143,426,true⟩, +⟨1,143,452,true⟩, +⟨1,143,454,true⟩, +⟨1,143,460,true⟩, +⟨1,143,462,true⟩, +⟨1,143,468,true⟩, +⟨1,143,470,true⟩, +⟨1,143,476,true⟩, +⟨1,143,478,true⟩, +⟨1,143,482,true⟩, +⟨1,143,483,true⟩, +⟨1,143,488,true⟩, +⟨1,143,495,true⟩, +⟨1,143,497,true⟩, +⟨1,143,501,true⟩, +⟨1,143,505,true⟩, +⟨1,143,509,true⟩, +⟨1,143,576,true⟩, +⟨1,143,578,true⟩, +⟨1,143,637,true⟩, +⟨1,143,639,true⟩, +⟨1,143,649,true⟩, +⟨1,143,651,true⟩, +⟨1,143,658,true⟩, +⟨1,143,659,true⟩, +⟨1,143,662,true⟩, +⟨1,143,663,true⟩, +⟨1,143,672,true⟩, +⟨1,143,674,true⟩, +⟨1,143,677,true⟩, +⟨1,143,678,true⟩, +⟨1,143,686,true⟩, +⟨1,143,687,true⟩, +⟨1,143,792,true⟩, +⟨1,143,843,true⟩, +⟨1,143,871,true⟩, +⟨1,143,911,true⟩, +⟨1,143,966,true⟩, +⟨1,143,974,true⟩, +⟨1,144,256,true⟩, +⟨1,144,262,true⟩, +⟨1,144,268,true⟩] +def chunk7 : List Event := [⟨1,144,274,true⟩, +⟨1,144,291,true⟩, +⟨1,144,295,true⟩, +⟨1,144,299,true⟩, +⟨1,144,303,true⟩, +⟨1,144,307,true⟩, +⟨1,144,311,true⟩, +⟨1,144,315,true⟩, +⟨1,144,319,true⟩, +⟨1,144,327,true⟩, +⟨1,144,355,true⟩, +⟨1,144,359,true⟩, +⟨1,144,363,true⟩, +⟨1,144,367,true⟩, +⟨1,144,371,true⟩, +⟨1,144,375,true⟩, +⟨1,144,379,true⟩, +⟨1,144,383,true⟩, +⟨1,144,419,true⟩, +⟨1,144,423,true⟩, +⟨1,144,427,true⟩, +⟨1,144,431,true⟩, +⟨1,144,435,true⟩, +⟨1,144,439,true⟩, +⟨1,144,443,true⟩, +⟨1,144,447,true⟩, +⟨1,144,483,true⟩, +⟨1,144,487,true⟩, +⟨1,144,491,true⟩, +⟨1,144,495,true⟩, +⟨1,144,499,true⟩, +⟨1,144,503,true⟩, +⟨1,144,507,true⟩, +⟨1,144,511,true⟩, +⟨1,144,516,true⟩, +⟨1,144,518,true⟩, +⟨1,144,532,true⟩, +⟨1,144,534,true⟩, +⟨1,144,688,true⟩, +⟨1,144,690,true⟩, +⟨1,144,692,true⟩, +⟨1,144,694,true⟩, +⟨1,144,706,true⟩, +⟨1,144,707,true⟩, +⟨1,144,710,true⟩, +⟨1,144,711,true⟩, +⟨1,144,722,true⟩, +⟨1,144,723,true⟩, +⟨1,144,726,true⟩, +⟨1,144,727,true⟩, +⟨1,145,256,true⟩, +⟨1,145,262,true⟩, +⟨1,145,268,true⟩, +⟨1,145,274,true⟩, +⟨1,145,289,true⟩, +⟨1,145,293,true⟩, +⟨1,145,297,true⟩, +⟨1,145,301,true⟩, +⟨1,145,307,true⟩, +⟨1,145,311,true⟩, +⟨1,145,315,true⟩, +⟨1,145,319,true⟩, +⟨1,145,324,true⟩, +⟨1,145,353,true⟩, +⟨1,145,357,true⟩, +⟨1,145,361,true⟩, +⟨1,145,365,true⟩, +⟨1,145,371,true⟩, +⟨1,145,375,true⟩, +⟨1,145,379,true⟩, +⟨1,145,383,true⟩, +⟨1,145,417,true⟩, +⟨1,145,421,true⟩, +⟨1,145,425,true⟩, +⟨1,145,429,true⟩, +⟨1,145,435,true⟩, +⟨1,145,439,true⟩, +⟨1,145,443,true⟩, +⟨1,145,447,true⟩, +⟨1,145,467,true⟩, +⟨1,145,468,true⟩, +⟨1,145,478,true⟩, +⟨1,145,479,true⟩, +⟨1,145,481,true⟩, +⟨1,145,485,true⟩, +⟨1,145,489,true⟩, +⟨1,145,493,true⟩, +⟨1,145,499,true⟩, +⟨1,145,503,true⟩, +⟨1,145,507,true⟩, +⟨1,145,511,true⟩, +⟨1,145,516,true⟩, +⟨1,145,518,true⟩, +⟨1,145,532,true⟩, +⟨1,145,534,true⟩, +⟨1,145,688,true⟩, +⟨1,145,692,true⟩, +⟨1,145,693,true⟩, +⟨1,145,694,true⟩, +⟨1,145,698,true⟩, +⟨1,145,702,true⟩, +⟨1,145,704,true⟩, +⟨1,145,705,true⟩, +⟨1,145,708,true⟩, +⟨1,145,709,true⟩, +⟨1,145,720,true⟩, +⟨1,145,721,true⟩, +⟨1,145,724,true⟩, +⟨1,145,725,true⟩, +⟨1,145,798,true⟩, +⟨1,145,812,true⟩, +⟨1,145,882,true⟩, +⟨1,145,963,true⟩, +⟨1,145,972,true⟩, +⟨1,146,256,true⟩, +⟨1,146,262,true⟩, +⟨1,146,268,true⟩, +⟨1,146,274,true⟩, +⟨1,146,291,true⟩, +⟨1,146,295,true⟩, +⟨1,146,299,true⟩, +⟨1,146,303,true⟩, +⟨1,146,305,true⟩, +⟨1,146,309,true⟩, +⟨1,146,313,true⟩, +⟨1,146,317,true⟩, +⟨1,146,322,true⟩, +⟨1,146,355,true⟩, +⟨1,146,359,true⟩, +⟨1,146,363,true⟩, +⟨1,146,367,true⟩, +⟨1,146,369,true⟩, +⟨1,146,373,true⟩, +⟨1,146,377,true⟩, +⟨1,146,381,true⟩, +⟨1,146,419,true⟩, +⟨1,146,423,true⟩, +⟨1,146,427,true⟩, +⟨1,146,431,true⟩, +⟨1,146,433,true⟩, +⟨1,146,437,true⟩, +⟨1,146,441,true⟩, +⟨1,146,445,true⟩, +⟨1,146,466,true⟩, +⟨1,146,469,true⟩, +⟨1,146,470,true⟩, +⟨1,146,471,true⟩, +⟨1,146,472,true⟩, +⟨1,146,473,true⟩, +⟨1,146,475,true⟩, +⟨1,146,476,true⟩, +⟨1,146,483,true⟩, +⟨1,146,487,true⟩, +⟨1,146,491,true⟩, +⟨1,146,495,true⟩, +⟨1,146,497,true⟩, +⟨1,146,501,true⟩, +⟨1,146,505,true⟩, +⟨1,146,509,true⟩, +⟨1,146,516,true⟩, +⟨1,146,518,true⟩, +⟨1,146,532,true⟩, +⟨1,146,534,true⟩, +⟨1,146,688,true⟩, +⟨1,146,692,true⟩, +⟨1,146,693,true⟩, +⟨1,146,704,true⟩, +⟨1,146,705,true⟩, +⟨1,146,708,true⟩, +⟨1,146,709,true⟩, +⟨1,146,720,true⟩, +⟨1,146,721,true⟩, +⟨1,146,724,true⟩, +⟨1,146,725,true⟩, +⟨1,146,826,true⟩, +⟨1,146,854,true⟩, +⟨1,146,868,true⟩, +⟨1,146,964,true⟩, +⟨1,146,971,true⟩, +⟨1,147,256,true⟩, +⟨1,147,262,true⟩, +⟨1,147,268,true⟩, +⟨1,147,274,true⟩, +⟨1,147,289,true⟩, +⟨1,147,293,true⟩, +⟨1,147,297,true⟩, +⟨1,147,301,true⟩, +⟨1,147,305,true⟩, +⟨1,147,309,true⟩, +⟨1,147,313,true⟩, +⟨1,147,317,true⟩, +⟨1,147,321,true⟩, +⟨1,147,353,true⟩, +⟨1,147,357,true⟩, +⟨1,147,361,true⟩, +⟨1,147,365,true⟩, +⟨1,147,369,true⟩, +⟨1,147,373,true⟩, +⟨1,147,377,true⟩, +⟨1,147,381,true⟩] +def chunk8 : List Event := [⟨1,147,417,true⟩, +⟨1,147,421,true⟩, +⟨1,147,425,true⟩, +⟨1,147,429,true⟩, +⟨1,147,433,true⟩, +⟨1,147,437,true⟩, +⟨1,147,441,true⟩, +⟨1,147,445,true⟩, +⟨1,147,481,true⟩, +⟨1,147,485,true⟩, +⟨1,147,489,true⟩, +⟨1,147,493,true⟩, +⟨1,147,497,true⟩, +⟨1,147,501,true⟩, +⟨1,147,505,true⟩, +⟨1,147,509,true⟩, +⟨1,147,516,true⟩, +⟨1,147,518,true⟩, +⟨1,147,532,true⟩, +⟨1,147,534,true⟩, +⟨1,147,688,true⟩, +⟨1,147,690,true⟩, +⟨1,147,692,true⟩, +⟨1,147,694,true⟩, +⟨1,147,706,true⟩, +⟨1,147,707,true⟩, +⟨1,147,710,true⟩, +⟨1,147,711,true⟩, +⟨1,147,722,true⟩, +⟨1,147,723,true⟩, +⟨1,147,726,true⟩, +⟨1,147,727,true⟩, +⟨1,147,798,true⟩, +⟨1,147,812,true⟩, +⟨1,147,826,true⟩, +⟨1,147,854,true⟩, +⟨1,147,868,true⟩, +⟨1,147,882,true⟩, +⟨1,148,256,true⟩, +⟨1,148,262,true⟩, +⟨1,148,268,true⟩, +⟨1,148,274,true⟩, +⟨1,148,289,true⟩, +⟨1,148,293,true⟩, +⟨1,148,297,true⟩, +⟨1,148,301,true⟩, +⟨1,148,307,true⟩, +⟨1,148,311,true⟩, +⟨1,148,315,true⟩, +⟨1,148,319,true⟩, +⟨1,148,335,true⟩, +⟨1,148,355,true⟩, +⟨1,148,359,true⟩, +⟨1,148,363,true⟩, +⟨1,148,367,true⟩, +⟨1,148,369,true⟩, +⟨1,148,373,true⟩, +⟨1,148,377,true⟩, +⟨1,148,381,true⟩, +⟨1,148,419,true⟩, +⟨1,148,423,true⟩, +⟨1,148,427,true⟩, +⟨1,148,431,true⟩, +⟨1,148,433,true⟩, +⟨1,148,437,true⟩, +⟨1,148,441,true⟩, +⟨1,148,445,true⟩, +⟨1,148,468,true⟩, +⟨1,148,469,true⟩, +⟨1,148,470,true⟩, +⟨1,148,471,true⟩, +⟨1,148,473,true⟩, +⟨1,148,475,true⟩, +⟨1,148,476,true⟩, +⟨1,148,478,true⟩, +⟨1,148,481,true⟩, +⟨1,148,485,true⟩, +⟨1,148,489,true⟩, +⟨1,148,493,true⟩, +⟨1,148,499,true⟩, +⟨1,148,503,true⟩, +⟨1,148,507,true⟩, +⟨1,148,511,true⟩, +⟨1,148,512,true⟩, +⟨1,148,514,true⟩, +⟨1,148,528,true⟩, +⟨1,148,530,true⟩, +⟨1,148,688,true⟩, +⟨1,148,690,true⟩, +⟨1,148,693,true⟩, +⟨1,148,698,true⟩, +⟨1,148,703,true⟩, +⟨1,148,706,true⟩, +⟨1,148,707,true⟩, +⟨1,148,710,true⟩, +⟨1,148,711,true⟩, +⟨1,148,722,true⟩, +⟨1,148,723,true⟩, +⟨1,148,726,true⟩, +⟨1,148,727,true⟩, +⟨1,148,737,true⟩, +⟨1,148,750,true⟩, +⟨1,148,854,true⟩, +⟨1,148,868,true⟩, +⟨1,148,882,true⟩, +⟨1,148,963,true⟩, +⟨1,148,971,true⟩, +⟨1,149,256,true⟩, +⟨1,149,262,true⟩, +⟨1,149,268,true⟩, +⟨1,149,274,true⟩, +⟨1,149,291,true⟩, +⟨1,149,295,true⟩, +⟨1,149,299,true⟩, +⟨1,149,303,true⟩, +⟨1,149,307,true⟩, +⟨1,149,311,true⟩, +⟨1,149,315,true⟩, +⟨1,149,319,true⟩, +⟨1,149,332,true⟩, +⟨1,149,353,true⟩, +⟨1,149,357,true⟩, +⟨1,149,361,true⟩, +⟨1,149,365,true⟩, +⟨1,149,369,true⟩, +⟨1,149,373,true⟩, +⟨1,149,377,true⟩, +⟨1,149,381,true⟩, +⟨1,149,417,true⟩, +⟨1,149,421,true⟩, +⟨1,149,425,true⟩, +⟨1,149,429,true⟩, +⟨1,149,433,true⟩, +⟨1,149,437,true⟩, +⟨1,149,441,true⟩, +⟨1,149,445,true⟩, +⟨1,149,483,true⟩, +⟨1,149,487,true⟩, +⟨1,149,491,true⟩, +⟨1,149,495,true⟩, +⟨1,149,499,true⟩, +⟨1,149,503,true⟩, +⟨1,149,507,true⟩, +⟨1,149,511,true⟩, +⟨1,149,512,true⟩, +⟨1,149,514,true⟩, +⟨1,149,528,true⟩, +⟨1,149,530,true⟩, +⟨1,149,688,true⟩, +⟨1,149,690,true⟩, +⟨1,149,692,true⟩, +⟨1,149,694,true⟩, +⟨1,149,704,true⟩, +⟨1,149,705,true⟩, +⟨1,149,708,true⟩, +⟨1,149,709,true⟩, +⟨1,149,720,true⟩, +⟨1,149,721,true⟩, +⟨1,149,724,true⟩, +⟨1,149,725,true⟩, +⟨1,149,737,true⟩, +⟨1,149,750,true⟩, +⟨1,149,798,true⟩, +⟨1,149,812,true⟩, +⟨1,149,854,true⟩, +⟨1,149,868,true⟩, +⟨1,150,256,true⟩, +⟨1,150,262,true⟩, +⟨1,150,268,true⟩, +⟨1,150,274,true⟩, +⟨1,150,289,true⟩, +⟨1,150,293,true⟩, +⟨1,150,297,true⟩, +⟨1,150,301,true⟩, +⟨1,150,305,true⟩, +⟨1,150,309,true⟩, +⟨1,150,313,true⟩, +⟨1,150,317,true⟩, +⟨1,150,330,true⟩, +⟨1,150,355,true⟩, +⟨1,150,359,true⟩, +⟨1,150,363,true⟩, +⟨1,150,367,true⟩, +⟨1,150,371,true⟩, +⟨1,150,375,true⟩, +⟨1,150,379,true⟩, +⟨1,150,383,true⟩, +⟨1,150,419,true⟩, +⟨1,150,423,true⟩, +⟨1,150,427,true⟩, +⟨1,150,431,true⟩, +⟨1,150,435,true⟩, +⟨1,150,439,true⟩, +⟨1,150,443,true⟩, +⟨1,150,447,true⟩, +⟨1,150,481,true⟩, +⟨1,150,485,true⟩, +⟨1,150,489,true⟩, +⟨1,150,493,true⟩, +⟨1,150,497,true⟩] +def chunk9 : List Event := [⟨1,150,501,true⟩, +⟨1,150,505,true⟩, +⟨1,150,509,true⟩, +⟨1,150,512,true⟩, +⟨1,150,514,true⟩, +⟨1,150,528,true⟩, +⟨1,150,530,true⟩, +⟨1,150,688,true⟩, +⟨1,150,690,true⟩, +⟨1,150,692,true⟩, +⟨1,150,694,true⟩, +⟨1,150,704,true⟩, +⟨1,150,705,true⟩, +⟨1,150,708,true⟩, +⟨1,150,709,true⟩, +⟨1,150,720,true⟩, +⟨1,150,721,true⟩, +⟨1,150,724,true⟩, +⟨1,150,725,true⟩, +⟨1,150,737,true⟩, +⟨1,150,750,true⟩, +⟨1,150,826,true⟩, +⟨1,150,882,true⟩, +⟨1,151,256,true⟩, +⟨1,151,262,true⟩, +⟨1,151,268,true⟩, +⟨1,151,274,true⟩, +⟨1,151,291,true⟩, +⟨1,151,295,true⟩, +⟨1,151,299,true⟩, +⟨1,151,303,true⟩, +⟨1,151,305,true⟩, +⟨1,151,309,true⟩, +⟨1,151,313,true⟩, +⟨1,151,317,true⟩, +⟨1,151,329,true⟩, +⟨1,151,353,true⟩, +⟨1,151,357,true⟩, +⟨1,151,361,true⟩, +⟨1,151,365,true⟩, +⟨1,151,371,true⟩, +⟨1,151,375,true⟩, +⟨1,151,379,true⟩, +⟨1,151,383,true⟩, +⟨1,151,417,true⟩, +⟨1,151,421,true⟩, +⟨1,151,425,true⟩, +⟨1,151,429,true⟩, +⟨1,151,435,true⟩, +⟨1,151,439,true⟩, +⟨1,151,443,true⟩, +⟨1,151,447,true⟩, +⟨1,151,466,true⟩, +⟨1,151,467,true⟩, +⟨1,151,472,true⟩, +⟨1,151,479,true⟩, +⟨1,151,483,true⟩, +⟨1,151,487,true⟩, +⟨1,151,491,true⟩, +⟨1,151,495,true⟩, +⟨1,151,497,true⟩, +⟨1,151,501,true⟩, +⟨1,151,505,true⟩, +⟨1,151,509,true⟩, +⟨1,151,512,true⟩, +⟨1,151,514,true⟩, +⟨1,151,528,true⟩, +⟨1,151,530,true⟩, +⟨1,151,688,true⟩, +⟨1,151,690,true⟩, +⟨1,151,693,true⟩, +⟨1,151,694,true⟩, +⟨1,151,702,true⟩, +⟨1,151,703,true⟩, +⟨1,151,706,true⟩, +⟨1,151,707,true⟩, +⟨1,151,710,true⟩, +⟨1,151,711,true⟩, +⟨1,151,722,true⟩, +⟨1,151,723,true⟩, +⟨1,151,726,true⟩, +⟨1,151,727,true⟩, +⟨1,151,737,true⟩, +⟨1,151,750,true⟩, +⟨1,151,798,true⟩, +⟨1,151,812,true⟩, +⟨1,151,826,true⟩, +⟨1,151,964,true⟩, +⟨1,151,972,true⟩, +⟨1,152,257,true⟩, +⟨1,152,263,true⟩, +⟨1,152,280,true⟩, +⟨1,152,286,true⟩, +⟨1,152,292,true⟩, +⟨1,152,294,true⟩, +⟨1,152,300,true⟩, +⟨1,152,302,true⟩, +⟨1,152,308,true⟩, +⟨1,152,310,true⟩, +⟨1,152,316,true⟩, +⟨1,152,318,true⟩, +⟨1,152,342,true⟩, +⟨1,152,356,true⟩, +⟨1,152,358,true⟩, +⟨1,152,364,true⟩, +⟨1,152,366,true⟩, +⟨1,152,372,true⟩, +⟨1,152,374,true⟩, +⟨1,152,380,true⟩, +⟨1,152,382,true⟩, +⟨1,152,420,true⟩, +⟨1,152,422,true⟩, +⟨1,152,428,true⟩, +⟨1,152,430,true⟩, +⟨1,152,436,true⟩, +⟨1,152,438,true⟩, +⟨1,152,444,true⟩, +⟨1,152,446,true⟩, +⟨1,152,484,true⟩, +⟨1,152,486,true⟩, +⟨1,152,492,true⟩, +⟨1,152,494,true⟩, +⟨1,152,500,true⟩, +⟨1,152,502,true⟩, +⟨1,152,508,true⟩, +⟨1,152,510,true⟩, +⟨1,152,516,true⟩, +⟨1,152,518,true⟩, +⟨1,152,548,true⟩, +⟨1,152,550,true⟩, +⟨1,152,690,true⟩, +⟨1,152,691,true⟩, +⟨1,152,694,true⟩, +⟨1,152,695,true⟩, +⟨1,152,704,true⟩, +⟨1,152,706,true⟩, +⟨1,152,708,true⟩, +⟨1,152,710,true⟩, +⟨1,152,724,true⟩, +⟨1,152,726,true⟩, +⟨1,152,766,true⟩, +⟨1,153,257,true⟩, +⟨1,153,263,true⟩, +⟨1,153,280,true⟩, +⟨1,153,286,true⟩, +⟨1,153,292,true⟩, +⟨1,153,294,true⟩, +⟨1,153,300,true⟩, +⟨1,153,302,true⟩, +⟨1,153,308,true⟩, +⟨1,153,310,true⟩, +⟨1,153,316,true⟩, +⟨1,153,318,true⟩, +⟨1,153,340,true⟩, +⟨1,153,352,true⟩, +⟨1,153,354,true⟩, +⟨1,153,360,true⟩, +⟨1,153,362,true⟩, +⟨1,153,368,true⟩, +⟨1,153,370,true⟩, +⟨1,153,376,true⟩, +⟨1,153,378,true⟩, +⟨1,153,420,true⟩, +⟨1,153,422,true⟩, +⟨1,153,428,true⟩, +⟨1,153,430,true⟩, +⟨1,153,436,true⟩, +⟨1,153,438,true⟩, +⟨1,153,444,true⟩, +⟨1,153,446,true⟩, +⟨1,153,450,true⟩, +⟨1,153,451,true⟩, +⟨1,153,452,true⟩, +⟨1,153,453,true⟩, +⟨1,153,454,true⟩, +⟨1,153,455,true⟩, +⟨1,153,456,true⟩, +⟨1,153,457,true⟩, +⟨1,153,459,true⟩, +⟨1,153,460,true⟩, +⟨1,153,462,true⟩, +⟨1,153,463,true⟩, +⟨1,153,480,true⟩, +⟨1,153,482,true⟩, +⟨1,153,488,true⟩, +⟨1,153,490,true⟩, +⟨1,153,496,true⟩, +⟨1,153,498,true⟩, +⟨1,153,504,true⟩, +⟨1,153,506,true⟩, +⟨1,153,516,true⟩, +⟨1,153,518,true⟩, +⟨1,153,548,true⟩, +⟨1,153,550,true⟩, +⟨1,153,688,true⟩, +⟨1,153,689,true⟩, +⟨1,153,692,true⟩, +⟨1,153,693,true⟩, +⟨1,153,704,true⟩, +⟨1,153,706,true⟩] +def chunk10 : List Event := [⟨1,153,708,true⟩, +⟨1,153,714,true⟩, +⟨1,153,718,true⟩, +⟨1,153,720,true⟩, +⟨1,153,722,true⟩, +⟨1,153,766,true⟩, +⟨1,153,796,true⟩, +⟨1,153,824,true⟩, +⟨1,153,880,true⟩, +⟨1,153,962,true⟩, +⟨1,153,969,true⟩, +⟨1,154,257,true⟩, +⟨1,154,263,true⟩, +⟨1,154,280,true⟩, +⟨1,154,286,true⟩, +⟨1,154,288,true⟩, +⟨1,154,290,true⟩, +⟨1,154,296,true⟩, +⟨1,154,298,true⟩, +⟨1,154,304,true⟩, +⟨1,154,306,true⟩, +⟨1,154,312,true⟩, +⟨1,154,314,true⟩, +⟨1,154,338,true⟩, +⟨1,154,356,true⟩, +⟨1,154,358,true⟩, +⟨1,154,364,true⟩, +⟨1,154,366,true⟩, +⟨1,154,372,true⟩, +⟨1,154,374,true⟩, +⟨1,154,380,true⟩, +⟨1,154,382,true⟩, +⟨1,154,416,true⟩, +⟨1,154,418,true⟩, +⟨1,154,424,true⟩, +⟨1,154,426,true⟩, +⟨1,154,432,true⟩, +⟨1,154,434,true⟩, +⟨1,154,440,true⟩, +⟨1,154,442,true⟩, +⟨1,154,450,true⟩, +⟨1,154,452,true⟩, +⟨1,154,456,true⟩, +⟨1,154,462,true⟩, +⟨1,154,484,true⟩, +⟨1,154,486,true⟩, +⟨1,154,492,true⟩, +⟨1,154,494,true⟩, +⟨1,154,500,true⟩, +⟨1,154,502,true⟩, +⟨1,154,508,true⟩, +⟨1,154,510,true⟩, +⟨1,154,516,true⟩, +⟨1,154,518,true⟩, +⟨1,154,548,true⟩, +⟨1,154,550,true⟩, +⟨1,154,688,true⟩, +⟨1,154,689,true⟩, +⟨1,154,692,true⟩, +⟨1,154,693,true⟩, +⟨1,154,704,true⟩, +⟨1,154,709,true⟩, +⟨1,154,710,true⟩, +⟨1,154,714,true⟩, +⟨1,154,720,true⟩, +⟨1,154,722,true⟩, +⟨1,154,766,true⟩, +⟨1,154,782,true⟩, +⟨1,154,810,true⟩, +⟨1,154,866,true⟩, +⟨1,154,936,true⟩, +⟨1,154,970,true⟩, +⟨1,155,257,true⟩, +⟨1,155,263,true⟩, +⟨1,155,280,true⟩, +⟨1,155,286,true⟩, +⟨1,155,288,true⟩, +⟨1,155,290,true⟩, +⟨1,155,296,true⟩, +⟨1,155,298,true⟩, +⟨1,155,304,true⟩, +⟨1,155,306,true⟩, +⟨1,155,312,true⟩, +⟨1,155,314,true⟩, +⟨1,155,336,true⟩, +⟨1,155,352,true⟩, +⟨1,155,354,true⟩, +⟨1,155,360,true⟩, +⟨1,155,362,true⟩, +⟨1,155,368,true⟩, +⟨1,155,370,true⟩, +⟨1,155,376,true⟩, +⟨1,155,378,true⟩, +⟨1,155,416,true⟩, +⟨1,155,418,true⟩, +⟨1,155,424,true⟩, +⟨1,155,426,true⟩, +⟨1,155,432,true⟩, +⟨1,155,434,true⟩, +⟨1,155,440,true⟩, +⟨1,155,442,true⟩, +⟨1,155,480,true⟩, +⟨1,155,482,true⟩, +⟨1,155,488,true⟩, +⟨1,155,490,true⟩, +⟨1,155,496,true⟩, +⟨1,155,498,true⟩, +⟨1,155,504,true⟩, +⟨1,155,506,true⟩, +⟨1,155,516,true⟩, +⟨1,155,518,true⟩, +⟨1,155,548,true⟩, +⟨1,155,550,true⟩, +⟨1,155,690,true⟩, +⟨1,155,691,true⟩, +⟨1,155,694,true⟩, +⟨1,155,695,true⟩, +⟨1,155,704,true⟩, +⟨1,155,706,true⟩, +⟨1,155,708,true⟩, +⟨1,155,710,true⟩, +⟨1,155,724,true⟩, +⟨1,155,726,true⟩, +⟨1,155,766,true⟩, +⟨1,155,782,true⟩, +⟨1,155,796,true⟩, +⟨1,155,810,true⟩, +⟨1,155,824,true⟩, +⟨1,155,866,true⟩, +⟨1,155,880,true⟩, +⟨1,156,257,true⟩, +⟨1,156,263,true⟩, +⟨1,156,280,true⟩, +⟨1,156,286,true⟩, +⟨1,156,288,true⟩, +⟨1,156,290,true⟩, +⟨1,156,296,true⟩, +⟨1,156,298,true⟩, +⟨1,156,308,true⟩, +⟨1,156,310,true⟩, +⟨1,156,316,true⟩, +⟨1,156,318,true⟩, +⟨1,156,351,true⟩, +⟨1,156,356,true⟩, +⟨1,156,358,true⟩, +⟨1,156,364,true⟩, +⟨1,156,366,true⟩, +⟨1,156,368,true⟩, +⟨1,156,370,true⟩, +⟨1,156,376,true⟩, +⟨1,156,378,true⟩, +⟨1,156,420,true⟩, +⟨1,156,422,true⟩, +⟨1,156,428,true⟩, +⟨1,156,430,true⟩, +⟨1,156,432,true⟩, +⟨1,156,434,true⟩, +⟨1,156,440,true⟩, +⟨1,156,442,true⟩, +⟨1,156,451,true⟩, +⟨1,156,452,true⟩, +⟨1,156,462,true⟩, +⟨1,156,463,true⟩, +⟨1,156,480,true⟩, +⟨1,156,482,true⟩, +⟨1,156,488,true⟩, +⟨1,156,490,true⟩, +⟨1,156,500,true⟩, +⟨1,156,502,true⟩, +⟨1,156,508,true⟩, +⟨1,156,510,true⟩, +⟨1,156,512,true⟩, +⟨1,156,514,true⟩, +⟨1,156,544,true⟩, +⟨1,156,546,true⟩, +⟨1,156,690,true⟩, +⟨1,156,691,true⟩, +⟨1,156,694,true⟩, +⟨1,156,695,true⟩, +⟨1,156,704,true⟩, +⟨1,156,708,true⟩, +⟨1,156,710,true⟩, +⟨1,156,714,true⟩, +⟨1,156,718,true⟩, +⟨1,156,719,true⟩, +⟨1,156,724,true⟩, +⟨1,156,726,true⟩, +⟨1,156,736,true⟩, +⟨1,156,764,true⟩, +⟨1,156,866,true⟩, +⟨1,156,880,true⟩, +⟨1,156,936,true⟩, +⟨1,156,969,true⟩, +⟨1,157,257,true⟩, +⟨1,157,263,true⟩, +⟨1,157,280,true⟩, +⟨1,157,286,true⟩, +⟨1,157,288,true⟩, +⟨1,157,290,true⟩, +⟨1,157,296,true⟩] +def chunk11 : List Event := [⟨1,157,298,true⟩, +⟨1,157,308,true⟩, +⟨1,157,310,true⟩, +⟨1,157,316,true⟩, +⟨1,157,318,true⟩, +⟨1,157,349,true⟩, +⟨1,157,352,true⟩, +⟨1,157,354,true⟩, +⟨1,157,360,true⟩, +⟨1,157,362,true⟩, +⟨1,157,372,true⟩, +⟨1,157,374,true⟩, +⟨1,157,380,true⟩, +⟨1,157,382,true⟩, +⟨1,157,420,true⟩, +⟨1,157,422,true⟩, +⟨1,157,428,true⟩, +⟨1,157,430,true⟩, +⟨1,157,432,true⟩, +⟨1,157,434,true⟩, +⟨1,157,440,true⟩, +⟨1,157,442,true⟩, +⟨1,157,484,true⟩, +⟨1,157,486,true⟩, +⟨1,157,492,true⟩, +⟨1,157,494,true⟩, +⟨1,157,496,true⟩, +⟨1,157,498,true⟩, +⟨1,157,504,true⟩, +⟨1,157,506,true⟩, +⟨1,157,512,true⟩, +⟨1,157,514,true⟩, +⟨1,157,544,true⟩, +⟨1,157,546,true⟩, +⟨1,157,688,true⟩, +⟨1,157,689,true⟩, +⟨1,157,692,true⟩, +⟨1,157,693,true⟩, +⟨1,157,704,true⟩, +⟨1,157,706,true⟩, +⟨1,157,708,true⟩, +⟨1,157,710,true⟩, +⟨1,157,720,true⟩, +⟨1,157,722,true⟩, +⟨1,157,736,true⟩, +⟨1,157,764,true⟩, +⟨1,157,796,true⟩, +⟨1,157,824,true⟩, +⟨1,157,866,true⟩, +⟨1,158,257,true⟩, +⟨1,158,263,true⟩, +⟨1,158,280,true⟩, +⟨1,158,286,true⟩, +⟨1,158,292,true⟩, +⟨1,158,294,true⟩, +⟨1,158,300,true⟩, +⟨1,158,302,true⟩, +⟨1,158,304,true⟩, +⟨1,158,306,true⟩, +⟨1,158,312,true⟩, +⟨1,158,314,true⟩, +⟨1,158,347,true⟩, +⟨1,158,356,true⟩, +⟨1,158,358,true⟩, +⟨1,158,364,true⟩, +⟨1,158,366,true⟩, +⟨1,158,368,true⟩, +⟨1,158,370,true⟩, +⟨1,158,376,true⟩, +⟨1,158,378,true⟩, +⟨1,158,416,true⟩, +⟨1,158,418,true⟩, +⟨1,158,424,true⟩, +⟨1,158,426,true⟩, +⟨1,158,436,true⟩, +⟨1,158,438,true⟩, +⟨1,158,444,true⟩, +⟨1,158,446,true⟩, +⟨1,158,480,true⟩, +⟨1,158,482,true⟩, +⟨1,158,488,true⟩, +⟨1,158,490,true⟩, +⟨1,158,500,true⟩, +⟨1,158,502,true⟩, +⟨1,158,508,true⟩, +⟨1,158,510,true⟩, +⟨1,158,512,true⟩, +⟨1,158,514,true⟩, +⟨1,158,544,true⟩, +⟨1,158,546,true⟩, +⟨1,158,688,true⟩, +⟨1,158,689,true⟩, +⟨1,158,692,true⟩, +⟨1,158,693,true⟩, +⟨1,158,704,true⟩, +⟨1,158,706,true⟩, +⟨1,158,708,true⟩, +⟨1,158,710,true⟩, +⟨1,158,720,true⟩, +⟨1,158,722,true⟩, +⟨1,158,736,true⟩, +⟨1,158,764,true⟩, +⟨1,158,782,true⟩, +⟨1,158,810,true⟩, +⟨1,158,880,true⟩, +⟨1,159,257,true⟩, +⟨1,159,263,true⟩, +⟨1,159,280,true⟩, +⟨1,159,286,true⟩, +⟨1,159,292,true⟩, +⟨1,159,294,true⟩, +⟨1,159,300,true⟩, +⟨1,159,302,true⟩, +⟨1,159,304,true⟩, +⟨1,159,306,true⟩, +⟨1,159,312,true⟩, +⟨1,159,314,true⟩, +⟨1,159,345,true⟩, +⟨1,159,352,true⟩, +⟨1,159,354,true⟩, +⟨1,159,360,true⟩, +⟨1,159,362,true⟩, +⟨1,159,372,true⟩, +⟨1,159,374,true⟩, +⟨1,159,380,true⟩, +⟨1,159,382,true⟩, +⟨1,159,416,true⟩, +⟨1,159,418,true⟩, +⟨1,159,424,true⟩, +⟨1,159,426,true⟩, +⟨1,159,436,true⟩, +⟨1,159,438,true⟩, +⟨1,159,444,true⟩, +⟨1,159,446,true⟩, +⟨1,159,452,true⟩, +⟨1,159,453,true⟩, +⟨1,159,454,true⟩, +⟨1,159,455,true⟩, +⟨1,159,457,true⟩, +⟨1,159,459,true⟩, +⟨1,159,460,true⟩, +⟨1,159,462,true⟩, +⟨1,159,484,true⟩, +⟨1,159,486,true⟩, +⟨1,159,492,true⟩, +⟨1,159,494,true⟩, +⟨1,159,496,true⟩, +⟨1,159,498,true⟩, +⟨1,159,504,true⟩, +⟨1,159,506,true⟩, +⟨1,159,512,true⟩, +⟨1,159,514,true⟩, +⟨1,159,544,true⟩, +⟨1,159,546,true⟩, +⟨1,159,690,true⟩, +⟨1,159,691,true⟩, +⟨1,159,694,true⟩, +⟨1,159,695,true⟩, +⟨1,159,704,true⟩, +⟨1,159,706,true⟩, +⟨1,159,709,true⟩, +⟨1,159,714,true⟩, +⟨1,159,719,true⟩, +⟨1,159,724,true⟩, +⟨1,159,726,true⟩, +⟨1,159,736,true⟩, +⟨1,159,764,true⟩, +⟨1,159,782,true⟩, +⟨1,159,796,true⟩, +⟨1,159,810,true⟩, +⟨1,159,824,true⟩, +⟨1,159,962,true⟩, +⟨1,159,970,true⟩, +⟨1,160,250,true⟩, +⟨1,160,260,true⟩, +⟨1,160,267,true⟩, +⟨1,160,279,true⟩, +⟨1,160,290,true⟩, +⟨1,160,294,true⟩, +⟨1,160,296,true⟩, +⟨1,160,300,true⟩, +⟨1,160,323,true⟩, +⟨1,160,327,true⟩, +⟨1,160,331,true⟩, +⟨1,160,335,true⟩, +⟨1,160,339,true⟩, +⟨1,160,343,true⟩, +⟨1,160,347,true⟩, +⟨1,160,351,true⟩, +⟨1,160,359,true⟩, +⟨1,160,373,true⟩, +⟨1,160,375,true⟩, +⟨1,160,377,true⟩, +⟨1,160,379,true⟩, +⟨1,160,386,true⟩, +⟨1,160,390,true⟩, +⟨1,160,392,true⟩, +⟨1,160,396,true⟩, +⟨1,160,404,true⟩, +⟨1,160,406,true⟩] +def chunk12 : List Event := [⟨1,160,412,true⟩, +⟨1,160,414,true⟩, +⟨1,160,419,true⟩, +⟨1,160,423,true⟩, +⟨1,160,427,true⟩, +⟨1,160,431,true⟩, +⟨1,160,451,true⟩, +⟨1,160,455,true⟩, +⟨1,160,459,true⟩, +⟨1,160,463,true⟩, +⟨1,160,467,true⟩, +⟨1,160,471,true⟩, +⟨1,160,475,true⟩, +⟨1,160,479,true⟩, +⟨1,160,500,true⟩, +⟨1,160,502,true⟩, +⟨1,160,508,true⟩, +⟨1,160,510,true⟩, +⟨1,160,564,true⟩, +⟨1,160,566,true⟩, +⟨1,160,633,true⟩, +⟨1,160,635,true⟩, +⟨1,160,653,true⟩, +⟨1,160,655,true⟩, +⟨1,160,656,true⟩, +⟨1,160,658,true⟩, +⟨1,160,660,true⟩, +⟨1,160,662,true⟩, +⟨1,160,674,true⟩, +⟨1,160,675,true⟩, +⟨1,160,678,true⟩, +⟨1,160,679,true⟩, +⟨1,160,729,true⟩, +⟨1,160,731,true⟩, +⟨1,160,780,true⟩, +⟨1,160,927,true⟩, +⟨1,161,250,true⟩, +⟨1,161,260,true⟩, +⟨1,161,267,true⟩, +⟨1,161,279,true⟩, +⟨1,161,288,true⟩, +⟨1,161,292,true⟩, +⟨1,161,298,true⟩, +⟨1,161,302,true⟩, +⟨1,161,321,true⟩, +⟨1,161,325,true⟩, +⟨1,161,329,true⟩, +⟨1,161,333,true⟩, +⟨1,161,339,true⟩, +⟨1,161,343,true⟩, +⟨1,161,347,true⟩, +⟨1,161,351,true⟩, +⟨1,161,357,true⟩, +⟨1,161,373,true⟩, +⟨1,161,375,true⟩, +⟨1,161,377,true⟩, +⟨1,161,379,true⟩, +⟨1,161,384,true⟩, +⟨1,161,388,true⟩, +⟨1,161,394,true⟩, +⟨1,161,398,true⟩, +⟨1,161,404,true⟩, +⟨1,161,406,true⟩, +⟨1,161,412,true⟩, +⟨1,161,414,true⟩, +⟨1,161,417,true⟩, +⟨1,161,421,true⟩, +⟨1,161,425,true⟩, +⟨1,161,429,true⟩, +⟨1,161,435,true⟩, +⟨1,161,436,true⟩, +⟨1,161,446,true⟩, +⟨1,161,447,true⟩, +⟨1,161,449,true⟩, +⟨1,161,453,true⟩, +⟨1,161,457,true⟩, +⟨1,161,461,true⟩, +⟨1,161,467,true⟩, +⟨1,161,471,true⟩, +⟨1,161,475,true⟩, +⟨1,161,479,true⟩, +⟨1,161,500,true⟩, +⟨1,161,502,true⟩, +⟨1,161,508,true⟩, +⟨1,161,510,true⟩, +⟨1,161,564,true⟩, +⟨1,161,566,true⟩, +⟨1,161,632,true⟩, +⟨1,161,634,true⟩, +⟨1,161,653,true⟩, +⟨1,161,655,true⟩, +⟨1,161,656,true⟩, +⟨1,161,660,true⟩, +⟨1,161,661,true⟩, +⟨1,161,662,true⟩, +⟨1,161,666,true⟩, +⟨1,161,670,true⟩, +⟨1,161,672,true⟩, +⟨1,161,673,true⟩, +⟨1,161,676,true⟩, +⟨1,161,677,true⟩, +⟨1,161,728,true⟩, +⟨1,161,730,true⟩, +⟨1,161,780,true⟩, +⟨1,161,844,true⟩, +⟨1,161,912,true⟩, +⟨1,161,926,true⟩, +⟨1,161,967,true⟩, +⟨1,161,976,true⟩, +⟨1,162,250,true⟩, +⟨1,162,260,true⟩, +⟨1,162,267,true⟩, +⟨1,162,279,true⟩, +⟨1,162,290,true⟩, +⟨1,162,294,true⟩, +⟨1,162,296,true⟩, +⟨1,162,300,true⟩, +⟨1,162,323,true⟩, +⟨1,162,327,true⟩, +⟨1,162,331,true⟩, +⟨1,162,335,true⟩, +⟨1,162,337,true⟩, +⟨1,162,341,true⟩, +⟨1,162,345,true⟩, +⟨1,162,349,true⟩, +⟨1,162,355,true⟩, +⟨1,162,369,true⟩, +⟨1,162,371,true⟩, +⟨1,162,381,true⟩, +⟨1,162,383,true⟩, +⟨1,162,384,true⟩, +⟨1,162,388,true⟩, +⟨1,162,394,true⟩, +⟨1,162,398,true⟩, +⟨1,162,404,true⟩, +⟨1,162,406,true⟩, +⟨1,162,412,true⟩, +⟨1,162,414,true⟩, +⟨1,162,419,true⟩, +⟨1,162,423,true⟩, +⟨1,162,427,true⟩, +⟨1,162,431,true⟩, +⟨1,162,434,true⟩, +⟨1,162,437,true⟩, +⟨1,162,438,true⟩, +⟨1,162,439,true⟩, +⟨1,162,440,true⟩, +⟨1,162,441,true⟩, +⟨1,162,443,true⟩, +⟨1,162,444,true⟩, +⟨1,162,451,true⟩, +⟨1,162,455,true⟩, +⟨1,162,459,true⟩, +⟨1,162,463,true⟩, +⟨1,162,465,true⟩, +⟨1,162,469,true⟩, +⟨1,162,473,true⟩, +⟨1,162,477,true⟩, +⟨1,162,496,true⟩, +⟨1,162,498,true⟩, +⟨1,162,504,true⟩, +⟨1,162,506,true⟩, +⟨1,162,564,true⟩, +⟨1,162,566,true⟩, +⟨1,162,633,true⟩, +⟨1,162,635,true⟩, +⟨1,162,652,true⟩, +⟨1,162,654,true⟩, +⟨1,162,656,true⟩, +⟨1,162,660,true⟩, +⟨1,162,661,true⟩, +⟨1,162,672,true⟩, +⟨1,162,673,true⟩, +⟨1,162,676,true⟩, +⟨1,162,677,true⟩, +⟨1,162,728,true⟩, +⟨1,162,730,true⟩, +⟨1,162,780,true⟩, +⟨1,162,858,true⟩, +⟨1,162,898,true⟩, +⟨1,162,926,true⟩, +⟨1,162,968,true⟩, +⟨1,162,975,true⟩, +⟨1,163,250,true⟩, +⟨1,163,260,true⟩, +⟨1,163,267,true⟩, +⟨1,163,279,true⟩, +⟨1,163,288,true⟩, +⟨1,163,292,true⟩, +⟨1,163,298,true⟩, +⟨1,163,302,true⟩, +⟨1,163,321,true⟩, +⟨1,163,325,true⟩, +⟨1,163,329,true⟩, +⟨1,163,333,true⟩, +⟨1,163,337,true⟩, +⟨1,163,341,true⟩, +⟨1,163,345,true⟩, +⟨1,163,349,true⟩, +⟨1,163,353,true⟩] +def chunk13 : List Event := [⟨1,163,369,true⟩, +⟨1,163,371,true⟩, +⟨1,163,381,true⟩, +⟨1,163,383,true⟩, +⟨1,163,386,true⟩, +⟨1,163,390,true⟩, +⟨1,163,392,true⟩, +⟨1,163,396,true⟩, +⟨1,163,404,true⟩, +⟨1,163,406,true⟩, +⟨1,163,412,true⟩, +⟨1,163,414,true⟩, +⟨1,163,417,true⟩, +⟨1,163,421,true⟩, +⟨1,163,425,true⟩, +⟨1,163,429,true⟩, +⟨1,163,449,true⟩, +⟨1,163,453,true⟩, +⟨1,163,457,true⟩, +⟨1,163,461,true⟩, +⟨1,163,465,true⟩, +⟨1,163,469,true⟩, +⟨1,163,473,true⟩, +⟨1,163,477,true⟩, +⟨1,163,496,true⟩, +⟨1,163,498,true⟩, +⟨1,163,504,true⟩, +⟨1,163,506,true⟩, +⟨1,163,564,true⟩, +⟨1,163,566,true⟩, +⟨1,163,632,true⟩, +⟨1,163,634,true⟩, +⟨1,163,652,true⟩, +⟨1,163,654,true⟩, +⟨1,163,656,true⟩, +⟨1,163,658,true⟩, +⟨1,163,660,true⟩, +⟨1,163,662,true⟩, +⟨1,163,674,true⟩, +⟨1,163,675,true⟩, +⟨1,163,678,true⟩, +⟨1,163,679,true⟩, +⟨1,163,729,true⟩, +⟨1,163,731,true⟩, +⟨1,163,780,true⟩, +⟨1,163,844,true⟩, +⟨1,163,858,true⟩, +⟨1,163,898,true⟩, +⟨1,163,912,true⟩, +⟨1,163,927,true⟩, +⟨1,164,250,true⟩, +⟨1,164,260,true⟩, +⟨1,164,267,true⟩, +⟨1,164,279,true⟩, +⟨1,164,288,true⟩, +⟨1,164,292,true⟩, +⟨1,164,298,true⟩, +⟨1,164,302,true⟩, +⟨1,164,323,true⟩, +⟨1,164,327,true⟩, +⟨1,164,331,true⟩, +⟨1,164,335,true⟩, +⟨1,164,339,true⟩, +⟨1,164,343,true⟩, +⟨1,164,347,true⟩, +⟨1,164,351,true⟩, +⟨1,164,366,true⟩, +⟨1,164,369,true⟩, +⟨1,164,371,true⟩, +⟨1,164,381,true⟩, +⟨1,164,383,true⟩, +⟨1,164,386,true⟩, +⟨1,164,390,true⟩, +⟨1,164,392,true⟩, +⟨1,164,396,true⟩, +⟨1,164,400,true⟩, +⟨1,164,402,true⟩, +⟨1,164,408,true⟩, +⟨1,164,410,true⟩, +⟨1,164,419,true⟩, +⟨1,164,423,true⟩, +⟨1,164,427,true⟩, +⟨1,164,431,true⟩, +⟨1,164,436,true⟩, +⟨1,164,437,true⟩, +⟨1,164,438,true⟩, +⟨1,164,439,true⟩, +⟨1,164,441,true⟩, +⟨1,164,443,true⟩, +⟨1,164,444,true⟩, +⟨1,164,446,true⟩, +⟨1,164,449,true⟩, +⟨1,164,453,true⟩, +⟨1,164,457,true⟩, +⟨1,164,461,true⟩, +⟨1,164,465,true⟩, +⟨1,164,469,true⟩, +⟨1,164,473,true⟩, +⟨1,164,477,true⟩, +⟨1,164,500,true⟩, +⟨1,164,502,true⟩, +⟨1,164,508,true⟩, +⟨1,164,510,true⟩, +⟨1,164,560,true⟩, +⟨1,164,562,true⟩, +⟨1,164,632,true⟩, +⟨1,164,634,true⟩, +⟨1,164,652,true⟩, +⟨1,164,654,true⟩, +⟨1,164,656,true⟩, +⟨1,164,658,true⟩, +⟨1,164,661,true⟩, +⟨1,164,666,true⟩, +⟨1,164,671,true⟩, +⟨1,164,674,true⟩, +⟨1,164,675,true⟩, +⟨1,164,678,true⟩, +⟨1,164,679,true⟩, +⟨1,164,729,true⟩, +⟨1,164,731,true⟩, +⟨1,164,740,true⟩, +⟨1,164,778,true⟩, +⟨1,164,844,true⟩, +⟨1,164,858,true⟩, +⟨1,164,898,true⟩, +⟨1,164,912,true⟩, +⟨1,164,927,true⟩, +⟨1,164,967,true⟩, +⟨1,164,975,true⟩, +⟨1,165,250,true⟩, +⟨1,165,260,true⟩, +⟨1,165,267,true⟩, +⟨1,165,279,true⟩, +⟨1,165,290,true⟩, +⟨1,165,294,true⟩, +⟨1,165,296,true⟩, +⟨1,165,300,true⟩, +⟨1,165,321,true⟩, +⟨1,165,325,true⟩, +⟨1,165,329,true⟩, +⟨1,165,333,true⟩, +⟨1,165,339,true⟩, +⟨1,165,343,true⟩, +⟨1,165,347,true⟩, +⟨1,165,351,true⟩, +⟨1,165,364,true⟩, +⟨1,165,369,true⟩, +⟨1,165,371,true⟩, +⟨1,165,381,true⟩, +⟨1,165,383,true⟩, +⟨1,165,384,true⟩, +⟨1,165,388,true⟩, +⟨1,165,394,true⟩, +⟨1,165,398,true⟩, +⟨1,165,400,true⟩, +⟨1,165,402,true⟩, +⟨1,165,408,true⟩, +⟨1,165,410,true⟩, +⟨1,165,417,true⟩, +⟨1,165,421,true⟩, +⟨1,165,425,true⟩, +⟨1,165,429,true⟩, +⟨1,165,451,true⟩, +⟨1,165,455,true⟩, +⟨1,165,459,true⟩, +⟨1,165,463,true⟩, +⟨1,165,465,true⟩, +⟨1,165,469,true⟩, +⟨1,165,473,true⟩, +⟨1,165,477,true⟩, +⟨1,165,500,true⟩, +⟨1,165,502,true⟩, +⟨1,165,508,true⟩, +⟨1,165,510,true⟩, +⟨1,165,560,true⟩, +⟨1,165,562,true⟩, +⟨1,165,633,true⟩, +⟨1,165,635,true⟩, +⟨1,165,652,true⟩, +⟨1,165,654,true⟩, +⟨1,165,656,true⟩, +⟨1,165,658,true⟩, +⟨1,165,660,true⟩, +⟨1,165,662,true⟩, +⟨1,165,672,true⟩, +⟨1,165,673,true⟩, +⟨1,165,676,true⟩, +⟨1,165,677,true⟩, +⟨1,165,728,true⟩, +⟨1,165,730,true⟩, +⟨1,165,740,true⟩, +⟨1,165,778,true⟩, +⟨1,165,858,true⟩, +⟨1,165,898,true⟩, +⟨1,165,926,true⟩, +⟨1,166,250,true⟩, +⟨1,166,260,true⟩, +⟨1,166,267,true⟩, +⟨1,166,279,true⟩, +⟨1,166,288,true⟩] +def chunk14 : List Event := [⟨1,166,292,true⟩, +⟨1,166,298,true⟩, +⟨1,166,302,true⟩, +⟨1,166,323,true⟩, +⟨1,166,327,true⟩, +⟨1,166,331,true⟩, +⟨1,166,335,true⟩, +⟨1,166,337,true⟩, +⟨1,166,341,true⟩, +⟨1,166,345,true⟩, +⟨1,166,349,true⟩, +⟨1,166,362,true⟩, +⟨1,166,373,true⟩, +⟨1,166,375,true⟩, +⟨1,166,377,true⟩, +⟨1,166,379,true⟩, +⟨1,166,384,true⟩, +⟨1,166,388,true⟩, +⟨1,166,394,true⟩, +⟨1,166,398,true⟩, +⟨1,166,400,true⟩, +⟨1,166,402,true⟩, +⟨1,166,408,true⟩, +⟨1,166,410,true⟩, +⟨1,166,419,true⟩, +⟨1,166,423,true⟩, +⟨1,166,427,true⟩, +⟨1,166,431,true⟩, +⟨1,166,449,true⟩, +⟨1,166,453,true⟩, +⟨1,166,457,true⟩, +⟨1,166,461,true⟩, +⟨1,166,467,true⟩, +⟨1,166,471,true⟩, +⟨1,166,475,true⟩, +⟨1,166,479,true⟩, +⟨1,166,496,true⟩, +⟨1,166,498,true⟩, +⟨1,166,504,true⟩, +⟨1,166,506,true⟩, +⟨1,166,560,true⟩, +⟨1,166,562,true⟩, +⟨1,166,632,true⟩, +⟨1,166,634,true⟩, +⟨1,166,653,true⟩, +⟨1,166,655,true⟩, +⟨1,166,656,true⟩, +⟨1,166,658,true⟩, +⟨1,166,660,true⟩, +⟨1,166,662,true⟩, +⟨1,166,672,true⟩, +⟨1,166,673,true⟩, +⟨1,166,676,true⟩, +⟨1,166,677,true⟩, +⟨1,166,728,true⟩, +⟨1,166,730,true⟩, +⟨1,166,740,true⟩, +⟨1,166,778,true⟩, +⟨1,166,844,true⟩, +⟨1,166,912,true⟩, +⟨1,166,926,true⟩, +⟨1,167,250,true⟩, +⟨1,167,260,true⟩, +⟨1,167,267,true⟩, +⟨1,167,279,true⟩, +⟨1,167,290,true⟩, +⟨1,167,294,true⟩, +⟨1,167,296,true⟩, +⟨1,167,300,true⟩, +⟨1,167,321,true⟩, +⟨1,167,325,true⟩, +⟨1,167,329,true⟩, +⟨1,167,333,true⟩, +⟨1,167,337,true⟩, +⟨1,167,341,true⟩, +⟨1,167,345,true⟩, +⟨1,167,349,true⟩, +⟨1,167,360,true⟩, +⟨1,167,373,true⟩, +⟨1,167,375,true⟩, +⟨1,167,377,true⟩, +⟨1,167,379,true⟩, +⟨1,167,386,true⟩, +⟨1,167,390,true⟩, +⟨1,167,392,true⟩, +⟨1,167,396,true⟩, +⟨1,167,400,true⟩, +⟨1,167,402,true⟩, +⟨1,167,408,true⟩, +⟨1,167,410,true⟩, +⟨1,167,417,true⟩, +⟨1,167,421,true⟩, +⟨1,167,425,true⟩, +⟨1,167,429,true⟩, +⟨1,167,434,true⟩, +⟨1,167,435,true⟩, +⟨1,167,440,true⟩, +⟨1,167,447,true⟩, +⟨1,167,451,true⟩, +⟨1,167,455,true⟩, +⟨1,167,459,true⟩, +⟨1,167,463,true⟩, +⟨1,167,467,true⟩, +⟨1,167,471,true⟩, +⟨1,167,475,true⟩, +⟨1,167,479,true⟩, +⟨1,167,496,true⟩, +⟨1,167,498,true⟩, +⟨1,167,504,true⟩, +⟨1,167,506,true⟩, +⟨1,167,560,true⟩, +⟨1,167,562,true⟩, +⟨1,167,633,true⟩, +⟨1,167,635,true⟩, +⟨1,167,653,true⟩, +⟨1,167,655,true⟩, +⟨1,167,656,true⟩, +⟨1,167,658,true⟩, +⟨1,167,661,true⟩, +⟨1,167,662,true⟩, +⟨1,167,670,true⟩, +⟨1,167,671,true⟩, +⟨1,167,674,true⟩, +⟨1,167,675,true⟩, +⟨1,167,678,true⟩, +⟨1,167,679,true⟩, +⟨1,167,729,true⟩, +⟨1,167,731,true⟩, +⟨1,167,740,true⟩, +⟨1,167,778,true⟩, +⟨1,167,927,true⟩, +⟨1,167,968,true⟩, +⟨1,167,976,true⟩, +⟨1,168,244,true⟩, +⟨1,168,265,true⟩, +⟨1,168,283,true⟩, +⟨1,168,306,true⟩, +⟨1,168,310,true⟩, +⟨1,168,312,true⟩, +⟨1,168,316,true⟩, +⟨1,168,325,true⟩, +⟨1,168,327,true⟩, +⟨1,168,329,true⟩, +⟨1,168,331,true⟩, +⟨1,168,338,true⟩, +⟨1,168,342,true⟩, +⟨1,168,344,true⟩, +⟨1,168,348,true⟩, +⟨1,168,357,true⟩, +⟨1,168,359,true⟩, +⟨1,168,361,true⟩, +⟨1,168,363,true⟩, +⟨1,168,375,true⟩, +⟨1,168,389,true⟩, +⟨1,168,391,true⟩, +⟨1,168,393,true⟩, +⟨1,168,395,true⟩, +⟨1,168,405,true⟩, +⟨1,168,407,true⟩, +⟨1,168,409,true⟩, +⟨1,168,411,true⟩, +⟨1,168,435,true⟩, +⟨1,168,439,true⟩, +⟨1,168,443,true⟩, +⟨1,168,447,true⟩, +⟨1,168,452,true⟩, +⟨1,168,454,true⟩, +⟨1,168,460,true⟩, +⟨1,168,462,true⟩, +⟨1,168,467,true⟩, +⟨1,168,471,true⟩, +⟨1,168,475,true⟩, +⟨1,168,479,true⟩, +⟨1,168,484,true⟩, +⟨1,168,486,true⟩, +⟨1,168,492,true⟩, +⟨1,168,494,true⟩, +⟨1,168,525,true⟩, +⟨1,168,527,true⟩, +⟨1,168,537,true⟩, +⟨1,168,539,true⟩, +⟨1,168,557,true⟩, +⟨1,168,559,true⟩, +⟨1,168,569,true⟩, +⟨1,168,571,true⟩, +⟨1,168,589,true⟩, +⟨1,168,591,true⟩, +⟨1,168,592,true⟩, +⟨1,168,594,true⟩, +⟨1,168,596,true⟩, +⟨1,168,598,true⟩, +⟨1,168,610,true⟩, +⟨1,168,611,true⟩, +⟨1,168,614,true⟩, +⟨1,168,615,true⟩, +⟨1,168,628,true⟩, +⟨1,168,630,true⟩, +⟨1,168,733,true⟩, +⟨1,168,735,true⟩, +⟨1,169,244,true⟩] +def chunk15 : List Event := [⟨1,169,265,true⟩, +⟨1,169,283,true⟩, +⟨1,169,304,true⟩, +⟨1,169,308,true⟩, +⟨1,169,314,true⟩, +⟨1,169,318,true⟩, +⟨1,169,321,true⟩, +⟨1,169,323,true⟩, +⟨1,169,333,true⟩, +⟨1,169,335,true⟩, +⟨1,169,338,true⟩, +⟨1,169,342,true⟩, +⟨1,169,344,true⟩, +⟨1,169,348,true⟩, +⟨1,169,357,true⟩, +⟨1,169,359,true⟩, +⟨1,169,361,true⟩, +⟨1,169,363,true⟩, +⟨1,169,372,true⟩, +⟨1,169,385,true⟩, +⟨1,169,387,true⟩, +⟨1,169,397,true⟩, +⟨1,169,399,true⟩, +⟨1,169,405,true⟩, +⟨1,169,407,true⟩, +⟨1,169,409,true⟩, +⟨1,169,411,true⟩, +⟨1,169,419,true⟩, +⟨1,169,420,true⟩, +⟨1,169,430,true⟩, +⟨1,169,431,true⟩, +⟨1,169,433,true⟩, +⟨1,169,437,true⟩, +⟨1,169,441,true⟩, +⟨1,169,445,true⟩, +⟨1,169,448,true⟩, +⟨1,169,450,true⟩, +⟨1,169,456,true⟩, +⟨1,169,458,true⟩, +⟨1,169,467,true⟩, +⟨1,169,471,true⟩, +⟨1,169,475,true⟩, +⟨1,169,479,true⟩, +⟨1,169,484,true⟩, +⟨1,169,486,true⟩, +⟨1,169,492,true⟩, +⟨1,169,494,true⟩, +⟨1,169,525,true⟩, +⟨1,169,527,true⟩, +⟨1,169,537,true⟩, +⟨1,169,539,true⟩, +⟨1,169,556,true⟩, +⟨1,169,558,true⟩, +⟨1,169,568,true⟩, +⟨1,169,570,true⟩, +⟨1,169,589,true⟩, +⟨1,169,591,true⟩, +⟨1,169,592,true⟩, +⟨1,169,596,true⟩, +⟨1,169,597,true⟩, +⟨1,169,598,true⟩, +⟨1,169,602,true⟩, +⟨1,169,606,true⟩, +⟨1,169,608,true⟩, +⟨1,169,609,true⟩, +⟨1,169,612,true⟩, +⟨1,169,613,true⟩, +⟨1,169,628,true⟩, +⟨1,169,630,true⟩, +⟨1,169,732,true⟩, +⟨1,169,734,true⟩, +⟨1,169,934,true⟩, +⟨1,169,940,true⟩, +⟨1,170,244,true⟩, +⟨1,170,265,true⟩, +⟨1,170,283,true⟩, +⟨1,170,306,true⟩, +⟨1,170,310,true⟩, +⟨1,170,312,true⟩, +⟨1,170,316,true⟩, +⟨1,170,325,true⟩, +⟨1,170,327,true⟩, +⟨1,170,329,true⟩, +⟨1,170,331,true⟩, +⟨1,170,336,true⟩, +⟨1,170,340,true⟩, +⟨1,170,346,true⟩, +⟨1,170,350,true⟩, +⟨1,170,353,true⟩, +⟨1,170,355,true⟩, +⟨1,170,365,true⟩, +⟨1,170,367,true⟩, +⟨1,170,370,true⟩, +⟨1,170,385,true⟩, +⟨1,170,387,true⟩, +⟨1,170,397,true⟩, +⟨1,170,399,true⟩, +⟨1,170,405,true⟩, +⟨1,170,407,true⟩, +⟨1,170,409,true⟩, +⟨1,170,411,true⟩, +⟨1,170,418,true⟩, +⟨1,170,421,true⟩, +⟨1,170,422,true⟩, +⟨1,170,423,true⟩, +⟨1,170,424,true⟩, +⟨1,170,425,true⟩, +⟨1,170,427,true⟩, +⟨1,170,428,true⟩, +⟨1,170,435,true⟩, +⟨1,170,439,true⟩, +⟨1,170,443,true⟩, +⟨1,170,447,true⟩, +⟨1,170,452,true⟩, +⟨1,170,454,true⟩, +⟨1,170,460,true⟩, +⟨1,170,462,true⟩, +⟨1,170,465,true⟩, +⟨1,170,469,true⟩, +⟨1,170,473,true⟩, +⟨1,170,477,true⟩, +⟨1,170,480,true⟩, +⟨1,170,482,true⟩, +⟨1,170,488,true⟩, +⟨1,170,490,true⟩, +⟨1,170,525,true⟩, +⟨1,170,527,true⟩, +⟨1,170,536,true⟩, +⟨1,170,538,true⟩, +⟨1,170,557,true⟩, +⟨1,170,559,true⟩, +⟨1,170,569,true⟩, +⟨1,170,571,true⟩, +⟨1,170,588,true⟩, +⟨1,170,590,true⟩, +⟨1,170,592,true⟩, +⟨1,170,596,true⟩, +⟨1,170,597,true⟩, +⟨1,170,608,true⟩, +⟨1,170,609,true⟩, +⟨1,170,612,true⟩, +⟨1,170,613,true⟩, +⟨1,170,628,true⟩, +⟨1,170,630,true⟩, +⟨1,170,732,true⟩, +⟨1,170,734,true⟩, +⟨1,170,935,true⟩, +⟨1,170,939,true⟩, +⟨1,171,244,true⟩, +⟨1,171,265,true⟩, +⟨1,171,283,true⟩, +⟨1,171,304,true⟩, +⟨1,171,308,true⟩, +⟨1,171,314,true⟩, +⟨1,171,318,true⟩, +⟨1,171,321,true⟩, +⟨1,171,323,true⟩, +⟨1,171,333,true⟩, +⟨1,171,335,true⟩, +⟨1,171,336,true⟩, +⟨1,171,340,true⟩, +⟨1,171,346,true⟩, +⟨1,171,350,true⟩, +⟨1,171,353,true⟩, +⟨1,171,355,true⟩, +⟨1,171,365,true⟩, +⟨1,171,367,true⟩, +⟨1,171,369,true⟩, +⟨1,171,389,true⟩, +⟨1,171,391,true⟩, +⟨1,171,393,true⟩, +⟨1,171,395,true⟩, +⟨1,171,405,true⟩, +⟨1,171,407,true⟩, +⟨1,171,409,true⟩, +⟨1,171,411,true⟩, +⟨1,171,433,true⟩, +⟨1,171,437,true⟩, +⟨1,171,441,true⟩, +⟨1,171,445,true⟩, +⟨1,171,448,true⟩, +⟨1,171,450,true⟩, +⟨1,171,456,true⟩, +⟨1,171,458,true⟩, +⟨1,171,465,true⟩, +⟨1,171,469,true⟩, +⟨1,171,473,true⟩, +⟨1,171,477,true⟩, +⟨1,171,480,true⟩, +⟨1,171,482,true⟩, +⟨1,171,488,true⟩, +⟨1,171,490,true⟩, +⟨1,171,525,true⟩, +⟨1,171,527,true⟩, +⟨1,171,536,true⟩, +⟨1,171,538,true⟩, +⟨1,171,556,true⟩, +⟨1,171,558,true⟩, +⟨1,171,568,true⟩, +⟨1,171,570,true⟩] +def chunk16 : List Event := [⟨1,171,588,true⟩, +⟨1,171,590,true⟩, +⟨1,171,592,true⟩, +⟨1,171,594,true⟩, +⟨1,171,596,true⟩, +⟨1,171,598,true⟩, +⟨1,171,610,true⟩, +⟨1,171,611,true⟩, +⟨1,171,614,true⟩, +⟨1,171,615,true⟩, +⟨1,171,628,true⟩, +⟨1,171,630,true⟩, +⟨1,171,733,true⟩, +⟨1,171,735,true⟩, +⟨1,172,244,true⟩, +⟨1,172,265,true⟩, +⟨1,172,283,true⟩, +⟨1,172,304,true⟩, +⟨1,172,308,true⟩, +⟨1,172,314,true⟩, +⟨1,172,318,true⟩, +⟨1,172,325,true⟩, +⟨1,172,327,true⟩, +⟨1,172,329,true⟩, +⟨1,172,331,true⟩, +⟨1,172,338,true⟩, +⟨1,172,342,true⟩, +⟨1,172,344,true⟩, +⟨1,172,348,true⟩, +⟨1,172,353,true⟩, +⟨1,172,355,true⟩, +⟨1,172,365,true⟩, +⟨1,172,367,true⟩, +⟨1,172,383,true⟩, +⟨1,172,389,true⟩, +⟨1,172,391,true⟩, +⟨1,172,393,true⟩, +⟨1,172,395,true⟩, +⟨1,172,401,true⟩, +⟨1,172,403,true⟩, +⟨1,172,413,true⟩, +⟨1,172,415,true⟩, +⟨1,172,418,true⟩, +⟨1,172,419,true⟩, +⟨1,172,422,true⟩, +⟨1,172,423,true⟩, +⟨1,172,424,true⟩, +⟨1,172,427,true⟩, +⟨1,172,428,true⟩, +⟨1,172,431,true⟩, +⟨1,172,435,true⟩, +⟨1,172,439,true⟩, +⟨1,172,443,true⟩, +⟨1,172,447,true⟩, +⟨1,172,448,true⟩, +⟨1,172,450,true⟩, +⟨1,172,456,true⟩, +⟨1,172,458,true⟩, +⟨1,172,465,true⟩, +⟨1,172,469,true⟩, +⟨1,172,473,true⟩, +⟨1,172,477,true⟩, +⟨1,172,484,true⟩, +⟨1,172,486,true⟩, +⟨1,172,492,true⟩, +⟨1,172,494,true⟩, +⟨1,172,524,true⟩, +⟨1,172,526,true⟩, +⟨1,172,537,true⟩, +⟨1,172,539,true⟩, +⟨1,172,557,true⟩, +⟨1,172,559,true⟩, +⟨1,172,568,true⟩, +⟨1,172,570,true⟩, +⟨1,172,588,true⟩, +⟨1,172,590,true⟩, +⟨1,172,592,true⟩, +⟨1,172,594,true⟩, +⟨1,172,597,true⟩, +⟨1,172,606,true⟩, +⟨1,172,607,true⟩, +⟨1,172,610,true⟩, +⟨1,172,611,true⟩, +⟨1,172,614,true⟩, +⟨1,172,615,true⟩, +⟨1,172,624,true⟩, +⟨1,172,626,true⟩, +⟨1,172,733,true⟩, +⟨1,172,735,true⟩, +⟨1,172,744,true⟩, +⟨1,172,834,true⟩, +⟨1,172,934,true⟩, +⟨1,172,939,true⟩, +⟨1,173,244,true⟩, +⟨1,173,265,true⟩, +⟨1,173,283,true⟩, +⟨1,173,306,true⟩, +⟨1,173,310,true⟩, +⟨1,173,312,true⟩, +⟨1,173,316,true⟩, +⟨1,173,321,true⟩, +⟨1,173,323,true⟩, +⟨1,173,333,true⟩, +⟨1,173,335,true⟩, +⟨1,173,338,true⟩, +⟨1,173,342,true⟩, +⟨1,173,344,true⟩, +⟨1,173,348,true⟩, +⟨1,173,353,true⟩, +⟨1,173,355,true⟩, +⟨1,173,365,true⟩, +⟨1,173,367,true⟩, +⟨1,173,380,true⟩, +⟨1,173,385,true⟩, +⟨1,173,387,true⟩, +⟨1,173,397,true⟩, +⟨1,173,399,true⟩, +⟨1,173,401,true⟩, +⟨1,173,403,true⟩, +⟨1,173,413,true⟩, +⟨1,173,415,true⟩, +⟨1,173,433,true⟩, +⟨1,173,437,true⟩, +⟨1,173,441,true⟩, +⟨1,173,445,true⟩, +⟨1,173,452,true⟩, +⟨1,173,454,true⟩, +⟨1,173,460,true⟩, +⟨1,173,462,true⟩, +⟨1,173,465,true⟩, +⟨1,173,469,true⟩, +⟨1,173,473,true⟩, +⟨1,173,477,true⟩, +⟨1,173,484,true⟩, +⟨1,173,486,true⟩, +⟨1,173,492,true⟩, +⟨1,173,494,true⟩, +⟨1,173,524,true⟩, +⟨1,173,526,true⟩, +⟨1,173,537,true⟩, +⟨1,173,539,true⟩, +⟨1,173,556,true⟩, +⟨1,173,558,true⟩, +⟨1,173,569,true⟩, +⟨1,173,571,true⟩, +⟨1,173,588,true⟩, +⟨1,173,590,true⟩, +⟨1,173,592,true⟩, +⟨1,173,594,true⟩, +⟨1,173,596,true⟩, +⟨1,173,598,true⟩, +⟨1,173,608,true⟩, +⟨1,173,609,true⟩, +⟨1,173,612,true⟩, +⟨1,173,613,true⟩, +⟨1,173,624,true⟩, +⟨1,173,626,true⟩, +⟨1,173,732,true⟩, +⟨1,173,734,true⟩, +⟨1,173,744,true⟩, +⟨1,173,834,true⟩, +⟨1,174,244,true⟩, +⟨1,174,265,true⟩, +⟨1,174,283,true⟩, +⟨1,174,304,true⟩, +⟨1,174,308,true⟩, +⟨1,174,314,true⟩, +⟨1,174,318,true⟩, +⟨1,174,325,true⟩, +⟨1,174,327,true⟩, +⟨1,174,329,true⟩, +⟨1,174,331,true⟩, +⟨1,174,336,true⟩, +⟨1,174,340,true⟩, +⟨1,174,346,true⟩, +⟨1,174,350,true⟩, +⟨1,174,357,true⟩, +⟨1,174,359,true⟩, +⟨1,174,361,true⟩, +⟨1,174,363,true⟩, +⟨1,174,378,true⟩, +⟨1,174,385,true⟩, +⟨1,174,387,true⟩, +⟨1,174,397,true⟩, +⟨1,174,399,true⟩, +⟨1,174,401,true⟩, +⟨1,174,403,true⟩, +⟨1,174,413,true⟩, +⟨1,174,415,true⟩, +⟨1,174,435,true⟩, +⟨1,174,439,true⟩, +⟨1,174,443,true⟩, +⟨1,174,447,true⟩, +⟨1,174,448,true⟩, +⟨1,174,450,true⟩, +⟨1,174,456,true⟩, +⟨1,174,458,true⟩, +⟨1,174,467,true⟩, +⟨1,174,471,true⟩, +⟨1,174,475,true⟩] +def chunk17 : List Event := [⟨1,174,479,true⟩, +⟨1,174,480,true⟩, +⟨1,174,482,true⟩, +⟨1,174,488,true⟩, +⟨1,174,490,true⟩, +⟨1,174,524,true⟩, +⟨1,174,526,true⟩, +⟨1,174,536,true⟩, +⟨1,174,538,true⟩, +⟨1,174,557,true⟩, +⟨1,174,559,true⟩, +⟨1,174,568,true⟩, +⟨1,174,570,true⟩, +⟨1,174,589,true⟩, +⟨1,174,591,true⟩, +⟨1,174,592,true⟩, +⟨1,174,594,true⟩, +⟨1,174,596,true⟩, +⟨1,174,598,true⟩, +⟨1,174,608,true⟩, +⟨1,174,609,true⟩, +⟨1,174,612,true⟩, +⟨1,174,613,true⟩, +⟨1,174,624,true⟩, +⟨1,174,626,true⟩, +⟨1,174,732,true⟩, +⟨1,174,734,true⟩, +⟨1,174,744,true⟩, +⟨1,174,834,true⟩, +⟨1,175,244,true⟩, +⟨1,175,265,true⟩, +⟨1,175,283,true⟩, +⟨1,175,306,true⟩, +⟨1,175,310,true⟩, +⟨1,175,312,true⟩, +⟨1,175,316,true⟩, +⟨1,175,321,true⟩, +⟨1,175,323,true⟩, +⟨1,175,333,true⟩, +⟨1,175,335,true⟩, +⟨1,175,336,true⟩, +⟨1,175,340,true⟩, +⟨1,175,346,true⟩, +⟨1,175,350,true⟩, +⟨1,175,357,true⟩, +⟨1,175,359,true⟩, +⟨1,175,361,true⟩, +⟨1,175,363,true⟩, +⟨1,175,377,true⟩, +⟨1,175,389,true⟩, +⟨1,175,391,true⟩, +⟨1,175,393,true⟩, +⟨1,175,395,true⟩, +⟨1,175,401,true⟩, +⟨1,175,403,true⟩, +⟨1,175,413,true⟩, +⟨1,175,415,true⟩, +⟨1,175,420,true⟩, +⟨1,175,421,true⟩, +⟨1,175,425,true⟩, +⟨1,175,430,true⟩, +⟨1,175,433,true⟩, +⟨1,175,437,true⟩, +⟨1,175,441,true⟩, +⟨1,175,445,true⟩, +⟨1,175,452,true⟩, +⟨1,175,454,true⟩, +⟨1,175,460,true⟩, +⟨1,175,462,true⟩, +⟨1,175,467,true⟩, +⟨1,175,471,true⟩, +⟨1,175,475,true⟩, +⟨1,175,479,true⟩, +⟨1,175,480,true⟩, +⟨1,175,482,true⟩, +⟨1,175,488,true⟩, +⟨1,175,490,true⟩, +⟨1,175,524,true⟩, +⟨1,175,526,true⟩, +⟨1,175,536,true⟩, +⟨1,175,538,true⟩, +⟨1,175,556,true⟩, +⟨1,175,558,true⟩, +⟨1,175,569,true⟩, +⟨1,175,571,true⟩, +⟨1,175,589,true⟩, +⟨1,175,591,true⟩, +⟨1,175,592,true⟩, +⟨1,175,594,true⟩, +⟨1,175,597,true⟩, +⟨1,175,598,true⟩, +⟨1,175,602,true⟩, +⟨1,175,607,true⟩, +⟨1,175,610,true⟩, +⟨1,175,611,true⟩, +⟨1,175,614,true⟩, +⟨1,175,615,true⟩, +⟨1,175,624,true⟩, +⟨1,175,626,true⟩, +⟨1,175,733,true⟩, +⟨1,175,735,true⟩, +⟨1,175,744,true⟩, +⟨1,175,834,true⟩, +⟨1,175,935,true⟩, +⟨1,175,940,true⟩, +⟨1,176,252,true⟩, +⟨1,176,258,true⟩, +⟨1,176,391,true⟩, +⟨1,176,512,true⟩, +⟨1,176,514,true⟩, +⟨1,176,516,true⟩, +⟨1,176,518,true⟩, +⟨1,176,523,true⟩, +⟨1,176,530,true⟩, +⟨1,176,531,true⟩, +⟨1,176,534,true⟩, +⟨1,176,535,true⟩, +⟨1,176,546,true⟩, +⟨1,176,547,true⟩, +⟨1,176,550,true⟩, +⟨1,176,551,true⟩, +⟨1,176,562,true⟩, +⟨1,176,563,true⟩, +⟨1,176,566,true⟩, +⟨1,176,567,true⟩, +⟨1,176,578,true⟩, +⟨1,176,579,true⟩, +⟨1,176,582,true⟩, +⟨1,176,583,true⟩, +⟨1,176,594,true⟩, +⟨1,176,595,true⟩, +⟨1,176,598,true⟩, +⟨1,176,599,true⟩, +⟨1,176,610,true⟩, +⟨1,176,611,true⟩, +⟨1,176,614,true⟩, +⟨1,176,615,true⟩, +⟨1,176,626,true⟩, +⟨1,176,627,true⟩, +⟨1,176,630,true⟩, +⟨1,176,631,true⟩, +⟨1,176,642,true⟩, +⟨1,176,643,true⟩, +⟨1,176,646,true⟩, +⟨1,176,647,true⟩, +⟨1,176,658,true⟩, +⟨1,176,659,true⟩, +⟨1,176,662,true⟩, +⟨1,176,663,true⟩, +⟨1,176,674,true⟩, +⟨1,176,675,true⟩, +⟨1,176,678,true⟩, +⟨1,176,679,true⟩, +⟨1,176,690,true⟩, +⟨1,176,691,true⟩, +⟨1,176,694,true⟩, +⟨1,176,695,true⟩, +⟨1,176,706,true⟩, +⟨1,176,707,true⟩, +⟨1,176,710,true⟩, +⟨1,176,711,true⟩, +⟨1,176,763,true⟩, +⟨1,177,252,true⟩, +⟨1,177,258,true⟩, +⟨1,177,389,true⟩, +⟨1,177,403,true⟩, +⟨1,177,404,true⟩, +⟨1,177,414,true⟩, +⟨1,177,415,true⟩, +⟨1,177,512,true⟩, +⟨1,177,516,true⟩, +⟨1,177,517,true⟩, +⟨1,177,518,true⟩, +⟨1,177,522,true⟩, +⟨1,177,526,true⟩, +⟨1,177,530,true⟩, +⟨1,177,531,true⟩, +⟨1,177,534,true⟩, +⟨1,177,535,true⟩, +⟨1,177,544,true⟩, +⟨1,177,545,true⟩, +⟨1,177,548,true⟩, +⟨1,177,549,true⟩, +⟨1,177,562,true⟩, +⟨1,177,563,true⟩, +⟨1,177,566,true⟩, +⟨1,177,567,true⟩, +⟨1,177,576,true⟩, +⟨1,177,577,true⟩, +⟨1,177,580,true⟩, +⟨1,177,581,true⟩, +⟨1,177,592,true⟩, +⟨1,177,593,true⟩, +⟨1,177,596,true⟩, +⟨1,177,597,true⟩, +⟨1,177,610,true⟩, +⟨1,177,611,true⟩, +⟨1,177,614,true⟩, +⟨1,177,615,true⟩, +⟨1,177,624,true⟩] +def chunk18 : List Event := [⟨1,177,625,true⟩, +⟨1,177,628,true⟩, +⟨1,177,629,true⟩, +⟨1,177,642,true⟩, +⟨1,177,643,true⟩, +⟨1,177,646,true⟩, +⟨1,177,647,true⟩, +⟨1,177,658,true⟩, +⟨1,177,659,true⟩, +⟨1,177,662,true⟩, +⟨1,177,663,true⟩, +⟨1,177,672,true⟩, +⟨1,177,673,true⟩, +⟨1,177,676,true⟩, +⟨1,177,677,true⟩, +⟨1,177,690,true⟩, +⟨1,177,691,true⟩, +⟨1,177,694,true⟩, +⟨1,177,695,true⟩, +⟨1,177,704,true⟩, +⟨1,177,705,true⟩, +⟨1,177,708,true⟩, +⟨1,177,709,true⟩, +⟨1,177,763,true⟩, +⟨1,177,776,true⟩, +⟨1,177,950,true⟩, +⟨1,178,252,true⟩, +⟨1,178,258,true⟩, +⟨1,178,387,true⟩, +⟨1,178,402,true⟩, +⟨1,178,405,true⟩, +⟨1,178,406,true⟩, +⟨1,178,407,true⟩, +⟨1,178,408,true⟩, +⟨1,178,409,true⟩, +⟨1,178,411,true⟩, +⟨1,178,412,true⟩, +⟨1,178,512,true⟩, +⟨1,178,516,true⟩, +⟨1,178,517,true⟩, +⟨1,178,523,true⟩, +⟨1,178,530,true⟩, +⟨1,178,531,true⟩, +⟨1,178,534,true⟩, +⟨1,178,535,true⟩, +⟨1,178,544,true⟩, +⟨1,178,545,true⟩, +⟨1,178,548,true⟩, +⟨1,178,549,true⟩, +⟨1,178,560,true⟩, +⟨1,178,561,true⟩, +⟨1,178,564,true⟩, +⟨1,178,565,true⟩, +⟨1,178,578,true⟩, +⟨1,178,579,true⟩, +⟨1,178,582,true⟩, +⟨1,178,583,true⟩, +⟨1,178,594,true⟩, +⟨1,178,595,true⟩, +⟨1,178,598,true⟩, +⟨1,178,599,true⟩, +⟨1,178,608,true⟩, +⟨1,178,609,true⟩, +⟨1,178,612,true⟩, +⟨1,178,613,true⟩, +⟨1,178,626,true⟩, +⟨1,178,627,true⟩, +⟨1,178,630,true⟩, +⟨1,178,631,true⟩, +⟨1,178,640,true⟩, +⟨1,178,641,true⟩, +⟨1,178,644,true⟩, +⟨1,178,645,true⟩, +⟨1,178,656,true⟩, +⟨1,178,657,true⟩, +⟨1,178,660,true⟩, +⟨1,178,661,true⟩, +⟨1,178,674,true⟩, +⟨1,178,675,true⟩, +⟨1,178,678,true⟩, +⟨1,178,679,true⟩, +⟨1,178,690,true⟩, +⟨1,178,691,true⟩, +⟨1,178,694,true⟩, +⟨1,178,695,true⟩, +⟨1,178,704,true⟩, +⟨1,178,705,true⟩, +⟨1,178,708,true⟩, +⟨1,178,709,true⟩, +⟨1,178,763,true⟩, +⟨1,178,776,true⟩, +⟨1,178,790,true⟩, +⟨1,178,941,true⟩, +⟨1,179,252,true⟩, +⟨1,179,258,true⟩, +⟨1,179,385,true⟩, +⟨1,179,512,true⟩, +⟨1,179,514,true⟩, +⟨1,179,516,true⟩, +⟨1,179,518,true⟩, +⟨1,179,523,true⟩, +⟨1,179,530,true⟩, +⟨1,179,531,true⟩, +⟨1,179,534,true⟩, +⟨1,179,535,true⟩, +⟨1,179,546,true⟩, +⟨1,179,547,true⟩, +⟨1,179,550,true⟩, +⟨1,179,551,true⟩, +⟨1,179,560,true⟩, +⟨1,179,561,true⟩, +⟨1,179,564,true⟩, +⟨1,179,565,true⟩, +⟨1,179,576,true⟩, +⟨1,179,577,true⟩, +⟨1,179,580,true⟩, +⟨1,179,581,true⟩, +⟨1,179,592,true⟩, +⟨1,179,593,true⟩, +⟨1,179,596,true⟩, +⟨1,179,597,true⟩, +⟨1,179,608,true⟩, +⟨1,179,609,true⟩, +⟨1,179,612,true⟩, +⟨1,179,613,true⟩, +⟨1,179,624,true⟩, +⟨1,179,625,true⟩, +⟨1,179,628,true⟩, +⟨1,179,629,true⟩, +⟨1,179,640,true⟩, +⟨1,179,641,true⟩, +⟨1,179,644,true⟩, +⟨1,179,645,true⟩, +⟨1,179,656,true⟩, +⟨1,179,657,true⟩, +⟨1,179,660,true⟩, +⟨1,179,661,true⟩, +⟨1,179,672,true⟩, +⟨1,179,673,true⟩, +⟨1,179,676,true⟩, +⟨1,179,677,true⟩, +⟨1,179,690,true⟩, +⟨1,179,691,true⟩, +⟨1,179,694,true⟩, +⟨1,179,695,true⟩, +⟨1,179,706,true⟩, +⟨1,179,707,true⟩, +⟨1,179,710,true⟩, +⟨1,179,711,true⟩, +⟨1,179,763,true⟩, +⟨1,179,790,true⟩, +⟨1,180,252,true⟩, +⟨1,180,258,true⟩, +⟨1,180,398,true⟩, +⟨1,180,403,true⟩, +⟨1,180,404,true⟩, +⟨1,180,414,true⟩, +⟨1,180,415,true⟩, +⟨1,180,512,true⟩, +⟨1,180,516,true⟩, +⟨1,180,518,true⟩, +⟨1,180,522,true⟩, +⟨1,180,523,true⟩, +⟨1,180,526,true⟩, +⟨1,180,527,true⟩, +⟨1,180,528,true⟩, +⟨1,180,529,true⟩, +⟨1,180,532,true⟩, +⟨1,180,533,true⟩, +⟨1,180,546,true⟩, +⟨1,180,547,true⟩, +⟨1,180,550,true⟩, +⟨1,180,551,true⟩, +⟨1,180,562,true⟩, +⟨1,180,563,true⟩, +⟨1,180,566,true⟩, +⟨1,180,567,true⟩, +⟨1,180,576,true⟩, +⟨1,180,577,true⟩, +⟨1,180,580,true⟩, +⟨1,180,581,true⟩, +⟨1,180,594,true⟩, +⟨1,180,595,true⟩, +⟨1,180,598,true⟩, +⟨1,180,599,true⟩, +⟨1,180,608,true⟩, +⟨1,180,609,true⟩, +⟨1,180,612,true⟩, +⟨1,180,613,true⟩, +⟨1,180,626,true⟩, +⟨1,180,627,true⟩, +⟨1,180,630,true⟩, +⟨1,180,631,true⟩, +⟨1,180,640,true⟩, +⟨1,180,641,true⟩, +⟨1,180,644,true⟩, +⟨1,180,645,true⟩, +⟨1,180,658,true⟩, +⟨1,180,659,true⟩, +⟨1,180,662,true⟩] +def chunk19 : List Event := [⟨1,180,663,true⟩, +⟨1,180,672,true⟩, +⟨1,180,673,true⟩, +⟨1,180,676,true⟩, +⟨1,180,677,true⟩, +⟨1,180,688,true⟩, +⟨1,180,689,true⟩, +⟨1,180,692,true⟩, +⟨1,180,693,true⟩, +⟨1,180,706,true⟩, +⟨1,180,707,true⟩, +⟨1,180,710,true⟩, +⟨1,180,711,true⟩, +⟨1,180,762,true⟩, +⟨1,180,941,true⟩, +⟨1,181,252,true⟩, +⟨1,181,258,true⟩, +⟨1,181,396,true⟩, +⟨1,181,512,true⟩, +⟨1,181,514,true⟩, +⟨1,181,516,true⟩, +⟨1,181,518,true⟩, +⟨1,181,523,true⟩, +⟨1,181,528,true⟩, +⟨1,181,529,true⟩, +⟨1,181,532,true⟩, +⟨1,181,533,true⟩, +⟨1,181,544,true⟩, +⟨1,181,545,true⟩, +⟨1,181,548,true⟩, +⟨1,181,549,true⟩, +⟨1,181,562,true⟩, +⟨1,181,563,true⟩, +⟨1,181,566,true⟩, +⟨1,181,567,true⟩, +⟨1,181,578,true⟩, +⟨1,181,579,true⟩, +⟨1,181,582,true⟩, +⟨1,181,583,true⟩, +⟨1,181,592,true⟩, +⟨1,181,593,true⟩, +⟨1,181,596,true⟩, +⟨1,181,597,true⟩, +⟨1,181,608,true⟩, +⟨1,181,609,true⟩, +⟨1,181,612,true⟩, +⟨1,181,613,true⟩, +⟨1,181,624,true⟩, +⟨1,181,625,true⟩, +⟨1,181,628,true⟩, +⟨1,181,629,true⟩, +⟨1,181,640,true⟩, +⟨1,181,641,true⟩, +⟨1,181,644,true⟩, +⟨1,181,645,true⟩, +⟨1,181,658,true⟩, +⟨1,181,659,true⟩, +⟨1,181,662,true⟩, +⟨1,181,663,true⟩, +⟨1,181,674,true⟩, +⟨1,181,675,true⟩, +⟨1,181,678,true⟩, +⟨1,181,679,true⟩, +⟨1,181,688,true⟩, +⟨1,181,689,true⟩, +⟨1,181,692,true⟩, +⟨1,181,693,true⟩, +⟨1,181,704,true⟩, +⟨1,181,705,true⟩, +⟨1,181,708,true⟩, +⟨1,181,709,true⟩, +⟨1,181,762,true⟩, +⟨1,181,776,true⟩, +⟨1,182,252,true⟩, +⟨1,182,258,true⟩, +⟨1,182,394,true⟩, +⟨1,182,512,true⟩, +⟨1,182,514,true⟩, +⟨1,182,516,true⟩, +⟨1,182,518,true⟩, +⟨1,182,523,true⟩, +⟨1,182,528,true⟩, +⟨1,182,529,true⟩, +⟨1,182,532,true⟩, +⟨1,182,533,true⟩, +⟨1,182,544,true⟩, +⟨1,182,545,true⟩, +⟨1,182,548,true⟩, +⟨1,182,549,true⟩, +⟨1,182,560,true⟩, +⟨1,182,561,true⟩, +⟨1,182,564,true⟩, +⟨1,182,565,true⟩, +⟨1,182,576,true⟩, +⟨1,182,577,true⟩, +⟨1,182,580,true⟩, +⟨1,182,581,true⟩, +⟨1,182,594,true⟩, +⟨1,182,595,true⟩, +⟨1,182,598,true⟩, +⟨1,182,599,true⟩, +⟨1,182,610,true⟩, +⟨1,182,611,true⟩, +⟨1,182,614,true⟩, +⟨1,182,615,true⟩, +⟨1,182,626,true⟩, +⟨1,182,627,true⟩, +⟨1,182,630,true⟩, +⟨1,182,631,true⟩, +⟨1,182,642,true⟩, +⟨1,182,643,true⟩, +⟨1,182,646,true⟩, +⟨1,182,647,true⟩, +⟨1,182,656,true⟩, +⟨1,182,657,true⟩, +⟨1,182,660,true⟩, +⟨1,182,661,true⟩, +⟨1,182,672,true⟩, +⟨1,182,673,true⟩, +⟨1,182,676,true⟩, +⟨1,182,677,true⟩, +⟨1,182,688,true⟩, +⟨1,182,689,true⟩, +⟨1,182,692,true⟩, +⟨1,182,693,true⟩, +⟨1,182,704,true⟩, +⟨1,182,705,true⟩, +⟨1,182,708,true⟩, +⟨1,182,709,true⟩, +⟨1,182,762,true⟩, +⟨1,182,776,true⟩, +⟨1,182,790,true⟩, +⟨1,183,252,true⟩, +⟨1,183,258,true⟩, +⟨1,183,392,true⟩, +⟨1,183,402,true⟩, +⟨1,183,405,true⟩, +⟨1,183,406,true⟩, +⟨1,183,407,true⟩, +⟨1,183,408,true⟩, +⟨1,183,409,true⟩, +⟨1,183,411,true⟩, +⟨1,183,412,true⟩, +⟨1,183,512,true⟩, +⟨1,183,516,true⟩, +⟨1,183,527,true⟩, +⟨1,183,528,true⟩, +⟨1,183,529,true⟩, +⟨1,183,532,true⟩, +⟨1,183,533,true⟩, +⟨1,183,546,true⟩, +⟨1,183,547,true⟩, +⟨1,183,550,true⟩, +⟨1,183,551,true⟩, +⟨1,183,560,true⟩, +⟨1,183,561,true⟩, +⟨1,183,564,true⟩, +⟨1,183,565,true⟩, +⟨1,183,578,true⟩, +⟨1,183,579,true⟩, +⟨1,183,582,true⟩, +⟨1,183,583,true⟩, +⟨1,183,592,true⟩, +⟨1,183,593,true⟩, +⟨1,183,596,true⟩, +⟨1,183,597,true⟩, +⟨1,183,610,true⟩, +⟨1,183,611,true⟩, +⟨1,183,614,true⟩, +⟨1,183,615,true⟩, +⟨1,183,624,true⟩, +⟨1,183,625,true⟩, +⟨1,183,628,true⟩, +⟨1,183,629,true⟩, +⟨1,183,642,true⟩, +⟨1,183,643,true⟩, +⟨1,183,646,true⟩, +⟨1,183,647,true⟩, +⟨1,183,656,true⟩, +⟨1,183,657,true⟩, +⟨1,183,660,true⟩, +⟨1,183,661,true⟩, +⟨1,183,674,true⟩, +⟨1,183,675,true⟩, +⟨1,183,678,true⟩, +⟨1,183,679,true⟩, +⟨1,183,688,true⟩, +⟨1,183,689,true⟩, +⟨1,183,692,true⟩, +⟨1,183,693,true⟩, +⟨1,183,706,true⟩, +⟨1,183,707,true⟩, +⟨1,183,710,true⟩, +⟨1,183,711,true⟩, +⟨1,183,762,true⟩, +⟨1,183,790,true⟩, +⟨1,183,950,true⟩, +⟨1,184,269,true⟩, +⟨1,184,275,true⟩, +⟨1,184,281,true⟩] +def chunk20 : List Event := [⟨1,184,287,true⟩, +⟨1,184,407,true⟩, +⟨1,184,532,true⟩, +⟨1,184,534,true⟩, +⟨1,184,548,true⟩, +⟨1,184,550,true⟩, +⟨1,184,564,true⟩, +⟨1,184,566,true⟩, +⟨1,184,580,true⟩, +⟨1,184,582,true⟩, +⟨1,184,596,true⟩, +⟨1,184,598,true⟩, +⟨1,184,612,true⟩, +⟨1,184,614,true⟩, +⟨1,184,628,true⟩, +⟨1,184,630,true⟩, +⟨1,184,644,true⟩, +⟨1,184,646,true⟩, +⟨1,184,660,true⟩, +⟨1,184,662,true⟩, +⟨1,184,676,true⟩, +⟨1,184,678,true⟩, +⟨1,184,692,true⟩, +⟨1,184,694,true⟩, +⟨1,184,708,true⟩, +⟨1,184,710,true⟩, +⟨1,184,720,true⟩, +⟨1,184,722,true⟩, +⟨1,184,724,true⟩, +⟨1,184,726,true⟩, +⟨1,184,907,true⟩, +⟨1,185,269,true⟩, +⟨1,185,275,true⟩, +⟨1,185,281,true⟩, +⟨1,185,287,true⟩, +⟨1,185,386,true⟩, +⟨1,185,388,true⟩, +⟨1,185,392,true⟩, +⟨1,185,398,true⟩, +⟨1,185,405,true⟩, +⟨1,185,532,true⟩, +⟨1,185,534,true⟩, +⟨1,185,548,true⟩, +⟨1,185,550,true⟩, +⟨1,185,564,true⟩, +⟨1,185,566,true⟩, +⟨1,185,580,true⟩, +⟨1,185,582,true⟩, +⟨1,185,592,true⟩, +⟨1,185,594,true⟩, +⟨1,185,608,true⟩, +⟨1,185,610,true⟩, +⟨1,185,628,true⟩, +⟨1,185,630,true⟩, +⟨1,185,644,true⟩, +⟨1,185,646,true⟩, +⟨1,185,656,true⟩, +⟨1,185,658,true⟩, +⟨1,185,672,true⟩, +⟨1,185,674,true⟩, +⟨1,185,688,true⟩, +⟨1,185,690,true⟩, +⟨1,185,704,true⟩, +⟨1,185,706,true⟩, +⟨1,185,720,true⟩, +⟨1,185,725,true⟩, +⟨1,185,726,true⟩, +⟨1,185,730,true⟩, +⟨1,185,735,true⟩, +⟨1,185,807,true⟩, +⟨1,185,821,true⟩, +⟨1,185,905,true⟩, +⟨1,185,960,true⟩, +⟨1,185,977,true⟩, +⟨1,186,269,true⟩, +⟨1,186,275,true⟩, +⟨1,186,281,true⟩, +⟨1,186,287,true⟩, +⟨1,186,387,true⟩, +⟨1,186,389,true⟩, +⟨1,186,393,true⟩, +⟨1,186,399,true⟩, +⟨1,186,403,true⟩, +⟨1,186,532,true⟩, +⟨1,186,534,true⟩, +⟨1,186,548,true⟩, +⟨1,186,550,true⟩, +⟨1,186,560,true⟩, +⟨1,186,562,true⟩, +⟨1,186,576,true⟩, +⟨1,186,578,true⟩, +⟨1,186,596,true⟩, +⟨1,186,598,true⟩, +⟨1,186,612,true⟩, +⟨1,186,614,true⟩, +⟨1,186,624,true⟩, +⟨1,186,626,true⟩, +⟨1,186,640,true⟩, +⟨1,186,642,true⟩, +⟨1,186,660,true⟩, +⟨1,186,662,true⟩, +⟨1,186,676,true⟩, +⟨1,186,678,true⟩, +⟨1,186,688,true⟩, +⟨1,186,690,true⟩, +⟨1,186,704,true⟩, +⟨1,186,706,true⟩, +⟨1,186,720,true⟩, +⟨1,186,726,true⟩, +⟨1,186,734,true⟩, +⟨1,186,735,true⟩, +⟨1,186,779,true⟩, +⟨1,186,793,true⟩, +⟨1,186,835,true⟩, +⟨1,186,849,true⟩, +⟨1,186,905,true⟩, +⟨1,186,959,true⟩, +⟨1,187,269,true⟩, +⟨1,187,275,true⟩, +⟨1,187,281,true⟩, +⟨1,187,287,true⟩, +⟨1,187,401,true⟩, +⟨1,187,532,true⟩, +⟨1,187,534,true⟩, +⟨1,187,548,true⟩, +⟨1,187,550,true⟩, +⟨1,187,560,true⟩, +⟨1,187,562,true⟩, +⟨1,187,576,true⟩, +⟨1,187,578,true⟩, +⟨1,187,592,true⟩, +⟨1,187,594,true⟩, +⟨1,187,608,true⟩, +⟨1,187,610,true⟩, +⟨1,187,624,true⟩, +⟨1,187,626,true⟩, +⟨1,187,640,true⟩, +⟨1,187,642,true⟩, +⟨1,187,656,true⟩, +⟨1,187,658,true⟩, +⟨1,187,672,true⟩, +⟨1,187,674,true⟩, +⟨1,187,692,true⟩, +⟨1,187,694,true⟩, +⟨1,187,708,true⟩, +⟨1,187,710,true⟩, +⟨1,187,720,true⟩, +⟨1,187,722,true⟩, +⟨1,187,724,true⟩, +⟨1,187,726,true⟩, +⟨1,187,779,true⟩, +⟨1,187,793,true⟩, +⟨1,187,807,true⟩, +⟨1,187,821,true⟩, +⟨1,187,835,true⟩, +⟨1,187,849,true⟩, +⟨1,187,907,true⟩, +⟨1,188,269,true⟩, +⟨1,188,275,true⟩, +⟨1,188,281,true⟩, +⟨1,188,287,true⟩, +⟨1,188,386,true⟩, +⟨1,188,387,true⟩, +⟨1,188,392,true⟩, +⟨1,188,399,true⟩, +⟨1,188,414,true⟩, +⟨1,188,528,true⟩, +⟨1,188,530,true⟩, +⟨1,188,544,true⟩, +⟨1,188,546,true⟩, +⟨1,188,564,true⟩, +⟨1,188,566,true⟩, +⟨1,188,580,true⟩, +⟨1,188,582,true⟩, +⟨1,188,596,true⟩, +⟨1,188,598,true⟩, +⟨1,188,612,true⟩, +⟨1,188,614,true⟩, +⟨1,188,624,true⟩, +⟨1,188,626,true⟩, +⟨1,188,640,true⟩, +⟨1,188,642,true⟩, +⟨1,188,656,true⟩, +⟨1,188,658,true⟩, +⟨1,188,672,true⟩, +⟨1,188,674,true⟩, +⟨1,188,692,true⟩, +⟨1,188,694,true⟩, +⟨1,188,708,true⟩, +⟨1,188,710,true⟩, +⟨1,188,720,true⟩, +⟨1,188,722,true⟩, +⟨1,188,725,true⟩, +⟨1,188,726,true⟩, +⟨1,188,731,true⟩, +⟨1,188,734,true⟩, +⟨1,188,765,true⟩, +⟨1,188,835,true⟩, +⟨1,188,849,true⟩, +⟨1,188,907,true⟩] +def chunk21 : List Event := [⟨1,188,959,true⟩, +⟨1,188,977,true⟩, +⟨1,189,269,true⟩, +⟨1,189,275,true⟩, +⟨1,189,281,true⟩, +⟨1,189,287,true⟩, +⟨1,189,412,true⟩, +⟨1,189,528,true⟩, +⟨1,189,530,true⟩, +⟨1,189,544,true⟩, +⟨1,189,546,true⟩, +⟨1,189,564,true⟩, +⟨1,189,566,true⟩, +⟨1,189,580,true⟩, +⟨1,189,582,true⟩, +⟨1,189,592,true⟩, +⟨1,189,594,true⟩, +⟨1,189,608,true⟩, +⟨1,189,610,true⟩, +⟨1,189,624,true⟩, +⟨1,189,626,true⟩, +⟨1,189,640,true⟩, +⟨1,189,642,true⟩, +⟨1,189,660,true⟩, +⟨1,189,662,true⟩, +⟨1,189,676,true⟩, +⟨1,189,678,true⟩, +⟨1,189,688,true⟩, +⟨1,189,690,true⟩, +⟨1,189,704,true⟩, +⟨1,189,706,true⟩, +⟨1,189,720,true⟩, +⟨1,189,722,true⟩, +⟨1,189,724,true⟩, +⟨1,189,726,true⟩, +⟨1,189,765,true⟩, +⟨1,189,807,true⟩, +⟨1,189,821,true⟩, +⟨1,189,835,true⟩, +⟨1,189,849,true⟩, +⟨1,189,905,true⟩, +⟨1,190,269,true⟩, +⟨1,190,275,true⟩, +⟨1,190,281,true⟩, +⟨1,190,287,true⟩, +⟨1,190,410,true⟩, +⟨1,190,528,true⟩, +⟨1,190,530,true⟩, +⟨1,190,544,true⟩, +⟨1,190,546,true⟩, +⟨1,190,560,true⟩, +⟨1,190,562,true⟩, +⟨1,190,576,true⟩, +⟨1,190,578,true⟩, +⟨1,190,596,true⟩, +⟨1,190,598,true⟩, +⟨1,190,612,true⟩, +⟨1,190,614,true⟩, +⟨1,190,628,true⟩, +⟨1,190,630,true⟩, +⟨1,190,644,true⟩, +⟨1,190,646,true⟩, +⟨1,190,656,true⟩, +⟨1,190,658,true⟩, +⟨1,190,672,true⟩, +⟨1,190,674,true⟩, +⟨1,190,688,true⟩, +⟨1,190,690,true⟩, +⟨1,190,704,true⟩, +⟨1,190,706,true⟩, +⟨1,190,720,true⟩, +⟨1,190,722,true⟩, +⟨1,190,724,true⟩, +⟨1,190,726,true⟩, +⟨1,190,765,true⟩, +⟨1,190,779,true⟩, +⟨1,190,793,true⟩, +⟨1,190,905,true⟩, +⟨1,191,269,true⟩, +⟨1,191,275,true⟩, +⟨1,191,281,true⟩, +⟨1,191,287,true⟩, +⟨1,191,388,true⟩, +⟨1,191,389,true⟩, +⟨1,191,393,true⟩, +⟨1,191,398,true⟩, +⟨1,191,408,true⟩, +⟨1,191,528,true⟩, +⟨1,191,530,true⟩, +⟨1,191,544,true⟩, +⟨1,191,546,true⟩, +⟨1,191,560,true⟩, +⟨1,191,562,true⟩, +⟨1,191,576,true⟩, +⟨1,191,578,true⟩, +⟨1,191,592,true⟩, +⟨1,191,594,true⟩, +⟨1,191,608,true⟩, +⟨1,191,610,true⟩, +⟨1,191,628,true⟩, +⟨1,191,630,true⟩, +⟨1,191,644,true⟩, +⟨1,191,646,true⟩, +⟨1,191,660,true⟩, +⟨1,191,662,true⟩, +⟨1,191,676,true⟩, +⟨1,191,678,true⟩, +⟨1,191,692,true⟩, +⟨1,191,694,true⟩, +⟨1,191,708,true⟩, +⟨1,191,710,true⟩, +⟨1,191,720,true⟩, +⟨1,191,722,true⟩, +⟨1,191,726,true⟩, +⟨1,191,730,true⟩, +⟨1,191,731,true⟩, +⟨1,191,765,true⟩, +⟨1,191,779,true⟩, +⟨1,191,793,true⟩, +⟨1,191,807,true⟩, +⟨1,191,821,true⟩, +⟨1,191,907,true⟩, +⟨1,191,960,true⟩, +⟨1,192,249,true⟩, +⟨1,192,255,true⟩, +⟨1,192,272,true⟩, +⟨1,192,278,true⟩, +⟨1,192,308,true⟩, +⟨1,192,310,true⟩, +⟨1,192,316,true⟩, +⟨1,192,318,true⟩, +⟨1,192,323,true⟩, +⟨1,192,327,true⟩, +⟨1,192,331,true⟩, +⟨1,192,335,true⟩, +⟨1,192,340,true⟩, +⟨1,192,342,true⟩, +⟨1,192,348,true⟩, +⟨1,192,350,true⟩, +⟨1,192,355,true⟩, +⟨1,192,359,true⟩, +⟨1,192,363,true⟩, +⟨1,192,367,true⟩, +⟨1,192,387,true⟩, +⟨1,192,391,true⟩, +⟨1,192,395,true⟩, +⟨1,192,399,true⟩, +⟨1,192,403,true⟩, +⟨1,192,407,true⟩, +⟨1,192,411,true⟩, +⟨1,192,415,true⟩, +⟨1,192,423,true⟩, +⟨1,192,437,true⟩, +⟨1,192,439,true⟩, +⟨1,192,441,true⟩, +⟨1,192,443,true⟩, +⟨1,192,450,true⟩, +⟨1,192,454,true⟩, +⟨1,192,456,true⟩, +⟨1,192,460,true⟩, +⟨1,192,469,true⟩, +⟨1,192,471,true⟩, +⟨1,192,473,true⟩, +⟨1,192,475,true⟩, +⟨1,192,482,true⟩, +⟨1,192,486,true⟩, +⟨1,192,488,true⟩, +⟨1,192,492,true⟩, +⟨1,192,612,true⟩, +⟨1,192,614,true⟩, +⟨1,192,626,true⟩, +⟨1,192,627,true⟩, +⟨1,192,630,true⟩, +⟨1,192,631,true⟩, +⟨1,192,640,true⟩, +⟨1,192,642,true⟩, +⟨1,192,644,true⟩, +⟨1,192,646,true⟩, +⟨1,192,669,true⟩, +⟨1,192,671,true⟩, +⟨1,192,681,true⟩, +⟨1,192,683,true⟩, +⟨1,192,701,true⟩, +⟨1,192,703,true⟩, +⟨1,192,713,true⟩, +⟨1,192,715,true⟩, +⟨1,192,915,true⟩, +⟨1,193,249,true⟩, +⟨1,193,255,true⟩, +⟨1,193,272,true⟩, +⟨1,193,278,true⟩, +⟨1,193,308,true⟩, +⟨1,193,310,true⟩, +⟨1,193,316,true⟩, +⟨1,193,318,true⟩, +⟨1,193,321,true⟩, +⟨1,193,325,true⟩, +⟨1,193,329,true⟩, +⟨1,193,333,true⟩, +⟨1,193,340,true⟩] +def chunk22 : List Event := [⟨1,193,342,true⟩, +⟨1,193,348,true⟩, +⟨1,193,350,true⟩, +⟨1,193,353,true⟩, +⟨1,193,357,true⟩, +⟨1,193,361,true⟩, +⟨1,193,365,true⟩, +⟨1,193,371,true⟩, +⟨1,193,372,true⟩, +⟨1,193,382,true⟩, +⟨1,193,383,true⟩, +⟨1,193,385,true⟩, +⟨1,193,389,true⟩, +⟨1,193,393,true⟩, +⟨1,193,397,true⟩, +⟨1,193,403,true⟩, +⟨1,193,407,true⟩, +⟨1,193,411,true⟩, +⟨1,193,415,true⟩, +⟨1,193,420,true⟩, +⟨1,193,437,true⟩, +⟨1,193,439,true⟩, +⟨1,193,441,true⟩, +⟨1,193,443,true⟩, +⟨1,193,448,true⟩, +⟨1,193,452,true⟩, +⟨1,193,458,true⟩, +⟨1,193,462,true⟩, +⟨1,193,469,true⟩, +⟨1,193,471,true⟩, +⟨1,193,473,true⟩, +⟨1,193,475,true⟩, +⟨1,193,480,true⟩, +⟨1,193,484,true⟩, +⟨1,193,490,true⟩, +⟨1,193,494,true⟩, +⟨1,193,612,true⟩, +⟨1,193,614,true⟩, +⟨1,193,624,true⟩, +⟨1,193,625,true⟩, +⟨1,193,628,true⟩, +⟨1,193,629,true⟩, +⟨1,193,640,true⟩, +⟨1,193,644,true⟩, +⟨1,193,645,true⟩, +⟨1,193,646,true⟩, +⟨1,193,650,true⟩, +⟨1,193,654,true⟩, +⟨1,193,669,true⟩, +⟨1,193,671,true⟩, +⟨1,193,680,true⟩, +⟨1,193,682,true⟩, +⟨1,193,701,true⟩, +⟨1,193,703,true⟩, +⟨1,193,712,true⟩, +⟨1,193,714,true⟩, +⟨1,193,770,true⟩, +⟨1,193,846,true⟩, +⟨1,193,914,true⟩, +⟨1,193,928,true⟩, +⟨1,193,980,true⟩, +⟨1,193,983,true⟩, +⟨1,194,249,true⟩, +⟨1,194,255,true⟩, +⟨1,194,272,true⟩, +⟨1,194,278,true⟩, +⟨1,194,304,true⟩, +⟨1,194,306,true⟩, +⟨1,194,312,true⟩, +⟨1,194,314,true⟩, +⟨1,194,323,true⟩, +⟨1,194,327,true⟩, +⟨1,194,331,true⟩, +⟨1,194,335,true⟩, +⟨1,194,336,true⟩, +⟨1,194,338,true⟩, +⟨1,194,344,true⟩, +⟨1,194,346,true⟩, +⟨1,194,355,true⟩, +⟨1,194,359,true⟩, +⟨1,194,363,true⟩, +⟨1,194,367,true⟩, +⟨1,194,370,true⟩, +⟨1,194,373,true⟩, +⟨1,194,374,true⟩, +⟨1,194,375,true⟩, +⟨1,194,376,true⟩, +⟨1,194,377,true⟩, +⟨1,194,379,true⟩, +⟨1,194,380,true⟩, +⟨1,194,385,true⟩, +⟨1,194,389,true⟩, +⟨1,194,393,true⟩, +⟨1,194,397,true⟩, +⟨1,194,403,true⟩, +⟨1,194,407,true⟩, +⟨1,194,411,true⟩, +⟨1,194,415,true⟩, +⟨1,194,418,true⟩, +⟨1,194,433,true⟩, +⟨1,194,435,true⟩, +⟨1,194,445,true⟩, +⟨1,194,447,true⟩, +⟨1,194,450,true⟩, +⟨1,194,454,true⟩, +⟨1,194,456,true⟩, +⟨1,194,460,true⟩, +⟨1,194,465,true⟩, +⟨1,194,467,true⟩, +⟨1,194,477,true⟩, +⟨1,194,479,true⟩, +⟨1,194,482,true⟩, +⟨1,194,486,true⟩, +⟨1,194,488,true⟩, +⟨1,194,492,true⟩, +⟨1,194,612,true⟩, +⟨1,194,614,true⟩, +⟨1,194,624,true⟩, +⟨1,194,625,true⟩, +⟨1,194,628,true⟩, +⟨1,194,629,true⟩, +⟨1,194,640,true⟩, +⟨1,194,644,true⟩, +⟨1,194,645,true⟩, +⟨1,194,668,true⟩, +⟨1,194,670,true⟩, +⟨1,194,681,true⟩, +⟨1,194,683,true⟩, +⟨1,194,700,true⟩, +⟨1,194,702,true⟩, +⟨1,194,713,true⟩, +⟨1,194,715,true⟩, +⟨1,194,846,true⟩, +⟨1,194,872,true⟩, +⟨1,194,900,true⟩, +⟨1,194,915,true⟩, +⟨1,194,928,true⟩, +⟨1,194,979,true⟩, +⟨1,194,984,true⟩, +⟨1,195,249,true⟩, +⟨1,195,255,true⟩, +⟨1,195,272,true⟩, +⟨1,195,278,true⟩, +⟨1,195,304,true⟩, +⟨1,195,306,true⟩, +⟨1,195,312,true⟩, +⟨1,195,314,true⟩, +⟨1,195,321,true⟩, +⟨1,195,325,true⟩, +⟨1,195,329,true⟩, +⟨1,195,333,true⟩, +⟨1,195,336,true⟩, +⟨1,195,338,true⟩, +⟨1,195,344,true⟩, +⟨1,195,346,true⟩, +⟨1,195,353,true⟩, +⟨1,195,357,true⟩, +⟨1,195,361,true⟩, +⟨1,195,365,true⟩, +⟨1,195,387,true⟩, +⟨1,195,391,true⟩, +⟨1,195,395,true⟩, +⟨1,195,399,true⟩, +⟨1,195,403,true⟩, +⟨1,195,407,true⟩, +⟨1,195,411,true⟩, +⟨1,195,415,true⟩, +⟨1,195,417,true⟩, +⟨1,195,433,true⟩, +⟨1,195,435,true⟩, +⟨1,195,445,true⟩, +⟨1,195,447,true⟩, +⟨1,195,448,true⟩, +⟨1,195,452,true⟩, +⟨1,195,458,true⟩, +⟨1,195,462,true⟩, +⟨1,195,465,true⟩, +⟨1,195,467,true⟩, +⟨1,195,477,true⟩, +⟨1,195,479,true⟩, +⟨1,195,480,true⟩, +⟨1,195,484,true⟩, +⟨1,195,490,true⟩, +⟨1,195,494,true⟩, +⟨1,195,612,true⟩, +⟨1,195,614,true⟩, +⟨1,195,626,true⟩, +⟨1,195,627,true⟩, +⟨1,195,630,true⟩, +⟨1,195,631,true⟩, +⟨1,195,640,true⟩, +⟨1,195,642,true⟩, +⟨1,195,644,true⟩, +⟨1,195,646,true⟩, +⟨1,195,668,true⟩, +⟨1,195,670,true⟩, +⟨1,195,680,true⟩, +⟨1,195,682,true⟩, +⟨1,195,700,true⟩, +⟨1,195,702,true⟩] +def chunk23 : List Event := [⟨1,195,712,true⟩, +⟨1,195,714,true⟩, +⟨1,195,770,true⟩, +⟨1,195,872,true⟩, +⟨1,195,900,true⟩, +⟨1,195,914,true⟩, +⟨1,196,249,true⟩, +⟨1,196,255,true⟩, +⟨1,196,272,true⟩, +⟨1,196,278,true⟩, +⟨1,196,308,true⟩, +⟨1,196,310,true⟩, +⟨1,196,316,true⟩, +⟨1,196,318,true⟩, +⟨1,196,323,true⟩, +⟨1,196,327,true⟩, +⟨1,196,331,true⟩, +⟨1,196,335,true⟩, +⟨1,196,340,true⟩, +⟨1,196,342,true⟩, +⟨1,196,348,true⟩, +⟨1,196,350,true⟩, +⟨1,196,355,true⟩, +⟨1,196,359,true⟩, +⟨1,196,363,true⟩, +⟨1,196,367,true⟩, +⟨1,196,370,true⟩, +⟨1,196,371,true⟩, +⟨1,196,374,true⟩, +⟨1,196,375,true⟩, +⟨1,196,376,true⟩, +⟨1,196,379,true⟩, +⟨1,196,380,true⟩, +⟨1,196,383,true⟩, +⟨1,196,387,true⟩, +⟨1,196,391,true⟩, +⟨1,196,395,true⟩, +⟨1,196,399,true⟩, +⟨1,196,401,true⟩, +⟨1,196,405,true⟩, +⟨1,196,409,true⟩, +⟨1,196,413,true⟩, +⟨1,196,431,true⟩, +⟨1,196,433,true⟩, +⟨1,196,435,true⟩, +⟨1,196,445,true⟩, +⟨1,196,447,true⟩, +⟨1,196,448,true⟩, +⟨1,196,452,true⟩, +⟨1,196,458,true⟩, +⟨1,196,462,true⟩, +⟨1,196,465,true⟩, +⟨1,196,467,true⟩, +⟨1,196,477,true⟩, +⟨1,196,479,true⟩, +⟨1,196,480,true⟩, +⟨1,196,484,true⟩, +⟨1,196,490,true⟩, +⟨1,196,494,true⟩, +⟨1,196,608,true⟩, +⟨1,196,610,true⟩, +⟨1,196,626,true⟩, +⟨1,196,627,true⟩, +⟨1,196,630,true⟩, +⟨1,196,631,true⟩, +⟨1,196,640,true⟩, +⟨1,196,642,true⟩, +⟨1,196,645,true⟩, +⟨1,196,654,true⟩, +⟨1,196,655,true⟩, +⟨1,196,668,true⟩, +⟨1,196,670,true⟩, +⟨1,196,680,true⟩, +⟨1,196,682,true⟩, +⟨1,196,700,true⟩, +⟨1,196,702,true⟩, +⟨1,196,712,true⟩, +⟨1,196,714,true⟩, +⟨1,196,820,true⟩, +⟨1,196,872,true⟩, +⟨1,196,900,true⟩, +⟨1,196,914,true⟩, +⟨1,196,979,true⟩, +⟨1,196,983,true⟩, +⟨1,197,249,true⟩, +⟨1,197,255,true⟩, +⟨1,197,272,true⟩, +⟨1,197,278,true⟩, +⟨1,197,308,true⟩, +⟨1,197,310,true⟩, +⟨1,197,316,true⟩, +⟨1,197,318,true⟩, +⟨1,197,321,true⟩, +⟨1,197,325,true⟩, +⟨1,197,329,true⟩, +⟨1,197,333,true⟩, +⟨1,197,340,true⟩, +⟨1,197,342,true⟩, +⟨1,197,348,true⟩, +⟨1,197,350,true⟩, +⟨1,197,353,true⟩, +⟨1,197,357,true⟩, +⟨1,197,361,true⟩, +⟨1,197,365,true⟩, +⟨1,197,385,true⟩, +⟨1,197,389,true⟩, +⟨1,197,393,true⟩, +⟨1,197,397,true⟩, +⟨1,197,401,true⟩, +⟨1,197,405,true⟩, +⟨1,197,409,true⟩, +⟨1,197,413,true⟩, +⟨1,197,428,true⟩, +⟨1,197,433,true⟩, +⟨1,197,435,true⟩, +⟨1,197,445,true⟩, +⟨1,197,447,true⟩, +⟨1,197,450,true⟩, +⟨1,197,454,true⟩, +⟨1,197,456,true⟩, +⟨1,197,460,true⟩, +⟨1,197,465,true⟩, +⟨1,197,467,true⟩, +⟨1,197,477,true⟩, +⟨1,197,479,true⟩, +⟨1,197,482,true⟩, +⟨1,197,486,true⟩, +⟨1,197,488,true⟩, +⟨1,197,492,true⟩, +⟨1,197,608,true⟩, +⟨1,197,610,true⟩, +⟨1,197,624,true⟩, +⟨1,197,625,true⟩, +⟨1,197,628,true⟩, +⟨1,197,629,true⟩, +⟨1,197,640,true⟩, +⟨1,197,642,true⟩, +⟨1,197,644,true⟩, +⟨1,197,646,true⟩, +⟨1,197,668,true⟩, +⟨1,197,670,true⟩, +⟨1,197,681,true⟩, +⟨1,197,683,true⟩, +⟨1,197,700,true⟩, +⟨1,197,702,true⟩, +⟨1,197,713,true⟩, +⟨1,197,715,true⟩, +⟨1,197,770,true⟩, +⟨1,197,820,true⟩, +⟨1,197,846,true⟩, +⟨1,197,872,true⟩, +⟨1,197,900,true⟩, +⟨1,197,915,true⟩, +⟨1,197,928,true⟩, +⟨1,198,249,true⟩, +⟨1,198,255,true⟩, +⟨1,198,272,true⟩, +⟨1,198,278,true⟩, +⟨1,198,304,true⟩, +⟨1,198,306,true⟩, +⟨1,198,312,true⟩, +⟨1,198,314,true⟩, +⟨1,198,323,true⟩, +⟨1,198,327,true⟩, +⟨1,198,331,true⟩, +⟨1,198,335,true⟩, +⟨1,198,336,true⟩, +⟨1,198,338,true⟩, +⟨1,198,344,true⟩, +⟨1,198,346,true⟩, +⟨1,198,355,true⟩, +⟨1,198,359,true⟩, +⟨1,198,363,true⟩, +⟨1,198,367,true⟩, +⟨1,198,385,true⟩, +⟨1,198,389,true⟩, +⟨1,198,393,true⟩, +⟨1,198,397,true⟩, +⟨1,198,401,true⟩, +⟨1,198,405,true⟩, +⟨1,198,409,true⟩, +⟨1,198,413,true⟩, +⟨1,198,426,true⟩, +⟨1,198,437,true⟩, +⟨1,198,439,true⟩, +⟨1,198,441,true⟩, +⟨1,198,443,true⟩, +⟨1,198,448,true⟩, +⟨1,198,452,true⟩, +⟨1,198,458,true⟩, +⟨1,198,462,true⟩, +⟨1,198,469,true⟩, +⟨1,198,471,true⟩, +⟨1,198,473,true⟩, +⟨1,198,475,true⟩, +⟨1,198,480,true⟩, +⟨1,198,484,true⟩, +⟨1,198,490,true⟩, +⟨1,198,494,true⟩, +⟨1,198,608,true⟩] +def chunk24 : List Event := [⟨1,198,610,true⟩, +⟨1,198,624,true⟩, +⟨1,198,625,true⟩, +⟨1,198,628,true⟩, +⟨1,198,629,true⟩, +⟨1,198,640,true⟩, +⟨1,198,642,true⟩, +⟨1,198,644,true⟩, +⟨1,198,646,true⟩, +⟨1,198,669,true⟩, +⟨1,198,671,true⟩, +⟨1,198,680,true⟩, +⟨1,198,682,true⟩, +⟨1,198,701,true⟩, +⟨1,198,703,true⟩, +⟨1,198,712,true⟩, +⟨1,198,714,true⟩, +⟨1,198,820,true⟩, +⟨1,198,846,true⟩, +⟨1,198,914,true⟩, +⟨1,198,928,true⟩, +⟨1,199,249,true⟩, +⟨1,199,255,true⟩, +⟨1,199,272,true⟩, +⟨1,199,278,true⟩, +⟨1,199,304,true⟩, +⟨1,199,306,true⟩, +⟨1,199,312,true⟩, +⟨1,199,314,true⟩, +⟨1,199,321,true⟩, +⟨1,199,325,true⟩, +⟨1,199,329,true⟩, +⟨1,199,333,true⟩, +⟨1,199,336,true⟩, +⟨1,199,338,true⟩, +⟨1,199,344,true⟩, +⟨1,199,346,true⟩, +⟨1,199,353,true⟩, +⟨1,199,357,true⟩, +⟨1,199,361,true⟩, +⟨1,199,365,true⟩, +⟨1,199,372,true⟩, +⟨1,199,373,true⟩, +⟨1,199,377,true⟩, +⟨1,199,382,true⟩, +⟨1,199,387,true⟩, +⟨1,199,391,true⟩, +⟨1,199,395,true⟩, +⟨1,199,399,true⟩, +⟨1,199,401,true⟩, +⟨1,199,405,true⟩, +⟨1,199,409,true⟩, +⟨1,199,413,true⟩, +⟨1,199,425,true⟩, +⟨1,199,437,true⟩, +⟨1,199,439,true⟩, +⟨1,199,441,true⟩, +⟨1,199,443,true⟩, +⟨1,199,450,true⟩, +⟨1,199,454,true⟩, +⟨1,199,456,true⟩, +⟨1,199,460,true⟩, +⟨1,199,469,true⟩, +⟨1,199,471,true⟩, +⟨1,199,473,true⟩, +⟨1,199,475,true⟩, +⟨1,199,482,true⟩, +⟨1,199,486,true⟩, +⟨1,199,488,true⟩, +⟨1,199,492,true⟩, +⟨1,199,608,true⟩, +⟨1,199,610,true⟩, +⟨1,199,626,true⟩, +⟨1,199,627,true⟩, +⟨1,199,630,true⟩, +⟨1,199,631,true⟩, +⟨1,199,640,true⟩, +⟨1,199,642,true⟩, +⟨1,199,645,true⟩, +⟨1,199,646,true⟩, +⟨1,199,650,true⟩, +⟨1,199,655,true⟩, +⟨1,199,669,true⟩, +⟨1,199,671,true⟩, +⟨1,199,681,true⟩, +⟨1,199,683,true⟩, +⟨1,199,701,true⟩, +⟨1,199,703,true⟩, +⟨1,199,713,true⟩, +⟨1,199,715,true⟩, +⟨1,199,770,true⟩, +⟨1,199,820,true⟩, +⟨1,199,915,true⟩, +⟨1,199,980,true⟩, +⟨1,199,984,true⟩, +⟨1,200,243,true⟩, +⟨1,200,253,true⟩, +⟨1,200,270,true⟩, +⟨1,200,282,true⟩, +⟨1,200,292,true⟩, +⟨1,200,294,true⟩, +⟨1,200,300,true⟩, +⟨1,200,302,true⟩, +⟨1,200,325,true⟩, +⟨1,200,327,true⟩, +⟨1,200,329,true⟩, +⟨1,200,331,true⟩, +⟨1,200,341,true⟩, +⟨1,200,343,true⟩, +⟨1,200,345,true⟩, +⟨1,200,347,true⟩, +⟨1,200,371,true⟩, +⟨1,200,375,true⟩, +⟨1,200,379,true⟩, +⟨1,200,383,true⟩, +⟨1,200,388,true⟩, +⟨1,200,390,true⟩, +⟨1,200,396,true⟩, +⟨1,200,398,true⟩, +⟨1,200,402,true⟩, +⟨1,200,406,true⟩, +⟨1,200,408,true⟩, +⟨1,200,412,true⟩, +⟨1,200,421,true⟩, +⟨1,200,423,true⟩, +⟨1,200,425,true⟩, +⟨1,200,427,true⟩, +⟨1,200,438,true⟩, +⟨1,200,453,true⟩, +⟨1,200,455,true⟩, +⟨1,200,457,true⟩, +⟨1,200,459,true⟩, +⟨1,200,469,true⟩, +⟨1,200,471,true⟩, +⟨1,200,473,true⟩, +⟨1,200,475,true⟩, +⟨1,200,498,true⟩, +⟨1,200,502,true⟩, +⟨1,200,504,true⟩, +⟨1,200,508,true⟩, +⟨1,200,521,true⟩, +⟨1,200,523,true⟩, +⟨1,200,541,true⟩, +⟨1,200,543,true⟩, +⟨1,200,557,true⟩, +⟨1,200,559,true⟩, +⟨1,200,562,true⟩, +⟨1,200,563,true⟩, +⟨1,200,566,true⟩, +⟨1,200,567,true⟩, +⟨1,200,576,true⟩, +⟨1,200,578,true⟩, +⟨1,200,580,true⟩, +⟨1,200,582,true⟩, +⟨1,200,605,true⟩, +⟨1,200,607,true⟩, +⟨1,200,617,true⟩, +⟨1,200,619,true⟩, +⟨1,200,676,true⟩, +⟨1,200,678,true⟩, +⟨1,200,701,true⟩, +⟨1,200,703,true⟩, +⟨1,200,717,true⟩, +⟨1,200,719,true⟩, +⟨1,200,759,true⟩, +⟨1,200,775,true⟩, +⟨1,200,878,true⟩, +⟨1,201,243,true⟩, +⟨1,201,253,true⟩, +⟨1,201,270,true⟩, +⟨1,201,282,true⟩, +⟨1,201,292,true⟩, +⟨1,201,294,true⟩, +⟨1,201,300,true⟩, +⟨1,201,302,true⟩, +⟨1,201,321,true⟩, +⟨1,201,323,true⟩, +⟨1,201,333,true⟩, +⟨1,201,335,true⟩, +⟨1,201,341,true⟩, +⟨1,201,343,true⟩, +⟨1,201,345,true⟩, +⟨1,201,347,true⟩, +⟨1,201,354,true⟩, +⟨1,201,356,true⟩, +⟨1,201,360,true⟩, +⟨1,201,366,true⟩, +⟨1,201,369,true⟩, +⟨1,201,373,true⟩, +⟨1,201,377,true⟩, +⟨1,201,381,true⟩, +⟨1,201,384,true⟩, +⟨1,201,386,true⟩, +⟨1,201,392,true⟩, +⟨1,201,394,true⟩, +⟨1,201,402,true⟩, +⟨1,201,406,true⟩, +⟨1,201,408,true⟩, +⟨1,201,412,true⟩, +⟨1,201,421,true⟩] +def chunk25 : List Event := [⟨1,201,423,true⟩, +⟨1,201,425,true⟩, +⟨1,201,427,true⟩, +⟨1,201,437,true⟩, +⟨1,201,449,true⟩, +⟨1,201,451,true⟩, +⟨1,201,461,true⟩, +⟨1,201,463,true⟩, +⟨1,201,469,true⟩, +⟨1,201,471,true⟩, +⟨1,201,473,true⟩, +⟨1,201,475,true⟩, +⟨1,201,496,true⟩, +⟨1,201,500,true⟩, +⟨1,201,506,true⟩, +⟨1,201,510,true⟩, +⟨1,201,521,true⟩, +⟨1,201,523,true⟩, +⟨1,201,541,true⟩, +⟨1,201,543,true⟩, +⟨1,201,556,true⟩, +⟨1,201,558,true⟩, +⟨1,201,560,true⟩, +⟨1,201,561,true⟩, +⟨1,201,564,true⟩, +⟨1,201,565,true⟩, +⟨1,201,576,true⟩, +⟨1,201,581,true⟩, +⟨1,201,582,true⟩, +⟨1,201,586,true⟩, +⟨1,201,591,true⟩, +⟨1,201,605,true⟩, +⟨1,201,607,true⟩, +⟨1,201,616,true⟩, +⟨1,201,618,true⟩, +⟨1,201,676,true⟩, +⟨1,201,678,true⟩, +⟨1,201,701,true⟩, +⟨1,201,703,true⟩, +⟨1,201,716,true⟩, +⟨1,201,718,true⟩, +⟨1,201,759,true⟩, +⟨1,201,774,true⟩, +⟨1,201,878,true⟩, +⟨1,201,944,true⟩, +⟨1,201,951,true⟩, +⟨1,202,243,true⟩, +⟨1,202,253,true⟩, +⟨1,202,270,true⟩, +⟨1,202,282,true⟩, +⟨1,202,288,true⟩, +⟨1,202,290,true⟩, +⟨1,202,296,true⟩, +⟨1,202,298,true⟩, +⟨1,202,325,true⟩, +⟨1,202,327,true⟩, +⟨1,202,329,true⟩, +⟨1,202,331,true⟩, +⟨1,202,337,true⟩, +⟨1,202,339,true⟩, +⟨1,202,349,true⟩, +⟨1,202,351,true⟩, +⟨1,202,355,true⟩, +⟨1,202,357,true⟩, +⟨1,202,361,true⟩, +⟨1,202,367,true⟩, +⟨1,202,371,true⟩, +⟨1,202,375,true⟩, +⟨1,202,379,true⟩, +⟨1,202,383,true⟩, +⟨1,202,384,true⟩, +⟨1,202,386,true⟩, +⟨1,202,392,true⟩, +⟨1,202,394,true⟩, +⟨1,202,402,true⟩, +⟨1,202,406,true⟩, +⟨1,202,408,true⟩, +⟨1,202,412,true⟩, +⟨1,202,417,true⟩, +⟨1,202,419,true⟩, +⟨1,202,429,true⟩, +⟨1,202,431,true⟩, +⟨1,202,435,true⟩, +⟨1,202,453,true⟩, +⟨1,202,455,true⟩, +⟨1,202,457,true⟩, +⟨1,202,459,true⟩, +⟨1,202,465,true⟩, +⟨1,202,467,true⟩, +⟨1,202,477,true⟩, +⟨1,202,479,true⟩, +⟨1,202,498,true⟩, +⟨1,202,502,true⟩, +⟨1,202,504,true⟩, +⟨1,202,508,true⟩, +⟨1,202,521,true⟩, +⟨1,202,523,true⟩, +⟨1,202,540,true⟩, +⟨1,202,542,true⟩, +⟨1,202,557,true⟩, +⟨1,202,559,true⟩, +⟨1,202,560,true⟩, +⟨1,202,561,true⟩, +⟨1,202,564,true⟩, +⟨1,202,565,true⟩, +⟨1,202,576,true⟩, +⟨1,202,582,true⟩, +⟨1,202,590,true⟩, +⟨1,202,591,true⟩, +⟨1,202,604,true⟩, +⟨1,202,606,true⟩, +⟨1,202,617,true⟩, +⟨1,202,619,true⟩, +⟨1,202,676,true⟩, +⟨1,202,678,true⟩, +⟨1,202,700,true⟩, +⟨1,202,702,true⟩, +⟨1,202,717,true⟩, +⟨1,202,719,true⟩, +⟨1,202,758,true⟩, +⟨1,202,775,true⟩, +⟨1,202,878,true⟩, +⟨1,202,942,true⟩, +⟨1,203,243,true⟩, +⟨1,203,253,true⟩, +⟨1,203,270,true⟩, +⟨1,203,282,true⟩, +⟨1,203,288,true⟩, +⟨1,203,290,true⟩, +⟨1,203,296,true⟩, +⟨1,203,298,true⟩, +⟨1,203,321,true⟩, +⟨1,203,323,true⟩, +⟨1,203,333,true⟩, +⟨1,203,335,true⟩, +⟨1,203,337,true⟩, +⟨1,203,339,true⟩, +⟨1,203,349,true⟩, +⟨1,203,351,true⟩, +⟨1,203,369,true⟩, +⟨1,203,373,true⟩, +⟨1,203,377,true⟩, +⟨1,203,381,true⟩, +⟨1,203,388,true⟩, +⟨1,203,390,true⟩, +⟨1,203,396,true⟩, +⟨1,203,398,true⟩, +⟨1,203,402,true⟩, +⟨1,203,406,true⟩, +⟨1,203,408,true⟩, +⟨1,203,412,true⟩, +⟨1,203,417,true⟩, +⟨1,203,419,true⟩, +⟨1,203,429,true⟩, +⟨1,203,431,true⟩, +⟨1,203,432,true⟩, +⟨1,203,449,true⟩, +⟨1,203,451,true⟩, +⟨1,203,461,true⟩, +⟨1,203,463,true⟩, +⟨1,203,465,true⟩, +⟨1,203,467,true⟩, +⟨1,203,477,true⟩, +⟨1,203,479,true⟩, +⟨1,203,496,true⟩, +⟨1,203,500,true⟩, +⟨1,203,506,true⟩, +⟨1,203,510,true⟩, +⟨1,203,521,true⟩, +⟨1,203,523,true⟩, +⟨1,203,540,true⟩, +⟨1,203,542,true⟩, +⟨1,203,556,true⟩, +⟨1,203,558,true⟩, +⟨1,203,562,true⟩, +⟨1,203,563,true⟩, +⟨1,203,566,true⟩, +⟨1,203,567,true⟩, +⟨1,203,576,true⟩, +⟨1,203,578,true⟩, +⟨1,203,580,true⟩, +⟨1,203,582,true⟩, +⟨1,203,604,true⟩, +⟨1,203,606,true⟩, +⟨1,203,616,true⟩, +⟨1,203,618,true⟩, +⟨1,203,676,true⟩, +⟨1,203,678,true⟩, +⟨1,203,700,true⟩, +⟨1,203,702,true⟩, +⟨1,203,716,true⟩, +⟨1,203,718,true⟩, +⟨1,203,758,true⟩, +⟨1,203,774,true⟩, +⟨1,203,878,true⟩, +⟨1,204,243,true⟩, +⟨1,204,253,true⟩, +⟨1,204,270,true⟩, +⟨1,204,282,true⟩, +⟨1,204,292,true⟩] +def chunk26 : List Event := [⟨1,204,294,true⟩, +⟨1,204,300,true⟩, +⟨1,204,302,true⟩, +⟨1,204,325,true⟩, +⟨1,204,327,true⟩, +⟨1,204,329,true⟩, +⟨1,204,331,true⟩, +⟨1,204,341,true⟩, +⟨1,204,343,true⟩, +⟨1,204,345,true⟩, +⟨1,204,347,true⟩, +⟨1,204,354,true⟩, +⟨1,204,355,true⟩, +⟨1,204,360,true⟩, +⟨1,204,367,true⟩, +⟨1,204,371,true⟩, +⟨1,204,375,true⟩, +⟨1,204,379,true⟩, +⟨1,204,383,true⟩, +⟨1,204,388,true⟩, +⟨1,204,390,true⟩, +⟨1,204,396,true⟩, +⟨1,204,398,true⟩, +⟨1,204,400,true⟩, +⟨1,204,404,true⟩, +⟨1,204,410,true⟩, +⟨1,204,414,true⟩, +⟨1,204,417,true⟩, +⟨1,204,419,true⟩, +⟨1,204,429,true⟩, +⟨1,204,431,true⟩, +⟨1,204,446,true⟩, +⟨1,204,449,true⟩, +⟨1,204,451,true⟩, +⟨1,204,461,true⟩, +⟨1,204,463,true⟩, +⟨1,204,465,true⟩, +⟨1,204,467,true⟩, +⟨1,204,477,true⟩, +⟨1,204,479,true⟩, +⟨1,204,496,true⟩, +⟨1,204,500,true⟩, +⟨1,204,506,true⟩, +⟨1,204,510,true⟩, +⟨1,204,520,true⟩, +⟨1,204,522,true⟩, +⟨1,204,541,true⟩, +⟨1,204,543,true⟩, +⟨1,204,557,true⟩, +⟨1,204,559,true⟩, +⟨1,204,562,true⟩, +⟨1,204,563,true⟩, +⟨1,204,566,true⟩, +⟨1,204,567,true⟩, +⟨1,204,576,true⟩, +⟨1,204,578,true⟩, +⟨1,204,581,true⟩, +⟨1,204,582,true⟩, +⟨1,204,587,true⟩, +⟨1,204,590,true⟩, +⟨1,204,604,true⟩, +⟨1,204,606,true⟩, +⟨1,204,616,true⟩, +⟨1,204,618,true⟩, +⟨1,204,672,true⟩, +⟨1,204,674,true⟩, +⟨1,204,700,true⟩, +⟨1,204,702,true⟩, +⟨1,204,716,true⟩, +⟨1,204,718,true⟩, +⟨1,204,759,true⟩, +⟨1,204,775,true⟩, +⟨1,204,876,true⟩, +⟨1,204,942,true⟩, +⟨1,204,951,true⟩, +⟨1,205,243,true⟩, +⟨1,205,253,true⟩, +⟨1,205,270,true⟩, +⟨1,205,282,true⟩, +⟨1,205,292,true⟩, +⟨1,205,294,true⟩, +⟨1,205,300,true⟩, +⟨1,205,302,true⟩, +⟨1,205,321,true⟩, +⟨1,205,323,true⟩, +⟨1,205,333,true⟩, +⟨1,205,335,true⟩, +⟨1,205,341,true⟩, +⟨1,205,343,true⟩, +⟨1,205,345,true⟩, +⟨1,205,347,true⟩, +⟨1,205,369,true⟩, +⟨1,205,373,true⟩, +⟨1,205,377,true⟩, +⟨1,205,381,true⟩, +⟨1,205,384,true⟩, +⟨1,205,386,true⟩, +⟨1,205,392,true⟩, +⟨1,205,394,true⟩, +⟨1,205,400,true⟩, +⟨1,205,404,true⟩, +⟨1,205,410,true⟩, +⟨1,205,414,true⟩, +⟨1,205,417,true⟩, +⟨1,205,419,true⟩, +⟨1,205,429,true⟩, +⟨1,205,431,true⟩, +⟨1,205,445,true⟩, +⟨1,205,453,true⟩, +⟨1,205,455,true⟩, +⟨1,205,457,true⟩, +⟨1,205,459,true⟩, +⟨1,205,465,true⟩, +⟨1,205,467,true⟩, +⟨1,205,477,true⟩, +⟨1,205,479,true⟩, +⟨1,205,498,true⟩, +⟨1,205,502,true⟩, +⟨1,205,504,true⟩, +⟨1,205,508,true⟩, +⟨1,205,520,true⟩, +⟨1,205,522,true⟩, +⟨1,205,541,true⟩, +⟨1,205,543,true⟩, +⟨1,205,556,true⟩, +⟨1,205,558,true⟩, +⟨1,205,560,true⟩, +⟨1,205,561,true⟩, +⟨1,205,564,true⟩, +⟨1,205,565,true⟩, +⟨1,205,576,true⟩, +⟨1,205,578,true⟩, +⟨1,205,580,true⟩, +⟨1,205,582,true⟩, +⟨1,205,604,true⟩, +⟨1,205,606,true⟩, +⟨1,205,617,true⟩, +⟨1,205,619,true⟩, +⟨1,205,672,true⟩, +⟨1,205,674,true⟩, +⟨1,205,700,true⟩, +⟨1,205,702,true⟩, +⟨1,205,717,true⟩, +⟨1,205,719,true⟩, +⟨1,205,759,true⟩, +⟨1,205,774,true⟩, +⟨1,205,876,true⟩, +⟨1,206,243,true⟩, +⟨1,206,253,true⟩, +⟨1,206,270,true⟩, +⟨1,206,282,true⟩, +⟨1,206,288,true⟩, +⟨1,206,290,true⟩, +⟨1,206,296,true⟩, +⟨1,206,298,true⟩, +⟨1,206,325,true⟩, +⟨1,206,327,true⟩, +⟨1,206,329,true⟩, +⟨1,206,331,true⟩, +⟨1,206,337,true⟩, +⟨1,206,339,true⟩, +⟨1,206,349,true⟩, +⟨1,206,351,true⟩, +⟨1,206,371,true⟩, +⟨1,206,375,true⟩, +⟨1,206,379,true⟩, +⟨1,206,383,true⟩, +⟨1,206,384,true⟩, +⟨1,206,386,true⟩, +⟨1,206,392,true⟩, +⟨1,206,394,true⟩, +⟨1,206,400,true⟩, +⟨1,206,404,true⟩, +⟨1,206,410,true⟩, +⟨1,206,414,true⟩, +⟨1,206,421,true⟩, +⟨1,206,423,true⟩, +⟨1,206,425,true⟩, +⟨1,206,427,true⟩, +⟨1,206,443,true⟩, +⟨1,206,449,true⟩, +⟨1,206,451,true⟩, +⟨1,206,461,true⟩, +⟨1,206,463,true⟩, +⟨1,206,469,true⟩, +⟨1,206,471,true⟩, +⟨1,206,473,true⟩, +⟨1,206,475,true⟩, +⟨1,206,496,true⟩, +⟨1,206,500,true⟩, +⟨1,206,506,true⟩, +⟨1,206,510,true⟩, +⟨1,206,520,true⟩, +⟨1,206,522,true⟩, +⟨1,206,540,true⟩, +⟨1,206,542,true⟩, +⟨1,206,557,true⟩, +⟨1,206,559,true⟩, +⟨1,206,560,true⟩, +⟨1,206,561,true⟩] +def chunk27 : List Event := [⟨1,206,564,true⟩, +⟨1,206,565,true⟩, +⟨1,206,576,true⟩, +⟨1,206,578,true⟩, +⟨1,206,580,true⟩, +⟨1,206,582,true⟩, +⟨1,206,605,true⟩, +⟨1,206,607,true⟩, +⟨1,206,616,true⟩, +⟨1,206,618,true⟩, +⟨1,206,672,true⟩, +⟨1,206,674,true⟩, +⟨1,206,701,true⟩, +⟨1,206,703,true⟩, +⟨1,206,716,true⟩, +⟨1,206,718,true⟩, +⟨1,206,758,true⟩, +⟨1,206,775,true⟩, +⟨1,206,876,true⟩, +⟨1,207,243,true⟩, +⟨1,207,253,true⟩, +⟨1,207,270,true⟩, +⟨1,207,282,true⟩, +⟨1,207,288,true⟩, +⟨1,207,290,true⟩, +⟨1,207,296,true⟩, +⟨1,207,298,true⟩, +⟨1,207,321,true⟩, +⟨1,207,323,true⟩, +⟨1,207,333,true⟩, +⟨1,207,335,true⟩, +⟨1,207,337,true⟩, +⟨1,207,339,true⟩, +⟨1,207,349,true⟩, +⟨1,207,351,true⟩, +⟨1,207,356,true⟩, +⟨1,207,357,true⟩, +⟨1,207,361,true⟩, +⟨1,207,366,true⟩, +⟨1,207,369,true⟩, +⟨1,207,373,true⟩, +⟨1,207,377,true⟩, +⟨1,207,381,true⟩, +⟨1,207,388,true⟩, +⟨1,207,390,true⟩, +⟨1,207,396,true⟩, +⟨1,207,398,true⟩, +⟨1,207,400,true⟩, +⟨1,207,404,true⟩, +⟨1,207,410,true⟩, +⟨1,207,414,true⟩, +⟨1,207,421,true⟩, +⟨1,207,423,true⟩, +⟨1,207,425,true⟩, +⟨1,207,427,true⟩, +⟨1,207,440,true⟩, +⟨1,207,453,true⟩, +⟨1,207,455,true⟩, +⟨1,207,457,true⟩, +⟨1,207,459,true⟩, +⟨1,207,469,true⟩, +⟨1,207,471,true⟩, +⟨1,207,473,true⟩, +⟨1,207,475,true⟩, +⟨1,207,498,true⟩, +⟨1,207,502,true⟩, +⟨1,207,504,true⟩, +⟨1,207,508,true⟩, +⟨1,207,520,true⟩, +⟨1,207,522,true⟩, +⟨1,207,540,true⟩, +⟨1,207,542,true⟩, +⟨1,207,556,true⟩, +⟨1,207,558,true⟩, +⟨1,207,562,true⟩, +⟨1,207,563,true⟩, +⟨1,207,566,true⟩, +⟨1,207,567,true⟩, +⟨1,207,576,true⟩, +⟨1,207,578,true⟩, +⟨1,207,582,true⟩, +⟨1,207,586,true⟩, +⟨1,207,587,true⟩, +⟨1,207,605,true⟩, +⟨1,207,607,true⟩, +⟨1,207,617,true⟩, +⟨1,207,619,true⟩, +⟨1,207,672,true⟩, +⟨1,207,674,true⟩, +⟨1,207,701,true⟩, +⟨1,207,703,true⟩, +⟨1,207,717,true⟩, +⟨1,207,719,true⟩, +⟨1,207,758,true⟩, +⟨1,207,774,true⟩, +⟨1,207,876,true⟩, +⟨1,207,944,true⟩, +⟨1,208,240,true⟩, +⟨1,208,246,true⟩, +⟨1,208,290,true⟩, +⟨1,208,294,true⟩, +⟨1,208,296,true⟩, +⟨1,208,300,true⟩, +⟨1,208,306,true⟩, +⟨1,208,310,true⟩, +⟨1,208,312,true⟩, +⟨1,208,316,true⟩, +⟨1,208,354,true⟩, +⟨1,208,358,true⟩, +⟨1,208,360,true⟩, +⟨1,208,364,true⟩, +⟨1,208,370,true⟩, +⟨1,208,374,true⟩, +⟨1,208,376,true⟩, +⟨1,208,380,true⟩, +⟨1,208,418,true⟩, +⟨1,208,422,true⟩, +⟨1,208,424,true⟩, +⟨1,208,428,true⟩, +⟨1,208,434,true⟩, +⟨1,208,438,true⟩, +⟨1,208,440,true⟩, +⟨1,208,444,true⟩, +⟨1,208,454,true⟩, +⟨1,208,482,true⟩, +⟨1,208,486,true⟩, +⟨1,208,488,true⟩, +⟨1,208,492,true⟩, +⟨1,208,498,true⟩, +⟨1,208,502,true⟩, +⟨1,208,504,true⟩, +⟨1,208,508,true⟩, +⟨1,208,514,true⟩, +⟨1,208,515,true⟩, +⟨1,208,518,true⟩, +⟨1,208,519,true⟩, +⟨1,208,528,true⟩, +⟨1,208,530,true⟩, +⟨1,208,532,true⟩, +⟨1,208,534,true⟩, +⟨1,208,546,true⟩, +⟨1,208,547,true⟩, +⟨1,208,550,true⟩, +⟨1,208,551,true⟩, +⟨1,208,569,true⟩, +⟨1,208,571,true⟩, +⟨1,208,585,true⟩, +⟨1,208,587,true⟩, +⟨1,208,601,true⟩, +⟨1,208,603,true⟩, +⟨1,208,617,true⟩, +⟨1,208,619,true⟩, +⟨1,208,633,true⟩, +⟨1,208,635,true⟩, +⟨1,208,649,true⟩, +⟨1,208,651,true⟩, +⟨1,208,665,true⟩, +⟨1,208,667,true⟩, +⟨1,208,681,true⟩, +⟨1,208,683,true⟩, +⟨1,208,692,true⟩, +⟨1,208,694,true⟩, +⟨1,208,722,true⟩, +⟨1,208,723,true⟩, +⟨1,208,726,true⟩, +⟨1,208,727,true⟩, +⟨1,208,749,true⟩, +⟨1,208,892,true⟩, +⟨1,209,240,true⟩, +⟨1,209,246,true⟩, +⟨1,209,288,true⟩, +⟨1,209,292,true⟩, +⟨1,209,298,true⟩, +⟨1,209,302,true⟩, +⟨1,209,306,true⟩, +⟨1,209,310,true⟩, +⟨1,209,312,true⟩, +⟨1,209,316,true⟩, +⟨1,209,339,true⟩, +⟨1,209,341,true⟩, +⟨1,209,345,true⟩, +⟨1,209,351,true⟩, +⟨1,209,352,true⟩, +⟨1,209,356,true⟩, +⟨1,209,362,true⟩, +⟨1,209,366,true⟩, +⟨1,209,370,true⟩, +⟨1,209,374,true⟩, +⟨1,209,376,true⟩, +⟨1,209,380,true⟩, +⟨1,209,416,true⟩, +⟨1,209,420,true⟩, +⟨1,209,426,true⟩, +⟨1,209,430,true⟩, +⟨1,209,434,true⟩, +⟨1,209,438,true⟩, +⟨1,209,440,true⟩, +⟨1,209,444,true⟩, +⟨1,209,453,true⟩, +⟨1,209,480,true⟩] +def chunk28 : List Event := [⟨1,209,484,true⟩, +⟨1,209,490,true⟩, +⟨1,209,494,true⟩, +⟨1,209,498,true⟩, +⟨1,209,502,true⟩, +⟨1,209,504,true⟩, +⟨1,209,508,true⟩, +⟨1,209,514,true⟩, +⟨1,209,515,true⟩, +⟨1,209,518,true⟩, +⟨1,209,519,true⟩, +⟨1,209,528,true⟩, +⟨1,209,534,true⟩, +⟨1,209,539,true⟩, +⟨1,209,542,true⟩, +⟨1,209,544,true⟩, +⟨1,209,545,true⟩, +⟨1,209,548,true⟩, +⟨1,209,549,true⟩, +⟨1,209,569,true⟩, +⟨1,209,571,true⟩, +⟨1,209,584,true⟩, +⟨1,209,586,true⟩, +⟨1,209,600,true⟩, +⟨1,209,602,true⟩, +⟨1,209,617,true⟩, +⟨1,209,619,true⟩, +⟨1,209,632,true⟩, +⟨1,209,634,true⟩, +⟨1,209,649,true⟩, +⟨1,209,651,true⟩, +⟨1,209,665,true⟩, +⟨1,209,667,true⟩, +⟨1,209,680,true⟩, +⟨1,209,682,true⟩, +⟨1,209,692,true⟩, +⟨1,209,694,true⟩, +⟨1,209,720,true⟩, +⟨1,209,721,true⟩, +⟨1,209,724,true⟩, +⟨1,209,725,true⟩, +⟨1,209,749,true⟩, +⟨1,209,800,true⟩, +⟨1,209,892,true⟩, +⟨1,209,954,true⟩, +⟨1,210,240,true⟩, +⟨1,210,246,true⟩, +⟨1,210,290,true⟩, +⟨1,210,294,true⟩, +⟨1,210,296,true⟩, +⟨1,210,300,true⟩, +⟨1,210,304,true⟩, +⟨1,210,308,true⟩, +⟨1,210,314,true⟩, +⟨1,210,318,true⟩, +⟨1,210,338,true⟩, +⟨1,210,340,true⟩, +⟨1,210,344,true⟩, +⟨1,210,350,true⟩, +⟨1,210,354,true⟩, +⟨1,210,358,true⟩, +⟨1,210,360,true⟩, +⟨1,210,364,true⟩, +⟨1,210,368,true⟩, +⟨1,210,372,true⟩, +⟨1,210,378,true⟩, +⟨1,210,382,true⟩, +⟨1,210,418,true⟩, +⟨1,210,422,true⟩, +⟨1,210,424,true⟩, +⟨1,210,428,true⟩, +⟨1,210,432,true⟩, +⟨1,210,436,true⟩, +⟨1,210,442,true⟩, +⟨1,210,446,true⟩, +⟨1,210,451,true⟩, +⟨1,210,482,true⟩, +⟨1,210,486,true⟩, +⟨1,210,488,true⟩, +⟨1,210,492,true⟩, +⟨1,210,496,true⟩, +⟨1,210,500,true⟩, +⟨1,210,506,true⟩, +⟨1,210,510,true⟩, +⟨1,210,514,true⟩, +⟨1,210,515,true⟩, +⟨1,210,518,true⟩, +⟨1,210,519,true⟩, +⟨1,210,528,true⟩, +⟨1,210,533,true⟩, +⟨1,210,534,true⟩, +⟨1,210,538,true⟩, +⟨1,210,539,true⟩, +⟨1,210,543,true⟩, +⟨1,210,544,true⟩, +⟨1,210,545,true⟩, +⟨1,210,548,true⟩, +⟨1,210,549,true⟩, +⟨1,210,568,true⟩, +⟨1,210,570,true⟩, +⟨1,210,585,true⟩, +⟨1,210,587,true⟩, +⟨1,210,601,true⟩, +⟨1,210,603,true⟩, +⟨1,210,616,true⟩, +⟨1,210,618,true⟩, +⟨1,210,633,true⟩, +⟨1,210,635,true⟩, +⟨1,210,648,true⟩, +⟨1,210,650,true⟩, +⟨1,210,664,true⟩, +⟨1,210,666,true⟩, +⟨1,210,681,true⟩, +⟨1,210,683,true⟩, +⟨1,210,692,true⟩, +⟨1,210,694,true⟩, +⟨1,210,720,true⟩, +⟨1,210,721,true⟩, +⟨1,210,724,true⟩, +⟨1,210,725,true⟩, +⟨1,210,749,true⟩, +⟨1,210,788,true⟩, +⟨1,210,892,true⟩, +⟨1,210,948,true⟩, +⟨1,210,952,true⟩, +⟨1,211,240,true⟩, +⟨1,211,246,true⟩, +⟨1,211,288,true⟩, +⟨1,211,292,true⟩, +⟨1,211,298,true⟩, +⟨1,211,302,true⟩, +⟨1,211,304,true⟩, +⟨1,211,308,true⟩, +⟨1,211,314,true⟩, +⟨1,211,318,true⟩, +⟨1,211,352,true⟩, +⟨1,211,356,true⟩, +⟨1,211,362,true⟩, +⟨1,211,366,true⟩, +⟨1,211,368,true⟩, +⟨1,211,372,true⟩, +⟨1,211,378,true⟩, +⟨1,211,382,true⟩, +⟨1,211,416,true⟩, +⟨1,211,420,true⟩, +⟨1,211,426,true⟩, +⟨1,211,430,true⟩, +⟨1,211,432,true⟩, +⟨1,211,436,true⟩, +⟨1,211,442,true⟩, +⟨1,211,446,true⟩, +⟨1,211,448,true⟩, +⟨1,211,480,true⟩, +⟨1,211,484,true⟩, +⟨1,211,490,true⟩, +⟨1,211,494,true⟩, +⟨1,211,496,true⟩, +⟨1,211,500,true⟩, +⟨1,211,506,true⟩, +⟨1,211,510,true⟩, +⟨1,211,514,true⟩, +⟨1,211,515,true⟩, +⟨1,211,518,true⟩, +⟨1,211,519,true⟩, +⟨1,211,528,true⟩, +⟨1,211,530,true⟩, +⟨1,211,532,true⟩, +⟨1,211,534,true⟩, +⟨1,211,546,true⟩, +⟨1,211,547,true⟩, +⟨1,211,550,true⟩, +⟨1,211,551,true⟩, +⟨1,211,568,true⟩, +⟨1,211,570,true⟩, +⟨1,211,584,true⟩, +⟨1,211,586,true⟩, +⟨1,211,600,true⟩, +⟨1,211,602,true⟩, +⟨1,211,616,true⟩, +⟨1,211,618,true⟩, +⟨1,211,632,true⟩, +⟨1,211,634,true⟩, +⟨1,211,648,true⟩, +⟨1,211,650,true⟩, +⟨1,211,664,true⟩, +⟨1,211,666,true⟩, +⟨1,211,680,true⟩, +⟨1,211,682,true⟩, +⟨1,211,692,true⟩, +⟨1,211,694,true⟩, +⟨1,211,722,true⟩, +⟨1,211,723,true⟩, +⟨1,211,726,true⟩, +⟨1,211,727,true⟩, +⟨1,211,749,true⟩, +⟨1,211,788,true⟩, +⟨1,211,800,true⟩, +⟨1,211,892,true⟩, +⟨1,212,240,true⟩, +⟨1,212,246,true⟩] +def chunk29 : List Event := [⟨1,212,290,true⟩, +⟨1,212,294,true⟩, +⟨1,212,296,true⟩, +⟨1,212,300,true⟩, +⟨1,212,306,true⟩, +⟨1,212,310,true⟩, +⟨1,212,312,true⟩, +⟨1,212,316,true⟩, +⟨1,212,340,true⟩, +⟨1,212,341,true⟩, +⟨1,212,345,true⟩, +⟨1,212,350,true⟩, +⟨1,212,354,true⟩, +⟨1,212,358,true⟩, +⟨1,212,360,true⟩, +⟨1,212,364,true⟩, +⟨1,212,370,true⟩, +⟨1,212,374,true⟩, +⟨1,212,376,true⟩, +⟨1,212,380,true⟩, +⟨1,212,416,true⟩, +⟨1,212,420,true⟩, +⟨1,212,426,true⟩, +⟨1,212,430,true⟩, +⟨1,212,432,true⟩, +⟨1,212,436,true⟩, +⟨1,212,442,true⟩, +⟨1,212,446,true⟩, +⟨1,212,462,true⟩, +⟨1,212,480,true⟩, +⟨1,212,484,true⟩, +⟨1,212,490,true⟩, +⟨1,212,494,true⟩, +⟨1,212,496,true⟩, +⟨1,212,500,true⟩, +⟨1,212,506,true⟩, +⟨1,212,510,true⟩, +⟨1,212,512,true⟩, +⟨1,212,513,true⟩, +⟨1,212,516,true⟩, +⟨1,212,517,true⟩, +⟨1,212,528,true⟩, +⟨1,212,530,true⟩, +⟨1,212,534,true⟩, +⟨1,212,535,true⟩, +⟨1,212,538,true⟩, +⟨1,212,546,true⟩, +⟨1,212,547,true⟩, +⟨1,212,550,true⟩, +⟨1,212,551,true⟩, +⟨1,212,569,true⟩, +⟨1,212,571,true⟩, +⟨1,212,585,true⟩, +⟨1,212,587,true⟩, +⟨1,212,600,true⟩, +⟨1,212,602,true⟩, +⟨1,212,616,true⟩, +⟨1,212,618,true⟩, +⟨1,212,633,true⟩, +⟨1,212,635,true⟩, +⟨1,212,649,true⟩, +⟨1,212,651,true⟩, +⟨1,212,664,true⟩, +⟨1,212,666,true⟩, +⟨1,212,680,true⟩, +⟨1,212,682,true⟩, +⟨1,212,688,true⟩, +⟨1,212,690,true⟩, +⟨1,212,722,true⟩, +⟨1,212,723,true⟩, +⟨1,212,726,true⟩, +⟨1,212,727,true⟩, +⟨1,212,748,true⟩, +⟨1,212,890,true⟩, +⟨1,212,952,true⟩, +⟨1,213,240,true⟩, +⟨1,213,246,true⟩, +⟨1,213,288,true⟩, +⟨1,213,292,true⟩, +⟨1,213,298,true⟩, +⟨1,213,302,true⟩, +⟨1,213,306,true⟩, +⟨1,213,310,true⟩, +⟨1,213,312,true⟩, +⟨1,213,316,true⟩, +⟨1,213,352,true⟩, +⟨1,213,356,true⟩, +⟨1,213,362,true⟩, +⟨1,213,366,true⟩, +⟨1,213,370,true⟩, +⟨1,213,374,true⟩, +⟨1,213,376,true⟩, +⟨1,213,380,true⟩, +⟨1,213,418,true⟩, +⟨1,213,422,true⟩, +⟨1,213,424,true⟩, +⟨1,213,428,true⟩, +⟨1,213,432,true⟩, +⟨1,213,436,true⟩, +⟨1,213,442,true⟩, +⟨1,213,446,true⟩, +⟨1,213,461,true⟩, +⟨1,213,482,true⟩, +⟨1,213,486,true⟩, +⟨1,213,488,true⟩, +⟨1,213,492,true⟩, +⟨1,213,496,true⟩, +⟨1,213,500,true⟩, +⟨1,213,506,true⟩, +⟨1,213,510,true⟩, +⟨1,213,512,true⟩, +⟨1,213,513,true⟩, +⟨1,213,516,true⟩, +⟨1,213,517,true⟩, +⟨1,213,528,true⟩, +⟨1,213,530,true⟩, +⟨1,213,532,true⟩, +⟨1,213,534,true⟩, +⟨1,213,544,true⟩, +⟨1,213,545,true⟩, +⟨1,213,548,true⟩, +⟨1,213,549,true⟩, +⟨1,213,569,true⟩, +⟨1,213,571,true⟩, +⟨1,213,584,true⟩, +⟨1,213,586,true⟩, +⟨1,213,601,true⟩, +⟨1,213,603,true⟩, +⟨1,213,616,true⟩, +⟨1,213,618,true⟩, +⟨1,213,632,true⟩, +⟨1,213,634,true⟩, +⟨1,213,649,true⟩, +⟨1,213,651,true⟩, +⟨1,213,664,true⟩, +⟨1,213,666,true⟩, +⟨1,213,681,true⟩, +⟨1,213,683,true⟩, +⟨1,213,688,true⟩, +⟨1,213,690,true⟩, +⟨1,213,720,true⟩, +⟨1,213,721,true⟩, +⟨1,213,724,true⟩, +⟨1,213,725,true⟩, +⟨1,213,748,true⟩, +⟨1,213,800,true⟩, +⟨1,213,890,true⟩, +⟨1,214,240,true⟩, +⟨1,214,246,true⟩, +⟨1,214,290,true⟩, +⟨1,214,294,true⟩, +⟨1,214,296,true⟩, +⟨1,214,300,true⟩, +⟨1,214,304,true⟩, +⟨1,214,308,true⟩, +⟨1,214,314,true⟩, +⟨1,214,318,true⟩, +⟨1,214,354,true⟩, +⟨1,214,358,true⟩, +⟨1,214,360,true⟩, +⟨1,214,364,true⟩, +⟨1,214,368,true⟩, +⟨1,214,372,true⟩, +⟨1,214,378,true⟩, +⟨1,214,382,true⟩, +⟨1,214,416,true⟩, +⟨1,214,420,true⟩, +⟨1,214,426,true⟩, +⟨1,214,430,true⟩, +⟨1,214,434,true⟩, +⟨1,214,438,true⟩, +⟨1,214,440,true⟩, +⟨1,214,444,true⟩, +⟨1,214,459,true⟩, +⟨1,214,480,true⟩, +⟨1,214,484,true⟩, +⟨1,214,490,true⟩, +⟨1,214,494,true⟩, +⟨1,214,498,true⟩, +⟨1,214,502,true⟩, +⟨1,214,504,true⟩, +⟨1,214,508,true⟩, +⟨1,214,512,true⟩, +⟨1,214,513,true⟩, +⟨1,214,516,true⟩, +⟨1,214,517,true⟩, +⟨1,214,528,true⟩, +⟨1,214,530,true⟩, +⟨1,214,532,true⟩, +⟨1,214,534,true⟩, +⟨1,214,544,true⟩, +⟨1,214,545,true⟩, +⟨1,214,548,true⟩, +⟨1,214,549,true⟩, +⟨1,214,568,true⟩, +⟨1,214,570,true⟩, +⟨1,214,585,true⟩, +⟨1,214,587,true⟩, +⟨1,214,600,true⟩, +⟨1,214,602,true⟩] +def chunk30 : List Event := [⟨1,214,617,true⟩, +⟨1,214,619,true⟩, +⟨1,214,633,true⟩, +⟨1,214,635,true⟩, +⟨1,214,648,true⟩, +⟨1,214,650,true⟩, +⟨1,214,665,true⟩, +⟨1,214,667,true⟩, +⟨1,214,680,true⟩, +⟨1,214,682,true⟩, +⟨1,214,688,true⟩, +⟨1,214,690,true⟩, +⟨1,214,720,true⟩, +⟨1,214,721,true⟩, +⟨1,214,724,true⟩, +⟨1,214,725,true⟩, +⟨1,214,748,true⟩, +⟨1,214,788,true⟩, +⟨1,214,890,true⟩, +⟨1,215,240,true⟩, +⟨1,215,246,true⟩, +⟨1,215,288,true⟩, +⟨1,215,292,true⟩, +⟨1,215,298,true⟩, +⟨1,215,302,true⟩, +⟨1,215,304,true⟩, +⟨1,215,308,true⟩, +⟨1,215,314,true⟩, +⟨1,215,318,true⟩, +⟨1,215,338,true⟩, +⟨1,215,339,true⟩, +⟨1,215,344,true⟩, +⟨1,215,351,true⟩, +⟨1,215,352,true⟩, +⟨1,215,356,true⟩, +⟨1,215,362,true⟩, +⟨1,215,366,true⟩, +⟨1,215,368,true⟩, +⟨1,215,372,true⟩, +⟨1,215,378,true⟩, +⟨1,215,382,true⟩, +⟨1,215,418,true⟩, +⟨1,215,422,true⟩, +⟨1,215,424,true⟩, +⟨1,215,428,true⟩, +⟨1,215,434,true⟩, +⟨1,215,438,true⟩, +⟨1,215,440,true⟩, +⟨1,215,444,true⟩, +⟨1,215,456,true⟩, +⟨1,215,482,true⟩, +⟨1,215,486,true⟩, +⟨1,215,488,true⟩, +⟨1,215,492,true⟩, +⟨1,215,498,true⟩, +⟨1,215,502,true⟩, +⟨1,215,504,true⟩, +⟨1,215,508,true⟩, +⟨1,215,512,true⟩, +⟨1,215,513,true⟩, +⟨1,215,516,true⟩, +⟨1,215,517,true⟩, +⟨1,215,528,true⟩, +⟨1,215,530,true⟩, +⟨1,215,533,true⟩, +⟨1,215,534,true⟩, +⟨1,215,535,true⟩, +⟨1,215,542,true⟩, +⟨1,215,543,true⟩, +⟨1,215,546,true⟩, +⟨1,215,547,true⟩, +⟨1,215,550,true⟩, +⟨1,215,551,true⟩, +⟨1,215,568,true⟩, +⟨1,215,570,true⟩, +⟨1,215,584,true⟩, +⟨1,215,586,true⟩, +⟨1,215,601,true⟩, +⟨1,215,603,true⟩, +⟨1,215,617,true⟩, +⟨1,215,619,true⟩, +⟨1,215,632,true⟩, +⟨1,215,634,true⟩, +⟨1,215,648,true⟩, +⟨1,215,650,true⟩, +⟨1,215,665,true⟩, +⟨1,215,667,true⟩, +⟨1,215,681,true⟩, +⟨1,215,683,true⟩, +⟨1,215,688,true⟩, +⟨1,215,690,true⟩, +⟨1,215,722,true⟩, +⟨1,215,723,true⟩, +⟨1,215,726,true⟩, +⟨1,215,727,true⟩, +⟨1,215,748,true⟩, +⟨1,215,788,true⟩, +⟨1,215,800,true⟩, +⟨1,215,890,true⟩, +⟨1,215,948,true⟩, +⟨1,215,954,true⟩, +⟨1,216,241,true⟩, +⟨1,216,247,true⟩, +⟨1,216,293,true⟩, +⟨1,216,295,true⟩, +⟨1,216,297,true⟩, +⟨1,216,299,true⟩, +⟨1,216,309,true⟩, +⟨1,216,311,true⟩, +⟨1,216,313,true⟩, +⟨1,216,315,true⟩, +⟨1,216,357,true⟩, +⟨1,216,359,true⟩, +⟨1,216,361,true⟩, +⟨1,216,363,true⟩, +⟨1,216,373,true⟩, +⟨1,216,375,true⟩, +⟨1,216,377,true⟩, +⟨1,216,379,true⟩, +⟨1,216,421,true⟩, +⟨1,216,423,true⟩, +⟨1,216,425,true⟩, +⟨1,216,427,true⟩, +⟨1,216,437,true⟩, +⟨1,216,439,true⟩, +⟨1,216,441,true⟩, +⟨1,216,443,true⟩, +⟨1,216,470,true⟩, +⟨1,216,485,true⟩, +⟨1,216,487,true⟩, +⟨1,216,489,true⟩, +⟨1,216,491,true⟩, +⟨1,216,501,true⟩, +⟨1,216,503,true⟩, +⟨1,216,505,true⟩, +⟨1,216,507,true⟩, +⟨1,216,514,true⟩, +⟨1,216,515,true⟩, +⟨1,216,518,true⟩, +⟨1,216,519,true⟩, +⟨1,216,530,true⟩, +⟨1,216,531,true⟩, +⟨1,216,534,true⟩, +⟨1,216,535,true⟩, +⟨1,216,544,true⟩, +⟨1,216,546,true⟩, +⟨1,216,548,true⟩, +⟨1,216,550,true⟩, +⟨1,216,573,true⟩, +⟨1,216,575,true⟩, +⟨1,216,589,true⟩, +⟨1,216,591,true⟩, +⟨1,216,605,true⟩, +⟨1,216,607,true⟩, +⟨1,216,621,true⟩, +⟨1,216,623,true⟩, +⟨1,216,637,true⟩, +⟨1,216,639,true⟩, +⟨1,216,653,true⟩, +⟨1,216,655,true⟩, +⟨1,216,669,true⟩, +⟨1,216,671,true⟩, +⟨1,216,685,true⟩, +⟨1,216,687,true⟩, +⟨1,216,708,true⟩, +⟨1,216,710,true⟩, +⟨1,216,724,true⟩, +⟨1,216,726,true⟩, +⟨1,216,906,true⟩, +⟨1,216,920,true⟩, +⟨1,217,241,true⟩, +⟨1,217,247,true⟩, +⟨1,217,293,true⟩, +⟨1,217,295,true⟩, +⟨1,217,297,true⟩, +⟨1,217,299,true⟩, +⟨1,217,309,true⟩, +⟨1,217,311,true⟩, +⟨1,217,313,true⟩, +⟨1,217,315,true⟩, +⟨1,217,323,true⟩, +⟨1,217,325,true⟩, +⟨1,217,329,true⟩, +⟨1,217,335,true⟩, +⟨1,217,353,true⟩, +⟨1,217,355,true⟩, +⟨1,217,365,true⟩, +⟨1,217,367,true⟩, +⟨1,217,369,true⟩, +⟨1,217,371,true⟩, +⟨1,217,381,true⟩, +⟨1,217,383,true⟩, +⟨1,217,421,true⟩, +⟨1,217,423,true⟩, +⟨1,217,425,true⟩, +⟨1,217,427,true⟩, +⟨1,217,437,true⟩, +⟨1,217,439,true⟩, +⟨1,217,441,true⟩, +⟨1,217,443,true⟩] +def chunk31 : List Event := [⟨1,217,469,true⟩, +⟨1,217,481,true⟩, +⟨1,217,483,true⟩, +⟨1,217,493,true⟩, +⟨1,217,495,true⟩, +⟨1,217,497,true⟩, +⟨1,217,499,true⟩, +⟨1,217,509,true⟩, +⟨1,217,511,true⟩, +⟨1,217,514,true⟩, +⟨1,217,515,true⟩, +⟨1,217,518,true⟩, +⟨1,217,519,true⟩, +⟨1,217,528,true⟩, +⟨1,217,529,true⟩, +⟨1,217,532,true⟩, +⟨1,217,533,true⟩, +⟨1,217,544,true⟩, +⟨1,217,549,true⟩, +⟨1,217,550,true⟩, +⟨1,217,558,true⟩, +⟨1,217,559,true⟩, +⟨1,217,573,true⟩, +⟨1,217,575,true⟩, +⟨1,217,588,true⟩, +⟨1,217,590,true⟩, +⟨1,217,605,true⟩, +⟨1,217,607,true⟩, +⟨1,217,620,true⟩, +⟨1,217,622,true⟩, +⟨1,217,637,true⟩, +⟨1,217,639,true⟩, +⟨1,217,652,true⟩, +⟨1,217,654,true⟩, +⟨1,217,669,true⟩, +⟨1,217,671,true⟩, +⟨1,217,684,true⟩, +⟨1,217,686,true⟩, +⟨1,217,708,true⟩, +⟨1,217,710,true⟩, +⟨1,217,720,true⟩, +⟨1,217,722,true⟩, +⟨1,217,802,true⟩, +⟨1,217,906,true⟩, +⟨1,217,918,true⟩, +⟨1,217,945,true⟩, +⟨1,217,956,true⟩, +⟨1,218,241,true⟩, +⟨1,218,247,true⟩, +⟨1,218,289,true⟩, +⟨1,218,291,true⟩, +⟨1,218,301,true⟩, +⟨1,218,303,true⟩, +⟨1,218,305,true⟩, +⟨1,218,307,true⟩, +⟨1,218,317,true⟩, +⟨1,218,319,true⟩, +⟨1,218,322,true⟩, +⟨1,218,324,true⟩, +⟨1,218,328,true⟩, +⟨1,218,334,true⟩, +⟨1,218,357,true⟩, +⟨1,218,359,true⟩, +⟨1,218,361,true⟩, +⟨1,218,363,true⟩, +⟨1,218,373,true⟩, +⟨1,218,375,true⟩, +⟨1,218,377,true⟩, +⟨1,218,379,true⟩, +⟨1,218,417,true⟩, +⟨1,218,419,true⟩, +⟨1,218,429,true⟩, +⟨1,218,431,true⟩, +⟨1,218,433,true⟩, +⟨1,218,435,true⟩, +⟨1,218,445,true⟩, +⟨1,218,447,true⟩, +⟨1,218,467,true⟩, +⟨1,218,485,true⟩, +⟨1,218,487,true⟩, +⟨1,218,489,true⟩, +⟨1,218,491,true⟩, +⟨1,218,501,true⟩, +⟨1,218,503,true⟩, +⟨1,218,505,true⟩, +⟨1,218,507,true⟩, +⟨1,218,514,true⟩, +⟨1,218,515,true⟩, +⟨1,218,518,true⟩, +⟨1,218,519,true⟩, +⟨1,218,528,true⟩, +⟨1,218,529,true⟩, +⟨1,218,532,true⟩, +⟨1,218,533,true⟩, +⟨1,218,544,true⟩, +⟨1,218,550,true⟩, +⟨1,218,554,true⟩, +⟨1,218,559,true⟩, +⟨1,218,572,true⟩, +⟨1,218,574,true⟩, +⟨1,218,589,true⟩, +⟨1,218,591,true⟩, +⟨1,218,604,true⟩, +⟨1,218,606,true⟩, +⟨1,218,621,true⟩, +⟨1,218,623,true⟩, +⟨1,218,636,true⟩, +⟨1,218,638,true⟩, +⟨1,218,653,true⟩, +⟨1,218,655,true⟩, +⟨1,218,668,true⟩, +⟨1,218,670,true⟩, +⟨1,218,685,true⟩, +⟨1,218,687,true⟩, +⟨1,218,708,true⟩, +⟨1,218,710,true⟩, +⟨1,218,720,true⟩, +⟨1,218,722,true⟩, +⟨1,218,786,true⟩, +⟨1,218,816,true⟩, +⟨1,218,906,true⟩, +⟨1,218,918,true⟩, +⟨1,218,943,true⟩, +⟨1,219,241,true⟩, +⟨1,219,247,true⟩, +⟨1,219,289,true⟩, +⟨1,219,291,true⟩, +⟨1,219,301,true⟩, +⟨1,219,303,true⟩, +⟨1,219,305,true⟩, +⟨1,219,307,true⟩, +⟨1,219,317,true⟩, +⟨1,219,319,true⟩, +⟨1,219,353,true⟩, +⟨1,219,355,true⟩, +⟨1,219,365,true⟩, +⟨1,219,367,true⟩, +⟨1,219,369,true⟩, +⟨1,219,371,true⟩, +⟨1,219,381,true⟩, +⟨1,219,383,true⟩, +⟨1,219,417,true⟩, +⟨1,219,419,true⟩, +⟨1,219,429,true⟩, +⟨1,219,431,true⟩, +⟨1,219,433,true⟩, +⟨1,219,435,true⟩, +⟨1,219,445,true⟩, +⟨1,219,447,true⟩, +⟨1,219,464,true⟩, +⟨1,219,481,true⟩, +⟨1,219,483,true⟩, +⟨1,219,493,true⟩, +⟨1,219,495,true⟩, +⟨1,219,497,true⟩, +⟨1,219,499,true⟩, +⟨1,219,509,true⟩, +⟨1,219,511,true⟩, +⟨1,219,514,true⟩, +⟨1,219,515,true⟩, +⟨1,219,518,true⟩, +⟨1,219,519,true⟩, +⟨1,219,530,true⟩, +⟨1,219,531,true⟩, +⟨1,219,534,true⟩, +⟨1,219,535,true⟩, +⟨1,219,544,true⟩, +⟨1,219,546,true⟩, +⟨1,219,548,true⟩, +⟨1,219,550,true⟩, +⟨1,219,572,true⟩, +⟨1,219,574,true⟩, +⟨1,219,588,true⟩, +⟨1,219,590,true⟩, +⟨1,219,604,true⟩, +⟨1,219,606,true⟩, +⟨1,219,620,true⟩, +⟨1,219,622,true⟩, +⟨1,219,636,true⟩, +⟨1,219,638,true⟩, +⟨1,219,652,true⟩, +⟨1,219,654,true⟩, +⟨1,219,668,true⟩, +⟨1,219,670,true⟩, +⟨1,219,684,true⟩, +⟨1,219,686,true⟩, +⟨1,219,708,true⟩, +⟨1,219,710,true⟩, +⟨1,219,724,true⟩, +⟨1,219,726,true⟩, +⟨1,219,786,true⟩, +⟨1,219,802,true⟩, +⟨1,219,816,true⟩, +⟨1,219,906,true⟩, +⟨1,219,920,true⟩, +⟨1,220,241,true⟩, +⟨1,220,247,true⟩, +⟨1,220,293,true⟩, +⟨1,220,295,true⟩, +⟨1,220,297,true⟩] +def chunk32 : List Event := [⟨1,220,299,true⟩, +⟨1,220,309,true⟩, +⟨1,220,311,true⟩, +⟨1,220,313,true⟩, +⟨1,220,315,true⟩, +⟨1,220,324,true⟩, +⟨1,220,325,true⟩, +⟨1,220,329,true⟩, +⟨1,220,334,true⟩, +⟨1,220,357,true⟩, +⟨1,220,359,true⟩, +⟨1,220,361,true⟩, +⟨1,220,363,true⟩, +⟨1,220,373,true⟩, +⟨1,220,375,true⟩, +⟨1,220,377,true⟩, +⟨1,220,379,true⟩, +⟨1,220,417,true⟩, +⟨1,220,419,true⟩, +⟨1,220,429,true⟩, +⟨1,220,431,true⟩, +⟨1,220,433,true⟩, +⟨1,220,435,true⟩, +⟨1,220,445,true⟩, +⟨1,220,447,true⟩, +⟨1,220,478,true⟩, +⟨1,220,481,true⟩, +⟨1,220,483,true⟩, +⟨1,220,493,true⟩, +⟨1,220,495,true⟩, +⟨1,220,497,true⟩, +⟨1,220,499,true⟩, +⟨1,220,509,true⟩, +⟨1,220,511,true⟩, +⟨1,220,512,true⟩, +⟨1,220,513,true⟩, +⟨1,220,516,true⟩, +⟨1,220,517,true⟩, +⟨1,220,530,true⟩, +⟨1,220,531,true⟩, +⟨1,220,534,true⟩, +⟨1,220,535,true⟩, +⟨1,220,544,true⟩, +⟨1,220,546,true⟩, +⟨1,220,549,true⟩, +⟨1,220,550,true⟩, +⟨1,220,554,true⟩, +⟨1,220,555,true⟩, +⟨1,220,573,true⟩, +⟨1,220,575,true⟩, +⟨1,220,589,true⟩, +⟨1,220,591,true⟩, +⟨1,220,604,true⟩, +⟨1,220,606,true⟩, +⟨1,220,620,true⟩, +⟨1,220,622,true⟩, +⟨1,220,637,true⟩, +⟨1,220,639,true⟩, +⟨1,220,653,true⟩, +⟨1,220,655,true⟩, +⟨1,220,668,true⟩, +⟨1,220,670,true⟩, +⟨1,220,684,true⟩, +⟨1,220,686,true⟩, +⟨1,220,704,true⟩, +⟨1,220,706,true⟩, +⟨1,220,724,true⟩, +⟨1,220,726,true⟩, +⟨1,220,816,true⟩, +⟨1,220,904,true⟩, +⟨1,220,920,true⟩, +⟨1,220,943,true⟩, +⟨1,220,956,true⟩, +⟨1,221,241,true⟩, +⟨1,221,247,true⟩, +⟨1,221,293,true⟩, +⟨1,221,295,true⟩, +⟨1,221,297,true⟩, +⟨1,221,299,true⟩, +⟨1,221,309,true⟩, +⟨1,221,311,true⟩, +⟨1,221,313,true⟩, +⟨1,221,315,true⟩, +⟨1,221,353,true⟩, +⟨1,221,355,true⟩, +⟨1,221,365,true⟩, +⟨1,221,367,true⟩, +⟨1,221,369,true⟩, +⟨1,221,371,true⟩, +⟨1,221,381,true⟩, +⟨1,221,383,true⟩, +⟨1,221,417,true⟩, +⟨1,221,419,true⟩, +⟨1,221,429,true⟩, +⟨1,221,431,true⟩, +⟨1,221,433,true⟩, +⟨1,221,435,true⟩, +⟨1,221,445,true⟩, +⟨1,221,447,true⟩, +⟨1,221,477,true⟩, +⟨1,221,485,true⟩, +⟨1,221,487,true⟩, +⟨1,221,489,true⟩, +⟨1,221,491,true⟩, +⟨1,221,501,true⟩, +⟨1,221,503,true⟩, +⟨1,221,505,true⟩, +⟨1,221,507,true⟩, +⟨1,221,512,true⟩, +⟨1,221,513,true⟩, +⟨1,221,516,true⟩, +⟨1,221,517,true⟩, +⟨1,221,528,true⟩, +⟨1,221,529,true⟩, +⟨1,221,532,true⟩, +⟨1,221,533,true⟩, +⟨1,221,544,true⟩, +⟨1,221,546,true⟩, +⟨1,221,548,true⟩, +⟨1,221,550,true⟩, +⟨1,221,573,true⟩, +⟨1,221,575,true⟩, +⟨1,221,588,true⟩, +⟨1,221,590,true⟩, +⟨1,221,604,true⟩, +⟨1,221,606,true⟩, +⟨1,221,621,true⟩, +⟨1,221,623,true⟩, +⟨1,221,637,true⟩, +⟨1,221,639,true⟩, +⟨1,221,652,true⟩, +⟨1,221,654,true⟩, +⟨1,221,668,true⟩, +⟨1,221,670,true⟩, +⟨1,221,685,true⟩, +⟨1,221,687,true⟩, +⟨1,221,704,true⟩, +⟨1,221,706,true⟩, +⟨1,221,720,true⟩, +⟨1,221,722,true⟩, +⟨1,221,802,true⟩, +⟨1,221,816,true⟩, +⟨1,221,904,true⟩, +⟨1,221,918,true⟩, +⟨1,222,241,true⟩, +⟨1,222,247,true⟩, +⟨1,222,289,true⟩, +⟨1,222,291,true⟩, +⟨1,222,301,true⟩, +⟨1,222,303,true⟩, +⟨1,222,305,true⟩, +⟨1,222,307,true⟩, +⟨1,222,317,true⟩, +⟨1,222,319,true⟩, +⟨1,222,357,true⟩, +⟨1,222,359,true⟩, +⟨1,222,361,true⟩, +⟨1,222,363,true⟩, +⟨1,222,373,true⟩, +⟨1,222,375,true⟩, +⟨1,222,377,true⟩, +⟨1,222,379,true⟩, +⟨1,222,421,true⟩, +⟨1,222,423,true⟩, +⟨1,222,425,true⟩, +⟨1,222,427,true⟩, +⟨1,222,437,true⟩, +⟨1,222,439,true⟩, +⟨1,222,441,true⟩, +⟨1,222,443,true⟩, +⟨1,222,475,true⟩, +⟨1,222,481,true⟩, +⟨1,222,483,true⟩, +⟨1,222,493,true⟩, +⟨1,222,495,true⟩, +⟨1,222,497,true⟩, +⟨1,222,499,true⟩, +⟨1,222,509,true⟩, +⟨1,222,511,true⟩, +⟨1,222,512,true⟩, +⟨1,222,513,true⟩, +⟨1,222,516,true⟩, +⟨1,222,517,true⟩, +⟨1,222,528,true⟩, +⟨1,222,529,true⟩, +⟨1,222,532,true⟩, +⟨1,222,533,true⟩, +⟨1,222,544,true⟩, +⟨1,222,546,true⟩, +⟨1,222,548,true⟩, +⟨1,222,550,true⟩, +⟨1,222,572,true⟩, +⟨1,222,574,true⟩, +⟨1,222,589,true⟩, +⟨1,222,591,true⟩, +⟨1,222,605,true⟩, +⟨1,222,607,true⟩, +⟨1,222,620,true⟩, +⟨1,222,622,true⟩, +⟨1,222,636,true⟩] +def chunk33 : List Event := [⟨1,222,638,true⟩, +⟨1,222,653,true⟩, +⟨1,222,655,true⟩, +⟨1,222,669,true⟩, +⟨1,222,671,true⟩, +⟨1,222,684,true⟩, +⟨1,222,686,true⟩, +⟨1,222,704,true⟩, +⟨1,222,706,true⟩, +⟨1,222,720,true⟩, +⟨1,222,722,true⟩, +⟨1,222,786,true⟩, +⟨1,222,904,true⟩, +⟨1,222,918,true⟩, +⟨1,223,241,true⟩, +⟨1,223,247,true⟩, +⟨1,223,289,true⟩, +⟨1,223,291,true⟩, +⟨1,223,301,true⟩, +⟨1,223,303,true⟩, +⟨1,223,305,true⟩, +⟨1,223,307,true⟩, +⟨1,223,317,true⟩, +⟨1,223,319,true⟩, +⟨1,223,322,true⟩, +⟨1,223,323,true⟩, +⟨1,223,328,true⟩, +⟨1,223,335,true⟩, +⟨1,223,353,true⟩, +⟨1,223,355,true⟩, +⟨1,223,365,true⟩, +⟨1,223,367,true⟩, +⟨1,223,369,true⟩, +⟨1,223,371,true⟩, +⟨1,223,381,true⟩, +⟨1,223,383,true⟩, +⟨1,223,421,true⟩, +⟨1,223,423,true⟩, +⟨1,223,425,true⟩, +⟨1,223,427,true⟩, +⟨1,223,437,true⟩, +⟨1,223,439,true⟩, +⟨1,223,441,true⟩, +⟨1,223,443,true⟩, +⟨1,223,472,true⟩, +⟨1,223,485,true⟩, +⟨1,223,487,true⟩, +⟨1,223,489,true⟩, +⟨1,223,491,true⟩, +⟨1,223,501,true⟩, +⟨1,223,503,true⟩, +⟨1,223,505,true⟩, +⟨1,223,507,true⟩, +⟨1,223,512,true⟩, +⟨1,223,513,true⟩, +⟨1,223,516,true⟩, +⟨1,223,517,true⟩, +⟨1,223,530,true⟩, +⟨1,223,531,true⟩, +⟨1,223,534,true⟩, +⟨1,223,535,true⟩, +⟨1,223,544,true⟩, +⟨1,223,546,true⟩, +⟨1,223,550,true⟩, +⟨1,223,555,true⟩, +⟨1,223,558,true⟩, +⟨1,223,572,true⟩, +⟨1,223,574,true⟩, +⟨1,223,588,true⟩, +⟨1,223,590,true⟩, +⟨1,223,605,true⟩, +⟨1,223,607,true⟩, +⟨1,223,621,true⟩, +⟨1,223,623,true⟩, +⟨1,223,636,true⟩, +⟨1,223,638,true⟩, +⟨1,223,652,true⟩, +⟨1,223,654,true⟩, +⟨1,223,669,true⟩, +⟨1,223,671,true⟩, +⟨1,223,685,true⟩, +⟨1,223,687,true⟩, +⟨1,223,704,true⟩, +⟨1,223,706,true⟩, +⟨1,223,724,true⟩, +⟨1,223,726,true⟩, +⟨1,223,786,true⟩, +⟨1,223,802,true⟩, +⟨1,223,904,true⟩, +⟨1,223,920,true⟩, +⟨1,223,945,true⟩, +⟨1,224,242,true⟩, +⟨1,224,264,true⟩, +⟨1,224,276,true⟩, +⟨1,224,291,true⟩, +⟨1,224,295,true⟩, +⟨1,224,299,true⟩, +⟨1,224,303,true⟩, +⟨1,224,322,true⟩, +⟨1,224,326,true⟩, +⟨1,224,328,true⟩, +⟨1,224,332,true⟩, +⟨1,224,338,true⟩, +⟨1,224,342,true⟩, +⟨1,224,344,true⟩, +⟨1,224,348,true⟩, +⟨1,224,372,true⟩, +⟨1,224,374,true⟩, +⟨1,224,380,true⟩, +⟨1,224,382,true⟩, +⟨1,224,386,true⟩, +⟨1,224,390,true⟩, +⟨1,224,392,true⟩, +⟨1,224,396,true⟩, +⟨1,224,402,true⟩, +⟨1,224,406,true⟩, +⟨1,224,408,true⟩, +⟨1,224,412,true⟩, +⟨1,224,418,true⟩, +⟨1,224,422,true⟩, +⟨1,224,424,true⟩, +⟨1,224,428,true⟩, +⟨1,224,450,true⟩, +⟨1,224,454,true⟩, +⟨1,224,456,true⟩, +⟨1,224,460,true⟩, +⟨1,224,466,true⟩, +⟨1,224,470,true⟩, +⟨1,224,472,true⟩, +⟨1,224,476,true⟩, +⟨1,224,486,true⟩, +⟨1,224,501,true⟩, +⟨1,224,503,true⟩, +⟨1,224,505,true⟩, +⟨1,224,507,true⟩, +⟨1,224,521,true⟩, +⟨1,224,523,true⟩, +⟨1,224,537,true⟩, +⟨1,224,539,true⟩, +⟨1,224,553,true⟩, +⟨1,224,555,true⟩, +⟨1,224,560,true⟩, +⟨1,224,562,true⟩, +⟨1,224,564,true⟩, +⟨1,224,566,true⟩, +⟨1,224,578,true⟩, +⟨1,224,579,true⟩, +⟨1,224,582,true⟩, +⟨1,224,583,true⟩, +⟨1,224,601,true⟩, +⟨1,224,603,true⟩, +⟨1,224,621,true⟩, +⟨1,224,623,true⟩, +⟨1,224,660,true⟩, +⟨1,224,662,true⟩, +⟨1,224,697,true⟩, +⟨1,224,699,true⟩, +⟨1,224,713,true⟩, +⟨1,224,715,true⟩, +⟨1,224,729,true⟩, +⟨1,224,731,true⟩, +⟨1,224,864,true⟩, +⟨1,225,242,true⟩, +⟨1,225,264,true⟩, +⟨1,225,276,true⟩, +⟨1,225,289,true⟩, +⟨1,225,293,true⟩, +⟨1,225,297,true⟩, +⟨1,225,301,true⟩, +⟨1,225,307,true⟩, +⟨1,225,308,true⟩, +⟨1,225,318,true⟩, +⟨1,225,319,true⟩, +⟨1,225,320,true⟩, +⟨1,225,324,true⟩, +⟨1,225,330,true⟩, +⟨1,225,334,true⟩, +⟨1,225,338,true⟩, +⟨1,225,342,true⟩, +⟨1,225,344,true⟩, +⟨1,225,348,true⟩, +⟨1,225,372,true⟩, +⟨1,225,374,true⟩, +⟨1,225,380,true⟩, +⟨1,225,382,true⟩, +⟨1,225,384,true⟩, +⟨1,225,388,true⟩, +⟨1,225,394,true⟩, +⟨1,225,398,true⟩, +⟨1,225,402,true⟩, +⟨1,225,406,true⟩, +⟨1,225,408,true⟩, +⟨1,225,412,true⟩, +⟨1,225,416,true⟩, +⟨1,225,420,true⟩, +⟨1,225,426,true⟩, +⟨1,225,430,true⟩, +⟨1,225,448,true⟩, +⟨1,225,452,true⟩, +⟨1,225,458,true⟩] +def chunk34 : List Event := [⟨1,225,462,true⟩, +⟨1,225,466,true⟩, +⟨1,225,470,true⟩, +⟨1,225,472,true⟩, +⟨1,225,476,true⟩, +⟨1,225,485,true⟩, +⟨1,225,501,true⟩, +⟨1,225,503,true⟩, +⟨1,225,505,true⟩, +⟨1,225,507,true⟩, +⟨1,225,521,true⟩, +⟨1,225,523,true⟩, +⟨1,225,537,true⟩, +⟨1,225,539,true⟩, +⟨1,225,552,true⟩, +⟨1,225,554,true⟩, +⟨1,225,560,true⟩, +⟨1,225,564,true⟩, +⟨1,225,565,true⟩, +⟨1,225,566,true⟩, +⟨1,225,570,true⟩, +⟨1,225,574,true⟩, +⟨1,225,576,true⟩, +⟨1,225,577,true⟩, +⟨1,225,580,true⟩, +⟨1,225,581,true⟩, +⟨1,225,600,true⟩, +⟨1,225,602,true⟩, +⟨1,225,621,true⟩, +⟨1,225,623,true⟩, +⟨1,225,660,true⟩, +⟨1,225,662,true⟩, +⟨1,225,697,true⟩, +⟨1,225,699,true⟩, +⟨1,225,712,true⟩, +⟨1,225,714,true⟩, +⟨1,225,728,true⟩, +⟨1,225,730,true⟩, +⟨1,225,772,true⟩, +⟨1,225,864,true⟩, +⟨1,225,946,true⟩, +⟨1,225,957,true⟩, +⟨1,226,242,true⟩, +⟨1,226,264,true⟩, +⟨1,226,276,true⟩, +⟨1,226,291,true⟩, +⟨1,226,295,true⟩, +⟨1,226,299,true⟩, +⟨1,226,303,true⟩, +⟨1,226,306,true⟩, +⟨1,226,309,true⟩, +⟨1,226,310,true⟩, +⟨1,226,311,true⟩, +⟨1,226,312,true⟩, +⟨1,226,313,true⟩, +⟨1,226,315,true⟩, +⟨1,226,316,true⟩, +⟨1,226,322,true⟩, +⟨1,226,326,true⟩, +⟨1,226,328,true⟩, +⟨1,226,332,true⟩, +⟨1,226,336,true⟩, +⟨1,226,340,true⟩, +⟨1,226,346,true⟩, +⟨1,226,350,true⟩, +⟨1,226,368,true⟩, +⟨1,226,370,true⟩, +⟨1,226,376,true⟩, +⟨1,226,378,true⟩, +⟨1,226,384,true⟩, +⟨1,226,388,true⟩, +⟨1,226,394,true⟩, +⟨1,226,398,true⟩, +⟨1,226,402,true⟩, +⟨1,226,406,true⟩, +⟨1,226,408,true⟩, +⟨1,226,412,true⟩, +⟨1,226,418,true⟩, +⟨1,226,422,true⟩, +⟨1,226,424,true⟩, +⟨1,226,428,true⟩, +⟨1,226,450,true⟩, +⟨1,226,454,true⟩, +⟨1,226,456,true⟩, +⟨1,226,460,true⟩, +⟨1,226,464,true⟩, +⟨1,226,468,true⟩, +⟨1,226,474,true⟩, +⟨1,226,478,true⟩, +⟨1,226,483,true⟩, +⟨1,226,497,true⟩, +⟨1,226,499,true⟩, +⟨1,226,509,true⟩, +⟨1,226,511,true⟩, +⟨1,226,521,true⟩, +⟨1,226,523,true⟩, +⟨1,226,536,true⟩, +⟨1,226,538,true⟩, +⟨1,226,553,true⟩, +⟨1,226,555,true⟩, +⟨1,226,560,true⟩, +⟨1,226,564,true⟩, +⟨1,226,565,true⟩, +⟨1,226,576,true⟩, +⟨1,226,577,true⟩, +⟨1,226,580,true⟩, +⟨1,226,581,true⟩, +⟨1,226,601,true⟩, +⟨1,226,603,true⟩, +⟨1,226,620,true⟩, +⟨1,226,622,true⟩, +⟨1,226,660,true⟩, +⟨1,226,662,true⟩, +⟨1,226,696,true⟩, +⟨1,226,698,true⟩, +⟨1,226,713,true⟩, +⟨1,226,715,true⟩, +⟨1,226,728,true⟩, +⟨1,226,730,true⟩, +⟨1,226,760,true⟩, +⟨1,226,864,true⟩, +⟨1,226,947,true⟩, +⟨1,226,955,true⟩, +⟨1,227,242,true⟩, +⟨1,227,264,true⟩, +⟨1,227,276,true⟩, +⟨1,227,289,true⟩, +⟨1,227,293,true⟩, +⟨1,227,297,true⟩, +⟨1,227,301,true⟩, +⟨1,227,320,true⟩, +⟨1,227,324,true⟩, +⟨1,227,330,true⟩, +⟨1,227,334,true⟩, +⟨1,227,336,true⟩, +⟨1,227,340,true⟩, +⟨1,227,346,true⟩, +⟨1,227,350,true⟩, +⟨1,227,368,true⟩, +⟨1,227,370,true⟩, +⟨1,227,376,true⟩, +⟨1,227,378,true⟩, +⟨1,227,386,true⟩, +⟨1,227,390,true⟩, +⟨1,227,392,true⟩, +⟨1,227,396,true⟩, +⟨1,227,402,true⟩, +⟨1,227,406,true⟩, +⟨1,227,408,true⟩, +⟨1,227,412,true⟩, +⟨1,227,416,true⟩, +⟨1,227,420,true⟩, +⟨1,227,426,true⟩, +⟨1,227,430,true⟩, +⟨1,227,448,true⟩, +⟨1,227,452,true⟩, +⟨1,227,458,true⟩, +⟨1,227,462,true⟩, +⟨1,227,464,true⟩, +⟨1,227,468,true⟩, +⟨1,227,474,true⟩, +⟨1,227,478,true⟩, +⟨1,227,480,true⟩, +⟨1,227,497,true⟩, +⟨1,227,499,true⟩, +⟨1,227,509,true⟩, +⟨1,227,511,true⟩, +⟨1,227,521,true⟩, +⟨1,227,523,true⟩, +⟨1,227,536,true⟩, +⟨1,227,538,true⟩, +⟨1,227,552,true⟩, +⟨1,227,554,true⟩, +⟨1,227,560,true⟩, +⟨1,227,562,true⟩, +⟨1,227,564,true⟩, +⟨1,227,566,true⟩, +⟨1,227,578,true⟩, +⟨1,227,579,true⟩, +⟨1,227,582,true⟩, +⟨1,227,583,true⟩, +⟨1,227,600,true⟩, +⟨1,227,602,true⟩, +⟨1,227,620,true⟩, +⟨1,227,622,true⟩, +⟨1,227,660,true⟩, +⟨1,227,662,true⟩, +⟨1,227,696,true⟩, +⟨1,227,698,true⟩, +⟨1,227,712,true⟩, +⟨1,227,714,true⟩, +⟨1,227,729,true⟩, +⟨1,227,731,true⟩, +⟨1,227,760,true⟩, +⟨1,227,772,true⟩, +⟨1,227,864,true⟩, +⟨1,228,242,true⟩, +⟨1,228,264,true⟩, +⟨1,228,276,true⟩, +⟨1,228,291,true⟩] +def chunk35 : List Event := [⟨1,228,295,true⟩, +⟨1,228,299,true⟩, +⟨1,228,303,true⟩, +⟨1,228,306,true⟩, +⟨1,228,307,true⟩, +⟨1,228,310,true⟩, +⟨1,228,311,true⟩, +⟨1,228,312,true⟩, +⟨1,228,315,true⟩, +⟨1,228,316,true⟩, +⟨1,228,319,true⟩, +⟨1,228,322,true⟩, +⟨1,228,326,true⟩, +⟨1,228,328,true⟩, +⟨1,228,332,true⟩, +⟨1,228,338,true⟩, +⟨1,228,342,true⟩, +⟨1,228,344,true⟩, +⟨1,228,348,true⟩, +⟨1,228,372,true⟩, +⟨1,228,374,true⟩, +⟨1,228,380,true⟩, +⟨1,228,382,true⟩, +⟨1,228,386,true⟩, +⟨1,228,390,true⟩, +⟨1,228,392,true⟩, +⟨1,228,396,true⟩, +⟨1,228,400,true⟩, +⟨1,228,404,true⟩, +⟨1,228,410,true⟩, +⟨1,228,414,true⟩, +⟨1,228,416,true⟩, +⟨1,228,420,true⟩, +⟨1,228,426,true⟩, +⟨1,228,430,true⟩, +⟨1,228,448,true⟩, +⟨1,228,452,true⟩, +⟨1,228,458,true⟩, +⟨1,228,462,true⟩, +⟨1,228,464,true⟩, +⟨1,228,468,true⟩, +⟨1,228,474,true⟩, +⟨1,228,478,true⟩, +⟨1,228,494,true⟩, +⟨1,228,497,true⟩, +⟨1,228,499,true⟩, +⟨1,228,509,true⟩, +⟨1,228,511,true⟩, +⟨1,228,520,true⟩, +⟨1,228,522,true⟩, +⟨1,228,537,true⟩, +⟨1,228,539,true⟩, +⟨1,228,553,true⟩, +⟨1,228,555,true⟩, +⟨1,228,560,true⟩, +⟨1,228,562,true⟩, +⟨1,228,565,true⟩, +⟨1,228,574,true⟩, +⟨1,228,575,true⟩, +⟨1,228,578,true⟩, +⟨1,228,579,true⟩, +⟨1,228,582,true⟩, +⟨1,228,583,true⟩, +⟨1,228,600,true⟩, +⟨1,228,602,true⟩, +⟨1,228,620,true⟩, +⟨1,228,622,true⟩, +⟨1,228,656,true⟩, +⟨1,228,658,true⟩, +⟨1,228,696,true⟩, +⟨1,228,698,true⟩, +⟨1,228,712,true⟩, +⟨1,228,714,true⟩, +⟨1,228,729,true⟩, +⟨1,228,731,true⟩, +⟨1,228,746,true⟩, +⟨1,228,862,true⟩, +⟨1,228,946,true⟩, +⟨1,228,955,true⟩, +⟨1,229,242,true⟩, +⟨1,229,264,true⟩, +⟨1,229,276,true⟩, +⟨1,229,289,true⟩, +⟨1,229,293,true⟩, +⟨1,229,297,true⟩, +⟨1,229,301,true⟩, +⟨1,229,320,true⟩, +⟨1,229,324,true⟩, +⟨1,229,330,true⟩, +⟨1,229,334,true⟩, +⟨1,229,338,true⟩, +⟨1,229,342,true⟩, +⟨1,229,344,true⟩, +⟨1,229,348,true⟩, +⟨1,229,372,true⟩, +⟨1,229,374,true⟩, +⟨1,229,380,true⟩, +⟨1,229,382,true⟩, +⟨1,229,384,true⟩, +⟨1,229,388,true⟩, +⟨1,229,394,true⟩, +⟨1,229,398,true⟩, +⟨1,229,400,true⟩, +⟨1,229,404,true⟩, +⟨1,229,410,true⟩, +⟨1,229,414,true⟩, +⟨1,229,418,true⟩, +⟨1,229,422,true⟩, +⟨1,229,424,true⟩, +⟨1,229,428,true⟩, +⟨1,229,450,true⟩, +⟨1,229,454,true⟩, +⟨1,229,456,true⟩, +⟨1,229,460,true⟩, +⟨1,229,464,true⟩, +⟨1,229,468,true⟩, +⟨1,229,474,true⟩, +⟨1,229,478,true⟩, +⟨1,229,493,true⟩, +⟨1,229,497,true⟩, +⟨1,229,499,true⟩, +⟨1,229,509,true⟩, +⟨1,229,511,true⟩, +⟨1,229,520,true⟩, +⟨1,229,522,true⟩, +⟨1,229,537,true⟩, +⟨1,229,539,true⟩, +⟨1,229,552,true⟩, +⟨1,229,554,true⟩, +⟨1,229,560,true⟩, +⟨1,229,562,true⟩, +⟨1,229,564,true⟩, +⟨1,229,566,true⟩, +⟨1,229,576,true⟩, +⟨1,229,577,true⟩, +⟨1,229,580,true⟩, +⟨1,229,581,true⟩, +⟨1,229,601,true⟩, +⟨1,229,603,true⟩, +⟨1,229,620,true⟩, +⟨1,229,622,true⟩, +⟨1,229,656,true⟩, +⟨1,229,658,true⟩, +⟨1,229,696,true⟩, +⟨1,229,698,true⟩, +⟨1,229,713,true⟩, +⟨1,229,715,true⟩, +⟨1,229,728,true⟩, +⟨1,229,730,true⟩, +⟨1,229,746,true⟩, +⟨1,229,772,true⟩, +⟨1,229,862,true⟩, +⟨1,230,242,true⟩, +⟨1,230,264,true⟩, +⟨1,230,276,true⟩, +⟨1,230,291,true⟩, +⟨1,230,295,true⟩, +⟨1,230,299,true⟩, +⟨1,230,303,true⟩, +⟨1,230,322,true⟩, +⟨1,230,326,true⟩, +⟨1,230,328,true⟩, +⟨1,230,332,true⟩, +⟨1,230,336,true⟩, +⟨1,230,340,true⟩, +⟨1,230,346,true⟩, +⟨1,230,350,true⟩, +⟨1,230,368,true⟩, +⟨1,230,370,true⟩, +⟨1,230,376,true⟩, +⟨1,230,378,true⟩, +⟨1,230,384,true⟩, +⟨1,230,388,true⟩, +⟨1,230,394,true⟩, +⟨1,230,398,true⟩, +⟨1,230,400,true⟩, +⟨1,230,404,true⟩, +⟨1,230,410,true⟩, +⟨1,230,414,true⟩, +⟨1,230,416,true⟩, +⟨1,230,420,true⟩, +⟨1,230,426,true⟩, +⟨1,230,430,true⟩, +⟨1,230,448,true⟩, +⟨1,230,452,true⟩, +⟨1,230,458,true⟩, +⟨1,230,462,true⟩, +⟨1,230,466,true⟩, +⟨1,230,470,true⟩, +⟨1,230,472,true⟩, +⟨1,230,476,true⟩, +⟨1,230,491,true⟩, +⟨1,230,501,true⟩, +⟨1,230,503,true⟩, +⟨1,230,505,true⟩, +⟨1,230,507,true⟩, +⟨1,230,520,true⟩, +⟨1,230,522,true⟩, +⟨1,230,536,true⟩, +⟨1,230,538,true⟩] +def chunk36 : List Event := [⟨1,230,553,true⟩, +⟨1,230,555,true⟩, +⟨1,230,560,true⟩, +⟨1,230,562,true⟩, +⟨1,230,564,true⟩, +⟨1,230,566,true⟩, +⟨1,230,576,true⟩, +⟨1,230,577,true⟩, +⟨1,230,580,true⟩, +⟨1,230,581,true⟩, +⟨1,230,600,true⟩, +⟨1,230,602,true⟩, +⟨1,230,621,true⟩, +⟨1,230,623,true⟩, +⟨1,230,656,true⟩, +⟨1,230,658,true⟩, +⟨1,230,697,true⟩, +⟨1,230,699,true⟩, +⟨1,230,712,true⟩, +⟨1,230,714,true⟩, +⟨1,230,728,true⟩, +⟨1,230,730,true⟩, +⟨1,230,746,true⟩, +⟨1,230,760,true⟩, +⟨1,230,862,true⟩, +⟨1,231,242,true⟩, +⟨1,231,264,true⟩, +⟨1,231,276,true⟩, +⟨1,231,289,true⟩, +⟨1,231,293,true⟩, +⟨1,231,297,true⟩, +⟨1,231,301,true⟩, +⟨1,231,308,true⟩, +⟨1,231,309,true⟩, +⟨1,231,313,true⟩, +⟨1,231,318,true⟩, +⟨1,231,320,true⟩, +⟨1,231,324,true⟩, +⟨1,231,330,true⟩, +⟨1,231,334,true⟩, +⟨1,231,336,true⟩, +⟨1,231,340,true⟩, +⟨1,231,346,true⟩, +⟨1,231,350,true⟩, +⟨1,231,368,true⟩, +⟨1,231,370,true⟩, +⟨1,231,376,true⟩, +⟨1,231,378,true⟩, +⟨1,231,386,true⟩, +⟨1,231,390,true⟩, +⟨1,231,392,true⟩, +⟨1,231,396,true⟩, +⟨1,231,400,true⟩, +⟨1,231,404,true⟩, +⟨1,231,410,true⟩, +⟨1,231,414,true⟩, +⟨1,231,418,true⟩, +⟨1,231,422,true⟩, +⟨1,231,424,true⟩, +⟨1,231,428,true⟩, +⟨1,231,450,true⟩, +⟨1,231,454,true⟩, +⟨1,231,456,true⟩, +⟨1,231,460,true⟩, +⟨1,231,466,true⟩, +⟨1,231,470,true⟩, +⟨1,231,472,true⟩, +⟨1,231,476,true⟩, +⟨1,231,488,true⟩, +⟨1,231,501,true⟩, +⟨1,231,503,true⟩, +⟨1,231,505,true⟩, +⟨1,231,507,true⟩, +⟨1,231,520,true⟩, +⟨1,231,522,true⟩, +⟨1,231,536,true⟩, +⟨1,231,538,true⟩, +⟨1,231,552,true⟩, +⟨1,231,554,true⟩, +⟨1,231,560,true⟩, +⟨1,231,562,true⟩, +⟨1,231,565,true⟩, +⟨1,231,566,true⟩, +⟨1,231,570,true⟩, +⟨1,231,575,true⟩, +⟨1,231,578,true⟩, +⟨1,231,579,true⟩, +⟨1,231,582,true⟩, +⟨1,231,583,true⟩, +⟨1,231,601,true⟩, +⟨1,231,603,true⟩, +⟨1,231,621,true⟩, +⟨1,231,623,true⟩, +⟨1,231,656,true⟩, +⟨1,231,658,true⟩, +⟨1,231,697,true⟩, +⟨1,231,699,true⟩, +⟨1,231,713,true⟩, +⟨1,231,715,true⟩, +⟨1,231,729,true⟩, +⟨1,231,731,true⟩, +⟨1,231,746,true⟩, +⟨1,231,760,true⟩, +⟨1,231,772,true⟩, +⟨1,231,862,true⟩, +⟨1,231,947,true⟩, +⟨1,231,957,true⟩, +⟨1,232,248,true⟩, +⟨1,232,254,true⟩, +⟨1,232,266,true⟩, +⟨1,232,284,true⟩, +⟨1,232,307,true⟩, +⟨1,232,311,true⟩, +⟨1,232,315,true⟩, +⟨1,232,319,true⟩, +⟨1,232,324,true⟩, +⟨1,232,326,true⟩, +⟨1,232,332,true⟩, +⟨1,232,334,true⟩, +⟨1,232,339,true⟩, +⟨1,232,343,true⟩, +⟨1,232,347,true⟩, +⟨1,232,351,true⟩, +⟨1,232,356,true⟩, +⟨1,232,358,true⟩, +⟨1,232,364,true⟩, +⟨1,232,366,true⟩, +⟨1,232,389,true⟩, +⟨1,232,391,true⟩, +⟨1,232,393,true⟩, +⟨1,232,395,true⟩, +⟨1,232,403,true⟩, +⟨1,232,407,true⟩, +⟨1,232,411,true⟩, +⟨1,232,415,true⟩, +⟨1,232,434,true⟩, +⟨1,232,438,true⟩, +⟨1,232,440,true⟩, +⟨1,232,444,true⟩, +⟨1,232,453,true⟩, +⟨1,232,455,true⟩, +⟨1,232,457,true⟩, +⟨1,232,459,true⟩, +⟨1,232,466,true⟩, +⟨1,232,470,true⟩, +⟨1,232,472,true⟩, +⟨1,232,476,true⟩, +⟨1,232,485,true⟩, +⟨1,232,487,true⟩, +⟨1,232,489,true⟩, +⟨1,232,491,true⟩, +⟨1,232,502,true⟩, +⟨1,232,596,true⟩, +⟨1,232,598,true⟩, +⟨1,232,624,true⟩, +⟨1,232,626,true⟩, +⟨1,232,628,true⟩, +⟨1,232,630,true⟩, +⟨1,232,642,true⟩, +⟨1,232,643,true⟩, +⟨1,232,646,true⟩, +⟨1,232,647,true⟩, +⟨1,232,665,true⟩, +⟨1,232,667,true⟩, +⟨1,232,685,true⟩, +⟨1,232,687,true⟩, +⟨1,232,697,true⟩, +⟨1,232,699,true⟩, +⟨1,232,717,true⟩, +⟨1,232,719,true⟩, +⟨1,232,733,true⟩, +⟨1,232,735,true⟩, +⟨1,233,248,true⟩, +⟨1,233,254,true⟩, +⟨1,233,266,true⟩, +⟨1,233,284,true⟩, +⟨1,233,291,true⟩, +⟨1,233,292,true⟩, +⟨1,233,302,true⟩, +⟨1,233,303,true⟩, +⟨1,233,305,true⟩, +⟨1,233,309,true⟩, +⟨1,233,313,true⟩, +⟨1,233,317,true⟩, +⟨1,233,320,true⟩, +⟨1,233,322,true⟩, +⟨1,233,328,true⟩, +⟨1,233,330,true⟩, +⟨1,233,339,true⟩, +⟨1,233,343,true⟩, +⟨1,233,347,true⟩, +⟨1,233,351,true⟩, +⟨1,233,356,true⟩, +⟨1,233,358,true⟩, +⟨1,233,364,true⟩, +⟨1,233,366,true⟩, +⟨1,233,385,true⟩, +⟨1,233,387,true⟩, +⟨1,233,397,true⟩, +⟨1,233,399,true⟩] +def chunk37 : List Event := [⟨1,233,403,true⟩, +⟨1,233,407,true⟩, +⟨1,233,411,true⟩, +⟨1,233,415,true⟩, +⟨1,233,432,true⟩, +⟨1,233,436,true⟩, +⟨1,233,442,true⟩, +⟨1,233,446,true⟩, +⟨1,233,449,true⟩, +⟨1,233,451,true⟩, +⟨1,233,461,true⟩, +⟨1,233,463,true⟩, +⟨1,233,466,true⟩, +⟨1,233,470,true⟩, +⟨1,233,472,true⟩, +⟨1,233,476,true⟩, +⟨1,233,485,true⟩, +⟨1,233,487,true⟩, +⟨1,233,489,true⟩, +⟨1,233,491,true⟩, +⟨1,233,500,true⟩, +⟨1,233,596,true⟩, +⟨1,233,598,true⟩, +⟨1,233,624,true⟩, +⟨1,233,628,true⟩, +⟨1,233,629,true⟩, +⟨1,233,630,true⟩, +⟨1,233,634,true⟩, +⟨1,233,638,true⟩, +⟨1,233,640,true⟩, +⟨1,233,641,true⟩, +⟨1,233,644,true⟩, +⟨1,233,645,true⟩, +⟨1,233,664,true⟩, +⟨1,233,666,true⟩, +⟨1,233,685,true⟩, +⟨1,233,687,true⟩, +⟨1,233,697,true⟩, +⟨1,233,699,true⟩, +⟨1,233,716,true⟩, +⟨1,233,718,true⟩, +⟨1,233,732,true⟩, +⟨1,233,734,true⟩, +⟨1,233,768,true⟩, +⟨1,233,916,true⟩, +⟨1,233,930,true⟩, +⟨1,233,981,true⟩, +⟨1,233,986,true⟩, +⟨1,234,248,true⟩, +⟨1,234,254,true⟩, +⟨1,234,266,true⟩, +⟨1,234,284,true⟩, +⟨1,234,290,true⟩, +⟨1,234,293,true⟩, +⟨1,234,294,true⟩, +⟨1,234,295,true⟩, +⟨1,234,296,true⟩, +⟨1,234,297,true⟩, +⟨1,234,299,true⟩, +⟨1,234,300,true⟩, +⟨1,234,307,true⟩, +⟨1,234,311,true⟩, +⟨1,234,315,true⟩, +⟨1,234,319,true⟩, +⟨1,234,324,true⟩, +⟨1,234,326,true⟩, +⟨1,234,332,true⟩, +⟨1,234,334,true⟩, +⟨1,234,337,true⟩, +⟨1,234,341,true⟩, +⟨1,234,345,true⟩, +⟨1,234,349,true⟩, +⟨1,234,352,true⟩, +⟨1,234,354,true⟩, +⟨1,234,360,true⟩, +⟨1,234,362,true⟩, +⟨1,234,385,true⟩, +⟨1,234,387,true⟩, +⟨1,234,397,true⟩, +⟨1,234,399,true⟩, +⟨1,234,403,true⟩, +⟨1,234,407,true⟩, +⟨1,234,411,true⟩, +⟨1,234,415,true⟩, +⟨1,234,434,true⟩, +⟨1,234,438,true⟩, +⟨1,234,440,true⟩, +⟨1,234,444,true⟩, +⟨1,234,453,true⟩, +⟨1,234,455,true⟩, +⟨1,234,457,true⟩, +⟨1,234,459,true⟩, +⟨1,234,464,true⟩, +⟨1,234,468,true⟩, +⟨1,234,474,true⟩, +⟨1,234,478,true⟩, +⟨1,234,481,true⟩, +⟨1,234,483,true⟩, +⟨1,234,493,true⟩, +⟨1,234,495,true⟩, +⟨1,234,498,true⟩, +⟨1,234,596,true⟩, +⟨1,234,598,true⟩, +⟨1,234,624,true⟩, +⟨1,234,628,true⟩, +⟨1,234,629,true⟩, +⟨1,234,640,true⟩, +⟨1,234,641,true⟩, +⟨1,234,644,true⟩, +⟨1,234,645,true⟩, +⟨1,234,665,true⟩, +⟨1,234,667,true⟩, +⟨1,234,684,true⟩, +⟨1,234,686,true⟩, +⟨1,234,696,true⟩, +⟨1,234,698,true⟩, +⟨1,234,717,true⟩, +⟨1,234,719,true⟩, +⟨1,234,732,true⟩, +⟨1,234,734,true⟩, +⟨1,234,756,true⟩, +⟨1,234,902,true⟩, +⟨1,234,930,true⟩, +⟨1,234,982,true⟩, +⟨1,234,985,true⟩, +⟨1,235,248,true⟩, +⟨1,235,254,true⟩, +⟨1,235,266,true⟩, +⟨1,235,284,true⟩, +⟨1,235,305,true⟩, +⟨1,235,309,true⟩, +⟨1,235,313,true⟩, +⟨1,235,317,true⟩, +⟨1,235,320,true⟩, +⟨1,235,322,true⟩, +⟨1,235,328,true⟩, +⟨1,235,330,true⟩, +⟨1,235,337,true⟩, +⟨1,235,341,true⟩, +⟨1,235,345,true⟩, +⟨1,235,349,true⟩, +⟨1,235,352,true⟩, +⟨1,235,354,true⟩, +⟨1,235,360,true⟩, +⟨1,235,362,true⟩, +⟨1,235,389,true⟩, +⟨1,235,391,true⟩, +⟨1,235,393,true⟩, +⟨1,235,395,true⟩, +⟨1,235,403,true⟩, +⟨1,235,407,true⟩, +⟨1,235,411,true⟩, +⟨1,235,415,true⟩, +⟨1,235,432,true⟩, +⟨1,235,436,true⟩, +⟨1,235,442,true⟩, +⟨1,235,446,true⟩, +⟨1,235,449,true⟩, +⟨1,235,451,true⟩, +⟨1,235,461,true⟩, +⟨1,235,463,true⟩, +⟨1,235,464,true⟩, +⟨1,235,468,true⟩, +⟨1,235,474,true⟩, +⟨1,235,478,true⟩, +⟨1,235,481,true⟩, +⟨1,235,483,true⟩, +⟨1,235,493,true⟩, +⟨1,235,495,true⟩, +⟨1,235,496,true⟩, +⟨1,235,596,true⟩, +⟨1,235,598,true⟩, +⟨1,235,624,true⟩, +⟨1,235,626,true⟩, +⟨1,235,628,true⟩, +⟨1,235,630,true⟩, +⟨1,235,642,true⟩, +⟨1,235,643,true⟩, +⟨1,235,646,true⟩, +⟨1,235,647,true⟩, +⟨1,235,664,true⟩, +⟨1,235,666,true⟩, +⟨1,235,684,true⟩, +⟨1,235,686,true⟩, +⟨1,235,696,true⟩, +⟨1,235,698,true⟩, +⟨1,235,716,true⟩, +⟨1,235,718,true⟩, +⟨1,235,733,true⟩, +⟨1,235,735,true⟩, +⟨1,235,756,true⟩, +⟨1,235,768,true⟩, +⟨1,235,902,true⟩, +⟨1,235,916,true⟩, +⟨1,236,248,true⟩, +⟨1,236,254,true⟩, +⟨1,236,266,true⟩, +⟨1,236,284,true⟩, +⟨1,236,292,true⟩, +⟨1,236,293,true⟩] +def chunk38 : List Event := [⟨1,236,294,true⟩, +⟨1,236,295,true⟩, +⟨1,236,297,true⟩, +⟨1,236,299,true⟩, +⟨1,236,300,true⟩, +⟨1,236,302,true⟩, +⟨1,236,307,true⟩, +⟨1,236,311,true⟩, +⟨1,236,315,true⟩, +⟨1,236,319,true⟩, +⟨1,236,324,true⟩, +⟨1,236,326,true⟩, +⟨1,236,332,true⟩, +⟨1,236,334,true⟩, +⟨1,236,339,true⟩, +⟨1,236,343,true⟩, +⟨1,236,347,true⟩, +⟨1,236,351,true⟩, +⟨1,236,356,true⟩, +⟨1,236,358,true⟩, +⟨1,236,364,true⟩, +⟨1,236,366,true⟩, +⟨1,236,389,true⟩, +⟨1,236,391,true⟩, +⟨1,236,393,true⟩, +⟨1,236,395,true⟩, +⟨1,236,401,true⟩, +⟨1,236,405,true⟩, +⟨1,236,409,true⟩, +⟨1,236,413,true⟩, +⟨1,236,432,true⟩, +⟨1,236,436,true⟩, +⟨1,236,442,true⟩, +⟨1,236,446,true⟩, +⟨1,236,449,true⟩, +⟨1,236,451,true⟩, +⟨1,236,461,true⟩, +⟨1,236,463,true⟩, +⟨1,236,464,true⟩, +⟨1,236,468,true⟩, +⟨1,236,474,true⟩, +⟨1,236,478,true⟩, +⟨1,236,481,true⟩, +⟨1,236,483,true⟩, +⟨1,236,493,true⟩, +⟨1,236,495,true⟩, +⟨1,236,511,true⟩, +⟨1,236,592,true⟩, +⟨1,236,594,true⟩, +⟨1,236,624,true⟩, +⟨1,236,626,true⟩, +⟨1,236,629,true⟩, +⟨1,236,634,true⟩, +⟨1,236,639,true⟩, +⟨1,236,642,true⟩, +⟨1,236,643,true⟩, +⟨1,236,646,true⟩, +⟨1,236,647,true⟩, +⟨1,236,664,true⟩, +⟨1,236,666,true⟩, +⟨1,236,684,true⟩, +⟨1,236,686,true⟩, +⟨1,236,696,true⟩, +⟨1,236,698,true⟩, +⟨1,236,716,true⟩, +⟨1,236,718,true⟩, +⟨1,236,733,true⟩, +⟨1,236,735,true⟩, +⟨1,236,742,true⟩, +⟨1,236,806,true⟩, +⟨1,236,902,true⟩, +⟨1,236,916,true⟩, +⟨1,236,981,true⟩, +⟨1,236,985,true⟩, +⟨1,237,248,true⟩, +⟨1,237,254,true⟩, +⟨1,237,266,true⟩, +⟨1,237,284,true⟩, +⟨1,237,305,true⟩, +⟨1,237,309,true⟩, +⟨1,237,313,true⟩, +⟨1,237,317,true⟩, +⟨1,237,320,true⟩, +⟨1,237,322,true⟩, +⟨1,237,328,true⟩, +⟨1,237,330,true⟩, +⟨1,237,339,true⟩, +⟨1,237,343,true⟩, +⟨1,237,347,true⟩, +⟨1,237,351,true⟩, +⟨1,237,356,true⟩, +⟨1,237,358,true⟩, +⟨1,237,364,true⟩, +⟨1,237,366,true⟩, +⟨1,237,385,true⟩, +⟨1,237,387,true⟩, +⟨1,237,397,true⟩, +⟨1,237,399,true⟩, +⟨1,237,401,true⟩, +⟨1,237,405,true⟩, +⟨1,237,409,true⟩, +⟨1,237,413,true⟩, +⟨1,237,434,true⟩, +⟨1,237,438,true⟩, +⟨1,237,440,true⟩, +⟨1,237,444,true⟩, +⟨1,237,453,true⟩, +⟨1,237,455,true⟩, +⟨1,237,457,true⟩, +⟨1,237,459,true⟩, +⟨1,237,464,true⟩, +⟨1,237,468,true⟩, +⟨1,237,474,true⟩, +⟨1,237,478,true⟩, +⟨1,237,481,true⟩, +⟨1,237,483,true⟩, +⟨1,237,493,true⟩, +⟨1,237,495,true⟩, +⟨1,237,509,true⟩, +⟨1,237,592,true⟩, +⟨1,237,594,true⟩, +⟨1,237,624,true⟩, +⟨1,237,626,true⟩, +⟨1,237,628,true⟩, +⟨1,237,630,true⟩, +⟨1,237,640,true⟩, +⟨1,237,641,true⟩, +⟨1,237,644,true⟩, +⟨1,237,645,true⟩, +⟨1,237,665,true⟩, +⟨1,237,667,true⟩, +⟨1,237,684,true⟩, +⟨1,237,686,true⟩, +⟨1,237,696,true⟩, +⟨1,237,698,true⟩, +⟨1,237,717,true⟩, +⟨1,237,719,true⟩, +⟨1,237,732,true⟩, +⟨1,237,734,true⟩, +⟨1,237,742,true⟩, +⟨1,237,768,true⟩, +⟨1,237,806,true⟩, +⟨1,237,902,true⟩, +⟨1,237,930,true⟩, +⟨1,238,248,true⟩, +⟨1,238,254,true⟩, +⟨1,238,266,true⟩, +⟨1,238,284,true⟩, +⟨1,238,307,true⟩, +⟨1,238,311,true⟩, +⟨1,238,315,true⟩, +⟨1,238,319,true⟩, +⟨1,238,324,true⟩, +⟨1,238,326,true⟩, +⟨1,238,332,true⟩, +⟨1,238,334,true⟩, +⟨1,238,337,true⟩, +⟨1,238,341,true⟩, +⟨1,238,345,true⟩, +⟨1,238,349,true⟩, +⟨1,238,352,true⟩, +⟨1,238,354,true⟩, +⟨1,238,360,true⟩, +⟨1,238,362,true⟩, +⟨1,238,385,true⟩, +⟨1,238,387,true⟩, +⟨1,238,397,true⟩, +⟨1,238,399,true⟩, +⟨1,238,401,true⟩, +⟨1,238,405,true⟩, +⟨1,238,409,true⟩, +⟨1,238,413,true⟩, +⟨1,238,432,true⟩, +⟨1,238,436,true⟩, +⟨1,238,442,true⟩, +⟨1,238,446,true⟩, +⟨1,238,449,true⟩, +⟨1,238,451,true⟩, +⟨1,238,461,true⟩, +⟨1,238,463,true⟩, +⟨1,238,466,true⟩, +⟨1,238,470,true⟩, +⟨1,238,472,true⟩, +⟨1,238,476,true⟩, +⟨1,238,485,true⟩, +⟨1,238,487,true⟩, +⟨1,238,489,true⟩, +⟨1,238,491,true⟩, +⟨1,238,507,true⟩, +⟨1,238,592,true⟩, +⟨1,238,594,true⟩, +⟨1,238,624,true⟩, +⟨1,238,626,true⟩, +⟨1,238,628,true⟩, +⟨1,238,630,true⟩, +⟨1,238,640,true⟩, +⟨1,238,641,true⟩, +⟨1,238,644,true⟩, +⟨1,238,645,true⟩, +⟨1,238,664,true⟩] +def chunk39 : List Event := [⟨1,238,666,true⟩, +⟨1,238,685,true⟩, +⟨1,238,687,true⟩, +⟨1,238,697,true⟩, +⟨1,238,699,true⟩, +⟨1,238,716,true⟩, +⟨1,238,718,true⟩, +⟨1,238,732,true⟩, +⟨1,238,734,true⟩, +⟨1,238,742,true⟩, +⟨1,238,756,true⟩, +⟨1,238,806,true⟩, +⟨1,238,916,true⟩, +⟨1,238,930,true⟩, +⟨1,239,248,true⟩, +⟨1,239,254,true⟩, +⟨1,239,266,true⟩, +⟨1,239,284,true⟩, +⟨1,239,290,true⟩, +⟨1,239,291,true⟩, +⟨1,239,296,true⟩, +⟨1,239,303,true⟩, +⟨1,239,305,true⟩, +⟨1,239,309,true⟩, +⟨1,239,313,true⟩, +⟨1,239,317,true⟩, +⟨1,239,320,true⟩, +⟨1,239,322,true⟩, +⟨1,239,328,true⟩, +⟨1,239,330,true⟩, +⟨1,239,337,true⟩, +⟨1,239,341,true⟩, +⟨1,239,345,true⟩, +⟨1,239,349,true⟩, +⟨1,239,352,true⟩, +⟨1,239,354,true⟩, +⟨1,239,360,true⟩, +⟨1,239,362,true⟩, +⟨1,239,389,true⟩, +⟨1,239,391,true⟩, +⟨1,239,393,true⟩, +⟨1,239,395,true⟩, +⟨1,239,401,true⟩, +⟨1,239,405,true⟩, +⟨1,239,409,true⟩, +⟨1,239,413,true⟩, +⟨1,239,434,true⟩, +⟨1,239,438,true⟩, +⟨1,239,440,true⟩, +⟨1,239,444,true⟩, +⟨1,239,453,true⟩, +⟨1,239,455,true⟩, +⟨1,239,457,true⟩, +⟨1,239,459,true⟩, +⟨1,239,466,true⟩, +⟨1,239,470,true⟩, +⟨1,239,472,true⟩, +⟨1,239,476,true⟩, +⟨1,239,485,true⟩, +⟨1,239,487,true⟩, +⟨1,239,489,true⟩, +⟨1,239,491,true⟩, +⟨1,239,505,true⟩, +⟨1,239,592,true⟩, +⟨1,239,594,true⟩, +⟨1,239,624,true⟩, +⟨1,239,626,true⟩, +⟨1,239,629,true⟩, +⟨1,239,630,true⟩, +⟨1,239,638,true⟩, +⟨1,239,639,true⟩, +⟨1,239,642,true⟩, +⟨1,239,643,true⟩, +⟨1,239,646,true⟩, +⟨1,239,647,true⟩, +⟨1,239,665,true⟩, +⟨1,239,667,true⟩, +⟨1,239,685,true⟩, +⟨1,239,687,true⟩, +⟨1,239,697,true⟩, +⟨1,239,699,true⟩, +⟨1,239,717,true⟩, +⟨1,239,719,true⟩, +⟨1,239,733,true⟩, +⟨1,239,735,true⟩, +⟨1,239,742,true⟩, +⟨1,239,756,true⟩, +⟨1,239,768,true⟩, +⟨1,239,806,true⟩, +⟨1,239,982,true⟩, +⟨1,239,986,true⟩, +⟨0,241,0,false⟩, +⟨1,241,787,true⟩, +⟨1,241,803,true⟩, +⟨1,241,817,true⟩, +⟨1,241,833,true⟩, +⟨0,242,0,false⟩, +⟨1,242,747,true⟩, +⟨1,242,761,true⟩, +⟨1,242,773,true⟩, +⟨0,244,0,false⟩, +⟨1,244,745,true⟩, +⟨0,248,0,true⟩, +⟨1,248,743,true⟩, +⟨1,248,757,true⟩, +⟨1,248,769,true⟩, +⟨1,248,861,true⟩, +⟨1,248,875,true⟩, +⟨1,248,889,true⟩, +⟨0,249,0,true⟩, +⟨1,249,771,true⟩, +⟨1,249,847,true⟩, +⟨1,249,873,true⟩, +⟨0,250,0,true⟩, +⟨1,250,741,true⟩, +⟨1,250,845,true⟩, +⟨1,250,859,true⟩, +⟨1,250,885,true⟩, +⟨0,254,0,false⟩, +⟨1,254,903,true⟩, +⟨1,254,917,true⟩, +⟨0,256,0,false⟩, +⟨1,256,739,true⟩, +⟨1,256,799,true⟩, +⟨1,256,855,true⟩, +⟨1,256,909,true⟩, +⟨0,257,0,false⟩, +⟨1,257,738,true⟩, +⟨1,257,783,true⟩, +⟨1,257,797,true⟩, +⟨1,257,839,true⟩, +⟨1,257,853,true⟩, +⟨1,257,895,true⟩, +⟨0,260,0,true⟩, +⟨1,260,913,true⟩, +⟨0,263,0,true⟩, +⟨1,263,825,true⟩, +⟨1,263,867,true⟩, +⟨0,267,0,false⟩, +⟨1,267,899,true⟩, +⟨0,268,0,false⟩, +⟨1,268,752,true⟩, +⟨1,268,785,true⟩, +⟨1,268,813,true⟩, +⟨1,268,841,true⟩, +⟨1,268,869,true⟩, +⟨1,268,923,true⟩, +⟨0,269,0,false⟩, +⟨1,269,753,true⟩, +⟨1,269,781,true⟩, +⟨1,269,809,true⟩, +⟨1,269,837,true⟩, +⟨1,269,865,true⟩, +⟨1,269,893,true⟩, +⟨0,272,0,true⟩, +⟨1,272,755,true⟩, +⟨1,272,822,true⟩, +⟨1,272,887,true⟩, +⟨1,272,901,true⟩, +⟨1,272,929,true⟩, +⟨0,274,0,true⟩, +⟨1,274,827,true⟩, +⟨1,274,883,true⟩, +⟨0,275,0,true⟩, +⟨1,275,795,true⟩, +⟨1,275,823,true⟩, +⟨1,275,851,true⟩, +⟨1,275,879,true⟩, +⟨0,283,0,true⟩, +⟨1,283,836,true⟩, +⟨0,284,0,true⟩, +⟨1,284,808,true⟩, +⟨1,284,931,true⟩, +⟨0,286,0,true⟩, +⟨1,286,919,true⟩, +⟨1,286,921,true⟩, +⟨0,287,0,true⟩, +⟨1,287,767,true⟩, +⟨0,736,0,false⟩, +⟨1,736,738,true⟩, +⟨1,736,838,true⟩, +⟨1,736,839,true⟩, +⟨1,736,852,true⟩, +⟨1,736,853,true⟩, +⟨0,737,0,false⟩, +⟨1,737,739,true⟩, +⟨1,737,908,true⟩, +⟨1,737,909,true⟩, +⟨0,740,0,true⟩, +⟨1,740,741,true⟩, +⟨0,742,0,true⟩, +⟨1,742,743,true⟩, +⟨1,742,874,true⟩, +⟨1,742,875,true⟩, +⟨1,742,888,true⟩, +⟨1,742,889,true⟩, +⟨0,744,0,false⟩, +⟨1,744,745,true⟩, +⟨0,746,0,false⟩, +⟨1,746,747,true⟩] +def chunk40 : List Event := [⟨0,748,0,false⟩, +⟨1,748,789,true⟩, +⟨1,748,801,true⟩, +⟨1,748,818,true⟩, +⟨1,748,830,true⟩, +⟨0,749,0,false⟩, +⟨1,749,789,true⟩, +⟨1,749,801,true⟩, +⟨1,749,819,true⟩, +⟨1,749,831,true⟩, +⟨0,750,0,false⟩, +⟨1,750,752,true⟩, +⟨1,750,784,true⟩, +⟨1,750,785,true⟩, +⟨1,750,840,true⟩, +⟨1,750,841,true⟩, +⟨1,750,922,true⟩, +⟨1,750,923,true⟩, +⟨0,756,0,true⟩, +⟨1,756,757,true⟩, +⟨1,756,860,true⟩, +⟨1,756,861,true⟩, +⟨1,756,888,true⟩, +⟨1,756,889,true⟩, +⟨0,760,0,false⟩, +⟨1,760,761,true⟩, +⟨0,762,0,false⟩, +⟨1,762,777,true⟩, +⟨1,762,791,true⟩, +⟨1,762,804,true⟩, +⟨1,762,815,true⟩, +⟨1,762,828,true⟩, +⟨0,763,0,false⟩, +⟨1,763,777,true⟩, +⟨1,763,791,true⟩, +⟨1,763,805,true⟩, +⟨1,763,815,true⟩, +⟨1,763,829,true⟩, +⟨0,764,0,true⟩, +⟨1,764,811,true⟩, +⟨1,764,881,true⟩, +⟨1,764,921,true⟩, +⟨0,765,0,true⟩, +⟨1,765,767,true⟩, +⟨0,766,0,true⟩, +⟨1,766,811,true⟩, +⟨1,766,881,true⟩, +⟨1,766,919,true⟩, +⟨0,768,0,true⟩, +⟨1,768,769,true⟩, +⟨1,768,860,true⟩, +⟨1,768,861,true⟩, +⟨1,768,874,true⟩, +⟨1,768,875,true⟩, +⟨0,770,0,true⟩, +⟨1,770,771,true⟩, +⟨0,772,0,false⟩, +⟨1,772,773,true⟩, +⟨0,776,0,false⟩, +⟨1,776,777,true⟩, +⟨1,776,804,true⟩, +⟨1,776,805,true⟩, +⟨1,776,814,true⟩, +⟨1,776,815,true⟩, +⟨0,779,0,false⟩, +⟨1,779,751,true⟩, +⟨1,779,753,true⟩, +⟨1,779,781,true⟩, +⟨1,779,863,true⟩, +⟨1,779,865,true⟩, +⟨1,779,891,true⟩, +⟨1,779,893,true⟩, +⟨0,782,0,false⟩, +⟨1,782,783,true⟩, +⟨1,782,838,true⟩, +⟨1,782,839,true⟩, +⟨1,782,894,true⟩, +⟨1,782,895,true⟩, +⟨0,786,0,false⟩, +⟨1,786,787,true⟩, +⟨1,786,832,true⟩, +⟨1,786,833,true⟩, +⟨0,788,0,false⟩, +⟨1,788,789,true⟩, +⟨1,788,830,true⟩, +⟨1,788,831,true⟩, +⟨0,790,0,false⟩, +⟨1,790,791,true⟩, +⟨1,790,804,true⟩, +⟨1,790,805,true⟩, +⟨1,790,814,true⟩, +⟨1,790,815,true⟩, +⟨1,790,828,true⟩, +⟨1,790,829,true⟩, +⟨0,792,0,true⟩, +⟨1,792,857,true⟩, +⟨1,792,897,true⟩, +⟨1,792,925,true⟩, +⟨0,793,0,true⟩, +⟨1,793,795,true⟩, +⟨1,793,877,true⟩, +⟨1,793,879,true⟩, +⟨0,794,0,true⟩, +⟨1,794,857,true⟩, +⟨1,794,897,true⟩, +⟨1,794,925,true⟩, +⟨0,796,0,false⟩, +⟨1,796,797,true⟩, +⟨1,796,852,true⟩, +⟨1,796,853,true⟩, +⟨1,796,894,true⟩, +⟨1,796,895,true⟩, +⟨0,798,0,false⟩, +⟨1,798,799,true⟩, +⟨1,798,908,true⟩, +⟨1,798,909,true⟩, +⟨0,800,0,false⟩, +⟨1,800,801,true⟩, +⟨1,800,818,true⟩, +⟨1,800,819,true⟩, +⟨0,802,0,false⟩, +⟨1,802,803,true⟩, +⟨1,802,832,true⟩, +⟨1,802,833,true⟩, +⟨0,806,0,true⟩, +⟨1,806,808,true⟩, +⟨0,807,0,false⟩, +⟨1,807,809,true⟩, +⟨1,807,863,true⟩, +⟨1,807,865,true⟩, +⟨1,807,891,true⟩, +⟨1,807,893,true⟩, +⟨0,810,0,true⟩, +⟨1,810,811,true⟩, +⟨1,810,919,true⟩, +⟨1,810,921,true⟩, +⟨0,812,0,false⟩, +⟨1,812,813,true⟩, +⟨1,812,840,true⟩, +⟨1,812,841,true⟩, +⟨1,812,922,true⟩, +⟨1,812,923,true⟩, +⟨0,816,0,false⟩, +⟨1,816,817,true⟩, +⟨1,816,832,true⟩, +⟨1,816,833,true⟩, +⟨0,820,0,true⟩, +⟨1,820,754,true⟩, +⟨1,820,755,true⟩, +⟨1,820,822,true⟩, +⟨0,821,0,true⟩, +⟨1,821,823,true⟩, +⟨1,821,877,true⟩, +⟨1,821,879,true⟩, +⟨0,824,0,true⟩, +⟨1,824,825,true⟩, +⟨0,826,0,true⟩, +⟨1,826,827,true⟩, +⟨0,834,0,true⟩, +⟨1,834,836,true⟩, +⟨0,835,0,false⟩, +⟨1,835,751,true⟩, +⟨1,835,753,true⟩, +⟨1,835,837,true⟩, +⟨1,835,863,true⟩, +⟨1,835,865,true⟩, +⟨0,844,0,true⟩, +⟨1,844,845,true⟩, +⟨1,844,884,true⟩, +⟨1,844,885,true⟩, +⟨0,846,0,true⟩, +⟨1,846,847,true⟩, +⟨0,849,0,true⟩, +⟨1,849,851,true⟩, +⟨1,849,877,true⟩, +⟨1,849,879,true⟩, +⟨0,854,0,false⟩, +⟨1,854,855,true⟩, +⟨1,854,908,true⟩, +⟨1,854,909,true⟩, +⟨0,858,0,true⟩, +⟨1,858,859,true⟩, +⟨1,858,884,true⟩, +⟨1,858,885,true⟩, +⟨0,866,0,true⟩, +⟨1,866,867,true⟩, +⟨0,868,0,false⟩, +⟨1,868,784,true⟩, +⟨1,868,785,true⟩, +⟨1,868,869,true⟩, +⟨1,868,922,true⟩, +⟨1,868,923,true⟩, +⟨0,872,0,true⟩, +⟨1,872,873,true⟩, +⟨0,880,0,true⟩, +⟨1,880,881,true⟩, +⟨1,880,919,true⟩, +⟨1,880,921,true⟩, +⟨0,882,0,true⟩, +⟨1,882,883,true⟩] +def chunk41 : List Event := [⟨0,896,0,true⟩, +⟨1,896,856,true⟩, +⟨1,896,857,true⟩, +⟨1,896,897,true⟩, +⟨0,898,0,false⟩, +⟨1,898,899,true⟩, +⟨0,900,0,true⟩, +⟨1,900,754,true⟩, +⟨1,900,755,true⟩, +⟨1,900,886,true⟩, +⟨1,900,887,true⟩, +⟨1,900,901,true⟩, +⟨0,902,0,false⟩, +⟨1,902,903,true⟩, +⟨0,912,0,true⟩, +⟨1,912,913,true⟩, +⟨0,916,0,false⟩, +⟨1,916,917,true⟩, +⟨0,924,0,true⟩, +⟨1,924,856,true⟩, +⟨1,924,857,true⟩, +⟨1,924,925,true⟩, +⟨0,928,0,true⟩, +⟨1,928,886,true⟩, +⟨1,928,887,true⟩, +⟨1,928,929,true⟩, +⟨0,930,0,true⟩, +⟨1,930,931,true⟩, +⟨0,932,0,false⟩, +⟨1,932,938,true⟩, +⟨0,933,0,false⟩, +⟨1,933,938,true⟩, +⟨0,936,0,false⟩, +⟨1,936,961,true⟩, +⟨0,937,0,false⟩, +⟨1,937,938,true⟩, +⟨0,941,0,false⟩, +⟨1,941,949,true⟩, +⟨0,942,0,false⟩, +⟨1,942,953,true⟩, +⟨0,943,0,false⟩, +⟨1,943,958,true⟩, +⟨0,944,0,false⟩, +⟨1,944,953,true⟩, +⟨0,945,0,false⟩, +⟨1,945,958,true⟩, +⟨0,951,0,false⟩, +⟨1,951,953,true⟩, +⟨0,956,0,false⟩, +⟨1,956,958,true⟩, +⟨0,959,0,true⟩, +⟨1,959,978,true⟩, +⟨0,960,0,true⟩, +⟨1,960,978,true⟩, +⟨0,977,0,true⟩, +⟨1,977,978,true⟩, +⟨0,240,0,false⟩, +⟨1,240,0,true⟩, +⟨1,241,0,true⟩, +⟨1,242,0,true⟩, +⟨0,243,0,false⟩, +⟨1,243,0,true⟩, +⟨1,244,0,true⟩, +⟨0,245,0,false⟩, +⟨1,245,0,true⟩, +⟨0,246,0,true⟩, +⟨1,246,1,true⟩, +⟨0,247,0,true⟩, +⟨1,247,1,true⟩, +⟨1,248,1,true⟩, +⟨1,249,1,true⟩, +⟨1,250,1,true⟩, +⟨0,251,0,true⟩, +⟨1,251,1,true⟩, +⟨0,252,0,false⟩, +⟨1,252,2,true⟩, +⟨0,253,0,false⟩, +⟨1,253,2,true⟩, +⟨1,254,2,true⟩, +⟨0,255,0,false⟩, +⟨1,255,2,true⟩, +⟨1,256,2,true⟩, +⟨1,257,2,true⟩, +⟨0,258,0,true⟩, +⟨1,258,3,true⟩, +⟨0,259,0,true⟩, +⟨1,259,3,true⟩, +⟨1,260,3,true⟩, +⟨0,261,0,true⟩, +⟨1,261,3,true⟩, +⟨0,262,0,true⟩, +⟨1,262,3,true⟩, +⟨1,263,3,true⟩, +⟨0,264,0,false⟩, +⟨1,264,4,true⟩, +⟨0,265,0,false⟩, +⟨1,265,4,true⟩, +⟨0,266,0,false⟩, +⟨1,266,4,true⟩, +⟨1,267,4,true⟩, +⟨1,268,4,true⟩, +⟨1,269,4,true⟩, +⟨0,270,0,true⟩, +⟨1,270,5,true⟩, +⟨0,271,0,true⟩, +⟨1,271,5,true⟩, +⟨1,272,5,true⟩, +⟨0,273,0,true⟩, +⟨1,273,5,true⟩, +⟨1,274,5,true⟩, +⟨1,275,5,true⟩, +⟨0,276,0,false⟩, +⟨1,276,6,true⟩, +⟨0,277,0,false⟩, +⟨1,277,6,true⟩, +⟨0,278,0,false⟩, +⟨1,278,6,true⟩, +⟨0,279,0,false⟩, +⟨1,279,6,true⟩, +⟨0,280,0,false⟩, +⟨1,280,6,true⟩, +⟨0,281,0,false⟩, +⟨1,281,6,true⟩, +⟨0,282,0,true⟩, +⟨1,282,7,true⟩, +⟨1,283,7,true⟩, +⟨1,284,7,true⟩, +⟨0,285,0,true⟩, +⟨1,285,7,true⟩, +⟨1,286,7,true⟩, +⟨1,287,7,true⟩, +⟨0,288,0,false⟩, +⟨1,288,8,true⟩, +⟨0,289,0,false⟩, +⟨1,289,8,true⟩, +⟨0,290,0,true⟩, +⟨1,290,9,true⟩, +⟨0,291,0,true⟩, +⟨1,291,9,true⟩, +⟨0,292,0,false⟩, +⟨1,292,10,true⟩, +⟨0,293,0,false⟩, +⟨1,293,10,true⟩, +⟨0,294,0,true⟩, +⟨1,294,11,true⟩, +⟨0,295,0,true⟩, +⟨1,295,11,true⟩, +⟨0,296,0,false⟩, +⟨1,296,12,true⟩, +⟨0,297,0,false⟩, +⟨1,297,12,true⟩, +⟨0,298,0,true⟩, +⟨1,298,13,true⟩, +⟨0,299,0,true⟩, +⟨1,299,13,true⟩, +⟨0,300,0,false⟩, +⟨1,300,14,true⟩, +⟨0,301,0,false⟩, +⟨1,301,14,true⟩, +⟨0,302,0,true⟩, +⟨1,302,15,true⟩, +⟨0,303,0,true⟩, +⟨1,303,15,true⟩, +⟨0,304,0,false⟩, +⟨1,304,16,true⟩, +⟨0,305,0,false⟩, +⟨1,305,16,true⟩, +⟨0,306,0,true⟩, +⟨1,306,17,true⟩, +⟨0,307,0,true⟩, +⟨1,307,17,true⟩, +⟨0,308,0,false⟩, +⟨1,308,18,true⟩, +⟨0,309,0,false⟩, +⟨1,309,18,true⟩, +⟨0,310,0,true⟩, +⟨1,310,19,true⟩, +⟨0,311,0,true⟩, +⟨1,311,19,true⟩, +⟨0,312,0,false⟩, +⟨1,312,20,true⟩, +⟨0,313,0,false⟩, +⟨1,313,20,true⟩, +⟨0,314,0,true⟩, +⟨1,314,21,true⟩, +⟨0,315,0,true⟩, +⟨1,315,21,true⟩, +⟨0,316,0,false⟩, +⟨1,316,22,true⟩, +⟨0,317,0,false⟩, +⟨1,317,22,true⟩, +⟨0,318,0,true⟩, +⟨1,318,23,true⟩, +⟨0,319,0,true⟩, +⟨1,319,23,true⟩, +⟨0,320,0,false⟩, +⟨1,320,24,true⟩, +⟨0,321,0,false⟩, +⟨1,321,24,true⟩, +⟨0,322,0,true⟩] +def chunk42 : List Event := [⟨1,322,25,true⟩, +⟨0,323,0,true⟩, +⟨1,323,25,true⟩, +⟨0,324,0,false⟩, +⟨1,324,26,true⟩, +⟨0,325,0,false⟩, +⟨1,325,26,true⟩, +⟨0,326,0,true⟩, +⟨1,326,27,true⟩, +⟨0,327,0,true⟩, +⟨1,327,27,true⟩, +⟨0,328,0,false⟩, +⟨1,328,28,true⟩, +⟨0,329,0,false⟩, +⟨1,329,28,true⟩, +⟨0,330,0,true⟩, +⟨1,330,29,true⟩, +⟨0,331,0,true⟩, +⟨1,331,29,true⟩, +⟨0,332,0,false⟩, +⟨1,332,30,true⟩, +⟨0,333,0,false⟩, +⟨1,333,30,true⟩, +⟨0,334,0,true⟩, +⟨1,334,31,true⟩, +⟨0,335,0,true⟩, +⟨1,335,31,true⟩, +⟨0,336,0,false⟩, +⟨1,336,32,true⟩, +⟨0,337,0,false⟩, +⟨1,337,32,true⟩, +⟨0,338,0,true⟩, +⟨1,338,33,true⟩, +⟨0,339,0,true⟩, +⟨1,339,33,true⟩, +⟨0,340,0,false⟩, +⟨1,340,34,true⟩, +⟨0,341,0,false⟩, +⟨1,341,34,true⟩, +⟨0,342,0,true⟩, +⟨1,342,35,true⟩, +⟨0,343,0,true⟩, +⟨1,343,35,true⟩, +⟨0,344,0,false⟩, +⟨1,344,36,true⟩, +⟨0,345,0,false⟩, +⟨1,345,36,true⟩, +⟨0,346,0,true⟩, +⟨1,346,37,true⟩, +⟨0,347,0,true⟩, +⟨1,347,37,true⟩, +⟨0,348,0,false⟩, +⟨1,348,38,true⟩, +⟨0,349,0,false⟩, +⟨1,349,38,true⟩, +⟨0,350,0,true⟩, +⟨1,350,39,true⟩, +⟨0,351,0,true⟩, +⟨1,351,39,true⟩, +⟨0,352,0,false⟩, +⟨1,352,40,true⟩, +⟨0,353,0,false⟩, +⟨1,353,40,true⟩, +⟨0,354,0,true⟩, +⟨1,354,41,true⟩, +⟨0,355,0,true⟩, +⟨1,355,41,true⟩, +⟨0,356,0,false⟩, +⟨1,356,42,true⟩, +⟨0,357,0,false⟩, +⟨1,357,42,true⟩, +⟨0,358,0,true⟩, +⟨1,358,43,true⟩, +⟨0,359,0,true⟩, +⟨1,359,43,true⟩, +⟨0,360,0,false⟩, +⟨1,360,44,true⟩, +⟨0,361,0,false⟩, +⟨1,361,44,true⟩, +⟨0,362,0,true⟩, +⟨1,362,45,true⟩, +⟨0,363,0,true⟩, +⟨1,363,45,true⟩, +⟨0,364,0,false⟩, +⟨1,364,46,true⟩, +⟨0,365,0,false⟩, +⟨1,365,46,true⟩, +⟨0,366,0,true⟩, +⟨1,366,47,true⟩, +⟨0,367,0,true⟩, +⟨1,367,47,true⟩, +⟨0,368,0,false⟩, +⟨1,368,48,true⟩, +⟨0,369,0,false⟩, +⟨1,369,48,true⟩, +⟨0,370,0,true⟩, +⟨1,370,49,true⟩, +⟨0,371,0,true⟩, +⟨1,371,49,true⟩, +⟨0,372,0,false⟩, +⟨1,372,50,true⟩, +⟨0,373,0,false⟩, +⟨1,373,50,true⟩, +⟨0,374,0,true⟩, +⟨1,374,51,true⟩, +⟨0,375,0,true⟩, +⟨1,375,51,true⟩, +⟨0,376,0,false⟩, +⟨1,376,52,true⟩, +⟨0,377,0,false⟩, +⟨1,377,52,true⟩, +⟨0,378,0,true⟩, +⟨1,378,53,true⟩, +⟨0,379,0,true⟩, +⟨1,379,53,true⟩, +⟨0,380,0,false⟩, +⟨1,380,54,true⟩, +⟨0,381,0,false⟩, +⟨1,381,54,true⟩, +⟨0,382,0,true⟩, +⟨1,382,55,true⟩, +⟨0,383,0,true⟩, +⟨1,383,55,true⟩, +⟨0,384,0,false⟩, +⟨1,384,56,true⟩, +⟨0,385,0,false⟩, +⟨1,385,56,true⟩, +⟨0,386,0,true⟩, +⟨1,386,57,true⟩, +⟨0,387,0,true⟩, +⟨1,387,57,true⟩, +⟨0,388,0,false⟩, +⟨1,388,58,true⟩, +⟨0,389,0,false⟩, +⟨1,389,58,true⟩, +⟨0,390,0,true⟩, +⟨1,390,59,true⟩, +⟨0,391,0,true⟩, +⟨1,391,59,true⟩, +⟨0,392,0,false⟩, +⟨1,392,60,true⟩, +⟨0,393,0,false⟩, +⟨1,393,60,true⟩, +⟨0,394,0,true⟩, +⟨1,394,61,true⟩, +⟨0,395,0,true⟩, +⟨1,395,61,true⟩, +⟨0,396,0,false⟩, +⟨1,396,62,true⟩, +⟨0,397,0,false⟩, +⟨1,397,62,true⟩, +⟨0,398,0,true⟩, +⟨1,398,63,true⟩, +⟨0,399,0,true⟩, +⟨1,399,63,true⟩, +⟨0,400,0,false⟩, +⟨1,400,64,true⟩, +⟨0,401,0,false⟩, +⟨1,401,64,true⟩, +⟨0,402,0,true⟩, +⟨1,402,65,true⟩, +⟨0,403,0,true⟩, +⟨1,403,65,true⟩, +⟨0,404,0,false⟩, +⟨1,404,66,true⟩, +⟨0,405,0,false⟩, +⟨1,405,66,true⟩, +⟨0,406,0,true⟩, +⟨1,406,67,true⟩, +⟨0,407,0,true⟩, +⟨1,407,67,true⟩, +⟨0,408,0,false⟩, +⟨1,408,68,true⟩, +⟨0,409,0,false⟩, +⟨1,409,68,true⟩, +⟨0,410,0,true⟩, +⟨1,410,69,true⟩, +⟨0,411,0,true⟩, +⟨1,411,69,true⟩, +⟨0,412,0,false⟩, +⟨1,412,70,true⟩, +⟨0,413,0,false⟩, +⟨1,413,70,true⟩, +⟨0,414,0,true⟩, +⟨1,414,71,true⟩, +⟨0,415,0,true⟩, +⟨1,415,71,true⟩, +⟨0,416,0,false⟩, +⟨1,416,72,true⟩, +⟨0,417,0,false⟩, +⟨1,417,72,true⟩, +⟨0,418,0,true⟩, +⟨1,418,73,true⟩, +⟨0,419,0,true⟩, +⟨1,419,73,true⟩, +⟨0,420,0,false⟩, +⟨1,420,74,true⟩, +⟨0,421,0,false⟩, +⟨1,421,74,true⟩, +⟨0,422,0,true⟩] +def chunk43 : List Event := [⟨1,422,75,true⟩, +⟨0,423,0,true⟩, +⟨1,423,75,true⟩, +⟨0,424,0,false⟩, +⟨1,424,76,true⟩, +⟨0,425,0,false⟩, +⟨1,425,76,true⟩, +⟨0,426,0,true⟩, +⟨1,426,77,true⟩, +⟨0,427,0,true⟩, +⟨1,427,77,true⟩, +⟨0,428,0,false⟩, +⟨1,428,78,true⟩, +⟨0,429,0,false⟩, +⟨1,429,78,true⟩, +⟨0,430,0,true⟩, +⟨1,430,79,true⟩, +⟨0,431,0,true⟩, +⟨1,431,79,true⟩, +⟨0,432,0,false⟩, +⟨1,432,80,true⟩, +⟨0,433,0,false⟩, +⟨1,433,80,true⟩, +⟨0,434,0,true⟩, +⟨1,434,81,true⟩, +⟨0,435,0,true⟩, +⟨1,435,81,true⟩, +⟨0,436,0,false⟩, +⟨1,436,82,true⟩, +⟨0,437,0,false⟩, +⟨1,437,82,true⟩, +⟨0,438,0,true⟩, +⟨1,438,83,true⟩, +⟨0,439,0,true⟩, +⟨1,439,83,true⟩, +⟨0,440,0,false⟩, +⟨1,440,84,true⟩, +⟨0,441,0,false⟩, +⟨1,441,84,true⟩, +⟨0,442,0,true⟩, +⟨1,442,85,true⟩, +⟨0,443,0,true⟩, +⟨1,443,85,true⟩, +⟨0,444,0,false⟩, +⟨1,444,86,true⟩, +⟨0,445,0,false⟩, +⟨1,445,86,true⟩, +⟨0,446,0,true⟩, +⟨1,446,87,true⟩, +⟨0,447,0,true⟩, +⟨1,447,87,true⟩, +⟨0,448,0,false⟩, +⟨1,448,88,true⟩, +⟨0,449,0,false⟩, +⟨1,449,88,true⟩, +⟨0,450,0,true⟩, +⟨1,450,89,true⟩, +⟨0,451,0,true⟩, +⟨1,451,89,true⟩, +⟨0,452,0,false⟩, +⟨1,452,90,true⟩, +⟨0,453,0,false⟩, +⟨1,453,90,true⟩, +⟨0,454,0,true⟩, +⟨1,454,91,true⟩, +⟨0,455,0,true⟩, +⟨1,455,91,true⟩, +⟨0,456,0,false⟩, +⟨1,456,92,true⟩, +⟨0,457,0,false⟩, +⟨1,457,92,true⟩, +⟨0,458,0,true⟩, +⟨1,458,93,true⟩, +⟨0,459,0,true⟩, +⟨1,459,93,true⟩, +⟨0,460,0,false⟩, +⟨1,460,94,true⟩, +⟨0,461,0,false⟩, +⟨1,461,94,true⟩, +⟨0,462,0,true⟩, +⟨1,462,95,true⟩, +⟨0,463,0,true⟩, +⟨1,463,95,true⟩, +⟨0,464,0,false⟩, +⟨1,464,96,true⟩, +⟨0,465,0,false⟩, +⟨1,465,96,true⟩, +⟨0,466,0,true⟩, +⟨1,466,97,true⟩, +⟨0,467,0,true⟩, +⟨1,467,97,true⟩, +⟨0,468,0,false⟩, +⟨1,468,98,true⟩, +⟨0,469,0,false⟩, +⟨1,469,98,true⟩, +⟨0,470,0,true⟩, +⟨1,470,99,true⟩, +⟨0,471,0,true⟩, +⟨1,471,99,true⟩, +⟨0,472,0,false⟩, +⟨1,472,100,true⟩, +⟨0,473,0,false⟩, +⟨1,473,100,true⟩, +⟨0,474,0,true⟩, +⟨1,474,101,true⟩, +⟨0,475,0,true⟩, +⟨1,475,101,true⟩, +⟨0,476,0,false⟩, +⟨1,476,102,true⟩, +⟨0,477,0,false⟩, +⟨1,477,102,true⟩, +⟨0,478,0,true⟩, +⟨1,478,103,true⟩, +⟨0,479,0,true⟩, +⟨1,479,103,true⟩, +⟨0,480,0,false⟩, +⟨1,480,104,true⟩, +⟨0,481,0,false⟩, +⟨1,481,104,true⟩, +⟨0,482,0,true⟩, +⟨1,482,105,true⟩, +⟨0,483,0,true⟩, +⟨1,483,105,true⟩, +⟨0,484,0,false⟩, +⟨1,484,106,true⟩, +⟨0,485,0,false⟩, +⟨1,485,106,true⟩, +⟨0,486,0,true⟩, +⟨1,486,107,true⟩, +⟨0,487,0,true⟩, +⟨1,487,107,true⟩, +⟨0,488,0,false⟩, +⟨1,488,108,true⟩, +⟨0,489,0,false⟩, +⟨1,489,108,true⟩, +⟨0,490,0,true⟩, +⟨1,490,109,true⟩, +⟨0,491,0,true⟩, +⟨1,491,109,true⟩, +⟨0,492,0,false⟩, +⟨1,492,110,true⟩, +⟨0,493,0,false⟩, +⟨1,493,110,true⟩, +⟨0,494,0,true⟩, +⟨1,494,111,true⟩, +⟨0,495,0,true⟩, +⟨1,495,111,true⟩, +⟨0,496,0,false⟩, +⟨1,496,112,true⟩, +⟨0,497,0,false⟩, +⟨1,497,112,true⟩, +⟨0,498,0,true⟩, +⟨1,498,113,true⟩, +⟨0,499,0,true⟩, +⟨1,499,113,true⟩, +⟨0,500,0,false⟩, +⟨1,500,114,true⟩, +⟨0,501,0,false⟩, +⟨1,501,114,true⟩, +⟨0,502,0,true⟩, +⟨1,502,115,true⟩, +⟨0,503,0,true⟩, +⟨1,503,115,true⟩, +⟨0,504,0,false⟩, +⟨1,504,116,true⟩, +⟨0,505,0,false⟩, +⟨1,505,116,true⟩, +⟨0,506,0,true⟩, +⟨1,506,117,true⟩, +⟨0,507,0,true⟩, +⟨1,507,117,true⟩, +⟨0,508,0,false⟩, +⟨1,508,118,true⟩, +⟨0,509,0,false⟩, +⟨1,509,118,true⟩, +⟨0,510,0,true⟩, +⟨1,510,119,true⟩, +⟨0,511,0,true⟩, +⟨1,511,119,true⟩, +⟨0,512,0,false⟩, +⟨1,512,64,true⟩, +⟨0,512,66,false⟩, +⟨0,67,69,false⟩, +⟨1,512,67,true⟩, +⟨0,513,0,false⟩, +⟨1,513,512,true⟩, +⟨0,514,0,true⟩, +⟨1,514,65,true⟩, +⟨0,514,67,true⟩, +⟨0,66,68,true⟩, +⟨1,514,66,true⟩, +⟨0,515,0,true⟩, +⟨1,515,514,true⟩, +⟨0,516,0,false⟩, +⟨1,516,68,true⟩, +⟨0,516,70,false⟩, +⟨0,71,73,false⟩, +⟨1,516,71,true⟩, +⟨0,517,0,false⟩, +⟨1,517,516,true⟩] +def chunk44 : List Event := [⟨0,518,0,true⟩, +⟨1,518,69,true⟩, +⟨0,518,71,true⟩, +⟨0,70,72,true⟩, +⟨1,518,70,true⟩, +⟨0,519,0,true⟩, +⟨1,519,518,true⟩, +⟨0,400,66,false⟩, +⟨0,410,71,false⟩, +⟨1,400,410,true⟩, +⟨0,520,0,false⟩, +⟨1,520,400,true⟩, +⟨0,402,67,true⟩, +⟨0,408,70,true⟩, +⟨1,402,408,true⟩, +⟨0,521,0,true⟩, +⟨1,521,402,true⟩, +⟨0,404,68,false⟩, +⟨0,414,73,false⟩, +⟨1,404,414,true⟩, +⟨0,522,0,false⟩, +⟨1,522,404,true⟩, +⟨0,406,69,true⟩, +⟨0,412,72,true⟩, +⟨1,406,412,true⟩, +⟨0,523,0,true⟩, +⟨1,523,406,true⟩, +⟨0,413,72,false⟩, +⟨0,401,66,false⟩, +⟨1,413,401,true⟩, +⟨0,524,0,false⟩, +⟨1,524,413,true⟩, +⟨0,409,70,true⟩, +⟨0,405,68,true⟩, +⟨1,409,405,true⟩, +⟨0,525,0,true⟩, +⟨1,525,409,true⟩, +⟨0,415,73,false⟩, +⟨0,403,67,false⟩, +⟨1,415,403,true⟩, +⟨0,526,0,false⟩, +⟨1,526,415,true⟩, +⟨0,411,71,true⟩, +⟨0,407,69,true⟩, +⟨1,411,407,true⟩, +⟨0,527,0,true⟩, +⟨1,527,411,true⟩, +⟨0,528,0,false⟩, +⟨1,528,32,true⟩, +⟨0,528,34,false⟩, +⟨0,35,37,false⟩, +⟨1,528,35,true⟩, +⟨0,529,0,false⟩, +⟨1,529,528,true⟩, +⟨0,530,0,true⟩, +⟨1,530,33,true⟩, +⟨0,530,35,true⟩, +⟨0,34,36,true⟩, +⟨1,530,34,true⟩, +⟨0,531,0,true⟩, +⟨1,531,530,true⟩, +⟨0,532,0,false⟩, +⟨1,532,36,true⟩, +⟨0,532,38,false⟩, +⟨0,39,41,false⟩, +⟨1,532,39,true⟩, +⟨0,533,0,false⟩, +⟨1,533,532,true⟩, +⟨0,534,0,true⟩, +⟨1,534,37,true⟩, +⟨0,534,39,true⟩, +⟨0,38,40,true⟩, +⟨1,534,38,true⟩, +⟨0,535,0,true⟩, +⟨1,535,534,true⟩, +⟨0,346,39,false⟩, +⟨0,336,34,false⟩, +⟨1,346,336,true⟩, +⟨0,536,0,false⟩, +⟨1,536,346,true⟩, +⟨0,344,38,true⟩, +⟨0,338,35,true⟩, +⟨1,344,338,true⟩, +⟨0,537,0,true⟩, +⟨1,537,344,true⟩, +⟨0,350,41,false⟩, +⟨0,340,36,false⟩, +⟨1,350,340,true⟩, +⟨0,538,0,false⟩, +⟨1,538,350,true⟩, +⟨0,348,40,true⟩, +⟨0,342,37,true⟩, +⟨1,348,342,true⟩, +⟨0,539,0,true⟩, +⟨1,539,348,true⟩, +⟨0,337,34,false⟩, +⟨0,349,40,false⟩, +⟨1,337,349,true⟩, +⟨0,540,0,false⟩, +⟨1,540,337,true⟩, +⟨0,341,36,true⟩, +⟨0,345,38,true⟩, +⟨1,341,345,true⟩, +⟨0,541,0,true⟩, +⟨1,541,341,true⟩, +⟨0,339,35,false⟩, +⟨0,351,41,false⟩, +⟨1,339,351,true⟩, +⟨0,542,0,false⟩, +⟨1,542,339,true⟩, +⟨0,343,37,true⟩, +⟨0,347,39,true⟩, +⟨1,343,347,true⟩, +⟨0,543,0,true⟩, +⟨1,543,343,true⟩, +⟨0,544,0,false⟩, +⟨1,544,24,true⟩, +⟨0,544,26,false⟩, +⟨0,27,29,false⟩, +⟨1,544,27,true⟩, +⟨0,545,0,false⟩, +⟨1,545,544,true⟩, +⟨0,546,0,true⟩, +⟨1,546,25,true⟩, +⟨0,546,27,true⟩, +⟨0,26,28,true⟩, +⟨1,546,26,true⟩, +⟨0,547,0,true⟩, +⟨1,547,546,true⟩, +⟨0,548,0,false⟩, +⟨1,548,28,true⟩, +⟨0,548,30,false⟩, +⟨0,31,33,false⟩, +⟨1,548,31,true⟩, +⟨0,549,0,false⟩, +⟨1,549,548,true⟩, +⟨0,550,0,true⟩, +⟨1,550,29,true⟩, +⟨0,550,31,true⟩, +⟨0,30,32,true⟩, +⟨1,550,30,true⟩, +⟨0,551,0,true⟩, +⟨1,551,550,true⟩, +⟨0,320,26,false⟩, +⟨0,330,31,false⟩, +⟨1,320,330,true⟩, +⟨0,552,0,false⟩, +⟨1,552,320,true⟩, +⟨0,328,30,true⟩, +⟨0,322,27,true⟩, +⟨1,328,322,true⟩, +⟨0,553,0,true⟩, +⟨1,553,328,true⟩, +⟨0,334,33,false⟩, +⟨0,324,28,false⟩, +⟨1,334,324,true⟩, +⟨0,554,0,false⟩, +⟨1,554,334,true⟩, +⟨0,326,29,true⟩, +⟨0,332,32,true⟩, +⟨1,326,332,true⟩, +⟨0,555,0,true⟩, +⟨1,555,326,true⟩, +⟨0,333,32,false⟩, +⟨0,321,26,false⟩, +⟨1,333,321,true⟩, +⟨0,556,0,false⟩, +⟨1,556,333,true⟩, +⟨0,325,28,true⟩, +⟨0,329,30,true⟩, +⟨1,325,329,true⟩, +⟨0,557,0,true⟩, +⟨1,557,325,true⟩, +⟨0,323,27,false⟩, +⟨0,335,33,false⟩, +⟨1,323,335,true⟩, +⟨0,558,0,false⟩, +⟨1,558,323,true⟩, +⟨0,331,31,true⟩, +⟨0,327,29,true⟩, +⟨1,331,327,true⟩, +⟨0,559,0,true⟩, +⟨1,559,331,true⟩, +⟨0,560,0,false⟩, +⟨1,560,16,true⟩, +⟨0,560,18,false⟩, +⟨0,19,21,false⟩, +⟨1,560,19,true⟩, +⟨0,561,0,false⟩, +⟨1,561,560,true⟩, +⟨0,562,0,true⟩, +⟨1,562,17,true⟩, +⟨0,562,19,true⟩, +⟨0,18,20,true⟩, +⟨1,562,18,true⟩, +⟨0,563,0,true⟩, +⟨1,563,562,true⟩, +⟨0,564,0,false⟩, +⟨1,564,20,true⟩, +⟨0,564,22,false⟩] +def chunk45 : List Event := [⟨0,23,25,false⟩, +⟨1,564,23,true⟩, +⟨0,565,0,false⟩, +⟨1,565,564,true⟩, +⟨0,566,0,true⟩, +⟨1,566,21,true⟩, +⟨0,566,23,true⟩, +⟨0,22,24,true⟩, +⟨1,566,22,true⟩, +⟨0,567,0,true⟩, +⟨1,567,566,true⟩, +⟨0,304,18,false⟩, +⟨0,314,23,false⟩, +⟨1,304,314,true⟩, +⟨0,568,0,false⟩, +⟨1,568,304,true⟩, +⟨0,312,22,true⟩, +⟨0,306,19,true⟩, +⟨1,312,306,true⟩, +⟨0,569,0,true⟩, +⟨1,569,312,true⟩, +⟨0,318,25,false⟩, +⟨0,308,20,false⟩, +⟨1,318,308,true⟩, +⟨0,570,0,false⟩, +⟨1,570,318,true⟩, +⟨0,310,21,true⟩, +⟨0,316,24,true⟩, +⟨1,310,316,true⟩, +⟨0,571,0,true⟩, +⟨1,571,310,true⟩, +⟨0,317,24,false⟩, +⟨0,305,18,false⟩, +⟨1,317,305,true⟩, +⟨0,572,0,false⟩, +⟨1,572,317,true⟩, +⟨0,309,20,true⟩, +⟨0,313,22,true⟩, +⟨1,309,313,true⟩, +⟨0,573,0,true⟩, +⟨1,573,309,true⟩, +⟨0,307,19,false⟩, +⟨0,319,25,false⟩, +⟨1,307,319,true⟩, +⟨0,574,0,false⟩, +⟨1,574,307,true⟩, +⟨0,315,23,true⟩, +⟨0,311,21,true⟩, +⟨1,315,311,true⟩, +⟨0,575,0,true⟩, +⟨1,575,315,true⟩, +⟨0,576,0,false⟩, +⟨1,576,40,true⟩, +⟨0,576,42,false⟩, +⟨0,43,45,false⟩, +⟨1,576,43,true⟩, +⟨0,577,0,false⟩, +⟨1,577,576,true⟩, +⟨0,578,0,true⟩, +⟨1,578,41,true⟩, +⟨0,578,43,true⟩, +⟨0,42,44,true⟩, +⟨1,578,42,true⟩, +⟨0,579,0,true⟩, +⟨1,579,578,true⟩, +⟨0,580,0,false⟩, +⟨1,580,44,true⟩, +⟨0,580,46,false⟩, +⟨0,47,49,false⟩, +⟨1,580,47,true⟩, +⟨0,581,0,false⟩, +⟨1,581,580,true⟩, +⟨0,582,0,true⟩, +⟨1,582,45,true⟩, +⟨0,582,47,true⟩, +⟨0,46,48,true⟩, +⟨1,582,46,true⟩, +⟨0,583,0,true⟩, +⟨1,583,582,true⟩, +⟨0,352,42,false⟩, +⟨0,362,47,false⟩, +⟨1,352,362,true⟩, +⟨0,584,0,false⟩, +⟨1,584,352,true⟩, +⟨0,354,43,true⟩, +⟨0,360,46,true⟩, +⟨1,354,360,true⟩, +⟨0,585,0,true⟩, +⟨1,585,354,true⟩, +⟨0,356,44,false⟩, +⟨0,366,49,false⟩, +⟨1,356,366,true⟩, +⟨0,586,0,false⟩, +⟨1,586,356,true⟩, +⟨0,358,45,true⟩, +⟨0,364,48,true⟩, +⟨1,358,364,true⟩, +⟨0,587,0,true⟩, +⟨1,587,358,true⟩, +⟨0,365,48,false⟩, +⟨0,353,42,false⟩, +⟨1,365,353,true⟩, +⟨0,588,0,false⟩, +⟨1,588,365,true⟩, +⟨0,361,46,true⟩, +⟨0,357,44,true⟩, +⟨1,361,357,true⟩, +⟨0,589,0,true⟩, +⟨1,589,361,true⟩, +⟨0,367,49,false⟩, +⟨0,355,43,false⟩, +⟨1,367,355,true⟩, +⟨0,590,0,false⟩, +⟨1,590,367,true⟩, +⟨0,363,47,true⟩, +⟨0,359,45,true⟩, +⟨1,363,359,true⟩, +⟨0,591,0,true⟩, +⟨1,591,363,true⟩, +⟨0,592,0,false⟩, +⟨1,592,72,true⟩, +⟨0,592,74,false⟩, +⟨0,75,77,false⟩, +⟨1,592,75,true⟩, +⟨0,593,0,false⟩, +⟨1,593,592,true⟩, +⟨0,594,0,true⟩, +⟨1,594,73,true⟩, +⟨0,594,75,true⟩, +⟨0,74,76,true⟩, +⟨1,594,74,true⟩, +⟨0,595,0,true⟩, +⟨1,595,594,true⟩, +⟨0,596,0,false⟩, +⟨1,596,76,true⟩, +⟨0,596,78,false⟩, +⟨0,79,81,false⟩, +⟨1,596,79,true⟩, +⟨0,597,0,false⟩, +⟨1,597,596,true⟩, +⟨0,598,0,true⟩, +⟨1,598,77,true⟩, +⟨0,598,79,true⟩, +⟨0,78,80,true⟩, +⟨1,598,78,true⟩, +⟨0,599,0,true⟩, +⟨1,599,598,true⟩, +⟨0,416,74,false⟩, +⟨0,426,79,false⟩, +⟨1,416,426,true⟩, +⟨0,600,0,false⟩, +⟨1,600,416,true⟩, +⟨0,424,78,true⟩, +⟨0,418,75,true⟩, +⟨1,424,418,true⟩, +⟨0,601,0,true⟩, +⟨1,601,424,true⟩, +⟨0,430,81,false⟩, +⟨0,420,76,false⟩, +⟨1,430,420,true⟩, +⟨0,602,0,false⟩, +⟨1,602,430,true⟩, +⟨0,422,77,true⟩, +⟨0,428,80,true⟩, +⟨1,422,428,true⟩, +⟨0,603,0,true⟩, +⟨1,603,422,true⟩, +⟨0,429,80,false⟩, +⟨0,417,74,false⟩, +⟨1,429,417,true⟩, +⟨0,604,0,false⟩, +⟨1,604,429,true⟩, +⟨0,421,76,true⟩, +⟨0,425,78,true⟩, +⟨1,421,425,true⟩, +⟨0,605,0,true⟩, +⟨1,605,421,true⟩, +⟨0,419,75,false⟩, +⟨0,431,81,false⟩, +⟨1,419,431,true⟩, +⟨0,606,0,false⟩, +⟨1,606,419,true⟩, +⟨0,427,79,true⟩, +⟨0,423,77,true⟩, +⟨1,427,423,true⟩, +⟨0,607,0,true⟩, +⟨1,607,427,true⟩, +⟨0,608,0,false⟩, +⟨1,608,112,true⟩, +⟨0,608,114,false⟩, +⟨0,115,117,false⟩, +⟨1,608,115,true⟩, +⟨0,609,0,false⟩, +⟨1,609,608,true⟩, +⟨0,610,0,true⟩, +⟨1,610,113,true⟩, +⟨0,610,115,true⟩, +⟨0,114,116,true⟩, +⟨1,610,114,true⟩, +⟨0,611,0,true⟩] +def chunk46 : List Event := [⟨1,611,610,true⟩, +⟨0,612,0,false⟩, +⟨1,612,116,true⟩, +⟨0,612,118,false⟩, +⟨0,119,121,false⟩, +⟨1,612,119,true⟩, +⟨0,613,0,false⟩, +⟨1,613,612,true⟩, +⟨0,614,0,true⟩, +⟨1,614,117,true⟩, +⟨0,614,119,true⟩, +⟨0,118,120,true⟩, +⟨1,614,118,true⟩, +⟨0,615,0,true⟩, +⟨1,615,614,true⟩, +⟨0,506,119,false⟩, +⟨0,496,114,false⟩, +⟨1,506,496,true⟩, +⟨0,616,0,false⟩, +⟨1,616,506,true⟩, +⟨0,504,118,true⟩, +⟨0,498,115,true⟩, +⟨1,504,498,true⟩, +⟨0,617,0,true⟩, +⟨1,617,504,true⟩, +⟨0,510,121,false⟩, +⟨0,500,116,false⟩, +⟨1,510,500,true⟩, +⟨0,618,0,false⟩, +⟨1,618,510,true⟩, +⟨0,508,120,true⟩, +⟨0,502,117,true⟩, +⟨1,508,502,true⟩, +⟨0,619,0,true⟩, +⟨1,619,508,true⟩, +⟨0,497,114,false⟩, +⟨0,509,120,false⟩, +⟨1,497,509,true⟩, +⟨0,620,0,false⟩, +⟨1,620,497,true⟩, +⟨0,501,116,true⟩, +⟨0,505,118,true⟩, +⟨1,501,505,true⟩, +⟨0,621,0,true⟩, +⟨1,621,501,true⟩, +⟨0,499,115,false⟩, +⟨0,511,121,false⟩, +⟨1,499,511,true⟩, +⟨0,622,0,false⟩, +⟨1,622,499,true⟩, +⟨0,503,117,true⟩, +⟨0,507,119,true⟩, +⟨1,503,507,true⟩, +⟨0,623,0,true⟩, +⟨1,623,503,true⟩, +⟨0,624,0,false⟩, +⟨1,624,8,true⟩, +⟨0,624,10,false⟩, +⟨0,11,13,false⟩, +⟨1,624,11,true⟩, +⟨0,625,0,false⟩, +⟨1,625,624,true⟩, +⟨0,626,0,true⟩, +⟨1,626,9,true⟩, +⟨0,626,11,true⟩, +⟨0,10,12,true⟩, +⟨1,626,10,true⟩, +⟨0,627,0,true⟩, +⟨1,627,626,true⟩, +⟨0,628,0,false⟩, +⟨1,628,12,true⟩, +⟨0,628,14,false⟩, +⟨0,15,17,false⟩, +⟨1,628,15,true⟩, +⟨0,629,0,false⟩, +⟨1,629,628,true⟩, +⟨0,630,0,true⟩, +⟨1,630,13,true⟩, +⟨0,630,15,true⟩, +⟨0,14,16,true⟩, +⟨1,630,14,true⟩, +⟨0,631,0,true⟩, +⟨1,631,630,true⟩, +⟨0,288,10,false⟩, +⟨0,298,15,false⟩, +⟨1,288,298,true⟩, +⟨0,632,0,false⟩, +⟨1,632,288,true⟩, +⟨0,290,11,true⟩, +⟨0,296,14,true⟩, +⟨1,290,296,true⟩, +⟨0,633,0,true⟩, +⟨1,633,290,true⟩, +⟨0,292,12,false⟩, +⟨0,302,17,false⟩, +⟨1,292,302,true⟩, +⟨0,634,0,false⟩, +⟨1,634,292,true⟩, +⟨0,294,13,true⟩, +⟨0,300,16,true⟩, +⟨1,294,300,true⟩, +⟨0,635,0,true⟩, +⟨1,635,294,true⟩, +⟨0,301,16,false⟩, +⟨0,289,10,false⟩, +⟨1,301,289,true⟩, +⟨0,636,0,false⟩, +⟨1,636,301,true⟩, +⟨0,297,14,true⟩, +⟨0,293,12,true⟩, +⟨1,297,293,true⟩, +⟨0,637,0,true⟩, +⟨1,637,297,true⟩, +⟨0,303,17,false⟩, +⟨0,291,11,false⟩, +⟨1,303,291,true⟩, +⟨0,638,0,false⟩, +⟨1,638,303,true⟩, +⟨0,299,15,true⟩, +⟨0,295,13,true⟩, +⟨1,299,295,true⟩, +⟨0,639,0,true⟩, +⟨1,639,299,true⟩, +⟨0,640,0,false⟩, +⟨1,640,48,true⟩, +⟨0,640,50,false⟩, +⟨0,51,53,false⟩, +⟨1,640,51,true⟩, +⟨0,641,0,false⟩, +⟨1,641,640,true⟩, +⟨0,642,0,true⟩, +⟨1,642,49,true⟩, +⟨0,642,51,true⟩, +⟨0,50,52,true⟩, +⟨1,642,50,true⟩, +⟨0,643,0,true⟩, +⟨1,643,642,true⟩, +⟨0,644,0,false⟩, +⟨1,644,52,true⟩, +⟨0,644,54,false⟩, +⟨0,55,57,false⟩, +⟨1,644,55,true⟩, +⟨0,645,0,false⟩, +⟨1,645,644,true⟩, +⟨0,646,0,true⟩, +⟨1,646,53,true⟩, +⟨0,646,55,true⟩, +⟨0,54,56,true⟩, +⟨1,646,54,true⟩, +⟨0,647,0,true⟩, +⟨1,647,646,true⟩, +⟨0,368,50,false⟩, +⟨0,378,55,false⟩, +⟨1,368,378,true⟩, +⟨0,648,0,false⟩, +⟨1,648,368,true⟩, +⟨0,376,54,true⟩, +⟨0,370,51,true⟩, +⟨1,376,370,true⟩, +⟨0,649,0,true⟩, +⟨1,649,376,true⟩, +⟨0,382,57,false⟩, +⟨0,372,52,false⟩, +⟨1,382,372,true⟩, +⟨0,650,0,false⟩, +⟨1,650,382,true⟩, +⟨0,374,53,true⟩, +⟨0,380,56,true⟩, +⟨1,374,380,true⟩, +⟨0,651,0,true⟩, +⟨1,651,374,true⟩, +⟨0,381,56,false⟩, +⟨0,369,50,false⟩, +⟨1,381,369,true⟩, +⟨0,652,0,false⟩, +⟨1,652,381,true⟩, +⟨0,373,52,true⟩, +⟨0,377,54,true⟩, +⟨1,373,377,true⟩, +⟨0,653,0,true⟩, +⟨1,653,373,true⟩, +⟨0,371,51,false⟩, +⟨0,383,57,false⟩, +⟨1,371,383,true⟩, +⟨0,654,0,false⟩, +⟨1,654,371,true⟩, +⟨0,379,55,true⟩, +⟨0,375,53,true⟩, +⟨1,379,375,true⟩, +⟨0,655,0,true⟩, +⟨1,655,379,true⟩, +⟨0,656,0,false⟩, +⟨1,656,80,true⟩, +⟨0,656,82,false⟩, +⟨0,83,85,false⟩, +⟨1,656,83,true⟩, +⟨0,657,0,false⟩, +⟨1,657,656,true⟩, +⟨0,658,0,true⟩, +⟨1,658,81,true⟩] +def chunk47 : List Event := [⟨0,658,83,true⟩, +⟨0,82,84,true⟩, +⟨1,658,82,true⟩, +⟨0,659,0,true⟩, +⟨1,659,658,true⟩, +⟨0,660,0,false⟩, +⟨1,660,84,true⟩, +⟨0,660,86,false⟩, +⟨0,87,89,false⟩, +⟨1,660,87,true⟩, +⟨0,661,0,false⟩, +⟨1,661,660,true⟩, +⟨0,662,0,true⟩, +⟨1,662,85,true⟩, +⟨0,662,87,true⟩, +⟨0,86,88,true⟩, +⟨1,662,86,true⟩, +⟨0,663,0,true⟩, +⟨1,663,662,true⟩, +⟨0,442,87,false⟩, +⟨0,432,82,false⟩, +⟨1,442,432,true⟩, +⟨0,664,0,false⟩, +⟨1,664,442,true⟩, +⟨0,434,83,true⟩, +⟨0,440,86,true⟩, +⟨1,434,440,true⟩, +⟨0,665,0,true⟩, +⟨1,665,434,true⟩, +⟨0,436,84,false⟩, +⟨0,446,89,false⟩, +⟨1,436,446,true⟩, +⟨0,666,0,false⟩, +⟨1,666,436,true⟩, +⟨0,444,88,true⟩, +⟨0,438,85,true⟩, +⟨1,444,438,true⟩, +⟨0,667,0,true⟩, +⟨1,667,444,true⟩, +⟨0,433,82,false⟩, +⟨0,445,88,false⟩, +⟨1,433,445,true⟩, +⟨0,668,0,false⟩, +⟨1,668,433,true⟩, +⟨0,441,86,true⟩, +⟨0,437,84,true⟩, +⟨1,441,437,true⟩, +⟨0,669,0,true⟩, +⟨1,669,441,true⟩, +⟨0,447,89,false⟩, +⟨0,435,83,false⟩, +⟨1,447,435,true⟩, +⟨0,670,0,false⟩, +⟨1,670,447,true⟩, +⟨0,439,85,true⟩, +⟨0,443,87,true⟩, +⟨1,439,443,true⟩, +⟨0,671,0,true⟩, +⟨1,671,439,true⟩, +⟨0,672,0,false⟩, +⟨1,672,104,true⟩, +⟨0,672,106,false⟩, +⟨0,107,109,false⟩, +⟨1,672,107,true⟩, +⟨0,673,0,false⟩, +⟨1,673,672,true⟩, +⟨0,674,0,true⟩, +⟨1,674,105,true⟩, +⟨0,674,107,true⟩, +⟨0,106,108,true⟩, +⟨1,674,106,true⟩, +⟨0,675,0,true⟩, +⟨1,675,674,true⟩, +⟨0,676,0,false⟩, +⟨1,676,108,true⟩, +⟨0,676,110,false⟩, +⟨0,111,113,false⟩, +⟨1,676,111,true⟩, +⟨0,677,0,false⟩, +⟨1,677,676,true⟩, +⟨0,678,0,true⟩, +⟨1,678,109,true⟩, +⟨0,678,111,true⟩, +⟨0,110,112,true⟩, +⟨1,678,110,true⟩, +⟨0,679,0,true⟩, +⟨1,679,678,true⟩, +⟨0,490,111,false⟩, +⟨0,480,106,false⟩, +⟨1,490,480,true⟩, +⟨0,680,0,false⟩, +⟨1,680,490,true⟩, +⟨0,482,107,true⟩, +⟨0,488,110,true⟩, +⟨1,482,488,true⟩, +⟨0,681,0,true⟩, +⟨1,681,482,true⟩, +⟨0,484,108,false⟩, +⟨0,494,113,false⟩, +⟨1,484,494,true⟩, +⟨0,682,0,false⟩, +⟨1,682,484,true⟩, +⟨0,492,112,true⟩, +⟨0,486,109,true⟩, +⟨1,492,486,true⟩, +⟨0,683,0,true⟩, +⟨1,683,492,true⟩, +⟨0,481,106,false⟩, +⟨0,493,112,false⟩, +⟨1,481,493,true⟩, +⟨0,684,0,false⟩, +⟨1,684,481,true⟩, +⟨0,489,110,true⟩, +⟨0,485,108,true⟩, +⟨1,489,485,true⟩, +⟨0,685,0,true⟩, +⟨1,685,489,true⟩, +⟨0,495,113,false⟩, +⟨0,483,107,false⟩, +⟨1,495,483,true⟩, +⟨0,686,0,false⟩, +⟨1,686,495,true⟩, +⟨0,487,109,true⟩, +⟨0,491,111,true⟩, +⟨1,487,491,true⟩, +⟨0,687,0,true⟩, +⟨1,687,487,true⟩, +⟨0,688,0,false⟩, +⟨1,688,96,true⟩, +⟨0,688,98,false⟩, +⟨0,99,101,false⟩, +⟨1,688,99,true⟩, +⟨0,689,0,false⟩, +⟨1,689,688,true⟩, +⟨0,690,0,true⟩, +⟨1,690,97,true⟩, +⟨0,690,99,true⟩, +⟨0,98,100,true⟩, +⟨1,690,98,true⟩, +⟨0,691,0,true⟩, +⟨1,691,690,true⟩, +⟨0,692,0,false⟩, +⟨1,692,100,true⟩, +⟨0,692,102,false⟩, +⟨0,103,105,false⟩, +⟨1,692,103,true⟩, +⟨0,693,0,false⟩, +⟨1,693,692,true⟩, +⟨0,694,0,true⟩, +⟨1,694,101,true⟩, +⟨0,694,103,true⟩, +⟨0,102,104,true⟩, +⟨1,694,102,true⟩, +⟨0,695,0,true⟩, +⟨1,695,694,true⟩, +⟨0,474,103,false⟩, +⟨0,464,98,false⟩, +⟨1,474,464,true⟩, +⟨0,696,0,false⟩, +⟨1,696,474,true⟩, +⟨0,466,99,true⟩, +⟨0,472,102,true⟩, +⟨1,466,472,true⟩, +⟨0,697,0,true⟩, +⟨1,697,466,true⟩, +⟨0,468,100,false⟩, +⟨0,478,105,false⟩, +⟨1,468,478,true⟩, +⟨0,698,0,false⟩, +⟨1,698,468,true⟩, +⟨0,476,104,true⟩, +⟨0,470,101,true⟩, +⟨1,476,470,true⟩, +⟨0,699,0,true⟩, +⟨1,699,476,true⟩, +⟨0,465,98,false⟩, +⟨0,477,104,false⟩, +⟨1,465,477,true⟩, +⟨0,700,0,false⟩, +⟨1,700,465,true⟩, +⟨0,473,102,true⟩, +⟨0,469,100,true⟩, +⟨1,473,469,true⟩, +⟨0,701,0,true⟩, +⟨1,701,473,true⟩, +⟨0,479,105,false⟩, +⟨0,467,99,false⟩, +⟨1,479,467,true⟩, +⟨0,702,0,false⟩, +⟨1,702,479,true⟩, +⟨0,471,101,true⟩, +⟨0,475,103,true⟩, +⟨1,471,475,true⟩, +⟨0,703,0,true⟩, +⟨1,703,471,true⟩, +⟨0,704,0,false⟩, +⟨1,704,88,true⟩, +⟨0,704,90,false⟩, +⟨0,91,93,false⟩, +⟨1,704,91,true⟩] +def chunk48 : List Event := [⟨0,705,0,false⟩, +⟨1,705,704,true⟩, +⟨0,706,0,true⟩, +⟨1,706,89,true⟩, +⟨0,706,91,true⟩, +⟨0,90,92,true⟩, +⟨1,706,90,true⟩, +⟨0,707,0,true⟩, +⟨1,707,706,true⟩, +⟨0,708,0,false⟩, +⟨1,708,92,true⟩, +⟨0,708,94,false⟩, +⟨0,95,97,false⟩, +⟨1,708,95,true⟩, +⟨0,709,0,false⟩, +⟨1,709,708,true⟩, +⟨0,710,0,true⟩, +⟨1,710,93,true⟩, +⟨0,710,95,true⟩, +⟨0,94,96,true⟩, +⟨1,710,94,true⟩, +⟨0,711,0,true⟩, +⟨1,711,710,true⟩, +⟨0,458,95,false⟩, +⟨0,448,90,false⟩, +⟨1,458,448,true⟩, +⟨0,712,0,false⟩, +⟨1,712,458,true⟩, +⟨0,450,91,true⟩, +⟨0,456,94,true⟩, +⟨1,450,456,true⟩, +⟨0,713,0,true⟩, +⟨1,713,450,true⟩, +⟨0,452,92,false⟩, +⟨0,462,97,false⟩, +⟨1,452,462,true⟩, +⟨0,714,0,false⟩, +⟨1,714,452,true⟩, +⟨0,460,96,true⟩, +⟨0,454,93,true⟩, +⟨1,460,454,true⟩, +⟨0,715,0,true⟩, +⟨1,715,460,true⟩, +⟨0,449,90,false⟩, +⟨0,461,96,false⟩, +⟨1,449,461,true⟩, +⟨0,716,0,false⟩, +⟨1,716,449,true⟩, +⟨0,457,94,true⟩, +⟨0,453,92,true⟩, +⟨1,457,453,true⟩, +⟨0,717,0,true⟩, +⟨1,717,457,true⟩, +⟨0,463,97,false⟩, +⟨0,451,91,false⟩, +⟨1,463,451,true⟩, +⟨0,718,0,false⟩, +⟨1,718,463,true⟩, +⟨0,455,93,true⟩, +⟨0,459,95,true⟩, +⟨1,455,459,true⟩, +⟨0,719,0,true⟩, +⟨1,719,455,true⟩, +⟨0,720,0,false⟩, +⟨1,720,56,true⟩, +⟨0,720,58,false⟩, +⟨0,59,61,false⟩, +⟨1,720,59,true⟩, +⟨0,721,0,false⟩, +⟨1,721,720,true⟩, +⟨0,722,0,true⟩, +⟨1,722,57,true⟩, +⟨0,722,59,true⟩, +⟨0,58,60,true⟩, +⟨1,722,58,true⟩, +⟨0,723,0,true⟩, +⟨1,723,722,true⟩, +⟨0,724,0,false⟩, +⟨1,724,60,true⟩, +⟨0,724,62,false⟩, +⟨0,63,65,false⟩, +⟨1,724,63,true⟩, +⟨0,725,0,false⟩, +⟨1,725,724,true⟩, +⟨0,726,0,true⟩, +⟨1,726,61,true⟩, +⟨0,726,63,true⟩, +⟨0,62,64,true⟩, +⟨1,726,62,true⟩, +⟨0,727,0,true⟩, +⟨1,727,726,true⟩, +⟨0,384,58,false⟩, +⟨0,394,63,false⟩, +⟨1,384,394,true⟩, +⟨0,728,0,false⟩, +⟨1,728,384,true⟩, +⟨0,386,59,true⟩, +⟨0,392,62,true⟩, +⟨1,386,392,true⟩, +⟨0,729,0,true⟩, +⟨1,729,386,true⟩, +⟨0,388,60,false⟩, +⟨0,398,65,false⟩, +⟨1,388,398,true⟩, +⟨0,730,0,false⟩, +⟨1,730,388,true⟩, +⟨0,390,61,true⟩, +⟨0,396,64,true⟩, +⟨1,390,396,true⟩, +⟨0,731,0,true⟩, +⟨1,731,390,true⟩, +⟨0,397,64,false⟩, +⟨0,385,58,false⟩, +⟨1,397,385,true⟩, +⟨0,732,0,false⟩, +⟨1,732,397,true⟩, +⟨0,393,62,true⟩, +⟨0,389,60,true⟩, +⟨1,393,389,true⟩, +⟨0,733,0,true⟩, +⟨1,733,393,true⟩, +⟨0,399,65,false⟩, +⟨0,387,59,false⟩, +⟨1,399,387,true⟩, +⟨0,734,0,false⟩, +⟨1,734,399,true⟩, +⟨0,395,63,true⟩, +⟨0,391,61,true⟩, +⟨1,395,391,true⟩, +⟨0,735,0,true⟩, +⟨1,735,395,true⟩, +⟨0,512,122,false⟩, +⟨0,514,123,false⟩, +⟨1,512,514,true⟩, +⟨0,736,4,false⟩, +⟨1,736,512,true⟩, +⟨0,737,4,false⟩, +⟨1,737,512,true⟩, +⟨0,516,124,true⟩, +⟨0,518,125,true⟩, +⟨1,516,518,true⟩, +⟨0,738,4,true⟩, +⟨1,738,516,true⟩, +⟨0,739,4,true⟩, +⟨1,739,516,true⟩, +⟨0,400,126,false⟩, +⟨0,402,127,false⟩, +⟨1,400,402,true⟩, +⟨0,740,3,false⟩, +⟨1,740,400,true⟩, +⟨0,404,128,true⟩, +⟨0,406,129,true⟩, +⟨1,404,406,true⟩, +⟨0,741,3,true⟩, +⟨1,741,404,true⟩, +⟨0,413,130,false⟩, +⟨0,409,131,false⟩, +⟨1,413,409,true⟩, +⟨0,742,3,false⟩, +⟨1,742,413,true⟩, +⟨0,415,132,true⟩, +⟨0,411,133,true⟩, +⟨1,415,411,true⟩, +⟨0,743,3,true⟩, +⟨1,743,415,true⟩, +⟨0,524,130,false⟩, +⟨0,526,132,false⟩, +⟨1,524,526,true⟩, +⟨0,744,2,false⟩, +⟨1,744,524,true⟩, +⟨0,525,131,true⟩, +⟨0,527,133,true⟩, +⟨1,525,527,true⟩, +⟨0,745,2,true⟩, +⟨1,745,525,true⟩, +⟨0,520,126,false⟩, +⟨0,522,128,false⟩, +⟨1,520,522,true⟩, +⟨0,746,2,false⟩, +⟨1,746,520,true⟩, +⟨0,521,127,true⟩, +⟨0,523,129,true⟩, +⟨1,521,523,true⟩, +⟨0,747,2,true⟩, +⟨1,747,521,true⟩, +⟨0,513,122,false⟩, +⟨0,517,124,false⟩, +⟨1,513,517,true⟩, +⟨0,748,2,false⟩, +⟨1,748,513,true⟩, +⟨0,515,123,true⟩, +⟨0,519,125,true⟩, +⟨1,515,519,true⟩, +⟨0,749,2,true⟩, +⟨1,749,515,true⟩, +⟨0,528,134,false⟩, +⟨0,530,135,false⟩, +⟨1,528,530,true⟩, +⟨0,750,6,false⟩, +⟨1,750,528,true⟩] +def chunk49 : List Event := [⟨0,751,6,false⟩, +⟨1,751,528,true⟩, +⟨0,532,136,true⟩, +⟨0,534,137,true⟩, +⟨1,532,534,true⟩, +⟨0,752,6,true⟩, +⟨1,752,532,true⟩, +⟨0,753,6,true⟩, +⟨1,753,532,true⟩, +⟨0,346,138,false⟩, +⟨0,344,139,false⟩, +⟨1,346,344,true⟩, +⟨0,754,7,false⟩, +⟨1,754,346,true⟩, +⟨0,350,140,true⟩, +⟨0,348,141,true⟩, +⟨1,350,348,true⟩, +⟨0,755,7,true⟩, +⟨1,755,350,true⟩, +⟨0,337,142,false⟩, +⟨0,341,143,false⟩, +⟨1,337,341,true⟩, +⟨0,756,3,false⟩, +⟨1,756,337,true⟩, +⟨0,339,144,true⟩, +⟨0,343,145,true⟩, +⟨1,339,343,true⟩, +⟨0,757,3,true⟩, +⟨1,757,339,true⟩, +⟨0,540,142,false⟩, +⟨0,542,144,false⟩, +⟨1,540,542,true⟩, +⟨0,758,0,false⟩, +⟨1,758,540,true⟩, +⟨0,541,143,true⟩, +⟨0,543,145,true⟩, +⟨1,541,543,true⟩, +⟨0,759,0,true⟩, +⟨1,759,541,true⟩, +⟨0,536,138,false⟩, +⟨0,538,140,false⟩, +⟨1,536,538,true⟩, +⟨0,760,2,false⟩, +⟨1,760,536,true⟩, +⟨0,537,139,true⟩, +⟨0,539,141,true⟩, +⟨1,537,539,true⟩, +⟨0,761,2,true⟩, +⟨1,761,537,true⟩, +⟨0,529,134,false⟩, +⟨0,533,136,false⟩, +⟨1,529,533,true⟩, +⟨0,762,2,false⟩, +⟨1,762,529,true⟩, +⟨0,531,135,true⟩, +⟨0,535,137,true⟩, +⟨1,531,535,true⟩, +⟨0,763,2,true⟩, +⟨1,763,531,true⟩, +⟨0,544,146,false⟩, +⟨0,546,147,false⟩, +⟨1,544,546,true⟩, +⟨0,764,9,false⟩, +⟨1,764,544,true⟩, +⟨0,765,9,false⟩, +⟨1,765,544,true⟩, +⟨0,548,148,true⟩, +⟨0,550,149,true⟩, +⟨1,548,550,true⟩, +⟨0,766,9,true⟩, +⟨1,766,548,true⟩, +⟨0,767,9,true⟩, +⟨1,767,548,true⟩, +⟨0,320,150,false⟩, +⟨0,328,151,false⟩, +⟨1,320,328,true⟩, +⟨0,768,3,false⟩, +⟨1,768,320,true⟩, +⟨0,334,152,true⟩, +⟨0,326,153,true⟩, +⟨1,334,326,true⟩, +⟨0,769,3,true⟩, +⟨1,769,334,true⟩, +⟨0,333,154,false⟩, +⟨0,325,155,false⟩, +⟨1,333,325,true⟩, +⟨0,770,3,false⟩, +⟨1,770,333,true⟩, +⟨0,323,156,true⟩, +⟨0,331,157,true⟩, +⟨1,323,331,true⟩, +⟨0,771,3,true⟩, +⟨1,771,323,true⟩, +⟨0,552,150,false⟩, +⟨0,554,152,false⟩, +⟨1,552,554,true⟩, +⟨0,772,2,false⟩, +⟨1,772,552,true⟩, +⟨0,553,151,true⟩, +⟨0,555,153,true⟩, +⟨1,553,555,true⟩, +⟨0,773,2,true⟩, +⟨1,773,553,true⟩, +⟨0,556,154,false⟩, +⟨0,558,156,false⟩, +⟨1,556,558,true⟩, +⟨0,774,0,false⟩, +⟨1,774,556,true⟩, +⟨0,557,155,true⟩, +⟨0,559,157,true⟩, +⟨1,557,559,true⟩, +⟨0,775,0,true⟩, +⟨1,775,557,true⟩, +⟨0,545,146,false⟩, +⟨0,549,148,false⟩, +⟨1,545,549,true⟩, +⟨0,776,2,false⟩, +⟨1,776,545,true⟩, +⟨0,547,147,true⟩, +⟨0,551,149,true⟩, +⟨1,547,551,true⟩, +⟨0,777,2,true⟩, +⟨1,777,547,true⟩, +⟨0,560,158,false⟩, +⟨0,562,159,false⟩, +⟨1,560,562,true⟩, +⟨0,778,0,false⟩, +⟨1,778,560,true⟩, +⟨0,779,6,false⟩, +⟨1,779,560,true⟩, +⟨0,564,160,true⟩, +⟨0,566,161,true⟩, +⟨1,564,566,true⟩, +⟨0,780,0,true⟩, +⟨1,780,564,true⟩, +⟨0,781,6,true⟩, +⟨1,781,564,true⟩, +⟨0,304,162,false⟩, +⟨0,312,163,false⟩, +⟨1,304,312,true⟩, +⟨0,782,4,false⟩, +⟨1,782,304,true⟩, +⟨0,318,164,true⟩, +⟨0,310,165,true⟩, +⟨1,318,310,true⟩, +⟨0,783,4,true⟩, +⟨1,783,318,true⟩, +⟨0,317,166,false⟩, +⟨0,309,167,false⟩, +⟨1,317,309,true⟩, +⟨0,784,6,false⟩, +⟨1,784,317,true⟩, +⟨0,307,168,true⟩, +⟨0,315,169,true⟩, +⟨1,307,315,true⟩, +⟨0,785,6,true⟩, +⟨1,785,307,true⟩, +⟨0,572,166,false⟩, +⟨0,574,168,false⟩, +⟨1,572,574,true⟩, +⟨0,786,2,false⟩, +⟨1,786,572,true⟩, +⟨0,573,167,true⟩, +⟨0,575,169,true⟩, +⟨1,573,575,true⟩, +⟨0,787,2,true⟩, +⟨1,787,573,true⟩, +⟨0,568,162,false⟩, +⟨0,570,164,false⟩, +⟨1,568,570,true⟩, +⟨0,788,2,false⟩, +⟨1,788,568,true⟩, +⟨0,569,163,true⟩, +⟨0,571,165,true⟩, +⟨1,569,571,true⟩, +⟨0,789,2,true⟩, +⟨1,789,569,true⟩, +⟨0,561,158,false⟩, +⟨0,565,160,false⟩, +⟨1,561,565,true⟩, +⟨0,790,2,false⟩, +⟨1,790,561,true⟩, +⟨0,563,159,true⟩, +⟨0,567,161,true⟩, +⟨1,563,567,true⟩, +⟨0,791,2,true⟩, +⟨1,791,563,true⟩, +⟨0,576,170,false⟩, +⟨0,578,171,false⟩, +⟨1,576,578,true⟩, +⟨0,792,7,false⟩, +⟨1,792,576,true⟩, +⟨0,793,7,false⟩, +⟨1,793,576,true⟩, +⟨0,580,172,true⟩, +⟨0,582,173,true⟩, +⟨1,580,582,true⟩, +⟨0,794,7,true⟩, +⟨1,794,580,true⟩, +⟨0,795,7,true⟩] +def chunk50 : List Event := [⟨1,795,580,true⟩, +⟨0,352,174,false⟩, +⟨0,354,175,false⟩, +⟨1,352,354,true⟩, +⟨0,796,4,false⟩, +⟨1,796,352,true⟩, +⟨0,356,176,true⟩, +⟨0,358,177,true⟩, +⟨1,356,358,true⟩, +⟨0,797,4,true⟩, +⟨1,797,356,true⟩, +⟨0,365,178,false⟩, +⟨0,361,179,false⟩, +⟨1,365,361,true⟩, +⟨0,798,4,false⟩, +⟨1,798,365,true⟩, +⟨0,367,180,true⟩, +⟨0,363,181,true⟩, +⟨1,367,363,true⟩, +⟨0,799,4,true⟩, +⟨1,799,367,true⟩, +⟨0,584,174,false⟩, +⟨0,586,176,false⟩, +⟨1,584,586,true⟩, +⟨0,800,2,false⟩, +⟨1,800,584,true⟩, +⟨0,585,175,true⟩, +⟨0,587,177,true⟩, +⟨1,585,587,true⟩, +⟨0,801,2,true⟩, +⟨1,801,585,true⟩, +⟨0,588,178,false⟩, +⟨0,590,180,false⟩, +⟨1,588,590,true⟩, +⟨0,802,2,false⟩, +⟨1,802,588,true⟩, +⟨0,589,179,true⟩, +⟨0,591,181,true⟩, +⟨1,589,591,true⟩, +⟨0,803,2,true⟩, +⟨1,803,589,true⟩, +⟨0,577,170,false⟩, +⟨0,581,172,false⟩, +⟨1,577,581,true⟩, +⟨0,804,2,false⟩, +⟨1,804,577,true⟩, +⟨0,579,171,true⟩, +⟨0,583,173,true⟩, +⟨1,579,583,true⟩, +⟨0,805,2,true⟩, +⟨1,805,579,true⟩, +⟨0,592,182,false⟩, +⟨0,594,183,false⟩, +⟨1,592,594,true⟩, +⟨0,806,9,false⟩, +⟨1,806,592,true⟩, +⟨0,807,6,false⟩, +⟨1,807,592,true⟩, +⟨0,596,184,true⟩, +⟨0,598,185,true⟩, +⟨1,596,598,true⟩, +⟨0,808,9,true⟩, +⟨1,808,596,true⟩, +⟨0,809,6,true⟩, +⟨1,809,596,true⟩, +⟨0,416,186,false⟩, +⟨0,424,187,false⟩, +⟨1,416,424,true⟩, +⟨0,810,9,false⟩, +⟨1,810,416,true⟩, +⟨0,430,188,true⟩, +⟨0,422,189,true⟩, +⟨1,430,422,true⟩, +⟨0,811,9,true⟩, +⟨1,811,430,true⟩, +⟨0,429,190,false⟩, +⟨0,421,191,false⟩, +⟨1,429,421,true⟩, +⟨0,812,6,false⟩, +⟨1,812,429,true⟩, +⟨0,419,192,true⟩, +⟨0,427,193,true⟩, +⟨1,419,427,true⟩, +⟨0,813,6,true⟩, +⟨1,813,419,true⟩, +⟨0,593,182,false⟩, +⟨0,597,184,false⟩, +⟨1,593,597,true⟩, +⟨0,814,2,false⟩, +⟨1,814,593,true⟩, +⟨0,595,183,true⟩, +⟨0,599,185,true⟩, +⟨1,595,599,true⟩, +⟨0,815,2,true⟩, +⟨1,815,595,true⟩, +⟨0,604,190,false⟩, +⟨0,606,192,false⟩, +⟨1,604,606,true⟩, +⟨0,816,2,false⟩, +⟨1,816,604,true⟩, +⟨0,605,191,true⟩, +⟨0,607,193,true⟩, +⟨1,605,607,true⟩, +⟨0,817,2,true⟩, +⟨1,817,605,true⟩, +⟨0,600,186,false⟩, +⟨0,602,188,false⟩, +⟨1,600,602,true⟩, +⟨0,818,2,false⟩, +⟨1,818,600,true⟩, +⟨0,601,187,true⟩, +⟨0,603,189,true⟩, +⟨1,601,603,true⟩, +⟨0,819,2,true⟩, +⟨1,819,601,true⟩, +⟨0,608,194,false⟩, +⟨0,610,195,false⟩, +⟨1,608,610,true⟩, +⟨0,820,7,false⟩, +⟨1,820,608,true⟩, +⟨0,821,7,false⟩, +⟨1,821,608,true⟩, +⟨0,612,196,true⟩, +⟨0,614,197,true⟩, +⟨1,612,614,true⟩, +⟨0,822,7,true⟩, +⟨1,822,612,true⟩, +⟨0,823,7,true⟩, +⟨1,823,612,true⟩, +⟨0,506,198,false⟩, +⟨0,504,199,false⟩, +⟨1,506,504,true⟩, +⟨0,824,5,false⟩, +⟨1,824,506,true⟩, +⟨0,510,200,true⟩, +⟨0,508,201,true⟩, +⟨1,510,508,true⟩, +⟨0,825,5,true⟩, +⟨1,825,510,true⟩, +⟨0,497,202,false⟩, +⟨0,501,203,false⟩, +⟨1,497,501,true⟩, +⟨0,826,7,false⟩, +⟨1,826,497,true⟩, +⟨0,499,204,true⟩, +⟨0,503,205,true⟩, +⟨1,499,503,true⟩, +⟨0,827,7,true⟩, +⟨1,827,499,true⟩, +⟨0,609,194,false⟩, +⟨0,613,196,false⟩, +⟨1,609,613,true⟩, +⟨0,828,2,false⟩, +⟨1,828,609,true⟩, +⟨0,611,195,true⟩, +⟨0,615,197,true⟩, +⟨1,611,615,true⟩, +⟨0,829,2,true⟩, +⟨1,829,611,true⟩, +⟨0,616,198,false⟩, +⟨0,618,200,false⟩, +⟨1,616,618,true⟩, +⟨0,830,2,false⟩, +⟨1,830,616,true⟩, +⟨0,617,199,true⟩, +⟨0,619,201,true⟩, +⟨1,617,619,true⟩, +⟨0,831,2,true⟩, +⟨1,831,617,true⟩, +⟨0,620,202,false⟩, +⟨0,622,204,false⟩, +⟨1,620,622,true⟩, +⟨0,832,2,false⟩, +⟨1,832,620,true⟩, +⟨0,621,203,true⟩, +⟨0,623,205,true⟩, +⟨1,621,623,true⟩, +⟨0,833,2,true⟩, +⟨1,833,621,true⟩, +⟨0,624,206,false⟩, +⟨0,626,207,false⟩, +⟨1,624,626,true⟩, +⟨0,834,9,false⟩, +⟨1,834,624,true⟩, +⟨0,835,6,false⟩, +⟨1,835,624,true⟩, +⟨0,628,208,true⟩, +⟨0,630,209,true⟩, +⟨1,628,630,true⟩, +⟨0,836,9,true⟩, +⟨1,836,628,true⟩, +⟨0,837,6,true⟩, +⟨1,837,628,true⟩, +⟨0,288,210,false⟩, +⟨0,290,211,false⟩, +⟨1,288,290,true⟩, +⟨0,838,4,false⟩, +⟨1,838,288,true⟩, +⟨0,292,212,true⟩, +⟨0,294,213,true⟩] +def chunk51 : List Event := [⟨1,292,294,true⟩, +⟨0,839,4,true⟩, +⟨1,839,292,true⟩, +⟨0,301,214,false⟩, +⟨0,297,215,false⟩, +⟨1,301,297,true⟩, +⟨0,840,6,false⟩, +⟨1,840,301,true⟩, +⟨0,303,216,true⟩, +⟨0,299,217,true⟩, +⟨1,303,299,true⟩, +⟨0,841,6,true⟩, +⟨1,841,303,true⟩, +⟨0,636,214,false⟩, +⟨0,638,216,false⟩, +⟨1,636,638,true⟩, +⟨0,842,0,false⟩, +⟨1,842,636,true⟩, +⟨0,637,215,true⟩, +⟨0,639,217,true⟩, +⟨1,637,639,true⟩, +⟨0,843,0,true⟩, +⟨1,843,637,true⟩, +⟨0,632,210,false⟩, +⟨0,634,212,false⟩, +⟨1,632,634,true⟩, +⟨0,844,3,false⟩, +⟨1,844,632,true⟩, +⟨0,633,211,true⟩, +⟨0,635,213,true⟩, +⟨1,633,635,true⟩, +⟨0,845,3,true⟩, +⟨1,845,633,true⟩, +⟨0,625,206,false⟩, +⟨0,629,208,false⟩, +⟨1,625,629,true⟩, +⟨0,846,3,false⟩, +⟨1,846,625,true⟩, +⟨0,627,207,true⟩, +⟨0,631,209,true⟩, +⟨1,627,631,true⟩, +⟨0,847,3,true⟩, +⟨1,847,627,true⟩, +⟨0,640,218,false⟩, +⟨0,642,219,false⟩, +⟨1,640,642,true⟩, +⟨0,848,0,false⟩, +⟨1,848,640,true⟩, +⟨0,849,7,false⟩, +⟨1,849,640,true⟩, +⟨0,644,220,true⟩, +⟨0,646,221,true⟩, +⟨1,644,646,true⟩, +⟨0,850,0,true⟩, +⟨1,850,644,true⟩, +⟨0,851,7,true⟩, +⟨1,851,644,true⟩, +⟨0,368,222,false⟩, +⟨0,376,223,false⟩, +⟨1,368,376,true⟩, +⟨0,852,4,false⟩, +⟨1,852,368,true⟩, +⟨0,382,224,true⟩, +⟨0,374,225,true⟩, +⟨1,382,374,true⟩, +⟨0,853,4,true⟩, +⟨1,853,382,true⟩, +⟨0,381,226,false⟩, +⟨0,373,227,false⟩, +⟨1,381,373,true⟩, +⟨0,854,4,false⟩, +⟨1,854,381,true⟩, +⟨0,371,228,true⟩, +⟨0,379,229,true⟩, +⟨1,371,379,true⟩, +⟨0,855,4,true⟩, +⟨1,855,371,true⟩, +⟨0,648,222,false⟩, +⟨0,650,224,false⟩, +⟨1,648,650,true⟩, +⟨0,856,7,false⟩, +⟨1,856,648,true⟩, +⟨0,649,223,true⟩, +⟨0,651,225,true⟩, +⟨1,649,651,true⟩, +⟨0,857,7,true⟩, +⟨1,857,649,true⟩, +⟨0,652,226,false⟩, +⟨0,654,228,false⟩, +⟨1,652,654,true⟩, +⟨0,858,3,false⟩, +⟨1,858,652,true⟩, +⟨0,653,227,true⟩, +⟨0,655,229,true⟩, +⟨1,653,655,true⟩, +⟨0,859,3,true⟩, +⟨1,859,653,true⟩, +⟨0,641,218,false⟩, +⟨0,645,220,false⟩, +⟨1,641,645,true⟩, +⟨0,860,3,false⟩, +⟨1,860,641,true⟩, +⟨0,643,219,true⟩, +⟨0,647,221,true⟩, +⟨1,643,647,true⟩, +⟨0,861,3,true⟩, +⟨1,861,643,true⟩, +⟨0,656,230,false⟩, +⟨0,658,231,false⟩, +⟨1,656,658,true⟩, +⟨0,862,0,false⟩, +⟨1,862,656,true⟩, +⟨0,863,6,false⟩, +⟨1,863,656,true⟩, +⟨0,660,232,true⟩, +⟨0,662,233,true⟩, +⟨1,660,662,true⟩, +⟨0,864,0,true⟩, +⟨1,864,660,true⟩, +⟨0,865,6,true⟩, +⟨1,865,660,true⟩, +⟨0,442,234,false⟩, +⟨0,434,235,false⟩, +⟨1,442,434,true⟩, +⟨0,866,5,false⟩, +⟨1,866,442,true⟩, +⟨0,436,236,true⟩, +⟨0,444,237,true⟩, +⟨1,436,444,true⟩, +⟨0,867,5,true⟩, +⟨1,867,436,true⟩, +⟨0,433,238,false⟩, +⟨0,441,239,false⟩, +⟨1,433,441,true⟩, +⟨0,868,6,false⟩, +⟨1,868,433,true⟩, +⟨0,447,240,true⟩, +⟨0,439,241,true⟩, +⟨1,447,439,true⟩, +⟨0,869,6,true⟩, +⟨1,869,447,true⟩, +⟨0,657,230,false⟩, +⟨0,661,232,false⟩, +⟨1,657,661,true⟩, +⟨0,870,0,false⟩, +⟨1,870,657,true⟩, +⟨0,659,231,true⟩, +⟨0,663,233,true⟩, +⟨1,659,663,true⟩, +⟨0,871,0,true⟩, +⟨1,871,659,true⟩, +⟨0,668,238,false⟩, +⟨0,670,240,false⟩, +⟨1,668,670,true⟩, +⟨0,872,3,false⟩, +⟨1,872,668,true⟩, +⟨0,669,239,true⟩, +⟨0,671,241,true⟩, +⟨1,669,671,true⟩, +⟨0,873,3,true⟩, +⟨1,873,669,true⟩, +⟨0,664,234,false⟩, +⟨0,666,236,false⟩, +⟨1,664,666,true⟩, +⟨0,874,3,false⟩, +⟨1,874,664,true⟩, +⟨0,665,235,true⟩, +⟨0,667,237,true⟩, +⟨1,665,667,true⟩, +⟨0,875,3,true⟩, +⟨1,875,665,true⟩, +⟨0,672,242,false⟩, +⟨0,674,243,false⟩, +⟨1,672,674,true⟩, +⟨0,876,0,false⟩, +⟨1,876,672,true⟩, +⟨0,877,7,false⟩, +⟨1,877,672,true⟩, +⟨0,676,244,true⟩, +⟨0,678,245,true⟩, +⟨1,676,678,true⟩, +⟨0,878,0,true⟩, +⟨1,878,676,true⟩, +⟨0,879,7,true⟩, +⟨1,879,676,true⟩, +⟨0,490,246,false⟩, +⟨0,482,247,false⟩, +⟨1,490,482,true⟩, +⟨0,880,9,false⟩, +⟨1,880,490,true⟩, +⟨0,484,248,true⟩, +⟨0,492,249,true⟩, +⟨1,484,492,true⟩, +⟨0,881,9,true⟩, +⟨1,881,484,true⟩, +⟨0,481,250,false⟩, +⟨0,489,251,false⟩, +⟨1,481,489,true⟩, +⟨0,882,7,false⟩, +⟨1,882,481,true⟩] +def chunk52 : List Event := [⟨0,495,252,true⟩, +⟨0,487,253,true⟩, +⟨1,495,487,true⟩, +⟨0,883,7,true⟩, +⟨1,883,495,true⟩, +⟨0,673,242,false⟩, +⟨0,677,244,false⟩, +⟨1,673,677,true⟩, +⟨0,884,3,false⟩, +⟨1,884,673,true⟩, +⟨0,675,243,true⟩, +⟨0,679,245,true⟩, +⟨1,675,679,true⟩, +⟨0,885,3,true⟩, +⟨1,885,675,true⟩, +⟨0,680,246,false⟩, +⟨0,682,248,false⟩, +⟨1,680,682,true⟩, +⟨0,886,7,false⟩, +⟨1,886,680,true⟩, +⟨0,681,247,true⟩, +⟨0,683,249,true⟩, +⟨1,681,683,true⟩, +⟨0,887,7,true⟩, +⟨1,887,681,true⟩, +⟨0,684,250,false⟩, +⟨0,686,252,false⟩, +⟨1,684,686,true⟩, +⟨0,888,3,false⟩, +⟨1,888,684,true⟩, +⟨0,685,251,true⟩, +⟨0,687,253,true⟩, +⟨1,685,687,true⟩, +⟨0,889,3,true⟩, +⟨1,889,685,true⟩, +⟨0,688,254,false⟩, +⟨0,690,255,false⟩, +⟨1,688,690,true⟩, +⟨0,890,0,false⟩, +⟨1,890,688,true⟩, +⟨0,891,6,false⟩, +⟨1,891,688,true⟩, +⟨0,692,256,true⟩, +⟨0,694,257,true⟩, +⟨1,692,694,true⟩, +⟨0,892,0,true⟩, +⟨1,892,692,true⟩, +⟨0,893,6,true⟩, +⟨1,893,692,true⟩, +⟨0,689,254,false⟩, +⟨0,693,256,false⟩, +⟨1,689,693,true⟩, +⟨0,894,4,false⟩, +⟨1,894,689,true⟩, +⟨0,691,255,true⟩, +⟨0,695,257,true⟩, +⟨1,691,695,true⟩, +⟨0,895,4,true⟩, +⟨1,895,691,true⟩, +⟨0,474,258,false⟩, +⟨0,466,259,false⟩, +⟨1,474,466,true⟩, +⟨0,896,7,false⟩, +⟨1,896,474,true⟩, +⟨0,468,260,true⟩, +⟨0,476,261,true⟩, +⟨1,468,476,true⟩, +⟨0,897,7,true⟩, +⟨1,897,468,true⟩, +⟨0,465,262,false⟩, +⟨0,473,263,false⟩, +⟨1,465,473,true⟩, +⟨0,898,6,false⟩, +⟨1,898,465,true⟩, +⟨0,479,264,true⟩, +⟨0,471,265,true⟩, +⟨1,479,471,true⟩, +⟨0,899,6,true⟩, +⟨1,899,479,true⟩, +⟨0,700,262,false⟩, +⟨0,702,264,false⟩, +⟨1,700,702,true⟩, +⟨0,900,7,false⟩, +⟨1,900,700,true⟩, +⟨0,701,263,true⟩, +⟨0,703,265,true⟩, +⟨1,701,703,true⟩, +⟨0,901,7,true⟩, +⟨1,901,701,true⟩, +⟨0,696,258,false⟩, +⟨0,698,260,false⟩, +⟨1,696,698,true⟩, +⟨0,902,4,false⟩, +⟨1,902,696,true⟩, +⟨0,697,259,true⟩, +⟨0,699,261,true⟩, +⟨1,697,699,true⟩, +⟨0,903,4,true⟩, +⟨1,903,697,true⟩, +⟨0,704,266,false⟩, +⟨0,706,267,false⟩, +⟨1,704,706,true⟩, +⟨0,904,0,false⟩, +⟨1,904,704,true⟩, +⟨0,905,0,false⟩, +⟨1,905,704,true⟩, +⟨0,708,268,true⟩, +⟨0,710,269,true⟩, +⟨1,708,710,true⟩, +⟨0,906,0,true⟩, +⟨1,906,708,true⟩, +⟨0,907,0,true⟩, +⟨1,907,708,true⟩, +⟨0,705,266,false⟩, +⟨0,709,268,false⟩, +⟨1,705,709,true⟩, +⟨0,908,4,false⟩, +⟨1,908,705,true⟩, +⟨0,707,267,true⟩, +⟨0,711,269,true⟩, +⟨1,707,711,true⟩, +⟨0,909,4,true⟩, +⟨1,909,707,true⟩, +⟨0,458,270,false⟩, +⟨0,450,271,false⟩, +⟨1,458,450,true⟩, +⟨0,910,0,false⟩, +⟨1,910,458,true⟩, +⟨0,452,272,true⟩, +⟨0,460,273,true⟩, +⟨1,452,460,true⟩, +⟨0,911,0,true⟩, +⟨1,911,452,true⟩, +⟨0,449,274,false⟩, +⟨0,457,275,false⟩, +⟨1,449,457,true⟩, +⟨0,912,5,false⟩, +⟨1,912,449,true⟩, +⟨0,463,276,true⟩, +⟨0,455,277,true⟩, +⟨1,463,455,true⟩, +⟨0,913,5,true⟩, +⟨1,913,463,true⟩, +⟨0,712,270,false⟩, +⟨0,714,272,false⟩, +⟨1,712,714,true⟩, +⟨0,914,0,false⟩, +⟨1,914,712,true⟩, +⟨0,713,271,true⟩, +⟨0,715,273,true⟩, +⟨1,713,715,true⟩, +⟨0,915,0,true⟩, +⟨1,915,713,true⟩, +⟨0,716,274,false⟩, +⟨0,718,276,false⟩, +⟨1,716,718,true⟩, +⟨0,916,4,false⟩, +⟨1,916,716,true⟩, +⟨0,717,275,true⟩, +⟨0,719,277,true⟩, +⟨1,717,719,true⟩, +⟨0,917,4,true⟩, +⟨1,917,717,true⟩, +⟨0,720,278,false⟩, +⟨0,722,279,false⟩, +⟨1,720,722,true⟩, +⟨0,918,0,false⟩, +⟨1,918,720,true⟩, +⟨0,919,9,false⟩, +⟨1,919,720,true⟩, +⟨0,724,280,true⟩, +⟨0,726,281,true⟩, +⟨1,724,726,true⟩, +⟨0,920,0,true⟩, +⟨1,920,724,true⟩, +⟨0,921,9,true⟩, +⟨1,921,724,true⟩, +⟨0,721,278,false⟩, +⟨0,725,280,false⟩, +⟨1,721,725,true⟩, +⟨0,922,6,false⟩, +⟨1,922,721,true⟩, +⟨0,723,279,true⟩, +⟨0,727,281,true⟩, +⟨1,723,727,true⟩, +⟨0,923,6,true⟩, +⟨1,923,723,true⟩, +⟨0,384,282,false⟩, +⟨0,386,283,false⟩, +⟨1,384,386,true⟩, +⟨0,924,7,false⟩, +⟨1,924,384,true⟩, +⟨0,388,284,true⟩, +⟨0,390,285,true⟩, +⟨1,388,390,true⟩, +⟨0,925,7,true⟩, +⟨1,925,388,true⟩, +⟨0,728,282,false⟩, +⟨0,730,284,false⟩, +⟨1,728,730,true⟩] +def chunk53 : List Event := [⟨0,926,0,false⟩, +⟨1,926,728,true⟩, +⟨0,729,283,true⟩, +⟨0,731,285,true⟩, +⟨1,729,731,true⟩, +⟨0,927,0,true⟩, +⟨1,927,729,true⟩, +⟨0,397,286,false⟩, +⟨0,393,287,false⟩, +⟨1,397,393,true⟩, +⟨0,928,7,false⟩, +⟨1,928,397,true⟩, +⟨0,399,288,true⟩, +⟨0,395,289,true⟩, +⟨1,399,395,true⟩, +⟨0,929,7,true⟩, +⟨1,929,399,true⟩, +⟨0,732,286,false⟩, +⟨0,734,288,false⟩, +⟨1,732,734,true⟩, +⟨0,930,9,false⟩, +⟨1,930,732,true⟩, +⟨0,733,287,true⟩, +⟨0,735,289,true⟩, +⟨1,733,735,true⟩, +⟨0,931,9,true⟩, +⟨1,931,733,true⟩, +⟨0,512,290,false⟩, +⟨0,516,291,false⟩, +⟨1,512,516,true⟩, +⟨0,519,301,false⟩, +⟨0,518,291,false⟩, +⟨1,519,518,true⟩, +⟨1,519,512,true⟩, +⟨0,523,299,false⟩, +⟨0,406,293,false⟩, +⟨1,523,406,true⟩, +⟨0,411,295,false⟩, +⟨1,406,411,true⟩, +⟨1,406,518,true⟩, +⟨1,523,512,true⟩, +⟨0,0,2,false⟩, +⟨1,523,0,true⟩, +⟨0,1,3,false⟩, +⟨1,523,1,true⟩, +⟨0,252,4,false⟩, +⟨1,523,252,true⟩, +⟨1,252,0,true⟩, +⟨1,252,1,true⟩, +⟨1,252,512,true⟩, +⟨1,252,523,true⟩, +⟨0,258,5,false⟩, +⟨1,523,258,true⟩, +⟨0,528,302,true⟩, +⟨0,532,303,true⟩, +⟨1,528,532,true⟩, +⟨0,533,312,true⟩, +⟨0,534,303,true⟩, +⟨1,532,533,true⟩, +⟨1,532,534,true⟩, +⟨0,240,2,true⟩, +⟨1,240,528,true⟩, +⟨0,246,3,true⟩, +⟨1,240,246,true⟩, +⟨0,4,6,true⟩, +⟨1,240,4,true⟩, +⟨0,5,7,true⟩, +⟨1,240,5,true⟩, +⟨0,544,314,false⟩, +⟨0,548,315,false⟩, +⟨1,544,548,true⟩, +⟨0,551,325,false⟩, +⟨0,550,315,false⟩, +⟨1,551,550,true⟩, +⟨1,551,544,true⟩, +⟨0,241,2,false⟩, +⟨1,241,544,true⟩, +⟨0,247,3,false⟩, +⟨1,241,247,true⟩, +⟨0,6,8,false⟩, +⟨1,241,6,true⟩, +⟨0,7,9,false⟩, +⟨1,241,7,true⟩, +⟨0,560,326,true⟩, +⟨0,564,327,true⟩, +⟨1,560,564,true⟩, +⟨0,567,337,true⟩, +⟨0,566,327,true⟩, +⟨1,567,566,true⟩, +⟨1,567,560,true⟩, +⟨0,571,335,true⟩, +⟨0,310,329,true⟩, +⟨1,571,310,true⟩, +⟨0,315,331,true⟩, +⟨1,310,315,true⟩, +⟨1,310,566,true⟩, +⟨1,571,560,true⟩, +⟨0,242,2,true⟩, +⟨1,242,560,true⟩, +⟨0,2,4,true⟩, +⟨1,242,2,true⟩, +⟨0,264,6,true⟩, +⟨1,242,264,true⟩, +⟨0,276,8,true⟩, +⟨1,242,276,true⟩, +⟨0,576,338,false⟩, +⟨0,580,339,false⟩, +⟨1,576,580,true⟩, +⟨0,583,349,false⟩, +⟨0,582,339,false⟩, +⟨1,583,582,true⟩, +⟨1,583,576,true⟩, +⟨0,243,2,false⟩, +⟨1,243,576,true⟩, +⟨0,253,4,false⟩, +⟨1,243,253,true⟩, +⟨0,270,7,false⟩, +⟨1,243,270,true⟩, +⟨0,282,9,false⟩, +⟨1,243,282,true⟩, +⟨0,592,350,true⟩, +⟨0,596,351,true⟩, +⟨1,592,596,true⟩, +⟨0,599,357,true⟩, +⟨0,598,351,true⟩, +⟨1,599,598,true⟩, +⟨1,599,592,true⟩, +⟨0,603,361,true⟩, +⟨0,422,353,true⟩, +⟨1,603,422,true⟩, +⟨0,427,355,true⟩, +⟨1,422,427,true⟩, +⟨1,422,598,true⟩, +⟨1,603,592,true⟩, +⟨0,244,2,true⟩, +⟨1,244,592,true⟩, +⟨0,3,5,true⟩, +⟨1,244,3,true⟩, +⟨0,265,6,true⟩, +⟨1,244,265,true⟩, +⟨0,283,9,true⟩, +⟨1,244,283,true⟩, +⟨0,608,362,false⟩, +⟨0,612,363,false⟩, +⟨1,608,612,true⟩, +⟨0,615,369,false⟩, +⟨0,614,363,false⟩, +⟨1,615,614,true⟩, +⟨1,615,608,true⟩, +⟨0,245,2,false⟩, +⟨1,245,608,true⟩, +⟨0,259,5,false⟩, +⟨1,245,259,true⟩, +⟨0,271,7,false⟩, +⟨1,245,271,true⟩, +⟨0,277,8,false⟩, +⟨1,245,277,true⟩, +⟨0,624,374,true⟩, +⟨0,628,375,true⟩, +⟨1,624,628,true⟩, +⟨0,631,385,true⟩, +⟨0,630,375,true⟩, +⟨1,631,630,true⟩, +⟨1,631,624,true⟩, +⟨0,635,383,true⟩, +⟨0,294,377,true⟩, +⟨1,635,294,true⟩, +⟨0,299,379,true⟩, +⟨1,294,299,true⟩, +⟨1,294,630,true⟩, +⟨1,635,624,true⟩, +⟨0,248,3,true⟩, +⟨1,248,624,true⟩, +⟨0,254,4,true⟩, +⟨1,248,254,true⟩, +⟨0,266,6,true⟩, +⟨1,248,266,true⟩, +⟨0,284,9,true⟩, +⟨1,248,284,true⟩, +⟨0,640,386,false⟩, +⟨0,644,387,false⟩, +⟨1,640,644,true⟩, +⟨0,647,397,false⟩, +⟨0,646,387,false⟩, +⟨1,647,646,true⟩, +⟨1,647,640,true⟩, +⟨0,651,393,false⟩, +⟨0,374,389,false⟩, +⟨1,651,374,true⟩, +⟨0,379,391,false⟩, +⟨1,374,379,true⟩, +⟨1,374,646,true⟩, +⟨1,651,640,true⟩, +⟨0,249,3,false⟩, +⟨1,249,640,true⟩, +⟨0,255,4,false⟩, +⟨1,249,255,true⟩, +⟨0,272,7,false⟩, +⟨1,249,272,true⟩, +⟨0,278,8,false⟩] +def chunk54 : List Event := [⟨1,249,278,true⟩, +⟨0,656,398,true⟩, +⟨0,660,399,true⟩, +⟨1,656,660,true⟩, +⟨0,663,405,true⟩, +⟨0,662,399,true⟩, +⟨1,663,662,true⟩, +⟨1,663,656,true⟩, +⟨0,667,409,true⟩, +⟨0,444,401,true⟩, +⟨1,667,444,true⟩, +⟨0,439,403,true⟩, +⟨1,444,439,true⟩, +⟨1,444,662,true⟩, +⟨1,667,656,true⟩, +⟨0,250,3,true⟩, +⟨1,250,656,true⟩, +⟨0,260,5,true⟩, +⟨1,250,260,true⟩, +⟨0,267,6,true⟩, +⟨1,250,267,true⟩, +⟨0,279,8,true⟩, +⟨1,250,279,true⟩, +⟨0,672,410,false⟩, +⟨0,676,411,false⟩, +⟨1,672,676,true⟩, +⟨0,679,417,false⟩, +⟨0,678,411,false⟩, +⟨1,679,678,true⟩, +⟨1,679,672,true⟩, +⟨0,683,419,false⟩, +⟨0,492,413,false⟩, +⟨1,683,492,true⟩, +⟨0,487,415,false⟩, +⟨1,492,487,true⟩, +⟨1,492,678,true⟩, +⟨1,683,672,true⟩, +⟨0,251,3,false⟩, +⟨1,251,672,true⟩, +⟨0,261,5,false⟩, +⟨1,251,261,true⟩, +⟨0,273,7,false⟩, +⟨1,251,273,true⟩, +⟨0,285,9,false⟩, +⟨1,251,285,true⟩, +⟨0,688,422,true⟩, +⟨0,692,423,true⟩, +⟨1,688,692,true⟩, +⟨0,695,425,true⟩, +⟨0,694,423,true⟩, +⟨1,695,694,true⟩, +⟨1,695,688,true⟩, +⟨0,699,433,true⟩, +⟨0,476,427,true⟩, +⟨1,699,476,true⟩, +⟨0,471,429,true⟩, +⟨1,476,471,true⟩, +⟨1,476,694,true⟩, +⟨1,699,688,true⟩, +⟨0,256,4,true⟩, +⟨1,256,688,true⟩, +⟨0,262,5,true⟩, +⟨1,256,262,true⟩, +⟨0,268,6,true⟩, +⟨1,256,268,true⟩, +⟨0,274,7,true⟩, +⟨1,256,274,true⟩, +⟨0,704,434,false⟩, +⟨0,708,435,false⟩, +⟨1,704,708,true⟩, +⟨0,711,437,false⟩, +⟨0,710,435,false⟩, +⟨1,711,710,true⟩, +⟨0,455,441,false⟩, +⟨0,460,439,false⟩, +⟨1,710,455,true⟩, +⟨1,710,460,true⟩, +⟨1,711,704,true⟩, +⟨0,715,443,false⟩, +⟨1,715,460,true⟩, +⟨1,715,704,true⟩, +⟨0,257,4,false⟩, +⟨1,257,704,true⟩, +⟨0,263,5,false⟩, +⟨1,257,263,true⟩, +⟨0,280,8,false⟩, +⟨1,257,280,true⟩, +⟨0,286,9,false⟩, +⟨1,257,286,true⟩, +⟨0,720,446,true⟩, +⟨0,724,447,true⟩, +⟨1,720,724,true⟩, +⟨0,727,449,true⟩, +⟨0,726,447,true⟩, +⟨1,727,726,true⟩, +⟨1,727,720,true⟩, +⟨0,269,6,true⟩, +⟨1,269,720,true⟩, +⟨0,275,7,true⟩, +⟨1,269,275,true⟩, +⟨0,281,8,true⟩, +⟨1,269,281,true⟩, +⟨0,287,9,true⟩, +⟨1,269,287,true⟩, +⟨0,736,290,false⟩, +⟨0,764,314,false⟩, +⟨1,736,764,true⟩, +⟨0,719,445,false⟩, +⟨0,455,470,false⟩, +⟨1,719,455,true⟩, +⟨1,719,736,true⟩, +⟨0,737,290,true⟩, +⟨0,750,302,true⟩, +⟨1,737,750,true⟩, +⟨0,703,431,true⟩, +⟨0,471,469,true⟩, +⟨1,703,471,true⟩, +⟨1,703,737,true⟩, +⟨0,738,291,false⟩, +⟨0,766,315,false⟩, +⟨1,738,766,true⟩, +⟨0,450,438,false⟩, +⟨0,457,440,false⟩, +⟨0,706,434,false⟩, +⟨1,450,457,true⟩, +⟨1,450,706,true⟩, +⟨0,450,470,false⟩, +⟨1,450,738,true⟩, +⟨0,739,291,true⟩, +⟨0,752,303,true⟩, +⟨1,739,752,true⟩, +⟨0,693,424,true⟩, +⟨1,694,692,true⟩, +⟨1,694,693,true⟩, +⟨0,694,469,true⟩, +⟨1,694,739,true⟩, +⟨0,400,292,false⟩, +⟨0,792,338,false⟩, +⟨1,400,792,true⟩, +⟨0,687,421,false⟩, +⟨0,487,468,false⟩, +⟨1,687,487,true⟩, +⟨1,687,400,true⟩, +⟨0,740,292,true⟩, +⟨0,778,326,true⟩, +⟨1,740,778,true⟩, +⟨0,671,407,true⟩, +⟨0,439,467,true⟩, +⟨1,671,439,true⟩, +⟨1,671,740,true⟩, +⟨0,404,293,false⟩, +⟨0,794,339,false⟩, +⟨1,404,794,true⟩, +⟨0,677,416,false⟩, +⟨1,678,676,true⟩, +⟨1,678,677,true⟩, +⟨0,678,468,false⟩, +⟨1,678,404,true⟩, +⟨0,741,293,true⟩, +⟨0,780,327,true⟩, +⟨1,741,780,true⟩, +⟨0,661,404,true⟩, +⟨1,662,660,true⟩, +⟨1,662,661,true⟩, +⟨0,662,467,true⟩, +⟨1,662,741,true⟩, +⟨0,413,294,false⟩, +⟨0,820,362,false⟩, +⟨1,413,820,true⟩, +⟨0,655,395,false⟩, +⟨0,379,466,false⟩, +⟨1,655,379,true⟩, +⟨1,655,413,true⟩, +⟨0,742,294,true⟩, +⟨0,806,350,true⟩, +⟨1,742,806,true⟩, +⟨0,639,381,true⟩, +⟨0,299,465,true⟩, +⟨1,639,299,true⟩, +⟨1,639,742,true⟩, +⟨0,415,295,false⟩, +⟨0,822,363,false⟩, +⟨1,415,822,true⟩, +⟨0,645,396,false⟩, +⟨1,646,644,true⟩, +⟨1,646,645,true⟩, +⟨0,646,466,false⟩, +⟨1,646,415,true⟩, +⟨0,743,295,true⟩, +⟨0,808,351,true⟩, +⟨1,743,808,true⟩, +⟨0,629,384,true⟩, +⟨1,630,628,true⟩, +⟨1,630,629,true⟩, +⟨0,630,465,true⟩, +⟨1,630,743,true⟩, +⟨0,524,296,false⟩, +⟨0,848,386,false⟩, +⟨1,524,848,true⟩, +⟨0,619,371,false⟩] +def chunk55 : List Event := [⟨0,508,365,false⟩, +⟨1,619,508,true⟩, +⟨1,619,524,true⟩, +⟨0,744,296,true⟩, +⟨0,834,374,true⟩, +⟨1,744,834,true⟩, +⟨0,607,359,true⟩, +⟨0,427,463,true⟩, +⟨1,607,427,true⟩, +⟨1,607,744,true⟩, +⟨0,525,297,false⟩, +⟨0,850,387,false⟩, +⟨1,525,850,true⟩, +⟨0,623,373,false⟩, +⟨0,503,367,false⟩, +⟨1,623,503,true⟩, +⟨1,623,525,true⟩, +⟨0,745,297,true⟩, +⟨0,836,375,true⟩, +⟨1,745,836,true⟩, +⟨0,597,356,true⟩, +⟨1,598,596,true⟩, +⟨1,598,597,true⟩, +⟨0,598,463,true⟩, +⟨1,598,745,true⟩, +⟨0,520,298,false⟩, +⟨0,876,410,false⟩, +⟨1,520,876,true⟩, +⟨0,587,345,false⟩, +⟨0,358,341,false⟩, +⟨1,587,358,true⟩, +⟨1,587,520,true⟩, +⟨0,746,298,true⟩, +⟨0,862,398,true⟩, +⟨1,746,862,true⟩, +⟨0,575,333,true⟩, +⟨0,315,461,true⟩, +⟨1,575,315,true⟩, +⟨1,575,746,true⟩, +⟨0,521,299,false⟩, +⟨0,878,411,false⟩, +⟨1,521,878,true⟩, +⟨0,591,347,false⟩, +⟨0,363,343,false⟩, +⟨1,591,363,true⟩, +⟨1,591,521,true⟩, +⟨0,747,299,true⟩, +⟨0,864,399,true⟩, +⟨1,747,864,true⟩, +⟨0,565,336,true⟩, +⟨1,566,564,true⟩, +⟨1,566,565,true⟩, +⟨0,566,461,true⟩, +⟨1,566,747,true⟩, +⟨0,513,300,false⟩, +⟨0,904,434,false⟩, +⟨1,513,904,true⟩, +⟨0,555,321,false⟩, +⟨0,326,317,false⟩, +⟨1,555,326,true⟩, +⟨1,555,513,true⟩, +⟨0,748,300,true⟩, +⟨0,890,422,true⟩, +⟨1,748,890,true⟩, +⟨0,535,313,true⟩, +⟨0,534,459,true⟩, +⟨1,535,534,true⟩, +⟨1,535,748,true⟩, +⟨0,515,301,false⟩, +⟨0,906,435,false⟩, +⟨1,515,906,true⟩, +⟨0,559,323,false⟩, +⟨0,331,319,false⟩, +⟨1,559,331,true⟩, +⟨1,559,515,true⟩, +⟨0,749,301,true⟩, +⟨0,892,423,true⟩, +⟨1,749,892,true⟩, +⟨0,539,311,true⟩, +⟨0,348,305,true⟩, +⟨1,539,348,true⟩, +⟨1,539,749,true⟩, +⟨0,751,302,false⟩, +⟨0,765,314,false⟩, +⟨1,751,765,true⟩, +⟨0,731,453,false⟩, +⟨0,390,451,false⟩, +⟨1,731,390,true⟩, +⟨1,731,751,true⟩, +⟨0,753,303,true⟩, +⟨0,767,315,true⟩, +⟨1,753,767,true⟩, +⟨0,735,457,true⟩, +⟨0,395,455,true⟩, +⟨1,735,395,true⟩, +⟨1,735,753,true⟩, +⟨0,346,304,false⟩, +⟨0,416,352,false⟩, +⟨1,346,416,true⟩, +⟨0,482,412,false⟩, +⟨0,489,414,false⟩, +⟨0,674,410,false⟩, +⟨1,482,489,true⟩, +⟨1,482,674,true⟩, +⟨0,482,468,false⟩, +⟨1,482,346,true⟩, +⟨0,754,304,true⟩, +⟨0,304,328,true⟩, +⟨1,754,304,true⟩, +⟨0,373,390,false⟩, +⟨0,376,388,false⟩, +⟨0,642,386,false⟩, +⟨1,373,376,true⟩, +⟨1,373,642,true⟩, +⟨0,373,466,true⟩, +⟨1,373,754,true⟩, +⟨0,350,305,false⟩, +⟨0,430,353,false⟩, +⟨1,350,430,true⟩, +⟨0,682,418,false⟩, +⟨1,682,489,true⟩, +⟨1,682,677,true⟩, +⟨0,682,468,false⟩, +⟨1,682,350,true⟩, +⟨0,755,305,true⟩, +⟨0,318,329,true⟩, +⟨1,755,318,true⟩, +⟨0,654,394,false⟩, +⟨1,654,376,true⟩, +⟨1,654,645,true⟩, +⟨0,654,466,true⟩, +⟨1,654,755,true⟩, +⟨0,337,306,false⟩, +⟨0,506,364,false⟩, +⟨1,337,506,true⟩, +⟨0,434,400,true⟩, +⟨0,441,402,true⟩, +⟨0,658,398,true⟩, +⟨1,434,441,true⟩, +⟨1,434,658,true⟩, +⟨0,434,467,false⟩, +⟨1,434,337,true⟩, +⟨0,756,306,true⟩, +⟨0,352,340,true⟩, +⟨1,756,352,true⟩, +⟨0,290,376,true⟩, +⟨0,297,378,true⟩, +⟨0,626,374,true⟩, +⟨1,290,297,true⟩, +⟨1,290,626,true⟩, +⟨0,290,465,true⟩, +⟨1,290,756,true⟩, +⟨0,339,307,false⟩, +⟨0,510,365,false⟩, +⟨1,339,510,true⟩, +⟨0,666,408,true⟩, +⟨1,666,441,true⟩, +⟨1,666,661,true⟩, +⟨0,666,467,false⟩, +⟨1,666,339,true⟩, +⟨0,757,307,true⟩, +⟨0,356,341,true⟩, +⟨1,757,356,true⟩, +⟨0,634,382,true⟩, +⟨1,634,297,true⟩, +⟨1,634,629,true⟩, +⟨0,634,465,true⟩, +⟨1,634,757,true⟩, +⟨0,540,308,false⟩, +⟨0,442,400,false⟩, +⟨1,540,442,true⟩, +⟨0,613,368,false⟩, +⟨1,614,612,true⟩, +⟨1,614,613,true⟩, +⟨0,614,464,false⟩, +⟨1,614,540,true⟩, +⟨0,758,308,true⟩, +⟨0,288,376,true⟩, +⟨1,758,288,true⟩, +⟨0,581,348,false⟩, +⟨1,582,580,true⟩, +⟨1,582,581,true⟩, +⟨0,582,462,true⟩, +⟨1,582,758,true⟩, +⟨0,541,309,false⟩, +⟨0,436,401,false⟩, +⟨1,541,436,true⟩, +⟨0,501,366,false⟩, +⟨0,504,364,false⟩, +⟨0,610,362,false⟩, +⟨1,501,504,true⟩, +⟨1,501,610,true⟩, +⟨0,501,464,false⟩, +⟨1,501,541,true⟩, +⟨0,759,309,true⟩, +⟨0,292,377,true⟩, +⟨1,759,292,true⟩, +⟨0,354,340,false⟩, +⟨0,361,342,false⟩, +⟨0,578,338,false⟩] +def chunk56 : List Event := [⟨1,354,361,true⟩, +⟨1,354,578,true⟩, +⟨0,354,462,true⟩, +⟨1,354,759,true⟩, +⟨0,536,310,false⟩, +⟨0,490,412,false⟩, +⟨1,536,490,true⟩, +⟨0,421,354,true⟩, +⟨0,424,352,true⟩, +⟨0,594,350,true⟩, +⟨1,421,424,true⟩, +⟨1,421,594,true⟩, +⟨0,421,463,false⟩, +⟨1,421,536,true⟩, +⟨0,760,310,true⟩, +⟨0,368,388,true⟩, +⟨1,760,368,true⟩, +⟨0,309,330,true⟩, +⟨0,312,328,true⟩, +⟨0,562,326,true⟩, +⟨1,309,312,true⟩, +⟨1,309,562,true⟩, +⟨0,309,461,true⟩, +⟨1,309,760,true⟩, +⟨0,537,311,false⟩, +⟨0,484,413,false⟩, +⟨1,537,484,true⟩, +⟨0,606,358,true⟩, +⟨1,606,424,true⟩, +⟨1,606,597,true⟩, +⟨0,606,463,false⟩, +⟨1,606,537,true⟩, +⟨0,761,311,true⟩, +⟨0,382,389,true⟩, +⟨1,761,382,true⟩, +⟨0,574,332,true⟩, +⟨1,574,312,true⟩, +⟨1,574,565,true⟩, +⟨0,574,461,true⟩, +⟨1,574,761,true⟩, +⟨0,529,312,false⟩, +⟨0,918,446,false⟩, +⟨1,529,918,true⟩, +⟨0,762,312,true⟩, +⟨0,689,424,true⟩, +⟨1,762,689,true⟩, +⟨0,527,297,true⟩, +⟨0,411,458,true⟩, +⟨1,527,411,true⟩, +⟨1,527,762,true⟩, +⟨0,531,313,false⟩, +⟨0,920,447,false⟩, +⟨1,531,920,true⟩, +⟨0,763,313,true⟩, +⟨0,691,425,true⟩, +⟨1,763,691,true⟩, +⟨0,517,300,false⟩, +⟨1,518,516,true⟩, +⟨1,518,517,true⟩, +⟨0,518,458,true⟩, +⟨1,518,763,true⟩, +⟨0,320,316,false⟩, +⟨0,497,366,false⟩, +⟨1,320,497,true⟩, +⟨0,686,420,false⟩, +⟨1,686,489,true⟩, +⟨1,686,674,true⟩, +⟨1,686,677,true⟩, +⟨0,686,468,false⟩, +⟨1,686,320,true⟩, +⟨0,768,316,true⟩, +⟨0,317,330,true⟩, +⟨1,768,317,true⟩, +⟨0,638,380,true⟩, +⟨1,638,297,true⟩, +⟨1,638,626,true⟩, +⟨1,638,629,true⟩, +⟨0,638,465,true⟩, +⟨1,638,768,true⟩, +⟨0,334,317,false⟩, +⟨0,499,367,false⟩, +⟨1,334,499,true⟩, +⟨0,492,468,false⟩, +⟨1,492,334,true⟩, +⟨0,769,317,true⟩, +⟨0,307,331,true⟩, +⟨1,769,307,true⟩, +⟨0,294,465,true⟩, +⟨1,294,769,true⟩, +⟨0,333,318,false⟩, +⟨0,429,354,false⟩, +⟨1,333,429,true⟩, +⟨0,670,406,true⟩, +⟨1,670,441,true⟩, +⟨1,670,658,true⟩, +⟨1,670,661,true⟩, +⟨0,670,467,false⟩, +⟨1,670,333,true⟩, +⟨0,770,318,true⟩, +⟨0,365,342,true⟩, +⟨1,770,365,true⟩, +⟨0,650,392,false⟩, +⟨1,650,376,true⟩, +⟨1,650,642,true⟩, +⟨1,650,645,true⟩, +⟨0,650,466,true⟩, +⟨1,650,770,true⟩, +⟨0,323,319,false⟩, +⟨0,419,355,false⟩, +⟨1,323,419,true⟩, +⟨0,444,467,false⟩, +⟨1,444,323,true⟩, +⟨0,771,319,true⟩, +⟨0,367,343,true⟩, +⟨1,771,367,true⟩, +⟨0,374,466,true⟩, +⟨1,374,771,true⟩, +⟨0,552,320,false⟩, +⟨0,481,414,false⟩, +⟨1,552,481,true⟩, +⟨0,622,372,false⟩, +⟨1,622,504,true⟩, +⟨1,622,613,true⟩, +⟨0,622,464,false⟩, +⟨1,622,552,true⟩, +⟨0,772,320,true⟩, +⟨0,301,378,true⟩, +⟨1,772,301,true⟩, +⟨0,570,334,true⟩, +⟨1,570,312,true⟩, +⟨1,570,562,true⟩, +⟨1,570,565,true⟩, +⟨0,570,461,true⟩, +⟨1,570,772,true⟩, +⟨0,553,321,false⟩, +⟨0,495,415,false⟩, +⟨1,553,495,true⟩, +⟨0,618,370,false⟩, +⟨1,618,504,true⟩, +⟨1,618,610,true⟩, +⟨1,618,613,true⟩, +⟨0,618,464,false⟩, +⟨1,618,553,true⟩, +⟨0,773,321,true⟩, +⟨0,303,379,true⟩, +⟨1,773,303,true⟩, +⟨0,310,461,true⟩, +⟨1,310,773,true⟩, +⟨0,556,322,false⟩, +⟨0,433,402,false⟩, +⟨1,556,433,true⟩, +⟨0,602,360,true⟩, +⟨1,602,424,true⟩, +⟨1,602,594,true⟩, +⟨1,602,597,true⟩, +⟨0,602,463,false⟩, +⟨1,602,556,true⟩, +⟨0,774,322,true⟩, +⟨0,381,390,true⟩, +⟨1,774,381,true⟩, +⟨0,586,344,false⟩, +⟨1,586,361,true⟩, +⟨1,586,581,true⟩, +⟨0,586,462,true⟩, +⟨1,586,774,true⟩, +⟨0,557,323,false⟩, +⟨0,447,403,false⟩, +⟨1,557,447,true⟩, +⟨0,422,463,false⟩, +⟨1,422,557,true⟩, +⟨0,775,323,true⟩, +⟨0,371,391,true⟩, +⟨1,775,371,true⟩, +⟨0,590,346,false⟩, +⟨1,590,361,true⟩, +⟨1,590,578,true⟩, +⟨1,590,581,true⟩, +⟨0,590,462,true⟩, +⟨1,590,775,true⟩, +⟨0,545,324,false⟩, +⟨0,721,448,false⟩, +⟨1,545,721,true⟩, +⟨0,776,324,true⟩, +⟨0,705,436,true⟩, +⟨1,776,705,true⟩, +⟨0,547,325,false⟩, +⟨0,723,449,false⟩, +⟨1,547,723,true⟩, +⟨0,777,325,true⟩, +⟨0,707,437,true⟩, +⟨1,777,707,true⟩, +⟨0,779,326,false⟩, +⟨0,793,338,false⟩, +⟨1,779,793,true⟩, +⟨0,725,448,true⟩, +⟨1,726,724,true⟩, +⟨1,726,725,true⟩, +⟨0,726,471,false⟩, +⟨1,726,779,true⟩, +⟨0,781,327,true⟩] +def chunk57 : List Event := [⟨0,795,339,true⟩, +⟨1,781,795,true⟩, +⟨0,386,450,true⟩, +⟨0,393,454,true⟩, +⟨0,722,446,true⟩, +⟨1,386,393,true⟩, +⟨1,386,722,true⟩, +⟨0,386,471,true⟩, +⟨1,386,781,true⟩, +⟨0,782,328,false⟩, +⟨0,810,352,false⟩, +⟨1,782,810,true⟩, +⟨0,709,436,false⟩, +⟨0,714,442,false⟩, +⟨1,709,457,true⟩, +⟨1,709,714,true⟩, +⟨0,709,470,false⟩, +⟨1,709,782,true⟩, +⟨0,783,329,true⟩, +⟨0,811,353,true⟩, +⟨1,783,811,true⟩, +⟨0,718,444,false⟩, +⟨1,718,706,true⟩, +⟨1,718,714,true⟩, +⟨0,718,470,true⟩, +⟨1,718,783,true⟩, +⟨0,784,330,false⟩, +⟨0,826,366,false⟩, +⟨1,784,826,true⟩, +⟨0,466,426,true⟩, +⟨0,473,428,true⟩, +⟨0,690,422,true⟩, +⟨1,466,473,true⟩, +⟨1,466,690,true⟩, +⟨0,466,469,false⟩, +⟨1,466,784,true⟩, +⟨0,785,331,true⟩, +⟨0,827,367,true⟩, +⟨1,785,827,true⟩, +⟨0,698,432,true⟩, +⟨1,698,473,true⟩, +⟨1,698,693,true⟩, +⟨0,698,469,true⟩, +⟨1,698,785,true⟩, +⟨0,572,332,false⟩, +⟨0,474,426,false⟩, +⟨1,572,474,true⟩, +⟨0,932,464,false⟩, +⟨1,932,572,true⟩, +⟨0,786,332,true⟩, +⟨0,636,380,true⟩, +⟨1,786,636,true⟩, +⟨0,549,324,false⟩, +⟨1,550,548,true⟩, +⟨1,550,549,true⟩, +⟨0,550,460,true⟩, +⟨1,550,786,true⟩, +⟨0,573,333,false⟩, +⟨0,468,427,false⟩, +⟨1,573,468,true⟩, +⟨0,933,464,false⟩, +⟨1,933,573,true⟩, +⟨0,787,333,true⟩, +⟨0,637,381,true⟩, +⟨1,787,637,true⟩, +⟨0,325,318,false⟩, +⟨0,328,316,false⟩, +⟨0,546,314,false⟩, +⟨1,325,328,true⟩, +⟨1,325,546,true⟩, +⟨0,325,460,true⟩, +⟨1,325,787,true⟩, +⟨0,568,334,false⟩, +⟨0,458,438,false⟩, +⟨1,568,458,true⟩, +⟨0,934,0,false⟩, +⟨1,934,568,true⟩, +⟨0,788,334,true⟩, +⟨0,648,392,true⟩, +⟨1,788,648,true⟩, +⟨0,543,309,true⟩, +⟨0,343,307,true⟩, +⟨1,543,343,true⟩, +⟨1,543,788,true⟩, +⟨0,569,335,false⟩, +⟨0,452,439,false⟩, +⟨1,569,452,true⟩, +⟨0,935,0,false⟩, +⟨1,935,569,true⟩, +⟨0,789,335,true⟩, +⟨0,649,393,true⟩, +⟨1,789,649,true⟩, +⟨0,341,306,true⟩, +⟨0,344,304,true⟩, +⟨0,530,302,true⟩, +⟨1,341,344,true⟩, +⟨1,341,530,true⟩, +⟨0,341,459,true⟩, +⟨1,341,789,true⟩, +⟨0,561,336,false⟩, +⟨0,384,450,false⟩, +⟨1,561,384,true⟩, +⟨0,790,336,true⟩, +⟨0,657,404,true⟩, +⟨1,790,657,true⟩, +⟨0,402,292,false⟩, +⟨0,409,294,false⟩, +⟨0,514,290,false⟩, +⟨1,402,409,true⟩, +⟨1,402,514,true⟩, +⟨0,402,458,true⟩, +⟨1,402,790,true⟩, +⟨0,563,337,false⟩, +⟨0,388,451,false⟩, +⟨1,563,388,true⟩, +⟨0,791,337,true⟩, +⟨0,659,405,true⟩, +⟨1,791,659,true⟩, +⟨0,522,298,false⟩, +⟨1,522,409,true⟩, +⟨1,522,517,true⟩, +⟨0,522,458,true⟩, +⟨1,522,791,true⟩, +⟨0,796,340,false⟩, +⟨0,824,364,false⟩, +⟨1,796,824,true⟩, +⟨0,710,470,false⟩, +⟨1,710,796,true⟩, +⟨0,797,341,true⟩, +⟨0,825,365,true⟩, +⟨1,797,825,true⟩, +⟨0,936,470,true⟩, +⟨1,936,797,true⟩, +⟨0,798,342,false⟩, +⟨0,812,354,false⟩, +⟨1,798,812,true⟩, +⟨0,702,430,true⟩, +⟨1,702,473,true⟩, +⟨1,702,690,true⟩, +⟨1,702,693,true⟩, +⟨0,702,469,false⟩, +⟨1,702,798,true⟩, +⟨0,799,343,true⟩, +⟨0,813,355,true⟩, +⟨1,799,813,true⟩, +⟨0,476,469,true⟩, +⟨1,476,799,true⟩, +⟨0,584,344,false⟩, +⟨0,449,440,false⟩, +⟨1,584,449,true⟩, +⟨0,937,464,false⟩, +⟨1,937,584,true⟩, +⟨0,800,344,true⟩, +⟨0,632,382,true⟩, +⟨1,800,632,true⟩, +⟨0,542,308,true⟩, +⟨1,542,344,true⟩, +⟨1,542,533,true⟩, +⟨0,542,459,true⟩, +⟨1,542,800,true⟩, +⟨0,585,345,false⟩, +⟨0,463,441,false⟩, +⟨1,585,463,true⟩, +⟨0,938,464,false⟩, +⟨1,938,585,true⟩, +⟨0,801,345,true⟩, +⟨0,633,383,true⟩, +⟨1,801,633,true⟩, +⟨0,538,310,true⟩, +⟨1,538,344,true⟩, +⟨1,538,530,true⟩, +⟨1,538,533,true⟩, +⟨0,538,459,true⟩, +⟨1,538,801,true⟩, +⟨0,588,346,false⟩, +⟨0,465,428,false⟩, +⟨1,588,465,true⟩, +⟨0,939,0,false⟩, +⟨1,939,588,true⟩, +⟨0,802,346,true⟩, +⟨0,652,394,true⟩, +⟨1,802,652,true⟩, +⟨0,558,322,false⟩, +⟨1,558,328,true⟩, +⟨1,558,549,true⟩, +⟨0,558,460,true⟩, +⟨1,558,802,true⟩, +⟨0,589,347,false⟩, +⟨0,479,429,false⟩, +⟨1,589,479,true⟩, +⟨0,940,0,false⟩, +⟨1,940,589,true⟩, +⟨0,803,347,true⟩, +⟨0,653,395,true⟩, +⟨1,803,653,true⟩, +⟨0,554,320,false⟩, +⟨1,554,328,true⟩, +⟨1,554,546,true⟩, +⟨1,554,549,true⟩, +⟨0,554,460,true⟩] +def chunk58 : List Event := [⟨1,554,803,true⟩, +⟨0,577,348,false⟩, +⟨0,728,452,false⟩, +⟨1,577,728,true⟩, +⟨0,804,348,true⟩, +⟨0,673,416,true⟩, +⟨1,804,673,true⟩, +⟨0,526,296,false⟩, +⟨1,526,409,true⟩, +⟨1,526,514,true⟩, +⟨1,526,517,true⟩, +⟨0,526,458,true⟩, +⟨1,526,804,true⟩, +⟨0,579,349,false⟩, +⟨0,729,453,false⟩, +⟨1,579,729,true⟩, +⟨0,805,349,true⟩, +⟨0,675,417,true⟩, +⟨1,805,675,true⟩, +⟨0,406,458,true⟩, +⟨1,406,805,true⟩, +⟨0,807,350,false⟩, +⟨0,821,362,false⟩, +⟨1,807,821,true⟩, +⟨0,730,452,true⟩, +⟨1,730,393,true⟩, +⟨1,730,725,true⟩, +⟨0,730,471,false⟩, +⟨1,730,807,true⟩, +⟨0,809,351,true⟩, +⟨0,823,363,true⟩, +⟨1,809,823,true⟩, +⟨0,734,456,true⟩, +⟨1,734,393,true⟩, +⟨1,734,722,true⟩, +⟨1,734,725,true⟩, +⟨0,734,471,true⟩, +⟨1,734,809,true⟩, +⟨0,593,356,false⟩, +⟨0,397,454,false⟩, +⟨1,593,397,true⟩, +⟨0,814,356,true⟩, +⟨0,625,384,true⟩, +⟨1,814,625,true⟩, +⟨0,252,458,true⟩, +⟨1,252,814,true⟩, +⟨0,595,357,false⟩, +⟨0,399,455,false⟩, +⟨1,595,399,true⟩, +⟨0,815,357,true⟩, +⟨0,627,385,true⟩, +⟨1,815,627,true⟩, +⟨0,941,458,true⟩, +⟨1,941,815,true⟩, +⟨0,604,358,false⟩, +⟨0,700,430,false⟩, +⟨1,604,700,true⟩, +⟨0,942,462,false⟩, +⟨1,942,604,true⟩, +⟨0,816,358,true⟩, +⟨0,668,406,true⟩, +⟨1,816,668,true⟩, +⟨0,943,460,true⟩, +⟨1,943,816,true⟩, +⟨0,605,359,false⟩, +⟨0,701,431,false⟩, +⟨1,605,701,true⟩, +⟨0,944,462,false⟩, +⟨1,944,605,true⟩, +⟨0,817,359,true⟩, +⟨0,669,407,true⟩, +⟨1,817,669,true⟩, +⟨0,945,460,true⟩, +⟨1,945,817,true⟩, +⟨0,600,360,false⟩, +⟨0,712,442,false⟩, +⟨1,600,712,true⟩, +⟨0,946,0,false⟩, +⟨1,946,600,true⟩, +⟨0,818,360,true⟩, +⟨0,680,418,true⟩, +⟨1,818,680,true⟩, +⟨0,532,459,true⟩, +⟨1,532,818,true⟩, +⟨0,601,361,false⟩, +⟨0,713,443,false⟩, +⟨1,601,713,true⟩, +⟨0,947,0,false⟩, +⟨1,947,601,true⟩, +⟨0,819,361,true⟩, +⟨0,681,419,true⟩, +⟨1,819,681,true⟩, +⟨0,948,0,true⟩, +⟨1,948,819,true⟩, +⟨0,609,368,false⟩, +⟨0,732,456,false⟩, +⟨1,609,732,true⟩, +⟨0,828,368,true⟩, +⟨0,641,396,true⟩, +⟨1,828,641,true⟩, +⟨0,949,458,true⟩, +⟨1,949,828,true⟩, +⟨0,611,369,false⟩, +⟨0,733,457,false⟩, +⟨1,611,733,true⟩, +⟨0,829,369,true⟩, +⟨0,643,397,true⟩, +⟨1,829,643,true⟩, +⟨0,950,0,true⟩, +⟨1,950,829,true⟩, +⟨0,616,370,false⟩, +⟨0,716,444,false⟩, +⟨1,616,716,true⟩, +⟨0,951,462,false⟩, +⟨1,951,616,true⟩, +⟨0,830,370,true⟩, +⟨0,664,408,true⟩, +⟨1,830,664,true⟩, +⟨0,952,0,true⟩, +⟨1,952,830,true⟩, +⟨0,617,371,false⟩, +⟨0,717,445,false⟩, +⟨1,617,717,true⟩, +⟨0,953,462,false⟩, +⟨1,953,617,true⟩, +⟨0,831,371,true⟩, +⟨0,665,409,true⟩, +⟨1,831,665,true⟩, +⟨0,954,0,true⟩, +⟨1,954,831,true⟩, +⟨0,620,372,false⟩, +⟨0,696,432,false⟩, +⟨1,620,696,true⟩, +⟨0,955,0,false⟩, +⟨1,955,620,true⟩, +⟨0,832,372,true⟩, +⟨0,684,420,true⟩, +⟨1,832,684,true⟩, +⟨0,956,460,true⟩, +⟨1,956,832,true⟩, +⟨0,621,373,false⟩, +⟨0,697,433,false⟩, +⟨1,621,697,true⟩, +⟨0,957,0,false⟩, +⟨1,957,621,true⟩, +⟨0,833,373,true⟩, +⟨0,685,421,true⟩, +⟨1,833,685,true⟩, +⟨0,958,460,true⟩, +⟨1,958,833,true⟩, +⟨0,835,374,false⟩, +⟨0,849,386,false⟩, +⟨1,835,849,true⟩, +⟨0,959,471,false⟩, +⟨1,959,835,true⟩, +⟨0,837,375,true⟩, +⟨0,851,387,true⟩, +⟨1,837,851,true⟩, +⟨0,960,471,true⟩, +⟨1,960,837,true⟩, +⟨0,838,376,false⟩, +⟨0,866,400,false⟩, +⟨1,838,866,true⟩, +⟨0,961,470,false⟩, +⟨1,961,838,true⟩, +⟨0,839,377,true⟩, +⟨0,867,401,true⟩, +⟨1,839,867,true⟩, +⟨0,962,0,true⟩, +⟨1,962,839,true⟩, +⟨0,840,378,false⟩, +⟨0,882,414,false⟩, +⟨1,840,882,true⟩, +⟨0,963,0,false⟩, +⟨1,963,840,true⟩, +⟨0,841,379,true⟩, +⟨0,883,415,true⟩, +⟨1,841,883,true⟩, +⟨0,964,0,true⟩, +⟨1,964,841,true⟩, +⟨0,842,380,false⟩, +⟨0,896,426,false⟩, +⟨1,842,896,true⟩, +⟨0,965,0,false⟩, +⟨1,965,842,true⟩, +⟨0,843,381,true⟩, +⟨0,897,427,true⟩, +⟨1,843,897,true⟩, +⟨0,966,0,true⟩, +⟨1,966,843,true⟩, +⟨0,844,382,false⟩, +⟨0,912,440,false⟩, +⟨1,844,912,true⟩, +⟨0,967,0,false⟩, +⟨1,967,844,true⟩, +⟨0,845,383,true⟩, +⟨0,913,441,true⟩, +⟨1,845,913,true⟩, +⟨0,968,0,true⟩, +⟨1,968,845,true⟩] +def chunk59 : List Event := [⟨0,846,384,false⟩, +⟨0,928,454,false⟩, +⟨1,846,928,true⟩, +⟨0,847,385,true⟩, +⟨0,929,455,true⟩, +⟨1,847,929,true⟩, +⟨0,852,388,false⟩, +⟨0,880,412,false⟩, +⟨1,852,880,true⟩, +⟨0,969,0,false⟩, +⟨1,969,852,true⟩, +⟨0,853,389,true⟩, +⟨0,881,413,true⟩, +⟨1,853,881,true⟩, +⟨0,970,0,true⟩, +⟨1,970,853,true⟩, +⟨0,854,390,false⟩, +⟨0,868,402,false⟩, +⟨1,854,868,true⟩, +⟨0,971,0,false⟩, +⟨1,971,854,true⟩, +⟨0,855,391,true⟩, +⟨0,869,403,true⟩, +⟨1,855,869,true⟩, +⟨0,972,0,true⟩, +⟨1,972,855,true⟩, +⟨0,856,392,false⟩, +⟨0,910,438,false⟩, +⟨1,856,910,true⟩, +⟨0,973,0,false⟩, +⟨1,973,856,true⟩, +⟨0,857,393,true⟩, +⟨0,911,439,true⟩, +⟨1,857,911,true⟩, +⟨0,974,0,true⟩, +⟨1,974,857,true⟩, +⟨0,858,394,false⟩, +⟨0,898,428,false⟩, +⟨1,858,898,true⟩, +⟨0,975,0,false⟩, +⟨1,975,858,true⟩, +⟨0,859,395,true⟩, +⟨0,899,429,true⟩, +⟨1,859,899,true⟩, +⟨0,976,0,true⟩, +⟨1,976,859,true⟩, +⟨0,860,396,false⟩, +⟨0,930,456,false⟩, +⟨1,860,930,true⟩, +⟨0,861,397,true⟩, +⟨0,931,457,true⟩, +⟨1,861,931,true⟩, +⟨0,863,398,false⟩, +⟨0,877,410,false⟩, +⟨1,863,877,true⟩, +⟨0,977,471,false⟩, +⟨1,977,863,true⟩, +⟨0,865,399,true⟩, +⟨0,879,411,true⟩, +⟨1,865,879,true⟩, +⟨0,978,471,true⟩, +⟨1,978,865,true⟩, +⟨0,870,404,false⟩, +⟨0,924,450,false⟩, +⟨1,870,924,true⟩, +⟨0,871,405,true⟩, +⟨0,925,451,true⟩, +⟨1,871,925,true⟩, +⟨0,872,406,false⟩, +⟨0,900,430,false⟩, +⟨1,872,900,true⟩, +⟨0,979,0,false⟩, +⟨1,979,872,true⟩, +⟨0,873,407,true⟩, +⟨0,901,431,true⟩, +⟨1,873,901,true⟩, +⟨0,980,0,true⟩, +⟨1,980,873,true⟩, +⟨0,874,408,false⟩, +⟨0,916,444,false⟩, +⟨1,874,916,true⟩, +⟨0,981,0,false⟩, +⟨1,981,874,true⟩, +⟨0,875,409,true⟩, +⟨0,917,445,true⟩, +⟨1,875,917,true⟩, +⟨0,982,0,true⟩, +⟨1,982,875,true⟩, +⟨0,884,416,false⟩, +⟨0,926,452,false⟩, +⟨1,884,926,true⟩, +⟨0,885,417,true⟩, +⟨0,927,453,true⟩, +⟨1,885,927,true⟩, +⟨0,886,418,false⟩, +⟨0,914,442,false⟩, +⟨1,886,914,true⟩, +⟨0,983,0,false⟩, +⟨1,983,886,true⟩, +⟨0,887,419,true⟩, +⟨0,915,443,true⟩, +⟨1,887,915,true⟩, +⟨0,984,0,true⟩, +⟨1,984,887,true⟩, +⟨0,888,420,false⟩, +⟨0,902,432,false⟩, +⟨1,888,902,true⟩, +⟨0,985,0,false⟩, +⟨1,985,888,true⟩, +⟨0,889,421,true⟩, +⟨0,903,433,true⟩, +⟨1,889,903,true⟩, +⟨0,986,0,true⟩, +⟨1,986,889,true⟩, +⟨0,891,422,false⟩, +⟨0,905,434,false⟩, +⟨1,891,905,true⟩, +⟨0,893,423,true⟩, +⟨0,907,435,true⟩, +⟨1,893,907,true⟩, +⟨0,894,424,false⟩, +⟨0,919,446,false⟩, +⟨1,894,919,true⟩, +⟨0,895,425,true⟩, +⟨0,921,447,true⟩, +⟨1,895,921,true⟩, +⟨0,908,436,false⟩, +⟨0,922,448,false⟩, +⟨1,908,922,true⟩, +⟨0,909,437,true⟩, +⟨0,923,449,true⟩, +⟨1,909,923,true⟩, +⟨0,753,497,false⟩, +⟨0,69,71,false⟩, +⟨1,753,69,true⟩, +⟨0,70,125,false⟩, +⟨1,753,70,true⟩, +⟨0,837,599,true⟩, +⟨0,809,573,true⟩, +⟨1,837,809,true⟩, +⟨0,407,133,true⟩, +⟨1,407,837,true⟩, +⟨0,865,621,false⟩, +⟨0,781,539,false⟩, +⟨1,865,781,true⟩, +⟨0,863,620,true⟩, +⟨0,779,538,true⟩, +⟨1,863,779,true⟩, +⟨0,835,598,false⟩, +⟨0,807,572,false⟩, +⟨1,835,807,true⟩, +⟨0,401,130,false⟩, +⟨1,401,835,true⟩, +⟨0,751,496,true⟩, +⟨0,64,66,true⟩, +⟨1,751,64,true⟩, +⟨0,67,122,true⟩, +⟨1,751,67,true⟩, +⟨0,412,129,false⟩, +⟨1,412,865,true⟩, +⟨0,410,126,true⟩, +⟨1,410,863,true⟩, +⟨0,735,497,false⟩, +⟨0,68,70,false⟩, +⟨1,735,68,true⟩, +⟨0,71,124,false⟩, +⟨1,735,71,true⟩, +⟨0,960,599,true⟩, +⟨0,730,572,true⟩, +⟨1,960,730,true⟩, +⟨0,405,131,true⟩, +⟨1,405,960,true⟩, +⟨0,977,620,false⟩, +⟨0,386,539,false⟩, +⟨1,977,386,true⟩, +⟨0,978,621,true⟩, +⟨0,726,538,true⟩, +⟨1,978,726,true⟩, +⟨0,959,598,false⟩, +⟨0,734,573,false⟩, +⟨1,959,734,true⟩, +⟨0,403,132,false⟩, +⟨1,403,959,true⟩, +⟨0,731,496,true⟩, +⟨0,65,67,true⟩, +⟨1,731,65,true⟩, +⟨0,66,123,true⟩, +⟨1,731,66,true⟩, +⟨0,414,128,false⟩, +⟨1,414,977,true⟩, +⟨0,408,127,true⟩, +⟨1,408,978,true⟩, +⟨0,738,474,false⟩, +⟨0,37,39,false⟩, +⟨1,738,37,true⟩, +⟨0,38,137,false⟩, +⟨1,738,38,true⟩, +⟨0,839,601,true⟩, +⟨0,797,557,true⟩, +⟨1,839,797,true⟩] +def chunk60 : List Event := [⟨0,853,611,false⟩, +⟨0,783,541,false⟩, +⟨1,853,783,true⟩, +⟨0,342,141,false⟩, +⟨1,342,853,true⟩, +⟨0,852,610,true⟩, +⟨0,782,540,true⟩, +⟨1,852,782,true⟩, +⟨0,336,138,true⟩, +⟨1,336,852,true⟩, +⟨0,838,600,false⟩, +⟨0,796,556,false⟩, +⟨1,838,796,true⟩, +⟨0,736,472,true⟩, +⟨0,32,34,true⟩, +⟨1,736,32,true⟩, +⟨0,35,134,true⟩, +⟨1,736,35,true⟩, +⟨0,349,142,false⟩, +⟨1,349,838,true⟩, +⟨0,347,145,true⟩, +⟨1,347,839,true⟩, +⟨0,450,474,false⟩, +⟨0,36,38,false⟩, +⟨1,450,36,true⟩, +⟨0,39,136,false⟩, +⟨1,450,39,true⟩, +⟨0,962,601,true⟩, +⟨0,710,556,true⟩, +⟨1,962,710,true⟩, +⟨0,969,610,false⟩, +⟨0,718,541,false⟩, +⟨1,969,718,true⟩, +⟨0,340,140,false⟩, +⟨1,340,969,true⟩, +⟨0,970,611,true⟩, +⟨0,709,540,true⟩, +⟨1,970,709,true⟩, +⟨0,338,139,true⟩, +⟨1,338,970,true⟩, +⟨0,961,600,false⟩, +⟨0,936,557,false⟩, +⟨1,961,936,true⟩, +⟨0,719,472,true⟩, +⟨0,33,35,true⟩, +⟨1,719,33,true⟩, +⟨0,34,135,true⟩, +⟨1,719,34,true⟩, +⟨0,351,144,false⟩, +⟨1,351,961,true⟩, +⟨0,345,143,true⟩, +⟨1,345,962,true⟩, +⟨0,739,475,false⟩, +⟨0,29,31,false⟩, +⟨1,739,29,true⟩, +⟨0,30,149,false⟩, +⟨1,739,30,true⟩, +⟨0,855,613,true⟩, +⟨0,799,559,true⟩, +⟨1,855,799,true⟩, +⟨0,327,157,true⟩, +⟨1,327,855,true⟩, +⟨0,841,603,false⟩, +⟨0,785,543,false⟩, +⟨1,841,785,true⟩, +⟨0,840,602,true⟩, +⟨0,784,542,true⟩, +⟨1,840,784,true⟩, +⟨0,854,612,false⟩, +⟨0,798,558,false⟩, +⟨1,854,798,true⟩, +⟨0,321,154,false⟩, +⟨1,321,854,true⟩, +⟨0,737,473,true⟩, +⟨0,24,26,true⟩, +⟨1,737,24,true⟩, +⟨0,27,146,true⟩, +⟨1,737,27,true⟩, +⟨0,332,153,false⟩, +⟨1,332,841,true⟩, +⟨0,330,150,true⟩, +⟨1,330,840,true⟩, +⟨0,694,475,false⟩, +⟨0,28,30,false⟩, +⟨1,694,28,true⟩, +⟨0,31,148,false⟩, +⟨1,694,31,true⟩, +⟨0,972,613,true⟩, +⟨0,702,558,true⟩, +⟨1,972,702,true⟩, +⟨0,963,602,false⟩, +⟨0,698,543,false⟩, +⟨1,963,698,true⟩, +⟨0,324,152,false⟩, +⟨1,324,963,true⟩, +⟨0,964,603,true⟩, +⟨0,466,542,true⟩, +⟨1,964,466,true⟩, +⟨0,322,151,true⟩, +⟨1,322,964,true⟩, +⟨0,971,612,false⟩, +⟨0,476,559,false⟩, +⟨1,971,476,true⟩, +⟨0,703,473,true⟩, +⟨0,25,27,true⟩, +⟨1,703,25,true⟩, +⟨0,26,147,true⟩, +⟨1,703,26,true⟩, +⟨0,335,156,false⟩, +⟨1,335,971,true⟩, +⟨0,329,155,true⟩, +⟨1,329,972,true⟩, +⟨0,404,478,false⟩, +⟨0,21,23,false⟩, +⟨1,404,21,true⟩, +⟨0,22,161,false⟩, +⟨1,404,22,true⟩, +⟨0,843,605,true⟩, +⟨0,334,520,true⟩, +⟨1,843,334,true⟩, +⟨0,311,169,true⟩, +⟨1,311,843,true⟩, +⟨0,857,615,false⟩, +⟨0,350,500,false⟩, +⟨1,857,350,true⟩, +⟨0,856,614,true⟩, +⟨0,346,498,true⟩, +⟨1,856,346,true⟩, +⟨0,842,604,false⟩, +⟨0,320,518,false⟩, +⟨1,842,320,true⟩, +⟨0,305,166,false⟩, +⟨1,305,842,true⟩, +⟨0,400,476,true⟩, +⟨0,16,18,true⟩, +⟨1,400,16,true⟩, +⟨0,19,158,true⟩, +⟨1,400,19,true⟩, +⟨0,316,165,false⟩, +⟨1,316,857,true⟩, +⟨0,314,162,true⟩, +⟨1,314,856,true⟩, +⟨0,678,478,false⟩, +⟨0,20,22,false⟩, +⟨1,678,20,true⟩, +⟨0,23,160,false⟩, +⟨1,678,23,true⟩, +⟨0,966,605,true⟩, +⟨0,686,518,true⟩, +⟨1,966,686,true⟩, +⟨0,973,614,false⟩, +⟨0,682,500,false⟩, +⟨1,973,682,true⟩, +⟨0,308,164,false⟩, +⟨1,308,973,true⟩, +⟨0,974,615,true⟩, +⟨0,482,498,true⟩, +⟨1,974,482,true⟩, +⟨0,306,163,true⟩, +⟨1,306,974,true⟩, +⟨0,965,604,false⟩, +⟨0,492,520,false⟩, +⟨1,965,492,true⟩, +⟨0,687,476,true⟩, +⟨0,17,19,true⟩, +⟨1,687,17,true⟩, +⟨0,18,159,true⟩, +⟨1,687,18,true⟩, +⟨0,319,168,false⟩, +⟨1,319,965,true⟩, +⟨0,313,167,true⟩, +⟨1,313,966,true⟩, +⟨0,741,479,false⟩, +⟨0,45,47,false⟩, +⟨1,741,45,true⟩, +⟨0,46,173,false⟩, +⟨1,741,46,true⟩, +⟨0,859,617,true⟩, +⟨0,323,524,true⟩, +⟨1,859,323,true⟩, +⟨0,359,181,true⟩, +⟨1,359,859,true⟩, +⟨0,845,607,false⟩, +⟨0,339,504,false⟩, +⟨1,845,339,true⟩, +⟨0,844,606,true⟩, +⟨0,337,502,true⟩, +⟨1,844,337,true⟩, +⟨0,858,616,false⟩, +⟨0,333,522,false⟩, +⟨1,858,333,true⟩, +⟨0,353,178,false⟩, +⟨1,353,858,true⟩, +⟨0,740,477,true⟩, +⟨0,40,42,true⟩, +⟨1,740,40,true⟩, +⟨0,43,170,true⟩, +⟨1,740,43,true⟩, +⟨0,364,177,false⟩, +⟨1,364,845,true⟩] +def chunk61 : List Event := [⟨0,362,174,true⟩, +⟨1,362,844,true⟩, +⟨0,662,479,false⟩, +⟨0,44,46,false⟩, +⟨1,662,44,true⟩, +⟨0,47,172,false⟩, +⟨1,662,47,true⟩, +⟨0,976,617,true⟩, +⟨0,670,522,true⟩, +⟨1,976,670,true⟩, +⟨0,357,179,true⟩, +⟨1,357,976,true⟩, +⟨0,967,606,false⟩, +⟨0,666,504,false⟩, +⟨1,967,666,true⟩, +⟨0,968,607,true⟩, +⟨0,434,502,true⟩, +⟨1,968,434,true⟩, +⟨0,975,616,false⟩, +⟨0,444,524,false⟩, +⟨1,975,444,true⟩, +⟨0,355,180,false⟩, +⟨1,355,975,true⟩, +⟨0,671,477,true⟩, +⟨0,41,43,true⟩, +⟨1,671,41,true⟩, +⟨0,42,171,true⟩, +⟨1,671,42,true⟩, +⟨0,366,176,false⟩, +⟨1,366,967,true⟩, +⟨0,360,175,true⟩, +⟨1,360,968,true⟩, +⟨0,415,482,false⟩, +⟨0,77,79,false⟩, +⟨1,415,77,true⟩, +⟨0,78,185,false⟩, +⟨1,415,78,true⟩, +⟨0,873,625,true⟩, +⟨0,771,525,true⟩, +⟨1,873,771,true⟩, +⟨0,423,193,true⟩, +⟨1,423,873,true⟩, +⟨0,887,631,false⟩, +⟨0,755,501,false⟩, +⟨1,887,755,true⟩, +⟨0,886,630,true⟩, +⟨0,754,499,true⟩, +⟨1,886,754,true⟩, +⟨0,872,624,false⟩, +⟨0,770,523,false⟩, +⟨1,872,770,true⟩, +⟨0,417,190,false⟩, +⟨1,417,872,true⟩, +⟨0,413,480,true⟩, +⟨0,72,74,true⟩, +⟨1,413,72,true⟩, +⟨0,75,182,true⟩, +⟨1,413,75,true⟩, +⟨0,428,189,false⟩, +⟨1,428,887,true⟩, +⟨0,426,186,true⟩, +⟨1,426,886,true⟩, +⟨0,646,482,false⟩, +⟨0,76,78,false⟩, +⟨1,646,76,true⟩, +⟨0,79,184,false⟩, +⟨1,646,79,true⟩, +⟨0,980,625,true⟩, +⟨0,650,523,true⟩, +⟨1,980,650,true⟩, +⟨0,983,630,false⟩, +⟨0,654,501,false⟩, +⟨1,983,654,true⟩, +⟨0,420,188,false⟩, +⟨1,420,983,true⟩, +⟨0,984,631,true⟩, +⟨0,373,499,true⟩, +⟨1,984,373,true⟩, +⟨0,418,187,true⟩, +⟨1,418,984,true⟩, +⟨0,979,624,false⟩, +⟨0,374,525,false⟩, +⟨1,979,374,true⟩, +⟨0,655,480,true⟩, +⟨0,73,75,true⟩, +⟨1,655,73,true⟩, +⟨0,74,183,true⟩, +⟨1,655,74,true⟩, +⟨0,431,192,false⟩, +⟨1,431,979,true⟩, +⟨0,425,191,true⟩, +⟨1,425,980,true⟩, +⟨0,743,483,false⟩, +⟨0,117,119,false⟩, +⟨1,743,117,true⟩, +⟨0,118,197,false⟩, +⟨1,743,118,true⟩, +⟨0,889,633,true⟩, +⟨0,769,521,true⟩, +⟨1,889,769,true⟩, +⟨0,875,627,false⟩, +⟨0,757,505,false⟩, +⟨1,875,757,true⟩, +⟨0,502,201,false⟩, +⟨1,502,875,true⟩, +⟨0,874,626,true⟩, +⟨0,756,503,true⟩, +⟨1,874,756,true⟩, +⟨0,496,198,true⟩, +⟨1,496,874,true⟩, +⟨0,888,632,false⟩, +⟨0,768,519,false⟩, +⟨1,888,768,true⟩, +⟨0,742,481,true⟩, +⟨0,112,114,true⟩, +⟨1,742,112,true⟩, +⟨0,115,194,true⟩, +⟨1,742,115,true⟩, +⟨0,509,202,false⟩, +⟨1,509,888,true⟩, +⟨0,507,205,true⟩, +⟨1,507,889,true⟩, +⟨0,630,483,false⟩, +⟨0,116,118,false⟩, +⟨1,630,116,true⟩, +⟨0,119,196,false⟩, +⟨1,630,119,true⟩, +⟨0,986,633,true⟩, +⟨0,638,519,true⟩, +⟨1,986,638,true⟩, +⟨0,981,626,false⟩, +⟨0,634,505,false⟩, +⟨1,981,634,true⟩, +⟨0,500,200,false⟩, +⟨1,500,981,true⟩, +⟨0,982,627,true⟩, +⟨0,290,503,true⟩, +⟨1,982,290,true⟩, +⟨0,498,199,true⟩, +⟨1,498,982,true⟩, +⟨0,985,632,false⟩, +⟨0,294,521,false⟩, +⟨1,985,294,true⟩, +⟨0,639,481,true⟩, +⟨0,113,115,true⟩, +⟨1,639,113,true⟩, +⟨0,114,195,true⟩, +⟨1,639,114,true⟩, +⟨0,511,204,false⟩, +⟨1,511,985,true⟩, +⟨0,505,203,true⟩, +⟨1,505,986,true⟩, +⟨0,525,486,false⟩, +⟨0,13,15,false⟩, +⟨1,525,13,true⟩, +⟨0,14,209,false⟩, +⟨1,525,14,true⟩, +⟨0,573,546,true⟩, +⟨0,553,528,true⟩, +⟨1,573,553,true⟩, +⟨0,295,217,true⟩, +⟨1,295,573,true⟩, +⟨0,585,562,false⟩, +⟨0,541,508,false⟩, +⟨1,585,541,true⟩, +⟨0,584,560,true⟩, +⟨0,540,506,true⟩, +⟨1,584,540,true⟩, +⟨0,572,544,false⟩, +⟨0,552,526,false⟩, +⟨1,572,552,true⟩, +⟨0,289,214,false⟩, +⟨1,289,572,true⟩, +⟨0,524,484,true⟩, +⟨0,8,10,true⟩, +⟨1,524,8,true⟩, +⟨0,11,206,true⟩, +⟨1,524,11,true⟩, +⟨0,300,213,false⟩, +⟨1,300,585,true⟩, +⟨0,298,210,true⟩, +⟨1,298,584,true⟩, +⟨0,623,486,false⟩, +⟨0,12,14,false⟩, +⟨1,623,12,true⟩, +⟨0,15,208,false⟩, +⟨1,623,15,true⟩, +⟨0,933,546,true⟩, +⟨0,622,526,true⟩, +⟨1,933,622,true⟩, +⟨0,293,215,true⟩, +⟨1,293,933,true⟩, +⟨0,937,560,false⟩, +⟨0,501,508,false⟩, +⟨1,937,501,true⟩, +⟨0,938,562,true⟩, +⟨0,614,506,true⟩, +⟨1,938,614,true⟩, +⟨0,932,544,false⟩, +⟨0,618,528,false⟩] +def chunk62 : List Event := [⟨1,932,618,true⟩, +⟨0,291,216,false⟩, +⟨1,291,932,true⟩, +⟨0,619,484,true⟩, +⟨0,9,11,true⟩, +⟨1,619,9,true⟩, +⟨0,10,207,true⟩, +⟨1,619,10,true⟩, +⟨0,302,212,false⟩, +⟨1,302,937,true⟩, +⟨0,296,211,true⟩, +⟨1,296,938,true⟩, +⟨0,745,487,false⟩, +⟨0,53,55,false⟩, +⟨1,745,53,true⟩, +⟨0,54,221,false⟩, +⟨1,745,54,true⟩, +⟨0,589,566,true⟩, +⟨0,557,532,true⟩, +⟨1,589,557,true⟩, +⟨0,375,229,true⟩, +⟨1,375,589,true⟩, +⟨0,569,550,false⟩, +⟨0,537,512,false⟩, +⟨1,569,537,true⟩, +⟨0,568,548,true⟩, +⟨0,536,510,true⟩, +⟨1,568,536,true⟩, +⟨0,588,564,false⟩, +⟨0,556,530,false⟩, +⟨1,588,556,true⟩, +⟨0,369,226,false⟩, +⟨1,369,588,true⟩, +⟨0,744,485,true⟩, +⟨0,48,50,true⟩, +⟨1,744,48,true⟩, +⟨0,51,218,true⟩, +⟨1,744,51,true⟩, +⟨0,380,225,false⟩, +⟨1,380,569,true⟩, +⟨0,378,222,true⟩, +⟨1,378,568,true⟩, +⟨0,598,487,false⟩, +⟨0,52,54,false⟩, +⟨1,598,52,true⟩, +⟨0,55,220,false⟩, +⟨1,598,55,true⟩, +⟨0,940,566,true⟩, +⟨0,602,530,true⟩, +⟨1,940,602,true⟩, +⟨0,934,548,false⟩, +⟨0,606,512,false⟩, +⟨1,934,606,true⟩, +⟨0,372,224,false⟩, +⟨1,372,934,true⟩, +⟨0,935,550,true⟩, +⟨0,421,510,true⟩, +⟨1,935,421,true⟩, +⟨0,370,223,true⟩, +⟨1,370,935,true⟩, +⟨0,939,564,false⟩, +⟨0,422,532,false⟩, +⟨1,939,422,true⟩, +⟨0,607,485,true⟩, +⟨0,49,51,true⟩, +⟨1,607,49,true⟩, +⟨0,50,219,true⟩, +⟨1,607,50,true⟩, +⟨0,383,228,false⟩, +⟨1,383,939,true⟩, +⟨0,377,227,true⟩, +⟨1,377,940,true⟩, +⟨0,521,490,false⟩, +⟨0,85,87,false⟩, +⟨1,521,85,true⟩, +⟨0,86,233,false⟩, +⟨1,521,86,true⟩, +⟨0,605,580,true⟩, +⟨0,775,533,true⟩, +⟨1,605,775,true⟩, +⟨0,617,592,false⟩, +⟨0,759,509,false⟩, +⟨1,617,759,true⟩, +⟨0,438,237,false⟩, +⟨1,438,617,true⟩, +⟨0,616,590,true⟩, +⟨0,758,507,true⟩, +⟨1,616,758,true⟩, +⟨0,432,234,true⟩, +⟨1,432,616,true⟩, +⟨0,604,578,false⟩, +⟨0,774,531,false⟩, +⟨1,604,774,true⟩, +⟨0,520,488,true⟩, +⟨0,80,82,true⟩, +⟨1,520,80,true⟩, +⟨0,83,230,true⟩, +⟨1,520,83,true⟩, +⟨0,445,238,false⟩, +⟨1,445,604,true⟩, +⟨0,443,241,true⟩, +⟨1,443,605,true⟩, +⟨0,591,490,false⟩, +⟨0,84,86,false⟩, +⟨1,591,84,true⟩, +⟨0,87,232,false⟩, +⟨1,591,87,true⟩, +⟨0,944,580,true⟩, +⟨0,586,531,true⟩, +⟨1,944,586,true⟩, +⟨0,437,239,true⟩, +⟨1,437,944,true⟩, +⟨0,951,590,false⟩, +⟨0,354,509,false⟩, +⟨1,951,354,true⟩, +⟨0,953,592,true⟩, +⟨0,582,507,true⟩, +⟨1,953,582,true⟩, +⟨0,942,578,false⟩, +⟨0,590,533,false⟩, +⟨1,942,590,true⟩, +⟨0,435,240,false⟩, +⟨1,435,942,true⟩, +⟨0,587,488,true⟩, +⟨0,81,83,true⟩, +⟨1,587,81,true⟩, +⟨0,82,231,true⟩, +⟨1,587,82,true⟩, +⟨0,446,236,false⟩, +⟨1,446,951,true⟩, +⟨0,440,235,true⟩, +⟨1,440,953,true⟩, +⟨0,747,491,false⟩, +⟨0,109,111,false⟩, +⟨1,747,109,true⟩, +⟨0,110,245,false⟩, +⟨1,747,110,true⟩, +⟨0,621,596,true⟩, +⟨0,773,529,true⟩, +⟨1,621,773,true⟩, +⟨0,601,584,false⟩, +⟨0,761,513,false⟩, +⟨1,601,761,true⟩, +⟨0,486,249,false⟩, +⟨1,486,601,true⟩, +⟨0,600,582,true⟩, +⟨0,760,511,true⟩, +⟨1,600,760,true⟩, +⟨0,480,246,true⟩, +⟨1,480,600,true⟩, +⟨0,620,594,false⟩, +⟨0,772,527,false⟩, +⟨1,620,772,true⟩, +⟨0,746,489,true⟩, +⟨0,104,106,true⟩, +⟨1,746,104,true⟩, +⟨0,107,242,true⟩, +⟨1,746,107,true⟩, +⟨0,493,250,false⟩, +⟨1,493,620,true⟩, +⟨0,491,253,true⟩, +⟨1,491,621,true⟩, +⟨0,566,491,false⟩, +⟨0,108,110,false⟩, +⟨1,566,108,true⟩, +⟨0,111,244,false⟩, +⟨1,566,111,true⟩, +⟨0,957,596,true⟩, +⟨0,570,527,true⟩, +⟨1,957,570,true⟩, +⟨0,485,251,true⟩, +⟨1,485,957,true⟩, +⟨0,946,582,false⟩, +⟨0,574,513,false⟩, +⟨1,946,574,true⟩, +⟨0,947,584,true⟩, +⟨0,309,511,true⟩, +⟨1,947,309,true⟩, +⟨0,955,594,false⟩, +⟨0,310,529,false⟩, +⟨1,955,310,true⟩, +⟨0,483,252,false⟩, +⟨1,483,955,true⟩, +⟨0,575,489,true⟩, +⟨0,105,107,true⟩, +⟨1,575,105,true⟩, +⟨0,106,243,true⟩, +⟨1,575,106,true⟩, +⟨0,494,248,false⟩, +⟨1,494,946,true⟩, +⟨0,488,247,true⟩, +⟨1,488,947,true⟩, +⟨0,515,494,false⟩, +⟨0,101,103,false⟩, +⟨1,515,101,true⟩, +⟨0,102,257,false⟩, +⟨1,515,102,true⟩, +⟨0,817,581,true⟩, +⟨0,803,567,true⟩, +⟨1,817,803,true⟩] +def chunk63 : List Event := [⟨0,833,597,false⟩, +⟨0,787,547,false⟩, +⟨1,833,787,true⟩, +⟨0,470,261,false⟩, +⟨1,470,833,true⟩, +⟨0,832,595,true⟩, +⟨0,786,545,true⟩, +⟨1,832,786,true⟩, +⟨0,464,258,true⟩, +⟨1,464,832,true⟩, +⟨0,816,579,false⟩, +⟨0,802,565,false⟩, +⟨1,816,802,true⟩, +⟨0,513,492,true⟩, +⟨0,96,98,true⟩, +⟨1,513,96,true⟩, +⟨0,99,254,true⟩, +⟨1,513,99,true⟩, +⟨0,477,262,false⟩, +⟨1,477,816,true⟩, +⟨0,475,265,true⟩, +⟨1,475,817,true⟩, +⟨0,559,494,false⟩, +⟨0,100,102,false⟩, +⟨1,559,100,true⟩, +⟨0,103,256,false⟩, +⟨1,559,103,true⟩, +⟨0,945,581,true⟩, +⟨0,558,565,true⟩, +⟨1,945,558,true⟩, +⟨0,469,263,true⟩, +⟨1,469,945,true⟩, +⟨0,956,595,false⟩, +⟨0,325,547,false⟩, +⟨1,956,325,true⟩, +⟨0,958,597,true⟩, +⟨0,550,545,true⟩, +⟨1,958,550,true⟩, +⟨0,943,579,false⟩, +⟨0,554,567,false⟩, +⟨1,943,554,true⟩, +⟨0,467,264,false⟩, +⟨1,467,943,true⟩, +⟨0,555,492,true⟩, +⟨0,97,99,true⟩, +⟨1,555,97,true⟩, +⟨0,98,255,true⟩, +⟨1,555,98,true⟩, +⟨0,478,260,false⟩, +⟨1,478,956,true⟩, +⟨0,472,259,true⟩, +⟨1,472,958,true⟩, +⟨0,749,495,false⟩, +⟨0,93,95,false⟩, +⟨1,749,93,true⟩, +⟨0,94,269,false⟩, +⟨1,749,94,true⟩, +⟨0,831,593,true⟩, +⟨0,801,563,true⟩, +⟨1,831,801,true⟩, +⟨0,819,585,false⟩, +⟨0,789,551,false⟩, +⟨1,819,789,true⟩, +⟨0,454,273,false⟩, +⟨1,454,819,true⟩, +⟨0,818,583,true⟩, +⟨0,788,549,true⟩, +⟨1,818,788,true⟩, +⟨0,448,270,true⟩, +⟨1,448,818,true⟩, +⟨0,830,591,false⟩, +⟨0,800,561,false⟩, +⟨1,830,800,true⟩, +⟨0,748,493,true⟩, +⟨0,88,90,true⟩, +⟨1,748,88,true⟩, +⟨0,91,266,true⟩, +⟨1,748,91,true⟩, +⟨0,461,274,false⟩, +⟨1,461,830,true⟩, +⟨0,459,277,true⟩, +⟨1,459,831,true⟩, +⟨0,539,495,false⟩, +⟨0,92,94,false⟩, +⟨1,539,92,true⟩, +⟨0,95,268,false⟩, +⟨1,539,95,true⟩, +⟨0,954,593,true⟩, +⟨0,542,561,true⟩, +⟨1,954,542,true⟩, +⟨0,453,275,true⟩, +⟨1,453,954,true⟩, +⟨0,532,583,false⟩, +⟨0,341,551,false⟩, +⟨1,532,341,true⟩, +⟨0,948,585,true⟩, +⟨0,543,549,true⟩, +⟨1,948,543,true⟩, +⟨0,952,591,false⟩, +⟨0,538,563,false⟩, +⟨1,952,538,true⟩, +⟨0,451,276,false⟩, +⟨1,451,952,true⟩, +⟨0,535,493,true⟩, +⟨0,89,91,true⟩, +⟨1,535,89,true⟩, +⟨0,90,267,true⟩, +⟨1,535,90,true⟩, +⟨0,462,272,false⟩, +⟨1,462,532,true⟩, +⟨0,456,271,true⟩, +⟨1,456,948,true⟩, +⟨0,763,517,false⟩, +⟨0,61,63,false⟩, +⟨1,763,61,true⟩, +⟨0,62,281,false⟩, +⟨1,763,62,true⟩, +⟨0,829,589,true⟩, +⟨0,815,577,true⟩, +⟨1,829,815,true⟩, +⟨0,391,289,true⟩, +⟨1,391,829,true⟩, +⟨0,805,571,false⟩, +⟨0,791,555,false⟩, +⟨1,805,791,true⟩, +⟨0,804,569,true⟩, +⟨0,790,553,true⟩, +⟨1,804,790,true⟩, +⟨0,828,587,false⟩, +⟨0,814,575,false⟩, +⟨1,828,814,true⟩, +⟨0,385,286,false⟩, +⟨1,385,828,true⟩, +⟨0,762,515,true⟩, +⟨0,56,58,true⟩, +⟨1,762,56,true⟩, +⟨0,59,278,true⟩, +⟨1,762,59,true⟩, +⟨0,396,285,false⟩, +⟨1,396,805,true⟩, +⟨0,394,282,true⟩, +⟨1,394,804,true⟩, +⟨0,518,517,false⟩, +⟨0,60,62,false⟩, +⟨1,518,60,true⟩, +⟨0,63,280,false⟩, +⟨1,518,63,true⟩, +⟨0,950,589,true⟩, +⟨0,252,575,true⟩, +⟨1,950,252,true⟩, +⟨0,389,287,true⟩, +⟨1,389,950,true⟩, +⟨0,526,569,false⟩, +⟨0,522,555,false⟩, +⟨1,526,522,true⟩, +⟨0,406,571,true⟩, +⟨0,402,553,true⟩, +⟨1,406,402,true⟩, +⟨0,949,587,false⟩, +⟨0,941,577,false⟩, +⟨1,949,941,true⟩, +⟨0,387,288,false⟩, +⟨1,387,949,true⟩, +⟨0,527,515,true⟩, +⟨0,57,59,true⟩, +⟨1,527,57,true⟩, +⟨0,58,279,true⟩, +⟨1,527,58,true⟩, +⟨0,398,284,false⟩, +⟨1,398,526,true⟩, +⟨0,392,283,true⟩, +⟨1,392,406,true⟩, +⟨0,704,470,false⟩, +⟨0,640,466,false⟩, +⟨1,704,640,true⟩, +⟨0,704,808,false⟩, +⟨0,255,466,false⟩, +⟨1,704,255,true⟩, +⟨0,278,466,false⟩, +⟨1,704,278,true⟩, +⟨0,624,465,true⟩, +⟨0,656,467,true⟩, +⟨1,624,656,true⟩, +⟨0,266,465,true⟩, +⟨1,266,624,true⟩, +⟨0,688,469,false⟩, +⟨0,720,471,false⟩, +⟨1,688,720,true⟩, +⟨0,907,635,false⟩, +⟨0,708,470,false⟩, +⟨1,907,708,true⟩, +⟨1,907,688,true⟩, +⟨0,576,462,true⟩, +⟨0,711,470,true⟩, +⟨1,576,711,true⟩, +⟨0,253,462,true⟩, +⟨1,576,253,true⟩, +⟨0,282,462,true⟩, +⟨1,576,282,true⟩, +⟨0,560,461,false⟩] +def chunk64 : List Event := [⟨0,592,463,false⟩, +⟨1,560,592,true⟩, +⟨0,264,461,false⟩, +⟨1,560,264,true⟩, +⟨0,810,540,false⟩, +⟨0,811,541,false⟩, +⟨1,592,810,true⟩, +⟨1,592,811,true⟩, +⟨1,592,560,true⟩, +⟨0,544,460,true⟩, +⟨0,727,471,true⟩, +⟨1,544,727,true⟩, +⟨0,6,460,true⟩, +⟨1,544,6,true⟩, +⟨0,7,460,true⟩, +⟨1,544,7,true⟩, +⟨0,599,463,false⟩, +⟨0,608,464,false⟩, +⟨1,599,608,true⟩, +⟨0,3,463,false⟩, +⟨1,599,3,true⟩, +⟨0,663,467,false⟩, +⟨0,672,468,false⟩, +⟨1,663,672,true⟩, +⟨0,567,461,true⟩, +⟨0,583,462,true⟩, +⟨1,567,583,true⟩, +⟨0,2,461,true⟩, +⟨1,567,2,true⟩, +⟨0,631,465,true⟩, +⟨0,647,466,true⟩, +⟨1,631,647,true⟩, +⟨0,512,458,false⟩, +⟨0,551,460,false⟩, +⟨1,512,551,true⟩, +⟨0,512,818,false⟩, +⟨0,1,458,false⟩, +⟨1,512,1,true⟩, +⟨0,640,808,false⟩, +⟨0,679,468,false⟩, +⟨1,640,679,true⟩, +⟨0,551,818,true⟩, +⟨0,715,470,true⟩, +⟨1,551,715,true⟩, +⟨0,280,470,true⟩, +⟨1,551,280,true⟩, +⟨0,286,470,true⟩, +⟨1,551,286,true⟩, +⟨0,603,463,false⟩, +⟨0,695,469,false⟩, +⟨1,603,695,true⟩, +⟨0,262,469,false⟩, +⟨1,603,262,true⟩, +⟨0,265,463,false⟩, +⟨1,603,265,true⟩, +⟨0,519,458,false⟩, +⟨0,528,459,false⟩, +⟨1,519,528,true⟩, +⟨0,519,820,false⟩, +⟨0,246,459,false⟩, +⟨1,519,246,true⟩, +⟨0,635,465,false⟩, +⟨0,683,468,false⟩, +⟨1,635,683,true⟩, +⟨0,528,820,true⟩, +⟨0,699,469,true⟩, +⟨1,528,699,true⟩, +⟨0,4,459,true⟩, +⟨1,528,4,true⟩, +⟨0,5,459,true⟩, +⟨1,528,5,true⟩, +⟨0,571,461,true⟩, +⟨0,615,464,true⟩, +⟨1,571,615,true⟩, +⟨0,276,461,true⟩, +⟨1,571,276,true⟩, +⟨0,651,466,true⟩, +⟨0,667,467,true⟩, +⟨1,651,667,true⟩, +⟨0,64,645,true⟩, +⟨0,119,718,true⟩, +⟨1,64,119,true⟩, +⟨0,32,657,true⟩, +⟨1,32,119,true⟩, +⟨0,16,681,true⟩, +⟨1,16,119,true⟩, +⟨0,9,735,true⟩, +⟨1,9,119,true⟩, +⟨0,8,729,true⟩, +⟨1,8,119,true⟩, +⟨0,118,712,true⟩, +⟨1,64,118,true⟩, +⟨1,32,118,true⟩, +⟨1,16,118,true⟩, +⟨0,1,828,true⟩, +⟨1,1,118,true⟩, +⟨0,0,458,true⟩, +⟨1,0,118,true⟩, +⟨0,117,712,true⟩, +⟨1,64,117,true⟩, +⟨1,32,117,true⟩, +⟨1,16,117,true⟩, +⟨0,2,827,true⟩, +⟨1,2,117,true⟩, +⟨1,0,117,true⟩, +⟨0,116,718,true⟩, +⟨1,64,116,true⟩, +⟨1,32,116,true⟩, +⟨1,16,116,true⟩, +⟨1,9,116,true⟩, +⟨1,8,116,true⟩, +⟨1,2,116,true⟩, +⟨1,1,116,true⟩, +⟨0,115,717,true⟩, +⟨1,64,115,true⟩, +⟨1,32,115,true⟩, +⟨1,16,115,true⟩, +⟨0,4,831,true⟩, +⟨1,4,115,true⟩, +⟨1,0,115,true⟩, +⟨0,114,723,true⟩, +⟨1,64,114,true⟩, +⟨1,32,114,true⟩, +⟨1,16,114,true⟩, +⟨1,9,114,true⟩, +⟨1,8,114,true⟩, +⟨1,4,114,true⟩, +⟨1,1,114,true⟩, +⟨0,113,723,true⟩, +⟨1,64,113,true⟩, +⟨1,32,113,true⟩, +⟨1,16,113,true⟩, +⟨1,9,113,true⟩, +⟨1,8,113,true⟩, +⟨1,4,113,true⟩, +⟨1,2,113,true⟩, +⟨0,112,717,true⟩, +⟨1,64,112,true⟩, +⟨1,32,112,true⟩, +⟨1,16,112,true⟩, +⟨1,4,112,true⟩, +⟨1,2,112,true⟩, +⟨1,1,112,true⟩, +⟨1,0,112,true⟩, +⟨0,111,766,true⟩, +⟨1,64,111,true⟩, +⟨1,32,111,true⟩, +⟨1,9,111,true⟩, +⟨1,1,111,true⟩, +⟨1,0,111,true⟩, +⟨0,110,760,true⟩, +⟨1,64,110,true⟩, +⟨1,32,110,true⟩, +⟨1,8,110,true⟩, +⟨1,1,110,true⟩, +⟨1,0,110,true⟩, +⟨0,109,760,true⟩, +⟨1,64,109,true⟩, +⟨1,32,109,true⟩, +⟨1,8,109,true⟩, +⟨1,2,109,true⟩, +⟨1,1,109,true⟩, +⟨0,108,766,true⟩, +⟨1,64,108,true⟩, +⟨1,32,108,true⟩, +⟨1,9,108,true⟩, +⟨1,2,108,true⟩, +⟨1,1,108,true⟩, +⟨0,107,765,true⟩, +⟨1,64,107,true⟩, +⟨1,32,107,true⟩, +⟨1,8,107,true⟩, +⟨1,4,107,true⟩, +⟨1,1,107,true⟩, +⟨0,106,771,true⟩, +⟨1,64,106,true⟩, +⟨1,32,106,true⟩, +⟨1,9,106,true⟩, +⟨1,4,106,true⟩, +⟨1,1,106,true⟩, +⟨0,105,771,true⟩, +⟨1,64,105,true⟩, +⟨1,32,105,true⟩, +⟨1,9,105,true⟩, +⟨1,4,105,true⟩, +⟨1,2,105,true⟩, +⟨1,1,105,true⟩, +⟨1,0,105,true⟩, +⟨0,104,765,true⟩, +⟨1,64,104,true⟩, +⟨1,32,104,true⟩, +⟨1,8,104,true⟩, +⟨1,4,104,true⟩, +⟨1,2,104,true⟩, +⟨1,1,104,true⟩, +⟨1,0,104,true⟩, +⟨0,103,778,true⟩, +⟨1,64,103,true⟩, +⟨1,32,103,true⟩, +⟨1,2,103,true⟩] +def chunk65 : List Event := [⟨1,1,103,true⟩, +⟨1,0,103,true⟩, +⟨0,102,772,true⟩, +⟨1,64,102,true⟩, +⟨1,32,102,true⟩, +⟨1,9,102,true⟩, +⟨1,8,102,true⟩, +⟨1,1,102,true⟩, +⟨0,101,772,true⟩, +⟨1,64,101,true⟩, +⟨1,32,101,true⟩, +⟨1,9,101,true⟩, +⟨1,8,101,true⟩, +⟨1,0,101,true⟩, +⟨0,100,778,true⟩, +⟨1,64,100,true⟩, +⟨1,32,100,true⟩, +⟨1,2,100,true⟩, +⟨0,99,777,true⟩, +⟨1,64,99,true⟩, +⟨1,32,99,true⟩, +⟨1,9,99,true⟩, +⟨1,8,99,true⟩, +⟨1,4,99,true⟩, +⟨1,2,99,true⟩, +⟨1,1,99,true⟩, +⟨0,98,783,true⟩, +⟨1,64,98,true⟩, +⟨1,32,98,true⟩, +⟨1,4,98,true⟩, +⟨1,1,98,true⟩, +⟨1,0,98,true⟩, +⟨0,97,783,true⟩, +⟨1,64,97,true⟩, +⟨1,32,97,true⟩, +⟨1,4,97,true⟩, +⟨0,96,777,true⟩, +⟨1,64,96,true⟩, +⟨1,32,96,true⟩, +⟨1,9,96,true⟩, +⟨1,8,96,true⟩, +⟨1,4,96,true⟩, +⟨1,2,96,true⟩, +⟨1,0,96,true⟩, +⟨0,95,790,true⟩, +⟨1,64,95,true⟩, +⟨1,16,95,true⟩, +⟨1,9,95,true⟩, +⟨1,2,95,true⟩, +⟨1,0,95,true⟩, +⟨0,94,784,true⟩, +⟨1,64,94,true⟩, +⟨1,16,94,true⟩, +⟨1,8,94,true⟩, +⟨1,2,94,true⟩, +⟨1,0,94,true⟩, +⟨0,93,784,true⟩, +⟨1,64,93,true⟩, +⟨1,16,93,true⟩, +⟨1,8,93,true⟩, +⟨1,2,93,true⟩, +⟨1,1,93,true⟩, +⟨0,92,790,true⟩, +⟨1,64,92,true⟩, +⟨1,16,92,true⟩, +⟨1,9,92,true⟩, +⟨1,2,92,true⟩, +⟨1,1,92,true⟩, +⟨0,91,789,true⟩, +⟨1,64,91,true⟩, +⟨1,16,91,true⟩, +⟨1,8,91,true⟩, +⟨1,4,91,true⟩, +⟨1,2,91,true⟩, +⟨0,90,795,true⟩, +⟨1,64,90,true⟩, +⟨1,16,90,true⟩, +⟨1,9,90,true⟩, +⟨1,4,90,true⟩, +⟨1,2,90,true⟩, +⟨0,89,795,true⟩, +⟨1,64,89,true⟩, +⟨1,16,89,true⟩, +⟨1,9,89,true⟩, +⟨1,4,89,true⟩, +⟨1,2,89,true⟩, +⟨1,1,89,true⟩, +⟨1,0,89,true⟩, +⟨0,88,789,true⟩, +⟨1,64,88,true⟩, +⟨1,16,88,true⟩, +⟨1,8,88,true⟩, +⟨1,4,88,true⟩, +⟨1,2,88,true⟩, +⟨1,1,88,true⟩, +⟨1,0,88,true⟩, +⟨0,87,754,true⟩, +⟨1,64,87,true⟩, +⟨1,16,87,true⟩, +⟨1,2,87,true⟩, +⟨1,1,87,true⟩, +⟨1,0,87,true⟩, +⟨0,86,748,true⟩, +⟨1,64,86,true⟩, +⟨1,16,86,true⟩, +⟨1,9,86,true⟩, +⟨1,8,86,true⟩, +⟨1,2,86,true⟩, +⟨0,85,748,true⟩, +⟨1,64,85,true⟩, +⟨1,16,85,true⟩, +⟨1,9,85,true⟩, +⟨1,8,85,true⟩, +⟨1,0,85,true⟩, +⟨0,84,754,true⟩, +⟨1,64,84,true⟩, +⟨1,16,84,true⟩, +⟨1,1,84,true⟩, +⟨0,83,753,true⟩, +⟨1,64,83,true⟩, +⟨1,16,83,true⟩, +⟨1,9,83,true⟩, +⟨1,8,83,true⟩, +⟨1,4,83,true⟩, +⟨1,2,83,true⟩, +⟨1,1,83,true⟩, +⟨0,82,759,true⟩, +⟨1,64,82,true⟩, +⟨1,16,82,true⟩, +⟨1,4,82,true⟩, +⟨1,2,82,true⟩, +⟨1,0,82,true⟩, +⟨0,81,759,true⟩, +⟨1,64,81,true⟩, +⟨1,16,81,true⟩, +⟨1,4,81,true⟩, +⟨0,80,753,true⟩, +⟨1,64,80,true⟩, +⟨1,16,80,true⟩, +⟨1,9,80,true⟩, +⟨1,8,80,true⟩, +⟨1,4,80,true⟩, +⟨1,1,80,true⟩, +⟨1,0,80,true⟩, +⟨0,79,706,true⟩, +⟨1,64,79,true⟩, +⟨1,8,79,true⟩, +⟨1,2,79,true⟩, +⟨1,1,79,true⟩, +⟨1,0,79,true⟩, +⟨0,78,700,true⟩, +⟨1,64,78,true⟩, +⟨1,9,78,true⟩, +⟨1,2,78,true⟩, +⟨1,1,78,true⟩, +⟨1,0,78,true⟩, +⟨0,77,700,true⟩, +⟨1,64,77,true⟩, +⟨1,9,77,true⟩, +⟨1,0,77,true⟩, +⟨0,76,706,true⟩, +⟨1,64,76,true⟩, +⟨1,8,76,true⟩, +⟨1,0,76,true⟩, +⟨0,75,705,true⟩, +⟨1,64,75,true⟩, +⟨1,9,75,true⟩, +⟨1,4,75,true⟩, +⟨1,2,75,true⟩, +⟨1,1,75,true⟩, +⟨0,74,711,true⟩, +⟨1,64,74,true⟩, +⟨1,8,74,true⟩, +⟨1,4,74,true⟩, +⟨1,2,74,true⟩, +⟨1,1,74,true⟩, +⟨0,73,711,true⟩, +⟨1,64,73,true⟩, +⟨1,8,73,true⟩, +⟨1,4,73,true⟩, +⟨0,72,705,true⟩, +⟨1,64,72,true⟩, +⟨1,9,72,true⟩, +⟨1,4,72,true⟩, +⟨0,71,646,true⟩, +⟨1,64,71,true⟩, +⟨1,9,71,true⟩, +⟨1,8,71,true⟩, +⟨1,4,71,true⟩, +⟨1,2,71,true⟩, +⟨1,1,71,true⟩, +⟨1,0,71,true⟩, +⟨0,70,640,true⟩, +⟨1,64,70,true⟩, +⟨1,2,70,true⟩, +⟨1,1,70,true⟩, +⟨0,69,640,true⟩, +⟨1,64,69,true⟩, +⟨1,2,69,true⟩, +⟨1,0,69,true⟩] +def chunk66 : List Event := [⟨0,68,646,true⟩, +⟨1,64,68,true⟩, +⟨1,9,68,true⟩, +⟨1,8,68,true⟩, +⟨1,4,68,true⟩, +⟨1,2,68,true⟩, +⟨0,67,645,true⟩, +⟨1,64,67,true⟩, +⟨1,1,67,true⟩, +⟨1,0,67,true⟩, +⟨0,66,651,true⟩, +⟨1,64,66,true⟩, +⟨1,9,66,true⟩, +⟨1,8,66,true⟩, +⟨1,4,66,true⟩, +⟨1,1,66,true⟩, +⟨0,65,651,true⟩, +⟨1,64,65,true⟩, +⟨1,9,65,true⟩, +⟨1,8,65,true⟩, +⟨1,4,65,true⟩, +⟨1,0,65,true⟩, +⟨1,32,64,true⟩, +⟨1,16,64,true⟩, +⟨1,4,64,true⟩, +⟨1,2,64,true⟩, +⟨1,1,64,true⟩, +⟨0,63,802,true⟩, +⟨1,32,63,true⟩, +⟨1,16,63,true⟩, +⟨1,9,63,true⟩, +⟨1,4,63,true⟩, +⟨1,0,63,true⟩, +⟨0,62,796,true⟩, +⟨1,32,62,true⟩, +⟨1,16,62,true⟩, +⟨1,8,62,true⟩, +⟨1,4,62,true⟩, +⟨1,0,62,true⟩, +⟨0,61,796,true⟩, +⟨1,32,61,true⟩, +⟨1,16,61,true⟩, +⟨1,8,61,true⟩, +⟨1,4,61,true⟩, +⟨1,1,61,true⟩, +⟨0,60,802,true⟩, +⟨1,32,60,true⟩, +⟨1,16,60,true⟩, +⟨1,9,60,true⟩, +⟨1,4,60,true⟩, +⟨1,1,60,true⟩, +⟨0,59,801,true⟩, +⟨1,32,59,true⟩, +⟨1,16,59,true⟩, +⟨1,8,59,true⟩, +⟨1,4,59,true⟩, +⟨1,2,59,true⟩, +⟨0,58,807,true⟩, +⟨1,32,58,true⟩, +⟨1,16,58,true⟩, +⟨1,9,58,true⟩, +⟨1,4,58,true⟩, +⟨1,2,58,true⟩, +⟨0,57,807,true⟩, +⟨1,32,57,true⟩, +⟨1,16,57,true⟩, +⟨1,9,57,true⟩, +⟨1,4,57,true⟩, +⟨1,2,57,true⟩, +⟨1,1,57,true⟩, +⟨1,0,57,true⟩, +⟨0,56,801,true⟩, +⟨1,32,56,true⟩, +⟨1,16,56,true⟩, +⟨1,8,56,true⟩, +⟨1,4,56,true⟩, +⟨1,2,56,true⟩, +⟨1,1,56,true⟩, +⟨1,0,56,true⟩, +⟨0,55,742,true⟩, +⟨1,32,55,true⟩, +⟨1,16,55,true⟩, +⟨1,4,55,true⟩, +⟨1,1,55,true⟩, +⟨1,0,55,true⟩, +⟨0,54,736,true⟩, +⟨1,32,54,true⟩, +⟨1,16,54,true⟩, +⟨1,9,54,true⟩, +⟨1,8,54,true⟩, +⟨1,4,54,true⟩, +⟨0,53,736,true⟩, +⟨1,32,53,true⟩, +⟨1,16,53,true⟩, +⟨1,9,53,true⟩, +⟨1,8,53,true⟩, +⟨1,4,53,true⟩, +⟨1,2,53,true⟩, +⟨1,1,53,true⟩, +⟨0,52,742,true⟩, +⟨1,32,52,true⟩, +⟨1,16,52,true⟩, +⟨1,4,52,true⟩, +⟨1,2,52,true⟩, +⟨1,0,52,true⟩, +⟨0,51,741,true⟩, +⟨1,32,51,true⟩, +⟨1,16,51,true⟩, +⟨1,9,51,true⟩, +⟨1,8,51,true⟩, +⟨1,0,51,true⟩, +⟨0,50,747,true⟩, +⟨1,32,50,true⟩, +⟨1,16,50,true⟩, +⟨1,1,50,true⟩, +⟨0,49,747,true⟩, +⟨1,32,49,true⟩, +⟨1,16,49,true⟩, +⟨1,2,49,true⟩, +⟨0,48,741,true⟩, +⟨1,32,48,true⟩, +⟨1,16,48,true⟩, +⟨1,9,48,true⟩, +⟨1,8,48,true⟩, +⟨1,2,48,true⟩, +⟨1,1,48,true⟩, +⟨1,0,48,true⟩, +⟨0,47,694,true⟩, +⟨1,32,47,true⟩, +⟨1,8,47,true⟩, +⟨1,4,47,true⟩, +⟨1,1,47,true⟩, +⟨1,0,47,true⟩, +⟨0,46,688,true⟩, +⟨1,32,46,true⟩, +⟨1,9,46,true⟩, +⟨1,4,46,true⟩, +⟨1,1,46,true⟩, +⟨1,0,46,true⟩, +⟨0,45,688,true⟩, +⟨1,32,45,true⟩, +⟨1,9,45,true⟩, +⟨1,4,45,true⟩, +⟨1,2,45,true⟩, +⟨1,1,45,true⟩, +⟨0,44,694,true⟩, +⟨1,32,44,true⟩, +⟨1,8,44,true⟩, +⟨1,4,44,true⟩, +⟨1,2,44,true⟩, +⟨1,1,44,true⟩, +⟨0,43,693,true⟩, +⟨1,32,43,true⟩, +⟨1,9,43,true⟩, +⟨1,0,43,true⟩, +⟨0,42,699,true⟩, +⟨1,32,42,true⟩, +⟨1,8,42,true⟩, +⟨1,0,42,true⟩, +⟨0,41,699,true⟩, +⟨1,32,41,true⟩, +⟨1,8,41,true⟩, +⟨1,2,41,true⟩, +⟨0,40,693,true⟩, +⟨1,32,40,true⟩, +⟨1,9,40,true⟩, +⟨1,2,40,true⟩, +⟨0,39,658,true⟩, +⟨1,32,39,true⟩, +⟨1,9,39,true⟩, +⟨1,8,39,true⟩, +⟨1,4,39,true⟩, +⟨1,2,39,true⟩, +⟨1,1,39,true⟩, +⟨1,0,39,true⟩, +⟨0,38,652,true⟩, +⟨1,32,38,true⟩, +⟨1,4,38,true⟩, +⟨1,1,38,true⟩, +⟨0,37,652,true⟩, +⟨1,32,37,true⟩, +⟨1,4,37,true⟩, +⟨1,0,37,true⟩, +⟨0,36,658,true⟩, +⟨1,32,36,true⟩, +⟨1,9,36,true⟩, +⟨1,8,36,true⟩, +⟨1,4,36,true⟩, +⟨1,2,36,true⟩, +⟨0,35,657,true⟩, +⟨1,32,35,true⟩, +⟨1,1,35,true⟩, +⟨1,0,35,true⟩, +⟨0,34,663,true⟩, +⟨1,32,34,true⟩, +⟨1,9,34,true⟩, +⟨1,8,34,true⟩, +⟨1,2,34,true⟩, +⟨1,1,34,true⟩, +⟨0,33,663,true⟩] +def chunk67 : List Event := [⟨1,32,33,true⟩, +⟨1,9,33,true⟩, +⟨1,8,33,true⟩, +⟨1,2,33,true⟩, +⟨1,0,33,true⟩, +⟨1,64,32,true⟩, +⟨1,8,32,true⟩, +⟨1,2,32,true⟩, +⟨1,0,32,true⟩, +⟨0,31,670,true⟩, +⟨1,16,31,true⟩, +⟨1,8,31,true⟩, +⟨1,4,31,true⟩, +⟨1,2,31,true⟩, +⟨1,0,31,true⟩, +⟨0,30,664,true⟩, +⟨1,16,30,true⟩, +⟨1,9,30,true⟩, +⟨1,4,30,true⟩, +⟨1,2,30,true⟩, +⟨1,0,30,true⟩, +⟨0,29,664,true⟩, +⟨1,16,29,true⟩, +⟨1,9,29,true⟩, +⟨1,4,29,true⟩, +⟨1,2,29,true⟩, +⟨1,1,29,true⟩, +⟨0,28,670,true⟩, +⟨1,16,28,true⟩, +⟨1,8,28,true⟩, +⟨1,4,28,true⟩, +⟨1,2,28,true⟩, +⟨1,1,28,true⟩, +⟨0,27,669,true⟩, +⟨1,16,27,true⟩, +⟨1,9,27,true⟩, +⟨1,0,27,true⟩, +⟨0,26,675,true⟩, +⟨1,16,26,true⟩, +⟨1,8,26,true⟩, +⟨1,0,26,true⟩, +⟨0,25,675,true⟩, +⟨1,16,25,true⟩, +⟨1,8,25,true⟩, +⟨1,1,25,true⟩, +⟨0,24,669,true⟩, +⟨1,16,24,true⟩, +⟨1,9,24,true⟩, +⟨1,1,24,true⟩, +⟨0,23,682,true⟩, +⟨1,16,23,true⟩, +⟨1,9,23,true⟩, +⟨1,8,23,true⟩, +⟨1,4,23,true⟩, +⟨1,2,23,true⟩, +⟨1,1,23,true⟩, +⟨1,0,23,true⟩, +⟨0,22,676,true⟩, +⟨1,16,22,true⟩, +⟨1,4,22,true⟩, +⟨1,2,22,true⟩, +⟨0,21,676,true⟩, +⟨1,16,21,true⟩, +⟨1,4,21,true⟩, +⟨1,0,21,true⟩, +⟨0,20,682,true⟩, +⟨1,16,20,true⟩, +⟨1,9,20,true⟩, +⟨1,8,20,true⟩, +⟨1,4,20,true⟩, +⟨1,1,20,true⟩, +⟨0,19,681,true⟩, +⟨1,16,19,true⟩, +⟨1,2,19,true⟩, +⟨1,0,19,true⟩, +⟨0,18,687,true⟩, +⟨1,16,18,true⟩, +⟨1,9,18,true⟩, +⟨1,8,18,true⟩, +⟨1,2,18,true⟩, +⟨1,1,18,true⟩, +⟨0,17,687,true⟩, +⟨1,16,17,true⟩, +⟨1,9,17,true⟩, +⟨1,8,17,true⟩, +⟨1,1,17,true⟩, +⟨1,0,17,true⟩, +⟨1,64,16,true⟩, +⟨1,8,16,true⟩, +⟨1,1,16,true⟩, +⟨1,0,16,true⟩, +⟨0,15,730,true⟩, +⟨1,9,15,true⟩, +⟨1,4,15,true⟩, +⟨1,2,15,true⟩, +⟨0,14,724,true⟩, +⟨1,8,14,true⟩, +⟨1,4,14,true⟩, +⟨1,2,14,true⟩, +⟨0,13,724,true⟩, +⟨1,8,13,true⟩, +⟨1,4,13,true⟩, +⟨1,1,13,true⟩, +⟨0,12,730,true⟩, +⟨1,9,12,true⟩, +⟨1,4,12,true⟩, +⟨1,1,12,true⟩, +⟨0,11,729,true⟩, +⟨1,8,11,true⟩, +⟨1,2,11,true⟩, +⟨1,1,11,true⟩, +⟨0,10,735,true⟩, +⟨1,9,10,true⟩, +⟨1,2,10,true⟩, +⟨1,1,10,true⟩, +⟨1,8,9,true⟩, +⟨1,4,9,true⟩, +⟨1,0,9,true⟩, +⟨1,9,64,true⟩, +⟨1,64,9,true⟩, +⟨1,9,64,true⟩, +⟨1,32,8,true⟩, +⟨1,16,8,true⟩, +⟨1,0,8,true⟩, +⟨0,7,813,true⟩, +⟨1,4,7,true⟩, +⟨1,2,7,true⟩, +⟨1,1,7,true⟩, +⟨0,6,813,true⟩, +⟨1,4,6,true⟩, +⟨1,2,6,true⟩, +⟨1,0,6,true⟩, +⟨0,5,831,true⟩, +⟨1,4,5,true⟩, +⟨1,1,5,true⟩, +⟨1,0,5,true⟩, +⟨1,64,4,true⟩, +⟨1,2,4,true⟩, +⟨1,4,32,true⟩, +⟨1,32,4,true⟩, +⟨1,4,32,true⟩, +⟨0,3,826,true⟩, +⟨1,2,3,true⟩, +⟨1,1,3,true⟩, +⟨1,0,3,true⟩, +⟨1,32,2,true⟩, +⟨1,1,2,true⟩, +⟨1,2,16,true⟩, +⟨1,16,2,true⟩, +⟨1,2,16,true⟩, +⟨1,16,1,true⟩, +⟨1,0,1,true⟩, +⟨1,1,9,true⟩, +⟨1,9,1,true⟩, +⟨1,1,9,true⟩, +⟨1,64,0,true⟩, +⟨1,32,0,true⟩, +⟨1,16,0,true⟩, +⟨2,0,987,true⟩, +⟨1,120,987,true⟩, +⟨1,121,987,true⟩, +⟨1,122,987,true⟩, +⟨1,123,987,true⟩, +⟨1,124,987,true⟩, +⟨1,125,987,true⟩, +⟨1,126,987,true⟩, +⟨1,127,987,true⟩, +⟨1,128,987,true⟩, +⟨1,129,987,true⟩, +⟨1,130,987,true⟩, +⟨1,131,987,true⟩, +⟨1,132,987,true⟩, +⟨1,133,987,true⟩, +⟨1,134,987,true⟩, +⟨1,135,987,true⟩, +⟨1,136,987,true⟩, +⟨1,137,987,true⟩, +⟨1,138,987,true⟩, +⟨1,139,987,true⟩, +⟨1,140,987,true⟩, +⟨1,141,987,true⟩, +⟨1,142,987,true⟩, +⟨1,143,987,true⟩, +⟨1,144,987,true⟩, +⟨1,145,987,true⟩, +⟨1,146,987,true⟩, +⟨1,147,987,true⟩, +⟨1,148,987,true⟩, +⟨1,149,987,true⟩, +⟨1,150,987,true⟩, +⟨1,151,987,true⟩, +⟨1,152,987,true⟩, +⟨1,153,987,true⟩, +⟨1,154,987,true⟩, +⟨1,155,987,true⟩, +⟨1,156,987,true⟩, +⟨1,157,987,true⟩, +⟨1,158,987,true⟩, +⟨1,159,987,true⟩, +⟨1,160,987,true⟩] +def chunk68 : List Event := [⟨1,161,987,true⟩, +⟨1,162,987,true⟩, +⟨1,163,987,true⟩, +⟨1,164,987,true⟩, +⟨1,165,987,true⟩, +⟨1,166,987,true⟩, +⟨1,167,987,true⟩, +⟨1,168,987,true⟩, +⟨1,169,987,true⟩, +⟨1,170,987,true⟩, +⟨1,171,987,true⟩, +⟨1,172,987,true⟩, +⟨1,173,987,true⟩, +⟨1,174,987,true⟩, +⟨1,175,987,true⟩, +⟨1,176,987,true⟩, +⟨1,177,987,true⟩, +⟨1,178,987,true⟩, +⟨1,179,987,true⟩, +⟨1,180,987,true⟩, +⟨1,181,987,true⟩, +⟨1,182,987,true⟩, +⟨1,183,987,true⟩, +⟨1,184,987,true⟩, +⟨1,185,987,true⟩, +⟨1,186,987,true⟩, +⟨1,187,987,true⟩, +⟨1,188,987,true⟩, +⟨1,189,987,true⟩, +⟨1,190,987,true⟩, +⟨1,191,987,true⟩, +⟨1,192,987,true⟩, +⟨1,193,987,true⟩, +⟨1,194,987,true⟩, +⟨1,195,987,true⟩, +⟨1,196,987,true⟩, +⟨1,197,987,true⟩, +⟨1,198,987,true⟩, +⟨1,199,987,true⟩, +⟨1,200,987,true⟩, +⟨1,201,987,true⟩, +⟨1,202,987,true⟩, +⟨1,203,987,true⟩, +⟨1,204,987,true⟩, +⟨1,205,987,true⟩, +⟨1,206,987,true⟩, +⟨1,207,987,true⟩, +⟨1,208,987,true⟩, +⟨1,209,987,true⟩, +⟨1,210,987,true⟩, +⟨1,211,987,true⟩, +⟨1,212,987,true⟩, +⟨1,213,987,true⟩, +⟨1,214,987,true⟩, +⟨1,215,987,true⟩, +⟨1,216,987,true⟩, +⟨1,217,987,true⟩, +⟨1,218,987,true⟩, +⟨1,219,987,true⟩, +⟨1,220,987,true⟩, +⟨1,221,987,true⟩, +⟨1,222,987,true⟩, +⟨1,223,987,true⟩, +⟨1,224,987,true⟩, +⟨1,225,987,true⟩, +⟨1,226,987,true⟩, +⟨1,227,987,true⟩, +⟨1,228,987,true⟩, +⟨1,229,987,true⟩, +⟨1,230,987,true⟩, +⟨1,231,987,true⟩, +⟨1,232,987,true⟩, +⟨1,233,987,true⟩, +⟨1,234,987,true⟩, +⟨1,235,987,true⟩, +⟨1,236,987,true⟩, +⟨1,237,987,true⟩, +⟨1,238,987,true⟩, +⟨1,239,987,true⟩, +⟨3,0,987,true⟩, +⟨2,1,987,true⟩, +⟨1,120,987,true⟩, +⟨1,123,987,true⟩, +⟨1,125,987,true⟩, +⟨1,126,987,true⟩, +⟨1,137,987,true⟩, +⟨1,139,987,true⟩, +⟨1,141,987,true⟩, +⟨1,143,987,true⟩, +⟨1,146,987,true⟩, +⟨1,147,987,true⟩, +⟨1,150,987,true⟩, +⟨1,151,987,true⟩, +⟨1,153,987,true⟩, +⟨1,155,987,true⟩, +⟨1,157,987,true⟩, +⟨1,159,987,true⟩, +⟨1,162,987,true⟩, +⟨1,163,987,true⟩, +⟨1,166,987,true⟩, +⟨1,167,987,true⟩, +⟨1,168,987,true⟩, +⟨1,171,987,true⟩, +⟨1,172,987,true⟩, +⟨1,175,987,true⟩, +⟨1,176,987,true⟩, +⟨1,177,987,true⟩, +⟨1,182,987,true⟩, +⟨1,183,987,true⟩, +⟨1,185,987,true⟩, +⟨1,187,987,true⟩, +⟨1,189,987,true⟩, +⟨1,191,987,true⟩, +⟨1,196,987,true⟩, +⟨1,197,987,true⟩, +⟨1,198,987,true⟩, +⟨1,199,987,true⟩, +⟨1,200,987,true⟩, +⟨1,202,987,true⟩, +⟨1,205,987,true⟩, +⟨1,207,987,true⟩, +⟨1,208,987,true⟩, +⟨1,209,987,true⟩, +⟨1,214,987,true⟩, +⟨1,215,987,true⟩, +⟨1,216,987,true⟩, +⟨1,218,987,true⟩, +⟨1,221,987,true⟩, +⟨1,223,987,true⟩, +⟨1,224,987,true⟩, +⟨1,225,987,true⟩, +⟨1,230,987,true⟩, +⟨1,231,987,true⟩, +⟨1,232,987,true⟩, +⟨1,235,987,true⟩, +⟨1,237,987,true⟩, +⟨1,238,987,true⟩, +⟨3,1,987,true⟩, +⟨2,2,987,true⟩, +⟨1,121,987,true⟩, +⟨1,123,987,true⟩, +⟨1,125,987,true⟩, +⟨1,127,987,true⟩, +⟨1,129,987,true⟩, +⟨1,131,987,true⟩, +⟨1,133,987,true⟩, +⟨1,135,987,true⟩, +⟨1,145,987,true⟩, +⟨1,147,987,true⟩, +⟨1,148,987,true⟩, +⟨1,150,987,true⟩, +⟨1,153,987,true⟩, +⟨1,155,987,true⟩, +⟨1,156,987,true⟩, +⟨1,158,987,true⟩, +⟨1,160,987,true⟩, +⟨1,163,987,true⟩, +⟨1,164,987,true⟩, +⟨1,167,987,true⟩, +⟨1,170,987,true⟩, +⟨1,171,987,true⟩, +⟨1,174,987,true⟩, +⟨1,175,987,true⟩, +⟨1,176,987,true⟩, +⟨1,178,987,true⟩, +⟨1,181,987,true⟩, +⟨1,183,987,true⟩, +⟨1,185,987,true⟩, +⟨1,187,987,true⟩, +⟨1,188,987,true⟩, +⟨1,190,987,true⟩, +⟨1,192,987,true⟩, +⟨1,194,987,true⟩, +⟨1,197,987,true⟩, +⟨1,199,987,true⟩, +⟨1,204,987,true⟩, +⟨1,205,987,true⟩, +⟨1,206,987,true⟩, +⟨1,207,987,true⟩, +⟨1,208,987,true⟩, +⟨1,210,987,true⟩, +⟨1,213,987,true⟩, +⟨1,215,987,true⟩, +⟨1,216,987,true⟩, +⟨1,218,987,true⟩, +⟨1,221,987,true⟩, +⟨1,223,987,true⟩, +⟨1,224,987,true⟩, +⟨1,227,987,true⟩, +⟨1,229,987,true⟩, +⟨1,230,987,true⟩, +⟨1,232,987,true⟩, +⟨1,233,987,true⟩, +⟨1,238,987,true⟩, +⟨1,239,987,true⟩, +⟨3,2,987,true⟩, +⟨2,4,987,true⟩, +⟨1,122,987,true⟩, +⟨1,123,987,true⟩, +⟨1,126,987,true⟩] +def chunk69 : List Event := [⟨1,127,987,true⟩, +⟨1,129,987,true⟩, +⟨1,131,987,true⟩, +⟨1,132,987,true⟩, +⟨1,134,987,true⟩, +⟨1,137,987,true⟩, +⟨1,139,987,true⟩, +⟨1,140,987,true⟩, +⟨1,142,987,true⟩, +⟨1,144,987,true⟩, +⟨1,147,987,true⟩, +⟨1,148,987,true⟩, +⟨1,151,987,true⟩, +⟨1,161,987,true⟩, +⟨1,163,987,true⟩, +⟨1,164,987,true⟩, +⟨1,166,987,true⟩, +⟨1,169,987,true⟩, +⟨1,171,987,true⟩, +⟨1,172,987,true⟩, +⟨1,174,987,true⟩, +⟨1,176,987,true⟩, +⟨1,179,987,true⟩, +⟨1,180,987,true⟩, +⟨1,183,987,true⟩, +⟨1,185,987,true⟩, +⟨1,186,987,true⟩, +⟨1,189,987,true⟩, +⟨1,190,987,true⟩, +⟨1,192,987,true⟩, +⟨1,194,987,true⟩, +⟨1,197,987,true⟩, +⟨1,199,987,true⟩, +⟨1,200,987,true⟩, +⟨1,202,987,true⟩, +⟨1,205,987,true⟩, +⟨1,207,987,true⟩, +⟨1,208,987,true⟩, +⟨1,211,987,true⟩, +⟨1,213,987,true⟩, +⟨1,214,987,true⟩, +⟨1,220,987,true⟩, +⟨1,221,987,true⟩, +⟨1,222,987,true⟩, +⟨1,223,987,true⟩, +⟨1,224,987,true⟩, +⟨1,226,987,true⟩, +⟨1,229,987,true⟩, +⟨1,231,987,true⟩, +⟨1,232,987,true⟩, +⟨1,234,987,true⟩, +⟨1,237,987,true⟩, +⟨1,239,987,true⟩, +⟨3,4,987,true⟩, +⟨2,8,987,true⟩, +⟨1,124,987,true⟩, +⟨1,125,987,true⟩, +⟨1,126,987,true⟩, +⟨1,127,987,true⟩, +⟨1,129,987,true⟩, +⟨1,130,987,true⟩, +⟨1,133,987,true⟩, +⟨1,134,987,true⟩, +⟨1,137,987,true⟩, +⟨1,138,987,true⟩, +⟨1,141,987,true⟩, +⟨1,142,987,true⟩, +⟨1,144,987,true⟩, +⟨1,147,987,true⟩, +⟨1,148,987,true⟩, +⟨1,151,987,true⟩, +⟨1,153,987,true⟩, +⟨1,154,987,true⟩, +⟨1,157,987,true⟩, +⟨1,158,987,true⟩, +⟨1,160,987,true⟩, +⟨1,163,987,true⟩, +⟨1,164,987,true⟩, +⟨1,167,987,true⟩, +⟨1,168,987,true⟩, +⟨1,171,987,true⟩, +⟨1,172,987,true⟩, +⟨1,175,987,true⟩, +⟨1,176,987,true⟩, +⟨1,179,987,true⟩, +⟨1,181,987,true⟩, +⟨1,182,987,true⟩, +⟨1,193,987,true⟩, +⟨1,194,987,true⟩, +⟨1,197,987,true⟩, +⟨1,198,987,true⟩, +⟨1,201,987,true⟩, +⟨1,202,987,true⟩, +⟨1,205,987,true⟩, +⟨1,206,987,true⟩, +⟨1,208,987,true⟩, +⟨1,211,987,true⟩, +⟨1,212,987,true⟩, +⟨1,215,987,true⟩, +⟨1,217,987,true⟩, +⟨1,218,987,true⟩, +⟨1,221,987,true⟩, +⟨1,222,987,true⟩, +⟨1,224,987,true⟩, +⟨1,227,987,true⟩, +⟨1,228,987,true⟩, +⟨1,231,987,true⟩, +⟨1,232,987,true⟩, +⟨1,235,987,true⟩, +⟨1,236,987,true⟩, +⟨1,239,987,true⟩, +⟨3,8,987,true⟩, +⟨2,9,987,true⟩, +⟨1,128,987,true⟩, +⟨1,129,987,true⟩, +⟨1,130,987,true⟩, +⟨1,131,987,true⟩, +⟨1,132,987,true⟩, +⟨1,133,987,true⟩, +⟨1,134,987,true⟩, +⟨1,135,987,true⟩, +⟨1,144,987,true⟩, +⟨1,145,987,true⟩, +⟨1,146,987,true⟩, +⟨1,147,987,true⟩, +⟨1,148,987,true⟩, +⟨1,149,987,true⟩, +⟨1,150,987,true⟩, +⟨1,151,987,true⟩, +⟨1,160,987,true⟩, +⟨1,161,987,true⟩, +⟨1,162,987,true⟩, +⟨1,163,987,true⟩, +⟨1,164,987,true⟩, +⟨1,165,987,true⟩, +⟨1,166,987,true⟩, +⟨1,167,987,true⟩, +⟨1,176,987,true⟩, +⟨1,177,987,true⟩, +⟨1,178,987,true⟩, +⟨1,179,987,true⟩, +⟨1,180,987,true⟩, +⟨1,181,987,true⟩, +⟨1,182,987,true⟩, +⟨1,183,987,true⟩, +⟨1,192,987,true⟩, +⟨1,193,987,true⟩, +⟨1,194,987,true⟩, +⟨1,195,987,true⟩, +⟨1,196,987,true⟩, +⟨1,197,987,true⟩, +⟨1,198,987,true⟩, +⟨1,199,987,true⟩, +⟨1,208,987,true⟩, +⟨1,209,987,true⟩, +⟨1,210,987,true⟩, +⟨1,211,987,true⟩, +⟨1,212,987,true⟩, +⟨1,213,987,true⟩, +⟨1,214,987,true⟩, +⟨1,215,987,true⟩, +⟨1,224,987,true⟩, +⟨1,225,987,true⟩, +⟨1,226,987,true⟩, +⟨1,227,987,true⟩, +⟨1,228,987,true⟩, +⟨1,229,987,true⟩, +⟨1,230,987,true⟩, +⟨1,231,987,true⟩, +⟨3,9,987,true⟩, +⟨2,16,987,true⟩, +⟨1,136,987,true⟩, +⟨1,137,987,true⟩, +⟨1,138,987,true⟩, +⟨1,139,987,true⟩, +⟨1,140,987,true⟩, +⟨1,141,987,true⟩, +⟨1,142,987,true⟩, +⟨1,143,987,true⟩, +⟨1,144,987,true⟩, +⟨1,145,987,true⟩, +⟨1,146,987,true⟩, +⟨1,147,987,true⟩, +⟨1,148,987,true⟩, +⟨1,149,987,true⟩, +⟨1,150,987,true⟩, +⟨1,151,987,true⟩, +⟨1,168,987,true⟩, +⟨1,169,987,true⟩, +⟨1,170,987,true⟩, +⟨1,171,987,true⟩, +⟨1,172,987,true⟩, +⟨1,173,987,true⟩, +⟨1,174,987,true⟩, +⟨1,175,987,true⟩, +⟨1,176,987,true⟩, +⟨1,177,987,true⟩, +⟨1,178,987,true⟩, +⟨1,179,987,true⟩, +⟨1,180,987,true⟩] +def chunk70 : List Event := [⟨1,181,987,true⟩, +⟨1,182,987,true⟩, +⟨1,183,987,true⟩, +⟨1,200,987,true⟩, +⟨1,201,987,true⟩, +⟨1,202,987,true⟩, +⟨1,203,987,true⟩, +⟨1,204,987,true⟩, +⟨1,205,987,true⟩, +⟨1,206,987,true⟩, +⟨1,207,987,true⟩, +⟨1,208,987,true⟩, +⟨1,209,987,true⟩, +⟨1,210,987,true⟩, +⟨1,211,987,true⟩, +⟨1,212,987,true⟩, +⟨1,213,987,true⟩, +⟨1,214,987,true⟩, +⟨1,215,987,true⟩, +⟨1,232,987,true⟩, +⟨1,233,987,true⟩, +⟨1,234,987,true⟩, +⟨1,235,987,true⟩, +⟨1,236,987,true⟩, +⟨1,237,987,true⟩, +⟨1,238,987,true⟩, +⟨1,239,987,true⟩, +⟨3,16,987,true⟩, +⟨2,32,987,true⟩, +⟨1,152,987,true⟩, +⟨1,153,987,true⟩, +⟨1,154,987,true⟩, +⟨1,155,987,true⟩, +⟨1,156,987,true⟩, +⟨1,157,987,true⟩, +⟨1,158,987,true⟩, +⟨1,159,987,true⟩, +⟨1,160,987,true⟩, +⟨1,161,987,true⟩, +⟨1,162,987,true⟩, +⟨1,163,987,true⟩, +⟨1,164,987,true⟩, +⟨1,165,987,true⟩, +⟨1,166,987,true⟩, +⟨1,167,987,true⟩, +⟨1,168,987,true⟩, +⟨1,169,987,true⟩, +⟨1,170,987,true⟩, +⟨1,171,987,true⟩, +⟨1,172,987,true⟩, +⟨1,173,987,true⟩, +⟨1,174,987,true⟩, +⟨1,175,987,true⟩, +⟨1,176,987,true⟩, +⟨1,177,987,true⟩, +⟨1,178,987,true⟩, +⟨1,179,987,true⟩, +⟨1,180,987,true⟩, +⟨1,181,987,true⟩, +⟨1,182,987,true⟩, +⟨1,183,987,true⟩, +⟨1,216,987,true⟩, +⟨1,217,987,true⟩, +⟨1,218,987,true⟩, +⟨1,219,987,true⟩, +⟨1,220,987,true⟩, +⟨1,221,987,true⟩, +⟨1,222,987,true⟩, +⟨1,223,987,true⟩, +⟨1,224,987,true⟩, +⟨1,225,987,true⟩, +⟨1,226,987,true⟩, +⟨1,227,987,true⟩, +⟨1,228,987,true⟩, +⟨1,229,987,true⟩, +⟨1,230,987,true⟩, +⟨1,231,987,true⟩, +⟨1,232,987,true⟩, +⟨1,233,987,true⟩, +⟨1,234,987,true⟩, +⟨1,235,987,true⟩, +⟨1,236,987,true⟩, +⟨1,237,987,true⟩, +⟨1,238,987,true⟩, +⟨1,239,987,true⟩, +⟨3,32,987,true⟩, +⟨2,64,987,true⟩, +⟨1,184,987,true⟩, +⟨1,185,987,true⟩, +⟨1,186,987,true⟩, +⟨1,187,987,true⟩, +⟨1,188,987,true⟩, +⟨1,189,987,true⟩, +⟨1,190,987,true⟩, +⟨1,191,987,true⟩, +⟨1,192,987,true⟩, +⟨1,193,987,true⟩, +⟨1,194,987,true⟩, +⟨1,195,987,true⟩, +⟨1,196,987,true⟩, +⟨1,197,987,true⟩, +⟨1,198,987,true⟩, +⟨1,199,987,true⟩, +⟨1,200,987,true⟩, +⟨1,201,987,true⟩, +⟨1,202,987,true⟩, +⟨1,203,987,true⟩, +⟨1,204,987,true⟩, +⟨1,205,987,true⟩, +⟨1,206,987,true⟩, +⟨1,207,987,true⟩, +⟨1,208,987,true⟩, +⟨1,209,987,true⟩, +⟨1,210,987,true⟩, +⟨1,211,987,true⟩, +⟨1,212,987,true⟩, +⟨1,213,987,true⟩, +⟨1,214,987,true⟩, +⟨1,215,987,true⟩, +⟨1,216,987,true⟩, +⟨1,217,987,true⟩, +⟨1,218,987,true⟩, +⟨1,219,987,true⟩, +⟨1,220,987,true⟩, +⟨1,221,987,true⟩, +⟨1,222,987,true⟩, +⟨1,223,987,true⟩, +⟨1,224,987,true⟩, +⟨1,225,987,true⟩, +⟨1,226,987,true⟩, +⟨1,227,987,true⟩, +⟨1,228,987,true⟩, +⟨1,229,987,true⟩, +⟨1,230,987,true⟩, +⟨1,231,987,true⟩, +⟨1,232,987,true⟩, +⟨1,233,987,true⟩, +⟨1,234,987,true⟩, +⟨1,235,987,true⟩, +⟨1,236,987,true⟩, +⟨1,237,987,true⟩, +⟨1,238,987,true⟩, +⟨1,239,987,true⟩, +⟨3,64,987,true⟩, +⟨1,16,0,true⟩, +⟨1,32,0,true⟩, +⟨1,64,0,true⟩, +⟨1,1,9,true⟩, +⟨1,9,1,true⟩, +⟨1,1,9,true⟩, +⟨1,0,1,true⟩, +⟨1,16,1,true⟩, +⟨1,2,16,true⟩, +⟨1,16,2,true⟩, +⟨1,2,16,true⟩, +⟨1,1,2,true⟩, +⟨1,32,2,true⟩, +⟨1,0,3,true⟩, +⟨1,1,3,true⟩, +⟨1,2,3,true⟩, +⟨1,4,32,true⟩, +⟨1,32,4,true⟩, +⟨1,4,32,true⟩, +⟨1,2,4,true⟩, +⟨1,64,4,true⟩, +⟨1,0,5,true⟩, +⟨1,1,5,true⟩, +⟨1,4,5,true⟩, +⟨1,0,6,true⟩, +⟨1,2,6,true⟩, +⟨1,4,6,true⟩, +⟨1,1,7,true⟩, +⟨1,2,7,true⟩, +⟨1,4,7,true⟩, +⟨1,0,8,true⟩, +⟨1,16,8,true⟩, +⟨1,32,8,true⟩, +⟨1,9,64,true⟩, +⟨1,64,9,true⟩, +⟨1,9,64,true⟩, +⟨1,0,9,true⟩, +⟨1,4,9,true⟩, +⟨1,8,9,true⟩, +⟨1,1,10,true⟩, +⟨1,2,10,true⟩, +⟨1,9,10,true⟩, +⟨1,1,11,true⟩, +⟨1,2,11,true⟩, +⟨1,8,11,true⟩, +⟨1,1,12,true⟩, +⟨1,4,12,true⟩, +⟨1,9,12,true⟩, +⟨1,1,13,true⟩, +⟨1,4,13,true⟩, +⟨1,8,13,true⟩, +⟨1,2,14,true⟩, +⟨1,4,14,true⟩, +⟨1,8,14,true⟩, +⟨1,2,15,true⟩, +⟨1,4,15,true⟩] +def chunk71 : List Event := [⟨1,9,15,true⟩, +⟨1,0,16,true⟩, +⟨1,1,16,true⟩, +⟨1,8,16,true⟩, +⟨1,64,16,true⟩, +⟨1,0,17,true⟩, +⟨1,1,17,true⟩, +⟨1,8,17,true⟩, +⟨1,9,17,true⟩, +⟨1,16,17,true⟩, +⟨1,1,18,true⟩, +⟨1,2,18,true⟩, +⟨1,8,18,true⟩, +⟨1,9,18,true⟩, +⟨1,16,18,true⟩, +⟨1,0,19,true⟩, +⟨1,2,19,true⟩, +⟨1,16,19,true⟩, +⟨1,1,20,true⟩, +⟨1,4,20,true⟩, +⟨1,8,20,true⟩, +⟨1,9,20,true⟩, +⟨1,16,20,true⟩, +⟨1,0,21,true⟩, +⟨1,4,21,true⟩, +⟨1,16,21,true⟩, +⟨1,2,22,true⟩, +⟨1,4,22,true⟩, +⟨1,16,22,true⟩, +⟨1,0,23,true⟩, +⟨1,1,23,true⟩, +⟨1,2,23,true⟩, +⟨1,4,23,true⟩, +⟨1,8,23,true⟩, +⟨1,9,23,true⟩, +⟨1,16,23,true⟩, +⟨1,1,24,true⟩, +⟨1,9,24,true⟩, +⟨1,16,24,true⟩, +⟨1,1,25,true⟩, +⟨1,8,25,true⟩, +⟨1,16,25,true⟩, +⟨1,0,26,true⟩, +⟨1,8,26,true⟩, +⟨1,16,26,true⟩, +⟨1,0,27,true⟩, +⟨1,9,27,true⟩, +⟨1,16,27,true⟩, +⟨1,1,28,true⟩, +⟨1,2,28,true⟩, +⟨1,4,28,true⟩, +⟨1,8,28,true⟩, +⟨1,16,28,true⟩, +⟨1,1,29,true⟩, +⟨1,2,29,true⟩, +⟨1,4,29,true⟩, +⟨1,9,29,true⟩, +⟨1,16,29,true⟩, +⟨1,0,30,true⟩, +⟨1,2,30,true⟩, +⟨1,4,30,true⟩, +⟨1,9,30,true⟩, +⟨1,16,30,true⟩, +⟨1,0,31,true⟩, +⟨1,2,31,true⟩, +⟨1,4,31,true⟩, +⟨1,8,31,true⟩, +⟨1,16,31,true⟩, +⟨1,0,32,true⟩, +⟨1,2,32,true⟩, +⟨1,8,32,true⟩, +⟨1,64,32,true⟩, +⟨1,0,33,true⟩, +⟨1,2,33,true⟩, +⟨1,8,33,true⟩, +⟨1,9,33,true⟩, +⟨1,32,33,true⟩, +⟨1,1,34,true⟩, +⟨1,2,34,true⟩, +⟨1,8,34,true⟩, +⟨1,9,34,true⟩, +⟨1,32,34,true⟩, +⟨1,0,35,true⟩, +⟨1,1,35,true⟩, +⟨1,32,35,true⟩, +⟨1,2,36,true⟩, +⟨1,4,36,true⟩, +⟨1,8,36,true⟩, +⟨1,9,36,true⟩, +⟨1,32,36,true⟩, +⟨1,0,37,true⟩, +⟨1,4,37,true⟩, +⟨1,32,37,true⟩, +⟨1,1,38,true⟩, +⟨1,4,38,true⟩, +⟨1,32,38,true⟩, +⟨1,0,39,true⟩, +⟨1,1,39,true⟩, +⟨1,2,39,true⟩, +⟨1,4,39,true⟩, +⟨1,8,39,true⟩, +⟨1,9,39,true⟩, +⟨1,32,39,true⟩, +⟨1,2,40,true⟩, +⟨1,9,40,true⟩, +⟨1,32,40,true⟩, +⟨1,2,41,true⟩, +⟨1,8,41,true⟩, +⟨1,32,41,true⟩, +⟨1,0,42,true⟩, +⟨1,8,42,true⟩, +⟨1,32,42,true⟩, +⟨1,0,43,true⟩, +⟨1,9,43,true⟩, +⟨1,32,43,true⟩, +⟨1,1,44,true⟩, +⟨1,2,44,true⟩, +⟨1,4,44,true⟩, +⟨1,8,44,true⟩, +⟨1,32,44,true⟩, +⟨1,1,45,true⟩, +⟨1,2,45,true⟩, +⟨1,4,45,true⟩, +⟨1,9,45,true⟩, +⟨1,32,45,true⟩, +⟨1,0,46,true⟩, +⟨1,1,46,true⟩, +⟨1,4,46,true⟩, +⟨1,9,46,true⟩, +⟨1,32,46,true⟩, +⟨1,0,47,true⟩, +⟨1,1,47,true⟩, +⟨1,4,47,true⟩, +⟨1,8,47,true⟩, +⟨1,32,47,true⟩, +⟨1,0,48,true⟩, +⟨1,1,48,true⟩, +⟨1,2,48,true⟩, +⟨1,8,48,true⟩, +⟨1,9,48,true⟩, +⟨1,16,48,true⟩, +⟨1,32,48,true⟩, +⟨1,2,49,true⟩, +⟨1,16,49,true⟩, +⟨1,32,49,true⟩, +⟨1,1,50,true⟩, +⟨1,16,50,true⟩, +⟨1,32,50,true⟩, +⟨1,0,51,true⟩, +⟨1,8,51,true⟩, +⟨1,9,51,true⟩, +⟨1,16,51,true⟩, +⟨1,32,51,true⟩, +⟨1,0,52,true⟩, +⟨1,2,52,true⟩, +⟨1,4,52,true⟩, +⟨1,16,52,true⟩, +⟨1,32,52,true⟩, +⟨1,1,53,true⟩, +⟨1,2,53,true⟩, +⟨1,4,53,true⟩, +⟨1,8,53,true⟩, +⟨1,9,53,true⟩, +⟨1,16,53,true⟩, +⟨1,32,53,true⟩, +⟨1,4,54,true⟩, +⟨1,8,54,true⟩, +⟨1,9,54,true⟩, +⟨1,16,54,true⟩, +⟨1,32,54,true⟩, +⟨1,0,55,true⟩, +⟨1,1,55,true⟩, +⟨1,4,55,true⟩, +⟨1,16,55,true⟩, +⟨1,32,55,true⟩, +⟨1,0,56,true⟩, +⟨1,1,56,true⟩, +⟨1,2,56,true⟩, +⟨1,4,56,true⟩, +⟨1,8,56,true⟩, +⟨1,16,56,true⟩, +⟨1,32,56,true⟩, +⟨1,0,57,true⟩, +⟨1,1,57,true⟩, +⟨1,2,57,true⟩, +⟨1,4,57,true⟩, +⟨1,9,57,true⟩, +⟨1,16,57,true⟩, +⟨1,32,57,true⟩, +⟨1,2,58,true⟩, +⟨1,4,58,true⟩, +⟨1,9,58,true⟩, +⟨1,16,58,true⟩, +⟨1,32,58,true⟩, +⟨1,2,59,true⟩, +⟨1,4,59,true⟩, +⟨1,8,59,true⟩, +⟨1,16,59,true⟩, +⟨1,32,59,true⟩, +⟨1,1,60,true⟩] +def chunk72 : List Event := [⟨1,4,60,true⟩, +⟨1,9,60,true⟩, +⟨1,16,60,true⟩, +⟨1,32,60,true⟩, +⟨1,1,61,true⟩, +⟨1,4,61,true⟩, +⟨1,8,61,true⟩, +⟨1,16,61,true⟩, +⟨1,32,61,true⟩, +⟨1,0,62,true⟩, +⟨1,4,62,true⟩, +⟨1,8,62,true⟩, +⟨1,16,62,true⟩, +⟨1,32,62,true⟩, +⟨1,0,63,true⟩, +⟨1,4,63,true⟩, +⟨1,9,63,true⟩, +⟨1,16,63,true⟩, +⟨1,32,63,true⟩, +⟨1,1,64,true⟩, +⟨1,2,64,true⟩, +⟨1,4,64,true⟩, +⟨1,16,64,true⟩, +⟨1,32,64,true⟩, +⟨1,0,65,true⟩, +⟨1,4,65,true⟩, +⟨1,8,65,true⟩, +⟨1,9,65,true⟩, +⟨1,64,65,true⟩, +⟨1,1,66,true⟩, +⟨1,4,66,true⟩, +⟨1,8,66,true⟩, +⟨1,9,66,true⟩, +⟨1,64,66,true⟩, +⟨1,0,67,true⟩, +⟨1,1,67,true⟩, +⟨1,64,67,true⟩, +⟨1,2,68,true⟩, +⟨1,4,68,true⟩, +⟨1,8,68,true⟩, +⟨1,9,68,true⟩, +⟨1,64,68,true⟩, +⟨1,0,69,true⟩, +⟨1,2,69,true⟩, +⟨1,64,69,true⟩, +⟨1,1,70,true⟩, +⟨1,2,70,true⟩, +⟨1,64,70,true⟩, +⟨1,0,71,true⟩, +⟨1,1,71,true⟩, +⟨1,2,71,true⟩, +⟨1,4,71,true⟩, +⟨1,8,71,true⟩, +⟨1,9,71,true⟩, +⟨1,64,71,true⟩, +⟨1,4,72,true⟩, +⟨1,9,72,true⟩, +⟨1,64,72,true⟩, +⟨1,4,73,true⟩, +⟨1,8,73,true⟩, +⟨1,64,73,true⟩, +⟨1,1,74,true⟩, +⟨1,2,74,true⟩, +⟨1,4,74,true⟩, +⟨1,8,74,true⟩, +⟨1,64,74,true⟩, +⟨1,1,75,true⟩, +⟨1,2,75,true⟩, +⟨1,4,75,true⟩, +⟨1,9,75,true⟩, +⟨1,64,75,true⟩, +⟨1,0,76,true⟩, +⟨1,8,76,true⟩, +⟨1,64,76,true⟩, +⟨1,0,77,true⟩, +⟨1,9,77,true⟩, +⟨1,64,77,true⟩, +⟨1,0,78,true⟩, +⟨1,1,78,true⟩, +⟨1,2,78,true⟩, +⟨1,9,78,true⟩, +⟨1,64,78,true⟩, +⟨1,0,79,true⟩, +⟨1,1,79,true⟩, +⟨1,2,79,true⟩, +⟨1,8,79,true⟩, +⟨1,64,79,true⟩, +⟨1,0,80,true⟩, +⟨1,1,80,true⟩, +⟨1,4,80,true⟩, +⟨1,8,80,true⟩, +⟨1,9,80,true⟩, +⟨1,16,80,true⟩, +⟨1,64,80,true⟩, +⟨1,4,81,true⟩, +⟨1,16,81,true⟩, +⟨1,64,81,true⟩, +⟨1,0,82,true⟩, +⟨1,2,82,true⟩, +⟨1,4,82,true⟩, +⟨1,16,82,true⟩, +⟨1,64,82,true⟩, +⟨1,1,83,true⟩, +⟨1,2,83,true⟩, +⟨1,4,83,true⟩, +⟨1,8,83,true⟩, +⟨1,9,83,true⟩, +⟨1,16,83,true⟩, +⟨1,64,83,true⟩, +⟨1,1,84,true⟩, +⟨1,16,84,true⟩, +⟨1,64,84,true⟩, +⟨1,0,85,true⟩, +⟨1,8,85,true⟩, +⟨1,9,85,true⟩, +⟨1,16,85,true⟩, +⟨1,64,85,true⟩, +⟨1,2,86,true⟩, +⟨1,8,86,true⟩, +⟨1,9,86,true⟩, +⟨1,16,86,true⟩, +⟨1,64,86,true⟩, +⟨1,0,87,true⟩, +⟨1,1,87,true⟩, +⟨1,2,87,true⟩, +⟨1,16,87,true⟩, +⟨1,64,87,true⟩, +⟨1,0,88,true⟩, +⟨1,1,88,true⟩, +⟨1,2,88,true⟩, +⟨1,4,88,true⟩, +⟨1,8,88,true⟩, +⟨1,16,88,true⟩, +⟨1,64,88,true⟩, +⟨1,0,89,true⟩, +⟨1,1,89,true⟩, +⟨1,2,89,true⟩, +⟨1,4,89,true⟩, +⟨1,9,89,true⟩, +⟨1,16,89,true⟩, +⟨1,64,89,true⟩, +⟨1,2,90,true⟩, +⟨1,4,90,true⟩, +⟨1,9,90,true⟩, +⟨1,16,90,true⟩, +⟨1,64,90,true⟩, +⟨1,2,91,true⟩, +⟨1,4,91,true⟩, +⟨1,8,91,true⟩, +⟨1,16,91,true⟩, +⟨1,64,91,true⟩, +⟨1,1,92,true⟩, +⟨1,2,92,true⟩, +⟨1,9,92,true⟩, +⟨1,16,92,true⟩, +⟨1,64,92,true⟩, +⟨1,1,93,true⟩, +⟨1,2,93,true⟩, +⟨1,8,93,true⟩, +⟨1,16,93,true⟩, +⟨1,64,93,true⟩, +⟨1,0,94,true⟩, +⟨1,2,94,true⟩, +⟨1,8,94,true⟩, +⟨1,16,94,true⟩, +⟨1,64,94,true⟩, +⟨1,0,95,true⟩, +⟨1,2,95,true⟩, +⟨1,9,95,true⟩, +⟨1,16,95,true⟩, +⟨1,64,95,true⟩, +⟨1,0,96,true⟩, +⟨1,2,96,true⟩, +⟨1,4,96,true⟩, +⟨1,8,96,true⟩, +⟨1,9,96,true⟩, +⟨1,32,96,true⟩, +⟨1,64,96,true⟩, +⟨1,4,97,true⟩, +⟨1,32,97,true⟩, +⟨1,64,97,true⟩, +⟨1,0,98,true⟩, +⟨1,1,98,true⟩, +⟨1,4,98,true⟩, +⟨1,32,98,true⟩, +⟨1,64,98,true⟩, +⟨1,1,99,true⟩, +⟨1,2,99,true⟩, +⟨1,4,99,true⟩, +⟨1,8,99,true⟩, +⟨1,9,99,true⟩, +⟨1,32,99,true⟩, +⟨1,64,99,true⟩, +⟨1,2,100,true⟩, +⟨1,32,100,true⟩, +⟨1,64,100,true⟩, +⟨1,0,101,true⟩, +⟨1,8,101,true⟩, +⟨1,9,101,true⟩, +⟨1,32,101,true⟩] +def chunk73 : List Event := [⟨1,64,101,true⟩, +⟨1,1,102,true⟩, +⟨1,8,102,true⟩, +⟨1,9,102,true⟩, +⟨1,32,102,true⟩, +⟨1,64,102,true⟩, +⟨1,0,103,true⟩, +⟨1,1,103,true⟩, +⟨1,2,103,true⟩, +⟨1,32,103,true⟩, +⟨1,64,103,true⟩, +⟨1,0,104,true⟩, +⟨1,1,104,true⟩, +⟨1,2,104,true⟩, +⟨1,4,104,true⟩, +⟨1,8,104,true⟩, +⟨1,32,104,true⟩, +⟨1,64,104,true⟩, +⟨1,0,105,true⟩, +⟨1,1,105,true⟩, +⟨1,2,105,true⟩, +⟨1,4,105,true⟩, +⟨1,9,105,true⟩, +⟨1,32,105,true⟩, +⟨1,64,105,true⟩, +⟨1,1,106,true⟩, +⟨1,4,106,true⟩, +⟨1,9,106,true⟩, +⟨1,32,106,true⟩, +⟨1,64,106,true⟩, +⟨1,1,107,true⟩, +⟨1,4,107,true⟩, +⟨1,8,107,true⟩, +⟨1,32,107,true⟩, +⟨1,64,107,true⟩, +⟨1,1,108,true⟩, +⟨1,2,108,true⟩, +⟨1,9,108,true⟩, +⟨1,32,108,true⟩, +⟨1,64,108,true⟩, +⟨1,1,109,true⟩, +⟨1,2,109,true⟩, +⟨1,8,109,true⟩, +⟨1,32,109,true⟩, +⟨1,64,109,true⟩, +⟨1,0,110,true⟩, +⟨1,1,110,true⟩, +⟨1,8,110,true⟩, +⟨1,32,110,true⟩, +⟨1,64,110,true⟩, +⟨1,0,111,true⟩, +⟨1,1,111,true⟩, +⟨1,9,111,true⟩, +⟨1,32,111,true⟩, +⟨1,64,111,true⟩, +⟨1,0,112,true⟩, +⟨1,1,112,true⟩, +⟨1,2,112,true⟩, +⟨1,4,112,true⟩, +⟨1,16,112,true⟩, +⟨1,32,112,true⟩, +⟨1,64,112,true⟩, +⟨1,2,113,true⟩, +⟨1,4,113,true⟩, +⟨1,8,113,true⟩, +⟨1,9,113,true⟩, +⟨1,16,113,true⟩, +⟨1,32,113,true⟩, +⟨1,64,113,true⟩, +⟨1,1,114,true⟩, +⟨1,4,114,true⟩, +⟨1,8,114,true⟩, +⟨1,9,114,true⟩, +⟨1,16,114,true⟩, +⟨1,32,114,true⟩, +⟨1,64,114,true⟩, +⟨1,0,115,true⟩, +⟨1,4,115,true⟩, +⟨1,16,115,true⟩, +⟨1,32,115,true⟩, +⟨1,64,115,true⟩, +⟨1,1,116,true⟩, +⟨1,2,116,true⟩, +⟨1,8,116,true⟩, +⟨1,9,116,true⟩, +⟨1,16,116,true⟩, +⟨1,32,116,true⟩, +⟨1,64,116,true⟩, +⟨1,0,117,true⟩, +⟨1,2,117,true⟩, +⟨1,16,117,true⟩, +⟨1,32,117,true⟩, +⟨1,64,117,true⟩, +⟨1,0,118,true⟩, +⟨1,1,118,true⟩, +⟨1,16,118,true⟩, +⟨1,32,118,true⟩, +⟨1,64,118,true⟩, +⟨1,8,119,true⟩, +⟨1,9,119,true⟩, +⟨1,16,119,true⟩, +⟨1,32,119,true⟩, +⟨1,64,119,true⟩, +⟨0,125,0,false⟩, +⟨1,125,523,true⟩, +⟨0,127,0,false⟩, +⟨1,127,523,true⟩, +⟨0,176,0,false⟩, +⟨1,176,523,true⟩, +⟨0,177,0,false⟩, +⟨1,177,523,true⟩, +⟨0,178,0,false⟩, +⟨1,178,523,true⟩, +⟨0,179,0,false⟩, +⟨1,179,523,true⟩, +⟨0,180,0,true⟩, +⟨0,523,458,true⟩, +⟨1,180,523,true⟩, +⟨0,181,0,true⟩, +⟨1,181,523,true⟩, +⟨0,182,0,true⟩, +⟨1,182,523,true⟩, +⟨0,183,0,true⟩, +⟨0,523,515,true⟩, +⟨1,183,523,true⟩, +⟨0,122,0,true⟩, +⟨1,122,240,true⟩, +⟨0,123,0,true⟩, +⟨1,123,240,true⟩, +⟨0,208,0,true⟩, +⟨1,208,240,true⟩, +⟨0,209,0,true⟩, +⟨1,209,240,true⟩, +⟨0,210,0,true⟩, +⟨1,210,240,true⟩, +⟨0,211,0,true⟩, +⟨1,211,240,true⟩, +⟨0,212,0,true⟩, +⟨0,240,459,true⟩, +⟨1,212,240,true⟩, +⟨0,213,0,true⟩, +⟨1,213,240,true⟩, +⟨0,214,0,true⟩, +⟨1,214,240,true⟩, +⟨0,215,0,true⟩, +⟨0,240,493,true⟩, +⟨1,215,240,true⟩, +⟨0,216,0,false⟩, +⟨1,216,241,true⟩, +⟨0,217,0,false⟩, +⟨1,217,241,true⟩, +⟨0,218,0,false⟩, +⟨1,218,241,true⟩, +⟨0,219,0,false⟩, +⟨1,219,241,true⟩, +⟨0,220,0,false⟩, +⟨0,241,460,false⟩, +⟨1,220,241,true⟩, +⟨0,221,0,false⟩, +⟨1,221,241,true⟩, +⟨0,222,0,false⟩, +⟨1,222,241,true⟩, +⟨0,223,0,true⟩, +⟨0,241,492,true⟩, +⟨1,223,241,true⟩, +⟨0,224,0,true⟩, +⟨1,224,242,true⟩, +⟨0,225,0,true⟩, +⟨1,225,242,true⟩, +⟨0,226,0,true⟩, +⟨1,226,242,true⟩, +⟨0,227,0,true⟩, +⟨1,227,242,true⟩, +⟨0,228,0,true⟩, +⟨0,242,461,true⟩, +⟨1,228,242,true⟩, +⟨0,229,0,true⟩, +⟨1,229,242,true⟩, +⟨0,230,0,true⟩, +⟨1,230,242,true⟩, +⟨0,231,0,true⟩, +⟨0,242,489,true⟩, +⟨1,231,242,true⟩, +⟨0,126,0,false⟩, +⟨1,126,243,true⟩, +⟨0,200,0,false⟩, +⟨1,200,243,true⟩, +⟨0,201,0,false⟩, +⟨1,201,243,true⟩, +⟨0,202,0,false⟩, +⟨1,202,243,true⟩, +⟨0,203,0,false⟩, +⟨1,203,243,true⟩, +⟨0,204,0,false⟩, +⟨0,243,462,false⟩, +⟨1,204,243,true⟩, +⟨0,205,0,false⟩, +⟨1,205,243,true⟩, +⟨0,206,0,false⟩, +⟨1,206,243,true⟩] +def chunk74 : List Event := [⟨0,207,0,true⟩, +⟨0,243,488,true⟩, +⟨1,207,243,true⟩, +⟨0,168,0,true⟩, +⟨1,168,244,true⟩, +⟨0,169,0,true⟩, +⟨1,169,244,true⟩, +⟨0,170,0,true⟩, +⟨1,170,244,true⟩, +⟨0,171,0,true⟩, +⟨1,171,244,true⟩, +⟨0,172,0,true⟩, +⟨0,244,463,true⟩, +⟨1,172,244,true⟩, +⟨0,173,0,true⟩, +⟨1,173,244,true⟩, +⟨0,174,0,true⟩, +⟨1,174,244,true⟩, +⟨0,175,0,true⟩, +⟨0,244,485,true⟩, +⟨1,175,244,true⟩, +⟨0,121,0,false⟩, +⟨1,121,245,true⟩, +⟨0,124,0,false⟩, +⟨1,124,245,true⟩, +⟨0,128,0,false⟩, +⟨1,128,245,true⟩, +⟨0,129,0,false⟩, +⟨1,129,245,true⟩, +⟨0,130,0,false⟩, +⟨1,130,245,true⟩, +⟨0,131,0,false⟩, +⟨1,131,245,true⟩, +⟨0,132,0,false⟩, +⟨0,245,464,false⟩, +⟨1,132,245,true⟩, +⟨0,133,0,false⟩, +⟨1,133,245,true⟩, +⟨0,134,0,false⟩, +⟨1,134,245,true⟩, +⟨0,135,0,true⟩, +⟨0,245,484,true⟩, +⟨1,135,245,true⟩, +⟨0,232,0,true⟩, +⟨1,232,248,true⟩, +⟨0,233,0,true⟩, +⟨1,233,248,true⟩, +⟨0,234,0,true⟩, +⟨1,234,248,true⟩, +⟨0,235,0,true⟩, +⟨1,235,248,true⟩, +⟨0,236,0,true⟩, +⟨0,248,465,true⟩, +⟨1,236,248,true⟩, +⟨0,237,0,true⟩, +⟨1,237,248,true⟩, +⟨0,238,0,true⟩, +⟨1,238,248,true⟩, +⟨0,239,0,true⟩, +⟨0,248,481,true⟩, +⟨1,239,248,true⟩, +⟨0,192,0,false⟩, +⟨1,192,249,true⟩, +⟨0,193,0,false⟩, +⟨1,193,249,true⟩, +⟨0,194,0,false⟩, +⟨1,194,249,true⟩, +⟨0,195,0,false⟩, +⟨1,195,249,true⟩, +⟨0,196,0,false⟩, +⟨0,249,466,false⟩, +⟨1,196,249,true⟩, +⟨0,197,0,false⟩, +⟨1,197,249,true⟩, +⟨0,198,0,false⟩, +⟨1,198,249,true⟩, +⟨0,199,0,true⟩, +⟨0,249,480,true⟩, +⟨1,199,249,true⟩, +⟨0,160,0,true⟩, +⟨1,160,250,true⟩, +⟨0,161,0,true⟩, +⟨1,161,250,true⟩, +⟨0,162,0,true⟩, +⟨1,162,250,true⟩, +⟨0,163,0,true⟩, +⟨1,163,250,true⟩, +⟨0,164,0,true⟩, +⟨0,250,467,true⟩, +⟨1,164,250,true⟩, +⟨0,165,0,true⟩, +⟨1,165,250,true⟩, +⟨0,166,0,true⟩, +⟨1,166,250,true⟩, +⟨0,167,0,true⟩, +⟨0,250,477,true⟩, +⟨1,167,250,true⟩, +⟨0,120,0,false⟩, +⟨1,120,251,true⟩, +⟨0,136,0,false⟩, +⟨1,136,251,true⟩, +⟨0,137,0,false⟩, +⟨1,137,251,true⟩, +⟨0,138,0,false⟩, +⟨1,138,251,true⟩, +⟨0,139,0,false⟩, +⟨1,139,251,true⟩, +⟨0,140,0,false⟩, +⟨0,251,468,false⟩, +⟨1,140,251,true⟩, +⟨0,141,0,false⟩, +⟨1,141,251,true⟩, +⟨0,142,0,false⟩, +⟨1,142,251,true⟩, +⟨0,143,0,true⟩, +⟨0,251,476,true⟩, +⟨1,143,251,true⟩, +⟨0,144,0,true⟩, +⟨1,144,256,true⟩, +⟨0,145,0,true⟩, +⟨1,145,256,true⟩, +⟨0,146,0,true⟩, +⟨1,146,256,true⟩, +⟨0,147,0,true⟩, +⟨1,147,256,true⟩, +⟨0,148,0,true⟩, +⟨0,256,469,true⟩, +⟨1,148,256,true⟩, +⟨0,149,0,true⟩, +⟨1,149,256,true⟩, +⟨0,150,0,true⟩, +⟨1,150,256,true⟩, +⟨0,151,0,true⟩, +⟨0,256,473,true⟩, +⟨1,151,256,true⟩, +⟨0,152,0,false⟩, +⟨1,152,257,true⟩, +⟨0,153,0,false⟩, +⟨1,153,257,true⟩, +⟨0,154,0,false⟩, +⟨1,154,257,true⟩, +⟨0,155,0,false⟩, +⟨1,155,257,true⟩, +⟨0,156,0,false⟩, +⟨0,257,470,false⟩, +⟨1,156,257,true⟩, +⟨0,157,0,false⟩, +⟨1,157,257,true⟩, +⟨0,158,0,false⟩, +⟨1,158,257,true⟩, +⟨0,159,0,true⟩, +⟨0,257,472,true⟩, +⟨1,159,257,true⟩, +⟨0,184,0,true⟩, +⟨1,184,269,true⟩, +⟨0,185,0,true⟩, +⟨1,185,269,true⟩, +⟨0,186,0,true⟩, +⟨1,186,269,true⟩, +⟨0,187,0,true⟩, +⟨1,187,269,true⟩, +⟨0,188,0,false⟩, +⟨0,269,471,false⟩, +⟨1,188,269,true⟩, +⟨0,189,0,false⟩, +⟨1,189,269,true⟩, +⟨0,190,0,false⟩, +⟨1,190,269,true⟩, +⟨0,191,0,true⟩, +⟨0,269,496,true⟩, +⟨1,191,269,true⟩, +⟨0,217,460,false⟩, +⟨1,217,529,true⟩, +⟨0,218,460,false⟩, +⟨1,218,529,true⟩, +⟨0,221,492,true⟩, +⟨0,529,514,true⟩, +⟨1,221,529,true⟩, +⟨0,222,492,true⟩, +⟨1,222,529,true⟩, +⟨0,216,460,false⟩, +⟨1,216,531,true⟩, +⟨0,219,460,false⟩, +⟨1,219,531,true⟩, +⟨0,220,492,true⟩, +⟨0,531,516,true⟩, +⟨1,220,531,true⟩, +⟨0,531,783,true⟩, +⟨1,223,531,true⟩, +⟨0,209,459,false⟩, +⟨1,209,545,true⟩, +⟨0,210,459,false⟩, +⟨1,210,545,true⟩, +⟨0,213,493,true⟩, +⟨0,545,534,true⟩, +⟨1,213,545,true⟩, +⟨0,214,493,true⟩, +⟨1,214,545,true⟩, +⟨0,177,458,true⟩, +⟨1,177,776,true⟩] +def chunk75 : List Event := [⟨0,178,458,true⟩, +⟨1,178,776,true⟩, +⟨0,181,515,true⟩, +⟨0,776,535,true⟩, +⟨1,181,776,true⟩, +⟨0,182,515,true⟩, +⟨1,182,776,true⟩, +⟨0,208,459,false⟩, +⟨1,208,547,true⟩, +⟨0,211,459,false⟩, +⟨1,211,547,true⟩, +⟨0,212,493,true⟩, +⟨0,547,536,true⟩, +⟨1,212,547,true⟩, +⟨0,547,795,true⟩, +⟨1,215,547,true⟩, +⟨0,176,458,true⟩, +⟨1,176,777,true⟩, +⟨0,179,458,true⟩, +⟨1,179,777,true⟩, +⟨0,180,515,true⟩, +⟨0,777,537,true⟩, +⟨1,180,777,true⟩, +⟨0,777,807,true⟩, +⟨1,183,777,true⟩, +⟨0,201,462,false⟩, +⟨1,201,561,true⟩, +⟨0,202,462,false⟩, +⟨1,202,561,true⟩, +⟨0,205,488,true⟩, +⟨0,561,552,true⟩, +⟨1,205,561,true⟩, +⟨0,206,488,true⟩, +⟨1,206,561,true⟩, +⟨0,200,462,false⟩, +⟨1,200,563,true⟩, +⟨0,203,462,false⟩, +⟨1,203,563,true⟩, +⟨0,204,488,true⟩, +⟨0,563,554,true⟩, +⟨1,204,563,true⟩, +⟨0,563,759,true⟩, +⟨1,207,563,true⟩, +⟨0,225,461,false⟩, +⟨1,225,577,true⟩, +⟨0,226,461,false⟩, +⟨1,226,577,true⟩, +⟨0,229,489,true⟩, +⟨0,577,568,true⟩, +⟨1,229,577,true⟩, +⟨0,230,489,true⟩, +⟨1,230,577,true⟩, +⟨0,224,461,false⟩, +⟨1,224,579,true⟩, +⟨0,227,461,false⟩, +⟨1,227,579,true⟩, +⟨0,228,489,true⟩, +⟨0,579,570,true⟩, +⟨1,228,579,true⟩, +⟨0,579,771,true⟩, +⟨1,231,579,true⟩, +⟨0,129,464,false⟩, +⟨1,129,593,true⟩, +⟨0,130,464,false⟩, +⟨1,130,593,true⟩, +⟨0,133,484,true⟩, +⟨0,593,574,true⟩, +⟨1,133,593,true⟩, +⟨0,134,484,true⟩, +⟨1,134,593,true⟩, +⟨0,128,464,false⟩, +⟨1,128,595,true⟩, +⟨0,131,464,false⟩, +⟨1,131,595,true⟩, +⟨0,132,484,true⟩, +⟨0,595,576,true⟩, +⟨1,132,595,true⟩, +⟨0,595,735,true⟩, +⟨1,135,595,true⟩, +⟨0,169,463,false⟩, +⟨1,169,609,true⟩, +⟨0,170,463,false⟩, +⟨1,170,609,true⟩, +⟨0,173,485,true⟩, +⟨0,609,586,true⟩, +⟨1,173,609,true⟩, +⟨0,174,485,true⟩, +⟨1,174,609,true⟩, +⟨0,168,463,false⟩, +⟨1,168,611,true⟩, +⟨0,171,463,false⟩, +⟨1,171,611,true⟩, +⟨0,172,485,true⟩, +⟨0,611,588,true⟩, +⟨1,172,611,true⟩, +⟨0,611,747,true⟩, +⟨1,175,611,true⟩, +⟨0,193,466,false⟩, +⟨1,193,846,true⟩, +⟨0,194,466,false⟩, +⟨1,194,846,true⟩, +⟨0,197,480,true⟩, +⟨0,846,608,true⟩, +⟨1,197,846,true⟩, +⟨0,198,480,true⟩, +⟨1,198,846,true⟩, +⟨0,192,466,true⟩, +⟨1,192,847,true⟩, +⟨0,195,466,true⟩, +⟨1,195,847,true⟩, +⟨0,196,480,true⟩, +⟨0,847,609,true⟩, +⟨1,196,847,true⟩, +⟨0,847,711,true⟩, +⟨1,199,847,true⟩, +⟨0,233,465,false⟩, +⟨1,233,860,true⟩, +⟨0,234,465,false⟩, +⟨1,234,860,true⟩, +⟨0,237,481,true⟩, +⟨0,860,618,true⟩, +⟨1,237,860,true⟩, +⟨0,238,481,true⟩, +⟨1,238,860,true⟩, +⟨0,232,465,true⟩, +⟨1,232,861,true⟩, +⟨0,235,465,true⟩, +⟨1,235,861,true⟩, +⟨0,236,481,true⟩, +⟨0,861,619,true⟩, +⟨1,236,861,true⟩, +⟨0,861,723,true⟩, +⟨1,239,861,true⟩, +⟨0,137,468,false⟩, +⟨1,137,870,true⟩, +⟨0,138,468,false⟩, +⟨1,138,870,true⟩, +⟨0,141,476,true⟩, +⟨0,870,622,true⟩, +⟨1,141,870,true⟩, +⟨0,142,476,true⟩, +⟨1,142,870,true⟩, +⟨0,136,468,true⟩, +⟨1,136,871,true⟩, +⟨0,139,468,true⟩, +⟨1,139,871,true⟩, +⟨0,140,476,true⟩, +⟨0,871,623,true⟩, +⟨1,140,871,true⟩, +⟨0,871,687,true⟩, +⟨1,143,871,true⟩, +⟨0,161,467,false⟩, +⟨1,161,884,true⟩, +⟨0,162,467,false⟩, +⟨1,162,884,true⟩, +⟨0,165,477,true⟩, +⟨0,884,628,true⟩, +⟨1,165,884,true⟩, +⟨0,166,477,true⟩, +⟨1,166,884,true⟩, +⟨0,160,467,true⟩, +⟨1,160,885,true⟩, +⟨0,163,467,true⟩, +⟨1,163,885,true⟩, +⟨0,164,477,true⟩, +⟨0,885,629,true⟩, +⟨1,164,885,true⟩, +⟨0,885,699,true⟩, +⟨1,167,885,true⟩, +⟨0,185,471,false⟩, +⟨1,185,891,true⟩, +⟨0,186,471,false⟩, +⟨1,186,891,true⟩, +⟨0,189,496,true⟩, +⟨0,891,634,true⟩, +⟨1,189,891,true⟩, +⟨0,190,496,true⟩, +⟨1,190,891,true⟩, +⟨0,184,471,true⟩, +⟨1,184,893,true⟩, +⟨0,187,471,true⟩, +⟨1,187,893,true⟩, +⟨0,188,496,true⟩, +⟨0,893,635,true⟩, +⟨1,188,893,true⟩, +⟨0,893,651,true⟩, +⟨1,191,893,true⟩, +⟨0,153,470,false⟩, +⟨1,153,894,true⟩, +⟨0,154,470,false⟩, +⟨1,154,894,true⟩, +⟨0,157,472,true⟩, +⟨0,894,636,true⟩, +⟨1,157,894,true⟩, +⟨0,158,472,true⟩, +⟨1,158,894,true⟩, +⟨0,152,470,true⟩, +⟨1,152,895,true⟩, +⟨0,155,470,true⟩, +⟨1,155,895,true⟩] +def chunk76 : List Event := [⟨0,156,472,true⟩, +⟨0,895,637,true⟩, +⟨1,156,895,true⟩, +⟨0,895,663,true⟩, +⟨1,159,895,true⟩, +⟨0,145,469,false⟩, +⟨1,145,908,true⟩, +⟨0,146,469,false⟩, +⟨1,146,908,true⟩, +⟨0,149,473,true⟩, +⟨0,908,638,true⟩, +⟨1,149,908,true⟩, +⟨0,150,473,true⟩, +⟨1,150,908,true⟩, +⟨0,144,469,true⟩, +⟨1,144,909,true⟩, +⟨0,147,469,true⟩, +⟨1,147,909,true⟩, +⟨0,148,473,true⟩, +⟨0,909,639,true⟩, +⟨1,148,909,true⟩, +⟨0,909,675,true⟩, +⟨1,151,909,true⟩, +⟨0,184,635,false⟩, +⟨1,184,753,true⟩, +⟨0,187,635,false⟩, +⟨1,187,753,true⟩, +⟨1,189,751,true⟩, +⟨1,190,751,true⟩, +⟨0,185,634,false⟩, +⟨1,185,735,true⟩, +⟨0,186,634,false⟩, +⟨1,186,735,true⟩, +⟨1,188,731,true⟩, +⟨0,731,651,true⟩, +⟨1,191,731,true⟩, +⟨0,152,637,false⟩, +⟨1,152,738,true⟩, +⟨0,155,637,false⟩, +⟨1,155,738,true⟩, +⟨1,157,736,true⟩, +⟨1,158,736,true⟩, +⟨0,153,636,false⟩, +⟨1,153,450,true⟩, +⟨0,154,636,false⟩, +⟨1,154,450,true⟩, +⟨1,156,719,true⟩, +⟨0,719,663,true⟩, +⟨1,159,719,true⟩, +⟨0,144,639,false⟩, +⟨1,144,739,true⟩, +⟨0,147,639,false⟩, +⟨1,147,739,true⟩, +⟨1,149,737,true⟩, +⟨1,150,737,true⟩, +⟨0,145,638,false⟩, +⟨1,145,694,true⟩, +⟨0,146,638,false⟩, +⟨1,146,694,true⟩, +⟨1,148,703,true⟩, +⟨0,703,675,true⟩, +⟨1,151,703,true⟩, +⟨0,136,623,false⟩, +⟨1,136,404,true⟩, +⟨0,139,623,false⟩, +⟨1,139,404,true⟩, +⟨1,141,400,true⟩, +⟨1,142,400,true⟩, +⟨0,137,622,false⟩, +⟨1,137,678,true⟩, +⟨0,138,622,false⟩, +⟨1,138,678,true⟩, +⟨1,140,687,true⟩, +⟨0,687,687,true⟩, +⟨1,143,687,true⟩, +⟨0,160,629,false⟩, +⟨1,160,741,true⟩, +⟨0,163,629,false⟩, +⟨1,163,741,true⟩, +⟨1,165,740,true⟩, +⟨1,166,740,true⟩, +⟨0,161,628,false⟩, +⟨1,161,662,true⟩, +⟨0,162,628,false⟩, +⟨1,162,662,true⟩, +⟨1,164,671,true⟩, +⟨0,671,699,true⟩, +⟨1,167,671,true⟩, +⟨0,192,609,false⟩, +⟨1,192,415,true⟩, +⟨0,195,609,false⟩, +⟨1,195,415,true⟩, +⟨1,197,413,true⟩, +⟨1,198,413,true⟩, +⟨0,193,608,false⟩, +⟨1,193,646,true⟩, +⟨0,194,608,false⟩, +⟨1,194,646,true⟩, +⟨1,196,655,true⟩, +⟨0,655,711,true⟩, +⟨1,199,655,true⟩, +⟨0,232,619,false⟩, +⟨1,232,743,true⟩, +⟨0,235,619,false⟩, +⟨1,235,743,true⟩, +⟨1,237,742,true⟩, +⟨1,238,742,true⟩, +⟨0,233,618,false⟩, +⟨1,233,630,true⟩, +⟨0,234,618,false⟩, +⟨1,234,630,true⟩, +⟨1,236,639,true⟩, +⟨0,639,723,true⟩, +⟨1,239,639,true⟩, +⟨0,128,576,false⟩, +⟨1,128,525,true⟩, +⟨0,131,576,false⟩, +⟨1,131,525,true⟩, +⟨1,133,524,true⟩, +⟨1,134,524,true⟩, +⟨0,129,574,false⟩, +⟨1,129,623,true⟩, +⟨0,130,574,false⟩, +⟨1,130,623,true⟩, +⟨1,132,619,true⟩, +⟨0,619,735,true⟩, +⟨1,135,619,true⟩, +⟨0,168,588,false⟩, +⟨1,168,745,true⟩, +⟨0,171,588,false⟩, +⟨1,171,745,true⟩, +⟨1,173,744,true⟩, +⟨1,174,744,true⟩, +⟨0,169,586,false⟩, +⟨1,169,598,true⟩, +⟨0,170,586,false⟩, +⟨1,170,598,true⟩, +⟨1,172,607,true⟩, +⟨0,607,747,true⟩, +⟨1,175,607,true⟩, +⟨0,200,554,false⟩, +⟨1,200,521,true⟩, +⟨0,203,554,false⟩, +⟨1,203,521,true⟩, +⟨1,205,520,true⟩, +⟨1,206,520,true⟩, +⟨0,201,552,false⟩, +⟨1,201,591,true⟩, +⟨0,202,552,false⟩, +⟨1,202,591,true⟩, +⟨1,204,587,true⟩, +⟨0,587,759,true⟩, +⟨1,207,587,true⟩, +⟨0,224,570,false⟩, +⟨1,224,747,true⟩, +⟨0,227,570,false⟩, +⟨1,227,747,true⟩, +⟨1,229,746,true⟩, +⟨1,230,746,true⟩, +⟨0,225,568,false⟩, +⟨1,225,566,true⟩, +⟨0,226,568,false⟩, +⟨1,226,566,true⟩, +⟨1,228,575,true⟩, +⟨0,575,771,true⟩, +⟨1,231,575,true⟩, +⟨0,216,516,false⟩, +⟨1,216,515,true⟩, +⟨0,219,516,false⟩, +⟨1,219,515,true⟩, +⟨1,221,513,true⟩, +⟨1,222,513,true⟩, +⟨0,217,514,false⟩, +⟨1,217,559,true⟩, +⟨0,218,514,false⟩, +⟨1,218,559,true⟩, +⟨1,220,555,true⟩, +⟨0,555,783,true⟩, +⟨1,223,555,true⟩, +⟨0,208,536,false⟩, +⟨1,208,749,true⟩, +⟨0,211,536,false⟩, +⟨1,211,749,true⟩, +⟨1,213,748,true⟩, +⟨1,214,748,true⟩, +⟨0,209,534,false⟩, +⟨1,209,539,true⟩, +⟨0,210,534,false⟩, +⟨1,210,539,true⟩, +⟨1,212,535,true⟩, +⟨0,535,795,true⟩, +⟨1,215,535,true⟩, +⟨0,176,537,false⟩, +⟨1,176,763,true⟩, +⟨0,179,537,false⟩, +⟨1,179,763,true⟩, +⟨1,181,762,true⟩, +⟨1,182,762,true⟩, +⟨0,177,535,false⟩, +⟨1,177,518,true⟩] +def chunk77 : List Event := [⟨0,178,535,false⟩, +⟨1,178,518,true⟩, +⟨1,180,527,true⟩, +⟨0,527,807,true⟩, +⟨1,183,527,true⟩, +⟨0,120,468,false⟩, +⟨1,120,704,true⟩, +⟨0,121,464,true⟩, +⟨1,121,576,true⟩, +⟨0,124,464,false⟩, +⟨0,576,811,false⟩, +⟨1,124,576,true⟩, +⟨0,122,459,true⟩, +⟨1,122,544,true⟩, +⟨0,123,459,true⟩, +⟨0,544,813,true⟩, +⟨1,123,544,true⟩, +⟨0,125,458,true⟩, +⟨1,125,551,true⟩, +⟨0,126,462,false⟩, +⟨1,126,603,true⟩, +⟨0,127,458,true⟩, +⟨1,127,528,true⟩, +⟨0,688,810,false⟩, +⟨1,120,688,true⟩, +⟨0,266,809,false⟩, +⟨1,120,266,true⟩, +⟨0,121,811,true⟩, +⟨0,560,812,true⟩, +⟨1,121,560,true⟩, +⟨0,907,810,true⟩, +⟨1,121,907,true⟩, +⟨0,122,813,false⟩, +⟨1,122,599,true⟩, +⟨1,122,663,true⟩, +⟨1,123,567,true⟩, +⟨1,123,631,true⟩, +⟨1,124,512,true⟩, +⟨1,124,640,true⟩, +⟨0,624,809,true⟩, +⟨1,125,624,true⟩, +⟨0,592,812,true⟩, +⟨1,125,592,true⟩, +⟨1,126,635,true⟩, +⟨1,126,519,true⟩, +⟨1,127,571,true⟩, +⟨1,127,651,true⟩, +⟨0,128,724,false⟩, +⟨0,295,725,false⟩, +⟨1,128,295,true⟩, +⟨0,585,726,false⟩, +⟨1,128,585,true⟩, +⟨0,129,730,true⟩, +⟨0,293,731,true⟩, +⟨1,129,293,true⟩, +⟨0,937,732,true⟩, +⟨1,129,937,true⟩, +⟨0,130,730,false⟩, +⟨0,938,733,false⟩, +⟨1,130,938,true⟩, +⟨0,291,734,false⟩, +⟨1,130,291,true⟩, +⟨0,131,724,true⟩, +⟨0,584,727,true⟩, +⟨1,131,584,true⟩, +⟨0,289,728,true⟩, +⟨1,131,289,true⟩, +⟨0,132,735,false⟩, +⟨0,932,734,false⟩, +⟨1,132,932,true⟩, +⟨0,302,732,false⟩, +⟨1,132,302,true⟩, +⟨0,133,729,true⟩, +⟨0,300,726,true⟩, +⟨1,133,300,true⟩, +⟨0,572,728,true⟩, +⟨1,133,572,true⟩, +⟨0,134,729,false⟩, +⟨0,298,727,false⟩, +⟨1,134,298,true⟩, +⟨0,573,725,false⟩, +⟨1,134,573,true⟩, +⟨0,933,731,true⟩, +⟨1,135,933,true⟩, +⟨0,296,733,true⟩, +⟨1,135,296,true⟩, +⟨0,136,676,false⟩, +⟨0,311,677,false⟩, +⟨1,136,311,true⟩, +⟨0,857,678,false⟩, +⟨1,136,857,true⟩, +⟨0,137,682,true⟩, +⟨0,966,683,true⟩, +⟨1,137,966,true⟩, +⟨0,308,684,true⟩, +⟨1,137,308,true⟩, +⟨0,138,682,false⟩, +⟨0,306,685,false⟩, +⟨1,138,306,true⟩, +⟨0,965,686,false⟩, +⟨1,138,965,true⟩, +⟨0,139,676,true⟩, +⟨0,856,679,true⟩, +⟨1,139,856,true⟩, +⟨0,305,680,true⟩, +⟨1,139,305,true⟩, +⟨0,140,687,false⟩, +⟨0,973,684,false⟩, +⟨1,140,973,true⟩, +⟨0,319,686,false⟩, +⟨1,140,319,true⟩, +⟨0,141,681,true⟩, +⟨0,316,678,true⟩, +⟨1,141,316,true⟩, +⟨0,842,680,true⟩, +⟨1,141,842,true⟩, +⟨0,142,681,false⟩, +⟨0,314,679,false⟩, +⟨1,142,314,true⟩, +⟨0,843,677,false⟩, +⟨1,142,843,true⟩, +⟨0,974,685,true⟩, +⟨1,143,974,true⟩, +⟨0,313,683,true⟩, +⟨1,143,313,true⟩, +⟨0,144,664,false⟩, +⟨0,327,665,false⟩, +⟨1,144,327,true⟩, +⟨0,841,666,false⟩, +⟨1,144,841,true⟩, +⟨0,145,670,true⟩, +⟨0,972,671,true⟩, +⟨1,145,972,true⟩, +⟨0,324,672,true⟩, +⟨1,145,324,true⟩, +⟨0,146,670,false⟩, +⟨0,322,673,false⟩, +⟨1,146,322,true⟩, +⟨0,971,674,false⟩, +⟨1,146,971,true⟩, +⟨0,147,664,true⟩, +⟨0,840,667,true⟩, +⟨1,147,840,true⟩, +⟨0,321,668,true⟩, +⟨1,147,321,true⟩, +⟨0,148,675,false⟩, +⟨0,963,672,false⟩, +⟨1,148,963,true⟩, +⟨0,335,674,false⟩, +⟨1,148,335,true⟩, +⟨0,149,669,true⟩, +⟨0,854,668,true⟩, +⟨1,149,854,true⟩, +⟨0,332,666,true⟩, +⟨1,149,332,true⟩, +⟨0,150,669,false⟩, +⟨0,855,665,false⟩, +⟨1,150,855,true⟩, +⟨0,330,667,false⟩, +⟨1,150,330,true⟩, +⟨0,964,673,true⟩, +⟨1,151,964,true⟩, +⟨0,329,671,true⟩, +⟨1,151,329,true⟩, +⟨0,152,652,false⟩, +⟨0,839,653,false⟩, +⟨1,152,839,true⟩, +⟨0,342,654,false⟩, +⟨1,152,342,true⟩, +⟨0,153,658,true⟩, +⟨0,962,659,true⟩, +⟨1,153,962,true⟩, +⟨0,340,660,true⟩, +⟨1,153,340,true⟩, +⟨0,154,658,false⟩, +⟨0,338,661,false⟩, +⟨1,154,338,true⟩, +⟨0,961,662,false⟩, +⟨1,154,961,true⟩, +⟨0,155,652,true⟩, +⟨0,336,655,true⟩, +⟨1,155,336,true⟩, +⟨0,838,656,true⟩, +⟨1,155,838,true⟩, +⟨0,156,663,false⟩, +⟨0,969,660,false⟩, +⟨1,156,969,true⟩, +⟨0,351,662,false⟩, +⟨1,156,351,true⟩, +⟨0,157,657,true⟩, +⟨0,853,654,true⟩, +⟨1,157,853,true⟩, +⟨0,349,656,true⟩, +⟨1,157,349,true⟩, +⟨0,158,657,false⟩, +⟨0,852,655,false⟩, +⟨1,158,852,true⟩, +⟨0,347,653,false⟩, +⟨1,158,347,true⟩, +⟨0,970,661,true⟩] +def chunk78 : List Event := [⟨1,159,970,true⟩, +⟨0,345,659,true⟩, +⟨1,159,345,true⟩, +⟨0,160,688,false⟩, +⟨0,359,689,false⟩, +⟨1,160,359,true⟩, +⟨0,845,690,false⟩, +⟨1,160,845,true⟩, +⟨0,161,694,true⟩, +⟨0,357,695,true⟩, +⟨1,161,357,true⟩, +⟨0,967,696,true⟩, +⟨1,161,967,true⟩, +⟨0,162,694,false⟩, +⟨0,355,698,false⟩, +⟨1,162,355,true⟩, +⟨0,968,697,false⟩, +⟨1,162,968,true⟩, +⟨0,163,688,true⟩, +⟨0,844,691,true⟩, +⟨1,163,844,true⟩, +⟨0,353,692,true⟩, +⟨1,163,353,true⟩, +⟨0,164,699,false⟩, +⟨0,975,698,false⟩, +⟨1,164,975,true⟩, +⟨0,366,696,false⟩, +⟨1,164,366,true⟩, +⟨0,165,693,true⟩, +⟨0,858,692,true⟩, +⟨1,165,858,true⟩, +⟨0,364,690,true⟩, +⟨1,165,364,true⟩, +⟨0,166,693,false⟩, +⟨0,859,689,false⟩, +⟨1,166,859,true⟩, +⟨0,362,691,false⟩, +⟨1,166,362,true⟩, +⟨0,360,697,true⟩, +⟨1,167,360,true⟩, +⟨0,976,695,true⟩, +⟨1,167,976,true⟩, +⟨0,168,736,false⟩, +⟨0,375,737,false⟩, +⟨1,168,375,true⟩, +⟨0,569,738,false⟩, +⟨1,168,569,true⟩, +⟨0,169,742,true⟩, +⟨0,940,743,true⟩, +⟨1,169,940,true⟩, +⟨0,372,744,true⟩, +⟨1,169,372,true⟩, +⟨0,170,742,false⟩, +⟨0,370,745,false⟩, +⟨1,170,370,true⟩, +⟨0,939,746,false⟩, +⟨1,170,939,true⟩, +⟨0,171,736,true⟩, +⟨0,568,739,true⟩, +⟨1,171,568,true⟩, +⟨0,369,740,true⟩, +⟨1,171,369,true⟩, +⟨0,172,747,false⟩, +⟨0,383,746,false⟩, +⟨1,172,383,true⟩, +⟨0,934,744,false⟩, +⟨1,172,934,true⟩, +⟨0,173,741,true⟩, +⟨0,588,740,true⟩, +⟨1,173,588,true⟩, +⟨0,380,738,true⟩, +⟨1,173,380,true⟩, +⟨0,174,741,false⟩, +⟨0,589,737,false⟩, +⟨1,174,589,true⟩, +⟨0,378,739,false⟩, +⟨1,174,378,true⟩, +⟨0,377,743,true⟩, +⟨1,175,377,true⟩, +⟨0,935,745,true⟩, +⟨1,175,935,true⟩, +⟨0,176,796,false⟩, +⟨0,805,798,false⟩, +⟨1,176,805,true⟩, +⟨0,391,797,false⟩, +⟨1,176,391,true⟩, +⟨0,177,802,true⟩, +⟨0,389,803,true⟩, +⟨1,177,389,true⟩, +⟨0,526,804,true⟩, +⟨1,177,526,true⟩, +⟨0,178,802,false⟩, +⟨0,406,805,false⟩, +⟨1,178,406,true⟩, +⟨0,387,806,false⟩, +⟨1,178,387,true⟩, +⟨0,179,796,true⟩, +⟨0,804,799,true⟩, +⟨1,179,804,true⟩, +⟨0,385,800,true⟩, +⟨1,179,385,true⟩, +⟨0,180,807,false⟩, +⟨0,949,806,false⟩, +⟨1,180,949,true⟩, +⟨0,398,804,false⟩, +⟨1,180,398,true⟩, +⟨0,181,801,true⟩, +⟨0,828,800,true⟩, +⟨1,181,828,true⟩, +⟨0,396,798,true⟩, +⟨1,181,396,true⟩, +⟨0,182,801,false⟩, +⟨0,829,797,false⟩, +⟨1,182,829,true⟩, +⟨0,394,799,false⟩, +⟨1,182,394,true⟩, +⟨0,950,803,true⟩, +⟨1,183,950,true⟩, +⟨0,392,805,true⟩, +⟨1,183,392,true⟩, +⟨0,184,640,false⟩, +⟨0,407,641,false⟩, +⟨1,184,407,true⟩, +⟨0,865,642,false⟩, +⟨1,184,865,true⟩, +⟨0,185,646,true⟩, +⟨0,405,647,true⟩, +⟨1,185,405,true⟩, +⟨0,977,648,true⟩, +⟨1,185,977,true⟩, +⟨0,186,646,false⟩, +⟨0,403,650,false⟩, +⟨1,186,403,true⟩, +⟨0,978,649,false⟩, +⟨1,186,978,true⟩, +⟨0,187,640,true⟩, +⟨0,863,643,true⟩, +⟨1,187,863,true⟩, +⟨0,401,644,true⟩, +⟨1,187,401,true⟩, +⟨0,188,651,false⟩, +⟨0,959,650,false⟩, +⟨1,188,959,true⟩, +⟨0,414,648,false⟩, +⟨1,188,414,true⟩, +⟨0,189,645,true⟩, +⟨0,835,644,true⟩, +⟨1,189,835,true⟩, +⟨0,412,642,true⟩, +⟨1,189,412,true⟩, +⟨0,190,645,false⟩, +⟨0,837,641,false⟩, +⟨1,190,837,true⟩, +⟨0,410,643,false⟩, +⟨1,190,410,true⟩, +⟨0,408,649,true⟩, +⟨1,191,408,true⟩, +⟨0,960,647,true⟩, +⟨1,191,960,true⟩, +⟨0,192,700,false⟩, +⟨0,423,701,false⟩, +⟨1,192,423,true⟩, +⟨0,887,702,false⟩, +⟨1,192,887,true⟩, +⟨0,193,706,true⟩, +⟨0,980,707,true⟩, +⟨1,193,980,true⟩, +⟨0,420,708,true⟩, +⟨1,193,420,true⟩, +⟨0,194,706,false⟩, +⟨0,418,709,false⟩, +⟨1,194,418,true⟩, +⟨0,979,710,false⟩, +⟨1,194,979,true⟩, +⟨0,195,700,true⟩, +⟨0,886,703,true⟩, +⟨1,195,886,true⟩, +⟨0,417,704,true⟩, +⟨1,195,417,true⟩, +⟨0,196,711,false⟩, +⟨0,983,708,false⟩, +⟨1,196,983,true⟩, +⟨0,431,710,false⟩, +⟨1,196,431,true⟩, +⟨0,197,705,true⟩, +⟨0,872,704,true⟩, +⟨1,197,872,true⟩, +⟨0,428,702,true⟩, +⟨1,197,428,true⟩, +⟨0,198,705,false⟩, +⟨0,873,701,false⟩, +⟨1,198,873,true⟩, +⟨0,426,703,false⟩, +⟨1,198,426,true⟩, +⟨0,984,709,true⟩, +⟨1,199,984,true⟩, +⟨0,425,707,true⟩, +⟨1,199,425,true⟩, +⟨0,200,748,false⟩, +⟨0,605,749,false⟩] +def chunk79 : List Event := [⟨1,200,605,true⟩, +⟨0,438,750,false⟩, +⟨1,200,438,true⟩, +⟨0,201,754,true⟩, +⟨0,437,755,true⟩, +⟨1,201,437,true⟩, +⟨0,951,756,true⟩, +⟨1,201,951,true⟩, +⟨0,202,754,false⟩, +⟨0,953,757,false⟩, +⟨1,202,953,true⟩, +⟨0,435,758,false⟩, +⟨1,202,435,true⟩, +⟨0,203,748,true⟩, +⟨0,432,751,true⟩, +⟨1,203,432,true⟩, +⟨0,604,752,true⟩, +⟨1,203,604,true⟩, +⟨0,204,759,false⟩, +⟨0,942,758,false⟩, +⟨1,204,942,true⟩, +⟨0,446,756,false⟩, +⟨1,204,446,true⟩, +⟨0,205,753,true⟩, +⟨0,617,750,true⟩, +⟨1,205,617,true⟩, +⟨0,445,752,true⟩, +⟨1,205,445,true⟩, +⟨0,206,753,false⟩, +⟨0,616,751,false⟩, +⟨1,206,616,true⟩, +⟨0,443,749,false⟩, +⟨1,206,443,true⟩, +⟨0,944,755,true⟩, +⟨1,207,944,true⟩, +⟨0,440,757,true⟩, +⟨1,207,440,true⟩, +⟨0,208,784,false⟩, +⟨0,831,785,false⟩, +⟨1,208,831,true⟩, +⟨0,454,786,false⟩, +⟨1,208,454,true⟩, +⟨0,209,790,true⟩, +⟨0,453,791,true⟩, +⟨1,209,453,true⟩, +⟨0,532,792,true⟩, +⟨1,209,532,true⟩, +⟨0,210,790,false⟩, +⟨0,451,794,false⟩, +⟨1,210,451,true⟩, +⟨0,948,793,false⟩, +⟨1,210,948,true⟩, +⟨0,211,784,true⟩, +⟨0,448,787,true⟩, +⟨1,211,448,true⟩, +⟨0,830,788,true⟩, +⟨1,211,830,true⟩, +⟨0,212,795,false⟩, +⟨0,952,794,false⟩, +⟨1,212,952,true⟩, +⟨0,462,792,false⟩, +⟨1,212,462,true⟩, +⟨0,213,789,true⟩, +⟨0,819,786,true⟩, +⟨1,213,819,true⟩, +⟨0,461,788,true⟩, +⟨1,213,461,true⟩, +⟨0,214,789,false⟩, +⟨0,818,787,false⟩, +⟨1,214,818,true⟩, +⟨0,459,785,false⟩, +⟨1,214,459,true⟩, +⟨0,456,793,true⟩, +⟨1,215,456,true⟩, +⟨0,954,791,true⟩, +⟨1,215,954,true⟩, +⟨0,216,772,false⟩, +⟨0,817,773,false⟩, +⟨1,216,817,true⟩, +⟨0,470,774,false⟩, +⟨1,216,470,true⟩, +⟨0,217,778,true⟩, +⟨0,469,779,true⟩, +⟨1,217,469,true⟩, +⟨0,956,780,true⟩, +⟨1,217,956,true⟩, +⟨0,218,778,false⟩, +⟨0,958,781,false⟩, +⟨1,218,958,true⟩, +⟨0,467,782,false⟩, +⟨1,218,467,true⟩, +⟨0,219,772,true⟩, +⟨0,464,775,true⟩, +⟨1,219,464,true⟩, +⟨0,816,776,true⟩, +⟨1,219,816,true⟩, +⟨0,220,783,false⟩, +⟨0,943,782,false⟩, +⟨1,220,943,true⟩, +⟨0,478,780,false⟩, +⟨1,220,478,true⟩, +⟨0,221,777,true⟩, +⟨0,477,776,true⟩, +⟨1,221,477,true⟩, +⟨0,833,774,true⟩, +⟨1,221,833,true⟩, +⟨0,222,777,false⟩, +⟨0,475,773,false⟩, +⟨1,222,475,true⟩, +⟨0,832,775,false⟩, +⟨1,222,832,true⟩, +⟨0,945,779,true⟩, +⟨1,223,945,true⟩, +⟨0,472,781,true⟩, +⟨1,223,472,true⟩, +⟨0,224,760,false⟩, +⟨0,621,761,false⟩, +⟨1,224,621,true⟩, +⟨0,486,762,false⟩, +⟨1,224,486,true⟩, +⟨0,225,766,true⟩, +⟨0,485,767,true⟩, +⟨1,225,485,true⟩, +⟨0,946,768,true⟩, +⟨1,225,946,true⟩, +⟨0,226,766,false⟩, +⟨0,947,769,false⟩, +⟨1,226,947,true⟩, +⟨0,483,770,false⟩, +⟨1,226,483,true⟩, +⟨0,227,760,true⟩, +⟨0,480,763,true⟩, +⟨1,227,480,true⟩, +⟨0,620,764,true⟩, +⟨1,227,620,true⟩, +⟨0,228,771,false⟩, +⟨0,955,770,false⟩, +⟨1,228,955,true⟩, +⟨0,494,768,false⟩, +⟨1,228,494,true⟩, +⟨0,229,765,true⟩, +⟨0,601,762,true⟩, +⟨1,229,601,true⟩, +⟨0,493,764,true⟩, +⟨1,229,493,true⟩, +⟨0,230,765,false⟩, +⟨0,600,763,false⟩, +⟨1,230,600,true⟩, +⟨0,491,761,false⟩, +⟨1,230,491,true⟩, +⟨0,957,767,true⟩, +⟨1,231,957,true⟩, +⟨0,488,769,true⟩, +⟨1,231,488,true⟩, +⟨0,232,712,false⟩, +⟨0,889,713,false⟩, +⟨1,232,889,true⟩, +⟨0,502,714,false⟩, +⟨1,232,502,true⟩, +⟨0,233,718,true⟩, +⟨0,986,719,true⟩, +⟨1,233,986,true⟩, +⟨0,500,720,true⟩, +⟨1,233,500,true⟩, +⟨0,234,718,false⟩, +⟨0,498,721,false⟩, +⟨1,234,498,true⟩, +⟨0,985,722,false⟩, +⟨1,234,985,true⟩, +⟨0,235,712,true⟩, +⟨0,496,715,true⟩, +⟨1,235,496,true⟩, +⟨0,888,716,true⟩, +⟨1,235,888,true⟩, +⟨0,236,723,false⟩, +⟨0,981,720,false⟩, +⟨1,236,981,true⟩, +⟨0,511,722,false⟩, +⟨1,236,511,true⟩, +⟨0,237,717,true⟩, +⟨0,875,714,true⟩, +⟨1,237,875,true⟩, +⟨0,509,716,true⟩, +⟨1,237,509,true⟩, +⟨0,238,717,false⟩, +⟨0,874,715,false⟩, +⟨1,238,874,true⟩, +⟨0,507,713,false⟩, +⟨1,238,507,true⟩, +⟨0,982,721,true⟩, +⟨1,239,982,true⟩, +⟨0,505,719,true⟩, +⟨1,239,505,true⟩, +⟨0,651,831,true⟩, +⟨0,667,831,true⟩, +⟨1,651,667,true⟩, +⟨0,571,831,true⟩, +⟨0,276,831,true⟩, +⟨1,571,276,true⟩, +⟨0,615,831,true⟩] +def chunk80 : List Event := [⟨1,571,615,true⟩, +⟨0,528,831,true⟩, +⟨1,528,5,true⟩, +⟨1,528,4,true⟩, +⟨0,699,831,true⟩, +⟨1,528,699,true⟩, +⟨0,635,830,true⟩, +⟨0,683,830,true⟩, +⟨1,635,683,true⟩, +⟨0,519,830,true⟩, +⟨0,246,830,true⟩, +⟨1,519,246,true⟩, +⟨1,519,528,true⟩, +⟨0,603,830,true⟩, +⟨0,265,830,true⟩, +⟨1,603,265,true⟩, +⟨0,262,830,true⟩, +⟨1,603,262,true⟩, +⟨0,695,830,true⟩, +⟨1,603,695,true⟩, +⟨0,551,829,true⟩, +⟨0,286,829,true⟩, +⟨1,551,286,true⟩, +⟨0,280,829,true⟩, +⟨1,551,280,true⟩, +⟨0,715,829,true⟩, +⟨1,551,715,true⟩, +⟨0,640,828,true⟩, +⟨0,679,828,true⟩, +⟨1,640,679,true⟩, +⟨0,512,828,true⟩, +⟨1,512,1,true⟩, +⟨1,512,551,true⟩, +⟨0,631,827,true⟩, +⟨0,647,827,true⟩, +⟨1,631,647,true⟩, +⟨0,567,827,true⟩, +⟨1,567,2,true⟩, +⟨0,583,827,true⟩, +⟨1,567,583,true⟩, +⟨0,663,826,true⟩, +⟨0,672,826,true⟩, +⟨1,663,672,true⟩, +⟨0,599,826,true⟩, +⟨1,599,3,true⟩, +⟨0,608,826,true⟩, +⟨1,599,608,true⟩, +⟨0,544,827,true⟩, +⟨1,544,7,true⟩, +⟨1,544,6,true⟩, +⟨0,727,813,true⟩, +⟨1,544,727,true⟩, +⟨0,592,829,true⟩, +⟨0,560,825,true⟩, +⟨1,592,560,true⟩, +⟨0,810,812,true⟩, +⟨0,811,812,true⟩, +⟨1,592,810,true⟩, +⟨1,592,811,true⟩, +⟨0,264,812,true⟩, +⟨1,560,264,true⟩, +⟨1,560,592,true⟩, +⟨0,576,828,true⟩, +⟨0,282,811,true⟩, +⟨1,576,282,true⟩, +⟨0,253,811,true⟩, +⟨1,576,253,true⟩, +⟨0,711,811,true⟩, +⟨1,576,711,true⟩, +⟨0,907,825,true⟩, +⟨0,688,824,true⟩, +⟨1,907,688,true⟩, +⟨0,708,810,true⟩, +⟨1,907,708,true⟩, +⟨0,720,810,true⟩, +⟨1,688,720,true⟩, +⟨0,266,824,true⟩, +⟨0,624,829,true⟩, +⟨1,266,624,true⟩, +⟨0,656,809,true⟩, +⟨1,624,656,true⟩, +⟨0,704,824,true⟩, +⟨0,278,824,true⟩, +⟨1,704,278,true⟩, +⟨0,255,824,true⟩, +⟨1,704,255,true⟩, +⟨1,704,640,true⟩, +⟨0,392,887,true⟩, +⟨0,406,882,true⟩, +⟨1,392,406,true⟩, +⟨0,398,884,true⟩, +⟨0,526,881,true⟩, +⟨1,398,526,true⟩, +⟨0,527,887,true⟩, +⟨1,527,58,true⟩, +⟨1,527,57,true⟩, +⟨0,387,882,true⟩, +⟨0,949,884,true⟩, +⟨1,387,949,true⟩, +⟨0,941,806,true⟩, +⟨1,949,941,true⟩, +⟨0,402,805,true⟩, +⟨1,406,402,true⟩, +⟨0,522,804,true⟩, +⟨1,526,522,true⟩, +⟨0,389,881,true⟩, +⟨0,950,887,true⟩, +⟨1,389,950,true⟩, +⟨0,252,803,true⟩, +⟨1,950,252,true⟩, +⟨0,518,802,true⟩, +⟨1,518,63,true⟩, +⟨1,518,60,true⟩, +⟨0,394,886,true⟩, +⟨0,804,883,true⟩, +⟨1,394,804,true⟩, +⟨0,396,885,true⟩, +⟨0,805,880,true⟩, +⟨1,396,805,true⟩, +⟨0,762,801,true⟩, +⟨1,762,59,true⟩, +⟨1,762,56,true⟩, +⟨0,385,883,true⟩, +⟨0,828,885,true⟩, +⟨1,385,828,true⟩, +⟨0,814,800,true⟩, +⟨1,828,814,true⟩, +⟨0,790,799,true⟩, +⟨1,804,790,true⟩, +⟨0,791,798,true⟩, +⟨1,805,791,true⟩, +⟨0,391,880,true⟩, +⟨0,829,886,true⟩, +⟨1,391,829,true⟩, +⟨0,815,797,true⟩, +⟨1,829,815,true⟩, +⟨0,763,796,true⟩, +⟨1,763,62,true⟩, +⟨1,763,61,true⟩, +⟨0,456,919,true⟩, +⟨0,948,914,true⟩, +⟨1,456,948,true⟩, +⟨0,462,916,true⟩, +⟨0,532,913,true⟩, +⟨1,462,532,true⟩, +⟨0,535,919,true⟩, +⟨1,535,90,true⟩, +⟨1,535,89,true⟩, +⟨0,451,914,true⟩, +⟨0,952,916,true⟩, +⟨1,451,952,true⟩, +⟨0,538,794,true⟩, +⟨1,952,538,true⟩, +⟨0,543,793,true⟩, +⟨1,948,543,true⟩, +⟨0,341,792,true⟩, +⟨1,532,341,true⟩, +⟨0,453,913,true⟩, +⟨0,954,919,true⟩, +⟨1,453,954,true⟩, +⟨0,542,791,true⟩, +⟨1,954,542,true⟩, +⟨0,539,790,true⟩, +⟨1,539,95,true⟩, +⟨1,539,92,true⟩, +⟨0,459,918,true⟩, +⟨0,831,912,true⟩, +⟨1,459,831,true⟩, +⟨0,461,917,true⟩, +⟨0,830,915,true⟩, +⟨1,461,830,true⟩, +⟨0,748,789,true⟩, +⟨1,748,91,true⟩, +⟨1,748,88,true⟩, +⟨0,800,788,true⟩, +⟨1,830,800,true⟩, +⟨0,448,915,true⟩, +⟨0,818,918,true⟩, +⟨1,448,818,true⟩, +⟨0,788,787,true⟩, +⟨1,818,788,true⟩, +⟨0,454,912,true⟩, +⟨0,819,917,true⟩, +⟨1,454,819,true⟩, +⟨0,789,786,true⟩, +⟨1,819,789,true⟩, +⟨0,801,785,true⟩, +⟨1,831,801,true⟩, +⟨0,749,784,true⟩, +⟨1,749,94,true⟩, +⟨1,749,93,true⟩, +⟨0,472,927,true⟩, +⟨0,958,922,true⟩, +⟨1,472,958,true⟩, +⟨0,478,924,true⟩, +⟨0,956,921,true⟩, +⟨1,478,956,true⟩, +⟨0,555,927,true⟩, +⟨1,555,98,true⟩, +⟨1,555,97,true⟩] +def chunk81 : List Event := [⟨0,467,922,true⟩, +⟨0,943,924,true⟩, +⟨1,467,943,true⟩, +⟨0,554,782,true⟩, +⟨1,943,554,true⟩, +⟨0,550,781,true⟩, +⟨1,958,550,true⟩, +⟨0,325,780,true⟩, +⟨1,956,325,true⟩, +⟨0,469,921,true⟩, +⟨0,945,927,true⟩, +⟨1,469,945,true⟩, +⟨0,558,779,true⟩, +⟨1,945,558,true⟩, +⟨0,559,778,true⟩, +⟨1,559,103,true⟩, +⟨1,559,100,true⟩, +⟨0,475,926,true⟩, +⟨0,817,920,true⟩, +⟨1,475,817,true⟩, +⟨0,477,925,true⟩, +⟨0,816,923,true⟩, +⟨1,477,816,true⟩, +⟨0,513,777,true⟩, +⟨1,513,99,true⟩, +⟨1,513,96,true⟩, +⟨0,802,776,true⟩, +⟨1,816,802,true⟩, +⟨0,464,923,true⟩, +⟨0,832,926,true⟩, +⟨1,464,832,true⟩, +⟨0,786,775,true⟩, +⟨1,832,786,true⟩, +⟨0,470,920,true⟩, +⟨0,833,925,true⟩, +⟨1,470,833,true⟩, +⟨0,787,774,true⟩, +⟨1,833,787,true⟩, +⟨0,803,773,true⟩, +⟨1,817,803,true⟩, +⟨0,515,772,true⟩, +⟨1,515,102,true⟩, +⟨1,515,101,true⟩, +⟨0,488,935,true⟩, +⟨0,947,930,true⟩, +⟨1,488,947,true⟩, +⟨0,494,932,true⟩, +⟨0,946,929,true⟩, +⟨1,494,946,true⟩, +⟨0,575,935,true⟩, +⟨1,575,106,true⟩, +⟨1,575,105,true⟩, +⟨0,483,930,true⟩, +⟨0,955,932,true⟩, +⟨1,483,955,true⟩, +⟨0,310,770,true⟩, +⟨1,955,310,true⟩, +⟨0,309,769,true⟩, +⟨1,947,309,true⟩, +⟨0,574,768,true⟩, +⟨1,946,574,true⟩, +⟨0,485,929,true⟩, +⟨0,957,935,true⟩, +⟨1,485,957,true⟩, +⟨0,570,767,true⟩, +⟨1,957,570,true⟩, +⟨0,566,766,true⟩, +⟨1,566,111,true⟩, +⟨1,566,108,true⟩, +⟨0,491,934,true⟩, +⟨0,621,928,true⟩, +⟨1,491,621,true⟩, +⟨0,493,933,true⟩, +⟨0,620,931,true⟩, +⟨1,493,620,true⟩, +⟨0,746,765,true⟩, +⟨1,746,107,true⟩, +⟨1,746,104,true⟩, +⟨0,772,764,true⟩, +⟨1,620,772,true⟩, +⟨0,480,931,true⟩, +⟨0,600,934,true⟩, +⟨1,480,600,true⟩, +⟨0,760,763,true⟩, +⟨1,600,760,true⟩, +⟨0,486,928,true⟩, +⟨0,601,933,true⟩, +⟨1,486,601,true⟩, +⟨0,761,762,true⟩, +⟨1,601,761,true⟩, +⟨0,773,761,true⟩, +⟨1,621,773,true⟩, +⟨0,747,760,true⟩, +⟨1,747,110,true⟩, +⟨1,747,109,true⟩, +⟨0,440,911,true⟩, +⟨0,953,906,true⟩, +⟨1,440,953,true⟩, +⟨0,446,908,true⟩, +⟨0,951,905,true⟩, +⟨1,446,951,true⟩, +⟨0,587,911,true⟩, +⟨1,587,82,true⟩, +⟨1,587,81,true⟩, +⟨0,435,906,true⟩, +⟨0,942,908,true⟩, +⟨1,435,942,true⟩, +⟨0,590,758,true⟩, +⟨1,942,590,true⟩, +⟨0,582,757,true⟩, +⟨1,953,582,true⟩, +⟨0,354,756,true⟩, +⟨1,951,354,true⟩, +⟨0,437,905,true⟩, +⟨0,944,911,true⟩, +⟨1,437,944,true⟩, +⟨0,586,755,true⟩, +⟨1,944,586,true⟩, +⟨0,591,754,true⟩, +⟨1,591,87,true⟩, +⟨1,591,84,true⟩, +⟨0,443,910,true⟩, +⟨0,605,904,true⟩, +⟨1,443,605,true⟩, +⟨0,445,909,true⟩, +⟨0,604,907,true⟩, +⟨1,445,604,true⟩, +⟨0,520,753,true⟩, +⟨1,520,83,true⟩, +⟨1,520,80,true⟩, +⟨0,774,752,true⟩, +⟨1,604,774,true⟩, +⟨0,432,907,true⟩, +⟨0,616,910,true⟩, +⟨1,432,616,true⟩, +⟨0,758,751,true⟩, +⟨1,616,758,true⟩, +⟨0,438,904,true⟩, +⟨0,617,909,true⟩, +⟨1,438,617,true⟩, +⟨0,759,750,true⟩, +⟨1,617,759,true⟩, +⟨0,775,749,true⟩, +⟨1,605,775,true⟩, +⟨0,521,748,true⟩, +⟨1,521,86,true⟩, +⟨1,521,85,true⟩, +⟨0,377,879,true⟩, +⟨0,940,873,true⟩, +⟨1,377,940,true⟩, +⟨0,383,876,true⟩, +⟨0,939,874,true⟩, +⟨1,383,939,true⟩, +⟨0,607,879,true⟩, +⟨1,607,50,true⟩, +⟨1,607,49,true⟩, +⟨0,422,746,true⟩, +⟨1,939,422,true⟩, +⟨0,370,874,true⟩, +⟨0,935,879,true⟩, +⟨1,370,935,true⟩, +⟨0,421,745,true⟩, +⟨1,935,421,true⟩, +⟨0,372,873,true⟩, +⟨0,934,876,true⟩, +⟨1,372,934,true⟩, +⟨0,606,744,true⟩, +⟨1,934,606,true⟩, +⟨0,602,743,true⟩, +⟨1,940,602,true⟩, +⟨0,598,742,true⟩, +⟨1,598,55,true⟩, +⟨1,598,52,true⟩, +⟨0,378,878,true⟩, +⟨0,568,875,true⟩, +⟨1,378,568,true⟩, +⟨0,380,877,true⟩, +⟨0,569,872,true⟩, +⟨1,380,569,true⟩, +⟨0,744,741,true⟩, +⟨1,744,51,true⟩, +⟨1,744,48,true⟩, +⟨0,369,875,true⟩, +⟨0,588,877,true⟩, +⟨1,369,588,true⟩, +⟨0,556,740,true⟩, +⟨1,588,556,true⟩, +⟨0,536,739,true⟩, +⟨1,568,536,true⟩, +⟨0,537,738,true⟩, +⟨1,569,537,true⟩, +⟨0,375,872,true⟩, +⟨0,589,878,true⟩, +⟨1,375,589,true⟩, +⟨0,557,737,true⟩, +⟨1,589,557,true⟩, +⟨0,745,736,true⟩, +⟨1,745,54,true⟩, +⟨1,745,53,true⟩, +⟨0,296,839,true⟩] +def chunk82 : List Event := [⟨0,938,834,true⟩, +⟨1,296,938,true⟩, +⟨0,302,836,true⟩, +⟨0,937,833,true⟩, +⟨1,302,937,true⟩, +⟨0,619,839,true⟩, +⟨1,619,10,true⟩, +⟨1,619,9,true⟩, +⟨0,291,834,true⟩, +⟨0,932,836,true⟩, +⟨1,291,932,true⟩, +⟨0,618,734,true⟩, +⟨1,932,618,true⟩, +⟨0,614,733,true⟩, +⟨1,938,614,true⟩, +⟨0,501,732,true⟩, +⟨1,937,501,true⟩, +⟨0,293,833,true⟩, +⟨0,933,839,true⟩, +⟨1,293,933,true⟩, +⟨0,622,731,true⟩, +⟨1,933,622,true⟩, +⟨0,623,730,true⟩, +⟨1,623,15,true⟩, +⟨1,623,12,true⟩, +⟨0,298,838,true⟩, +⟨0,584,835,true⟩, +⟨1,298,584,true⟩, +⟨0,300,837,true⟩, +⟨0,585,832,true⟩, +⟨1,300,585,true⟩, +⟨0,524,729,true⟩, +⟨1,524,11,true⟩, +⟨1,524,8,true⟩, +⟨0,289,835,true⟩, +⟨0,572,837,true⟩, +⟨1,289,572,true⟩, +⟨0,552,728,true⟩, +⟨1,572,552,true⟩, +⟨0,540,727,true⟩, +⟨1,584,540,true⟩, +⟨0,541,726,true⟩, +⟨1,585,541,true⟩, +⟨0,295,832,true⟩, +⟨0,573,838,true⟩, +⟨1,295,573,true⟩, +⟨0,553,725,true⟩, +⟨1,573,553,true⟩, +⟨0,525,724,true⟩, +⟨1,525,14,true⟩, +⟨1,525,13,true⟩, +⟨0,505,943,true⟩, +⟨0,986,937,true⟩, +⟨1,505,986,true⟩, +⟨0,511,940,true⟩, +⟨0,985,938,true⟩, +⟨1,511,985,true⟩, +⟨0,639,943,true⟩, +⟨1,639,114,true⟩, +⟨1,639,113,true⟩, +⟨0,294,722,true⟩, +⟨1,985,294,true⟩, +⟨0,498,938,true⟩, +⟨0,982,943,true⟩, +⟨1,498,982,true⟩, +⟨0,290,721,true⟩, +⟨1,982,290,true⟩, +⟨0,500,937,true⟩, +⟨0,981,940,true⟩, +⟨1,500,981,true⟩, +⟨0,634,720,true⟩, +⟨1,981,634,true⟩, +⟨0,638,719,true⟩, +⟨1,986,638,true⟩, +⟨0,630,718,true⟩, +⟨1,630,119,true⟩, +⟨1,630,116,true⟩, +⟨0,507,942,true⟩, +⟨0,889,936,true⟩, +⟨1,507,889,true⟩, +⟨0,509,941,true⟩, +⟨0,888,939,true⟩, +⟨1,509,888,true⟩, +⟨0,742,717,true⟩, +⟨1,742,115,true⟩, +⟨1,742,112,true⟩, +⟨0,768,716,true⟩, +⟨1,888,768,true⟩, +⟨0,496,939,true⟩, +⟨0,874,942,true⟩, +⟨1,496,874,true⟩, +⟨0,756,715,true⟩, +⟨1,874,756,true⟩, +⟨0,502,936,true⟩, +⟨0,875,941,true⟩, +⟨1,502,875,true⟩, +⟨0,757,714,true⟩, +⟨1,875,757,true⟩, +⟨0,769,713,true⟩, +⟨1,889,769,true⟩, +⟨0,743,712,true⟩, +⟨1,743,118,true⟩, +⟨1,743,117,true⟩, +⟨0,425,903,true⟩, +⟨0,980,897,true⟩, +⟨1,425,980,true⟩, +⟨0,431,900,true⟩, +⟨0,979,898,true⟩, +⟨1,431,979,true⟩, +⟨0,655,903,true⟩, +⟨1,655,74,true⟩, +⟨1,655,73,true⟩, +⟨0,374,710,true⟩, +⟨1,979,374,true⟩, +⟨0,418,898,true⟩, +⟨0,984,903,true⟩, +⟨1,418,984,true⟩, +⟨0,373,709,true⟩, +⟨1,984,373,true⟩, +⟨0,420,897,true⟩, +⟨0,983,900,true⟩, +⟨1,420,983,true⟩, +⟨0,654,708,true⟩, +⟨1,983,654,true⟩, +⟨0,650,707,true⟩, +⟨1,980,650,true⟩, +⟨0,646,706,true⟩, +⟨1,646,79,true⟩, +⟨1,646,76,true⟩, +⟨0,426,902,true⟩, +⟨0,886,899,true⟩, +⟨1,426,886,true⟩, +⟨0,428,901,true⟩, +⟨0,887,896,true⟩, +⟨1,428,887,true⟩, +⟨0,413,705,true⟩, +⟨1,413,75,true⟩, +⟨1,413,72,true⟩, +⟨0,417,899,true⟩, +⟨0,872,901,true⟩, +⟨1,417,872,true⟩, +⟨0,770,704,true⟩, +⟨1,872,770,true⟩, +⟨0,754,703,true⟩, +⟨1,886,754,true⟩, +⟨0,755,702,true⟩, +⟨1,887,755,true⟩, +⟨0,423,896,true⟩, +⟨0,873,902,true⟩, +⟨1,423,873,true⟩, +⟨0,771,701,true⟩, +⟨1,873,771,true⟩, +⟨0,415,700,true⟩, +⟨1,415,78,true⟩, +⟨1,415,77,true⟩, +⟨0,360,871,true⟩, +⟨0,968,866,true⟩, +⟨1,360,968,true⟩, +⟨0,366,868,true⟩, +⟨0,967,865,true⟩, +⟨1,366,967,true⟩, +⟨0,671,871,true⟩, +⟨1,671,42,true⟩, +⟨1,671,41,true⟩, +⟨0,355,866,true⟩, +⟨0,975,868,true⟩, +⟨1,355,975,true⟩, +⟨0,444,698,true⟩, +⟨1,975,444,true⟩, +⟨0,434,697,true⟩, +⟨1,968,434,true⟩, +⟨0,666,696,true⟩, +⟨1,967,666,true⟩, +⟨0,357,865,true⟩, +⟨0,976,871,true⟩, +⟨1,357,976,true⟩, +⟨0,670,695,true⟩, +⟨1,976,670,true⟩, +⟨0,662,694,true⟩, +⟨1,662,47,true⟩, +⟨1,662,44,true⟩, +⟨0,362,870,true⟩, +⟨0,844,867,true⟩, +⟨1,362,844,true⟩, +⟨0,364,869,true⟩, +⟨0,845,864,true⟩, +⟨1,364,845,true⟩, +⟨0,740,693,true⟩, +⟨1,740,43,true⟩, +⟨1,740,40,true⟩, +⟨0,353,867,true⟩, +⟨0,858,869,true⟩, +⟨1,353,858,true⟩, +⟨0,333,692,true⟩, +⟨1,858,333,true⟩, +⟨0,337,691,true⟩, +⟨1,844,337,true⟩, +⟨0,339,690,true⟩, +⟨1,845,339,true⟩, +⟨0,359,864,true⟩] +def chunk83 : List Event := [⟨0,859,870,true⟩, +⟨1,359,859,true⟩, +⟨0,323,689,true⟩, +⟨1,859,323,true⟩, +⟨0,741,688,true⟩, +⟨1,741,46,true⟩, +⟨1,741,45,true⟩, +⟨0,313,847,true⟩, +⟨0,966,841,true⟩, +⟨1,313,966,true⟩, +⟨0,319,844,true⟩, +⟨0,965,842,true⟩, +⟨1,319,965,true⟩, +⟨0,687,847,true⟩, +⟨1,687,18,true⟩, +⟨1,687,17,true⟩, +⟨0,492,686,true⟩, +⟨1,965,492,true⟩, +⟨0,306,842,true⟩, +⟨0,974,847,true⟩, +⟨1,306,974,true⟩, +⟨0,482,685,true⟩, +⟨1,974,482,true⟩, +⟨0,308,841,true⟩, +⟨0,973,844,true⟩, +⟨1,308,973,true⟩, +⟨0,682,684,true⟩, +⟨1,973,682,true⟩, +⟨0,686,683,true⟩, +⟨1,966,686,true⟩, +⟨0,678,682,true⟩, +⟨1,678,23,true⟩, +⟨1,678,20,true⟩, +⟨0,314,846,true⟩, +⟨0,856,843,true⟩, +⟨1,314,856,true⟩, +⟨0,316,845,true⟩, +⟨0,857,840,true⟩, +⟨1,316,857,true⟩, +⟨0,400,681,true⟩, +⟨1,400,19,true⟩, +⟨1,400,16,true⟩, +⟨0,305,843,true⟩, +⟨0,842,845,true⟩, +⟨1,305,842,true⟩, +⟨0,320,680,true⟩, +⟨1,842,320,true⟩, +⟨0,346,679,true⟩, +⟨1,856,346,true⟩, +⟨0,350,678,true⟩, +⟨1,857,350,true⟩, +⟨0,311,840,true⟩, +⟨0,843,846,true⟩, +⟨1,311,843,true⟩, +⟨0,334,677,true⟩, +⟨1,843,334,true⟩, +⟨0,404,676,true⟩, +⟨1,404,22,true⟩, +⟨1,404,21,true⟩, +⟨0,329,855,true⟩, +⟨0,972,849,true⟩, +⟨1,329,972,true⟩, +⟨0,335,852,true⟩, +⟨0,971,850,true⟩, +⟨1,335,971,true⟩, +⟨0,703,855,true⟩, +⟨1,703,26,true⟩, +⟨1,703,25,true⟩, +⟨0,476,674,true⟩, +⟨1,971,476,true⟩, +⟨0,322,850,true⟩, +⟨0,964,855,true⟩, +⟨1,322,964,true⟩, +⟨0,466,673,true⟩, +⟨1,964,466,true⟩, +⟨0,324,849,true⟩, +⟨0,963,852,true⟩, +⟨1,324,963,true⟩, +⟨0,698,672,true⟩, +⟨1,963,698,true⟩, +⟨0,702,671,true⟩, +⟨1,972,702,true⟩, +⟨0,694,670,true⟩, +⟨1,694,31,true⟩, +⟨1,694,28,true⟩, +⟨0,330,854,true⟩, +⟨0,840,851,true⟩, +⟨1,330,840,true⟩, +⟨0,332,853,true⟩, +⟨0,841,848,true⟩, +⟨1,332,841,true⟩, +⟨0,737,669,true⟩, +⟨1,737,27,true⟩, +⟨1,737,24,true⟩, +⟨0,321,851,true⟩, +⟨0,854,853,true⟩, +⟨1,321,854,true⟩, +⟨0,798,668,true⟩, +⟨1,854,798,true⟩, +⟨0,784,667,true⟩, +⟨1,840,784,true⟩, +⟨0,785,666,true⟩, +⟨1,841,785,true⟩, +⟨0,327,848,true⟩, +⟨0,855,854,true⟩, +⟨1,327,855,true⟩, +⟨0,799,665,true⟩, +⟨1,855,799,true⟩, +⟨0,739,664,true⟩, +⟨1,739,30,true⟩, +⟨1,739,29,true⟩, +⟨0,345,863,true⟩, +⟨0,962,857,true⟩, +⟨1,345,962,true⟩, +⟨0,351,860,true⟩, +⟨0,961,858,true⟩, +⟨1,351,961,true⟩, +⟨0,719,863,true⟩, +⟨1,719,34,true⟩, +⟨1,719,33,true⟩, +⟨0,936,662,true⟩, +⟨1,961,936,true⟩, +⟨0,338,858,true⟩, +⟨0,970,863,true⟩, +⟨1,338,970,true⟩, +⟨0,709,661,true⟩, +⟨1,970,709,true⟩, +⟨0,340,857,true⟩, +⟨0,969,860,true⟩, +⟨1,340,969,true⟩, +⟨0,718,660,true⟩, +⟨1,969,718,true⟩, +⟨0,710,659,true⟩, +⟨1,962,710,true⟩, +⟨0,450,658,true⟩, +⟨1,450,39,true⟩, +⟨1,450,36,true⟩, +⟨0,347,862,true⟩, +⟨0,839,856,true⟩, +⟨1,347,839,true⟩, +⟨0,349,861,true⟩, +⟨0,838,859,true⟩, +⟨1,349,838,true⟩, +⟨0,736,657,true⟩, +⟨1,736,35,true⟩, +⟨1,736,32,true⟩, +⟨0,796,656,true⟩, +⟨1,838,796,true⟩, +⟨0,336,859,true⟩, +⟨0,852,862,true⟩, +⟨1,336,852,true⟩, +⟨0,782,655,true⟩, +⟨1,852,782,true⟩, +⟨0,342,856,true⟩, +⟨0,853,861,true⟩, +⟨1,342,853,true⟩, +⟨0,783,654,true⟩, +⟨1,853,783,true⟩, +⟨0,797,653,true⟩, +⟨1,839,797,true⟩, +⟨0,738,652,true⟩, +⟨1,738,38,true⟩, +⟨1,738,37,true⟩, +⟨0,408,895,true⟩, +⟨0,978,890,true⟩, +⟨1,408,978,true⟩, +⟨0,414,892,true⟩, +⟨0,977,889,true⟩, +⟨1,414,977,true⟩, +⟨0,731,895,true⟩, +⟨1,731,66,true⟩, +⟨1,731,65,true⟩, +⟨0,403,890,true⟩, +⟨0,959,892,true⟩, +⟨1,403,959,true⟩, +⟨0,734,650,true⟩, +⟨1,959,734,true⟩, +⟨0,726,649,true⟩, +⟨1,978,726,true⟩, +⟨0,386,648,true⟩, +⟨1,977,386,true⟩, +⟨0,405,889,true⟩, +⟨0,960,895,true⟩, +⟨1,405,960,true⟩, +⟨0,730,647,true⟩, +⟨1,960,730,true⟩, +⟨0,735,646,true⟩, +⟨1,735,71,true⟩, +⟨1,735,68,true⟩, +⟨0,410,894,true⟩, +⟨0,863,891,true⟩, +⟨1,410,863,true⟩, +⟨0,412,893,true⟩, +⟨0,865,888,true⟩, +⟨1,412,865,true⟩, +⟨0,751,645,true⟩, +⟨1,751,67,true⟩, +⟨1,751,64,true⟩, +⟨0,401,891,true⟩, +⟨0,835,893,true⟩] +def chunk84 : List Event := [⟨1,401,835,true⟩, +⟨0,807,644,true⟩, +⟨1,835,807,true⟩, +⟨0,779,643,true⟩, +⟨1,863,779,true⟩, +⟨0,781,642,true⟩, +⟨1,865,781,true⟩, +⟨0,407,888,true⟩, +⟨0,837,894,true⟩, +⟨1,407,837,true⟩, +⟨0,809,641,true⟩, +⟨1,837,809,true⟩, +⟨0,753,640,true⟩, +⟨1,753,70,true⟩, +⟨1,753,69,true⟩, +⟨0,909,855,true⟩, +⟨0,923,639,true⟩, +⟨1,909,923,true⟩, +⟨0,908,669,true⟩, +⟨0,922,638,true⟩, +⟨1,908,922,true⟩, +⟨0,895,863,true⟩, +⟨0,921,637,true⟩, +⟨1,895,921,true⟩, +⟨0,894,657,true⟩, +⟨0,919,636,true⟩, +⟨1,894,919,true⟩, +⟨0,893,895,true⟩, +⟨1,893,907,true⟩, +⟨0,891,645,true⟩, +⟨0,905,634,true⟩, +⟨1,891,905,true⟩, +⟨1,986,889,true⟩, +⟨0,903,633,true⟩, +⟨1,889,903,true⟩, +⟨1,985,888,true⟩, +⟨0,902,632,true⟩, +⟨1,888,902,true⟩, +⟨1,984,887,true⟩, +⟨0,915,631,true⟩, +⟨1,887,915,true⟩, +⟨1,983,886,true⟩, +⟨0,914,630,true⟩, +⟨1,886,914,true⟩, +⟨0,885,871,true⟩, +⟨0,927,629,true⟩, +⟨1,885,927,true⟩, +⟨0,884,693,true⟩, +⟨0,926,628,true⟩, +⟨1,884,926,true⟩, +⟨1,982,875,true⟩, +⟨0,917,627,true⟩, +⟨1,875,917,true⟩, +⟨1,981,874,true⟩, +⟨0,916,626,true⟩, +⟨1,874,916,true⟩, +⟨1,980,873,true⟩, +⟨0,901,625,true⟩, +⟨1,873,901,true⟩, +⟨1,979,872,true⟩, +⟨0,900,624,true⟩, +⟨1,872,900,true⟩, +⟨0,871,847,true⟩, +⟨0,925,623,true⟩, +⟨1,871,925,true⟩, +⟨0,870,681,true⟩, +⟨0,924,622,true⟩, +⟨1,870,924,true⟩, +⟨1,978,865,true⟩, +⟨0,879,621,true⟩, +⟨1,865,879,true⟩, +⟨1,977,863,true⟩, +⟨0,877,620,true⟩, +⟨1,863,877,true⟩, +⟨0,861,943,true⟩, +⟨0,931,619,true⟩, +⟨1,861,931,true⟩, +⟨0,860,717,true⟩, +⟨0,930,618,true⟩, +⟨1,860,930,true⟩, +⟨1,976,859,true⟩, +⟨0,899,617,true⟩, +⟨1,859,899,true⟩, +⟨1,975,858,true⟩, +⟨0,898,616,true⟩, +⟨1,858,898,true⟩, +⟨1,974,857,true⟩, +⟨0,911,615,true⟩, +⟨1,857,911,true⟩, +⟨1,973,856,true⟩, +⟨0,910,614,true⟩, +⟨1,856,910,true⟩, +⟨1,972,855,true⟩, +⟨0,869,613,true⟩, +⟨1,855,869,true⟩, +⟨1,971,854,true⟩, +⟨0,868,612,true⟩, +⟨1,854,868,true⟩, +⟨1,970,853,true⟩, +⟨0,881,611,true⟩, +⟨1,853,881,true⟩, +⟨1,969,852,true⟩, +⟨0,880,610,true⟩, +⟨1,852,880,true⟩, +⟨0,847,903,true⟩, +⟨0,929,609,true⟩, +⟨1,847,929,true⟩, +⟨0,846,705,true⟩, +⟨0,928,608,true⟩, +⟨1,846,928,true⟩, +⟨1,968,845,true⟩, +⟨0,913,607,true⟩, +⟨1,845,913,true⟩, +⟨1,967,844,true⟩, +⟨0,912,606,true⟩, +⟨1,844,912,true⟩, +⟨1,966,843,true⟩, +⟨0,897,605,true⟩, +⟨1,843,897,true⟩, +⟨1,965,842,true⟩, +⟨0,896,604,true⟩, +⟨1,842,896,true⟩, +⟨1,964,841,true⟩, +⟨0,883,603,true⟩, +⟨1,841,883,true⟩, +⟨1,963,840,true⟩, +⟨0,882,602,true⟩, +⟨1,840,882,true⟩, +⟨1,962,839,true⟩, +⟨0,867,601,true⟩, +⟨1,839,867,true⟩, +⟨1,961,838,true⟩, +⟨0,866,600,true⟩, +⟨1,838,866,true⟩, +⟨1,960,837,true⟩, +⟨0,851,599,true⟩, +⟨1,837,851,true⟩, +⟨1,959,835,true⟩, +⟨0,849,598,true⟩, +⟨1,835,849,true⟩, +⟨1,958,833,true⟩, +⟨0,685,597,true⟩, +⟨1,833,685,true⟩, +⟨1,957,621,true⟩, +⟨0,697,596,true⟩, +⟨1,621,697,true⟩, +⟨1,956,832,true⟩, +⟨0,684,595,true⟩, +⟨1,832,684,true⟩, +⟨1,955,620,true⟩, +⟨0,696,594,true⟩, +⟨1,620,696,true⟩, +⟨1,954,831,true⟩, +⟨0,665,593,true⟩, +⟨1,831,665,true⟩, +⟨1,953,617,true⟩, +⟨0,717,592,true⟩, +⟨1,617,717,true⟩, +⟨1,952,830,true⟩, +⟨0,664,591,true⟩, +⟨1,830,664,true⟩, +⟨1,951,616,true⟩, +⟨0,716,590,true⟩, +⟨1,616,716,true⟩, +⟨1,950,829,true⟩, +⟨0,643,589,true⟩, +⟨1,829,643,true⟩, +⟨0,611,879,true⟩, +⟨0,733,588,true⟩, +⟨1,611,733,true⟩, +⟨1,949,828,true⟩, +⟨0,641,587,true⟩, +⟨1,828,641,true⟩, +⟨0,609,741,true⟩, +⟨0,732,586,true⟩, +⟨1,609,732,true⟩, +⟨1,948,819,true⟩, +⟨0,681,585,true⟩, +⟨1,819,681,true⟩, +⟨1,947,601,true⟩, +⟨0,713,584,true⟩, +⟨1,601,713,true⟩, +⟨1,532,818,true⟩, +⟨0,680,583,true⟩, +⟨1,818,680,true⟩, +⟨1,946,600,true⟩, +⟨0,712,582,true⟩, +⟨1,600,712,true⟩, +⟨1,945,817,true⟩, +⟨0,669,581,true⟩, +⟨1,817,669,true⟩, +⟨1,944,605,true⟩, +⟨0,701,580,true⟩, +⟨1,605,701,true⟩, +⟨1,943,816,true⟩, +⟨0,668,579,true⟩, +⟨1,816,668,true⟩, +⟨1,942,604,true⟩, +⟨0,700,578,true⟩, +⟨1,604,700,true⟩] +def chunk85 : List Event := [⟨1,941,815,true⟩, +⟨0,627,577,true⟩, +⟨1,815,627,true⟩, +⟨0,595,839,true⟩, +⟨0,399,576,true⟩, +⟨1,595,399,true⟩, +⟨1,252,814,true⟩, +⟨0,625,575,true⟩, +⟨1,814,625,true⟩, +⟨0,593,729,true⟩, +⟨0,397,574,true⟩, +⟨1,593,397,true⟩, +⟨1,734,809,true⟩, +⟨0,393,471,true⟩, +⟨0,722,471,true⟩, +⟨0,725,471,true⟩, +⟨1,734,393,true⟩, +⟨1,734,722,true⟩, +⟨1,734,725,true⟩, +⟨0,823,573,true⟩, +⟨1,809,823,true⟩, +⟨1,730,807,true⟩, +⟨1,730,393,true⟩, +⟨1,730,725,true⟩, +⟨0,821,572,true⟩, +⟨1,807,821,true⟩, +⟨1,406,805,true⟩, +⟨0,675,571,true⟩, +⟨1,805,675,true⟩, +⟨0,579,935,true⟩, +⟨0,729,570,true⟩, +⟨1,579,729,true⟩, +⟨1,526,804,true⟩, +⟨0,409,458,true⟩, +⟨0,514,458,true⟩, +⟨0,517,458,true⟩, +⟨1,526,409,true⟩, +⟨1,526,514,true⟩, +⟨1,526,517,true⟩, +⟨0,673,569,true⟩, +⟨1,804,673,true⟩, +⟨0,577,765,true⟩, +⟨0,728,568,true⟩, +⟨1,577,728,true⟩, +⟨1,554,803,true⟩, +⟨0,328,460,true⟩, +⟨0,546,460,true⟩, +⟨0,549,460,true⟩, +⟨1,554,328,true⟩, +⟨1,554,546,true⟩, +⟨1,554,549,true⟩, +⟨0,653,567,true⟩, +⟨1,803,653,true⟩, +⟨1,940,589,true⟩, +⟨0,479,566,true⟩, +⟨1,589,479,true⟩, +⟨1,558,802,true⟩, +⟨1,558,328,true⟩, +⟨1,558,549,true⟩, +⟨0,652,565,true⟩, +⟨1,802,652,true⟩, +⟨1,939,588,true⟩, +⟨0,465,564,true⟩, +⟨1,588,465,true⟩, +⟨1,538,801,true⟩, +⟨0,344,459,true⟩, +⟨0,530,459,true⟩, +⟨0,533,459,true⟩, +⟨1,538,344,true⟩, +⟨1,538,530,true⟩, +⟨1,538,533,true⟩, +⟨0,633,563,true⟩, +⟨1,801,633,true⟩, +⟨1,938,585,true⟩, +⟨0,463,562,true⟩, +⟨1,585,463,true⟩, +⟨1,542,800,true⟩, +⟨1,542,344,true⟩, +⟨1,542,533,true⟩, +⟨0,632,561,true⟩, +⟨1,800,632,true⟩, +⟨1,937,584,true⟩, +⟨0,449,560,true⟩, +⟨1,584,449,true⟩, +⟨1,476,799,true⟩, +⟨0,813,559,true⟩, +⟨1,799,813,true⟩, +⟨1,702,798,true⟩, +⟨0,473,469,true⟩, +⟨0,690,469,true⟩, +⟨0,693,469,true⟩, +⟨1,702,473,true⟩, +⟨1,702,690,true⟩, +⟨1,702,693,true⟩, +⟨0,812,558,true⟩, +⟨1,798,812,true⟩, +⟨1,936,797,true⟩, +⟨0,825,557,true⟩, +⟨1,797,825,true⟩, +⟨1,710,796,true⟩, +⟨0,824,556,true⟩, +⟨1,796,824,true⟩, +⟨1,522,791,true⟩, +⟨1,522,409,true⟩, +⟨1,522,517,true⟩, +⟨0,659,555,true⟩, +⟨1,791,659,true⟩, +⟨0,563,911,true⟩, +⟨0,388,554,true⟩, +⟨1,563,388,true⟩, +⟨1,402,790,true⟩, +⟨1,402,409,true⟩, +⟨1,402,514,true⟩, +⟨0,657,553,true⟩, +⟨1,790,657,true⟩, +⟨0,561,753,true⟩, +⟨0,384,552,true⟩, +⟨1,561,384,true⟩, +⟨1,341,789,true⟩, +⟨1,341,344,true⟩, +⟨1,341,530,true⟩, +⟨0,649,551,true⟩, +⟨1,789,649,true⟩, +⟨1,935,569,true⟩, +⟨0,452,550,true⟩, +⟨1,569,452,true⟩, +⟨1,543,788,true⟩, +⟨0,343,549,true⟩, +⟨1,543,343,true⟩, +⟨0,648,549,true⟩, +⟨1,788,648,true⟩, +⟨1,934,568,true⟩, +⟨0,458,548,true⟩, +⟨1,568,458,true⟩, +⟨1,325,787,true⟩, +⟨1,325,328,true⟩, +⟨1,325,546,true⟩, +⟨0,637,547,true⟩, +⟨1,787,637,true⟩, +⟨1,933,573,true⟩, +⟨0,468,546,true⟩, +⟨1,573,468,true⟩, +⟨1,550,786,true⟩, +⟨0,548,460,true⟩, +⟨1,550,548,true⟩, +⟨1,550,549,true⟩, +⟨0,636,545,true⟩, +⟨1,786,636,true⟩, +⟨1,932,572,true⟩, +⟨0,474,544,true⟩, +⟨1,572,474,true⟩, +⟨1,698,785,true⟩, +⟨1,698,473,true⟩, +⟨1,698,693,true⟩, +⟨0,827,543,true⟩, +⟨1,785,827,true⟩, +⟨1,466,784,true⟩, +⟨1,466,473,true⟩, +⟨1,466,690,true⟩, +⟨0,826,542,true⟩, +⟨1,784,826,true⟩, +⟨1,718,783,true⟩, +⟨0,706,470,true⟩, +⟨0,714,470,true⟩, +⟨1,718,706,true⟩, +⟨1,718,714,true⟩, +⟨1,783,811,true⟩, +⟨1,709,782,true⟩, +⟨0,457,470,true⟩, +⟨1,709,457,true⟩, +⟨1,709,714,true⟩, +⟨1,782,810,true⟩, +⟨1,386,781,true⟩, +⟨1,386,393,true⟩, +⟨1,386,722,true⟩, +⟨0,795,539,true⟩, +⟨1,781,795,true⟩, +⟨1,726,779,true⟩, +⟨0,724,471,true⟩, +⟨1,726,724,true⟩, +⟨1,726,725,true⟩, +⟨0,793,538,true⟩, +⟨1,779,793,true⟩, +⟨0,777,887,true⟩, +⟨0,707,537,true⟩, +⟨1,777,707,true⟩, +⟨0,547,919,true⟩, +⟨0,723,536,true⟩, +⟨1,547,723,true⟩, +⟨0,776,801,true⟩, +⟨0,705,535,true⟩, +⟨1,776,705,true⟩, +⟨0,545,789,true⟩, +⟨0,721,534,true⟩, +⟨1,545,721,true⟩, +⟨1,590,775,true⟩, +⟨0,361,462,true⟩, +⟨0,578,462,true⟩, +⟨0,581,462,true⟩, +⟨1,590,361,true⟩] +def chunk86 : List Event := [⟨1,590,578,true⟩, +⟨1,590,581,true⟩, +⟨0,371,533,true⟩, +⟨1,775,371,true⟩, +⟨1,422,557,true⟩, +⟨0,447,532,true⟩, +⟨1,557,447,true⟩, +⟨1,586,774,true⟩, +⟨1,586,361,true⟩, +⟨1,586,581,true⟩, +⟨0,381,531,true⟩, +⟨1,774,381,true⟩, +⟨1,602,556,true⟩, +⟨0,424,463,true⟩, +⟨0,594,463,true⟩, +⟨0,597,463,true⟩, +⟨1,602,424,true⟩, +⟨1,602,594,true⟩, +⟨1,602,597,true⟩, +⟨0,433,530,true⟩, +⟨1,556,433,true⟩, +⟨1,310,773,true⟩, +⟨0,303,529,true⟩, +⟨1,773,303,true⟩, +⟨1,618,553,true⟩, +⟨0,504,464,true⟩, +⟨0,610,464,true⟩, +⟨0,613,464,true⟩, +⟨1,618,504,true⟩, +⟨1,618,610,true⟩, +⟨1,618,613,true⟩, +⟨0,495,528,true⟩, +⟨1,553,495,true⟩, +⟨1,570,772,true⟩, +⟨0,312,461,true⟩, +⟨0,562,461,true⟩, +⟨0,565,461,true⟩, +⟨1,570,312,true⟩, +⟨1,570,562,true⟩, +⟨1,570,565,true⟩, +⟨0,301,527,true⟩, +⟨1,772,301,true⟩, +⟨1,622,552,true⟩, +⟨1,622,504,true⟩, +⟨1,622,613,true⟩, +⟨0,481,526,true⟩, +⟨1,552,481,true⟩, +⟨1,374,771,true⟩, +⟨0,367,525,true⟩, +⟨1,771,367,true⟩, +⟨1,444,323,true⟩, +⟨0,419,524,true⟩, +⟨1,323,419,true⟩, +⟨1,650,770,true⟩, +⟨0,376,466,true⟩, +⟨0,642,466,true⟩, +⟨0,645,466,true⟩, +⟨1,650,376,true⟩, +⟨1,650,642,true⟩, +⟨1,650,645,true⟩, +⟨0,365,523,true⟩, +⟨1,770,365,true⟩, +⟨1,670,333,true⟩, +⟨0,441,467,true⟩, +⟨0,658,467,true⟩, +⟨0,661,467,true⟩, +⟨1,670,441,true⟩, +⟨1,670,658,true⟩, +⟨1,670,661,true⟩, +⟨0,429,522,true⟩, +⟨1,333,429,true⟩, +⟨1,294,769,true⟩, +⟨0,307,521,true⟩, +⟨1,769,307,true⟩, +⟨1,492,334,true⟩, +⟨0,499,520,true⟩, +⟨1,334,499,true⟩, +⟨1,638,768,true⟩, +⟨0,297,465,true⟩, +⟨0,626,465,true⟩, +⟨0,629,465,true⟩, +⟨1,638,297,true⟩, +⟨1,638,626,true⟩, +⟨1,638,629,true⟩, +⟨0,317,519,true⟩, +⟨1,768,317,true⟩, +⟨1,686,320,true⟩, +⟨0,489,468,true⟩, +⟨0,674,468,true⟩, +⟨0,677,468,true⟩, +⟨1,686,489,true⟩, +⟨1,686,674,true⟩, +⟨1,686,677,true⟩, +⟨0,497,518,true⟩, +⟨1,320,497,true⟩, +⟨1,518,763,true⟩, +⟨0,516,458,true⟩, +⟨1,518,516,true⟩, +⟨1,518,517,true⟩, +⟨0,691,517,true⟩, +⟨1,763,691,true⟩, +⟨0,531,927,true⟩, +⟨0,920,516,true⟩, +⟨1,531,920,true⟩, +⟨1,527,762,true⟩, +⟨0,411,515,true⟩, +⟨1,527,411,true⟩, +⟨0,689,515,true⟩, +⟨1,762,689,true⟩, +⟨0,529,777,true⟩, +⟨0,918,514,true⟩, +⟨1,529,918,true⟩, +⟨1,574,761,true⟩, +⟨1,574,312,true⟩, +⟨1,574,565,true⟩, +⟨0,382,513,true⟩, +⟨1,761,382,true⟩, +⟨1,606,537,true⟩, +⟨1,606,424,true⟩, +⟨1,606,597,true⟩, +⟨0,484,512,true⟩, +⟨1,537,484,true⟩, +⟨1,309,760,true⟩, +⟨1,309,312,true⟩, +⟨1,309,562,true⟩, +⟨0,368,511,true⟩, +⟨1,760,368,true⟩, +⟨1,421,536,true⟩, +⟨1,421,424,true⟩, +⟨1,421,594,true⟩, +⟨0,490,510,true⟩, +⟨1,536,490,true⟩, +⟨1,354,759,true⟩, +⟨1,354,361,true⟩, +⟨1,354,578,true⟩, +⟨0,292,509,true⟩, +⟨1,759,292,true⟩, +⟨1,501,541,true⟩, +⟨1,501,504,true⟩, +⟨1,501,610,true⟩, +⟨0,436,508,true⟩, +⟨1,541,436,true⟩, +⟨1,582,758,true⟩, +⟨0,580,462,true⟩, +⟨1,582,580,true⟩, +⟨1,582,581,true⟩, +⟨0,288,507,true⟩, +⟨1,758,288,true⟩, +⟨1,614,540,true⟩, +⟨0,612,464,true⟩, +⟨1,614,612,true⟩, +⟨1,614,613,true⟩, +⟨0,442,506,true⟩, +⟨1,540,442,true⟩, +⟨1,634,757,true⟩, +⟨1,634,297,true⟩, +⟨1,634,629,true⟩, +⟨0,356,505,true⟩, +⟨1,757,356,true⟩, +⟨1,666,339,true⟩, +⟨1,666,441,true⟩, +⟨1,666,661,true⟩, +⟨0,510,504,true⟩, +⟨1,339,510,true⟩, +⟨1,290,756,true⟩, +⟨1,290,297,true⟩, +⟨1,290,626,true⟩, +⟨0,352,503,true⟩, +⟨1,756,352,true⟩, +⟨1,434,337,true⟩, +⟨1,434,441,true⟩, +⟨1,434,658,true⟩, +⟨0,506,502,true⟩, +⟨1,337,506,true⟩, +⟨1,654,755,true⟩, +⟨1,654,376,true⟩, +⟨1,654,645,true⟩, +⟨0,318,501,true⟩, +⟨1,755,318,true⟩, +⟨1,682,350,true⟩, +⟨1,682,489,true⟩, +⟨1,682,677,true⟩, +⟨0,430,500,true⟩, +⟨1,350,430,true⟩, +⟨1,373,754,true⟩, +⟨1,373,376,true⟩, +⟨1,373,642,true⟩, +⟨0,304,499,true⟩, +⟨1,754,304,true⟩, +⟨1,482,346,true⟩, +⟨1,482,489,true⟩, +⟨1,482,674,true⟩, +⟨0,416,498,true⟩, +⟨1,346,416,true⟩, +⟨1,735,753,true⟩, +⟨0,395,497,true⟩, +⟨1,735,395,true⟩, +⟨0,767,497,true⟩, +⟨1,753,767,true⟩, +⟨1,731,751,true⟩] +def chunk87 : List Event := [⟨0,390,496,true⟩, +⟨1,731,390,true⟩, +⟨0,765,496,true⟩, +⟨1,751,765,true⟩, +⟨1,539,749,true⟩, +⟨0,348,495,true⟩, +⟨1,539,348,true⟩, +⟨0,892,495,true⟩, +⟨1,749,892,true⟩, +⟨1,559,515,true⟩, +⟨0,331,494,true⟩, +⟨1,559,331,true⟩, +⟨0,906,494,true⟩, +⟨1,515,906,true⟩, +⟨1,535,748,true⟩, +⟨0,534,493,true⟩, +⟨1,535,534,true⟩, +⟨0,890,493,true⟩, +⟨1,748,890,true⟩, +⟨1,555,513,true⟩, +⟨0,326,492,true⟩, +⟨1,555,326,true⟩, +⟨0,904,492,true⟩, +⟨1,513,904,true⟩, +⟨1,566,747,true⟩, +⟨0,564,461,true⟩, +⟨1,566,564,true⟩, +⟨1,566,565,true⟩, +⟨0,864,491,true⟩, +⟨1,747,864,true⟩, +⟨1,591,521,true⟩, +⟨0,363,490,true⟩, +⟨1,591,363,true⟩, +⟨0,878,490,true⟩, +⟨1,521,878,true⟩, +⟨1,575,746,true⟩, +⟨0,315,489,true⟩, +⟨1,575,315,true⟩, +⟨0,862,489,true⟩, +⟨1,746,862,true⟩, +⟨1,587,520,true⟩, +⟨0,358,488,true⟩, +⟨1,587,358,true⟩, +⟨0,876,488,true⟩, +⟨1,520,876,true⟩, +⟨1,598,745,true⟩, +⟨0,596,463,true⟩, +⟨1,598,596,true⟩, +⟨1,598,597,true⟩, +⟨0,836,487,true⟩, +⟨1,745,836,true⟩, +⟨1,623,525,true⟩, +⟨0,503,486,true⟩, +⟨1,623,503,true⟩, +⟨0,850,486,true⟩, +⟨1,525,850,true⟩, +⟨1,607,744,true⟩, +⟨0,427,485,true⟩, +⟨1,607,427,true⟩, +⟨0,834,485,true⟩, +⟨1,744,834,true⟩, +⟨1,619,524,true⟩, +⟨0,508,484,true⟩, +⟨1,619,508,true⟩, +⟨0,848,484,true⟩, +⟨1,524,848,true⟩, +⟨1,630,743,true⟩, +⟨0,628,465,true⟩, +⟨1,630,628,true⟩, +⟨1,630,629,true⟩, +⟨0,808,483,true⟩, +⟨1,743,808,true⟩, +⟨1,646,415,true⟩, +⟨0,644,466,true⟩, +⟨1,646,644,true⟩, +⟨1,646,645,true⟩, +⟨0,822,482,true⟩, +⟨1,415,822,true⟩, +⟨1,639,742,true⟩, +⟨0,299,481,true⟩, +⟨1,639,299,true⟩, +⟨0,806,481,true⟩, +⟨1,742,806,true⟩, +⟨1,655,413,true⟩, +⟨0,379,480,true⟩, +⟨1,655,379,true⟩, +⟨0,820,480,true⟩, +⟨1,413,820,true⟩, +⟨1,662,741,true⟩, +⟨0,660,467,true⟩, +⟨1,662,660,true⟩, +⟨1,662,661,true⟩, +⟨0,780,479,true⟩, +⟨1,741,780,true⟩, +⟨1,678,404,true⟩, +⟨0,676,468,true⟩, +⟨1,678,676,true⟩, +⟨1,678,677,true⟩, +⟨0,794,478,true⟩, +⟨1,404,794,true⟩, +⟨1,671,740,true⟩, +⟨0,439,477,true⟩, +⟨1,671,439,true⟩, +⟨0,778,477,true⟩, +⟨1,740,778,true⟩, +⟨1,687,400,true⟩, +⟨0,487,476,true⟩, +⟨1,687,487,true⟩, +⟨0,792,476,true⟩, +⟨1,400,792,true⟩, +⟨1,694,739,true⟩, +⟨0,692,469,true⟩, +⟨1,694,692,true⟩, +⟨1,694,693,true⟩, +⟨0,752,475,true⟩, +⟨1,739,752,true⟩, +⟨1,450,738,true⟩, +⟨1,450,457,true⟩, +⟨1,450,706,true⟩, +⟨0,766,474,true⟩, +⟨1,738,766,true⟩, +⟨1,703,737,true⟩, +⟨0,471,473,true⟩, +⟨1,703,471,true⟩, +⟨0,750,473,true⟩, +⟨1,737,750,true⟩, +⟨1,719,736,true⟩, +⟨0,455,472,true⟩, +⟨1,719,455,true⟩, +⟨0,764,472,true⟩, +⟨1,736,764,true⟩, +⟨0,269,895,true⟩, +⟨0,287,471,true⟩, +⟨1,269,287,true⟩, +⟨0,281,471,true⟩, +⟨1,269,281,true⟩, +⟨0,275,471,true⟩, +⟨1,269,275,true⟩, +⟨1,269,720,true⟩, +⟨1,727,720,true⟩, +⟨1,727,726,true⟩, +⟨1,720,724,true⟩, +⟨0,257,863,true⟩, +⟨1,257,286,true⟩, +⟨1,257,280,true⟩, +⟨0,263,470,true⟩, +⟨1,257,263,true⟩, +⟨1,257,704,true⟩, +⟨1,715,704,true⟩, +⟨0,460,470,true⟩, +⟨1,715,460,true⟩, +⟨1,711,704,true⟩, +⟨1,710,455,true⟩, +⟨1,710,460,true⟩, +⟨1,711,710,true⟩, +⟨1,704,708,true⟩, +⟨0,256,855,true⟩, +⟨0,274,469,true⟩, +⟨1,256,274,true⟩, +⟨0,268,469,true⟩, +⟨1,256,268,true⟩, +⟨1,256,262,true⟩, +⟨1,256,688,true⟩, +⟨1,699,688,true⟩, +⟨1,476,471,true⟩, +⟨1,476,694,true⟩, +⟨1,699,476,true⟩, +⟨1,695,688,true⟩, +⟨1,695,694,true⟩, +⟨1,688,692,true⟩, +⟨0,251,847,true⟩, +⟨0,285,468,true⟩, +⟨1,251,285,true⟩, +⟨0,273,468,true⟩, +⟨1,251,273,true⟩, +⟨0,261,468,true⟩, +⟨1,251,261,true⟩, +⟨1,251,672,true⟩, +⟨1,683,672,true⟩, +⟨1,492,487,true⟩, +⟨1,492,678,true⟩, +⟨1,683,492,true⟩, +⟨1,679,672,true⟩, +⟨1,679,678,true⟩, +⟨1,672,676,true⟩, +⟨0,250,871,true⟩, +⟨0,279,467,true⟩, +⟨1,250,279,true⟩, +⟨0,267,467,true⟩, +⟨1,250,267,true⟩, +⟨0,260,467,true⟩, +⟨1,250,260,true⟩, +⟨1,250,656,true⟩, +⟨1,667,656,true⟩, +⟨1,444,439,true⟩, +⟨1,444,662,true⟩, +⟨1,667,444,true⟩, +⟨1,663,656,true⟩, +⟨1,663,662,true⟩, +⟨1,656,660,true⟩] +def chunk88 : List Event := [⟨0,249,903,true⟩, +⟨1,249,278,true⟩, +⟨0,272,466,true⟩, +⟨1,249,272,true⟩, +⟨1,249,255,true⟩, +⟨1,249,640,true⟩, +⟨1,651,640,true⟩, +⟨1,374,379,true⟩, +⟨1,374,646,true⟩, +⟨1,651,374,true⟩, +⟨1,647,640,true⟩, +⟨1,647,646,true⟩, +⟨1,640,644,true⟩, +⟨0,248,943,true⟩, +⟨0,284,465,true⟩, +⟨1,248,284,true⟩, +⟨1,248,266,true⟩, +⟨0,254,465,true⟩, +⟨1,248,254,true⟩, +⟨1,248,624,true⟩, +⟨1,635,624,true⟩, +⟨1,294,299,true⟩, +⟨1,294,630,true⟩, +⟨1,635,294,true⟩, +⟨1,631,624,true⟩, +⟨1,631,630,true⟩, +⟨1,624,628,true⟩, +⟨0,245,839,true⟩, +⟨0,277,464,true⟩, +⟨1,245,277,true⟩, +⟨0,271,464,true⟩, +⟨1,245,271,true⟩, +⟨0,259,464,true⟩, +⟨1,245,259,true⟩, +⟨1,245,608,true⟩, +⟨1,615,608,true⟩, +⟨1,615,614,true⟩, +⟨1,608,612,true⟩, +⟨0,244,879,true⟩, +⟨0,283,463,true⟩, +⟨1,244,283,true⟩, +⟨1,244,265,true⟩, +⟨1,244,3,true⟩, +⟨1,244,592,true⟩, +⟨1,603,592,true⟩, +⟨1,422,427,true⟩, +⟨1,422,598,true⟩, +⟨1,603,422,true⟩, +⟨1,599,592,true⟩, +⟨1,599,598,true⟩, +⟨1,592,596,true⟩, +⟨0,243,911,true⟩, +⟨1,243,282,true⟩, +⟨0,270,462,true⟩, +⟨1,243,270,true⟩, +⟨1,243,253,true⟩, +⟨1,243,576,true⟩, +⟨1,583,576,true⟩, +⟨1,583,582,true⟩, +⟨1,576,580,true⟩, +⟨0,242,935,true⟩, +⟨1,242,276,true⟩, +⟨1,242,264,true⟩, +⟨1,242,2,true⟩, +⟨1,242,560,true⟩, +⟨1,571,560,true⟩, +⟨1,310,315,true⟩, +⟨1,310,566,true⟩, +⟨1,571,310,true⟩, +⟨1,567,560,true⟩, +⟨1,567,566,true⟩, +⟨1,560,564,true⟩, +⟨0,241,927,true⟩, +⟨1,241,7,true⟩, +⟨1,241,6,true⟩, +⟨0,247,460,true⟩, +⟨1,241,247,true⟩, +⟨1,241,544,true⟩, +⟨1,551,544,true⟩, +⟨1,551,550,true⟩, +⟨1,544,548,true⟩, +⟨0,240,919,true⟩, +⟨1,240,5,true⟩, +⟨1,240,4,true⟩, +⟨1,240,246,true⟩, +⟨1,240,528,true⟩, +⟨1,532,533,true⟩, +⟨1,532,534,true⟩, +⟨1,528,532,true⟩, +⟨0,523,887,true⟩, +⟨0,258,458,true⟩, +⟨1,523,258,true⟩, +⟨1,252,0,true⟩, +⟨1,252,1,true⟩, +⟨1,252,512,true⟩, +⟨1,252,523,true⟩, +⟨1,523,252,true⟩, +⟨1,523,1,true⟩, +⟨1,523,0,true⟩, +⟨1,523,512,true⟩, +⟨1,406,411,true⟩, +⟨1,406,518,true⟩, +⟨1,523,406,true⟩, +⟨1,519,512,true⟩, +⟨1,519,518,true⟩, +⟨1,512,516,true⟩, +⟨1,931,733,true⟩, +⟨1,733,735,true⟩, +⟨1,930,732,true⟩, +⟨1,732,734,true⟩, +⟨1,929,399,true⟩, +⟨1,399,395,true⟩, +⟨1,928,397,true⟩, +⟨1,397,393,true⟩, +⟨1,927,729,true⟩, +⟨1,729,731,true⟩, +⟨1,926,728,true⟩, +⟨1,728,730,true⟩, +⟨1,925,388,true⟩, +⟨1,388,390,true⟩, +⟨1,924,384,true⟩, +⟨1,384,386,true⟩, +⟨1,923,723,true⟩, +⟨1,723,727,true⟩, +⟨1,922,721,true⟩, +⟨1,721,725,true⟩, +⟨1,921,724,true⟩, +⟨1,920,724,true⟩, +⟨1,724,726,true⟩, +⟨1,919,720,true⟩, +⟨1,918,720,true⟩, +⟨1,720,722,true⟩, +⟨1,917,717,true⟩, +⟨1,717,719,true⟩, +⟨1,916,716,true⟩, +⟨1,716,718,true⟩, +⟨1,915,713,true⟩, +⟨1,713,715,true⟩, +⟨1,914,712,true⟩, +⟨1,712,714,true⟩, +⟨1,913,463,true⟩, +⟨1,463,455,true⟩, +⟨1,912,449,true⟩, +⟨1,449,457,true⟩, +⟨1,911,452,true⟩, +⟨1,452,460,true⟩, +⟨1,910,458,true⟩, +⟨1,458,450,true⟩, +⟨1,909,707,true⟩, +⟨1,707,711,true⟩, +⟨1,908,705,true⟩, +⟨1,705,709,true⟩, +⟨1,907,708,true⟩, +⟨1,906,708,true⟩, +⟨1,708,710,true⟩, +⟨1,905,704,true⟩, +⟨1,904,704,true⟩, +⟨1,704,706,true⟩, +⟨1,903,697,true⟩, +⟨1,697,699,true⟩, +⟨1,902,696,true⟩, +⟨1,696,698,true⟩, +⟨1,901,701,true⟩, +⟨1,701,703,true⟩, +⟨1,900,700,true⟩, +⟨1,700,702,true⟩, +⟨1,899,479,true⟩, +⟨1,479,471,true⟩, +⟨1,898,465,true⟩, +⟨1,465,473,true⟩, +⟨1,897,468,true⟩, +⟨1,468,476,true⟩, +⟨1,896,474,true⟩, +⟨1,474,466,true⟩, +⟨1,895,691,true⟩, +⟨1,691,695,true⟩, +⟨1,894,689,true⟩, +⟨1,689,693,true⟩, +⟨1,893,692,true⟩, +⟨1,892,692,true⟩, +⟨1,692,694,true⟩, +⟨1,891,688,true⟩, +⟨1,890,688,true⟩, +⟨1,688,690,true⟩, +⟨1,889,685,true⟩, +⟨1,685,687,true⟩, +⟨1,888,684,true⟩, +⟨1,684,686,true⟩, +⟨1,887,681,true⟩, +⟨1,681,683,true⟩, +⟨1,886,680,true⟩, +⟨1,680,682,true⟩, +⟨1,885,675,true⟩, +⟨1,675,679,true⟩, +⟨1,884,673,true⟩, +⟨1,673,677,true⟩, +⟨1,883,495,true⟩, +⟨1,495,487,true⟩, +⟨1,882,481,true⟩, +⟨1,481,489,true⟩] +def chunk89 : List Event := [⟨1,881,484,true⟩, +⟨1,484,492,true⟩, +⟨1,880,490,true⟩, +⟨1,490,482,true⟩, +⟨1,879,676,true⟩, +⟨1,878,676,true⟩, +⟨1,676,678,true⟩, +⟨1,877,672,true⟩, +⟨1,876,672,true⟩, +⟨1,672,674,true⟩, +⟨1,875,665,true⟩, +⟨1,665,667,true⟩, +⟨1,874,664,true⟩, +⟨1,664,666,true⟩, +⟨1,873,669,true⟩, +⟨1,669,671,true⟩, +⟨1,872,668,true⟩, +⟨1,668,670,true⟩, +⟨1,871,659,true⟩, +⟨1,659,663,true⟩, +⟨1,870,657,true⟩, +⟨1,657,661,true⟩, +⟨1,869,447,true⟩, +⟨1,447,439,true⟩, +⟨1,868,433,true⟩, +⟨1,433,441,true⟩, +⟨1,867,436,true⟩, +⟨1,436,444,true⟩, +⟨1,866,442,true⟩, +⟨1,442,434,true⟩, +⟨1,865,660,true⟩, +⟨1,864,660,true⟩, +⟨1,660,662,true⟩, +⟨1,863,656,true⟩, +⟨1,862,656,true⟩, +⟨1,656,658,true⟩, +⟨1,861,643,true⟩, +⟨1,643,647,true⟩, +⟨1,860,641,true⟩, +⟨1,641,645,true⟩, +⟨1,859,653,true⟩, +⟨1,653,655,true⟩, +⟨1,858,652,true⟩, +⟨1,652,654,true⟩, +⟨1,857,649,true⟩, +⟨1,649,651,true⟩, +⟨1,856,648,true⟩, +⟨1,648,650,true⟩, +⟨1,855,371,true⟩, +⟨1,371,379,true⟩, +⟨1,854,381,true⟩, +⟨1,381,373,true⟩, +⟨1,853,382,true⟩, +⟨1,382,374,true⟩, +⟨1,852,368,true⟩, +⟨1,368,376,true⟩, +⟨1,851,644,true⟩, +⟨1,850,644,true⟩, +⟨1,644,646,true⟩, +⟨1,849,640,true⟩, +⟨1,848,640,true⟩, +⟨1,640,642,true⟩, +⟨1,847,627,true⟩, +⟨1,627,631,true⟩, +⟨1,846,625,true⟩, +⟨1,625,629,true⟩, +⟨1,845,633,true⟩, +⟨1,633,635,true⟩, +⟨1,844,632,true⟩, +⟨1,632,634,true⟩, +⟨1,843,637,true⟩, +⟨1,637,639,true⟩, +⟨1,842,636,true⟩, +⟨1,636,638,true⟩, +⟨1,841,303,true⟩, +⟨1,303,299,true⟩, +⟨1,840,301,true⟩, +⟨1,301,297,true⟩, +⟨1,839,292,true⟩, +⟨1,292,294,true⟩, +⟨1,838,288,true⟩, +⟨1,288,290,true⟩, +⟨1,837,628,true⟩, +⟨1,836,628,true⟩, +⟨1,628,630,true⟩, +⟨1,835,624,true⟩, +⟨1,834,624,true⟩, +⟨1,624,626,true⟩, +⟨1,833,621,true⟩, +⟨1,621,623,true⟩, +⟨1,832,620,true⟩, +⟨1,620,622,true⟩, +⟨1,831,617,true⟩, +⟨1,617,619,true⟩, +⟨1,830,616,true⟩, +⟨1,616,618,true⟩, +⟨1,829,611,true⟩, +⟨1,611,615,true⟩, +⟨1,828,609,true⟩, +⟨1,609,613,true⟩, +⟨1,827,499,true⟩, +⟨1,499,503,true⟩, +⟨1,826,497,true⟩, +⟨1,497,501,true⟩, +⟨1,825,510,true⟩, +⟨1,510,508,true⟩, +⟨1,824,506,true⟩, +⟨1,506,504,true⟩, +⟨1,823,612,true⟩, +⟨1,822,612,true⟩, +⟨1,612,614,true⟩, +⟨1,821,608,true⟩, +⟨1,820,608,true⟩, +⟨1,608,610,true⟩, +⟨1,819,601,true⟩, +⟨1,601,603,true⟩, +⟨1,818,600,true⟩, +⟨1,600,602,true⟩, +⟨1,817,605,true⟩, +⟨1,605,607,true⟩, +⟨1,816,604,true⟩, +⟨1,604,606,true⟩, +⟨1,815,595,true⟩, +⟨1,595,599,true⟩, +⟨1,814,593,true⟩, +⟨1,593,597,true⟩, +⟨1,813,419,true⟩, +⟨1,419,427,true⟩, +⟨1,812,429,true⟩, +⟨1,429,421,true⟩, +⟨1,811,430,true⟩, +⟨1,430,422,true⟩, +⟨1,810,416,true⟩, +⟨1,416,424,true⟩, +⟨1,809,596,true⟩, +⟨1,808,596,true⟩, +⟨1,596,598,true⟩, +⟨1,807,592,true⟩, +⟨1,806,592,true⟩, +⟨1,592,594,true⟩, +⟨1,805,579,true⟩, +⟨1,579,583,true⟩, +⟨1,804,577,true⟩, +⟨1,577,581,true⟩, +⟨1,803,589,true⟩, +⟨1,589,591,true⟩, +⟨1,802,588,true⟩, +⟨1,588,590,true⟩, +⟨1,801,585,true⟩, +⟨1,585,587,true⟩, +⟨1,800,584,true⟩, +⟨1,584,586,true⟩, +⟨1,799,367,true⟩, +⟨1,367,363,true⟩, +⟨1,798,365,true⟩, +⟨1,365,361,true⟩, +⟨1,797,356,true⟩, +⟨1,356,358,true⟩, +⟨1,796,352,true⟩, +⟨1,352,354,true⟩, +⟨1,795,580,true⟩, +⟨1,794,580,true⟩, +⟨1,580,582,true⟩, +⟨1,793,576,true⟩, +⟨1,792,576,true⟩, +⟨1,576,578,true⟩, +⟨1,791,563,true⟩, +⟨1,563,567,true⟩, +⟨1,790,561,true⟩, +⟨1,561,565,true⟩, +⟨1,789,569,true⟩, +⟨1,569,571,true⟩, +⟨1,788,568,true⟩, +⟨1,568,570,true⟩, +⟨1,787,573,true⟩, +⟨1,573,575,true⟩, +⟨1,786,572,true⟩, +⟨1,572,574,true⟩, +⟨1,785,307,true⟩, +⟨1,307,315,true⟩, +⟨1,784,317,true⟩, +⟨1,317,309,true⟩, +⟨1,783,318,true⟩, +⟨1,318,310,true⟩, +⟨1,782,304,true⟩, +⟨1,304,312,true⟩, +⟨1,781,564,true⟩, +⟨1,780,564,true⟩, +⟨1,564,566,true⟩, +⟨1,779,560,true⟩, +⟨1,778,560,true⟩, +⟨1,560,562,true⟩, +⟨1,777,547,true⟩, +⟨1,547,551,true⟩, +⟨1,776,545,true⟩, +⟨1,545,549,true⟩, +⟨1,775,557,true⟩, +⟨1,557,559,true⟩, +⟨1,774,556,true⟩, +⟨1,556,558,true⟩] +def chunk90 : List Event := [⟨1,773,553,true⟩, +⟨1,553,555,true⟩, +⟨1,772,552,true⟩, +⟨1,552,554,true⟩, +⟨1,771,323,true⟩, +⟨1,323,331,true⟩, +⟨1,770,333,true⟩, +⟨1,333,325,true⟩, +⟨1,769,334,true⟩, +⟨1,334,326,true⟩, +⟨1,768,320,true⟩, +⟨1,320,328,true⟩, +⟨1,767,548,true⟩, +⟨1,766,548,true⟩, +⟨1,548,550,true⟩, +⟨1,765,544,true⟩, +⟨1,764,544,true⟩, +⟨1,544,546,true⟩, +⟨1,763,531,true⟩, +⟨1,531,535,true⟩, +⟨1,762,529,true⟩, +⟨1,529,533,true⟩, +⟨1,761,537,true⟩, +⟨1,537,539,true⟩, +⟨1,760,536,true⟩, +⟨1,536,538,true⟩, +⟨1,759,541,true⟩, +⟨1,541,543,true⟩, +⟨1,758,540,true⟩, +⟨1,540,542,true⟩, +⟨1,757,339,true⟩, +⟨1,339,343,true⟩, +⟨1,756,337,true⟩, +⟨1,337,341,true⟩, +⟨1,755,350,true⟩, +⟨1,350,348,true⟩, +⟨1,754,346,true⟩, +⟨1,346,344,true⟩, +⟨1,753,532,true⟩, +⟨1,752,532,true⟩, +⟨1,532,534,true⟩, +⟨1,751,528,true⟩, +⟨1,750,528,true⟩, +⟨1,528,530,true⟩, +⟨1,749,515,true⟩, +⟨1,515,519,true⟩, +⟨1,748,513,true⟩, +⟨1,513,517,true⟩, +⟨1,747,521,true⟩, +⟨1,521,523,true⟩, +⟨1,746,520,true⟩, +⟨1,520,522,true⟩, +⟨1,745,525,true⟩, +⟨1,525,527,true⟩, +⟨1,744,524,true⟩, +⟨1,524,526,true⟩, +⟨1,743,415,true⟩, +⟨1,415,411,true⟩, +⟨1,742,413,true⟩, +⟨1,413,409,true⟩, +⟨1,741,404,true⟩, +⟨1,404,406,true⟩, +⟨1,740,400,true⟩, +⟨1,400,402,true⟩, +⟨1,739,516,true⟩, +⟨1,738,516,true⟩, +⟨1,516,518,true⟩, +⟨1,737,512,true⟩, +⟨1,736,512,true⟩, +⟨1,512,514,true⟩, +⟨1,735,395,true⟩, +⟨1,395,391,true⟩, +⟨1,734,399,true⟩, +⟨1,399,387,true⟩, +⟨1,733,393,true⟩, +⟨1,393,389,true⟩, +⟨1,732,397,true⟩, +⟨1,397,385,true⟩, +⟨1,731,390,true⟩, +⟨1,390,396,true⟩, +⟨1,730,388,true⟩, +⟨1,388,398,true⟩, +⟨1,729,386,true⟩, +⟨1,386,392,true⟩, +⟨1,728,384,true⟩, +⟨1,384,394,true⟩, +⟨1,727,726,true⟩, +⟨1,726,62,true⟩, +⟨1,726,61,true⟩, +⟨1,725,724,true⟩, +⟨1,724,63,true⟩, +⟨1,724,60,true⟩, +⟨1,723,722,true⟩, +⟨1,722,58,true⟩, +⟨1,722,57,true⟩, +⟨1,721,720,true⟩, +⟨1,720,59,true⟩, +⟨1,720,56,true⟩, +⟨1,719,455,true⟩, +⟨1,455,459,true⟩, +⟨1,718,463,true⟩, +⟨1,463,451,true⟩, +⟨1,717,457,true⟩, +⟨1,457,453,true⟩, +⟨1,716,449,true⟩, +⟨1,449,461,true⟩, +⟨1,715,460,true⟩, +⟨1,460,454,true⟩, +⟨1,714,452,true⟩, +⟨1,452,462,true⟩, +⟨1,713,450,true⟩, +⟨1,450,456,true⟩, +⟨1,712,458,true⟩, +⟨1,458,448,true⟩, +⟨1,711,710,true⟩, +⟨1,710,94,true⟩, +⟨1,710,93,true⟩, +⟨1,709,708,true⟩, +⟨1,708,95,true⟩, +⟨1,708,92,true⟩, +⟨1,707,706,true⟩, +⟨1,706,90,true⟩, +⟨1,706,89,true⟩, +⟨1,705,704,true⟩, +⟨1,704,91,true⟩, +⟨1,704,88,true⟩, +⟨1,703,471,true⟩, +⟨1,471,475,true⟩, +⟨1,702,479,true⟩, +⟨1,479,467,true⟩, +⟨1,701,473,true⟩, +⟨1,473,469,true⟩, +⟨1,700,465,true⟩, +⟨1,465,477,true⟩, +⟨1,699,476,true⟩, +⟨1,476,470,true⟩, +⟨1,698,468,true⟩, +⟨1,468,478,true⟩, +⟨1,697,466,true⟩, +⟨1,466,472,true⟩, +⟨1,696,474,true⟩, +⟨1,474,464,true⟩, +⟨1,695,694,true⟩, +⟨1,694,102,true⟩, +⟨1,694,101,true⟩, +⟨1,693,692,true⟩, +⟨1,692,103,true⟩, +⟨1,692,100,true⟩, +⟨1,691,690,true⟩, +⟨1,690,98,true⟩, +⟨1,690,97,true⟩, +⟨1,689,688,true⟩, +⟨1,688,99,true⟩, +⟨1,688,96,true⟩, +⟨1,687,487,true⟩, +⟨1,487,491,true⟩, +⟨1,686,495,true⟩, +⟨1,495,483,true⟩, +⟨1,685,489,true⟩, +⟨1,489,485,true⟩, +⟨1,684,481,true⟩, +⟨1,481,493,true⟩, +⟨1,683,492,true⟩, +⟨1,492,486,true⟩, +⟨1,682,484,true⟩, +⟨1,484,494,true⟩, +⟨1,681,482,true⟩, +⟨1,482,488,true⟩, +⟨1,680,490,true⟩, +⟨1,490,480,true⟩, +⟨1,679,678,true⟩, +⟨1,678,110,true⟩, +⟨1,678,109,true⟩, +⟨1,677,676,true⟩, +⟨1,676,111,true⟩, +⟨1,676,108,true⟩, +⟨1,675,674,true⟩, +⟨1,674,106,true⟩, +⟨1,674,105,true⟩, +⟨1,673,672,true⟩, +⟨1,672,107,true⟩, +⟨1,672,104,true⟩, +⟨1,671,439,true⟩, +⟨1,439,443,true⟩, +⟨1,670,447,true⟩, +⟨1,447,435,true⟩, +⟨1,669,441,true⟩, +⟨1,441,437,true⟩, +⟨1,668,433,true⟩, +⟨1,433,445,true⟩, +⟨1,667,444,true⟩, +⟨1,444,438,true⟩, +⟨1,666,436,true⟩, +⟨1,436,446,true⟩, +⟨1,665,434,true⟩, +⟨1,434,440,true⟩, +⟨1,664,442,true⟩, +⟨1,442,432,true⟩, +⟨1,663,662,true⟩, +⟨1,662,86,true⟩] +def chunk91 : List Event := [⟨1,662,85,true⟩, +⟨1,661,660,true⟩, +⟨1,660,87,true⟩, +⟨1,660,84,true⟩, +⟨1,659,658,true⟩, +⟨1,658,82,true⟩, +⟨1,658,81,true⟩, +⟨1,657,656,true⟩, +⟨1,656,83,true⟩, +⟨1,656,80,true⟩, +⟨1,655,379,true⟩, +⟨1,379,375,true⟩, +⟨1,654,371,true⟩, +⟨1,371,383,true⟩, +⟨1,653,373,true⟩, +⟨1,373,377,true⟩, +⟨1,652,381,true⟩, +⟨1,381,369,true⟩, +⟨1,651,374,true⟩, +⟨1,374,380,true⟩, +⟨1,650,382,true⟩, +⟨1,382,372,true⟩, +⟨1,649,376,true⟩, +⟨1,376,370,true⟩, +⟨1,648,368,true⟩, +⟨1,368,378,true⟩, +⟨1,647,646,true⟩, +⟨1,646,54,true⟩, +⟨1,646,53,true⟩, +⟨1,645,644,true⟩, +⟨1,644,55,true⟩, +⟨1,644,52,true⟩, +⟨1,643,642,true⟩, +⟨1,642,50,true⟩, +⟨1,642,49,true⟩, +⟨1,641,640,true⟩, +⟨1,640,51,true⟩, +⟨1,640,48,true⟩, +⟨1,639,299,true⟩, +⟨1,299,295,true⟩, +⟨1,638,303,true⟩, +⟨1,303,291,true⟩, +⟨1,637,297,true⟩, +⟨1,297,293,true⟩, +⟨1,636,301,true⟩, +⟨1,301,289,true⟩, +⟨1,635,294,true⟩, +⟨1,294,300,true⟩, +⟨1,634,292,true⟩, +⟨1,292,302,true⟩, +⟨1,633,290,true⟩, +⟨1,290,296,true⟩, +⟨1,632,288,true⟩, +⟨1,288,298,true⟩, +⟨1,631,630,true⟩, +⟨1,630,14,true⟩, +⟨1,630,13,true⟩, +⟨1,629,628,true⟩, +⟨1,628,15,true⟩, +⟨1,628,12,true⟩, +⟨1,627,626,true⟩, +⟨1,626,10,true⟩, +⟨1,626,9,true⟩, +⟨1,625,624,true⟩, +⟨1,624,11,true⟩, +⟨1,624,8,true⟩, +⟨1,623,503,true⟩, +⟨1,503,507,true⟩, +⟨1,622,499,true⟩, +⟨1,499,511,true⟩, +⟨1,621,501,true⟩, +⟨1,501,505,true⟩, +⟨1,620,497,true⟩, +⟨1,497,509,true⟩, +⟨1,619,508,true⟩, +⟨1,508,502,true⟩, +⟨1,618,510,true⟩, +⟨1,510,500,true⟩, +⟨1,617,504,true⟩, +⟨1,504,498,true⟩, +⟨1,616,506,true⟩, +⟨1,506,496,true⟩, +⟨1,615,614,true⟩, +⟨1,614,118,true⟩, +⟨1,614,117,true⟩, +⟨1,613,612,true⟩, +⟨1,612,119,true⟩, +⟨1,612,116,true⟩, +⟨1,611,610,true⟩, +⟨1,610,114,true⟩, +⟨1,610,113,true⟩, +⟨1,609,608,true⟩, +⟨1,608,115,true⟩, +⟨1,608,112,true⟩, +⟨1,607,427,true⟩, +⟨1,427,423,true⟩, +⟨1,606,419,true⟩, +⟨1,419,431,true⟩, +⟨1,605,421,true⟩, +⟨1,421,425,true⟩, +⟨1,604,429,true⟩, +⟨1,429,417,true⟩, +⟨1,603,422,true⟩, +⟨1,422,428,true⟩, +⟨1,602,430,true⟩, +⟨1,430,420,true⟩, +⟨1,601,424,true⟩, +⟨1,424,418,true⟩, +⟨1,600,416,true⟩, +⟨1,416,426,true⟩, +⟨1,599,598,true⟩, +⟨1,598,78,true⟩, +⟨1,598,77,true⟩, +⟨1,597,596,true⟩, +⟨1,596,79,true⟩, +⟨1,596,76,true⟩, +⟨1,595,594,true⟩, +⟨1,594,74,true⟩, +⟨1,594,73,true⟩, +⟨1,593,592,true⟩, +⟨1,592,75,true⟩, +⟨1,592,72,true⟩, +⟨1,591,363,true⟩, +⟨1,363,359,true⟩, +⟨1,590,367,true⟩, +⟨1,367,355,true⟩, +⟨1,589,361,true⟩, +⟨1,361,357,true⟩, +⟨1,588,365,true⟩, +⟨1,365,353,true⟩, +⟨1,587,358,true⟩, +⟨1,358,364,true⟩, +⟨1,586,356,true⟩, +⟨1,356,366,true⟩, +⟨1,585,354,true⟩, +⟨1,354,360,true⟩, +⟨1,584,352,true⟩, +⟨1,352,362,true⟩, +⟨1,583,582,true⟩, +⟨1,582,46,true⟩, +⟨1,582,45,true⟩, +⟨1,581,580,true⟩, +⟨1,580,47,true⟩, +⟨1,580,44,true⟩, +⟨1,579,578,true⟩, +⟨1,578,42,true⟩, +⟨1,578,41,true⟩, +⟨1,577,576,true⟩, +⟨1,576,43,true⟩, +⟨1,576,40,true⟩, +⟨1,575,315,true⟩, +⟨1,315,311,true⟩, +⟨1,574,307,true⟩, +⟨1,307,319,true⟩, +⟨1,573,309,true⟩, +⟨1,309,313,true⟩, +⟨1,572,317,true⟩, +⟨1,317,305,true⟩, +⟨1,571,310,true⟩, +⟨1,310,316,true⟩, +⟨1,570,318,true⟩, +⟨1,318,308,true⟩, +⟨1,569,312,true⟩, +⟨1,312,306,true⟩, +⟨1,568,304,true⟩, +⟨1,304,314,true⟩, +⟨1,567,566,true⟩, +⟨1,566,22,true⟩, +⟨1,566,21,true⟩, +⟨1,565,564,true⟩, +⟨1,564,23,true⟩, +⟨1,564,20,true⟩, +⟨1,563,562,true⟩, +⟨1,562,18,true⟩, +⟨1,562,17,true⟩, +⟨1,561,560,true⟩, +⟨1,560,19,true⟩, +⟨1,560,16,true⟩, +⟨1,559,331,true⟩, +⟨1,331,327,true⟩, +⟨1,558,323,true⟩, +⟨1,323,335,true⟩, +⟨1,557,325,true⟩, +⟨1,325,329,true⟩, +⟨1,556,333,true⟩, +⟨1,333,321,true⟩, +⟨1,555,326,true⟩, +⟨1,326,332,true⟩, +⟨1,554,334,true⟩, +⟨1,334,324,true⟩, +⟨1,553,328,true⟩, +⟨1,328,322,true⟩, +⟨1,552,320,true⟩, +⟨1,320,330,true⟩, +⟨1,551,550,true⟩, +⟨1,550,30,true⟩, +⟨1,550,29,true⟩, +⟨1,549,548,true⟩, +⟨1,548,31,true⟩, +⟨1,548,28,true⟩] +def chunk92 : List Event := [⟨1,547,546,true⟩, +⟨1,546,26,true⟩, +⟨1,546,25,true⟩, +⟨1,545,544,true⟩, +⟨1,544,27,true⟩, +⟨1,544,24,true⟩, +⟨1,543,343,true⟩, +⟨1,343,347,true⟩, +⟨1,542,339,true⟩, +⟨1,339,351,true⟩, +⟨1,541,341,true⟩, +⟨1,341,345,true⟩, +⟨1,540,337,true⟩, +⟨1,337,349,true⟩, +⟨1,539,348,true⟩, +⟨1,348,342,true⟩, +⟨1,538,350,true⟩, +⟨1,350,340,true⟩, +⟨1,537,344,true⟩, +⟨1,344,338,true⟩, +⟨1,536,346,true⟩, +⟨1,346,336,true⟩, +⟨1,535,534,true⟩, +⟨1,534,38,true⟩, +⟨1,534,37,true⟩, +⟨1,533,532,true⟩, +⟨1,532,39,true⟩, +⟨1,532,36,true⟩, +⟨1,531,530,true⟩, +⟨1,530,34,true⟩, +⟨1,530,33,true⟩, +⟨1,529,528,true⟩, +⟨1,528,35,true⟩, +⟨1,528,32,true⟩, +⟨1,527,411,true⟩, +⟨1,411,407,true⟩, +⟨1,526,415,true⟩, +⟨1,415,403,true⟩, +⟨1,525,409,true⟩, +⟨1,409,405,true⟩, +⟨1,524,413,true⟩, +⟨1,413,401,true⟩, +⟨1,523,406,true⟩, +⟨1,406,412,true⟩, +⟨1,522,404,true⟩, +⟨1,404,414,true⟩, +⟨1,521,402,true⟩, +⟨1,402,408,true⟩, +⟨1,520,400,true⟩, +⟨1,400,410,true⟩, +⟨1,519,518,true⟩, +⟨1,518,70,true⟩, +⟨1,518,69,true⟩, +⟨1,517,516,true⟩, +⟨1,516,71,true⟩, +⟨1,516,68,true⟩, +⟨1,515,514,true⟩, +⟨1,514,66,true⟩, +⟨1,514,65,true⟩, +⟨1,513,512,true⟩, +⟨1,512,67,true⟩, +⟨1,512,64,true⟩, +⟨1,511,119,true⟩, +⟨1,510,119,true⟩, +⟨1,509,118,true⟩, +⟨1,508,118,true⟩, +⟨1,507,117,true⟩, +⟨1,506,117,true⟩, +⟨1,505,116,true⟩, +⟨1,504,116,true⟩, +⟨1,503,115,true⟩, +⟨1,502,115,true⟩, +⟨1,501,114,true⟩, +⟨1,500,114,true⟩, +⟨1,499,113,true⟩, +⟨1,498,113,true⟩, +⟨1,497,112,true⟩, +⟨1,496,112,true⟩, +⟨1,495,111,true⟩, +⟨1,494,111,true⟩, +⟨1,493,110,true⟩, +⟨1,492,110,true⟩, +⟨1,491,109,true⟩, +⟨1,490,109,true⟩, +⟨1,489,108,true⟩, +⟨1,488,108,true⟩, +⟨1,487,107,true⟩, +⟨1,486,107,true⟩, +⟨1,485,106,true⟩, +⟨1,484,106,true⟩, +⟨1,483,105,true⟩, +⟨1,482,105,true⟩, +⟨1,481,104,true⟩, +⟨1,480,104,true⟩, +⟨1,479,103,true⟩, +⟨1,478,103,true⟩, +⟨1,477,102,true⟩, +⟨1,476,102,true⟩, +⟨1,475,101,true⟩, +⟨1,474,101,true⟩, +⟨1,473,100,true⟩, +⟨1,472,100,true⟩, +⟨1,471,99,true⟩, +⟨1,470,99,true⟩, +⟨1,469,98,true⟩, +⟨1,468,98,true⟩, +⟨1,467,97,true⟩, +⟨1,466,97,true⟩, +⟨1,465,96,true⟩, +⟨1,464,96,true⟩, +⟨1,463,95,true⟩, +⟨1,462,95,true⟩, +⟨1,461,94,true⟩, +⟨1,460,94,true⟩, +⟨1,459,93,true⟩, +⟨1,458,93,true⟩, +⟨1,457,92,true⟩, +⟨1,456,92,true⟩, +⟨1,455,91,true⟩, +⟨1,454,91,true⟩, +⟨1,453,90,true⟩, +⟨1,452,90,true⟩, +⟨1,451,89,true⟩, +⟨1,450,89,true⟩, +⟨1,449,88,true⟩, +⟨1,448,88,true⟩, +⟨1,447,87,true⟩, +⟨1,446,87,true⟩, +⟨1,445,86,true⟩, +⟨1,444,86,true⟩, +⟨1,443,85,true⟩, +⟨1,442,85,true⟩, +⟨1,441,84,true⟩, +⟨1,440,84,true⟩, +⟨1,439,83,true⟩, +⟨1,438,83,true⟩, +⟨1,437,82,true⟩, +⟨1,436,82,true⟩, +⟨1,435,81,true⟩, +⟨1,434,81,true⟩, +⟨1,433,80,true⟩, +⟨1,432,80,true⟩, +⟨1,431,79,true⟩, +⟨1,430,79,true⟩, +⟨1,429,78,true⟩, +⟨1,428,78,true⟩, +⟨1,427,77,true⟩, +⟨1,426,77,true⟩, +⟨1,425,76,true⟩, +⟨1,424,76,true⟩, +⟨1,423,75,true⟩, +⟨1,422,75,true⟩, +⟨1,421,74,true⟩, +⟨1,420,74,true⟩, +⟨1,419,73,true⟩, +⟨1,418,73,true⟩, +⟨1,417,72,true⟩, +⟨1,416,72,true⟩, +⟨1,415,71,true⟩, +⟨1,414,71,true⟩, +⟨1,413,70,true⟩, +⟨1,412,70,true⟩, +⟨1,411,69,true⟩, +⟨1,410,69,true⟩, +⟨1,409,68,true⟩, +⟨1,408,68,true⟩, +⟨1,407,67,true⟩, +⟨1,406,67,true⟩, +⟨1,405,66,true⟩, +⟨1,404,66,true⟩, +⟨1,403,65,true⟩, +⟨1,402,65,true⟩, +⟨1,401,64,true⟩, +⟨1,400,64,true⟩, +⟨1,399,63,true⟩, +⟨1,398,63,true⟩, +⟨1,397,62,true⟩, +⟨1,396,62,true⟩, +⟨1,395,61,true⟩, +⟨1,394,61,true⟩, +⟨1,393,60,true⟩, +⟨1,392,60,true⟩, +⟨1,391,59,true⟩, +⟨1,390,59,true⟩, +⟨1,389,58,true⟩, +⟨1,388,58,true⟩, +⟨1,387,57,true⟩, +⟨1,386,57,true⟩, +⟨1,385,56,true⟩, +⟨1,384,56,true⟩, +⟨1,383,55,true⟩, +⟨1,382,55,true⟩, +⟨1,381,54,true⟩, +⟨1,380,54,true⟩, +⟨1,379,53,true⟩, +⟨1,378,53,true⟩, +⟨1,377,52,true⟩, +⟨1,376,52,true⟩, +⟨1,375,51,true⟩, +⟨1,374,51,true⟩] +def chunk93 : List Event := [⟨1,373,50,true⟩, +⟨1,372,50,true⟩, +⟨1,371,49,true⟩, +⟨1,370,49,true⟩, +⟨1,369,48,true⟩, +⟨1,368,48,true⟩, +⟨1,367,47,true⟩, +⟨1,366,47,true⟩, +⟨1,365,46,true⟩, +⟨1,364,46,true⟩, +⟨1,363,45,true⟩, +⟨1,362,45,true⟩, +⟨1,361,44,true⟩, +⟨1,360,44,true⟩, +⟨1,359,43,true⟩, +⟨1,358,43,true⟩, +⟨1,357,42,true⟩, +⟨1,356,42,true⟩, +⟨1,355,41,true⟩, +⟨1,354,41,true⟩, +⟨1,353,40,true⟩, +⟨1,352,40,true⟩, +⟨1,351,39,true⟩, +⟨1,350,39,true⟩, +⟨1,349,38,true⟩, +⟨1,348,38,true⟩, +⟨1,347,37,true⟩, +⟨1,346,37,true⟩, +⟨1,345,36,true⟩, +⟨1,344,36,true⟩, +⟨1,343,35,true⟩, +⟨1,342,35,true⟩, +⟨1,341,34,true⟩, +⟨1,340,34,true⟩, +⟨1,339,33,true⟩, +⟨1,338,33,true⟩, +⟨1,337,32,true⟩, +⟨1,336,32,true⟩, +⟨1,335,31,true⟩, +⟨1,334,31,true⟩, +⟨1,333,30,true⟩, +⟨1,332,30,true⟩, +⟨1,331,29,true⟩, +⟨1,330,29,true⟩, +⟨1,329,28,true⟩, +⟨1,328,28,true⟩, +⟨1,327,27,true⟩, +⟨1,326,27,true⟩, +⟨1,325,26,true⟩, +⟨1,324,26,true⟩, +⟨1,323,25,true⟩, +⟨1,322,25,true⟩, +⟨1,321,24,true⟩, +⟨1,320,24,true⟩, +⟨1,319,23,true⟩, +⟨1,318,23,true⟩, +⟨1,317,22,true⟩, +⟨1,316,22,true⟩, +⟨1,315,21,true⟩, +⟨1,314,21,true⟩, +⟨1,313,20,true⟩, +⟨1,312,20,true⟩, +⟨1,311,19,true⟩, +⟨1,310,19,true⟩, +⟨1,309,18,true⟩, +⟨1,308,18,true⟩, +⟨1,307,17,true⟩, +⟨1,306,17,true⟩, +⟨1,305,16,true⟩, +⟨1,304,16,true⟩, +⟨1,303,15,true⟩, +⟨1,302,15,true⟩, +⟨1,301,14,true⟩, +⟨1,300,14,true⟩, +⟨1,299,13,true⟩, +⟨1,298,13,true⟩, +⟨1,297,12,true⟩, +⟨1,296,12,true⟩, +⟨1,295,11,true⟩, +⟨1,294,11,true⟩, +⟨1,293,10,true⟩, +⟨1,292,10,true⟩, +⟨1,291,9,true⟩, +⟨1,290,9,true⟩, +⟨1,289,8,true⟩, +⟨1,288,8,true⟩, +⟨1,287,7,true⟩, +⟨1,286,7,true⟩, +⟨1,285,7,true⟩, +⟨1,284,7,true⟩, +⟨1,283,7,true⟩, +⟨1,282,7,true⟩, +⟨1,281,6,true⟩, +⟨1,280,6,true⟩, +⟨1,279,6,true⟩, +⟨1,278,6,true⟩, +⟨1,277,6,true⟩, +⟨1,276,6,true⟩, +⟨1,275,5,true⟩, +⟨1,274,5,true⟩, +⟨1,273,5,true⟩, +⟨1,272,5,true⟩, +⟨1,271,5,true⟩, +⟨1,270,5,true⟩, +⟨1,269,4,true⟩, +⟨1,268,4,true⟩, +⟨1,267,4,true⟩, +⟨1,266,4,true⟩, +⟨1,265,4,true⟩, +⟨1,264,4,true⟩, +⟨1,263,3,true⟩, +⟨1,262,3,true⟩, +⟨1,261,3,true⟩, +⟨1,260,3,true⟩, +⟨1,259,3,true⟩, +⟨1,258,3,true⟩, +⟨1,257,2,true⟩, +⟨1,256,2,true⟩, +⟨1,255,2,true⟩, +⟨1,254,2,true⟩, +⟨1,253,2,true⟩, +⟨1,252,2,true⟩, +⟨1,251,1,true⟩, +⟨1,250,1,true⟩, +⟨1,249,1,true⟩, +⟨1,248,1,true⟩, +⟨1,247,1,true⟩, +⟨1,246,1,true⟩, +⟨1,245,0,true⟩, +⟨1,244,0,true⟩, +⟨1,243,0,true⟩, +⟨1,242,0,true⟩, +⟨1,241,0,true⟩, +⟨1,240,0,true⟩, +⟨1,241,787,true⟩, +⟨1,241,803,true⟩, +⟨1,241,817,true⟩, +⟨1,241,833,true⟩, +⟨1,242,747,true⟩, +⟨1,242,761,true⟩, +⟨1,242,773,true⟩, +⟨1,244,745,true⟩, +⟨1,248,743,true⟩, +⟨1,248,757,true⟩, +⟨1,248,769,true⟩, +⟨1,248,861,true⟩, +⟨1,248,875,true⟩, +⟨1,248,889,true⟩, +⟨1,249,771,true⟩, +⟨1,249,847,true⟩, +⟨1,249,873,true⟩, +⟨1,250,741,true⟩, +⟨1,250,845,true⟩, +⟨1,250,859,true⟩, +⟨1,250,885,true⟩, +⟨1,254,903,true⟩, +⟨1,254,917,true⟩, +⟨1,256,739,true⟩, +⟨1,256,799,true⟩, +⟨1,256,855,true⟩, +⟨1,256,909,true⟩, +⟨1,257,738,true⟩, +⟨1,257,783,true⟩, +⟨1,257,797,true⟩, +⟨1,257,839,true⟩, +⟨1,257,853,true⟩, +⟨1,257,895,true⟩, +⟨1,260,913,true⟩, +⟨1,263,825,true⟩, +⟨1,263,867,true⟩, +⟨1,267,899,true⟩, +⟨1,268,752,true⟩, +⟨1,268,785,true⟩, +⟨1,268,813,true⟩, +⟨1,268,841,true⟩, +⟨1,268,869,true⟩, +⟨1,268,923,true⟩, +⟨1,269,753,true⟩, +⟨1,269,781,true⟩, +⟨1,269,809,true⟩, +⟨1,269,837,true⟩, +⟨1,269,865,true⟩, +⟨1,269,893,true⟩, +⟨1,272,755,true⟩, +⟨1,272,822,true⟩, +⟨1,272,887,true⟩, +⟨1,272,901,true⟩, +⟨1,272,929,true⟩, +⟨1,274,827,true⟩, +⟨1,274,883,true⟩, +⟨1,275,795,true⟩, +⟨1,275,823,true⟩, +⟨1,275,851,true⟩, +⟨1,275,879,true⟩, +⟨1,283,836,true⟩, +⟨1,284,808,true⟩, +⟨1,284,931,true⟩, +⟨1,286,919,true⟩, +⟨1,286,921,true⟩, +⟨1,287,767,true⟩] +def chunk94 : List Event := [⟨1,736,738,true⟩, +⟨1,736,838,true⟩, +⟨1,736,839,true⟩, +⟨1,736,852,true⟩, +⟨1,736,853,true⟩, +⟨1,737,739,true⟩, +⟨1,737,908,true⟩, +⟨1,737,909,true⟩, +⟨1,740,741,true⟩, +⟨1,742,743,true⟩, +⟨1,742,874,true⟩, +⟨1,742,875,true⟩, +⟨1,742,888,true⟩, +⟨1,742,889,true⟩, +⟨1,744,745,true⟩, +⟨1,746,747,true⟩, +⟨1,748,789,true⟩, +⟨1,748,801,true⟩, +⟨1,748,818,true⟩, +⟨1,748,830,true⟩, +⟨1,749,789,true⟩, +⟨1,749,801,true⟩, +⟨1,749,819,true⟩, +⟨1,749,831,true⟩, +⟨1,750,752,true⟩, +⟨1,750,784,true⟩, +⟨1,750,785,true⟩, +⟨1,750,840,true⟩, +⟨1,750,841,true⟩, +⟨1,750,922,true⟩, +⟨1,750,923,true⟩, +⟨1,756,757,true⟩, +⟨1,756,860,true⟩, +⟨1,756,861,true⟩, +⟨1,756,888,true⟩, +⟨1,756,889,true⟩, +⟨1,760,761,true⟩, +⟨1,762,777,true⟩, +⟨1,762,791,true⟩, +⟨1,762,804,true⟩, +⟨1,762,815,true⟩, +⟨1,762,828,true⟩, +⟨1,763,777,true⟩, +⟨1,763,791,true⟩, +⟨1,763,805,true⟩, +⟨1,763,815,true⟩, +⟨1,763,829,true⟩, +⟨1,764,811,true⟩, +⟨1,764,881,true⟩, +⟨1,764,921,true⟩, +⟨1,765,767,true⟩, +⟨1,766,811,true⟩, +⟨1,766,881,true⟩, +⟨1,766,919,true⟩, +⟨1,768,769,true⟩, +⟨1,768,860,true⟩, +⟨1,768,861,true⟩, +⟨1,768,874,true⟩, +⟨1,768,875,true⟩, +⟨1,770,771,true⟩, +⟨1,772,773,true⟩, +⟨1,776,777,true⟩, +⟨1,776,804,true⟩, +⟨1,776,805,true⟩, +⟨1,776,814,true⟩, +⟨1,776,815,true⟩, +⟨1,779,751,true⟩, +⟨1,779,753,true⟩, +⟨1,779,781,true⟩, +⟨1,779,863,true⟩, +⟨1,779,865,true⟩, +⟨1,779,891,true⟩, +⟨1,779,893,true⟩, +⟨1,782,783,true⟩, +⟨1,782,838,true⟩, +⟨1,782,839,true⟩, +⟨1,782,894,true⟩, +⟨1,782,895,true⟩, +⟨1,786,787,true⟩, +⟨1,786,832,true⟩, +⟨1,786,833,true⟩, +⟨1,788,789,true⟩, +⟨1,788,830,true⟩, +⟨1,788,831,true⟩, +⟨1,790,791,true⟩, +⟨1,790,804,true⟩, +⟨1,790,805,true⟩, +⟨1,790,814,true⟩, +⟨1,790,815,true⟩, +⟨1,790,828,true⟩, +⟨1,790,829,true⟩, +⟨1,792,857,true⟩, +⟨1,792,897,true⟩, +⟨1,792,925,true⟩, +⟨1,793,795,true⟩, +⟨1,793,877,true⟩, +⟨1,793,879,true⟩, +⟨1,794,857,true⟩, +⟨1,794,897,true⟩, +⟨1,794,925,true⟩, +⟨1,796,797,true⟩, +⟨1,796,852,true⟩, +⟨1,796,853,true⟩, +⟨1,796,894,true⟩, +⟨1,796,895,true⟩, +⟨1,798,799,true⟩, +⟨1,798,908,true⟩, +⟨1,798,909,true⟩, +⟨1,800,801,true⟩, +⟨1,800,818,true⟩, +⟨1,800,819,true⟩, +⟨1,802,803,true⟩, +⟨1,802,832,true⟩, +⟨1,802,833,true⟩, +⟨1,806,808,true⟩, +⟨1,807,809,true⟩, +⟨1,807,863,true⟩, +⟨1,807,865,true⟩, +⟨1,807,891,true⟩, +⟨1,807,893,true⟩, +⟨1,810,811,true⟩, +⟨1,810,919,true⟩, +⟨1,810,921,true⟩, +⟨1,812,813,true⟩, +⟨1,812,840,true⟩, +⟨1,812,841,true⟩, +⟨1,812,922,true⟩, +⟨1,812,923,true⟩, +⟨1,816,817,true⟩, +⟨1,816,832,true⟩, +⟨1,816,833,true⟩, +⟨1,820,754,true⟩, +⟨1,820,755,true⟩, +⟨1,820,822,true⟩, +⟨1,821,823,true⟩, +⟨1,821,877,true⟩, +⟨1,821,879,true⟩, +⟨1,824,825,true⟩, +⟨1,826,827,true⟩, +⟨1,834,836,true⟩, +⟨1,835,751,true⟩, +⟨1,835,753,true⟩, +⟨1,835,837,true⟩, +⟨1,835,863,true⟩, +⟨1,835,865,true⟩, +⟨1,844,845,true⟩, +⟨1,844,884,true⟩, +⟨1,844,885,true⟩, +⟨1,846,847,true⟩, +⟨1,849,851,true⟩, +⟨1,849,877,true⟩, +⟨1,849,879,true⟩, +⟨1,854,855,true⟩, +⟨1,854,908,true⟩, +⟨1,854,909,true⟩, +⟨1,858,859,true⟩, +⟨1,858,884,true⟩, +⟨1,858,885,true⟩, +⟨1,866,867,true⟩, +⟨1,868,784,true⟩, +⟨1,868,785,true⟩, +⟨1,868,869,true⟩, +⟨1,868,922,true⟩, +⟨1,868,923,true⟩, +⟨1,872,873,true⟩, +⟨1,880,881,true⟩, +⟨1,880,919,true⟩, +⟨1,880,921,true⟩, +⟨1,882,883,true⟩, +⟨1,896,856,true⟩, +⟨1,896,857,true⟩, +⟨1,896,897,true⟩, +⟨1,898,899,true⟩, +⟨1,900,754,true⟩, +⟨1,900,755,true⟩, +⟨1,900,886,true⟩, +⟨1,900,887,true⟩, +⟨1,900,901,true⟩, +⟨1,902,903,true⟩, +⟨1,912,913,true⟩, +⟨1,916,917,true⟩, +⟨1,924,856,true⟩, +⟨1,924,857,true⟩, +⟨1,924,925,true⟩, +⟨1,928,886,true⟩, +⟨1,928,887,true⟩, +⟨1,928,929,true⟩, +⟨1,930,931,true⟩, +⟨1,932,938,true⟩, +⟨1,933,938,true⟩, +⟨1,936,961,true⟩, +⟨1,937,938,true⟩, +⟨1,941,949,true⟩, +⟨1,942,953,true⟩, +⟨1,943,958,true⟩, +⟨1,944,953,true⟩, +⟨1,945,958,true⟩, +⟨1,951,953,true⟩, +⟨1,956,958,true⟩, +⟨1,959,978,true⟩] +def chunk95 : List Event := [⟨1,960,978,true⟩, +⟨1,977,978,true⟩] +def forwardChunks : List (List Event) := [chunk0,chunk1,chunk2,chunk3,chunk4,chunk5,chunk6,chunk7,chunk8,chunk9,chunk10,chunk11,chunk12,chunk13,chunk14,chunk15,chunk16,chunk17,chunk18,chunk19,chunk20,chunk21,chunk22,chunk23,chunk24,chunk25,chunk26,chunk27,chunk28,chunk29,chunk30,chunk31,chunk32,chunk33,chunk34,chunk35,chunk36,chunk37,chunk38,chunk39,chunk40,chunk41,chunk42,chunk43,chunk44,chunk45,chunk46,chunk47,chunk48,chunk49,chunk50,chunk51,chunk52,chunk53,chunk54,chunk55,chunk56,chunk57,chunk58,chunk59,chunk60,chunk61,chunk62,chunk63,chunk64,chunk65,chunk66,chunk67,chunk68,chunk69,chunk70,chunk71,chunk72,chunk73,chunk74,chunk75,chunk76,chunk77,chunk78,chunk79,chunk80,chunk81,chunk82,chunk83,chunk84,chunk85,chunk86,chunk87,chunk88,chunk89,chunk90,chunk91,chunk92,chunk93,chunk94,chunk95] +def forwardWord : List Event := forwardChunks.flatten +end SourceMatrix diff --git a/research/lean-multi-host-source/NOTICE.md b/research/lean-multi-host-source/NOTICE.md new file mode 100644 index 0000000000..952612f428 --- /dev/null +++ b/research/lean-multi-host-source/NOTICE.md @@ -0,0 +1,54 @@ +# Attribution and scope + +Apache-2.0, under the repository license. This contribution was prepared with +substantial OpenAI Codex assistance. It is an independent verification effort; +no priority or improved integer-multiplication bound is claimed. + +The human contributor initiated and coordinated this AI-assisted verification +effort. They do not claim to have independently derived or personally checked +the mathematics. Codex agents developed the formalization, ran the reported +checks, and prepared the technical reviews and documentation. Separate agent +reviews are not independent human mathematical review. + +The unchanged source word and geometry are inherited from the contributors +credited in PR442 and its ancestors, including Dylan Crow (with Anthropic +Claude assistance), Jacob Sussman, Zhihao Chen (with OpenAI Codex assistance), +and the earlier source527/PR234/PR266/PR315/PR346/PR352/PR363 contributors. +Their existing notices and repository history remain authoritative. + +The multiple-host algebra reuses the preceding local WholeHosting package. +The gauge convention and partial-swap identities follow existing +`research/machine-transfer-verification/transfer-proof/framed/FramedXor.lean` +and `AddressGauges.lean` at pinned main. New adaptations explicitly separate +generic simulation lemmas from concrete source instantiation. + +The refreshed audit also reviewed PR509 at +`7b9c720ecc9f483c383e7cd9c2ab81f06ee5df59`, which formalizes the generic +Lemma G frame-conjugation, replay, and bit-entrance principles. Those +principles are overlapping existing work, not a novelty claim here. This +package targets the additional literal PR442 event, frame, owner, and +clean-private-register obligations. See `overlap-review.md`. + +The closing audit also reviewed PR513's sequential completed-bank theorem +and five-stage source bindings at +`005dd3f4e3cba8d1761abc4ab391aaf6d14d6f73`. Its generic completion algebra +overlaps with this contribution's framework; it retains the physical +arbitrary-dirty-input endpoint as a supplier premise. No novelty for generic +completion algebra is claimed here. + +The external-review refresh also inspected PR516 at +`1c6b6ff9366a94e1f86a6c5d661a7df75c6ff814`. It supplies overlapping generic +owner, realized-word, helper and scheduling results while taking concrete +endpoint and chart data as premises. This delivery makes no novelty claim +for those generic principles. Its distinct review target is the literal +selected PR442 supplier obligations; see `EXTERNAL-OVERLAP-REVIEW.md` for the +bounded search and its limits. + +The input snapshots preserve the pinned generated source bytes. Compression +of previously uncompressed JSON uses deterministic gzip; the uncompressed +hashes identify the original files exactly. No source algorithm was changed. + +PR448's split-stream gain remains unestablished. Nothing here assumes its +missing interface or supplies an uncharged additional register. This package +does not establish a compiler, physical resource bill, asymptotic transfer, +or unconditional integer-multiplication theorem. diff --git a/research/lean-multi-host-source/OwnerTransport.lean b/research/lean-multi-host-source/OwnerTransport.lean new file mode 100644 index 0000000000..0d7f411d3e --- /dev/null +++ b/research/lean-multi-host-source/OwnerTransport.lean @@ -0,0 +1,479 @@ +import FramedReplay + +/-! +Raw owner-chart routing for the source-permitted owner `(F,d sigma⁻¹)`. +A logical address a in a role is represented at sigma(a) in the owner +cover chart. Thus its chart-relative read from source s while writing +destination t uses sigma_s ∘ sigma_t⁻¹. The native-coordinate bridge below +proves that g_r sigma_r=d makes this a same-native-address XOR, not an +additional physical routing layer. The theorems below use actual inverse laws and +physical owner injectivity; frame-label equality cannot imply them. + +This is the coordinate realization permitted by PR442 PROOF.md §2 (whole +residual isometry plus the charged slot permutation and U_q). It does not +assert that the symbolic JSON contains numerical routing matrices. +Apache-2.0. Prepared with substantial OpenAI Codex assistance. +-/ +namespace OwnerTransport +open FramedReplay + +abbrev Raw (S X : Type) := S → Row X +abbrev Logical (R X : Type) := R → Row X + +def gather {R S X : Type} (owner : R → S) (chart : R → Gauge X) + (raw : Raw S X) : Logical R X := + fun r => ((raw (owner r)).1, fun a => (raw (owner r)).2 ((chart r).forward a)) + +noncomputable def write {R S X : Type} (owner : R → S) (chart : R → Gauge X) + (raw : Raw S X) (r : R) (row : Row X) : Raw S X := by + classical + exact fun s => if s = owner r then + (row.1, fun a => row.2 ((chart r).inverse a)) else raw s + +noncomputable def replace {R X : Type} (s : Logical R X) (r : R) (row : Row X) : Logical R X := by + classical + exact fun t => if t = r then row else s t + +/-- All other physical streams, including retained streams outside the +local role image, survive every routed write unchanged. -/ +theorem write_other {R S X : Type} (owner : R → S) (chart : R → Gauge X) + (raw : Raw S X) (r : R) (row : Row X) (s : S) (hne : s ≠ owner r) : + write owner chart raw r row s = raw s := by + classical + simp only [write, if_neg hne] + +theorem gather_write {R S X : Type} (owner : R → S) (chart : R → Gauge X) + (hinj : ∀ {r s}, owner r = owner s → r = s) + (raw : Raw S X) (r : R) (row : Row X) : + gather owner chart (write owner chart raw r row) = + replace (gather owner chart raw) r row := by + classical + funext s + by_cases hs : s = r + · subst s + simp only [gather, write, replace] + congr 1 + funext a + exact congrArg row.2 ((chart r).inverse_forward a) + · have ho : owner s ≠ owner r := fun h => hs (hinj h) + simp only [gather, write, replace, if_neg ho, if_neg hs] + +/-- Raw XOR has the literal source-to-destination chart route. -/ +noncomputable def rawXor {R S X : Type} (owner : R → S) (chart : R → Gauge X) + (raw : Raw S X) (x y : R) : Raw S X := by + classical + exact fun s => if s = owner x then + ((raw s).1, fun a => (raw s).2 a ^^ + (raw (owner y)).2 ((chart y).forward ((chart x).inverse a))) + else raw s + +theorem rawXor_write {R S X : Type} (owner : R → S) (chart : R → Gauge X) + (raw : Raw S X) (x y : R) : + rawXor owner chart raw x y = write owner chart raw x + ((gather owner chart raw x).1, + fun a => (gather owner chart raw x).2 a ^^ (gather owner chart raw y).2 a) := by + classical + funext s + by_cases hs : s = owner x + · subst s + simp only [rawXor, write, gather, (chart x).forward_inverse] + · simp only [rawXor, write, if_neg hs] + +/-- Raw MOVE/COPY routing also transports the old and new local frame +operators. Omitting the owner charts from this expression changes the map. -/ +noncomputable def rawTransport {R S X : Type} (owner : R → S) (chart : R → Gauge X) + (raw : Raw S X) (source dest : R) (newFrame : Gauge X) : Raw S X := by + classical + exact fun s => if s = owner dest then + (newFrame, fun a => (raw (owner source)).2 + ((chart source).forward ((raw (owner source)).1.forward + (newFrame.inverse ((chart dest).inverse a))))) + else raw s + +theorem rawTransport_write {R S X : Type} (owner : R → S) (chart : R → Gauge X) + (raw : Raw S X) (source dest : R) (newFrame : Gauge X) : + rawTransport owner chart raw source dest newFrame = + write owner chart raw dest (reframe newFrame (gather owner chart raw source)) := by + classical + rfl + +noncomputable def rawStep {R S X : Type} (owner : R → S) (chart : R → Gauge X) + (raw : Raw S X) (op : Nat) (x y : R) (odd : Bool) (newFrame : Gauge X) : Raw S X := + match op with + | 0 => rawTransport owner chart raw x x newFrame + | 1 => if odd then rawXor owner chart raw x y else raw + | 2 => rawTransport owner chart raw x y newFrame + | _ => write owner chart raw y (newFrame, fun _ => false) + +noncomputable def logicalStep {R X : Type} (s : Logical R X) + (op : Nat) (x y : R) (odd : Bool) (newFrame : Gauge X) : Logical R X := + match op with + | 0 => replace s x (reframe newFrame (s x)) + | 1 => if odd then replace s x ((s x).1, fun a => (s x).2 a ^^ (s y).2 a) else s + | 2 => replace s y (reframe newFrame (s x)) + | _ => replace s y (newFrame, fun _ => false) + +/-- Every raw event refines the common-chart FramedReplay row operation; +this theorem includes address routing and all retained non-owner streams. -/ +theorem gather_step {R S X : Type} (owner : R → S) (chart : R → Gauge X) + (hinj : ∀ {r s}, owner r = owner s → r = s) + (raw : Raw S X) (op : Nat) (x y : R) (odd : Bool) (newFrame : Gauge X) : + gather owner chart (rawStep owner chart raw op x y odd newFrame) = + logicalStep (gather owner chart raw) op x y odd newFrame := by + cases op with + | zero => + simp only [rawStep, logicalStep, rawTransport_write, gather_write owner chart hinj] + | succ op => + cases op with + | zero => + cases odd <;> simp only [rawStep, logicalStep, Bool.false_eq_true, ↓reduceIte, + rawXor_write, gather_write owner chart hinj] + | succ op => + cases op with + | zero => + simp only [rawStep, logicalStep, rawTransport_write, gather_write owner chart hinj] + | succ op => + simp only [rawStep, logicalStep, gather_write owner chart hinj] + +/-- The function-store operation above is exactly the tree-store operation +used by the checked literal framed replay, within its actual index bound. -/ +theorem logicalStep_tree {X : Type} (s : Store X) (depth : Nat) + (full : TreeReplay.Tree.Full depth s) (e : Event X) (i : Nat) + (hx : e.scalar.x < 2 ^ depth) (hy : e.scalar.y < 2 ^ depth) + (hi : i < 2 ^ depth) : + logicalStep (fun j => s.get j) e.scalar.op e.scalar.x e.scalar.y + e.scalar.odd e.newFrame i = (physicalStep s e).get i := by + classical + obtain ⟨⟨op, x, y, odd⟩, newFrame⟩ := e + cases op with + | zero => + simp only [logicalStep, physicalStep, replace, + TreeReplay.Tree.get_put depth s full x i _ hx hi] + simp only [eq_comm] + | succ op => + cases op with + | zero => + cases odd <;> simp only [logicalStep, physicalStep, replace, + Bool.false_eq_true, ↓reduceIte, + TreeReplay.Tree.get_put depth s full x i _ hx hi] <;> + simp only [eq_comm] + | succ op => + cases op with + | zero => + simp only [logicalStep, physicalStep, replace, + TreeReplay.Tree.get_put depth s full y i _ hy hi] + simp only [eq_comm] + | succ op => + simp only [logicalStep, physicalStep, replace, + TreeReplay.Tree.get_put depth s full y i _ hy hi] + simp only [eq_comm] + +theorem rawStep_other {R S X : Type} (owner : R → S) (chart : R → Gauge X) + (raw : Raw S X) (op : Nat) (x y : R) (odd : Bool) (newFrame : Gauge X) + (s : S) (hx : s ≠ owner x) (hy : s ≠ owner y) : + rawStep owner chart raw op x y odd newFrame s = raw s := by + classical + cases op with + | zero => simp only [rawStep, rawTransport, if_neg hx] + | succ op => + cases op with + | zero => cases odd <;> simp [rawStep, rawXor, hx] + | succ op => + cases op with + | zero => simp only [rawStep, rawTransport, if_neg hy] + | succ op => simp only [rawStep, write, if_neg hy] + +structure RouteEvent (R X : Type) where + op : Nat + x : R + y : R + odd : Bool + newFrame : Gauge X + +def RouteEvent.framed {n : Nat} {X : Type} (e : RouteEvent (Fin n) X) : Event X := + ⟨⟨e.op, e.x.val, e.y.val, e.odd⟩, e.newFrame⟩ + +noncomputable def runRaw {R S X : Type} (owner : R → S) (chart : R → Gauge X) + (events : List (RouteEvent R X)) (raw : Raw S X) : Raw S X := + events.foldl (fun s e => rawStep owner chart s e.op e.x e.y e.odd e.newFrame) raw + +theorem replace_fin_tree {n : Nat} {X : Type} (s : Store X) (depth : Nat) + (full : TreeReplay.Tree.Full depth s) (bound : n ≤ 2 ^ depth) + (f : Logical (Fin n) X) (rel : ∀ r, f r = s.get r.val) + (x r : Fin n) (row : Row X) : + replace f x row r = (s.put x.val row).get r.val := by + classical + rw [TreeReplay.Tree.get_put depth s full x.val r.val row + (Nat.lt_of_lt_of_le x.isLt bound) (Nat.lt_of_lt_of_le r.isLt bound)] + by_cases he : r = x + · subst r + simp [replace] + · have hv : x.val ≠ r.val := fun h => he (Fin.ext h.symm) + simp only [replace, if_neg he, if_neg hv, rel] + +theorem logicalStep_fin_tree {n : Nat} {X : Type} (s : Store X) (depth : Nat) + (full : TreeReplay.Tree.Full depth s) (bound : n ≤ 2 ^ depth) + (f : Logical (Fin n) X) (rel : ∀ r, f r = s.get r.val) + (e : RouteEvent (Fin n) X) (r : Fin n) : + logicalStep f e.op e.x e.y e.odd e.newFrame r = + (physicalStep s e.framed).get r.val := by + have hp := replace_fin_tree s depth full bound f rel + obtain ⟨op, x, y, odd, frame⟩ := e + cases op with + | zero => simpa only [logicalStep, RouteEvent.framed, physicalStep, rel] using + (hp x r (reframe frame (f x))) + | succ op => + cases op with + | zero => + cases odd + · exact rel r + · simpa only [logicalStep, RouteEvent.framed, physicalStep, ↓reduceIte, rel] using + (hp x r ((f x).1, fun a => (f x).2 a ^^ (f y).2 a)) + | succ op => + cases op with + | zero => simpa only [logicalStep, RouteEvent.framed, physicalStep, rel] using + (hp y r (reframe frame (f x))) + | succ op => simpa only [logicalStep, RouteEvent.framed, physicalStep, rel] using + (hp y r (frame, fun _ => false)) + +theorem physicalStep_full {X : Type} (s : Store X) (depth : Nat) + (full : TreeReplay.Tree.Full depth s) (e : Event X) : + TreeReplay.Tree.Full depth (physicalStep s e) := by + obtain ⟨⟨op, x, y, odd⟩, frame⟩ := e + cases op with + | zero => exact TreeReplay.Tree.full_put _ _ full _ _ + | succ op => + cases op with + | zero => cases odd <;> first | exact full | exact TreeReplay.Tree.full_put _ _ full _ _ + | succ op => cases op <;> exact TreeReplay.Tree.full_put _ _ full _ _ + +/-- A complete sequence of physically routed operations, retaining all +non-owner streams, refines the exact framed tree interpreter used by the +source-word certificate. This is an execution equality, not a postulated +endpoint contract. The clean-work guards remain those of FramedReplay. -/ +theorem gather_run_framed {n : Nat} {S X : Type} + (owner : Fin n → S) (chart : Fin n → Gauge X) + (hinj : ∀ {r s}, owner r = owner s → r = s) + (events : List (RouteEvent (Fin n) X)) (raw : Raw S X) + (s : Store X) (depth : Nat) (full : TreeReplay.Tree.Full depth s) + (bound : n ≤ 2 ^ depth) + (rel : ∀ r, gather owner chart raw r = s.get r.val) : + ∀ r, gather owner chart (runRaw owner chart events raw) r = + (runPhysical (events.map RouteEvent.framed) s).get r.val := by + induction events generalizing raw s with + | nil => exact rel + | cons e es ih => + apply ih _ _ (physicalStep_full s depth full e.framed) + intro r + rw [congrFun (gather_step owner chart hinj raw e.op e.x e.y e.odd e.newFrame) r] + exact logicalStep_fin_tree s depth full bound _ rel e r + +/-- Every retained physical stream outside this invocation's actual owner +image survives the entire same chronological routed word unchanged. -/ +theorem runRaw_other {R S X : Type} (owner : R → S) (chart : R → Gauge X) + (events : List (RouteEvent R X)) (raw : Raw S X) (s : S) + (outside : ∀ r, s ≠ owner r) : + runRaw owner chart events raw s = raw s := by + induction events generalizing raw with + | nil => rfl + | cons e es ih => + change runRaw owner chart es + (rawStep owner chart raw e.op e.x e.y e.odd e.newFrame) s = raw s + rw [ih] + exact rawStep_other owner chart raw e.op e.x e.y e.odd e.newFrame s + (outside e.x) (outside e.y) + +def identityGauge (X : Type) : Gauge X := ⟨id, id, fun _ => rfl, fun _ => rfl⟩ + +/-- Extend the actual charts of the selected owners to a coordinate chart +on every retained stream. Other streams use their native coordinates. -/ +noncomputable def extendCover {R S X : Type} (owner : R → S) + (cover : R → Gauge X) (s : S) : Gauge X := by + classical + exact if h : ∃ r, owner r = s then cover h.choose else identityGauge X + +theorem extendCover_owner {R S X : Type} (owner : R → S) + (hinj : ∀ {r s}, owner r = owner s → r = s) + (cover : R → Gauge X) (r : R) : + extendCover owner cover (owner r) = cover r := by + classical + have h : ∃ t, owner t = owner r := ⟨r, rfl⟩ + simp only [extendCover, dif_pos h] + exact congrArg cover (hinj h.choose_spec) + +/-- Arbitrary dirty original/retained payloads and one designated initially +blank private row. This describes allowed initial data; it does not erase +an arbitrary dirty private row during execution. Frame labels are metadata. -/ +noncomputable def initialRaw {R S X : Type} (owner : R → S) + (frames : R → Gauge X) (privateRow : R) (payload : S → X → Bool) : Raw S X := by + classical + exact fun s => (extendCover owner frames s, + if s = owner privateRow then fun _ => false else payload s) + +theorem initialRaw_other {R S X : Type} (owner : R → S) + (frames : R → Gauge X) (privateRow : R) (payload : S → X → Bool) + (s : S) (hs : s ≠ owner privateRow) : + (initialRaw owner frames privateRow payload s).2 = payload s := by + classical + simp only [initialRaw, if_neg hs] + +theorem gather_initialRaw {R S X : Type} [DecidableEq R] (owner : R → S) (chart : R → Gauge X) + (hinj : ∀ {r s}, owner r = owner s → r = s) + (frames : R → Gauge X) (privateRow : R) (payload : S → X → Bool) (r : R) : + gather owner chart (initialRaw owner frames privateRow payload) r = + (frames r, if r = privateRow then fun _ => false + else fun a => payload (owner r) ((chart r).forward a)) := by + classical + simp only [gather, initialRaw, extendCover_owner owner hinj] + by_cases hr : r = privateRow + · subst r + simp only [↓reduceIte] + · have ho : owner r ≠ owner privateRow := fun h => hr (hinj h) + simp only [if_neg hr, if_neg ho] + +def fromNative {S X : Type} (cover : S → Gauge X) (native : Raw S X) : Raw S X := + fun s => ((native s).1, fun a => (native s).2 ((cover s).forward a)) + +/-- When g_r sigma_r=d, the apparent raw chart route is precisely a +same-native-address read; it is not a second physical routing layer. -/ +theorem route_native_address {R S X : Type} (owner : R → S) + (chart : R → Gauge X) (cover : S → Gauge X) (d : Gauge X) + (common : ∀ r a, (cover (owner r)).forward ((chart r).forward a) = d.forward a) + (x y : R) (a : X) : + (cover (owner y)).forward ((chart y).forward ((chart x).inverse a)) = + (cover (owner x)).forward a := by + rw [common, ← common x ((chart x).inverse a), (chart x).forward_inverse] + +theorem inverse_common_cover {R S X : Type} (owner : R → S) + (chart : R → Gauge X) (cover : S → Gauge X) (d : Gauge X) + (common : ∀ r a, (cover (owner r)).forward ((chart r).forward a) = d.forward a) + (r : R) (a : X) : + (chart r).inverse ((cover (owner r)).inverse a) = d.inverse a := by + have h := common r ((chart r).inverse ((cover (owner r)).inverse a)) + rw [(chart r).forward_inverse, (cover (owner r)).forward_inverse] at h + have hi := congrArg d.inverse h + rw [d.inverse_forward] at hi + exact hi.symm + +noncomputable def nativeXor {R S X : Type} (owner : R → S) + (native : Raw S X) (x y : R) : Raw S X := by + classical + exact fun s => if s = owner x then + ((native s).1, fun a => (native s).2 a ^^ (native (owner y)).2 a) + else native s + +theorem rawXor_fromNative {R S X : Type} (owner : R → S) + (chart : R → Gauge X) (cover : S → Gauge X) (d : Gauge X) + (common : ∀ r a, (cover (owner r)).forward ((chart r).forward a) = d.forward a) + (native : Raw S X) (x y : R) : + rawXor owner chart (fromNative cover native) x y = + fromNative cover (nativeXor owner native x y) := by + classical + funext s + by_cases hs : s = owner x + · subst s + simp only [rawXor, nativeXor, fromNative, ↓reduceIte] + rw [show (fun a => (native (owner x)).2 ((cover (owner x)).forward a) ^^ + (native (owner y)).2 ((cover (owner y)).forward ((chart y).forward ((chart x).inverse a)))) = + (fun a => (native (owner x)).2 ((cover (owner x)).forward a) ^^ + (native (owner y)).2 ((cover (owner x)).forward a)) by + funext a + rw [route_native_address owner chart cover d common]] + · simp only [rawXor, nativeXor, fromNative, if_neg hs] + +noncomputable def nativeTransport {R S X : Type} (owner : R → S) + (d : Gauge X) (native : Raw S X) (source dest : R) (newFrame : Gauge X) : Raw S X := by + classical + exact fun s => if s = owner dest then + (newFrame, fun a => (native (owner source)).2 + (d.forward ((native (owner source)).1.forward (newFrame.inverse (d.inverse a))))) + else native s + +/-- Raw MOVE/COPY is the source's native D_d-frame transport. This removes +both cover-class chart maps and leaves the actual common invocation d. -/ +theorem rawTransport_fromNative {R S X : Type} (owner : R → S) + (chart : R → Gauge X) (cover : S → Gauge X) (d : Gauge X) + (common : ∀ r a, (cover (owner r)).forward ((chart r).forward a) = d.forward a) + (native : Raw S X) (source dest : R) (newFrame : Gauge X) : + rawTransport owner chart (fromNative cover native) source dest newFrame = + fromNative cover (nativeTransport owner d native source dest newFrame) := by + classical + funext s + by_cases hs : s = owner dest + · subst s + simp only [rawTransport, nativeTransport, fromNative, ↓reduceIte] + apply Prod.ext + · rfl + · funext a + dsimp only + rw [common] + have h := inverse_common_cover owner chart cover d common dest + ((cover (owner dest)).forward a) + rw [(cover (owner dest)).inverse_forward] at h + rw [h] + · simp only [rawTransport, nativeTransport, fromNative, if_neg hs] + +noncomputable def nativeStep {R S X : Type} (owner : R → S) (d : Gauge X) + (native : Raw S X) (op : Nat) (x y : R) (odd : Bool) (newFrame : Gauge X) : Raw S X := + match op with + | 0 => nativeTransport owner d native x x newFrame + | 1 => if odd then nativeXor owner native x y else native + | 2 => nativeTransport owner d native x y newFrame + | _ => write owner (fun _ => identityGauge X) native y (newFrame, fun _ => false) + +theorem rawStep_fromNative {R S X : Type} (owner : R → S) + (chart : R → Gauge X) (cover : S → Gauge X) (d : Gauge X) + (common : ∀ r a, (cover (owner r)).forward ((chart r).forward a) = d.forward a) + (native : Raw S X) (op : Nat) (x y : R) (odd : Bool) (newFrame : Gauge X) : + rawStep owner chart (fromNative cover native) op x y odd newFrame = + fromNative cover (nativeStep owner d native op x y odd newFrame) := by + classical + cases op with + | zero => exact rawTransport_fromNative owner chart cover d common native x x newFrame + | succ op => + cases op with + | zero => + cases odd + · rfl + · exact rawXor_fromNative owner chart cover d common native x y + | succ op => + cases op with + | zero => exact rawTransport_fromNative owner chart cover d common native x y newFrame + | succ op => + funext s + by_cases hs : s = owner y <;> + simp only [rawStep, nativeStep, write, fromNative, hs, ↓reduceIte] + +noncomputable def runNative {R S X : Type} (owner : R → S) (d : Gauge X) + (events : List (RouteEvent R X)) (native : Raw S X) : Raw S X := + events.foldl (fun s e => nativeStep owner d s e.op e.x e.y e.odd e.newFrame) native + +/-- Complete-word native/raw equality, including the private copied row. +Only the actual common-cover equation is required, not an endpoint premise. -/ +theorem runRaw_fromNative {R S X : Type} (owner : R → S) + (chart : R → Gauge X) (cover : S → Gauge X) (d : Gauge X) + (common : ∀ r a, (cover (owner r)).forward ((chart r).forward a) = d.forward a) + (events : List (RouteEvent R X)) (native : Raw S X) : + runRaw owner chart events (fromNative cover native) = + fromNative cover (runNative owner d events native) := by + induction events generalizing native with + | nil => rfl + | cons e es ih => + change runRaw owner chart es + (rawStep owner chart (fromNative cover native) e.op e.x e.y e.odd e.newFrame) = _ + rw [rawStep_fromNative owner chart cover d common, ih] + rfl + +end OwnerTransport +#print axioms OwnerTransport.write_other +#print axioms OwnerTransport.gather_write +#print axioms OwnerTransport.rawXor_write +#print axioms OwnerTransport.gather_step +#print axioms OwnerTransport.logicalStep_tree +#print axioms OwnerTransport.rawStep_other +#print axioms OwnerTransport.gather_run_framed +#print axioms OwnerTransport.runRaw_other +#print axioms OwnerTransport.route_native_address +#print axioms OwnerTransport.rawXor_fromNative +#print axioms OwnerTransport.rawTransport_fromNative +#print axioms OwnerTransport.runRaw_fromNative diff --git a/research/lean-multi-host-source/Ownership.lean b/research/lean-multi-host-source/Ownership.lean new file mode 100644 index 0000000000..5aafc83ee9 --- /dev/null +++ b/research/lean-multi-host-source/Ownership.lean @@ -0,0 +1,112 @@ +import OwnershipData + +/-! +Constructive ownership for the literal PR442 stage-2, replica-0 invocation. +`owner` is the actual formula `(family, d ∘ sigma⁻¹)` with arbitrary source +charts for the 240 data roles and our explicit slot-permutation charts for +all 747 helpers. The family outer chart is instantiated by the actual source +port basis in OwnershipGeometry; the inverse law here is an explicit premise. + +Injection holds at a fixed cover invocation. No assertion of disjoint owners +across different cover elements is made. Apache-2.0. Prepared with substantial +OpenAI Codex assistance. +-/ +namespace SourceOwnership + +abbrev Vec (K : Type) := Axis → K + +def reindex {K : Type} (t : Tag) (v : Vec K) : Vec K := fun i => v (invPerm t i) +def unindex {K : Type} (t : Tag) (v : Vec K) : Vec K := fun i => v (perm t i) + +theorem unindex_reindex {K : Type} (t : Tag) (v : Vec K) : + unindex t (reindex t v) = v := by + funext i + simp only [unindex, reindex, perm_inverse] + +theorem reindex_unindex {K : Type} (t : Tag) (v : Vec K) : + reindex t (unindex t v) = v := by + funext i + simp only [unindex, reindex, inverse_perm] + +/-- Transport of the full residual coordinate projector, for every vector. -/ +theorem residual_projector_transport {K : Type} (zero : K) (t : Tag) (v : Vec K) : + reindex t (fun i => if sourceMask t i then v i else zero) = + fun i => if targetMask t i then reindex t v i else zero := by + funext i + have hm := perm_support t (invPerm t i) + rw [inverse_perm] at hm + simp only [reindex, ← hm] + +theorem perm_tag_injective {a b : Tag} (h : perm a = perm b) : a = b := by + apply fingerprint_injective a b + unfold fingerprint + rw [h] + +/-- Distinct literal permutations give distinct actions over any set with + two distinct values. Descriptor inequality alone is not used. -/ +theorem unindex_tag_injective {K : Type} (lo hi : K) (hne : lo ≠ hi) + {a b : Tag} (h : @unindex K a = @unindex K b) : a = b := by + apply perm_tag_injective + funext i + apply Classical.byContradiction + intro hn + let v : Vec K := fun j => if j = perm a i then lo else hi + have he := congrFun (congrFun h v) i + have hn' : perm b i ≠ perm a i := fun hh => hn hh.symm + simp only [unindex, v, if_pos rfl, if_neg hn'] at he + exact hne he + +theorem family_data_general (r : Role) (hr : r.val < 240) : family r = r.val := by + exact family_data ⟨r.val, hr⟩ + +theorem same_family_data {r s : Role} (hf : family r = family s) (hr : r.val < 240) : r = s := by + have hfr := family_data_general r hr + by_cases hs : s.val < 240 + · apply Fin.ext + rw [← hfr, hf, family_data_general s hs] + · have hfs := (helper_range s (Nat.le_of_not_lt hs)).1 + omega + +/-- Helpers first undo the common family chart, then undo their explicit +slot permutation. Data inverse charts are exactly the supplied source maps. -/ +def sigmaInverse {K : Type} + (dataInverse : Role → Vec K → Vec K) + (familyInverse : Nat → Vec K → Vec K) (r : Role) : Vec K → Vec K := + if r.val < 240 then dataInverse r + else fun v => unindex (tag r) (familyInverse (family r) v) + +/-- Physical class as an actual function on address vectors. A proof that +these functions lie in the orthogonal cover is provided separately. -/ +def owner {K : Type} + (dataInverse : Role → Vec K → Vec K) + (familyInverse : Nat → Vec K → Vec K) + (d : Vec K → Vec K) (r : Role) : Nat × (Vec K → Vec K) := + (family r, fun v => d (sigmaInverse dataInverse familyInverse r v)) + +/-- All 987 roles have distinct physical owners at every fixed injective +cover map d. The common outer family chart has the displayed actual inverse; +there is no physical-aliasing premise. -/ +theorem owners_injective {K : Type} (lo hi : K) (hne : lo ≠ hi) + (dataInverse : Role → Vec K → Vec K) + (familyForward familyInverse : Nat → Vec K → Vec K) + (hinv : ∀ f v, familyInverse f (familyForward f v) = v) + (d : Vec K → Vec K) (hd : ∀ {x y}, d x = d y → x = y) + {r s : Role} + (h : owner dataInverse familyInverse d r = owner dataInverse familyInverse d s) : r = s := by + have hf : family r = family s := congrArg Prod.fst h + by_cases hr : r.val < 240 + · exact same_family_data hf hr + by_cases hs : s.val < 240 + · exact (same_family_data hf.symm hs).symm + apply family_tag_injective hf + apply unindex_tag_injective lo hi hne + funext v + have ho := congrFun (congrArg Prod.snd h) (familyForward (family r) v) + have he := hd ho + simp only [sigmaInverse, if_neg hr, if_neg hs, ← hf, hinv] at he + exact he + +end SourceOwnership +#print axioms SourceOwnership.residual_projector_transport +#print axioms SourceOwnership.unindex_tag_injective +#print axioms SourceOwnership.owners_injective diff --git a/research/lean-multi-host-source/OwnershipData.lean b/research/lean-multi-host-source/OwnershipData.lean new file mode 100644 index 0000000000..4fdabbbf95 --- /dev/null +++ b/research/lean-multi-host-source/OwnershipData.lean @@ -0,0 +1,83 @@ +import Std + +/-! Literal ownership certificate for PR442 stage2/replica0, all987roles. +Generated by generate_ownership_data.py. The extractor is not kernel verified. +Apache-2.0. Prepared with substantial OpenAI Codex assistance. -/ +set_option maxRecDepth 1000000 +set_option maxHeartbeats 0 +namespace SourceOwnership + +inductive Lookup where + | leaf : Nat → Lookup + | node : Lookup → Lookup → Lookup + +def lookup : Lookup → Nat → Nat + | .leaf n, _ => n + | .node l r, i => if i % 2 == 0 then lookup l (i / 2) else lookup r (i / 2) + +def familyTable : Lookup := (.node (.node (.node (.node (.node (.node (.node (.node (.node (.node (.leaf 0) (.leaf 598)) (.node (.leaf 513) (.leaf 679))) (.node (.node (.leaf 128) (.leaf 641)) (.node (.leaf 555) (.leaf 696)))) (.node (.node (.node (.leaf 64) (.leaf 619)) (.node (.leaf 534) (.leaf 289))) (.node (.node (.leaf 192) (.leaf 662)) (.node (.leaf 577) (.leaf 711))))) (.node (.node (.node (.node (.leaf 32) (.leaf 609)) (.node (.leaf 523) (.leaf 685))) (.node (.node (.leaf 160) (.leaf 651)) (.node (.leaf 566) (.leaf 703)))) (.node (.node (.node (.leaf 96) (.leaf 630)) (.node (.leaf 545) (.leaf 692))) (.node (.node (.leaf 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(.leaf 11)) (.node (.leaf 14) (.leaf 11)))) (.node (.node (.node (.leaf 14) (.leaf 15)) (.node (.leaf 14) (.leaf 11))) (.node (.node (.leaf 14) (.leaf 11)) (.node (.leaf 6) (.leaf 11))))) (.leaf 39)) (.node (.node (.node (.node (.leaf 23) (.node (.leaf 23) (.leaf 27))) (.node (.node (.leaf 23) (.leaf 27)) (.node (.leaf 23) (.leaf 27)))) (.node (.node (.node (.leaf 23) (.leaf 6)) (.node (.leaf 23) (.leaf 27))) (.node (.node (.leaf 23) (.leaf 27)) (.node (.leaf 23) (.leaf 27))))) (.leaf 55))) (.node (.node (.node (.node (.node (.node (.leaf 1) (.leaf 6)) (.node (.leaf 0) (.leaf 19))) (.node (.node (.leaf 0) (.leaf 19)) (.node (.leaf 0) (.leaf 19)))) (.node (.node (.node (.leaf 0) (.leaf 23)) (.node (.leaf 0) (.leaf 19))) (.node (.node (.leaf 0) (.leaf 19)) (.node (.leaf 15) (.leaf 19))))) (.leaf 47)) (.node (.leaf 31) (.leaf 63))))))) + +abbrev Role := Fin 987 +abbrev Tag := Fin 16 +abbrev Axis := Fin 64 + +def family (r : Role) : Nat := lookup familyTable r.val +def tag (r : Role) : Tag := ⟨lookup tagTable r.val % 16, Nat.mod_lt _ (by decide)⟩ +def perm (t : Tag) (i : Axis) : Axis := + ⟨lookup permTable (64 * t.val + i.val) % 64, Nat.mod_lt _ (by decide)⟩ +def invPerm (t : Tag) (i : Axis) : Axis := + ⟨lookup invPermTable (64 * t.val + i.val) % 64, Nat.mod_lt _ (by decide)⟩ +def sourceMask (t : Tag) (i : Axis) : Bool := (lookup sourceBits t.val).testBit i.val +def targetMask (t : Tag) (i : Axis) : Bool := (lookup targetBits t.val).testBit i.val + +theorem perm_inverse : ∀ (t : Tag) (i : Axis), invPerm t (perm t i) = i := by decide +theorem inverse_perm : ∀ (t : Tag) (i : Axis), perm t (invPerm t i) = i := by decide +theorem perm_support : ∀ (t : Tag) (i : Axis), targetMask t (perm t i) = sourceMask t i := by decide + +def fingerprint (t : Tag) : Nat := + (List.range 8).foldl (fun n i => n + (perm t ⟨i % 64, Nat.mod_lt _ (by decide)⟩).val * 64^i) 0 + +theorem fingerprint_injective : ∀ (a b : Tag), fingerprint a = fingerprint b → a = b := by decide + +theorem owner_inverse : ∀ r : Role, lookup inverseOwnerTable (16 * family r + (tag r).val) = r.val := by decide + +theorem family_tag_injective {r s : Role} (hf : family r = family s) (ht : tag r = tag s) : r = s := by + apply Fin.ext + rw [← owner_inverse r, ← owner_inverse s, hf, ht] + +theorem family_data : ∀ r : Fin 240, family ⟨r.val, Nat.lt_trans r.isLt (by decide)⟩ = r.val := by decide + +theorem helper_range : ∀ r : Role, 240 ≤ r.val → 240 ≤ family r ∧ family r < 720 := by decide + +theorem helper_frame : ∀ r : Role, 240 ≤ r.val → lookup initialFrameTable r.val = lookup tagInitialFrame (tag r).val := by decide + +theorem helper_child : ∀ r : Role, 240 ≤ r.val → ((tag r).val ≥ 7 ↔ family r ≥ 480) := by decide + +end SourceOwnership +#print axioms SourceOwnership.perm_inverse +#print axioms SourceOwnership.perm_support +#print axioms SourceOwnership.fingerprint_injective +#print axioms SourceOwnership.family_tag_injective +#print axioms SourceOwnership.helper_frame diff --git a/research/lean-multi-host-source/OwnershipGeometry.lean b/research/lean-multi-host-source/OwnershipGeometry.lean new file mode 100644 index 0000000000..f2fe46c25d --- /dev/null +++ b/research/lean-multi-host-source/OwnershipGeometry.lean @@ -0,0 +1,334 @@ +import Ownership +import PortGeometry +import OwnerTransport +import AddressPairs + +/-! +Actual admissible slot charts for every helper of PR442 stage2/replica0. +The source allows a slot isometry followed, when necessary, by U_q ⊕ I. +We construct this choice explicitly: one of the 16 checked permutations, +then the literal source port basis for families 480..719. The inverse +family-chart premise of Ownership.owners_injective is discharged here. + +The generic intermediate theorem allows arbitrary bijective data charts, +since their families are separate. The exported source construction fixes +all 240 charts to the literal stage-2 data route from PortGeometry. +This file does not infer any global bound from ownership. +Apache-2.0. Prepared with substantial OpenAI Codex assistance. +-/ +namespace SourceOwnership +open scoped BigOperators + +/-- Literal permutation, including its checked inverse on all 64 axes. -/ +def axisEquiv (t : Tag) : Axis ≃ Axis where + toFun := perm t + invFun := invPerm t + left_inv := perm_inverse t + right_inv := inverse_perm t + +def slotChart (K : Type) (t : Tag) : Vec K ≃ Vec K where + toFun := reindex t + invFun := unindex t + left_inv := unindex_reindex t + right_inv := reindex_unindex t + +theorem slotChart_dot (K : Type) [CommSemiring K] (t : Tag) (v w : Vec K) : + (∑ i, slotChart K t v i * slotChart K t w i) = ∑ i, v i * w i := by + exact (axisEquiv t).symm.sum_comp (fun i => v i * w i) + +theorem slotChart_add (K : Type) [Add K] (t : Tag) (v w : Vec K) : + slotChart K t (v + w) = slotChart K t v + slotChart K t w := rfl + +theorem slotChart_smul (K : Type) [Mul K] (t : Tag) (c : K) (v : Vec K) : + slotChart K t (fun i => c * v i) = fun i => c * slotChart K t v i := rfl + +/-- Child1's pending block is wholly exterior. Child2 uses the actual port +basis on U0; the table theorem helper_child binds this branch to the source. -/ +def familyChart (K : Type) [Field K] (h2 : (2 : K) ≠ 0) (f : Nat) : + Vec K ≃ Vec K := + if 480 ≤ f then PortGeometry.chart64 K h2 ⟨f % 120, Nat.mod_lt _ (by decide)⟩ + else Equiv.refl _ + +theorem familyChart_dot (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (f : Nat) (v w : Vec K) : + (∑ i, familyChart K h2 f v i * familyChart K h2 f w i) = ∑ i, v i * w i := by + unfold familyChart + split + · exact PortGeometry.chart64_dot K h2 _ v w + · rfl + +theorem familyChart_add (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (f : Nat) (v w : Vec K) : + familyChart K h2 f (v + w) = familyChart K h2 f v + familyChart K h2 f w := by + unfold familyChart + split + · exact PortGeometry.chart64_add K h2 _ v w + · rfl + +theorem familyChart_smul (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (f : Nat) (c : K) (v : Vec K) : + familyChart K h2 f (fun i => c * v i) = fun i => c * familyChart K h2 f v i := by + unfold familyChart + split + · exact PortGeometry.chart64_smul K h2 _ c v + · rfl + +def actualSigma (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (dataCharts : Role → Vec K ≃ Vec K) (r : Role) : Vec K ≃ Vec K := + if r.val < 240 then dataCharts r + else (slotChart K (tag r)).trans (familyChart K h2 (family r)) + +theorem helper_sigma_dot (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (dataCharts : Role → Vec K ≃ Vec K) (r : Role) (hr : 240 ≤ r.val) + (v w : Vec K) : + (∑ i, actualSigma K h2 dataCharts r v i * actualSigma K h2 dataCharts r w i) = + ∑ i, v i * w i := by + rw [actualSigma, if_neg (Nat.not_lt.mpr hr)] + change (∑ i, familyChart K h2 (family r) (slotChart K (tag r) v) i * + familyChart K h2 (family r) (slotChart K (tag r) w) i) = _ + rw [familyChart_dot, slotChart_dot] + +theorem helper_sigma_add (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (dataCharts : Role → Vec K ≃ Vec K) (r : Role) (hr : 240 ≤ r.val) + (v w : Vec K) : + actualSigma K h2 dataCharts r (v + w) = + actualSigma K h2 dataCharts r v + actualSigma K h2 dataCharts r w := by + simp only [actualSigma, if_neg (Nat.not_lt.mpr hr), Equiv.trans_apply, + slotChart_add, familyChart_add] + +theorem helper_sigma_smul (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (dataCharts : Role → Vec K ≃ Vec K) (r : Role) (hr : 240 ≤ r.val) + (c : K) (v : Vec K) : + actualSigma K h2 dataCharts r (fun i => c * v i) = + fun i => c * actualSigma K h2 dataCharts r v i := by + simp only [actualSigma, if_neg (Nat.not_lt.mpr hr), Equiv.trans_apply, + slotChart_smul, familyChart_smul] + +/-- Forward stage2 uses the same literal rho on source and target ports. +The owner formula is d rho, hence sigma is rho inverse. -/ +def sourceDataCharts (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (r : Role) : Vec K ≃ Vec K := + (PortGeometry.dataRoute64 K h2 ⟨r.val % 120, Nat.mod_lt _ (by decide)⟩).symm + +def physicalOwner (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (dataCharts : Role → Vec K ≃ Vec K) (d : Vec K ≃ Vec K) : + Role → Nat × (Vec K → Vec K) := + owner (fun r => (dataCharts r).symm) (fun f => (familyChart K h2 f).symm) d + +theorem physicalOwner_formula (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (dataCharts : Role → Vec K ≃ Vec K) (d : Vec K ≃ Vec K) (r : Role) : + physicalOwner K h2 dataCharts d r = + (family r, fun v => d ((actualSigma K h2 dataCharts r).symm v)) := by + unfold physicalOwner owner sigmaInverse actualSigma + split <;> rfl + +theorem physicalOwner_common (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (dataCharts : Role → Vec K ≃ Vec K) (d : Vec K ≃ Vec K) (r : Role) (v : Vec K) : + (physicalOwner K h2 dataCharts d r).2 (actualSigma K h2 dataCharts r v) = d v := by + rw [physicalOwner_formula] + exact congrArg d ((actualSigma K h2 dataCharts r).symm_apply_apply v) + +/-- Source-specific nonaliasing of every one of the 987 actual live roles, +for every fixed invertible cover element d and every admitted odd field. +The helper sigma maps are constructed, not assumed distinct. -/ +theorem physicalOwner_injective (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (dataCharts : Role → Vec K ≃ Vec K) (d : Vec K ≃ Vec K) : + Function.Injective (physicalOwner K h2 dataCharts d) := by + intro r s h + exact owners_injective (0 : K) 1 zero_ne_one + (fun r => (dataCharts r).symm) + (fun f => familyChart K h2 f) (fun f => (familyChart K h2 f).symm) + (fun f v => (familyChart K h2 f).symm_apply_apply v) d + (fun h => d.injective h) h + +/-- Gauge for simultaneous transport of the two address halves. -/ +def pairGauge {K : Type} (e : Vec K ≃ Vec K) : FramedReplay.Gauge (Vec K × Vec K) where + forward p := (e p.1, e p.2) + inverse p := (e.symm p.1, e.symm p.2) + inverse_forward p := by simp only [Equiv.symm_apply_apply] + forward_inverse p := by simp only [Equiv.apply_symm_apply] + +theorem family_lt (r : Role) : family r < 720 := by + by_cases hr : r.val < 240 + · rw [family_data_general r hr] + omega + · exact (helper_range r (Nat.le_of_not_lt hr)).2 + +abbrev ActiveRole := Fin 988 + +/-- The source mapper uses `[LIVE, ['private',0]]` for local register987. +The hosted template has LIVE9457 and explicitly reserves nine private rows; +this invocation uses one such row. Its frame is still tracked separately. -/ +def activeOwner (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (dataCharts : Role → Vec K ≃ Vec K) (d : Vec K ≃ Vec K) + (r : ActiveRole) : Nat × (Vec K → Vec K) := + if hr : r.val < 987 then physicalOwner K h2 dataCharts d ⟨r.val, hr⟩ + else (9457, id) + +def activeSigma (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (dataCharts : Role → Vec K ≃ Vec K) (r : ActiveRole) : Vec K ≃ Vec K := + if hr : r.val < 987 then actualSigma K h2 dataCharts ⟨r.val, hr⟩ + else Equiv.refl _ + +theorem activeOwner_injective (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (dataCharts : Role → Vec K ≃ Vec K) (d : Vec K ≃ Vec K) : + Function.Injective (activeOwner K h2 dataCharts d) := by + intro r s h + by_cases hr : r.val < 987 + · by_cases hs : s.val < 987 + · simp only [activeOwner, dif_pos hr, dif_pos hs] at h + have he := physicalOwner_injective K h2 dataCharts d h + exact Fin.ext (congrArg (fun t : Role => t.val) he) + · have hf := congrArg Prod.fst h + simp only [activeOwner, dif_pos hr, dif_neg hs, physicalOwner, owner] at hf + have hl := family_lt (⟨r.val, hr⟩ : Role) + omega + · by_cases hs : s.val < 987 + · have hf := congrArg Prod.fst h + simp only [activeOwner, dif_neg hr, dif_pos hs, physicalOwner, owner] at hf + have hl := family_lt (⟨s.val, hs⟩ : Role) + omega + · apply Fin.ext + omega + +/-- The generic raw-to-common-chart event theorem with all ownership and +slot-chart nonaliasing premises discharged for the selected source call. -/ +theorem active_gather_step (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (dataCharts : Role → Vec K ≃ Vec K) (d : Vec K ≃ Vec K) + (raw : OwnerTransport.Raw (Nat × (Vec K → Vec K)) (Vec K × Vec K)) + (op : Nat) (x y : ActiveRole) (odd : Bool) + (newFrame : FramedReplay.Gauge (Vec K × Vec K)) : + let own := activeOwner K h2 dataCharts d + let charts := fun r => pairGauge (activeSigma K h2 dataCharts r) + OwnerTransport.gather own charts + (OwnerTransport.rawStep own charts raw op x y odd newFrame) = + OwnerTransport.logicalStep (OwnerTransport.gather own charts raw) + op x y odd newFrame := by + exact OwnerTransport.gather_step _ _ + (fun h => activeOwner_injective K h2 dataCharts d h) _ _ _ _ _ _ + +def sourceActiveOwner (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (d : Vec K ≃ Vec K) := activeOwner K h2 (sourceDataCharts K h2) d + +def sourceActiveChart (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (r : ActiveRole) : FramedReplay.Gauge (Vec K × Vec K) := + pairGauge (activeSigma K h2 (sourceDataCharts K h2) r) + +theorem sourceActiveOwner_injective (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (d : Vec K ≃ Vec K) : Function.Injective (sourceActiveOwner K h2 d) := + activeOwner_injective K h2 (sourceDataCharts K h2) d + +/-- All 988 actual role charts and owners instantiate the whole raw-word +refinement. Only the chosen framed event list and matching initial data are +arguments; no owner or slot-chart hypothesis remains. -/ +theorem source_gather_run (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (d : Vec K ≃ Vec K) + (events : List (OwnerTransport.RouteEvent ActiveRole (Vec K × Vec K))) + (raw : OwnerTransport.Raw (Nat × (Vec K → Vec K)) (Vec K × Vec K)) + (s : FramedReplay.Store (Vec K × Vec K)) + (full : TreeReplay.Tree.Full 10 s) + (rel : ∀ r, OwnerTransport.gather (sourceActiveOwner K h2 d) + (sourceActiveChart K h2) raw r = s.get r.val) : + ∀ r, OwnerTransport.gather (sourceActiveOwner K h2 d) (sourceActiveChart K h2) + (OwnerTransport.runRaw (sourceActiveOwner K h2 d) (sourceActiveChart K h2) events raw) r = + (FramedReplay.runPhysical (events.map OwnerTransport.RouteEvent.framed) s).get r.val := + OwnerTransport.gather_run_framed _ _ + (fun h => sourceActiveOwner_injective K h2 d h) events raw s 10 full (by decide) rel + +/-- Exact zip/unzip conjugation places the same literal charts on the +pointwise paired-address type used by MultiHosting. -/ +def sourceActiveAddressChart (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (r : ActiveRole) : FramedReplay.Gauge (WholeHosting.Address Axis K) := + AddressPairs.gauge (sourceActiveChart K h2 r) + +def familyAddressChart (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (f : Nat) : FramedReplay.Gauge (WholeHosting.Address Axis K) := + AddressPairs.gauge (pairGauge (familyChart K h2 f)) + +theorem helper_address_forward (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (r : ActiveRole) (hr : 240 ≤ r.val) (hl : r.val < 987) + (a : WholeHosting.Address Axis K) : + (sourceActiveAddressChart K h2 r).forward a = + (familyAddressChart K h2 (family ⟨r.val, hl⟩)).forward + (reindex (tag ⟨r.val, hl⟩) a) := by + simp only [sourceActiveAddressChart, sourceActiveChart, activeSigma, dif_pos hl, + actualSigma, if_neg (Nat.not_lt.mpr hr), familyAddressChart, + AddressPairs.gauge, pairGauge, Equiv.trans_apply, slotChart] + rfl + +theorem helper_address_inverse (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (r : ActiveRole) (hr : 240 ≤ r.val) (hl : r.val < 987) + (a : WholeHosting.Address Axis K) : + (sourceActiveAddressChart K h2 r).inverse a = + unindex (tag ⟨r.val, hl⟩) + ((familyAddressChart K h2 (family ⟨r.val, hl⟩)).inverse a) := by + simp only [sourceActiveAddressChart, sourceActiveChart, activeSigma, dif_pos hl, + actualSigma, if_neg (Nat.not_lt.mpr hr), familyAddressChart, + AddressPairs.gauge, pairGauge, Equiv.symm_trans_apply, slotChart] + rfl + +theorem source_address_gather_run (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (d : Vec K ≃ Vec K) + (events : List (OwnerTransport.RouteEvent ActiveRole (WholeHosting.Address Axis K))) + (raw : OwnerTransport.Raw (Nat × (Vec K → Vec K)) (WholeHosting.Address Axis K)) + (s : FramedReplay.Store (WholeHosting.Address Axis K)) + (full : TreeReplay.Tree.Full 10 s) + (rel : ∀ r, OwnerTransport.gather (sourceActiveOwner K h2 d) + (sourceActiveAddressChart K h2) raw r = s.get r.val) : + ∀ r, OwnerTransport.gather (sourceActiveOwner K h2 d) (sourceActiveAddressChart K h2) + (OwnerTransport.runRaw (sourceActiveOwner K h2 d) (sourceActiveAddressChart K h2) events raw) r = + (FramedReplay.runPhysical (events.map OwnerTransport.RouteEvent.framed) s).get r.val := + OwnerTransport.gather_run_framed _ _ + (fun h => sourceActiveOwner_injective K h2 d h) events raw s 10 full (by decide) rel + +/-- On live owners this is exactly their cover element g=d sigma⁻¹. +The private identifier `(9457,id)` names reserved private0, not a cover class: +its per-invocation native chart is d, while its local slot chart is identity. +This states that convention explicitly rather than inferring d from id. -/ +def sourceRoleCover (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (d : Vec K ≃ Vec K) (r : ActiveRole) : + FramedReplay.Gauge (WholeHosting.Address Axis K) := + AddressPairs.gauge + (pairGauge ((activeSigma K h2 (sourceDataCharts K h2) r).symm.trans d)) + +noncomputable def sourceNativeCover (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (d : Vec K ≃ Vec K) : + (Nat × (Vec K → Vec K)) → FramedReplay.Gauge (WholeHosting.Address Axis K) := + OwnerTransport.extendCover (sourceActiveOwner K h2 d) (sourceRoleCover K h2 d) + +/-- Actual common-cover cancellation, including the private scratch row. -/ +theorem source_common_cover (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (d : Vec K ≃ Vec K) (r : ActiveRole) (a : WholeHosting.Address Axis K) : + (sourceNativeCover K h2 d (sourceActiveOwner K h2 d r)).forward + ((sourceActiveAddressChart K h2 r).forward a) = + (AddressPairs.gauge (pairGauge d)).forward a := by + rw [sourceNativeCover, OwnerTransport.extendCover_owner _ + (fun h => sourceActiveOwner_injective K h2 d h)] + simp only [sourceRoleCover, sourceActiveAddressChart, sourceActiveChart, + AddressPairs.gauge, AddressPairs.split_join, pairGauge, Equiv.trans_apply, + Equiv.symm_apply_apply] + +/-- The exact same complete raw word is a native word whose XOR operations +read the same native address and whose transports are conjugated only by d. +Owner-chart routing is a coordinate description, not an uncharged interface. -/ +theorem source_native_run (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (d : Vec K ≃ Vec K) + (events : List (OwnerTransport.RouteEvent ActiveRole (WholeHosting.Address Axis K))) + (native : OwnerTransport.Raw (Nat × (Vec K → Vec K)) (WholeHosting.Address Axis K)) : + OwnerTransport.runRaw (sourceActiveOwner K h2 d) (sourceActiveAddressChart K h2) + events (OwnerTransport.fromNative (sourceNativeCover K h2 d) native) = + OwnerTransport.fromNative (sourceNativeCover K h2 d) + (OwnerTransport.runNative (sourceActiveOwner K h2 d) + (AddressPairs.gauge (pairGauge d)) events native) := + OwnerTransport.runRaw_fromNative _ _ _ _ (source_common_cover K h2 d) events native + +end SourceOwnership +#print axioms SourceOwnership.slotChart_dot +#print axioms SourceOwnership.helper_sigma_dot +#print axioms SourceOwnership.physicalOwner_injective +#print axioms SourceOwnership.activeOwner_injective +#print axioms SourceOwnership.active_gather_step +#print axioms SourceOwnership.sourceActiveOwner_injective +#print axioms SourceOwnership.source_address_gather_run +#print axioms SourceOwnership.source_common_cover +#print axioms SourceOwnership.source_native_run diff --git a/research/lean-multi-host-source/ParentOwnership.lean b/research/lean-multi-host-source/ParentOwnership.lean new file mode 100644 index 0000000000..7ff4009d76 --- /dev/null +++ b/research/lean-multi-host-source/ParentOwnership.lean @@ -0,0 +1,314 @@ +import ParentOwnershipData +import OwnershipGeometry + +/-! +Actual original-bank owners of the selected PR442 forward invocation. +The 59 permutation charts are checked, not assumed distinct. The 61 route +slots are separate: different residual subspaces can share one permutation. +Data roles use the same literal source port charts as the hosted invocation. +Private role 987 belongs to the original template's family 14259. +Apache-2.0. Prepared with substantial OpenAI Codex assistance. +-/ +namespace ParentOwnership +open SourceOwnership (lookup) +open scoped BigOperators + +abbrev Vec (K : Type) := Axis → K + +def reindex {K : Type} (t : Tag) (v : Vec K) : Vec K := fun i => v (invPerm t i) +def unindex {K : Type} (t : Tag) (v : Vec K) : Vec K := fun i => v (perm t i) + +theorem unindex_reindex {K : Type} (t : Tag) (v : Vec K) : + unindex t (reindex t v) = v := by + funext i + simp only [unindex, reindex, perm_inverse] + +theorem reindex_unindex {K : Type} (t : Tag) (v : Vec K) : + reindex t (unindex t v) = v := by + funext i + simp only [unindex, reindex, inverse_perm] + +/-- The support statement is indexed by route slot, not permutation tag. -/ +theorem residual_projector_transport {K : Type} (zero : K) (s : Slot) (v : Vec K) : + reindex (slotTag s) (fun i => if sourceMask s i then v i else zero) = + fun i => if targetMask s i then reindex (slotTag s) v i else zero := by + funext i + have hm := perm_support s (invPerm (slotTag s) i) + rw [inverse_perm] at hm + simp only [reindex, ← hm] + +theorem perm_tag_injective {a b : Tag} (h : perm a = perm b) : a = b := by + apply fingerprint_injective a b + unfold fingerprint + rw [h] + +theorem unindex_tag_injective {K : Type} (lo hi : K) (hne : lo ≠ hi) + {a b : Tag} (h : @unindex K a = @unindex K b) : a = b := by + apply perm_tag_injective + funext i + apply Classical.byContradiction + intro hn + let v : Vec K := fun j => if j = perm a i then lo else hi + have he := congrFun (congrFun h v) i + have hn' : perm b i ≠ perm a i := fun hh => hn hh.symm + simp only [unindex, v, if_pos rfl, if_neg hn'] at he + exact hne he + +theorem family_data_general (r : Role) (hr : r.val < 240) : family r = r.val := + family_data ⟨r.val, hr⟩ + +theorem same_family_data {r s : Role} (hf : family r = family s) + (hr : r.val < 240) : r = s := by + have hfr := family_data_general r hr + by_cases hs : s.val < 240 + · apply Fin.ext + rw [← hfr, hf, family_data_general s hs] + · have hfs := (helper_range s (Nat.le_of_not_lt hs)).1 + omega + +def sigmaInverse {K : Type} (dataInverse : Role → Vec K → Vec K) + (r : Role) : Vec K → Vec K := + if r.val < 240 then dataInverse r else unindex (tag r) + +def owner {K : Type} (dataInverse : Role → Vec K → Vec K) + (d : Vec K → Vec K) (r : Role) : Nat × (Vec K → Vec K) := + (family r, fun v => d (sigmaInverse dataInverse r v)) + +/-- No nonaliasing premise: literal family/tag inversion and faithful +permutation actions establish injectivity for every fixed injective d. -/ +theorem owners_injective {K : Type} (lo hi : K) (hne : lo ≠ hi) + (dataInverse : Role → Vec K → Vec K) + (d : Vec K → Vec K) (hd : ∀ {x y}, d x = d y → x = y) + {r s : Role} (h : owner dataInverse d r = owner dataInverse d s) : r = s := by + have hf : family r = family s := congrArg Prod.fst h + by_cases hr : r.val < 240 + · exact same_family_data hf hr + by_cases hs : s.val < 240 + · exact (same_family_data hf.symm hs).symm + apply family_tag_injective hf + apply unindex_tag_injective lo hi hne + funext v + have ho := congrFun (congrArg Prod.snd h) v + have he := hd ho + simpa only [sigmaInverse, if_neg hr, if_neg hs] using he + +def axisEquiv (t : Tag) : Axis ≃ Axis where + toFun := perm t + invFun := invPerm t + left_inv := perm_inverse t + right_inv := inverse_perm t + +def slotChart (K : Type) (t : Tag) : Vec K ≃ Vec K where + toFun := reindex t + invFun := unindex t + left_inv := unindex_reindex t + right_inv := reindex_unindex t + +theorem slotChart_dot (K : Type) [CommSemiring K] (t : Tag) (v w : Vec K) : + (∑ i, slotChart K t v i * slotChart K t w i) = ∑ i, v i * w i := by + exact (axisEquiv t).symm.sum_comp (fun i => v i * w i) + +theorem slotChart_add (K : Type) [Add K] (t : Tag) (v w : Vec K) : + slotChart K t (v + w) = slotChart K t v + slotChart K t w := rfl + +theorem slotChart_smul (K : Type) [Mul K] (t : Tag) (c : K) (v : Vec K) : + slotChart K t (fun i => c * v i) = fun i => c * slotChart K t v i := rfl + +def sourceDataCharts (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (r : Role) : Vec K ≃ Vec K := SourceOwnership.sourceDataCharts K h2 r + +def actualSigma (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (r : Role) : Vec K ≃ Vec K := + if r.val < 240 then sourceDataCharts K h2 r else slotChart K (tag r) + +theorem helper_sigma_dot (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (r : Role) (hr : 240 ≤ r.val) (v w : Vec K) : + (∑ i, actualSigma K h2 r v i * actualSigma K h2 r w i) = ∑ i, v i * w i := by + rw [actualSigma, if_neg (Nat.not_lt.mpr hr)] + exact slotChart_dot K (tag r) v w + +theorem helper_sigma_add (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (r : Role) (hr : 240 ≤ r.val) (v w : Vec K) : + actualSigma K h2 r (v + w) = actualSigma K h2 r v + actualSigma K h2 r w := by + simp only [actualSigma, if_neg (Nat.not_lt.mpr hr), slotChart_add] + +theorem helper_sigma_smul (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (r : Role) (hr : 240 ≤ r.val) (c : K) (v : Vec K) : + actualSigma K h2 r (fun i => c * v i) = fun i => c * actualSigma K h2 r v i := by + simp only [actualSigma, if_neg (Nat.not_lt.mpr hr), slotChart_smul] + +theorem helper_residual_transport (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (r : Role) (hr : 240 ≤ r.val) (v : Vec K) : + actualSigma K h2 r (fun i => if sourceMask (slot r) i then v i else 0) = + fun i => if targetMask (slot r) i then actualSigma K h2 r v i else 0 := by + simp only [actualSigma, if_neg (Nat.not_lt.mpr hr)] + exact residual_projector_transport 0 (slot r) v + +def physicalOwner (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (d : Vec K ≃ Vec K) : Role → Nat × (Vec K → Vec K) := + owner (fun r => (sourceDataCharts K h2 r).symm) d + +theorem physicalOwner_formula (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (d : Vec K ≃ Vec K) (r : Role) : + physicalOwner K h2 d r = (family r, fun v => d ((actualSigma K h2 r).symm v)) := by + unfold physicalOwner owner sigmaInverse actualSigma + split <;> rfl + +theorem physicalOwner_injective (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (d : Vec K ≃ Vec K) : Function.Injective (physicalOwner K h2 d) := by + intro r s h + exact owners_injective (0 : K) 1 zero_ne_one + (fun r => (sourceDataCharts K h2 r).symm) d (fun h => d.injective h) h + +theorem family_lt (r : Role) : family r < 14259 := by + by_cases hr : r.val < 240 + · rw [family_data_general r hr] + omega + · exact (helper_range r (Nat.le_of_not_lt hr)).2 + +abbrev ActiveRole := Fin 988 + +def sourceActiveOwner (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (d : Vec K ≃ Vec K) (r : ActiveRole) : Nat × (Vec K → Vec K) := + if hr : r.val < 987 then physicalOwner K h2 d ⟨r.val, hr⟩ else (14259, id) + +/-- Every active parent owner avoids the families used for retained hosts. -/ +theorem sourceActiveOwner_avoids_host_families (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (d : Vec K ≃ Vec K) (r : ActiveRole) (f : Nat) + (hf : 240 ≤ f) (hf' : f < 7680) : + (sourceActiveOwner K h2 d r).1 ≠ f := by + by_cases hr : r.val < 987 + · simp only [sourceActiveOwner, dif_pos hr, physicalOwner, owner] + by_cases hd : r.val < 240 + · rw [family_data_general ⟨r.val, hr⟩ hd] + change r.val ≠ f + omega + · have hb := (helper_range ⟨r.val, hr⟩ (Nat.le_of_not_lt hd)).1 + omega + · simp only [sourceActiveOwner, dif_neg hr] + omega + +def sourceActiveSigma (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (r : ActiveRole) : Vec K ≃ Vec K := + if hr : r.val < 987 then actualSigma K h2 ⟨r.val, hr⟩ else Equiv.refl _ + +def sourceActiveChart (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (r : ActiveRole) : FramedReplay.Gauge (Vec K × Vec K) := + SourceOwnership.pairGauge (sourceActiveSigma K h2 r) + +theorem sourceActiveOwner_injective (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (d : Vec K ≃ Vec K) : Function.Injective (sourceActiveOwner K h2 d) := by + intro r s h + by_cases hr : r.val < 987 + · by_cases hs : s.val < 987 + · simp only [sourceActiveOwner, dif_pos hr, dif_pos hs] at h + have he := physicalOwner_injective K h2 d h + exact Fin.ext (congrArg (fun t : Role => t.val) he) + · have hf := congrArg Prod.fst h + simp only [sourceActiveOwner, dif_pos hr, dif_neg hs, physicalOwner, owner] at hf + have hl := family_lt (⟨r.val, hr⟩ : Role) + omega + · by_cases hs : s.val < 987 + · have hf := congrArg Prod.fst h + simp only [sourceActiveOwner, dif_neg hr, dif_pos hs, physicalOwner, owner] at hf + have hl := family_lt (⟨s.val, hs⟩ : Role) + omega + · apply Fin.ext + omega + +/-- Original-bank charts instantiate the raw-word ownership refinement for +all 988 roles. The event trace and its initial-state relation are arguments. -/ +theorem source_gather_run (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (d : Vec K ≃ Vec K) + (events : List (OwnerTransport.RouteEvent ActiveRole (Vec K × Vec K))) + (raw : OwnerTransport.Raw (Nat × (Vec K → Vec K)) (Vec K × Vec K)) + (s : FramedReplay.Store (Vec K × Vec K)) + (full : TreeReplay.Tree.Full 10 s) + (rel : ∀ r, OwnerTransport.gather (sourceActiveOwner K h2 d) + (sourceActiveChart K h2) raw r = s.get r.val) : + ∀ r, OwnerTransport.gather (sourceActiveOwner K h2 d) (sourceActiveChart K h2) + (OwnerTransport.runRaw (sourceActiveOwner K h2 d) (sourceActiveChart K h2) events raw) r = + (FramedReplay.runPhysical (events.map OwnerTransport.RouteEvent.framed) s).get r.val := + OwnerTransport.gather_run_framed _ _ + (fun h => sourceActiveOwner_injective K h2 d h) events raw s 10 full (by decide) rel + +def sourceActiveAddressChart (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (r : ActiveRole) : FramedReplay.Gauge (WholeHosting.Address Axis K) := + AddressPairs.gauge (sourceActiveChart K h2 r) + +theorem helper_address_forward (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (r : ActiveRole) (hr : 240 ≤ r.val) (hl : r.val < 987) + (a : WholeHosting.Address Axis K) : + (sourceActiveAddressChart K h2 r).forward a = reindex (tag ⟨r.val, hl⟩) a := by + simp only [sourceActiveAddressChart, sourceActiveChart, sourceActiveSigma, dif_pos hl, + actualSigma, if_neg (Nat.not_lt.mpr hr), AddressPairs.gauge, + SourceOwnership.pairGauge, slotChart] + rfl + +theorem helper_address_inverse (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (r : ActiveRole) (hr : 240 ≤ r.val) (hl : r.val < 987) + (a : WholeHosting.Address Axis K) : + (sourceActiveAddressChart K h2 r).inverse a = unindex (tag ⟨r.val, hl⟩) a := by + simp only [sourceActiveAddressChart, sourceActiveChart, sourceActiveSigma, dif_pos hl, + actualSigma, if_neg (Nat.not_lt.mpr hr), AddressPairs.gauge, + SourceOwnership.pairGauge, slotChart] + rfl + +theorem source_address_gather_run (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (d : Vec K ≃ Vec K) + (events : List (OwnerTransport.RouteEvent ActiveRole (WholeHosting.Address Axis K))) + (raw : OwnerTransport.Raw (Nat × (Vec K → Vec K)) (WholeHosting.Address Axis K)) + (s : FramedReplay.Store (WholeHosting.Address Axis K)) + (full : TreeReplay.Tree.Full 10 s) + (rel : ∀ r, OwnerTransport.gather (sourceActiveOwner K h2 d) + (sourceActiveAddressChart K h2) raw r = s.get r.val) : + ∀ r, OwnerTransport.gather (sourceActiveOwner K h2 d) (sourceActiveAddressChart K h2) + (OwnerTransport.runRaw (sourceActiveOwner K h2 d) (sourceActiveAddressChart K h2) events raw) r = + (FramedReplay.runPhysical (events.map OwnerTransport.RouteEvent.framed) s).get r.val := + OwnerTransport.gather_run_framed _ _ + (fun h => sourceActiveOwner_injective K h2 d h) events raw s 10 full (by decide) rel + +/-- The reserved private identifier names family14259; its native chart is d. +Every live role uses the actual common-cover chart d ∘ sigma⁻¹. -/ +def sourceRoleCover (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (d : Vec K ≃ Vec K) (r : ActiveRole) : + FramedReplay.Gauge (WholeHosting.Address Axis K) := + AddressPairs.gauge + (SourceOwnership.pairGauge ((sourceActiveSigma K h2 r).symm.trans d)) + +noncomputable def sourceNativeCover (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (d : Vec K ≃ Vec K) : + (Nat × (Vec K → Vec K)) → FramedReplay.Gauge (WholeHosting.Address Axis K) := + OwnerTransport.extendCover (sourceActiveOwner K h2 d) (sourceRoleCover K h2 d) + +theorem source_common_cover (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (d : Vec K ≃ Vec K) (r : ActiveRole) (a : WholeHosting.Address Axis K) : + (sourceNativeCover K h2 d (sourceActiveOwner K h2 d r)).forward + ((sourceActiveAddressChart K h2 r).forward a) = + (AddressPairs.gauge (SourceOwnership.pairGauge d)).forward a := by + rw [sourceNativeCover, OwnerTransport.extendCover_owner _ + (fun h => sourceActiveOwner_injective K h2 d h)] + simp only [sourceRoleCover, sourceActiveAddressChart, sourceActiveChart, + AddressPairs.gauge, AddressPairs.split_join, SourceOwnership.pairGauge, Equiv.trans_apply, + Equiv.symm_apply_apply] + +theorem source_native_run (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (d : Vec K ≃ Vec K) + (events : List (OwnerTransport.RouteEvent ActiveRole (WholeHosting.Address Axis K))) + (native : OwnerTransport.Raw (Nat × (Vec K → Vec K)) (WholeHosting.Address Axis K)) : + OwnerTransport.runRaw (sourceActiveOwner K h2 d) (sourceActiveAddressChart K h2) + events (OwnerTransport.fromNative (sourceNativeCover K h2 d) native) = + OwnerTransport.fromNative (sourceNativeCover K h2 d) + (OwnerTransport.runNative (sourceActiveOwner K h2 d) + (AddressPairs.gauge (SourceOwnership.pairGauge d)) events native) := + OwnerTransport.runRaw_fromNative _ _ _ _ (source_common_cover K h2 d) events native + +end ParentOwnership +#print axioms ParentOwnership.unindex_tag_injective +#print axioms ParentOwnership.owners_injective +#print axioms ParentOwnership.helper_residual_transport +#print axioms ParentOwnership.sourceActiveOwner_injective +#print axioms ParentOwnership.source_gather_run + +#print axioms ParentOwnership.source_common_cover +#print axioms ParentOwnership.source_native_run diff --git a/research/lean-multi-host-source/ParentOwnershipData.lean b/research/lean-multi-host-source/ParentOwnershipData.lean new file mode 100644 index 0000000000..de74658134 --- /dev/null +++ b/research/lean-multi-host-source/ParentOwnershipData.lean @@ -0,0 +1,78 @@ +import OwnershipData +/-! +Literal original-bank ownership certificate for PR442 stage2/replica0. +Generated by generate_parent_ownership.py. Extraction is not kernel verified. +Apache-2.0. Prepared with substantial OpenAI Codex assistance. +-/ +set_option maxRecDepth 1000000 +set_option maxHeartbeats 0 +namespace ParentOwnership +open SourceOwnership (Lookup lookup) + +def familyTable : Lookup := (.node (.node (.node (.node (.node (.node (.node (.node (.node (.node (.leaf 0) (.leaf 9270)) (.node (.leaf 9158) (.leaf 9300))) (.node (.node (.leaf 128) (.leaf 9286)) (.node (.leaf 9254) (.leaf 9306)))) (.node (.node (.node (.leaf 64) (.leaf 9278)) (.node (.leaf 9222) (.leaf 9148))) (.node (.node (.leaf 192) (.leaf 9294)) (.node (.leaf 9262) (.leaf 9312))))) (.node (.node (.node (.node (.leaf 32) (.leaf 9274)) (.node (.leaf 9190) (.leaf 9302))) (.node (.node (.leaf 160) (.leaf 9290)) (.node (.leaf 9258) (.leaf 9309)))) (.node (.node (.node (.leaf 96) (.leaf 9282)) (.node (.leaf 9250) (.leaf 9305))) (.node (.node (.leaf 224) (.leaf 9298)) (.node (.leaf 9266) (.leaf 0)))))) (.node (.node (.node (.node (.node (.leaf 16) (.leaf 9272)) (.node (.leaf 9174) (.leaf 9144))) (.node (.node (.leaf 144) (.leaf 9288)) (.node (.leaf 9256) (.leaf 9308)))) (.node (.node (.node (.leaf 80) (.leaf 9280)) (.node (.leaf 9238) (.leaf 9304))) (.node (.node (.leaf 208) (.leaf 9296)) (.node (.leaf 9264) (.leaf 9314))))) (.node (.node (.node (.node (.leaf 48) (.leaf 9276)) (.node (.leaf 9206) (.leaf 9303))) (.node (.node (.leaf 176) (.leaf 9292)) (.node (.leaf 9260) (.leaf 9310)))) (.node (.node (.node (.leaf 112) (.leaf 9284)) (.node (.leaf 9252) (.leaf 9306))) (.node (.leaf 9142) (.node (.leaf 9268) (.leaf 0))))))) (.node (.node (.node (.node (.node (.node (.leaf 8) (.leaf 9271)) (.node (.leaf 9166) (.leaf 9300))) (.node (.node (.leaf 136) (.leaf 9287)) (.node (.leaf 9255) (.leaf 9307)))) (.node (.node (.node (.leaf 72) (.leaf 9279)) (.node (.leaf 9230) (.leaf 9148))) (.node (.node (.leaf 200) (.leaf 9295)) (.node (.leaf 9263) (.leaf 9313))))) (.node (.node (.node (.node (.leaf 40) (.leaf 9275)) (.node (.leaf 9198) (.leaf 9146))) (.node (.node (.leaf 168) (.leaf 9291)) (.node (.leaf 9259) (.leaf 9310)))) (.node (.node (.node (.leaf 104) (.leaf 9283)) (.node (.leaf 9251) (.leaf 9306))) (.node (.node (.leaf 232) (.leaf 9298)) (.node (.leaf 9267) (.leaf 0)))))) (.node (.node (.node (.node (.node (.leaf 24) (.leaf 9273)) (.node (.leaf 9182) (.leaf 9301))) (.node (.node (.leaf 152) (.leaf 9289)) (.node (.leaf 9257) (.leaf 9308)))) (.node (.node (.node (.leaf 88) (.leaf 9281)) (.node (.leaf 9249) (.leaf 9149))) (.node (.node (.leaf 216) (.leaf 9297)) (.node (.leaf 9265) (.leaf 9315))))) (.node (.node (.node (.node (.leaf 56) (.leaf 9277)) (.node (.leaf 9214) (.leaf 9303))) (.node (.node (.leaf 184) (.leaf 9293)) (.node (.leaf 9261) (.leaf 9311)))) (.node (.node (.node (.leaf 120) (.leaf 9285)) (.node (.leaf 9253) (.leaf 9152))) (.node (.node (.leaf 9150) (.leaf 9299)) (.node (.leaf 9269) (.leaf 0)))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf 4) (.leaf 9270)) (.node (.leaf 9162) (.leaf 9300))) (.node (.node (.leaf 132) (.leaf 9286)) (.node (.leaf 9254) (.leaf 9307)))) (.node (.node (.node (.leaf 68) (.leaf 9278)) (.node (.leaf 9226) (.leaf 9148))) (.node (.node (.leaf 196) (.leaf 9294)) (.node (.leaf 9262) (.leaf 9312))))) (.node (.node (.node (.node (.leaf 36) (.leaf 9274)) (.node (.leaf 9194) (.leaf 9145))) (.node (.node (.leaf 164) (.leaf 9290)) (.node (.leaf 9258) (.leaf 9309)))) (.node (.node (.node (.leaf 100) (.leaf 9282)) (.node (.leaf 9250) (.leaf 9305))) (.node (.node (.leaf 228) (.leaf 9298)) (.node (.leaf 9266) (.leaf 0)))))) (.node (.node (.node (.node (.node (.leaf 20) (.leaf 9272)) (.node (.leaf 9178) (.leaf 9301))) (.node (.node (.leaf 148) (.leaf 9288)) (.node (.leaf 9256) (.leaf 9308)))) (.node (.node (.node (.leaf 84) (.leaf 9280)) (.node (.leaf 9242) (.leaf 9149))) (.node (.node (.leaf 212) (.leaf 9296)) (.node (.leaf 9264) (.leaf 9314))))) (.node (.node (.node (.node (.leaf 52) (.leaf 9276)) (.node (.leaf 9210) (.leaf 9303))) (.node (.node (.leaf 180) (.leaf 9292)) (.node (.leaf 9260) (.leaf 9311)))) (.node (.node (.node (.leaf 116) (.leaf 9284)) (.node (.leaf 9252) (.leaf 9151))) (.node (.node (.leaf 9146) (.leaf 9299)) (.node (.leaf 9268) (.leaf 0))))))) (.node (.node (.node (.node (.node (.node (.leaf 12) (.leaf 9271)) (.node (.leaf 9170) (.leaf 9301))) (.node (.node (.leaf 140) (.leaf 9287)) (.node (.leaf 9255) (.leaf 9153)))) (.node (.node (.node (.leaf 76) (.leaf 9279)) (.node (.leaf 9234) (.leaf 9304))) (.node (.node (.leaf 204) (.leaf 9295)) (.node (.leaf 9263) (.leaf 9313))))) (.node (.node (.node (.node (.leaf 44) (.leaf 9275)) (.node (.leaf 9202) (.leaf 9303))) (.node (.node (.leaf 172) (.leaf 9291)) (.node (.leaf 9259) (.leaf 9310)))) (.node (.node (.node (.leaf 108) (.leaf 9283)) (.node (.leaf 9251) (.leaf 9306))) (.node (.node (.leaf 236) (.leaf 9298)) (.node (.leaf 9267) (.leaf 0)))))) (.node (.node (.node (.node (.node (.leaf 28) (.leaf 9273)) (.node (.leaf 9186) (.leaf 9302))) (.node (.node (.leaf 156) (.leaf 9289)) (.node (.leaf 9257) (.leaf 9308)))) (.node (.node (.node (.leaf 92) (.leaf 9281)) (.node (.leaf 9249) (.leaf 9150))) (.node (.node (.leaf 220) (.leaf 9297)) (.node (.leaf 9265) (.leaf 0))))) (.node (.node (.node (.node (.leaf 60) (.leaf 9277)) (.node (.leaf 9218) (.leaf 9147))) (.node (.node (.leaf 188) (.leaf 9293)) (.node (.leaf 9261) (.leaf 9312)))) (.node (.node (.node (.leaf 124) (.leaf 9285)) (.node (.leaf 9253) (.leaf 9306))) (.node (.node (.leaf 9154) (.leaf 9299)) (.node (.leaf 9269) (.leaf 0))))))))) (.node (.node (.node (.node (.node (.node (.node (.node (.leaf 2) (.leaf 9270)) (.node (.leaf 9160) (.leaf 9300))) (.node (.node (.leaf 130) (.leaf 9286)) (.node (.leaf 9254) (.leaf 9307)))) (.node (.node (.node (.leaf 66) (.leaf 9278)) (.node (.leaf 9224) (.leaf 9303))) (.node (.node (.leaf 194) (.leaf 9294)) (.node (.leaf 9262) (.leaf 9312))))) (.node (.node (.node (.node (.leaf 34) (.leaf 9274)) (.node (.leaf 9192) (.leaf 9302))) (.node (.node (.leaf 162) (.leaf 9290)) (.node (.leaf 9258) (.leaf 9309)))) (.node (.node (.node (.leaf 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(.leaf 9306))) (.node (.node (.leaf 9152) (.leaf 9299)) (.node (.leaf 9269) (.leaf 0)))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf 6) (.leaf 9270)) (.node (.leaf 9164) (.leaf 9300))) (.node (.node (.leaf 134) (.leaf 9286)) (.node (.leaf 9254) (.leaf 9307)))) (.node (.node (.node (.leaf 70) (.leaf 9278)) (.node (.leaf 9228) (.leaf 9148))) (.node (.node (.leaf 198) (.leaf 9294)) (.node (.leaf 9262) (.leaf 9313))))) (.node (.node (.node (.node (.leaf 38) (.leaf 9274)) (.node (.leaf 9196) (.leaf 9302))) (.node (.node (.leaf 166) (.leaf 9290)) (.node (.leaf 9258) (.leaf 9309)))) (.node (.node (.node (.leaf 102) (.leaf 9282)) (.node (.leaf 9250) (.leaf 9305))) (.node (.node (.leaf 230) (.leaf 9298)) (.node (.leaf 9266) (.leaf 0)))))) (.node (.node (.node (.node (.node (.leaf 22) (.leaf 9272)) (.node (.leaf 9180) (.leaf 9301))) (.node (.node (.leaf 150) (.leaf 9288)) (.node (.leaf 9256) (.leaf 9308)))) (.node (.node (.node (.leaf 86) (.leaf 9280)) (.node (.leaf 9244) (.leaf 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(.leaf 63) (.node (.leaf 63) (.node (.leaf 63) (.leaf 0))))) (.node (.node (.leaf 63) (.node (.leaf 63) (.node (.leaf 63) (.leaf 0)))) (.node (.leaf 63) (.node (.leaf 63) (.node (.leaf 63) (.leaf 0))))))))))))) + +abbrev Role := Fin 987 +abbrev Tag := Fin 59 +abbrev Slot := Fin 61 +abbrev Axis := Fin 64 + +def family (r : Role) : Nat := lookup familyTable r.val +def slot (r : Role) : Slot := ⟨lookup slotTable r.val % 61, Nat.mod_lt _ (by decide)⟩ +def slotTag (s : Slot) : Tag := ⟨lookup slotTagTable s.val % 59, Nat.mod_lt _ (by decide)⟩ +def tag (r : Role) : Tag := slotTag (slot r) +def perm (t : Tag) (i : Axis) : Axis := + ⟨lookup permTable (64*t.val+i.val) % 64, Nat.mod_lt _ (by decide)⟩ +def invPerm (t : Tag) (i : Axis) : Axis := + ⟨lookup invPermTable (64*t.val+i.val) % 64, Nat.mod_lt _ (by decide)⟩ +def sourceMask (t : Slot) (i : Axis) : Bool := (lookup sourceBits t.val).testBit i.val +def targetMask (t : Slot) (i : Axis) : Bool := (lookup targetBits t.val).testBit i.val + +theorem perm_inverse : ∀ (t : Tag) (i : Axis), invPerm t (perm t i) = i := by decide +theorem inverse_perm : ∀ (t : Tag) (i : Axis), perm t (invPerm t i) = i := by decide +theorem perm_support : ∀ (s : Slot) (i : Axis), targetMask s (perm (slotTag s) i) = sourceMask s i := by decide + +def fingerprint (t : Tag) : Nat := + (List.range 8).foldl (fun n i => n + (perm t ⟨i % 64, Nat.mod_lt _ (by decide)⟩).val * 64^i) 0 + +theorem fingerprint_injective : ∀ (a b : Tag), fingerprint a = fingerprint b → a = b := by decide + +theorem owner_inverse : ∀ r : Role, lookup inverseOwnerTable (59*family r+(tag r).val) = r.val := by decide + +theorem family_tag_injective {r s : Role} (hf : family r = family s) (ht : tag r = tag s) : r = s := by + apply Fin.ext + rw [← owner_inverse r, ← owner_inverse s, hf, ht] + +theorem family_data : ∀ r : Fin 240, family ⟨r.val, Nat.lt_trans r.isLt (by decide)⟩ = r.val := by decide + +theorem helper_range : ∀ r : Role, 240 ≤ r.val → 7680 ≤ family r ∧ family r < 14259 := by decide + +theorem helper_frame : ∀ r : Role, 240 ≤ r.val → lookup initialFrameTable r.val = lookup slotInitialFrame (slot r).val := by decide + +end ParentOwnership +#print axioms ParentOwnership.perm_inverse +#print axioms ParentOwnership.perm_support +#print axioms ParentOwnership.fingerprint_injective +#print axioms ParentOwnership.family_tag_injective +#print axioms ParentOwnership.helper_frame diff --git a/research/lean-multi-host-source/PayloadGuards.lean b/research/lean-multi-host-source/PayloadGuards.lean new file mode 100644 index 0000000000..6105ae5cb8 --- /dev/null +++ b/research/lean-multi-host-source/PayloadGuards.lean @@ -0,0 +1,58 @@ +import TreeReplay + +/-! +Transport the symbolic copy/erase preconditions to whole arbitrary dirty +payloads at every point in the normalized run. Equality here is equality +of entire functions, not merely a check at one address. +-/ +namespace TreeReplay +open LinearReplay (Event evalRow evalRow_zero) + +def PayloadClean {X : Type u} (s : Tree (X → Bool)) (e : Event) : Prop := + (e.op = 2 → s.get e.y = fun _ => false) ∧ + (e.op = 3 → s.get e.x = s.get e.y) + +def PayloadCleanRun {X : Type u} : List Event → Tree (X → Bool) → Prop + | [], _ => True + | e :: es, s => PayloadClean s e ∧ + PayloadCleanRun es (step (fun _ => false) (fun a b x => a x ^^ b x) s e) + +theorem payload_checks_sound {X : Type u} (n : Nat) (input : Nat → X → Bool) + (s : Tree Nat) (e : Event) (h : rowChecks s e = true) : + PayloadClean (evalPayloadRows n input s) e := by + constructor + · intro hop + have hy : s.get e.y = 0 := by + simp only [rowChecks, hop, Bool.and_eq_true, beq_iff_eq] at h + exact h.2 + apply funext + intro x + change ((s.map (fun row x => evalRow n (fun i => input i x) row)).get e.y) x = false + rw [Tree.map_get, hy] + exact evalRow_zero n (fun i => input i x) + · intro hop + have hxy : s.get e.x = s.get e.y := by + simp only [rowChecks, hop, Bool.and_eq_true, beq_iff_eq] at h + exact h.2 + change (s.map _).get e.x = (s.map _).get e.y + rw [Tree.map_get, Tree.map_get, hxy] + +theorem checked_payload_guards_sound {X : Type u} (n : Nat) (input : Nat → X → Bool) + (es : List Event) (s : Tree Nat × Bool) (h : (runCheckedRows es s).2 = true) : + PayloadCleanRun es (evalPayloadRows n input s.1) := by + induction es generalizing s with + | nil => trivial + | cons e es ih => + have hfirst := checked_flag_mono es (checkedRowStep s e) h + have hparts := Bool.and_eq_true_iff.mp hfirst + constructor + · exact payload_checks_sound n input s.1 e hparts.2 + · have hi := ih (checkedRowStep s e) h + have hstep : evalPayloadRows n input (rowStep s.1 e) = + step (fun _ => false) (fun a b x => a x ^^ b x) (evalPayloadRows n input s.1) e := by + apply step_map 0 (fun _ => false) (· ^^^ ·) (fun a b x => a x ^^ b x) + · funext x; exact evalRow_zero n (fun i => input i x) + · intro a b; funext x; exact LinearReplay.evalRow_xor n (fun i => input i x) a b + simpa only [checkedRowStep, hstep] using hi + +end TreeReplay diff --git a/research/lean-multi-host-source/PhysicalSourceConnection.lean b/research/lean-multi-host-source/PhysicalSourceConnection.lean new file mode 100644 index 0000000000..9a78d48f18 --- /dev/null +++ b/research/lean-multi-host-source/PhysicalSourceConnection.lean @@ -0,0 +1,243 @@ +import SourceConnection +import SourceFramed + +/-! +An endpoint contract for the actual framed invocation, retaining all 747 +host streams, all 240 data streams and arbitrary untouched exterior state. +The old helper bank is threaded through its actual outputs. COPY/ERASE +guards and clean-temporary restoration follow from SourceFramed for every +dirty input. + +`HelperRelative` is an explicit remaining geometry obligation in this file: +the source's actual initial/final gauges must compose to its declared +residual swap. Distinct physical ownership and the identification of the +gather/scatter maps with source charts are also supplied separately. No +claim that an arbitrary supplied gauge family is the source's geometry is +made here. +-/ +namespace PhysicalSourceConnection +open TreeReplay WholeHosting SourceConnection +set_option maxRecDepth 100000 +set_option maxHeartbeats 0 + +-- Prevent elaboration from reducing the full literal execution or frame tables. +-- These remain ordinary transparent definitions checked by the kernel. +attribute [local irreducible] SourceFramed.final SourceFrameTrace.state0 SourceFrameTrace.state96 + +abbrev Address64 (K : Type) := Address SourceOwnership.Axis K +abbrev Gauges (K : Type) := Nat → FramedReplay.Gauge (Address64 K) + +def relative {K : Type} (gauges : Gauges K) (h : Host) (a : Address64 K) : Address64 K := + (gauges (SourceFrameTrace.state0.frames.get (240 + h.val))).forward + ((gauges (SourceFrameTrace.state96.frames.get (240 + h.val))).inverse a) + +def HelperRelative {K : Type} (gauges : Gauges K) : Prop := + ∀ h a, relative gauges h a = + swapAddress (SourceOwnership.sourceMask (SourceOwnership.tag (role h))) a + +def physicalData {K : Type} (gauges : Gauges K) + (data : Data → Streams K) (helpers : Host → Streams K) : Data → Streams K := + fun i => ((SourceFramed.final gauges (packed data helpers)).get i.val).2 + +def physicalHelpers {K : Type} (gauges : Gauges K) + (data : Data → Streams K) (helpers : Host → Streams K) : Host → Streams K := + fun h => ((SourceFramed.final gauges (packed data helpers)).get (240 + h.val)).2 + +theorem helper_endpoints {K : Type} (gauges : Gauges K) + (data : Data → Streams K) (helpers : Host → Streams K) : + physicalHelpers gauges data helpers = fun h a => helpers h (relative gauges h a) := by + have he := congrArg + (fun values : Fin 1024 → Streams K => fun h : Host => values ⟨240 + h.val, by omega⟩) + (SourceFramed.all_physical_endpoints gauges (packed data helpers)) + apply he.trans + funext h a + have hr : 240 + h.val < 987 := by omega + have ht : ¬ 240 + h.val < 240 := by omega + simp only [SourceMatrix.endpointPayload, hr, ht, and_false, ↓reduceIte, + SourceFramed.normalizedInput, packed_helper, relative] + +theorem helper_endpoint {K : Type} (gauges : Gauges K) + (data : Data → Streams K) (helpers : Host → Streams K) (h : Host) : + physicalHelpers gauges data helpers h = fun a => helpers h (relative gauges h a) := + congrFun (helper_endpoints gauges data helpers) h + +#print axioms helper_endpoints +#print axioms helper_endpoint + +theorem physical_data_endpoints {K : Type} (gauges : Gauges K) + (data : Data → Streams K) (helpers : Host → Streams K) : + physicalData gauges data helpers = fun i a => + SourceMatrix.endpointPayload (SourceFramed.normalizedInput gauges (packed data helpers)) + i.val ((gauges (SourceFrameTrace.state96.frames.get i.val)).inverse a) := by + exact congrArg + (fun values : Fin 1024 → Streams K => fun i : Data => values ⟨i.val, by omega⟩) + (SourceFramed.all_physical_endpoints gauges (packed data helpers)) + +/-- Independence is proved from the literal word for every dirty bank. +The zero bank below is only a name for the resulting data-only function. -/ +theorem data_independent {K : Type} (gauges : Gauges K) (data : Data → Streams K) + (left right : Host → Streams K) : physicalData gauges data left = physicalData gauges data right := by + rw [physical_data_endpoints, physical_data_endpoints] + funext i a + have hi : i.val < 987 := by omega + by_cases ht : 120 ≤ i.val + · have hs : i.val - 120 < 240 := by omega + simp [SourceMatrix.endpointPayload, SourceFramed.normalizedInput, + packed, hi, ht, i.isLt, hs] + · simp [SourceMatrix.endpointPayload, SourceFramed.normalizedInput, + packed, hi, ht, i.isLt] + +#print axioms physical_data_endpoints +#print axioms data_independent + +def dataEndpoint {K : Type} (gauges : Gauges K) (data : Data → Streams K) : Data → Streams K := + physicalData gauges data (fun _ _ => false) + +theorem data_endpoint {K : Type} (gauges : Gauges K) + (data : Data → Streams K) (helpers : Host → Streams K) : + physicalData gauges data helpers = dataEndpoint gauges data := + data_independent gauges data helpers (fun _ _ => false) + +def scatterHost {K : Type} (h : Host) (v : Streams K) : Streams K := + fun a => v (SourceOwnership.unindex (SourceOwnership.tag (role h)) a) + +/-- This uses arbitrary-helper endpoint identity first, then the actual +relative frame equation. It does not equate physical initial data with the +convenient normalized input used by SourceConnection.invoke. -/ +theorem hosted_endpoint {K : Type} (gauges : Gauges K) (geometry : HelperRelative gauges) + (data : Data → Streams K) (hosts : Host → Streams K) (h : Host) : + scatterHost h (physicalHelpers gauges data (fun j => hostInput j (hosts j)) h) = + bitAction (residual h) (hosts h) := by + rw [helper_endpoint] + funext a + change hosts h (SourceOwnership.reindex (SourceOwnership.tag (role h)) + (relative gauges h (SourceOwnership.unindex (SourceOwnership.tag (role h)) a))) = _ + rw [geometry] + exact congrArg (hosts h) (swap_conjugacy _ a) + +def event {K : Type} {Tail : Type v} (gauges : Gauges K) + (dataInput dataOutput : Data → Streams K → Streams K) : + MultiHosting.WindowEvent Host SourceOwnership.Axis (Retained K Tail) where + idle := fun _ _ => false + residual := residual + other s := (fun i => dataOutput i (dataEndpoint gauges (fun j => dataInput j (s.1 j)) i), s.2) + +def original {K : Type} {Tail : Type v} (gauges : Gauges K) + (dataInput dataOutput : Data → Streams K → Streams K) + (oldInput oldOutput : Host → Streams K → Streams K) + (s : MultiHosting.WindowState Host SourceOwnership.Axis K Bool (Retained K Tail) × + (Host → Streams K)) := + let data := fun i => dataInput i (s.1.2.1 i) + let helpers := fun h => oldInput h (s.2 h) + ((s.1.1, (fun i : Data => dataOutput i (physicalData gauges data helpers i), s.1.2.2)), + fun h : Host => oldOutput h (physicalHelpers gauges data helpers h)) + +def relocated {K : Type} {Tail : Type v} (gauges : Gauges K) + (dataInput dataOutput : Data → Streams K → Streams K) + (s : MultiHosting.WindowState Host SourceOwnership.Axis K Bool (Retained K Tail) × Unit) := + let data := fun i => dataInput i (s.1.2.1 i) + let helpers := fun h => hostInput h (s.1.1 h) + ((fun h : Host => scatterHost h (physicalHelpers gauges data helpers h), + (fun i : Data => dataOutput i (physicalData gauges data helpers i), s.1.2.2)), s.2) + +theorem original_retained {K : Type} {Tail : Type v} (gauges : Gauges K) + (dataInput dataOutput : Data → Streams K → Streams K) + (oldInput oldOutput : Host → Streams K → Streams K) + (s : MultiHosting.WindowState Host SourceOwnership.Axis K Bool (Retained K Tail)) + (bank : Host → Streams K) : + (original gauges dataInput dataOutput oldInput oldOutput (s, bank)).1 = + (event gauges dataInput dataOutput).base s := by + apply Prod.ext + · funext h; exact (bitAction_empty (s.1 h)).symm + · apply Prod.ext + · funext i + exact congrArg (dataOutput i) (congrFun + (data_endpoint gauges (fun j => dataInput j (s.2.1 j)) + (fun h => oldInput h (bank h))) i) + · rfl + +theorem relocated_retained {K : Type} {Tail : Type v} (gauges : Gauges K) + (geometry : HelperRelative gauges) + (dataInput dataOutput : Data → Streams K → Streams K) + (s : MultiHosting.WindowState Host SourceOwnership.Axis K Bool (Retained K Tail)) + (bank : Unit) : + (relocated gauges dataInput dataOutput (s, bank)).1 = + (event gauges dataInput dataOutput).hosted s := by + apply Prod.ext + · funext h + change scatterHost h (physicalHelpers gauges _ _ h) = + bitAction (residual h) (bitAction (fun _ => false) (s.1 h)) + rw [bitAction_empty] + exact hosted_endpoint gauges geometry _ s.1 h + · apply Prod.ext + · funext i + exact congrArg (dataOutput i) (congrFun + (data_endpoint gauges (fun j => dataInput j (s.2.1 j)) + (fun h => hostInput h (s.1 h))) i) + · rfl + +def contract {K : Type} {Tail : Type v} (gauges : Gauges K) (geometry : HelperRelative gauges) + (dataInput dataOutput : Data → Streams K → Streams K) + (oldInput oldOutput : Host → Streams K → Streams K) : + MultiHosting.PhysicalContract (K := K) (A := Bool) + (event (Tail := Tail) gauges dataInput dataOutput) (Host → Streams K) Unit where + original := original gauges dataInput dataOutput oldInput oldOutput + relocated := relocated gauges dataInput dataOutput + original_retained := original_retained gauges dataInput dataOutput oldInput oldOutput + relocated_retained := relocated_retained gauges geometry dataInput dataOutput + +/-- Actual child pending coordinates in the selected stage-2 invocation. +Child 1 has coordinates 15..21; child 2 has coordinates 1..28. -/ +def pendingTag (t : SourceOwnership.Tag) : Mask SourceOwnership.Axis := fun i => + if SourceOwnership.lookup SourceOwnership.tagChild t.val = 1 then + decide (15 ≤ i.val ∧ i.val < 22) + else decide (1 ≤ i.val ∧ i.val < 29) + +theorem tag_child_cases : ∀ t : SourceOwnership.Tag, + SourceOwnership.lookup SourceOwnership.tagChild t.val = 1 ∨ + SourceOwnership.lookup SourceOwnership.tagChild t.val = 2 := by decide + +theorem tag_pending_contains : ∀ (t : SourceOwnership.Tag) (i : SourceOwnership.Axis), + SourceOwnership.targetMask t i = true → pendingTag t i = true := by decide + +def pending : MultiHosting.HostMask Host SourceOwnership.Axis := + fun h => pendingTag (SourceOwnership.tag (role h)) + +/-- Application to this one invocation. The remaining pending swap is +explicitly charged on each affected host. This is not a whole-cover sweep +or an asymptotic cost/bound theorem. `geometry` is discharged by the concrete +source gauge connector, not by this abstract application. -/ +theorem selected_invocation_completion {K : Type} {Tail : Type v} (gauges : Gauges K) + (geometry : HelperRelative gauges) + (dataInput dataOutput : Data → Streams K → Streams K) + (oldInput oldOutput : Host → Streams K → Streams K) + (s : MultiHosting.WindowState Host SourceOwnership.Axis K Bool (Retained K Tail)) + (oldBank : Host → Streams K) (newBank : Unit) : + MultiHosting.onHosts (MultiHosting.remainders pending [event (Tail := Tail) gauges dataInput dataOutput]) + (relocated gauges dataInput dataOutput (s, newBank)).1 = + MultiHosting.onHosts pending + (original gauges dataInput dataOutput oldInput oldOutput (s, oldBank)).1 := by + have hd : ∀ h, DisjointMasks + (MultiHosting.residuals [event (Tail := Tail) gauges dataInput dataOutput] h) := by + intro h + simp [MultiHosting.residuals, DisjointMasks, MasksDisjoint, maskUnion] + have hs : ∀ h, MaskSubset + (MultiHosting.masksUnion [event (Tail := Tail) gauges dataInput dataOutput] h) (pending h) := by + intro h i hi + have ht : SourceOwnership.targetMask (SourceOwnership.tag (role h)) i = true := by + simpa [MultiHosting.masksUnion, MultiHosting.residuals, event, maskUnion, + unionMask, residual] using hi + exact tag_pending_contains _ i ht + exact MultiHosting.physical_multi_hosting + (.cons (contract gauges geometry dataInput dataOutput oldInput oldOutput) .nil) + pending hd hs s oldBank newBank + +#print axioms data_endpoint +#print axioms hosted_endpoint +#print axioms original_retained +#print axioms relocated_retained +#print axioms tag_child_cases +#print axioms tag_pending_contains +#print axioms selected_invocation_completion + +end PhysicalSourceConnection diff --git a/research/lean-multi-host-source/PortData.lean b/research/lean-multi-host-source/PortData.lean new file mode 100644 index 0000000000..1e26926f7f --- /dev/null +++ b/research/lean-multi-host-source/PortData.lean @@ -0,0 +1,917 @@ +import Std + +/-! +Literal port charts and rho15 matrices from PR442's inherited GEOMETRY.json. +Apache-2.0. Prepared with substantial OpenAI Codex assistance. +Generated by generate_port_data.py; its JSON parser is not kernel verified. +Source SHA-256: fc7b29b16ee754ca9717973b745d6322bbf8351a5e35e3fc9e0fbf7a88dc0317 +Each basis is exactly 2 B_q = [q | 2 complement_columns]; each route is 4 rho15. +Every port carries small kernel-checked column, row and route certificates. +Balanced lookup selects certified records, avoiding one large normalizer cache. +-/ +namespace PortGeometry +set_option maxHeartbeats 0 +set_option maxRecDepth 100000 + +inductive IntLookup where + | leaf : Int → IntLookup + | node : IntLookup → IntLookup → IntLookup + +def intLookup : IntLookup → Nat → Int + | .leaf n, _ => n + | .node l r, i => if i % 2 == 0 then intLookup l (i / 2) else intLookup r (i / 2) + +def columnDot (b : Fin 8 → Fin 8 → Int) (i j : Fin 8) : Int := + b 0 i * b 0 j + (b 1 i * b 1 j + (b 2 i * b 2 j + (b 3 i * b 3 j + + (b 4 i * b 4 j + (b 5 i * b 5 j + (b 6 i * b 6 j + (b 7 i * b 7 j + 0))))))) + +def rowDot (b : Fin 8 → Fin 8 → Int) (i j : Fin 8) : Int := + b i 0 * b j 0 + (b i 1 * b j 1 + (b i 2 * b j 2 + (b i 3 * b j 3 + + (b i 4 * b j 4 + (b i 5 * b j 5 + (b i 6 * b j 6 + (b i 7 * b j 7 + 0))))))) + +def routeExpected (b : Fin 8 → Fin 8 → Int) (i j : Fin 15) : Int := + if hi : i.val < 8 then + if hj : j.val < 8 then b ⟨i.val, hi⟩ 0 * b ⟨j.val, hj⟩ 0 + else 2 * b ⟨i.val, hi⟩ ⟨j.val - 7, by omega⟩ + else if hj : j.val < 8 then 2 * b ⟨j.val, hj⟩ ⟨i.val - 7, by omega⟩ + else 0 + +structure CertifiedPort where + basis : Fin 8 → Fin 8 → Int + route : Fin 15 → Fin 15 → Int + column_correct : ∀ i j, columnDot basis i j = if i = j then 4 else 0 + row_correct : ∀ i j, rowDot basis i j = if i = j then 4 else 0 + route_correct : ∀ i j, route i j = routeExpected basis i j + +def certified0 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0))) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.leaf (0)) (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified1 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (-2))))))) (.node (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (-2)))) (.leaf (0)))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0))) (.leaf (0))) (.leaf (0)))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.leaf (0)) (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (-4))))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (-4)) (.leaf (0))))) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0))) (.leaf (0)))) (.node (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (-4)) (.leaf (0)))))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0))) (.leaf (0)))) (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (-4)))) (.leaf (0)))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified2 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (-2)))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.leaf (0)) (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0)))) (.node (.leaf (0)) (.node (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (-4)))) (.leaf (0)))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (-4))) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.leaf (0)) (.node (.leaf (-4)) (.leaf (0)))) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (-4)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified3 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.leaf (0)))) (.node (.node (.leaf (0)) (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0)))) (.leaf (0))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.node (.leaf (-4)) (.leaf (0))) (.leaf (0)))) (.leaf (0)))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (-4))) (.leaf (0))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0))) (.leaf (0))) (.leaf (0)))) (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.node (.leaf (0)) (.leaf (-4))) (.leaf (0))) (.leaf (0)))) (.node (.leaf (0)) (.node (.node (.node (.leaf (-4)) (.leaf (0))) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified4 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (-2)))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0)))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (-4)))) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.leaf (0)) (.node (.node (.node (.leaf (0)) (.leaf (-4))) (.leaf (0))) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (-4)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.node (.leaf (-4)) (.leaf (0))) (.leaf (0)))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified5 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0)))) (.node (.leaf (0)) (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))) (.leaf (0))))) (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.leaf (0)))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.leaf (0)) (.node (.leaf (-4)) (.leaf (0)))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (-4))) (.leaf (0))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0))) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))))))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (-4))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))) (.leaf (0)))) (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0)))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.leaf (0)) (.node (.node (.node (.leaf (-4)) (.leaf (0))) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified6 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0)))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0)))) (.node (.leaf (0)) (.node (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.node (.node (.leaf (0)) (.leaf (-4))) (.leaf (0))) (.leaf (0)))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (-4))) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.leaf (0)) (.node (.leaf (-4)) (.leaf (0)))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0))) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.node (.leaf (-4)) (.leaf (0))) (.leaf (0)))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified7 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.leaf (0)) (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (-2)))) (.leaf (0))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.leaf (0)))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (-4)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.leaf (0)) (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (-4))) (.leaf (0))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0))) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (-4)))) (.leaf (0)))) (.node (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.node (.node (.leaf (-4)) (.leaf (0))) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0))) (.leaf (0)))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified8 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1))))) (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.node (.leaf (1)) (.leaf (-1)))) (.leaf (0))) (.node (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1))))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0))))))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (1)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0)))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (1)) (.leaf (2))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (1)) (.leaf (0)))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2))))) (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))) (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0)))) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0)))) (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified9 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1))))) (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.node (.leaf (1)) (.leaf (-1)))) (.leaf (0))) (.node (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1))))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (-2))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (1)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (-2)))) (.node 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(.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2))))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified10 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1))))) (.node (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (1))) (.leaf (0)))) (.node (.node (.node (.leaf (1)) (.node (.leaf (1)) (.leaf (-1)))) (.leaf (0))) (.node (.node (.node (.leaf (0)) 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(.node (.node (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1))))) (.node (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (1))) (.leaf (0)))) (.node (.node (.node (.leaf (1)) (.node (.leaf (1)) (.leaf (-1)))) (.leaf (0))) (.node (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1))))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (-2))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (-1)) (.leaf (2))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0)))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf 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(.leaf (0)) (.node (.leaf (-1)) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0)))))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf 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(.node (.leaf (1)) (.leaf (2))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0)))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (-1)) (.leaf (2))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (-1)) (.leaf (0)))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (-2))))) (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0))))) (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0)))))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified13 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1))))) (.node (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (1))) (.leaf (0)))) (.node (.node (.node (.leaf (1)) (.node (.leaf (1)) (.leaf (-1)))) (.leaf (0))) (.node (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1))))))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))))) (.node (.node (.node (.node 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(.leaf (0)) (.leaf (-2))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2))))) (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2))))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified14 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1))))) (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.node (.leaf (1)) (.leaf (-1)))) (.leaf (0))) (.node (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1))))))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (-2))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0))))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0))))))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (-1)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (-1)) (.leaf (0)))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.leaf (0)) (.node 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(.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0)))) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0)))) (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0)))))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified15 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1))))) (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.node (.leaf (1)) (.leaf (-1)))) (.leaf (0))) (.node (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1))))))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0))))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (-1)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0)))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (-1)) (.leaf (2))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (1)) (.leaf (0)))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2))))) (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))) (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0)))) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0)))) (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2))))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified16 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.node (.leaf (1)) (.leaf (-1)))) (.leaf (0))) (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.node (.leaf (-1)) (.leaf (1)))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0)))) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0)))) (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified17 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.leaf (1)) (.node (.leaf (1)) (.leaf (-1)))) (.leaf (0))) (.node (.node (.leaf (1)) (.node (.leaf (-1)) (.leaf (1)))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (1))) (.leaf (0))) (.node (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (1))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0)))) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified18 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (1))) (.leaf (0))) (.node (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (1))) (.leaf (0)))) (.node (.node (.node (.leaf (1)) (.node (.leaf (1)) (.leaf (-1)))) (.leaf (0))) (.node (.node (.leaf (1)) (.node (.leaf (-1)) (.leaf (1)))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified19 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.node (.leaf (1)) (.leaf (-1)))) (.leaf (0))) (.node (.node (.node (.leaf (-1)) (.leaf (1))) (.node (.leaf (1)) (.leaf (-1)))) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0)))) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified20 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.leaf (1)) (.node (.leaf (-1)) (.leaf (1)))) (.leaf (0))) (.node (.node (.leaf (1)) (.node (.leaf (1)) (.leaf (-1)))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (1))) (.leaf (0))) (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (1))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0)))) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified21 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.node (.node (.leaf (-1)) (.leaf (1))) (.node (.leaf (1)) (.leaf (-1)))) (.leaf (0))) (.node (.node (.node (.leaf (-1)) (.leaf (1))) (.node (.leaf (-1)) (.leaf (1)))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified22 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.node (.leaf (-1)) (.leaf (1)))) (.leaf (0))) (.node (.node (.node (.leaf (-1)) (.leaf (1))) (.node (.leaf (-1)) (.leaf (1)))) (.leaf (0)))) (.node (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0)))) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified23 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (-1))) (.leaf (0))) (.node (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (-1))) (.leaf (0)))) (.node (.node (.node (.leaf (-1)) (.node (.leaf (1)) (.leaf (-1)))) (.leaf (0))) (.node (.node (.leaf (-1)) (.node (.leaf (-1)) (.leaf (1)))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0)))) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0)))) (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified24 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1))))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (2))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (2))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0))))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0))))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.leaf (0)) (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (-2))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (-2))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0))))) (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (2))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (-2))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))))) (.node (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0)))))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (-2))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (2))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified25 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1))))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (2))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (-2))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2)))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0))))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.leaf (0)) (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (-2))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (2))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2)))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (2))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (2))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (0)))))) (.node (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (2))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (2))))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified26 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1))))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (2))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (2))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0))))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.leaf (0)) (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (2))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (2))))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2)))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (2))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (-2))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))))) (.node (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (-2))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (2))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified27 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1))))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (2))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (-2))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.leaf (0)) (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (2))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (-2))))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0))))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (2))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (2))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2)))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (0)))))) (.node (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0)))))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (2))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (2))))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified28 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1))))))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (-2))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (2))))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.leaf (0)) (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (2))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (-2))))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0))))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (2))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (2))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2)))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (0)))))) (.node (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0)))))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (2))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (2))))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified29 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1))))))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (-2))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (-2))))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2)))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0))))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.leaf (0)) (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (2))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (2))))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2)))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (2))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (-2))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))))) (.node (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (-2))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (2))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified30 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1))))))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (-2))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (2))))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0))))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.leaf (0)) (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (-2))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (2))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2)))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (2))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (2))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (0)))))) (.node (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (2))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (2))))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified31 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node 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(.leaf (0)) (.node (.leaf (-2)) (.leaf (0))))) (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (2))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (-2))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))))) (.node (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0)))))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (-2))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (2))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified32 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))) (.leaf (0))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (0))) (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (0)))) (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (0))) (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (2))) (.node (.leaf (1)) (.leaf (2)))) (.leaf (0))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0)))) (.leaf (0))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (-2))) (.node (.leaf (1)) (.leaf (-2)))) (.leaf (0))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.leaf (0)) (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (2))) (.node (.leaf (1)) (.leaf (-2)))) (.leaf (0))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))) (.leaf (0)))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (-2))) (.node (.leaf (1)) (.leaf (2)))) (.leaf (0))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0)))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified33 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))) (.leaf (0))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (2))) (.node (.leaf (1)) (.leaf (-2)))) (.leaf (0))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (-2))) (.node (.leaf (1)) (.leaf (2)))) (.leaf (0))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.leaf (0)) (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (2))) (.node (.leaf (1)) (.leaf (2)))) (.leaf (0))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))) (.leaf (0)))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (2))) (.node (.leaf (-1)) (.leaf (2)))) (.leaf (0))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified34 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (2))) (.node (.leaf (-1)) (.leaf (2)))) (.leaf (0))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0)))) (.leaf (0))))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (2))) (.node (.leaf (1)) (.leaf (2)))) (.leaf (0))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.leaf (0)) (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (2))) (.node (.leaf (-1)) (.leaf (-2)))) (.leaf (0))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))) (.leaf (0)))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (-2))) (.node (.leaf (-1)) (.leaf (2)))) (.leaf (0))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified35 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (0))) (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (0)))) (.node (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (0))) (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (2))) (.node (.leaf (-1)) (.leaf (-2)))) (.leaf (0))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (2))) (.node (.leaf (1)) (.leaf (-2)))) (.leaf (0))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.leaf (0)) (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (2))) (.node (.leaf (-1)) (.leaf (2)))) (.leaf (0))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))) (.leaf (0)))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (2))) (.node (.leaf (1)) (.leaf (2)))) (.leaf (0))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0)))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified36 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))) (.leaf (0))))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (-2))) (.node (.leaf (1)) (.leaf (2)))) (.leaf (0))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (2))) (.node (.leaf (1)) (.leaf (-2)))) (.leaf (0))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.leaf (0)) (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (2))) (.node (.leaf (-1)) (.leaf (2)))) (.leaf (0))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))) (.leaf (0)))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (2))) (.node (.leaf (1)) (.leaf (2)))) (.leaf (0))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0)))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified37 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))) (.leaf (0))))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (0))) (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (0)))) (.node (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (0))) (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (-2))) (.node (.leaf (1)) (.leaf (-2)))) (.leaf (0))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0)))) (.leaf (0))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (2))) (.node (.leaf (1)) (.leaf (2)))) (.leaf (0))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.leaf (0)) (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) 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(.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.leaf (0)) (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (2))) (.node (.leaf (1)) (.leaf (2)))) (.leaf (0))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))) (.leaf (0)))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (2))) (.node (.leaf (-1)) (.leaf (2)))) (.leaf (0))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified39 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (0)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (-2))) (.node (.leaf (-1)) (.leaf (-2)))) (.leaf (0))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf 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(.node (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (2))) (.node (.leaf (1)) (.leaf (-2)))) (.leaf (0))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))) (.leaf (0)))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (-2))) (.node (.leaf (1)) (.leaf (2)))) (.leaf (0))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0)))) (.leaf (0))))) (.node (.node (.node 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(1)) (.leaf (0)))))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified41 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (0)) (.leaf (-1))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (0)) (.leaf (1))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (0)) (.leaf (1)))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (0)) (.leaf (1)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (0)))))) (.node (.leaf (0)) (.node (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))))))) (.node (.node (.node 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column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified42 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (0)) (.leaf (1))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (0)) (.leaf (-1))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (0)) (.leaf (1)))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (1)) (.leaf 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+ route_correct := by decide + +def certified43 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (0)) (.leaf (-1))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (0)) (.leaf (1))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (0)) (.leaf (-1)))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node 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(.leaf (0))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified44 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (0)) (.leaf (1))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (0)) (.leaf (1))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (0)) (.leaf (-1)))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (0)) (.leaf (1)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2))))) (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (1)) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))))) (.node (.leaf (0)) (.node (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0)))))))) (.node (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2))))) (.node (.node 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(.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified45 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (0)) (.leaf (-1))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (0)) (.leaf (-1))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (0)) (.leaf (1)))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (0)) (.leaf (1)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2))))) (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (1)) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (0)))))) (.node (.leaf (0)) (.node (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))))))) (.node (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (-1)) 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(.leaf (2))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (0)))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2))))) (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified46 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (0)) (.leaf (1))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (0)) (.leaf (1))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (0)) (.leaf (1)))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (0)) (.leaf (1)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2))))) (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))))) (.node (.leaf (0)) (.node (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))))))) (.node (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (-1)) 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(-2))) (.node (.leaf (1)) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (0)))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified47 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (0)) (.leaf (-1))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (0)) (.leaf (-1))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (0)) (.leaf (-1)))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (0)) (.leaf (1)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2))))) (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (0)))))) (.node (.leaf (0)) (.node (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0)))))))) (.node (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))))) (.node (.leaf (0)) (.node (.leaf 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(.leaf (0)) (.node (.leaf (1)) (.leaf (0)))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2))))) (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (1)) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified48 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.node (.leaf (1)) (.leaf (-1)))) (.leaf (0))) (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.node (.leaf (-1)) (.leaf (1)))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (2)))) (.leaf (0))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (2)))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) 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(0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0)))) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0)))) (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0))))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified49 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (-1)))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (1)))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (1))) (.leaf (0))) (.node (.node (.node (.leaf (-1)) (.leaf (1))) 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(.node (.node (.leaf (0)) (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified50 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (1))) (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.node (.leaf (1)) (.leaf (-1)))) (.leaf (0))) (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.node (.leaf (-1)) (.leaf (1)))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node 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(-1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0)))) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0)))) (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0))))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0)))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified51 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (-1)))) (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (0)))) (.node (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (1)))) (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (1))) (.leaf (0))) (.node (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (1))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (-2)))) (.leaf (0))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (-2)))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))))) (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (-2)))) (.leaf (0))) (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (2)))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf 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column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified52 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (1)))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (1)))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (1))) (.leaf (0))) (.node (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (1))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (0)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (-2)))) (.leaf (0))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (-2)))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0)))) (.leaf (0))))) (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (-2)))) (.leaf (0))) (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (2)))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.node (.leaf (-1)) (.leaf (2))) (.node (.leaf (-1)) (.leaf (2)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (1)) (.leaf (2))) (.node (.leaf (1)) (.leaf (2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0)))) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (0)) 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(.node (.node (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.node (.leaf (1)) (.leaf (-1)))) (.leaf (0))) (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.node (.leaf (-1)) (.leaf (1)))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (0)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (-2)))) (.leaf (0))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (2)))) (.leaf (0)))) (.node 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(0))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (0)) (.leaf (-1)))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (0)) (.leaf (1)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (1)) 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(.node (.leaf (2)) (.leaf (0))))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (-2)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (2))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified57 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (0)) (.leaf (-1))))) (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (0)) (.leaf (-1))))) (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.node (.leaf (-1)) (.leaf (1)))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (0)) (.leaf (1)))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (0)) (.leaf (1)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (-2))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf 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(.leaf (2))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0)))) (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (2)))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (2))))) (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified58 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (0)) (.leaf (1))))) (.node (.node (.leaf (1)) (.node (.leaf (-1)) (.leaf (1)))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (0)) (.leaf (1))))) (.node (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (1))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (0)) (.leaf (-1)))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf 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(.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (-2)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (2))))) (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (1)) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified64 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node 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(.node (.leaf (1)) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified65 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))) (.leaf (0))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) 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by decide + row_correct := by decide + route_correct := by decide + +def certified66 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))) (.leaf (0))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (2))) (.leaf (0))) (.node (.node (.leaf (-1)) (.leaf (2))) (.leaf (0)))) (.node (.node (.node (.leaf (1)) (.leaf (-2))) (.leaf (0))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (2))) (.leaf (0))) (.node (.node (.leaf (1)) (.leaf (2))) (.leaf (0)))) (.node (.node (.node (.leaf (-1)) (.leaf (2))) (.leaf (0))) (.node (.node (.leaf (-1)) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (2))) (.leaf (0))) (.node (.node (.leaf (-1)) (.leaf (-2))) (.leaf (0)))) (.node (.node (.node (.leaf (1)) (.leaf (2))) (.leaf (0))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))) (.leaf (0))))) (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (-2))) (.leaf (0))) (.node (.node (.leaf (-1)) (.leaf (2))) (.leaf (0)))) (.node (.node (.node (.leaf (1)) (.leaf (2))) (.leaf (0))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified67 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))) (.leaf (0))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (2))) (.leaf (0))) (.node (.node (.leaf (-1)) (.leaf (-2))) (.leaf (0)))) (.node (.node (.node (.leaf (1)) (.leaf (-2))) (.leaf (0))) (.node (.node (.leaf (-1)) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (2))) (.leaf (0))) (.node (.node (.leaf (1)) (.leaf (-2))) (.leaf (0)))) (.node (.node (.node (.leaf (-1)) (.leaf (2))) (.leaf (0))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (2)) 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(2)))) (.leaf (0))))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (-2))) (.leaf (0))) (.node (.node (.leaf (1)) (.leaf (2))) (.leaf (0)))) (.node (.node (.node (.leaf (-1)) (.leaf (2))) (.leaf (0))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (2))) (.leaf (0))) (.node (.node (.leaf (1)) (.leaf (-2))) (.leaf (0)))) (.node (.node (.node (.leaf (-1)) (.leaf (2))) (.leaf (0))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (2))) (.leaf (0))) (.node (.node (.leaf (-1)) (.leaf (2))) (.leaf (0)))) (.node (.node (.node (.leaf (1)) (.leaf (2))) (.leaf (0))) (.node (.node (.leaf (-1)) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))) (.leaf (0))))) (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (2))) (.leaf (0))) (.node (.node (.leaf (1)) (.leaf (2))) (.leaf (0)))) (.node (.node (.node (.leaf (-1)) (.leaf (-2))) (.leaf (0))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified69 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))) (.leaf (0))))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (-1)) 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(.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))) (.leaf (0))))) (.node (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (-2))) (.leaf (0))) (.node (.node (.leaf (-1)) (.leaf (2))) (.leaf (0)))) (.node (.node (.node (.leaf (1)) (.leaf (2))) (.leaf (0))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified70 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))) (.leaf (0))))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (-2))) (.leaf (0))) (.node (.node (.leaf (-1)) (.leaf (2))) (.leaf (0)))) (.node (.node (.node (.leaf (-1)) (.leaf (-2))) (.leaf (0))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (-2))) (.leaf (0))) (.node (.node (.leaf (1)) (.leaf (2))) (.leaf (0)))) (.node (.node (.node (.leaf (1)) (.leaf (2))) (.leaf (0))) (.node (.node (.leaf (-1)) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (2)) (.leaf (0))) 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(0))))) (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (2))) (.leaf (0))) (.node (.node (.leaf (-1)) (.leaf (2))) (.leaf (0)))) (.node (.node (.node (.leaf (-1)) (.leaf (2))) (.leaf (0))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified71 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf 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(-1))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (1)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (2))))) (.node (.leaf (0)) (.node (.node (.leaf (1)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0)))))) (.node (.leaf (0)) (.node (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (-2))))) (.node (.leaf (0)) (.node (.node (.leaf (1)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0)))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.leaf (0)) (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0)))) (.leaf (0))) (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0))))))) (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0)))) (.leaf (0))) (.node (.leaf (0)) (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))) (.leaf (0))))) (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (-2))))) (.node (.leaf (0)) (.node (.node (.leaf (1)) (.leaf (-2))) (.node (.leaf (1)) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.leaf (0)) (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0))))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (2))))) (.node (.leaf (0)) (.node (.node (.leaf (1)) (.leaf (-2))) (.node (.leaf (1)) (.leaf (0)))))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified73 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (-1))))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (1)))))) (.node (.node 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(.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified74 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (0))) (.node (.leaf (0)) (.leaf (1))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (-1))))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (1)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (2))))) (.node (.leaf (0)) (.node (.node (.leaf (1)) (.leaf (-2))) (.node (.leaf (1)) (.leaf (0)))))) (.node (.leaf (0)) (.node (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (2))))) (.node (.leaf (0)) (.node (.node (.leaf (-1)) (.leaf (2))) (.node (.leaf (-1)) (.leaf (0)))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.leaf (0)) (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0))))))) 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(-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (2))))) (.node (.leaf (0)) (.node (.node (.leaf (1)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0)))))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified75 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (-1))))) (.node (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (-1)))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf 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(.leaf (0))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))) (.leaf (0))))) (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (2))))) (.node (.leaf (0)) (.node (.node (.leaf (1)) (.leaf (2))) (.node (.leaf (-1)) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0))))))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (2))))) (.node (.leaf (0)) (.node (.node (.leaf (-1)) (.leaf (-2))) (.node (.leaf (1)) (.leaf (0)))))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified76 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (1))))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (-1)))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (0))) (.node (.leaf (0)) (.leaf (1))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (2))))) (.node (.leaf (0)) (.node (.node (.leaf (-1)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0)))))) (.node (.leaf (0)) (.node (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (-2))))) (.node (.leaf (0)) (.node (.node (.leaf (-1)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0)))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.leaf (0)) (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))))) (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (2)) (.leaf 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(0))))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (2))))) (.node (.leaf (0)) (.node (.node (.leaf (-1)) (.leaf (-2))) (.node (.leaf (1)) (.leaf (0)))))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified77 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (-1))))) (.node (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (1)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (-2))))) (.node (.leaf (0)) (.node (.node (.leaf (-1)) (.leaf (2))) (.node (.leaf (-1)) (.leaf (0)))))) (.node (.leaf (0)) (.node (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (2))))) (.node (.leaf (0)) (.node (.node (.leaf (-1)) (.leaf (2))) (.node (.leaf (-1)) (.leaf (0)))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.leaf (0)) (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0))))))) (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.leaf (0)) (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))) (.leaf (0))))) (.node (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (-2))))) (.node (.leaf (0)) (.node (.node (.leaf (1)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (2))))) (.node (.leaf (0)) (.node (.node (.leaf (1)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0)))))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified78 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (1))))) (.node (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (1)))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (2))))) (.node (.leaf (0)) (.node (.node (.leaf (-1)) (.leaf (-2))) (.node (.leaf (1)) (.leaf (0)))))) (.node (.leaf (0)) (.node (.node (.node (.leaf (4)) (.leaf 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(.node (.node (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))) (.leaf (0))))) (.node (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (2))))) (.node (.leaf (0)) (.node (.node (.leaf (1)) (.leaf (-2))) (.node (.leaf (-1)) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.leaf (0)) (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (2))))) (.node (.leaf (0)) (.node (.node (.leaf (-1)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0)))))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified79 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (-1))))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (1)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (-2))))) (.node (.leaf (0)) (.node (.node (.leaf (-1)) (.leaf (-2))) (.node (.leaf (-1)) (.leaf (0)))))) (.node (.leaf (0)) (.node (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (-2))))) (.node (.leaf (0)) (.node (.node (.leaf (1)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0)))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.leaf (0)) (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0)))) (.leaf (0))) (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0))))))) (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0)))) (.leaf (0))) (.node (.leaf (0)) (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))) (.leaf (0))))) (.node (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (-2))))) (.node (.leaf (0)) (.node (.node (.leaf (1)) (.leaf (-2))) (.node (.leaf (1)) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.leaf (0)) (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0))))))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (2))))) (.node (.leaf (0)) (.node (.node (.leaf (1)) (.leaf (-2))) (.node (.leaf (1)) (.leaf (0)))))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified80 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.node (.leaf (-1)) (.leaf (1)))) (.leaf (0))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0)))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf 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(.leaf (0))) (.leaf (0))) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (1)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (1)) (.leaf (-2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (1)) (.leaf (2))) (.leaf (0))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0))))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0)))) (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))) (.leaf (0))))) (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (1)) (.leaf (2))) (.leaf (0))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified81 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.leaf (1)) (.node (.leaf (-1)) (.leaf (1)))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (1))) (.leaf (0))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0)))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.node (.leaf (1)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (1)) (.leaf (2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0)))) (.node 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(.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified82 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.leaf (1)) (.node (.leaf (-1)) (.leaf (1)))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (1))) (.leaf (0))))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))) (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0)))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.node (.leaf (-1)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (2)))) (.node 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(.node (.node (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (1)) (.leaf (-2))) (.leaf (0))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))) (.leaf (0))))) (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (1)) (.leaf (-2))) (.leaf (0))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified83 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.node (.leaf (-1)) (.leaf (1)))) (.leaf (0))))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))) (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0)))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (-1)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (-1)) (.leaf (2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))) (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0)))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (-1)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (-1)) (.leaf (-2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.node (.leaf (1)) (.leaf (-2))) (.leaf (0))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0))))) (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0)))) (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))) (.leaf (0))))) (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.node (.leaf (1)) (.leaf (-2))) (.leaf (0))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified84 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.node (.leaf (-1)) (.leaf (1)))) (.leaf (0))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0)))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (1)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (-1)) (.leaf (2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0)))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (1)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (-1)) (.leaf (-2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (1)) (.leaf (2))) (.leaf (0))) (.node (.node (.leaf (-1)) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0))))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0)))) (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))) (.leaf (0))))) (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.node (.leaf (-1)) (.leaf (-2))) (.leaf (0))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified85 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.leaf (1)) (.node (.leaf (-1)) (.leaf (1)))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (1))) (.leaf (0))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0)))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.node (.leaf (1)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (-1)) (.leaf (2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0)))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (0)))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (-1)) (.leaf (2))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (1)) (.leaf (2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (-1)) 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(.leaf (0)))) (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified86 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.leaf (1)) (.node (.leaf (-1)) (.leaf (1)))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (1))) (.leaf (0))))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf 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(1))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (0)) (.leaf (1))))) (.node (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.node (.leaf (1)) (.leaf (-1)))) (.leaf (0))) (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.node (.leaf (-1)) (.leaf (1)))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (-1))))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (1)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (2))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (2)))) (.leaf (0)))) (.node (.leaf (0)) (.node (.node (.node (.leaf (4)) (.leaf 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(1)) (.leaf (0)))))) (.node (.node (.leaf (0)) (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (1)) (.leaf (-2))) (.node (.leaf (1)) (.leaf (2))))) (.node (.leaf (0)) (.node (.node (.leaf (1)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0)))))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified89 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (-1))))) (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (-1)))))) (.node (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.node (.leaf (1)) (.leaf (-1)))) (.leaf (0))) (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.node (.leaf (-1)) (.leaf 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(.node (.leaf (0)) (.node (.node (.leaf (-1)) (.leaf (-2))) (.node (.leaf (1)) (.leaf (0)))))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified90 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (-1)))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (1)))) (.node (.leaf (0)) (.leaf (1))))) (.node (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (1))) (.leaf (0))) (.node (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (1))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (-1))))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (1)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (2))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (-2)))) (.leaf (0)))) (.node (.leaf (0)) (.node (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (2))))) (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (2)))) (.leaf (0)))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (1)) (.leaf (-2))) (.node (.leaf (1)) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0))))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (-1)) (.leaf (2))) (.node (.leaf (-1)) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.leaf (0)) (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0)))) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4)))) (.leaf (0))) (.leaf (0))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (1)) (.leaf (2))) (.node (.leaf (-1)) (.leaf (-2))))) (.node (.leaf (0)) (.node (.node (.leaf (1)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0)))))) (.node (.node (.leaf (0)) (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0))))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (1)) (.leaf (-2))) (.node (.leaf (-1)) (.leaf (2))))) (.node (.leaf (0)) (.node (.node (.leaf (1)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0)))))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified91 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.leaf (0)) 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(2))))) (.node (.leaf (0)) (.node (.node (.leaf (-1)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0)))))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified93 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (0)) (.leaf (-1))))) (.node (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.node (.leaf (1)) (.leaf (-1)))) (.leaf (0))) (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.node (.leaf (-1)) (.leaf (1)))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (-1))))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf 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(.node (.node (.node (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (-1)))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (1))))) (.node (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (1)))) (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (1)))))) (.node (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (1))) (.leaf (0))) (.node (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (1))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (2))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (-2)))) (.leaf (0)))) (.node (.leaf 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(.node (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (2)))) (.node (.node (.leaf (1)) (.leaf (2))) (.leaf (0)))) (.node (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (2)))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified98 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (1))) (.leaf (0)))) (.node (.node (.node (.leaf (1)) 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(0)))) (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (1))) (.leaf (0)))) (.node (.node (.node (.leaf (1)) (.node (.leaf (1)) (.leaf (-1)))) (.leaf (0))) (.node (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (1)) (.leaf (0))))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (1)) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (1)) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) 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route_correct := by decide + +def certified100 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.node (.leaf (1)) (.leaf (-1)))) (.leaf (0))) (.node (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (-1)) (.leaf (0))))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (1)) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (1)) (.leaf (0))))) (.node (.leaf 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(0)))) (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (2)))) (.node (.node (.leaf (1)) (.leaf (2))) (.leaf (0)))) (.node (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (2)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0)))) (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))))))) (.node (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (2)))) (.node (.node (.leaf (-1)) (.leaf (2))) (.leaf (0)))) (.node (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (-2)))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (-2)) (.leaf (0))) (.node (.leaf (-2)) (.leaf (0))))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified101 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (1)) (.leaf (-1))) (.node (.leaf (1)) (.leaf (-1)))) (.leaf (0))) (.node (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (-1)) (.leaf (0)))) (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (-1)) (.leaf (0))))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (-1)) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (1)) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (0)))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (-1)) (.leaf (-2)))) (.node (.node (.leaf (-1)) (.leaf (2))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf 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(0)) (.leaf (2))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.leaf (0)) (.node (.node (.leaf (-1)) (.leaf (1))) (.node (.leaf (1)) (.leaf (-1))))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (-1)) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node 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by decide + row_correct := by decide + route_correct := by decide + +def certified105 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.leaf (0)) (.node (.leaf (1)) (.node (.leaf (1)) (.leaf (-1))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.leaf (0)) (.node (.node (.leaf (-1)) (.leaf (1))) (.leaf (1)))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1))))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (-1)) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node 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(.node (.leaf (0)) (.leaf (2))))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (-1)) (.leaf (2)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (1)) (.leaf (0)))))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified106 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (1)) (.leaf (-1))) (.leaf (1)))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-1)) (.node (.leaf (1)) (.leaf (-1))))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1))))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (0)) (.leaf (1))) 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(.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (0)) (.leaf (-2))))) (.leaf (0))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0))))) (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))))))) (.node (.node (.node (.leaf (0)) (.node (.node (.node 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(.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (-1)) (.leaf (0))))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (-1)) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (1)) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (2)))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))))))) (.node (.node (.node (.leaf (0)) (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0)))) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (2)))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))) (.leaf (0)))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (-2)))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0)))) (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))))))) (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (-2)))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified113 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) 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(.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (2)))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified114 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (-1)) (.leaf (0))))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (1)) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (1)) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (2)))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node 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(0))))) (.node (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (-2)))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified115 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (1)) (.leaf (0))))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (1)) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (1)) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (-2)))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (0)) 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(.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified116 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (1)) (.leaf (0))))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (1)) (.leaf (0))) 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(4)) (.leaf (0))) (.leaf (0)))) (.leaf (0)))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (-2)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0)))) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))))))) (.node (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (2)))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified117 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (-1)) (.leaf (0))))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (1)) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (1)) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (-2)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))))))) (.node (.node (.node (.leaf (0)) (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (2)))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))) (.leaf (0)))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (2)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))))))) (.node (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (-2)))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified118 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (1)) (.leaf (0))))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (-1)) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (1)) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (2)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))))))) (.node (.node (.node (.leaf (0)) (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0)))) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (2)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))) (.leaf (0)))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (2)))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0))))))) (.node (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (2)))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +def certified119 : CertifiedPort where + basis := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.leaf (2))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.leaf (0))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (1)))) (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (-1)) (.leaf (0))))))) (.node (.node (.node (.leaf (0)) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (0)) (.leaf (1))) (.node (.leaf (-1)) (.leaf (0)))))) (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-1)))) (.node (.node (.leaf (0)) (.leaf (-1))) (.node (.leaf (1)) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (2)))))))) (8 * i.val + j.val) + route := fun i j => intLookup (.node (.node (.node (.node (.node (.node (.node (.node (.leaf (1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (-1)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (-1)) (.leaf (-2)))) (.node (.node (.leaf (-1)) (.leaf (0))) (.leaf (0))))) (.node (.leaf (0)) (.node (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0))) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0)))) (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))))))) (.node (.node (.node (.leaf (0)) (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0)))) (.node (.node (.leaf (2)) (.leaf (0))) (.leaf (0)))))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (2)))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0))))) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0))))))))) (.node (.node (.node (.node (.node (.node (.node (.leaf (0)) (.leaf (4))) (.leaf (0))) (.leaf (0))) (.leaf (0))) (.node (.node (.leaf (0)) (.node (.node (.leaf (4)) (.leaf (0))) (.leaf (0)))) (.leaf (0)))) (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (2)))) (.node (.node (.leaf (0)) (.leaf (-2))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (-2)))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))) (.node (.leaf (0)) (.node (.leaf (2)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (-2)) (.leaf (0)))) (.node (.node (.leaf (-2)) (.leaf (0))) (.leaf (0))))))) (.node (.node (.node (.node (.node (.node (.leaf (-1)) (.leaf (0))) (.node (.leaf (0)) (.leaf (-2)))) (.node (.node (.leaf (0)) (.leaf (2))) (.node (.leaf (1)) (.leaf (0))))) (.node (.node (.leaf (0)) (.node (.leaf (1)) (.leaf (-2)))) (.node (.node (.leaf (1)) (.leaf (0))) (.leaf (0))))) (.node (.node (.node (.leaf (0)) (.node (.leaf (4)) (.leaf (0)))) (.leaf (0))) (.leaf (0)))) (.node (.node (.node (.leaf (0)) (.node (.leaf (0)) (.node (.leaf (0)) (.leaf (4))))) (.leaf (0))) (.leaf (0)))))) (16 * i.val + j.val) + column_correct := by decide + row_correct := by decide + route_correct := by decide + +inductive PortLookup where + | leaf : CertifiedPort → PortLookup + | node : PortLookup → PortLookup → PortLookup + +def lookupPort : PortLookup → Nat → CertifiedPort + | .leaf p, _ => p + | .node l r, i => if i % 2 == 0 then lookupPort l (i / 2) else lookupPort r (i / 2) + +def certifiedTable : PortLookup := (.node (.node (.node (.node (.node (.node (.node (.leaf (certified0)) (.leaf (certified64))) (.node (.leaf (certified32)) (.leaf (certified96)))) (.node (.node (.leaf (certified16)) (.leaf (certified80))) (.node (.leaf (certified48)) (.leaf (certified112))))) (.node (.node (.node (.leaf (certified8)) (.leaf (certified72))) (.node (.leaf (certified40)) (.leaf (certified104)))) (.node (.node (.leaf (certified24)) (.leaf (certified88))) (.node (.leaf (certified56)) (.leaf (certified0)))))) (.node (.node (.node (.node (.leaf (certified4)) (.leaf (certified68))) (.node (.leaf (certified36)) (.leaf (certified100)))) (.node (.node (.leaf (certified20)) (.leaf (certified84))) (.node (.leaf (certified52)) (.leaf (certified116))))) (.node (.node (.node (.leaf (certified12)) (.leaf (certified76))) (.node (.leaf (certified44)) (.leaf (certified108)))) (.node (.node (.leaf (certified28)) (.leaf (certified92))) (.node (.leaf (certified60)) (.leaf (certified0))))))) (.node (.node (.node (.node (.node (.leaf (certified2)) (.leaf (certified66))) (.node (.leaf (certified34)) (.leaf (certified98)))) (.node (.node (.leaf (certified18)) (.leaf (certified82))) (.node (.leaf (certified50)) (.leaf (certified114))))) (.node (.node (.node (.leaf (certified10)) (.leaf (certified74))) (.node (.leaf (certified42)) (.leaf (certified106)))) (.node (.node (.leaf (certified26)) (.leaf (certified90))) (.node (.leaf (certified58)) (.leaf (certified0)))))) (.node (.node (.node (.node (.leaf (certified6)) (.leaf (certified70))) (.node (.leaf (certified38)) (.leaf (certified102)))) (.node (.node (.leaf (certified22)) (.leaf (certified86))) (.node (.leaf (certified54)) (.leaf (certified118))))) (.node (.node (.node (.leaf (certified14)) (.leaf (certified78))) (.node (.leaf (certified46)) (.leaf (certified110)))) (.node (.node (.leaf (certified30)) (.leaf (certified94))) (.node (.leaf (certified62)) (.leaf (certified0)))))))) (.node (.node (.node (.node (.node (.node (.leaf (certified1)) (.leaf (certified65))) (.node (.leaf (certified33)) (.leaf (certified97)))) (.node (.node (.leaf (certified17)) (.leaf (certified81))) (.node (.leaf (certified49)) (.leaf (certified113))))) (.node (.node (.node (.leaf (certified9)) (.leaf (certified73))) (.node (.leaf (certified41)) (.leaf (certified105)))) (.node (.node (.leaf (certified25)) (.leaf (certified89))) (.node (.leaf (certified57)) (.leaf (certified0)))))) (.node (.node (.node (.node (.leaf (certified5)) (.leaf (certified69))) (.node (.leaf (certified37)) (.leaf (certified101)))) (.node (.node (.leaf (certified21)) (.leaf (certified85))) (.node (.leaf (certified53)) (.leaf (certified117))))) (.node (.node (.node (.leaf (certified13)) (.leaf (certified77))) (.node (.leaf (certified45)) (.leaf (certified109)))) (.node (.node (.leaf (certified29)) (.leaf (certified93))) (.node (.leaf (certified61)) (.leaf (certified0))))))) (.node (.node (.node (.node (.node (.leaf (certified3)) (.leaf (certified67))) (.node (.leaf (certified35)) (.leaf (certified99)))) (.node (.node (.leaf (certified19)) (.leaf (certified83))) (.node (.leaf (certified51)) (.leaf (certified115))))) (.node (.node (.node (.leaf (certified11)) (.leaf (certified75))) (.node (.leaf (certified43)) (.leaf (certified107)))) (.node (.node (.leaf (certified27)) (.leaf (certified91))) (.node (.leaf (certified59)) (.leaf (certified0)))))) (.node (.node (.node (.node (.leaf (certified7)) (.leaf (certified71))) (.node (.leaf (certified39)) (.leaf (certified103)))) (.node (.node (.leaf (certified23)) (.leaf (certified87))) (.node (.leaf (certified55)) (.leaf (certified119))))) (.node (.node (.node (.leaf (certified15)) (.leaf (certified79))) (.node (.leaf (certified47)) (.leaf (certified111)))) (.node (.node (.leaf (certified31)) (.leaf (certified95))) (.node (.leaf (certified63)) (.leaf (certified0))))))))) + +def portData (port : Fin 120) : CertifiedPort := lookupPort certifiedTable port.val + +def doubledBasis (port : Fin 120) : Fin 8 → Fin 8 → Int := (portData port).basis + +def quarteredRoute (port : Fin 120) : Fin 15 → Fin 15 → Int := (portData port).route + +def expectedQuarteredRoute (port : Fin 120) (i j : Fin 15) : Int := + routeExpected (doubledBasis port) i j + +def doubledDot (port : Fin 120) (i j : Fin 8) : Int := columnDot (doubledBasis port) i j + +theorem doubled_orthogonal_entries (port : Fin 120) (i j : Fin 8) : + doubledDot port i j = if i = j then 4 else 0 := + (portData port).column_correct i j + +theorem quarteredRoute_exact (port : Fin 120) (i j : Fin 15) : + quarteredRoute port i j = expectedQuarteredRoute port i j := + (portData port).route_correct i j + +end PortGeometry +#print axioms PortGeometry.doubled_orthogonal_entries +#print axioms PortGeometry.quarteredRoute_exact diff --git a/research/lean-multi-host-source/PortGeometry.lean b/research/lean-multi-host-source/PortGeometry.lean new file mode 100644 index 0000000000..6cf1a2144d --- /dev/null +++ b/research/lean-multi-host-source/PortGeometry.lean @@ -0,0 +1,396 @@ +import PortRowData +import Mathlib.Data.Matrix.Mul +import Mathlib.Tactic.FieldSimp +import Mathlib.Tactic.Ring +import Mathlib.Tactic.NormNum +import Mathlib.Algebra.BigOperators.Fin + +/-! +The concrete dyadic port charts used by the selected source construction. +Apache-2.0. Prepared with substantial OpenAI Codex assistance. + +`basis` is the source matrix B_q = [q/2 | complement_columns], obtained by +casting the literal integer table `2 B_q` then dividing by two. This is valid +in every field in which two is nonzero, including admitted odd finite fields; +no rational-to-finite-field ring homomorphism is assumed. Its transpose is +the inverse. `chart64` applies this basis to coordinates 0..7 and fixes 8..63. +These proofs establish the chart, not local-word endpoint correctness or +physical ownership, which must be supplied separately. +-/ +namespace PortGeometry +open scoped Matrix BigOperators + +def integerBasis (port : Fin 120) : Matrix (Fin 8) (Fin 8) Int := + Matrix.of (doubledBasis port) + +theorem doubled_orthogonal (port : Fin 120) : + (integerBasis port).transpose * integerBasis port = + (4 : Int) • (1 : Matrix (Fin 8) (Fin 8) Int) := by + ext i j + have h := doubled_orthogonal_entries port i j + by_cases hij : i = j <;> + simpa [Matrix.mul_apply, Matrix.transpose_apply, Fin.sum_univ_succ, + Matrix.smul_apply, Matrix.one_apply, doubledDot, columnDot, hij, smul_eq_mul, + integerBasis] using h + +theorem doubled_row_orthogonal (port : Fin 120) : + integerBasis port * (integerBasis port).transpose = + (4 : Int) • (1 : Matrix (Fin 8) (Fin 8) Int) := by + ext i j + have h := doubled_row_orthogonal_entries port i j + by_cases hij : i = j <;> + simpa [Matrix.mul_apply, Matrix.transpose_apply, Fin.sum_univ_succ, + Matrix.smul_apply, Matrix.one_apply, doubledRowDot, rowDot, hij, smul_eq_mul, + integerBasis] using h + +def castBasis (K : Type*) [Field K] (port : Fin 120) : Matrix (Fin 8) (Fin 8) K := + Matrix.map (integerBasis port) (Int.castRingHom K) + +def basis (K : Type*) [Field K] (port : Fin 120) : Matrix (Fin 8) (Fin 8) K := + (2 : K)⁻¹ • castBasis K port + +theorem basis_entry (K : Type*) [Field K] (port : Fin 120) (i j : Fin 8) : + basis K port i j = (doubledBasis port i j : K) / 2 := by + simp [basis, castBasis, integerBasis, Matrix.map, Matrix.smul_apply, div_eq_mul_inv, + smul_eq_mul, mul_comm] + +theorem cast_orthogonal (K : Type*) [Field K] (port : Fin 120) : + (castBasis K port).transpose * castBasis K port = + (4 : K) • (1 : Matrix (Fin 8) (Fin 8) K) := by + have h := congrArg (fun m : Matrix (Fin 8) (Fin 8) Int => m.map (Int.castRingHom K)) + (doubled_orthogonal port) + rw [Matrix.map_mul] at h + change (castBasis K port).transpose * castBasis K port = _ at h + rw [h] + ext i j + by_cases hij : i = j <;> + simp [Matrix.map, Matrix.smul_apply, Matrix.one_apply, hij, smul_eq_mul] + +theorem cast_row_orthogonal (K : Type*) [Field K] (port : Fin 120) : + castBasis K port * (castBasis K port).transpose = + (4 : K) • (1 : Matrix (Fin 8) (Fin 8) K) := by + have h := congrArg (fun m : Matrix (Fin 8) (Fin 8) Int => m.map (Int.castRingHom K)) + (doubled_row_orthogonal port) + rw [Matrix.map_mul] at h + change castBasis K port * (castBasis K port).transpose = _ at h + rw [h] + ext i j + by_cases hij : i = j <;> + simp [Matrix.map, Matrix.smul_apply, Matrix.one_apply, hij, smul_eq_mul] + +/-- Checked orthogonality survives reduction to any field of characteristic +other than two. This quantifies over the field; it is not a numerical sample. -/ +theorem basis_transpose_mul (K : Type*) [Field K] (h2 : (2 : K) ≠ 0) + (port : Fin 120) : (basis K port).transpose * basis K port = 1 := by + unfold basis + rw [Matrix.transpose_smul, Matrix.smul_mul, Matrix.mul_smul, cast_orthogonal] + have hs : (2 : K)⁻¹ * ((2 : K)⁻¹ * 4) = 1 := by + field_simp [h2] + ring + simp only [smul_smul, hs, one_smul] + +theorem basis_mul_transpose (K : Type*) [Field K] (h2 : (2 : K) ≠ 0) + (port : Fin 120) : basis K port * (basis K port).transpose = 1 := by + unfold basis + rw [Matrix.transpose_smul, Matrix.smul_mul, Matrix.mul_smul, cast_row_orthogonal] + have hs : (2 : K)⁻¹ * ((2 : K)⁻¹ * 4) = 1 := by + field_simp [h2] + ring + simp only [smul_smul, hs, one_smul] + +/-- Coordinate-to-ambient map on U0, with the literal source transpose as +inverse. Every coordinate value is arbitrary. -/ +def chart8 (K : Type*) [Field K] (h2 : (2 : K) ≠ 0) (port : Fin 120) : + (Fin 8 → K) ≃ (Fin 8 → K) where + toFun v := basis K port *ᵥ v + invFun v := (basis K port).transpose *ᵥ v + left_inv v := by + dsimp only + rw [Matrix.mulVec_mulVec, basis_transpose_mul K h2, Matrix.one_mulVec] + right_inv v := by + dsimp only + rw [Matrix.mulVec_mulVec, basis_mul_transpose K h2, Matrix.one_mulVec] + +theorem chart8_dot (K : Type*) [Field K] (h2 : (2 : K) ≠ 0) (port : Fin 120) + (v w : Fin 8 → K) : (chart8 K h2 port v) ⬝ᵥ (chart8 K h2 port w) = v ⬝ᵥ w := by + change (basis K port *ᵥ v) ⬝ᵥ (basis K port *ᵥ w) = _ + rw [Matrix.dotProduct_mulVec, Matrix.vecMul_mulVec, basis_transpose_mul K h2, + Matrix.vecMul_one] + +def firstEight {K : Type*} (v : Fin 64 → K) : Fin 8 → K := + fun j => v (Fin.castAdd 56 j) + +theorem firstEight_add {K : Type*} [Add K] (v w : Fin 64 → K) : + firstEight (v + w) = firstEight v + firstEight w := rfl + +theorem firstEight_smul {K : Type*} [Mul K] (c : K) (v : Fin 64 → K) : + firstEight (c • v) = c • firstEight v := rfl + +def extendEight {K : Type*} (f : (Fin 8 → K) → (Fin 8 → K)) + (v : Fin 64 → K) : Fin 64 → K := + fun i => if hi : i.val < 8 then f (firstEight v) ⟨i.val, hi⟩ else v i + +theorem firstEight_extendEight {K : Type*} (f : (Fin 8 → K) → (Fin 8 → K)) + (v : Fin 64 → K) : firstEight (extendEight f v) = f (firstEight v) := by + funext j + simp [firstEight, extendEight, j.isLt] + +theorem extendEight_comp {K : Type*} (f g : (Fin 8 → K) → (Fin 8 → K)) + (v : Fin 64 → K) : extendEight f (extendEight g v) = extendEight (f ∘ g) v := by + funext i + by_cases hi : i.val < 8 + · simp [extendEight, hi, firstEight_extendEight] + · simp [extendEight, hi] + +theorem extendEight_id {K : Type*} (v : Fin 64 → K) : extendEight id v = v := by + funext i + by_cases hi : i.val < 8 <;> simp [extendEight, firstEight, hi] + +def liftChart {K : Type*} (chart : (Fin 8 → K) ≃ (Fin 8 → K)) : + (Fin 64 → K) ≃ (Fin 64 → K) where + toFun := extendEight chart + invFun := extendEight chart.symm + left_inv v := by + rw [extendEight_comp] + have hi : (chart.symm ∘ chart : (Fin 8 → K) → (Fin 8 → K)) = id := by + funext x + exact chart.symm_apply_apply x + rw [hi, extendEight_id] + right_inv v := by + rw [extendEight_comp] + have hi : (chart ∘ chart.symm : (Fin 8 → K) → (Fin 8 → K)) = id := by + funext x + exact chart.apply_symm_apply x + rw [hi, extendEight_id] + +def chart64 (K : Type*) [Field K] (h2 : (2 : K) ≠ 0) (port : Fin 120) : + (Fin 64 → K) ≃ (Fin 64 → K) := liftChart (chart8 K h2 port) + +theorem chart64_firstEight (K : Type*) [Field K] (h2 : (2 : K) ≠ 0) + (port : Fin 120) (v : Fin 64 → K) : + firstEight (chart64 K h2 port v) = basis K port *ᵥ firstEight v := + firstEight_extendEight _ v + +theorem chart64_outside (K : Type*) [Field K] (h2 : (2 : K) ≠ 0) + (port : Fin 120) (v : Fin 64 → K) (i : Fin 64) (hi : 8 ≤ i.val) : + chart64 K h2 port v i = v i := by + simp [chart64, liftChart, extendEight, Nat.not_lt.mpr hi] + +theorem chart64_bijective (K : Type*) [Field K] (h2 : (2 : K) ≠ 0) + (port : Fin 120) : Function.Bijective (chart64 K h2 port) := + (chart64 K h2 port).bijective + +theorem chart64_add (K : Type*) [Field K] (h2 : (2 : K) ≠ 0) (port : Fin 120) + (v w : Fin 64 → K) : + chart64 K h2 port (v + w) = chart64 K h2 port v + chart64 K h2 port w := by + funext i + by_cases hi : i.val < 8 + · simp [chart64, liftChart, extendEight, chart8, firstEight_add, hi, + Matrix.mulVec_add, Pi.add_apply] + · simp [chart64, liftChart, extendEight, hi] + +theorem chart64_smul (K : Type*) [Field K] (h2 : (2 : K) ≠ 0) (port : Fin 120) + (c : K) (v : Fin 64 → K) : + chart64 K h2 port (c • v) = c • chart64 K h2 port v := by + funext i + by_cases hi : i.val < 8 + · simp [chart64, liftChart, extendEight, chart8, firstEight_smul, hi, + Matrix.mulVec_smul, Pi.smul_apply] + · simp [chart64, liftChart, extendEight, hi] + +/-- Preservation of the ambient dot form, required for genuine orthogonal +cover membership. Bijectivity alone would not establish this property. -/ +theorem chart64_dot (K : Type*) [Field K] (h2 : (2 : K) ≠ 0) (port : Fin 120) + (v w : Fin 64 → K) : + (∑ i, chart64 K h2 port v i * chart64 K h2 port w i) = ∑ i, v i * w i := by + rw [Fin.sum_univ_add (a := 8) (b := 56), Fin.sum_univ_add (a := 8) (b := 56)] + apply congrArg₂ (· + ·) + · have h := chart8_dot K h2 port (firstEight v) (firstEight w) + change (∑ i : Fin 8, chart64 K h2 port v (Fin.castAdd 56 i) * + chart64 K h2 port w (Fin.castAdd 56 i)) = _ + simpa [dotProduct, chart64, liftChart, extendEight, firstEight, Fin.isLt, Fin.castAdd] using h + · apply Finset.sum_congr rfl + intro i _ + rw [chart64_outside K h2 port v _ (by exact Nat.le_add_right 8 i.val), + chart64_outside K h2 port w _ (by exact Nat.le_add_right 8 i.val)] + +theorem chart64_symm_dot (K : Type*) [Field K] (h2 : (2 : K) ≠ 0) (port : Fin 120) + (v w : Fin 64 → K) : + (∑ i, (chart64 K h2 port).symm v i * (chart64 K h2 port).symm w i) = + ∑ i, v i * w i := by + have h := chart64_dot K h2 port ((chart64 K h2 port).symm v) + ((chart64 K h2 port).symm w) + simpa only [Equiv.apply_symm_apply] using h.symm + +theorem chart64_symm_add (K : Type*) [Field K] (h2 : (2 : K) ≠ 0) (port : Fin 120) + (v w : Fin 64 → K) : + (chart64 K h2 port).symm (v + w) = + (chart64 K h2 port).symm v + (chart64 K h2 port).symm w := by + apply (chart64 K h2 port).injective + rw [Equiv.apply_symm_apply, chart64_add, Equiv.apply_symm_apply, Equiv.apply_symm_apply] + +theorem chart64_symm_smul (K : Type*) [Field K] (h2 : (2 : K) ≠ 0) (port : Fin 120) + (c : K) (v : Fin 64 → K) : + (chart64 K h2 port).symm (c • v) = c • (chart64 K h2 port).symm v := by + apply (chart64 K h2 port).injective + rw [Equiv.apply_symm_apply, chart64_smul, Equiv.apply_symm_apply] + +/-- Stage 2 exchanges the seven q-perpendicular coordinates 1..7 with the +second exterior block 15..21. The port direction (coordinate 0) is fixed. -/ +def stage2Index (i : Fin 64) : Fin 64 := + if h : 1 ≤ i.val ∧ i.val < 8 then ⟨i.val + 14, by omega⟩ + else if h : 15 ≤ i.val ∧ i.val < 22 then ⟨i.val - 14, by omega⟩ + else i + +theorem stage2Index_involutive : Function.Involutive stage2Index := by + change ∀ i : Fin 64, stage2Index (stage2Index i) = i + decide + +def stage2Permutation : Equiv.Perm (Fin 64) where + toFun := stage2Index + invFun := stage2Index + left_inv := stage2Index_involutive + right_inv := stage2Index_involutive + +def stage2Coordinates {K : Type*} : (Fin 64 → K) ≃ (Fin 64 → K) where + toFun v := v ∘ stage2Index + invFun v := v ∘ stage2Index + left_inv v := by funext i; exact congrArg v (stage2Index_involutive i) + right_inv v := by funext i; exact congrArg v (stage2Index_involutive i) + +theorem stage2Coordinates_dot (K : Type*) [Field K] (v w : Fin 64 → K) : + (∑ i, stage2Coordinates v i * stage2Coordinates w i) = ∑ i, v i * w i := + Fintype.sum_equiv stage2Permutation _ _ (fun _ => rfl) + +/-- Concrete stage-2 data-port route B_q P B_q⁻¹. `sourceRoute64_eq` below +identifies this with the literal source rho15 matrix. This chart result does +not alone establish a complete provider's primitive execution or endpoint. -/ +def dataRoute64 (K : Type*) [Field K] (h2 : (2 : K) ≠ 0) (port : Fin 120) : + (Fin 64 → K) ≃ (Fin 64 → K) := + (chart64 K h2 port).symm.trans (stage2Coordinates.trans (chart64 K h2 port)) + +theorem dataRoute64_dot (K : Type*) [Field K] (h2 : (2 : K) ≠ 0) (port : Fin 120) + (v w : Fin 64 → K) : + (∑ i, dataRoute64 K h2 port v i * dataRoute64 K h2 port w i) = ∑ i, v i * w i := by + change (∑ i, chart64 K h2 port (stage2Coordinates ((chart64 K h2 port).symm v)) i * + chart64 K h2 port (stage2Coordinates ((chart64 K h2 port).symm w)) i) = _ + rw [chart64_dot, stage2Coordinates_dot, chart64_symm_dot] + +theorem dataRoute64_add (K : Type*) [Field K] (h2 : (2 : K) ≠ 0) (port : Fin 120) + (v w : Fin 64 → K) : + dataRoute64 K h2 port (v + w) = dataRoute64 K h2 port v + dataRoute64 K h2 port w := by + change chart64 K h2 port (stage2Coordinates ((chart64 K h2 port).symm (v + w))) = _ + rw [chart64_symm_add] + change chart64 K h2 port (stage2Coordinates ((chart64 K h2 port).symm v) + + stage2Coordinates ((chart64 K h2 port).symm w)) = _ + exact chart64_add K h2 port _ _ + +theorem dataRoute64_smul (K : Type*) [Field K] (h2 : (2 : K) ≠ 0) (port : Fin 120) + (c : K) (v : Fin 64 → K) : + dataRoute64 K h2 port (c • v) = c • dataRoute64 K h2 port v := by + change chart64 K h2 port (stage2Coordinates ((chart64 K h2 port).symm (c • v))) = _ + rw [chart64_symm_smul] + change chart64 K h2 port (c • stage2Coordinates ((chart64 K h2 port).symm v)) = _ + exact chart64_smul K h2 port _ _ + +theorem dataRoute64_involutive (K : Type*) [Field K] (h2 : (2 : K) ≠ 0) + (port : Fin 120) : Function.Involutive (dataRoute64 K h2 port) := by + intro v + change chart64 K h2 port (stage2Coordinates ((chart64 K h2 port).symm + (chart64 K h2 port (stage2Coordinates ((chart64 K h2 port).symm v))))) = v + rw [Equiv.symm_apply_apply] + change chart64 K h2 port ((stage2Coordinates : (Fin 64 → K) ≃ _).symm + (stage2Coordinates ((chart64 K h2 port).symm v))) = v + rw [Equiv.symm_apply_apply, Equiv.apply_symm_apply] + +/-- The literal source rho15 matrix, reduced by its true denominator four. +PortData checks its integer entries against the source port basis. -/ +def route15 (K : Type*) [Field K] (port : Fin 120) : Matrix (Fin 15) (Fin 15) K := + fun i j => (quarteredRoute port i j : K) / 4 + +def expectedRoute15 (K : Type*) [Field K] (port : Fin 120) (i j : Fin 15) : K := + if hi : i.val < 8 then + if hj : j.val < 8 then + basis K port ⟨i.val, hi⟩ 0 * basis K port ⟨j.val, hj⟩ 0 + else basis K port ⟨i.val, hi⟩ ⟨j.val - 7, by omega⟩ + else if hj : j.val < 8 then + basis K port ⟨j.val, hj⟩ ⟨i.val - 7, by omega⟩ + else 0 + +theorem route15_entry (K : Type*) [Field K] (h2 : (2 : K) ≠ 0) + (port : Fin 120) (i j : Fin 15) : route15 K port i j = expectedRoute15 K port i j := by + have h4 : (4 : K) ≠ 0 := by + convert mul_ne_zero h2 h2 using 1 + norm_num + simp only [route15, quarteredRoute_exact, expectedRoute15, expectedQuarteredRoute, + routeExpected] + split_ifs <;> simp [basis_entry] <;> + field_simp [h2, h4] <;> ring + +def gatherStage2 {K : Type*} (v : Fin 64 → K) (i : Fin 15) : K := + if hi : i.val < 8 then v ⟨i.val, Nat.lt_trans hi (by decide)⟩ + else v ⟨i.val + 7, by omega⟩ + +/-- Literal rho15 acting on the source-listed axes [0..7,15..21]. All other +coordinates are retained exactly; its conjugacy with the concrete isometry +is established by `sourceRoute64_eq`. -/ +def sourceRoute64 (K : Type*) [Field K] (port : Fin 120) (v : Fin 64 → K) + (i : Fin 64) : K := + if hi : i.val < 8 then (route15 K port *ᵥ gatherStage2 v) ⟨i.val, Nat.lt_trans hi (by decide)⟩ + else if hi : 15 ≤ i.val ∧ i.val < 22 then + (route15 K port *ᵥ gatherStage2 v) ⟨i.val - 7, by omega⟩ + else v i + +theorem sourceRoute64_eq (K : Type*) [Field K] (h2 : (2 : K) ≠ 0) + (port : Fin 120) (v : Fin 64 → K) : sourceRoute64 K port v = dataRoute64 K h2 port v := by + funext i + by_cases hi : i.val < 8 + · simp [sourceRoute64, hi, Matrix.mulVec, dotProduct, Fin.sum_univ_succ, + route15_entry K h2, expectedRoute15, gatherStage2, + dataRoute64, chart64, liftChart, extendEight, chart8, + stage2Coordinates, firstEight, stage2Index, Matrix.transpose_apply] + ring + · by_cases hj : 15 ≤ i.val ∧ i.val < 22 + · have hsub : i.val - 14 < 8 := by omega + have hsub' : ¬i.val - 7 < 8 := by omega + have hsub'' : i.val - 7 - 7 = i.val - 14 := by omega + simp [sourceRoute64, hi, hj, Matrix.mulVec, dotProduct, Fin.sum_univ_succ, + route15_entry K h2, expectedRoute15, gatherStage2, + dataRoute64, chart64, liftChart, extendEight, chart8, + stage2Coordinates, firstEight, stage2Index, Matrix.transpose_apply, + hsub, hsub', hsub''] + · simp [sourceRoute64, hi, hj, dataRoute64, chart64, liftChart, + extendEight, stage2Coordinates, stage2Index] + +end PortGeometry + +#print axioms PortGeometry.cast_orthogonal +#print axioms PortGeometry.doubled_orthogonal +#print axioms PortGeometry.doubled_row_orthogonal +#print axioms PortGeometry.cast_row_orthogonal +#print axioms PortGeometry.basis_entry +#print axioms PortGeometry.basis_transpose_mul +#print axioms PortGeometry.basis_mul_transpose +#print axioms PortGeometry.firstEight_extendEight +#print axioms PortGeometry.firstEight_add +#print axioms PortGeometry.firstEight_smul +#print axioms PortGeometry.extendEight_comp +#print axioms PortGeometry.extendEight_id +#print axioms PortGeometry.chart64_firstEight +#print axioms PortGeometry.chart64_outside +#print axioms PortGeometry.chart64_bijective +#print axioms PortGeometry.chart64_add +#print axioms PortGeometry.chart64_smul +#print axioms PortGeometry.chart8_dot +#print axioms PortGeometry.chart64_dot +#print axioms PortGeometry.chart64_symm_dot +#print axioms PortGeometry.chart64_symm_add +#print axioms PortGeometry.chart64_symm_smul +#print axioms PortGeometry.stage2Index_involutive +#print axioms PortGeometry.stage2Coordinates_dot +#print axioms PortGeometry.dataRoute64_dot +#print axioms PortGeometry.dataRoute64_add +#print axioms PortGeometry.dataRoute64_smul +#print axioms PortGeometry.dataRoute64_involutive +#print axioms PortGeometry.route15_entry +#print axioms PortGeometry.sourceRoute64_eq diff --git a/research/lean-multi-host-source/PortRowData.lean b/research/lean-multi-host-source/PortRowData.lean new file mode 100644 index 0000000000..6d62a55576 --- /dev/null +++ b/research/lean-multi-host-source/PortRowData.lean @@ -0,0 +1,14 @@ +import PortData + +/-! Reverse orthogonality extracted from the checked exact source table. +Apache-2.0. Prepared with substantial OpenAI Codex assistance. -/ +namespace PortGeometry + +def doubledRowDot (port : Fin 120) (i j : Fin 8) : Int := rowDot (doubledBasis port) i j + +theorem doubled_row_orthogonal_entries (port : Fin 120) (i j : Fin 8) : + doubledRowDot port i j = if i = j then 4 else 0 := + (portData port).row_correct i j + +end PortGeometry +#print axioms PortGeometry.doubled_row_orthogonal_entries diff --git a/research/lean-multi-host-source/README.md b/research/lean-multi-host-source/README.md new file mode 100644 index 0000000000..043f5eb045 --- /dev/null +++ b/research/lean-multi-host-source/README.md @@ -0,0 +1,143 @@ +# One concrete invocation of whole-residual hosting + +This is Task B of the local verification contribution. Task A, the abstract +multi-host theorem and recovery of the previous single-host theorem, is +separately committed as `13611a8958fc71046a83d8431d2bd6335e6a3e2f` in +`../lean-multi-host-framework`. Its success does not establish this source +connection. + +The selected source is PR442 at +`4e16d001d505d4f21dd2bcfc44591f9be4c279bd`, stage 2, replica 0, pair 0, +forward orientation. It uses the inherited R747 word: 19,002 events, +987 live roles, and one clean private temporary. All 747 helpers may contain +arbitrary, correlated dirty payloads. The original and relocated templates +contain the identical local word. + +**Historical build status: PASS.** The coherent source build checked all 52 modules +(50 in this directory and two local dependencies) with `lean -t 0` and +audited 930 named theorem closures, using only standard +Lean axioms. Hash-checked resume retained successful builds from the same +initially empty directory. See [replay-result.json](replay-result.json) and +[VALIDATION.md](VALIDATION.md). Source extraction also passed independently. + +## What the concrete checks establish + +`SourceEndpoint.lean` reflects the complete literal word into a symbolic +matrix and proves its interpretation for every Boolean payload function. +Every target row receives its corresponding source row, all other live +normalized rows are restored, and the private row starts and ends at zero. +All nine COPY and nine ERASE guards hold throughout the actual sequence. +This is an arbitrary-input theorem, not a sample of input assignments. + +`SourceFramed.lean` joins the scalar certificate to the literal chronological +frame trace. It proves the decoded and physical endpoint for a family of +genuine address gauges, including every frame-label and clean-private guard. +The concrete geometry and ownership modules discharge the identification of +those gauges and nominal roles with the source. + +The final statements are collected in `SourceInvocation.lean`: + +| Declaration | Obligation | +| --- | --- | +| `actualContract` | Construct the old/new invocation contract from their literal execution folds. | +| `selected_call_completion` | Apply the multi-host theorem to this invocation and its remaining pending swaps. | +| `selected_native_completion` | Compare those same executions in common native coordinates. | +| `selected_matrix_realization`, `selected_original_matrix_realization` | Identify active-role gathers of both complete execution folds with the source matrix word; exterior preservation is proved separately. | +| `selected_data_formula` | Display the data endpoint with actual entrance/exit frames and port charts. | +| `selected_native_clean`, `selected_temporary_restoration` | Establish chronological COPY/ERASE legality and return the private row blank. | + +The permanent axiom-audit inventory now includes the constructed definition +`SourceInvocation.actualContract`, alongside the 930 named theorem declarations: +931 declarations in total. The historical 930-declaration receipt does not +certify that expanded inventory. The current fresh-build result and receipt +are reported separately in +[`../lean-external-review/VALIDATION.md`](../lean-external-review/VALIDATION.md). + +The geometry uses exact integer witnesses, cast into any field with +`2 ≠ 0`. Projectors have denominator dividing four; complete basis inverses +have denominator dividing 256. This avoids assuming a rational-to-field +map that would be invalid in positive characteristic. The actual stage-2 +exterior factor is included in both endpoint gauges and cancels formally. + +The relocated layout has 747 distinct helper streams on 317 family labels; +a stream owner includes its cover map. The original bank uses 172 families, +61 slot descriptions, and 59 distinct coordinate permutations. Owner +injectivity concerns the actual functions on coordinates, not nominal tag +inequality. The source permits a choice of slot isometry; the certificates +construct one exact permitted choice from the literal slot descriptors. + +The native-coordinate bridge identifies an ADD with reading the same +native address in its two streams. Its identity is +`g_source σ_source σ_target⁻¹ = g_target`, where `g σ = d` is the common +invocation chart. This uses one stream per helper. It assumes no split-helper +interface from PR448. + +Both native executions use one common cover-chart extension on the union +of their active owners. The intersection is proved to consist exactly of +the shared data owners, where the charts agree. This is necessary to make +equal retained raw inputs denote equal native inputs in both layouts. + +The private identifier names the source's reserved clean storage. For this +fixed invocation its native chart is the common cover chart `d`; the +identifier's placeholder is not an assertion that `d` is identity. The +source explicitly reserves private storage. The 36 extra leaves of the +certificate's binary tree are inaccessible padding, not algorithm registers. + +## Comparison boundary + +The comparison's retained state includes all 747 affected host streams, +all 240 active data streams, and arbitrary payloads outside the union of +the two layouts' active owner sets. Original helper-bank outputs +are returned and threaded as auxiliary outputs. They are not silently +asserted equal to their initial values. `selected_native_clean` and +`selected_temporary_restoration` prove temporary cleanliness for the actual trace. + +The common slot universe is a device for this local comparison. The input +embeddings assign defaults to slots unused by a layout; this is not equality +of arbitrary complete global allocations. Separately, the raw/native +execution theorem permits arbitrary payloads on all actual exterior streams +and proves they are preserved. The host observations use an explicit, +invertible family coordinate chart, so their complete payloads are retained. + +The corollary applies the multi-host theorem to one complete invocation: +all 19,002 instructions form the single event in its event list. +Consequently, the theorem's disjointness condition between separate events +is vacuous here; cross-invocation disjointness is not exercised. The proved +injectivity of physical owners within this invocation is a separate result. + +The pending-coordinate ranges 15..21 and 1..28 (half-open `[15,22)` and +`[1,29)`) are hand-supplied in `PhysicalSourceConnection.pendingTag`. +For these ranges, Lean's `tag_pending_contains` checks that they contain +the corresponding target masks. Neither Lean nor the source-extraction +check binds these ranges to the source schedule. The comparison applies +the remaining pending swaps immediately after the invocation; it does not +establish the full cover sweep or identify this immediate completion with +the later child schedule of the full algorithm. It also does not establish +a physical instruction-cost bill, an all-size compiler, analytic transfer, +or a higher κ. PR448's advertised split gain remains unestablished. + +## Reproduction and review + +See [BUILD.md](BUILD.md) for the pinned Lean/Mathlib build and replay commands, +[source-versions.json](source-versions.json) for the source and input hashes, +and [proof-manifest.json](proof-manifest.json) for the local module inventory. +`check_sources.py` checks the raw source binding and regenerates the literal +certificates. JSON extraction is a reproducible external boundary; Lean +checks the mathematical statements about those embedded literals. + +`SourceControls.lean` proves that deleting an actual ADD changes the next +certified checkpoint despite preserving that chunk's clean-work checks. +It also applies the first actual COPY instruction to a state with a dirty +private temporary and proves that its guard rejects the overwrite. These +are focused controls, not full replays of the corrupted word. + +The overlap search and its limits are in `overlap-review.md`. In particular, +PR509 already formalizes overlapping generic transport and replay principles; +the contribution here is the concrete source obligations. Attribution is +recorded in `NOTICE.md`. + +For the external-review delivery, start with +[`../lean-external-review/README.md`](../lean-external-review/README.md). +It provides the cumulative public-base patch, all local dependencies, exact +setup and reproduction instructions, a refreshed bounded overlap review, +and an explicit audit of these claims in [EXTERNAL-CLAIM-REVIEW.md](EXTERNAL-CLAIM-REVIEW.md). diff --git a/research/lean-multi-host-source/RowEvaluation.lean b/research/lean-multi-host-source/RowEvaluation.lean new file mode 100644 index 0000000000..9fca5a2e5f --- /dev/null +++ b/research/lean-multi-host-source/RowEvaluation.lean @@ -0,0 +1,47 @@ +import Std + +/-! +A Nat encodes a row of coefficients over F₂. `evalRow n u r` interprets +the first n coefficients against an entirely arbitrary Boolean input u. +There is no restriction on correlations among the inputs. Applying this +theorem pointwise also permits arbitrary Boolean-valued payload functions. +-/ +namespace LinearReplay + +def evalRow : Nat → (Nat → Bool) → Nat → Bool + | 0, _, _ => false + | n + 1, u, row => evalRow n u row ^^ (row.testBit n && u n) + +@[simp] theorem evalRow_zero (n : Nat) (u : Nat → Bool) : evalRow n u 0 = false := by + induction n with + | zero => rfl + | succ n ih => simp [evalRow, ih] + +theorem evalRow_xor (n : Nat) (u : Nat → Bool) (r s : Nat) : + evalRow n u (r ^^^ s) = (evalRow n u r ^^ evalRow n u s) := by + induction n with + | zero => rfl + | succ n ih => + simp only [evalRow, ih, Nat.testBit_xor] + cases evalRow n u r <;> cases evalRow n u s <;> + cases r.testBit n <;> cases s.testBit n <;> cases u n <;> rfl + +theorem evalRow_basis (n : Nat) (u : Nat → Bool) (i : Nat) : + evalRow n u (2 ^ i) = if i < n then u i else false := by + induction n with + | zero => simp [evalRow] + | succ n ih => + rw [evalRow, ih, Nat.testBit_two_pow] + by_cases h : i < n + · have hne : i ≠ n := by omega + simp [h, hne, Nat.lt_succ_of_lt h] + · by_cases heq : i = n + · subst i; simp + · have hn : ¬ i < n + 1 := by omega + simp [h, heq, hn] + +theorem evalRow_shift_basis (n : Nat) (u : Nat → Bool) (i : Nat) : + evalRow n u (1 <<< i) = if i < n then u i else false := by + simpa [Nat.shiftLeft_eq] using evalRow_basis n u i + +end LinearReplay diff --git a/research/lean-multi-host-source/SelectedGeometry.lean b/research/lean-multi-host-source/SelectedGeometry.lean new file mode 100644 index 0000000000..81207f6f78 --- /dev/null +++ b/research/lean-multi-host-source/SelectedGeometry.lean @@ -0,0 +1,51 @@ +import HelperGeometryData +import FrameGeometry +import FrameTraceTables +import FrameLabelData +import PhysicalSourceConnection +import AddressPairs + +/-! +Actual stage-2 address gauges, including the common exterior E₂ swap on +coordinates 8..21. The helper relative-frame premise is discharged from the +literal trace and frame tables. Modulo indexing only totalizes the public +Nat API: every source frame label has separately been checked below 944. +-/ +namespace SelectedGeometry + +def gauges (K : Type) [Field K] (h2 : (2 : K) ≠ 0) : PhysicalSourceConnection.Gauges K := + fun n => AddressPairs.gauge + (FrameGeometry.gaugeStage2 K h2 ⟨n % 944, Nat.mod_lt _ (by decide)⟩) + +theorem gauges_tag (K : Type) [Field K] (h2 : (2 : K) ≠ 0) (t : SourceOwnership.Tag) : + gauges K h2 (SourceOwnership.lookup SourceOwnership.tagInitialFrame t.val) = + AddressPairs.gauge (FrameGeometry.gaugeStage2 K h2 (tagFrame t)) := by + have hf : (⟨SourceOwnership.lookup SourceOwnership.tagInitialFrame t.val % 944, + Nat.mod_lt _ (by decide)⟩ : Fin 944) = tagFrame t := by + apply Fin.ext + exact Nat.mod_eq_of_lt (tag_frame_bound t) + exact congrArg (fun f => AddressPairs.gauge (FrameGeometry.gaugeStage2 K h2 f)) hf + +theorem helper_relative (K : Type) [Field K] (h2 : (2 : K) ≠ 0) : + PhysicalSourceConnection.HelperRelative (gauges K h2) := by + intro h a + have hi := SourceFrameTrace.initial_owner_frames (SourceConnection.role h) + have hr := SourceOwnership.helper_frame (SourceConnection.role h) (by + change 240 ≤ 240 + h.val + omega) + have hf := SourceFrameTrace.helper_final_frames h + have hi' : SourceFrameTrace.state0.frames.get (240 + h.val) = + SourceOwnership.lookup SourceOwnership.tagInitialFrame + (SourceOwnership.tag (SourceConnection.role h)).val := hi.trans hr + unfold PhysicalSourceConnection.relative + rw [hi', hf, gauges_tag] + change (AddressPairs.gauge + (FrameGeometry.gaugeStage2 K h2 (tagFrame (SourceOwnership.tag (SourceConnection.role h))))).forward + ((AddressPairs.gauge (FrameGeometry.gaugeStage2 K h2 1)).inverse a) = _ + apply AddressPairs.relative_coordinate + intro p + exact FrameGeometry.stage2_helper_endpoint K h2 _ _ + (tag_residual_diagonal (SourceOwnership.tag (SourceConnection.role h))) + (source_mask_outside (SourceOwnership.tag (SourceConnection.role h))) p + +end SelectedGeometry diff --git a/research/lean-multi-host-source/SourceCommonCover.lean b/research/lean-multi-host-source/SourceCommonCover.lean new file mode 100644 index 0000000000..72b14e7f68 --- /dev/null +++ b/research/lean-multi-host-source/SourceCommonCover.lean @@ -0,0 +1,114 @@ +import SourceInvocationState + +/-! +One physical native-coordinate convention for both executions. The two +active owner images overlap exactly on their common data roles. In +particular the hosted private key 9457 is outside the selected original +bank families, whose literal maximum is 9315. A shared cover extension is +essential: choosing identity independently on each inactive image would +give different native interpretations to the same retained host payload. +Apache-2.0. Prepared with substantial OpenAI Codex assistance. +-/ +namespace SourceInvocation +open SourceConnection FramedReplay +set_option maxRecDepth 100000 +set_option maxHeartbeats 0 + +variable (K : Type) [Field K] (h2 : (2 : K) ≠ 0) +variable (d : SourceOwnership.Vec K ≃ SourceOwnership.Vec K) + +theorem parent_family_lt_private : ∀ r : ParentOwnership.Role, + ParentOwnership.family r < 9457 := by decide + +/-- Equality of actual owner keys forces the same data role on both sides; +no original helper or either private temporary participates in an overlap. -/ +theorem owner_overlap_data (r s : SourceRaw.Role) + (he : oldOwner K h2 d r = newOwner K h2 d s) : + ∃ i : Data, r = SourceLayouts.dataRole i ∧ s = SourceLayouts.dataRole i := by + have hf := congrArg Prod.fst he + by_cases hr : r.val < 987 + · by_cases hs : s.val < 987 + · simp only [oldOwner, newOwner, ParentOwnership.sourceActiveOwner, + SourceOwnership.sourceActiveOwner, SourceOwnership.activeOwner, + dif_pos hr, dif_pos hs, ParentOwnership.physicalOwner, ParentOwnership.owner, + SourceOwnership.physicalOwner, SourceOwnership.owner] at hf + have hn := SourceOwnership.family_lt (⟨s.val, hs⟩ : SourceOwnership.Role) + have hrd : r.val < 240 := by + by_contra nh + have ho := (ParentOwnership.helper_range ⟨r.val, hr⟩ + (show 240 ≤ r.val from Nat.le_of_not_lt nh)).1 + omega + rw [ParentOwnership.family_data_general _ hrd] at hf + have hsd : s.val < 240 := by + by_contra nh + have ho := (SourceOwnership.helper_range ⟨s.val, hs⟩ + (show 240 ≤ s.val from Nat.le_of_not_lt nh)).1 + change r.val = SourceOwnership.family ⟨s.val, hs⟩ at hf + omega + rw [SourceOwnership.family_data_general _ hsd] at hf + refine ⟨⟨r.val, hrd⟩, ?_, ?_⟩ + · apply Fin.ext; rfl + · apply Fin.ext; exact hf.symm + · simp only [oldOwner, newOwner, ParentOwnership.sourceActiveOwner, + SourceOwnership.sourceActiveOwner, SourceOwnership.activeOwner, + dif_pos hr, dif_neg hs, ParentOwnership.physicalOwner, ParentOwnership.owner] at hf + have hp := parent_family_lt_private ⟨r.val, hr⟩ + omega + · by_cases hs : s.val < 987 + · simp only [oldOwner, newOwner, ParentOwnership.sourceActiveOwner, + SourceOwnership.sourceActiveOwner, SourceOwnership.activeOwner, + dif_neg hr, dif_pos hs, SourceOwnership.physicalOwner, SourceOwnership.owner] at hf + have hn := SourceOwnership.family_lt (⟨s.val, hs⟩ : SourceOwnership.Role) + omega + · simp only [oldOwner, newOwner, ParentOwnership.sourceActiveOwner, + SourceOwnership.sourceActiveOwner, SourceOwnership.activeOwner, + dif_neg hr, dif_neg hs] at hf + omega + +theorem owner_overlap_charts (r s : SourceRaw.Role) + (he : oldOwner K h2 d r = newOwner K h2 d s) : + oldChart K h2 r = newChart K h2 s := by + obtain ⟨i, rfl, rfl⟩ := owner_overlap_data K h2 d r s he + exact SourceLayouts.data_chart_eq K h2 i + +noncomputable def commonNativeCover : + Slot K → Gauge (WholeHosting.Address SourceOwnership.Axis K) := by + classical + exact fun p => if ∃ r, newOwner K h2 d r = p then + SourceOwnership.sourceNativeCover K h2 d p + else ParentOwnership.sourceNativeCover K h2 d p + +theorem commonNativeCover_new (r : SourceRaw.Role) : + commonNativeCover K h2 d (newOwner K h2 d r) = + SourceOwnership.sourceNativeCover K h2 d (newOwner K h2 d r) := by + classical + exact if_pos ⟨r, rfl⟩ + +theorem new_common_cover (r : SourceRaw.Role) + (a : WholeHosting.Address SourceOwnership.Axis K) : + (commonNativeCover K h2 d (newOwner K h2 d r)).forward + ((newChart K h2 r).forward a) = + (AddressPairs.gauge (SourceOwnership.pairGauge d)).forward a := by + rw [commonNativeCover_new] + exact SourceOwnership.source_common_cover K h2 d r a + +theorem old_common_cover (r : SourceRaw.Role) + (a : WholeHosting.Address SourceOwnership.Axis K) : + (commonNativeCover K h2 d (oldOwner K h2 d r)).forward + ((oldChart K h2 r).forward a) = + (AddressPairs.gauge (SourceOwnership.pairGauge d)).forward a := by + classical + unfold commonNativeCover + split + · next h => + obtain ⟨s, he⟩ := h + rw [owner_overlap_charts K h2 d r s he.symm, ← he] + exact SourceOwnership.source_common_cover K h2 d s a + · exact ParentOwnership.source_common_cover K h2 d r a + +#print axioms parent_family_lt_private +#print axioms owner_overlap_data +#print axioms old_common_cover +#print axioms new_common_cover + +end SourceInvocation diff --git a/research/lean-multi-host-source/SourceConnection.lean b/research/lean-multi-host-source/SourceConnection.lean new file mode 100644 index 0000000000..7eb5c83693 --- /dev/null +++ b/research/lean-multi-host-source/SourceConnection.lean @@ -0,0 +1,193 @@ +import SourceEndpoint +import MultiHosting +import Ownership + +/-! +The literal normalized invocation supplies the complete, arbitrary-input +endpoint for all 747 helper roles and all 240 data roles. The adapters below +express gather/scatter in the fixed owner charts. Their identification with +the physical source execution is a separate theorem: in particular, the +actual initial/final frames must implement `hostOutput`, and the source's +owner charts must implement `hostInput`. The adapter must not be reported +as that physical identification by itself. + +In particular, the literal physical initial decoder also contains its +initial frame. `hostInput` below is a convenient normalized representative, +not a claim about intermediate physical inputs. Connecting the two uses the +proved independence of data outputs from every dirty helper and the proved +identity on every normalized helper, followed by the actual initial/final +frame composition. The clean temporary is restored by +`SourceMatrix.arbitrary_dirty_temp_restored` and its chronological guards by +`SourceMatrix.actual_payload_clean`. +-/ +namespace SourceConnection +open TreeReplay WholeHosting +set_option maxRecDepth 100000 +set_option maxHeartbeats 0 + +abbrev Host := Fin 747 +abbrev Data := Fin 240 +abbrev Values (X : Type u) := X → Bool + +def packed {X : Type u} (data : Data → Values X) (helpers : Host → Values X) + (i : Nat) : Values X := + if hi : i < 240 then data ⟨i, hi⟩ + else if hr : i < 987 then helpers ⟨i - 240, by omega⟩ + else fun _ => false + +theorem packed_data {X : Type u} (data : Data → Values X) (helpers : Host → Values X) + (i : Data) : packed data helpers i.val = data i := by + simp [packed, i.isLt] + +theorem packed_helper {X : Type u} (data : Data → Values X) (helpers : Host → Values X) + (h : Host) : packed data helpers (240 + h.val) = helpers h := by + have hi : ¬ 240 + h.val < 240 := by omega + have hr : 240 + h.val < 987 := by omega + simp [packed, hi, hr] + +def dataOther {X : Type u} (data : Data → Values X) : Data → Values X := + fun i => if hi : 120 ≤ i.val then + fun x => data i x ^^ data ⟨i.val - 120, by omega⟩ x + else data i + +/-- This actually evaluates the certified literal word, not an assumed +closed-form endpoint. The clean temporary is included in the tree. -/ +def invoke {X : Type u} (data : Data → Values X) (helpers : Host → Values X) : + (Data → Values X) × (Host → Values X) := + let input := packed data helpers + let output := runPayloads SourceMatrix.forwardWord + (Tree.tabulate 10 (fun i => if i < 987 then input i else fun _ => false)) + (fun i => output.get i.val, fun h => output.get (240 + h.val)) + +theorem invoke_endpoint {X : Type u} (data : Data → Values X) (helpers : Host → Values X) : + invoke data helpers = (dataOther data, helpers) := by + have hwhole := SourceMatrix.arbitrary_dirty_payloads (packed data helpers) + have hprojected := congrArg (fun output : Tree (Values X) => + ((fun i : Data => output.get i.val), (fun h : Host => output.get (240 + h.val)))) hwhole + apply hprojected.trans + apply Prod.ext + · funext i + change (Tree.tabulate 10 (SourceMatrix.endpointPayload (packed data helpers))).get i.val = _ + rw [Tree.get_tabulate 10 _ i.val (by omega)] + unfold SourceMatrix.endpointPayload + have hir : i.val < 987 := by omega + by_cases hi : 120 ≤ i.val + · have hs : i.val - 120 < 240 := by omega + simp [dataOther, hi, hir, i.isLt, packed, hs] + · simp [dataOther, hi, hir, i.isLt, packed] + · funext h + change (Tree.tabulate 10 (SourceMatrix.endpointPayload (packed data helpers))).get (240 + h.val) = _ + rw [Tree.get_tabulate 10 _ (240 + h.val) (by omega)] + have hr : 240 + h.val < 987 := by omega + have hn : ¬ 240 + h.val < 240 := by omega + simp only [SourceMatrix.endpointPayload, hr, hn, and_false, ↓reduceIte, packed_helper] + +def role (h : Host) : SourceOwnership.Role := ⟨240 + h.val, by omega⟩ +def residual (h : Host) : Mask SourceOwnership.Axis := + SourceOwnership.targetMask (SourceOwnership.tag (role h)) + +/-- Complete paired-address conjugacy, including both entries at every +coordinate. This is stronger than just matching mask descriptors. -/ +theorem swap_conjugacy {K : Type} (t : SourceOwnership.Tag) + (a : Address SourceOwnership.Axis K) : + SourceOwnership.reindex t + (swapAddress (SourceOwnership.sourceMask t) (SourceOwnership.unindex t a)) = + swapAddress (SourceOwnership.targetMask t) a := by + funext i + have hm := SourceOwnership.perm_support t (SourceOwnership.invPerm t i) + rw [SourceOwnership.inverse_perm] at hm + simp only [SourceOwnership.reindex, SourceOwnership.unindex, swapAddress, + SourceOwnership.inverse_perm, ← hm] + +def hostInput {K : Type} (h : Host) (v : Stream SourceOwnership.Axis K Bool) : + Stream SourceOwnership.Axis K Bool := + fun a => v (SourceOwnership.reindex (SourceOwnership.tag (role h)) a) + +def hostOutput {K : Type} (h : Host) (v : Stream SourceOwnership.Axis K Bool) : + Stream SourceOwnership.Axis K Bool := + fun a => v (swapAddress (SourceOwnership.sourceMask (SourceOwnership.tag (role h))) + (SourceOwnership.unindex (SourceOwnership.tag (role h)) a)) + +theorem host_transport {K : Type} (h : Host) (v : Stream SourceOwnership.Axis K Bool) : + hostOutput h (hostInput h v) = bitAction (residual h) v := by + funext a + exact congrArg v (swap_conjugacy (SourceOwnership.tag (role h)) a) + +abbrev Streams (K : Type) := Stream SourceOwnership.Axis K Bool +abbrev Retained (K : Type) (Tail : Type v) := (Data → Streams K) × Tail + +/-- Data gather/scatter maps are common to the original and relocated +layouts. All data outputs and the untouched exterior state are retained. -/ +def event {K : Type} {Tail : Type v} + (dataInput dataOutput : Data → Streams K → Streams K) : + MultiHosting.WindowEvent Host SourceOwnership.Axis (Retained K Tail) where + idle := fun _ _ => false + residual := residual + other s := (fun i => dataOutput i (dataOther (fun j => dataInput j (s.1 j)) i), s.2) + +/-- Old helpers are a separate bank; its actual normalized endpoint and +chosen physical output charts are returned, not reset between invocations. -/ +def original {K : Type} {Tail : Type v} + (dataInput dataOutput : Data → Streams K → Streams K) + (oldInput oldOutput : Host → Streams K → Streams K) + (s : MultiHosting.WindowState Host SourceOwnership.Axis K Bool (Retained K Tail) × + (Host → Streams K)) := + let result := invoke (fun i => dataInput i (s.1.2.1 i)) (fun h => oldInput h (s.2 h)) + ((s.1.1, (fun i => dataOutput i (result.1 i), s.1.2.2)), + fun h => oldOutput h (result.2 h)) + +def relocated {K : Type} {Tail : Type v} + (dataInput dataOutput : Data → Streams K → Streams K) + (s : MultiHosting.WindowState Host SourceOwnership.Axis K Bool (Retained K Tail) × Unit) := + let result := invoke (fun i => dataInput i (s.1.2.1 i)) (fun h => hostInput h (s.1.1 h)) + ((fun h => hostOutput h (result.2 h), (fun i => dataOutput i (result.1 i), s.1.2.2)), s.2) + +theorem original_retained {K : Type} {Tail : Type v} + (dataInput dataOutput : Data → Streams K → Streams K) + (oldInput oldOutput : Host → Streams K → Streams K) + (s : MultiHosting.WindowState Host SourceOwnership.Axis K Bool (Retained K Tail)) + (bank : Host → Streams K) : + (original dataInput dataOutput oldInput oldOutput (s, bank)).1 = + (event dataInput dataOutput).base s := by + simp only [original, invoke_endpoint, event, MultiHosting.WindowEvent.base] + apply Prod.ext + · funext h; exact (bitAction_empty (s.1 h)).symm + · rfl + +theorem original_bank_output {K : Type} {Tail : Type v} + (dataInput dataOutput : Data → Streams K → Streams K) + (oldInput oldOutput : Host → Streams K → Streams K) + (s : MultiHosting.WindowState Host SourceOwnership.Axis K Bool (Retained K Tail)) + (bank : Host → Streams K) : + (original dataInput dataOutput oldInput oldOutput (s, bank)).2 = + fun h => oldOutput h (oldInput h (bank h)) := by + simp only [original, invoke_endpoint] + +theorem relocated_retained {K : Type} {Tail : Type v} + (dataInput dataOutput : Data → Streams K → Streams K) + (s : MultiHosting.WindowState Host SourceOwnership.Axis K Bool (Retained K Tail)) + (bank : Unit) : + (relocated dataInput dataOutput (s, bank)).1 = (event dataInput dataOutput).hosted s := by + simp only [relocated, invoke_endpoint, event, MultiHosting.WindowEvent.hosted, + MultiHosting.WindowEvent.base, MultiHosting.onHosts] + apply Prod.ext + · funext h + change hostOutput h (hostInput h (s.1 h)) = + bitAction (residual h) (bitAction (fun _ => false) (s.1 h)) + rw [host_transport, bitAction_empty] + · rfl + +/-- A contract for the literal normalized word with the displayed coordinate +adapters. It is a physical source contract only after those adapters and the +987 distinct role owners are identified with the actual source execution. -/ +def normalizedContract {K : Type} {Tail : Type v} + (dataInput dataOutput : Data → Streams K → Streams K) + (oldInput oldOutput : Host → Streams K → Streams K) : + MultiHosting.PhysicalContract (K := K) (A := Bool) (event (Tail := Tail) dataInput dataOutput) + (Host → Streams K) Unit where + original := original dataInput dataOutput oldInput oldOutput + relocated := relocated dataInput dataOutput + original_retained := original_retained dataInput dataOutput oldInput oldOutput + relocated_retained := relocated_retained dataInput dataOutput + +end SourceConnection diff --git a/research/lean-multi-host-source/SourceControls.lean b/research/lean-multi-host-source/SourceControls.lean new file mode 100644 index 0000000000..070536782c --- /dev/null +++ b/research/lean-multi-host-source/SourceControls.lean @@ -0,0 +1,58 @@ +import MatrixCertificate +set_option maxRecDepth 100000 +set_option maxHeartbeats 0 + +/-! +Focused source controls. These retain the distinction between arbitrary +original inputs and the required clean private register. The mutation is an +intentional alteration of one actual instruction, not a claim about the +submitted program. +-/ +namespace SourceControls +open LinearReplay (Event) +open TreeReplay SourceMatrix + +/-- Event 218 of the actual word, at offset 18 in its second chunk. -/ +theorem actual_add_event : chunk1[18]? = some (⟨1,126,243,true⟩ : Event) := by rfl + +def omittedAdd : List Event := chunk1.set 18 ⟨1,126,243,false⟩ + +/-- Omitting this source XOR loses exactly original variable 243 from row126. -/ +theorem omitted_add_changes_row : + (runCheckedRows omittedAdd state1).1.get 126 ^^^ state2.1.get 126 = + 1 <<< 243 := by rfl + +/-- The missing XOR is not detected merely by clean-work checks. -/ +theorem omitted_add_keeps_guards : + (runCheckedRows omittedAdd state1).2 = true := by rfl + +/-- Event13558 is the first actual COPY, into private role987. -/ +theorem actual_first_copy : chunk67[158]? = some (⟨2,0,987,true⟩ : Event) := by rfl + +def firstCopy : Event := ⟨2,0,987,true⟩ +def dirtyPrivate : Tree Nat := initial.put 987 (1 <<< 243) + +theorem dirty_private_copy_rejected : rowChecks dirtyPrivate firstCopy = false := by rfl + +theorem dirty_private_copy_would_overwrite : + (rowStep dirtyPrivate firstCopy).get 987 = 1 := by rfl + +/-- This is a result of the actual complete word, using its checked certificate. -/ +theorem literal_helper_three_survives : + (runRows forwardWord initial).get 243 = 1 <<< 243 := by + rw [literal_word_rows] + rfl + +/-- The complete word cannot have the often-mistaken all-zero helper endpoint. -/ +theorem literal_helper_three_not_zero : + (runRows forwardWord initial).get 243 ≠ 0 := by + rw [literal_helper_three_survives] + decide + +#print axioms omitted_add_changes_row +#print axioms omitted_add_keeps_guards +#print axioms dirty_private_copy_rejected +#print axioms dirty_private_copy_would_overwrite +#print axioms literal_helper_three_survives +#print axioms literal_helper_three_not_zero +end SourceControls diff --git a/research/lean-multi-host-source/SourceDataBehavior.lean b/research/lean-multi-host-source/SourceDataBehavior.lean new file mode 100644 index 0000000000..c0acdf492e --- /dev/null +++ b/research/lean-multi-host-source/SourceDataBehavior.lean @@ -0,0 +1,130 @@ +import SourceInvocationComparison + +/-! +The data operation of the selected call, with its actual unequal entrance +and exit frames displayed. The scalar certificate adds source i to target +120+i. Physical streams additionally undergo the stated frame and port-chart +pullbacks; this file does not identify those pullbacks with identity maps. +All data and helper payloads are arbitrary Boolean functions. +Apache-2.0. Prepared with substantial OpenAI Codex assistance. +-/ +namespace SourceDataBehavior +open SourceConnection FramedReplay +set_option maxRecDepth 100000 +set_option maxHeartbeats 0 +attribute [local irreducible] SourceFramed.final SourceRaw.final + +def first (i : Fin 120) : Data := ⟨i.val, by omega⟩ +def second (i : Fin 120) : Data := ⟨120 + i.val, by omega⟩ + +theorem first_initial_frame : ∀ i : Fin 120, + SourceFrameTrace.state0.frames.get (first i).val = i.val + 2 := by decide +theorem second_initial_frame : ∀ i : Fin 120, + SourceFrameTrace.state0.frames.get (second i).val = 0 := by decide +theorem first_final_frame : ∀ i : Fin 120, + SourceFrameTrace.state96.frames.get (first i).val = 1 := by decide +theorem second_final_frame : ∀ i : Fin 120, + SourceFrameTrace.state96.frames.get (second i).val = i.val + 824 := by decide + +theorem framed_first {K : Type} (gauges : PhysicalSourceConnection.Gauges K) + (data : Data → Streams K) (helpers : Host → Streams K) (i : Fin 120) : + PhysicalSourceConnection.physicalData gauges data helpers (first i) = + fun a => data (first i) + ((gauges (i.val + 2)).forward ((gauges 1).inverse a)) := by + have he := congrFun + (PhysicalSourceConnection.physical_data_endpoints gauges data helpers) (first i) + apply he.trans + funext a + have hi : (first i).val < 987 := by simp only [first]; omega + have hn : ¬ 120 ≤ (first i).val := by simp only [first]; omega + simp only [SourceMatrix.endpointPayload, hi, hn, false_and, ↓reduceIte, + SourceFramed.normalizedInput, packed_data, first_initial_frame, first_final_frame] + +theorem framed_second {K : Type} (gauges : PhysicalSourceConnection.Gauges K) + (data : Data → Streams K) (helpers : Host → Streams K) (i : Fin 120) : + PhysicalSourceConnection.physicalData gauges data helpers (second i) = + fun a => data (second i) + ((gauges 0).forward ((gauges (i.val + 824)).inverse a)) ^^ + data (first i) + ((gauges (i.val + 2)).forward ((gauges (i.val + 824)).inverse a)) := by + have he := congrFun + (PhysicalSourceConnection.physical_data_endpoints gauges data helpers) (second i) + apply he.trans + funext a + have hi : (second i).val < 987 := by simp only [second]; omega + have ht : 120 ≤ (second i).val ∧ (second i).val < 240 := by simp only [second]; omega + have hs : (second i).val - 120 = (first i).val := by simp only [first, second]; omega + simp only [SourceMatrix.endpointPayload, hi, ht, and_self, ↓reduceIte, hs, + SourceFramed.normalizedInput, packed_data, first_initial_frame, + second_initial_frame, second_final_frame] + +/-- Complete output data function, in the actual owner-coordinate chart. -/ +def dataFormula (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (gauges : SourceInvocation.Gauges K) (data : Data → Streams K) (i : Data) : Streams K := + SourceInvocation.dataOutput K h2 i + (fun a => if ht : 120 ≤ i.val then + SourceInvocation.dataInput K h2 i (data i) + ((gauges 0).forward ((gauges (i.val - 120 + 824)).inverse a)) ^^ + SourceInvocation.dataInput K h2 ⟨i.val - 120, by omega⟩ (data ⟨i.val - 120, by omega⟩) + ((gauges (i.val - 120 + 2)).forward + ((gauges (i.val - 120 + 824)).inverse a)) + else SourceInvocation.dataInput K h2 i (data i) + ((gauges (i.val + 2)).forward ((gauges 1).inverse a))) + +theorem framed_data_formula (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (gauges : SourceInvocation.Gauges K) (data : Data → Streams K) + (helpers : Host → Streams K) (i : Data) : + SourceInvocation.dataOutput K h2 i + (PhysicalSourceConnection.physicalData gauges + (fun j => SourceInvocation.dataInput K h2 j (data j)) helpers i) = + dataFormula K h2 gauges data i := by + by_cases ht : 120 ≤ i.val + · let j : Fin 120 := ⟨i.val - 120, by omega⟩ + have hj : second j = i := by apply Fin.ext; simp only [second, j]; omega + rw [← hj, framed_second] + unfold dataFormula + have hjt : 120 ≤ (second j).val := by simp only [second]; omega + simp only [dif_pos hjt] + simp only [second, Nat.add_sub_cancel_left] + rfl + · let j : Fin 120 := ⟨i.val, by omega⟩ + have hj : first j = i := rfl + rw [← hj, framed_first] + unfold dataFormula + have hjt : ¬ 120 ≤ (first j).val := ht + simp only [hjt, ↓reduceDIte] + rfl + +/-- The actual old-bank invocation has this exact data endpoint, for every +independent dirty bank input. -/ +theorem old_data_formula (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (d : SourceOwnership.Vec K ≃ SourceOwnership.Vec K) + (gauges : SourceInvocation.Gauges K) (s : SourceInvocation.State K h2 d) + (bank : Host → Streams K) (i : Data) : + (SourceInvocation.oldRaw K h2 d gauges s bank + (SourceInvocation.oldOwner K h2 d (SourceLayouts.dataRole i))).2 = + dataFormula K h2 gauges s.2.1 i := + (SourceInvocation.oldRaw_data K h2 d gauges s bank i).trans + (framed_data_formula K h2 gauges s.2.1 _ i) + +/-- The actual hosted invocation has the identical formula for all data, +despite every retained host carrying an arbitrary dirty stream. -/ +theorem new_data_formula (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (d : SourceOwnership.Vec K ≃ SourceOwnership.Vec K) + (gauges : SourceInvocation.Gauges K) (s : SourceInvocation.State K h2 d) (i : Data) : + (SourceInvocation.newRaw K h2 d gauges s + (SourceInvocation.newOwner K h2 d (SourceLayouts.dataRole i))).2 = + dataFormula K h2 gauges s.2.1 i := + (SourceInvocation.newRaw_data K h2 d gauges s i).trans + (framed_data_formula K h2 gauges s.2.1 _ i) + +#print axioms first_initial_frame +#print axioms second_initial_frame +#print axioms first_final_frame +#print axioms second_final_frame +#print axioms framed_first +#print axioms framed_second +#print axioms framed_data_formula +#print axioms old_data_formula +#print axioms new_data_formula +end SourceDataBehavior diff --git a/research/lean-multi-host-source/SourceEndpoint.lean b/research/lean-multi-host-source/SourceEndpoint.lean new file mode 100644 index 0000000000..7a5900f3c8 --- /dev/null +++ b/research/lean-multi-host-source/SourceEndpoint.lean @@ -0,0 +1,84 @@ +import MatrixCertificate +import SourceTables +import PayloadGuards + +/-! +The literal 19,002-event normalized word is correct for every assignment to +all 987 dirty original roles, including arbitrary dirty helper values. +There is exactly one designated clean temporary (role 987). The result +also holds for entire arbitrary Boolean-valued streams, pointwise in an +address of any type. Physical frames and role ownership are separate +source obligations and are not inferred from this normalized identity. +-/ +namespace SourceMatrix +open TreeReplay +set_option maxRecDepth 100000 +set_option maxHeartbeats 0 + +theorem arbitrary_dirty_bools (input : Nat → Bool) : + runBools forwardWord (dirtyInput 10 987 input) = + Tree.tabulate 10 (endpointValue input) := by + have hi := (congrArg (evalRows 987 input) initial_formula).trans + (evalRows_basisRows 10 987 input) + have ho := (congrArg (evalRows 987 input) expected_formula).trans + (evalRows_endpoint input) + exact (congrArg (runBools forwardWord) hi).symm.trans + ((evalRows_run 987 input forwardWord initial).symm.trans + ((congrArg (evalRows 987 input) literal_word_rows).trans ho)) + +theorem arbitrary_dirty_guards (input : Nat → Bool) : + (runCheckedBools forwardWord (dirtyInput 10 987 input, true)).2 = true := by + have h : (runCheckedRows forwardWord (initial, true)).2 = true := + congrArg Prod.snd literal_word_checked + have hs := checked_guards_sound 987 input forwardWord (initial, true) h + have hi := (congrArg (evalRows 987 input) initial_formula).trans + (evalRows_basisRows 10 987 input) + exact (congrArg (fun s => (runCheckedBools forwardWord (s, true)).2) hi).symm.trans hs + +theorem arbitrary_dirty_payloads {X : Type u} (input : Nat → X → Bool) : + runPayloads forwardWord + (Tree.tabulate 10 (fun i => if i < 987 then input i else fun _ => false)) = + Tree.tabulate 10 (endpointPayload input) := by + have hi := (congrArg (evalPayloadRows 987 input) initial_formula).trans + (evalPayloadRows_basisRows 10 987 input) + have ho := (congrArg (evalPayloadRows 987 input) expected_formula).trans + (evalPayloadRows_endpoint input) + exact (congrArg (runPayloads forwardWord) hi).symm.trans + ((evalPayloadRows_run 987 input forwardWord initial).symm.trans + ((congrArg (evalPayloadRows 987 input) literal_word_rows).trans ho)) + +theorem actual_payload_clean {X : Type u} (input : Nat → X → Bool) : + PayloadCleanRun forwardWord + (Tree.tabulate 10 (fun i => if i < 987 then input i else fun _ => false)) := by + have h : (runCheckedRows forwardWord (initial, true)).2 = true := + congrArg Prod.snd literal_word_checked + have hs := checked_payload_guards_sound 987 input forwardWord (initial, true) h + have hi := (congrArg (evalPayloadRows 987 input) initial_formula).trans + (evalPayloadRows_basisRows 10 987 input) + exact Eq.mp (congrArg (PayloadCleanRun forwardWord) hi) hs + +/-- The temporary is restored for every dirty payload assignment. -/ +theorem arbitrary_dirty_temp_restored {X : Type u} (input : Nat → X → Bool) : + (runPayloads forwardWord + (Tree.tabulate 10 (fun i => if i < 987 then input i else fun _ => false))).get 987 = + fun _ => false := by + rw [arbitrary_dirty_payloads, Tree.get_tabulate 10 _ 987 (by decide)] + rfl + +/-- Every original role is accounted for in the endpoint equation. -/ +theorem arbitrary_dirty_original_roles {X : Type u} (input : Nat → X → Bool) + (i : Nat) (hi : i < 987) : + (runPayloads forwardWord + (Tree.tabulate 10 (fun i => if i < 987 then input i else fun _ => false))).get i = + if 120 ≤ i ∧ i < 240 then fun x => input i x ^^ input (i - 120) x else input i := by + rw [arbitrary_dirty_payloads, Tree.get_tabulate 10 _ i (by omega)] + simp only [endpointPayload, hi, ↓reduceIte] + +#print axioms arbitrary_dirty_bools +#print axioms arbitrary_dirty_guards +#print axioms arbitrary_dirty_payloads +#print axioms actual_payload_clean +#print axioms arbitrary_dirty_temp_restored +#print axioms arbitrary_dirty_original_roles + +end SourceMatrix diff --git a/research/lean-multi-host-source/SourceFramed.lean b/research/lean-multi-host-source/SourceFramed.lean new file mode 100644 index 0000000000..0b0b8efaa6 --- /dev/null +++ b/research/lean-multi-host-source/SourceFramed.lean @@ -0,0 +1,132 @@ +import FrameTraceData +import FrameTraceRefinement +import SourceEndpoint + +/-! +The actual 19,002-event frame trace, executed on arbitrary dirty physical +payloads in all 987 original roles and one blank temporary. Its projection +is exactly the word checked by the whole symbolic matrix certificate. +The other 36 tree leaves are representation padding; the checked finite-role +projection proves that the word never accesses them as registers. + +This discharges every chronological frame-label and COPY/ERASE cleanliness +guard, for a supplied family of genuine address gauges. It does not assert +that a nominal register is a distinct owned physical stream, or that those +gauges are the actual source projectors; those concrete geometry and ownership +certificates are separate. Rows here use a common invocation address chart. +-/ +namespace SourceFramed +open TreeReplay (Tree) +set_option maxRecDepth 100000 +set_option maxHeartbeats 0 + +def normalizedInput {X : Type} (gauges : Nat → FramedReplay.Gauge X) + (input : Nat → X → Bool) (i : Nat) : X → Bool := + fun a => input i ((gauges (SourceFrameTrace.state0.frames.get i)).forward a) + +def initial {X : Type} (gauges : Nat → FramedReplay.Gauge X) + (input : Nat → X → Bool) : FramedReplay.Store X := + Tree.tabulate 10 (fun i => (gauges (SourceFrameTrace.state0.frames.get i), + if i < 987 then input i else fun _ => false)) + +def final {X : Type} (gauges : Nat → FramedReplay.Gauge X) + (input : Nat → X → Bool) : FramedReplay.Store X := + FramedReplay.runPhysical + (SourceFrameTrace.forward.map (FrameTrace.toPhysical gauges)) (initial gauges input) + +theorem initial_matches {X : Type} (gauges : Nat → FramedReplay.Gauge X) + (input : Nat → X → Bool) : + FrameTrace.Matches gauges SourceFrameTrace.state0 (initial gauges input) := by + unfold FrameTrace.Matches initial + rw [Tree.map_tabulate] + change Tree.tabulate 10 (fun i => gauges (SourceFrameTrace.state0.frames.get i)) = _ + simpa only [Tree.map_tabulate, Function.comp_def] using + congrArg (Tree.map gauges) SourceFrameTrace.initial_tabulate + +theorem initial_decoded {X : Type} (gauges : Nat → FramedReplay.Gauge X) + (input : Nat → X → Bool) : + FramedReplay.decode (initial gauges input) = + Tree.tabulate 10 (fun i => if i < 987 then normalizedInput gauges input i + else fun _ => false) := by + unfold FramedReplay.decode initial + rw [Tree.map_tabulate] + apply congrArg (Tree.tabulate 10) + funext i + change FramedReplay.decodeRow + (gauges (SourceFrameTrace.state0.frames.get i), + if i < 987 then input i else fun _ => false) = + (if i < 987 then normalizedInput gauges input i else fun _ => false) + by_cases hi : i < 987 + · simp only [if_pos hi] + rfl + · simp only [if_neg hi] + rfl + +theorem actual_valid {X : Type} (gauges : Nat → FramedReplay.Gauge X) + (input : Nat → X → Bool) : + FramedReplay.ValidTrace + (SourceFrameTrace.forward.map (FrameTrace.toPhysical gauges)) (initial gauges input) := by + apply FrameTrace.valid_trace gauges SourceFrameTrace.forward SourceFrameTrace.state0 + (initial gauges input) (initial_matches gauges input) SourceFrameTrace.forward_valid + rw [SourceFrameTrace.scalar_word, initial_decoded] + exact SourceMatrix.actual_payload_clean _ + +theorem final_matches {X : Type} (gauges : Nat → FramedReplay.Gauge X) + (input : Nat → X → Bool) : + FrameTrace.Matches gauges SourceFrameTrace.state96 (final gauges input) := by + have h := FrameTrace.matches_run gauges SourceFrameTrace.forward SourceFrameTrace.state0 + (initial gauges input) (initial_matches gauges input) true + rw [SourceFrameTrace.forward_checked] at h + exact h + +/-- Whole-store endpoint for arbitrary and correlated physical dirty payloads. -/ +theorem actual_decoded_endpoint {X : Type} (gauges : Nat → FramedReplay.Gauge X) + (input : Nat → X → Bool) : + FramedReplay.decode (final gauges input) = + Tree.tabulate 10 (SourceMatrix.endpointPayload (normalizedInput gauges input)) := by + unfold final + rw [FramedReplay.decode_run _ _ (actual_valid gauges input), + FrameTrace.scalar_projection, SourceFrameTrace.scalar_word, initial_decoded, + SourceMatrix.arbitrary_dirty_payloads] + +/-- Physical endpoint in each final row's own chart, including all original +roles and the blank temporary. No arbitrary dirty input was specialized. -/ +theorem actual_physical_endpoint {X : Type} (gauges : Nat → FramedReplay.Gauge X) + (input : Nat → X → Bool) (i : Nat) (hi : i < 1024) (a : X) : + ((final gauges input).get i).2 a = + SourceMatrix.endpointPayload (normalizedInput gauges input) i + ((gauges (SourceFrameTrace.state96.frames.get i)).inverse a) := by + have h := congrArg (fun t => Tree.get t i) (actual_decoded_endpoint gauges input) + rw [FramedReplay.decode, Tree.map_get, Tree.get_tabulate 10 _ i hi] at h + have hf := FrameTrace.matches_get gauges SourceFrameTrace.state96 + (final gauges input) (final_matches gauges input) i + have ha := congrFun h ((gauges (SourceFrameTrace.state96.frames.get i)).inverse a) + simp only [FramedReplay.decodeRow, hf, FramedReplay.Gauge.forward_inverse] at ha + exact ha + +theorem actual_temporary_restored {X : Type} (gauges : Nat → FramedReplay.Gauge X) + (input : Nat → X → Bool) : + ((final gauges input).get 987).2 = fun _ => false := by + funext a + rw [actual_physical_endpoint gauges input 987 (by decide) a] + rfl + +/-- A function-level endpoint avoids reducing the literal interpreter when +later proofs select several physical outputs at once. -/ +theorem all_physical_endpoints {X : Type} (gauges : Nat → FramedReplay.Gauge X) + (input : Nat → X → Bool) : + (fun r : Fin 1024 => ((final gauges input).get r.val).2) = + (fun r a => SourceMatrix.endpointPayload (normalizedInput gauges input) r.val + ((gauges (SourceFrameTrace.state96.frames.get r.val)).inverse a)) := by + funext r a + exact actual_physical_endpoint gauges input r.val r.isLt a + +#print axioms initial_matches +#print axioms initial_decoded +#print axioms actual_valid +#print axioms final_matches +#print axioms actual_decoded_endpoint +#print axioms actual_physical_endpoint +#print axioms actual_temporary_restored +#print axioms all_physical_endpoints +end SourceFramed diff --git a/research/lean-multi-host-source/SourceInitialPayload.lean b/research/lean-multi-host-source/SourceInitialPayload.lean new file mode 100644 index 0000000000..ee2cf6fe65 --- /dev/null +++ b/research/lean-multi-host-source/SourceInitialPayload.lean @@ -0,0 +1,81 @@ +import SourceInvocationState + +/-! +The explicit raw input constructions preserve all displayed arbitrary inputs. +The 240 data streams and all 747 retained hosts agree between the original +and relocated calls. The original helper bank remains an independent, +arbitrary input. These identities concern physical owner-cover payloads, +before any framed instruction executes. +Apache-2.0. Prepared with substantial OpenAI Codex assistance. +-/ +namespace SourceInvocation +open SourceConnection FramedReplay + +variable (K : Type) [Field K] (h2 : (2 : K) ≠ 0) +variable (d : SourceOwnership.Vec K ≃ SourceOwnership.Vec K) + +theorem newPayload_host (s : State K h2 d) (h : Host) : + newPayload K h2 d s (hostOwner K h2 d h) = + fun a => s.1 h ((hostChart K h2 h).inverse a) := by + unfold newPayload hostOwner + rw [InvocationPayload.realize_owner _ (newChart K h2) + (fun he => newOwner_injective K h2 d he)] + funext a + change packed _ _ (240 + h.val) _ = _ + rw [packed_helper] + change s.1 h (SourceOwnership.reindex (SourceOwnership.tag (role h)) + ((SourceOwnership.sourceActiveAddressChart K h2 (SourceLayouts.hostRole h)).inverse a)) = _ + rw [SourceLayouts.host_chart_inverse, SourceOwnership.reindex_unindex] + rfl + +theorem oldPayload_data (s : State K h2 d) (bank : Host → Streams K) (i : Data) : + oldPayload K h2 d s bank (oldOwner K h2 d (SourceLayouts.dataRole i)) = s.2.1 i := by + unfold oldPayload + rw [InvocationPayload.realize_owner _ (oldChart K h2) + (fun he => oldOwner_injective K h2 d he)] + funext a + change packed _ _ i.val _ = _ + rw [packed_data] + change s.2.1 i ((SourceOwnership.sourceActiveAddressChart K h2 + (SourceLayouts.dataRole i)).forward + ((ParentOwnership.sourceActiveAddressChart K h2 (SourceLayouts.dataRole i)).inverse a)) = _ + rw [SourceLayouts.data_chart_eq] + exact congrArg (s.2.1 i) (Gauge.forward_inverse _ a) + +theorem newPayload_data (s : State K h2 d) (i : Data) : + newPayload K h2 d s (newOwner K h2 d (SourceLayouts.dataRole i)) = s.2.1 i := by + unfold newPayload + rw [InvocationPayload.realize_owner _ (newChart K h2) + (fun he => newOwner_injective K h2 d he)] + funext a + change packed _ _ i.val _ = _ + rw [packed_data] + exact congrArg (s.2.1 i) ((newChart K h2 (SourceLayouts.dataRole i)).forward_inverse a) + +theorem oldPayload_bank (s : State K h2 d) (bank : Host → Streams K) (h : Host) : + oldPayload K h2 d s bank (oldOwner K h2 d (SourceLayouts.hostRole h)) = bank h := by + unfold oldPayload + rw [InvocationPayload.realize_owner _ (oldChart K h2) + (fun he => oldOwner_injective K h2 d he)] + funext a + change packed _ _ (240 + h.val) _ = _ + rw [packed_helper] + exact congrArg (bank h) ((oldChart K h2 (SourceLayouts.hostRole h)).forward_inverse a) + +theorem shared_host_input (s : State K h2 d) (bank : Host → Streams K) (h : Host) : + oldPayload K h2 d s bank (hostOwner K h2 d h) = + newPayload K h2 d s (hostOwner K h2 d h) := by + rw [oldPayload_host, newPayload_host] + +theorem shared_data_input (s : State K h2 d) (bank : Host → Streams K) (i : Data) : + oldPayload K h2 d s bank (oldOwner K h2 d (SourceLayouts.dataRole i)) = + newPayload K h2 d s (newOwner K h2 d (SourceLayouts.dataRole i)) := by + rw [oldPayload_data, newPayload_data] + +#print axioms newPayload_host +#print axioms oldPayload_data +#print axioms newPayload_data +#print axioms oldPayload_bank +#print axioms shared_host_input + +end SourceInvocation diff --git a/research/lean-multi-host-source/SourceInvocation.lean b/research/lean-multi-host-source/SourceInvocation.lean new file mode 100644 index 0000000000..3146d327c4 --- /dev/null +++ b/research/lean-multi-host-source/SourceInvocation.lean @@ -0,0 +1,195 @@ +import SourceInvocationComparison +import SourceInitialPayload +import SourceNativeInvocation +import SelectedGeometry +import SourceMoveGeometry +import SourceDataBehavior + +/-! +The selected PR442 stage2/replica0 invocation, connected to MultiHosting. + +The maps below are the literal source data routes, the 747 constructed host +owners/charts, the original parent-bank owners/charts, and all 19,002 source +events. No geometry, ownership, clean-work or input-matching premise is +assumed. Every retained host, all 240 data streams, the exterior of both +active owner images, and all 747 old-bank inputs are arbitrary Boolean +functions on paired 64-dimensional addresses. + +This is one local invocation. The displayed completion applies the remaining +pending swaps immediately in the abstract window. It does not prove their +later positions in the real recursive schedule, a whole-cover sweep, a global +bank renumbering, a register-cost saving, or a new kappa bound. +-/ +namespace SourceInvocation +open SourceConnection FramedReplay +variable (K : Type) [Field K] (h2 : (2 : K) ≠ 0) +variable (d : SourceOwnership.Vec K ≃ SourceOwnership.Vec K) +set_option maxRecDepth 100000 +set_option maxHeartbeats 0 +attribute [local irreducible] SourceRaw.final SourceFramed.final + +/-- A concrete physical contract for the actual old and relocated raw +instruction folds. Even the original-bank outputs are the actual outputs +of that fold; they have not been replaced with their initial values. -/ +noncomputable def actualContract : + MultiHosting.PhysicalContract (K := K) (A := Bool) + (PhysicalSourceConnection.event (Tail := Tail K h2 d) + (SelectedGeometry.gauges K h2) (dataInput K h2) (dataOutput K h2)) + (Host → Streams K) Unit where + original := oldResult K h2 d (SelectedGeometry.gauges K h2) + relocated := newResult K h2 d (SelectedGeometry.gauges K h2) + original_retained s bank := + (congrArg Prod.fst (oldResult_framed K h2 d (SelectedGeometry.gauges K h2) s bank)).trans + (PhysicalSourceConnection.original_retained _ _ _ _ _ s bank) + relocated_retained s bank := + (congrArg Prod.fst (newResult_framed K h2 d (SelectedGeometry.gauges K h2) s bank)).trans + (PhysicalSourceConnection.relocated_retained _ (SelectedGeometry.helper_relative K h2) + _ _ s bank) + +/-- All retained outputs of this actual invocation satisfy the multi-host +completion equation, for arbitrary dirty input. The only algebraic condition +is characteristic different from two; d is any invertible cover map. +Child-1 pending coordinates are 15..21 and child-2 coordinates are 1..28. -/ +theorem selected_call_completion (s : State K h2 d) (oldBank : Host → Streams K) : + MultiHosting.onHosts + (MultiHosting.remainders PhysicalSourceConnection.pending + [PhysicalSourceConnection.event (Tail := Tail K h2 d) (SelectedGeometry.gauges K h2) + (dataInput K h2) (dataOutput K h2)]) + (newResult K h2 d (SelectedGeometry.gauges K h2) (s, ())).1 = + MultiHosting.onHosts PhysicalSourceConnection.pending + (oldResult K h2 d (SelectedGeometry.gauges K h2) (s, oldBank)).1 := by + have hn := congrArg + (fun out : State K h2 d × Unit => + MultiHosting.onHosts + (MultiHosting.remainders PhysicalSourceConnection.pending + [PhysicalSourceConnection.event (Tail := Tail K h2 d) (SelectedGeometry.gauges K h2) + (dataInput K h2) (dataOutput K h2)]) out.1) + (newResult_framed K h2 d (SelectedGeometry.gauges K h2) s ()) + have ho := congrArg + (fun out : State K h2 d × (Host → Streams K) => + MultiHosting.onHosts PhysicalSourceConnection.pending out.1) + (oldResult_framed K h2 d (SelectedGeometry.gauges K h2) s oldBank) + exact hn.trans ((PhysicalSourceConnection.selected_invocation_completion + (SelectedGeometry.gauges K h2) (SelectedGeometry.helper_relative K h2) + (dataInput K h2) (dataOutput K h2) (oldInput K h2) (oldOutput K h2) + s oldBank ()).trans ho.symm) + +/-- The same completion equation for the native source folds themselves, +read in the common retained coordinate charts. The preceding input identity +lemmas guarantee that these runs start with the same retained native data. -/ +theorem selected_native_completion (s : State K h2 d) (oldBank : Host → Streams K) : + MultiHosting.onHosts + (MultiHosting.remainders PhysicalSourceConnection.pending + [PhysicalSourceConnection.event (Tail := Tail K h2 d) (SelectedGeometry.gauges K h2) + (dataInput K h2) (dataOutput K h2)]) + (newNativeResult K h2 d (SelectedGeometry.gauges K h2) (s, ())).1 = + MultiHosting.onHosts PhysicalSourceConnection.pending + (oldNativeResult K h2 d (SelectedGeometry.gauges K h2) (s, oldBank)).1 := by + have hn := congrArg + (fun out : State K h2 d × Unit => + MultiHosting.onHosts + (MultiHosting.remainders PhysicalSourceConnection.pending + [PhysicalSourceConnection.event (Tail := Tail K h2 d) (SelectedGeometry.gauges K h2) + (dataInput K h2) (dataOutput K h2)]) out.1) + (newResult_native K h2 d (SelectedGeometry.gauges K h2) s ()) + have ho := congrArg + (fun out : State K h2 d × (Host → Streams K) => + MultiHosting.onHosts PhysicalSourceConnection.pending out.1) + (oldResult_native K h2 d (SelectedGeometry.gauges K h2) s oldBank) + exact hn.symm.trans ((selected_call_completion K h2 d s oldBank).trans ho) + +/-- Concrete data behavior, including each port's actual initial/final +frame and its literal rho chart. The target term is XOR source; the displayed +coordinate pullbacks are retained rather than silently made identities. -/ +theorem selected_data_formula (s : State K h2 d) (oldBank : Host → Streams K) (i : Data) : + (oldRaw K h2 d (SelectedGeometry.gauges K h2) s oldBank + (oldOwner K h2 d (SourceLayouts.dataRole i))).2 = + SourceDataBehavior.dataFormula K h2 (SelectedGeometry.gauges K h2) s.2.1 i ∧ + (newRaw K h2 d (SelectedGeometry.gauges K h2) s + (newOwner K h2 d (SourceLayouts.dataRole i))).2 = + SourceDataBehavior.dataFormula K h2 (SelectedGeometry.gauges K h2) s.2.1 i := + ⟨SourceDataBehavior.old_data_formula K h2 d _ s oldBank i, + SourceDataBehavior.new_data_formula K h2 d _ s i⟩ + +/-- These are two coordinate descriptions of the very same native source +fold, with all initial payloads constructed explicitly. Thus the contract +above does not posit an extra routed interface for the physical XOR gates. -/ +theorem selected_native_realization (s : State K h2 d) (oldBank : Host → Streams K) : + oldRaw K h2 d (SelectedGeometry.gauges K h2) s oldBank = + OwnerTransport.fromNative (commonNativeCover K h2 d) + (oldNative K h2 d (SelectedGeometry.gauges K h2) s oldBank) ∧ + newRaw K h2 d (SelectedGeometry.gauges K h2) s = + OwnerTransport.fromNative (commonNativeCover K h2 d) + (newNative K h2 d (SelectedGeometry.gauges K h2) s) := + ⟨old_native_realization K h2 d _ s oldBank, new_native_realization K h2 d _ s⟩ + +/-- COPY blankness and ERASE equality follow the actual native trajectories; +there is no clean assumption on any of the 987 original streams. -/ +theorem selected_native_clean (s : State K h2 d) (oldBank : Host → Streams K) : + SourceRawGuards.NativeCleanRun (oldOwner K h2 d) (nativeGauge K d) + (SourceFrameTrace.forward.map (SourceFrameTrace.toRoute (SelectedGeometry.gauges K h2))) + (SourceRaw.initial (oldOwner K h2 d) (SelectedGeometry.gauges K h2) + (nativePayload K (commonNativeCover K h2 d) (oldPayload K h2 d s oldBank))) ∧ + SourceRawGuards.NativeCleanRun (newOwner K h2 d) (nativeGauge K d) + (SourceFrameTrace.forward.map (SourceFrameTrace.toRoute (SelectedGeometry.gauges K h2))) + (SourceRaw.initial (newOwner K h2 d) (SelectedGeometry.gauges K h2) + (nativePayload K (commonNativeCover K h2 d) (newPayload K h2 d s))) := + ⟨old_native_clean K h2 d _ s oldBank, new_native_clean K h2 d _ s⟩ + +/-- The complete actual relocated raw invocation also realizes the literal +matrix operators: every MOVE is D_(Pnew-Pold), and COPY uses the full local +8-coordinate transport. This equality includes frame metadata and payloads. -/ +theorem selected_matrix_realization (s : State K h2 d) : + (fun r => OwnerTransport.gather (newOwner K h2 d) (newChart K h2) + (newRaw K h2 d (SelectedGeometry.gauges K h2) s) r) = + fun r => (SourceMoveGeometry.matrixRun K h2 SourceFrameTrace.forward + (SourceFramed.initial (SelectedGeometry.gauges K h2) + (packed (fun i => dataInput K h2 i (s.2.1 i)) + (fun h => hostInput h (s.1 h))))).get r.val := by + have hg := funext (InvocationPayload.realized_gather (newOwner K h2 d) (newChart K h2) + (fun h => newOwner_injective K h2 d h) (SelectedGeometry.gauges K h2) + (fun i => dataInput K h2 i (s.2.1 i)) (fun h => hostInput h (s.1 h)) + (tailPayload K h2 d s)) + exact hg.trans (congrArg + (fun store : FramedReplay.Store (WholeHosting.Address SourceOwnership.Axis K) => + fun r : SourceRaw.Role => store.get r.val) + (SourceMoveGeometry.actual_matrix_run K h2 _).symm) + +/-- The original-bank invocation uses the same certified matrix word. -/ +theorem selected_original_matrix_realization (s : State K h2 d) + (bank : Host → Streams K) : + (fun r => OwnerTransport.gather (oldOwner K h2 d) (oldChart K h2) + (oldRaw K h2 d (SelectedGeometry.gauges K h2) s bank) r) = + fun r => (SourceMoveGeometry.matrixRun K h2 SourceFrameTrace.forward + (SourceFramed.initial (SelectedGeometry.gauges K h2) + (packed (fun i => dataInput K h2 i (s.2.1 i)) + (fun h => oldInput K h2 h (bank h))))).get r.val := by + have hg := funext (InvocationPayload.realized_gather (oldOwner K h2 d) (oldChart K h2) + (fun h => oldOwner_injective K h2 d h) (SelectedGeometry.gauges K h2) + (fun i => dataInput K h2 i (s.2.1 i)) (fun h => oldInput K h2 h (bank h)) + (hostPayload K h2 d s)) + exact hg.trans (congrArg + (fun store : FramedReplay.Store (WholeHosting.Address SourceOwnership.Axis K) => + fun r : SourceRaw.Role => store.get r.val) + (SourceMoveGeometry.actual_matrix_run K h2 _).symm) + +/-- Both physical private temporaries are returned blank. -/ +theorem selected_temporary_restoration (s : State K h2 d) (oldBank : Host → Streams K) : + (oldNative K h2 d (SelectedGeometry.gauges K h2) s oldBank + (oldOwner K h2 d SourceRaw.privateRow)).2 = (fun _ => false) ∧ + (newNative K h2 d (SelectedGeometry.gauges K h2) s + (newOwner K h2 d SourceRaw.privateRow)).2 = (fun _ => false) := + ⟨old_native_temporary_restored K h2 d _ s oldBank, + new_native_temporary_restored K h2 d _ s⟩ + +end SourceInvocation + +#print axioms SourceInvocation.selected_call_completion +#print axioms SourceInvocation.selected_native_realization +#print axioms SourceInvocation.selected_native_clean +#print axioms SourceInvocation.selected_matrix_realization +#print axioms SourceInvocation.selected_original_matrix_realization +#print axioms SourceInvocation.selected_temporary_restoration + +#print axioms SourceInvocation.selected_native_completion +#print axioms SourceInvocation.selected_data_formula diff --git a/research/lean-multi-host-source/SourceInvocationComparison.lean b/research/lean-multi-host-source/SourceInvocationComparison.lean new file mode 100644 index 0000000000..d34464400e --- /dev/null +++ b/research/lean-multi-host-source/SourceInvocationComparison.lean @@ -0,0 +1,138 @@ +import SourceInvocationState +import PhysicalSourceConnection + +/-! Comparison of actual raw outputs with the framed hosting contract. +All maps and owner layouts are concrete. These lemmas expose every output +class, including the original bank, instead of discarding affected rows. -/ +namespace SourceInvocation +open SourceConnection FramedReplay +variable (K : Type) [Field K] (h2 : (2 : K) ≠ 0) +variable (d : SourceOwnership.Vec K ≃ SourceOwnership.Vec K) +set_option maxRecDepth 100000 +set_option maxHeartbeats 0 +attribute [local irreducible] SourceRaw.final SourceFramed.final + +theorem oldRaw_data (gauges : Gauges K) (s : State K h2 d) + (bank : Host → Streams K) (i : Data) : + (oldRaw K h2 d gauges s bank (oldOwner K h2 d (SourceLayouts.dataRole i))).2 = + dataOutput K h2 i + (PhysicalSourceConnection.physicalData gauges + (fun j => dataInput K h2 j (s.2.1 j)) + (fun h => oldInput K h2 h (bank h)) i) := by + funext a + have he := InvocationPayload.realized_payload (oldOwner K h2 d) (oldChart K h2) + (fun h => oldOwner_injective K h2 d h) gauges + (fun j => dataInput K h2 j (s.2.1 j)) + (fun h => oldInput K h2 h (bank h)) (hostPayload K h2 d s) + (SourceLayouts.dataRole i) a + have hc : oldChart K h2 (SourceLayouts.dataRole i) = + newChart K h2 (SourceLayouts.dataRole i) := SourceLayouts.data_chart_eq K h2 i + rw [hc] at he + exact he + +theorem newRaw_data (gauges : Gauges K) (s : State K h2 d) (i : Data) : + (newRaw K h2 d gauges s (newOwner K h2 d (SourceLayouts.dataRole i))).2 = + dataOutput K h2 i + (PhysicalSourceConnection.physicalData gauges + (fun j => dataInput K h2 j (s.2.1 j)) + (fun h => hostInput h (s.1 h)) i) := by + funext a + exact InvocationPayload.realized_payload (newOwner K h2 d) (newChart K h2) + (fun h => newOwner_injective K h2 d h) gauges + (fun j => dataInput K h2 j (s.2.1 j)) + (fun h => hostInput h (s.1 h)) (tailPayload K h2 d s) + (SourceLayouts.dataRole i) a + +theorem oldRaw_bank (gauges : Gauges K) (s : State K h2 d) + (bank : Host → Streams K) (h : Host) : + (oldRaw K h2 d gauges s bank (oldOwner K h2 d (SourceLayouts.hostRole h))).2 = + oldOutput K h2 h + (PhysicalSourceConnection.physicalHelpers gauges + (fun j => dataInput K h2 j (s.2.1 j)) + (fun j => oldInput K h2 j (bank j)) h) := by + funext a + exact InvocationPayload.realized_payload (oldOwner K h2 d) (oldChart K h2) + (fun he => oldOwner_injective K h2 d he) gauges + (fun j => dataInput K h2 j (s.2.1 j)) + (fun j => oldInput K h2 j (bank j)) (hostPayload K h2 d s) + (SourceLayouts.hostRole h) a + +theorem oldRaw_host (gauges : Gauges K) (s : State K h2 d) + (bank : Host → Streams K) (h : Host) : + (oldRaw K h2 d gauges s bank (hostOwner K h2 d h)).2 = + fun a => s.1 h ((hostChart K h2 h).inverse a) := by + exact (SourceRaw.other_payload_preserved (oldOwner K h2 d) (oldChart K h2) + gauges (oldPayload K h2 d s bank) (hostOwner K h2 d h) + (host_not_old K h2 d h)).trans (oldPayload_host K h2 d s bank h) + +theorem newRaw_host (gauges : Gauges K) (s : State K h2 d) (h : Host) + (a : WholeHosting.Address SourceOwnership.Axis K) : + (newRaw K h2 d gauges s (hostOwner K h2 d h)).2 ((hostChart K h2 h).forward a) = + PhysicalSourceConnection.scatterHost h + (PhysicalSourceConnection.physicalHelpers gauges + (fun j => dataInput K h2 j (s.2.1 j)) + (fun j => hostInput j (s.1 j)) h) a := by + have he := InvocationPayload.realized_payload (newOwner K h2 d) (newChart K h2) + (fun he => newOwner_injective K h2 d he) gauges + (fun j => dataInput K h2 j (s.2.1 j)) + (fun j => hostInput j (s.1 j)) (tailPayload K h2 d s) + (SourceLayouts.hostRole h) ((hostChart K h2 h).forward a) + have hc : (newChart K h2 (SourceLayouts.hostRole h)).inverse + ((hostChart K h2 h).forward a) = + SourceOwnership.unindex (SourceOwnership.tag (role h)) a := by + exact (SourceLayouts.host_chart_inverse K h2 h _).trans + (congrArg (SourceOwnership.unindex (SourceOwnership.tag (role h))) + ((hostChart K h2 h).inverse_forward a)) + rw [hc] at he + exact he + +theorem oldRaw_outside (gauges : Gauges K) (s : State K h2 d) + (bank : Host → Streams K) (t : TailKey K h2 d) : + (oldRaw K h2 d gauges s bank t.val).2 = s.2.2 t := + (SourceRaw.other_payload_preserved (oldOwner K h2 d) (oldChart K h2) + gauges (oldPayload K h2 d s bank) t.val t.property.1).trans + (oldPayload_outside K h2 d s bank t) + +theorem newRaw_outside (gauges : Gauges K) (s : State K h2 d) + (t : TailKey K h2 d) : (newRaw K h2 d gauges s t.val).2 = s.2.2 t := + (SourceRaw.other_payload_preserved (newOwner K h2 d) (newChart K h2) + gauges (newPayload K h2 d s) t.val t.property.2).trans + (newPayload_outside K h2 d s t) + +/-- Equality includes the actual old-bank outputs as well as all retained +rows. No dirty-bank output is silently removed from this correspondence. -/ +theorem oldResult_framed (gauges : Gauges K) (s : State K h2 d) + (bank : Host → Streams K) : + oldResult K h2 d gauges (s, bank) = + PhysicalSourceConnection.original gauges (dataInput K h2) (dataOutput K h2) + (oldInput K h2) (oldOutput K h2) (s, bank) := by + apply Prod.ext + · apply Prod.ext + · funext h a + exact (congrFun (oldRaw_host K h2 d gauges s bank h) + ((hostChart K h2 h).forward a)).trans + (congrArg (s.1 h) ((hostChart K h2 h).inverse_forward a)) + · apply Prod.ext + · funext i + exact oldRaw_data K h2 d gauges s bank i + · funext t + exact oldRaw_outside K h2 d gauges s bank t + · funext h + exact oldRaw_bank K h2 d gauges s bank h + +theorem newResult_framed (gauges : Gauges K) (s : State K h2 d) (bank : Unit) : + newResult K h2 d gauges (s, bank) = + PhysicalSourceConnection.relocated gauges (dataInput K h2) (dataOutput K h2) + (s, bank) := by + apply Prod.ext + · apply Prod.ext + · funext h a + exact newRaw_host K h2 d gauges s h a + · apply Prod.ext + · funext i + exact newRaw_data K h2 d gauges s i + · funext t + exact newRaw_outside K h2 d gauges s t + · rfl + +end SourceInvocation diff --git a/research/lean-multi-host-source/SourceInvocationState.lean b/research/lean-multi-host-source/SourceInvocationState.lean new file mode 100644 index 0000000000..2d1d98831b --- /dev/null +++ b/research/lean-multi-host-source/SourceInvocationState.lean @@ -0,0 +1,135 @@ +import SourceLayouts +import InvocationPayload + +/-! Concrete raw input and output layouts for the single selected call. +Both embeddings expose every retained host, all data and the entire exterior +of the union of the two active owner images. The old bank is an arbitrary +separate input and an actual returned output. This common universe is a +local comparison device, not a global allocation or bank-renumbering claim. -/ +namespace SourceInvocation +open SourceConnection FramedReplay + +abbrev Slot (K : Type) := Nat × (SourceOwnership.Vec K → SourceOwnership.Vec K) +abbrev RawPayload (K : Type) := Slot K → Streams K +abbrev Gauges (K : Type) := Nat → Gauge (WholeHosting.Address SourceOwnership.Axis K) + +variable (K : Type) [Field K] (h2 : (2 : K) ≠ 0) +variable (d : SourceOwnership.Vec K ≃ SourceOwnership.Vec K) + +def oldOwner := ParentOwnership.sourceActiveOwner K h2 d +def newOwner := SourceOwnership.sourceActiveOwner K h2 d +def oldChart := ParentOwnership.sourceActiveAddressChart K h2 +def newChart := SourceOwnership.sourceActiveAddressChart K h2 + +def hostOwner (h : Host) : Slot K := newOwner K h2 d (SourceLayouts.hostRole h) +def hostChart (h : Host) := SourceOwnership.familyAddressChart K h2 + (SourceOwnership.family (role h)) + +def Outside (p : Slot K) : Prop := + (∀ r, p ≠ oldOwner K h2 d r) ∧ (∀ r, p ≠ newOwner K h2 d r) +abbrev TailKey := {p : Slot K // Outside K h2 d p} +abbrev Tail := TailKey K h2 d → Streams K +abbrev State := MultiHosting.WindowState Host SourceOwnership.Axis K Bool + (Retained K (Tail K h2 d)) + +noncomputable def tailPayload (s : State K h2 d) : RawPayload K := by + classical + exact fun p => if hp : Outside K h2 d p then s.2.2 ⟨p, hp⟩ else fun _ => false + +noncomputable def hostPayload (s : State K h2 d) : RawPayload K := + InvocationPayload.extend (hostOwner K h2 d) + (fun h a => s.1 h ((hostChart K h2 h).inverse a)) (tailPayload K h2 d s) + +def dataInput (i : Data) (v : Streams K) : Streams K := + fun a => v ((newChart K h2 (SourceLayouts.dataRole i)).forward a) +def dataOutput (i : Data) (v : Streams K) : Streams K := + fun a => v ((newChart K h2 (SourceLayouts.dataRole i)).inverse a) +def oldInput (h : Host) (v : Streams K) : Streams K := + fun a => v ((oldChart K h2 (SourceLayouts.hostRole h)).forward a) +def oldOutput (h : Host) (v : Streams K) : Streams K := + fun a => v ((oldChart K h2 (SourceLayouts.hostRole h)).inverse a) + +noncomputable def oldPayload (s : State K h2 d) (bank : Host → Streams K) : RawPayload K := + InvocationPayload.realize (oldOwner K h2 d) (oldChart K h2) + (packed (fun i => dataInput K h2 i (s.2.1 i)) + (fun h => oldInput K h2 h (bank h))) (hostPayload K h2 d s) + +noncomputable def newPayload (s : State K h2 d) : RawPayload K := + InvocationPayload.realize (newOwner K h2 d) (newChart K h2) + (packed (fun i => dataInput K h2 i (s.2.1 i)) + (fun h => hostInput h (s.1 h))) (tailPayload K h2 d s) + +noncomputable def oldRaw (gauges : Gauges K) (s : State K h2 d) (bank : Host → Streams K) := + SourceRaw.final (oldOwner K h2 d) (oldChart K h2) gauges (oldPayload K h2 d s bank) +noncomputable def newRaw (gauges : Gauges K) (s : State K h2 d) := + SourceRaw.final (newOwner K h2 d) (newChart K h2) gauges (newPayload K h2 d s) + +noncomputable def oldResult (gauges : Gauges K) + (sb : State K h2 d × (Host → Streams K)) : State K h2 d × (Host → Streams K) := + let raw := oldRaw K h2 d gauges sb.1 sb.2 + ((fun h a => (raw (hostOwner K h2 d h)).2 ((hostChart K h2 h).forward a), + (fun i => (raw (oldOwner K h2 d (SourceLayouts.dataRole i))).2, + fun t => (raw t.val).2)), + fun h => (raw (oldOwner K h2 d (SourceLayouts.hostRole h))).2) + +noncomputable def newResult (gauges : Gauges K) + (sb : State K h2 d × Unit) : State K h2 d × Unit := + let raw := newRaw K h2 d gauges sb.1 + ((fun h a => (raw (hostOwner K h2 d h)).2 ((hostChart K h2 h).forward a), + (fun i => (raw (newOwner K h2 d (SourceLayouts.dataRole i))).2, + fun t => (raw t.val).2)), sb.2) + +theorem oldOwner_injective : Function.Injective (oldOwner K h2 d) := + ParentOwnership.sourceActiveOwner_injective K h2 d +theorem newOwner_injective : Function.Injective (newOwner K h2 d) := + SourceOwnership.sourceActiveOwner_injective K h2 d + +theorem hostOwner_injective : Function.Injective (hostOwner K h2 d) := by + intro r s h + have he := newOwner_injective K h2 d h + apply Fin.ext + have hv := congrArg Fin.val he + change 240 + r.val = 240 + s.val at hv + omega + +theorem host_not_old (h : Host) (r : SourceRaw.Role) : + hostOwner K h2 d h ≠ oldOwner K h2 d r := by + exact fun he => SourceLayouts.parent_owner_ne_host K h2 d r h he.symm + +theorem tailPayload_outside (s : State K h2 d) (t : TailKey K h2 d) : + tailPayload K h2 d s t.val = s.2.2 t := by + classical + simp only [tailPayload, dif_pos t.property] + +theorem hostPayload_host (s : State K h2 d) (h : Host) : + hostPayload K h2 d s (hostOwner K h2 d h) = + fun a => s.1 h ((hostChart K h2 h).inverse a) := + InvocationPayload.extend_owner _ (fun he => hostOwner_injective K h2 d he) _ _ h + +theorem hostPayload_outside (s : State K h2 d) (t : TailKey K h2 d) : + hostPayload K h2 d s t.val = s.2.2 t := by + rw [hostPayload, InvocationPayload.extend_outside] + · exact tailPayload_outside K h2 d s t + · intro h + exact t.property.2 (SourceLayouts.hostRole h) + +theorem oldPayload_host (s : State K h2 d) (bank : Host → Streams K) (h : Host) : + oldPayload K h2 d s bank (hostOwner K h2 d h) = + fun a => s.1 h ((hostChart K h2 h).inverse a) := by + rw [oldPayload, InvocationPayload.realize, InvocationPayload.extend_outside] + · exact hostPayload_host K h2 d s h + · exact host_not_old K h2 d h + +theorem oldPayload_outside (s : State K h2 d) (bank : Host → Streams K) + (t : TailKey K h2 d) : oldPayload K h2 d s bank t.val = s.2.2 t := by + rw [oldPayload, InvocationPayload.realize, InvocationPayload.extend_outside] + · exact hostPayload_outside K h2 d s t + · exact t.property.1 + +theorem newPayload_outside (s : State K h2 d) (t : TailKey K h2 d) : + newPayload K h2 d s t.val = s.2.2 t := by + rw [newPayload, InvocationPayload.realize, InvocationPayload.extend_outside] + · exact tailPayload_outside K h2 d s t + · exact t.property.2 + +end SourceInvocation diff --git a/research/lean-multi-host-source/SourceLayouts.lean b/research/lean-multi-host-source/SourceLayouts.lean new file mode 100644 index 0000000000..f39a13d4d7 --- /dev/null +++ b/research/lean-multi-host-source/SourceLayouts.lean @@ -0,0 +1,93 @@ +import ParentOwnership +import SourceConnection + +/-! +Relations between the two literal owner layouts for the selected invocation. +The 240 data owners and their actual route charts agree. Every one of the +747 hosted helper owners lies outside the entire original active owner +image, including its private temporary. No descriptor-uniqueness premise +or assumed physical nonaliasing is used. +Apache-2.0. Prepared with substantial OpenAI Codex assistance. +-/ +namespace SourceLayouts +open SourceConnection + +def dataRole (i : Data) : SourceOwnership.ActiveRole := ⟨i.val, by omega⟩ +def hostRole (h : Host) : SourceOwnership.ActiveRole := ⟨240 + h.val, by omega⟩ + +theorem data_owner_eq (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (d : SourceOwnership.Vec K ≃ SourceOwnership.Vec K) (i : Data) : + ParentOwnership.sourceActiveOwner K h2 d (dataRole i) = + SourceOwnership.sourceActiveOwner K h2 d (dataRole i) := by + have hi : (dataRole i).val < 987 := by simp only [dataRole]; omega + have hid : (dataRole i).val < 240 := i.isLt + simp only [ParentOwnership.sourceActiveOwner, SourceOwnership.sourceActiveOwner, + SourceOwnership.activeOwner, dif_pos hi, + ParentOwnership.physicalOwner, ParentOwnership.owner, + SourceOwnership.physicalOwner, SourceOwnership.owner, + ParentOwnership.sigmaInverse, SourceOwnership.sigmaInverse, if_pos hid, + ParentOwnership.sourceDataCharts] + rw [ParentOwnership.family_data_general _ hid, + SourceOwnership.family_data_general _ hid] + +theorem data_chart_eq (K : Type) [Field K] (h2 : (2 : K) ≠ 0) (i : Data) : + ParentOwnership.sourceActiveAddressChart K h2 (dataRole i) = + SourceOwnership.sourceActiveAddressChart K h2 (dataRole i) := by + have hi : (dataRole i).val < 987 := by simp only [dataRole]; omega + have hid : (dataRole i).val < 240 := i.isLt + simp only [ParentOwnership.sourceActiveAddressChart, + SourceOwnership.sourceActiveAddressChart, ParentOwnership.sourceActiveChart, + SourceOwnership.sourceActiveChart, ParentOwnership.sourceActiveSigma, + SourceOwnership.activeSigma, dif_pos hi, ParentOwnership.actualSigma, + SourceOwnership.actualSigma, if_pos hid, ParentOwnership.sourceDataCharts] + +theorem host_family (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (d : SourceOwnership.Vec K ≃ SourceOwnership.Vec K) (h : Host) : + (SourceOwnership.sourceActiveOwner K h2 d (hostRole h)).1 = + SourceOwnership.family (role h) := by + have hh : (hostRole h).val < 987 := by simp only [hostRole]; omega + simp only [SourceOwnership.sourceActiveOwner, SourceOwnership.activeOwner, + dif_pos hh, SourceOwnership.physicalOwner, SourceOwnership.owner] + rfl + +theorem parent_owner_ne_host (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (d : SourceOwnership.Vec K ≃ SourceOwnership.Vec K) + (r : ParentOwnership.ActiveRole) (h : Host) : + ParentOwnership.sourceActiveOwner K h2 d r ≠ + SourceOwnership.sourceActiveOwner K h2 d (hostRole h) := by + have hr : 240 ≤ (role h).val := by simp only [role]; omega + have hf := SourceOwnership.helper_range (role h) hr + have hn := ParentOwnership.sourceActiveOwner_avoids_host_families K h2 d r + (SourceOwnership.family (role h)) hf.1 (by omega) + intro he + apply hn + exact (congrArg Prod.fst he).trans (host_family K h2 d h) + +theorem host_ne_parent_owner (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (d : SourceOwnership.Vec K ≃ SourceOwnership.Vec K) + (h : Host) (r : ParentOwnership.ActiveRole) : + SourceOwnership.sourceActiveOwner K h2 d (hostRole h) ≠ + ParentOwnership.sourceActiveOwner K h2 d r := + Ne.symm (parent_owner_ne_host K h2 d r h) + +theorem host_chart_forward (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (h : Host) (a : WholeHosting.Address SourceOwnership.Axis K) : + (SourceOwnership.sourceActiveAddressChart K h2 (hostRole h)).forward a = + (SourceOwnership.familyAddressChart K h2 (SourceOwnership.family (role h))).forward + (SourceOwnership.reindex (SourceOwnership.tag (role h)) a) := by + exact SourceOwnership.helper_address_forward K h2 (hostRole h) + (by simp only [hostRole]; omega) (by simp only [hostRole]; omega) a + +theorem host_chart_inverse (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (h : Host) (a : WholeHosting.Address SourceOwnership.Axis K) : + (SourceOwnership.sourceActiveAddressChart K h2 (hostRole h)).inverse a = + SourceOwnership.unindex (SourceOwnership.tag (role h)) + ((SourceOwnership.familyAddressChart K h2 (SourceOwnership.family (role h))).inverse a) := by + exact SourceOwnership.helper_address_inverse K h2 (hostRole h) + (by simp only [hostRole]; omega) (by simp only [hostRole]; omega) a + +#print axioms data_owner_eq +#print axioms data_chart_eq +#print axioms parent_owner_ne_host + +end SourceLayouts diff --git a/research/lean-multi-host-source/SourceMoveGeometry.lean b/research/lean-multi-host-source/SourceMoveGeometry.lean new file mode 100644 index 0000000000..840443f923 --- /dev/null +++ b/research/lean-multi-host-source/SourceMoveGeometry.lean @@ -0,0 +1,327 @@ +import FrameMoveData +import FrameLabelData +import SelectedGeometry +import FrameTraceRoutes + +/-! +The actual MOVE records execute the source operation D_(Pnew-Pold). +Every used absorption equation is selected by membership in the literal +19,002-event word. The common stage-2 exterior swap E2 is present in the +gauges and cancels explicitly. No payload is assumed zero or independent. + +The full replay equality below replaces MOVE by its matrix residual action +and COPY by the checked full-local-eight-coordinate transport. +The native-step equality additionally includes conjugation by the common +invocation chart d; it retains every physical stream other than the target. +Apache-2.0. Prepared with substantial OpenAI Codex assistance. +-/ +namespace SourceMoveGeometry +open FrameGeometry SourceFrameMoves +open scoped Matrix BigOperators +set_option maxRecDepth 100000 +set_option maxHeartbeats 0 + +/-- Both nesting equations follow from the checked pair of this MOVE. -/ +theorem move_projectors (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (e : FrameTrace.Entry) (he : e ∈ SourceFrameTrace.forward) (hop : e.scalar.op = 0) : + projector K (oldIndex e) * projector K (newIndex e) = projector K (oldIndex e) ∧ + projector K (newIndex e) * projector K (oldIndex e) = projector K (oldIndex e) := by + have h := move_absorbs e he hop + constructor + · apply normalized_absorption K h2 + ext i j + simpa [Matrix.mul_apply, Fin.sum_univ_succ, Matrix.smul_apply, dot8, scaledMatrix] using h.1 i j + · apply normalized_absorption K h2 + ext i j + simpa [Matrix.mul_apply, Fin.sum_univ_succ, Matrix.smul_apply, dot8, scaledMatrix] using h.2 i j + +/-- D of the new-minus-old local projector, identity on the other 56 axes. -/ +def residual64 (K : Type) [Field K] (e : FrameTrace.Entry) : + AddressPairs.Vectors (Fin 64) K → AddressPairs.Vectors (Fin 64) K := + liftPair (partialSwap (projector K (newIndex e) - projector K (oldIndex e))) + +theorem move_stage2_relative (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (e : FrameTrace.Entry) (he : e ∈ SourceFrameTrace.forward) (hop : e.scalar.op = 0) + (p : AddressPairs.Vectors (Fin 64) K) : + (gaugeStage2 K h2 (oldIndex e)).forward + ((gaugeStage2 K h2 (newIndex e)).inverse p) = residual64 K e p := by + rw [stage2_relative_transport] + change liftPair (partialSwap (projector K (oldIndex e))) + (liftPair (partialSwap (projector K (newIndex e))) p) = _ + rw [liftPair_comp] + have h : partialSwap (projector K (oldIndex e)) ∘ + partialSwap (projector K (newIndex e)) = + partialSwap (projector K (newIndex e) - projector K (oldIndex e)) := by + funext q + exact partialSwap_nested_reverse _ _ (move_projectors K h2 e he hop).1 q + rw [h] + rfl + +def residualAddress (K : Type) [Field K] (e : FrameTrace.Entry) + (a : PhysicalSourceConnection.Address64 K) : PhysicalSourceConnection.Address64 K := + AddressPairs.join (residual64 K e (AddressPairs.split a)) + +/-- Exact relative map used by the selected source gauge provider. -/ +theorem move_relative (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (e : FrameTrace.Entry) (he : e ∈ SourceFrameTrace.forward) (hop : e.scalar.op = 0) + (a : PhysicalSourceConnection.Address64 K) : + (SelectedGeometry.gauges K h2 e.oldFrame).forward + ((SelectedGeometry.gauges K h2 e.newFrame).inverse a) = residualAddress K e a := by + change (AddressPairs.gauge (gaugeStage2 K h2 (oldIndex e))).forward + ((AddressPairs.gauge (gaugeStage2 K h2 (newIndex e))).inverse a) = _ + rw [AddressPairs.relative_gauge, move_stage2_relative K h2 e he hop] + rfl + +def fullSwap64 (K : Type) : AddressPairs.Vectors (Fin 64) K → AddressPairs.Vectors (Fin 64) K := + liftPair (fun p => (p.2, p.1)) + +def fullSwapAddress (K : Type) (a : PhysicalSourceConnection.Address64 K) := + AddressPairs.join (fullSwap64 K (AddressPairs.split a)) + +theorem copy_stage2_relative (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (p : AddressPairs.Vectors (Fin 64) K) : + (gaugeStage2 K h2 1).forward ((gaugeStage2 K h2 0).inverse p) = fullSwap64 K p := by + rw [stage2_relative_transport] + change liftPair (partialSwap (projector K 1)) + (liftPair (partialSwap (projector K 0)) p) = _ + rw [liftPair_comp] + have h : partialSwap (projector K 1) ∘ partialSwap (projector K 0) = + fun p => (p.2, p.1) := by + funext q + rw [projector_full K h2, projector_zero K] + apply Prod.ext <;> funext i <;> + simp only [Function.comp_apply, partialSwap, Matrix.zero_mulVec, add_zero, + sub_zero, Matrix.one_mulVec, Pi.add_apply, Pi.sub_apply] <;> ring + rw [h] + rfl + +/-- Actual COPY records have old frame 1 and new frame 0, checked on the +literal word. Their full E2 factors cancel, leaving exactly eight axes. -/ +theorem copy_relative (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (e : FrameTrace.Entry) (he : e ∈ SourceFrameTrace.forward) (hop : e.scalar.op = 2) + (a : PhysicalSourceConnection.Address64 K) : + (SelectedGeometry.gauges K h2 e.oldFrame).forward + ((SelectedGeometry.gauges K h2 e.newFrame).inverse a) = fullSwapAddress K a := by + obtain ⟨ho, hn⟩ := SourceFrameLabels.copy_frames e he hop + rw [ho, hn] + change (AddressPairs.gauge (gaugeStage2 K h2 1)).forward + ((AddressPairs.gauge (gaugeStage2 K h2 0)).inverse a) = _ + rw [AddressPairs.relative_gauge, copy_stage2_relative K h2] + rfl + +/-- The source row and temporary at each actual ERASE use the same full/zero +pair. This identifies the transport appearing in the equality guard. -/ +theorem erase_relative (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (e : FrameTrace.Entry) (he : e ∈ SourceFrameTrace.forward) (hop : e.scalar.op = 3) + (a : PhysicalSourceConnection.Address64 K) : + (SelectedGeometry.gauges K h2 e.oldFrame).forward + ((SelectedGeometry.gauges K h2 e.newFrame).inverse a) = fullSwapAddress K a := by + obtain ⟨ho, hn⟩ := SourceFrameLabels.erase_frames e he hop + rw [ho, hn] + change (AddressPairs.gauge (gaugeStage2 K h2 1)).forward + ((AddressPairs.gauge (gaugeStage2 K h2 0)).inverse a) = _ + rw [AddressPairs.relative_gauge, copy_stage2_relative K h2] + rfl + +def matrixMove (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (s : FramedReplay.Store (PhysicalSourceConnection.Address64 K)) (e : FrameTrace.Entry) := + s.put e.scalar.x (SelectedGeometry.gauges K h2 e.newFrame, + fun a => (s.get e.scalar.x).2 (residualAddress K e a)) + +/-- At a checked occurrence, the old frame is the actual current row frame. +Consequently reframe executes D_(Pnew-Pold) on every arbitrary dirty payload. -/ +theorem physicalStep_move (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (e : FrameTrace.Entry) (he : e ∈ SourceFrameTrace.forward) (hop : e.scalar.op = 0) + (labels : FrameTrace.State) (s : FramedReplay.Store (PhysicalSourceConnection.Address64 K)) + (same : FrameTrace.Matches (SelectedGeometry.gauges K h2) labels s) + (checked : FrameTrace.check labels e = true) : + FramedReplay.physicalStep s (FrameTrace.toPhysical (SelectedGeometry.gauges K h2) e) = + matrixMove K h2 s e := by + have old : labels.frames.get e.scalar.x = e.oldFrame := by + simp only [FrameTrace.check, hop, Bool.and_eq_true, beq_iff_eq] at checked + exact checked.1.2 + have hf := FrameTrace.matches_get _ _ _ same e.scalar.x + rw [old] at hf + simp only [FramedReplay.physicalStep, FrameTrace.toPhysical, hop, Nat.zero_lt_succ, + ↓reduceIte, FramedReplay.reframe, hf, matrixMove] + congr 1 + apply Prod.ext + · rfl + · funext a + exact congrArg (s.get e.scalar.x).2 (move_relative K h2 e he hop a) + +def matrixCopy (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (s : FramedReplay.Store (PhysicalSourceConnection.Address64 K)) (e : FrameTrace.Entry) := + s.put e.scalar.y (SelectedGeometry.gauges K h2 e.newFrame, + fun a => (s.get e.scalar.x).2 (fullSwapAddress K a)) + +/-- Operational COPY equality. Legality also requires the destination to be +blank; SourceFramed.actual_valid proves that separate guard at every COPY. -/ +theorem physicalStep_copy (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (e : FrameTrace.Entry) (he : e ∈ SourceFrameTrace.forward) (hop : e.scalar.op = 2) + (labels : FrameTrace.State) (s : FramedReplay.Store (PhysicalSourceConnection.Address64 K)) + (same : FrameTrace.Matches (SelectedGeometry.gauges K h2) labels s) + (checked : FrameTrace.check labels e = true) : + FramedReplay.physicalStep s (FrameTrace.toPhysical (SelectedGeometry.gauges K h2) e) = + matrixCopy K h2 s e := by + have old : labels.frames.get e.scalar.x = e.oldFrame := by + simp only [FrameTrace.check, hop, Bool.and_eq_true, beq_iff_eq] at checked + omega + have hf := FrameTrace.matches_get _ _ _ same e.scalar.x + rw [old] at hf + simp only [FramedReplay.physicalStep, FrameTrace.toPhysical, hop, Nat.reduceLT, + ↓reduceIte, FramedReplay.reframe, hf, matrixCopy] + congr 1 + apply Prod.ext + · rfl + · funext a + exact congrArg (s.get e.scalar.x).2 (copy_relative K h2 e he hop a) + +/-- The operational replay uses the explicit matrix operation at each MOVE. -/ +def matrixStep (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (s : FramedReplay.Store (PhysicalSourceConnection.Address64 K)) (e : FrameTrace.Entry) := + if e.scalar.op = 0 then matrixMove K h2 s e + else if e.scalar.op = 2 then matrixCopy K h2 s e + else FramedReplay.physicalStep s (FrameTrace.toPhysical (SelectedGeometry.gauges K h2) e) + +def matrixRun (K : Type) [Field K] (h2 : (2 : K) ≠ 0) (es : List FrameTrace.Entry) + (s : FramedReplay.Store (PhysicalSourceConnection.Address64 K)) := + es.foldl (matrixStep K h2) s + +theorem matrix_run_eq (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (es : List FrameTrace.Entry) (members : ∀ e ∈ es, e ∈ SourceFrameTrace.forward) + (labels : FrameTrace.State) (s : FramedReplay.Store (PhysicalSourceConnection.Address64 K)) + (same : FrameTrace.Matches (SelectedGeometry.gauges K h2) labels s) + (checked : FrameTrace.Valid es labels) : + matrixRun K h2 es s = FramedReplay.runPhysical + (es.map (FrameTrace.toPhysical (SelectedGeometry.gauges K h2))) s := by + induction es generalizing labels s with + | nil => rfl + | cons e es ih => + have step : matrixStep K h2 s e = FramedReplay.physicalStep s + (FrameTrace.toPhysical (SelectedGeometry.gauges K h2) e) := by + unfold matrixStep + split + · exact (physicalStep_move K h2 e (members e (by simp)) ‹_› labels s same checked.1).symm + · split + · exact (physicalStep_copy K h2 e (members e (by simp)) ‹_› labels s same checked.1).symm + · rfl + change matrixRun K h2 es (matrixStep K h2 s e) = + FramedReplay.runPhysical (es.map (FrameTrace.toPhysical (SelectedGeometry.gauges K h2))) + (FramedReplay.physicalStep s (FrameTrace.toPhysical (SelectedGeometry.gauges K h2) e)) + rw [step] + exact ih (fun a ha => members a (by simp [ha])) (FrameTrace.next labels e) _ + (FrameTrace.matches_step _ _ _ _ same) checked.2 + +/-- The actual 19,002-event run is the same run with all MOVE/COPY operations +interpreted by their certified matrix operators, for every dirty input. -/ +theorem actual_matrix_run (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + (input : Nat → PhysicalSourceConnection.Address64 K → Bool) : + matrixRun K h2 SourceFrameTrace.forward + (SourceFramed.initial (SelectedGeometry.gauges K h2) input) = + SourceFramed.final (SelectedGeometry.gauges K h2) input := + matrix_run_eq K h2 _ (fun _ h => h) SourceFrameTrace.state0 _ + (SourceFramed.initial_matches _ _) SourceFrameTrace.forward_valid + +/-- Native physical MOVE: pull back the dirty target by d D_(new-old) d⁻¹. +Only the target stream changes; the frame metadata records the new frame. -/ +noncomputable def nativeMatrixMove (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + {R S : Type} (owner : R → S) (d : FramedReplay.Gauge (PhysicalSourceConnection.Address64 K)) + (native : OwnerTransport.Raw S (PhysicalSourceConnection.Address64 K)) (x : R) + (e : FrameTrace.Entry) : OwnerTransport.Raw S (PhysicalSourceConnection.Address64 K) := by + classical + exact fun s => if s = owner x then + (SelectedGeometry.gauges K h2 e.newFrame, fun a => (native s).2 + (d.forward (residualAddress K e (d.inverse a)))) + else native s + +/-- The owner-routing interpreter's MOVE is exactly the physical conjugate, +not an abstract reframe operation disconnected from the source projector. -/ +theorem nativeStep_move (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + {R S : Type} (owner : R → S) (d : FramedReplay.Gauge (PhysicalSourceConnection.Address64 K)) + (native : OwnerTransport.Raw S (PhysicalSourceConnection.Address64 K)) (x y : R) + (e : FrameTrace.Entry) (he : e ∈ SourceFrameTrace.forward) (hop : e.scalar.op = 0) + (old : (native (owner x)).1 = SelectedGeometry.gauges K h2 e.oldFrame) : + OwnerTransport.nativeStep owner d native e.scalar.op x y e.scalar.odd + (SelectedGeometry.gauges K h2 e.newFrame) = nativeMatrixMove K h2 owner d native x e := by + classical + funext s + by_cases hs : s = owner x + · subst s + simp only [OwnerTransport.nativeStep, hop, OwnerTransport.nativeTransport, + nativeMatrixMove, ↓reduceIte, old] + apply Prod.ext + · rfl + · funext a + exact congrArg (fun b => (native (owner x)).2 (d.forward b)) + (move_relative K h2 e he hop (d.inverse a)) + · simp only [OwnerTransport.nativeStep, hop, OwnerTransport.nativeTransport, + nativeMatrixMove, if_neg hs] + +/-- The same equality for the exact finite-role event encoding consumed by +the checked source native run. Membership ranges were checked separately by +FrameTraceRoutes; the encoded role below is the actual target role. -/ +theorem nativeRoute_move (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + {S : Type} (owner : Fin 988 → S) + (d : FramedReplay.Gauge (PhysicalSourceConnection.Address64 K)) + (native : OwnerTransport.Raw S (PhysicalSourceConnection.Address64 K)) + (e : FrameTrace.Entry) (he : e ∈ SourceFrameTrace.forward) (hop : e.scalar.op = 0) + (old : (native (owner (SourceFrameTrace.toRoute (SelectedGeometry.gauges K h2) e).x)).1 = + SelectedGeometry.gauges K h2 e.oldFrame) : + let routed := SourceFrameTrace.toRoute (SelectedGeometry.gauges K h2) e + OwnerTransport.nativeStep owner d native routed.op routed.x routed.y routed.odd routed.newFrame = + nativeMatrixMove K h2 owner d native routed.x e := by + dsimp only + have h := nativeStep_move K h2 owner d native + (SourceFrameTrace.toRoute (SelectedGeometry.gauges K h2) e).x + (SourceFrameTrace.toRoute (SelectedGeometry.gauges K h2) e).y e he hop old + simpa only [SourceFrameTrace.toRoute, hop, Nat.zero_lt_succ, ↓reduceIte] using h + +noncomputable def nativeMatrixCopy (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + {R S : Type} (owner : R → S) (d : FramedReplay.Gauge (PhysicalSourceConnection.Address64 K)) + (native : OwnerTransport.Raw S (PhysicalSourceConnection.Address64 K)) (x y : R) + (e : FrameTrace.Entry) : OwnerTransport.Raw S (PhysicalSourceConnection.Address64 K) := by + classical + exact fun s => if s = owner y then + (SelectedGeometry.gauges K h2 e.newFrame, fun a => (native (owner x)).2 + (d.forward (fullSwapAddress K (d.inverse a)))) + else native s + +/-- Native COPY is conjugation of the full eight-coordinate swap. The +separate native clean-work guard remains mandatory for a legal COPY. -/ +theorem nativeStep_copy (K : Type) [Field K] (h2 : (2 : K) ≠ 0) + {R S : Type} (owner : R → S) (d : FramedReplay.Gauge (PhysicalSourceConnection.Address64 K)) + (native : OwnerTransport.Raw S (PhysicalSourceConnection.Address64 K)) (x y : R) + (e : FrameTrace.Entry) (he : e ∈ SourceFrameTrace.forward) (hop : e.scalar.op = 2) + (old : (native (owner x)).1 = SelectedGeometry.gauges K h2 e.oldFrame) : + OwnerTransport.nativeStep owner d native e.scalar.op x y e.scalar.odd + (SelectedGeometry.gauges K h2 e.newFrame) = nativeMatrixCopy K h2 owner d native x y e := by + classical + funext s + by_cases hs : s = owner y + · subst s + simp only [OwnerTransport.nativeStep, hop, OwnerTransport.nativeTransport, + nativeMatrixCopy, ↓reduceIte, old] + apply Prod.ext + · rfl + · funext a + exact congrArg (fun b => (native (owner x)).2 (d.forward b)) + (copy_relative K h2 e he hop (d.inverse a)) + · simp only [OwnerTransport.nativeStep, hop, OwnerTransport.nativeTransport, + nativeMatrixCopy, if_neg hs] + +end SourceMoveGeometry + +#print axioms SourceMoveGeometry.move_projectors +#print axioms SourceMoveGeometry.move_stage2_relative +#print axioms SourceMoveGeometry.move_relative +#print axioms SourceMoveGeometry.copy_stage2_relative +#print axioms SourceMoveGeometry.copy_relative +#print axioms SourceMoveGeometry.erase_relative +#print axioms SourceMoveGeometry.physicalStep_move +#print axioms SourceMoveGeometry.physicalStep_copy +#print axioms SourceMoveGeometry.matrix_run_eq +#print axioms SourceMoveGeometry.actual_matrix_run +#print axioms SourceMoveGeometry.nativeStep_move +#print axioms SourceMoveGeometry.nativeRoute_move +#print axioms SourceMoveGeometry.nativeStep_copy diff --git a/research/lean-multi-host-source/SourceNativeInvocation.lean b/research/lean-multi-host-source/SourceNativeInvocation.lean new file mode 100644 index 0000000000..61592703a5 --- /dev/null +++ b/research/lean-multi-host-source/SourceNativeInvocation.lean @@ -0,0 +1,221 @@ +import SourceCommonCover +import SourceInitialPayload +import SourceRawGuards + +/-! The concrete owner-coordinate executions are the literal native +instruction sequence in different coordinates. In particular ADD reads +one native address in both physical streams; COPY/ERASE legality is proved +along that same trajectory. Private scratch uses the explicit cover chart d. +-/ +namespace SourceInvocation +open SourceConnection FramedReplay OwnerTransport +variable (K : Type) [Field K] (h2 : (2 : K) ≠ 0) +variable (d : SourceOwnership.Vec K ≃ SourceOwnership.Vec K) + +noncomputable def nativePayload (cover : Slot K → Gauge (WholeHosting.Address SourceOwnership.Axis K)) + (payload : RawPayload K) : RawPayload K := fun s a => payload s ((cover s).inverse a) + +def nativeGauge := AddressPairs.gauge (SourceOwnership.pairGauge d) + +noncomputable def oldNative (gauges : Gauges K) (s : State K h2 d) (bank : Host → Streams K) := + runNative (oldOwner K h2 d) (nativeGauge K d) + (SourceFrameTrace.forward.map (SourceFrameTrace.toRoute gauges)) + (SourceRaw.initial (oldOwner K h2 d) gauges + (nativePayload K (commonNativeCover K h2 d) (oldPayload K h2 d s bank))) + +noncomputable def newNative (gauges : Gauges K) (s : State K h2 d) := + runNative (newOwner K h2 d) (nativeGauge K d) + (SourceFrameTrace.forward.map (SourceFrameTrace.toRoute gauges)) + (SourceRaw.initial (newOwner K h2 d) gauges + (nativePayload K (commonNativeCover K h2 d) (newPayload K h2 d s))) + +omit [Field K] in +theorem native_payload_roundtrip + (cover : Slot K → Gauge (WholeHosting.Address SourceOwnership.Axis K)) (payload : RawPayload K) : + (fun s a => nativePayload K cover payload s ((cover s).forward a)) = payload := by + funext s a + exact congrArg (payload s) ((cover s).inverse_forward a) + +theorem old_native_realization (gauges : Gauges K) (s : State K h2 d) + (bank : Host → Streams K) : + oldRaw K h2 d gauges s bank = + fromNative (commonNativeCover K h2 d) + (oldNative K h2 d gauges s bank) := by + have h := SourceRawGuards.native_run_refines (oldOwner K h2 d) (oldChart K h2) + gauges (commonNativeCover K h2 d) (nativeGauge K d) + (old_common_cover K h2 d) + (nativePayload K (commonNativeCover K h2 d) (oldPayload K h2 d s bank)) + rw [native_payload_roundtrip] at h + exact h + +theorem new_native_realization (gauges : Gauges K) (s : State K h2 d) : + newRaw K h2 d gauges s = + fromNative (commonNativeCover K h2 d) + (newNative K h2 d gauges s) := by + have h := SourceRawGuards.native_run_refines (newOwner K h2 d) (newChart K h2) + gauges (commonNativeCover K h2 d) (nativeGauge K d) + (new_common_cover K h2 d) + (nativePayload K (commonNativeCover K h2 d) (newPayload K h2 d s)) + rw [native_payload_roundtrip] at h + exact h + +theorem old_native_clean (gauges : Gauges K) (s : State K h2 d) (bank : Host → Streams K) : + SourceRawGuards.NativeCleanRun (oldOwner K h2 d) (nativeGauge K d) + (SourceFrameTrace.forward.map (SourceFrameTrace.toRoute gauges)) + (SourceRaw.initial (oldOwner K h2 d) gauges + (nativePayload K (commonNativeCover K h2 d) (oldPayload K h2 d s bank))) := + SourceRawGuards.actual_native_clean (oldOwner K h2 d) (oldChart K h2) + (fun h => oldOwner_injective K h2 d h) gauges + (commonNativeCover K h2 d) (nativeGauge K d) + (old_common_cover K h2 d) _ + +theorem new_native_clean (gauges : Gauges K) (s : State K h2 d) : + SourceRawGuards.NativeCleanRun (newOwner K h2 d) (nativeGauge K d) + (SourceFrameTrace.forward.map (SourceFrameTrace.toRoute gauges)) + (SourceRaw.initial (newOwner K h2 d) gauges + (nativePayload K (commonNativeCover K h2 d) (newPayload K h2 d s))) := + SourceRawGuards.actual_native_clean (newOwner K h2 d) (newChart K h2) + (fun h => newOwner_injective K h2 d h) gauges + (commonNativeCover K h2 d) (nativeGauge K d) + (new_common_cover K h2 d) _ + +theorem old_native_temporary_restored (gauges : Gauges K) (s : State K h2 d) + (bank : Host → Streams K) : + (oldNative K h2 d gauges s bank (oldOwner K h2 d SourceRaw.privateRow)).2 = fun _ => false := + SourceRawGuards.native_private_restored (oldOwner K h2 d) (oldChart K h2) + (fun h => oldOwner_injective K h2 d h) gauges + (commonNativeCover K h2 d) (nativeGauge K d) + (old_common_cover K h2 d) _ + +theorem new_native_temporary_restored (gauges : Gauges K) (s : State K h2 d) : + (newNative K h2 d gauges s (newOwner K h2 d SourceRaw.privateRow)).2 = fun _ => false := + SourceRawGuards.native_private_restored (newOwner K h2 d) (newChart K h2) + (fun h => newOwner_injective K h2 d h) gauges + (commonNativeCover K h2 d) (nativeGauge K d) + (new_common_cover K h2 d) _ + +/-- The original and hosted native executions start from the same dirty +physical payload at every retained host. A single cover chart is essential +here; independent extensions outside each active image would not suffice. -/ +theorem native_shared_host_input (s : State K h2 d) (bank : Host → Streams K) (h : Host) : + nativePayload K (commonNativeCover K h2 d) (oldPayload K h2 d s bank) + (hostOwner K h2 d h) = + nativePayload K (commonNativeCover K h2 d) (newPayload K h2 d s) + (hostOwner K h2 d h) := by + funext a + exact congrFun (shared_host_input K h2 d s bank h) _ + +theorem native_shared_data_input (s : State K h2 d) (bank : Host → Streams K) (i : Data) : + nativePayload K (commonNativeCover K h2 d) (oldPayload K h2 d s bank) + (oldOwner K h2 d (SourceLayouts.dataRole i)) = + nativePayload K (commonNativeCover K h2 d) (newPayload K h2 d s) + (newOwner K h2 d (SourceLayouts.dataRole i)) := by + have ho : oldOwner K h2 d (SourceLayouts.dataRole i) = + newOwner K h2 d (SourceLayouts.dataRole i) := SourceLayouts.data_owner_eq K h2 d i + funext a + change oldPayload K h2 d s bank _ ((commonNativeCover K h2 d _).inverse a) = + newPayload K h2 d s _ ((commonNativeCover K h2 d _).inverse a) + rw [oldPayload_data, newPayload_data, ho] + +theorem native_shared_tail_input (s : State K h2 d) (bank : Host → Streams K) + (t : TailKey K h2 d) : + nativePayload K (commonNativeCover K h2 d) (oldPayload K h2 d s bank) t.val = + nativePayload K (commonNativeCover K h2 d) (newPayload K h2 d s) t.val := by + funext a + exact congrFun ((oldPayload_outside K h2 d s bank t).trans + (newPayload_outside K h2 d s t).symm) _ + +/-- The private-row initialization also preserves those shared retained +inputs. This statement concerns the actual initialized native states. -/ +theorem initialized_native_host_input (gauges : Gauges K) + (s : State K h2 d) (bank : Host → Streams K) (h : Host) : + (SourceRaw.initial (oldOwner K h2 d) gauges + (nativePayload K (commonNativeCover K h2 d) (oldPayload K h2 d s bank)) + (hostOwner K h2 d h)).2 = + (SourceRaw.initial (newOwner K h2 d) gauges + (nativePayload K (commonNativeCover K h2 d) (newPayload K h2 d s)) + (hostOwner K h2 d h)).2 := by + have hn : hostOwner K h2 d h ≠ newOwner K h2 d SourceRaw.privateRow := by + intro he + have hv := congrArg Fin.val (newOwner_injective K h2 d he) + change 240 + h.val = 987 at hv + omega + exact (OwnerTransport.initialRaw_other (oldOwner K h2 d) (SourceRaw.frames gauges) + SourceRaw.privateRow _ _ (host_not_old K h2 d h SourceRaw.privateRow)).trans + ((native_shared_host_input K h2 d s bank h).trans + (OwnerTransport.initialRaw_other (newOwner K h2 d) (SourceRaw.frames gauges) + SourceRaw.privateRow _ _ hn).symm) + +theorem initialized_native_data_input (gauges : Gauges K) + (s : State K h2 d) (bank : Host → Streams K) (i : Data) : + (SourceRaw.initial (oldOwner K h2 d) gauges + (nativePayload K (commonNativeCover K h2 d) (oldPayload K h2 d s bank)) + (oldOwner K h2 d (SourceLayouts.dataRole i))).2 = + (SourceRaw.initial (newOwner K h2 d) gauges + (nativePayload K (commonNativeCover K h2 d) (newPayload K h2 d s)) + (newOwner K h2 d (SourceLayouts.dataRole i))).2 := by + have ho : oldOwner K h2 d (SourceLayouts.dataRole i) ≠ + oldOwner K h2 d SourceRaw.privateRow := by + intro he + have hv := congrArg Fin.val (oldOwner_injective K h2 d he) + change i.val = 987 at hv + omega + have hn : newOwner K h2 d (SourceLayouts.dataRole i) ≠ + newOwner K h2 d SourceRaw.privateRow := by + intro he + have hv := congrArg Fin.val (newOwner_injective K h2 d he) + change i.val = 987 at hv + omega + exact (OwnerTransport.initialRaw_other (oldOwner K h2 d) (SourceRaw.frames gauges) + SourceRaw.privateRow _ _ ho).trans + ((native_shared_data_input K h2 d s bank i).trans + (OwnerTransport.initialRaw_other (newOwner K h2 d) (SourceRaw.frames gauges) + SourceRaw.privateRow _ _ hn).symm) + +theorem initialized_native_tail_input (gauges : Gauges K) + (s : State K h2 d) (bank : Host → Streams K) (t : TailKey K h2 d) : + (SourceRaw.initial (oldOwner K h2 d) gauges + (nativePayload K (commonNativeCover K h2 d) (oldPayload K h2 d s bank)) t.val).2 = + (SourceRaw.initial (newOwner K h2 d) gauges + (nativePayload K (commonNativeCover K h2 d) (newPayload K h2 d s)) t.val).2 := by + exact (OwnerTransport.initialRaw_other (oldOwner K h2 d) (SourceRaw.frames gauges) + SourceRaw.privateRow _ _ (t.property.1 SourceRaw.privateRow)).trans + ((native_shared_tail_input K h2 d s bank t).trans + (OwnerTransport.initialRaw_other (newOwner K h2 d) (SourceRaw.frames gauges) + SourceRaw.privateRow _ _ (t.property.2 SourceRaw.privateRow)).symm) + +/-- Native outputs are read in the same fixed retained coordinate charts. +The definition spells out the read-back from the native instruction fold. -/ +noncomputable def oldNativeResult (gauges : Gauges K) + (sb : State K h2 d × (Host → Streams K)) : State K h2 d × (Host → Streams K) := + let raw := fromNative (commonNativeCover K h2 d) (oldNative K h2 d gauges sb.1 sb.2) + ((fun h a => (raw (hostOwner K h2 d h)).2 ((hostChart K h2 h).forward a), + (fun i => (raw (oldOwner K h2 d (SourceLayouts.dataRole i))).2, + fun t => (raw t.val).2)), + fun h => (raw (oldOwner K h2 d (SourceLayouts.hostRole h))).2) + +noncomputable def newNativeResult (gauges : Gauges K) + (sb : State K h2 d × Unit) : State K h2 d × Unit := + let raw := fromNative (commonNativeCover K h2 d) (newNative K h2 d gauges sb.1) + ((fun h a => (raw (hostOwner K h2 d h)).2 ((hostChart K h2 h).forward a), + (fun i => (raw (newOwner K h2 d (SourceLayouts.dataRole i))).2, + fun t => (raw t.val).2)), sb.2) + +theorem oldResult_native (gauges : Gauges K) (s : State K h2 d) (bank : Host → Streams K) : + oldResult K h2 d gauges (s, bank) = oldNativeResult K h2 d gauges (s, bank) := by + exact congrArg (fun raw : Raw (Slot K) (WholeHosting.Address SourceOwnership.Axis K) => + ((fun h a => (raw (hostOwner K h2 d h)).2 ((hostChart K h2 h).forward a), + (fun i => (raw (oldOwner K h2 d (SourceLayouts.dataRole i))).2, + fun t : TailKey K h2 d => (raw t.val).2)), + fun h => (raw (oldOwner K h2 d (SourceLayouts.hostRole h))).2)) + (old_native_realization K h2 d gauges s bank) + +theorem newResult_native (gauges : Gauges K) (s : State K h2 d) (bank : Unit) : + newResult K h2 d gauges (s, bank) = newNativeResult K h2 d gauges (s, bank) := by + exact congrArg (fun raw : Raw (Slot K) (WholeHosting.Address SourceOwnership.Axis K) => + ((fun h a => (raw (hostOwner K h2 d h)).2 ((hostChart K h2 h).forward a), + (fun i => (raw (newOwner K h2 d (SourceLayouts.dataRole i))).2, + fun t : TailKey K h2 d => (raw t.val).2)), bank)) + (new_native_realization K h2 d gauges s) + +end SourceInvocation diff --git a/research/lean-multi-host-source/SourceRaw.lean b/research/lean-multi-host-source/SourceRaw.lean new file mode 100644 index 0000000000..38c282495b --- /dev/null +++ b/research/lean-multi-host-source/SourceRaw.lean @@ -0,0 +1,124 @@ +import SourceFramed +import FrameTraceRoutes +import OwnerTransport + +/-! +Whole-word realization on distinct raw physical owners, with arbitrary +payloads on every original and exterior stream. There is one designated +initially blank private row987. Frame labels are initialized metadata, not +constraints on dirty contents. The final SourceInvocation module supplies +the source-specific owner/chart maps; this module assumes their injectivity. +-/ +namespace SourceRaw +open TreeReplay (Tree) +open FramedReplay OwnerTransport +set_option maxRecDepth 100000 +set_option maxHeartbeats 0 + +abbrev Role := Fin 988 +def privateRow : Role := ⟨987, by decide⟩ + +def frames {X : Type} (gauges : Nat → Gauge X) (r : Role) : Gauge X := + gauges (SourceFrameTrace.state0.frames.get r.val) + +def input {S X : Type} (owner : Role → S) (chart : Role → Gauge X) + (payload : S → X → Bool) (i : Nat) : X → Bool := + if hi : i < 988 then fun a => payload (owner ⟨i, hi⟩) ((chart ⟨i, hi⟩).forward a) + else fun _ => false + +noncomputable def initial {S X : Type} (owner : Role → S) + (gauges : Nat → Gauge X) (payload : S → X → Bool) : Raw S X := + initialRaw owner (frames gauges) privateRow payload + +noncomputable def final {S X : Type} (owner : Role → S) (chart : Role → Gauge X) + (gauges : Nat → Gauge X) (payload : S → X → Bool) : Raw S X := + runRaw owner chart (SourceFrameTrace.forward.map (SourceFrameTrace.toRoute gauges)) + (initial owner gauges payload) + +theorem gather_initial {S X : Type} (owner : Role → S) (chart : Role → Gauge X) + (hinj : ∀ {r s}, owner r = owner s → r = s) + (gauges : Nat → Gauge X) (payload : S → X → Bool) (r : Role) : + gather owner chart (initial owner gauges payload) r = + (SourceFramed.initial gauges (input owner chart payload)).get r.val := by + rw [initial, gather_initialRaw owner chart hinj] + rw [SourceFramed.initial, Tree.get_tabulate 10 _ r.val (by omega)] + by_cases hr : r = privateRow + · subst r + simp only [privateRow, frames, ↓reduceIte, Nat.lt_irrefl] + · have hval : r.val < 987 := by + have hn : r.val ≠ 987 := fun h => hr (Fin.ext h) + omega + simp only [frames, if_neg hr, if_pos hval, input, dif_pos r.isLt] + +/-- Every physical role follows the exact chronological framed source word. +The finite-role projection is an equality of the literal event lists. -/ +theorem gather_final {S X : Type} (owner : Role → S) (chart : Role → Gauge X) + (hinj : ∀ {r s}, owner r = owner s → r = s) + (gauges : Nat → Gauge X) (payload : S → X → Bool) (r : Role) : + gather owner chart (final owner chart gauges payload) r = + (SourceFramed.final gauges (input owner chart payload)).get r.val := by + have h := gather_run_framed owner chart hinj + (SourceFrameTrace.forward.map (SourceFrameTrace.toRoute gauges)) + (initial owner gauges payload) + (SourceFramed.initial gauges (input owner chart payload)) 10 + (Tree.full_tabulate _ _) (by decide) + (gather_initial owner chart hinj gauges payload) r + rw [SourceFrameTrace.route_projection] at h + exact h + +/-- The same execution satisfies every COPY/ERASE guard for arbitrary dirty +payloads, including correlations among original and retained exterior rows. -/ +theorem actual_valid {S X : Type} (owner : Role → S) (chart : Role → Gauge X) + (gauges : Nat → Gauge X) (payload : S → X → Bool) : + FramedReplay.ValidTrace + (SourceFrameTrace.forward.map (FrameTrace.toPhysical gauges)) + (SourceFramed.initial gauges (input owner chart payload)) := + SourceFramed.actual_valid gauges _ + +/-- Exact raw payload endpoint. The inverse chart is the proved scatter +map; all dirty inputs remain universally quantified. -/ +theorem payload_endpoint {S X : Type} (owner : Role → S) (chart : Role → Gauge X) + (hinj : ∀ {r s}, owner r = owner s → r = s) + (gauges : Nat → Gauge X) (payload : S → X → Bool) (r : Role) (a : X) : + (final owner chart gauges payload (owner r)).2 a = + SourceMatrix.endpointPayload + (SourceFramed.normalizedInput gauges (input owner chart payload)) r.val + ((gauges (SourceFrameTrace.state96.frames.get r.val)).inverse + ((chart r).inverse a)) := by + have h := congrArg Prod.snd (gather_final owner chart hinj gauges payload r) + have ha := congrFun h ((chart r).inverse a) + simp only [gather, (chart r).forward_inverse] at ha + rw [ha] + exact SourceFramed.actual_physical_endpoint gauges _ r.val (by omega) _ + +theorem private_restored {S X : Type} (owner : Role → S) (chart : Role → Gauge X) + (hinj : ∀ {r s}, owner r = owner s → r = s) + (gauges : Nat → Gauge X) (payload : S → X → Bool) : + (final owner chart gauges payload (owner privateRow)).2 = fun _ => false := by + funext a + rw [payload_endpoint owner chart hinj gauges payload privateRow a] + rfl + +/-- Every row outside the actual owner image is preserved, including its +payload and metadata. This supplies the retained exterior state. -/ +theorem other_preserved {S X : Type} (owner : Role → S) (chart : Role → Gauge X) + (gauges : Nat → Gauge X) (payload : S → X → Bool) (s : S) + (outside : ∀ r, s ≠ owner r) : + final owner chart gauges payload s = initial owner gauges payload s := + runRaw_other owner chart _ _ s outside + +theorem other_payload_preserved {S X : Type} (owner : Role → S) (chart : Role → Gauge X) + (gauges : Nat → Gauge X) (payload : S → X → Bool) (s : S) + (outside : ∀ r, s ≠ owner r) : + (final owner chart gauges payload s).2 = payload s := by + rw [other_preserved owner chart gauges payload s outside] + exact initialRaw_other owner (frames gauges) privateRow payload s (outside privateRow) + +#print axioms gather_initial +#print axioms gather_final +#print axioms actual_valid +#print axioms payload_endpoint +#print axioms private_restored +#print axioms other_preserved +#print axioms other_payload_preserved +end SourceRaw diff --git a/research/lean-multi-host-source/SourceRawGuards.lean b/research/lean-multi-host-source/SourceRawGuards.lean new file mode 100644 index 0000000000..f3402e09cf --- /dev/null +++ b/research/lean-multi-host-source/SourceRawGuards.lean @@ -0,0 +1,216 @@ +import SourceRaw + +/-! COPY blankness and ERASE uncomputation guards along the actual raw and +native executions. Guards follow each preceding physical output; no fresh +reinitialization or endpoint assumption is inserted between events. -/ +namespace SourceRawGuards +open FramedReplay OwnerTransport +set_option maxRecDepth 100000 +set_option maxHeartbeats 0 + +def RawClean {R S X : Type} (owner : R → S) (chart : R → Gauge X) + (raw : Raw S X) (e : RouteEvent R X) : Prop := + (e.op = 2 → (raw (owner e.y)).2 = fun _ => false) ∧ + (e.op = 3 → ∀ a, (raw (owner e.y)).2 a = + (raw (owner e.x)).2 ((chart e.x).forward + ((raw (owner e.x)).1.forward ((raw (owner e.y)).1.inverse + ((chart e.y).inverse a))))) + +noncomputable def RawCleanRun {R S X : Type} (owner : R → S) (chart : R → Gauge X) : + List (RouteEvent R X) → Raw S X → Prop + | [], _ => True + | e :: es, raw => RawClean owner chart raw e ∧ RawCleanRun owner chart es + (rawStep owner chart raw e.op e.x e.y e.odd e.newFrame) + +theorem raw_clean_of_framed {n : Nat} {S X : Type} (owner : Fin n → S) + (chart : Fin n → Gauge X) (raw : Raw S X) (s : Store X) + (rel : ∀ r, gather owner chart raw r = s.get r.val) + (e : RouteEvent (Fin n) X) (valid : ValidStep s e.framed) : + RawClean owner chart raw e := by + constructor + · intro hop + have hv : decodeRow (s.get e.y.val) = fun _ => false := by + simpa only [ValidStep, RouteEvent.framed, hop] using valid + have hg : decodeRow (gather owner chart raw e.y) = fun _ => false := by + rw [rel]; exact hv + funext a + have h := physical_blank_of_decoded_blank _ hg ((chart e.y).inverse a) + simpa only [gather, (chart e.y).forward_inverse] using h + · intro hop a + have hv : decodeRow (s.get e.x.val) = decodeRow (s.get e.y.val) := by + simpa only [ValidStep, RouteEvent.framed, hop] using valid + have hg : decodeRow (gather owner chart raw e.x) = + decodeRow (gather owner chart raw e.y) := by + rw [rel, rel]; exact hv + have h := erase_guard_transport _ _ hg ((chart e.y).inverse a) + simpa only [gather, (chart e.y).forward_inverse] using h + +theorem raw_clean_run_of_framed {n : Nat} {S X : Type} (owner : Fin n → S) + (chart : Fin n → Gauge X) (hinj : ∀ {r s}, owner r = owner s → r = s) + (events : List (RouteEvent (Fin n) X)) (raw : Raw S X) + (s : Store X) (depth : Nat) (full : TreeReplay.Tree.Full depth s) + (bound : n ≤ 2 ^ depth) (rel : ∀ r, gather owner chart raw r = s.get r.val) + (valid : ValidTrace (events.map RouteEvent.framed) s) : + RawCleanRun owner chart events raw := by + induction events generalizing raw s with + | nil => trivial + | cons e es ih => + refine ⟨raw_clean_of_framed owner chart raw s rel e valid.1, ?_⟩ + apply ih _ _ (physicalStep_full s depth full e.framed) _ valid.2 + intro r + rw [congrFun (gather_step owner chart hinj raw e.op e.x e.y e.odd e.newFrame) r] + exact logicalStep_fin_tree s depth full bound _ rel e r + +def NativeClean {R S X : Type} (owner : R → S) (d : Gauge X) + (native : Raw S X) (e : RouteEvent R X) : Prop := + (e.op = 2 → (native (owner e.y)).2 = fun _ => false) ∧ + (e.op = 3 → ∀ a, (native (owner e.y)).2 a = + (native (owner e.x)).2 (d.forward + ((native (owner e.x)).1.forward ((native (owner e.y)).1.inverse (d.inverse a))))) + +noncomputable def NativeCleanRun {R S X : Type} (owner : R → S) (d : Gauge X) : + List (RouteEvent R X) → Raw S X → Prop + | [], _ => True + | e :: es, native => NativeClean owner d native e ∧ NativeCleanRun owner d es + (nativeStep owner d native e.op e.x e.y e.odd e.newFrame) + +theorem native_clean_of_raw {R S X : Type} (owner : R → S) + (chart : R → Gauge X) (cover : S → Gauge X) (d : Gauge X) + (common : ∀ r a, (cover (owner r)).forward ((chart r).forward a) = d.forward a) + (native : Raw S X) (e : RouteEvent R X) + (clean : RawClean owner chart (fromNative cover native) e) : + NativeClean owner d native e := by + constructor + · intro hop + funext a + have h := congrFun (clean.1 hop) ((cover (owner e.y)).inverse a) + simpa only [fromNative, (cover (owner e.y)).forward_inverse] using h + · intro hop a + have h := clean.2 hop ((cover (owner e.y)).inverse a) + simp only [fromNative, (cover (owner e.y)).forward_inverse] at h + rw [common, inverse_common_cover owner chart cover d common e.y a] at h + exact h + +theorem native_clean_run_of_raw {R S X : Type} (owner : R → S) + (chart : R → Gauge X) (cover : S → Gauge X) (d : Gauge X) + (common : ∀ r a, (cover (owner r)).forward ((chart r).forward a) = d.forward a) + (events : List (RouteEvent R X)) (native : Raw S X) + (clean : RawCleanRun owner chart events (fromNative cover native)) : + NativeCleanRun owner d events native := by + induction events generalizing native with + | nil => trivial + | cons e es ih => + refine ⟨native_clean_of_raw owner chart cover d common native e clean.1, ?_⟩ + apply ih + have h := clean.2 + rw [rawStep_fromNative owner chart cover d common] at h + exact h + +theorem actual_raw_clean {S X : Type} (owner : SourceRaw.Role → S) + (chart : SourceRaw.Role → Gauge X) (hinj : ∀ {r s}, owner r = owner s → r = s) + (gauges : Nat → Gauge X) (payload : S → X → Bool) : + RawCleanRun owner chart (SourceFrameTrace.forward.map (SourceFrameTrace.toRoute gauges)) + (SourceRaw.initial owner gauges payload) := by + apply raw_clean_run_of_framed owner chart hinj _ _ + (SourceFramed.initial gauges (SourceRaw.input owner chart payload)) 10 + (TreeReplay.Tree.full_tabulate _ _) (by decide) + (SourceRaw.gather_initial owner chart hinj gauges payload) + rw [SourceFrameTrace.route_projection] + exact SourceFramed.actual_valid gauges _ + +/-- Preparing a blank private row and the fixed frame metadata commutes +with expressing all physical streams in their cover charts. -/ +theorem initial_fromNative {S X : Type} (owner : SourceRaw.Role → S) + (gauges : Nat → Gauge X) (cover : S → Gauge X) (payload : S → X → Bool) : + SourceRaw.initial owner gauges (fun s a => payload s ((cover s).forward a)) = + fromNative cover (SourceRaw.initial owner gauges payload) := by + classical + funext s + by_cases hs : s = owner SourceRaw.privateRow <;> + simp only [SourceRaw.initial, initialRaw, fromNative, hs, ↓reduceIte] + +theorem actual_native_clean {S X : Type} (owner : SourceRaw.Role → S) + (chart : SourceRaw.Role → Gauge X) (hinj : ∀ {r s}, owner r = owner s → r = s) + (gauges : Nat → Gauge X) (cover : S → Gauge X) (d : Gauge X) + (common : ∀ r a, (cover (owner r)).forward ((chart r).forward a) = d.forward a) + (payload : S → X → Bool) : + NativeCleanRun owner d (SourceFrameTrace.forward.map (SourceFrameTrace.toRoute gauges)) + (SourceRaw.initial owner gauges payload) := by + apply native_clean_run_of_raw owner chart cover d common + rw [← initial_fromNative] + exact actual_raw_clean owner chart hinj gauges _ + +theorem native_run_refines {S X : Type} (owner : SourceRaw.Role → S) + (chart : SourceRaw.Role → Gauge X) (gauges : Nat → Gauge X) + (cover : S → Gauge X) (d : Gauge X) + (common : ∀ r a, (cover (owner r)).forward ((chart r).forward a) = d.forward a) + (payload : S → X → Bool) : + SourceRaw.final owner chart gauges (fun s a => payload s ((cover s).forward a)) = + fromNative cover (runNative owner d + (SourceFrameTrace.forward.map (SourceFrameTrace.toRoute gauges)) + (SourceRaw.initial owner gauges payload)) := by + unfold SourceRaw.final + rw [initial_fromNative, runRaw_fromNative owner chart cover d common] + +/-- Exact source-native endpoint, derived from the same native execution +whose physical COPY/ERASE guards were checked above. -/ +theorem native_payload_endpoint {S X : Type} (owner : SourceRaw.Role → S) + (chart : SourceRaw.Role → Gauge X) (hinj : ∀ {r s}, owner r = owner s → r = s) + (gauges : Nat → Gauge X) (cover : S → Gauge X) (d : Gauge X) + (common : ∀ r a, (cover (owner r)).forward ((chart r).forward a) = d.forward a) + (payload : S → X → Bool) (r : SourceRaw.Role) (a : X) : + ((runNative owner d + (SourceFrameTrace.forward.map (SourceFrameTrace.toRoute gauges)) + (SourceRaw.initial owner gauges payload)) (owner r)).2 a = + SourceMatrix.endpointPayload + (SourceFramed.normalizedInput gauges (SourceRaw.input owner chart + (fun s a => payload s ((cover s).forward a)))) r.val + ((gauges (SourceFrameTrace.state96.frames.get r.val)).inverse (d.inverse a)) := by + have h := SourceRaw.payload_endpoint owner chart hinj gauges + (fun s a => payload s ((cover s).forward a)) r ((cover (owner r)).inverse a) + rw [native_run_refines owner chart gauges cover d common] at h + simp only [fromNative, (cover (owner r)).forward_inverse] at h + rw [inverse_common_cover owner chart cover d common] at h + exact h + +theorem native_private_restored {S X : Type} (owner : SourceRaw.Role → S) + (chart : SourceRaw.Role → Gauge X) (hinj : ∀ {r s}, owner r = owner s → r = s) + (gauges : Nat → Gauge X) (cover : S → Gauge X) (d : Gauge X) + (common : ∀ r a, (cover (owner r)).forward ((chart r).forward a) = d.forward a) + (payload : S → X → Bool) : + ((runNative owner d + (SourceFrameTrace.forward.map (SourceFrameTrace.toRoute gauges)) + (SourceRaw.initial owner gauges payload)) (owner SourceRaw.privateRow)).2 = + fun _ => false := by + funext a + rw [native_payload_endpoint owner chart hinj gauges cover d common payload + SourceRaw.privateRow a] + rfl + +theorem native_other_preserved {S X : Type} (owner : SourceRaw.Role → S) + (chart : SourceRaw.Role → Gauge X) (gauges : Nat → Gauge X) + (cover : S → Gauge X) (d : Gauge X) + (common : ∀ r a, (cover (owner r)).forward ((chart r).forward a) = d.forward a) + (payload : S → X → Bool) (s : S) (outside : ∀ r, s ≠ owner r) : + ((runNative owner d + (SourceFrameTrace.forward.map (SourceFrameTrace.toRoute gauges)) + (SourceRaw.initial owner gauges payload)) s).2 = payload s := by + have h := SourceRaw.other_payload_preserved owner chart gauges + (fun s a => payload s ((cover s).forward a)) s outside + rw [native_run_refines owner chart gauges cover d common] at h + funext a + have ha := congrFun h ((cover s).inverse a) + simpa only [fromNative, (cover s).forward_inverse] using ha + +#print axioms raw_clean_of_framed +#print axioms raw_clean_run_of_framed +#print axioms native_clean_of_raw +#print axioms native_clean_run_of_raw +#print axioms actual_raw_clean +#print axioms initial_fromNative +#print axioms actual_native_clean +#print axioms native_run_refines +#print axioms native_payload_endpoint +#print axioms native_private_restored +#print axioms native_other_preserved +end SourceRawGuards diff --git a/research/lean-multi-host-source/SourceTables.lean b/research/lean-multi-host-source/SourceTables.lean new file mode 100644 index 0000000000..4cb798e810 --- /dev/null +++ b/research/lean-multi-host-source/SourceTables.lean @@ -0,0 +1,21 @@ +import MatrixData +import EndpointInterpretation + +/-! +Kernel comparisons bind the generated literal matrices to their intended +initial and endpoint formulas. These equalities are not assumptions supplied +by the generator. +-/ +namespace SourceMatrix +open TreeReplay +set_option maxRecDepth 100000 +set_option maxHeartbeats 0 + +theorem initial_formula : initial = basisRows 10 987 := by rfl + +theorem expected_formula : expected = Tree.tabulate 10 endpointRow := by rfl + +#print axioms initial_formula +#print axioms expected_formula + +end SourceMatrix diff --git a/research/lean-multi-host-source/TreeReplay.lean b/research/lean-multi-host-source/TreeReplay.lean new file mode 100644 index 0000000000..a48e1cf93d --- /dev/null +++ b/research/lean-multi-host-source/TreeReplay.lean @@ -0,0 +1,322 @@ +import LinearReplay + +/-! +An executable binary register store with the same linear semantics as +`LinearReplay`. Low bits of a register index choose successive branches. +The source certificate uses a full tree of depth 10 and verifies every +access is below 988; no out-of-range index is thereby allowed to alias a +physical register. The generic reflection result itself is shape-agnostic. +-/ +namespace TreeReplay +open LinearReplay (Event evalRow evalRow_zero evalRow_xor) +universe u v + +inductive Tree (α : Type u) where + | leaf : α → Tree α + | node : Tree α → Tree α → Tree α + deriving DecidableEq + +namespace Tree + +def get : Tree α → Nat → α + | .leaf a, _ => a + | .node l r, i => if i % 2 == 0 then l.get (i / 2) else r.get (i / 2) + +def put : Tree α → Nat → α → Tree α + | .leaf _, _, a => .leaf a + | .node l r, i, a => + if i % 2 == 0 then .node (l.put (i / 2) a) r else .node l (r.put (i / 2) a) + +def map (f : α → β) : Tree α → Tree β + | .leaf a => .leaf (f a) + | .node l r => .node (l.map f) (r.map f) + +theorem map_get (f : α → β) (s : Tree α) (i : Nat) : + (s.map f).get i = f (s.get i) := by + induction s generalizing i with + | leaf a => rfl + | node l r ihl ihr => + simp only [get, map] + split <;> simp_all + +theorem map_put (f : α → β) (s : Tree α) (i : Nat) (a : α) : + (s.put i a).map f = (s.map f).put i (f a) := by + induction s generalizing i with + | leaf b => rfl + | node l r ihl ihr => + simp only [put, map] + split <;> simp_all [map] + +theorem map_map (f : α → β) (g : β → γ) (s : Tree α) : + (s.map f).map g = s.map (g ∘ f) := by + induction s with + | leaf a => rfl + | node l r ihl ihr => simp [map, ihl, ihr] + +/-- Full binary store; the least significant index bit chooses the root branch. -/ +def tabulate : Nat → (Nat → α) → Tree α + | 0, f => .leaf (f 0) + | d + 1, f => .node (tabulate d (fun i => f (2 * i))) + (tabulate d (fun i => f (2 * i + 1))) + +theorem map_tabulate (f : α → β) (d : Nat) (g : Nat → α) : + (tabulate d g).map f = tabulate d (f ∘ g) := by + induction d generalizing g with + | zero => rfl + | succ d ih => simp [tabulate, map, ih, Function.comp_def] + +theorem get_tabulate (d : Nat) (f : Nat → α) (i : Nat) (h : i < 2 ^ d) : + (tabulate d f).get i = f i := by + induction d generalizing f i with + | zero => + have hi : i = 0 := by simp at h; omega + subst i; rfl + | succ d ih => + have hdiv : i / 2 < 2 ^ d := by + rw [Nat.pow_succ] at h + omega + simp only [tabulate, get] + split + · rw [ih _ _ hdiv] + congr 1 + rename_i hz + have hm : i % 2 = 0 := by simpa using hz + omega + · rw [ih _ _ hdiv] + congr 1 + rename_i hz + have hm : i % 2 ≠ 0 := by simpa using hz + omega + +def Full : Nat → Tree α → Prop + | 0, .leaf _ => True + | d + 1, .node l r => Full d l ∧ Full d r + | _, _ => False + +theorem full_tabulate (d : Nat) (f : Nat → α) : Full d (tabulate d f) := by + induction d generalizing f with + | zero => trivial + | succ d ih => exact ⟨ih _, ih _⟩ + +theorem full_put (d : Nat) (s : Tree α) (h : Full d s) (i : Nat) (a : α) : + Full d (s.put i a) := by + induction d generalizing s i with + | zero => cases s <;> simp_all [Full, put] + | succ d ih => + cases s with + | leaf b => cases h + | node l r => + simp only [put] + split <;> exact ⟨by first | exact ih _ h.1 _ | exact h.1, + by first | exact ih _ h.2 _ | exact h.2⟩ + +/-- Within a full store, an update changes exactly the selected register. -/ +theorem get_put (d : Nat) (s : Tree α) (h : Full d s) (i j : Nat) (a : α) + (hi : i < 2 ^ d) (hj : j < 2 ^ d) : + (s.put i a).get j = if i = j then a else s.get j := by + induction d generalizing s i j with + | zero => + have hi0 : i = 0 := by simp at hi; omega + have hj0 : j = 0 := by simp at hj; omega + subst i; subst j + cases s <;> simp_all [Full, put, get] + | succ d ih => + cases s with + | leaf b => cases h + | node l r => + have hid : i / 2 < 2 ^ d := by rw [Nat.pow_succ] at hi; omega + have hjd : j / 2 < 2 ^ d := by rw [Nat.pow_succ] at hj; omega + by_cases hip : i % 2 = 0 <;> by_cases hjp : j % 2 = 0 + · simp only [put, get, hip, hjp, beq_self_eq_true, ite_true] + rw [ih l h.1 _ _ hid hjd] + have heq : (i / 2 = j / 2) ↔ i = j := by omega + simp only [heq] + · have hij : i ≠ j := by omega + simp [put, get, hip, hjp, hij] + · have hij : i ≠ j := by omega + simp [put, get, hip, hjp, hij] + · simp only [put, get, beq_iff_eq, hip, hjp, ↓reduceIte] + rw [ih r h.2 _ _ hid hjd] + have heq : (i / 2 = j / 2) ↔ i = j := by omega + simp only [heq] + +end Tree + +def step (zero : α) (xor : α → α → α) (s : Tree α) (e : Event) : Tree α := + match e.op with + | 0 => s + | 1 => if e.odd then s.put e.x (xor (s.get e.x) (s.get e.y)) else s + | 2 => s.put e.y (s.get e.x) + | _ => s.put e.y zero + +def run (zero : α) (xor : α → α → α) (es : List Event) (s : Tree α) : Tree α := + es.foldl (step zero xor) s + +def rowStep := step (0 : Nat) (· ^^^ ·) +def boolStep := step false (· ^^ ·) +def runRows := run (0 : Nat) (· ^^^ ·) +def runBools := run false (· ^^ ·) + +def rowChecks (s : Tree Nat) (e : Event) : Bool := + match e.op with + | 0 => e.x < 987 + | 1 => e.x < 987 && e.y <= 987 && e.x != e.y + | 2 => e.x < 987 && e.y == 987 && s.get e.y == 0 + | 3 => e.x < 987 && e.y == 987 && s.get e.x == s.get e.y + | _ => false + +def checkedRowStep (s : Tree Nat × Bool) (e : Event) : Tree Nat × Bool := + (rowStep s.1 e, s.2 && rowChecks s.1 e) + +def runCheckedRows (es : List Event) (s : Tree Nat × Bool) : Tree Nat × Bool := + es.foldl checkedRowStep s + +def evalRows (n : Nat) (u : Nat → Bool) (s : Tree Nat) : Tree Bool := + s.map (evalRow n u) + +theorem step_map (zero : α) (zero' : β) (xor : α → α → α) (xor' : β → β → β) + (f : α → β) (hzero : f zero = zero') + (hxor : ∀ a b, f (xor a b) = xor' (f a) (f b)) (s : Tree α) (e : Event) : + (step zero xor s e).map f = step zero' xor' (s.map f) e := by + obtain ⟨op, x, y, odd⟩ := e + cases op with + | zero => rfl + | succ op => + cases op with + | zero => cases odd <;> simp [step, Tree.map_put, Tree.map_get, hxor] + | succ op => + cases op with + | zero => simp [step, Tree.map_put, Tree.map_get] + | succ op => simp [step, Tree.map_put, hzero] + +theorem run_map (zero : α) (zero' : β) (xor : α → α → α) (xor' : β → β → β) + (f : α → β) (hzero : f zero = zero') + (hxor : ∀ a b, f (xor a b) = xor' (f a) (f b)) (es : List Event) (s : Tree α) : + (run zero xor es s).map f = run zero' xor' es (s.map f) := by + induction es generalizing s with + | nil => rfl + | cons e es ih => + change (run zero xor es (step zero xor s e)).map f = + run zero' xor' es (step zero' xor' (s.map f) e) + rw [ih, step_map zero zero' xor xor' f hzero hxor] + +theorem evalRows_step (n : Nat) (u : Nat → Bool) (s : Tree Nat) (e : Event) : + evalRows n u (rowStep s e) = boolStep (evalRows n u s) e := by + exact step_map 0 false (· ^^^ ·) (· ^^ ·) (evalRow n u) + (evalRow_zero n u) (evalRow_xor n u) s e + +theorem evalRows_run (n : Nat) (u : Nat → Bool) (es : List Event) (s : Tree Nat) : + evalRows n u (runRows es s) = runBools es (evalRows n u s) := by + exact run_map 0 false (· ^^^ ·) (· ^^ ·) (evalRow n u) + (evalRow_zero n u) (evalRow_xor n u) es s + +theorem checked_projection (es : List Event) (s : Tree Nat × Bool) : + (runCheckedRows es s).1 = runRows es s.1 := by + induction es generalizing s with + | nil => rfl + | cons e es ih => exact ih (checkedRowStep s e) + +def boolChecks (s : Tree Bool) (e : Event) : Bool := + match e.op with + | 0 => e.x < 987 + | 1 => e.x < 987 && e.y <= 987 && e.x != e.y + | 2 => e.x < 987 && e.y == 987 && !(s.get e.y) + | 3 => e.x < 987 && e.y == 987 && s.get e.x == s.get e.y + | _ => false + +def checkedBoolStep (s : Tree Bool × Bool) (e : Event) : Tree Bool × Bool := + (boolStep s.1 e, s.2 && boolChecks s.1 e) + +def runCheckedBools (es : List Event) (s : Tree Bool × Bool) : Tree Bool × Bool := + es.foldl checkedBoolStep s + +theorem evalRows_get (n : Nat) (u : Nat → Bool) (s : Tree Nat) (i : Nat) : + (evalRows n u s).get i = evalRow n u (s.get i) := Tree.map_get _ _ _ + +theorem checks_sound (n : Nat) (u : Nat → Bool) (s : Tree Nat) (e : Event) + (h : rowChecks s e = true) : boolChecks (evalRows n u s) e = true := by + obtain ⟨op, x, y, odd⟩ := e + cases op with + | zero => exact h + | succ op => + cases op with + | zero => exact h + | succ op => + cases op with + | zero => + simp only [rowChecks, Bool.and_eq_true, beq_iff_eq] at h + simp only [boolChecks, Bool.and_eq_true, beq_iff_eq, evalRows_get] + exact ⟨h.1, by simp [h.2]⟩ + | succ op => + cases op with + | zero => + simp only [rowChecks, Bool.and_eq_true, beq_iff_eq] at h + simp only [boolChecks, Bool.and_eq_true, beq_iff_eq, evalRows_get] + exact ⟨h.1, congrArg (evalRow n u) h.2⟩ + | succ op => cases h + +theorem checked_flag_mono (es : List Event) (s : Tree Nat × Bool) + (h : (runCheckedRows es s).2 = true) : s.2 = true := by + induction es generalizing s with + | nil => exact h + | cons e es ih => + have h' := ih (checkedRowStep s e) h + exact (Bool.and_eq_true_iff.mp h').1 + +theorem checked_guards_sound (n : Nat) (u : Nat → Bool) (es : List Event) + (s : Tree Nat × Bool) (h : (runCheckedRows es s).2 = true) : + (runCheckedBools es (evalRows n u s.1, s.2)).2 = true := by + induction es generalizing s with + | nil => exact h + | cons e es ih => + have hfirst := checked_flag_mono es (checkedRowStep s e) h + have hparts := Bool.and_eq_true_iff.mp hfirst + have hb := checks_sound n u s.1 e hparts.2 + have hi := ih (checkedRowStep s e) h + simpa only [runCheckedBools, List.foldl_cons, checkedBoolStep, + evalRows_step, checkedRowStep, hparts.1, hparts.2, hb] using hi + +def basisRows (depth n : Nat) : Tree Nat := + Tree.tabulate depth fun i => if i < n then 1 <<< i else 0 + +def dirtyInput (depth n : Nat) (u : Nat → Bool) : Tree Bool := + Tree.tabulate depth fun i => if i < n then u i else false + +theorem evalRows_basisRows (depth n : Nat) (u : Nat → Bool) : + evalRows n u (basisRows depth n) = dirtyInput depth n u := by + simp only [evalRows, basisRows, dirtyInput, Tree.map_tabulate] + congr 1 + funext i + by_cases h : i < n <;> simp [h, LinearReplay.evalRow_shift_basis] + +theorem dirtyInput_get (depth n : Nat) (u : Nat → Bool) (i : Nat) + (h : i < 2 ^ depth) : + (dirtyInput depth n u).get i = if i < n then u i else false := + Tree.get_tabulate _ _ _ h + +/-- Interpret rows as entire arbitrary Boolean payloads, without restricting +their dependence on one another or on an address of any type. -/ +def evalPayloadRows {X : Type v} (n : Nat) (u : Nat → X → Bool) (s : Tree Nat) : Tree (X → Bool) := + s.map fun row address => evalRow n (fun i => u i address) row + +def runPayloads {X : Type v} (es : List Event) (s : Tree (X → Bool)) : Tree (X → Bool) := + run (fun _ => false) (fun a b x => a x ^^ b x) es s + +theorem evalPayloadRows_run {X : Type v} (n : Nat) (u : Nat → X → Bool) (es : List Event) (s : Tree Nat) : + evalPayloadRows n u (runRows es s) = runPayloads es (evalPayloadRows n u s) := by + apply run_map 0 (fun _ => false) (· ^^^ ·) (fun a b x => a x ^^ b x) + · funext x + exact evalRow_zero n (fun i => u i x) + · intro a b + funext x + exact evalRow_xor n (fun i => u i x) a b + +theorem evalPayloadRows_basisRows {X : Type v} (depth n : Nat) (u : Nat → X → Bool) : + evalPayloadRows n u (basisRows depth n) = + Tree.tabulate depth (fun i => if i < n then u i else fun _ => false) := by + simp only [evalPayloadRows, basisRows, Tree.map_tabulate] + congr 1 + funext i address + by_cases h : i < n <;> simp [h, LinearReplay.evalRow_shift_basis] + +end TreeReplay diff --git a/research/lean-multi-host-source/VALIDATION.md b/research/lean-multi-host-source/VALIDATION.md new file mode 100644 index 0000000000..6316efd618 --- /dev/null +++ b/research/lean-multi-host-source/VALIDATION.md @@ -0,0 +1,114 @@ +# Validation and remaining scope + +Current fresh-build status and receipts are recorded in +[`../lean-external-review/VALIDATION.md`](../lean-external-review/VALIDATION.md). +The current permanent inventory contains 931 declarations, including +`SourceInvocation.actualContract`. The 930-declaration historical receipts +below do not certify the expanded inventory. No Lean proof source changed. + +The earlier external-review validation reran Task A and source extraction +fresh; Task B explicitly reused all +52 receipt-anchored modules and reran the 930-declaration axiom inventory. +That historical resumed receipt reports zero fresh Task B modules. The original receipt did +not record byte hashes of the installed Lean distribution, Mathlib or its eight +manifest dependencies, so the resumed PASS cannot establish the external-library +bytes used in the original compilation. The linked delivery validation names +those dependencies and explains how fresh reproduction recompiles all 52 modules +and records the dependency hashes for a new run. + +**PASS:** the coherent package replay completed at +2026-10-11 23:59:17 UTC. `replay-result.json` records 52 source-built modules +with `lean -t 0` and 930 audited named theorem closures. Every source hash +matched that historical module inventory. Only `propext`, `Quot.sound`, and +`Classical.choice` occur. `source-binding-result.json` separately records the +successful source-extraction replay. + +The build began in an empty directory. After the frame certificate passed, +the runner rejected an outdated geometry source hash from its initial +manifest. Resuming with the frozen final manifest reused only hash-verified +successful builds from that same directory; all remaining sources were +compiled there and the complete axiom audit ran afterward. No development +model or external component-build artifact was imported into this replay. + +Recorded module wall times total 2,756.5 seconds (about 46 minutes), including +2,070.0 seconds for `FrameData`. These are reproduction observations under +shared machine load, not an isolated performance benchmark. Mathlib preparation +is separate from these local-module timings. + +## Separate results + +Task A is local commit `13611a8958fc71046a83d8431d2bd6335e6a3e2f`. Its own +fresh replay checked the multi-host theorem, exact single-host recovery, +physical adapter, and boundary controls. Its endpoint contracts are premises. + +Task B constructs one such contract from the actual selected PR442 +invocation. The final entry module is `SourceInvocation.lean`. It accepts a +field with `2 ≠ 0`, an invertible invocation chart, arbitrary retained state, +and arbitrary original-bank dirt. Ownership injectivity, helper-relative +geometry, input matching, and clean-work guards are proved inside the +dependency chain, rather than supplied as additional hypotheses. + +## Concrete evidence + +- The complete 19,002-event word has a checked symbolic endpoint for all + 987 live input streams and its one designated clean private row. Boolean + payloads are arbitrary functions and may be correlated. +- All 944 frame matrices have integer projector and complete-basis + certificates; all 3,357 distinct MOVE pairs have both absorption equations. + Matrix wrappers explicitly select matrix multiplication for the finite + tables, whose stored representation is an ordinary function type. +- Literal trace checks select those certified pairs for all 4,291 actual + MOVEs. COPY and ERASE have their exact full/zero frame pair and chronological + guards. Both complete matrix-run equalities refer to the same actual folds + used by the invocation contract. +- The 747 hosted owners and original bank owners are injective in their + actual family-and-cover-map representation. Both executions use one shared + cover extension, with equality of retained native inputs proved after + private-row initialization. The review caught and corrected the earlier + use of incompatible extensions. +- All affected hosts and data streams are retained. Original-bank outputs + are the real outputs of the old execution and are threaded as auxiliary + state. They are not silently replaced with their initial values. + +The component receipt `review-receipts/final-bridge-components.json` records +the final bridge source and artifact hashes. The independent native-input +review has its own receipt and log. Reviews disclose their authorship overlap; +they are separate agent reviews, not independent human audits. + +## Reproduction boundary + +`check_sources.py` verifies six source snapshots, reconstructs the original +binary records, independently compares all normalized events in order, and +regenerates the literal certificates. This extraction uses Python and SymPy; +it is not a verified JSON parser or source compiler. Lean checks the resulting +embedded mathematical statements. Exact versions are in `source-versions.json`. + +The package replay starts from manifested sources and uses `lean -t 0`. +It accepts only `propext`, `Quot.sound`, and `Classical.choice` in transitive +axiom closures. No project axiom, `sorry`, `admit`, `native_decide`, or unsafe +proof mechanism is permitted. Generated checkpoint theorems comprise much of +the declaration inventory; their count is not a count of new mathematical ideas. + +## Limits + +The result concerns one complete forward invocation, with explicit local +embeddings. All 19,002 instructions form one event in the multi-host theorem's +event list. Pairwise disjointness between separate events is vacuous in this +application; cross-invocation disjointness is not exercised. The separately +proved owner injectivity concerns this invocation only. + +The pending-coordinate ranges 15..21 and 1..28 (half-open `[15,22)` and +`[1,29)`) are hand-supplied. Lean checks their containment of the target masks +through `PhysicalSourceConnection.tag_pending_contains`; nothing in Lean +or the source-extraction check binds those ranges to the source schedule. +The remaining pending swaps are applied immediately after the invocation. +The result does not prove +the later recursive child schedule, complete cover sweep, equivalence of +arbitrary global allocations, resource charging, all-size compilation, or +an integer-multiplication bound. A continuation that observes or reuses old +auxiliary outputs needs the appropriate separate scope or restoration proof. + +The two mutation controls check a corrupted next checkpoint and a dirty-private +first-COPY state; they are not full executions of corrupted programs. PR448's +split-stream gain remains unestablished. No source algorithm or claimed κ was +changed. This validation preceded publication on the public review branch. diff --git a/research/lean-multi-host-source/check_sources.py b/research/lean-multi-host-source/check_sources.py new file mode 100644 index 0000000000..d463f0b060 --- /dev/null +++ b/research/lean-multi-host-source/check_sources.py @@ -0,0 +1,133 @@ +#!/usr/bin/env python3 +"""Reproduce the source-to-literal boundary; this Python parser is not a Lean proof.""" +import argparse +import gzip +import hashlib +import json +from pathlib import Path +import re +import subprocess +import struct +import sys +import tempfile + +ROOT = Path(__file__).resolve().parent + + +def require(ok, message): + if not ok: + raise RuntimeError(message) + + +def check(): + versions = json.loads((ROOT / 'source-versions.json').read_text()) + with tempfile.TemporaryDirectory(prefix='source-binding-') as tmp: + work = Path(tmp) + inputs = {} + for name, expected in versions['inputs'].items(): + blob = (ROOT / 'inputs' / name).read_bytes() + require(hashlib.sha256(blob).hexdigest() == expected['sha256_compressed'], name) + raw = gzip.decompress(blob) + require(hashlib.sha256(raw).hexdigest() == expected['sha256_uncompressed'], name) + path = work / name.removesuffix('.gz') + path.write_bytes(raw) + inputs[name] = json.loads(raw) if path.suffix == '.json' else raw + template = inputs['hosted-template.json.gz'] + parent = inputs['parent-template.json.gz'] + events = template['local_programs']['forward'] + require(events == parent['local_programs']['forward'], 'Parent/hosted word changed') + require(len(events) == 19002, 'Event count changed') + raw_records = list(struct.iter_unpack('<6i', inputs['records.bin.gz'])) + reconstructed = [] + for op, x, y, c, f, z in raw_records: + require(op in range(4), 'Unknown record opcode') + if op < 2: + # The exporter uses ADD's last field for the five word + # phases (D, A, scatter, B, C), not an address reflection. + require(z == 0 if op == 0 else 1 <= z <= 5, + 'Unexpected MOVE padding or ADD word-phase annotation') + reconstructed.append([op, x, y, c, f, 0]) + else: + require(z == (8 if op == 2 else 0), 'Wrong COPY/ERASE rank field') + reconstructed.append([op, x, y, c, f, z, 0]) + require(reconstructed == events, 'Forward word differs from original binary records') + canonical = json.dumps(events, separators=(',', ':')).encode() + require(hashlib.sha256(canonical).hexdigest() == + versions['selected_invocation']['canonical_forward_sha256'], + 'Wrong canonical forward word hash') + call = next(c for c in template['calls'] if c['stage'] == 2 and c['replica'] == 0) + require(call['pair'] == 0 and call['orientation'] == 'forward', 'Wrong invocation') + require(len(call['owners']) == 987, 'Wrong role count') + require(all(e[-1] == 0 for e in events), 'Unexpected reflected event') + frames = inputs['frames.json.gz']['frames'] + for e in events: + require(len(e) == (6 if e[0] < 2 else 7), 'Wrong opcode-dependent record length') + if e[0] == 1: + require(e[3] == 1, 'ADD coefficient is not the literal +1') + elif e[0] == 0: + require(e[4] == frames[str(e[3])]['dim'] - frames[str(e[2])]['dim'], + 'MOVE rank annotation disagrees with source dimensions') + # An independent literal parser checks chronological event preservation; + # it does not rely on the checkpoint generator's symbolic execution. + matrix_source = (ROOT / 'MatrixData.lean').read_text() + chunks = re.findall(r'def chunk(\d+) : List Event := \[(.*?)\]', matrix_source, re.S) + require([int(i) for i, _ in chunks] == list(range(96)), 'Wrong chunk inventory') + actual = [] + for _, body in chunks: + tuples = re.findall(r'⟨(\d+),(\d+),(\d+),(true|false)⟩', body) + require(re.sub(r'⟨\d+,\d+,\d+,(?:true|false)⟩|[\s,]', '', body) == '', + 'Unparsed event text') + actual.extend((int(o), int(x), int(y), b == 'true') for o, x, y, b in tuples) + expected_events = [(e[0], e[1], e[2], bool(e[3] & 1)) for e in events] + require(actual == expected_events, 'Normalized literal word differs from source') + require('def forwardWord : List Event := forwardChunks.flatten' in matrix_source, + 'Word definition changed') + chunks_text = re.search(r'def forwardChunks : List \(List Event\) := \[(.*?)\]', + matrix_source, re.S).group(1) + require(chunks_text.split(',') == ['chunk' + str(i) for i in range(96)], + 'Chunk order changed') + + def run(script, *args): + result = subprocess.run([sys.executable, str(ROOT / script), *map(str, args)], + text=True, stdout=subprocess.PIPE, + stderr=subprocess.STDOUT, timeout=300) + require(result.returncode == 0, script + '\n' + result.stdout) + + run('generate_matrix.py', ROOT / 'inputs/hosted-template.json.gz', work / 'matrix') + for name in ('MatrixData.lean', 'MatrixCheckpoints.lean', 'MatrixCertificate.lean'): + require((work / 'matrix' / name).read_bytes() == (ROOT / name).read_bytes(), + 'Non-reproducible generated file: ' + name) + run('generate_port_data.py', work / 'geometry.json', '--check') + run('generate_frame_data.py', work / 'frames.json', + ROOT / 'inputs/hosted-template.json.gz', '--check') + run('generate_ownership_data.py', '--template', ROOT / 'inputs/hosted-template.json.gz', + '--states', work / 'states.json', '--frames', work / 'frames.json', + '--out', work / 'OwnershipData.lean') + require((work / 'OwnershipData.lean').read_bytes() == (ROOT / 'OwnershipData.lean').read_bytes(), + 'Non-reproducible ownership data') + run('generate_parent_ownership.py', '--template', ROOT / 'inputs/parent-template.json.gz', + '--states', work / 'states.json', '--frames', work / 'frames.json', + '--out', work / 'ParentOwnershipData.lean') + require((work / 'ParentOwnershipData.lean').read_bytes() == + (ROOT / 'ParentOwnershipData.lean').read_bytes(), + 'Non-reproducible original-bank ownership data') + run('generate_frame_trace.py', ROOT / 'inputs/hosted-template.json.gz', + work / 'states.json', work / 'FrameTraceData.lean') + for name in ('FrameTraceLiterals.lean', 'FrameTraceCheckpoints.lean', 'FrameTraceData.lean'): + require((work / name).read_bytes() == (ROOT / name).read_bytes(), + 'Non-reproducible frame trace data: ' + name) + run('generate_frame_moves.py', '--template', ROOT / 'inputs/hosted-template.json.gz', + '--out', ROOT / 'FrameMoveData.lean', '--check') + return {'status': 'PASS', 'literal_events_in_order': 19002, 'live_roles': 987, + 'source_input_hashes_checked': len(versions['inputs']), + 'scope': 'Reproducible extraction; mathematical certificates are checked separately by Lean.'} + + +if __name__ == '__main__': + p = argparse.ArgumentParser(description=__doc__) + p.add_argument('--receipt', type=Path) + a = p.parse_args() + result = check() + if a.receipt: + a.receipt.write_text(json.dumps(result, indent=2) + '\n') + print(json.dumps(result)) diff --git a/research/lean-multi-host-source/closing-lean-overlap.md b/research/lean-multi-host-source/closing-lean-overlap.md new file mode 100644 index 0000000000..437ec19ca7 --- /dev/null +++ b/research/lean-multi-host-source/closing-lean-overlap.md @@ -0,0 +1,114 @@ +# Closing overlap review: PR513 and PR511 + +Read-only review completed 2026-10-11 UTC, following the closing snapshot +at `overlap-closing-refresh.json` in the contribution package. No GitHub +comments, publications or repository mutations were made by this audit. + +## Exact evidence boundary + +| PR | Inspected head | Changed files | Changed Lean files | +| --- | --- | ---: | ---: | +| [513](https://github.com/CrocSwap/integer-mult-bounds/pull/513) | `005dd3f4e3cba8d1761abc4ab391aaf6d14d6f73` | 20 | 8 | +| [511](https://github.com/CrocSwap/integer-mult-bounds/pull/511) | `79f7c03c7f820ab89955b75ef239cbaccc627e6e` | 17 | 4 | + +Both API heads matched the requested pins. Each compare against main +`12a4934d15006e8c10f9b2264f13f8f341be802b` reports one added commit. +Both recursive Git trees are untruncated (162 and 158 Lean files, +respectively). All 37 changed files were fetched from the exact commits; +their Git blob hashes were independently recomputed and matched the tree. +All eight PR513 Lean SHA-256 entries also match its manifest. + +The original API responses and fetched files were retained locally during +this audit. The shipped [URL/hash inventory](review-receipts/closing-overlap-fetch-manifest.json) +identifies the inspected files without requiring that local directory. +The review inspected the new theorem statements/proofs and source-binding +definitions, supporting theorem interfaces, README/provenance and manifests. +It did not independently rebuild these Lean 4.21.0 packages or reproduce +their advertised build receipts. Their kernel-check claims remain their +supplied evidence, distinct from this source review. + +## PR513: meaningful generic overlap, different concrete target + +`SequentialCompleteBank.sequential_complete_bank` +([exact source, line 82](https://github.com/CrocSwap/integer-mult-bounds/blob/005dd3f4e3cba8d1761abc4ab391aaf6d14d6f73/research/lean-sequential-bank-bindings/SequentialCompleteBank.lean#L82)) +composes completed local words. Its arguments explicitly include: + +- An arbitrary word for each role and an endpoint premise quantified over + every bank state and every remaining state (lines 84–89). +- One exact common chart and a supplied projector for each role. +- A disjointness premise and a complete partition of the identity + (lines 90–91). + +It proves the full bank swap and chronological evolution of the remaining +state. `completed_words_separate` at line 51 separately proves the product +endpoint composition. The implementation correctly reconciles its two list +orders by reversal. These overlap with the generic completed-word, +arbitrary-dirty-state, common-chart and disjoint-projector principles used +by our abstract framework. The contribution should claim no novelty for +those principles. Five supporting modules are acknowledged as unchanged +reuse; the three additions are this composition adapter and two selected +five-stage source bindings. + +The source bindings concern main's `research/five-stage-gen4-banks`, with +dimension 120, local dimension 24, 1,760 ports and 60 physical replicas. +They do not concern the PR442 R747 invocation: + +- `CurrentFiveStageBankAddressFactor.address_factor` + ([line 26](https://github.com/CrocSwap/integer-mult-bounds/blob/005dd3f4e3cba8d1761abc4ab391aaf6d14d6f73/research/lean-sequential-bank-bindings/CurrentFiveStageBankAddressFactor.lean#L26)) + proves the factor-order identity `route (d*tau) N = route d (N*tau^-1)` + for supplied group laws and normalizers. +- `CurrentFiveStageBankSourceSchedule.lowerStage` accepts the local record + list as an argument (line 101). `NormalizerFactors` accepts its matrix + factors (line 162). `chronologicalWord` accepts cover enumeration and all + local stage/idle/bridge/terminal words (line 191). +- `replica_major_stage_word` + ([line 204](https://github.com/CrocSwap/integer-mult-bounds/blob/005dd3f4e3cba8d1761abc4ab391aaf6d14d6f73/research/lean-sequential-bank-bindings/CurrentFiveStageBankSourceSchedule.lean#L204)) + connects those supplied words to the literal replica-major stage order. + It does not supply their physical endpoints or their matrix entries. + +The source header explicitly says that no matrix, finite-record digest, +physical endpoint, arbitrary-dirty provider or cost is certified here +(lines 8–11). Its provenance also distinguishes the selected transformed +local record list from the raw producer list and keeps the complete +physical endpoint as a supplier obligation. This is a precise, appropriate +boundary, not evidence of an error in PR513. + +No changed file provides the concrete 19,002-event PR442 word, the computed +987-row symbolic endpoint, its chronological nine COPY/nine ERASE guards, +the 944 actual frame matrices, the 747 hosted owner/chart assignments, or +the 172-family original-bank ownership/refinement. Those are precisely the +additional obligations pursued by our Task B. PR513 therefore does not +already discharge that selected concrete target. Its generic algebra can +be cited as overlapping existing work; importing it would not remove the +remaining source-specific proof work. + +## PR511: checked counting machinery, no target overlap + +`BinaryCountDispatcher.count_run` +([line 249](https://github.com/CrocSwap/integer-mult-bounds/blob/79f7c03c7f820ab89955b75ef239cbaccc627e6e/research/lean-binary-count-dispatcher/BinaryCountDispatcher.lean#L249)) +proves termination of an explicit seven-state two-tape binary dispatcher +within the carry-pass read receipt plus `2 * input.length + 1` transitions. +`counter_value` at line 261 gives +`(initial value + input length) mod 2^width`; empty input, zero width and +overflow are within that modular statement. Its four changed Lean files +are `BinaryCarryIncrement`, `BinaryCountDispatcher`, `CarryTape` and +`CarryTapePass`. + +The two external foundations are pinned to PR488 +`edd3102b415df5b9d6f633ac0a4dedcf69c58525`; their identities are recorded in +`FOUNDATIONS.json`. This audit did not re-fetch/rebuild those unchanged +foundations. The package explicitly leaves actual source prelude/caller, +width allocation and Plan/Budget composition open. It has no frame, +whole-residual hosting, physical owner or PR442 invocation endpoint result. + +## Bounded conclusion + +Neither of these exact new heads resolves the selected concrete PR442 +obligation. PR513 materially reinforces the need to describe the useful +contribution as discharging concrete supplier premises, not discovering +generic conjugation, partition or completed-word composition algebra. +PR511 adds independent compiler-helper work. This conclusion is limited to +the pinned changed files and their exposed interfaces; it is not an +exhaustive novelty claim over historical branches or external repositories. +Neither package establishes a new kappa bound, and neither changes the +unestablished status of PR448's advertised split-stream gain. diff --git a/research/lean-multi-host-source/generate_frame_data.py b/research/lean-multi-host-source/generate_frame_data.py new file mode 100644 index 0000000000..74e4ec9eb0 --- /dev/null +++ b/research/lean-multi-host-source/generate_frame_data.py @@ -0,0 +1,160 @@ +#!/usr/bin/env python3 +"""Emit untrusted witnesses; Lean checks every integer matrix identity. + +The source frame rows are literal. SymPy computes witnesses only: projectors +and an inverse of [B; A]. No SymPy answer is a trusted proof. --check rerenders +the entire file, including its source hashes and actual MOVE transition set. +""" +import argparse +import gzip +import hashlib +import json +from pathlib import Path +import sympy as sp + + +def array(rows): + return '#[' + ', '.join('#[' + ', '.join(map(str, row)) + ']' for row in rows) + ']' + + +def branch(names, start=0): + if len(names) == 1: + return names[0] + half = len(names) // 2 + return f'(if n < {start + half} then {branch(names[:half], start)} else {branch(names[half:], start + half)})' + + +def render(frames_path, template_path): + raw = frames_path.read_bytes() + template_raw = template_path.read_bytes() + frames = json.loads(raw)['frames'] + template = json.loads(gzip.decompress(template_raw)) + assert sorted(map(int, frames)) == list(range(944)) + matrices = [] + lines = ['''import Std + +/-! +Literal PR442 inherited frame rows, with independently checked integer +witnesses. Apache-2.0. Prepared with substantial OpenAI Codex assistance. +The balanced lookup stores proofs alongside each frame; no native_decide, +external solver axiom, or sampled field arithmetic is used. +''', f'frames.json SHA-256: {hashlib.sha256(raw).hexdigest()}', + f'GLOBAL-TEMPLATE.json.gz SHA-256: {hashlib.sha256(template_raw).hexdigest()}', + '''-/ +namespace FrameGeometry +set_option maxRecDepth 100000 +set_option maxHeartbeats 0 + +abbrev IntMatrix8 := Fin 8 → Fin 8 → Int +def entry (a : Array (Array Int)) : IntMatrix8 := + fun i j => (a.getD i.val #[]).getD j.val 0 + +def dot8 (a b : IntMatrix8) (i j : Fin 8) : Int := + a i 0 * b 0 j + (a i 1 * b 1 j + (a i 2 * b 2 j + + (a i 3 * b 3 j + (a i 4 * b 4 j + (a i 5 * b 5 j + + (a i 6 * b 6 j + (a i 7 * b 7 j + 0))))))) + +structure FrameDatum where + dimension : Nat + scaled : Array (Array Int) + /-- Exactly the source's B rows followed by its A rows. -/ + stack : Array (Array Int) + /-- Untrusted witness for 256 times the inverse of stack. -/ + inverse256 : Array (Array Int) + +def ValidFrame (d : FrameDatum) : Prop := + d.dimension ≤ 8 ∧ + (∀ i j : Fin 8, dot8 (entry d.scaled) (entry d.scaled) i j = 4 * entry d.scaled i j) ∧ + (∀ i j : Fin 8, entry d.scaled i j = entry d.scaled j i) ∧ + (∀ i j : Fin 8, dot8 (entry d.scaled) (fun a b => entry d.stack b a) i j = + if j.val < d.dimension then 4 * entry d.stack j i else 0) ∧ + (∀ i j : Fin 8, dot8 (entry d.stack) (entry d.inverse256) i j = + if i = j then 256 else 0) ∧ + (∀ i j : Fin 8, dot8 (entry d.inverse256) (entry d.stack) i j = + if i = j then 256 else 0) + +instance (d : FrameDatum) : Decidable (ValidFrame d) := by + unfold ValidFrame + infer_instance + +abbrev CertifiedFrame := { d : FrameDatum // ValidFrame d } +'''] + for n in range(944): + f = frames[str(n)] + rows = f['B'] + f['A'] + assert len(rows) == 8 and all(len(r) == 8 for r in rows) + assert len(f['B']) == f['dim'] + stack = sp.Matrix(rows) + inv = 256 * stack.inv() + b = sp.Matrix(f['B']) if f['B'] else sp.zeros(0, 8) + p = b.T * (b * b.T).inv() * b if f['B'] else sp.zeros(8) + scaled = 4 * p + assert all(x.q == 1 for x in inv) and all(x.q == 1 for x in scaled) + matrices.append(scaled) + lines.append(f'def certified{n} : CertifiedFrame :=\n ⟨{{ dimension := {f["dim"]}, scaled := {array(scaled.tolist())},\n' + f' stack := {array(rows)},\n inverse256 := {array(inv.tolist())} }}, by decide⟩\n') + lines.append('def lookup (n : Nat) : CertifiedFrame :=\n ' + branch([f'certified{n}' for n in range(944)])) + lines.append(''' +def frame (f : Fin 944) : FrameDatum := (lookup f.val).val +def scaled (f : Fin 944) : IntMatrix8 := entry (frame f).scaled +def stack (f : Fin 944) : IntMatrix8 := entry (frame f).stack +def inverse256 (f : Fin 944) : IntMatrix8 := entry (frame f).inverse256 + +theorem frame_valid (f : Fin 944) : ValidFrame (frame f) := (lookup f.val).property +theorem scaled_idempotent_entries (f : Fin 944) (i j : Fin 8) : + dot8 (scaled f) (scaled f) i j = 4 * scaled f i j := (frame_valid f).2.1 i j +theorem scaled_symmetric_entries (f : Fin 944) (i j : Fin 8) : + scaled f i j = scaled f j i := (frame_valid f).2.2.1 i j +theorem scaled_stack_entries (f : Fin 944) (i j : Fin 8) : + dot8 (scaled f) (fun a b => stack f b a) i j = + if j.val < (frame f).dimension then 4 * stack f j i else 0 := + (frame_valid f).2.2.2.1 i j +theorem stack_inverse_entries (f : Fin 944) (i j : Fin 8) : + dot8 (stack f) (inverse256 f) i j = if i = j then 256 else 0 := + (frame_valid f).2.2.2.2.1 i j +theorem inverse_stack_entries (f : Fin 944) (i j : Fin 8) : + dot8 (inverse256 f) (stack f) i j = if i = j then 256 else 0 := + (frame_valid f).2.2.2.2.2 i j + +def Absorbs (small large : Fin 944) : Prop := + (∀ i j : Fin 8, dot8 (scaled small) (scaled large) i j = 4 * scaled small i j) ∧ + (∀ i j : Fin 8, dot8 (scaled large) (scaled small) i j = 4 * scaled small i j) +''') + lines.append('instance (small large : Fin 944) : Decidable (Absorbs small large) := by\n unfold Absorbs\n infer_instance\n') + pairs = sorted({(e[2], e[3]) for e in template['local_programs']['forward'] if e[0] == 0}) + for k, (a, b) in enumerate(pairs): + assert matrices[a] * matrices[b] == 4 * matrices[a] + assert matrices[b] * matrices[a] == 4 * matrices[a] + lines.append(f'def transition{k} : {{ p : Fin 944 × Fin 944 // Absorbs p.1 p.2 }} :=\n ⟨({a}, {b}), by decide⟩') + lines.append(f'def transitionLookup (n : Nat) : {{ p : Fin 944 × Fin 944 // Absorbs p.1 p.2 }} :=\n ' + branch([f'transition{k}' for k in range(len(pairs))])) + lines.append(f'''def transition (n : Fin {len(pairs)}) : Fin 944 × Fin 944 := (transitionLookup n.val).val +theorem transition_absorbs (n : Fin {len(pairs)}) : Absorbs (transition n).1 (transition n).2 := + (transitionLookup n.val).property +end FrameGeometry +#print axioms FrameGeometry.frame_valid +#print axioms FrameGeometry.scaled_idempotent_entries +#print axioms FrameGeometry.scaled_symmetric_entries +#print axioms FrameGeometry.scaled_stack_entries +#print axioms FrameGeometry.stack_inverse_entries +#print axioms FrameGeometry.inverse_stack_entries +#print axioms FrameGeometry.transition_absorbs +''') + return '\n'.join(lines) + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument('frames', type=Path) + parser.add_argument('template', type=Path) + parser.add_argument('--output', type=Path, default=Path(__file__).with_name('FrameData.lean')) + parser.add_argument('--check', action='store_true') + args = parser.parse_args() + expected = render(args.frames, args.template) + if args.check: + assert args.output.read_text() == expected, 'FrameData.lean differs from the supplied source' + else: + args.output.write_text(expected) + + +if __name__ == '__main__': + main() diff --git a/research/lean-multi-host-source/generate_frame_moves.py b/research/lean-multi-host-source/generate_frame_moves.py new file mode 100644 index 0000000000..ac8247ee5c --- /dev/null +++ b/research/lean-multi-host-source/generate_frame_moves.py @@ -0,0 +1,114 @@ +#!/usr/bin/env python3 +"""Bind each literal MOVE to FrameData's certified source transition. +Apache-2.0. Prepared with substantial OpenAI Codex assistance. +""" +import argparse +import gzip +import hashlib +import json +from pathlib import Path + + +def search(pairs, start=0): + if len(pairs) == 1: + return str(start) + half = len(pairs) // 2 + old, new = pairs[half] + return (f'(if n < {944 * old + new} then {search(pairs[:half], start)} ' + f'else {search(pairs[half:], start + half)})') + + +def render(template): + raw = template.read_bytes() + if template.suffix == '.gz': + raw = gzip.decompress(raw) + assert hashlib.sha256(raw).hexdigest() == 'dd7833dcaff8c84b258847f4c4d65b6402c702700ae37d2c464083ee37b24126' + events = json.loads(raw)['local_programs']['forward'] + pairs = sorted({(e[2], e[3]) for e in events if e[0] == 0}) + assert len(events) == 19002 and len(pairs) == 3357 + assert sum(e[0] == 0 for e in events) == 4291 + assert all(0 <= a < 944 and 0 <= b < 944 for a, b in pairs) + return '''import FrameData +import FrameTraceLiterals + +/-! +Each of the actual4291 MOVE events selects one of FrameData's3357 certified +transition pairs. The balanced index is only an untrusted search aid; the +kernel checks the selected pair against the literal old/new frame labels. +Apache-2.0. Prepared with substantial OpenAI Codex assistance. +-/ +namespace SourceFrameMoves +set_option maxRecDepth 100000 +set_option maxHeartbeats 0 + +''' + f'def pairSearch (n : Nat) : Nat :=\n {search(pairs)}\n\n' + '''def moveIndex (e : FrameTrace.Entry) : Fin 3357 := + ⟨pairSearch (944 * e.oldFrame + e.newFrame) % 3357, Nat.mod_lt _ (by decide)⟩ + +def moveCheck (e : FrameTrace.Entry) : Bool := + decide (e.scalar.op = 0 → + (FrameGeometry.transition (moveIndex e)).1.val = e.oldFrame ∧ + (FrameGeometry.transition (moveIndex e)).2.val = e.newFrame) + +theorem moves_checked : SourceFrameTrace.forward.all moveCheck = true := by decide + +theorem move_pair (e : FrameTrace.Entry) (he : e ∈ SourceFrameTrace.forward) + (hop : e.scalar.op = 0) : + (FrameGeometry.transition (moveIndex e)).1.val = e.oldFrame ∧ + (FrameGeometry.transition (moveIndex e)).2.val = e.newFrame := by + have h := List.all_eq_true.mp moves_checked e he + exact of_decide_eq_true h hop + +theorem move_range (e : FrameTrace.Entry) (he : e ∈ SourceFrameTrace.forward) + (hop : e.scalar.op = 0) : e.oldFrame < 944 ∧ e.newFrame < 944 := by + obtain ⟨ha, hb⟩ := move_pair e he hop + exact ⟨ha ▸ (FrameGeometry.transition (moveIndex e)).1.isLt, + hb ▸ (FrameGeometry.transition (moveIndex e)).2.isLt⟩ + +def oldIndex (e : FrameTrace.Entry) : Fin 944 := + ⟨e.oldFrame % 944, Nat.mod_lt _ (by decide)⟩ + +def newIndex (e : FrameTrace.Entry) : Fin 944 := + ⟨e.newFrame % 944, Nat.mod_lt _ (by decide)⟩ + +theorem move_transition (e : FrameTrace.Entry) (he : e ∈ SourceFrameTrace.forward) + (hop : e.scalar.op = 0) : + FrameGeometry.transition (moveIndex e) = (oldIndex e, newIndex e) := by + obtain ⟨ha, hb⟩ := move_pair e he hop + obtain ⟨hra, hrb⟩ := move_range e he hop + apply Prod.ext + · apply Fin.ext + simpa only [oldIndex, Nat.mod_eq_of_lt hra] using ha + · apply Fin.ext + simpa only [newIndex, Nat.mod_eq_of_lt hrb] using hb + +/-- Every actual source MOVE satisfies the checked nested-projector identity. -/ +theorem move_absorbs (e : FrameTrace.Entry) (he : e ∈ SourceFrameTrace.forward) + (hop : e.scalar.op = 0) : FrameGeometry.Absorbs (oldIndex e) (newIndex e) := by + have h := FrameGeometry.transition_absorbs (moveIndex e) + rw [move_transition e he hop] at h + exact h + +end SourceFrameMoves +#print axioms SourceFrameMoves.moves_checked +#print axioms SourceFrameMoves.move_range +#print axioms SourceFrameMoves.move_transition +#print axioms SourceFrameMoves.move_absorbs +''' + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument('--template', type=Path, required=True) + parser.add_argument('--out', type=Path, required=True) + parser.add_argument('--check', action='store_true') + args = parser.parse_args() + source = render(args.template) + if args.check: + assert args.out.read_text() == source, 'FrameMoveData.lean changed' + else: + args.out.write_text(source) + print(f'PASS: 4291 literal MOVE events, 3357 certified pairs; {len(source)} source characters') + + +if __name__ == '__main__': + main() diff --git a/research/lean-multi-host-source/generate_frame_trace.py b/research/lean-multi-host-source/generate_frame_trace.py new file mode 100644 index 0000000000..5cea58d0b6 --- /dev/null +++ b/research/lean-multi-host-source/generate_frame_trace.py @@ -0,0 +1,60 @@ +"""Emit actual frame-label trajectory certificate and scalar-word identity. +The generator is untrusted: Lean checks every checkpoint and every scalar +projection chunk. Bind these raw entries to the original event JSON in replay. +""" +import argparse,gzip,json,hashlib +from pathlib import Path +p=argparse.ArgumentParser();p.add_argument('template',type=Path);p.add_argument('states',type=Path);p.add_argument('out',type=Path);a=p.parse_args() +t=json.loads(gzip.decompress(a.template.read_bytes()));states=json.loads(a.states.read_bytes());word=t['local_programs']['forward'];assert len(word)==19002 +entries=[] +for e in word: + op,x,y,c,f=e[:5];assert op in range(4) + if op==0:old,new,rank=y,c,f + elif op==1:old,new,rank=f,f,0 + else:old,new,rank=c,f,e[5] + entries.append((op,x,y,bool(c&1),old,new,rank)) +cur=[states['initial'][str(i)] for i in range(987)]+[0]*37;center=None;snaps=[(cur[:],center)] +for k,e in enumerate(entries): + op,x,y,odd,old,new,rank=e + assert x<987 + if op==0: + assert cur[x]==old and center!=x;cur[x]=new + elif op==1: + assert y<=987 and x!=y and cur[x]==cur[y]==old and center!=x and(y!=987 or center is not None) + elif op==2: + assert y==987 and cur[x]==old and center is None and rank==8;cur[y]=new;center=x + else: + assert y==987 and cur[x]==old and cur[y]==new and center==x and rank==0;cur[y]=0;center=None + if (k+1)%200==0 or k+1==len(entries):snaps.append((cur[:],center)) +assert cur[:987]==[states['final'][str(i)]for i in range(987)] and center is None and cur[987:]==[0]*37 +# Hash-cons only the96checkpoint trees, not an asserted computation result. +nodes=[];cache={} +def intern(xs): + key=('leaf',xs[0])if len(xs)==1 else('node',intern(xs[::2]),intern(xs[1::2])) + if key not in cache:cache[key]=len(nodes);nodes.append(key) + return cache[key] +roots=[intern(xs)for xs,_ in snaps] +defs=['import FrameTraceCore','set_option maxRecDepth 100000','set_option maxHeartbeats 0','namespace SourceFrameTrace','open FrameTrace','open TreeReplay (Tree)'] +checks=['import FrameTraceLiterals','import MatrixData','set_option maxRecDepth 100000','set_option maxHeartbeats 0','namespace SourceFrameTrace','open FrameTrace','open TreeReplay (Tree)'] +cert=['import FrameTraceCheckpoints','set_option maxRecDepth 100000','set_option maxHeartbeats 0','namespace SourceFrameTrace','open FrameTrace','open TreeReplay (Tree)'] +for i,n in enumerate(nodes):defs.append(f'def node{i} : Tree Nat := '+(f'.leaf {n[1]}'if n[0]=='leaf'else f'.node node{n[1]} node{n[2]}')) +for i,(_,center)in enumerate(snaps):defs.append(f'def state{i} : State := ⟨node{roots[i]}, '+('none'if center is None else f'some {center}')+'⟩') +N=len(snaps)-1 +checks.append('theorem initial_tabulate : Tree.tabulate 10 (fun i => state0.frames.get i) = state0.frames := by decide') +checks.append(f'theorem final_tabulate : Tree.tabulate 10 (fun i => state{N}.frames.get i) = state{N}.frames := by decide') +for i in range(N): + es=entries[200*i:200*(i+1)];defs.append(f'def chunk{i} : List Entry := ['+',\n'.join('⟨⟨%d,%d,%d,%s⟩,%d,%d,%d⟩'%(op,x,y,str(odd).lower(),old,new,rank)for op,x,y,odd,old,new,rank in es)+']') + checks.append(f'theorem project{i} : chunk{i}.map Entry.scalar = SourceMatrix.chunk{i} := rfl') + checks.append(f'theorem checkpoint{i} : runChecked chunk{i} (state{i},true) = (state{i+1},true) := by decide') +defs.append('def chunks : List (List Entry) := ['+','.join(f'chunk{i}'for i in range(N))+']') +defs.append('def forward : List Entry := chunks.flatten') +cert.append('theorem scalar_word : forward.map Entry.scalar = SourceMatrix.forwardWord := by\n simp only [forward, chunks, List.flatten_cons, List.flatten_nil, List.map_append, List.map_nil, '+', '.join(f'project{i}'for i in range(N))+', SourceMatrix.forwardWord, SourceMatrix.forwardChunks]') +checks.append('theorem combine (p q : List Entry) (s t u : State × Bool) (h : runChecked p s = t) (k : runChecked q t = u) : runChecked (p ++ q) s = u := by\n simp only [runChecked, List.foldl_append]\n rw [show List.foldl checkedStep s p = t from h]\n exact k') +defs.append(f'def suffix{N} : List Entry := []') +for i in reversed(range(N)):defs.append(f'def suffix{i} : List Entry := chunk{i} ++ suffix{i+1}') +checks.append(f'theorem finish{N} : runChecked suffix{N} (state{N},true) = (state{N},true) := rfl') +for i in reversed(range(N)):checks.append(f'theorem finish{i} : runChecked suffix{i} (state{i},true) = (state{N},true) := combine chunk{i} suffix{i+1} (state{i},true) (state{i+1},true) (state{N},true) checkpoint{i} finish{i+1}') +cert+=['theorem forward_checked : runChecked forward (state0,true) = (state96,true) := finish0','theorem forward_valid : Valid forward state0 := checked_valid forward (state0,true) (congrArg Prod.snd forward_checked)','#print axioms scalar_word','#print axioms forward_checked','#print axioms forward_valid'] +outputs={a.out.with_name('FrameTraceLiterals.lean'):defs,a.out.with_name('FrameTraceCheckpoints.lean'):checks,a.out:cert} +for path,lines in outputs.items():path.write_text('\n'.join(lines+['end SourceFrameTrace'])+'\n') +print(json.dumps({'events':len(entries),'chunks':N,'nodes':len(nodes),'source_word_sha256':hashlib.sha256(json.dumps(word,separators=(',',':')).encode()).hexdigest(),'output_sha256':{p.name:hashlib.sha256(p.read_bytes()).hexdigest()for p in outputs}})) diff --git a/research/lean-multi-host-source/generate_matrix.py b/research/lean-multi-host-source/generate_matrix.py new file mode 100644 index 0000000000..cc3bcb7983 --- /dev/null +++ b/research/lean-multi-host-source/generate_matrix.py @@ -0,0 +1,103 @@ +"""Generate untrusted symbolic checkpoints for kernel verification. +Every event is retained; Python's matrix results are checked by Lean rfl. +""" +import argparse,gzip,hashlib,json +from pathlib import Path +ap=argparse.ArgumentParser();ap.add_argument('template',type=Path);ap.add_argument('out',type=Path);a=ap.parse_args();a.out.mkdir(parents=True,exist_ok=True) +raw=gzip.decompress(a.template.read_bytes());assert hashlib.sha256(raw).hexdigest()=='dd7833dcaff8c84b258847f4c4d65b6402c702700ae37d2c464083ee37b24126' +es=json.loads(raw)['local_programs']['forward'];assert len(es)==19002 +chunk_size=200;N=(len(es)+chunk_size-1)//chunk_size +nodes={};roots=[] +def tree(rows): + key=('l',rows[0]) if len(rows)==1 else ('n',tree(rows[::2]),tree(rows[1::2])) + return nodes.setdefault(key,len(nodes)) +s=[1<=2 else 6) + if op==1: + assert 0<=y<=987 and x!=y + if e[3]&1:s[x]^=s[y] + elif op==2: + assert y==987 and s[y]==0;s[y]=s[x] + elif op==3: + assert y==987 and s[y]==s[x];s[y]=0 + if (i+1)%chunk_size==0 or i+1==len(es):roots.append(tree(s)) +expected=[((1< s + | es :: rest, s => runCheckedChunks rest (runCheckedRows es s) + +theorem combine (es : List Event) (rest : List (List Event)) + (s t u : Tree Nat × Bool) (h : runCheckedRows es s = t) + (tail : runCheckedChunks rest t = u) : runCheckedChunks (es :: rest) s = u := by + simp only [runCheckedChunks] + rw [h] + exact tail + +theorem chunks_flatten (chunks : List (List Event)) (s : Tree Nat × Bool) : + runCheckedChunks chunks s = runCheckedRows chunks.flatten s := by + induction chunks generalizing s with + | nil => rfl + | cons es rest ih => + simp only [runCheckedChunks, ih, List.flatten_cons, runCheckedRows, List.foldl_append] +'''] +for i in range(N): + lines+=['theorem checkpoint%d : runCheckedRows chunk%d state%d = state%d := by rfl'%(i,i,i,i+1)] +lines+=['def suffix%d : List (List Event) := []'%N] +for i in reversed(range(N)):lines+=['def suffix%d : List (List Event) := chunk%d :: suffix%d'%(i,i,i+1)] +lines+=['theorem finish%d : runCheckedChunks suffix%d state%d = state%d := rfl'%(N,N,N,N)] +for i in reversed(range(N)): + lines+=['theorem finish%d : runCheckedChunks suffix%d state%d = state%d :=\n combine chunk%d suffix%d state%d state%d state%d checkpoint%d finish%d'%(i,i,i,N,i,i+1,i,i+1,N,i,i+1)] +lines+=['theorem runFull_checked : runCheckedChunks forwardChunks (initial,true) = (expected,true) := finish0'] +prefix='\n'.join(lines)+'\n#print axioms runFull_checked\nend SourceMatrix\n' +a.out.joinpath('MatrixCheckpoints.lean').write_text(prefix) +wrapper='''import MatrixCheckpoints +namespace SourceMatrix +open TreeReplay + +theorem literal_word_checked : runCheckedRows forwardWord (initial,true) = (expected,true) := + (chunks_flatten forwardChunks (initial,true)).symm.trans runFull_checked + +theorem literal_word_rows : runRows forwardWord initial = expected := + (checked_projection forwardWord (initial,true)).symm.trans + (congrArg Prod.fst literal_word_checked) + +#print axioms literal_word_checked +#print axioms literal_word_rows +end SourceMatrix +''' +a.out.joinpath('MatrixCertificate.lean').write_text(wrapper) +print(json.dumps({'events':len(es),'chunks':N,'nodes':len(nodes),'sizes':{name:a.out.joinpath(name).stat().st_size for name in ['MatrixData.lean','MatrixCheckpoints.lean','MatrixCertificate.lean']}})) diff --git a/research/lean-multi-host-source/generate_ownership_data.py b/research/lean-multi-host-source/generate_ownership_data.py new file mode 100644 index 0000000000..9ef05d9b36 --- /dev/null +++ b/research/lean-multi-host-source/generate_ownership_data.py @@ -0,0 +1,98 @@ +#!/usr/bin/env python3 +"""Extract constructive owner permutations from the pinned actual stage-2 call. +Offline provenance bridge, not a kernel-verified JSON parser. Apache-2.0. +Prepared with substantial OpenAI Codex assistance. +""" +import argparse, gzip, hashlib, json +from pathlib import Path + +def sha(p): return hashlib.sha256(p.read_bytes()).hexdigest() +def arr(xs): return '#[' + ', '.join(map(str,xs)) + ']' +def tree(xs, default=0): + n=1 + while n=240}) + assert len(keys)==16 + ps=[];ins=[];srcbits=[];tarbits=[];details=[] + for child,off,w,fr in keys: + f=fs[str(fr)];src=[row.index(1) for row in f['A']] + assert all(row==[int(j==src[i]) for j in range(8)] for i,row in enumerate(f['A'])) + occupied=sorted(set(range(8))-set(src));assert len(occupied)==f['dim']==8-w + assert sorted(f['B'])==sorted([[2*int(j==i) for j in range(8)] for i in occupied]) + assert child in (1,2) + dst=list(range((15 if child==1 else 1)+off,(15 if child==1 else 1)+off+w)) + assert len(src)==len(dst)==w + perm=dict(zip(src,dst));perm.update(zip([i for i in range(64) if i not in src],[i for i in range(64) if i not in dst]));perm=[perm[i] for i in range(64)] + assert sorted(perm)==list(range(64));inv=[perm.index(i) for i in range(64)] + ps.append(perm);ins.append(inv);srcbits.append(sum(1<=240] + codes=[16*f+tag for f,tag in zip(fams,tags)];assert len(set(codes))==987 + inverse=[987]*(720*16) + for i,code in enumerate(codes):inverse[code]=i + assert all(240<=f<720 for f in fams[240:]);assert all((tag>=7)==(f>=480) for f,tag in zip(fams[240:],tags[240:])) + # A tiny faithful permutation fingerprint; digits are base64 images of axes0..7. + fingerprints=[sum(p[i]*64**i for i in range(8)) for p in ps] + assert len(set(fingerprints))==16 + out='''import Std\n\n/-! Literal ownership certificate for PR442 stage2/replica0, all987roles.\nGenerated by generate_ownership_data.py. The extractor is not kernel verified.\nApache-2.0. Prepared with substantial OpenAI Codex assistance. -/\nset_option maxRecDepth 1000000\nset_option maxHeartbeats 0\nnamespace SourceOwnership\n\ninductive Lookup where\n | leaf : Nat → Lookup\n | node : Lookup → Lookup → Lookup\n\ndef lookup : Lookup → Nat → Nat\n | .leaf n, _ => n\n | .node l r, i => if i % 2 == 0 then lookup l (i / 2) else lookup r (i / 2)\n\n''' + for name,vals in [('familyTable',fams),('tagTable',tags),('initialFrameTable',[s['initial'][str(i)] for i in range(987)]),('inverseOwnerTable',inverse),('sourceBits',srcbits),('targetBits',tarbits),('tagInitialFrame',[k[3] for k in keys]),('tagChild',[k[0] for k in keys]),('tagOffset',[k[1] for k in keys]),('tagWidth',[k[2] for k in keys])]:out+=f'def {name} : Lookup := {tree(vals)}\n\n' + for name,vals in [('permTable',ps),('invPermTable',ins)]:out+=f'def {name} : Lookup := '+tree([x for v in vals for x in v])+'\n\n' + out+='''abbrev Role := Fin 987 +abbrev Tag := Fin 16 +abbrev Axis := Fin 64 + +def family (r : Role) : Nat := lookup familyTable r.val +def tag (r : Role) : Tag := ⟨lookup tagTable r.val % 16, Nat.mod_lt _ (by decide)⟩ +def perm (t : Tag) (i : Axis) : Axis := + ⟨lookup permTable (64 * t.val + i.val) % 64, Nat.mod_lt _ (by decide)⟩ +def invPerm (t : Tag) (i : Axis) : Axis := + ⟨lookup invPermTable (64 * t.val + i.val) % 64, Nat.mod_lt _ (by decide)⟩ +def sourceMask (t : Tag) (i : Axis) : Bool := (lookup sourceBits t.val).testBit i.val +def targetMask (t : Tag) (i : Axis) : Bool := (lookup targetBits t.val).testBit i.val + +theorem perm_inverse : ∀ (t : Tag) (i : Axis), invPerm t (perm t i) = i := by decide +theorem inverse_perm : ∀ (t : Tag) (i : Axis), perm t (invPerm t i) = i := by decide +theorem perm_support : ∀ (t : Tag) (i : Axis), targetMask t (perm t i) = sourceMask t i := by decide + +def fingerprint (t : Tag) : Nat := + (List.range 8).foldl (fun n i => n + (perm t ⟨i % 64, Nat.mod_lt _ (by decide)⟩).val * 64^i) 0 + +theorem fingerprint_injective : ∀ (a b : Tag), fingerprint a = fingerprint b → a = b := by decide + +theorem owner_inverse : ∀ r : Role, lookup inverseOwnerTable (16 * family r + (tag r).val) = r.val := by decide + +theorem family_tag_injective {r s : Role} (hf : family r = family s) (ht : tag r = tag s) : r = s := by + apply Fin.ext + rw [← owner_inverse r, ← owner_inverse s, hf, ht] + +theorem family_data : ∀ r : Fin 240, family ⟨r.val, Nat.lt_trans r.isLt (by decide)⟩ = r.val := by decide + +theorem helper_range : ∀ r : Role, 240 ≤ r.val → 240 ≤ family r ∧ family r < 720 := by decide + +theorem helper_frame : ∀ r : Role, 240 ≤ r.val → lookup initialFrameTable r.val = lookup tagInitialFrame (tag r).val := by decide + +theorem helper_child : ∀ r : Role, 240 ≤ r.val → ((tag r).val ≥ 7 ↔ family r ≥ 480) := by decide + +end SourceOwnership +#print axioms SourceOwnership.perm_inverse +#print axioms SourceOwnership.perm_support +#print axioms SourceOwnership.fingerprint_injective +#print axioms SourceOwnership.family_tag_injective +#print axioms SourceOwnership.helper_frame +''' + a.out.write_text(out) + receipt=dict(source_commit='4e16d001d505d4f21dd2bcfc44591f9be4c279bd',template_sha256=sha(a.template),template_raw_sha256=hashlib.sha256(raw).hexdigest(),states_sha256=sha(a.states),frames_sha256=sha(a.frames),call={k:c[k] for k in ('stage','replica','pair','orientation','local_hash')},roles=[dict(role=i,family=fams[i],tag=tags[i],initial_frame=s['initial'][str(i)],source_route=c['owners'][i][1]) for i in range(987)],charts=details,construction='Map sorted local residual coordinate axes onto sorted actual pending axes; complete by order-preserving bijection of complements. For child2 postcompose by actual B_port⊕I56; child1 has identity postcomposition.',output_sha256=sha(a.out)) + if a.receipt:a.receipt.write_text(json.dumps(receipt,indent=2)+'\n') + print('PASS: 987 roles, 747 helpers, 317 helper families, 16 constructive chart permutations') +if __name__=='__main__':main() diff --git a/research/lean-multi-host-source/generate_parent_ownership.py b/research/lean-multi-host-source/generate_parent_ownership.py new file mode 100644 index 0000000000..f2a57f77af --- /dev/null +++ b/research/lean-multi-host-source/generate_parent_ownership.py @@ -0,0 +1,115 @@ +#!/usr/bin/env python3 +"""Construct parent-bank charts for the pinned original stage-2 invocation. +The emitted finite statements are checked by Lean; JSON extraction is external. +Apache-2.0. Prepared with substantial OpenAI Codex assistance. +""" +import argparse,gzip,hashlib,json +from pathlib import Path + +def read_json(p): + raw=p.read_bytes() + return json.loads(gzip.decompress(raw) if p.suffix=='.gz' else raw) +def sha(p):return hashlib.sha256(p.read_bytes()).hexdigest() +def tree(xs,default=0): + n=1 + while n=240}) + assert len(keys)==61 + ps=[];ins=[];srcbits=[];tarbits=[];details=[] + for off,w,fr in keys: + f=fs[str(fr)];src=[row.index(1) for row in f['A']] + assert src==sorted(src) + assert all(row==[int(j==src[i])for j in range(8)]for i,row in enumerate(f['A'])) + occupied=sorted(set(range(8))-set(src));assert len(occupied)==f['dim']==8-w + assert sorted(f['B'])==sorted([[2*int(j==i)for j in range(8)]for i in occupied]) + dst=list(range(off,off+w));assert 0<=off=240];tags=[slot_tags[z]for z in slots] + assert len(set(fams[240:]))==172 + assert all(7680<=f<14259 for f in fams[240:]) + codes=[59*f+tag for f,tag in zip(fams,tags)];assert len(set(codes))==987 + inverse=[987]*(max(codes)+1) + for i,code in enumerate(codes):inverse[code]=i + fingerprints=[sum(p[i]*64**i for i in range(8))for p in ps];assert len(set(fingerprints))==59 + out='''import OwnershipData +/-! +Literal original-bank ownership certificate for PR442 stage2/replica0. +Generated by generate_parent_ownership.py. Extraction is not kernel verified. +Apache-2.0. Prepared with substantial OpenAI Codex assistance. +-/ +set_option maxRecDepth 1000000 +set_option maxHeartbeats 0 +namespace ParentOwnership +open SourceOwnership (Lookup lookup) + +''' + for name,vals in [('familyTable',fams),('slotTable',slots),('slotTagTable',slot_tags),('initialFrameTable',[s['initial'][str(i)]for i in range(987)]),('inverseOwnerTable',inverse),('sourceBits',srcbits),('targetBits',tarbits),('slotInitialFrame',[k[2]for k in keys]),('slotOffset',[k[0]for k in keys]),('slotWidth',[k[1]for k in keys]),('permTable',[x for p in ps for x in p]),('invPermTable',[x for p in ins for x in p])]: + out+=f'def {name} : Lookup := {tree(vals,987 if name=="inverseOwnerTable" else 0)}\n\n' + out+='''abbrev Role := Fin 987 +abbrev Tag := Fin 59 +abbrev Slot := Fin 61 +abbrev Axis := Fin 64 + +def family (r : Role) : Nat := lookup familyTable r.val +def slot (r : Role) : Slot := ⟨lookup slotTable r.val % 61, Nat.mod_lt _ (by decide)⟩ +def slotTag (s : Slot) : Tag := ⟨lookup slotTagTable s.val % 59, Nat.mod_lt _ (by decide)⟩ +def tag (r : Role) : Tag := slotTag (slot r) +def perm (t : Tag) (i : Axis) : Axis := + ⟨lookup permTable (64*t.val+i.val) % 64, Nat.mod_lt _ (by decide)⟩ +def invPerm (t : Tag) (i : Axis) : Axis := + ⟨lookup invPermTable (64*t.val+i.val) % 64, Nat.mod_lt _ (by decide)⟩ +def sourceMask (t : Slot) (i : Axis) : Bool := (lookup sourceBits t.val).testBit i.val +def targetMask (t : Slot) (i : Axis) : Bool := (lookup targetBits t.val).testBit i.val + +theorem perm_inverse : ∀ (t : Tag) (i : Axis), invPerm t (perm t i) = i := by decide +theorem inverse_perm : ∀ (t : Tag) (i : Axis), perm t (invPerm t i) = i := by decide +theorem perm_support : ∀ (s : Slot) (i : Axis), targetMask s (perm (slotTag s) i) = sourceMask s i := by decide + +def fingerprint (t : Tag) : Nat := + (List.range 8).foldl (fun n i => n + (perm t ⟨i % 64, Nat.mod_lt _ (by decide)⟩).val * 64^i) 0 + +theorem fingerprint_injective : ∀ (a b : Tag), fingerprint a = fingerprint b → a = b := by decide + +theorem owner_inverse : ∀ r : Role, lookup inverseOwnerTable (59*family r+(tag r).val) = r.val := by decide + +theorem family_tag_injective {r s : Role} (hf : family r = family s) (ht : tag r = tag s) : r = s := by + apply Fin.ext + rw [← owner_inverse r, ← owner_inverse s, hf, ht] + +theorem family_data : ∀ r : Fin 240, family ⟨r.val, Nat.lt_trans r.isLt (by decide)⟩ = r.val := by decide + +theorem helper_range : ∀ r : Role, 240 ≤ r.val → 7680 ≤ family r ∧ family r < 14259 := by decide + +theorem helper_frame : ∀ r : Role, 240 ≤ r.val → lookup initialFrameTable r.val = lookup slotInitialFrame (slot r).val := by decide + +end ParentOwnership +#print axioms ParentOwnership.perm_inverse +#print axioms ParentOwnership.perm_support +#print axioms ParentOwnership.fingerprint_injective +#print axioms ParentOwnership.family_tag_injective +#print axioms ParentOwnership.helper_frame +''' + a.out.write_text(out) + if a.receipt:a.receipt.write_text(json.dumps(dict(source_commit='4e16d001d505d4f21dd2bcfc44591f9be4c279bd',template_sha256=sha(a.template),template_raw_sha256=hashlib.sha256(raw).hexdigest(),states_sha256=sha(a.states),frames_sha256=sha(a.frames),private_family=14259,call={k:c[k]for k in ('stage','replica','pair','orientation','local_hash')},roles=[dict(role=i,family=fams[i],tag=tags[i],slot=slots[i],initial_frame=s['initial'][str(i)],source_route=c['owners'][i][1])for i in range(987)],charts=details,permutations=ps,construction='Map each sorted local residual coordinate basis onto its actual bank interval; complete by the increasing bijection of complements. No exterior family-chart postcomposition.',output_sha256=sha(a.out)),indent=2)+'\n') + print(f'PASS: 987 roles,747 helpers,172 bank families,61 slots,59 permutations; source {a.out.stat().st_size} bytes') +if __name__=='__main__':main() diff --git a/research/lean-multi-host-source/generate_port_data.py b/research/lean-multi-host-source/generate_port_data.py new file mode 100644 index 0000000000..c08512b4e7 --- /dev/null +++ b/research/lean-multi-host-source/generate_port_data.py @@ -0,0 +1,199 @@ +#!/usr/bin/env python3 +"""Generate the literal dyadic port-basis certificate from pinned GEOMETRY.json. + +Parsing and code generation are untrusted; Lean checks the emitted finite +orthogonality proposition. Source SHA-256 and exact entry reconstruction are +recorded here to make the source-to-literal boundary reproducible. +""" +import argparse +from fractions import Fraction +import hashlib +import json +from pathlib import Path + + +def tree(values): + size = 1 + while size < len(values): + size *= 2 + values = list(values) + [0] * (size - len(values)) + def go(xs): + if all(x == xs[0] for x in xs): + return f"(.leaf ({xs[0]}))" + return f"(.node {go(xs[::2])} {go(xs[1::2])})" + return go(values) + + +def render(path: Path) -> str: + raw = path.read_bytes() + geometry = json.loads(raw) + ports = geometry["ports"] + assert len(ports) == 120 + matrices, routes = [], [] + for index, port in enumerate(ports): + assert port["port"] == index + assert len(port["q"]) == 8 + assert len(port["complement_columns"]) == 8 + rows = [] + for q, complement in zip(port["q"], port["complement_columns"]): + assert len(complement) == 7 + row = [Fraction(q)] + [2 * Fraction(x) for x in complement] + assert all(x.denominator == 1 for x in row) + rows.append([x.numerator for x in row]) + matrices.append(rows) + assert len(port["rho15"]) == 15 + route = [] + for row in port["rho15"]: + assert len(row) == 15 + row = [4 * Fraction(x) for x in row] + assert all(x.denominator == 1 for x in row) + route.append([x.numerator for x in row]) + routes.append(route) + stage2 = next(route for route in port["routes"] if route["stage"] == 2) + assert stage2["axes"] == list(range(8)) + list(range(15, 22)) + # Informative generator check; the generated Lean theorem independently + # checks the complete same integer identities in the kernel. + for matrix in matrices: + for i in range(8): + for j in range(8): + assert sum(matrix[k][i] * matrix[k][j] for k in range(8)) == (4 if i == j else 0) + assert sum(matrix[i][k] * matrix[j][k] for k in range(8)) == (4 if i == j else 0) + for basis, route in zip(matrices, routes): + for i in range(15): + for j in range(15): + if i < 8 and j < 8: + expected = basis[i][0] * basis[j][0] + elif i < 8: + expected = 2 * basis[i][j - 7] + elif j < 8: + expected = 2 * basis[j][i - 7] + else: + expected = 0 + assert route[i][j] == expected + header = f'''import Std + +/-! +Literal port charts and rho15 matrices from PR442's inherited GEOMETRY.json. +Apache-2.0. Prepared with substantial OpenAI Codex assistance. +Generated by generate_port_data.py; its JSON parser is not kernel verified. +Source SHA-256: {hashlib.sha256(raw).hexdigest()} +Each basis is exactly 2 B_q = [q | 2 complement_columns]; each route is 4 rho15. +Every port carries small kernel-checked column, row and route certificates. +Balanced lookup selects certified records, avoiding one large normalizer cache. +-/ +namespace PortGeometry +set_option maxHeartbeats 0 +set_option maxRecDepth 100000 + +inductive IntLookup where + | leaf : Int → IntLookup + | node : IntLookup → IntLookup → IntLookup + +def intLookup : IntLookup → Nat → Int + | .leaf n, _ => n + | .node l r, i => if i % 2 == 0 then intLookup l (i / 2) else intLookup r (i / 2) + +def columnDot (b : Fin 8 → Fin 8 → Int) (i j : Fin 8) : Int := + b 0 i * b 0 j + (b 1 i * b 1 j + (b 2 i * b 2 j + (b 3 i * b 3 j + + (b 4 i * b 4 j + (b 5 i * b 5 j + (b 6 i * b 6 j + (b 7 i * b 7 j + 0))))))) + +def rowDot (b : Fin 8 → Fin 8 → Int) (i j : Fin 8) : Int := + b i 0 * b j 0 + (b i 1 * b j 1 + (b i 2 * b j 2 + (b i 3 * b j 3 + + (b i 4 * b j 4 + (b i 5 * b j 5 + (b i 6 * b j 6 + (b i 7 * b j 7 + 0))))))) + +def routeExpected (b : Fin 8 → Fin 8 → Int) (i j : Fin 15) : Int := + if hi : i.val < 8 then + if hj : j.val < 8 then b ⟨i.val, hi⟩ 0 * b ⟨j.val, hj⟩ 0 + else 2 * b ⟨i.val, hi⟩ ⟨j.val - 7, by omega⟩ + else if hj : j.val < 8 then 2 * b ⟨j.val, hj⟩ ⟨i.val - 7, by omega⟩ + else 0 + +structure CertifiedPort where + basis : Fin 8 → Fin 8 → Int + route : Fin 15 → Fin 15 → Int + column_correct : ∀ i j, columnDot basis i j = if i = j then 4 else 0 + row_correct : ∀ i j, rowDot basis i j = if i = j then 4 else 0 + route_correct : ∀ i j, route i j = routeExpected basis i j + +''' + lines = [header] + for index, (b, r) in enumerate(zip(matrices, routes)): + btree = tree([x for row in b for x in row]) + rtree = tree([r[i][j] if i < 15 and j < 15 else 0 + for i in range(16) for j in range(16)]) + lines.append(f"def certified{index} : CertifiedPort where\n" + f" basis := fun i j => intLookup {btree} (8 * i.val + j.val)\n" + f" route := fun i j => intLookup {rtree} (16 * i.val + j.val)\n" + " column_correct := by decide\n row_correct := by decide\n" + " route_correct := by decide\n\n") + lines.append('''inductive PortLookup where + | leaf : CertifiedPort → PortLookup + | node : PortLookup → PortLookup → PortLookup + +def lookupPort : PortLookup → Nat → CertifiedPort + | .leaf p, _ => p + | .node l r, i => if i % 2 == 0 then lookupPort l (i / 2) else lookupPort r (i / 2) + +''') + names = [f'certified{i}' for i in range(120)] + ['certified0'] * 8 + lines.append('def certifiedTable : PortLookup := ' + tree(names) + '\n\n') + lines.append('''def portData (port : Fin 120) : CertifiedPort := lookupPort certifiedTable port.val + +def doubledBasis (port : Fin 120) : Fin 8 → Fin 8 → Int := (portData port).basis + +def quarteredRoute (port : Fin 120) : Fin 15 → Fin 15 → Int := (portData port).route + +def expectedQuarteredRoute (port : Fin 120) (i j : Fin 15) : Int := + routeExpected (doubledBasis port) i j + +def doubledDot (port : Fin 120) (i j : Fin 8) : Int := columnDot (doubledBasis port) i j + +theorem doubled_orthogonal_entries (port : Fin 120) (i j : Fin 8) : + doubledDot port i j = if i = j then 4 else 0 := + (portData port).column_correct i j + +theorem quarteredRoute_exact (port : Fin 120) (i j : Fin 15) : + quarteredRoute port i j = expectedQuarteredRoute port i j := + (portData port).route_correct i j + +end PortGeometry +#print axioms PortGeometry.doubled_orthogonal_entries +#print axioms PortGeometry.quarteredRoute_exact +''') + return ''.join(lines) + + +ROW_CERTIFICATE = '''import PortData + +/-! Reverse orthogonality extracted from the checked exact source table. +Apache-2.0. Prepared with substantial OpenAI Codex assistance. -/ +namespace PortGeometry + +def doubledRowDot (port : Fin 120) (i j : Fin 8) : Int := rowDot (doubledBasis port) i j + +theorem doubled_row_orthogonal_entries (port : Fin 120) (i j : Fin 8) : + doubledRowDot port i j = if i = j then 4 else 0 := + (portData port).row_correct i j + +end PortGeometry +#print axioms PortGeometry.doubled_row_orthogonal_entries +''' + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("geometry", type=Path) + parser.add_argument("--output", type=Path, default=Path(__file__).with_name("PortData.lean")) + parser.add_argument("--check", action="store_true") + args = parser.parse_args() + expected = render(args.geometry) + if args.check: + assert args.output.read_text() == expected, "PortData.lean does not match supplied source" + assert args.output.with_name("PortRowData.lean").read_text() == ROW_CERTIFICATE + else: + args.output.write_text(expected) + args.output.with_name("PortRowData.lean").write_text(ROW_CERTIFICATE) + + +if __name__ == "__main__": + main() diff --git a/research/lean-multi-host-source/independent-word-binding.json b/research/lean-multi-host-source/independent-word-binding.json new file mode 100644 index 0000000000..658376975b --- /dev/null +++ b/research/lean-multi-host-source/independent-word-binding.json @@ -0,0 +1,114 @@ +{ + "status": "PASS_INDEPENDENT_WORD_BINDING", + "records": 19002, + "record_bytes": 456048, + "record_sha256": "99cb283793818ad03f8f16f95a8eb23d0b18769d0657d58043fb7a427471c35d", + "raw_forward_canonical_sha256": "4ed9ed1f7756ea6ff2c299b61ed1dc3fe0fa5bbbb91b5170133596b452c8085e", + "opcode_counts": { + "1": 14693, + "0": 4291, + "2": 9, + "3": 9 + }, + "lean_chunks": 96, + "chunk_lengths": [ + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 200, + 2 + ], + "comparison": "all ordered projected events, every raw record reconstructed, parent=hosted forward word, selected stage2replica0pair0forward call unique", + "independent_frame_centre_check": "PASS: exact current frames, monotone frame ranks, equal-frame XOR, no centre writes, private reads only while open, 9 paired rank8 copies/erasures, final frame table" +} diff --git a/research/lean-multi-host-source/inputs/frames.json.gz b/research/lean-multi-host-source/inputs/frames.json.gz new file mode 100644 index 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asynchronous whole owners", + "head": "246bfacd4cb4072836ae3147099f548bb728229f", + "updated_at": "2026-10-11T23:22:36Z" + }, + { + "number": 510, + "title": "Bit word R480 at nine stages: c = 0.001587447106092548137108 (+1.41% over #493)", + "head": "64edee18af02aab0c1696b677a0287dd0146381b", + "updated_at": "2026-10-11T23:11:52Z" + }, + { + "number": 513, + "title": "[Lean] Add sequential completed-bank source bindings", + "head": "005dd3f4e3cba8d1761abc4ab391aaf6d14d6f73", + "updated_at": "2026-10-11T23:10:56Z" + }, + { + "number": 477, + "title": "Add categorized experiment log: 100 ideas, 300 trials, and recorded failures", + "head": "a5b588d7f16be383ec80e6c5adaa1a75049cb758", + "updated_at": "2026-10-11T23:06:05Z" + }, + { + "number": 512, + "title": "Conditional \u03ba = 0.001388049083313897: fresh partial-own asynchronous whole-owner certificate", + "head": "73d367fe754cf5921cd954221133b20ac752f932", + "updated_at": "2026-10-11T23:05:48Z" + }, + { + "number": 473, + "title": 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"number": 493, + "title": "Conditional \u03ba = 0.001303530097714685: an E8 bit word with 489 helpers, sources as carriers (0.001325 with #484's draft complex supplier)", + "head": "c3a9a436b84fe44fdc223a5784d84736d1c2d3c7", + "updated_at": "2026-10-11T22:09:48Z" + }, + { + "number": 505, + "title": "Asynchronous whole-owner replicas: kappa 0.001357701757628940 (+1.9236% over #496)", + "head": "4ee769c8e28837482272b5f4742497da8e2fc9d4", + "updated_at": "2026-10-11T22:05:40Z" + }, + { + "number": 499, + "title": "Retimed complex word (#495) on cross-copy hosting with #493's bit word: conditional \u03ba 1.452948511251494e-3 (stacked on #494)", + "head": "0f3e55dbf6b29a28bf462b4b3ec2a3ef06a28f5d", + "updated_at": "2026-10-11T22:00:08Z" + }, + { + "number": 485, + "title": "Method + bounds (no frontier claim): kernel width rule, EXACT pivot maximum 112 and a seeded 112-pivot selection on the R715 word", + "head": "af51ea7ad6570f04c8424be7cc6f4070bfd1e6ff", + "updated_at": 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494, + "title": "Under review (split-residual interface): #493's R489 bit word with #448's cross-copy complex supplier; computed \u03ba = 0.001435468764627892 not established", + "head": "419907c71246c050f1c3fd2a504469b74bf7798e", + "updated_at": "2026-10-11T21:15:59Z" + }, + { + "number": 480, + "title": "Under review (split-residual interface): cross-copy hosting on #472's R715 eleven-stage word; computed \u03ba = 0.001372550159367980 not established", + "head": "668c7dd0fa76d0da4289c9dea63b965e730142d0", + "updated_at": "2026-10-11T21:15:57Z" + }, + { + "number": 448, + "title": "Under review (split-residual interface): cross-copy idle-axis hosting, one residual on two copies of one idle child; computed \u03ba = 0.001330733966732373 not established", + "head": "359022bcd71143e45d48def0dd005bf67f339aa7", + "updated_at": "2026-10-11T21:15:56Z" + }, + { + "number": 484, + "title": "Complex supplier b \u2248 1.327\u00b710\u207b\u00b3 (+4.7%) on whole-residual hosting: shared-donor kernel and entrance gauges with paid residual wrappers (conditional on two lemmas)", + "head": "d30a05f90190dff6435e62ebed95aff9a0ddb610", + "updated_at": "2026-10-11T21:12:48Z" + }, + { + "number": 497, + "title": "Conditional \u03ba = 0.001325117552367841: moment-directed complex hosting", + "head": "b1972da7c6d11eb9745273d81bbba3fe9e565e88", + "updated_at": "2026-10-11T21:00:36Z" + }, + { + "number": 496, + "title": "Conditional \u03ba = 0.001332077359286333: pooled whole-owner complex supply", + "head": "00cf70efd6a8637531deafef698157ca83e249ee", + "updated_at": "2026-10-11T20:57:04Z" + }, + { + "number": 491, + "title": "R715 count-only fallback correction: conditional \u03ba = 0.001296611983223706", + "head": "996f67f7c21b8e56b4a2b0174c419ce48c480414", + "updated_at": "2026-10-11T20:56:33Z" + }, + { + "number": 495, + "title": "Add combined E8 witness at \u03ba = 0.001307044366925301", + "head": "355d9f7ff293e291676ff4a32eed434419692576", + "updated_at": "2026-10-11T20:44:01Z" + }, + { + "number": 466, + "title": "Conditional \u03ba = 0.001274415506145115: complex response kernel + rank151/mixed bit word on #451 (+0.670%)", + "head": "c2f8e18b1b3e39abb5d2f63b9ee4582c96cd75de", + "updated_at": "2026-10-11T20:18:17Z" + }, + { + "number": 489, + "title": "Replace local Gaussian inverse branches with two convolutions", + "head": "8922e3b3f0fd7772b0fb42028eb2532984c3ab42", + "updated_at": "2026-10-11T20:18:08Z" + }, + { + "number": 492, + "title": "Conditional kappa = 0.001297375468897877: response retiming and stage-conditioned donor flags (+0.05929% over #483)", + "head": "0c9eb6f80cef2e5797e5b7af940f447c0bdf25ad", + "updated_at": "2026-10-11T20:07:32Z" + }, + { + "number": 490, + "title": "Conditional \u03ba = 0.001295625678120464: whole-owner GL cover with sharp fallback", + "head": "63e9d2c22a02fdf40df824ba95d21cd2d6f01db7", + "updated_at": "2026-10-11T19:58:25Z" + }, + { + "number": 488, + "title": "[Lean] Verification of binary input preparation, \u03ba=0.000661885549259598", + "head": "edd3102b415df5b9d6f633ac0a4dedcf69c58525", + "updated_at": "2026-10-11T19:50:47Z" + }, + { + "number": 458, + "title": "Conditional \u03ba = 0.001274032589159993: complex kernel with paid residual adapters", + "head": "44e9eae8287951c1e6dbbd3c553f5743fe2240b0", + "updated_at": "2026-10-11T19:46:04Z" + }, + { + "number": 487, + "title": "[Lean] Verification of selected 1320-port bijection, \u03ba=0.000661885549259598", + "head": "15b49f66cb2d2663fb71672f4d594e755bd93938", + "updated_at": "2026-10-11T19:45:38Z" + }, + { + "number": 486, + "title": "Build binary compression halo boxes with fused streaming and sparse repair", + "head": "f14e5881b7681641fade599b5389995843088e20", + "updated_at": "2026-10-11T19:43:25Z" + }, + { + "number": 483, + "title": "Conditional kappa = 0.001296606691405309: response-kernel cancellation and nested-donor flags on R715", + "head": "3738c3ce2d04d6a6c6363408ff9402286f592bc7", + "updated_at": "2026-10-11T19:33:13Z" + }, + { + "number": 186, + "title": "Shared-edge supplier, coordinated frames and entrance banks: conditional kappa = 6.61885549259598e-4", + "head": "bea1d52fd330c699903f81612ee58be81697d1eb", + "updated_at": "2026-10-11T19:28:42Z" + }, + { + "number": 482, + "title": "Conditional \u03ba = 0.001168862033074029: R715 target factors in non-hosting banks", + "head": "ab81e78de235ed11d4279ee89b0824650c372e17", + "updated_at": "2026-10-11T19:18:57Z" + }, + { + "number": 481, + "title": "Batch Gaussian boundary right-hand sides to reduce their cost", + "head": "5f3db6a11198bab07d8effe8f0c9f5df9c3f2eb7", + "updated_at": "2026-10-11T19:06:42Z" + }, + { + "number": 479, + "title": "Remove the chirp-generation dimension factor with exact streamed phases", + "head": "40dd01058439cdffae3e3b41c4fe52edaccf5f91", + "updated_at": "2026-10-11T18:34:44Z" + }, + { + "number": 478, + "title": "Conditional kappa = 0.001295508560071773: fourteen target factors on PR473 (+0.1226%)", + "head": "bea1d52fd330c699903f81612ee58be81697d1eb", + "updated_at": "2026-10-11T18:31:32Z" + }, + { + "number": 476, + "title": "Conditional kappa = 0.001291542455423938: two-layer target factoring on R715 (+0.1461% over #470)", + "head": "e850569c33ad1d5771e2f8b1c6dfe7a445396167", + "updated_at": "2026-10-11T18:14:32Z" + }, + { + "number": 475, + "title": "Remove compact FFT reservation and top-bit costs with complementary reservoirs", + "head": "5996e33ecad6a0ccd578aec58831457829d75575", + "updated_at": "2026-10-11T18:13:47Z" + }, + { + "number": 376, + "title": "Conditional \u03ba=0.0011208649522582786: split centres with complete signed admission", + "head": "5522b4edf9748ccda787df81f0a83eda83cdc4e8", + "updated_at": "2026-10-11T18:08:52Z" + }, + { + "number": 468, + "title": "Prove nine calls are necessary for three abelian bit registers", + "head": "07a78bf335b0b5039a1fecd7cd74a0fe1d1605ea", + "updated_at": "2026-10-11T18:08:13Z" + }, + { + "number": 470, + "title": "Conditional \u03ba = 0.001291474845253222: retimed kernel and reordered R715 deliveries", + "head": "aaf3ef64672cb96d2f0cfe36410640ee59c07c9f", + "updated_at": "2026-10-11T18:07:43Z" + }, + { + "number": 474, + "title": "Bind the selected gen4 certificate to fresh replay outputs", + "head": "6563bc97e4c0f86d4ff9b11476ae925a6be7ff7f", + "updated_at": "2026-10-11T18:04:47Z" + }, + { + "number": 397, + "title": "Formalize the indexed B_K scalar bridge and bind the pinned B3 word", + "head": "cb6455fa1e9af68be47c33948d3d1a6f0717a5e4", + "updated_at": "2026-10-11T18:03:59Z" + }, + { + "number": 469, + "title": "Conditional \u03ba = 0.001350580884553120: gate-frame retiming of #450's eleven-stage cross-copy word (+0.2105%)", + "head": "a820816f07f60544bd38c6f12c38a9c25066ddf0", + "updated_at": "2026-10-11T18:03:40Z" + }, + { + "number": 275, + "title": "Finite assembly, source-basis cost reduction, and E8 verification", + "head": "e500c9c4217483de882cf06e6e80b25b70ea1ca5", + "updated_at": "2026-10-11T18:01:04Z" + }, + { + "number": 450, + "title": "Conditional \u03ba = 0.001347744547714835: eleven-stage cross-copy hosting with target mixing (+1.278% over #448)", + "head": "350943275564c53b209c1277aac7d691807726be", + "updated_at": "2026-10-11T17:45:50Z" + }, + { + "number": 464, + "title": "Conditional \u03ba = 0.001347744550711765: sharper bit bad-class charge on #450's word", + "head": "8c546e9918ae37d842916d89ffe28f2c08cdb3d3", + "updated_at": "2026-10-11T17:45:22Z" + }, + { + "number": 471, + "title": "Conditional kappa = 0.001274548075945587: full-nine-axis kernel normalization and same-owner spectator borrowing", + "head": "56b3da6aa1295d37ce43f1753479bfe4737b7ac3", + "updated_at": "2026-10-11T17:43:32Z" + }, + { + "number": 467, + "title": "Conditional \u03ba = 0.001289283116193775: R715 shared kernel, retiming and whole pooling", + "head": "e28109cd3fe2f2853449e4c49a55887790e16ba2", + "updated_at": "2026-10-11T17:39:33Z" + }, + { + "number": 463, + "title": "Conditional \u03ba = 0.001283479303751122: E8 bit word R715 (carrier lower bound + F2 overlap cancellation) with #458's complex supplier (+0.711% over #460)", + "head": "cdf0c1c6540df987467988fd771340670f4136f3", + "updated_at": "2026-10-11T17:34:40Z" + }, + { + "number": 454, + "title": "Conditional \u03ba = 0.001266536148630310: target mixing with whole-residual hosting", + "head": "d14eb0dd425bd681e3b43f208d089e679d600176", + "updated_at": "2026-10-11T17:33:36Z" + }, + { + "number": 460, + "title": "Conditional \u03ba = 0.001274415506145115: paid complex kernel + rank151 target mixing", + "head": "b98bbb4bc398ad67a41f123c6c301628c37e1d6b", + "updated_at": "2026-10-11T17:32:26Z" + }, + { + "number": 462, + "title": "Conditional \u03ba = 0.001274494971185576: four-replica whole bit hosting", + "head": "a63b25e65578816d78843c0e25131d9be7567cd2", + "updated_at": "2026-10-11T17:26:20Z" + }, + { + "number": 465, + "title": "Conditional kappa = 0.001283479306671789: certified R715 assembly with sharp bit charge", + "head": "22c2a15c232084a31b6c8f0263e2e8ce831047ea", + "updated_at": "2026-10-11T17:08:50Z" + }, + { + "number": 459, + "title": "Conditional \u03ba = 0.001266536148630309: rank151 kernel + target-prefix mixing on #451, complex-bound (+0.0477%)", + "head": "e037bc50c3d5efc1bec0d258a9f274f79ba45ec7", + "updated_at": "2026-10-11T17:03:10Z" + }, + { + "number": 451, + "title": "Conditional \u03ba = 0.001265931727546219: dual eleven-stage whole-residual hosting", + "head": "f3a38153678b55063fc005901cc968266166507d", + "updated_at": "2026-10-11T16:50:58Z" + }, + { + "number": 461, + "title": "Conditional kappa = 0.001274032592088050: sharper bit bad-class charge on #458", + "head": "dc297912ad446779f983818816617c03dfc76e16", + "updated_at": "2026-10-11T16:50:06Z" + }, + { + "number": 457, + "title": "Conditional \u03ba = 0.001266309796182835: rank151 bit kernel on #451's dual eleven-stage hosting (+0.0299%)", + "head": "3e89db7725785f8e8e172d04d1d4804f57db72f3", + "updated_at": "2026-10-11T16:49:06Z" + }, + { + "number": 456, + "title": "Conditional \u03ba = 0.001266564732900111: seven-replica whole-residual hosting", + "head": "fb010029442f39315333d56c1427df4eabe2960e", + "updated_at": "2026-10-11T16:26:10Z" + }, + { + "number": 455, + "title": "research: whole-residual replica pooling and program portfolios, conditional kappa = 0.001266541949425315", + "head": "f76fc4e36030d4e00b4cbb83b1dbc661a0974c4e", + "updated_at": "2026-10-11T16:11:46Z" + }, + { + "number": 453, + "title": "Under review: rank137 cross-copy candidate; inherited operator obstruction", + "head": "cff79050526545e7b66d24a7f4c65f22c1da8618", + "updated_at": "2026-10-11T15:59:15Z" + }, + { + "number": 445, + "title": "Conditional \u03ba = 0.001263365464781156: eleven-stage R740 hosting with complete row bound", + "head": "40ab91daf2b5e87fc4071dedae1699d5d7e7cecc", + "updated_at": "2026-10-11T15:58:55Z" + }, + { + "number": 446, + "title": "Format obstructions (no new \u03ba): exact bounds on window width, copy cost and label dimension", + "head": "309482849b6ddf34db998f53612d34c19f6e3233", + "updated_at": "2026-10-11T15:55:07Z" + }, + { + "number": 444, + "title": "Conditional \u03ba = 0.001246073505487942: R740 replicated kernel with idle-data hosting", + "head": "8c4242ea61c67827fe62b07b2edc093d7ddfa631", + "updated_at": "2026-10-11T15:41:40Z" + }, + { + "number": 200, + "title": "A stronger bit supplier: fixed-coordinate and face-diagonal bit local circuit on PR168 v4 (effective bit saving 6.7734e-4)", + "head": "a1175449f34d39ff933d9d8ab23ced1f32b290ec", + "updated_at": "2026-10-11T15:29:55Z" + }, + { + "number": 443, + "title": "Conditional \u03ba = 0.001138823042306561: retain rank138 with complete 32-replica banks", + "head": "5a514e94f156edcc5fd827b87494d962f79d0f6c", + "updated_at": "2026-10-11T15:28:13Z" + }, + { + "number": 452, + "title": "Speed up pinned E8 replay with shared prefixes and exact admission", + "head": "8a8079ec31abac7ccc4a0eae89df83b309fafbe1", + "updated_at": "2026-10-11T15:11:54Z" + }, + { + "number": 449, + "title": "[Draft] Complex supplier b \u2248 1.334e-3 (+5.2%): shared-donor kernel and entrance gauges on the E8 complex word", + "head": "7fac5292693bf738ff5eed6ec754f8ec22ebcf8e", + "updated_at": "2026-10-11T14:57:18Z" + }, + { + "number": 439, + "title": "Conditional \u03ba = 0.001133928043872860: R740 shared-donor kernel with explicit residual bank routes", + "head": "fa3a588ec1e383083abb8de9c51904fb9d689ad4", + "updated_at": "2026-10-11T14:47:32Z" + }, + { + "number": 447, + "title": "Conditional \u03ba = 0.001265848755025709: rank147 kernel with eleven-stage hosting", + "head": "d3cf3079091bb7e93a23e9cd98e82ccb89697328", + "updated_at": "2026-10-11T14:44:15Z" + }, + { + "number": 434, + "title": "Conditional kappa 0.001249035299298004: hosting-selected rank147 kernel", + "head": "6c0c0522665dda10201673c17fbb589f737d226c", + "updated_at": "2026-10-11T14:12:58Z" + }, + { + "number": 436, + "title": "Conditional \u03ba = 1.128983115440183e-3: an E8 bit word with 740 helpers under #433's complex supplier", + "head": "8f6b8297b08ad863940d5168a2db5402fad3690f", + "updated_at": "2026-10-11T14:11:28Z" + }, + { + "number": 437, + "title": "\u03ba = 1.128922474816875e-3: twelve early-final-use bit-helper resets", + "head": "ba6c10ba78e788764cfaa250d6a250d278580482", + "updated_at": "2026-10-11T13:24:46Z" + }, + { + "number": 425, + "title": "\u03ba = 1.048005508028206e-3: mutable-basis Hamming packets (\u22482^-9.89814; conditional; complex +4.97%)", + "head": "e11ccea1d092beb1b01b4ee4ce49da478234254c", + "updated_at": "2026-10-11T13:23:19Z" + }, + { + "number": 431, + "title": "Candidate conditional kappa 0.001056975315151441: Hamming complex and retimed bit composition", + "head": "71c5988803b1fc66fc9e8c2bc50949033be06e37", + "updated_at": "2026-10-11T13:23:16Z" + }, + { + "number": 433, + "title": "Split centres and source-basis reuse for conditional \u03ba = 0.001120864952258278", + "head": "6d9244518175caf9e0089f92486959bc2c317273", + "updated_at": "2026-10-11T13:23:14Z" + }, + { + "number": 442, + "title": "Conditional \u03ba \u2248 1.2375517e-3: idle-axis hosting of helper residuals (+9.2% over #434)", + "head": "4e16d001d505d4f21dd2bcfc44591f9be4c279bd", + "updated_at": "2026-10-11T13:18:56Z" + }, + { + "number": 441, + "title": "\u03ba = 1.138798055343319e-3: R740 block retiming after shared-donor kernel", + "head": "6160c13526f5f957902910b462164c93c1d8f39a", + "updated_at": "2026-10-11T13:17:26Z" + }, + { + "number": 440, + "title": "\u03ba = 1.136403735815528e-3: R740 shared-donor kernel with 57 primitive frame changes", + "head": "bd03373b6d4d4e380d0b6ea7d55cd2ac8f163544", + "updated_at": "2026-10-11T13:04:16Z" + }, + { + "number": 438, + "title": "\u03ba = 0.001133508328719775: early resets + kernel re-derived on the R747 bit word (+0.41% over #435)", + "head": "e3b56de7869f6af88d48ac0ab1d7959c4c9e6176", + "updated_at": "2026-10-11T12:36:25Z" + }, + { + "number": 426, + "title": "Conditional kappa 0.001018766833114736: checker-clean chronological gauges and R767 reuse", + "head": "88d552526893cd15325948bb1487e9a4d4bf32f6", + "updated_at": "2026-10-11T12:25:07Z" + }, + { + "number": 432, + "title": "Best gx/gxcore-clean \u03ba = 1.019752143318808\u00b710\u207b\u00b3: our #424 layers, 14 gate-frame retimings and a target-172 prefix on #426's R779 word (+9.85\u00b710\u207b\u2077 over #426)", + "head": "642b702149b975e3a535f139243cd3afd286e868", + "updated_at": "2026-10-11T12:24:12Z" + }, + { + "number": 424, + "title": "Conditional \u03ba = 1.018509848057013\u00b710\u207b\u00b3: checker-clean entrance enlargements, closure and rank-two gauges with a target-125 helper prefix on our #419 word (+1.75\u00b710\u207b\u2077 over #423)", + "head": "92c6ea78f5cf726dc7621854d53140512ba1c46a", + "updated_at": "2026-10-11T12:23:54Z" + }, + { + "number": 435, + "title": "\u03ba = 0.001128832830332521: #417's shared-donor kernel on #433's R758 bit word (+0.71%)", + "head": "2c9c833ac8709402c37fc88a6a23393fb0d397fb", + "updated_at": "2026-10-11T12:21:29Z" + }, + { + "number": 419, + "title": "Conditional \u03ba = 1.017962405296845\u00b710\u207b\u00b3: checker-clean grouped and frame-closure entrance promotions with a target-124 helper prefix on our #412 word (+3.9\u00b710\u207b\u2078 over #418; #414\u2013#416 fail gx E4/gxcore E5)", + "head": "70a276cb948e5be6071cde3f1bebdaf2f995ab8e", + "updated_at": "2026-10-11T11:59:38Z" + }, + { + "number": 422, + "title": "Candidate conditional kappa 0.001018475695250068: grouped entrance capacity and shared-frame enlargement", + "head": "dc7a552857c04f936daad0dc8e8b0164e5797f1a", + "updated_at": "2026-10-11T11:55:14Z" + }, + { + "number": 429, + "title": "Candidate conditional kappa 0.001019646575559504: R779 gauged helper inlining", + "head": "b25cbe3350e32efb211508c1dd41a134770fba16", + "updated_at": "2026-10-11T11:52:18Z" + }, + { + "number": 417, + "title": "E8 bit supplier c \u2248 1.044064\u00b710\u207b\u00b3 in the nine-stage word (+2.2 % bit cap; no new \u03ba, complex-bound)", + "head": "3f681fb571036ca4a267570318260b0d083f7b9d", + "updated_at": "2026-10-11T11:43:12Z" + }, + { + "number": 387, + "title": "Conditional kappa 0.000998634658090835: finite bootstrap and exact coarse precision", + "head": "d9fb9410b1ae6f6ada376a1e7fd12bc176e476ea", + "updated_at": "2026-10-11T11:38:41Z" + }, + { + "number": 352, + "title": "\u03ba = 8.01083628465007e-4: #346's w3 bit word with Sussman's Lean-checked E8 unit as the complex supplier (+0.96 % over #350)", + "head": "04b4c3c478b5bd8797d2663d89d8db4dfd0ad9f2", + "updated_at": "2026-10-11T11:38:38Z" + }, + { + "number": 412, + "title": "Conditional \u03ba = 1.017776060460931\u00b710\u207b\u00b3: checker-clean composition of sequential and enlarged entrance gauges with re-pivoting and padding fusion (+1.47\u00b710\u207b\u2077 over #411; #406/#408\u2013#410 fail gx E4)", + "head": "616d9d678c00d79693b869934464003ba5b8d1b1", + "updated_at": "2026-10-11T11:37:44Z" + }, + { + "number": 390, + "title": "E8 prefix restoration and heterogeneous helper banks: conditional kappa = 1.000220222889528e-3", + "head": "0e790f2dfb64e17bdee154aee151bb0c1dddb28e", + "updated_at": "2026-10-11T11:37:42Z" + } + ], + "448_comments": [ + { + "id": 6113791847, + "html_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/448#issuecomment-6113791847", + "updated_at": "2026-10-11T21:10:32Z", + "body": "Independent replay and a note on the split-residual interface (from an outside batch; no claim of our own)\n\n**Replay.** At the pinned head `359022bc`, `research/cross-copy-hosting/verify.py` passes from a fresh detached worktree with a fresh output directory and reproduces \u03ba = 0.001330733967 exactly. The same holds for #480 at `668c7dd0`, which reproduces 0.001372550159. This is part of a batch of 39 pinned frontier replays; 34 of them pass.\n\n**Ledger of the produced templates.** We wrote a checker that shares no code with the package. It reads `bit/` and `complex/GLOBAL-TEMPLATE.json.gz` and finds the following.\n- **Coordinate accounting is consistent.** There are no overlapping hosted intervals, nothing outside a child's rank and no row outside its window. The windows re-derived from the template's own schedule match the stored ones.\n- **The split is used heavily.** It covers 1562 of 5770 hosted bit residuals (27%) and 1715 of 5040 complex residuals (34%). In #480's bit template it is 14612 of 62920 (23%), and 1807 of 8140 in #450 and #469. None of the 61 whole-hosting templates we checked (#434 \u2026 #493) contains a split.\n- **The owner table names one family per split helper.** Each split helper has one entry in `calls[].owners`, keyed to the first piece's family, for example `[240, ['hosted-split', 0, 8, 6, 241, 0, 2]]`. The second family appears only inside the descriptor. #442's audit enforces \"each helper has exactly one owner\".\n\n**Where we think the review point is.** In your \u00a77 reply on #451, the open question is whether one local register's route may land in two families. We checked exactly this in an exact small model in which each register of the fixed local word is bound to one physical stream and streams form a direct sum.\n- **The model.** The word uses its helper as genuinely dirty scratch (`x += A h; h \u2190 F_R h; x \u2212= A F_R\u207b\u00b9 h; x \u2190 T x`). The coordinate factors are the bit `D_S` and the complex `C_S`, the same as in the #451 note and in `toy_two_family_check.py`.\n- **Whole hosting (#442) works.** It equals the original program in all 13 cases.\n- **A single-register split does not.** We enumerated every single-register binding and coordinate placement of a split residual: 152 programs over 18 cases (bit q = 3, 5; complex q = 2; m \u2264 8). None of them equals the original program.\n- **Two registers do.** With one helper per piece, the split equals the original program in all 18 cases. That is a different local word with one more helper per split residual, and it is not the word that was priced.\n\n`toy_two_family_check.py` composes `D_a^A \u2297 D_b^B` with the remainder children. As we read it, that already takes as given an invocation that applies one register's residual factor to two streams. Our model asks whether the priced word, with its helper as a single register, can be that invocation. It cannot when a register lives in one stream. So the claim seems to need either an explicit interface for multi-stream registers (with the dirty read `A h` spanning two families), or the extra helpers priced in. We have not computed \u03ba with the extra helpers.\n\nCode and data:\n- [report](https://github.com/hipotures/rad/blob/c6d971dabdde94e1c5ec1521c44ca63fd41debf9/research/integer-multiplication-bounds/campaigns/frontier-batch-20261011/report.md)\n- [stream model](https://github.com/hipotures/rad/blob/c6d971dabdde94e1c5ec1521c44ca63fd41debf9/research/integer-multiplication-bounds/campaigns/frontier-batch-20261011/code/job1_stream_model.py), about 10 s\n- [template ledger](https://github.com/hipotures/rad/blob/c6d971dabdde94e1c5ec1521c44ca63fd41debf9/research/integer-multiplication-bounds/campaigns/frontier-batch-20261011/code/job2_hosting_ledger.py)\n\nThis is our model of the declared execution, not a proof that no other realisation exists. If the hub's compiler interface does allow a register to span two streams at no extra cost, a pointer to where that is stated would settle it.\n\n---\n*This analysis was carried out by Claude Opus 5.5 (Anthropic) under human supervision.*\n" + }, + { + "id": 6113842081, + "html_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/448#issuecomment-6113842081", + "updated_at": "2026-10-11T21:15:52Z", + "body": "Thank you for the replay and for the stream model; this is the right level to settle it at, and I think your reading is the faithful one.\n\nWhere #448 \u00a72 and \u00a77 go wrong, stated plainly: the two-family argument takes the invocation's action on a split residual to be `D_a^A \u2297 D_b^B` *as given*. That presupposes that one local register can be read and written across two streams, which is exactly what your single-register enumeration tests and refutes (the dirty read `x += A h` has to see both pieces). The hub never states a multi-stream register interface; every owner table binds a register to one family, and I cannot point to a place where the compiler admits otherwise. So the realisation that does exist is your two-register control, and it is a different local word.\n\nPricing that word kills the gain. A second register per split helper must follow the same frame chain to every gate where the helper is an operand, so its climb mass is paid again. On #448's bit template your ledger counts 1,562 split residuals per replica, about 174 per invocation; at the word's average helper cost (\u224829 \u03a6-units per helper per invocation at m = 64) that is roughly +5,000 per invocation, against about 2,100 per invocation saved by removing the remainder children. The complex side is similar. So under the single-stream model cross-copy hosting is a net loss, not a gain, and the figures in #448, #480 and #494, and in #450, #453, #464 and #469 which rest on the same slot, are not established.\n\nI am retitling #448, #480 and #494 as under review on this point and leaving them as drafts with the packages intact, so the record of what was computed stays reproducible. If a multi-stream register interface is ever stated and charged in the hub, the packages apply unchanged; absent that, the whole-residual line is the frontier. Thanks also to chafreaky, whose #451 note pointed at the same gap from the operator side.\n" + } + ] +} diff --git a/research/lean-multi-host-source/overlap-closing-trees.json b/research/lean-multi-host-source/overlap-closing-trees.json new file mode 100644 index 0000000000..14226c1e85 --- /dev/null +++ b/research/lean-multi-host-source/overlap-closing-trees.json @@ -0,0 +1,654 @@ +{ + "checked_at_utc": "2026-10-11T23:26:49.896899+00:00", + "main_lean_count": 154, + "trees": { + "514": { + "head": "246bfacd4cb4072836ae3147099f548bb728229f", + "truncated": false, + "lean": { + "formal/lean/AuditAll.lean": "a8b583018023dc06928ff47fb0a4c887866f6fd8", + "formal/lean/KappaCheck.lean": "fae11c72de3ca0a2cedd9eb1655671054590769d", + "formal/lean/KappaCheck/Certificates.lean": "e7823cb19b5aee9dfc5c3a3a4b48aa4d92467b3f", + "formal/lean/KappaCheck/CrocSwap.lean": "340496d1883cadbad960cbe3b181b78cbc50e80c", + "formal/lean/KappaCheck/Frames.lean": "fc4295f7be2ebbafd39d8de2309e21bedba9de51", + 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487, + "title": "[Lean] Verification of selected 1320-port bijection, \u03ba=0.000661885549259598", + "head": "15b49f66cb2d2663fb71672f4d594e755bd93938", + "updated_at": "2026-10-11T19:45:38Z" + }, + { + "number": 486, + "title": "Build binary compression halo boxes with fused streaming and sparse repair", + "head": "f14e5881b7681641fade599b5389995843088e20", + "updated_at": "2026-10-11T19:43:25Z" + }, + { + "number": 483, + "title": "Conditional kappa = 0.001296606691405309: response-kernel cancellation and nested-donor flags on R715", + "head": "3738c3ce2d04d6a6c6363408ff9402286f592bc7", + "updated_at": "2026-10-11T19:33:13Z" + }, + { + "number": 186, + "title": "Shared-edge supplier, coordinated frames and entrance banks: conditional kappa = 6.61885549259598e-4", + "head": "bea1d52fd330c699903f81612ee58be81697d1eb", + "updated_at": "2026-10-11T19:28:42Z" + }, + { + "number": 482, + "title": "Conditional \u03ba = 0.001168862033074029: R715 target factors in non-hosting banks", + "head": "ab81e78de235ed11d4279ee89b0824650c372e17", + "updated_at": "2026-10-11T19:18:57Z" + }, + { + "number": 481, + "title": "Batch Gaussian boundary right-hand sides to reduce their cost", + "head": "5f3db6a11198bab07d8effe8f0c9f5df9c3f2eb7", + "updated_at": "2026-10-11T19:06:42Z" + }, + { + "number": 479, + "title": "Remove the chirp-generation dimension factor with exact streamed phases", + "head": "40dd01058439cdffae3e3b41c4fe52edaccf5f91", + "updated_at": "2026-10-11T18:34:44Z" + }, + { + "number": 478, + "title": "Conditional kappa = 0.001295508560071773: fourteen target factors on PR473 (+0.1226%)", + "head": "bea1d52fd330c699903f81612ee58be81697d1eb", + "updated_at": "2026-10-11T18:31:32Z" + }, + { + "number": 476, + "title": "Conditional kappa = 0.001291542455423938: two-layer target factoring on R715 (+0.1461% over #470)", + "head": "e850569c33ad1d5771e2f8b1c6dfe7a445396167", + "updated_at": "2026-10-11T18:14:32Z" + }, + { + "number": 475, + "title": "Remove compact FFT reservation and top-bit costs with complementary reservoirs", + "head": "5996e33ecad6a0ccd578aec58831457829d75575", + "updated_at": "2026-10-11T18:13:47Z" + }, + { + "number": 376, + "title": "Conditional \u03ba=0.0011208649522582786: split centres with complete signed admission", + "head": "5522b4edf9748ccda787df81f0a83eda83cdc4e8", + "updated_at": "2026-10-11T18:08:52Z" + }, + { + "number": 468, + "title": "Prove nine calls are necessary for three abelian bit registers", + "head": "07a78bf335b0b5039a1fecd7cd74a0fe1d1605ea", + "updated_at": "2026-10-11T18:08:13Z" + }, + { + "number": 470, + "title": "Conditional \u03ba = 0.001291474845253222: retimed kernel and reordered R715 deliveries", + "head": "aaf3ef64672cb96d2f0cfe36410640ee59c07c9f", + "updated_at": "2026-10-11T18:07:43Z" + }, + { + "number": 474, + "title": "Bind the selected gen4 certificate to fresh replay outputs", + "head": "6563bc97e4c0f86d4ff9b11476ae925a6be7ff7f", + "updated_at": "2026-10-11T18:04:47Z" + }, + { + "number": 397, + "title": "Formalize the indexed B_K scalar bridge and bind the pinned B3 word", + "head": "cb6455fa1e9af68be47c33948d3d1a6f0717a5e4", + "updated_at": "2026-10-11T18:03:59Z" + }, + { + "number": 469, + "title": "Conditional \u03ba = 0.001350580884553120: gate-frame retiming of #450's eleven-stage cross-copy word (+0.2105%)", + "head": "a820816f07f60544bd38c6f12c38a9c25066ddf0", + "updated_at": "2026-10-11T18:03:40Z" + }, + { + "number": 275, + "title": "Finite assembly, source-basis cost reduction, and E8 verification", + "head": "e500c9c4217483de882cf06e6e80b25b70ea1ca5", + "updated_at": "2026-10-11T18:01:04Z" + }, + { + "number": 450, + "title": "Conditional \u03ba = 0.001347744547714835: eleven-stage cross-copy hosting with target mixing (+1.278% over #448)", + "head": "350943275564c53b209c1277aac7d691807726be", + "updated_at": "2026-10-11T17:45:50Z" + }, + { + "number": 464, + "title": "Conditional \u03ba = 0.001347744550711765: sharper bit bad-class charge on #450's word", + "head": "8c546e9918ae37d842916d89ffe28f2c08cdb3d3", + "updated_at": "2026-10-11T17:45:22Z" + }, + { + "number": 471, + "title": "Conditional kappa = 0.001274548075945587: full-nine-axis kernel normalization and same-owner spectator borrowing", + "head": "56b3da6aa1295d37ce43f1753479bfe4737b7ac3", + "updated_at": "2026-10-11T17:43:32Z" + }, + { + "number": 467, + "title": "Conditional \u03ba = 0.001289283116193775: R715 shared kernel, retiming and whole pooling", + "head": "e28109cd3fe2f2853449e4c49a55887790e16ba2", + "updated_at": "2026-10-11T17:39:33Z" + }, + { + "number": 463, + "title": "Conditional \u03ba = 0.001283479303751122: E8 bit word R715 (carrier lower bound + F2 overlap cancellation) with #458's complex supplier (+0.711% over #460)", + "head": "cdf0c1c6540df987467988fd771340670f4136f3", + "updated_at": "2026-10-11T17:34:40Z" + }, + { + "number": 454, + "title": "Conditional \u03ba = 0.001266536148630310: target mixing with whole-residual hosting", + "head": "d14eb0dd425bd681e3b43f208d089e679d600176", + "updated_at": "2026-10-11T17:33:36Z" + }, + { + "number": 460, + "title": "Conditional \u03ba = 0.001274415506145115: paid complex kernel + rank151 target mixing", + "head": "b98bbb4bc398ad67a41f123c6c301628c37e1d6b", + "updated_at": "2026-10-11T17:32:26Z" + }, + { + "number": 462, + "title": "Conditional \u03ba = 0.001274494971185576: four-replica whole bit hosting", + "head": "a63b25e65578816d78843c0e25131d9be7567cd2", + "updated_at": "2026-10-11T17:26:20Z" + }, + { + "number": 465, + "title": "Conditional kappa = 0.001283479306671789: certified R715 assembly with sharp bit charge", + "head": "22c2a15c232084a31b6c8f0263e2e8ce831047ea", + "updated_at": "2026-10-11T17:08:50Z" + }, + { + "number": 459, + "title": "Conditional \u03ba = 0.001266536148630309: rank151 kernel + target-prefix mixing on #451, complex-bound (+0.0477%)", + "head": "e037bc50c3d5efc1bec0d258a9f274f79ba45ec7", + "updated_at": "2026-10-11T17:03:10Z" + }, + { + "number": 451, + "title": "Conditional \u03ba = 0.001265931727546219: dual eleven-stage whole-residual hosting", + "head": "f3a38153678b55063fc005901cc968266166507d", + "updated_at": "2026-10-11T16:50:58Z" + }, + { + "number": 461, + "title": "Conditional kappa = 0.001274032592088050: sharper bit bad-class charge on #458", + "head": "dc297912ad446779f983818816617c03dfc76e16", + "updated_at": "2026-10-11T16:50:06Z" + }, + { + "number": 457, + "title": "Conditional \u03ba = 0.001266309796182835: rank151 bit kernel on #451's dual eleven-stage hosting (+0.0299%)", + "head": "3e89db7725785f8e8e172d04d1d4804f57db72f3", + "updated_at": "2026-10-11T16:49:06Z" + }, + { + "number": 456, + "title": "Conditional \u03ba = 0.001266564732900111: seven-replica whole-residual hosting", + "head": "fb010029442f39315333d56c1427df4eabe2960e", + "updated_at": "2026-10-11T16:26:10Z" + }, + { + "number": 455, + "title": "research: whole-residual replica pooling and program portfolios, conditional kappa = 0.001266541949425315", + "head": "f76fc4e36030d4e00b4cbb83b1dbc661a0974c4e", + "updated_at": "2026-10-11T16:11:46Z" + }, + { + "number": 453, + "title": "Under review: rank137 cross-copy candidate; inherited operator obstruction", + "head": "cff79050526545e7b66d24a7f4c65f22c1da8618", + "updated_at": "2026-10-11T15:59:15Z" + }, + { + "number": 445, + "title": "Conditional \u03ba = 0.001263365464781156: eleven-stage R740 hosting with complete row bound", + "head": "40ab91daf2b5e87fc4071dedae1699d5d7e7cecc", + "updated_at": "2026-10-11T15:58:55Z" + }, + { + "number": 446, + "title": "Format obstructions (no new \u03ba): exact bounds on window width, copy cost and label dimension", + "head": "309482849b6ddf34db998f53612d34c19f6e3233", + "updated_at": "2026-10-11T15:55:07Z" + }, + { + "number": 444, + "title": "Conditional \u03ba = 0.001246073505487942: R740 replicated kernel with idle-data hosting", + "head": "8c4242ea61c67827fe62b07b2edc093d7ddfa631", + "updated_at": "2026-10-11T15:41:40Z" + }, + { + "number": 200, + "title": "A stronger bit supplier: fixed-coordinate and face-diagonal bit local circuit on PR168 v4 (effective bit saving 6.7734e-4)", + "head": "a1175449f34d39ff933d9d8ab23ced1f32b290ec", + "updated_at": "2026-10-11T15:29:55Z" + }, + { + "number": 443, + "title": "Conditional \u03ba = 0.001138823042306561: retain rank138 with complete 32-replica banks", + "head": "5a514e94f156edcc5fd827b87494d962f79d0f6c", + "updated_at": "2026-10-11T15:28:13Z" + }, + { + "number": 452, + "title": "Speed up pinned E8 replay with shared prefixes and exact admission", + "head": "8a8079ec31abac7ccc4a0eae89df83b309fafbe1", + "updated_at": "2026-10-11T15:11:54Z" + }, + { + "number": 449, + "title": "[Draft] Complex supplier b \u2248 1.334e-3 (+5.2%): shared-donor kernel and entrance gauges on the E8 complex word", + "head": "7fac5292693bf738ff5eed6ec754f8ec22ebcf8e", + "updated_at": "2026-10-11T14:57:18Z" + }, + { + "number": 439, + "title": "Conditional \u03ba = 0.001133928043872860: R740 shared-donor kernel with explicit residual bank routes", + "head": "fa3a588ec1e383083abb8de9c51904fb9d689ad4", + "updated_at": "2026-10-11T14:47:32Z" + }, + { + "number": 447, + "title": "Conditional \u03ba = 0.001265848755025709: rank147 kernel with eleven-stage hosting", + "head": "d3cf3079091bb7e93a23e9cd98e82ccb89697328", + "updated_at": "2026-10-11T14:44:15Z" + }, + { + "number": 434, + "title": "Conditional kappa 0.001249035299298004: hosting-selected rank147 kernel", + "head": "6c0c0522665dda10201673c17fbb589f737d226c", + "updated_at": "2026-10-11T14:12:58Z" + }, + { + "number": 436, + "title": "Conditional \u03ba = 1.128983115440183e-3: an E8 bit word with 740 helpers under #433's complex supplier", + "head": "8f6b8297b08ad863940d5168a2db5402fad3690f", + "updated_at": "2026-10-11T14:11:28Z" + }, + { + "number": 437, + "title": "\u03ba = 1.128922474816875e-3: twelve early-final-use bit-helper resets", + "head": "ba6c10ba78e788764cfaa250d6a250d278580482", + "updated_at": "2026-10-11T13:24:46Z" + }, + { + "number": 425, + "title": "\u03ba = 1.048005508028206e-3: mutable-basis Hamming packets (\u22482^-9.89814; conditional; complex +4.97%)", + "head": "e11ccea1d092beb1b01b4ee4ce49da478234254c", + "updated_at": "2026-10-11T13:23:19Z" + }, + { + "number": 431, + "title": "Candidate conditional kappa 0.001056975315151441: Hamming complex and retimed bit composition", + "head": "71c5988803b1fc66fc9e8c2bc50949033be06e37", + "updated_at": "2026-10-11T13:23:16Z" + }, + { + "number": 433, + "title": "Split centres and source-basis reuse for conditional \u03ba = 0.001120864952258278", + "head": "6d9244518175caf9e0089f92486959bc2c317273", + "updated_at": "2026-10-11T13:23:14Z" + }, + { + "number": 442, + "title": "Conditional \u03ba \u2248 1.2375517e-3: idle-axis hosting of helper residuals (+9.2% over #434)", + "head": "4e16d001d505d4f21dd2bcfc44591f9be4c279bd", + "updated_at": "2026-10-11T13:18:56Z" + }, + { + "number": 441, + "title": "\u03ba = 1.138798055343319e-3: R740 block retiming after shared-donor kernel", + "head": "6160c13526f5f957902910b462164c93c1d8f39a", + "updated_at": "2026-10-11T13:17:26Z" + }, + { + "number": 440, + "title": "\u03ba = 1.136403735815528e-3: R740 shared-donor kernel with 57 primitive frame changes", + "head": "bd03373b6d4d4e380d0b6ea7d55cd2ac8f163544", + "updated_at": "2026-10-11T13:04:16Z" + }, + { + "number": 438, + "title": "\u03ba = 0.001133508328719775: early resets + kernel re-derived on the R747 bit word (+0.41% over #435)", + "head": "e3b56de7869f6af88d48ac0ab1d7959c4c9e6176", + "updated_at": "2026-10-11T12:36:25Z" + }, + { + "number": 426, + "title": "Conditional kappa 0.001018766833114736: checker-clean chronological gauges and R767 reuse", + "head": "88d552526893cd15325948bb1487e9a4d4bf32f6", + "updated_at": "2026-10-11T12:25:07Z" + }, + { + "number": 432, + "title": "Best gx/gxcore-clean \u03ba = 1.019752143318808\u00b710\u207b\u00b3: our #424 layers, 14 gate-frame retimings and a target-172 prefix on #426's R779 word (+9.85\u00b710\u207b\u2077 over #426)", + "head": "642b702149b975e3a535f139243cd3afd286e868", + "updated_at": "2026-10-11T12:24:12Z" + }, + { + "number": 424, + "title": "Conditional \u03ba = 1.018509848057013\u00b710\u207b\u00b3: checker-clean entrance enlargements, closure and rank-two gauges with a target-125 helper prefix on our #419 word (+1.75\u00b710\u207b\u2077 over #423)", + "head": "92c6ea78f5cf726dc7621854d53140512ba1c46a", + "updated_at": "2026-10-11T12:23:54Z" + }, + { + "number": 435, + "title": "\u03ba = 0.001128832830332521: #417's shared-donor kernel on #433's R758 bit word (+0.71%)", + "head": "2c9c833ac8709402c37fc88a6a23393fb0d397fb", + "updated_at": "2026-10-11T12:21:29Z" + }, + { + "number": 419, + "title": "Conditional \u03ba = 1.017962405296845\u00b710\u207b\u00b3: checker-clean grouped and frame-closure entrance promotions with a target-124 helper prefix on our #412 word (+3.9\u00b710\u207b\u2078 over #418; #414\u2013#416 fail gx E4/gxcore E5)", + "head": "70a276cb948e5be6071cde3f1bebdaf2f995ab8e", + "updated_at": "2026-10-11T11:59:38Z" + }, + { + "number": 422, + "title": "Candidate conditional kappa 0.001018475695250068: grouped entrance capacity and shared-frame enlargement", + "head": "dc7a552857c04f936daad0dc8e8b0164e5797f1a", + "updated_at": "2026-10-11T11:55:14Z" + }, + { + "number": 429, + "title": "Candidate conditional kappa 0.001019646575559504: R779 gauged helper inlining", + "head": "b25cbe3350e32efb211508c1dd41a134770fba16", + "updated_at": "2026-10-11T11:52:18Z" + }, + { + "number": 417, + "title": "E8 bit supplier c \u2248 1.044064\u00b710\u207b\u00b3 in the nine-stage word (+2.2 % bit cap; no new \u03ba, complex-bound)", + "head": "3f681fb571036ca4a267570318260b0d083f7b9d", + "updated_at": "2026-10-11T11:43:12Z" + }, + { + "number": 387, + "title": "Conditional kappa 0.000998634658090835: finite bootstrap and exact coarse precision", + "head": "d9fb9410b1ae6f6ada376a1e7fd12bc176e476ea", + "updated_at": "2026-10-11T11:38:41Z" + }, + { + "number": 352, + "title": "\u03ba = 8.01083628465007e-4: #346's w3 bit word with Sussman's Lean-checked E8 unit as the complex supplier (+0.96 % over #350)", + "head": "04b4c3c478b5bd8797d2663d89d8db4dfd0ad9f2", + "updated_at": "2026-10-11T11:38:38Z" + }, + { + "number": 412, + "title": "Conditional \u03ba = 1.017776060460931\u00b710\u207b\u00b3: checker-clean composition of sequential and enlarged entrance gauges with re-pivoting and padding fusion (+1.47\u00b710\u207b\u2077 over #411; #406/#408\u2013#410 fail gx E4)", + "head": "616d9d678c00d79693b869934464003ba5b8d1b1", + "updated_at": "2026-10-11T11:37:44Z" + }, + { + "number": 390, + "title": "E8 prefix restoration and heterogeneous helper banks: conditional kappa = 1.000220222889528e-3", + "head": "0e790f2dfb64e17bdee154aee151bb0c1dddb28e", + "updated_at": "2026-10-11T11:37:42Z" + }, + { + "number": 385, + "title": "Retimed nine-stage complex + kernel bit: conditional kappa 0.000998390813251625", + "head": "ad7647ef25b1df0e51189a41072d08a928d759d5", + "updated_at": "2026-10-11T11:37:37Z" + }, + { + "number": 382, + "title": "Conditional \u03ba = 9.98243154231047\u00b710\u207b\u2074: our retimed + kernel E8 bit word in B\u2083 (unsplit) with #377's nine-stage complex component (+0.26 % over #381)", + "head": "536329e6cddd37d70a6b52cbe2c2604ea18c5e83", + "updated_at": "2026-10-11T11:37:36Z" + }, + { + "number": 380, + "title": "Conditional \u03ba = 9.67261003170394e-4: seven-stage E8 bit with nine-stage complex (+1.32149% over #378)", + "head": "6e95ce5fb4112e5e98382886d7904aee29e31c56", + "updated_at": "2026-10-11T11:37:35Z" + }, + { + "number": 377, + "title": "\u03ba = 9.98243154231047e-4: nine-stage complex E8 (\u22482^-9.9683; complex +14.036%, bit side pending)", + "head": "d0a620fcc99ba012468d61d01f5bb14007076d50", + "updated_at": "2026-10-11T11:37:34Z" + } + ] +} diff --git a/research/lean-multi-host-source/overlap-final-trees.json b/research/lean-multi-host-source/overlap-final-trees.json new file mode 100644 index 0000000000..60e369b485 --- /dev/null +++ b/research/lean-multi-host-source/overlap-final-trees.json @@ -0,0 +1,40 @@ +{ + "checked_at_utc": "2026-10-11T23:04:05.492595+00:00", + "heads": { + "refs/heads/main": "12a4934d15006e8c10f9b2264f13f8f341be802b", + "refs/pull/397/head": "cb6455fa1e9af68be47c33948d3d1a6f0717a5e4", + "refs/pull/442/head": "4e16d001d505d4f21dd2bcfc44591f9be4c279bd", + "refs/pull/448/head": "359022bcd71143e45d48def0dd005bf67f339aa7" + }, + "tree_comparisons": { + "473": { + "commit": "9a2e1d4a7739aa4439982d6baea9ffca66bb8ae3", + "truncated": false, + "lean_count": 154, + "changed_or_new_lean": {}, + "deleted_lean": [] + }, + "477": { + "commit": "61dcaf133eade170f253775e56e3d479fddc400c", + "truncated": false, + "lean_count": 154, + "changed_or_new_lean": {}, + "deleted_lean": [] + }, + "508": { + "commit": "3213fc136270ca8372ce9f8fbb828e78ba96cecf", + "truncated": false, + "lean_count": 154, + "changed_or_new_lean": {}, + "deleted_lean": [] + }, + "510": { + "commit": "64edee18af02aab0c1696b677a0287dd0146381b", + "truncated": false, + "lean_count": 154, + "changed_or_new_lean": {}, + "deleted_lean": [] + } + }, + "scope": "Complete untruncated trees of changed/new candidates; no newly changed Lean provider in these heads. Latest100 PR screening is bounded, not exhaustive." +} diff --git a/research/lean-multi-host-source/overlap-review.md b/research/lean-multi-host-source/overlap-review.md new file mode 100644 index 0000000000..de31d546c0 --- /dev/null +++ b/research/lean-multi-host-source/overlap-review.md @@ -0,0 +1,82 @@ +# Overlap audit and target selection + +The audit preceded implementation. The full initial record is in +`../lean-multi-host-framework/overlap-audit.json`; the final read-only refresh +is recorded in `overlap-final-refresh.json` and `overlap-final-trees.json`. + +Main, PR397, PR442, and PR448 remained at their previously inspected exact +heads. `source-versions.json` pins them and Jacob Sussman's linked +`wht-power-saving-lean` repository. The initial audit inspected the existing +dirty-wrapper, framed-XOR, address-gauge, localization, and scheduling work. +Generic conjugation and scheduling algebra are existing work. + +The latest PR448 discussion still includes its author's acknowledgement +(comment 6113842081, updated 2026-10-11 21:15:52 UTC): the proposed split action +presupposes an unstated multi-stream register interface; using a second +register changes the local word and requires charging its frame chain. This +contribution assumes neither that interface nor the advertised gain. + +The refresh screened the latest 100 updated PRs. Complete, untruncated trees +of changed PR473 and PR477 and new PR508 and PR510 each contained the same +154 Lean blobs as pinned main. Their newer Python/C++ constructions do not +provide a new Lean instantiation of this source obligation. This bounded +search does not assert that every historical branch or external repository +has been searched. + +## New overlapping Lean work: PR509 + +PR509, *Lemma G of #484: clean proof and Lean 4 formalisation of its core*, +was reviewed at `7b9c720ecc9f483c383e7cd9c2ab81f06ee5df59`. All 195 changed +paths were inspected for the relevant subtree; all 18 new subtree files +were fetched by exact commit and checked against its manifest. Six are Lean +files. This was a source review, not an independent build of its Lean 4.21.0 +package or replay of its Python instance checks. + +Its `LemmaG.Stream.conj` and `conj_matrix` establish common-frame transport +for labelled streams given well-labelledness and exact relabel recipes. +`scalRun_eq_sum` and `S_rowform` establish the arbitrary-input interpretation +of symbolic scalar execution. `row_unit` derives helper behavior from an +assumed unit endpoint row. `BitEntrance` proves doubled-address identities. +These substantially overlap with the generic principles supporting this +package; no novelty for those principles is claimed here. + +The concrete target remains open in that head. It contains no embedded +19,002-event PR442 word, computed 987-row endpoint, checked 944-frame matrix +table, actual 747-helper ownership map, or original 172-bank ownership +certificate. Its emitted-word labels, transition recipes, matrix endpoint, +accounting, and adapter hypotheses remain Python checks. Its selected word +is the complex PR484 variant with 800 live columns. + +Its copy/clear linear semantics also do not supply the clean-private guards +required here: copy overwrites and clear assigns zero, while admissibility +tracks labels. That is a different abstraction boundary, not a criticism of +its stated theorem. It has no concrete cover-class aliasing model. + +The useful target is therefore the additional concrete PR442 word, frames, +owners, and dirty-input obligations, followed by their explicit connection +to the separately checked multi-host theorem. + +## Closing refresh at 23:26 UTC + +`overlap-closing-refresh.json` rechecks the latest 100 updated PRs and the +pinned main, PR397, PR442, PR448, PR509, and Jacob Sussman heads. All those +pinned heads are unchanged, and PR448's latest discussion remains the same +interface acknowledgement. The changed PR473/477 heads and new PR512/514 +each still have precisely main's 154 Lean blobs; the complete tree evidence +is in `overlap-closing-trees.json`. + +Two new Lean PRs required source review. PR513 +(`005dd3f4e3cba8d1761abc4ab391aaf6d14d6f73`) adds a sequential completed-bank +theorem and concrete five-stage route/schedule bindings. Its generic +completion algebra substantially overlaps with Task A. It still assumes the +universal local physical endpoint as a supplier premise and does not certify +the actual PR442 word, frames, owner functions, or dirty-input endpoint. +PR511 (`79f7c03c7f820ab89955b75ef239cbaccc627e6e`) concerns a fixed-width +binary count dispatcher. Neither resolves this selected concrete obligation. + +`closing-lean-overlap.md` records the exact statement review and its limits. +All 37 changed files were fetched by exact head and checked against Git blob +hashes; PR513's eight Lean manifest hashes also matched. This was a source +review, not an independent rebuild of their Lean 4.21 packages. The concrete +source obligations remain the contribution; generic composition principles +are not presented as new. diff --git a/research/lean-multi-host-source/parent-ownership-review.md b/research/lean-multi-host-source/parent-ownership-review.md new file mode 100644 index 0000000000..0c2db1a55f --- /dev/null +++ b/research/lean-multi-host-source/parent-ownership-review.md @@ -0,0 +1,13 @@ +# Actual original-bank ownership review + +The selected source is PR442 commit `4e16d001d505d4f21dd2bcfc44591f9be4c279bd`, stage 2, replica 0, pair 0, forward. The original parent template has 987 live local roles and private family 14259. Its uncompressed SHA256 is `f9ce9ac945d9e8ea737dc5e456e366a7e2a21d8b989d24b742d7f124d26fb32f`; the other vendored input hashes are in `source-versions.json`. + +`generate_parent_ownership.py` reads every selected original owner and the corresponding source entrance frame. Its 747 helpers occupy 172 original bank families. For each route it maps the sorted residual standard basis to the specified bank interval, then completes the coordinate permutation by the increasing bijection between the complements. This explicitly chooses an isometry satisfying the source's interval descriptor; the source descriptor does not specify the complementary-axis ordering. Parent helpers have no additional B-port family chart. Data roles use the same source stage 2 port charts as the hosted call, with inverse convention chosen so the owner chart is `d * rho`. + +There are 61 route slots but 59 distinct permutations. Three slots share the identity permutation: offset 0 / width 7 / frame 9, offset 0 / width 8 / frame 0, and offset 4 / width 4 / frame 458. The Lean tables keep slot metadata separate from permutation tags. Treating slots as distinct actions would have invalidated the function-injectivity proof. + +`ParentOwnershipData.lean` checks both permutation inverse laws, the source-to-bank support equation for all 61 slots and 64 axes, faithfulness of all 59 permutation tags, and the inverse owner lookup for all 987 roles. Each helper family is at least 7680 and below 14259; data families are 0 through 239. The tables regenerate byte for byte (SHA256 `737ae7eb42e3d287db5fcd840eecef3c80bc0e01238bba2c8ba8cfbd162c3220`). Their Lean4.33.0 kernel build took 114.2 seconds on this machine. The generic owner-injectivity and coordinate-chart proofs were separately compiled against these tables. The complete `ParentOwnership.lean` module then compiled in 1.6 seconds using the checked data and source port charts; its reported theorem closures contain only `propext`, `Classical.choice`, and `Quot.sound`. The package-wide replay supplies the final import check. + +`ParentOwnership.lean` derives injectivity of actual owner functions for any fixed invertible cover and field with 2 nonzero. Descriptor inequality alone is not an assumption. The private row is separated by its reserved family 14259. Every parent active owner avoids host families 240 through 7679. The full-word gather theorem and native-cover theorem instantiate the generic raw-word semantics with these actual charts; callers still supply the concrete event word and initial-state relation. The private identifier `(14259,id)` denotes reserved scratch, while its per-invocation native chart is explicitly the common cover d. + +JSON extraction and the interpretation of the upstream route descriptor are outside the Lean kernel. The kernel certifies the resulting literal table and its mathematical properties. These files establish no improved kappa, all-size compiler, or interface for PR448's disputed two-stream split. diff --git a/research/lean-multi-host-source/proof-manifest.json b/research/lean-multi-host-source/proof-manifest.json new file mode 100644 index 0000000000..bc5c7c970d --- /dev/null +++ b/research/lean-multi-host-source/proof-manifest.json @@ -0,0 +1,1413 @@ +{ + "source_base_commit": "13611a8958fc71046a83d8431d2bd6335e6a3e2f", + "lean_commit": "d8b18978322de05a8f3dba51ef03cf5461676c17", + "mathlib_commit": "db584cd6d46c92f209a44c0f1c829460d327499d", + "modules": [ + { + "module": "RowEvaluation", + "source": "RowEvaluation.lean", + "sha256": "509b73251fd10153294d0c28ccf14285a3460b2a962ef4af0f03e658352ef055", + "imports": [ + "Std" + ] + }, + { + "module": "LinearReplay", + "source": "LinearReplay.lean", + "sha256": "50df4826c9531e5139bcd0161f77ced299a448793d1c97fea76c9a696ef215da", + "imports": [ + "RowEvaluation" + ] + }, + { + "module": "TreeReplay", + "source": "TreeReplay.lean", + "sha256": "d804569626c5569f8e1200458662871fcc666069e837022a9dbbf1ec877d8579", + "imports": [ + "LinearReplay" + ] + }, + { + "module": "FramedReplay", + "source": "FramedReplay.lean", + "sha256": "29c8a3767d9c34d4496855f93aa9b82945e4ea18b3923096d2cad7e52c0fbefc", + "imports": [ + "TreeReplay" + ] + }, + { + "module": "CoordinateSwap", + "source": "../lean-whole-residual-hosting/CoordinateSwap.lean", + "sha256": "74d47e67dad5e8d548e69b008de19b65cfd138d3be71cf80d0b6c6990cf65841", + "imports": [ + "Std" + ] + }, + { + "module": "AddressPairs", + "source": "AddressPairs.lean", + "sha256": "b451ac52482c143103142d1736c72c5126a374e5351fe0442beafc9f9d017be4", + "imports": [ + "FramedReplay", + "CoordinateSwap" + ] + }, + { + "module": "EndpointInterpretation", + "source": "EndpointInterpretation.lean", + "sha256": "174de6a410ad642cb55e4f21b7470a979a33275d4fc2e346caff0f3db90f1615", + "imports": [ + "TreeReplay" + ] + }, + { + "module": "FrameData", + "source": "FrameData.lean", + "sha256": "8bcdc93969f06caae9a438d59cd5e8cc052573daef4f0a9c16141b4815b68ce3", + "imports": [ + "Std" + ] + }, + { + "module": "FrameGeometry", + "source": "FrameGeometry.lean", + "sha256": "3fc83e60717189241a2656f70a98e0781536bea37f2727dad63b5cc0091e1c55", + "imports": [ + "FrameData", + "FramedReplay", + "Mathlib.Data.Matrix.Mul", + "Mathlib.Algebra.BigOperators.Fin", + "Mathlib.Tactic.FieldSimp", + "Mathlib.Tactic.Ring", + "Mathlib.Tactic.NormNum" + ] + }, + { + "module": "FrameTraceCore", + "source": "FrameTraceCore.lean", + "sha256": "426213f93d311bd7d42934649844d545e5a1a3e0dd3233f7804a360f2546d135", + "imports": [ + "FramedReplay" + ] + }, + { + "module": "FrameTraceLiterals", + "source": "FrameTraceLiterals.lean", + "sha256": "950b19499a2310ff5dc148138b8439ec46e3847caef544192cd0df4da6907264", + "imports": [ + "FrameTraceCore" + ] + }, + { + "module": "FrameLabelData", + "source": "FrameLabelData.lean", + "sha256": "9d3dac6340d136903ec092363afe017141c3916f9e6b4dc64aeed48430ebede3", + "imports": [ + "FrameTraceLiterals" + ] + }, + { + "module": "FrameMoveData", + "source": "FrameMoveData.lean", + "sha256": "070793e71a93cb9f2e925520022e1c8d3f8000553e3c384279eea118197ac325", + "imports": [ + "FrameData", + "FrameTraceLiterals" + ] + }, + { + "module": "MatrixData", + "source": "MatrixData.lean", + "sha256": "dfb7acb5dcb1d6b7978d80d4105c602be82d72305811f3a04a814ffd97bbdc64", + "imports": [ + "TreeReplay" + ] + }, + { + "module": "FrameTraceCheckpoints", + "source": "FrameTraceCheckpoints.lean", + "sha256": "117ecd55d92e17358f282a9c1ee0b0b1dc85fd79cf236c9e5d624d13ceed94c0", + "imports": [ + "FrameTraceLiterals", + "MatrixData" + ] + }, + { + "module": "FrameTraceData", + "source": "FrameTraceData.lean", + "sha256": "438f2df31174c3f51a51ebfdc12942125a32d7ba22da38e4deae69b4b412b571", + "imports": [ + "FrameTraceCheckpoints" + ] + }, + { + "module": "PayloadGuards", + "source": "PayloadGuards.lean", + "sha256": "23ec801ecd085f21a5fe6162dbcac474ff59702fc26c08fbd42d9c2fc09a09af", + "imports": [ + "TreeReplay" + ] + }, + { + "module": "FrameTraceRefinement", + "source": "FrameTraceRefinement.lean", + "sha256": "9dd2c00b89db52e10a6031fabc95b47ccbf8a06c289f5f499516603bc369db18", + "imports": [ + "FrameTraceCore", + "PayloadGuards" + ] + }, + { + "module": "OwnerTransport", + "source": "OwnerTransport.lean", + "sha256": "cdc9374538c716c85a3dfed949395a92d738f2bf6cba108d1a9f0ea2270ffc5c", + "imports": [ + "FramedReplay" + ] + }, + { + "module": "FrameTraceRoutes", + "source": "FrameTraceRoutes.lean", + "sha256": "ecfab2d1002c9f610174451c77fcafb5668e0d2c732d76de20e4a2b71e14f500", + "imports": [ + "FrameTraceLiterals", + "OwnerTransport" + ] + }, + { + "module": "OwnershipData", + "source": "OwnershipData.lean", + "sha256": "fa08b345a9763529ff8ad62f58ed472362aadfd3410cbaf02774339e4f13ee6a", + "imports": [ + "Std" + ] + }, + { + "module": "FrameTraceTables", + "source": "FrameTraceTables.lean", + "sha256": "f024344645891f85a073840da3e8546ba95ee5dbf5024a5db73136cf4e99f1c1", + "imports": [ + "FrameTraceLiterals", + "OwnershipData" + ] + }, + { + "module": "HelperGeometryData", + "source": "HelperGeometryData.lean", + "sha256": "41fdf73b03bcec19dc2455eb83b3ddbbd245e8b1c564dbef4676f25bd0a9c098", + "imports": [ + "FrameData", + "OwnershipData" + ] + }, + { + "module": "MatrixCheckpoints", + "source": "MatrixCheckpoints.lean", + "sha256": "da82943b96f829953ecb9e353e6a976f902db85cfa088acf2844d98c812f4588", + "imports": [ + "MatrixData" + ] + }, + { + "module": "MatrixCertificate", + "source": "MatrixCertificate.lean", + "sha256": "fba26c2d7aa7696707cbe8a1af8584db6a0dcb7af71a4040d94677e738a039d8", + "imports": [ + "MatrixCheckpoints" + ] + }, + { + "module": "SourceTables", + "source": "SourceTables.lean", + "sha256": "ebddbb922cfacb255104f693d8ede32cfcff0e69a9c2dd9d99a118177a87d949", + "imports": [ + "MatrixData", + "EndpointInterpretation" + ] + }, + { + "module": "SourceEndpoint", + "source": "SourceEndpoint.lean", + "sha256": "77b72ee70ffaf36a3a9f7fff0cee7d6be964b54a855483d9503208a747230bf9", + "imports": [ + "MatrixCertificate", + "SourceTables", + "PayloadGuards" + ] + }, + { + "module": "SourceFramed", + "source": "SourceFramed.lean", + "sha256": "503b3eec4ed209f966495f7eaa63ef0a92c1c611356b548f45574491fc6c4e2e", + "imports": [ + "FrameTraceData", + "FrameTraceRefinement", + "SourceEndpoint" + ] + }, + { + "module": "SourceRaw", + "source": "SourceRaw.lean", + "sha256": "dc499a037e1a930aa245d70496dfb1d51301d3b9f03716f5276733bd0081122d", + "imports": [ + "SourceFramed", + "FrameTraceRoutes", + "OwnerTransport" + ] + }, + { + "module": "MultiHosting", + "source": "../lean-multi-host-framework/MultiHosting.lean", + "sha256": "dc6188687ac8e089c64bf5ab7cd4c8c1a83f378d3c46bb1265a1b6ad43d199d6", + "imports": [ + "CoordinateSwap" + ] + }, + { + "module": "Ownership", + "source": "Ownership.lean", + "sha256": "a18ecfb59c4641ecf86eb672764dc6491e524d01b74392f34549c6013f9c4f76", + "imports": [ + "OwnershipData" + ] + }, + { + "module": "SourceConnection", + "source": "SourceConnection.lean", + "sha256": "b09db0d3b2ae6b3261f22f5ab9a656d963dc50c2582feedf57dc481f282ff80d", + "imports": [ + "SourceEndpoint", + "MultiHosting", + "Ownership" + ] + }, + { + "module": "InvocationPayload", + "source": "InvocationPayload.lean", + "sha256": "9a481f2ca0c796f88d0dc1b8a6a9fd17654a0c4d1c6c33c6e626753132cab0dc", + "imports": [ + "SourceRaw", + "SourceConnection" + ] + }, + { + "module": "PortData", + "source": "PortData.lean", + "sha256": "756e51c88c58f684c3ba0550d5b74dcd49b9225e4210409babf0aa99c53b1612", + "imports": [ + "Std" + ] + }, + { + "module": "PortRowData", + "source": "PortRowData.lean", + "sha256": "9f56dcd13f2f57ef914da0cda053f4408c06bf09ee8e4b399b67b990f1fcc7b0", + "imports": [ + "PortData" + ] + }, + { + "module": "PortGeometry", + "source": "PortGeometry.lean", + "sha256": "68b39cc27ed66768224c152c667272ac070403aac5730f21f6cbaac6c6b15cc6", + "imports": [ + "PortRowData", + "Mathlib.Data.Matrix.Mul", + "Mathlib.Tactic.FieldSimp", + "Mathlib.Tactic.Ring", + "Mathlib.Tactic.NormNum", + "Mathlib.Algebra.BigOperators.Fin" + ] + }, + { + "module": "OwnershipGeometry", + "source": "OwnershipGeometry.lean", + "sha256": "3acf8a6cfb8b086f06e65b79bd21aec3463723acc525dc69ae667fb5de4d7abd", + "imports": [ + "Ownership", + "PortGeometry", + "OwnerTransport", + "AddressPairs" + ] + }, + { + "module": "ParentOwnershipData", + "source": "ParentOwnershipData.lean", + "sha256": "737ae7eb42e3d287db5fcd840eecef3c80bc0e01238bba2c8ba8cfbd162c3220", + "imports": [ + "OwnershipData" + ] + }, + { + "module": "ParentOwnership", + "source": "ParentOwnership.lean", + "sha256": "dcff8654aee65aeee400fde68508a837f40acfc4214d21cf9061812ef9aa2968", + "imports": [ + "ParentOwnershipData", + "OwnershipGeometry" + ] + }, + { + "module": "PhysicalSourceConnection", + "source": "PhysicalSourceConnection.lean", + "sha256": "b32dfc5118a8de6fc0e8d52e13b06642927cc601c499865612207dd480ee92ae", + "imports": [ + "SourceConnection", + "SourceFramed" + ] + }, + { + "module": "SelectedGeometry", + "source": "SelectedGeometry.lean", + "sha256": "903f9eb72723a940aca4af8f05da79293be237ccd2cf2d5454c7badd867c8ac3", + "imports": [ + "HelperGeometryData", + "FrameGeometry", + "FrameTraceTables", + "FrameLabelData", + "PhysicalSourceConnection", + "AddressPairs" + ] + }, + { + "module": "SourceLayouts", + "source": "SourceLayouts.lean", + "sha256": "2c599203d826ad088103c93647de9ada2d38d73c0f508097b19f0dad0ca6ea42", + "imports": [ + "ParentOwnership", + "SourceConnection" + ] + }, + { + "module": "SourceInvocationState", + "source": "SourceInvocationState.lean", + "sha256": "f5a6f137e6ba2508eb114fedab0015b997e0ec86fbe17205a0829803dce56487", + "imports": [ + "SourceLayouts", + "InvocationPayload" + ] + }, + { + "module": "SourceCommonCover", + "source": "SourceCommonCover.lean", + "sha256": "97c76f69c1634410407e9d5560cfe55c8587b7e63c1146bcfd623b8fdfd78909", + "imports": [ + "SourceInvocationState" + ] + }, + { + "module": "SourceControls", + "source": "SourceControls.lean", + "sha256": "39ce81e3fbe6294c89729d7e2dcf8d4d1148b935d659b46780c472340c90c389", + "imports": [ + "MatrixCertificate" + ] + }, + { + "module": "SourceInvocationComparison", + "source": "SourceInvocationComparison.lean", + "sha256": "2c85d4f9d80c4a6ef7dfdc95322d00773e256bd3dd1a3ebe55eb23fa603121f2", + "imports": [ + "SourceInvocationState", + "PhysicalSourceConnection" + ] + }, + { + "module": "SourceDataBehavior", + "source": "SourceDataBehavior.lean", + "sha256": "75c803c8ef2f6034a7f885514b1bcc98772bbe8336d37bbaaf01a5928b128632", + "imports": [ + "SourceInvocationComparison" + ] + }, + { + "module": "SourceInitialPayload", + "source": "SourceInitialPayload.lean", + "sha256": "c577217a4eff88a5d5c4d8925156dc7c916ef7f0c64fc69321272d09126b155d", + "imports": [ + "SourceInvocationState" + ] + }, + { + "module": "SourceRawGuards", + "source": "SourceRawGuards.lean", + "sha256": "05f194304748c031bfdd9a452dba90bee6ee6a8c605e9ecd8fff853a6f514cd8", + "imports": [ + "SourceRaw" + ] + }, + { + "module": "SourceNativeInvocation", + "source": "SourceNativeInvocation.lean", + "sha256": "ac45da5c2e74495809d4c6ae8415df921154182854249546caa6209e16778021", + "imports": [ + "SourceCommonCover", + "SourceInitialPayload", + "SourceRawGuards" + ] + }, + { + "module": "SourceMoveGeometry", + "source": "SourceMoveGeometry.lean", + "sha256": "21dd5f55077f2e92ebb023639f1a007ab5c3644b88b5fe238101ca71e2dd7a01", + "imports": [ + "FrameMoveData", + "FrameLabelData", + "SelectedGeometry", + "FrameTraceRoutes" + ] + }, + { + "module": "SourceInvocation", + "source": "SourceInvocation.lean", + "sha256": "45ea3b2f9165a94a651f47beb93a5e74250b94538936ff18e81f8b5939e5e782", + "imports": [ + "SourceInvocationComparison", + "SourceInitialPayload", + "SourceNativeInvocation", + "SelectedGeometry", + "SourceMoveGeometry", + "SourceDataBehavior" + ] + } + ], + "audit_declarations": [ + "LinearReplay.evalRow_zero", + "LinearReplay.evalRow_xor", + "LinearReplay.evalRow_basis", + "LinearReplay.evalRow_shift_basis", + "LinearReplay.map_getD", + "LinearReplay.step_map", + "LinearReplay.run_map", + "LinearReplay.evalRows_step", + "LinearReplay.evalRows_run", + "LinearReplay.checked_projection", + "LinearReplay.evalRows_basisRows", + "LinearReplay.evalRows_getD", + "LinearReplay.checks_sound", + "LinearReplay.checked_flag_mono", + "LinearReplay.checked_guards_sound", + "TreeReplay.Tree.map_get", + "TreeReplay.Tree.map_put", + "TreeReplay.Tree.map_map", + "TreeReplay.Tree.map_tabulate", + "TreeReplay.Tree.get_tabulate", + "TreeReplay.Tree.full_tabulate", + "TreeReplay.Tree.full_put", + "TreeReplay.Tree.get_put", + "TreeReplay.step_map", + "TreeReplay.run_map", + "TreeReplay.evalRows_step", + "TreeReplay.evalRows_run", + "TreeReplay.checked_projection", + "TreeReplay.evalRows_get", + "TreeReplay.checks_sound", + "TreeReplay.checked_flag_mono", + "TreeReplay.checked_guards_sound", + "TreeReplay.evalRows_basisRows", + "TreeReplay.dirtyInput_get", + "TreeReplay.evalPayloadRows_run", + "TreeReplay.evalPayloadRows_basisRows", + "FramedReplay.decode_reframe", + "FramedReplay.put_get", + "FramedReplay.decode_xor", + "FramedReplay.decode_step", + "FramedReplay.physical_blank_of_decoded_blank", + "FramedReplay.erase_guard_transport", + "FramedReplay.decode_run", + "WholeHosting.masksDisjoint_symm", + "WholeHosting.swapAddress_involution", + "WholeHosting.swapAddress_commute", + "WholeHosting.swapAddress_disjoint_union", + "WholeHosting.bitAction_involution", + "WholeHosting.bitAction_commute", + "WholeHosting.bitAction_disjoint_comp", + "WholeHosting.remainder_disjoint", + "WholeHosting.union_remainder", + "WholeHosting.bitAction_complete", + "WholeHosting.bitAction_empty", + "WholeHosting.bitFactors_union", + "WholeHosting.bitFactors_complete", + "AddressPairs.split_join", + "AddressPairs.join_split", + "AddressPairs.relative_gauge", + "AddressPairs.join_swap", + "AddressPairs.relative_coordinate", + "SourceMatrix.evalRow_endpoint", + "SourceMatrix.evalRows_endpoint", + "SourceMatrix.evalPayloadRows_endpoint", + "FrameGeometry.frame_valid", + "FrameGeometry.scaled_idempotent_entries", + "FrameGeometry.scaled_symmetric_entries", + "FrameGeometry.scaled_stack_entries", + "FrameGeometry.stack_inverse_entries", + "FrameGeometry.inverse_stack_entries", + "FrameGeometry.transition_absorbs", + "FrameGeometry.scaled_full_entries", + "FrameGeometry.scaled_zero_entries", + "FrameGeometry.scaled_idempotent", + "FrameGeometry.scaled_symmetric", + "FrameGeometry.stack_inverse", + "FrameGeometry.inverse_stack", + "FrameGeometry.cast_mul_factor", + "FrameGeometry.four_ne_zero", + "FrameGeometry.two_fifty_six_ne_zero", + "FrameGeometry.projector_idempotent", + "FrameGeometry.projector_symmetric", + "FrameGeometry.projector_full", + "FrameGeometry.projector_zero", + "FrameGeometry.scaled_stack", + "FrameGeometry.cast_transpose", + "FrameGeometry.cast_product", + "FrameGeometry.cast_selector", + "FrameGeometry.projector_stack", + "FrameGeometry.transition_scaled_left", + "FrameGeometry.transition_scaled_right", + "FrameGeometry.normalized_absorption", + "FrameGeometry.transition_projectors", + "FrameGeometry.stack_right_inverse", + "FrameGeometry.stack_left_inverse", + "FrameGeometry.partialSwap_involution", + "FrameGeometry.partialSwap_nested", + "FrameGeometry.partialSwap_nested_reverse", + "FrameGeometry.full_after_frame", + "FrameGeometry.frame_after_full", + "FrameGeometry.firstEight_replaceFirst", + "FrameGeometry.replaceFirst_twice", + "FrameGeometry.replaceFirst_firstEight", + "FrameGeometry.liftPair_comp", + "FrameGeometry.liftPair_id", + "FrameGeometry.partialSwap_coordinate", + "FrameGeometry.coordinate_residual", + "FrameGeometry.residual_partialSwap", + "FrameGeometry.full_after_frame64_coordinate", + "FrameGeometry.frame_after_full64_coordinate", + "FrameGeometry.coordinateSwap64_involution", + "FrameGeometry.stage2_relative_transport", + "FrameGeometry.stage2_helper_endpoint", + "FrameTrace.flag_mono", + "FrameTrace.checked_valid", + "FrameTrace.scalar_projection", + "SourceFrameLabels.labels_checked", + "SourceFrameLabels.labels_valid", + "SourceFrameLabels.label_range", + "SourceFrameLabels.copy_frames", + "SourceFrameLabels.erase_frames", + "SourceFrameMoves.moves_checked", + "SourceFrameMoves.move_pair", + "SourceFrameMoves.move_range", + "SourceFrameMoves.move_transition", + "SourceFrameMoves.move_absorbs", + "SourceFrameTrace.initial_tabulate", + "SourceFrameTrace.final_tabulate", + "SourceFrameTrace.project0", + "SourceFrameTrace.checkpoint0", + "SourceFrameTrace.project1", + "SourceFrameTrace.checkpoint1", + "SourceFrameTrace.project2", + "SourceFrameTrace.checkpoint2", + "SourceFrameTrace.project3", + "SourceFrameTrace.checkpoint3", + "SourceFrameTrace.project4", + 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"SourceFrameTrace.checkpoint77", + "SourceFrameTrace.project78", + "SourceFrameTrace.checkpoint78", + "SourceFrameTrace.project79", + "SourceFrameTrace.checkpoint79", + "SourceFrameTrace.project80", + "SourceFrameTrace.checkpoint80", + "SourceFrameTrace.project81", + "SourceFrameTrace.checkpoint81", + "SourceFrameTrace.project82", + "SourceFrameTrace.checkpoint82", + "SourceFrameTrace.project83", + "SourceFrameTrace.checkpoint83", + "SourceFrameTrace.project84", + "SourceFrameTrace.checkpoint84", + "SourceFrameTrace.project85", + "SourceFrameTrace.checkpoint85", + "SourceFrameTrace.project86", + "SourceFrameTrace.checkpoint86", + "SourceFrameTrace.project87", + "SourceFrameTrace.checkpoint87", + "SourceFrameTrace.project88", + "SourceFrameTrace.checkpoint88", + "SourceFrameTrace.project89", + "SourceFrameTrace.checkpoint89", + "SourceFrameTrace.project90", + "SourceFrameTrace.checkpoint90", + "SourceFrameTrace.project91", + "SourceFrameTrace.checkpoint91", + "SourceFrameTrace.project92", + "SourceFrameTrace.checkpoint92", + "SourceFrameTrace.project93", + "SourceFrameTrace.checkpoint93", + "SourceFrameTrace.project94", + "SourceFrameTrace.checkpoint94", + "SourceFrameTrace.project95", + "SourceFrameTrace.checkpoint95", + "SourceFrameTrace.combine", + "SourceFrameTrace.finish96", + "SourceFrameTrace.finish95", + "SourceFrameTrace.finish94", + "SourceFrameTrace.finish93", + "SourceFrameTrace.finish92", + "SourceFrameTrace.finish91", + "SourceFrameTrace.finish90", + "SourceFrameTrace.finish89", + "SourceFrameTrace.finish88", + "SourceFrameTrace.finish87", + "SourceFrameTrace.finish86", + "SourceFrameTrace.finish85", + "SourceFrameTrace.finish84", + "SourceFrameTrace.finish83", + "SourceFrameTrace.finish82", + "SourceFrameTrace.finish81", + "SourceFrameTrace.finish80", + "SourceFrameTrace.finish79", + "SourceFrameTrace.finish78", + "SourceFrameTrace.finish77", + "SourceFrameTrace.finish76", + "SourceFrameTrace.finish75", + "SourceFrameTrace.finish74", + "SourceFrameTrace.finish73", + "SourceFrameTrace.finish72", + "SourceFrameTrace.finish71", + "SourceFrameTrace.finish70", + "SourceFrameTrace.finish69", + "SourceFrameTrace.finish68", + "SourceFrameTrace.finish67", + "SourceFrameTrace.finish66", + "SourceFrameTrace.finish65", + "SourceFrameTrace.finish64", + "SourceFrameTrace.finish63", + "SourceFrameTrace.finish62", + "SourceFrameTrace.finish61", + "SourceFrameTrace.finish60", + "SourceFrameTrace.finish59", + "SourceFrameTrace.finish58", + "SourceFrameTrace.finish57", + "SourceFrameTrace.finish56", + "SourceFrameTrace.finish55", + "SourceFrameTrace.finish54", + "SourceFrameTrace.finish53", + "SourceFrameTrace.finish52", + "SourceFrameTrace.finish51", + "SourceFrameTrace.finish50", + "SourceFrameTrace.finish49", + "SourceFrameTrace.finish48", + "SourceFrameTrace.finish47", + "SourceFrameTrace.finish46", + "SourceFrameTrace.finish45", + "SourceFrameTrace.finish44", + "SourceFrameTrace.finish43", + "SourceFrameTrace.finish42", + "SourceFrameTrace.finish41", + "SourceFrameTrace.finish40", + "SourceFrameTrace.finish39", + "SourceFrameTrace.finish38", + "SourceFrameTrace.finish37", + "SourceFrameTrace.finish36", + "SourceFrameTrace.finish35", + "SourceFrameTrace.finish34", + "SourceFrameTrace.finish33", + "SourceFrameTrace.finish32", + "SourceFrameTrace.finish31", + "SourceFrameTrace.finish30", + "SourceFrameTrace.finish29", + "SourceFrameTrace.finish28", + "SourceFrameTrace.finish27", + "SourceFrameTrace.finish26", + "SourceFrameTrace.finish25", + "SourceFrameTrace.finish24", + "SourceFrameTrace.finish23", + "SourceFrameTrace.finish22", + "SourceFrameTrace.finish21", + "SourceFrameTrace.finish20", + "SourceFrameTrace.finish19", + "SourceFrameTrace.finish18", + "SourceFrameTrace.finish17", + "SourceFrameTrace.finish16", + "SourceFrameTrace.finish15", + "SourceFrameTrace.finish14", + "SourceFrameTrace.finish13", + "SourceFrameTrace.finish12", + "SourceFrameTrace.finish11", + "SourceFrameTrace.finish10", + "SourceFrameTrace.finish9", + "SourceFrameTrace.finish8", + "SourceFrameTrace.finish7", + "SourceFrameTrace.finish6", + "SourceFrameTrace.finish5", + "SourceFrameTrace.finish4", + "SourceFrameTrace.finish3", + "SourceFrameTrace.finish2", + "SourceFrameTrace.finish1", + "SourceFrameTrace.finish0", + "SourceFrameTrace.scalar_word", + "SourceFrameTrace.forward_checked", + "SourceFrameTrace.forward_valid", + "TreeReplay.payload_checks_sound", + "TreeReplay.checked_payload_guards_sound", + "FrameTrace.matches_get", + "FrameTrace.matches_step", + "FrameTrace.add_frames_equal", + "FrameTrace.matches_run", + "FrameTrace.valid_step", + "FrameTrace.valid_trace", + "FrameTrace.decoded_run", + "OwnerTransport.write_other", + "OwnerTransport.gather_write", + "OwnerTransport.rawXor_write", + "OwnerTransport.rawTransport_write", + "OwnerTransport.gather_step", + "OwnerTransport.logicalStep_tree", + "OwnerTransport.rawStep_other", + "OwnerTransport.replace_fin_tree", + "OwnerTransport.logicalStep_fin_tree", + "OwnerTransport.physicalStep_full", + "OwnerTransport.gather_run_framed", + "OwnerTransport.runRaw_other", + "OwnerTransport.extendCover_owner", + "OwnerTransport.initialRaw_other", + "OwnerTransport.gather_initialRaw", + "OwnerTransport.route_native_address", + "OwnerTransport.inverse_common_cover", + "OwnerTransport.rawXor_fromNative", + "OwnerTransport.rawTransport_fromNative", + "OwnerTransport.rawStep_fromNative", + "OwnerTransport.runRaw_fromNative", + "SourceFrameTrace.indices_checked", + "SourceFrameTrace.indices_bound", + "SourceFrameTrace.route_projection", + "SourceOwnership.perm_inverse", + "SourceOwnership.inverse_perm", + "SourceOwnership.perm_support", + "SourceOwnership.fingerprint_injective", + "SourceOwnership.owner_inverse", + "SourceOwnership.family_tag_injective", + "SourceOwnership.family_data", + "SourceOwnership.helper_range", + "SourceOwnership.helper_frame", + "SourceOwnership.helper_child", + "SourceFrameTrace.initial_owner_frames", + "SourceFrameTrace.helper_final_frames", + "SourceFrameTrace.initial_frame_range", + "SourceFrameTrace.final_frame_range", + "SelectedGeometry.tag_frame_bound", + "SelectedGeometry.tag_residual_diagonal", + "SelectedGeometry.source_mask_outside", + "SourceMatrix.combine", + "SourceMatrix.chunks_flatten", + "SourceMatrix.checkpoint0", + "SourceMatrix.checkpoint1", + "SourceMatrix.checkpoint2", + "SourceMatrix.checkpoint3", + "SourceMatrix.checkpoint4", + "SourceMatrix.checkpoint5", + "SourceMatrix.checkpoint6", + "SourceMatrix.checkpoint7", + "SourceMatrix.checkpoint8", + "SourceMatrix.checkpoint9", + "SourceMatrix.checkpoint10", + "SourceMatrix.checkpoint11", + "SourceMatrix.checkpoint12", + "SourceMatrix.checkpoint13", + "SourceMatrix.checkpoint14", + "SourceMatrix.checkpoint15", + "SourceMatrix.checkpoint16", + "SourceMatrix.checkpoint17", + "SourceMatrix.checkpoint18", + "SourceMatrix.checkpoint19", + "SourceMatrix.checkpoint20", + "SourceMatrix.checkpoint21", + "SourceMatrix.checkpoint22", + "SourceMatrix.checkpoint23", + "SourceMatrix.checkpoint24", + "SourceMatrix.checkpoint25", + "SourceMatrix.checkpoint26", + "SourceMatrix.checkpoint27", + "SourceMatrix.checkpoint28", + "SourceMatrix.checkpoint29", + "SourceMatrix.checkpoint30", + "SourceMatrix.checkpoint31", + "SourceMatrix.checkpoint32", + "SourceMatrix.checkpoint33", + "SourceMatrix.checkpoint34", + "SourceMatrix.checkpoint35", + "SourceMatrix.checkpoint36", + "SourceMatrix.checkpoint37", + "SourceMatrix.checkpoint38", + "SourceMatrix.checkpoint39", + "SourceMatrix.checkpoint40", + "SourceMatrix.checkpoint41", + "SourceMatrix.checkpoint42", + "SourceMatrix.checkpoint43", + "SourceMatrix.checkpoint44", + "SourceMatrix.checkpoint45", + "SourceMatrix.checkpoint46", + "SourceMatrix.checkpoint47", + "SourceMatrix.checkpoint48", + "SourceMatrix.checkpoint49", + "SourceMatrix.checkpoint50", + "SourceMatrix.checkpoint51", + "SourceMatrix.checkpoint52", + "SourceMatrix.checkpoint53", + "SourceMatrix.checkpoint54", + "SourceMatrix.checkpoint55", + "SourceMatrix.checkpoint56", + "SourceMatrix.checkpoint57", + "SourceMatrix.checkpoint58", + "SourceMatrix.checkpoint59", + "SourceMatrix.checkpoint60", + "SourceMatrix.checkpoint61", + "SourceMatrix.checkpoint62", + "SourceMatrix.checkpoint63", + "SourceMatrix.checkpoint64", + "SourceMatrix.checkpoint65", + "SourceMatrix.checkpoint66", + "SourceMatrix.checkpoint67", + "SourceMatrix.checkpoint68", + "SourceMatrix.checkpoint69", + "SourceMatrix.checkpoint70", + "SourceMatrix.checkpoint71", + "SourceMatrix.checkpoint72", + "SourceMatrix.checkpoint73", + "SourceMatrix.checkpoint74", + "SourceMatrix.checkpoint75", + "SourceMatrix.checkpoint76", + "SourceMatrix.checkpoint77", + "SourceMatrix.checkpoint78", + "SourceMatrix.checkpoint79", + "SourceMatrix.checkpoint80", + "SourceMatrix.checkpoint81", + "SourceMatrix.checkpoint82", + "SourceMatrix.checkpoint83", + "SourceMatrix.checkpoint84", + "SourceMatrix.checkpoint85", + "SourceMatrix.checkpoint86", + "SourceMatrix.checkpoint87", + "SourceMatrix.checkpoint88", + "SourceMatrix.checkpoint89", + "SourceMatrix.checkpoint90", + "SourceMatrix.checkpoint91", + "SourceMatrix.checkpoint92", + "SourceMatrix.checkpoint93", + "SourceMatrix.checkpoint94", + "SourceMatrix.checkpoint95", + "SourceMatrix.finish96", + "SourceMatrix.finish95", + "SourceMatrix.finish94", + "SourceMatrix.finish93", + "SourceMatrix.finish92", + "SourceMatrix.finish91", + "SourceMatrix.finish90", + "SourceMatrix.finish89", + "SourceMatrix.finish88", + "SourceMatrix.finish87", + "SourceMatrix.finish86", + "SourceMatrix.finish85", + "SourceMatrix.finish84", + "SourceMatrix.finish83", + "SourceMatrix.finish82", + "SourceMatrix.finish81", + "SourceMatrix.finish80", + "SourceMatrix.finish79", + "SourceMatrix.finish78", + "SourceMatrix.finish77", + "SourceMatrix.finish76", + "SourceMatrix.finish75", + "SourceMatrix.finish74", + "SourceMatrix.finish73", + "SourceMatrix.finish72", + "SourceMatrix.finish71", + "SourceMatrix.finish70", + "SourceMatrix.finish69", + "SourceMatrix.finish68", + "SourceMatrix.finish67", + "SourceMatrix.finish66", + "SourceMatrix.finish65", + "SourceMatrix.finish64", + "SourceMatrix.finish63", + "SourceMatrix.finish62", + "SourceMatrix.finish61", + "SourceMatrix.finish60", + "SourceMatrix.finish59", + "SourceMatrix.finish58", + "SourceMatrix.finish57", + "SourceMatrix.finish56", + "SourceMatrix.finish55", + "SourceMatrix.finish54", + "SourceMatrix.finish53", + "SourceMatrix.finish52", + "SourceMatrix.finish51", + "SourceMatrix.finish50", + "SourceMatrix.finish49", + "SourceMatrix.finish48", + "SourceMatrix.finish47", + "SourceMatrix.finish46", + "SourceMatrix.finish45", + "SourceMatrix.finish44", + "SourceMatrix.finish43", + "SourceMatrix.finish42", + "SourceMatrix.finish41", + "SourceMatrix.finish40", + "SourceMatrix.finish39", + "SourceMatrix.finish38", + "SourceMatrix.finish37", + "SourceMatrix.finish36", + "SourceMatrix.finish35", + "SourceMatrix.finish34", + "SourceMatrix.finish33", + "SourceMatrix.finish32", + "SourceMatrix.finish31", + "SourceMatrix.finish30", + "SourceMatrix.finish29", + "SourceMatrix.finish28", + "SourceMatrix.finish27", + "SourceMatrix.finish26", + "SourceMatrix.finish25", + "SourceMatrix.finish24", + "SourceMatrix.finish23", + "SourceMatrix.finish22", + "SourceMatrix.finish21", + "SourceMatrix.finish20", + "SourceMatrix.finish19", + "SourceMatrix.finish18", + "SourceMatrix.finish17", + "SourceMatrix.finish16", + "SourceMatrix.finish15", + "SourceMatrix.finish14", + "SourceMatrix.finish13", + "SourceMatrix.finish12", + "SourceMatrix.finish11", + "SourceMatrix.finish10", + "SourceMatrix.finish9", + "SourceMatrix.finish8", + "SourceMatrix.finish7", + "SourceMatrix.finish6", + "SourceMatrix.finish5", + "SourceMatrix.finish4", + "SourceMatrix.finish3", + "SourceMatrix.finish2", + "SourceMatrix.finish1", + "SourceMatrix.finish0", + "SourceMatrix.runFull_checked", + "SourceMatrix.literal_word_checked", + "SourceMatrix.literal_word_rows", + "SourceMatrix.initial_formula", + "SourceMatrix.expected_formula", + "SourceMatrix.arbitrary_dirty_bools", + "SourceMatrix.arbitrary_dirty_guards", + "SourceMatrix.arbitrary_dirty_payloads", + "SourceMatrix.actual_payload_clean", + "SourceMatrix.arbitrary_dirty_temp_restored", + "SourceMatrix.arbitrary_dirty_original_roles", + "SourceFramed.initial_matches", + "SourceFramed.initial_decoded", + "SourceFramed.actual_valid", + "SourceFramed.final_matches", + "SourceFramed.actual_decoded_endpoint", + "SourceFramed.actual_physical_endpoint", + "SourceFramed.actual_temporary_restored", + "SourceFramed.all_physical_endpoints", + "SourceRaw.gather_initial", + "SourceRaw.gather_final", + "SourceRaw.actual_valid", + "SourceRaw.payload_endpoint", + "SourceRaw.private_restored", + "SourceRaw.other_preserved", + "SourceRaw.other_payload_preserved", + "MultiHosting.base_commutes", + "MultiHosting.runBase_commutes", + "MultiHosting.delay_residuals", + "MultiHosting.multi_hosting", + "MultiHosting.multi_hosting_in_context", + "MultiHosting.PhysicalImplementations.original_projection", + "MultiHosting.PhysicalImplementations.relocated_projection", + "MultiHosting.physical_multi_hosting", + "MultiHosting.physical_multi_hosting_in_context", + "SourceOwnership.unindex_reindex", + "SourceOwnership.reindex_unindex", + "SourceOwnership.residual_projector_transport", + "SourceOwnership.perm_tag_injective", + "SourceOwnership.unindex_tag_injective", + "SourceOwnership.family_data_general", + "SourceOwnership.same_family_data", + "SourceOwnership.owners_injective", + "SourceConnection.packed_data", + "SourceConnection.packed_helper", + "SourceConnection.invoke_endpoint", + "SourceConnection.swap_conjugacy", + "SourceConnection.host_transport", + "SourceConnection.original_retained", + "SourceConnection.original_bank_output", + "SourceConnection.relocated_retained", + "InvocationPayload.extend_owner", + "InvocationPayload.extend_outside", + "InvocationPayload.realize_owner", + "InvocationPayload.input_realize", + "InvocationPayload.input_realize_packed", + "InvocationPayload.realized_gather", + "InvocationPayload.realized_payload", + "InvocationPayload.realized_payloads", + "PortGeometry.doubled_orthogonal_entries", + "PortGeometry.quarteredRoute_exact", + "PortGeometry.doubled_row_orthogonal_entries", + "PortGeometry.doubled_orthogonal", + "PortGeometry.doubled_row_orthogonal", + "PortGeometry.basis_entry", + "PortGeometry.cast_orthogonal", + "PortGeometry.cast_row_orthogonal", + "PortGeometry.basis_transpose_mul", + "PortGeometry.basis_mul_transpose", + "PortGeometry.chart8_dot", + "PortGeometry.firstEight_add", + "PortGeometry.firstEight_smul", + "PortGeometry.firstEight_extendEight", + "PortGeometry.extendEight_comp", + "PortGeometry.extendEight_id", + "PortGeometry.chart64_firstEight", + "PortGeometry.chart64_outside", + "PortGeometry.chart64_bijective", + "PortGeometry.chart64_add", + "PortGeometry.chart64_smul", + "PortGeometry.chart64_dot", + "PortGeometry.chart64_symm_dot", + "PortGeometry.chart64_symm_add", + "PortGeometry.chart64_symm_smul", + "PortGeometry.stage2Index_involutive", + "PortGeometry.stage2Coordinates_dot", + "PortGeometry.dataRoute64_dot", + "PortGeometry.dataRoute64_add", + "PortGeometry.dataRoute64_smul", + "PortGeometry.dataRoute64_involutive", + "PortGeometry.route15_entry", + "PortGeometry.sourceRoute64_eq", + "SourceOwnership.slotChart_dot", + "SourceOwnership.slotChart_add", + "SourceOwnership.slotChart_smul", + "SourceOwnership.familyChart_dot", + "SourceOwnership.familyChart_add", + "SourceOwnership.familyChart_smul", + "SourceOwnership.helper_sigma_dot", + "SourceOwnership.helper_sigma_add", + "SourceOwnership.helper_sigma_smul", + "SourceOwnership.physicalOwner_formula", + "SourceOwnership.physicalOwner_common", + "SourceOwnership.physicalOwner_injective", + "SourceOwnership.family_lt", + "SourceOwnership.activeOwner_injective", + "SourceOwnership.active_gather_step", + "SourceOwnership.sourceActiveOwner_injective", + "SourceOwnership.source_gather_run", + "SourceOwnership.helper_address_forward", + "SourceOwnership.helper_address_inverse", + "SourceOwnership.source_address_gather_run", + "SourceOwnership.source_common_cover", + "SourceOwnership.source_native_run", + "ParentOwnership.perm_inverse", + "ParentOwnership.inverse_perm", + "ParentOwnership.perm_support", + "ParentOwnership.fingerprint_injective", + "ParentOwnership.owner_inverse", + "ParentOwnership.family_tag_injective", + "ParentOwnership.family_data", + "ParentOwnership.helper_range", + "ParentOwnership.helper_frame", + "ParentOwnership.unindex_reindex", + "ParentOwnership.reindex_unindex", + "ParentOwnership.residual_projector_transport", + "ParentOwnership.perm_tag_injective", + "ParentOwnership.unindex_tag_injective", + "ParentOwnership.family_data_general", + "ParentOwnership.same_family_data", + "ParentOwnership.owners_injective", + "ParentOwnership.slotChart_dot", + "ParentOwnership.slotChart_add", + "ParentOwnership.slotChart_smul", + "ParentOwnership.helper_sigma_dot", + "ParentOwnership.helper_sigma_add", + "ParentOwnership.helper_sigma_smul", + "ParentOwnership.helper_residual_transport", + "ParentOwnership.physicalOwner_formula", + "ParentOwnership.physicalOwner_injective", + "ParentOwnership.family_lt", + "ParentOwnership.sourceActiveOwner_avoids_host_families", + "ParentOwnership.sourceActiveOwner_injective", + "ParentOwnership.source_gather_run", + "ParentOwnership.helper_address_forward", + "ParentOwnership.helper_address_inverse", + "ParentOwnership.source_address_gather_run", + "ParentOwnership.source_common_cover", + "ParentOwnership.source_native_run", + "PhysicalSourceConnection.helper_endpoints", + "PhysicalSourceConnection.helper_endpoint", + "PhysicalSourceConnection.physical_data_endpoints", + "PhysicalSourceConnection.data_independent", + "PhysicalSourceConnection.data_endpoint", + "PhysicalSourceConnection.hosted_endpoint", + "PhysicalSourceConnection.original_retained", + "PhysicalSourceConnection.relocated_retained", + "PhysicalSourceConnection.tag_child_cases", + "PhysicalSourceConnection.tag_pending_contains", + "PhysicalSourceConnection.selected_invocation_completion", + "SelectedGeometry.gauges_tag", + "SelectedGeometry.helper_relative", + "SourceLayouts.data_owner_eq", + "SourceLayouts.data_chart_eq", + "SourceLayouts.host_family", + "SourceLayouts.parent_owner_ne_host", + "SourceLayouts.host_ne_parent_owner", + "SourceLayouts.host_chart_forward", + "SourceLayouts.host_chart_inverse", + "SourceInvocation.oldOwner_injective", + "SourceInvocation.newOwner_injective", + "SourceInvocation.hostOwner_injective", + "SourceInvocation.host_not_old", + "SourceInvocation.tailPayload_outside", + "SourceInvocation.hostPayload_host", + "SourceInvocation.hostPayload_outside", + "SourceInvocation.oldPayload_host", + "SourceInvocation.oldPayload_outside", + "SourceInvocation.newPayload_outside", + "SourceInvocation.parent_family_lt_private", + "SourceInvocation.owner_overlap_data", + "SourceInvocation.owner_overlap_charts", + "SourceInvocation.commonNativeCover_new", + "SourceInvocation.new_common_cover", + "SourceInvocation.old_common_cover", + "SourceControls.actual_add_event", + "SourceControls.omitted_add_changes_row", + "SourceControls.omitted_add_keeps_guards", + "SourceControls.actual_first_copy", + "SourceControls.dirty_private_copy_rejected", + "SourceControls.dirty_private_copy_would_overwrite", + "SourceControls.literal_helper_three_survives", + "SourceControls.literal_helper_three_not_zero", + "SourceInvocation.oldRaw_data", + "SourceInvocation.newRaw_data", + "SourceInvocation.oldRaw_bank", + "SourceInvocation.oldRaw_host", + "SourceInvocation.newRaw_host", + "SourceInvocation.oldRaw_outside", + "SourceInvocation.newRaw_outside", + "SourceInvocation.oldResult_framed", + "SourceInvocation.newResult_framed", + "SourceDataBehavior.first_initial_frame", + "SourceDataBehavior.second_initial_frame", + "SourceDataBehavior.first_final_frame", + "SourceDataBehavior.second_final_frame", + "SourceDataBehavior.framed_first", + "SourceDataBehavior.framed_second", + "SourceDataBehavior.framed_data_formula", + "SourceDataBehavior.old_data_formula", + "SourceDataBehavior.new_data_formula", + "SourceInvocation.newPayload_host", + "SourceInvocation.oldPayload_data", + "SourceInvocation.newPayload_data", + "SourceInvocation.oldPayload_bank", + "SourceInvocation.shared_host_input", + "SourceInvocation.shared_data_input", + "SourceRawGuards.raw_clean_of_framed", + "SourceRawGuards.raw_clean_run_of_framed", + "SourceRawGuards.native_clean_of_raw", + "SourceRawGuards.native_clean_run_of_raw", + "SourceRawGuards.actual_raw_clean", + "SourceRawGuards.initial_fromNative", + "SourceRawGuards.actual_native_clean", + "SourceRawGuards.native_run_refines", + "SourceRawGuards.native_payload_endpoint", + "SourceRawGuards.native_private_restored", + "SourceRawGuards.native_other_preserved", + "SourceInvocation.native_payload_roundtrip", + "SourceInvocation.old_native_realization", + "SourceInvocation.new_native_realization", + "SourceInvocation.old_native_clean", + "SourceInvocation.new_native_clean", + "SourceInvocation.old_native_temporary_restored", + "SourceInvocation.new_native_temporary_restored", + "SourceInvocation.native_shared_host_input", + "SourceInvocation.native_shared_data_input", + "SourceInvocation.native_shared_tail_input", + "SourceInvocation.initialized_native_host_input", + "SourceInvocation.initialized_native_data_input", + "SourceInvocation.initialized_native_tail_input", + "SourceInvocation.oldResult_native", + "SourceInvocation.newResult_native", + "SourceMoveGeometry.move_projectors", + "SourceMoveGeometry.move_stage2_relative", + "SourceMoveGeometry.move_relative", + "SourceMoveGeometry.copy_stage2_relative", + "SourceMoveGeometry.copy_relative", + "SourceMoveGeometry.erase_relative", + "SourceMoveGeometry.physicalStep_move", + "SourceMoveGeometry.physicalStep_copy", + "SourceMoveGeometry.matrix_run_eq", + "SourceMoveGeometry.actual_matrix_run", + "SourceMoveGeometry.nativeStep_move", + "SourceMoveGeometry.nativeRoute_move", + "SourceMoveGeometry.nativeStep_copy", + "SourceInvocation.actualContract", + "SourceInvocation.selected_call_completion", + "SourceInvocation.selected_native_completion", + "SourceInvocation.selected_data_formula", + "SourceInvocation.selected_native_realization", + "SourceInvocation.selected_native_clean", + "SourceInvocation.selected_matrix_realization", + "SourceInvocation.selected_original_matrix_realization", + "SourceInvocation.selected_temporary_restoration" + ], + "scope": { + "selected_source": "PR442 stage2 replica0 pair0 forward, 19002 literal events", + "framework": "Task A is separately committed and separately replayed.", + "certificate_boundary": "Lean proves statements about embedded literals; JSON extraction is reproduced externally.", + "limits": "No complete cover sweep, later real child schedule, physical cost, all-size compiler, or kappa bound." + } +} diff --git a/research/lean-multi-host-source/replay-result.json b/research/lean-multi-host-source/replay-result.json new file mode 100644 index 0000000000..e8328d68ef --- /dev/null +++ b/research/lean-multi-host-source/replay-result.json @@ -0,0 +1,3493 @@ +{ + "status": "PASS", + "lean": "Lean (version 4.33.0, x86_64-unknown-linux-gnu, commit d8b18978322de05a8f3dba51ef03cf5461676c17, Release)", + "trust_level": 0, + "lean_commit": "d8b18978322de05a8f3dba51ef03cf5461676c17", + "completed_utc": "2026-10-11T23:59:17.947059+00:00", + "manifest_sha256": "3ea081c5c7769718a30793b5f9a7de545b69152032845a134e646efcbd452312", + "mathlib_commit": "db584cd6d46c92f209a44c0f1c829460d327499d", + "modules": { + "RowEvaluation": { + "seconds": 0.564, + "sha256": 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"ecfab2d1002c9f610174451c77fcafb5668e0d2c732d76de20e4a2b71e14f500", + "output": "'SourceFrameTrace.indices_checked' does not depend on any axioms\n'SourceFrameTrace.indices_bound' depends on axioms: [propext, Quot.sound]\n'SourceFrameTrace.route_projection' depends on axioms: [propext, Quot.sound]\n", + "dependency_hashes": { + "FrameTraceLiterals": "9779f56e4ef00fdf27bb628ac42e84555cf46311b5e4e6511d2cfa589d697855", + "OwnerTransport": "d31a7db371484909c0690643cc1aae97a2a969a32a4847a2a5c9865b21d14ac6" + }, + "olean_sha256": "08952412510ed043bb62bb4119e8d518689ae1fe2b2f088cb22fb0caaf51f055" + }, + "OwnershipData": { + "seconds": 22.622, + "sha256": "fa08b345a9763529ff8ad62f58ed472362aadfd3410cbaf02774339e4f13ee6a", + "output": "'SourceOwnership.perm_inverse' does not depend on any axioms\n'SourceOwnership.perm_support' depends on axioms: [propext]\n'SourceOwnership.fingerprint_injective' does not depend on any axioms\n'SourceOwnership.family_tag_injective' does not depend on any axioms\n'SourceOwnership.helper_frame' does not depend on any axioms\n", + "dependency_hashes": {}, + "olean_sha256": "12d926f52897e6f28caa4b18562c7835ecf54d0feda224b31cde76ce9e32b8bf" + }, + "FrameTraceTables": { + "seconds": 9.151, + "sha256": "f024344645891f85a073840da3e8546ba95ee5dbf5024a5db73136cf4e99f1c1", + "output": "'SourceFrameTrace.initial_owner_frames' does not depend on any axioms\n'SourceFrameTrace.helper_final_frames' does not depend on any axioms\n'SourceFrameTrace.initial_frame_range' does not depend on any axioms\n'SourceFrameTrace.final_frame_range' does not depend on any axioms\n", + "dependency_hashes": { + "FrameTraceLiterals": "9779f56e4ef00fdf27bb628ac42e84555cf46311b5e4e6511d2cfa589d697855", + "OwnershipData": "12d926f52897e6f28caa4b18562c7835ecf54d0feda224b31cde76ce9e32b8bf" + }, + "olean_sha256": "91474282fb597a37d6d3474dcf8c2456d276eae84b714f2b9231db1f823f2b79" + }, + "HelperGeometryData": { + "seconds": 1.971, + "sha256": 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Quot.sound]\n'SourceMatrix.literal_word_rows' depends on axioms: [propext, Quot.sound]\n", + "dependency_hashes": { + "MatrixCheckpoints": "a7e7e84b1a781cc9d00049f8ee37319771c0b995da54f412bf644aef63b583a8" + }, + "olean_sha256": "9da0fae827a4f60fb440a7105800a620bec06ce23fd78ca4be8ea73ffdaa469b" + }, + "SourceTables": { + "seconds": 2.047, + "sha256": "ebddbb922cfacb255104f693d8ede32cfcff0e69a9c2dd9d99a118177a87d949", + "output": "'SourceMatrix.initial_formula' does not depend on any axioms\n'SourceMatrix.expected_formula' depends on axioms: [propext]\n", + "dependency_hashes": { + "MatrixData": "c3bcad1f60feef6e82d8056fb8e9c1c4952ce32f9892829e00213d880a0fac41", + "EndpointInterpretation": "f3f154d170081ad6663022ff70e21a755334b2dd6739c0d02624be16ca0f7c9f" + }, + "olean_sha256": "8f9e973937a8117eedb4c6742cc2b261be32cd1f9881a4c205429490650b8de6" + }, + "SourceEndpoint": { + "seconds": 0.547, + "sha256": "77b72ee70ffaf36a3a9f7fff0cee7d6be964b54a855483d9503208a747230bf9", + "output": 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+ "output": "'SourceFramed.initial_matches' depends on axioms: [propext]\n'SourceFramed.initial_decoded' depends on axioms: [propext, Quot.sound]\n'SourceFramed.actual_valid' depends on axioms: [propext, Quot.sound]\n'SourceFramed.final_matches' depends on axioms: [propext, Quot.sound]\n'SourceFramed.actual_decoded_endpoint' depends on axioms: [propext, Quot.sound]\n'SourceFramed.actual_physical_endpoint' depends on axioms: [propext, Quot.sound]\n'SourceFramed.actual_temporary_restored' depends on axioms: [propext, Quot.sound]\n'SourceFramed.all_physical_endpoints' depends on axioms: [propext, Quot.sound]\n", + "dependency_hashes": { + "FrameTraceData": "b2d95b9eb66a14ffc488d09b2103526ce64a0d662df7028409180cc7a0a607f4", + "FrameTraceRefinement": "1354555744c259a3d99e3e78bcfe73f4a28cd84a6b373683ed180cbc668c2c78", + "SourceEndpoint": "dfa95b142e70b85c7061cbb0c523f469a0a58735f5476d192565bafb34d54e04" + }, + "olean_sha256": "9468c77001af2dbe1b42855b2c08a95ef2e09e74e41ee7cdc6d50e73fa938772" 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[propext, Quot.sound]\n", + "dependency_hashes": { + "CoordinateSwap": "e48b7c60f8435bb45dd435dc8234348cbaa1cff43cc77465788c7b5266e2dc19" + }, + "olean_sha256": "621a1db3e156afafb9038056dc6f223f34588052369cd3c9268dc9414206a93f" + }, + "Ownership": { + "seconds": 0.469, + "sha256": "a18ecfb59c4641ecf86eb672764dc6491e524d01b74392f34549c6013f9c4f76", + "output": "'SourceOwnership.residual_projector_transport' depends on axioms: [propext, Quot.sound]\n'SourceOwnership.unindex_tag_injective' depends on axioms: [propext, Classical.choice, Quot.sound]\n'SourceOwnership.owners_injective' depends on axioms: [propext, Classical.choice, Quot.sound]\n", + "dependency_hashes": { + "OwnershipData": "12d926f52897e6f28caa4b18562c7835ecf54d0feda224b31cde76ce9e32b8bf" + }, + "olean_sha256": "547804c6899e5da7d0eeeead8ddd59fc38694e397dba73a2577b66949e707b3a" + }, + "SourceConnection": { + "seconds": 0.671, + "sha256": "b09db0d3b2ae6b3261f22f5ab9a656d963dc50c2582feedf57dc481f282ff80d", + "output": "", + 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[propext, Quot.sound]\n'PortGeometry.quarteredRoute_exact' depends on axioms: [propext, Quot.sound]\n", + "dependency_hashes": {}, + "olean_sha256": "0c4af9ed631e6148449c8b7e8ba6eb0b4afd5998530849a9912cf6c624b28adf" + }, + "PortRowData": { + "seconds": 0.365, + "sha256": "9f56dcd13f2f57ef914da0cda053f4408c06bf09ee8e4b399b67b990f1fcc7b0", + "output": "'PortGeometry.doubled_row_orthogonal_entries' depends on axioms: [propext, Quot.sound]\n", + "dependency_hashes": { + "PortData": "0c4af9ed631e6148449c8b7e8ba6eb0b4afd5998530849a9912cf6c624b28adf" + }, + "olean_sha256": "1387b375a44a58a99bad1202ca5b4cac95288e9e10b2784bced95a747a7cc290" + }, + "PortGeometry": { + "seconds": 4.108, + "sha256": "68b39cc27ed66768224c152c667272ac070403aac5730f21f6cbaac6c6b15cc6", + "output": "'PortGeometry.cast_orthogonal' depends on axioms: [propext, Classical.choice, Quot.sound]\n'PortGeometry.doubled_orthogonal' depends on axioms: [propext, Classical.choice, Quot.sound]\n'PortGeometry.doubled_row_orthogonal' depends on axioms: [propext, Classical.choice, Quot.sound]\n'PortGeometry.cast_row_orthogonal' depends on axioms: [propext, Classical.choice, Quot.sound]\n'PortGeometry.basis_entry' depends on axioms: [propext, Classical.choice, Quot.sound]\n'PortGeometry.basis_transpose_mul' depends on axioms: [propext, Classical.choice, Quot.sound]\n'PortGeometry.basis_mul_transpose' depends on axioms: [propext, Classical.choice, Quot.sound]\n'PortGeometry.firstEight_extendEight' depends on axioms: [propext, Quot.sound]\n'PortGeometry.firstEight_add' does not depend on any axioms\n'PortGeometry.firstEight_smul' does not depend on any axioms\n'PortGeometry.extendEight_comp' depends on axioms: [propext, Quot.sound]\n'PortGeometry.extendEight_id' depends on axioms: [propext, Quot.sound]\n'PortGeometry.chart64_firstEight' depends on axioms: [propext, Classical.choice, Quot.sound]\n'PortGeometry.chart64_outside' depends on axioms: [propext, Classical.choice, Quot.sound]\n'PortGeometry.chart64_bijective' depends on axioms: [propext, Classical.choice, Quot.sound]\n'PortGeometry.chart64_add' depends on axioms: [propext, Classical.choice, Quot.sound]\n'PortGeometry.chart64_smul' depends on axioms: [propext, Classical.choice, Quot.sound]\n'PortGeometry.chart8_dot' depends on axioms: [propext, Classical.choice, Quot.sound]\n'PortGeometry.chart64_dot' depends on axioms: [propext, Classical.choice, Quot.sound]\n'PortGeometry.chart64_symm_dot' depends on axioms: [propext, Classical.choice, Quot.sound]\n'PortGeometry.chart64_symm_add' depends on axioms: [propext, Classical.choice, Quot.sound]\n'PortGeometry.chart64_symm_smul' depends on axioms: [propext, Classical.choice, Quot.sound]\n'PortGeometry.stage2Index_involutive' depends on axioms: [propext, Quot.sound]\n'PortGeometry.stage2Coordinates_dot' depends on axioms: [propext, Classical.choice, Quot.sound]\n'PortGeometry.dataRoute64_dot' depends on axioms: [propext, Classical.choice, Quot.sound]\n'PortGeometry.dataRoute64_add' depends on axioms: [propext, Classical.choice, Quot.sound]\n'PortGeometry.dataRoute64_smul' depends on axioms: [propext, Classical.choice, Quot.sound]\n'PortGeometry.dataRoute64_involutive' depends on axioms: [propext, Classical.choice, Quot.sound]\n'PortGeometry.route15_entry' depends on axioms: [propext, Classical.choice, Quot.sound]\n'PortGeometry.sourceRoute64_eq' depends on axioms: [propext, Classical.choice, Quot.sound]\n", + "dependency_hashes": { + "PortRowData": "1387b375a44a58a99bad1202ca5b4cac95288e9e10b2784bced95a747a7cc290" + }, + "olean_sha256": "f89d8e98e2b3614ea7233f9570a398ce8cdb35c340ba8cc95bff942077350d60" + }, + "OwnershipGeometry": { + "seconds": 1.496, + "sha256": "3acf8a6cfb8b086f06e65b79bd21aec3463723acc525dc69ae667fb5de4d7abd", + "output": "'SourceOwnership.slotChart_dot' depends on axioms: [propext, Classical.choice, Quot.sound]\n'SourceOwnership.helper_sigma_dot' depends on axioms: [propext, Classical.choice, Quot.sound]\n'SourceOwnership.physicalOwner_injective' depends on axioms: [propext, Classical.choice, Quot.sound]\n'SourceOwnership.activeOwner_injective' depends on axioms: [propext, Classical.choice, Quot.sound]\n'SourceOwnership.active_gather_step' depends on axioms: [propext, Classical.choice, Quot.sound]\n'SourceOwnership.sourceActiveOwner_injective' depends on axioms: [propext, Classical.choice, Quot.sound]\n'SourceOwnership.source_address_gather_run' depends on axioms: [propext, Classical.choice, Quot.sound]\n'SourceOwnership.source_common_cover' depends on axioms: [propext, Classical.choice, Quot.sound]\n'SourceOwnership.source_native_run' depends on axioms: [propext, Classical.choice, Quot.sound]\n", + "dependency_hashes": { + "Ownership": "547804c6899e5da7d0eeeead8ddd59fc38694e397dba73a2577b66949e707b3a", + "PortGeometry": "f89d8e98e2b3614ea7233f9570a398ce8cdb35c340ba8cc95bff942077350d60", + "OwnerTransport": "d31a7db371484909c0690643cc1aae97a2a969a32a4847a2a5c9865b21d14ac6", + "AddressPairs": 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"PhysicalSourceConnection.selected_invocation_completion": [ + "propext", + "Quot.sound" + ], + "SelectedGeometry.gauges_tag": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SelectedGeometry.helper_relative": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceLayouts.data_owner_eq": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceLayouts.data_chart_eq": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceLayouts.host_family": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceLayouts.parent_owner_ne_host": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceLayouts.host_ne_parent_owner": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceLayouts.host_chart_forward": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceLayouts.host_chart_inverse": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.oldOwner_injective": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.newOwner_injective": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.hostOwner_injective": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.host_not_old": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.tailPayload_outside": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.hostPayload_host": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.hostPayload_outside": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.oldPayload_host": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.oldPayload_outside": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.newPayload_outside": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.parent_family_lt_private": [], + "SourceInvocation.owner_overlap_data": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.owner_overlap_charts": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.commonNativeCover_new": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.new_common_cover": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.old_common_cover": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceControls.actual_add_event": [ + "propext" + ], + "SourceControls.omitted_add_changes_row": [ + "propext" + ], + "SourceControls.omitted_add_keeps_guards": [ + "propext" + ], + "SourceControls.actual_first_copy": [ + "propext" + ], + "SourceControls.dirty_private_copy_rejected": [], + "SourceControls.dirty_private_copy_would_overwrite": [ + "propext" + ], + "SourceControls.literal_helper_three_survives": [ + "propext", + "Quot.sound" + ], + "SourceControls.literal_helper_three_not_zero": [ + "propext", + "Quot.sound" + ], + "SourceInvocation.oldRaw_data": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.newRaw_data": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.oldRaw_bank": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.oldRaw_host": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.newRaw_host": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.oldRaw_outside": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.newRaw_outside": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.oldResult_framed": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.newResult_framed": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceDataBehavior.first_initial_frame": [ + "propext", + "Quot.sound" + ], + "SourceDataBehavior.second_initial_frame": [ + "propext", + "Quot.sound" + ], + "SourceDataBehavior.first_final_frame": [ + "propext", + "Quot.sound" + ], + "SourceDataBehavior.second_final_frame": [ + "propext", + "Quot.sound" + ], + "SourceDataBehavior.framed_first": [ + "propext", + "Quot.sound" + ], + "SourceDataBehavior.framed_second": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceDataBehavior.framed_data_formula": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceDataBehavior.old_data_formula": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceDataBehavior.new_data_formula": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.newPayload_host": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.oldPayload_data": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.newPayload_data": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.oldPayload_bank": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.shared_host_input": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.shared_data_input": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceRawGuards.raw_clean_of_framed": [ + "Quot.sound" + ], + "SourceRawGuards.raw_clean_run_of_framed": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceRawGuards.native_clean_of_raw": [ + "Quot.sound" + ], + "SourceRawGuards.native_clean_run_of_raw": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceRawGuards.actual_raw_clean": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceRawGuards.initial_fromNative": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceRawGuards.actual_native_clean": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceRawGuards.native_run_refines": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceRawGuards.native_payload_endpoint": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceRawGuards.native_private_restored": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceRawGuards.native_other_preserved": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.native_payload_roundtrip": [ + "Quot.sound" + ], + "SourceInvocation.old_native_realization": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.new_native_realization": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.old_native_clean": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.new_native_clean": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.old_native_temporary_restored": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.new_native_temporary_restored": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.native_shared_host_input": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.native_shared_data_input": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.native_shared_tail_input": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.initialized_native_host_input": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.initialized_native_data_input": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.initialized_native_tail_input": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.oldResult_native": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.newResult_native": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceMoveGeometry.move_projectors": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceMoveGeometry.move_stage2_relative": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceMoveGeometry.move_relative": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceMoveGeometry.copy_stage2_relative": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceMoveGeometry.copy_relative": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceMoveGeometry.erase_relative": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceMoveGeometry.physicalStep_move": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceMoveGeometry.physicalStep_copy": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceMoveGeometry.matrix_run_eq": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceMoveGeometry.actual_matrix_run": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceMoveGeometry.nativeStep_move": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceMoveGeometry.nativeRoute_move": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceMoveGeometry.nativeStep_copy": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.selected_call_completion": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.selected_native_completion": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.selected_data_formula": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.selected_native_realization": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.selected_native_clean": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.selected_matrix_realization": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.selected_original_matrix_realization": [ + "propext", + "Classical.choice", + "Quot.sound" + ], + "SourceInvocation.selected_temporary_restoration": [ + "propext", + "Classical.choice", + "Quot.sound" + ] + }, + "scope": { + "selected_source": "PR442 stage2 replica0 pair0 forward, 19002 literal events", + "framework": "Task A is separately committed and separately replayed.", + "certificate_boundary": "Lean proves statements about embedded literals; JSON extraction is reproduced externally.", + "limits": "No complete cover sweep, later real child schedule, physical cost, all-size compiler, or kappa bound." + } +} diff --git a/research/lean-multi-host-source/replay.py b/research/lean-multi-host-source/replay.py new file mode 100644 index 0000000000..a8d6de14f6 --- /dev/null +++ b/research/lean-multi-host-source/replay.py @@ -0,0 +1,343 @@ +#!/usr/bin/env python3 +"""Build manifested local proofs from fresh sources at Lean trust level zero.""" +import argparse +from datetime import datetime, timezone +import hashlib +import json +import os +from pathlib import Path +import re +import subprocess +import tempfile +import time + +ROOT = Path(__file__).resolve().parent + + +def require(ok, message): + if not ok: + raise RuntimeError(message) + + + +def sha256_file(path): + digest = hashlib.sha256() + with path.open('rb') as stream: + for block in iter(lambda: stream.read(1024 * 1024), b''): + digest.update(block) + return digest.hexdigest() + + +def object_sha256(value): + return hashlib.sha256(json.dumps(value, sort_keys=True, separators=(',', ':')).encode()).hexdigest() + + +def footprint(root, files=None): + """Hash actual bytes, including companion olean/IR/native artifacts, not .hash claims.""" + if files is None: + files = sorted(p for p in root.rglob('*') if p.is_file()) if root.exists() else [] + records = [(str(p.relative_to(root)), p.stat().st_size, sha256_file(p)) for p in files] + return {'sha256': object_sha256(records), 'files': len(records), + 'bytes': sum(row[1] for row in records)} + + +def git_snapshot(root, expected): + revision = subprocess.check_output(['git', 'rev-parse', 'HEAD'], cwd=root, text=True).strip() + require(revision == expected, 'Wrong dependency revision: ' + str(root)) + dirty = subprocess.check_output(['git', 'status', '--porcelain', '--untracked-files=no'], + cwd=root, text=True) + require(not dirty, 'Modified tracked dependency sources: ' + str(root)) + extra = subprocess.check_output(['git', 'ls-files', '--others', '--exclude-standard', '-z'], + cwd=root).decode().split('\0') + require(not any(x.endswith('.lean') for x in extra), + 'Untracked Lean dependency sources: ' + str(root)) + tracked = subprocess.check_output(['git', 'ls-files', '-z'], cwd=root).decode().split('\0') + files = [root / x for x in sorted(tracked) if x and (root / x).is_file()] + return {'commit': revision, 'tracked_sources': footprint(root, files), + 'build_artifacts': footprint(root / '.lake' / 'build'), + 'lake_configuration_artifacts': footprint(root / '.lake', + sorted(x for x in (root / '.lake').glob('*') if x.is_file()))} + + +def external_environment(lean, env, mathlib, manifest, search_paths): + """Current observation, not an attestation of a historical build environment.""" + prefix = Path(subprocess.check_output([str(lean), '--print-prefix'], env=env, + text=True).strip()).resolve(strict=True) + require(lean == prefix / 'bin' / 'lean', 'Compiler is outside its reported toolchain prefix') + snapshot = {'schema': 1, 'toolchain': footprint(prefix), + 'lean_binary_sha256': sha256_file(lean), 'dependencies': {}} + allowed = {prefix / 'lib' / 'lean': 'toolchain/lib/lean'} + if mathlib is not None: + snapshot['dependencies']['Mathlib'] = git_snapshot(mathlib, manifest['mathlib_commit']) + allowed[(mathlib / '.lake/build/lib/lean').resolve()] = 'Mathlib/.lake/build/lib/lean' + deps = json.loads((mathlib / 'lake-manifest.json').read_text()) + for package in deps['packages']: + require(package['type'] == 'git' and not package.get('subDir'), + 'Unsupported dependency layout: ' + package['name']) + directory = (mathlib / deps['packagesDir'] / package['name']).resolve(strict=True) + snapshot['dependencies'][package['name']] = git_snapshot(directory, package['rev']) + allowed[(directory / '.lake/build/lib/lean').resolve()] = package['name'] + '/.lake/build/lib/lean' + require(all(path in allowed for path in search_paths), 'Unexpected library search path') + snapshot['library_search_order'] = [allowed[path] for path in search_paths] + return {'sha256': object_sha256(snapshot), 'components': snapshot, + 'meaning': 'Observed current bytes and clean pinned Git sources; not historical provenance.'} + + +def module_artifacts(build, name): + suffixes = ['.olean', '.olean.private', '.olean.server', '.ir', '.ir.sig', '.so'] + return {suffix: sha256_file(build / (name + suffix)) for suffix in suffixes + if (build / (name + suffix)).is_file()} + + +def validate_build_artifact_inventory(build, modules): + """The first LEAN_PATH entry must not shadow external library modules.""" + suffixes = ('.olean', '.olean.private', '.olean.server', '.ir', '.ir.sig', '.so') + allowed = {name + suffix for name in [*modules, 'ClosureAudit'] for suffix in suffixes} + for path in build.rglob('*'): + require(not (path.is_symlink() and path.is_dir()), + 'Symlinked directory in resumed build: ' + str(path.relative_to(build))) + if path.is_file() and path.name.endswith(suffixes): + require(path.relative_to(build).as_posix() in allowed, + 'Unmanifested library artifact in resumed build: ' + str(path.relative_to(build))) + + +def write_json_atomic(path, value): + staging = path.with_name(path.name + '.tmp') + staging.write_text(json.dumps(value, indent=2) + '\n') + staging.replace(path) + + +def legacy_receipt(path, commit, manifest, version): + """Anchor legacy progress to the committed successful receipt, not mutable progress alone.""" + raw = path.read_bytes() + repository = Path(subprocess.check_output(['git', 'rev-parse', '--show-toplevel'], + cwd=ROOT, text=True).strip()) + revision = subprocess.check_output(['git', 'rev-parse', commit + '^{commit}'], + cwd=repository, text=True).strip() + relative = (ROOT / 'replay-result.json').relative_to(repository).as_posix() + committed = subprocess.check_output(['git', 'show', revision + ':' + relative], cwd=repository) + require(raw == committed, 'Legacy receipt differs from the specified committed replay-result.json') + receipt = json.loads(raw) + require(receipt['status'] == 'PASS' and receipt['trust_level'] == 0 and receipt['lean'] == version, + 'Legacy receipt is not a matching successful trust-zero replay') + require(receipt['lean_commit'] == manifest['lean_commit'] and + receipt['mathlib_commit'] == manifest['mathlib_commit'], 'Legacy source pins changed') + positions = {name: i for i, name in enumerate(receipt['modules'])} + for name, record in receipt['modules'].items(): + require(all(dep in positions and positions[dep] < positions[name] + for dep in record['dependency_hashes']), 'Unordered legacy dependencies: ' + name) + require(all(value == receipt['modules'][dep]['olean_sha256'] + for dep, value in record['dependency_hashes'].items()), + 'Inconsistent legacy dependency receipt: ' + name) + return receipt, {'sha256': hashlib.sha256(raw).hexdigest(), 'git_commit': revision, + 'repository_path': relative} + + + +def legacy_reuse_record(name, cached, original, anchor, environment_sha, allowed): + require(allowed, + 'Legacy cache has no historical external fingerprint: ' + name + + '; use the explicit receipt-anchored legacy mode or a fresh build') + fields = ['sha256', 'dependency_hashes', 'olean_sha256', 'seconds', 'output'] + require(all(key in original and cached.get(key) == original[key] for key in fields), + 'Legacy progress differs from committed successful receipt: ' + name) + return dict(cached, historical_external_environment='unrecorded', + last_observed_environment_sha256=environment_sha, legacy_receipt=anchor) + +def cache_matches(cached, source, expected_sha, source_copy, artifacts, dependencies, + dependency_artifacts, dependency_sources, environment_sha): + if not (cached and cached.get('sha256') == expected_sha and + source_copy.is_file() and source_copy.read_bytes() == source and + cached.get('dependency_hashes') == dependencies and + artifacts.get('.olean') == cached.get('olean_sha256')): + return False + if cached.get('environment_sha256'): + return (cached['environment_sha256'] == environment_sha and + cached.get('artifacts') == artifacts and + cached.get('dependency_artifacts') == dependency_artifacts and + cached.get('dependency_source_sha256') == dependency_sources) + # Old receipts bound only a single .olean, so extra unrecorded companion parts cannot be reused. + return (set(artifacts) == {'.olean'} and + cached.get('last_observed_environment_sha256', environment_sha) == environment_sha) + + +def main(): + p = argparse.ArgumentParser(description=__doc__) + p.add_argument('--lean', required=True, type=Path) + p.add_argument('--mathlib', type=Path, help='pinned Mathlib checkout with required modules built') + p.add_argument('--receipt', type=Path) + p.add_argument('--build-dir', type=Path, help='new directory for retained sources and logs') + p.add_argument('--module-timeout', type=int, default=7200, + help='seconds allowed per module (large kernel certificates can take tens of minutes)') + p.add_argument('--resume', action='store_true', + help='resume this script\'s retained build, verifying source, dependency, and artifact hashes') + p.add_argument('--allow-legacy-resume', action='store_true', + help='explicitly reuse receipt-anchored old artifacts with unrecorded historical external environment') + p.add_argument('--legacy-receipt', type=Path, + help='successful old replay-result.json matching the committed receipt') + p.add_argument('--legacy-commit', default='HEAD', + help='Git commit containing the old replay-result.json (default HEAD)') + a = p.parse_args() + require(not a.allow_legacy_resume or (a.resume and a.legacy_receipt), + '--allow-legacy-resume requires --resume and --legacy-receipt') + lean = a.lean.resolve(strict=True) + env = dict(os.environ) + env.pop('LEAN_PATH', None) + env.pop('LEAN_SRC_PATH', None) + env.pop('LEAN_SYSROOT', None) + env['PATH'] = str(lean.parent) + os.pathsep + env.get('PATH', '') + version = subprocess.check_output([str(lean), '--version'], env=env, text=True).strip() + require(version.startswith('Lean (version 4.33.0,'), 'Lean 4.33.0 required') + manifest_bytes = (ROOT / 'proof-manifest.json').read_bytes() + manifest = json.loads(manifest_bytes) + revision = subprocess.check_output([str(lean), '--githash'], env=env, text=True).strip() + require(revision == manifest['lean_commit'], 'Wrong Lean revision') + mathlib_path = '' + mathlib = None + search_paths = [] + if any(i.startswith('Mathlib.') for m in manifest['modules'] for i in m['imports']): + require(a.mathlib is not None, '--mathlib required') + mathlib = a.mathlib.resolve(strict=True) + revision = subprocess.check_output(['git', 'rev-parse', 'HEAD'], cwd=mathlib, + text=True).strip() + require(revision == manifest['mathlib_commit'], 'Wrong Mathlib revision') + require((mathlib / 'lake-manifest.json').read_bytes() == + (ROOT / 'mathlib-lake-manifest.json').read_bytes(), 'Wrong Mathlib dependencies') + path = subprocess.check_output([str(lean.parent / 'lake'), 'env', 'printenv', 'LEAN_PATH'], + cwd=mathlib, env=env, text=True).strip() + search_paths = [(mathlib / x).resolve() for x in path.split(os.pathsep) if x] + mathlib_path = os.pathsep.join(map(str, search_paths)) + external = external_environment(lean, env, mathlib, manifest, search_paths) + old_receipt, old_anchor = (None, None) + if a.allow_legacy_resume: + old_receipt, old_anchor = legacy_receipt(a.legacy_receipt, a.legacy_commit, manifest, version) + tmp = None + if a.build_dir: + build = a.build_dir.resolve() + if not a.resume: + build.mkdir(parents=True, exist_ok=False) + else: + require(not a.resume, '--resume requires --build-dir') + tmp = tempfile.TemporaryDirectory(prefix='multi-host-source-') + build = Path(tmp.name) + progress_path = build / 'build-progress.json' + identity = {'lean': version, 'mathlib_commit': manifest.get('mathlib_commit')} + progress = {'identity': identity, 'modules': {}} + if a.resume: + validate_build_artifact_inventory(build, [m['module'] for m in manifest['modules']]) + progress = json.loads(progress_path.read_text()) + require(progress['identity'] == identity, 'Resumed toolchain changed') + reports, results = {}, {} + fresh, reused, legacy = [], [], [] + write_json_atomic(build / 'external-environment.json', external) + try: + env['LEAN_PATH'] = str(build) + (os.pathsep + mathlib_path if mathlib_path else '') + prior = [] + for m in manifest['modules']: + name = m['module'] + source = (ROOT / m['source']).read_bytes() + require(hashlib.sha256(source).hexdigest() == m['sha256'], 'Source mismatch: ' + name) + code = re.sub(r'--[^\n]*', '', re.sub(r'/\-[\s\S]*?\-/', '', source.decode())) + require(not re.search(r'\b(sorry|admit|native_decide|unsafe)\b', code), + 'Forbidden proof escape: ' + name) + require(not re.search(r'^\s*(axiom|opaque)\s', code, re.M), 'Project axiom: ' + name) + imports = re.findall(r'^import (\S+)$', code, re.M) + require(imports == m['imports'], 'Import mismatch: ' + name) + require(all(x == 'Std' or x in prior or x.startswith('Mathlib.') for x in imports), + 'Unmanifested dependency: ' + name) + dependency_hashes = {x: hashlib.sha256((build / (x + '.olean')).read_bytes()).hexdigest() + for x in imports if x in prior} + dependency_artifacts = {x: module_artifacts(build, x) for x in imports if x in prior} + dependency_sources = {x: results[x]['sha256'] for x in imports if x in prior} + cached = progress['modules'].get(name) + artifact = build / (name + '.olean') + artifacts = module_artifacts(build, name) + is_match = a.resume and cache_matches(cached, source, m['sha256'], + build / (name + '.lean'), artifacts, dependency_hashes, dependency_artifacts, + dependency_sources, external['sha256']) + if is_match and not cached.get('environment_sha256'): + original = old_receipt['modules'].get(name, {}) if old_receipt else {} + cached = legacy_reuse_record(name, cached, original, old_anchor, + external['sha256'], a.allow_legacy_resume) + legacy.append(name) + if is_match: + results[name] = cached + progress['modules'][name] = cached + write_json_atomic(progress_path, progress) + reused.append(name) + prior.append(name) + label = 'legacy reuse; historical external environment unrecorded' if name in legacy else 'verified cached build' + print(name + ': PASS (' + label + ')', flush=True) + continue + (build / (name + '.lean')).write_bytes(source) + start = time.monotonic() + result = subprocess.run([str(lean), '-t', '0', '-o', name + '.olean', name + '.lean'], + cwd=build, env=env, text=True, stdout=subprocess.PIPE, + stderr=subprocess.STDOUT, timeout=a.module_timeout) + (build / (name + '.log')).write_text(result.stdout) + require(result.returncode == 0 and 'sorry' not in result.stdout, + name + '\n' + result.stdout) + fresh.append(name) + results[name] = {'environment_sha256': external['sha256'], + 'historical_external_environment': 'fingerprinted_at_compile', + 'artifacts': module_artifacts(build, name), + 'dependency_artifacts': dependency_artifacts, + 'dependency_source_sha256': dependency_sources, + 'seconds': round(time.monotonic() - start, 3), + 'sha256': m['sha256'], 'output': result.stdout, + 'dependency_hashes': dependency_hashes, + 'olean_sha256': hashlib.sha256(artifact.read_bytes()).hexdigest()} + progress['modules'][name] = results[name] + write_json_atomic(progress_path, progress) + prior.append(name) + print(name + ': PASS', flush=True) + audit = '\n'.join('import ' + m['module'] for m in manifest['modules']) + '\n' + audit += '\n'.join('#print axioms ' + name for name in manifest['audit_declarations']) + '\n' + (build / 'ClosureAudit.lean').write_text(audit) + result = subprocess.run([str(lean), '-t', '0', 'ClosureAudit.lean'], cwd=build, + env=env, text=True, stdout=subprocess.PIPE, + stderr=subprocess.STDOUT, timeout=300) + require(result.returncode == 0, result.stdout) + (build / 'ClosureAudit.log').write_text(result.stdout) + for line in result.stdout.splitlines(): + match = re.fullmatch(r"'([^']+)' does not depend on any axioms", line) + if match: + name, axioms = match[1], [] + else: + match = re.fullmatch(r"'([^']+)' depends on axioms: \[([^]]*)\]", line) + require(match is not None, 'Unexpected audit output: ' + line) + name, axioms = match[1], match[2].split(', ') + require(name not in reports, 'Duplicate audit declaration') + require(set(axioms) <= {'propext', 'Quot.sound', 'Classical.choice'}, + 'Unexpected transitive axioms: ' + line) + reports[name] = axioms + require(list(reports) == manifest['audit_declarations'], 'Axiom inventory mismatch') + external_after = external_environment(lean, env, mathlib, manifest, search_paths) + require(external_after['sha256'] == external['sha256'], 'External environment changed during replay') + receipt = {'status': 'PASS', 'lean': version, 'trust_level': 0, + 'lean_commit': manifest['lean_commit'], + 'completed_utc': datetime.now(timezone.utc).isoformat(), + 'manifest_sha256': hashlib.sha256(manifest_bytes).hexdigest(), + 'mathlib_commit': manifest.get('mathlib_commit'), + 'external_environment': external, + 'replay_mode': 'resumed' if a.resume else 'fresh', + 'fresh_modules_compiled': len(fresh), 'reused_modules': len(reused), + 'legacy_reused_modules': len(legacy), + 'fresh_module_names': fresh, 'reused_module_names': reused, + 'legacy_module_names': legacy, + 'historical_external_environment': 'unrecorded_for_legacy_modules' if legacy else 'fingerprinted_at_compile', + 'closure_audit': 'rerun now with lean -t 0; axiom inventory, not leanchecker --fresh', + 'modules': results, 'axioms': reports, + 'scope': manifest['scope']} + if a.receipt: + a.receipt.write_text(json.dumps(receipt, indent=2) + '\n') + print(json.dumps({'status': 'PASS', 'fresh_modules': len(fresh), + 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assertion): + assert assertion, label + checks.append(label) + + def rejects(label, action): + try: + action() + except RuntimeError: + checks.append(label) + else: + raise AssertionError(label) + + with tempfile.TemporaryDirectory(prefix='reuse-policy-fixture-') as directory: + build = Path(directory) + source = b'def fixture := True\n' + source_copy = build / 'Fixture.lean' + source_copy.write_bytes(source) + artifact = build / 'Fixture.olean' + artifact.write_bytes(b'cache-policy fixture, not a Lean artifact') + sha = hashlib.sha256(source).hexdigest() + artifact_sha = replay.sha256_file(artifact) + deps = {'Earlier': 'a' * 64} + dep_artifacts = {'Earlier': {'.olean': 'a' * 64}} + dep_sources = {'Earlier': 'b' * 64} + old = {'sha256': sha, 'dependency_hashes': deps, + 'olean_sha256': artifact_sha, 'seconds': 1.0, 'output': ''} + args = dict(source=source, expected_sha=sha, source_copy=source_copy, + artifacts={'.olean': artifact_sha}, dependencies=deps, + dependency_artifacts=dep_artifacts, + dependency_sources=dep_sources, environment_sha='current') + anchor = {'fixture': True} + check('unchanged legacy cache matches before policy gate', replay.cache_matches(old, **args)) + rejects('legacy reuse without explicit flag rejected', + lambda: replay.legacy_reuse_record('Fixture', old, old, anchor, 'current', False)) + reused = replay.legacy_reuse_record('Fixture', old, old, anchor, 'current', True) + check('explicit legacy keeps historical environment unrecorded', + reused['historical_external_environment'] == 'unrecorded' and + 'environment_sha256' not in reused) + rejects('mutable progress cannot override committed artifact receipt', + lambda: replay.legacy_reuse_record('Fixture', dict(old, olean_sha256='altered'), + old, anchor, 'current', True)) + source_copy.write_bytes(source + b'-- changed\n') + check('changed copied source rejected', not replay.cache_matches(old, **args)) + source_copy.write_bytes(source) + artifact.write_bytes(b'altered fixture') + changed = dict(args, artifacts=replay.module_artifacts(build, 'Fixture')) + check('changed compiled bytes rejected', not replay.cache_matches(old, **changed)) + check('changed dependency hash rejected', not replay.cache_matches( + old, **dict(args, dependencies={'Earlier': 'changed'}))) + check('unrecorded legacy companion rejected', not replay.cache_matches( + old, **dict(args, artifacts={'.olean': artifact_sha, '.olean.private': 'extra'}))) + fresh = dict(old, environment_sha256='current', artifacts=args['artifacts'], + dependency_artifacts=dep_artifacts, dependency_source_sha256=dep_sources) + check('matching environment-bound cache accepted', replay.cache_matches(fresh, **args)) + check('changed external environment invalidates new cache', not replay.cache_matches( + fresh, **dict(args, environment_sha='changed'))) + check('changed dependency companion invalidates new cache', not replay.cache_matches( + fresh, **dict(args, dependency_artifacts={'Earlier': {'.olean': 'a' * 64, '.ir': 'new'}}))) + check('changed dependency source invalidates new cache', not replay.cache_matches( + fresh, **dict(args, dependency_sources={'Earlier': 'changed'}))) + repeated = replay.legacy_reuse_record('Fixture', reused, old, anchor, 'current', True) + check('subsequent legacy resume stays historically unrecorded', + repeated['historical_external_environment'] == 'unrecorded' and + 'environment_sha256' not in repeated) + check('previously observed changed environment invalidates legacy cache', + not replay.cache_matches(reused, **dict(args, environment_sha='changed'))) + before = replay.footprint(build) + artifact.write_bytes(b'another fixture') + check('footprint hashes actual bytes', replay.footprint(build) != before) + replay.validate_build_artifact_inventory(build, ['Fixture']) + checks.append('manifested artifact inventory accepted') + for name in ['Std.olean', 'Mathlib/Algebra/Group/Defs.olean', + 'Extra.olean.private', 'Extra.ir.sig', 'libInjected.so']: + extra = build / name + extra.parent.mkdir(parents=True, exist_ok=True) + extra.write_bytes(b'fixture') + rejects('unmanifested shadow artifact rejected: ' + name, + lambda: replay.validate_build_artifact_inventory(build, ['Fixture'])) + extra.unlink() + (build / 'Shadow').symlink_to(build.parent, target_is_directory=True) + rejects('symlinked search subtree rejected', + lambda: replay.validate_build_artifact_inventory(build, ['Fixture'])) + print(json.dumps({'status': 'PASS', 'checks': checks, 'count': len(checks), + 'scope': 'Policy fixtures only; no Lean compilation.'}, indent=2)) + + +if __name__ == '__main__': + main() diff --git a/research/lean-multi-host-source/review-receipts/external-build/environment.json b/research/lean-multi-host-source/review-receipts/external-build/environment.json new file mode 100644 index 0000000000..8a850659e8 --- /dev/null +++ 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+[{"url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/issues/comments/6113791847","html_url":"https://github.com/CrocSwap/integer-mult-bounds/pull/448#issuecomment-6113791847","issue_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/issues/448","id":6113791847,"node_id":"IC_kwDOU-508s8AAAABbGkPZw","user":{"login":"hipotures","id":584360,"node_id":"MDQ6VXNlcjU4NDM2MA==","avatar_url":"https://avatars.githubusercontent.com/u/584360?v=4","gravatar_id":"","url":"https://api.github.com/users/hipotures","html_url":"https://github.com/hipotures","followers_url":"https://api.github.com/users/hipotures/followers","following_url":"https://api.github.com/users/hipotures/following{/other_user}","gists_url":"https://api.github.com/users/hipotures/gists{/gist_id}","starred_url":"https://api.github.com/users/hipotures/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/hipotures/subscriptions","organizations_url":"https://api.github.com/users/hipotures/orgs","repos_url":"https://api.github.com/users/hipotures/repos","events_url":"https://api.github.com/users/hipotures/events{/privacy}","received_events_url":"https://api.github.com/users/hipotures/received_events","type":"User","user_view_type":"public","site_admin":false},"created_at":"2026-10-11T21:10:32Z","updated_at":"2026-10-11T21:10:32Z","body":"Independent replay and a note on the split-residual interface (from an outside batch; no claim of our own)\n\n**Replay.** At the pinned head `359022bc`, `research/cross-copy-hosting/verify.py` passes from a fresh detached worktree with a fresh output directory and reproduces κ = 0.001330733967 exactly. The same holds for #480 at `668c7dd0`, which reproduces 0.001372550159. This is part of a batch of 39 pinned frontier replays; 34 of them pass.\n\n**Ledger of the produced templates.** We wrote a checker that shares no code with the package. It reads `bit/` and `complex/GLOBAL-TEMPLATE.json.gz` and finds the following.\n- **Coordinate accounting is consistent.** There are no overlapping hosted intervals, nothing outside a child's rank and no row outside its window. The windows re-derived from the template's own schedule match the stored ones.\n- **The split is used heavily.** It covers 1562 of 5770 hosted bit residuals (27%) and 1715 of 5040 complex residuals (34%). In #480's bit template it is 14612 of 62920 (23%), and 1807 of 8140 in #450 and #469. None of the 61 whole-hosting templates we checked (#434 … #493) contains a split.\n- **The owner table names one family per split helper.** Each split helper has one entry in `calls[].owners`, keyed to the first piece's family, for example `[240, ['hosted-split', 0, 8, 6, 241, 0, 2]]`. The second family appears only inside the descriptor. #442's audit enforces \"each helper has exactly one owner\".\n\n**Where we think the review point is.** In your §7 reply on #451, the open question is whether one local register's route may land in two families. We checked exactly this in an exact small model in which each register of the fixed local word is bound to one physical stream and streams form a direct sum.\n- **The model.** The word uses its helper as genuinely dirty scratch (`x += A h; h ← F_R h; x −= A F_R⁻¹ h; x ← T x`). The coordinate factors are the bit `D_S` and the complex `C_S`, the same as in the #451 note and in `toy_two_family_check.py`.\n- **Whole hosting (#442) works.** It equals the original program in all 13 cases.\n- **A single-register split does not.** We enumerated every single-register binding and coordinate placement of a split residual: 152 programs over 18 cases (bit q = 3, 5; complex q = 2; m ≤ 8). None of them equals the original program.\n- **Two registers do.** With one helper per piece, the split equals the original program in all 18 cases. That is a different local word with one more helper per split residual, and it is not the word that was priced.\n\n`toy_two_family_check.py` composes `D_a^A ⊗ D_b^B` with the remainder children. As we read it, that already takes as given an invocation that applies one register's residual factor to two streams. Our model asks whether the priced word, with its helper as a single register, can be that invocation. It cannot when a register lives in one stream. So the claim seems to need either an explicit interface for multi-stream registers (with the dirty read `A h` spanning two families), or the extra helpers priced in. We have not computed κ with the extra helpers.\n\nCode and data:\n- [report](https://github.com/hipotures/rad/blob/c6d971dabdde94e1c5ec1521c44ca63fd41debf9/research/integer-multiplication-bounds/campaigns/frontier-batch-20261011/report.md)\n- [stream model](https://github.com/hipotures/rad/blob/c6d971dabdde94e1c5ec1521c44ca63fd41debf9/research/integer-multiplication-bounds/campaigns/frontier-batch-20261011/code/job1_stream_model.py), about 10 s\n- [template ledger](https://github.com/hipotures/rad/blob/c6d971dabdde94e1c5ec1521c44ca63fd41debf9/research/integer-multiplication-bounds/campaigns/frontier-batch-20261011/code/job2_hosting_ledger.py)\n\nThis is our model of the declared execution, not a proof that no other realisation exists. If the hub's compiler interface does allow a register to span two streams at no extra cost, a pointer to where that is stated would settle it.\n\n---\n*This analysis was carried out by Claude Opus 5.5 (Anthropic) under human supervision.*\n","author_association":"CONTRIBUTOR","reactions":{"url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/issues/comments/6113791847/reactions","total_count":0,"+1":0,"-1":0,"laugh":0,"hooray":0,"confused":0,"heart":0,"rocket":0,"eyes":0},"performed_via_github_app":null,"minimized":null},{"url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/issues/comments/6113842081","html_url":"https://github.com/CrocSwap/integer-mult-bounds/pull/448#issuecomment-6113842081","issue_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/issues/448","id":6113842081,"node_id":"IC_kwDOU-508s8AAAABbGnToQ","user":{"login":"higherbeing","id":7227029,"node_id":"MDQ6VXNlcjcyMjcwMjk=","avatar_url":"https://avatars.githubusercontent.com/u/7227029?v=4","gravatar_id":"","url":"https://api.github.com/users/higherbeing","html_url":"https://github.com/higherbeing","followers_url":"https://api.github.com/users/higherbeing/followers","following_url":"https://api.github.com/users/higherbeing/following{/other_user}","gists_url":"https://api.github.com/users/higherbeing/gists{/gist_id}","starred_url":"https://api.github.com/users/higherbeing/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/higherbeing/subscriptions","organizations_url":"https://api.github.com/users/higherbeing/orgs","repos_url":"https://api.github.com/users/higherbeing/repos","events_url":"https://api.github.com/users/higherbeing/events{/privacy}","received_events_url":"https://api.github.com/users/higherbeing/received_events","type":"User","user_view_type":"public","site_admin":false},"created_at":"2026-10-11T21:15:52Z","updated_at":"2026-10-11T21:15:52Z","body":"Thank you for the replay and for the stream model; this is the right level to settle it at, and I think your reading is the faithful one.\n\nWhere #448 §2 and §7 go wrong, stated plainly: the two-family argument takes the invocation's action on a split residual to be `D_a^A ⊗ D_b^B` *as given*. That presupposes that one local register can be read and written across two streams, which is exactly what your single-register enumeration tests and refutes (the dirty read `x += A h` has to see both pieces). The hub never states a multi-stream register interface; every owner table binds a register to one family, and I cannot point to a place where the compiler admits otherwise. So the realisation that does exist is your two-register control, and it is a different local word.\n\nPricing that word kills the gain. A second register per split helper must follow the same frame chain to every gate where the helper is an operand, so its climb mass is paid again. On #448's bit template your ledger counts 1,562 split residuals per replica, about 174 per invocation; at the word's average helper cost (≈29 Φ-units per helper per invocation at m = 64) that is roughly +5,000 per invocation, against about 2,100 per invocation saved by removing the remainder children. The complex side is similar. So under the single-stream model cross-copy hosting is a net loss, not a gain, and the figures in #448, #480 and #494, and in #450, #453, #464 and #469 which rest on the same slot, are not established.\n\nI am retitling #448, #480 and #494 as under review on this point and leaving them as drafts with the packages intact, so the record of what was computed stays reproducible. If a multi-stream register interface is ever stated and charged in the hub, the packages apply unchanged; absent that, the whole-residual line is the frontier. Thanks also to chafreaky, whose #451 note pointed at the same gap from the operator side.\n","author_association":"NONE","reactions":{"url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/issues/comments/6113842081/reactions","total_count":0,"+1":0,"-1":0,"laugh":0,"hooray":0,"confused":0,"heart":0,"rocket":0,"eyes":0},"performed_via_github_app":null,"minimized":null}] \ No newline at end of file diff --git a/research/lean-multi-host-source/review-receipts/external-overlap/448-review-comments.json b/research/lean-multi-host-source/review-receipts/external-overlap/448-review-comments.json new file mode 100644 index 0000000000..0637a088a0 --- /dev/null +++ b/research/lean-multi-host-source/review-receipts/external-overlap/448-review-comments.json @@ -0,0 +1 @@ +[] \ No newline at end of file diff --git a/research/lean-multi-host-source/review-receipts/external-overlap/448-reviews.json b/research/lean-multi-host-source/review-receipts/external-overlap/448-reviews.json new file mode 100644 index 0000000000..0637a088a0 --- /dev/null +++ b/research/lean-multi-host-source/review-receipts/external-overlap/448-reviews.json @@ -0,0 +1 @@ +[] \ No newline at end of file diff --git a/research/lean-multi-host-source/review-receipts/external-overlap/Jacob.json b/research/lean-multi-host-source/review-receipts/external-overlap/Jacob.json new file mode 100644 index 0000000000..f8ad5541b9 --- /dev/null +++ b/research/lean-multi-host-source/review-receipts/external-overlap/Jacob.json @@ -0,0 +1 @@ +{"sha":"9c94857bbaee886f8649edee0bc2d3c738f9555e","node_id":"C_kwDOVCd5qNoAKDljOTQ4NTdiYmFlZTg4NmY4NjQ5ZWRlZTBiYzJkM2M3MzhmOTU1NWU","commit":{"author":{"name":"Jacob Sussman","email":"95983206+jacobalansussman@users.noreply.github.com","date":"2026-10-11T00:24:08Z"},"committer":{"name":"Jacob Sussman","email":"95983206+jacobalansussman@users.noreply.github.com","date":"2026-10-11T00:24:08Z"},"message":"Fourth result: the last comparator verdicts on Linux\n\nChanges README.md, VERIFY.md, RELATED-WORK.md and notes/e8-results.json:\n\n- The comparator accepted the third result (comparator/UniformFourier.json)\n in a tree compiled from nothing, at the third attempt.\n- It accepted the two configurations of pull request #2, by Chafik Boukhalfa,\n for which he reports his own runs with the real sandbox.\n- Each of these runs had a stand-in for the comparator's sandbox; no run\n here used the real one.\n- Wording about the Linux runs made exact after an audit of the logs: the\n memory convention, and \"Replayed lines\" in place of \"modules replayed\".\n\nNo Lean file, tool or certificate is changed. 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-91,9 +91,9 @@ f664fde5fcfecfad564c3d42daa8011e3e5f10a745510b265d626e04a5470a97 OAI/Computabil\n 43fe1a7d39fefc06a20809e3179e293229d61c752a079cff4bbc6772edae698a OAI/Computability/FourierTransform/WorkingPreparation.lean\n cf9342af428783f0ff0eb72ccb497e1ea4b8e2cb4e5ecab3774c00d173a4b473 OAI/Computability/FourierTransform/WorkingTransform.lean\n 69c01258184100e5aef1cc0e1463e62df7f83eff03fd6142d68a451856fb7fab ORIGIN.md\n-d114f440d0031cec8285d591885477ee970813373a93ae4d6aa5aae79ed5c717 README.md\n-d0de9dee734d50b97d9ab1b5d8c098836bc8c8c0d37cbd7c59444140bb53def3 RELATED-WORK.md\n-28c6ad423f48ef9f62cbf0c65aa682a13b44e642697f51783a48426204a5f278 VERIFY.md\n+2029b33bbad4879630097164322b0ac3d4ea10db15f7aa93d75b5a16bb617483 README.md\n+e9e6eab12d40f6d82402a6c74c9814dd27c9e796aa2c1948c69ed09fba83d8f5 RELATED-WORK.md\n+a7a14de579569f56a18cf4dd07a4738e74d7e9eb8700b5c63d96253cb93b22be VERIFY.md\n ce638be547cac9eabc1eb6285b1a5b32b06024ef088c331dc2f585fdb7cdf006 WHTCheck/Solution.lean\n c49dfe44a9f096c2173f17b46c38d4f1d335a0c5a36b45093e6a86755919860b Work/Block/Address.lean\n 95b246e3b7be76957c7f4bf121309c370068a4ce43ffe11f2b8736334be6334e Work/Block/Batches.lean\n@@ -395,7 +395,7 @@ c802cbb96d8fa898e02c7fda6c91a5b48394fc67cd988f8ed417a65e53556123 comparator/Uni\n 3a7cabde26b0c210cb99f8ad8d523ff7969aea6bc949b6e009a20963802161fa lake-manifest.json\n 8927b3ee27366af0a026fbaefbc0c5d87fcbfc9138a68ab0938bf71e6cc9f8b5 lakefile.lean\n d5edba4e4b8faad9c1baeadb265716d20d03be4d1a2647dc5e35b0c0325bea7b lean-toolchain\n-0a11432484aecb3a9fbd43c137315d72746560c9b40ec4de694eb961b82f2e40 notes/e8-results.json\n+2ddd1bca7abb61ff98d9c3e5033d53c10af29053714ea04147115100464924bf notes/e8-results.json\n af7edbb4745eeafc14c3305e42ac08ec6e4a8ccba68f29267ff3a29d417a8d30 notes/for-network-coding-readers.md\n f3cfe8288367e0c3ee14bb737677a84f82acc1ea6a268dff751ff7eb815aac69 notes/how-the-e8-unit-was-found.md\n 6e8955b86adb6c878dbd1c57a6f7a9f3e9479380c64f51c9a596e76a843271f4 notes/network-coding/README.md"},{"sha":"1ebcd0462239a3107a63a031f0136c5b7ca574f4","filename":"README.md","status":"modified","additions":58,"deletions":18,"changes":76,"blob_url":"https://github.com/jacobalansussman/wht-power-saving-lean/blob/9c94857bbaee886f8649edee0bc2d3c738f9555e/README.md","raw_url":"https://github.com/jacobalansussman/wht-power-saving-lean/raw/9c94857bbaee886f8649edee0bc2d3c738f9555e/README.md","contents_url":"https://api.github.com/repos/jacobalansussman/wht-power-saving-lean/contents/README.md?ref=9c94857bbaee886f8649edee0bc2d3c738f9555e","patch":"@@ -119,9 +119,11 @@ is what that rests on.\n five-stage layout of this repository. He reports the Lean build and the comparator runs.\n - On 10 October 2026 the agents built his pull request on a Linux machine. All 54 Lean modules that it adds\n compiled. His three theorems depend only on the three standard axioms. `tools/Compare.lean` printed\n- `RESULT: PASS` for his Walsh-Hadamard statement and for his Fourier statements. The agents did not run\n- the official comparator on his files; he reports those runs himself. On my Mac the build could not\n- finish, because two of his modules need about 13 GB of memory each. Section 9 has the details.\n+ `RESULT: PASS` for his Walsh-Hadamard statement and for his Fourier statements. After the build, the\n+ agents ran the official comparator on the two configurations for which he reports runs, with a stand-in\n+ for its sandbox. It accepted both. He reports his own comparator runs, made with the real sandbox. On my\n+ Mac the build could not finish, because two of his modules need about 13 GB of memory each. Section 9 has\n+ the details.\n - shea256's repository now gives that same figure, where it had 6.7e-4 on 9 October. It reports its own\n rebuild of that proof and says that it \"does not claim a new exponent of our own\". That rebuild is\n reported by its author. It was not repeated here.\n@@ -443,11 +445,13 @@ and a comparator run on Linux. With the unchanged generators I reproduced his 41\n byte, and my checker and `gxdry.py` accept his certificate at 7547361. On 10 October 2026 the agents built\n his pull request on a Linux machine. All 54 Lean modules that it adds compiled. His three theorems depend\n only on the three standard axioms. `tools/Compare.lean` printed `RESULT: PASS` for his Walsh-Hadamard\n-statement and for his Fourier statements. The agents did not run the official comparator on his files; he\n-reports those runs himself. On my Mac the build could not finish, because two of his modules need about\n-13 GB of memory each. So in his pull request 7.547361e-4 is a Lean theorem, and it is his result. Section 9\n-has the details of the build. The pull request is not merged: I would rather this repository make that\n-circuit with its own scripts, which `tools/rebuild/` now does, than carry generated files.\n+statement and for his Fourier statements. After the build, the agents ran the official comparator on the\n+two configurations for which he reports runs, with a stand-in for its sandbox. It accepted both, each with\n+`Your solution is okay!` (74 and 73 minutes; 14.4 and 14.5 GB). He reports his own comparator runs, made\n+with the real sandbox. On my Mac the build could not finish, because two of his modules need about 13 GB of\n+memory each. So in his pull request 7.547361e-4 is a Lean theorem, and it is his result. Section 9 has the\n+details of the build and of those runs. The pull request is not merged: I would rather this repository make\n+that circuit with its own scripts, which `tools/rebuild/` now does, than carry generated files.\n \n **What is mine:** the Lean proof of the general frame lemma for this RAM model, the generalised engine, the\n extended certificate checker (section 5), the bridged five-stage layout in which their circuit is placed\n@@ -808,6 +812,8 @@ times and memory.\n 150 s; 15.7 and 16.0 GB); the comparator printed `Your solution is okay!` for both configurations (406 s\n and 432 s). The stand-in there is built on Linux namespaces, and the comparator replayed modules that had\n been compiled before the run. The machine was shared with other jobs, so its times are upper bounds.\n+ Memory on that machine, here and in the next point, is the kbytes figure that GNU `time` printed, divided\n+ by a million. A kbyte there is 1024 bytes, so in units of 10^9 bytes each figure is 2.4 % higher.\n - **The third revision, built from nothing on Linux.** On 10 October 2026 the whole published third revision\n was also built from nothing on that machine. It was cloned from GitHub, and all 342 Lean modules of the\n repository were compiled from source with the commands of VERIFY.md (94 minutes; largest process 10.5 GB).\n@@ -823,10 +829,14 @@ times and memory.\n - third result, `comparator/UniformFourier.json`: 108 minutes, 11.4 GB.\n \n The runs shared the machine, so the times are upper bounds. Two negative controls, one on the statement of\n- the second result and one on the Fourier statement of the third, were refused with exit code 1. One run\n- was still going when this text was written: the comparator for the third result in a tree where nothing\n- had been compiled before. It is the third attempt in that tree, and each attempt continued the build of\n- the one before. It has no verdict here.\n+ the second result and one on the Fourier statement of the third, were refused with exit code 1.\n+\n+ The agents also ran the comparator for the third result in a tree where none of the repository's modules\n+ had been compiled before. Mathlib's compiled files came from its cache. The comparator accepted the\n+ result, with `Your solution is okay!` and exit code 0. That was the third attempt in that tree, and each\n+ attempt continued the build of the one before. In the three attempts together, 314 modules of the\n+ repository were compiled inside the stand-in. The last attempt took 127 minutes and 11.4 GB. This verdict\n+ came after the fourth revision was published (section 9).\n - **No real sandbox on that Linux machine.** The comparator's sandbox needs Landlock, a feature of the Linux\n kernel. The Linux kernel of that machine has no Landlock, so the comparator's real sandbox could not run\n there either (limits, below).\n@@ -1082,7 +1092,10 @@ in section 9, and nothing else in it has changed).\n these modules.\n - In every comparator run the modules of the proof had been compiled beforehand, outside the sandbox, so the\n comparator replayed existing build products. Mathlib was not rebuilt from source, and the Lean toolchain and\n- the comparator programs were the ones already installed. See VERIFY.md, section 8.\n+ the comparator programs were the ones already installed. See VERIFY.md, section 8. One later run is the\n+ exception: on 10 October 2026, on the Linux machine, the comparator for the third result ran in a tree\n+ where none of the repository's modules had been compiled before, and it accepted the result at the third\n+ attempt (section 3).\n - New in the second revision: on 2026-10-09 the second result had not yet had the rebuild from nothing that\n the first result had.\n The copy of the repository in which the comparator passed took the compiled files of its 25 certificate\n@@ -1407,13 +1420,16 @@ kept out of the prose so that the prose can be read.\n \n ### For the opening and what is new\n \n-The four texts of this README:\n+The four texts of this README, and one follow-up:\n \n - First text (first result): commit `024f763`, 2026-10-09.\n - Second text (second result): commit `fdfb781`, with its note on open directions in commit `e0bbe1c`,\n 2026-10-09.\n - Third text (third result): commits `6a1d04f` and `f010392`, 2026-10-09.\n-- Fourth text (fourth result): this one, 2026-10-10.\n+- Fourth text (fourth result): commit `5ba3046`, 2026-10-10.\n+- Follow-up to the fourth text: this one. It adds the comparator verdicts on the Linux machine that arrived\n+ after the fourth text was published, and it corrects wording about the runs on that machine. It changes no\n+ Lean file and no figure of a result.\n \n OpenAI's work that the statement and the cost model come from: [openai/math](https://github.com/openai/math),\n family 130, commit `fd4aeeb`.\n@@ -1480,13 +1496,27 @@ result on his own hand-over pairs:\n build of the published tree of this repository (commit `f010392`).\n - All 54 Lean modules that the pull request adds compiled, with no error.\n - The two heaviest modules, `Work.GCert.Data.Gen.P233Scal0` and `Work.GCert.Data.Gen.P233Scal1`, built in\n- 574 s and 642 s. The largest process of each held about 13 GB (13.3 GB and 13.4 GB). The 54 modules took\n- 66 minutes in all, on a machine that other jobs shared.\n+ 574 s and 642 s. The largest process of each held about 13 GB (12.7 GiB and 12.8 GiB). The 54 modules\n+ took 66 minutes in all, on a machine that other jobs shared.\n - His three theorems, `wht_main_block_B2Gp233x`, `transform_mainY` and `convolution_mainY`, depend on\n `propext`, `Classical.choice` and `Quot.sound`, and on no other axiom.\n - `tools/Compare.lean` printed `RESULT: PASS` for his Walsh-Hadamard challenge and solution and for his\n Fourier challenge and solution, with the constant counts that he states (38871; 43381 and 43404).\n-- Not run in that build: the official comparator on his two configurations. He reports those runs himself.\n+- Not run in that build: the official comparator. The agents ran it afterwards on\n+ `comparator/B2Gp233x.json` and `comparator/UniformFourier233.json`, the two configurations for which he\n+ reports runs. They used a second copy of that tree and the stand-in for the sandbox (section 3). The\n+ comparator accepted both, each with `Lean default kernel accepts the solution`, `Your solution is okay!`\n+ and exit code 0. Each log has 176 `Replayed` lines and no `Built` line, so no module was compiled inside\n+ the runs.\n+ - `comparator/B2Gp233x.json`: started at 22:58 on 2026-10-10, ended at 00:12 on 2026-10-11; 74 minutes,\n+ 14.4 GB.\n+ - `comparator/UniformFourier233.json`: started at 23:00 on 2026-10-10, ended at 00:13 on 2026-10-11;\n+ 73 minutes, 14.5 GB.\n+ - The runs shared the machine, so the times are upper bounds.\n+ - The memory is counted as in section 3: the kbytes figure that GNU `time` printed (14443212 and\n+ 14501748), divided by a million.\n+ - These are not runs with the comparator's real sandbox. He reports his own runs, with the real `landrun`\n+ sandbox.\n - Mathlib was not compiled there. Its compiled files came from Mathlib's cache.\n - The Python checks of his certificate were made on the Mac earlier that day, not on the Linux machine\n (\"Whose circuit this is\").\n@@ -1611,3 +1641,13 @@ the seconds are the duration of the run.\n \n **The fourth result.** It was found, built and checked on 2026-10-10. Its runs, with commands, times and\n memory, are in [VERIFY.md](VERIFY.md), section 10.\n+\n+**The comparator for the third result in a tree compiled from nothing, on the Linux machine** (section 3).\n+All times are UTC, on 2026-10-10.\n+\n+- The first attempt started at 20:40 and the second at 21:17. Neither gave a verdict: the agents stopped\n+ both during the build, to keep the shared machine within its memory.\n+- The third attempt started at 21:23 and ended at 23:30, with `Your solution is okay!` and exit code 0.\n+- That was after the fourth text was published, so the fourth text said that the run had no verdict. The\n+ follow-up text has the verdict.\n+- The exact time and memory are in [VERIFY.md](VERIFY.md), section 8, point 14."},{"sha":"363c5657a9d478d417f51e420103afe352418f63","filename":"RELATED-WORK.md","status":"modified","additions":16,"deletions":5,"changes":21,"blob_url":"https://github.com/jacobalansussman/wht-power-saving-lean/blob/9c94857bbaee886f8649edee0bc2d3c738f9555e/RELATED-WORK.md","raw_url":"https://github.com/jacobalansussman/wht-power-saving-lean/raw/9c94857bbaee886f8649edee0bc2d3c738f9555e/RELATED-WORK.md","contents_url":"https://api.github.com/repos/jacobalansussman/wht-power-saving-lean/contents/RELATED-WORK.md?ref=9c94857bbaee886f8649edee0bc2d3c738f9555e","patch":"@@ -538,7 +538,7 @@ a claim of its authors, as everywhere in this file.\n |---|---|---|---|\n | 7795/10^7 (7795973/10^10) | [#327](https://github.com/CrocSwap/integer-mult-bounds/pull/327), DreamingOfClouds, 18:51, open; h = 20, 6,455 helpers | \"two independent rational moment engines\"; its author reports that it was \"kernel-checked in Lean with Jacob Sussman's unchanged generator\". Not built here | 1.1240 times it |\n | 7635/10^7 (7635875/10^10 by `gxdry.py` here) | [#304](https://github.com/CrocSwap/integer-mult-bounds/pull/304), DreamingOfClouds, 12:01 UTC on 2026-10-10, open; h = 22, 9,160 helpers | scripts; its description said \"no Lean build\" | 1.1475 times it |\n-| 7547361/10^10 | the circuit of #193 with the pairs of #233 (Chafik Boukhalfa, chafreaky); his pull request #2 of this repository, open | pull request #2 reports a Lean kernel check of the Walsh-Hadamard statement at this figure and of the Fourier statement at 7547360/10^10, `tools/Compare.lean` \"PASS for both\" and a comparator run on Linux, \"both accepted\". The agents built the pull request on a Linux machine on 2026-10-10: all 54 Lean modules that it adds compiled, and `tools/Compare.lean` printed `RESULT: PASS` for both statements; they did not run the comparator on it (the record below). In this repository's own rebuild the figure is a price by `gxdry.py`, and `tools/rebuild/` reproduces it (README, \"Whose circuit this is\") | 1.1610 times it |\n+| 7547361/10^10 | the circuit of #193 with the pairs of #233 (Chafik Boukhalfa, chafreaky); his pull request #2 of this repository, open | pull request #2 reports a Lean kernel check of the Walsh-Hadamard statement at this figure and of the Fourier statement at 7547360/10^10, `tools/Compare.lean` \"PASS for both\" and a comparator run on Linux, \"both accepted\". The agents built the pull request on a Linux machine on 2026-10-10: all 54 Lean modules that it adds compiled, and `tools/Compare.lean` printed `RESULT: PASS` for both statements; after the build they ran the official comparator on the two configurations for which he reports runs, with a stand-in for its sandbox, and it accepted both (the record below). In this repository's own rebuild the figure is a price by `gxdry.py`, and `tools/rebuild/` reproduces it (README, \"Whose circuit this is\") | 1.1610 times it |\n | 7474547/10^10 | the second result of this repository | a Lean theorem here | 1.1723 times it |\n \n Among those 100 pull requests, the largest kappa in a title was 7.77268e-4 (eumemic,\n@@ -599,15 +599,26 @@ machine.\n machine.\n - **The build:** all 54 Lean modules that the pull request adds compiled, with no error.\n - **The two heaviest modules:** `Work.GCert.Data.Gen.P233Scal0` and `Work.GCert.Data.Gen.P233Scal1` built in\n- 574 s and 642 s. The largest process of each held about 13 GB (13.3 GB and 13.4 GB). The 54 modules took 66\n- minutes in all, on a machine that other jobs shared.\n+ 574 s and 642 s. The largest process of each held about 13 GB (12.7 GiB and 12.8 GiB). The 54 modules took\n+ 66 minutes in all, on a machine that other jobs shared.\n - **The axioms:** his three theorems, `wht_main_block_B2Gp233x`, `transform_mainY` and `convolution_mainY`,\n depend on `propext`, `Classical.choice` and `Quot.sound`, and on no other axiom.\n - **The statement check:** `tools/Compare.lean` printed `RESULT: PASS` for his Walsh-Hadamard challenge and\n solution and for his Fourier challenge and solution, with the constant counts that he states (38871; 43381\n and 43404).\n-- **Not run in that build:** the official comparator on his two configurations. He reports those runs\n- himself.\n+- **Not run in that build:** the official comparator. The agents ran it afterwards on\n+ `comparator/B2Gp233x.json` and `comparator/UniformFourier233.json`, the two configurations for which he\n+ reports runs. They used a second copy of that tree and a stand-in for the sandbox (README, section 3).\n+- **The comparator runs made afterwards:** the comparator accepted both configurations, each with\n+ `Lean default kernel accepts the solution`, `Your solution is okay!` and exit code 0. Each log has 176\n+ `Replayed` lines and no `Built` line. The time is the wall clock of the run, and the memory is the maximum\n+ resident set size that GNU `time` printed.\n+ - `comparator/B2Gp233x.json`: 22:58 on 2026-10-10 to 00:12 on 2026-10-11; 4455 s (1:14:15), 14443212 kB.\n+ - `comparator/UniformFourier233.json`: 23:00 on 2026-10-10 to 00:13 on 2026-10-11; 4388 s (1:13:07),\n+ 14501748 kB.\n+ - The runs shared the machine, so the times are upper bounds.\n+ - These are not runs with the comparator's real sandbox: the kernel of that machine has no Landlock. He\n+ reports his own runs, with the real `landrun` sandbox.\n - **Mathlib** was not compiled there. Its compiled files came from Mathlib's cache.\n - **The Python checks** of his certificate were made on the Mac earlier that day, not on the Linux machine\n (README, \"Whose circuit this is\")."},{"sha":"5a391a18e84724e3c72c620e1a49f103aa620a90","filename":"VERIFY.md","status":"modified","additions":21,"deletions":7,"changes":28,"blob_url":"https://github.com/jacobalansussman/wht-power-saving-lean/blob/9c94857bbaee886f8649edee0bc2d3c738f9555e/VERIFY.md","raw_url":"https://github.com/jacobalansussman/wht-power-saving-lean/raw/9c94857bbaee886f8649edee0bc2d3c738f9555e/VERIFY.md","contents_url":"https://api.github.com/repos/jacobalansussman/wht-power-saving-lean/contents/VERIFY.md?ref=9c94857bbaee886f8649edee0bc2d3c738f9555e","patch":"@@ -386,7 +386,9 @@ Read these before relying on the result.\n the comparator runs, outside its sandbox. The comparator's README lists as an assumption that the solution\n was not compiled before. To meet it, run section 5 directly after `lake exe cache get`: the comparator then\n builds every module itself. It was not run in that order here; it compiles several kernel checks of a\n- certificate at the same time and may need more than 16 GB.\n+ certificate at the same time and may need more than 16 GB. On 2026-10-10 it was run in that order on the\n+ Linux machine, for `comparator/UniformFourier.json` only, and it accepted the third result at the third\n+ attempt, each attempt continuing the build of the one before (point 14).\n 4. **Mathlib was not rebuilt from source.** Its compiled files came from Mathlib's cache server for the pinned\n revision (`lake exe cache get`), as is usual.\n 5. **Not fetched fresh for this test:** the Lean toolchain v4.34.1 and the `comparator` and `lean4export`\n@@ -458,9 +460,19 @@ Read these before relying on the result.\n and the two runs for the first result used the same copy of the tree, partly at the same time. The run for\n the second result used a second copy. The two negative controls were\n refused with exit code 1 (a challenge with 7474548 for the second result, and one for the Fourier statement\n- of the third). One run was still going when this text was written: the comparator with\n- `comparator/UniformFourier.json` in a tree where nothing had been compiled before. It is the third attempt\n- in that tree, and each attempt continued the build of the one before. It has no verdict here.\n+ of the third).\n+\n+ The agents also ran the comparator with `comparator/UniformFourier.json` in a tree where none of the\n+ repository's modules had been compiled before. Mathlib's compiled files came from its cache. The comparator\n+ accepted the third result there: `Build completed successfully (9236 jobs)`,\n+ `Lean default kernel accepts the solution`, `Your solution is okay!` and exit code 0. That was the third\n+ attempt in that tree, and each attempt continued the build of the one before. The first two attempts gave\n+ no verdict: the agents stopped both during the build, to keep the shared machine within its memory. In the\n+ third, a helper that the agents ran outside the stand-in paused and resumed Lean processes for the same\n+ reason. The logs of the three attempts have 132, 1 and 181 `Built` lines, so 314 modules of the\n+ repository were compiled inside the stand-in. The last attempt: 7639 s (2:07:18), 11402808 kB. This verdict\n+ came after the fourth revision was published; the text published then said that the run had no verdict.\n+\n None of these runs used the comparator's real sandbox (point 1).\n \n ## 9. Measurements of the first publication (2026-10-09, 194 modules)\n@@ -636,9 +648,11 @@ Measured, Mac (the stand-in of section 5, `enable_nanoda` false): for both confi\n `Lean default kernel accepts the solution` and `Your solution is okay!`, exit code 0; 85 s and 6.05 GB for\n `comparator/B2Ge8x.json`, 89 s and 6.09 GB for `comparator/UniformFourierE8.json`; 171 modules replayed, none\n built. Linux: the same two lines for both configurations, exit code 0; 406 s and 6.80 GB, 432 s and 6.68 GB;\n-171 modules replayed, none built. The sandbox there was a stand-in built on Linux namespaces, not `landrun`,\n-because that kernel has no Landlock; the stand-in was not tested on its own in these runs. This is not a run\n-with the real sandbox. The times are from a machine under load.\n+171 `Replayed` lines and no `Built` line in each log. A memory figure in GB for the Linux machine, here and in\n+the rest of this file, is the kbytes figure that GNU `time` printed, divided by a million; a kbyte there is\n+1024 bytes, so in units of 10^9 bytes each figure is 2.4 % higher. The sandbox there was a stand-in built on\n+Linux namespaces, not `landrun`, because that kernel has no Landlock; the stand-in was not tested on its own\n+in these runs. This is not a run with the real sandbox. The times are from a machine under load.\n \n ### 10.4 Regenerate the generated files, and check the certificate in Python (no Lean needed)\n "},{"sha":"7b37c02b7b9787ffd9d5b02216807ddbff4ddebf","filename":"notes/e8-results.json","status":"modified","additions":2,"deletions":2,"changes":4,"blob_url":"https://github.com/jacobalansussman/wht-power-saving-lean/blob/9c94857bbaee886f8649edee0bc2d3c738f9555e/notes%2Fe8-results.json","raw_url":"https://github.com/jacobalansussman/wht-power-saving-lean/raw/9c94857bbaee886f8649edee0bc2d3c738f9555e/notes%2Fe8-results.json","contents_url":"https://api.github.com/repos/jacobalansussman/wht-power-saving-lean/contents/notes%2Fe8-results.json?ref=9c94857bbaee886f8649edee0bc2d3c738f9555e","patch":"@@ -68,7 +68,7 @@\n \"axioms\": \"[propext, Classical.choice, Quot.sound]\",\n \"compare_lean\": \"RESULT: PASS on the Mac and on Linux\",\n \"comparator\": \"Your solution is okay! on the Mac (stand-in tools/landrun-macos-shim.sh) and on Linux (a stand-in built on namespaces; that kernel has no Landlock); no run with the real landrun\",\n- \"peak_memory\": \"build: 6.15 GB resident on the Mac, 6.69 GB on Linux; tools/Compare.lean: 7.32 GB resident and about 9.8 GB of footprint (sampled) on the Mac, 16.0 GB resident on Linux; comparator: 6.09 GB on the Mac, 6.80 GB on Linux\"\n+ \"peak_memory\": \"build: 6.15 GB resident on the Mac, 6.69 GB on Linux; tools/Compare.lean: 7.32 GB resident and about 9.8 GB of footprint (sampled) on the Mac, 16.0 GB resident on Linux; comparator: 6.09 GB on the Mac, 6.80 GB on Linux; each Linux figure is the kbytes figure that GNU time printed, divided by a million\"\n },\n \"fourier_and_convolution\": {\n \"theorems\": [\"transform_mainE8\", \"convolution_mainE8\"],\n@@ -147,7 +147,7 @@\n \"noise\": \"optima of the programme with equal objective value differ by 0.3 to 0.6 percent in the figure; the four best files of the round lie within 0.1 percent\"\n },\n \"outside_certificates_priced_here\": [\n- {\"source\": \"pull request #2 to this repository (Chafik Boukhalfa, account chafreaky)\", \"label_width_h\": 22, \"helpers\": 9412, \"figure_integer\": 7547361, \"saving\": \"7.5474e-4\", \"status\": \"price as computed here; a Lean theorem in his pull request, which the agents built on Linux on 2026-10-10\", \"lean_by_its_author\": \"the pull request reports a Lean kernel check at this figure (theorem wht_main_block_B2Gp233x), tools/Compare.lean PASS and a comparator run on Linux\", \"lean_built_by_the_agents\": \"on 2026-10-10 the agents built the pull request on a Linux machine: all 54 Lean modules that it adds compiled; its three theorems depend only on propext, Classical.choice and Quot.sound; tools/Compare.lean printed RESULT: PASS for the Walsh-Hadamard statement and for the Fourier statements; the agents did not run the official comparator on it; on the Mac the build could not finish, because two of its modules need about 13 GB of memory each; the pull request is not merged\"},\n+ {\"source\": \"pull request #2 to this repository (Chafik Boukhalfa, account chafreaky)\", \"label_width_h\": 22, \"helpers\": 9412, \"figure_integer\": 7547361, \"saving\": \"7.5474e-4\", \"status\": \"price as computed here; a Lean theorem in his pull request, which the agents built on Linux on 2026-10-10\", \"lean_by_its_author\": \"the pull request reports a Lean kernel check at this figure (theorem wht_main_block_B2Gp233x), tools/Compare.lean PASS and a comparator run on Linux\", \"lean_built_by_the_agents\": \"on 2026-10-10 the agents built the pull request on a Linux machine: all 54 Lean modules that it adds compiled; its three theorems depend only on propext, Classical.choice and Quot.sound; tools/Compare.lean printed RESULT: PASS for the Walsh-Hadamard statement and for the Fourier statements; after the build the agents ran the official comparator on the two configurations for which its author reports runs, comparator/B2Gp233x.json and comparator/UniformFourier233.json, with a stand-in for its sandbox (that kernel has no Landlock), and it printed Your solution is okay! for both, exit code 0 (4455 s and 14.4 GB; 4388 s and 14.5 GB; the runs ended on 2026-10-11; each memory figure is the kbytes figure that GNU time printed, divided by a million); no run with the real landrun by the agents, and the author reports his own runs with it; on the Mac the build could not finish, because two of its modules need about 13 GB of memory each; the pull request is not merged\"},\n {\"source\": \"hub #304 (DreamingOfClouds)\", \"label_width_h\": 22, \"helpers\": 9160, \"figure_integer\": 7635875, \"saving\": \"7.6359e-4\", \"status\": \"price\"}\n ],\n \"floors\": {"}]} \ No newline at end of file diff --git a/research/lean-multi-host-source/review-receipts/external-overlap/files.json b/research/lean-multi-host-source/review-receipts/external-overlap/files.json new file mode 100644 index 0000000000..e60bad101c --- /dev/null +++ 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Original\n commits, licenses and AI-assistance disclosures are preserved. Douglas Colkitt\n performed the maintainer review and integration with OpenAI Codex assistance.\n \n+### Historical source527 checkpoint\n+\n+**eumemic's [#210](https://github.com/CrocSwap/integer-mult-bounds/pull/210),\n+κ=0.000710046193349537**, is now preserved as a complete historical package,\n+with its [review and reproduction record](docs/research/community-pr210-review.md).\n+eumemic contributed internal response cancellation, source reuse, target\n+transformations and the final composition. Its cumulative credits include\n+Henry Grant / hcg890 and Jacob Sussman (five-stage geometry), Evan McKinney\n+(completed banks), Rohan Arun (width-120 banking and helper refinements),\n+Chafik Boukhalfa (physical helper/checkers), Avi Eisenberg (complex helper),\n+Dugongue (coordinated frames and retiming), and Romyxen / sennemmi\n+(nineteen operation-frame improvements), with the full predecessor chain\n+retained in the original notices. Gabriele Nespoli's parallel fixed-prime\n+and finite-depth refinement remains acknowledged in the published\n+[round-nine ledger](research/community-round9-audit/INDEX.md).\n+\n ### Preceding coordinated-frame checkpoint\n \n **Current reviewed construction: #186 on #181 and #168, κ=0.000661885549259598.**"},{"sha":"61fc5ef410326fe5492bb32cd73220918c775d2d","filename":"Makefile","status":"modified","additions":9,"deletions":1,"changes":10,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/Makefile","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/Makefile","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/Makefile?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -46,6 +46,14 @@ gen4-bank-verify: selected-record-check\n \t@work=$$(mktemp -d \"$${TMPDIR:-/tmp}/integer-mult-gen4.XXXXXX\"); \\\n \tpython3 -B research/five-stage-gen4-banks/verify.py --output \"$$work/replay\"\n \n+.PHONY: source527-record-check source527-verify\n+source527-record-check:\n+\tpython3 -B scripts/verify_selected_result.py --record certificates/checkpoints/source527.json\n+\n+source527-verify: source527-record-check\n+\t@work=$$(mktemp -d \"$${TMPDIR:-/tmp}/integer-mult-source527.XXXXXX\"); \\\n+\tpython3 -B research/five-stage-source527-banks/verify.py --output \"$$work/replay\"\n+\n verify-community: community-audit-check community-followup-check copied-reversed-producer copied-reversed-check copied-fixed-reversed-producer copied-fixed-reversed-check\n \t$(MAKE) copied-fixed-verify\n \t$(MAKE) climbed-48-verify\n@@ -57,7 +65,7 @@ verify-producers:\n \t$(MAKE) endpoint-gauge-producer endpoint-gauge-certificate\n \t$(MAKE) partial-swap-producer partial-swap-certificate\n \n-verify-certificates:\n+verify-certificates: source527-record-check\n \tpython3 scripts/prime_field_network.py\n \tpython3 scripts/complex_network.py\n \tpython3 scripts/fast_gaussian.py"},{"sha":"66bf6782f7c5011869f98fb3c3a3063cfd547aa9","filename":"README.md","status":"modified","additions":28,"deletions":0,"changes":28,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/README.md","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/README.md","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/README.md?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -39,6 +39,34 @@ python3 -m pip install -r research/five-stage-gen4-banks/requirements.txt\n make gen4-bank-verify\n ```\n \n+## Historical audited checkpoint: 527 reused sources\n+\n+**eumemic's [#210](https://github.com/CrocSwap/integer-mult-bounds/pull/210)**,\n+pinned at `298f7c1`, gives the conditional witness\n+**κ = 710046193349537 / 10¹⁸ = 0.000710046193349537**.\n+This is the intermediate result announced before the gen4 update above.\n+Its complete source package and audit are now preserved on main; the newer\n+gen4 result remains selected.\n+\n+The construction combines internal response cancellations and source reuse\n+with Henry Grant and Jacob Sussman's five-stage geometry, Evan McKinney's\n+completed-bank method and Rohan Arun's width-120 banking work. Chafik\n+Boukhalfa's physical helper/checkers, Avi Eisenberg's complex helper,\n+Dugongue's refinements and Romyxen / sennemmi's operation frames remain\n+credited in the source notices. All eight mandatory finite stages passed,\n+with every one of the 121 pinned inputs unchanged. The retained all-size\n+interfaces remain conditional.\n+\n+[Checkpoint and publication review](docs/research/community-pr210-review.md) ·\n+[Exact certificate](research/community-round9-audit/pr210-certificate.json) ·\n+[Construction source](research/five-stage-source527-banks/PROOF.md) ·\n+[Full round-nine review](research/community-round9-audit/REPORT.md)\n+\n+```sh\n+python3 -m pip install -r research/five-stage-source527-banks/requirements.txt\n+make source527-verify\n+```\n+\n ## Preceding reviewed result: coordinated frames and completed entrance banks\n \n [Dugongue's #186](https://github.com/CrocSwap/integer-mult-bounds/pull/186)"},{"sha":"a26075c52736ae571ef1b9878a2059142e80bea1","filename":"certificates/checkpoints/source527.json","status":"added","additions":30,"deletions":0,"changes":30,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/certificates%2Fcheckpoints%2Fsource527.json","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/certificates%2Fcheckpoints%2Fsource527.json","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/certificates%2Fcheckpoints%2Fsource527.json?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,30 @@\n+{\n+ \"status\": \"Published historical checkpoint; superseded by gen4\",\n+ \"kappa\": \"710046193349537/1000000000000000000\",\n+ \"decimal\": \"0.000710046193349537\",\n+ \"source_prs\": [\n+ 210,\n+ 234,\n+ 209,\n+ 237,\n+ 197,\n+ 200,\n+ 193,\n+ 207,\n+ 216,\n+ 211,\n+ 230\n+ ],\n+ \"audited_source_head\": \"298f7c112889f799e8e2040099fbc325d0ccd0f6\",\n+ \"source_manifest\": \"research/five-stage-source527-banks/MANIFEST.json\",\n+ \"certificate\": \"research/community-round9-audit/pr210-certificate.json\",\n+ \"certificate_sha256\": \"5c1619604173dda4ff06efecd01bf7e48d017b17770ed35bb9f2f903930b5f08\",\n+ \"proof\": \"research/five-stage-source527-banks/PROOF.md\",\n+ \"proof_supplements\": {\n+ \"research/five-stage-source527-banks/BANK-PROOF.md\": \"9f3525c8e8b798119d81ca1af67424107a87aa0e98a326244149602fafa805ea\"\n+ },\n+ \"review\": \"docs/research/community-pr210-review.md\",\n+ \"validation\": \"docs/research/community-pr210-integration.json\",\n+ \"reproduce\": \"make source527-verify\",\n+ \"scope\": \"Conditional finite construction under inherited all-size compiler, chart, routing/restoration, prime, precision/recovery, complex symbolic and analytic interfaces. Full theorem not formalized.\"\n+}"},{"sha":"df15fd4c53f79288174403a069574997570ce4d8","filename":"docs/research/community-pr210-integration.json","status":"added","additions":203,"deletions":0,"changes":203,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/docs%2Fresearch%2Fcommunity-pr210-integration.json","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/docs%2Fresearch%2Fcommunity-pr210-integration.json","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/docs%2Fresearch%2Fcommunity-pr210-integration.json?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,203 @@\n+{\n+ \"status\": \"EXACT_HISTORICAL_CHECKPOINT_IMPORTED\",\n+ \"date\": \"2026-10-10\",\n+ \"source_head\": \"298f7c112889f799e8e2040099fbc325d0ccd0f6\",\n+ \"package_manifest_sha256\": \"d51e8cc118ef245e100ae74f4029d80371b8309e3e58daaff9983311c79a8780\",\n+ \"package_files\": 121,\n+ \"package_and_workflow_git_blobs_match_source\": true,\n+ \"prior_full_replay\": \"research/community-round9-audit/pr210-verification.json\",\n+ \"fresh_full_replay_this_import\": false,\n+ \"review_reuse_basis\": \"All 121 consumed inputs and original manifest match completed eight-stage immutable replay. Exact source git blob identity checked independently.\",\n+ \"historical_record\": \"certificates/checkpoints/source527.json\",\n+ \"selected_gen4_kappa\": \"90446448750933/125000000000000000\",\n+ \"selected_record_sha256\": \"df836c6d34509e980d067bd5678489c968bc6e329af9dd82c6207abf6443da89\",\n+ \"audit_snapshot_files\": 174,\n+ \"audit_snapshot_copy\": \"Original 174 files imported byte for byte; later publication context supplied separately.\",\n+ \"original_whitespace_preserved\": true,\n+ \"formal_scope\": \"PR236 completed review receipts are included as historical evidence; its standalone source package is not integrated.\",\n+ \"fresh_checks\": [\n+ \"complete package manifest\",\n+ \"git blob equality to frozen source\",\n+ \"historical record and proof/certificate bindings\",\n+ \"current gen4 record unchanged\",\n+ \"four selected-record corruption tests\",\n+ \"all original 174 review files byte-identical\",\n+ \"new documentation links\"\n+ ],\n+ 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0.000710046193349537.**\n+\n+The result was announced after its audit but before its standalone package\n+was imported into main. The subsequent gen4 publication moved main directly\n+from 0.000661885549259598 to 0.000723571590007464. This import fills the\n+historical publication gap; it does not lower the current selected result.\n+\n+## Construction and evidence\n+\n+The [complete source package](../../research/five-stage-source527-banks/README.md)\n+and its original workflow are imported without changes from the pinned head.\n+All 121 package inputs and the manifest match the completed eight-stage\n+replay. The import receipt also checks git blob identity. Original whitespace\n+is retained where changing it would invalidate the audited source pins.\n+\n+- [Full finite replay](../../research/community-round9-audit/pr210-verification.json):\n+ banks, bit, complex, finite, math, primes, raw and scalar stages all passed,\n+ including missing-stage and corruption controls.\n+- [Exact certificate](../../research/community-round9-audit/pr210-certificate.json):\n+ two moment engines, three finite ordinary-leaf levels, all 47 strict\n+ constraints and seven margins; the next headline grid point is rejected.\n+- [Additional complex scalar audit](../../research/community-round9-audit/pr210-complex-scalar.json):\n+ both signed directions, all 12,052 formal columns and 9,412 dirty roles,\n+ with independently propagated bounds and omitted-addition controls.\n+- [Full original round-nine report](../../research/community-round9-audit/REPORT.md)\n+ and [per-PR ledger](../../research/community-round9-audit/INDEX.md): historical\n+ review scope, individual findings and limitations, including verification\n+ contributions. These records do not imply that every reviewed PR is merged.\n+- [Publication checks](community-pr210-integration.json): exact import,\n+ preserved certificate and proof hashes, historical record validation and\n+ confirmation that the gen4 selection is unchanged.\n+\n+The full numerical replay is reused from the completed audit because every\n+consumed source byte is unchanged. Import-time checks freshly validate the\n+manifest, source tree and certificate bindings. A fresh complete replay is\n+available through:\n+\n+```sh\n+python3 -m pip install -r research/five-stage-source527-banks/requirements.txt\n+make source527-verify\n+```\n+\n+For just the publication bindings, run `make source527-record-check`.\n+\n+## Attribution\n+\n+eumemic supplies the final source527 composition, internal cancellations,\n+target transformations and source reuse. The construction credits Henry Grant\n+/ hcg890 and Jacob Sussman's five-stage layout/complex baseline; Rohan Arun's\n+width-120 banking and helper refinements; Evan McKinney's completed-bank\n+method; Chafik Boukhalfa's physical helper/checkers; Avi Eisenberg's complex\n+helper; Dugongue's coordinated-frame lineage; and Romyxen / sennemmi's nineteen\n+operation-frame improvements. The complete upstream notices, licenses and\n+AI-assistance disclosures remain in the original package. Parallel work,\n+including Gabriele Nespoli's fixed-prime/finite-depth refinement, retains its\n+own entry in the published review ledger.\n+\n+## Boundaries\n+\n+This is a conditional finite construction. Uniform compilation,\n+common-ancestor/weighted charts, paid routing and restored rows,\n+prime supply, precision/recovery, complex symbolic correctness and the\n+all-size analytic reduction remain inherited dependencies. It is not a\n+complete formal proof of integer multiplication or a practical benchmark.\n+\n+Later revisions of PR210 are not silently included. The copied round-nine\n+report states what had and had not been published when its review finished;\n+this document records the later publication. The report's PR236 Lean receipts\n+are published as review evidence, but the standalone PR236 source package\n+and the seven separately prepared tooling PRs are not integrated by this change."},{"sha":"231059a18d3a186330f315e5cd414214c97679a1","filename":"research/community-round9-audit/INDEX.md","status":"added","additions":61,"deletions":0,"changes":61,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2FINDEX.md","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2FINDEX.md","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2FINDEX.md?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,61 @@\n+# Per-PR review index\n+\n+Pinned round-9 snapshot: 51 new PRs and four changed heads. See [review-ledger.json](review-ledger.json) for exact heads, evidence and limitations, and [REPORT.md](REPORT.md) for recommendations. Finite passes remain conditional on inherited interfaces. All scheduled checks have finished; findings requiring changes and conditional scope remain explicit.\n+\n+| PR | Contributor | Disposition |\n+|---|---|---|\n+| [#240](https://github.com/CrocSwap/integer-mult-bounds/pull/240) | rohanarun | complete-changed-work-replay-passed |\n+| [#239](https://github.com/CrocSwap/integer-mult-bounds/pull/239) | RichardHoekstra | focused-review-passed |\n+| [#237](https://github.com/CrocSwap/integer-mult-bounds/pull/237) | rohanarun | changed-banks-replay-passed |\n+| [#236](https://github.com/CrocSwap/integer-mult-bounds/pull/236) | jamesyc | complete-kernel-replay-passed-with-portability-note |\n+| [#235](https://github.com/CrocSwap/integer-mult-bounds/pull/235) | gabriele-nespoli | changed-work-replay-passed |\n+| [#234](https://github.com/CrocSwap/integer-mult-bounds/pull/234) | hcg890 | complete-finite-replay-passed |\n+| [#233](https://github.com/CrocSwap/integer-mult-bounds/pull/233) | chafreaky | complete-finite-replay-passed |\n+| [#232](https://github.com/CrocSwap/integer-mult-bounds/pull/232) | maxime-fleury | priced-target-replay-passed-with-path-fix-needed |\n+| [#231](https://github.com/CrocSwap/integer-mult-bounds/pull/231) | GamingPuzzled | scoped-proof-and-check-passed |\n+| [#230](https://github.com/CrocSwap/integer-mult-bounds/pull/230) | sennemmi | complete-offline-finite-replay-passed |\n+| [#229](https://github.com/CrocSwap/integer-mult-bounds/pull/229) | maxime-fleury | priced-target-arithmetic-replay-passed |\n+| [#228](https://github.com/CrocSwap/integer-mult-bounds/pull/228) | tehruhn | scoped-replay-passed |\n+| [#227](https://github.com/CrocSwap/integer-mult-bounds/pull/227) | Dugongue | complete-native-finite-replay-passed |\n+| [#226](https://github.com/CrocSwap/integer-mult-bounds/pull/226) | pCwOrM | changes-needed-arithmetic-passes |\n+| [#225](https://github.com/CrocSwap/integer-mult-bounds/pull/225) | chafreaky | scoped-replay-passed |\n+| [#224](https://github.com/CrocSwap/integer-mult-bounds/pull/224) | maxime-fleury | priced-target-arithmetic-replay-passed |\n+| [#223](https://github.com/CrocSwap/integer-mult-bounds/pull/223) | ikeboy | complete-changed-work-replay-passed |\n+| [#222](https://github.com/CrocSwap/integer-mult-bounds/pull/222) | romainhedouin | finite-regeneration-passed |\n+| [#221](https://github.com/CrocSwap/integer-mult-bounds/pull/221) | maxime-fleury | scoped-ceiling-replay-passed |\n+| [#220](https://github.com/CrocSwap/integer-mult-bounds/pull/220) | maxime-fleury | documentation-review-passed |\n+| [#218](https://github.com/CrocSwap/integer-mult-bounds/pull/218) | GamingPuzzled | scoped-replay-passed |\n+| [#217](https://github.com/CrocSwap/integer-mult-bounds/pull/217) | hcg890 | complete-finite-stages-passed-with-environment-note |\n+| [#216](https://github.com/CrocSwap/integer-mult-bounds/pull/216) | Dugongue | native-replay-passed-packaging-fix-needed |\n+| [#215](https://github.com/CrocSwap/integer-mult-bounds/pull/215) | GamingPuzzled | scoped-documentation-reviewed |\n+| [#214](https://github.com/CrocSwap/integer-mult-bounds/pull/214) | antoine-olivier | independent-audit-documentation-reviewed |\n+| [#213](https://github.com/CrocSwap/integer-mult-bounds/pull/213) | sennemmi | parameter-followup-replay-passed |\n+| [#212](https://github.com/CrocSwap/integer-mult-bounds/pull/212) | chafreaky | scoped-ceiling-review-passed |\n+| [#211](https://github.com/CrocSwap/integer-mult-bounds/pull/211) | rohanarun | complete-changed-work-replay-passed |\n+| [#210](https://github.com/CrocSwap/integer-mult-bounds/pull/210) | eumemic | complete-finite-replay-passed |\n+| [#209](https://github.com/CrocSwap/integer-mult-bounds/pull/209) | jacobalansussman | documentation-review-passed |\n+| [#208](https://github.com/CrocSwap/integer-mult-bounds/pull/208) | maxime-fleury | priced-target-arithmetic-replay-passed |\n+| [#207](https://github.com/CrocSwap/integer-mult-bounds/pull/207) | Dugongue | complete-finite-replay-passed |\n+| [#205](https://github.com/CrocSwap/integer-mult-bounds/pull/205) | rohanarun | changed-work-and-parent-replays-passed-with-portability-note |\n+| [#204](https://github.com/CrocSwap/integer-mult-bounds/pull/204) | maxime-fleury | arithmetic-followup-replay-passed |\n+| [#203](https://github.com/CrocSwap/integer-mult-bounds/pull/203) | huxint | scoped-replay-passed |\n+| [#202](https://github.com/CrocSwap/integer-mult-bounds/pull/202) | chafreaky | canonical-hash-reproduction-fix-needed |\n+| [#201](https://github.com/CrocSwap/integer-mult-bounds/pull/201) | DaysSky | scoped-ceiling-review-passed |\n+| [#200](https://github.com/CrocSwap/integer-mult-bounds/pull/200) | chafreaky | complete-finite-replay-passed |\n+| [#199](https://github.com/CrocSwap/integer-mult-bounds/pull/199) | maxime-fleury | arithmetic-and-donor-diagnostic-replay-passed |\n+| [#198](https://github.com/CrocSwap/integer-mult-bounds/pull/198) | sennemmi | stale-provenance-and-canonical-reproduction-fixes-needed |\n+| [#197](https://github.com/CrocSwap/integer-mult-bounds/pull/197) | evmckinney9 | changed-work-and-parent-replays-passed-with-portability-note |\n+| [#196](https://github.com/CrocSwap/integer-mult-bounds/pull/196) | chafreaky | complete-finite-replay-passed |\n+| [#195](https://github.com/CrocSwap/integer-mult-bounds/pull/195) | huxint | complete-finite-replay-passed |\n+| [#194](https://github.com/CrocSwap/integer-mult-bounds/pull/194) | ikeboy | canonical-hash-reproduction-fix-needed |\n+| [#193](https://github.com/CrocSwap/integer-mult-bounds/pull/193) | ikeboy | finite-replay-passed-with-strict-portability-adapter |\n+| [#192](https://github.com/CrocSwap/integer-mult-bounds/pull/192) | DaysSky | scoped-ceiling-review-passed |\n+| [#191](https://github.com/CrocSwap/integer-mult-bounds/pull/191) | ikeboy | canonical-hash-reproduction-fix-needed |\n+| [#190](https://github.com/CrocSwap/integer-mult-bounds/pull/190) | romainhedouin | full-affected-suite-passed |\n+| [#189](https://github.com/CrocSwap/integer-mult-bounds/pull/189) | chafreaky | complete-finite-replay-passed |\n+| [#188](https://github.com/CrocSwap/integer-mult-bounds/pull/188) | huxint | complete-finite-replay-passed-with-portability-fixes-needed |\n+| [#187](https://github.com/CrocSwap/integer-mult-bounds/pull/187) | rohanarun | complete-finite-replay-passed |\n+| [#186](https://github.com/CrocSwap/integer-mult-bounds/pull/186) | Dugongue | complete-native-finite-replay-passed |\n+| [#180](https://github.com/CrocSwap/integer-mult-bounds/pull/180) | M6LI | independent-finite-replay-passed |\n+| [#178](https://github.com/CrocSwap/integer-mult-bounds/pull/178) | rohanarun | receipt-only-update |\n+| [#162](https://github.com/CrocSwap/integer-mult-bounds/pull/162) | DaysSky | scoped-replay-passed |"},{"sha":"fd7e1642d545af4b57719b4585d9a381e797ccf1","filename":"research/community-round9-audit/PUBLICATION.md","status":"added","additions":16,"deletions":0,"changes":16,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2FPUBLICATION.md","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2FPUBLICATION.md","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2FPUBLICATION.md?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,16 @@\n+# Publication context\n+\n+The original files in this directory are the frozen review snapshot completed\n+on 2026-10-10. Statements in REPORT.md about unpublished work describe that\n+review's completion, not the current repository state.\n+\n+The standalone audited PR210 source527 package is now published as a\n+[historical checkpoint](../../docs/research/community-pr210-review.md).\n+The current selected result is the separately audited\n+[gen4 checkpoint](../../docs/research/community-pr279-review.md).\n+\n+Publication of this review directory preserves its evidence and attribution;\n+it does not merge every PR in the ledger. In particular, PR236's full kernel\n+rebuild receipts are included, but its standalone source package and the\n+seven tooling/documentation PRs prepared in the review remain separate\n+integration work. Original execution records and dispositions are unchanged."},{"sha":"0a7ecf0bdde9a446440bb19b672513b7ab20e6da","filename":"research/community-round9-audit/REPORT.md","status":"added","additions":78,"deletions":0,"changes":78,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2FREPORT.md","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2FREPORT.md","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2FREPORT.md?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,78 @@\n+# Community round 9: pinned queue review\n+\n+The 2026-10-09 snapshot contains 179 open PRs (20 drafts), including **51 new PRs and four changed heads** relative to round 8. All 55 have individual dispositions in [INDEX.md](INDEX.md) and exact heads, evidence and limitations in [review-ledger.json](review-ledger.json). This review covers the pinned snapshot, not later remote changes. Prior snapshot inclusion is not mathematical approval.\n+\n+All scheduled finite, arithmetic and formal checks have finished. **PR236’s full accepted-set Lean rebuild and final integrity audit pass.** No PR has been publicly reviewed, merged, closed or pushed during this review; the selected record remains unchanged.\n+\n+## Strongest completed finite replay\n+\n+PR **#210**, head `298f7c112889f799e8e2040099fbc325d0ccd0f6`, passes all eight mandatory stages with all 121 inputs unchanged:\n+\n+**κ = 710046193349537 / 10^18 = 0.000710046193349537**, approximately **7.28%** above the published selected witness, 0.000661885549259598.\n+\n+The replay reconstructs the 527-source helper, five-stage bit word, exact geometry, formal bit columns, prime witnesses, stage-private completed banks, complex ledger, paid moments and three finite leaf levels. All 47 strict constraints and seven margins pass; the next headline grid point fails. See the [verification receipt](pr210-verification.json).\n+\n+A separate maintainer [complex scalar replay](complex_scalar_replay.py) checks both signed shear directions on all 12,052 formal columns, restores 9,412 dirty roles, and rejects an omitted addition in each direction. Its signed-digit packing uses independently propagated majorants. This is a scalar projection check, not a proof of complex address geometry.\n+\n+These are **conditional finite certificates**. Inherited uniform compiler, common-chart/weighted complex realization, paid routing and restored-row, precision/recovery, and all-size analytic interfaces remain dependencies. No new all-size theorem or complete Lean multiplication proof is claimed.\n+\n+## Local integration preparation\n+\n+The local branch `review/community-round9-ready` at `053d35d`, in `/tmp/integer-mult-round9-ready`, contains reviewed work from **#239, #222, #218, #231, #209, #190 and #220**, plus narrowly scoped maintainer documentation and Darwin RSS-unit fixes. Original authorship and source references are preserved. It has not been published or merged.\n+\n+- #239: dual-Gram oracle, 32 tests and identical independent audit payloads pass. Concurrent timings are not a robust speed benchmark.\n+- #222: six regenerated artifacts match pinned baseline payloads; independent checker and corruption controls pass. The full eight-file submission is included.\n+- #218: the complete parallel verifier and independent serial/fork parity checks pass.\n+- #231: the scoped parity lemma was reviewed and checked exhaustively for k=3 through 6.\n+- #190: the full affected `make verify-joint` suite passes after removing hashes of unconsumed metadata.\n+- #209 and #220: attribution and reproducibility guidance, respectively.\n+\n+## Finite constructions and lineage\n+\n+Completed original finite replays include #162, #180, #187, #189, #195, #196, #200, #207, #227/current #186, #230, #233 and #234. Their individual scopes differ; consult the ledger rather than interpreting this list as identical coverage. In particular, #180 reuses its previously audited native baseline, and #233 improves its complex supplier while its combined bound remains bit-limited.\n+\n+Changed-work replays for #197/#205, #211/#223, #237 and #240 freshly reconstruct the new charts, banks or source/frame work and reuse explicitly identified parent audits. #235 independently reproduces its new prime-density and seven-level arithmetic from fresh parent outputs, giving κ=0.000708582414684555347682; its original combined driver and `Prime.lean` were not rebuilt. #213's five-level arithmetic passes and its unchanged physical/admission records match freshly audited #211. #178 changes receipts/documentation only relative to its prior reviewed head.\n+\n+The complete #230 immutable offline run passes the deterministic 14-move/19-frame search, actual 471-source formal columns in F2 and both integer signs, retiming/endpoints, frames, charts/banks, complex flow/lift/contract and final assembly. Its κ=0.000694787513005285 is historical; the plateau contribution is retained in newer #210.\n+\n+Current #186 duplicates #227 exactly and was audited once under that identity. Its historical frozen publication remains untouched. Later descendants do not automatically validate every earlier head.\n+\n+## Reproduction findings and required fixes\n+\n+| PR | Finding and review outcome |\n+|---|---|\n+| #188 | Original Darwin `RLIMIT_AS` failure, followed by a last-bit discovery-root mismatch. A documented adapter removes only the unsupported memory cap and normalizes only that named diagnostic after exact comparison of all other fields. Complete replay passes and the entire final certificate matches exactly. CPU/alarm limits remain; no memory-cap claim. |\n+| #193 | Original canonical comparison fails. A fresh six-stage replay through #217's strict semantic adapter passes, validating actual hash links, exact maps/topology/kernel payloads, four accepting and 22 rejecting controls. Only two named discovery-root display differences and derived hash/gzip representation differences are permitted. This is an adapted pass, not an original default-command pass. |\n+| #191/#194/#202 | Fresh source-pinned diagnostics complete all six original stages and isolate exactly ten differing SHA256 leaves per head; every other reported field, including exact arithmetic, program identity and κ, matches. These are canonical hash-reproduction findings. Underlying historical payload equivalence is not established merely by ignoring the hashes, and #193's accepted normalization is not automatically extended. |\n+| #198 | Original aggregate fails 22 stale source pins; full source-assisted replay also fails canonical comparison. Scoped bit checks pass geometry/formal/terminal/moments but fail bundled prime-record equality. Independent regeneration shows every exact frame/basis/determinant/factor witness matches: only generator `script_sha256` is stale. Repair source provenance carefully; no wholesale repinning or original aggregate success is endorsed. |\n+| #216 | Five archive parts are at the package root, while the manifest expects `baseline/`. Copying the same hash-verified bytes into the expected disposable locations makes the complete native replay pass. Correct file placement before integration. |\n+| #217 | Fresh changed-bit stages and strict adapted complex stages, effective packing, scalar bills and final assembly pass. The original aggregate dependency-version gate was not passed. Installed NumPy2.4.6/SciPy1.17.1 differ from documented2.3.5/1.17.0. |\n+| #226 | Historical producer, arithmetic and five tests pass. New standalone verifier has an incorrect input root, treats missing hashed files as optional, and relies on stored margins. New Lean file has malformed encoding and is absent from default build targets. Repair packaging, verification and proof scope. |\n+| #232 | Original complete-corpus comparison fails only on a saved absolute Windows path. Strict path-only audit adapter passes all remaining original tests. Also remains a proposal with missing construction bodies, as below. |\n+| #236 | Original driver fails on Darwin `RLIMIT_AS`. The disclosed resource-policy adapter passes the complete kernel rebuild and final integrity audit without the advertised address-space cap. Correct the platform policy before claiming portable or Linux memory-capped execution. |\n+\n+Scientific-library version differences also apply where explicitly noted in the ledger. Do not describe those runs as reproductions of the pinned dependency environment. See [environment.json](environment.json).\n+\n+## Arithmetic, scoped barriers and research proposals\n+\n+#199 and #204 reproduce their exact finite-depth arithmetic, including κ=1693287/2500000000 for the next composition. Their commands inherit physical suppliers; they do not independently prove those constructions. #199's separate donor diagnostic reproduces its entire saved JSON: no eligible donor endpoint lies in any of the 220 unpaired birth frames. This is a scoped obstruction, not a universal reuse barrier.\n+\n+#192/#201/#212 pass their scoped ceiling calculations. #221's fresh 1,200-round calculation reproduces κ<0.0006968 for PR217's fixed word and bank model. These are not barriers for newer families. #203's architecture diagnostic and #225's conditional DFT-transfer arithmetic pass within their stated models. #215's scoped gauge note and #214's independent Linux audit report were reviewed; #214's own reported environment remains distinct from our corroborating runs.\n+\n+**#208, #224, #229 and #232 are priced research targets, not stronger finite certificates.** Their arithmetic/model checks pass, with #232's disclosed path normalization. #229's five-family, six-family and instantiation outputs reproduce byte for byte. #224 explicitly leaves C1–C5 and R1–R4 open. #232's importer correctly rejects ten absent implementation bodies and reports zero of six required exports implemented. Larger numbers in these proposals must not displace the strongest completed construction.\n+\n+## Attribution\n+\n+Preserve each contributor's mechanism and parallel work: source-assisted suppliers, completed banks, frame and scalar schedules, source reuse, plateau refinements, five-stage construction, width-120 banks, arithmetic, verification, tooling and documentation. The ledger links each result to its original author and exact head. Historical or superseded numerical contributions still deserve credit; numerical precedence and integration readiness are separate questions.\n+\n+## Completed formalization audit\n+\n+PR236 targets the historical conditional **κ=4609169/10^10** checkpoint. The full accepted set now passes: **3,606 modules, 14,320 audited declarations and 2,816 axiom-free declarations**. All observed transitive axioms are within `propext`, `Quot.sound` and `Classical.choice`.\n+\n+The full run rebuilt 3,602 modules and reused four dependency-closed modules freshly compiled earlier in this audit. The final [integrity check](pr236-final-integrity.json) independently reconstructs the complete receipt/dependency accounting and rechecks source, object, log, compiler and map hashes, source/import bindings and axiom output. It reuses the audited driver's source-plan and axiom parsers; it is not a second proof kernel. The terminal [summary](pr236-full-summary.json), [build log](pr236-full-build.log.txt), and [7,215-file evidence archive](pr236-kernel-evidence.tar.gz) are retained; the [archive manifest](pr236-evidence-manifest.json) records successful hash-checked readback.\n+\n+Original archive/source hashes and 11 driver fixtures pass. The original Darwin resource policy fails on `RLIMIT_AS`; the saved adapter omits only that unsupported address-space cap, retaining the official Lean4.21.0 compiler, original per-module timeouts, source/dependency checks and axiom audits. This is not a Linux memory-capped reproduction. The installed official standard library remains an explicit trust boundary and was not rebuilt.\n+\n+The [theorem scope review](pr236-scope-review.md) separates coefficient and dirty-response identities, finite assembly and local scratch statements from the remaining all-size obligations. The successful finite formalization does not establish the complete asymptotic multiplication theorem or a new numerical frontier.\n+\n+The [execution record](running-checks.json) now has no outstanding build. All 55 new/changed heads have completed review dispositions; this does not mean all are approved or that the 124 unchanged prior-snapshot entries received new full audits. No public review, merge, close, push or selected-record update was performed."},{"sha":"581762b7ed4649a2eb893e5ff7a0241ff4eb4717","filename":"research/community-round9-audit/complete_pr217_changed_audit.py","status":"added","additions":25,"deletions":0,"changes":25,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fcomplete_pr217_changed_audit.py","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fcomplete_pr217_changed_audit.py","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fcomplete_pr217_changed_audit.py?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,25 @@\n+\"\"\"Complete PR217 assembly using separately executed fresh complex/bit stages.\n+Original aggregate was not run: installed scientific versions differ from its pins.\n+\"\"\"\n+from pathlib import Path\n+import sys,importlib.util,json,hashlib,copy\n+sys.dont_write_bytecode=True\n+base=Path('/tmp/integer-mult-export217/research/butterfly-coordinated-bit-211');sys.path.insert(0,str(base))\n+spec=importlib.util.spec_from_file_location('butterfly_verifier',base/'verify.py');v=importlib.util.module_from_spec(spec);spec.loader.exec_module(v)\n+c=Path('/tmp/integer-mult-export193');b=Path('/tmp/integer-mult-export202');out=Path('/tmp/integer-mult-pr217-changed')\n+v.check_package();before=v.check_sources(c,b)\n+accepted=json.loads(Path('/tmp/integer-mult-pr193-portable/complex-acceptance.json').read_text())\n+controls=json.loads(Path('/tmp/integer-mult-pr193-portable/adapter-controls.json').read_text())\n+assert accepted['stages_executed']==6 and accepted['source_pins']==before['complex']\n+assert controls['status']=='PASS two-root portability controls' and len(controls['accepted'])==4 and len(controls['rejected'])==22\n+fresh=v.read(out/'effective-bit/receipt.json');v.admit(fresh);v.admit_artifacts(out,fresh)\n+bad=copy.deepcopy(fresh);bad['terminal']['formal']=[]\n+try:v.admit(bad)\n+except AssertionError:pass\n+else:raise AssertionError('Truncated terminal receipt admitted')\n+packed=v.effective_packing.run(b,fresh);v.write(out/'packing-scalar.json',packed)\n+math=v.js(v.verify_math.run(c,b,fresh,packed));assert math==v.read(base/'certificate.json')\n+v.write(out/'certificate.json',math)\n+assert v.check_sources(c,b)==before;v.check_package()\n+v.write(out/'maintainer-completion.json',dict(status='PASS_FRESH_STAGES_AND_CHANGED_ASSEMBLY',kappa=math['kappa'],original_aggregate_executed=False,installed_scientific_versions={'numpy':'2.4.6','scipy':'1.17.1'},unchanged_parent_complex_stages=6,exact_packing_and_all47=True,scope='Conditional finite supplier; original dependency-version gate not passed, no all-size theorem'))\n+print('PASS fresh PR217 stages and assembly; kappa='+math['kappa'])"},{"sha":"394ca90716cdf4ee3dc42d6550e68ce0783b1736","filename":"research/community-round9-audit/completion-audit.json","status":"added","additions":428,"deletions":0,"changes":428,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fcompletion-audit.json","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fcompletion-audit.json","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fcompletion-audit.json?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,428 @@\n+{\n+ \"status\": \"REVIEW_BATCH_COMPLETE\",\n+ \"objective\": \"Process the open PR queue for PRs not previously covered\",\n+ \"completed_at\": \"2026-10-10T03:05:50.621549+00:00\",\n+ \"snapshot_open_prs\": 179,\n+ \"reviewed_new_prs\": 51,\n+ \"reviewed_changed_heads\": 4,\n+ \"unchanged_prior_snapshot_prs\": 124,\n+ \"scope\": \"Pinned queue snapshot; review dispositions are not blanket mathematical approval or publication.\",\n+ \"reviewed_heads\": [\n+ {\n+ \"pr\": 240,\n+ \"author\": \"rohanarun\",\n+ \"head\": \"1068237fdb977f45e68107d118d0eaf0c7a4b516\",\n+ \"disposition\": \"complete-changed-work-replay-passed\",\n+ \"evidence_files\": 2\n+ },\n+ {\n+ \"pr\": 239,\n+ \"author\": \"RichardHoekstra\",\n+ \"head\": \"fd687eecd781631bc38ae8b03a83d00c13f05aa7\",\n+ \"disposition\": \"focused-review-passed\",\n+ \"evidence_files\": 2\n+ },\n+ {\n+ \"pr\": 237,\n+ \"author\": \"rohanarun\",\n+ \"head\": \"a8b0ce212bc9f09353a8161bf8a5cee9cefd600c\",\n+ \"disposition\": \"changed-banks-replay-passed\",\n+ \"evidence_files\": 3\n+ },\n+ {\n+ \"pr\": 236,\n+ \"author\": \"jamesyc\",\n+ \"head\": \"f825b6fdfd763f189db3aa1c02fdd5d604c85a01\",\n+ \"disposition\": \"complete-kernel-replay-passed-with-portability-note\",\n+ 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five-stage complex helper.\n+\n+This checks the literal scalar schedule with recursive calls replaced by the\n+identity, as appropriate to the scalar contract. It does not check the address\n+frames, the recursive operators, or the analytic transfer theorem.\n+Douglas Colkitt, with OpenAI Codex assistance. Apache-2.0.\n+\"\"\"\n+import argparse\n+import gzip\n+import hashlib\n+import importlib.util\n+import json\n+from pathlib import Path\n+import sys\n+import time\n+\n+\n+def need(ok, message):\n+ if not ok:\n+ raise ValueError(message)\n+\n+\n+def replay(package, direction):\n+ path = package / 'code/complex_scalars.py'\n+ spec = importlib.util.spec_from_file_location('submitted_complex_schedule', path)\n+ module = importlib.util.module_from_spec(spec)\n+ spec.loader.exec_module(module)\n+ source = package / 'inputs/complex/gcert1-p11-pr193.json.gz'\n+ c = json.loads(gzip.decompress(source.read_bytes()))\n+ n, v = 2*c['v']+c['R'], c['v']\n+ need((n, v) == (12052, 1320), 'Unexpected source')\n+ events = list(module.inv_schedule(direction, module.flat(c['A']), module.flat(c['B']), c))\n+\n+ def execute(initial, absolute=False, omit=None):\n+ # A row is an integer numerator vector / (2**u * 3**v). The same\n+ # denominator updates work for its packed encoding and its L1 majorant.\n+ rows = dict(initial)\n+ maxima = [0, 0, 0]\n+ for index, (_, event) in enumerate(events):\n+ if index == omit:\n+ continue\n+ op = event[0]\n+ if op == 'recursive_center':\n+ continue\n+ target = event[1]\n+ if op == 'clear':\n+ rows[target] = (0, 0, 0)\n+ elif op == 'copy':\n+ rows[target] = rows[event[2]]\n+ else:\n+ need(op == 'add', 'Unknown scalar opcode')\n+ _, _, source, a, b = event\n+ need(b in (1, 2, 3, 6), 'Unsupported denominator')\n+ x, u, w = rows[target]\n+ y, j, k = rows[source]\n+ j += int(b % 2 == 0)\n+ k += int(b % 3 == 0)\n+ new_u, new_w = max(u, j), max(w, k)\n+ coefficient = abs(a) if absolute else a\n+ rows[target] = (x * 2**(new_u-u) * 3**(new_w-w)\n+ + coefficient*y * 2**(new_u-j) * 3**(new_w-k), new_u, new_w)\n+ if absolute:\n+ x, u, w = rows[target]\n+ maxima = [max(maxima[0], x.bit_length()), max(maxima[1], u), max(maxima[2], w)]\n+ return rows, maxima\n+\n+ bound, maxima = execute({('L', i): (1, 0, 0) for i in range(n)}, absolute=True)\n+ # Include the final expected vector after clearing that row's denominator.\n+ max_difference = 0\n+ for i in range(n):\n+ b, u, w = bound[('L', i)]\n+ rhs_l1 = 2 if (direction == 'forward' and v <= i < 2*v) or (direction == 'backward' and i < v) else 1\n+ max_difference = max(max_difference, b + rhs_l1 * 2**u * 3**w)\n+ width = max_difference.bit_length()+2\n+ radix = 1 << width\n+ need(radix > 2*max_difference, 'Insufficient separation for signed digits')\n+ need(width < 128, 'Unexpectedly large packing; inspect before allocating')\n+ print(direction, 'columns', n, 'digit bits', width, 'bound bits', maxima, flush=True)\n+ units = [1 << (width*i) for i in range(n)]\n+ rows, _ = execute({('L', i): (units[i], 0, 0) for i in range(n)})\n+ for i in range(n):\n+ expected = units[i]\n+ if direction == 'forward' and v <= i < 2*v:\n+ expected += units[i-v]\n+ if direction == 'backward' and i < v:\n+ expected -= units[i+v]\n+ x, u, w = rows[('L', i)]\n+ need(x == expected * 2**u * 3**w, f'Wrong {direction} live row {i}')\n+ need(all(value[0] == 0 for role, value in rows.items() if role[0] != 'L'), 'Temporary not cleared')\n+\n+ # A deterministic corruption must change the map. Check the complete packed\n+ # map again; selected impulse columns can miss a legitimate changed column.\n+ mutation = next(i for i, (phase, e) in enumerate(events)\n+ if phase == 'main' and e[0] == 'add'\n+ and e[1][0] == e[2][0] == 'L'\n+ and (v <= e[1][1] < 2*v if direction == 'forward' else e[2][1] < 2*v and e[2][1] >= v))\n+ bad, _ = execute({('L', i): (units[i], 0, 0) for i in range(n)}, omit=mutation)\n+ detected = any(rows[r][0]*2**bad[r][1]*3**bad[r][2] != bad[r][0]*2**rows[r][1]*3**rows[r][2] for r in rows)\n+ need(detected, 'Omitted scalar addition was not detected by controls')\n+ return dict(direction=direction, columns=n, arbitrary_dirty=c['R'], live_rows=n,\n+ digit_bits=width, maximum_final_difference_majorant=max_difference,\n+ prefix_numerator_bits=maxima[0], max_denominator_powers=maxima[1:],\n+ live_shear_and_restoration=True, temporaries_cleared=True,\n+ omitted_addition_rejected=True, events=len(events),\n+ schedule_source_sha256=hashlib.sha256(path.read_bytes()).hexdigest(),\n+ certificate_sha256=hashlib.sha256(source.read_bytes()).hexdigest())\n+\n+\n+def main():\n+ need(not sys.flags.optimize, 'Run without -O')\n+ parser = argparse.ArgumentParser(description=__doc__)\n+ parser.add_argument('package', type=Path)\n+ parser.add_argument('--output', type=Path, required=True)\n+ args = parser.parse_args()\n+ start = time.monotonic()\n+ results = [replay(args.package, direction) for direction in ('forward', 'backward')]\n+ result = dict(status='PASS exact complete scalar schedule', checks=results, seconds=time.monotonic()-start,\n+ scope='All scalar columns and arbitrary dirty restoration only; recursive center operators are identity in this scalar projection. Address geometry and all-size transfer are separate obligations.')\n+ args.output.write_text(json.dumps(result, indent=2)+'\\n')\n+ print(json.dumps(result), flush=True)\n+\n+\n+if __name__ == '__main__':\n+ main()"},{"sha":"8667fa22ad331b5e07e7fbf06aa40dd026d5cfb8","filename":"research/community-round9-audit/diagnose_canonical_replay.py","status":"added","additions":46,"deletions":0,"changes":46,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fdiagnose_canonical_replay.py","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fdiagnose_canonical_replay.py","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fdiagnose_canonical_replay.py?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,46 @@\n+\"\"\"Run original pinned supplier build and report every saved-certificate difference.\n+This diagnoses a failed default comparison; it does not normalize or accept it.\n+\"\"\"\n+import hashlib\n+import json\n+import sys\n+from pathlib import Path\n+\n+root = Path(sys.argv[1]).resolve()\n+output = Path(sys.argv[2]).resolve()\n+package = root / 'research/source-assisted-v4'\n+sys.path.insert(0, str(package))\n+import verify\n+\n+assert not sys.flags.optimize\n+if hasattr(sys, 'set_int_max_str_digits'):\n+ sys.set_int_max_str_digits(0)\n+before = verify.pins()\n+built = verify.build()\n+assert verify.pins() == before, 'source bindings changed'\n+saved = json.loads((package / 'certificate.json').read_text())\n+differences = []\n+\n+def walk(a, b, path=''):\n+ if isinstance(a, dict) and isinstance(b, dict):\n+ for key in sorted(a.keys() | b.keys()):\n+ if key not in a or key not in b:\n+ differences.append(dict(path=path+'/'+key, kind='missing', built=a.get(key), saved=b.get(key)))\n+ else:\n+ walk(a[key], b[key], path+'/'+key)\n+ elif isinstance(a, list) and isinstance(b, list) and len(a) == len(b):\n+ for i, (x, y) in enumerate(zip(a, b)):\n+ walk(x, y, path+'/'+str(i))\n+ elif a != b:\n+ differences.append(dict(path=path, kind='different', built=a, saved=b))\n+\n+walk(built, saved)\n+output.mkdir(parents=True, exist_ok=True)\n+(output/'built.json').write_text(json.dumps(built, indent=2, sort_keys=True)+'\\n')\n+receipt = dict(status='DIAGNOSTIC_ONLY', source_pins_unchanged=True,\n+ source_files=len(before), source_pin_digest=hashlib.sha256(json.dumps(before, sort_keys=True).encode()).hexdigest(),\n+ saved_certificate_sha256=hashlib.sha256((package/'certificate.json').read_bytes()).hexdigest(),\n+ built_certificate_sha256=hashlib.sha256((output/'built.json').read_bytes()).hexdigest(),\n+ identical=(built == saved), differences=differences)\n+(output/'comparison.json').write_text(json.dumps(receipt, indent=2, sort_keys=True)+'\\n')\n+print(json.dumps(receipt, indent=2, sort_keys=True))"},{"sha":"3b3a250bc5cde8d373edbcb75371446f8eafdbe2","filename":"research/community-round9-audit/disposable-cleanup.json","status":"added","additions":113,"deletions":0,"changes":113,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fdisposable-cleanup.json","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fdisposable-cleanup.json","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fdisposable-cleanup.json?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,113 @@\n+{\n+ \"at\": \"2026-10-10T00:04:25.857303+00:00\",\n+ \"directories\": [\n+ {\n+ \"pr\": 180,\n+ \"directory\": \"/tmp/integer-mult-export180\",\n+ \"pinned_source_head\": \"33f3f1e3eba2797caf9c355bcca1cbdb800bfd24\",\n+ \"reason\": \"completed disposable replay; evidence saved in review folder; source recoverable from local pinned git ref\"\n+ },\n+ {\n+ \"pr\": 188,\n+ \"directory\": \"/tmp/integer-mult-export188\",\n+ \"pinned_source_head\": \"c6eea3e8a46bf122878b512590f9f91a20260800\",\n+ \"reason\": \"completed disposable replay; evidence saved in review folder; source recoverable from local pinned git ref\"\n+ },\n+ {\n+ \"pr\": 189,\n+ \"directory\": \"/tmp/integer-mult-export189\",\n+ \"pinned_source_head\": \"0a4091175b3981267a97a62ab7492cb9ba528916\",\n+ \"reason\": \"completed disposable replay; evidence saved in review folder; source recoverable from local pinned git ref\"\n+ },\n+ {\n+ \"pr\": 191,\n+ \"directory\": \"/tmp/integer-mult-export191\",\n+ \"pinned_source_head\": \"15fa62d52bd7d08f29fd09fffe33dfc7a15ba8a0\",\n+ \"reason\": \"completed disposable replay; evidence saved in review folder; source recoverable from local pinned git ref\"\n+ },\n+ {\n+ \"pr\": 194,\n+ \"directory\": \"/tmp/integer-mult-export194\",\n+ \"pinned_source_head\": \"a8c87783785be6fe20c4a8bb2ac4b3eec295a179\",\n+ \"reason\": \"completed disposable replay; evidence saved in review folder; source recoverable from local pinned git ref\"\n+ },\n+ {\n+ \"pr\": 195,\n+ \"directory\": \"/tmp/integer-mult-export195\",\n+ \"pinned_source_head\": \"d3e6b83af33c3aad940e737776937706e25b0b19\",\n+ \"reason\": \"completed disposable replay; evidence saved in review folder; source recoverable from local pinned git ref\"\n+ },\n+ {\n+ \"pr\": 196,\n+ \"directory\": \"/tmp/integer-mult-export196\",\n+ \"pinned_source_head\": \"5b09c35ee837e0157342a7cd1fbd933467cfe90b\",\n+ \"reason\": \"completed disposable replay; evidence saved in review folder; source recoverable from local pinned git ref\"\n+ },\n+ {\n+ \"pr\": 198,\n+ \"directory\": \"/tmp/integer-mult-export198\",\n+ \"pinned_source_head\": \"a22b271a06c6e61b7dcd2ec4859e6ccd532b1f6a\",\n+ \"reason\": \"completed disposable replay; evidence saved in review folder; source recoverable from local pinned git ref\"\n+ },\n+ {\n+ \"pr\": 200,\n+ \"directory\": \"/tmp/integer-mult-export200\",\n+ \"pinned_source_head\": \"a1175449f34d39ff933d9d8ab23ced1f32b290ec\",\n+ \"reason\": \"completed disposable replay; evidence saved in review folder; source recoverable from local pinned git ref\"\n+ },\n+ {\n+ \"pr\": 207,\n+ \"directory\": \"/tmp/integer-mult-export207\",\n+ \"pinned_source_head\": \"cd14825023b75af4f5919a30e5e6d548b6ade5bc\",\n+ \"reason\": \"completed disposable replay; evidence saved in review folder; source recoverable from local pinned git ref\"\n+ },\n+ {\n+ \"pr\": 216,\n+ \"directory\": \"/tmp/integer-mult-export216\",\n+ \"pinned_source_head\": \"34abdc58ed77329c8bf9af5634531fc41939ba3c\",\n+ \"reason\": \"completed disposable replay; evidence saved in review folder; source recoverable from local pinned git ref\"\n+ },\n+ {\n+ \"pr\": 223,\n+ \"directory\": \"/tmp/integer-mult-export223\",\n+ \"pinned_source_head\": \"8786fec0148a41409874cad133123da227d93751\",\n+ \"reason\": \"completed disposable replay; evidence saved in review folder; source recoverable from local pinned git ref\"\n+ },\n+ {\n+ \"pr\": 227,\n+ \"directory\": \"/tmp/integer-mult-export227\",\n+ \"pinned_source_head\": \"418bd6a80f3190d1998780a2fb7f66a073367de1\",\n+ \"reason\": \"completed disposable replay; evidence saved in review folder; source recoverable from local pinned git ref\"\n+ },\n+ {\n+ \"pr\": 233,\n+ \"directory\": \"/tmp/integer-mult-export233\",\n+ \"pinned_source_head\": \"109a857a329d18ed5552d5573f17ddfa886ae57f\",\n+ \"reason\": \"completed disposable replay; evidence saved in review folder; source recoverable from local pinned git ref\"\n+ },\n+ {\n+ \"pr\": 234,\n+ \"directory\": \"/tmp/integer-mult-export234\",\n+ \"pinned_source_head\": \"af3fe331ca60c936229e060681ffccbc1c208678\",\n+ \"reason\": \"completed disposable replay; evidence saved in review folder; source recoverable from local pinned git ref\"\n+ },\n+ {\n+ \"pr\": 235,\n+ \"directory\": \"/tmp/integer-mult-export235\",\n+ \"pinned_source_head\": \"63e3e9e2f852c72634d4b09d0bbb8fcf1081481d\",\n+ \"reason\": \"completed disposable replay; evidence saved in review folder; source recoverable from local pinned git ref\"\n+ },\n+ {\n+ \"pr\": 237,\n+ \"directory\": \"/tmp/integer-mult-export237\",\n+ \"pinned_source_head\": \"a8b0ce212bc9f09353a8161bf8a5cee9cefd600c\",\n+ \"reason\": \"completed disposable replay; evidence saved in review folder; source recoverable from local pinned git ref\"\n+ },\n+ {\n+ \"pr\": 240,\n+ \"directory\": \"/tmp/integer-mult-export240\",\n+ \"pinned_source_head\": \"1068237fdb977f45e68107d118d0eaf0c7a4b516\",\n+ \"reason\": \"completed disposable replay; evidence saved in review folder; source recoverable from local pinned git ref\"\n+ }\n+ ]\n+}"},{"sha":"d6182837d1591f50c66612cc3cb2678129ee370b","filename":"research/community-round9-audit/environment.json","status":"added","additions":9,"deletions":0,"changes":9,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fenvironment.json","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fenvironment.json","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fenvironment.json?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,9 @@\n+{\n+ \"platform\": \"macOS-26.6.2-arm64-arm-64bit-Mach-O\",\n+ \"python\": \"3.14.6 (main, Jun 10 2026, 10:03:53) [Clang 21.0.0 (clang-2100.0.123.102)]\",\n+ \"review_python\": \"3.14.6 (main, Jun 10 2026, 10:03:53) [Clang 21.0.0 (clang-2100.0.123.102)]\\n1.14.0\",\n+ \"scientific_python\": \"3.13.0 (main, Oct 7 2024, 05:02:14) [Clang 16.0.0 (clang-1600.0.26.4)]\\n2.4.6 1.17.1\",\n+ \"cxx\": \"Apple clang version 21.0.0 (clang-2100.3.34.2)\",\n+ \"lean\": \"Lean (version 4.21.0, arm64-apple-darwin23.6.0, commit 6741444a63ee, Release)\",\n+ \"scope\": \"Pinned queue review. Installed scientific versions differ from some requested pins. Darwin memory-limit adapters are individually disclosed; no Linux or global suite pass claimed.\"\n+}"},{"sha":"e742356a25c0aceec390c678287e90a20ae604b5","filename":"research/community-round9-audit/finalize_pr236_audit.py","status":"added","additions":106,"deletions":0,"changes":106,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Ffinalize_pr236_audit.py","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Ffinalize_pr236_audit.py","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Ffinalize_pr236_audit.py?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,106 @@\n+\"\"\"Check a terminal full PR236 build and emit an integrity/axiom receipt.\n+\n+Does not run Lean or turn partial receipts into a full result. The build lock\n+must be released and the original driver must report the complete accepted set.\n+Uses that audited driver's source-plan and axiom parsers, then independently\n+reconstructs the complete receipt/dependency/hash accounting.\n+\"\"\"\n+import argparse\n+import fcntl\n+import hashlib\n+import importlib.util\n+import json\n+from pathlib import Path\n+\n+\n+def check(condition, message):\n+ if not condition:\n+ raise RuntimeError(message)\n+\n+\n+def sha(path):\n+ return hashlib.sha256(path.read_bytes()).hexdigest()\n+\n+\n+def main():\n+ parser = argparse.ArgumentParser(description=__doc__)\n+ parser.add_argument('--build', required=True, type=Path)\n+ parser.add_argument('--source-root', required=True, type=Path)\n+ parser.add_argument('--map', required=True, type=Path)\n+ parser.add_argument('--driver', required=True, type=Path)\n+ parser.add_argument('--lean', required=True, type=Path)\n+ parser.add_argument('--receipt', required=True, type=Path)\n+ args = parser.parse_args()\n+ build = args.build.resolve()\n+ with (build/'build.lock').open('a+') as lock:\n+ try:\n+ fcntl.flock(lock, fcntl.LOCK_EX | fcntl.LOCK_NB)\n+ except BlockingIOError:\n+ print('BUILD_STILL_RUNNING: no final receipt written')\n+ return 3\n+ summary = json.loads((build/'SUMMARY.json').read_text())\n+ check(summary.get('status') == 'FULL_ACCEPTED_SET_COMPILED', 'No completed full build')\n+ check(summary.get('kernel_compiled') is True and summary.get('full_accepted_set') is True,\n+ 'Summary does not assert a full kernel build')\n+ spec = importlib.util.spec_from_file_location('pr236_audited_driver', args.driver)\n+ driver = importlib.util.module_from_spec(spec)\n+ spec.loader.exec_module(driver)\n+ plan, modules, dependencies, order, map_hash = driver.load_plan(args.map, args.source_root)\n+ compiler = driver.toolchain_identity(args.lean.resolve())\n+ check(summary['map_sha256'] == map_hash, 'Map changed')\n+ check(summary['source_commit'] == plan['target_commit'], 'Wrong scientific target')\n+ check(summary['compiler'] == compiler, 'Compiler identity changed')\n+ check(summary['accepted_modules'] == summary['selected_modules'] == len(modules), 'Module coverage')\n+ check(summary['selected_declarations'] == plan['accepted_declarations'], 'Declaration coverage')\n+ check(set(summary['receipts']) == set(modules), 'Summary receipt coverage')\n+ visited = summary['rebuilt'] + summary['reused']\n+ check(len(visited) == len(set(visited)) == len(modules) and set(visited) == set(modules),\n+ 'Rebuilt/reused coverage')\n+ check({p.stem for p in (build/'receipts').glob('*.json')} == set(modules), 'On-disk receipt coverage')\n+ done = {}\n+ declarations = axiom_free = 0\n+ used_axioms = set()\n+ for name in order:\n+ m = modules[name]\n+ receipt = json.loads((build/'receipts'/f'{name}.json').read_text())\n+ check(receipt['status'] == 'PASS' and receipt['compiler_exit'] == 0, f'Compiler failure: {name}')\n+ check(receipt['module'] == name and receipt['map_sha256_when_built'] == map_hash,\n+ f'Receipt identity: {name}')\n+ object_path = build/'objects'/(name.replace('.', '/')+'.olean')\n+ source_path = build/'sources'/(name.replace('.', '/')+'.lean')\n+ log_path = build/'logs'/f'{name}.log'\n+ check(sha(source_path) == m['source_sha256'], f'Compiled source changed: {name}')\n+ check(sha(object_path) == receipt['object_sha256'], f'Object changed: {name}')\n+ check(sha(log_path) == receipt['log_sha256'], f'Log changed: {name}')\n+ expected_key = dict(policy=driver.POLICY, compiler=compiler,\n+ source_sha256=m['source_sha256'], imports=m['imports'],\n+ expected_axiom_commands=m['expected_axiom_commands'],\n+ dependencies={n:done[n]['object_sha256'] for n in dependencies[name]},\n+ timeout_seconds=m.get('timeout_seconds',60), address_space_bytes=None,\n+ lean_jobs=1, lean_stack_kib=65536, allowed_axioms=sorted(driver.ALLOWED_AXIOMS))\n+ check(receipt['build_key'] == expected_key, f'Build/dependency policy changed: {name}')\n+ audit = driver.audit_output(log_path.read_text(), m['expected_axiom_commands'])\n+ check(receipt['audit'] == audit, f'Axiom receipt changed: {name}')\n+ check(hashlib.sha256(json.dumps(receipt, sort_keys=True).encode()).hexdigest()\n+ == summary['receipts'][name], f'Summary binding changed: {name}')\n+ declarations += audit['declarations']\n+ axiom_free += audit['axiom_free']\n+ used_axioms.update(audit['axioms'])\n+ done[name] = receipt\n+ check(declarations == plan['accepted_declarations'], 'Audited declaration coverage')\n+ result = dict(status='FULL_KERNEL_RECEIPTS_REVALIDATED', accepted_modules=len(done),\n+ audited_declarations=declarations, axiom_free_declarations=axiom_free,\n+ allowed_axioms=sorted(driver.ALLOWED_AXIOMS), observed_axioms=sorted(used_axioms),\n+ source_commit=plan['target_commit'], map_sha256=map_hash,\n+ summary_sha256=sha(build/'SUMMARY.json'), driver_sha256=sha(args.driver),\n+ compiler=compiler, address_space_bytes=None,\n+ resource_policy='Darwin audit adapter; no address-space cap; original per-module timeouts',\n+ reused_modules=summary['reused'], rebuilt_modules=len(summary['rebuilt']),\n+ scope=plan['scope'], installed_standard_library_rebuilt=False)\n+ args.receipt.write_text(json.dumps(result,indent=2,sort_keys=True)+'\\n')\n+ print(json.dumps(result,indent=2,sort_keys=True))\n+ return 0\n+\n+\n+if __name__ == '__main__':\n+ raise SystemExit(main())"},{"sha":"b5b91d99bb002241d0ece08689a5e8e4820d3ab3","filename":"research/community-round9-audit/pr162-replay.log.txt","status":"added","additions":6,"deletions":0,"changes":6,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr162-replay.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr162-replay.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr162-replay.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,6 @@\n+[ 19s] PASS control: #161's arcs give #161's certified record exactly; its physical record prices to complex 5885669/10^10 and kappa 5878747/10^10 (next points rejected)\n+[ 40s] PASS extended word: 6249 arcs (48 new), R 15963; repository verify() passes (1742400 signed scalar pairs, 2970 gauges)\n+[ 57s] PASS physical layer: repository checker passes; 8298 moved frames, 2970 pairs (2970 late), W 15633, deficit 1320, replay restored with controls flipped_signed_operation, late_read_before_donor_death, omitted_recipient_read rejected\n+[ 57s] PASS complex saving 5908857/10000000000 = 5.9088570e-04 (next rejected, gap 1.199e-10); bit supplier unchanged at 5.9307713e-04\n+[ 57s] PASS kappa 5901881/10000000000 = 5.9018810e-04 (next 2950941/5000000000 rejected); complex side binds; 47 constraints, 7 margins; largest child 20\n+[ 57s] gain over #161: complex +0.394%, kappa +0.394%"},{"sha":"c8a1b449398f843166f962a953112496e566a881","filename":"research/community-round9-audit/pr178-diff-review.json","status":"added","additions":12,"deletions":0,"changes":12,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr178-diff-review.json","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr178-diff-review.json","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr178-diff-review.json?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,12 @@\n+{\n+ \"pr\": 178,\n+ \"base\": \"2c4a380126640abfcdce398ced255d1dd5d1d007\",\n+ \"head\": \"0bffdfa5aafdc23e668e035ae2b179212b4b3d9a\",\n+ \"changed_files\": [\n+ \"research/paired-cube-frame-refinement/README.md\",\n+ \"research/paired-cube-frame-refinement/SOURCE.json\",\n+ \"research/paired-cube-frame-refinement/validation.json\"\n+ ],\n+ \"diff_sha256\": \"2c8674c594e3c1ccdf28a8e6a375ce6769d7709e8f506928f72b04d4d64fb8f1\",\n+ \"scope\": \"Compared prior/current heads: only README, SOURCE.json and validation.json changed. The mathematical witness and verifier code are unchanged; retain earlier review scope rather than imply a new construction check.\"\n+}"},{"sha":"55ebb5e2df1803ec14a48eb77c5ea63a4d7c600d","filename":"research/community-round9-audit/pr178-reviewed.diff","status":"added","additions":91,"deletions":0,"changes":91,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr178-reviewed.diff","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr178-reviewed.diff","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr178-reviewed.diff?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,91 @@\n+diff --git a/research/paired-cube-frame-refinement/README.md b/research/paired-cube-frame-refinement/README.md\n+index 5374408..594e6c8 100644\n+--- a/research/paired-cube-frame-refinement/README.md\n++++ b/research/paired-cube-frame-refinement/README.md\n+@@ -30,9 +30,11 @@ assembly checks all 47 strict inequalities and seven margins. The adjacent\n+ 10^-14 complex point fails the same conservative rational moment enclosure;\n+ this concerns that fixed enclosure and parameter choice only.\n+ \n+-Validation status: fresh producer, focused baseline, candidate physical and\n+-reflected-word checks, independent full formal execution, and exact assembly\n+-passed locally. The packaged gate is checked before submission. Full repository\n+-verification and research-head GitHub CI are pending; keep this PR draft until\n+-both complete. Finite verification does not establish the inherited all-size\n+-interfaces. See PROOF.md and NOTICE.\n++Validation status: full repository `make -j1 verify` and the packaged verifier\n++passed on frozen research commit `2c4a380126640abfcdce398ced255d1dd5d1d007`\n++on 2026-10-09, in 3340.2324075698853 seconds. The run completed 79 isolated\n++test modules, 20 patch checks and the package's ten corruption controls, with\n++no source drift. All 48 research-head GitHub CI checks passed. See\n++validation.json for the source-bound receipt and evidence hashes. Finite\n++verification does not establish the inherited all-size interfaces. See PROOF.md\n++and NOTICE.\n+diff --git a/research/paired-cube-frame-refinement/SOURCE.json b/research/paired-cube-frame-refinement/SOURCE.json\n+index 7d50608..4bd6c7b 100644\n+--- a/research/paired-cube-frame-refinement/SOURCE.json\n++++ b/research/paired-cube-frame-refinement/SOURCE.json\n+@@ -1060,7 +1060,7 @@\n+ \"research/paired-cube-frame-refinement/EXPERIMENTS.json\": \"9dab9ba8dec1845c35a36f93c8a2150334b637b89f31cb307c008a872406b4b9\",\n+ \"research/paired-cube-frame-refinement/NOTICE\": \"66c90eaaf6256566584b35731e15417a261ce3392f6b125e89ec951949018a6f\",\n+ \"research/paired-cube-frame-refinement/PROOF.md\": \"29e18c2f41d9bc900771b359cd6e7779a60f1cf69872c2ca71e6c5d520f38a81\",\n+- \"research/paired-cube-frame-refinement/README.md\": \"f593b0858536b9e98e5b24857a5ca1d4fddbca18171da974a5d05010ad5910e6\",\n++ \"research/paired-cube-frame-refinement/README.md\": \"ccea702f57321f4ba35fda3b9ca51b80217abff05326a0fbddd8dd87ee3fb472\",\n+ \"research/paired-cube-frame-refinement/arithmetic.py\": \"a1fffbeb24370e6c1ec080ef9354e980243e64661b42883c9184908bc9e5b306\",\n+ \"research/paired-cube-frame-refinement/audit/check_sinks.py\": \"d70903464b3caabc0920aee8953978a27a6874a655ecb66cadacf77a31df11af\",\n+ \"research/paired-cube-frame-refinement/audit/formal_sinks.py\": \"d7fefe86e637584ad1bf53c8f7714b88d5abed92eaa29d110ef099536e51f516\",\n+diff --git a/research/paired-cube-frame-refinement/validation.json b/research/paired-cube-frame-refinement/validation.json\n+new file mode 100644\n+index 0000000..4fbbd45\n+--- /dev/null\n++++ b/research/paired-cube-frame-refinement/validation.json\n+@@ -0,0 +1,50 @@\n++{\n++ \"status\": \"PASS full frozen research-head verification\",\n++ \"pull_request\": \"https://github.com/CrocSwap/integer-mult-bounds/pull/178\",\n++ \"tested_research_commit\": \"2c4a380126640abfcdce398ced255d1dd5d1d007\",\n++ \"verification_started_at\": \"2026-10-09T11:13:05.858300+00:00\",\n++ \"verification_completed_at\": \"2026-10-09T12:08:46.090649+00:00\",\n++ \"elapsed_seconds\": 3340.2324075698853,\n++ \"platform\": \"Linux Daytona python:3.11-slim with g++ and libboost-dev\",\n++ \"compiler\": \"c++ -include algorithm\",\n++ \"commands\": [\n++ [\n++ \"make\",\n++ \"-j1\",\n++ \"verify\"\n++ ],\n++ [\n++ \"python\",\n++ \"research/paired-cube-frame-refinement/verify.py\"\n++ ]\n++ ],\n++ \"coverage\": {\n++ \"isolated_test_modules\": 79,\n++ \"patch_apply_checks\": 20,\n++ \"packaged_mutation_controls\": 10,\n++ \"assembly_strict_constraints\": 47,\n++ \"assembly_margins\": 7,\n++ \"formal_columns_both_signs\": 13655,\n++ \"dirty_registers_restored\": 11015\n++ },\n++ \"source_drift\": {\n++ \"git_status\": \"\",\n++ \"patch_bytes\": 0,\n++ \"tracked_drift\": []\n++ },\n++ \"source_pins_verified\": 1682,\n++ \"evidence\": {\n++ \"archive_name\": \"full-verify-evidence.tar.gz\",\n++ \"archive_sha256\": \"e8277c1f7164ab8871ab5b6d799dc1254159367e4110ef3968b9e303c7cb8cbd\",\n++ \"full_log_sha256\": \"3871c4f2d466a78f0f5cd5b475480f0508be387a63031b0e1bef462ca8a34e3f\",\n++ \"runner_sha256\": \"dd9b9f4fd6dd49c53c765ca89600bf97a817d3e4decf4a496e0377654ddd1b19\"\n++ },\n++ \"github_ci\": {\n++ \"research_head\": \"2c4a380126640abfcdce398ced255d1dd5d1d007\",\n++ \"checked_at\": \"2026-10-09T12:19:24.567222+00:00\",\n++ \"completed_successful_checks\": 48,\n++ \"failed_checks\": 0,\n++ \"pending_checks\": 0\n++ },\n++ \"scope\": \"Full verification and CI apply to the frozen research commit above. A following receipt/documentation-only commit is not claimed to have been the tested research head. Conditional all-size interfaces remain unproved by finite tests.\"\n++}"},{"sha":"2f910819d3d63e5a63c40556766062b421cafdce","filename":"research/community-round9-audit/pr180-arithmetic.log.txt","status":"added","additions":1,"deletions":0,"changes":1,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr180-arithmetic.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr180-arithmetic.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr180-arithmetic.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1 @@\n+PASS pinned186 conditional kappa=330942774629799608347/500000000000000000000000; both full moments,47 strict constraints,7 margins,first atom and next grids; complex limiter; separate finite scalar/bank checks and inherited all-size contracts remain explicit"},{"sha":"48b2cc043fc35dea2c7b388f8875b4481f0257ab","filename":"research/community-round9-audit/pr180-check_banks-optimized.log.txt","status":"added","additions":144,"deletions":0,"changes":144,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr180-check_banks-optimized.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr180-check_banks-optimized.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr180-check_banks-optimized.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,144 @@\n+{\n+ \"address_maps\": [\n+ {\n+ \"blocks\": 18,\n+ \"rings\": {\n+ \"0\": {\n+ \"False\": {\n+ \"endpoint_columns\": 144,\n+ \"inverse_columns\": 144\n+ },\n+ \"True\": {\n+ \"endpoint_columns\": 144,\n+ \"inverse_columns\": 144\n+ },\n+ \"controls\": {\n+ \"inconsistent_common_chart\": \"endpoint column 71\",\n+ \"omit\": \"endpoint column 68\",\n+ \"repeat\": \"endpoint column 68\"\n+ }\n+ },\n+ \"2\": {\n+ \"False\": {\n+ \"endpoint_columns\": 144,\n+ \"inverse_columns\": 144\n+ },\n+ \"True\": {\n+ \"endpoint_columns\": 144,\n+ \"inverse_columns\": 144\n+ },\n+ \"controls\": {\n+ \"inconsistent_common_chart\": \"endpoint column 71\",\n+ \"omit\": \"endpoint column 68\",\n+ \"repeat\": \"endpoint column 68\"\n+ }\n+ }\n+ },\n+ \"width\": 4\n+ },\n+ {\n+ \"blocks\": 3,\n+ \"rings\": {\n+ \"0\": {\n+ \"False\": {\n+ \"endpoint_columns\": 144,\n+ \"inverse_columns\": 144\n+ },\n+ \"True\": {\n+ \"endpoint_columns\": 144,\n+ \"inverse_columns\": 144\n+ },\n+ \"controls\": {\n+ \"inconsistent_common_chart\": \"endpoint column 71\",\n+ \"omit\": \"endpoint column 48\",\n+ \"repeat\": \"endpoint column 48\"\n+ }\n+ },\n+ \"2\": {\n+ \"False\": {\n+ \"endpoint_columns\": 144,\n+ \"inverse_columns\": 144\n+ },\n+ \"True\": {\n+ \"endpoint_columns\": 144,\n+ \"inverse_columns\": 144\n+ },\n+ \"controls\": {\n+ \"inconsistent_common_chart\": \"endpoint column 71\",\n+ \"omit\": \"endpoint column 48\",\n+ \"repeat\": \"endpoint column 48\"\n+ }\n+ }\n+ },\n+ \"width\": 24\n+ }\n+ ],\n+ \"all_basis_columns_per_ring\": 144,\n+ \"allocation\": {\n+ \"aliases\": 1760,\n+ \"deficit\": 1936,\n+ \"edge_count\": 296710,\n+ \"entrance_rank20\": 2200,\n+ \"literal_stock\": 177432,\n+ \"logical_roles\": 19788,\n+ \"mass\": 1417520,\n+ \"normalized_stock\": \"59144/3\",\n+ \"physical_roles\": 18028,\n+ \"recipient_rank21_internal\": 1760,\n+ \"removed_rank60\": 2200,\n+ \"replicas\": 9,\n+ \"retained_child_histogram\": {\n+ \"1\": 125448,\n+ \"2\": 62908,\n+ \"3\": 29616,\n+ \"4\": 8970,\n+ \"5\": 7800,\n+ \"6\": 3660,\n+ \"7\": 3312,\n+ \"8\": 2802,\n+ \"9\": 1812,\n+ \"10\": 2508,\n+ \"11\": 1158,\n+ \"12\": 4320,\n+ \"13\": 1590,\n+ \"14\": 3234,\n+ \"15\": 1230,\n+ \"16\": 3216,\n+ \"17\": 1164,\n+ \"18\": 1332,\n+ \"19\": 918,\n+ \"20\": 5280,\n+ \"21\": 11160,\n+ \"22\": 13272\n+ },\n+ \"retained_rank21_children\": 11160,\n+ \"selected_banks_per_stage\": 1100,\n+ \"undeferred_banks_per_stage\": 47484,\n+ \"undeferred_roles\": 15828\n+ },\n+ \"bank_profile_sha256\": \"29489011434764f2a0c934222e553b22428ee2de5b890b850caf43dc6feb32e2\",\n+ \"ledger_controls\": {\n+ \"eight_replicas_not_integral\": \"selected bank allocation nonintegral\",\n+ \"fallback_count_unscaled\": \"fallback bill divided by3\",\n+ \"omit_rank21_children\": \"retained internal rank21 children deleted\",\n+ \"rank21_as_new_entrances\": \"recipient splice double counted\"\n+ },\n+ \"native_input_sha256\": {\n+ \"references/paired-cube/bit-physical/word_p12.json.gz\": \"6f10239e8e2946263c7959392edd7c4e48661708a4d83222acb7cf6297783928\",\n+ \"research/paired-cube-bit/out/profile_p12.json\": \"12187fd2e4c66349c3c111311f00d57fe2180a0dcf11973457821b28b76c39b9\"\n+ },\n+ \"optimized\": true,\n+ \"original_histogram_sha256\": \"6735294e8639da09eb3eb2234cbc5814298442a6c946b5534bcf6e48903547f3\",\n+ \"scale3\": {\n+ \"bad_fraction\": \"1/10000000000000000\",\n+ \"characteristic_and_fallback_coefficients_unchanged\": true,\n+ \"deficit\": 5808,\n+ \"edge_count\": 890130,\n+ \"fallback_children_per_edge\": 165888,\n+ \"mass\": 4252560,\n+ \"stock\": 59144\n+ },\n+ \"scope\": \"Exact finite address maps/inverses over Z and F2 and declared replica allocation; native word byte pins and physical entrance classes/deadlines only. No producer/native module imported; no weighted compiler, tensor/Clifford, common-chart existence, multibank paid routing/restoration, all-size or new moment acceptance.\",\n+ \"seconds\": 1.1085584169995855,\n+ \"status\": \"finite_bank_endpoint_and_allocation_pass\"\n+}"},{"sha":"df2b11532a444ad71a1677ecbd5ada209c0669fc","filename":"research/community-round9-audit/pr180-check_banks.log.txt","status":"added","additions":144,"deletions":0,"changes":144,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr180-check_banks.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr180-check_banks.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr180-check_banks.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,144 @@\n+{\n+ \"address_maps\": [\n+ {\n+ \"blocks\": 18,\n+ \"rings\": {\n+ \"0\": {\n+ \"False\": {\n+ \"endpoint_columns\": 144,\n+ \"inverse_columns\": 144\n+ },\n+ \"True\": {\n+ \"endpoint_columns\": 144,\n+ \"inverse_columns\": 144\n+ },\n+ \"controls\": {\n+ \"inconsistent_common_chart\": \"endpoint column 71\",\n+ \"omit\": \"endpoint column 68\",\n+ \"repeat\": \"endpoint column 68\"\n+ }\n+ },\n+ \"2\": {\n+ \"False\": {\n+ \"endpoint_columns\": 144,\n+ \"inverse_columns\": 144\n+ },\n+ \"True\": {\n+ \"endpoint_columns\": 144,\n+ \"inverse_columns\": 144\n+ },\n+ \"controls\": {\n+ \"inconsistent_common_chart\": \"endpoint column 71\",\n+ \"omit\": \"endpoint column 68\",\n+ \"repeat\": \"endpoint column 68\"\n+ }\n+ }\n+ },\n+ \"width\": 4\n+ },\n+ {\n+ \"blocks\": 3,\n+ \"rings\": {\n+ \"0\": {\n+ \"False\": {\n+ \"endpoint_columns\": 144,\n+ \"inverse_columns\": 144\n+ },\n+ \"True\": {\n+ \"endpoint_columns\": 144,\n+ \"inverse_columns\": 144\n+ },\n+ \"controls\": {\n+ \"inconsistent_common_chart\": \"endpoint column 71\",\n+ \"omit\": \"endpoint column 48\",\n+ \"repeat\": \"endpoint column 48\"\n+ }\n+ },\n+ \"2\": {\n+ \"False\": {\n+ \"endpoint_columns\": 144,\n+ \"inverse_columns\": 144\n+ },\n+ \"True\": {\n+ \"endpoint_columns\": 144,\n+ \"inverse_columns\": 144\n+ },\n+ \"controls\": {\n+ \"inconsistent_common_chart\": \"endpoint column 71\",\n+ \"omit\": \"endpoint column 48\",\n+ \"repeat\": \"endpoint column 48\"\n+ }\n+ }\n+ },\n+ \"width\": 24\n+ }\n+ ],\n+ \"all_basis_columns_per_ring\": 144,\n+ \"allocation\": {\n+ \"aliases\": 1760,\n+ \"deficit\": 1936,\n+ \"edge_count\": 296710,\n+ \"entrance_rank20\": 2200,\n+ \"literal_stock\": 177432,\n+ \"logical_roles\": 19788,\n+ \"mass\": 1417520,\n+ \"normalized_stock\": \"59144/3\",\n+ \"physical_roles\": 18028,\n+ \"recipient_rank21_internal\": 1760,\n+ \"removed_rank60\": 2200,\n+ \"replicas\": 9,\n+ \"retained_child_histogram\": {\n+ \"1\": 125448,\n+ \"2\": 62908,\n+ \"3\": 29616,\n+ \"4\": 8970,\n+ \"5\": 7800,\n+ \"6\": 3660,\n+ \"7\": 3312,\n+ \"8\": 2802,\n+ \"9\": 1812,\n+ \"10\": 2508,\n+ \"11\": 1158,\n+ \"12\": 4320,\n+ \"13\": 1590,\n+ \"14\": 3234,\n+ \"15\": 1230,\n+ \"16\": 3216,\n+ \"17\": 1164,\n+ \"18\": 1332,\n+ \"19\": 918,\n+ \"20\": 5280,\n+ \"21\": 11160,\n+ \"22\": 13272\n+ },\n+ \"retained_rank21_children\": 11160,\n+ \"selected_banks_per_stage\": 1100,\n+ \"undeferred_banks_per_stage\": 47484,\n+ \"undeferred_roles\": 15828\n+ },\n+ \"bank_profile_sha256\": \"29489011434764f2a0c934222e553b22428ee2de5b890b850caf43dc6feb32e2\",\n+ \"ledger_controls\": {\n+ \"eight_replicas_not_integral\": \"selected bank allocation nonintegral\",\n+ \"fallback_count_unscaled\": \"fallback bill divided by3\",\n+ \"omit_rank21_children\": \"retained internal rank21 children deleted\",\n+ \"rank21_as_new_entrances\": \"recipient splice double counted\"\n+ },\n+ \"native_input_sha256\": {\n+ \"references/paired-cube/bit-physical/word_p12.json.gz\": \"6f10239e8e2946263c7959392edd7c4e48661708a4d83222acb7cf6297783928\",\n+ \"research/paired-cube-bit/out/profile_p12.json\": \"12187fd2e4c66349c3c111311f00d57fe2180a0dcf11973457821b28b76c39b9\"\n+ },\n+ \"optimized\": false,\n+ \"original_histogram_sha256\": \"6735294e8639da09eb3eb2234cbc5814298442a6c946b5534bcf6e48903547f3\",\n+ \"scale3\": {\n+ \"bad_fraction\": \"1/10000000000000000\",\n+ \"characteristic_and_fallback_coefficients_unchanged\": true,\n+ \"deficit\": 5808,\n+ \"edge_count\": 890130,\n+ \"fallback_children_per_edge\": 165888,\n+ \"mass\": 4252560,\n+ \"stock\": 59144\n+ },\n+ \"scope\": \"Exact finite address maps/inverses over Z and F2 and declared replica allocation; native word byte pins and physical entrance classes/deadlines only. No producer/native module imported; no weighted compiler, tensor/Clifford, common-chart existence, multibank paid routing/restoration, all-size or new moment acceptance.\",\n+ \"seconds\": 1.055727917000695,\n+ \"status\": \"finite_bank_endpoint_and_allocation_pass\"\n+}"},{"sha":"ac7675469a580e2c941deb4c22dd92eb5369ed54","filename":"research/community-round9-audit/pr180-scalar.log.txt","status":"added","additions":72,"deletions":0,"changes":72,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr180-scalar.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr180-scalar.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr180-scalar.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,72 @@\n+{\n+ \"aliases\": 2310,\n+ \"controls\": {\n+ \"omit_compensated_read\": {\n+ \"reason\": \"target bank row 942\",\n+ \"rejected\": true\n+ },\n+ \"omit_post_shear\": {\n+ \"reason\": \"target bank row 297\",\n+ \"rejected\": true\n+ },\n+ \"wrong_dirty_inverse\": {\n+ \"reason\": \"dirty restore row 28\",\n+ \"rejected\": true\n+ },\n+ \"wrong_pivot_sign\": {\n+ \"reason\": \"target bank row 672\",\n+ \"rejected\": true\n+ },\n+ \"wrong_reflection_sign\": {\n+ \"reason\": \"target bank row 8\",\n+ \"rejected\": true\n+ }\n+ },\n+ \"elapsed_seconds\": 48.48919145900072,\n+ \"event_sha256\": \"955c165a922de2a901e6b9a2c2ee71836443379d56e3f355b89c0b5c29209f7d\",\n+ \"limits\": {\n+ \"required_external_memory_limit_bytes\": 4294967296,\n+ \"seconds\": 180,\n+ \"workers\": 1\n+ },\n+ \"native_response_correspondence\": {\n+ \"exact_all_center_and_side_responses_equal\": true,\n+ \"operations\": 32971,\n+ \"per_role_order_preserved\": true,\n+ \"response_sha256\": \"698e3c06c77929653877a6d93aa359bf31c80858b4c78767ebce98b3b87847f9\",\n+ \"roles\": 13042\n+ },\n+ \"positive\": {\n+ \"forward\": {\n+ \"all_absent_coefficients_checked\": true,\n+ \"dirty_rows\": 10686,\n+ \"events\": 87195,\n+ \"formal_basis\": 13326,\n+ \"forward\": true,\n+ \"largest_final_denominator\": 6,\n+ \"reflected\": false,\n+ \"ring\": \"Q via integer numerators/adaptive denominators\",\n+ \"source_rows\": 1320,\n+ \"target_rows\": 1320\n+ },\n+ \"reflected\": {\n+ \"all_absent_coefficients_checked\": true,\n+ \"dirty_rows\": 10686,\n+ \"events\": 87195,\n+ \"formal_basis\": 13326,\n+ \"forward\": false,\n+ \"largest_final_denominator\": 24,\n+ \"reflected\": true,\n+ \"ring\": \"Q via integer numerators/adaptive denominators\",\n+ \"source_rows\": 1320,\n+ \"target_rows\": 1320\n+ }\n+ },\n+ \"reflection_gates\": 330,\n+ \"retained_dirty\": 10686,\n+ \"role_count\": 13042,\n+ \"scope\": \"Exact finite scalar maps on the full source, target and retained dirty basis; sink eligibility checks. Full frame/phase/all-size proof not certified.\",\n+ \"sink_count\": 46,\n+ \"sparse_term_additions\": 130405468,\n+ \"status\": \"computed_pass\"\n+}"},{"sha":"c51047b61d0dbd0fb18a472e8d3cd512da4a6903","filename":"research/community-round9-audit/pr180-test_refinement-optimized.log.txt","status":"added","additions":5,"deletions":0,"changes":5,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr180-test_refinement-optimized.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr180-test_refinement-optimized.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr180-test_refinement-optimized.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,5 @@\n+...........\n+----------------------------------------------------------------------\n+Ran 11 tests in 0.437s\n+\n+OK"},{"sha":"e54ff12974715b1cf482c558e66311c9c1d98ad2","filename":"research/community-round9-audit/pr180-test_refinement.log.txt","status":"added","additions":5,"deletions":0,"changes":5,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr180-test_refinement.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr180-test_refinement.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr180-test_refinement.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,5 @@\n+...........\n+----------------------------------------------------------------------\n+Ran 11 tests in 0.375s\n+\n+OK"},{"sha":"84faabb38668db693e640c2ddd8ffe3888a314b9","filename":"research/community-round9-audit/pr180-test_source-optimized.log.txt","status":"added","additions":5,"deletions":0,"changes":5,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr180-test_source-optimized.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr180-test_source-optimized.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr180-test_source-optimized.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,5 @@\n+........\n+----------------------------------------------------------------------\n+Ran 8 tests in 0.287s\n+\n+OK"},{"sha":"2e994a4217af7b4d260cd4be97ddb9252811547a","filename":"research/community-round9-audit/pr180-test_source.log.txt","status":"added","additions":5,"deletions":0,"changes":5,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr180-test_source.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr180-test_source.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr180-test_source.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,5 @@\n+........\n+----------------------------------------------------------------------\n+Ran 8 tests in 0.275s\n+\n+OK"},{"sha":"497f8c866e5e611a6080b7677ad6ce63806c224b","filename":"research/community-round9-audit/pr187-replay.log.txt","status":"added","additions":225,"deletions":0,"changes":225,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr187-replay.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr187-replay.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr187-replay.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,225 @@\n+PASS 1733 immutable source pins\n+PASS actual emitted histogram and scalar guard; exact paid moments; finite leaf bootstrap; 47 constraints,7 margins,8 controls andadjacentgrids\n+kappa=330877589979561/500000000000000000\n+network captured\n+{\"R\": 19348, \"physical_R\": 17588, \"ops\": 64824, \"cut\": 30224, \"low_matrices\": 7672, \"low_controls\": 5280, \"pairs\": 1760, \"gauges\": 3960}\n+{\n+ \"status\": \"PASS\",\n+ \"h\": 24,\n+ \"used_frames\": 24161,\n+ \"parent_covered_frames\": 23869,\n+ \"parent_covered_bases\": 23869,\n+ \"supplemental_frames\": 292,\n+ \"supplemental_bases\": 292,\n+ \"parent_witness_sha256\": \"8a9a48e52117e2b0fb6b8f929a762b76cac88045f91a7e610d2b23c84c629da5\",\n+ \"parent_arithmetic_sha256\": \"98cd03bc9582e7bd0ab194c191ea8eea940539e510051443ab9fd3e572a364ab\",\n+ \"frame_source_sha256\": \"d2347635891e70918171b96ae33c9cb667cec11cdb7b8f634685b3df8c7effc1\",\n+ \"used_frame_basis_manifest_sha256\": \"952e47141b19a3ee0acfc74f3ebdc79a5ae87b1439bca635fe9519439d0a0edb\",\n+ \"stripped_primes\": [\n+ 2,\n+ 3,\n+ 5,\n+ 7,\n+ 11,\n+ 13,\n+ 17,\n+ 19,\n+ 23,\n+ 29,\n+ 31\n+ ],\n+ \"prime_lower_bound\": 1208925819614629174706176,\n+ \"prime_guard_unchanged\": true,\n+ \"maximum_supplemental_determinant_bits\": 79,\n+ \"maximum_supplemental_remaining_factor\": 1,\n+ \"adverse_controls\": [\n+ \"zero_determinant\",\n+ \"incorrect_factor_identity\",\n+ \"factor_at_or_above_inherited_prime_floor\",\n+ \"missing_supplemental_basis\"\n+ ],\n+ \"scope\": \"Canonical basis hashes bind all emitted frames to pinned retained exact Gram witnesses or explicitly recomputed supplemental Bareiss witnesses. Retained determinant values rely on the independently verified immutable parent witness; factor identities are rechecked here. Every q>2^80 remains valid. Complement formula denominators 3 and5 are already excluded.\"\n+}\n+{\n+ \"status\": \"PASS\",\n+ \"scope\": \"Exact emitted elementary-word geometry, source-control chronology, target chronology, all paid chains; independent dirty replay separate\",\n+ \"source_head\": \"2c4a380126640abfcdce398ced255d1dd5d1d007\",\n+ \"R\": 19348,\n+ \"physical_R\": 17588,\n+ \"m\": 72,\n+ \"W_per_vertex\": 21108,\n+ \"rank_per_vertex\": 1517840,\n+ \"deficit_per_vertex\": 1936,\n+ \"operations\": 64824,\n+ \"source_controls\": 5280,\n+ \"span_membership_checks\": 1680600,\n+ \"local_histogram\": {\n+ \"1\": 33896,\n+ \"2\": 19356,\n+ \"3\": 9872,\n+ \"4\": 2990,\n+ \"5\": 2600,\n+ \"6\": 1220,\n+ \"7\": 1104,\n+ \"8\": 934,\n+ \"9\": 604,\n+ \"10\": 836,\n+ \"11\": 386,\n+ \"12\": 1440,\n+ \"13\": 530,\n+ \"14\": 1078,\n+ \"15\": 410,\n+ \"16\": 1072,\n+ \"17\": 388,\n+ \"18\": 444,\n+ \"19\": 306,\n+ \"21\": 2840,\n+ \"22\": 3104\n+ },\n+ \"source_data_histogram\": {\n+ \"1\": 1760,\n+ \"2\": 880,\n+ \"20\": 880,\n+ \"22\": 880\n+ },\n+ \"target_data_histogram\": {\n+ \"1\": 4400,\n+ \"20\": 880,\n+ \"21\": 880\n+ },\n+ \"child_histogram\": {\n+ \"1\": 120168,\n+ \"2\": 64228,\n+ \"3\": 29616,\n+ \"4\": 8970,\n+ \"5\": 7800,\n+ \"6\": 3660,\n+ \"7\": 3312,\n+ \"8\": 2802,\n+ \"9\": 1812,\n+ \"10\": 2508,\n+ \"11\": 1158,\n+ \"12\": 4320,\n+ \"13\": 1590,\n+ \"14\": 3234,\n+ \"15\": 1230,\n+ \"16\": 3216,\n+ \"17\": 1164,\n+ \"18\": 1332,\n+ \"19\": 918,\n+ \"20\": 5280,\n+ \"21\": 11160,\n+ \"22\": 11952,\n+ \"60\": 2200\n+ },\n+ \"exact_network_histogram_equal\": true,\n+ \"word_sha256\": \"3c188c2527b3b96443e241f2f0d07c120feb1e784c2ff7f49c3e1e10eaea5f0b\"\n+}\n+{\n+ \"elementary_forward_xors\": 64824,\n+ \"elementary_inverse_xors\": 64824,\n+ \"old_value_response_xors\": 743312,\n+ \"root_read_xors\": 14080,\n+ \"partner_mix_forward_inverse_xors\": 1760,\n+ \"partner_delivery_xors\": 1760,\n+ \"total_scalar_xors\": 890560,\n+ \"original_X_controls\": 5280,\n+ \"nongauged_response_xors\": 737152,\n+ \"gauged_response_xors\": 6160,\n+ \"payload_coefficient_alphabet\": [\n+ 0,\n+ 1\n+ ],\n+ \"maximum_absolute_payload_shear_coefficient\": 1,\n+ \"integer_non_cancelling_majorants\": {\n+ \"maximum_aux_old_read_row_l1\": 2820,\n+ \"sum_aux_old_read_row_l1\": 5442384,\n+ \"maximum_X_adjoint_row_l1\": 3049,\n+ \"maximum_forward_and_inverse_row_l1\": 442955,\n+ \"interpretation\": \"Noncancelling defining-integer-word coefficient majorants, not exact coefficient maxima or an integer identity. F2 adjoints are separately stored in emitted word.\"\n+ },\n+ \"note\": \"XOR scalar transcript counts only. Frame adapters, inverses and base-case bit implementation remain covered by assembled supplier guard. Every emitted payload shear already has unit coefficient overF2; no decomposition needed.\"\n+}\n+{\n+ \"status\": \"PASS\",\n+ \"word_sha256\": \"3c188c2527b3b96443e241f2f0d07c120feb1e784c2ff7f49c3e1e10eaea5f0b\",\n+ \"logical_auxiliary_roles\": 19348,\n+ \"physical_auxiliary_roles\": 17588,\n+ \"source_columns\": 1760,\n+ \"target_columns\": 1760,\n+ \"dirty_columns\": 17588,\n+ \"total_independent_columns\": 21108,\n+ \"literal_elementary_operations\": 890560,\n+ \"forward_auxiliary_operations\": 64824,\n+ \"original_source_control_operations\": 5280,\n+ \"gauges\": 3960,\n+ \"pairs\": 1760,\n+ \"baseline\": {\n+ \"exact_map\": true,\n+ \"bad_source_rows\": 0,\n+ \"bad_target_rows\": 0,\n+ \"bad_dirty_rows\": 0,\n+ \"first_bad_rows\": []\n+ },\n+ \"full_time_reverse\": {\n+ \"exact_map\": true,\n+ \"bad_source_rows\": 0,\n+ \"bad_target_rows\": 0,\n+ \"bad_dirty_rows\": 0,\n+ \"first_bad_rows\": []\n+ },\n+ \"negative_controls\": {\n+ \"omit_forward_new_X\": {\n+ \"exact_map\": false,\n+ \"bad_source_rows\": 0,\n+ \"bad_target_rows\": 76,\n+ \"bad_dirty_rows\": 1,\n+ \"first_bad_rows\": [\n+ 1760,\n+ 1761,\n+ 1762\n+ ]\n+ },\n+ \"omit_inverse_new_X\": {\n+ \"exact_map\": false,\n+ \"bad_source_rows\": 0,\n+ \"bad_target_rows\": 0,\n+ \"bad_dirty_rows\": 1,\n+ \"first_bad_rows\": [\n+ 9680\n+ ]\n+ },\n+ \"omit_compensated_read\": {\n+ \"exact_map\": false,\n+ \"bad_source_rows\": 0,\n+ \"bad_target_rows\": 1,\n+ \"bad_dirty_rows\": 0,\n+ \"first_bad_rows\": [\n+ 1915\n+ ]\n+ }\n+ },\n+ \"integer_lift\": {\n+ \"exact_unit_shear_inverse_certified\": true,\n+ \"global_inverse_argument\": \"Literal reverse word with negated unit coefficients; adjacent inverse pairs cancel over Z on all coordinates.\",\n+ \"integer_decoder_identity_claimed\": false,\n+ \"sample_replays\": [\n+ {\n+ \"seed\": 1701,\n+ \"source_and_dirty_restored\": true,\n+ \"bit_decoder_parity\": true,\n+ \"whole_word_signed_inverse_restored\": true\n+ },\n+ {\n+ \"seed\": 3402,\n+ \"source_and_dirty_restored\": true,\n+ \"bit_decoder_parity\": true,\n+ \"whole_word_signed_inverse_restored\": true\n+ }\n+ ]\n+ },\n+ \"mutation_new_X_operation\": 11880,\n+ \"elapsed_seconds\": 7.096212584001478,\n+ \"scope\": \"Exact F2 scalar maps: Y+=X, all original X and arbitrary dirty Z restored, every Y column retained. Whole-word inverse has same scalar map in F2. Actual complemented-frame geometry uses the separate reflection lemma and forward frame certification.\"\n+}\n+PASS literal emitted BIT word, conservative geometry, paid histogram, scalar count, all-column forward/reflection and mutation controls"},{"sha":"8bc9243fb91650ae9e5465321df1ffd8fc9282ed","filename":"research/community-round9-audit/pr188-adapted.log.txt","status":"added","additions":20,"deletions":0,"changes":20,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr188-adapted.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr188-adapted.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr188-adapted.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,20 @@\n+Rebuilding signed complex word, full intersections and scalar decoder...\n+Regenerating paired-cube signed DAG from inherited PR117 restrictions\n+Replaying frozen carrier matching and full binary intersections\n+Selecting chronological partial gauges and constructing signed physical M\n+Independently checking signed scalar identity, K, physical word, intersections and target chains\n+Checking independent terminal plan and all rational columns of the actual new executor...\n+Regenerating merged bit word from frozen arcs...\n+Traceback (most recent call last):\n+ File \"/private/tmp/integer-mult-export188/research/paired-cube-terminal-reuse/verify.py\", line 117, in \n+ if __name__=='__main__':main()\n+ ~~~~^^\n+ File \"/private/tmp/integer-mult-export188/research/paired-cube-terminal-reuse/verify.py\", line 109, in main\n+ result=verify();encoded=json.dumps(result,indent=2,sort_keys=True)+'\\n'\n+ File \"/private/tmp/integer-mult-export188/research/paired-cube-terminal-reuse/verify.py\", line 86, in verify\n+ require(bp==json.loads((HERE/'selected/bit/profile.json').read_text()),'Frozen bit row differs')\n+ ~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n+ File \"/private/tmp/integer-mult-export188/research/paired-cube-terminal-reuse/verify.py\", line 30, in require\n+ if not ok:raise ValueError(message)\n+ ^^^^^^^^^^^^^^^^^^^^^^^^^\n+ValueError: Frozen bit row differs"},{"sha":"287168886a2c229ad7e6d67720350a1cf04269b0","filename":"research/community-round9-audit/pr188-darwin-sitecustomize.py","status":"added","additions":9,"deletions":0,"changes":9,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr188-darwin-sitecustomize.py","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr188-darwin-sitecustomize.py","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr188-darwin-sitecustomize.py?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,9 @@\n+\"\"\"Maintainer audit only: retain CPU limits, omit unsupported Darwin RLIMIT_AS.\"\"\"\n+import resource, sys\n+_original_setrlimit = resource.setrlimit\n+def _portable_setrlimit(which, limits):\n+ if sys.platform == \"darwin\" and which == resource.RLIMIT_AS:\n+ print(\"MAINTAINER ADAPTER: RLIMIT_AS omitted on Darwin; no address-space cap claimed\", file=sys.stderr)\n+ return\n+ return _original_setrlimit(which, limits)\n+resource.setrlimit = _portable_setrlimit"},{"sha":"0f8682049533ef1eb3e0cbac6fa73321cc7e7dc9","filename":"research/community-round9-audit/pr188-native-failure.log.txt","status":"added","additions":28,"deletions":0,"changes":28,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr188-native-failure.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr188-native-failure.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr188-native-failure.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,28 @@\n+Rebuilding signed complex word, full intersections and scalar decoder...\n+Regenerating paired-cube signed DAG from inherited PR117 restrictions\n+Replaying frozen carrier matching and full binary intersections\n+Selecting chronological partial gauges and constructing signed physical M\n+Independently checking signed scalar identity, K, physical word, intersections and target chains\n+Checking independent terminal plan and all rational columns of the actual new executor...\n+Traceback (most recent call last):\n+ File \"/private/tmp/integer-mult-export188/research/paired-cube-terminal-reuse/verify.py\", line 117, in \n+ if __name__=='__main__':main()\n+ ~~~~^^\n+ File \"/private/tmp/integer-mult-export188/research/paired-cube-terminal-reuse/verify.py\", line 109, in main\n+ result=verify();encoded=json.dumps(result,indent=2,sort_keys=True)+'\\n'\n+ File \"/private/tmp/integer-mult-export188/research/paired-cube-terminal-reuse/verify.py\", line 76, in verify\n+ complex_result=terminal.certify(g,witness,word,row,before,frames,pairs)\n+ File \"/private/tmp/integer-mult-export188/research/paired-cube-terminal-reuse/terminal.py\", line 185, in certify\n+ plan=independent_plan(g,witness,word,row,profile,frames,pairs)\n+ File \"/private/tmp/integer-mult-export188/research/paired-cube-terminal-reuse/terminal.py\", line 45, in independent_plan\n+ raise ValueError('Independent terminal compiler rejected the word:\\n'+result.stderr)\n+ValueError: Independent terminal compiler rejected the word:\n+Traceback (most recent call last):\n+ File \"/private/tmp/integer-mult-export188/research/paired-cube-terminal-reuse/references/pr166_check_sink_accumulator.py\", line 203, in \n+ if __name__=='__main__':main()\n+ ~~~~^^\n+ File \"/private/tmp/integer-mult-export188/research/paired-cube-terminal-reuse/references/pr166_check_sink_accumulator.py\", line 20, in main\n+ resource.setrlimit(resource.RLIMIT_CPU,(60,60));resource.setrlimit(resource.RLIMIT_AS,(768*1024**2,768*1024**2));signal.alarm(60)\n+ ~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n+ValueError: current limit exceeds maximum limit\n+"},{"sha":"33740543878a5fa1117f142160215cbca1acc7ca","filename":"research/community-round9-audit/pr188-portable-fresh.json","status":"added","additions":2923,"deletions":0,"changes":2923,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr188-portable-fresh.json","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr188-portable-fresh.json","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr188-portable-fresh.json?ref=12a4934d15006e8c10f9b2264f13f8f341be802b"},{"sha":"18a28a163794b93328fecdd8a457a427976ca89f","filename":"research/community-round9-audit/pr188-portable.log.txt","status":"added","additions":10,"deletions":0,"changes":10,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr188-portable.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr188-portable.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr188-portable.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,10 @@\n+Rebuilding signed complex word, full intersections and scalar decoder...\n+Regenerating paired-cube signed DAG from inherited PR117 restrictions\n+Replaying frozen carrier matching and full binary intersections\n+Selecting chronological partial gauges and constructing signed physical M\n+Independently checking signed scalar identity, K, physical word, intersections and target chains\n+Checking independent terminal plan and all rational columns of the actual new executor...\n+Regenerating merged bit word from frozen arcs...\n+Checking every bit column over F2 and Z, and every rational frame determinant...\n+Certifying both paid suppliers, finite bridge and 47 strict balanced-assembly inequalities...\n+{\"status\": \"PASS_ADAPTED_PR188_COMPLETE_FINITE_REPLAY\", \"kappa\": \"308013811/500000000000\", \"diagnostic_normalization\": [{\"field\": \"numerical_root\", \"actual\": 0.0006467468629597348, \"expected\": 0.0006467468629597346, \"all_exact_fields_identical\": true}], \"rlimit_as_applied\": false, \"original_driver_pass\": false}"},{"sha":"b9530b20da005b58ded6f5d0379216e58372ede9","filename":"research/community-round9-audit/pr188-profile-diagnostic.log.txt","status":"added","additions":1,"deletions":0,"changes":1,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr188-profile-diagnostic.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr188-profile-diagnostic.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr188-profile-diagnostic.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1 @@\n+/numerical_root 0.0006467468629597348 0.0006467468629597346"},{"sha":"0edbc25385cf4d3763cfc2f183a1fe01eaecf084","filename":"research/community-round9-audit/pr188_portable_audit.py","status":"added","additions":24,"deletions":0,"changes":24,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr188_portable_audit.py","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr188_portable_audit.py","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr188_portable_audit.py?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,24 @@\n+\"\"\"Audit-only Darwin replay: omit unsupported RLIMIT_AS via saved sitecustomize;\n+permit only the diagnosed last-bit discovery numerical_root comparison.\n+All exact fields and final certificate must still match; original sources stay pinned.\n+\"\"\"\n+import importlib.util,inspect,json,math,sys\n+from pathlib import Path\n+sys.dont_write_bytecode=True\n+base=Path('/tmp/integer-mult-export188/research/paired-cube-terminal-reuse')\n+sys.path.insert(0,str(base))\n+spec=importlib.util.spec_from_file_location('pr188_target',base/'verify.py');m=importlib.util.module_from_spec(spec);spec.loader.exec_module(m)\n+original=m.require;records=[]\n+def require(ok,message):\n+ if message=='Frozen bit row differs' and not ok:\n+ actual=inspect.currentframe().f_back.f_locals['bp'];expected=json.loads((base/'selected/bit/profile.json').read_text())\n+ a=dict(actual);b=dict(expected);ra=a.pop('numerical_root');rb=b.pop('numerical_root')\n+ assert a==b and type(ra)is float and math.isfinite(ra) and format(ra,'.12e')==format(rb,'.12e')\n+ records.append(dict(field='numerical_root',actual=ra,expected=rb,all_exact_fields_identical=True))\n+ return\n+ original(ok,message)\n+m.require=require\n+result=m.verify();expected=json.loads((base/'certificate.json').read_text())\n+Path('/tmp/integer-mult-pr188-portable-fresh.json').write_text(json.dumps(result,indent=2))\n+assert result==expected, 'Complete final exact certificate differs'\n+print(json.dumps(dict(status='PASS_ADAPTED_PR188_COMPLETE_FINITE_REPLAY',kappa=result['kappa'],diagnostic_normalization=records,rlimit_as_applied=False,original_driver_pass=False)))"},{"sha":"ee75915923ddb09cfff2f5fa56985bbb4a42b54d","filename":"research/community-round9-audit/pr189-replay.log.txt","status":"added","additions":3,"deletions":0,"changes":3,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr189-replay.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr189-replay.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr189-replay.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,3 @@\n+Checking new signed complex word, all formal columns, frames and exact moment.\n+Checking the new bit local circuit, our physical frames, aliases and 34 terminal sinks, full F2 identity and paid moment envelope.\n+PASS paired-cube-twin-local-168 kappa=330877589979561/500000000000000000; complete complex and bit words, 47 constraints, seven margins, and 21 assembly controls."},{"sha":"e7f93c3e92589af7bf0df2a8f57db49d30914e5b","filename":"research/community-round9-audit/pr190-replay.log.txt","status":"added","additions":60,"deletions":0,"changes":60,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr190-replay.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr190-replay.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr190-replay.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,60 @@\n+python3 scripts/experiments/verify_skip_frame.py\n+PASS h=23: full dirty basis, exact frame path, every fixed-basis profile\n+PASS h=25: full dirty basis, exact frame path, every fixed-basis profile\n+PASS conditional kappa=4669442391/100000000000000; bit saving=116741511/2500000000000\n+PASS exact recurrence, 47 strict inequalities, seven margins, eventual cutoffs\n+python3 scripts/experiments/verify_joint_dual.py\n+built 23 36626 regions\n+augment 100 11854\n+augment 200 11954\n+matched 11974 seconds 2.4223971366882324\n+compile 23 0 6 reclaimed 0 seconds 2.430819034576416\n+compile 23 5000 16729 reclaimed 19 seconds 2.9099831581115723\n+compile 23 10000 20965 reclaimed 172 seconds 9.442233085632324\n+compile 23 15000 22929 reclaimed 607 seconds 16.081545114517212\n+compile 23 20000 25536 reclaimed 1200 seconds 26.98870015144348\n+compile 23 25000 28333 reclaimed 1562 seconds 50.42971992492676\n+compile 23 30000 30127 reclaimed 1786 seconds 93.22463607788086\n+compile 23 35000 30688 reclaimed 1853 seconds 117.51345014572144\n+PASS h=23: full dirty basis, exact frame path, every fixed-basis profile\n+built 25 48675 regions\n+augment 100 16090\n+augment 200 16190\n+matched 16276 seconds 9.98438286781311\n+compile 25 0 6 reclaimed 0 seconds 9.999056100845337\n+compile 25 5000 19564 reclaimed 0 seconds 10.440004110336304\n+compile 25 10000 25624 reclaimed 50 seconds 24.693618059158325\n+compile 25 15000 28089 reclaimed 718 seconds 41.2987539768219\n+compile 25 20000 29883 reclaimed 986 seconds 59.171961069107056\n+compile 25 25000 32329 reclaimed 1785 seconds 101.57689905166626\n+compile 25 30000 35471 reclaimed 2135 seconds 206.77248406410217\n+compile 25 35000 37806 reclaimed 2408 seconds 318.29451417922974\n+compile 25 40000 39609 reclaimed 2613 seconds 385.54773807525635\n+compile 25 45000 40338 reclaimed 2711 seconds 410.10110902786255\n+PASS h=25: full dirty basis, exact frame path, every fixed-basis profile\n+PASS conditional kappa=4764513337/100000000000000; bit saving=2382370177/50000000000000\n+PASS exact recurrence, 47 strict inequalities, seven margins, eventual cutoffs\n+python3 -m unittest discover -s tests -p 'test_joint_reclaim.py' -v\n+test_aliased_terminal_role_is_rejected (test_joint_reclaim.JointReclamationControls.test_aliased_terminal_role_is_rejected) ... ok\n+test_cancelled_repetitions_of_paid_scatter_are_rejected (test_joint_reclaim.JointReclamationControls.test_cancelled_repetitions_of_paid_scatter_are_rejected) ... ok\n+test_complete_pr58_profile_fails_new_bit_saving (test_joint_reclaim.JointReclamationControls.test_complete_pr58_profile_fails_new_bit_saving) ... ok\n+test_missing_copied_center_is_rejected (test_joint_reclaim.JointReclamationControls.test_missing_copied_center_is_rejected) ... ok\n+test_missing_scatter_is_rejected_by_each_helper (test_joint_reclaim.JointReclamationControls.test_missing_scatter_is_rejected_by_each_helper) ... ok\n+test_negative_operation_frame_index_is_rejected (test_joint_reclaim.JointReclamationControls.test_negative_operation_frame_index_is_rejected) ... ok\n+test_non_nested_operation_frame_is_rejected (test_joint_reclaim.JointReclamationControls.test_non_nested_operation_frame_is_rejected) ... ok\n+test_omitted_literal_xor_is_rejected (test_joint_reclaim.JointReclamationControls.test_omitted_literal_xor_is_rejected) ... ok\n+test_omitted_transition_cannot_reduce_paid_profile (test_joint_reclaim.JointReclamationControls.test_omitted_transition_cannot_reduce_paid_profile) ... ok\n+test_optimized_helpers_reject_unchecked_word (test_joint_reclaim.JointReclamationControls.test_optimized_helpers_reject_unchecked_word) ... ok\n+test_optimized_python_is_rejected_by_every_new_entry (test_joint_reclaim.JointReclamationControls.test_optimized_python_is_rejected_by_every_new_entry) ... ok\n+test_scatter_order_preserves_the_complete_basis_receipt (test_joint_reclaim.JointReclamationControls.test_scatter_order_preserves_the_complete_basis_receipt) ... ok\n+test_selected_words_pass_independent_replay (test_joint_reclaim.JointReclamationControls.test_selected_words_pass_independent_replay) ... ok\n+test_self_cancelling_uncharged_scatter_is_rejected (test_joint_reclaim.JointReclamationControls.test_self_cancelling_uncharged_scatter_is_rejected) ... ok\n+test_self_xor_is_rejected (test_joint_reclaim.JointReclamationControls.test_self_xor_is_rejected) ... ok\n+test_understated_physical_width_is_rejected (test_joint_reclaim.JointReclamationControls.test_understated_physical_width_is_rejected) ... ok\n+\n+----------------------------------------------------------------------\n+Ran 16 tests in 49.830s\n+\n+OK\n+python3 scripts/audit_joint_candidate.py --check docs/research/community-round2-arithmetic.json\n+PASS independent PR60/61 moments, complete child ledger, assembly and Lean source binding"},{"sha":"863251e01bd586a38e684cd13553ddd31fc58401","filename":"research/community-round9-audit/pr191-canonical-comparison.json","status":"added","additions":71,"deletions":0,"changes":71,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr191-canonical-comparison.json","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr191-canonical-comparison.json","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr191-canonical-comparison.json?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,71 @@\n+{\n+ \"built_certificate_sha256\": \"aaa5178b4c0b9f99dbaf4039949b4047d12792d9193141aa0900d99b92ebae1c\",\n+ \"differences\": [\n+ {\n+ \"built\": \"5effdca9917bb75babc843dd0240fe990943f066c1e4b9f0fb63da1a0d34f34f\",\n+ \"kind\": 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No frozen large cache is required.\",\n+ \"scalar_coefficients\": [\n+ [\n+ -2,\n+ 1\n+ ],\n+ [\n+ -1,\n+ 1\n+ ],\n+ [\n+ -1,\n+ 2\n+ ],\n+ [\n+ 1,\n+ 2\n+ ],\n+ [\n+ 1,\n+ 1\n+ ],\n+ [\n+ 2,\n+ 1\n+ ]\n+ ],\n+ \"scalar_denominator_lcm\": \"2\",\n+ \"signature\": \"GPT-6 Astra\",\n+ \"source_data_histogram\": {\n+ \"1\": 1320,\n+ \"18\": 1320,\n+ \"2\": 1320\n+ },\n+ \"status\": \"Exact local invertible flow, exact all-column fresh identity, paid source controls, target read chains, and integer histogram certified. 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Not an exact supplier certificate.\",\n+ \"v\": 1320,\n+ \"vectors\": 24788\n+ },\n+ \"gain_over_pr186\": \"124191790067/110314258209933\",\n+ \"kappa\": \"6626307/10000000000\",\n+ \"lift\": {\n+ \"all_actual_coefficients_dyadic\": true,\n+ \"certificate_path\": \"research/source-assisted-v4/.work/lift.certificate.json.gz\",\n+ \"certificate_sha256\": \"5effdca9917bb75babc843dd0240fe990943f066c1e4b9f0fb63da1a0d34f34f\",\n+ \"checker_path\": \"research/source-assisted/decision/exact_complex_flow_lift.py\",\n+ \"checker_sha256\": \"9d841bcfdc7c9c19b31791e8d7cfebd223d80d5e9ecd376d26257244f5323f2e\",\n+ \"coefficient_numerator_lcm\": \"2\",\n+ \"coefficients\": [\n+ [\n+ -2,\n+ 1\n+ ],\n+ [\n+ -1,\n+ 1\n+ ],\n+ [\n+ -1,\n+ 2\n+ ],\n+ [\n+ 1,\n+ 2\n+ ],\n+ [\n+ 1,\n+ 1\n+ ],\n+ [\n+ 2,\n+ 1\n+ ]\n+ ],\n+ \"denominator_lcm\": \"2\",\n+ \"exact_scalar_program_sha256\": \"8f0c50142fd8eee2c7056a8e13b391823df51b9aca518b7c64bf23d1616ec6b1\",\n+ \"inverse_elementary_gates\": 60915,\n+ \"kernel_reuses\": 707,\n+ \"max_abs_numerator\": \"2\",\n+ \"max_denominator\": \"2\",\n+ \"nodes\": 18662,\n+ \"physical_R\": 10824,\n+ \"signature\": \"GPT-6 Astra\",\n+ \"source_control_vertices\": 130,\n+ \"source_erasures\": 1412,\n+ \"status\": \"Exact rational local lifts and inverse gate programs verified; monotone flow and zero-fresh kernel reuse DAG verified.\",\n+ \"witness_path\": \"research/source-assisted-v4/.work/flow.witness.json\",\n+ \"witness_sha256\": \"b2e9d6c2c50d74db4c400dd52650f09bc711ca8a0b1ac1939d90cb30662c8ef4\"\n+ },\n+ \"lift_certificate_sha256\": \"5effdca9917bb75babc843dd0240fe990943f066c1e4b9f0fb63da1a0d34f34f\",\n+ \"scope\": \"PR184 contract, finite bridge and bit supplier unchanged; the complex supplier is PR184's source-parity local word and frame flow on PR168 v4's query modules and physical layer. No new flattened bit transcript or full Clifford/router replay, as in PR184.\",\n+ \"status\": \"PASS conditional finite witness\",\n+ \"witness_sha256\": \"b2e9d6c2c50d74db4c400dd52650f09bc711ca8a0b1ac1939d90cb30662c8ef4\"\n+}"},{"sha":"7ce90253dd3312e48c252adf44995933765372b2","filename":"research/community-round9-audit/pr191-queue-0.log.txt","status":"added","additions":8,"deletions":0,"changes":8,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr191-queue-0.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr191-queue-0.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr191-queue-0.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,8 @@\n+Traceback (most recent call last):\n+ File \"/private/tmp/integer-mult-export191/research/source-assisted-v4/verify.py\", line 150, in \n+ main()\n+ ~~~~^^\n+ File \"/private/tmp/integer-mult-export191/research/source-assisted-v4/verify.py\", line 145, in main\n+ assert result == read(target), 'Canonical certificate does not reproduce'\n+ ^^^^^^^^^^^^^^^^^^^^^^\n+AssertionError: Canonical certificate does not reproduce"},{"sha":"02b89361b3749d019b497cc17cc356a736c415fc","filename":"research/community-round9-audit/pr192-replay.log.txt","status":"added","additions":40,"deletions":0,"changes":40,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr192-replay.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr192-replay.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr192-replay.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,40 @@\n+[ 0s] rebuilt the pinned files of #168 (commit 4a3c769) from baseline-pr168.tar.gz; hashes match SOURCE.json\n+Regenerating paired-cube signed DAG from inherited PR117 restrictions\n+Replaying frozen carrier matching and full binary intersections\n+Selecting chronological partial gauges and constructing signed physical M\n+Independently checking signed scalar identity, K, physical word, intersections and target chains\n+[ 24s] tree /private/var/folders/sd/yrr853rn73qdgdgdmps82gfh0000gn/T/kappa-ceiling-pr168-0erhl_ni (physical layer): h 22, v 1320, centre loss 440, deficit D = 2v - 3 loss = 1320\n+[ 24s] fact 1, complex: certified saving 6.5632000e-04 < D/C = 6.5690113e-04 (gap 0.088%)\n+[ 24s] fact 1, bit: certified coarse saving 6.6002530e-04 < D/C = 6.6058615e-04 (gap 0.085%)\n+[ 24s] fact 2 (balanced prefix): kappa 3279447/5000000000 < G(min(complex 2051/3125000, bit coarse 6600253/10000000000)) = 6.5588951e-04\n+[ 90s] self-test: the tree layout lies inside every derived frame bound; its slot chains reproduce the certified complex ledger exactly; every slot floor is below its actual chain\n+[ 248s] fact 4: 11015 physical slots (2310 reuse pairs, 47 sinks); 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\"2200\",\n+ \"7\": \"3762\",\n+ \"8\": \"2808\",\n+ \"9\": \"1944\"\n+ },\n+ \"m\": 72,\n+ \"mass\": \"1515392\",\n+ \"maxchild\": 60\n+ },\n+ \"effective_saving\": \"133575648846809489/200000000000000000000\",\n+ \"effective_saving_decimal\": \"6.678782442340e-04\",\n+ \"ideal_moment_upper\": \"168072904686372575392663389853985508233749/168072904699027902633448979930087889567744\",\n+ \"ordinary_leaf_saving\": \"384599/10000000000\",\n+ \"saving\": \"6682989/10000000000\",\n+ \"strict_gap_lower\": \"5911615430598974531639452298701600939983271/82066847997572218082738759731488227328000000000000000\",\n+ \"strict_gap_lower_decimal\": \"7.203414746444e-11\"\n+ },\n+ \"bit_source\": \"research/paired-cube-twin-local-168/certificate.json bit.profile (PR189)\",\n+ \"complex\": {\n+ \"bad_moment_upper\": \"0\",\n+ \"counts\": {\n+ \"W\": \"12052\",\n+ \"delta\": \"1320\",\n+ \"edge_count\": \"213147\",\n+ \"histogram\": {\n+ \"1\": \"87534\",\n+ \"10\": \"2790\",\n+ \"11\": \"1062\",\n+ 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\"checked_source_columns\": 1320,\n+ \"checked_target_rows\": 1320,\n+ \"controls_before_original_K\": true,\n+ \"original_source_V_before_all_controls\": true,\n+ \"positive_target_data_histogram\": {\n+ \"1\": 3960,\n+ \"18\": 1320\n+ },\n+ \"read_counts\": {\n+ \"center\": 22,\n+ \"deferred\": 2310,\n+ \"side\": 3135\n+ },\n+ \"source_controls_at_paid_parity_frames\": true,\n+ \"target_chains_nested\": true,\n+ \"target_data_histogram\": {\n+ \"0\": 6270,\n+ \"1\": 3960,\n+ \"18\": 1320\n+ }\n+ },\n+ \"complex_lift_certificate_sha256\": \"85a482d8153b972cdb695ecebe1b802ac3414ba0e03fd8fdfe93aae0a73f2c24\"\n+ },\n+ \"finite_bridge\": {\n+ \"proof\": \"FINITE_BRIDGE.txt\",\n+ \"representation\": \"Exact powers of two with proved dominating bounds\",\n+ \"rows\": {\n+ \"coefficient\": 20161,\n+ \"degree\": 1000000,\n+ \"degree_gap\": \"23971789/25\",\n+ \"suffix_slope\": 4000000\n+ },\n+ \"semantic\": {\n+ \"B_upper\": {\n+ \"base\": 2,\n+ \"exponent\": 100001\n+ },\n+ \"C0\": {\n+ 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\"434b81507ebb6e20aa73508d9ac01011fa1b785204363a5eee2eea59256e4b70\",\n+ \"research/source-assisted-v4/.work/aligned/cache/graph.json\": \"a4d350feb76f2ddcffa409d079bf479c04afd65af2d6b6e96a2ea157019d78d5\",\n+ \"research/source-assisted-v4/.work/aligned/cache/record.json\": \"e31f5c73f2744965f63243953858a57ffd099c4a6352a080c3ac74e2b8dd1486\",\n+ \"research/source-assisted-v4/.work/aligned/cache/selection.json\": \"dfc2cd63e23473ee2a55aca490bde08566b5a8828a9826b9bea8e2ca84fbe22a\",\n+ \"research/source-assisted-v4/.work/aligned/references/paired-cube/physical/frames.json\": \"1a6c215cdc58216f7ec96fb898a471e25d094fd86de085f6c06e86fd8997bfad\",\n+ \"research/source-assisted-v4/.work/aligned/references/paired-cube/physical/pairs.json\": \"abf341935148071a2222fe61c430e4e2fe3d16a64db14ab4eed9cd9a5a0f54d3\",\n+ \"research/source-assisted-v4/.work/flow.json\": \"e5024707ca0669de4fa5ee07d5d01d9e61ca2bf32b1229642c717f2d67138959\",\n+ \"research/source-assisted-v4/.work/flow.witness.json\": \"51da02c6cd844276ca26608f1b714ab07d476ec25634ad1a9b461ccda2fbe457\",\n+ \"research/source-assisted-v4/.work/lift.certificate.json.gz\": \"85a482d8153b972cdb695ecebe1b802ac3414ba0e03fd8fdfe93aae0a73f2c24\",\n+ \"research/source-assisted-v4/.work/lift.json\": \"c4b11be0de29399a37a45f176e0c14c0b20c43ab15b6c4b1116bdff589e5001e\",\n+ \"research/source-assisted-v4/contract_v4.py\": \"67da183217adbe28915391c8cd0c8c4ec9c9dedead54a641a2de23834df2342c\",\n+ \"research/source-assisted-v4/data/kernel-pairs.json\": \"f1535677d1ec225a3a132b2da0f6da9613b7b814227647b288c4e298ec26d8d3\",\n+ \"research/source-assisted-v4/data/physical-pairs.json\": \"7095501f054e9ec18aa212bfed1b01e497ca2ae997f4c9ece2779909b3fd72e2\",\n+ \"research/source-assisted-v4/source_aligned_local_v4.py\": \"3e11a7418bf1f3b51674b45e4dded184cf1599338c4c3911e145f58c8c15a969\",\n+ \"research/source-assisted-v4/verify.py\": \"41e73269755771828a33c85ba9d171ff9df36315430205889b321b35c4193aaa\",\n+ \"research/source-assisted/decision/complex_frame_flow.py\": \"5ea4f32f4eb0b19816a0b98272592f9dc0e9cbc448ce5eb7907ba113233dcc86\",\n+ \"research/source-assisted/decision/exact_complex_flow_lift.py\": \"9d841bcfdc7c9c19b31791e8d7cfebd223d80d5e9ecd376d26257244f5323f2e\"\n+ },\n+ \"rank_per_vertex\": 794112,\n+ \"regeneration\": \"Run source_aligned_local_v4.py, PR184 complex_frame_flow.py with source purification and frozen kernel reuse, PR184 exact_complex_flow_lift.py, and this checker on the PR168 v4 producer cache. No frozen large cache is required.\",\n+ \"scalar_coefficients\": [\n+ [\n+ -2,\n+ 1\n+ ],\n+ [\n+ -1,\n+ 1\n+ ],\n+ [\n+ -1,\n+ 2\n+ ],\n+ [\n+ 1,\n+ 2\n+ ],\n+ [\n+ 1,\n+ 1\n+ ],\n+ [\n+ 2,\n+ 1\n+ ]\n+ ],\n+ \"scalar_denominator_lcm\": \"2\",\n+ \"signature\": \"GPT-6 Astra\",\n+ \"source_data_histogram\": {\n+ \"1\": 1320,\n+ \"18\": 1320,\n+ \"2\": 1320\n+ },\n+ \"status\": \"Exact local invertible flow, exact all-column fresh identity, paid source controls, target read chains, and integer histogram certified. A literal globally renumbered operation program is not exported; dense initial dirty-response subtraction is defined by the exact certified flow.\",\n+ \"target_data_histogram\": {\n+ \"0\": 6270,\n+ \"1\": 3960,\n+ \"18\": 1320\n+ },\n+ \"terminal_sink_substitutions\": 0,\n+ \"v\": 1320\n+ },\n+ \"complex_saving\": \"219037/312500000\",\n+ \"flow\": {\n+ \"baseline_entropy\": \"2.264636168006e+06\",\n+ \"birth_histogram\": {\n+ \"1:1\": 2640,\n+ \"1:10\": 22,\n+ \"1:3\": 2016,\n+ \"1:5\": 154,\n+ \"1:6\": 88,\n+ \"2:10\": 74,\n+ \"2:11\": 5,\n+ \"2:12\": 57,\n+ \"2:13\": 11,\n+ \"2:14\": 92,\n+ \"2:15\": 47,\n+ \"2:16\": 37,\n+ \"2:17\": 39,\n+ \"2:3\": 1548,\n+ \"2:4\": 503,\n+ \"2:5\": 396,\n+ \"2:6\": 94,\n+ \"2:7\": 23,\n+ \"2:8\": 241,\n+ \"2:9\": 5\n+ },\n+ \"cache_sha256\": {\n+ \"frames.json\": \"434b81507ebb6e20aa73508d9ac01011fa1b785204363a5eee2eea59256e4b70\",\n+ \"graph.json\": \"a4d350feb76f2ddcffa409d079bf479c04afd65af2d6b6e96a2ea157019d78d5\",\n+ \"record.json\": \"e31f5c73f2744965f63243953858a57ffd099c4a6352a080c3ac74e2b8dd1486\",\n+ \"selection.json\": \"dfc2cd63e23473ee2a55aca490bde08566b5a8828a9826b9bea8e2ca84fbe22a\"\n+ },\n+ \"child_histogram\": {\n+ \"1\": 87534,\n+ \"10\": 2790,\n+ \"11\": 1062,\n+ \"12\": 3591,\n+ \"13\": 381,\n+ \"14\": 2226,\n+ \"15\": 5637,\n+ \"16\": 264,\n+ \"17\": 243,\n+ \"18\": 7959,\n+ \"19\": 501,\n+ \"2\": 39834,\n+ \"20\": 66,\n+ \"3\": 29769,\n+ \"4\": 12627,\n+ \"5\": 5850,\n+ \"6\": 4815,\n+ \"7\": 2118,\n+ \"8\": 4593,\n+ \"9\": 1287\n+ },\n+ \"deficit\": 1320,\n+ \"edge_basis_values\": 42787,\n+ \"edge_distinct_values\": 42787,\n+ \"edge_nullity_histogram\": {\n+ \"0\": 41912\n+ },\n+ \"edge_removed_values\": 0,\n+ \"entropy\": \"1.881413992826e+06\",\n+ \"entropy_ratio\": \"8.307798044588e-01\",\n+ \"field_prime\": 1000003,\n+ \"frames\": 18532,\n+ \"h\": 22,\n+ \"incoming_dependencies\": 24,\n+ \"kernel_reuses\": 0,\n+ \"local_histogram\": {\n+ \"1\": 23898,\n+ \"10\": 930,\n+ \"11\": 354,\n+ \"12\": 1197,\n+ \"13\": 127,\n+ \"14\": 742,\n+ \"15\": 1879,\n+ \"16\": 88,\n+ \"17\": 81,\n+ \"18\": 13,\n+ \"19\": 167,\n+ \"2\": 11078,\n+ \"20\": 22,\n+ \"3\": 9923,\n+ \"4\": 4209,\n+ \"5\": 1950,\n+ \"6\": 1605,\n+ \"7\": 706,\n+ \"8\": 1531,\n+ \"9\": 429\n+ },\n+ \"loss\": 440,\n+ \"new_R\": 9412,\n+ \"new_W\": 12052,\n+ \"numerical_local_root\": \"7.009184438594e-04\",\n+ \"original_physical_roles\": 13372,\n+ \"original_role_crossings\": 46747,\n+ \"outgoing_dependencies\": 8116,\n+ \"retirement_histogram\": {\n+ \"1:12\": 66,\n+ \"1:20\": 198,\n+ \"1:3\": 84,\n+ \"1:6\": 4,\n+ \"2:10\": 63,\n+ \"2:11\": 1,\n+ \"2:12\": 103,\n+ \"2:13\": 26,\n+ \"2:14\": 117,\n+ \"2:15\": 87,\n+ \"2:16\": 293,\n+ \"2:17\": 177,\n+ \"2:18\": 651,\n+ \"2:19\": 3410,\n+ \"2:20\": 1320,\n+ \"2:21\": 2640,\n+ \"2:3\": 83,\n+ \"2:4\": 13,\n+ \"2:5\": 42,\n+ \"2:6\": 3,\n+ \"2:8\": 30,\n+ \"2:9\": 1\n+ },\n+ \"source_control_erasures\": 0,\n+ \"source_sha256\": {\n+ \"references/paired-cube/physical/frames.json\": \"1a6c215cdc58216f7ec96fb898a471e25d094fd86de085f6c06e86fd8997bfad\",\n+ \"references/paired-cube/physical/pairs.json\": \"abf341935148071a2222fe61c430e4e2fe3d16a64db14ab4eed9cd9a5a0f54d3\"\n+ },\n+ \"status\": \"Modular equal-frame flow price, retaining dirty kernel lifts and complete full-frame cleanup. Not an exact supplier certificate.\",\n+ \"v\": 1320,\n+ \"vectors\": 26200\n+ },\n+ \"gain_over_pr186\": \"2773425370201/330942774629799\",\n+ \"gain_over_pr191\": \"48017/6626307\",\n+ \"gain_over_pr193\": \"6613/1661968\",\n+ \"kappa\": \"1668581/2500000000\",\n+ \"lift\": {\n+ \"all_actual_coefficients_dyadic\": true,\n+ \"certificate_path\": \"research/source-assisted-v4/.work/lift.certificate.json.gz\",\n+ \"certificate_sha256\": \"85a482d8153b972cdb695ecebe1b802ac3414ba0e03fd8fdfe93aae0a73f2c24\",\n+ \"checker_path\": \"research/source-assisted/decision/exact_complex_flow_lift.py\",\n+ \"checker_sha256\": \"9d841bcfdc7c9c19b31791e8d7cfebd223d80d5e9ecd376d26257244f5323f2e\",\n+ \"coefficient_numerator_lcm\": \"2\",\n+ \"coefficients\": [\n+ [\n+ -2,\n+ 1\n+ ],\n+ [\n+ -1,\n+ 1\n+ ],\n+ [\n+ -1,\n+ 2\n+ ],\n+ [\n+ 1,\n+ 2\n+ ],\n+ [\n+ 1,\n+ 1\n+ ],\n+ [\n+ 2,\n+ 1\n+ ]\n+ ],\n+ \"denominator_lcm\": \"2\",\n+ \"exact_scalar_program_sha256\": \"3b4e671d7c6630570b04788bb2c81629e2c52f8dc2fcc5805952f0b403921027\",\n+ \"inverse_elementary_gates\": 58165,\n+ \"kernel_reuses\": 0,\n+ \"max_abs_numerator\": \"2\",\n+ \"max_denominator\": \"2\",\n+ \"nodes\": 18532,\n+ \"physical_R\": 9412,\n+ \"signature\": \"GPT-6 Astra\",\n+ \"source_control_vertices\": 0,\n+ \"source_erasures\": 0,\n+ \"status\": \"Exact rational local lifts and inverse gate programs verified; monotone flow and zero-fresh kernel reuse DAG verified.\",\n+ \"witness_path\": \"research/source-assisted-v4/.work/flow.witness.json\",\n+ \"witness_sha256\": \"51da02c6cd844276ca26608f1b714ab07d476ec25634ad1a9b461ccda2fbe457\"\n+ },\n+ \"lift_certificate_sha256\": \"85a482d8153b972cdb695ecebe1b802ac3414ba0e03fd8fdfe93aae0a73f2c24\",\n+ \"scope\": \"PR184 contract and finite bridge unchanged; the bit supplier is PR189 (verified by its own verify.py); the complex supplier is PR184's source-parity local word and frame flow on PR168 v4's query modules and physical layer, with donor/recipient pairs that avoid parity purification. No new flattened bit transcript or full Clifford/router replay, as in PR184.\",\n+ \"status\": \"PASS conditional finite witness\",\n+ \"witness_sha256\": \"51da02c6cd844276ca26608f1b714ab07d476ec25634ad1a9b461ccda2fbe457\"\n+}"},{"sha":"a6ef11382e99b4bbfc1776552e69767ab7ebcb80","filename":"research/community-round9-audit/pr194-queue-0.log.txt","status":"added","additions":8,"deletions":0,"changes":8,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr194-queue-0.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr194-queue-0.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr194-queue-0.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,8 @@\n+Traceback (most recent call last):\n+ File \"/private/tmp/integer-mult-export194/research/source-assisted-v4/verify.py\", line 167, in \n+ main()\n+ ~~~~^^\n+ File \"/private/tmp/integer-mult-export194/research/source-assisted-v4/verify.py\", line 162, in main\n+ assert result == read(target), 'Canonical certificate does not reproduce'\n+ ^^^^^^^^^^^^^^^^^^^^^^\n+AssertionError: Canonical certificate does not reproduce"},{"sha":"4d678d04b51b21bcc5b933e7fdcaedca77aec6a3","filename":"research/community-round9-audit/pr195-replay.log.txt","status":"added","additions":3,"deletions":0,"changes":3,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr195-replay.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr195-replay.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr195-replay.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,3 @@\n+Replaying the complete pinned PR186 complex and bank-bit certificate...\n+Checking new frames, signed formal columns, terminal chronology and both sink directions...\n+PASS kappa=331325992674373/500000000000000000; full parent replay, both new complex directions, 46 terminals and exact assembly (285.8s)"},{"sha":"7f2c4a46fee1766a724e21185cebc020f904a68c","filename":"research/community-round9-audit/pr196-replay.log.txt","status":"added","additions":3,"deletions":0,"changes":3,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr196-replay.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr196-replay.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr196-replay.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,3 @@\n+Checking new signed complex word, all formal columns, frames and exact moment.\n+Checking the new bit local circuit, our physical frames, aliases and 34 terminal sinks, full F2 identity and paid moment envelope.\n+PASS paired-cube-diagonal-local-168 kappa=166261725903847/250000000000000000; complete complex and bit words, 47 constraints, seven margins, and 21 assembly controls."},{"sha":"9529a874d7aa8de7c07e5a1804c671041d5345a8","filename":"research/community-round9-audit/pr197-arithmetic.log.txt","status":"added","additions":2,"deletions":0,"changes":2,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr197-arithmetic.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr197-arithmetic.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr197-arithmetic.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,2 @@\n+PASS exact packed profile, two moment engines, finite leaf composition, 47 constraints and seven margins\n+conditional kappa = 135216063303877/200000000000000000"},{"sha":"d321d01c300b3b02e3c37559772fba4bf6d94f6e","filename":"research/community-round9-audit/pr197-banks.json","status":"added","additions":69,"deletions":0,"changes":69,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr197-banks.json","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr197-banks.json","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr197-banks.json?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,69 @@\n+{\n+ \"status\": \"PASS_FRESH_BANK_CERTIFICATE_EQUALITY\",\n+ \"pr\": 197,\n+ \"physical\": {\n+ \"status\": \"PASS exact actual-chain chart and incidence checks\",\n+ \"source_commit\": \"201737a1ec4f936e166e2481fb9e88104cb2ccc7\",\n+ \"word_sha256\": \"3c188c2527b3b96443e241f2f0d07c120feb1e784c2ff7f49c3e1e10eaea5f0b\",\n+ \"physical_roles\": 17588,\n+ \"interior_splices\": 1760,\n+ \"gauge_roles\": 2200,\n+ \"distinct_gauges\": 220,\n+ \"copies\": 3,\n+ \"banks\": 47264,\n+ \"patterns\": [\n+ {\n+ \"rank4\": 6,\n+ \"rank24\": 2,\n+ \"count\": 3300\n+ },\n+ {\n+ \"rank4\": 0,\n+ \"rank24\": 3,\n+ \"count\": 43964\n+ }\n+ ],\n+ \"incidences\": 158292,\n+ \"W\": 57824,\n+ \"m\": 72,\n+ \"rank_mass\": 4157520,\n+ \"deficit\": 5808,\n+ \"maxchild\": 22,\n+ \"child_histogram\": {\n+ \"1\": 360504,\n+ \"2\": 192684,\n+ \"3\": 88848,\n+ \"4\": 26910,\n+ \"5\": 23400,\n+ \"6\": 10980,\n+ \"7\": 9936,\n+ \"8\": 8406,\n+ \"9\": 5436,\n+ \"10\": 7524,\n+ \"11\": 3474,\n+ \"12\": 12960,\n+ \"13\": 4770,\n+ \"14\": 9702,\n+ \"15\": 3690,\n+ \"16\": 9648,\n+ \"17\": 3492,\n+ \"18\": 3996,\n+ \"19\": 2754,\n+ \"20\": 15840,\n+ \"21\": 33480,\n+ \"22\": 35856\n+ },\n+ \"chart_sha256\": \"24ad4add234c38be945378df5748ea4c4f054780e3a617c2b7be12e5049ad553\",\n+ \"incidence_sha256\": \"310591cedba5a950c1e44d9adf686c9df104c07ba03d04c50db87c22b44e3ef6\",\n+ \"max_chart_factors\": 186,\n+ \"max_num\": 5,\n+ \"max_den\": 18,\n+ \"conservative_selector_calls\": 5859111150,\n+ \"color_stats\": {\n+ \"swaps\": 733,\n+ \"longest_swapped_path\": 11\n+ },\n+ \"conflicting_assignment_rejected\": true\n+ },\n+ \"scope\": \"Fresh exact bank/chart allocation only; parent supplier and default source-pin/arithmetic replay recorded separately\"\n+}"},{"sha":"575e2a8474e2d910c24b5f54fb65ea021519cc1e","filename":"research/community-round9-audit/pr198-bit-scoped.log.txt","status":"added","additions":11,"deletions":0,"changes":11,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr198-bit-scoped.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr198-bit-scoped.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr198-bit-scoped.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,11 @@\n+bound 62018 bits 24 columns 21074\n+Traceback (most recent call last):\n+ File \"/private/tmp/integer-mult-export198/research/paired-cube-twin-local-168/bit/prove.py\", line 114, in \n+ if __name__=='__main__':main()\n+ ~~~~^^\n+ File \"/private/tmp/integer-mult-export198/research/paired-cube-twin-local-168/bit/prove.py\", line 104, in main\n+ need(primes==json.loads(gzip.decompress((HERE/'prime-witnesses.json.gz').read_bytes())),'source-bound all-frame prime witness reproduction')\n+ ~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n+ File \"/private/tmp/integer-mult-export198/research/paired-cube-twin-local-168/bit/base_word.py\", line 22, in need\n+ raise ValueError(msg)\n+ValueError: source-bound all-frame prime witness reproduction"},{"sha":"0331948cc4700e8627c7b6bd989c13cc2abe9669","filename":"research/community-round9-audit/pr198-prime-diagnostic.json","status":"added","additions":10,"deletions":0,"changes":10,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr198-prime-diagnostic.json","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr198-prime-diagnostic.json","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr198-prime-diagnostic.json?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,10 @@\n+{\n+ \"different_top_fields\": [\n+ \"script_sha256\"\n+ ],\n+ \"all_exact_frame_witnesses_identical\": true,\n+ \"script_sha256\": {\n+ \"fresh\": \"36bf9e0fc54c6c1e739801fd9240b20beaf5235758aef271be50943414109a1c\",\n+ \"saved\": \"37808c871602ca1cb3073044bee9f365c7ee350ed05fbb954b1f19be9cb3fb5d\"\n+ }\n+}"},{"sha":"36c96354756f9cc8c7208dd5141aedce817f434c","filename":"research/community-round9-audit/pr198-queue-0.log.txt","status":"added","additions":11,"deletions":0,"changes":11,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr198-queue-0.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr198-queue-0.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr198-queue-0.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,11 @@\n+Traceback (most recent call last):\n+ File \"/private/tmp/integer-mult-export198/research/paired-cube-twin-local-168/verify.py\", line 63, in \n+ if __name__=='__main__':main()\n+ ~~~~^^\n+ File \"/private/tmp/integer-mult-export198/research/paired-cube-twin-local-168/verify.py\", line 54, in main\n+ before=None if args.write else pins()\n+ ~~~~^^\n+ File \"/private/tmp/integer-mult-export198/research/paired-cube-twin-local-168/verify.py\", line 22, in pins\n+ assert values==manifest['files'],'Pinned construction or dependency bytes changed'\n+ ^^^^^^^^^^^^^^^^^^^^^^^^^\n+AssertionError: Pinned construction or dependency bytes changed"},{"sha":"59505d9aa6fd8e186f2c9899dca52fa29bca7ef2","filename":"research/community-round9-audit/pr198-queue-1.log.txt","status":"added","additions":17,"deletions":0,"changes":17,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr198-queue-1.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr198-queue-1.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr198-queue-1.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,17 @@\n+Certificate mismatch at $.assembly.construction_receipts.complex_lift_certificate_sha256: generated=\"85a482d8153b972cdb695ecebe1b802ac3414ba0e03fd8fdfe93aae0a73f2c24\" saved=\"1d81a79bda88b8a0ef64b7ae815c0d20cf1eee7f4714053530805bbb39e89ef2\"\n+Certificate mismatch at $.assembly.source_sha256.complex: generated=\"b47ae85d3010bcbf2a7b8770dc92243235fc3f8ec9d689e53e927ff50e40747f\" saved=\"df6f8b65d97063042c2cc35256ff5a78d3a7692e8701872d6b78eece0b333681\"\n+Certificate mismatch at $.complex_profile.exact_lift_certificate_sha256: generated=\"85a482d8153b972cdb695ecebe1b802ac3414ba0e03fd8fdfe93aae0a73f2c24\" saved=\"1d81a79bda88b8a0ef64b7ae815c0d20cf1eee7f4714053530805bbb39e89ef2\"\n+Certificate mismatch at $.complex_profile.proof_chain_sha256.research/source-assisted-v4/.work/aligned/cache/record.json: generated=\"e31f5c73f2744965f63243953858a57ffd099c4a6352a080c3ac74e2b8dd1486\" saved=\"2065cbaa22c87198a4d535119534e05fab4a258445ecda00cf3cbb9151cfcc30\"\n+Certificate mismatch at $.complex_profile.proof_chain_sha256.research/source-assisted-v4/.work/flow.json: generated=\"e5024707ca0669de4fa5ee07d5d01d9e61ca2bf32b1229642c717f2d67138959\" saved=\"ecc1b61843c40303516f05721d708e3f8183ba9c7fea2551da45028d557f7af3\"\n+Certificate mismatch at $.complex_profile.proof_chain_sha256.research/source-assisted-v4/.work/lift.certificate.json.gz: generated=\"85a482d8153b972cdb695ecebe1b802ac3414ba0e03fd8fdfe93aae0a73f2c24\" saved=\"1d81a79bda88b8a0ef64b7ae815c0d20cf1eee7f4714053530805bbb39e89ef2\"\n+Certificate mismatch at $.complex_profile.proof_chain_sha256.research/source-assisted-v4/.work/lift.json: generated=\"c4b11be0de29399a37a45f176e0c14c0b20c43ab15b6c4b1116bdff589e5001e\" saved=\"c41fee34c5c6e036ed9242ea6c19f32988aa21753b83e79513c890804cc469ae\"\n+Certificate mismatch at $.flow.cache_sha256.record.json: generated=\"e31f5c73f2744965f63243953858a57ffd099c4a6352a080c3ac74e2b8dd1486\" saved=\"2065cbaa22c87198a4d535119534e05fab4a258445ecda00cf3cbb9151cfcc30\"\n+Certificate mismatch at $.lift.certificate_sha256: generated=\"85a482d8153b972cdb695ecebe1b802ac3414ba0e03fd8fdfe93aae0a73f2c24\" saved=\"1d81a79bda88b8a0ef64b7ae815c0d20cf1eee7f4714053530805bbb39e89ef2\"\n+Certificate mismatch at $.lift_certificate_sha256: generated=\"85a482d8153b972cdb695ecebe1b802ac3414ba0e03fd8fdfe93aae0a73f2c24\" saved=\"1d81a79bda88b8a0ef64b7ae815c0d20cf1eee7f4714053530805bbb39e89ef2\"\n+Traceback (most recent call last):\n+ File \"/private/tmp/integer-mult-export198/research/source-assisted-v4/verify.py\", line 210, in \n+ main()\n+ ~~~~^^\n+ File \"/private/tmp/integer-mult-export198/research/source-assisted-v4/verify.py\", line 205, in main\n+ raise AssertionError('Canonical certificate does not reproduce')\n+AssertionError: Canonical certificate does not reproduce"},{"sha":"db088909e5b2f935e64f17976b842931ec884aed","filename":"research/community-round9-audit/pr198-stale-source-pins.json","status":"added","additions":112,"deletions":0,"changes":112,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr198-stale-source-pins.json","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr198-stale-source-pins.json","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr198-stale-source-pins.json?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,112 @@\n+[\n+ {\n+ \"path\": \".gitattributes\",\n+ \"expected\": \"eddd6423bbf2bafb17ecd446d7bfc7dea8a7537e7658cfe4839219f62a043b5c\",\n+ \"actual\": \"672dd6ef1e36d19844f103f05bfb6843d462e35f98946fe86a557896bfee97ae\"\n+ },\n+ {\n+ \"path\": \".github/workflows/verify.yml\",\n+ \"expected\": \"767d03b8206012c0715656e89b04e4816ca7206a4110a8e58d91c7589081e898\",\n+ \"actual\": \"0b0ebae2889ce3f73a620fff094f9720847d19ec553512c905397f4c8f2d3989\"\n+ },\n+ {\n+ \"path\": \"CITATION.cff\",\n+ \"expected\": \"c9ca9b580debf6e379225a217d0876b47b87a25c57beed72a082e742742aba8f\",\n+ \"actual\": \"551e27b08d995d60e39575cd17566bcd8db1e07a67be8685d473b4019224dac5\"\n+ },\n+ {\n+ \"path\": \"CONTRIBUTING.md\",\n+ \"expected\": \"6e02aa4d12b0ee585e6bc66e7f2a55a615c4fd8d234de9f5d5e056e12dbafaaf\",\n+ \"actual\": \"6657473df7f81c51680c0187cf2251f67bfbe42202ba4226b8e038abb7d19507\"\n+ },\n+ {\n+ \"path\": \"CONTRIBUTORS.md\",\n+ \"expected\": \"ec32d62fff5b19a582323ddf69090a95cbd8a0e5974c643f6096c5a41fb73326\",\n+ \"actual\": \"b68a5c7cc97e3fedb061676721472b755175b8102351353e5487dc7ff17389fd\"\n+ },\n+ {\n+ \"path\": \"Makefile\",\n+ \"expected\": \"85f7531c0c7705457a278537252c3d54970c0f3944089f8d5a83f43bb9e4d4cc\",\n+ \"actual\": \"768131bd4ce18433f6abccdc9812a38c92e11220e3a1019c6d95334b42f529d1\"\n+ },\n+ {\n+ \"path\": \"NOTICE\",\n+ \"expected\": \"c9850418622aea8d1382a230306c940947b5da818f4854b4b272ed60cf239f6c\",\n+ \"actual\": \"b49022cb4104d90b182e4c335f670faf45529025b15db77bf0291835083c28bd\"\n+ },\n+ {\n+ \"path\": \"README.md\",\n+ \"expected\": \"ac1d3d09e6400f65884142e3c15903455940133c581aa7f6786d94ad7c3b9f5b\",\n+ \"actual\": \"d104c31d5b7e0d3a8d011a0e3517ab615e5b499b3dc05684f7ad3cadcd28bdae\"\n+ },\n+ {\n+ \"path\": \"SOURCES.json\",\n+ \"expected\": \"296143c503c07ff86fcc0766d538cafc1b8530d1747c45b3125dcaeb937a3510\",\n+ \"actual\": \"e4e785a201a8345e871abf6753ba7a10d57654ac4b62fc007bcdddabe6311441\"\n+ },\n+ {\n+ \"path\": \"certificates/joint-dual-kappa.json\",\n+ \"expected\": \"82def00bd2c38daafec4c588de3532328d4ad674eeb872fd8eb0618948605241\",\n+ \"actual\": \"9801147b1502cf1e43d5fa39aa37f5291f03b48c30c4dd4f272e0877894a1c24\"\n+ },\n+ {\n+ \"path\": \"certificates/joint-dual-validation.json\",\n+ \"expected\": \"7a0fb71551b2c6f9e2ce0f4fdc39f8d566c8ebbbdd2b1cc2fc69de44070a9f87\",\n+ \"actual\": \"064f279be38a19e8f7422a5c56a864aa0ffbe4c1582dcbf7e93c963550c7d6d9\"\n+ },\n+ {\n+ \"path\": \"certificates/selected-result.json\",\n+ \"expected\": \"9b236d6a5925c2f5768dfd5b200eca93bba76b2dbf23b5aaaefeb1542ebc59da\",\n+ \"actual\": \"434456fb153101c31aa69fe5abb67a33f2cfbcb083dbae7ee0f8ff0872d2b20d\"\n+ },\n+ {\n+ \"path\": \"certificates/skip-frame-kappa.json\",\n+ \"expected\": \"d6d2ed145539af1acfe95c0df1ceac155fa359d43590ac772cbe1938f92f0092\",\n+ \"actual\": \"9f57831c261dfb6b3bfbe94be75bfa5a3faa05768b7d500281e7398623ad115a\"\n+ },\n+ {\n+ \"path\": \"certificates/skip-frame-validation.json\",\n+ \"expected\": \"ac9903607751f8d58ff5fb79cc5eab6e5a5f5b462edd08c631765632837a6565\",\n+ \"actual\": \"29062e44d551124fbf961b49a77f4229901fc206bb142571497ca43e88f4b47c\"\n+ },\n+ {\n+ \"path\": \"docs/reproducibility.md\",\n+ \"expected\": \"7751615091eabd9c357c770ba7a7d18f1bf69922d9dd390681ff387838224de7\",\n+ \"actual\": \"a689b06481b951dbe7588d19479c320a47f97314da1f3faea3c88643a7b32654\"\n+ },\n+ {\n+ \"path\": \"docs/research/contribution-review.md\",\n+ \"expected\": \"b16811a69d97349a828c3c463ffef24855e343ec1abeb7794d23be02941f4325\",\n+ \"actual\": \"eb559c32da33f11507824a849fafe1e14fca82cba6bfb506f44c297efa54d4be\"\n+ },\n+ {\n+ \"path\": \"docs/research/current-status.md\",\n+ \"expected\": \"77abf3b177eb67adbd8cdb6f52313c5e65a52e7d78f363f19d0cdb2c50825241\",\n+ \"actual\": \"c60af6041963234126583602bbb7ba7025930c4becf0f7001ccf42ffb2695fd6\"\n+ },\n+ {\n+ \"path\": \"research/joint-dual/SOURCE.json\",\n+ \"expected\": \"ef8fc24da50fbefb5643deb0ec26c826bc158b080ea4ccf61b038948dbd305b6\",\n+ \"actual\": \"4f3c15b82a2d97335d4fe95fb8bcb96bd2a921087da289d9da16c68213a17f17\"\n+ },\n+ {\n+ \"path\": \"research/pair-assembly/frame/frame-certificate.json\",\n+ \"expected\": \"646c98ac6b48b7f90c900f7c2ba7e2fc607e1577d9f0a5d07ed109b3923c562a\",\n+ \"actual\": \"eb5e8d25c4404703cc968acb4cc4642555ae56c3e93c1bb6a1e073fad72294e6\"\n+ },\n+ {\n+ \"path\": \"scripts/experiments/binary_frame_profile_prepare.py\",\n+ \"expected\": \"8a50381cab00b33e62b3a057d199ba5e19647929135c95b0fd63fc8a8ef7c9b3\",\n+ \"actual\": \"16dea3d3ef3dc90db928ed3e35d002f6926d2e7388da4766fc2fd725550f739e\"\n+ },\n+ {\n+ \"path\": \"scripts/experiments/binary_frame_replay.py\",\n+ \"expected\": \"392e78e62d7685c99a5888a7da743ea6c3dcad631af4a743c91e0c09348442bc\",\n+ \"actual\": \"1a572dbb33faba6695b3293768a7e61392d11cb4c2d5f708eedcd2cb95d0aff9\"\n+ },\n+ {\n+ \"path\": \"tests/test_joint_reclaim.py\",\n+ \"expected\": \"e2cfc99a52283c4912f970f83c7da5481ba9840d5f999f7e0e5468e8e8862a41\",\n+ \"actual\": \"c4e2817bf6e699f462aa3c589ee45e24ab0dcad6bcdb6152ca2a1e16ac7bffeb\"\n+ }\n+]"},{"sha":"3085ec2b60edb077957f3fc7d3d19ea894a6797c","filename":"research/community-round9-audit/pr198_prime_diagnostic.py","status":"added","additions":13,"deletions":0,"changes":13,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr198_prime_diagnostic.py","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr198_prime_diagnostic.py","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr198_prime_diagnostic.py?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,13 @@\n+import sys,json,gzip\n+from pathlib import Path\n+base=Path('/tmp/integer-mult-export198/research/paired-cube-twin-local-168/bit');sys.path.insert(0,str(base))\n+from word import Candidate\n+from prime_witnesses import certificate\n+w=Candidate();w.exact_frames();w.row();r=certificate(w);old=json.loads(gzip.decompress((base/'prime-witnesses.json.gz').read_bytes()))\n+different=[k for k in r if r[k]!=old.get(k)]\n+result=dict(different_top_fields=different,all_exact_frame_witnesses_identical=r['frame_witnesses']==old['frame_witnesses'])\n+if 'input_sha256'in different:result['input_hash_differences']={k:[v,old['input_sha256'].get(k)] for k,v in r['input_sha256'].items()if v!=old['input_sha256'].get(k)}\n+for k in different:\n+ if k not in ('frame_witnesses','input_sha256'):result[k]={'fresh':r[k],'saved':old.get(k)}\n+print(json.dumps(result,indent=2))\n+Path('/tmp/integer-mult-pr198-prime-fresh.json').write_text(json.dumps(r))"},{"sha":"db9778d192c39fa148b467aad0c56fe60140fd94","filename":"research/community-round9-audit/pr199-donor-reuse.json","status":"added","additions":15,"deletions":0,"changes":15,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr199-donor-reuse.json","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr199-donor-reuse.json","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr199-donor-reuse.json?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,15 @@\n+{\n+ \"gauges\": 3960,\n+ \"pairs\": 1760,\n+ \"unpaired\": 2200,\n+ \"unpaired_by_birth_frame_dim\": {\n+ \"20\": 2200\n+ },\n+ \"paired_by_birth_frame_dim\": {\n+ \"21\": 1760\n+ },\n+ \"donor_end_frames\": 8628,\n+ \"unpaired_birth_frames\": 220,\n+ \"unpaired_birth_frames_admitting_a_donor\": 0,\n+ \"detail\": []\n+}"},{"sha":"cec8e1a1243df86cbbb3d6f68bed89e4b7755516","filename":"research/community-round9-audit/pr199-replay.log.txt","status":"added","additions":25,"deletions":0,"changes":25,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr199-replay.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr199-replay.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr199-replay.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,25 @@\n+[reproduce] PR194 kappa = 1668581/2500000000 vs certificate 1668581/2500000000 -> EXACT\n+[reproduce] complex=0.0007009184 bit_coarse=0.0006682989 bit_effective=0.000667878244234047 atom=0.000667878245 OLD=3.84599e-05\n+[depth 0] leaf=0.000667878244234047 kappa=1668581/2500000000 (0.0006674324) gain vs record=+0.0000% [47 constraints, 7 margins]\n+[depth 1] leaf=0.000668298618876214 kappa=3339261/5000000000 (0.0006678522) gain vs record=+0.0629% [47 constraints, 7 margins]\n+[depth 2] leaf=0.000668298899812125 kappa=267141/400000000 (0.0006678525) gain vs record=+0.0629% [47 constraints, 7 margins]\n+[depth 3] leaf=0.000668298899999874 kappa=267141/400000000 (0.0006678525) gain vs record=+0.0629% [47 constraints, 7 margins]\n+[control] depth 0 = record 1668581/2500000000; untolled limit C gives 267141/400000000 vs claimed 267141/400000000 (edge of the 10^-10 grid)\n+[control] strict tolls hold: 0.000667878244234047 < 0.000668298899812125 < 0.0006682989 < 0.999331701100188\n+[best] depth 2: kappa=267141/400000000 vs record 1668581/2500000000 (+0.0629%)\n+[write] /private/tmp/integer-mult-export199/research/bit-leaf-bootstrap-189/bootstrap-result.json\n+[bit supplier] m=72 W=20634 deficit=1936 sinks=34 coarse=6777739/10000000000 (0.0006777739)\n+[complex] saving=219037/312500000 (0.0007009184)\n+[legacy] effective=338670433250477381/500000000000000000000 (0.000677340866500955) slack below coarse=4.33033e-07\n+[depth 0] leaf=0.000677340866500955 kappa=6768823/10000000000 (0.0006768823) [47 constraints, 7 margins]\n+[depth 1] leaf=0.000677773606501196 kappa=1354629/2000000000 (0.0006773145) [47 constraints, 7 margins]\n+[depth 2] leaf=0.000677773899801074 kappa=1693287/2500000000 (0.0006773148) [47 constraints, 7 margins]\n+[depth 3] leaf=0.000677773899999865 kappa=1693287/2500000000 (0.0006773148) [47 constraints, 7 margins]\n+[best] depth 2: kappa=1693287/2500000000\n+ vs #197: +0.1826%\n+ vs #199: +1.4168%\n+[write] /private/tmp/integer-mult-export199/research/bit-leaf-bootstrap-189/.work/next-composition-result.json\n+PASS pinned inputs, exact PR194 reproduction, bootstrap depths 0-3, 47 strict constraints and 7 margins per depth\n+record kappa=267141/400000000 (0.0006678525), gain vs PR194 = +0.0629%\n+next composition (PR200 bit + bootstrap) kappa=1693287/2500000000 (0.0006773148), gain vs #197 = +0.1826%\n+Physical words are inherited pinned inputs; this command does not replay them."},{"sha":"777b7d8e76ec1966b7f75b79f5cfe9e04f183072","filename":"research/community-round9-audit/pr199-reuse.log.txt","status":"added","additions":6,"deletions":0,"changes":6,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr199-reuse.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr199-reuse.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr199-reuse.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,6 @@\n+gauges=3960 pairs=1760 unpaired=2200\n+unpaired by birth-frame dim: {20: 2200}\n+paired by birth-frame dim: {21: 1760}\n+distinct donor end frames (non-gauge, non-root, phase-2 operands): 8628\n+unpaired birth frames: 220; of these, containing at least one donor end frame: 0\n+verdict: no unpaired gauge can receive a donor"},{"sha":"dcbf53dfe795487a3575f0a5f123cefcb02e91bb","filename":"research/community-round9-audit/pr200-replay.log.txt","status":"added","additions":3,"deletions":0,"changes":3,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr200-replay.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr200-replay.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr200-replay.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,3 @@\n+Checking new signed complex word, all formal columns, frames and exact moment.\n+Checking the fixed-coordinate/face-diagonal bit local circuit, our physical frames, aliases and 34 terminal sinks, full F2 identity and paid moment envelope.\n+PASS paired-cube-diagonal-bit-168 kappa=166261725903847/250000000000000000; complete complex and bit words, 47 constraints, seven margins, and 21 assembly controls."},{"sha":"df838c1c5099002fefb6770054392bfdffd206df","filename":"research/community-round9-audit/pr202-canonical-comparison.json","status":"added","additions":71,"deletions":0,"changes":71,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr202-canonical-comparison.json","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr202-canonical-comparison.json","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr202-canonical-comparison.json?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,71 @@\n+{\n+ \"built_certificate_sha256\": \"51f075b42f4e32981808be2d215d1172161217926be3160f0e796ed528bcd0f5\",\n+ \"differences\": [\n+ {\n+ \"built\": \"85a482d8153b972cdb695ecebe1b802ac3414ba0e03fd8fdfe93aae0a73f2c24\",\n+ \"kind\": \"different\",\n+ \"path\": \"/assembly/construction_receipts/complex_lift_certificate_sha256\",\n+ \"saved\": \"462521350b4f1b133f4bde6c793afdf735e84f8da918a169f1d030fc61727ee0\"\n+ },\n+ {\n+ \"built\": \"e7145de93a9d46a776572afa5421f5d777109524b7f41c13003b56c8e4136a41\",\n+ \"kind\": \"different\",\n+ \"path\": \"/assembly/source_sha256/complex\",\n+ \"saved\": \"b80de5b00f7551cbbece1d2ec4a85f1433eb62d208df6cb11270087dcdfde3a3\"\n+ },\n+ {\n+ \"built\": \"85a482d8153b972cdb695ecebe1b802ac3414ba0e03fd8fdfe93aae0a73f2c24\",\n+ \"kind\": \"different\",\n+ \"path\": \"/complex_profile/exact_lift_certificate_sha256\",\n+ \"saved\": \"462521350b4f1b133f4bde6c793afdf735e84f8da918a169f1d030fc61727ee0\"\n+ },\n+ {\n+ \"built\": \"e31f5c73f2744965f63243953858a57ffd099c4a6352a080c3ac74e2b8dd1486\",\n+ \"kind\": \"different\",\n+ \"path\": \"/complex_profile/proof_chain_sha256/research/source-assisted-v4/.work/aligned/cache/record.json\",\n+ \"saved\": \"2065cbaa22c87198a4d535119534e05fab4a258445ecda00cf3cbb9151cfcc30\"\n+ },\n+ {\n+ \"built\": \"e5024707ca0669de4fa5ee07d5d01d9e61ca2bf32b1229642c717f2d67138959\",\n+ \"kind\": \"different\",\n+ \"path\": \"/complex_profile/proof_chain_sha256/research/source-assisted-v4/.work/flow.json\",\n+ \"saved\": \"ecc1b61843c40303516f05721d708e3f8183ba9c7fea2551da45028d557f7af3\"\n+ },\n+ {\n+ \"built\": \"85a482d8153b972cdb695ecebe1b802ac3414ba0e03fd8fdfe93aae0a73f2c24\",\n+ \"kind\": \"different\",\n+ \"path\": \"/complex_profile/proof_chain_sha256/research/source-assisted-v4/.work/lift.certificate.json.gz\",\n+ \"saved\": \"462521350b4f1b133f4bde6c793afdf735e84f8da918a169f1d030fc61727ee0\"\n+ },\n+ {\n+ \"built\": \"c4b11be0de29399a37a45f176e0c14c0b20c43ab15b6c4b1116bdff589e5001e\",\n+ \"kind\": \"different\",\n+ \"path\": \"/complex_profile/proof_chain_sha256/research/source-assisted-v4/.work/lift.json\",\n+ \"saved\": \"89b0d949852a5c22909256f03be040ce57450062c901a64a71a0e1cbb6bda8a1\"\n+ },\n+ {\n+ \"built\": \"e31f5c73f2744965f63243953858a57ffd099c4a6352a080c3ac74e2b8dd1486\",\n+ \"kind\": \"different\",\n+ \"path\": \"/flow/cache_sha256/record.json\",\n+ \"saved\": \"2065cbaa22c87198a4d535119534e05fab4a258445ecda00cf3cbb9151cfcc30\"\n+ },\n+ {\n+ \"built\": \"85a482d8153b972cdb695ecebe1b802ac3414ba0e03fd8fdfe93aae0a73f2c24\",\n+ \"kind\": \"different\",\n+ \"path\": \"/lift/certificate_sha256\",\n+ \"saved\": \"462521350b4f1b133f4bde6c793afdf735e84f8da918a169f1d030fc61727ee0\"\n+ },\n+ {\n+ \"built\": \"85a482d8153b972cdb695ecebe1b802ac3414ba0e03fd8fdfe93aae0a73f2c24\",\n+ \"kind\": \"different\",\n+ \"path\": \"/lift_certificate_sha256\",\n+ \"saved\": \"462521350b4f1b133f4bde6c793afdf735e84f8da918a169f1d030fc61727ee0\"\n+ }\n+ ],\n+ \"identical\": false,\n+ \"saved_certificate_sha256\": \"6fb7df88e8d6635e15a53e1e5c88a47265f5c1706937e390eca01a91749aad9d\",\n+ \"source_files\": 51,\n+ \"source_pin_digest\": \"492e79f42346eb54ad77ddff9331a086f2afbe640abc99a983081558b9712a0d\",\n+ \"source_pins_unchanged\": true,\n+ \"status\": \"DIAGNOSTIC_ONLY\"\n+}"},{"sha":"df838c1c5099002fefb6770054392bfdffd206df","filename":"research/community-round9-audit/pr202-canonical-diagnostic.log.txt","status":"added","additions":71,"deletions":0,"changes":71,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr202-canonical-diagnostic.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr202-canonical-diagnostic.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr202-canonical-diagnostic.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,71 @@\n+{\n+ \"built_certificate_sha256\": \"51f075b42f4e32981808be2d215d1172161217926be3160f0e796ed528bcd0f5\",\n+ \"differences\": [\n+ {\n+ \"built\": \"85a482d8153b972cdb695ecebe1b802ac3414ba0e03fd8fdfe93aae0a73f2c24\",\n+ \"kind\": \"different\",\n+ \"path\": \"/assembly/construction_receipts/complex_lift_certificate_sha256\",\n+ \"saved\": \"462521350b4f1b133f4bde6c793afdf735e84f8da918a169f1d030fc61727ee0\"\n+ },\n+ {\n+ \"built\": \"e7145de93a9d46a776572afa5421f5d777109524b7f41c13003b56c8e4136a41\",\n+ \"kind\": \"different\",\n+ \"path\": \"/assembly/source_sha256/complex\",\n+ \"saved\": \"b80de5b00f7551cbbece1d2ec4a85f1433eb62d208df6cb11270087dcdfde3a3\"\n+ },\n+ {\n+ \"built\": \"85a482d8153b972cdb695ecebe1b802ac3414ba0e03fd8fdfe93aae0a73f2c24\",\n+ \"kind\": \"different\",\n+ \"path\": \"/complex_profile/exact_lift_certificate_sha256\",\n+ \"saved\": \"462521350b4f1b133f4bde6c793afdf735e84f8da918a169f1d030fc61727ee0\"\n+ },\n+ {\n+ \"built\": \"e31f5c73f2744965f63243953858a57ffd099c4a6352a080c3ac74e2b8dd1486\",\n+ \"kind\": \"different\",\n+ \"path\": 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A literal globally renumbered operation program is not exported; dense initial dirty-response subtraction is defined by the exact certified flow.\",\n+ \"target_data_histogram\": {\n+ \"0\": 6270,\n+ \"1\": 3960,\n+ \"18\": 1320\n+ },\n+ \"terminal_sink_substitutions\": 0,\n+ \"v\": 1320\n+ },\n+ \"complex_saving\": \"219037/312500000\",\n+ \"flow\": {\n+ \"baseline_entropy\": \"2.264636168006e+06\",\n+ \"birth_histogram\": {\n+ \"1:1\": 2640,\n+ \"1:10\": 22,\n+ \"1:3\": 2016,\n+ \"1:5\": 154,\n+ \"1:6\": 88,\n+ \"2:10\": 74,\n+ \"2:11\": 5,\n+ \"2:12\": 57,\n+ \"2:13\": 11,\n+ \"2:14\": 92,\n+ \"2:15\": 47,\n+ \"2:16\": 37,\n+ \"2:17\": 39,\n+ \"2:3\": 1548,\n+ \"2:4\": 503,\n+ \"2:5\": 396,\n+ \"2:6\": 94,\n+ \"2:7\": 23,\n+ \"2:8\": 241,\n+ \"2:9\": 5\n+ },\n+ \"cache_sha256\": {\n+ \"frames.json\": \"434b81507ebb6e20aa73508d9ac01011fa1b785204363a5eee2eea59256e4b70\",\n+ \"graph.json\": \"a4d350feb76f2ddcffa409d079bf479c04afd65af2d6b6e96a2ea157019d78d5\",\n+ \"record.json\": \"e31f5c73f2744965f63243953858a57ffd099c4a6352a080c3ac74e2b8dd1486\",\n+ \"selection.json\": \"dfc2cd63e23473ee2a55aca490bde08566b5a8828a9826b9bea8e2ca84fbe22a\"\n+ },\n+ \"child_histogram\": {\n+ \"1\": 87534,\n+ \"10\": 2790,\n+ \"11\": 1062,\n+ \"12\": 3591,\n+ \"13\": 381,\n+ \"14\": 2226,\n+ \"15\": 5637,\n+ \"16\": 264,\n+ \"17\": 243,\n+ \"18\": 7959,\n+ \"19\": 501,\n+ \"2\": 39834,\n+ \"20\": 66,\n+ \"3\": 29769,\n+ \"4\": 12627,\n+ \"5\": 5850,\n+ \"6\": 4815,\n+ \"7\": 2118,\n+ \"8\": 4593,\n+ \"9\": 1287\n+ },\n+ \"deficit\": 1320,\n+ \"edge_basis_values\": 42787,\n+ \"edge_distinct_values\": 42787,\n+ \"edge_nullity_histogram\": {\n+ \"0\": 41912\n+ },\n+ \"edge_removed_values\": 0,\n+ \"entropy\": \"1.881413992826e+06\",\n+ \"entropy_ratio\": \"8.307798044588e-01\",\n+ \"field_prime\": 1000003,\n+ \"frames\": 18532,\n+ \"h\": 22,\n+ \"incoming_dependencies\": 24,\n+ \"kernel_reuses\": 0,\n+ \"local_histogram\": {\n+ \"1\": 23898,\n+ \"10\": 930,\n+ \"11\": 354,\n+ \"12\": 1197,\n+ \"13\": 127,\n+ \"14\": 742,\n+ \"15\": 1879,\n+ \"16\": 88,\n+ \"17\": 81,\n+ \"18\": 13,\n+ \"19\": 167,\n+ \"2\": 11078,\n+ \"20\": 22,\n+ \"3\": 9923,\n+ \"4\": 4209,\n+ \"5\": 1950,\n+ \"6\": 1605,\n+ \"7\": 706,\n+ \"8\": 1531,\n+ \"9\": 429\n+ },\n+ \"loss\": 440,\n+ \"new_R\": 9412,\n+ \"new_W\": 12052,\n+ \"numerical_local_root\": \"7.009184438594e-04\",\n+ \"original_physical_roles\": 13372,\n+ \"original_role_crossings\": 46747,\n+ \"outgoing_dependencies\": 8116,\n+ \"retirement_histogram\": {\n+ \"1:12\": 66,\n+ \"1:20\": 198,\n+ \"1:3\": 84,\n+ \"1:6\": 4,\n+ \"2:10\": 63,\n+ \"2:11\": 1,\n+ \"2:12\": 103,\n+ \"2:13\": 26,\n+ \"2:14\": 117,\n+ \"2:15\": 87,\n+ \"2:16\": 293,\n+ \"2:17\": 177,\n+ \"2:18\": 651,\n+ \"2:19\": 3410,\n+ \"2:20\": 1320,\n+ \"2:21\": 2640,\n+ \"2:3\": 83,\n+ \"2:4\": 13,\n+ \"2:5\": 42,\n+ \"2:6\": 3,\n+ \"2:8\": 30,\n+ \"2:9\": 1\n+ },\n+ \"source_control_erasures\": 0,\n+ \"source_sha256\": {\n+ \"references/paired-cube/physical/frames.json\": \"1a6c215cdc58216f7ec96fb898a471e25d094fd86de085f6c06e86fd8997bfad\",\n+ \"references/paired-cube/physical/pairs.json\": \"abf341935148071a2222fe61c430e4e2fe3d16a64db14ab4eed9cd9a5a0f54d3\"\n+ },\n+ \"status\": \"Modular equal-frame flow price, retaining dirty kernel lifts and complete full-frame cleanup. Not an exact supplier certificate.\",\n+ \"v\": 1320,\n+ \"vectors\": 26200\n+ },\n+ \"gain_over_pr186\": \"7498375370201/330942774629799\",\n+ \"gain_over_pr191\": \"142516/6626307\",\n+ \"gain_over_pr193\": \"120951/6647872\",\n+ \"kappa\": \"6768823/10000000000\",\n+ \"lift\": {\n+ \"all_actual_coefficients_dyadic\": true,\n+ \"certificate_path\": \"research/source-assisted-v4/.work/lift.certificate.json.gz\",\n+ \"certificate_sha256\": \"85a482d8153b972cdb695ecebe1b802ac3414ba0e03fd8fdfe93aae0a73f2c24\",\n+ \"checker_path\": \"research/source-assisted/decision/exact_complex_flow_lift.py\",\n+ \"checker_sha256\": \"9d841bcfdc7c9c19b31791e8d7cfebd223d80d5e9ecd376d26257244f5323f2e\",\n+ \"coefficient_numerator_lcm\": \"2\",\n+ \"coefficients\": [\n+ [\n+ -2,\n+ 1\n+ ],\n+ [\n+ -1,\n+ 1\n+ ],\n+ [\n+ -1,\n+ 2\n+ ],\n+ [\n+ 1,\n+ 2\n+ ],\n+ [\n+ 1,\n+ 1\n+ ],\n+ [\n+ 2,\n+ 1\n+ ]\n+ ],\n+ \"denominator_lcm\": \"2\",\n+ \"exact_scalar_program_sha256\": \"3b4e671d7c6630570b04788bb2c81629e2c52f8dc2fcc5805952f0b403921027\",\n+ \"inverse_elementary_gates\": 58165,\n+ \"kernel_reuses\": 0,\n+ \"max_abs_numerator\": \"2\",\n+ \"max_denominator\": \"2\",\n+ \"nodes\": 18532,\n+ \"physical_R\": 9412,\n+ \"signature\": \"GPT-6 Astra\",\n+ \"source_control_vertices\": 0,\n+ \"source_erasures\": 0,\n+ \"status\": \"Exact rational local lifts and inverse gate programs verified; monotone flow and zero-fresh kernel reuse DAG verified.\",\n+ \"witness_path\": \"research/source-assisted-v4/.work/flow.witness.json\",\n+ \"witness_sha256\": \"51da02c6cd844276ca26608f1b714ab07d476ec25634ad1a9b461ccda2fbe457\"\n+ },\n+ \"lift_certificate_sha256\": \"85a482d8153b972cdb695ecebe1b802ac3414ba0e03fd8fdfe93aae0a73f2c24\",\n+ \"scope\": \"PR184 contract and finite bridge unchanged; the bit supplier is PR189 (verified by its own verify.py); the complex supplier is PR184's source-parity local word and frame flow on PR168 v4's query modules and physical layer, with donor/recipient pairs that avoid parity purification. No new flattened bit transcript or full Clifford/router replay, as in PR184.\",\n+ \"status\": \"PASS conditional finite witness\",\n+ \"witness_sha256\": \"51da02c6cd844276ca26608f1b714ab07d476ec25634ad1a9b461ccda2fbe457\"\n+}"},{"sha":"dc2e9dd21dfe3052dfb36d08d2dc3bd12b61aedc","filename":"research/community-round9-audit/pr202-queue-0.log.txt","status":"added","additions":8,"deletions":0,"changes":8,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr202-queue-0.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr202-queue-0.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr202-queue-0.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,8 @@\n+Traceback (most recent call last):\n+ File \"/private/tmp/integer-mult-export202/research/source-assisted-v4/verify.py\", line 167, in \n+ main()\n+ ~~~~^^\n+ File \"/private/tmp/integer-mult-export202/research/source-assisted-v4/verify.py\", line 162, in main\n+ assert result == read(target), 'Canonical certificate does not reproduce'\n+ ^^^^^^^^^^^^^^^^^^^^^^\n+AssertionError: Canonical certificate does not reproduce"},{"sha":"f8a225505d5f7a99d29b4da8cbc9af3a231dd76a","filename":"research/community-round9-audit/pr203-replay.log.txt","status":"added","additions":24,"deletions":0,"changes":24,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr203-replay.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr203-replay.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr203-replay.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,24 @@\n+PASS exact data/family ceilings and the sharp rank-minimal center controls\n+.......\n+----------------------------------------------------------------------\n+Ran 7 tests in 0.431s\n+\n+OK\n+PASS all 87 topologies and all scalar permutations; independent full-word controls\n+PASS 1/16: case 0, W=10, all 6^14 assignments excluded\n+PASS 2/16: case 3, W=9, all 6^14 assignments excluded\n+PASS 3/16: case 4, W=9, all 6^14 assignments excluded\n+PASS 4/16: case 13, W=9, all 6^14 assignments excluded\n+PASS 5/16: case 16, W=8, all 6^14 assignments excluded\n+PASS 6/16: case 34, W=9, all 6^14 assignments excluded\n+PASS 7/16: case 36, W=8, all 6^14 assignments excluded\n+PASS 8/16: case 37, W=8, all 6^14 assignments excluded\n+PASS 9/16: case 41, W=8, all 6^14 assignments excluded\n+PASS 10/16: case 43, W=7, all 6^14 assignments excluded\n+PASS 11/16: case 47, W=9, all 6^14 assignments excluded\n+PASS 12/16: case 50, W=8, all 6^14 assignments excluded\n+PASS 13/16: case 60, W=8, all 6^14 assignments excluded\n+PASS 14/16: case 62, W=7, all 6^14 assignments excluded\n+PASS 15/16: case 67, W=9, all 6^14 assignments excluded\n+PASS 16/16: case 70, W=8, all 6^14 assignments excluded\n+PASS conditional architecture audit; no new multiplication exponent"},{"sha":"d6812f3f9d3ed4e565cd4b2ff75895abebc6c7ff","filename":"research/community-round9-audit/pr204-replay.log.txt","status":"added","additions":15,"deletions":0,"changes":15,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr204-replay.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr204-replay.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr204-replay.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,15 @@\n+[pins] 21 package and input files match SOURCE.json\n+[regenerate] certificate.json reproduced exactly from the vendored pins\n+[pins] complex saving = 219037/312500000 (PR194 as published, kappa 1668581/2500000000), binding branch = bit at every depth\n+[cross-check] depth 0 kappa = 6768823/10000000000 equals PR200's announced value for this composition\n+[cross-check] PR184 legacy leaf 0.000677340866500955 vs PR200 published 0.000677340914792209 (delta 4.83e-11): one grid step at depth 0, identical at depth 2\n+[claim] kappa = 1693287/2500000000 (0.0006773148) at depth 2; vs #197 +0.1826%, vs PR200 announced +0.0639%\n+[ceiling] C/(1+C) = 0.000677314833683646; the claim sits 3.37e-11 below it, under one grid unit (1e-10)\n+[tolls] a_0 < a_1 < ... < a_2 < C < 1 - a_2\n+[adjacent grid] minimum margin = 0.00067731481317472 lies in (kappa, kappa + 1e-10)\n+[controls] rejected: bit profile with a perturbed W, leaf at or above the coarse saving, unbootstrapped depth-0 value offered as the claim\n+[levers] three published values reproduced exactly; banking the rank-60 exterior corrections is worth +0.8484% of kappa (0.000677314882 -> 0.0006830612994), which this package models and does not build\n+[audit] 3 banked rows priced to their own certificates exactly; the frontier is PR207 coordinated crossover at 0.000683190455036641, and its cheapest admissible ledger would reach 0.001207154248 (+76.6%), a bound rather than a construction\n+[targets] the frontier is bit at 213497/312500000; taking the bit word's rank-1 children into larger ones reaches the complex side's 0.0007004273 (+2.52%), and soaking both words' cheap children buys +15.98%, rising to +76.48% at the cheapest admissible ledgers\n+[first rung] coarsening 57/1000 of the mass in the bit word's smallest children reaches the complex side (bit coarse 700971690742463/1000000000000000000 vs the 350459170788869778860671/500000000000000000000000000 it needs)\n+PASS composed-diagonal-bit-bootstrap kappa = 1693287/2500000000 at depth 2; 47 strict constraints and 7 margins per depth"},{"sha":"15b6ee9fd9712de0260a6b5203cb13233cae0c0c","filename":"research/community-round9-audit/pr205-arithmetic.log.txt","status":"added","additions":2,"deletions":0,"changes":2,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr205-arithmetic.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr205-arithmetic.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr205-arithmetic.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,2 @@\n+PASS exact charts and banks on PR200, two moment engines, finite leaf composition, 47 constraints and seven margins\n+conditional kappa = 683061299399923/1000000000000000000"},{"sha":"1b0e54ead7f6b47edcc99ba09070174ec2c2ae27","filename":"research/community-round9-audit/pr205-banks.json","status":"added","additions":70,"deletions":0,"changes":70,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr205-banks.json","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr205-banks.json","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr205-banks.json?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,70 @@\n+{\n+ \"status\": \"PASS_FRESH_BANK_CERTIFICATE_EQUALITY\",\n+ \"pr\": 205,\n+ \"physical\": {\n+ \"status\": \"PASS exact actual-chain chart and incidence checks\",\n+ \"source_package\": \"research/paired-cube-diagonal-bit-168\",\n+ \"word_sha256\": \"0728ed1c7320430a87709b1034485cbabefec85d532b48897f74136cf3954218\",\n+ \"physical_roles\": 17114,\n+ \"interior_splices\": 1760,\n+ \"terminal_sinks\": 34,\n+ \"gauge_roles\": 2200,\n+ \"distinct_gauges\": 220,\n+ \"copies\": 3,\n+ \"banks\": 45842,\n+ \"patterns\": [\n+ {\n+ \"rank4\": 6,\n+ \"rank24\": 2,\n+ \"count\": 3300\n+ },\n+ {\n+ \"rank4\": 0,\n+ \"rank24\": 3,\n+ \"count\": 42542\n+ }\n+ ],\n+ \"incidences\": 154026,\n+ \"W\": 56402,\n+ \"m\": 72,\n+ \"rank_mass\": 4055136,\n+ \"deficit\": 5808,\n+ \"maxchild\": 22,\n+ \"child_histogram\": {\n+ \"1\": 377316,\n+ \"2\": 175962,\n+ \"3\": 92790,\n+ \"4\": 28764,\n+ \"5\": 24210,\n+ \"6\": 12456,\n+ \"7\": 12240,\n+ \"8\": 7542,\n+ \"9\": 5256,\n+ \"10\": 6066,\n+ \"11\": 3636,\n+ \"12\": 12186,\n+ \"13\": 4878,\n+ \"14\": 11016,\n+ \"15\": 2592,\n+ \"16\": 8964,\n+ \"17\": 4068,\n+ \"18\": 4842,\n+ \"19\": 1944,\n+ \"20\": 15840,\n+ \"21\": 45054,\n+ \"22\": 20016\n+ },\n+ \"chart_sha256\": \"22662b8580d62f26f50a7773ac45a40d4ffa8352bba5317ec3b2c0ce5897a810\",\n+ \"incidence_sha256\": \"76bff256b747bd188fdfa679059c8340cab7d8e1208db4b818d770ea08711117\",\n+ \"max_chart_factors\": 171,\n+ \"max_num\": 5,\n+ \"max_den\": 18,\n+ \"conservative_selector_calls\": 5368513266,\n+ \"color_stats\": {\n+ \"swaps\": 733,\n+ \"longest_swapped_path\": 11\n+ },\n+ \"conflicting_assignment_rejected\": true\n+ },\n+ \"scope\": \"Fresh exact bank/chart allocation only; parent supplier and default source-pin/arithmetic replay recorded separately\"\n+}"},{"sha":"a4f9fb71597f94fe8b949a19f72760cb3ab8f7ed","filename":"research/community-round9-audit/pr207-replay.log.txt","status":"added","additions":157,"deletions":0,"changes":157,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr207-replay.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr207-replay.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr207-replay.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,157 @@\n+PASS full exact rational value, geometry and alias checks; changes 302\n+PASS FULL_FINITE_REPLAY_PASS 169475279115177/250000000000000000\n+{\n+ \"status\": \"PASS_ADMITTED_FRAME_BANK_COMPOSITION\",\n+ \"output\": \"/private/var/folders/sd/yrr853rn73qdgdgdmps82gfh0000gn/T/crossover-pr200-vlw_tys1/source/research/coordinated-crossover-pr200/geometry/packed-frames.json\",\n+ \"changed_ops\": 302,\n+ \"stock\": \"56402/3\",\n+ \"rank\": 1351712,\n+ \"coarse\": \"136731504666219/200000000000000000\",\n+ \"ordinary\": \"546573370825043616599485038841961823/800000000000000000000000000000000000000\",\n+ \"ordinary_float\": 0.0006832167135313045,\n+ \"frames\": 24602\n+}\n+{\n+ \"status\": \"PASS_ALL_ACTUAL_GAUGE_CHARTS_AND_ROUTING_BILL\",\n+ \"source_pin\": \"a1175449f34d39ff933d9d8ab23ced1f32b290ec\",\n+ \"retained_factorizer_sha256\": \"56822a01bfc646b0f3b28d3ebc60aeb6acf380d53bbed96780992ea66ad1bec7\",\n+ \"gauges\": 2200,\n+ \"distinct_gauge_frames\": 220,\n+ \"max_chart_factors\": 186,\n+ \"max_factor_numerator\": 5,\n+ \"max_denominator_or_inverse_denominator\": 18,\n+ \"max_inverse_numerator\": 18,\n+ \"max_basis_numerator\": 2,\n+ \"chart_witness_sha256\": \"f81a21df89d4702b70564f9577b5506504de429ca5df253e78bd28f2685cd432\",\n+ \"greedy_distinct_scalars\": [\n+ 1,\n+ 2,\n+ 3,\n+ 4,\n+ 5,\n+ 6,\n+ 7,\n+ 8,\n+ 9,\n+ 10,\n+ 11,\n+ 12,\n+ 13,\n+ 14,\n+ 15,\n+ 16,\n+ 17,\n+ 18\n+ ],\n+ \"cleared_normalizer_difference_bound\": 11664,\n+ \"permutation_transpositions_bound\": 71,\n+ \"extra_distinct_scalar_coordinate_scales_bound\": 72,\n+ \"combined_chart_factor_bound\": 329,\n+ \"nine_full_replicas\": true,\n+ \"total_stage_core_occurrences\": 27,\n+ \"literal_persistent_stock\": 169206,\n+ \"conservative_extra_selector_calls\": 21900544398,\n+ \"selector_calls_below_2pow40\": true,\n+ \"prime_guard\": \"Every nonzero factor/inverse denominator and fixed scalar is smaller than2^80; all actual changes are invertible for every inherited primeq>2^80. Distinct normalizers remain distinct by cleared entry bounds.\",\n+ \"routing_payment\": \"These finite extra calls use inherited completed old ordinary selector; they are O(K V w^(1-a_old)), absorbed by strict finite-leaf atom/row toll as in PR197 PROOF5. No extra positive-rank children and no new external row reserve.\",\n+ \"scope\": \"Exact finite address chart, inverse, unit and replicated routing bill on same220gauge frames; allsize weighted/restored selector guarantee stays inherited.\"\n+}\n+PASS_LITERAL_DISTINCT_NORMALIZERS\n+{\"stage\": \"exact_completions\", \"nodes\": 0, \"denominator_lcm\": \"1\", \"seconds\": 70.13149750000048}\n+{\"stage\": \"exact_completions\", \"nodes\": 4000, \"denominator_lcm\": \"2\", \"seconds\": 71.73180345800029}\n+{\"stage\": \"exact_completions\", \"nodes\": 8000, \"denominator_lcm\": \"2\", \"seconds\": 74.087349292}\n+{\"stage\": \"exact_completions\", \"nodes\": 12000, \"denominator_lcm\": \"2\", \"seconds\": 83.44241104200046}\n+{\"stage\": \"exact_completions\", \"nodes\": 16000, \"denominator_lcm\": \"2\", \"seconds\": 90.47279745800006}\n+{\n+ \"signature\": \"GPT-6 Astra\",\n+ \"status\": \"Exact rational local lifts and inverse gate programs verified; monotone flow and zero-fresh kernel reuse DAG verified.\",\n+ \"nodes\": 18532,\n+ \"inverse_elementary_gates\": 58165,\n+ \"source_control_vertices\": 0,\n+ \"source_erasures\": 0,\n+ \"kernel_reuses\": 0,\n+ \"physical_R\": 9412,\n+ \"denominator_lcm\": \"2\",\n+ \"coefficient_numerator_lcm\": \"2\",\n+ \"max_abs_numerator\": \"2\",\n+ \"max_denominator\": \"2\",\n+ \"all_actual_coefficients_dyadic\": true,\n+ \"coefficients\": [\n+ [\n+ -2,\n+ 1\n+ ],\n+ [\n+ -1,\n+ 1\n+ ],\n+ [\n+ -1,\n+ 2\n+ ],\n+ [\n+ 1,\n+ 2\n+ ],\n+ [\n+ 1,\n+ 1\n+ ],\n+ [\n+ 2,\n+ 1\n+ ]\n+ ],\n+ \"certificate_path\": \"/private/var/folders/sd/yrr853rn73qdgdgdmps82gfh0000gn/T/crossover-pr200-vlw_tys1/source/research/source-assisted-v4/.work/lift.certificate.json.gz\",\n+ \"certificate_sha256\": \"72a9626394aff05457ba5d25fc312608effba611f1f184ad8a6ddf186c7b150f\",\n+ \"exact_scalar_program_sha256\": \"3b4e671d7c6630570b04788bb2c81629e2c52f8dc2fcc5805952f0b403921027\",\n+ \"witness_path\": \"/private/var/folders/sd/yrr853rn73qdgdgdmps82gfh0000gn/T/crossover-pr200-vlw_tys1/source/research/source-assisted-v4/.work/flow.witness.json\",\n+ \"witness_sha256\": \"51da02c6cd844276ca26608f1b714ab07d476ec25634ad1a9b461ccda2fbe457\",\n+ \"checker_path\": \"decision/exact_complex_flow_lift.py\",\n+ \"checker_sha256\": \"9d841bcfdc7c9c19b31791e8d7cfebd223d80d5e9ecd376d26257244f5323f2e\",\n+ \"seconds\": 94.29781220800032\n+}\n+{\n+ \"status\": \"Exact local invertible flow, exact all-column fresh identity, paid source controls, target read chains, and integer histogram certified. A literal globally renumbered operation program is not exported; dense initial dirty-response subtraction is defined by the exact certified flow.\",\n+ \"physical_R\": 9412,\n+ \"m\": 66,\n+ \"W_per_vertex\": 12052,\n+ \"deficit_per_vertex\": 1320,\n+ \"numerical_local_root\": 0.0007009184438593612,\n+ \"contract_checks\": {\n+ \"all_fresh_columns_equal_identity\": true,\n+ \"arithmetic\": \"integers, endpoint scaled by 6\",\n+ \"checked_source_columns\": 1320,\n+ \"checked_target_rows\": 1320,\n+ \"source_controls_at_paid_parity_frames\": true,\n+ \"original_source_V_before_all_controls\": true,\n+ \"controls_before_original_K\": true,\n+ \"all_centers_in_phase1\": true,\n+ \"all_target_cap_reads_in_phase2\": true,\n+ \"target_chains_nested\": true,\n+ \"read_counts\": {\n+ \"center\": 22,\n+ \"side\": 3135,\n+ \"deferred\": 2310\n+ },\n+ \"target_data_histogram\": {\n+ \"0\": 6270,\n+ \"1\": 3960,\n+ \"18\": 1320\n+ },\n+ \"positive_target_data_histogram\": {\n+ \"1\": 3960,\n+ \"18\": 1320\n+ }\n+ },\n+ \"seconds\": 4.30832937500054\n+}\n+{\n+ \"status\": \"PASS_EXACT_47_CONSTRAINT_ASSEMBLY\",\n+ \"kappa\": \"1366380910073/2000000000000000\",\n+ \"kappa_float\": 0.0006831904550365,\n+ \"bit_ordinary\": \"4375408149318106538866216854671930632866706725794304565219529058788314814256861959639757/6400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\",\n+ \"a_complex\": \"700918443859411/1000000000000000000\"\n+}\n+PASS full offline bit/frame/bank/chart/complex-lift/contract replay, independent paid moments, 47 inequalities and controls; kappa=1366380910073/2000000000000000\n+PASS immutable manual-upload package; no network, git, or publication required"},{"sha":"7452270c5fb37ab3e4641481474ca353d812cada","filename":"research/community-round9-audit/pr208-replay.log.txt","status":"added","additions":19,"deletions":0,"changes":19,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr208-replay.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr208-replay.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr208-replay.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,19 @@\n+[pins] 25 package and input files match SOURCE.json\n+[regenerate] certificate.json reproduced exactly from the vendored pins\n+[pins] complex saving = 219037/312500000 (PR194 as published, kappa 1668581/2500000000), binding branch = bit at every depth\n+[cross-check] depth 0 kappa = 6768823/10000000000 equals PR200's announced value for this composition\n+[cross-check] PR184 legacy leaf 0.000677340866500955 vs PR200 published 0.000677340914792209 (delta 4.83e-11): one grid step at depth 0, identical at depth 2\n+[claim] kappa = 1693287/2500000000 (0.0006773148) at depth 2; vs #197 +0.1826%, vs PR200 announced +0.0639%\n+[ceiling] C/(1+C) = 0.000677314833683646; the claim sits 3.37e-11 below it, under one grid unit (1e-10)\n+[tolls] a_0 < a_1 < ... < a_2 < C < 1 - a_2\n+[adjacent grid] minimum margin = 0.00067731481317472 lies in (kappa, kappa + 1e-10)\n+[controls] rejected: bit profile with a perturbed W, leaf at or above the coarse saving, unbootstrapped depth-0 value offered as the claim\n+[levers] three published values reproduced exactly; banking the rank-60 exterior corrections is worth +0.8484% of kappa (0.000677314882 -> 0.0006830612994), which this package models and does not build\n+[audit] 3 banked rows priced to their own certificates exactly; the frontier is PR207 coordinated crossover at 0.000683190455036641, and its cheapest admissible ledger would reach 0.001207154248 (+76.6%), a bound rather than a construction\n+[targets] the frontier is bit at 213497/312500000; taking the bit word's rank-1 children into larger ones reaches the complex side's 0.0007004273 (+2.52%), and soaking both words' cheap children buys +15.98%, rising to +76.48% at the cheapest admissible ledgers\n+[first rung] coarsening 57/1000 of the mass in the bit word's smallest children reaches the complex side (bit coarse 700971690742463/1000000000000000000 vs the 350459170788869778860671/500000000000000000000000000 it needs)\n+[rungs] absorbing whole families into the banks, two tiers. Sound schedules (each family's blocks tile the bank by themselves): the bit word can bank ranks [6, 8, 18], the complex word rank [11] -- 1 new residual type on rank 6 is 54531/78125000 (+2.17%), two types reach the unmoved complex cap at 7004273/10000000000 (+2.52%), and three types (adding the complex word's own rank 11) reach 3541457/5000000000 (+3.67%)\n+[rungs certified shape] with the absorbed family's rank free, only the volume must fill whole banks: 750 candidate pairs, 725 of them above the frontier, 1 new residual type reaching 7004273/10000000000 (+2.52%), 3 types 1819669/2500000000 (+6.54%), and 8 types 3066221/2500000000 (+79.52%)\n+[banks] the queue's own banked rows removed rank-60 exteriors from a width-72 word (60 does not divide 72), volume 396000 = 72 x 5500, with blocks of 4 and 24 tiling the width as 18 x 4, 3 x 24 or 6 x 4 + 2 x 24 -- so an absorbed family's rank is free, the volume condition is the certified one, and the certified-shape ladder is the primary one at 7004273/10000000000 (+2.52%) for a single new residual type\n+[allocation] against the suppliers' own rules, no rung of this ladder is bankable by the construction as published: it banks one family -- the selected entrance-gauge exteriors, already taken in this word -- and retains every other, with alias children, source births and deleted terminals excluded outright. The schedule a builder would hand its generator is fixed here: the cheapest certified rung is bit rank 22, 6116 banks of 72 registers, volume 440352, retained W 50286; the two-family tiling rung is ranks 6 and 8, 1824 banks in 608 whole banks per stage, retained W 54578\n+PASS composed-diagonal-bit-bootstrap kappa = 1693287/2500000000 at depth 2; 47 strict constraints and 7 margins per depth"},{"sha":"88f0b3d0cbfc6c41a78bc3bb219911142bf845f2","filename":"research/community-round9-audit/pr209-diff-review.json","status":"added","additions":10,"deletions":0,"changes":10,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr209-diff-review.json","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr209-diff-review.json","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr209-diff-review.json?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,10 @@\n+{\n+ \"pr\": 209,\n+ \"base\": \"3b6b66891c0ac888521cf591fe306c6286601d4f\",\n+ \"head\": \"a7aeea067ec1e2b7e91b0ecec660512b7cafca26\",\n+ \"changed_files\": [\n+ \"CONTRIBUTORS.md\"\n+ ],\n+ \"diff_sha256\": \"8914e0ea54ebb061653c39fb30bf8b62c84741f1e15e06d827a11e9f24336184\",\n+ \"scope\": \"One attribution bullet, appropriately scoped to separate family-130 RAM/Fourier Lean development. Publication source supplies the later five-stage lineage; no independent Lean rebuild of that linked project in this review.\"\n+}"},{"sha":"d9e27b66d89a56f13f391383265f2df9e36105a1","filename":"research/community-round9-audit/pr209-reviewed.diff","status":"added","additions":9,"deletions":0,"changes":9,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr209-reviewed.diff","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr209-reviewed.diff","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr209-reviewed.diff?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,9 @@\n+diff --git a/CONTRIBUTORS.md b/CONTRIBUTORS.md\n+index 049b44a..ee8e4b1 100644\n+--- a/CONTRIBUTORS.md\n++++ b/CONTRIBUTORS.md\n+@@ -211,3 +211,4 @@ verified posts, profile associations and unresolved account identities.\n+ \n+ - **Michiel Kosters** ([research repository](https://github.com/michielkosters/mathematics_ai/tree/2e0aa64ca09c87fc94f8575f59493f70cf929d71/problems/integer-multiplication-109); Douglas associates @one_line_proof) developed a parallel weighted-hypergraph/coordinate-frame candidate, compressed centers and aligned bit pairing. Our [review](research/parallel-announcements/README.md) reproduces the finite certificate with its transfer/precision limitations explicit.\n+ - **Abe / @abe_asfaw**, via a suggestion supplied by Douglas, identified the redundant complex center and its historical 26.5% numerical gain. We [checked the scalar identity, counts and assembly arithmetic](research/parallel-announcements/README.md), and credit this parallel observation alongside the already preserved rank-h center research.\n++- **Jacob Sussman** ([jacobalansussman](https://github.com/jacobalansussman/wht-power-saving-lean/tree/fdfb7815c15ec43af0fb54818a6a57ae4025126b)) published a separate Lean 4 development on the Fourier side (OpenAI's family 130, not this project's multiplication theorem): a proof of #130's general frame lemma for that RAM model, and a kernel check of #193's complex word, rebuilt from the published data, inside a five-stage layout. It was built with AI agents (Claude) and makes no κ claim. Nothing in it has been replayed or reviewed here."},{"sha":"2a709edbef4467899a763d2ace0cd8b94f43aee4","filename":"research/community-round9-audit/pr210-banks.json","status":"added","additions":3825,"deletions":0,"changes":3825,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr210-banks.json","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr210-banks.json","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr210-banks.json?ref=12a4934d15006e8c10f9b2264f13f8f341be802b"},{"sha":"22fe6ee4aee6ca058ee99dc441e87a179335232f","filename":"research/community-round9-audit/pr210-bit.json","status":"added","additions":393,"deletions":0,"changes":393,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr210-bit.json","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr210-bit.json","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr210-bit.json?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,393 @@\n+{\n+ \"geometry\": {\n+ \"all_1760_ports_coordinate_permutation_equivalent\": true,\n+ \"checked_actual_entrances\": [\n+ {\n+ \"completion_rank\": 100,\n+ \"distinct_windows\": 5,\n+ \"local_frame\": 127239,\n+ \"local_rank\": 20\n+ },\n+ {\n+ \"completion_rank\": 100,\n+ \"distinct_windows\": 5,\n+ \"local_frame\": 127241,\n+ \"local_rank\": 20\n+ }\n+ ],\n+ \"checked_actual_ports\": [\n+ {\n+ \"boundaries\": 8,\n+ \"idle_ranks\": [\n+ 46,\n+ 46,\n+ 23,\n+ 23,\n+ 50,\n+ 50,\n+ 4,\n+ 4\n+ ],\n+ \"labels\": [\n+ 0,\n+ 2,\n+ 4\n+ ],\n+ \"port\": 0,\n+ \"routes\": 5\n+ },\n+ {\n+ \"boundaries\": 8,\n+ \"idle_ranks\": [\n+ 46,\n+ 46,\n+ 23,\n+ 23,\n+ 50,\n+ 50,\n+ 4,\n+ 4\n+ ],\n+ \"labels\": [\n+ 19,\n+ 21,\n+ 23\n+ ],\n+ \"port\": 1759,\n+ \"routes\": 5\n+ }\n+ ],\n+ \"checked_new_sparse_source_frames\": 31,\n+ \"clean_fingerprint\": {\n+ \"scalar_word_sha256\": \"e675d4eb9d90ff0b44279fae0b46f1a8b39f65421cc38454b70a6b75d0e10b42\"\n+ },\n+ \"distinct_entrances_noncommuting\": false,\n+ \"m\": 120,\n+ \"scope\": \"Exact rational h24/m120 route and idle matrices for actual source ports and actual independent entrance bases. Coordinate-permutation/direct-sum arguments cover the remaining ports and independent entrances. No scalar payload replay.\",\n+ \"script_sha256\": \"bff96140e93c0cea01ed618b49b913f913c12d99ebb0e4e4342336cf5a102800\",\n+ \"seconds\": 2.8829491670003335,\n+ \"source_pins\": {},\n+ \"status\": \"PASS_EXACT_H24_CALLABLE_LOWERING_GEOMETRY\",\n+ \"terminal_exchange_frame_identity_checked\": true,\n+ \"wrong_duplicate_window_rejected\": true,\n+ \"wrong_equal_rank_correction_rejected\": true\n+ },\n+ \"global_result\": {\n+ \"bank_F2_endpoint_after_terminal_relabel\": [\n+ 1,\n+ 2,\n+ 4,\n+ 8\n+ ],\n+ \"bank_F2_endpoint_before_terminal_relabel\": [\n+ 2,\n+ 1,\n+ 8,\n+ 4\n+ ],\n+ \"bridge_additions\": 10560,\n+ \"controls_rejected\": [\n+ \"unremapped local temporary collides with arbitrary live helper\",\n+ \"literal inverse of erased copy loses arbitrary center contribution\",\n+ \"omitted bridge 0\",\n+ \"omitted bridge 1\",\n+ \"omitted bridge 2\",\n+ \"omitted bridge 3\",\n+ \"omitted bridge 4\",\n+ \"omitted bridge 5\",\n+ \"stage4 helper route aliases stage3 window\"\n+ ],\n+ 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6418,\n+ \"1/3\": 3960,\n+ \"2\": 561\n+ },\n+ \"old_response\": {\n+ \"-1\": 2277,\n+ \"-1/2\": 9185,\n+ \"-1/3\": 3960,\n+ \"-2\": 2389,\n+ \"1\": 26677,\n+ \"1/2\": 2112,\n+ \"1/6\": 25080,\n+ \"2\": 561\n+ }\n+ },\n+ \"other_main_recursive_calls\": \"70147 existing live-label transitions, unchanged; not scalar macros\",\n+ \"phases\": {\n+ \"cleanup\": {\n+ \"Gaussian_primitive_steps\": 129658,\n+ \"add\": 40231,\n+ \"all_macros\": 40231,\n+ \"divisor3_exposure\": 0,\n+ \"halving_exposure\": 6015,\n+ \"real_component_primitive_steps\": 259316,\n+ \"scalar_log2_magnitude_charge\": 43181,\n+ \"scalar_macros\": 40231\n+ },\n+ \"main\": {\n+ \"Gaussian_primitive_steps\": 312920,\n+ \"add\": 80843,\n+ \"all_macros\": 80909,\n+ \"clear\": 44,\n+ \"divisor3_exposure\": 29040,\n+ \"halving_exposure\": 38357,\n+ \"real_component_primitive_steps\": 625840,\n+ \"recursive_centers\": 22,\n+ \"recursive_rank_mass\": 440,\n+ \"scalar_log2_magnitude_charge\": 83793,\n+ \"scalar_macros\": 80887\n+ },\n+ \"old_response\": {\n+ \"Gaussian_primitive_steps\": 303914,\n+ \"add\": 72241,\n+ \"all_macros\": 91065,\n+ \"clear\": 9412,\n+ \"copy\": 9412,\n+ \"divisor3_exposure\": 29040,\n+ \"halving_exposure\": 36377,\n+ \"real_component_primitive_steps\": 607828,\n+ \"scalar_log2_magnitude_charge\": 75191,\n+ \"scalar_macros\": 91065\n+ }\n+ },\n+ \"schedule_sha256\": \"0e8809c4cce8f981e68b435f9a5529f10f6bd5ae7697c69124c82711c4ac79b3\",\n+ \"totals\": {\n+ \"Gaussian_primitive_steps\": 746492,\n+ \"add\": 193315,\n+ \"all_macros\": 212205,\n+ \"clear\": 9456,\n+ \"copy\": 9412,\n+ \"divisor3_exposure\": 58080,\n+ \"halving_exposure\": 80749,\n+ \"real_component_primitive_steps\": 1492984,\n+ \"recursive_centers\": 22,\n+ \"scalar_log2_magnitude_charge\": 202165,\n+ \"scalar_macros\": 212183\n+ }\n+ },\n+ \"scratch\": {\n+ \"additional_recursive_calls\": 0,\n+ \"extra_external_row_coordinate\": false,\n+ \"live_roles\": 14692,\n+ \"physical_roles_per_cover\": 24127\n+ },\n+ \"scratch_lifecycle_checks\": {\n+ \"backward\": {\n+ \"center_children\": 22,\n+ \"coefficient_work_cleared_per_add\": true,\n+ \"complete_stream_fraction\": \"1/(14692*|Orth(110,2)|)\",\n+ \"moment_live_width\": 14692,\n+ \"new_recursive_children\": 0,\n+ \"new_work_stock_only\": 9413,\n+ \"tableau_absent_from_all_children\": true,\n+ \"tableau_cleared_before_entire_main_phase\": true\n+ },\n+ \"forward\": {\n+ \"center_children\": 22,\n+ \"coefficient_work_cleared_per_add\": true,\n+ \"complete_stream_fraction\": \"1/(14692*|Orth(110,2)|)\",\n+ \"moment_live_width\": 14692,\n+ \"new_recursive_children\": 0,\n+ \"new_work_stock_only\": 9413,\n+ \"tableau_absent_from_all_children\": true,\n+ \"tableau_cleared_before_entire_main_phase\": true\n+ }\n+ },\n+ \"template_tests\": {\n+ \"checks_passed\": 7,\n+ \"published_full_scalar_replay\": false,\n+ \"tiny_exact_template_columns_checked\": 7,\n+ \"unreversed_transpose_rejected\": true,\n+ \"wrong_inverse_sign_rejected\": true\n+ }\n+ },\n+ \"splice\": {\n+ \"certificate_sha256\": \"15251deb0c11e0504d7b297c9786818888a93f08b92b03c6c122784b70488633\",\n+ \"controls\": [\n+ {\n+ \"name\": \"drop_final_climb\",\n+ \"orientation\": \"forward\",\n+ \"reason\": \"final climbs omitted before cleanup\",\n+ \"rejected\": true\n+ },\n+ {\n+ \"name\": \"cleanup_before_final_climbs\",\n+ \"orientation\": \"forward\",\n+ \"reason\": \"strict old/A/copy/B/final/adapter/cleanup chronology\",\n+ \"rejected\": true\n+ },\n+ {\n+ \"name\": \"drop_final_frame_adapter\",\n+ \"orientation\": \"forward\",\n+ \"reason\": \"missing or reordered exact final adapter\",\n+ \"rejected\": true\n+ },\n+ {\n+ \"name\": \"wrong_common_exact_gate_label\",\n+ \"orientation\": \"forward\",\n+ \"reason\": \"scalar incidence uses wrong exact label\",\n+ \"rejected\": true\n+ },\n+ {\n+ \"name\": \"drop_center_child\",\n+ \"orientation\": \"forward\",\n+ \"reason\": \"center source frame\",\n+ \"rejected\": true\n+ },\n+ {\n+ \"name\": \"tableau_not_erased_before_child\",\n+ \"orientation\": \"forward\",\n+ \"reason\": \"old-response tableau survived before label recursion\",\n+ \"rejected\": true\n+ },\n+ {\n+ \"name\": \"wrong_cleanup_sign\",\n+ \"orientation\": \"forward\",\n+ \"reason\": \"complete scalar program differs from checked bill\",\n+ \"rejected\": true\n+ },\n+ {\n+ \"name\": \"drop_final_climb\",\n+ \"orientation\": \"backward\",\n+ \"reason\": \"final climbs omitted before cleanup\",\n+ \"rejected\": true\n+ },\n+ {\n+ \"name\": \"cleanup_before_final_climbs\",\n+ \"orientation\": \"backward\",\n+ \"reason\": \"strict old/A/copy/B/final/adapter/cleanup chronology\",\n+ \"rejected\": true\n+ },\n+ {\n+ \"name\": \"drop_final_frame_adapter\",\n+ \"orientation\": \"backward\",\n+ \"reason\": \"missing or reordered exact final adapter\",\n+ \"rejected\": true\n+ },\n+ {\n+ \"name\": \"wrong_common_exact_gate_label\",\n+ \"orientation\": \"backward\",\n+ \"reason\": \"scalar incidence uses wrong exact label\",\n+ \"rejected\": true\n+ },\n+ {\n+ \"name\": \"drop_center_child\",\n+ \"orientation\": \"backward\",\n+ \"reason\": \"center source frame\",\n+ \"rejected\": true\n+ },\n+ {\n+ \"name\": \"tableau_not_erased_before_child\",\n+ \"orientation\": \"backward\",\n+ \"reason\": \"old-response tableau survived before label recursion\",\n+ \"rejected\": true\n+ },\n+ {\n+ \"name\": \"wrong_cleanup_sign\",\n+ \"orientation\": \"backward\",\n+ \"reason\": \"complete scalar program differs from checked bill\",\n+ \"rejected\": true\n+ },\n+ {\n+ \"name\": \"wrong_helper_owner\",\n+ \"reason\": \"five-window exact source/tape/namespace contract changed\",\n+ \"rejected\": true\n+ },\n+ {\n+ \"name\": \"rank_only_frame\",\n+ \"reason\": \"five-window exact source/tape/namespace contract changed\",\n+ \"rejected\": true\n+ },\n+ {\n+ \"name\": \"scratch_alias\",\n+ \"reason\": \"five-window exact source/tape/namespace contract changed\",\n+ \"rejected\": true\n+ },\n+ {\n+ \"name\": \"wrong_live_normalization\",\n+ \"reason\": \"five-window exact source/tape/namespace contract changed\",\n+ \"rejected\": true\n+ },\n+ {\n+ \"name\": \"free_RAM\",\n+ \"reason\": \"five-window exact source/tape/namespace contract changed\",\n+ \"rejected\": true\n+ },\n+ {\n+ \"name\": \"missing_tableau\",\n+ \"reason\": \"five-window exact source/tape/namespace contract changed\",\n+ \"rejected\": true\n+ }\n+ ],\n+ \"global_contract\": {\n+ \"chronology\": [\n+ \"stage0\",\n+ \"stage1\",\n+ \"climbA\",\n+ \"bridgeA\",\n+ \"stage2\",\n+ \"climbB\",\n+ \"bridgeB\",\n+ \"stage3\",\n+ \"stage4\",\n+ \"final_climbs\",\n+ \"bridgeC\",\n+ \"terminal_shifts\",\n+ \"signed_exchange\"\n+ ],\n+ \"exact_frame_bindings\": {\n+ \"sfin\": {\n+ \"anchor\": \"sfin :\",\n+ \"declaration_line\": \"sfin : \\u2200 g, W4 (s4.symm g) * (W3 (s3.symm g) * (W2 (s2.symm g) * (W1 (s1.symm g) * (G0 g).Xm.\\u03a6 1))) = kernel \\u03b1\",\n+ \"line\": 82,\n+ \"source\": \"Work/GCert/Chain/NetDef.lean\",\n+ \"url\": \"https://github.com/jacobalansussman/wht-power-saving-lean/blob/f010392c923279e3dd59ef3aa5fedad23affc5fd/Work/GCert/Chain/NetDef.lean#L82\"\n+ },\n+ \"term\": {\n+ \"anchor\": \"term :\",\n+ \"declaration_line\": \"term : \\u2200 g t, kernel \\u03b1 * (G0 g).Xm.\\u03a6 (tt (I.tv t)) = shift (u g t) * YF g t\",\n+ \"line\": 94,\n+ \"source\": \"Work/GCert/Chain/NetDef.lean\",\n+ \"url\": \"https://github.com/jacobalansussman/wht-power-saving-lean/blob/f010392c923279e3dd59ef3aa5fedad23affc5fd/Work/GCert/Chain/NetDef.lean#L94\"\n+ },\n+ \"x01\": {\n+ \"anchor\": \"x01 :\",\n+ \"declaration_line\": \"x01 : \\u2200 g t, (G0 g).Xm.\\u03a6 1 = (G1 (r1 t g)).Xm.\\u03a6 (tt (I.tv t))\",\n+ \"line\": 73,\n+ \"source\": \"Work/GCert/Chain/NetDef.lean\",\n+ \"url\": \"https://github.com/jacobalansussman/wht-power-saving-lean/blob/f010392c923279e3dd59ef3aa5fedad23affc5fd/Work/GCert/Chain/NetDef.lean#L73\"\n+ },\n+ \"x12\": {\n+ \"anchor\": \"x12 :\",\n+ \"declaration_line\": \"x12 : \\u2200 g t, (G1 (r1 t g)).Xm.\\u03a6 1 = (G2 (r2 t g)).Xm.\\u03a6 (tt (I.tv t))\",\n+ \"line\": 75,\n+ \"source\": \"Work/GCert/Chain/NetDef.lean\",\n+ \"url\": \"https://github.com/jacobalansussman/wht-power-saving-lean/blob/f010392c923279e3dd59ef3aa5fedad23affc5fd/Work/GCert/Chain/NetDef.lean#L75\"\n+ },\n+ \"x23\": {\n+ \"anchor\": \"x23 :\",\n+ \"declaration_line\": \"x23 : \\u2200 g t, (G2 (r2 t g)).Xm.\\u03a6 1 = (G3 (r3 t g)).Xm.\\u03a6 (tt (I.tv t))\",\n+ \"line\": 77,\n+ \"source\": \"Work/GCert/Chain/NetDef.lean\",\n+ \"url\": \"https://github.com/jacobalansussman/wht-power-saving-lean/blob/f010392c923279e3dd59ef3aa5fedad23affc5fd/Work/GCert/Chain/NetDef.lean#L77\"\n+ },\n+ \"x34\": {\n+ \"anchor\": \"x34 :\",\n+ \"declaration_line\": \"x34 : \\u2200 g t, (G3 (r3 t g)).Xm.\\u03a6 1 = (G4 (r4 t g)).Xm.\\u03a6 (tt (I.tv t))\",\n+ \"line\": 79,\n+ \"source\": \"Work/GCert/Chain/NetDef.lean\",\n+ \"url\": \"https://github.com/jacobalansussman/wht-power-saving-lean/blob/f010392c923279e3dd59ef3aa5fedad23affc5fd/Work/GCert/Chain/NetDef.lean#L79\"\n+ },\n+ \"y01\": {\n+ \"anchor\": \"y01 :\",\n+ \"declaration_line\": \"y01 : \\u2200 g t, (G0 g).Xm.\\u03a6 (1 + tt (I.tv t)) = (G1 (r1 t g)).Xm.\\u03a6 0\",\n+ \"line\": 74,\n+ \"source\": \"Work/GCert/Chain/NetDef.lean\",\n+ \"url\": \"https://github.com/jacobalansussman/wht-power-saving-lean/blob/f010392c923279e3dd59ef3aa5fedad23affc5fd/Work/GCert/Chain/NetDef.lean#L74\"\n+ },\n+ \"y12\": {\n+ \"anchor\": \"y12 :\",\n+ \"declaration_line\": \"y12 : \\u2200 g t, (G1 (r1 t g)).Xm.\\u03a6 (1 + tt (I.tv t)) = (G2 (r2 t g)).Xm.\\u03a6 0\",\n+ \"line\": 76,\n+ \"source\": \"Work/GCert/Chain/NetDef.lean\",\n+ \"url\": \"https://github.com/jacobalansussman/wht-power-saving-lean/blob/f010392c923279e3dd59ef3aa5fedad23affc5fd/Work/GCert/Chain/NetDef.lean#L76\"\n+ },\n+ \"y23\": {\n+ \"anchor\": \"y23 :\",\n+ \"declaration_line\": \"y23 : \\u2200 g t, (G2 (r2 t g)).Xm.\\u03a6 (1 + tt (I.tv t)) = (G3 (r3 t g)).Xm.\\u03a6 0\",\n+ \"line\": 78,\n+ \"source\": \"Work/GCert/Chain/NetDef.lean\",\n+ \"url\": \"https://github.com/jacobalansussman/wht-power-saving-lean/blob/f010392c923279e3dd59ef3aa5fedad23affc5fd/Work/GCert/Chain/NetDef.lean#L78\"\n+ },\n+ \"y34\": {\n+ \"anchor\": \"y34 :\",\n+ \"declaration_line\": \"y34 : \\u2200 g t, (G3 (r3 t g)).Xm.\\u03a6 (1 + tt (I.tv t)) = (G4 (r4 t g)).Xm.\\u03a6 0\",\n+ \"line\": 80,\n+ \"source\": \"Work/GCert/Chain/NetDef.lean\",\n+ \"url\": \"https://github.com/jacobalansussman/wht-power-saving-lean/blob/f010392c923279e3dd59ef3aa5fedad23affc5fd/Work/GCert/Chain/NetDef.lean#L80\"\n+ }\n+ },\n+ \"family\": \"baseline5stageComplex\",\n+ \"global_bound_exponent\": 6050,\n+ \"helper_policy\": \"arbitrary_input; inherited_dirty_lift; Z5=kernel\",\n+ \"label_policy\": \"identical_exact_representative_and_paid_rank_zero_reconciliation\",\n+ \"live\": 14692,\n+ \"local_bound_exponent\": 48,\n+ \"m\": 110,\n+ \"maintained_guard_changed\": false,\n+ \"odd_grid\": \"2^(-P)3^(-G(D+1)); no return rounding\",\n+ \"physical\": 24127,\n+ \"primitive_policy\": \"charged_fixed_tape_complete_streams\",\n+ \"primitive_recipe\": {\n+ \"center_backward\": \"zero at frame zero; accumulate transpose scatter; exact residual to retained frame; subtract into original; erase\",\n+ \"center_forward\": \"copy at retained frame; exact residual to frame zero; scatter; erase\",\n+ \"cross_phase\": \"i^(2xy) = i^x i^y i^(-(x xor y)); at most three parity-phase scans\",\n+ \"entry_exit\": \"WinB.old_to_new and WinB.new_to_old, lowered as paid exact rank-zero Clifford operators\",\n+ \"live_child\": \"exact target representative times inverse current representative; two rank-zero factors around one C tensor child\",\n+ \"phase_scan\": \"evaluate fixed Z4 quadratic descriptors per record, multiply by fourth root, record suffix pays descriptor arithmetic\",\n+ \"rank_zero\": \"binary Gaussian elimination; affine bit flips; Z4 linear phases and even cross terms; exact scalar fourth root\",\n+ \"role_route\": \"permutation on all complete live/work roles, at most W_physical^2 complete-stream exchanges on fixed tapes\",\n+ \"row_stock\": \"split only live complete rows; scalar-only work creates no row coordinate or recursive branch\",\n+ \"scalar\": \"copy source to W; optional double/halve/divide3; signed accumulate; clear W\",\n+ \"selected_bit\": \"compact-control-movement proposition, complete restored borrowed fields, paid repair, no RAM lookup\"\n+ },\n+ \"recursive_volume_denominator\": 14692,\n+ \"scratch_namespace\": {\n+ \"centers\": [\n+ 14692,\n+ 14714\n+ ],\n+ \"coefficient\": [\n+ 24126,\n+ 24127\n+ ],\n+ \"tableau\": [\n+ 14714,\n+ 24126\n+ ]\n+ },\n+ \"stage_recipe\": [\n+ {\n+ \"active_pair\": 1,\n+ \"bank_owner\": \"d\",\n+ \"exterior_subset\": \"empty\",\n+ \"helper_owner\": \"d\",\n+ \"native_frame\": \"(G0 d).X.Phi(frames[f])\",\n+ \"old_frame\": \"(G0 d).Xm.Phi(P)\",\n+ \"orientation\": \"forward\",\n+ \"stage\": 0,\n+ \"window\": \"G0\"\n+ },\n+ {\n+ \"active_pair\": 1,\n+ \"bank_owner\": \"r1(t)^(-1)(d)\",\n+ \"exterior_subset\": \"qS bs1 l\",\n+ \"helper_owner\": \"s1(d)\",\n+ \"native_frame\": \"(G1 d).X.Phi(frames[f])\",\n+ \"old_frame\": \"(G1 d).Xm.Phi(P)\",\n+ \"orientation\": \"backward\",\n+ \"stage\": 1,\n+ \"window\": \"G1\"\n+ },\n+ {\n+ \"active_pair\": 1,\n+ \"bank_owner\": \"r2(t)^(-1)(d)\",\n+ \"exterior_subset\": \"qS bs2 l\",\n+ \"helper_owner\": \"s2(d)\",\n+ \"native_frame\": \"(G2 d).X.Phi(frames[f])\",\n+ \"old_frame\": \"(G2 d).Xm.Phi(P)\",\n+ \"orientation\": \"forward\",\n+ \"stage\": 2,\n+ \"window\": \"G2\"\n+ },\n+ {\n+ \"active_pair\": 2,\n+ \"bank_owner\": \"r3(t)^(-1)(d)\",\n+ \"exterior_subset\": \"qS bs3 l\",\n+ \"helper_owner\": \"s3(d)\",\n+ \"native_frame\": \"(G3 d).X.Phi(frames[f])\",\n+ \"old_frame\": \"(G3 d).Xm.Phi(P)\",\n+ \"orientation\": \"backward\",\n+ \"stage\": 3,\n+ \"window\": 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\"accepted\": {\n+ \"saving\": \"171078960107339/250000000000000000\",\n+ \"lower\": \"3304804687499999996771405325082960189736345242324091468618865791/3304804687500000000000000000000000000000000000000000000000000000\",\n+ \"upper\": \"2203203124999999997847603550055306793157563539718798610767322967/2203203125000000000000000000000000000000000000000000000000000000\",\n+ \"strict_gap_lower\": \"1625348795138405329078087754605107701019/451216000000000000000000000000000000000000000000000\"\n+ },\n+ \"next_excluded\": {\n+ \"saving\": \"684315840429357/1000000000000000000\",\n+ \"lower\": \"220320312500000000245640538235013054437599001104928200990645937/220320312500000000000000000000000000000000000000000000000000000\",\n+ \"upper\": \"6609609375000000007369216147050391633127970167528178065408615429/6609609375000000000000000000000000000000000000000000000000000000\",\n+ \"strict_gap_lower\": \"4876043553767370246147767230868278741577/1353648000000000000000000000000000000000000000000000\"\n+ }\n+ },\n+ \"bit_coarse_relative_gain\": \"5767448072061/678548392357295\",\n+ \"stock_relative_reduction\": \"2750/30951\",\n+ \"ordinary_chain\": [\n+ \"67811433917228834656124539327071113021/100000000000000000000000000000000000000000\",\n+ \"17107789916095283651025662505333308177788503624360561119/25000000000000000000000000000000000000000000000000000000000\",\n+ \"4276973984532914552551086058834440860404075524266507475651790194509952341/6250000000000000000000000000000000000000000000000000000000000000000000000000\",\n+ \"1069243500667763570993285042141947175981048664467967881924465976234543947863836349134330599/1562500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\"\n+ ],\n+ \"extra_selector_calls\": 5368513266,\n+ \"selector_toll_gap\": \"1560361512998661367679006714957858052824018951335532032118075534023765456052136163650865669401/1562500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\",\n+ \"comparison_pr207_kappa\": \"1366380910073/2000000000000000\",\n+ \"comparison_pr205_kappa\": \"683061299399923/1000000000000000000\",\n+ \"before_packing\": {\n+ \"kappa\": \"338827405863723/500000000000000000\",\n+ \"binding\": \"bit\"\n+ },\n+ \"after_packing\": {\n+ \"kappa\": \"683847872495777/1000000000000000000\",\n+ \"assembly\": {\n+ \"parameters\": {\n+ \"a_bit\": \"1069243500667763570993285042141947175981048664467967881924465976234543947863836349134330599/1562500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\",\n+ \"a_complex\": \"700918443859411/1000000000000000000\",\n+ \"tau\": \"1561430756499332236429006714957858052824018951335532032118075534023765456052136163650865669401/1562500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\",\n+ \"sigma\": \"999299081556140589/1000000000000000000\",\n+ \"eta\": \"1/1000000000000000000000000\",\n+ \"beta\": \"1/1000000000000000000000000\",\n+ \"q\": 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\"657417459277/683190455036500\",\n+ \"controls\": [\n+ \"changed rank mass\"\n+ ]\n+ },\n+ \"independent\": {\n+ \"status\": \"PASS\",\n+ \"moment_intervals\": {\n+ \"complex\": {\n+ \"accepted_lower\": \"151303260229760552849231624798695928011617003747957445895984727/151303260229760553131497868256997591293731175633361087898845184\",\n+ \"accepted_upper\": \"1664335862527366081341547872785655208127787041227531904856155057/1664335862527366084446476550826973504231042931966971966887297024\",\n+ \"next_lower\": \"1664335862527366085285815072313660921079442613294059590682498373/1664335862527366084446476550826973504231042931966971966887297024\",\n+ \"next_upper\": \"72362428805537655881991959665811344394758374491046069160122671/72362428805537655845498980470737978444827953563781389864665088\"\n+ },\n+ \"bit_before\": {\n+ \"accepted_lower\": 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\"10372297619510143596562190064648835114394124441832510479677700436312004908739/10372297619510143606695298683039808628935694876327943591690240000000000000000\",\n+ \"next_lower\": \"13829730159346858157679504732416265699030774350928862666935041706926030070479/13829730159346858142260398244053078171914259835103924788920320000000000000000\",\n+ \"next_upper\": \"41489190478040574473038514197248797097092323052786588000812341185231262689911/41489190478040574426781194732159234515742779505311774366760960000000000000000\"\n+ }\n+ },\n+ \"finite_leaf_levels\": 3,\n+ \"adjacent_final_grids_checked\": 2\n+ },\n+ \"bank_controls\": {\n+ \"formal_columns_per_case\": 144,\n+ \"weighted_partition_cases\": 12,\n+ \"rejected\": [\n+ \"repeated block mod 9\",\n+ \"omitted block mod 9\",\n+ \"repeated block mod 25\",\n+ \"omitted block mod 25\",\n+ \"repeated block mod 125\",\n+ \"omitted block mod 125\"\n+ ]\n+ }\n+ }\n+}"},{"sha":"875b8922d85958b649279f5d251f4e5f588c4a18","filename":"research/community-round9-audit/pr212-replay.log.txt","status":"added","additions":39,"deletions":0,"changes":39,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr212-replay.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr212-replay.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr212-replay.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,39 @@\n+[ 0s] rebuilt the pinned files of #200 (commit a117544) from baseline-pr200.tar.gz; hashes match SOURCE.json\n+[ 23s] #200 bit word: h 24, v 1760, centre loss 528, deficit D = 2v - 3 loss = 1936, 41288 operations, 18908 roles, 1760 reuse pairs, 34 sinks\n+[ 23s] fact 1: certified coarse saving 6.7777395e-04 < D/C = 6.7837287e-04 (gap 0.088%)\n+[ 352s] self-test: #200's layout lies inside every derived frame bound; its slot chains reproduce the certified pre-sink ledger exactly (W 20668, rank 1486160); the terminal record substitutes [3, 21] per sink and stage; every slot floor is below its actual chain\n+[ 614s] fact 4, #200's own ledger: certified C = 2853888, floor C >= 2804210; coarse < 6904/10^7 = 6.9040000e-04 (certified 6.7777395e-04 is 98.2% of it); kappa < 6900/10^7\n+[ 614s] fact 4, banked ledger (#205/#206/#207 accounting on this word): D/C of #200's layout = 6.8414215e-04; floor C >= 2780144; coarse < 6964/10^7; kappa < 6959/10^7\n+[ 614s] without coupling the two registers of an operation: coarse < 7056/10^7 (own), 7118/10^7 (banked)\n+[ 614s] PASS results equal expected.json\n+{\n+ \"D\": 1936,\n+ \"certified_coarse\": \"677773948354561/1000000000000000000\",\n+ \"certified_kappa\": \"166261725903847/250000000000000000\",\n+ \"h\": 24,\n+ \"loss\": 528,\n+ \"m\": 72,\n+ \"operations\": 41288,\n+ \"package\": \"research/paired-cube-diagonal-bit-168\",\n+ \"results\": {\n+ \"banked\": {\n+ \"C_certified_layout\": 2829821.258057245,\n+ \"C_floor\": 2780143.846154924,\n+ \"coarse_ceiling\": \"6964/10^7\",\n+ \"coarse_ceiling_uncoupled\": \"7118/10^7\",\n+ \"kappa_ceiling\": \"6959/10^7\"\n+ },\n+ \"own\": {\n+ \"C_certified_layout\": 2853887.7035540473,\n+ \"C_floor\": 2804210.291651726,\n+ \"coarse_ceiling\": \"6904/10^7\",\n+ \"coarse_ceiling_uncoupled\": \"7056/10^7\",\n+ \"kappa_ceiling\": \"6900/10^7\"\n+ }\n+ },\n+ \"reuse_pairs\": 1760,\n+ \"roles\": 18908,\n+ \"rounds\": 1200,\n+ \"sinks\": 34,\n+ \"v\": 1760\n+}"},{"sha":"ba32315a2f7e1531dc7f624861e3ecf392f09177","filename":"research/community-round9-audit/pr213-arithmetic.log.txt","status":"added","additions":2,"deletions":0,"changes":2,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr213-arithmetic.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr213-arithmetic.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr213-arithmetic.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,2 @@\n+PASS PR200 frame/terminal/prime re-admission, exact charts and banks, two moment engines, finite leaf composition, 47 constraints\n+conditional kappa = 683847872497761/1000000000000000000"},{"sha":"4642fdd54adf76666b1bf81c1f8d62f85b2df419","filename":"research/community-round9-audit/pr214-README.md","status":"added","additions":280,"deletions":0,"changes":280,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr214-README.md","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr214-README.md","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr214-README.md?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,280 @@\n+# Independent reproductions and audit notes: #207, #202, #197, #199\n+\n+Snapshot: 2026-10-09, runs between 13:43Z and 17:33Z; PR heads re-read at 17:35Z.\n+CI states and the sources cited in items 1 to 3 re-read at 18:05Z; all heads\n+unchanged. Repository base at the time: `main` =\n+`3b6b66891c0ac888521cf591fe306c6286601d4f`.\n+\n+This directory records independent replays of four open submissions, with\n+pinned heads, exact commands and outputs. It is a reproduction report, not a\n+review disposition and not an acceptance of any bound. A passing verifier is a\n+finite certificate check under the inherited conditional interfaces. It is not\n+a formal verification of the multiplication theorem. Every κ below is\n+conditional, as in the submissions themselves.\n+\n+Each item carries one of three labels:\n+\n+- **reproduced**: the submission's own verifier ran unmodified at the pinned\n+ head and printed the claimed value;\n+- **not reproduced**: the submission's own verifier failed in our environment;\n+- **audit finding**: an observation from reading the sources, the CI records\n+ or a diagnostic run. It is not a claim of mathematical error.\n+\n+## Environment (all runs)\n+\n+- Linux x86_64 (kernel 6.18.33.2, WSL2), Ubuntu 24.04.5 LTS.\n+- CPython 3.13.16 in a virtual environment with numpy 2.3.5 and scipy 1.17.0.\n+ These equal the pins in the packages' requirement files. No package was\n+ installed or upgraded for these runs.\n+- Fresh clones; heads fetched from `pull//head` and checked out detached.\n+ No source file was modified. All verifiers were run with `-B`.\n+- Wall times come from `/usr/bin/time -v` or from bash `time`. Peak memory is\n+ given where `/usr/bin/time -v` recorded it.\n+- One control run used CPython 3.12.3 (system interpreter) with the same numpy\n+ and scipy. It is reported only under item 2.\n+\n+## Summary\n+\n+| Item | PR | Head run (now) | Command | Exit | Wall | Printed κ | Label |\n+|---|---|---|---|---|---|---|---|\n+| 1 | [#207](https://github.com/CrocSwap/integer-mult-bounds/pull/207) | `cd14825023b7` (unchanged) | `python -B research/coordinated-crossover-pr200/verify.py` | 0 | 2:22.76 | 1366380910073/2000000000000000 = 6.831904550365e-4 | reproduced |\n+| 2a | [#202](https://github.com/CrocSwap/integer-mult-bounds/pull/202) | `8d8d67bcf69c` (unchanged) | `python -B research/paired-cube-diagonal-bit-168/verify.py` | 0 | 2:36.64 | 166261725903847/250000000000000000 = 6.65046903615388e-4 (package's own κ) | reproduced |\n+| 2b | #202 | `8d8d67bcf69c` (unchanged) | `python -B research/source-assisted-v4/verify.py` | non-zero (AssertionError) | 1:00.09 | none (fails before printing) | not reproduced; audit finding |\n+| 3 | [#197](https://github.com/CrocSwap/integer-mult-bounds/pull/197) | `8c5e1cf07c23` (unchanged) | see item 3 | 0 | 2:01.30 | 135216063303877/200000000000000000 = 6.76080316519385e-4 | reproduced; audit finding |\n+| 4 | [#199](https://github.com/CrocSwap/integer-mult-bounds/pull/199) | `5c1fb8346615` (current head) | see item 4 | 0 | 0:10.25 | none (diagnostic; output sha256 `30418cac…a61c` = committed) | reproduced |\n+\n+Full SHAs, interpreter and package versions per run are in\n+[receipts.json](receipts.json).\n+\n+## 1. #207: reproduced\n+\n+- Head `cd14825023b75af4f5919a30e5e6d548b6ade5bc`. Its merge base with `main`\n+ is `3b6b66891c0ac888521cf591fe306c6286601d4f`. The head is unchanged at 17:35Z.\n+- Command, from the repository root, as in the PR body:\n+ `python -B research/coordinated-crossover-pr200/verify.py`.\n+- Exit code 0; wall time 2:22.76 (17:05:22Z to 17:07:45Z); peak RSS\n+ 2,155,372 kB. `git status --porcelain` was empty after the run.\n+- Final lines printed:\n+ `PASS full offline bit/frame/bank/chart/complex-lift/contract replay, independent paid moments, 47 inequalities and controls; kappa=1366380910073/2000000000000000`\n+ and `PASS immutable manual-upload package; no network, git, or publication required`.\n+ Intermediate records include `PASS_ADMITTED_FRAME_BANK_COMPOSITION`,\n+ `PASS_ALL_ACTUAL_GAUGE_CHARTS_AND_ROUTING_BILL`,\n+ `PASS_LITERAL_DISTINCT_NORMALIZERS` and `PASS_EXACT_47_CONSTRAINT_ASSEMBLY`.\n+- The printed κ equals the PR's claim exactly.\n+- Note: the complex-lift step printed `certificate_sha256`\n+ `72a9626394aff05457ba5d25fc312608effba611f1f184ad8a6ddf186c7b150f`. The\n+ verifier does not compare this hash, and #207's `certificate.json` does not\n+ record it. For the complex lift, `verify_inner.py:23` asserts that\n+ `exact_scalar_program_sha256` equals #202's committed value\n+ (`3b4e671d7c6630570b04788bb2c81629e2c52f8dc2fcc5805952f0b403921027`), and\n+ `verify_inner.py:29-30` asserts that the mathematical fields of the replayed\n+ complex profile (`m`, `W_per_vertex`, `rank_per_vertex`,\n+ `deficit_per_vertex`, `child_histogram`, `contract_checks`,\n+ `exact_scalar_program_sha256`) equal #202's committed `complex_profile`.\n+ Both checks passed. This design matters for item 2b.\n+- CI: the six workflow runs recorded for this head (for example run\n+ 37955916437, \"Verify research artifacts\") are awaiting maintainer approval\n+ (`action_required`).\n+\n+## 2. #202: bit package reproduced; headline verifier not reproduced here\n+\n+Head `8d8d67bcf69c5ea67d3a29dbc64ba588156d6e8d`, tree\n+`4d07f3f18343da5a0f474d6d830afe64c0c18505`. The head is unchanged at 17:35Z.\n+No CI run exists for this head. The PR is in conflict with `main`\n+(`CONFLICTING`), and GitHub does not run `pull_request` workflows on a\n+conflicting PR. Its workflow `.github/workflows/source-assisted-v4.yml` would\n+run `python -B research/source-assisted-v4/verify.py` under Python 3.13\n+(lines 26 and 30).\n+\n+**2a. Bit package (reproduced).**\n+`python -B research/paired-cube-diagonal-bit-168/verify.py` exited 0 in\n+2:36.64 (peak RSS 2,194,084 kB). The working tree was clean before and after.\n+It printed\n+`PASS paired-cube-diagonal-bit-168 kappa=166261725903847/250000000000000000; complete complex and bit words, 47 constraints, seven margins, and 21 assembly controls.`\n+This κ is the package's own assembly, not the #202 headline. The run\n+regenerates the bit certificate that #202's assembly reads, and the script\n+asserts that the regenerated result equals the committed `certificate.json`.\n+\n+**2b. Headline verifier (not reproduced in this environment).**\n+The 6.768823e-4 headline is checked by `research/source-assisted-v4/verify.py`.\n+In our environment this verifier stops at `verify.py:162` with\n+`AssertionError: Canonical certificate does not reproduce`, after 1:00.09.\n+\n+The diagnostic [certificate_diff.py](certificate_diff.py), copied into a #202\n+checkout at `8d8d67b` and run from its root, calls the PR's own `build()` and\n+compares the result leaf by leaf with the committed certificate. It modifies\n+no tracked file; like `verify.py`, `build()` creates and then deletes the\n+package's temporary `.work/` directory (`verify.py:29`, `89-91`, `145`).\n+Exactly 7 leaves differ:\n+\n+| Leaf | Built here | Committed at `8d8d67b` |\n+|---|---|---|\n+| `/lift_certificate_sha256`, `/lift/certificate_sha256`, `/complex_profile/exact_lift_certificate_sha256`, `/assembly/construction_receipts/complex_lift_certificate_sha256`, `/complex_profile/proof_chain_sha256/…/.work/lift.certificate.json.gz` | `1d81a79bda88…9ef2` | `462521350b4f…7ee0` |\n+| `/complex_profile/proof_chain_sha256/…/.work/lift.json` | `c41fee34c5c6…` | `89b0d949852a…` |\n+| `/assembly/source_sha256/complex` | `7374c75b7d6e…f0cb` | `b80de5b00f75…e3a3` |\n+\n+All seven come from one value: the sha256 of the compressed lift certificate\n+`lift.certificate.json.gz`, which\n+`research/source-assisted/decision/exact_complex_flow_lift.py:408-409` writes\n+with `gzip.compress(..., compresslevel=9, mtime=0)`. `lift.json` records that\n+hash (same file, line 419), the complex profile records both files' hashes,\n+and `/assembly/source_sha256/complex` is the sha256 of the complex profile\n+file (`research/source-assisted-v4/assemble.py:89`).\n+\n+Every other leaf is equal, including κ = 6768823/10^10, the complex saving,\n+the bit effective saving and the assembly records. Two independent builds in\n+fresh clones (15:12Z, and 17:25Z with this script, whose code has not changed\n+since, only its docstring: exit 0, 1:01.63) gave identical values. In this\n+environment the build is therefore stable from run to run.\n+\n+Observations (audit findings, from `git show` / `git diff`, GitHub's compare\n+and CI records):\n+\n+1. #194 at `a8c87783785be6fe20c4a8bb2ac4b3eec295a179` commits exactly the\n+ values built here (`1d81a79b…`, `c41fee34…`, `7374c75b…`). Its\n+ `source-assisted-v4/verify.py` passes in the same environment (exit 0,\n+ 0:57.89). #194's CI ran the same command and passed under CPython 3.13.16\n+ with numpy 2.3.5 and scipy 1.17.0, the versions used here (workflow\n+ `source-assisted-v4.yml`, run 37931952877, job 113824581619).\n+2. #202 is #194 plus one commit: GitHub's compare `a8c8778...8d8d67b` reports\n+ 1 commit ahead and 0 behind. In that commit the `SOURCE.json` pins change\n+ only for the bit-certificate path, `assemble.py`, `pin_sources.py`,\n+ `NOTICE`, `PROOF.md` and `README.md`. The pins of `verify.py`,\n+ `contract_v4.py`, `source_aligned_local_v4.py` and `data/*.json` are\n+ unchanged, and `research/source-assisted/` is unchanged. Between the two\n+ committed certificates, the `/lift` record differs only by\n+ `certificate_sha256`, and `/complex_profile` only by the three lift hashes\n+ above; `exact_scalar_program_sha256` (`3b4e671d…1027`) and the witness hash\n+ are identical. The other differences come from the new bit supplier and κ.\n+3. Control run with CPython 3.12.3, the system interpreter (same numpy and\n+ scipy): #194's own `source-assisted-v4/verify.py` also fails the same\n+ assertion (exit 1, 1:05.71). Which leaves differ under 3.12.3 was not\n+ recorded. The canonical check is therefore sensitive to the environment;\n+ we did not separate the interpreter from the zlib build it uses.\n+\n+Reading: every leaf of #202's certificate that does not derive from the lift\n+gzip hash reproduces here. With unchanged lift inputs, our environment and\n+#194's CI produce the same gzip hash, and #202's committed hash is a different\n+one. This points to an environment-sensitive step (interpreter or zlib\n+build), which we have not isolated. It is a reproducibility observation, not a\n+claim about the mathematics of #202. Two remedies seem possible, at the\n+author's or maintainers' discretion. One is to record the reference\n+environment (interpreter and zlib versions) and regenerate the canonical\n+certificate in it. The other is to check the lift through\n+`exact_scalar_program_sha256` and the mathematical fields of the complex\n+profile rather than through the compressed file's hash, as #207's verifier\n+does (item 1, `verify_inner.py:23` and `29-30`).\n+\n+#207 consumes #202's complex supplier at `8d8d67b` and passes (item 1). This is\n+consistent with the reading above.\n+\n+## 3. #197: reproduced\n+\n+- Head `8c5e1cf07c23d843642bf2d4c76f882669edc43f` (tree\n+ `98ee8c8e5c0f2214a9250f8390fbffea11ba1652`), unchanged at 17:35Z. CI: the\n+ four workflow runs recorded for this head (including run 37936952135,\n+ \"Verify packed source-assisted bit supplier\") are awaiting maintainer\n+ approval (`action_required`). The pinned unmerged dependencies were\n+ checked out as separate worktrees: #187 at\n+ `201737a1ec4f936e166e2481fb9e88104cb2ccc7` and #193 at\n+ `187e1010ac8b259af8e9b5166f68b64bc27b4b47`. Both heads are unchanged.\n+- Command, as in the PR body (with our worktree paths):\n+ `python -B research/packed-source-assisted-bit/verify.py --complex-root <#193 worktree> --bit-root <#187 worktree> --full`.\n+- Recorded run, in a fresh clone: exit code 0; wall time 2:01.30 (17:30:47Z to\n+ 17:32:49Z); peak RSS 594,180 kB as reported by `/usr/bin/time -v`; stderr\n+ empty. `git status --porcelain` was empty before and after regeneration. The\n+ committed `certificate.json` (sha256\n+ `c18fe983eb863661a69b0c2d89771acf9d11b7f460b1b04afcac6f2fea799886`) is\n+ therefore regenerated byte for byte. An earlier run in another clone gave the\n+ same output in 1:35.68; its exit code was not captured.\n+- 8 PASS records: `PASS source-assisted-v4 kappa = 103873/156250000`,\n+ `PASS 1733 immutable source pins`,\n+ `PASS actual emitted histogram and scalar guard; …; 47 constraints,7 margins,8 controls …`,\n+ three JSON records with `\"status\": \"PASS\"` (frames, emitted word, F2 scalar\n+ map with three negative controls rejected),\n+ `PASS literal emitted BIT word, conservative geometry, paid histogram, scalar count, all-column forward/reflection and mutation controls`\n+ and `PASS exact packed profile, two moment engines, finite leaf composition, 47 constraints and seven margins`.\n+- Printed `conditional kappa = 135216063303877/200000000000000000`\n+ = 6.76080316519385e-4, equal to the PR's claim. This is 1.2957% above #194's\n+ 1668581/2500000000.\n+\n+Audit finding (reading, not a counterexample): the removal of the 6,600\n+rank-60 exterior children rests on the bank-endpoint identity of `PROOF.md`\n+§4, which the PR proves on paper (`PROOF.md:81-93`: for disjoint projectors,\n+D_P D_Q = D_(P+Q) = D_Q D_P; \"This is an operator identity on arbitrary bank\n+contents\"). Its finite controls, on all 144 formal columns over Z/9, Z/25 and\n+Z/125, \"support the identity above; they do not simulate the full cover or\n+prove the inherited Clifford interface\" (`PROOF.md:95-98`). On the full cover\n+the removal therefore rests on the paper argument, not on the replayed\n+checks. `main` already holds the maintainer review of a comparable removal\n+of rank-60 exterior corrections for #186, which #197 cites as \"#186's related\n+bank construction\": `research/community-round8-audit/BANK-SCHEDULE.md:6-8`\n+states that #186's coordinate-projector calculation proves a bank's endpoint,\n+with a comparable limit (\"does not instantiate the 72-dimensional production\n+word\", lines 94-95), and `CONTRIBUTING.md:13` asks readers to consult it. We\n+did not check whether #197's banks match that schedule. The package also\n+depends on the unmerged #187 and #193 checkouts, so it is not self-contained.\n+\n+What remains useful now that #205 and #207 report higher κ:\n+\n+- #205 (draft, `95c58706ad23`) states that it applies #197's completed-bank\n+ packing and reuses or adapts its code. It removes the same 6,600 rank-60\n+ exterior children. #207 cites #197 for its three-level bootstrap. This\n+ reproduction is an independent data point that the reference implementation\n+ of the packing regenerates exactly from pinned inputs.\n+- Any construction that removes these children by the same identity relies on\n+ the same paper argument. We did not assess whether the full-column bank\n+ checks of #205 or #207 cover this step for their own words.\n+\n+## 4. #199: donor-reuse diagnostic reproduced byte for byte\n+\n+- Run in a fresh clone at the current #199 head\n+ `5c1fb8346615968844bc182a5376c399109670ca` (tree\n+ `f08f784c50504ace4fa659867e954b18210851a1`), with the #189 package at\n+ `0a4091175b3981267a97a62ab7492cb9ba528916`. `research/paired-cube-bit` was\n+ extracted from #189 as well, because the #189 package imports it.\n+- Command, from `research/bit-leaf-bootstrap-189`:\n+ `python -B bit_reuse_maximal.py --package <#189 checkout>/research/paired-cube-twin-local-168 --out `\n+ (`bit_reuse_maximal.py` sha256\n+ `91792e33ff057080c91369b788c88b9cc01e1df6ce2bcd173e67d68132cd4a61`).\n+- Exit code 0; wall time 0:10.25 (17:30:48Z to 17:30:58Z); peak RSS\n+ 553,200 kB. The working tree was clean after the run.\n+- Output: gauges 3960, pairs 1760, unpaired 2200 (birth-frame dimension 20),\n+ 8628 distinct donor end frames, 220 unpaired birth frames, of which 0 contain\n+ a donor end frame; verdict \"no unpaired gauge can receive a donor\". The output\n+ sha256 `30418cac689093de5b4d3cb7d6eeae450f8a74de5be7d66cc9be6087ed3ea61c`\n+ equals that of the committed `bit-reuse-maximal.json`, and a JSON comparison\n+ prints `EQUAL`.\n+- An earlier run at the previous head `2a10ca79d7f2` gave the same output\n+ sha256. The two files involved are unchanged between the two heads. The new\n+ composition files of #199 (`next_bit_composition.py`,\n+ `next-composition-result.json`) were not replayed.\n+- Scope: this reproduces a finite exhaustive diagnostic over distinct frames\n+ for #189's bit word. It does not reproduce any κ.\n+\n+## What this submission adds, and predecessors\n+\n+All constructions, certificates and verifiers are the cited authors' work\n+(#207, #202, #200, #197, #194, #193, #189, #187, #185 and their lineage). This\n+directory adds only independent replays at pinned heads, one diagnostic\n+script (it modifies no tracked file), and the reproducibility observation of\n+item 2b. It changes no generator, certificate, test or `upstream/` file. It\n+claims no bound.\n+\n+## Not addressed here\n+\n+- Item 3: a review of the paper argument of `PROOF.md` §4 of #197 on the full\n+ cover, and of its counterpart in #205. This report replays finite checks\n+ only.\n+- Item 2b: which part of the environment (interpreter or zlib build) changes\n+ the lift gzip hash.\n+- For all items: the retained conditional interfaces stated by each\n+ submission (Clifford/tensor realization, weighted local-ring compilation,\n+ restored rows, fixed tape, routing, prime supply, precision and analytic\n+ transfer). A finite replay does not establish them.\n+- #205, #206, #208 and the new composition files of #199 were not replayed.\n+\n+## Disclosure\n+\n+Prepared with Claude (Anthropic) agents; runs executed locally; reviewed by the\n+submitter. New material is under the repository's Apache-2.0 license."},{"sha":"95216209a346f4fe3d9d72d4f49a2c85e75e01e2","filename":"research/community-round9-audit/pr214-certificate_diff.py","status":"added","additions":52,"deletions":0,"changes":52,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr214-certificate_diff.py","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr214-certificate_diff.py","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr214-certificate_diff.py?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,52 @@\n+\"\"\"Diagnostic for #202 (head 8d8d67bcf69c5ea67d3a29dbc64ba588156d6e8d).\n+\n+`research/source-assisted-v4/verify.py` asserts that its rebuilt certificate equals\n+the committed one (\"Canonical certificate does not reproduce\"). This script calls\n+the package's own `build()`, then prints every leaf of the rebuilt certificate that\n+differs from the committed `certificate.json`. It modifies no tracked file, but\n+`build()` creates and then deletes the package's temporary directory\n+`research/source-assisted-v4/.work/` (verify.py:29, 89-91, 145).\n+\n+The package exists only at the #202 head, not on main or in this PR. Usage: copy\n+this file into a checkout of #202 at 8d8d67b, under\n+`research/independent-reproduction-20261009/`, then from that checkout's root:\n+ python -B research/independent-reproduction-20261009/certificate_diff.py\n+\"\"\"\n+import sys\n+from pathlib import Path\n+\n+PKG = Path('research/source-assisted-v4').resolve()\n+sys.path.insert(0, str(PKG))\n+import verify # noqa: E402 (the package's own module)\n+\n+if hasattr(sys, 'set_int_max_str_digits'):\n+ sys.set_int_max_str_digits(0)\n+built = verify.build()\n+committed = verify.read(PKG / 'certificate.json')\n+\n+\n+def short(x):\n+ s = repr(x)\n+ return s if len(s) <= 160 else s[:150] + '...(' + str(len(s)) + ')'\n+\n+\n+def walk(a, b, path, out):\n+ if isinstance(a, dict) and isinstance(b, dict):\n+ for k in sorted(set(a) | set(b)):\n+ if k not in a or k not in b:\n+ out.append((path + '/' + k, 'only-built' if k in a else 'only-committed', short(a.get(k, b.get(k)))))\n+ else:\n+ walk(a[k], b[k], path + '/' + k, out)\n+ elif isinstance(a, list) and isinstance(b, list) and len(a) == len(b):\n+ for i, (x, y) in enumerate(zip(a, b)):\n+ walk(x, y, path + '[' + str(i) + ']', out)\n+ elif a != b:\n+ out.append((path, short(a), short(b)))\n+\n+\n+diffs = []\n+walk(built, committed, '', diffs)\n+print('python', sys.version.split()[0])\n+print('differing leaves:', len(diffs))\n+for p, x, y in diffs[:40]:\n+ print(p, '\\n built :', x, '\\n committed:', y)"},{"sha":"909045dc30cd73b6376f8390df94f19b20e040c7","filename":"research/community-round9-audit/pr214-receipts.json","status":"added","additions":180,"deletions":0,"changes":180,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr214-receipts.json","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr214-receipts.json","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr214-receipts.json?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,180 @@\n+{\n+ \"snapshot\": \"2026-10-09\",\n+ \"heads_reread_utc\": \"2026-10-09T17:35:47Z\",\n+ \"ci_and_sources_reread_utc\": \"2026-10-09T18:05Z\",\n+ \"main_at_snapshot\": \"3b6b66891c0ac888521cf591fe306c6286601d4f\",\n+ \"platform\": \"Linux 6.18.33.2 (WSL2) x86_64, Ubuntu 24.04.5 LTS\",\n+ \"scope\": \"Independent replays of submitted verifiers and one diagnostic that modifies no tracked file. Not a review disposition, not acceptance of any bound, not a formal verification. All kappa values are conditional on each submission's retained interfaces.\",\n+ \"labels\": {\n+ \"reproduced\": \"submission's own verifier ran unmodified at the pinned head and printed the claimed value\",\n+ \"not reproduced\": \"submission's own verifier failed in this environment\",\n+ \"audit finding\": \"observation from reading sources, CI records or a diagnostic run; not a claim of mathematical error\"\n+ },\n+ \"runs\": [\n+ {\n+ \"item\": \"1\",\n+ \"pr\": 207,\n+ \"head_run\": \"cd14825023b75af4f5919a30e5e6d548b6ade5bc\",\n+ \"head_now\": \"cd14825023b75af4f5919a30e5e6d548b6ade5bc\",\n+ \"merge_base_main\": \"3b6b66891c0ac888521cf591fe306c6286601d4f\",\n+ \"command\": \"python -B research/coordinated-crossover-pr200/verify.py\",\n+ \"python\": \"3.13.16\",\n+ \"packages\": {\"numpy\": \"2.3.5\", \"scipy\": \"1.17.0\"},\n+ \"start_utc\": \"2026-10-09T17:05:22Z\",\n+ \"end_utc\": \"2026-10-09T17:07:45Z\",\n+ \"exit\": 0,\n+ \"wall\": \"2:22.76\",\n+ \"max_rss_kb\": 2155372,\n+ \"tree_clean_after\": true,\n+ \"printed_kappa\": \"1366380910073/2000000000000000\",\n+ \"kappa_decimal\": \"0.0006831904550365\",\n+ \"claimed_kappa\": \"1366380910073/2000000000000000\",\n+ \"final_lines\": [\n+ \"PASS full offline bit/frame/bank/chart/complex-lift/contract replay, independent paid moments, 47 inequalities and controls; kappa=1366380910073/2000000000000000\",\n+ \"PASS immutable manual-upload package; no network, git, or publication required\"\n+ ],\n+ \"lift_certificate_sha256_printed\": \"72a9626394aff05457ba5d25fc312608effba611f1f184ad8a6ddf186c7b150f\",\n+ \"exact_scalar_program_sha256\": \"3b4e671d7c6630570b04788bb2c81629e2c52f8dc2fcc5805952f0b403921027\",\n+ \"note\": \"The lift certificate file hash is not compared and not recorded in #207's certificate.json. verify_inner.py:23 compares exact_scalar_program_sha256 with #202's committed value; verify_inner.py:29-30 compares the mathematical fields of the replayed complex profile (m, W_per_vertex, rank_per_vertex, deficit_per_vertex, child_histogram, contract_checks, exact_scalar_program_sha256) with #202's committed complex_profile.\",\n+ \"ci\": {\"runs_at_head\": 6, \"conclusion\": \"action_required (awaiting maintainer approval)\", \"example_run\": 37955916437},\n+ \"label\": \"reproduced\"\n+ },\n+ {\n+ \"item\": \"2a\",\n+ \"pr\": 202,\n+ \"head_run\": \"8d8d67bcf69c5ea67d3a29dbc64ba588156d6e8d\",\n+ \"tree\": \"4d07f3f18343da5a0f474d6d830afe64c0c18505\",\n+ \"head_now\": \"8d8d67bcf69c5ea67d3a29dbc64ba588156d6e8d\",\n+ \"command\": \"python -B research/paired-cube-diagonal-bit-168/verify.py\",\n+ \"python\": \"3.13.16\",\n+ \"packages\": {\"numpy\": \"2.3.5\", \"scipy\": \"1.17.0\"},\n+ \"start_utc\": \"2026-10-09T17:06:03Z\",\n+ \"end_utc\": \"2026-10-09T17:08:40Z\",\n+ \"exit\": 0,\n+ \"wall\": \"2:36.64\",\n+ \"max_rss_kb\": 2194084,\n+ \"tree_clean_after\": true,\n+ \"printed_kappa\": \"166261725903847/250000000000000000\",\n+ \"kappa_decimal\": \"0.000665046903615388\",\n+ \"final_lines\": [\n+ \"PASS paired-cube-diagonal-bit-168 kappa=166261725903847/250000000000000000; complete complex and bit words, 47 constraints, seven margins, and 21 assembly controls.\"\n+ ],\n+ \"note\": \"This is the package's own assembly, not the #202 headline. The verifier regenerates the bit certificate read by #202's assembly and asserts equality with the committed certificate.json.\",\n+ \"label\": \"reproduced\"\n+ },\n+ {\n+ \"item\": \"2b\",\n+ \"pr\": 202,\n+ \"head_run\": \"8d8d67bcf69c5ea67d3a29dbc64ba588156d6e8d\",\n+ \"head_now\": \"8d8d67bcf69c5ea67d3a29dbc64ba588156d6e8d\",\n+ \"command\": \"python -B research/source-assisted-v4/verify.py\",\n+ \"python\": \"3.13.16\",\n+ \"packages\": {\"numpy\": \"2.3.5\", \"scipy\": \"1.17.0\"},\n+ \"job_start_utc\": \"2026-10-09T15:10:10Z\",\n+ \"exit\": \"non-zero (uncaught AssertionError)\",\n+ \"wall\": \"1:00.09\",\n+ \"printed_kappa\": null,\n+ \"claimed_kappa\": \"6768823/10000000000\",\n+ \"error\": \"verify.py:162 AssertionError: Canonical certificate does not reproduce\",\n+ \"ci\": {\"runs_at_head\": 0, \"mergeable\": \"CONFLICTING\", \"reason\": \"GitHub does not run pull_request workflows on a PR with a merge conflict\", \"workflow\": \".github/workflows/source-assisted-v4.yml (python-version 3.13, runs python -B research/source-assisted-v4/verify.py; lines 26, 30)\"},\n+ \"diagnostic\": {\n+ \"script\": \"certificate_diff.py\",\n+ \"usage\": \"copied into a #202 checkout at 8d8d67b and run from its root\",\n+ \"side_effects\": \"modifies no tracked file; verify.build() creates and deletes research/source-assisted-v4/.work/ (verify.py:29, 89-91, 145)\",\n+ \"runs\": [\n+ {\"approx_utc\": \"2026-10-09T15:12Z\", \"python\": \"3.13.16\", \"differing_leaves\": 7},\n+ {\"start_utc\": \"2026-10-09T17:24:52Z\", \"python\": \"3.13.16\", \"script_sha256\": \"7d3ed605127b312df8893674be570107051e00e7b6df7a4b6568a56d43bdd0da\", \"script_note\": \"hash of the version run; the committed file differs from it only in its docstring\", \"exit\": 0, \"wall\": \"1:01.63\", \"max_rss_kb\": 594180, \"differing_leaves\": 7}\n+ ],\n+ \"differing_leaves\": {\n+ \"/lift_certificate_sha256\": [\"1d81a79bda88b8a0ef64b7ae815c0d20cf1eee7f4714053530805bbb39e89ef2\", \"462521350b4f1b133f4bde6c793afdf735e84f8da918a169f1d030fc61727ee0\"],\n+ \"/lift/certificate_sha256\": [\"1d81a79bda88b8a0ef64b7ae815c0d20cf1eee7f4714053530805bbb39e89ef2\", \"462521350b4f1b133f4bde6c793afdf735e84f8da918a169f1d030fc61727ee0\"],\n+ \"/complex_profile/exact_lift_certificate_sha256\": [\"1d81a79bda88b8a0ef64b7ae815c0d20cf1eee7f4714053530805bbb39e89ef2\", \"462521350b4f1b133f4bde6c793afdf735e84f8da918a169f1d030fc61727ee0\"],\n+ \"/assembly/construction_receipts/complex_lift_certificate_sha256\": [\"1d81a79bda88b8a0ef64b7ae815c0d20cf1eee7f4714053530805bbb39e89ef2\", \"462521350b4f1b133f4bde6c793afdf735e84f8da918a169f1d030fc61727ee0\"],\n+ \"/complex_profile/proof_chain_sha256/research/source-assisted-v4/.work/lift.certificate.json.gz\": [\"1d81a79bda88b8a0ef64b7ae815c0d20cf1eee7f4714053530805bbb39e89ef2\", \"462521350b4f1b133f4bde6c793afdf735e84f8da918a169f1d030fc61727ee0\"],\n+ \"/complex_profile/proof_chain_sha256/research/source-assisted-v4/.work/lift.json\": [\"c41fee34c5c6e036ed9242ea6c19f32988aa21753b83e79513c890804cc469ae\", \"89b0d949852a5c22909256f03be040ce57450062c901a64a71a0e1cbb6bda8a1\"],\n+ \"/assembly/source_sha256/complex\": [\"7374c75b7d6eaec051d0a451fbc1487acf443ecc3f6c39424af5ebcf0ee8f0cb\", \"b80de5b00f7551cbbece1d2ec4a85f1433eb62d208df6cb11270087dcdfde3a3\"]\n+ },\n+ \"differing_leaves_order\": [\"built here\", \"committed at 8d8d67b\"],\n+ \"all_other_leaves_equal\": true,\n+ \"single_source\": \"All 7 leaves derive from the sha256 of lift.certificate.json.gz, written by research/source-assisted/decision/exact_complex_flow_lift.py:408-409 with gzip.compress(..., compresslevel=9, mtime=0); lift.json records it (line 419); the complex profile records the lift hashes; /assembly/source_sha256/complex is the sha256 of the complex profile file (research/source-assisted-v4/assemble.py:89).\"\n+ },\n+ \"comparison_with_pr194\": {\n+ \"pr194_head\": \"a8c87783785be6fe20c4a8bb2ac4b3eec295a179\",\n+ \"pr194_committed_lift_certificate_sha256\": \"1d81a79bda88b8a0ef64b7ae815c0d20cf1eee7f4714053530805bbb39e89ef2\",\n+ \"pr194_committed_lift_json_sha256\": \"c41fee34c5c6e036ed9242ea6c19f32988aa21753b83e79513c890804cc469ae\",\n+ \"pr194_committed_source_sha256_complex\": \"7374c75b7d6eaec051d0a451fbc1487acf443ecc3f6c39424af5ebcf0ee8f0cb\",\n+ \"exact_scalar_program_sha256_both\": \"3b4e671d7c6630570b04788bb2c81629e2c52f8dc2fcc5805952f0b403921027\",\n+ \"unchanged_pins_between_heads\": [\"research/source-assisted-v4/verify.py\", \"research/source-assisted-v4/contract_v4.py\", \"research/source-assisted-v4/source_aligned_local_v4.py\", \"research/source-assisted-v4/data/kernel-pairs.json\", \"research/source-assisted-v4/data/physical-pairs.json\", \"research/source-assisted/ (no diff)\"],\n+ \"changed_pins_between_heads\": [\"bit certificate path\", \"research/source-assisted-v4/assemble.py\", \"research/source-assisted-v4/pin_sources.py\", \"research/source-assisted-v4/NOTICE\", \"research/source-assisted-v4/PROOF.md\", \"research/source-assisted-v4/README.md\"],\n+ \"pr202_vs_pr194_compare\": \"a8c8778...8d8d67b: ahead 1, behind 0 (one commit, 8d8d67b)\",\n+ \"committed_certificates_complex_side\": \"/lift differs only by certificate_sha256; /complex_profile only by the three lift hashes; exact_scalar_program_sha256 and witness_sha256 identical; other differences come from the new bit supplier and kappa\",\n+ \"pr194_ci\": {\"workflow\": \".github/workflows/source-assisted-v4.yml\", \"run\": 37931952877, \"job\": 113824581619, \"conclusion\": \"success\", \"python\": \"3.13.16\", \"packages\": {\"numpy\": \"2.3.5\", \"scipy\": \"1.17.0\"}, \"printed\": \"PASS source-assisted-v4 kappa = 1668581/2500000000 (0.0006674324)\"}\n+ },\n+ \"control_runs_pr194\": [\n+ {\"command\": \"python -B research/source-assisted-v4/verify.py\", \"python\": \"3.13.16\", \"packages\": {\"numpy\": \"2.3.5\", \"scipy\": \"1.17.0\"}, \"start_utc\": \"2026-10-09T13:47:30Z\", \"exit\": 0, \"wall\": \"0:57.89\", \"printed\": \"PASS source-assisted-v4 kappa = 1668581/2500000000 (0.0006674324)\"},\n+ {\"command\": \"python -B research/source-assisted-v4/verify.py\", \"python\": \"3.12.3\", \"packages\": {\"numpy\": \"2.3.5\", \"scipy\": \"1.17.0\"}, \"start_utc\": \"2026-10-09T13:44:07Z\", \"exit\": 1, \"wall\": \"1:05.71\", \"printed\": \"AssertionError: Canonical certificate does not reproduce\", \"differing_leaves\": \"not recorded\"}\n+ ],\n+ \"reading\": \"Every leaf not derived from the lift gzip hash reproduces. With unchanged lift inputs, this environment and #194's CI (CPython 3.13.16) give the same gzip hash; #202's committed hash differs. The canonical check is environment-sensitive (interpreter or zlib build; #194's check also fails under CPython 3.12.3); the cause is not isolated. No claim about the mathematics of #202. Possible remedies: record the reference environment and regenerate, or check the lift through exact_scalar_program_sha256 and the mathematical fields of the complex profile as #207's verify_inner.py:23 and 29-30 do.\",\n+ \"label\": \"not reproduced; audit finding\"\n+ },\n+ {\n+ \"item\": \"3\",\n+ \"pr\": 197,\n+ \"head_run\": \"8c5e1cf07c23d843642bf2d4c76f882669edc43f\",\n+ \"head_now\": \"8c5e1cf07c23d843642bf2d4c76f882669edc43f\",\n+ \"dependencies\": {\"pr187\": \"201737a1ec4f936e166e2481fb9e88104cb2ccc7\", \"pr193\": \"187e1010ac8b259af8e9b5166f68b64bc27b4b47\"},\n+ \"dependencies_now\": {\"pr187\": \"201737a1ec4f936e166e2481fb9e88104cb2ccc7\", \"pr193\": \"187e1010ac8b259af8e9b5166f68b64bc27b4b47\"},\n+ \"command\": \"python -B research/packed-source-assisted-bit/verify.py --complex-root --bit-root --full\",\n+ \"python\": \"3.13.16\",\n+ \"packages\": {\"numpy\": \"2.3.5\", \"scipy\": \"1.17.0\"},\n+ \"tree\": \"98ee8c8e5c0f2214a9250f8390fbffea11ba1652\",\n+ \"start_utc\": \"2026-10-09T17:30:47Z\",\n+ \"end_utc\": \"2026-10-09T17:32:49Z\",\n+ \"exit\": 0,\n+ \"wall\": \"2:01.30\",\n+ \"max_rss_kb\": 594180,\n+ \"stderr\": \"empty\",\n+ \"tree_clean_before\": true,\n+ \"tree_clean_after\": true,\n+ \"certificate_json_sha256_after_regeneration\": \"c18fe983eb863661a69b0c2d89771acf9d11b7f460b1b04afcac6f2fea799886\",\n+ \"source_json_sha256\": \"0fd4b4913ad0a4dea0f894b98732123378c1de5f440eac63e49d6123f9e03a9f\",\n+ \"stdout_sha256\": \"06b43a2ec68ef3e884ccc3648431d53a26503225f4a3354f12df415a9646b7ba\",\n+ \"stdout_note\": \"stdout contains timing fields; its hash is not expected to be stable across runs\",\n+ \"earlier_run\": {\"job_start_utc\": \"2026-10-09T15:01:24Z\", \"wall\": \"1:35.68\", \"exit\": \"not captured\", \"printed_kappa\": \"135216063303877/200000000000000000\", \"tree_clean_after\": true},\n+ \"pass_records\": 8,\n+ \"printed_kappa\": \"135216063303877/200000000000000000\",\n+ \"kappa_decimal\": \"0.000676080316519385\",\n+ \"claimed_kappa\": \"0.000676080316519385\",\n+ \"audit_finding\": \"Removal of 6,600 rank-60 exterior children rests on the bank-endpoint identity proved on paper in PROOF.md section 4 (lines 81-93, 'an operator identity on arbitrary bank contents'); the finite controls on 144 formal columns over Z/9, Z/25 and Z/125 'support the identity above; they do not simulate the full cover or prove the inherited Clifford interface' (PROOF.md:95-98). Maintainer review of a comparable removal for #186 on main: research/community-round8-audit/BANK-SCHEDULE.md:6-8, 94-95 (cited by CONTRIBUTING.md:13); match of #197's banks with that schedule not checked. Depends on unmerged #187 and #193.\",\n+ \"ci\": {\"runs_at_head\": 4, \"conclusion\": \"action_required (awaiting maintainer approval)\", \"example_run\": 37936952135},\n+ \"label\": \"reproduced; audit finding\"\n+ },\n+ {\n+ \"item\": \"4\",\n+ \"pr\": 199,\n+ \"head_run\": \"5c1fb8346615968844bc182a5376c399109670ca\",\n+ \"tree\": \"f08f784c50504ace4fa659867e954b18210851a1\",\n+ \"head_now\": \"5c1fb8346615968844bc182a5376c399109670ca\",\n+ \"pr189_head\": \"0a4091175b3981267a97a62ab7492cb9ba528916\",\n+ \"command\": \"python -B bit_reuse_maximal.py --package /research/paired-cube-twin-local-168 --out \",\n+ \"cwd\": \"research/bit-leaf-bootstrap-189\",\n+ \"script_sha256\": \"91792e33ff057080c91369b788c88b9cc01e1df6ce2bcd173e67d68132cd4a61\",\n+ \"python\": \"3.13.16\",\n+ \"packages\": {\"numpy\": \"2.3.5\", \"scipy\": \"1.17.0\"},\n+ \"start_utc\": \"2026-10-09T17:30:48Z\",\n+ \"end_utc\": \"2026-10-09T17:30:58Z\",\n+ \"exit\": 0,\n+ \"wall\": \"0:10.25\",\n+ \"max_rss_kb\": 553200,\n+ \"tree_clean_after\": true,\n+ \"earlier_run\": {\"head\": \"2a10ca79d7f2100f9c36ccb6e4b083454e264285\", \"job_start_utc\": \"2026-10-09T14:39:56Z\", \"output_sha256\": \"30418cac689093de5b4d3cb7d6eeae450f8a74de5be7d66cc9be6087ed3ea61c\", \"exit\": \"0 (inferred: the driving script continued under set -e)\"},\n+ \"not_replayed\": [\"research/bit-leaf-bootstrap-189/next_bit_composition.py\", \"research/bit-leaf-bootstrap-189/next-composition-result.json\"],\n+ \"printed\": {\"gauges\": 3960, \"pairs\": 1760, \"unpaired\": 2200, \"unpaired_birth_frame_dim\": 20, \"donor_end_frames\": 8628, \"unpaired_birth_frames\": 220, \"containing_a_donor\": 0, \"verdict\": \"no unpaired gauge can receive a donor\"},\n+ \"output_sha256\": \"30418cac689093de5b4d3cb7d6eeae450f8a74de5be7d66cc9be6087ed3ea61c\",\n+ \"committed_sha256\": \"30418cac689093de5b4d3cb7d6eeae450f8a74de5be7d66cc9be6087ed3ea61c\",\n+ \"json_compare\": \"EQUAL\",\n+ \"label\": \"reproduced\"\n+ }\n+ ],\n+ \"disclosure\": 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4055136\n+}"},{"sha":"4b1e7aeff2deccfde94e71749a080a769a5f166d","filename":"research/community-round9-audit/pr216-original-failure.log.txt","status":"added","additions":74,"deletions":0,"changes":74,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr216-original-failure.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr216-original-failure.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr216-original-failure.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,74 @@\n+sha256sum: baseline/baseline-pr202.part01: No such file or directory\n+sha256sum: baseline/baseline-pr202.part02: No such file or directory\n+sha256sum: baseline/baseline-pr202.part03: No such file or directory\n+sha256sum: baseline/baseline-pr202.part04: No such file or directory\n+sha256sum: baseline/baseline-pr202.part05: No such file or directory\n+baseline/arithmetic.py: OK\n+baseline/BANK-CHART-PROOF.md: OK\n+baseline/BASELINE.json: OK\n+baseline/BOOTSTRAP-REVIEW.md: OK\n+baseline/certificate.json: OK\n+baseline/CROSSOVERS.md: OK\n+baseline/FILES.json: OK\n+baseline/frames/opframe-bases.json: OK\n+baseline/frames/verify-bit-frames.py: OK\n+baseline/geometry/audit-gauge-charts.py: OK\n+baseline/geometry/BANK-PROOF-PR200.md: OK\n+baseline/geometry/base_two_moment.py: OK\n+baseline/geometry/check-normalizer-routing.py: OK\n+baseline/geometry/pack-admitted-frames.py: OK\n+baseline/geometry/pack-pr200.py: OK\n+baseline/geometry/retained-packing.py: OK\n+baseline/LICENSE: OK\n+baseline/NOTICE: OK\n+baseline/PR-STATEMENT.md: OK\n+baseline/PR205-COMPARISON.md: OK\n+baseline/PROOF.md: OK\n+baseline/README.md: OK\n+baseline/requirements.txt: OK\n+baseline/verify_inner.py: OK\n+baseline/verify.py: OK\n+certificate.json: OK\n+LICENSE: OK\n+native-inputs.zip: OK\n+native/bit-columns.cpp: OK\n+native/frame-admission.cpp: OK\n+native/native-deps.zip: OK\n+native/native-pricing.cpp: OK\n+NOTICE: OK\n+NOTICE-PR211: OK\n+PR-STATEMENT.md: OK\n+PRIVACY.md: OK\n+PROOF.md: OK\n+PUBLIC-SOURCES.json: OK\n+README.md: OK\n+receipts/ALL-COLUMNS.json: OK\n+receipts/ASSEMBLY.json: OK\n+receipts/FRAME-ADMISSION.json: OK\n+receipts/INDEPENDENT-ASSEMBLY.json: OK\n+receipts/native-pricing-admitted-replay.json: OK\n+receipts/native-pricing-admitted-reprice.json: OK\n+receipts/PACKAGED-REPLAY.json: OK\n+RESEARCH-STATUS.md: OK\n+research/CENTRE-EXTENSION-PROOF.md: OK\n+research/CENTRE-EXTENSION.json: OK\n+research/CLOSURE-CHECKS.md: OK\n+research/FIFTH-BOOTSTRAP-COMPARISON.json: OK\n+research/FINAL-CUT-NOMINATION.json: OK\n+research/HYBRID-CAP-CHECKS.txt: OK\n+research/HYBRID-CAP-PROOF.md: OK\n+research/hybrid-cap.cpp: OK\n+research/LATE-REFINEMENT-SUMMARY.md: OK\n+research/LATEST-PUBLIC-ASSESSMENT.md: OK\n+research/MAJORIZATION-CUT.md: OK\n+research/omitted-label-compiler.zip: OK\n+research/omitted-label-structural.zip: OK\n+research/PR210-NAIVE-UNION-FAILURE.txt: OK\n+research/PR210-PLATEAU-UNION-FAILURE.txt: OK\n+research/W-PADDING-PROOF.md: OK\n+verify.ps1: OK\n+verify.sh: OK\n+witnesses/additional-bases.json: OK\n+witnesses/bit-profile.json: OK\n+witnesses/complex-profile.json: OK\n+witnesses/merged-bases.json: OK"},{"sha":"73514d06ecdc76003fcc95656fd541146ac74f15","filename":"research/community-round9-audit/pr216-repaired.log.txt","status":"added","additions":210,"deletions":0,"changes":210,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr216-repaired.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr216-repaired.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr216-repaired.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,210 @@\n+baseline/arithmetic.py: OK\n+baseline/BANK-CHART-PROOF.md: OK\n+baseline/baseline-pr202.part01: OK\n+baseline/baseline-pr202.part02: OK\n+baseline/baseline-pr202.part03: OK\n+baseline/baseline-pr202.part04: OK\n+baseline/baseline-pr202.part05: OK\n+baseline/BASELINE.json: OK\n+baseline/BOOTSTRAP-REVIEW.md: OK\n+baseline/certificate.json: OK\n+baseline/CROSSOVERS.md: OK\n+baseline/FILES.json: OK\n+baseline/frames/opframe-bases.json: OK\n+baseline/frames/verify-bit-frames.py: OK\n+baseline/geometry/audit-gauge-charts.py: OK\n+baseline/geometry/BANK-PROOF-PR200.md: OK\n+baseline/geometry/base_two_moment.py: OK\n+baseline/geometry/check-normalizer-routing.py: OK\n+baseline/geometry/pack-admitted-frames.py: OK\n+baseline/geometry/pack-pr200.py: OK\n+baseline/geometry/retained-packing.py: OK\n+baseline/LICENSE: OK\n+baseline/NOTICE: OK\n+baseline/PR-STATEMENT.md: OK\n+baseline/PR205-COMPARISON.md: OK\n+baseline/PROOF.md: OK\n+baseline/README.md: OK\n+baseline/requirements.txt: OK\n+baseline/verify_inner.py: OK\n+baseline/verify.py: OK\n+certificate.json: OK\n+LICENSE: OK\n+native-inputs.zip: OK\n+native/bit-columns.cpp: OK\n+native/frame-admission.cpp: OK\n+native/native-deps.zip: OK\n+native/native-pricing.cpp: OK\n+NOTICE: OK\n+NOTICE-PR211: OK\n+PR-STATEMENT.md: OK\n+PRIVACY.md: OK\n+PROOF.md: OK\n+PUBLIC-SOURCES.json: OK\n+README.md: OK\n+receipts/ALL-COLUMNS.json: OK\n+receipts/ASSEMBLY.json: OK\n+receipts/FRAME-ADMISSION.json: OK\n+receipts/INDEPENDENT-ASSEMBLY.json: OK\n+receipts/native-pricing-admitted-replay.json: OK\n+receipts/native-pricing-admitted-reprice.json: OK\n+receipts/PACKAGED-REPLAY.json: OK\n+RESEARCH-STATUS.md: OK\n+research/CENTRE-EXTENSION-PROOF.md: OK\n+research/CENTRE-EXTENSION.json: OK\n+research/CLOSURE-CHECKS.md: OK\n+research/FIFTH-BOOTSTRAP-COMPARISON.json: OK\n+research/FINAL-CUT-NOMINATION.json: OK\n+research/HYBRID-CAP-CHECKS.txt: OK\n+research/HYBRID-CAP-PROOF.md: OK\n+research/hybrid-cap.cpp: OK\n+research/LATE-REFINEMENT-SUMMARY.md: OK\n+research/LATEST-PUBLIC-ASSESSMENT.md: OK\n+research/MAJORIZATION-CUT.md: OK\n+research/omitted-label-compiler.zip: OK\n+research/omitted-label-structural.zip: OK\n+research/PR210-NAIVE-UNION-FAILURE.txt: OK\n+research/PR210-PLATEAU-UNION-FAILURE.txt: OK\n+research/W-PADDING-PROOF.md: OK\n+verify.ps1: OK\n+verify.sh: OK\n+witnesses/additional-bases.json: OK\n+witnesses/bit-profile.json: OK\n+witnesses/complex-profile.json: OK\n+witnesses/merged-bases.json: OK\n+{\n+ \"changes\": 6258,\n+ \"new_graph\": {\n+ \"entropy\": 866269.8481223907,\n+ \"histogram\": {\n+ \"0\": 36229,\n+ \"1\": 38530,\n+ \"10\": 767,\n+ \"11\": 445,\n+ \"12\": 1487,\n+ \"13\": 534,\n+ \"14\": 1106,\n+ \"15\": 315,\n+ \"16\": 1032,\n+ \"17\": 496,\n+ \"18\": 444,\n+ \"19\": 310,\n+ \"2\": 18094,\n+ \"20\": 880,\n+ \"21\": 5006,\n+ \"22\": 1320,\n+ \"3\": 10175,\n+ \"4\": 2924,\n+ \"5\": 2482,\n+ \"6\": 1496,\n+ \"7\": 1218,\n+ \"8\": 617,\n+ \"9\": 613\n+ },\n+ \"mass\": 405456\n+ },\n+ \"prime_frames\": 4346,\n+ \"public_relative_changes\": 2268,\n+ \"status\": \"PASS_NATIVE_EXACT_FRAME_PATH_AND_PRIME_ADMISSION\",\n+ \"value_checks\": 149024\n+}\n+bound 39780 bits 24 columns 20634\n+F2 all columns PASS\n+Z forward all columns PASS\n+Z reflected all columns PASS\n+{\n+ \"F2_identity\": true,\n+ \"controls\": {\n+ \"omit-ancestor-response\": \"REJECTED\",\n+ \"omit-pre-target\": \"REJECTED\",\n+ \"omit-write\": \"REJECTED\"\n+ },\n+ \"dirty_columns\": 17114,\n+ \"formal_columns\": 20634,\n+ \"integer_bound\": \"39780\",\n+ \"integer_defining_decoder\": true,\n+ \"literal_inverse\": true,\n+ \"milliseconds\": 72123,\n+ \"packed_digit_bits\": 24,\n+ \"scope\": \"Pinned PR200 scalar word with terminal/gauge/alias/partner inventory; operation frame changes preserve this exact scalar execution.\",\n+ \"source_and_dirty_restoration\": true,\n+ \"source_columns\": 1760,\n+ \"status\": \"PASS_NATIVE_ALL_F2_AND_INTEGER_COLUMNS\",\n+ \"target_columns\": 1760\n+}\n+\"PASS_NATIVE_EXACT_47_CONSTRAINT_ASSEMBLY\"; output /tmp/coordinated-crossover-v2.PSyYno/results/ASSEMBLY.json\n+baseline/arithmetic.py: OK\n+baseline/BANK-CHART-PROOF.md: OK\n+baseline/baseline-pr202.part01: OK\n+baseline/baseline-pr202.part02: OK\n+baseline/baseline-pr202.part03: OK\n+baseline/baseline-pr202.part04: OK\n+baseline/baseline-pr202.part05: OK\n+baseline/BASELINE.json: OK\n+baseline/BOOTSTRAP-REVIEW.md: OK\n+baseline/certificate.json: OK\n+baseline/CROSSOVERS.md: OK\n+baseline/FILES.json: OK\n+baseline/frames/opframe-bases.json: OK\n+baseline/frames/verify-bit-frames.py: OK\n+baseline/geometry/audit-gauge-charts.py: OK\n+baseline/geometry/BANK-PROOF-PR200.md: OK\n+baseline/geometry/base_two_moment.py: OK\n+baseline/geometry/check-normalizer-routing.py: OK\n+baseline/geometry/pack-admitted-frames.py: OK\n+baseline/geometry/pack-pr200.py: OK\n+baseline/geometry/retained-packing.py: OK\n+baseline/LICENSE: OK\n+baseline/NOTICE: OK\n+baseline/PR-STATEMENT.md: OK\n+baseline/PR205-COMPARISON.md: OK\n+baseline/PROOF.md: OK\n+baseline/README.md: OK\n+baseline/requirements.txt: OK\n+baseline/verify_inner.py: OK\n+baseline/verify.py: OK\n+certificate.json: OK\n+LICENSE: OK\n+native-inputs.zip: OK\n+native/bit-columns.cpp: OK\n+native/frame-admission.cpp: OK\n+native/native-deps.zip: OK\n+native/native-pricing.cpp: OK\n+NOTICE: OK\n+NOTICE-PR211: OK\n+PR-STATEMENT.md: OK\n+PRIVACY.md: OK\n+PROOF.md: OK\n+PUBLIC-SOURCES.json: OK\n+README.md: OK\n+receipts/ALL-COLUMNS.json: OK\n+receipts/ASSEMBLY.json: OK\n+receipts/FRAME-ADMISSION.json: OK\n+receipts/INDEPENDENT-ASSEMBLY.json: OK\n+receipts/native-pricing-admitted-replay.json: OK\n+receipts/native-pricing-admitted-reprice.json: OK\n+receipts/PACKAGED-REPLAY.json: OK\n+RESEARCH-STATUS.md: OK\n+research/CENTRE-EXTENSION-PROOF.md: OK\n+research/CENTRE-EXTENSION.json: OK\n+research/CLOSURE-CHECKS.md: OK\n+research/FIFTH-BOOTSTRAP-COMPARISON.json: OK\n+research/FINAL-CUT-NOMINATION.json: OK\n+research/HYBRID-CAP-CHECKS.txt: OK\n+research/HYBRID-CAP-PROOF.md: OK\n+research/hybrid-cap.cpp: OK\n+research/LATE-REFINEMENT-SUMMARY.md: OK\n+research/LATEST-PUBLIC-ASSESSMENT.md: OK\n+research/MAJORIZATION-CUT.md: OK\n+research/omitted-label-compiler.zip: OK\n+research/omitted-label-structural.zip: OK\n+research/PR210-NAIVE-UNION-FAILURE.txt: OK\n+research/PR210-PLATEAU-UNION-FAILURE.txt: OK\n+research/W-PADDING-PROOF.md: OK\n+verify.ps1: OK\n+verify.sh: OK\n+witnesses/additional-bases.json: OK\n+witnesses/bit-profile.json: OK\n+witnesses/complex-profile.json: OK\n+witnesses/merged-bases.json: OK\n+PASS: conditional kappa=0.000683864313137600; fresh receipts: /tmp/coordinated-crossover-v2.PSyYno/results"},{"sha":"6a2a649f5e1c9af3ece78bd135868ddb3da0e08d","filename":"research/community-round9-audit/pr217-bit-receipt.json","status":"added","additions":1362,"deletions":0,"changes":1362,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr217-bit-receipt.json","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr217-bit-receipt.json","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr217-bit-receipt.json?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,1362 @@\n+{\n+ \"abstract_profile\": {\n+ \"R\": 18908,\n+ \"W_per_vertex\": 22428,\n+ \"c\": 24140,\n+ \"child_histogram\": {\n+ \"1\": 123936,\n+ \"10\": 2892,\n+ \"11\": 2190,\n+ \"12\": 2364,\n+ \"13\": 1614,\n+ \"14\": 2766,\n+ \"15\": 894,\n+ \"16\": 2574,\n+ \"17\": 1368,\n+ \"18\": 816,\n+ \"19\": 696,\n+ \"2\": 63820,\n+ \"20\": 9240,\n+ \"21\": 10560,\n+ \"22\": 7992,\n+ \"3\": 23802,\n+ \"4\": 18660,\n+ \"5\": 6954,\n+ \"6\": 5376,\n+ \"60\": 2200,\n+ \"63\": 1760,\n+ \"7\": 3324,\n+ \"8\": 4170,\n+ \"9\": 2166\n+ },\n+ \"deficit_per_vertex\": 1936,\n+ \"h\": 24,\n+ \"loss\": 528,\n+ \"m\": 72,\n+ \"matched\": 11856,\n+ \"maxchild\": 63,\n+ \"plain_frames\": 7728,\n+ \"q\": 6624,\n+ \"rank_per_vertex\": 1612880,\n+ \"remaining_internal_histogram\": {\n+ \"0\": 7262,\n+ \"1\": 33392,\n+ \"10\": 964,\n+ \"11\": 730,\n+ \"12\": 788,\n+ \"13\": 538,\n+ \"14\": 922,\n+ \"15\": 298,\n+ \"16\": 858,\n+ \"17\": 456,\n+ \"18\": 272,\n+ \"19\": 232,\n+ \"2\": 20100,\n+ \"20\": 2200,\n+ \"21\": 2200,\n+ \"22\": 1344,\n+ \"3\": 8374,\n+ \"4\": 6220,\n+ \"5\": 2318,\n+ \"6\": 1792,\n+ \"7\": 1108,\n+ \"8\": 1390,\n+ \"9\": 722\n+ },\n+ \"selected_rank_histogram\": {\n+ \"20\": 2200,\n+ \"21\": 1760\n+ },\n+ \"selected_roles\": 3960,\n+ \"source_data_histogram\": {\n+ \"1\": 1760,\n+ \"2\": 880,\n+ \"20\": 880,\n+ \"22\": 880\n+ },\n+ \"target_data_histogram\": {\n+ \"0\": 10560,\n+ \"1\": 4400,\n+ \"20\": 880,\n+ \"21\": 880\n+ },\n+ \"v\": 1760\n+ },\n+ \"baseline_formal\": [\n+ {\n+ \"all_dirty_and_source_columns_restored\": true,\n+ \"defining_decoder\": true,\n+ \"formal_variables\": 20668,\n+ \"identity\": true,\n+ \"ring\": \"2\",\n+ \"target_contract\": \"F2 identity\"\n+ },\n+ {\n+ \"all_dirty_and_source_columns_restored\": true,\n+ \"defining_decoder\": true,\n+ \"formal_variables\": 20668,\n+ \"identity\": false,\n+ \"ring\": \"0\",\n+ \"target_contract\": \"integer defining decoder\"\n+ }\n+ ],\n+ \"baseline_profile\": {\n+ \"R\": 17148,\n+ \"W_per_vertex\": 20668,\n+ \"changed_operation_frames\": 11671,\n+ \"child_histogram\": {\n+ \"1\": 127458,\n+ \"10\": 2292,\n+ \"11\": 1335,\n+ \"12\": 4398,\n+ \"13\": 1602,\n+ \"14\": 3462,\n+ \"15\": 945,\n+ \"16\": 3096,\n+ \"17\": 1488,\n+ \"18\": 1131,\n+ \"19\": 1131,\n+ \"2\": 59356,\n+ \"20\": 5280,\n+ \"21\": 14001,\n+ \"22\": 7791,\n+ \"3\": 30699,\n+ \"4\": 8715,\n+ \"5\": 7518,\n+ \"6\": 4365,\n+ \"60\": 2200,\n+ \"7\": 3711,\n+ \"8\": 1839,\n+ \"9\": 1668\n+ },\n+ \"deficit_per_vertex\": 1936,\n+ \"foreign_producer_replays\": 0,\n+ \"frames_not_contained_in_original\": 259,\n+ \"h\": 24,\n+ \"loss\": 528,\n+ \"m\": 72,\n+ \"maxchild\": 60,\n+ \"physical_internal_histogram\": {\n+ \"1\": 36326,\n+ \"10\": 764,\n+ \"11\": 445,\n+ \"12\": 1466,\n+ \"13\": 534,\n+ \"14\": 1154,\n+ \"15\": 315,\n+ \"16\": 1032,\n+ \"17\": 496,\n+ \"18\": 377,\n+ \"19\": 377,\n+ \"2\": 17732,\n+ \"21\": 3787,\n+ \"22\": 1717,\n+ \"3\": 10233,\n+ \"4\": 2905,\n+ \"5\": 2506,\n+ \"6\": 1455,\n+ \"7\": 1237,\n+ \"8\": 613,\n+ \"9\": 556\n+ },\n+ \"physical_target_histogram\": {\n+ \"1\": 4400,\n+ \"20\": 880,\n+ \"21\": 880\n+ },\n+ \"rank_per_vertex\": 1486160,\n+ \"reused_registers\": 1760,\n+ \"selected_rank_histogram\": {\n+ \"20\": 2200\n+ },\n+ \"selected_roles\": 2200,\n+ \"v\": 1760,\n+ \"virtual_R\": 18908\n+ },\n+ \"fresh_complex_proof_executed\": false,\n+ \"loader_sha256\": \"5aa9f19fe7e4f669499a4f0f916017f9042519d245202b8619ca609997b4e62c\",\n+ \"metadata\": {\n+ \"base_head\": \"a1175449f34d39ff933d9d8ab23ced1f32b290ec\",\n+ \"butterflies\": 440,\n+ \"butterfly_origin_head\": \"cd14825023b75af4f5919a30e5e6d548b6ade5bc\",\n+ \"changed_gate_controls\": 880,\n+ \"changed_graph_nodes\": 880,\n+ \"emitted_bytes\": {\n+ \"frames_p12.json\": 20965491,\n+ \"graph_p12.json\": 932763,\n+ \"word_p12.json\": 2357688\n+ },\n+ \"emitted_sha256\": {\n+ \"frames_p12.json\": \"4e0fce06f07a044e68583d3fe96594b5ad67fe0d19cfd43a97495c57823ae351\",\n+ \"graph_p12.json\": \"2bb271df49780365b22b286d9f7166b1fdf3c67ff7d679ba43ca633fc884bdcc\",\n+ \"word_p12.json\": \"ef77a7d30390a21c18ed70a905e1e6c7a07c29439a523da69e3c97ab5ac94356\"\n+ },\n+ \"full_serialization_canonical\": true,\n+ \"immutable_overlay_sha256\": 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34\n+}"},{"sha":"021682258f1448ba74a33d713a40737fe71ac88f","filename":"research/community-round9-audit/pr217-preflight.log.txt","status":"added","additions":1,"deletions":0,"changes":1,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr217-preflight.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr217-preflight.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr217-preflight.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1 @@\n+PASS public-source preflight; no supplier proof executed"},{"sha":"762b0db4368d224dca43d2c2b4b8c7bb55787726","filename":"research/community-round9-audit/pr217-tests.log.txt","status":"added","additions":5,"deletions":0,"changes":5,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr217-tests.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr217-tests.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr217-tests.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,5 @@\n+..........\n+----------------------------------------------------------------------\n+Ran 10 tests in 0.178s\n+\n+OK"},{"sha":"1650fe93d57e3fc642264ed490559dbd98f0d134","filename":"research/community-round9-audit/pr218-parity.json","status":"added","additions":50,"deletions":0,"changes":50,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr218-parity.json","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr218-parity.json","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr218-parity.json?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,50 @@\n+[\n+ {\n+ \"nondegenerate\": false,\n+ \"jobs\": 1,\n+ \"failures\": 77,\n+ \"matches_serial_oracle\": true\n+ },\n+ {\n+ \"nondegenerate\": false,\n+ \"jobs\": 4,\n+ \"failures\": 77,\n+ \"matches_serial_oracle\": true\n+ },\n+ {\n+ \"nondegenerate\": false,\n+ \"jobs\": 0,\n+ \"failures\": 77,\n+ \"matches_serial_oracle\": true\n+ },\n+ {\n+ \"nondegenerate\": false,\n+ \"jobs\": -1,\n+ \"failures\": 77,\n+ \"matches_serial_oracle\": true\n+ },\n+ {\n+ \"nondegenerate\": true,\n+ \"jobs\": 1,\n+ \"failures\": 118,\n+ \"matches_serial_oracle\": true\n+ },\n+ {\n+ \"nondegenerate\": true,\n+ \"jobs\": 4,\n+ \"failures\": 118,\n+ \"matches_serial_oracle\": true\n+ },\n+ {\n+ \"nondegenerate\": true,\n+ \"jobs\": 0,\n+ \"failures\": 118,\n+ \"matches_serial_oracle\": true\n+ },\n+ {\n+ \"nondegenerate\": true,\n+ \"jobs\": -1,\n+ \"failures\": 118,\n+ \"matches_serial_oracle\": true\n+ }\n+]"},{"sha":"d06a21131f8411eb18485dfe78c6107c8f1711aa","filename":"research/community-round9-audit/pr218-replay.log.txt","status":"added","additions":5,"deletions":0,"changes":5,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr218-replay.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr218-replay.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr218-replay.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,5 @@\n+[ 4s] PASS exact composed plan, chronological ledger and unchanged set of new frame pairs\n+[ 670s] PASS exact rational nesting (4878 new pairs; all inherited pairs checked)\n+[ 677s] PASS complete F2 and integer scalar maps with independent arbitrary data, targets and dirty registers\n+[ 684s] PASS stale-value, premature-read and incorrect-inverse negative controls\n+[ 685s] PASS kappa=472154791/1000000000000 = 0.000472154791; full fallback, both suppliers and 47 constraints"},{"sha":"67f6bc5aa7bf12a8abbb26c0b69e43a2b292f71b","filename":"research/community-round9-audit/pr221-ceiling.log.txt","status":"added","additions":37,"deletions":0,"changes":37,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr221-ceiling.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr221-ceiling.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr221-ceiling.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,37 @@\n+[ 27s] #200 bit word: h 24, v 1760, centre loss 528, deficit D = 2v - 3 loss = 1936, 41288 operations, 18908 roles, 1760 reuse pairs, 34 sinks\n+[ 27s] fact 1: certified coarse saving 6.7938424e-04 < D/C = 6.7998615e-04 (gap 0.089%)\n+[ 265s] self-test: #200's layout lies inside every derived frame bound; its slot chains reproduce the certified pre-sink ledger exactly (W 20668, rank 1486160); the terminal record substitutes [3, 21] per sink and stage; every slot floor is below its actual chain\n+[ 491s] fact 4, #200's own ledger: certified C = 2847117, floor C >= 2800700; coarse < 6913/10^7 = 6.9130000e-04 (certified 6.7938424e-04 is 98.3% of it); kappa < 6908/10^7\n+[ 491s] fact 4, banked ledger (#205/#206/#207 accounting on this word): D/C of #200's layout = 6.8578301e-04; floor C >= 2776634; coarse < 6973/10^7; kappa < 6968/10^7\n+[ 491s] without coupling the two registers of an operation: coarse < 7065/10^7 (own), 7128/10^7 (banked)\n+{\n+ \"D\": 1936,\n+ \"certified_coarse\": \"679384236170571/1000000000000000000\",\n+ \"certified_kappa\": null,\n+ \"h\": 24,\n+ \"loss\": 528,\n+ \"m\": 72,\n+ \"operations\": 41288,\n+ \"package\": \"research/paired-cube-diagonal-bit-168\",\n+ \"results\": {\n+ \"banked\": {\n+ \"C_certified_layout\": 2823050.382288007,\n+ \"C_floor\": 2776633.5777524863,\n+ \"coarse_ceiling\": \"6973/10^7\",\n+ \"coarse_ceiling_uncoupled\": \"7128/10^7\",\n+ \"kappa_ceiling\": \"6968/10^7\"\n+ },\n+ \"own\": {\n+ \"C_certified_layout\": 2847116.8277848093,\n+ \"C_floor\": 2800700.0232492886,\n+ \"coarse_ceiling\": \"6913/10^7\",\n+ \"coarse_ceiling_uncoupled\": \"7065/10^7\",\n+ \"kappa_ceiling\": \"6908/10^7\"\n+ }\n+ },\n+ \"reuse_pairs\": 1760,\n+ \"roles\": 18908,\n+ \"rounds\": 1200,\n+ \"sinks\": 34,\n+ \"v\": 1760\n+}"},{"sha":"0bcf2ea92dc5171a360f18ace68de5253fa221c6","filename":"research/community-round9-audit/pr221-emitted.log.txt","status":"added","additions":6,"deletions":0,"changes":6,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr221-emitted.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr221-emitted.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr221-emitted.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,6 @@\n+[33.6s] candidate built\n+ frames_p12.json 4e0fce06f07a044e matches expected-bit.json\n+ graph_p12.json 2bb271df49780365 matches expected-bit.json\n+ word_p12.json ef77a7d30390a21c matches expected-bit.json\n+word: ops 41288 roles 18908 v 1760 h 24 pairs 1760 gauges 3960 changed frames 11671\n+wrote /tmp/integer-mult-pr221-emitted"},{"sha":"eeabb0e179cbf681fd20f16b0756cecad4000a9e","filename":"research/community-round9-audit/pr221-transfer.log.txt","status":"added","additions":34,"deletions":0,"changes":34,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr221-transfer.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr221-transfer.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr221-transfer.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,34 @@\n+skeleton (must be identical for one operation-index space to exist)\n+ arcs A=11856 B=11856 identical\n+ order A=25900 B=25900 identical\n+ pairs A=1760 B=1760 identical\n+ gauges A=3960 B=3960 identical\n+ rootroles A=6624 B=6624 identical\n+ phase1 A=17688 B=17688 identical\n+ plain A=7728 B=7728 identical\n+ sources A=1760 B=1760 identical\n+ reads A=1760 B=1760 identical\n+ ops A=41288 B=41288 same length\n+\n+what PR217 rewrote in that shared index space\n+ operations whose content differs: 880 of 41288\n+ operation frames that differ: 7068 of 41288\n+\n+PR216 admission records, keyed by operation index\n+ current bases (input) 6191 records, 6191 distinct indices, max 35154, on a rewritten op: 3\n+ complete override list 6258 records, 6258 distinct indices, max 35154, on a rewritten op: 3\n+ canonical subspaces 2268 records, 2268 distinct indices, max 30329, on a rewritten op: 0\n+\n+the ceiling this package measured for PR217's own word\n+ #217 achieved kappa = 684696826673891/10^15\n+ #216 achieved kappa (plain word) = 427415195711/625000000000000\n+ floor: any frame layout of the word < 6968/10^7\n+ so a combined layout on this word can add at most +1.77% to the record\n+ while #216's own layout sits -0.122% below it, on the plain word\n+\n+PASS structural comparison (one index space, 880 rewritten operations, 7068 rewritten frames)\n+OPEN combination: the merge is well defined at the index level -- almost every\n+ admitted record addresses an operation PR217 left untouched -- but PR216\n+ admits its cuts with the scalar word fixed and PR217's rewrite is in those\n+ operations, so a merged layout needs fresh global admission and a fresh\n+ column replay, and the ceiling above bounds what it can reach."},{"sha":"9b28e3b820a9339e7c1d2983fc6ba819409ad12b","filename":"research/community-round9-audit/pr221-tree-ready.log.txt","status":"added","additions":3,"deletions":0,"changes":3,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr221-tree-ready.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr221-tree-ready.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr221-tree-ready.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,3 @@\n+tree: /private/tmp/integer-mult-pr221-tree-ready/research/paired-cube-diagonal-bit-168\n+pre-sink W 20668 rank 1486160 deficit 1936\n+post-terminal W 20634 rank 1483712 deficit 1936"},{"sha":"4a2940d89b998146a894b97f5202bcdaa719cf65","filename":"research/community-round9-audit/pr222-replay.log.txt","status":"added","additions":15,"deletions":0,"changes":15,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr222-replay.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr222-replay.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr222-replay.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,15 @@\n+main archive: 1700 files, sha256 2f8b42946202... matches research/coordinated-frames-and-entrance-banks/BASELINE.json (PR181 @ 7fb2194)\n+ PASS generator input data/arcs_p12.json equals main's research/paired-cube-bit/data/arcs_p12.json\n+ PASS generator input data/pair_module_p12.json equals main's research/paired-cube-bit/data/pair_module_p12.json\n+ PASS generator input data/qmod_p12.json equals main's research/paired-cube-bit/data/qmod_p12.json\n+fresh run of the generator: 15.1 s\n+ PASS graph_p12.json equals main's research/paired-cube-bit/out/graph_p12.json byte for byte\n+ PASS profile_p12.json equals main's research/paired-cube-bit/out/profile_p12.json byte for byte\n+ PASS word_p12.json equals main's research/paired-cube-bit/out/word_p12.json byte for byte\n+ PASS frames_p12.json equals main's research/paired-cube-bit/out/frames_p12.json byte for byte\n+ PASS kchron_p12.json equals main's research/paired-cube-bit/out/kchron_p12.json byte for byte\n+ PASS word_p12.json.gz equals main's research/paired-cube-bit/out/word_p12.json.gz (decompressed)\n+ PASS main's independent check_paired_cube_bit.py passes on the regenerated word (PASS: all 5 mutation controls rejected)\n+main's frozen physical layer (references/paired-cube/bit-physical) is NOT reproduced by this generator; relation, for information:\n+ same op count (41288) and op node multiset: True; same sources: True; ops reordered at 13120 positions; 98.4% of the regenerated frame records appear in its frames (ids renumbered)\n+PASS: the fast generator reproduces main's base bit word (10/10 checks)"},{"sha":"3a1cd3cbc6ee5e07924600170d5d09d0aa236193","filename":"research/community-round9-audit/pr223-changed.log.txt","status":"added","additions":2094,"deletions":0,"changes":2094,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr223-changed.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr223-changed.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr223-changed.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,2094 @@\n+PASS served word (re-derived and fully checked), exact charts and banks, two moment engines, finite leaf composition, 47 constraints and seven margins\n+conditional kappa = 34607230212503/50000000000000000\n+PASS served word (re-derived and fully checked), exact 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longest 21 output /var/folders/sd/yrr853rn73qdgdgdmps82gfh0000gn/T/climbed-producers-3a36zxny/h23.bin.round3_rankone_certified_profiles.json\n+PASS h=23 scalar, dense audit, pinned-links profile, independent recount, full timeline and dirty basis (both orientations)\n+Rebuilding climbed PR48 producer h=25\n+profiles 10000 of 185987\n+profiles 20000 of 185987\n+profiles 30000 of 185987\n+profiles 40000 of 185987\n+profiles 50000 of 185987\n+profiles 60000 of 185987\n+profiles 70000 of 185987\n+profiles 80000 of 185987\n+profiles 90000 of 185987\n+CRT matrices 7158 differing modular profiles 0\n+RANKONE h 25 longest 23 output /var/folders/sd/yrr853rn73qdgdgdmps82gfh0000gn/T/climbed-producers-3a36zxny/h25.bin.round3_rankone_certified_profiles.json\n+PASS h=25 scalar, dense audit, pinned-links profile, independent recount, full timeline and dirty basis (both orientations)"},{"sha":"aee061cc9f36af0fab00d171b5d9b685ee5b522b","filename":"research/community-round9-audit/pr226-standalone-failure.log.txt","status":"added","additions":5,"deletions":0,"changes":5,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr226-standalone-failure.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr226-standalone-failure.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr226-standalone-failure.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,5 @@\n+============================================================================\n+ SCHÖNHAGE TRILINEAR MULTIPLICATION TENSOR — ARITHMETIC VERIFIER\n+ Complexity Bound: T(n) = O(n (log n)^{1 - kappa})\n+============================================================================\n+[FAIL] certificate.json not found!"},{"sha":"3df11c85b9011799e9736725d1cb60581210cc77","filename":"research/community-round9-audit/pr226-tests.log.txt","status":"added","additions":5,"deletions":0,"changes":5,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr226-tests.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr226-tests.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr226-tests.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,5 @@\n+.....\n+----------------------------------------------------------------------\n+Ran 5 tests in 0.473s\n+\n+OK"},{"sha":"9636395af4c1a75241cbd46dd9570808e1989ecb","filename":"research/community-round9-audit/pr227-ACTUAL-SIGNALS.json","status":"added","additions":15,"deletions":0,"changes":15,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr227-ACTUAL-SIGNALS.json","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr227-ACTUAL-SIGNALS.json","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr227-ACTUAL-SIGNALS.json?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,15 @@\n+{\n+ \"auxiliary_updates\": 40758,\n+ \"borrowed_original_source_slots\": 469,\n+ \"both_operands_and_postsum_checked\": true,\n+ \"candidate_override_entries\": 2315,\n+ \"checked_early_source_mixes\": 469,\n+ \"forward_operations\": 41288,\n+ \"literal_source_label_memberships\": 3433472,\n+ \"omitted_first_copy_operations\": 440,\n+ \"physical_alias_mapping\": true,\n+ \"redirected_terminal_writes\": 90,\n+ \"scope\": \"Exact positive source supports follow actual original-X borrowed endpoints, source injections,physical alias donor contents,440 copy omissions,440 early and29prephase mixes at literal mix frames,and both gate operands/post-sums; complete scalar restoration and uniform prime/chronology/bank admissions separate\",\n+ \"status\": \"PASS_SOURCE469_ACTUAL_PHYSICAL_FRESH_SPANS\",\n+ \"unique_frame_label_memberships\": 924426\n+}"},{"sha":"44276cb38cc73701496a81cdb0a4dd4525f0b25d","filename":"research/community-round9-audit/pr227-ALL-COLUMNS.json","status":"added","additions":99,"deletions":0,"changes":99,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr227-ALL-COLUMNS.json","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr227-ALL-COLUMNS.json","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr227-ALL-COLUMNS.json?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,99 @@\n+{\n+ \"F2_identity\": true,\n+ \"borrowed_source_slots\": 469,\n+ \"changed_integer_adjoint_rows\": 440,\n+ \"control_failure_witnesses\": {\n+ \"old_adjoint\": \"target formal column failure target=0 input_column=3530\",\n+ \"omit-ancestor-response\": \"target formal column failure target=8 input_column=3850\",\n+ \"omit-new12\": \"target formal column failure target=216 input_column=17192\",\n+ \"omit-new13\": \"target formal column failure target=872 input_column=17525\",\n+ \"omit-new18\": \"target formal column failure target=864 input_column=17760\",\n+ \"omit-new19\": \"target formal column failure target=40 input_column=138\",\n+ \"omit-new2\": \"target formal column failure target=32 input_column=114\",\n+ \"omit-new4\": \"target formal column failure target=24 input_column=322\",\n+ \"omit-pre-target\": \"target formal column failure target=9 input_column=2\",\n+ \"omit-write\": \"target formal column failure target=8 input_column=128\",\n+ \"omit_early_mix\": \"target formal column failure target=5 input_column=3\",\n+ \"omit_gauge_compensation\": \"target formal column failure target=1624 input_column=1634\",\n+ \"omit_gauge_mix\": \"target formal column failure target=1636 input_column=1634\",\n+ \"undo_before_restore\": \"dirty 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no ghost dirty slots; independently recomputed full adjoint with omitted copies; physical source-frame, aliases, bank endpoints and paid pricing require separate admission.\",\n+ \"source_and_dirty_restoration\": true,\n+ \"source_columns\": 1760,\n+ \"status\": \"PASS_NATIVE_ALL_F2_AND_INTEGER_COLUMNS\",\n+ \"target_columns\": 1760,\n+ \"unchanged_gauge_adjoint_coefficients\": 6592\n+}\n+Actual charts=231 maxops=310 maxnum=8 maxden=72\n+{\n+ \"assignments\": 3595320,\n+ \"charts\": 231,\n+ \"literal_stock\": 1316658,\n+ \"max_factors\": 310,\n+ \"selector_calls\": 235098710064,\n+ \"status\": \"PASS_NATIVE_COMPLETE_BANKS_CHARTS_NORMALIZERS\"\n+}\n+\"PASS_NATIVE_EXACT_47_CONSTRAINT_ASSEMBLY\"; output /var/folders/sd/yrr853rn73qdgdgdmps82gfh0000gn/T//source-borrow-crossover-73E3OU/results/ASSEMBLY.json\n+\"PASS_INDEPENDENT_BASE2_DEGREE16_MOMENT_AND_ASSEMBLY\" kappa=1736938487903/2500000000000000\n+PASS immutable complete exact result: \"1736938487903/2500000000000000\"\n+ACTIVE-PRIMES-PROOF.md: OK\n+certificate.json: OK\n+LICENSE: OK\n+native-inputs.zip: OK\n+native/actual-signals.cpp: OK\n+native/all-active-primes.cpp: OK\n+native/bit-columns.cpp: OK\n+native/frame-algebra.hpp: OK\n+native/frozen-result.cpp: OK\n+native/independent-pricing.cpp: OK\n+native/joint-banks.cpp: OK\n+native/native-deps.zip: OK\n+native/native-pricing.cpp: OK\n+native/new-frame-algebra.hpp: OK\n+native/reference-frame-admission.cpp: OK\n+native/source-boundary.cpp: OK\n+native/source-entrances.cpp: OK\n+native/source-frame-admission.cpp: OK\n+native/source440-frame-admission.cpp: OK\n+NOTICE: OK\n+NOTICE-COMPOSITION: OK\n+NOTICE-PR211: OK\n+PR-STATEMENT.md: OK\n+PRIVACY.md: OK\n+PROOF.md: OK\n+README.md: OK\n+receipts/ACTUAL-SIGNALS.json: OK\n+receipts/ALL-ACTIVE-PRIMES.json: OK\n+receipts/ALL-COLUMNS.json: OK\n+receipts/BANKS.json: OK\n+receipts/FRAME-ADMISSION.json: OK\n+receipts/FRAME-PROVENANCE.json: OK\n+receipts/INDEPENDENT-ARITHMETIC.json: OK\n+receipts/PROFILE.json: OK\n+receipts/PUBLIC-BASELINE-COMPARISON.json: OK\n+receipts/SEARCH-NOMINATION.json: OK\n+receipts/SOURCE-BOUNDARY.json: OK\n+receipts/SOURCE-ENTRANCES.json: OK\n+research/BUTTERFLY-PROOF.md: OK\n+research/INNOVATION-EXTRACTOR-PROOF.md: OK\n+research/README.md: OK\n+research/READONLY-SHARING-PROOF.md: OK\n+research/READONLY-SHARING-SCALAR-PROOF.md: OK\n+research/source-greatest.cpp: OK\n+research/SUFFICIENT-CROSSOVERS.md: OK\n+SCALAR-PROOF.md: OK\n+SOURCE-BORROW-PROOF.md: OK\n+SOURCE-ENTRANCES-PROOF.md: OK\n+SOURCES.md: OK\n+upstream/GAUGE-SOURCE-BORROWING.md: OK\n+upstream/NEW-SOURCE-GAUGES.md: OK\n+upstream/SOURCE-BORROWING.md: OK\n+VALIDATION.md: OK\n+verify.ps1: OK\n+verify.sh: OK\n+witnesses/candidate-bases.json: OK\n+witnesses/complex-profile.json: OK\n+witnesses/empty-bases.json: OK\n+witnesses/new-73-contractions.json: OK\n+witnesses/source440-candidate-bases.json: OK\n+witnesses/source469-packed-reference.json: OK\n+PASS fresh offline replay; 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\"PASS_EXACT_47_CONSTRAINT_ASSEMBLY\"\r\n+}\r"},{"sha":"399fb9a1b65b252df44fb96cd56f25700aaff2c5","filename":"research/community-round9-audit/pr230-replay.log.txt","status":"added","additions":260,"deletions":0,"changes":260,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr230-replay.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr230-replay.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr230-replay.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,260 @@\n+PASS deterministic plateau reproduction; 14 moves, 19 operation frames; 107.0s\n+PASS exact frames and alias endpoints\n+bound 39780 bits 24 columns 20634\n+PASS full reflected supplier replay\n+PASS joint gauge whole-word and prime admission {'1': 126249, '2': 60538, '3': 30663, '4': 8706, '5': 7473, '6': 4551, '7': 3762, '8': 1935, '9': 1815, '10': 2337, '11': 1338, '12': 4518, '13': 1734, '14': 3312, '15': 873, '16': 3042, '17': 1452, '18': 1404, '19': 846, '20': 5148, '21': 14886, '22': 6672, '36': 18, '39': 48, '54': 13, '57': 3, '60': 2200}\n+PASS omitted new compensation read rejected\n+PASS reversed nested gauge read order rejected\n+PASS omitted nested rank19 compensation rejected\n+PASS omitted rank12 shared gauge compensation rejected\n+PASS omitted rank13 shared gauge compensation rejected\n+PASS F2 {'mode': 'F2', 'direction': 1, 'formal_columns': 20194, 'sources': 1760, 'targets': 1760, 'dirty': 16674, 'all_targets': True, 'all_source_and_dirty_restored': True} seconds 0.9533260839998547\n+bound 37624 bits 24\n+PASS integer 1 seconds 67.36971929199899\n+PASS integer -1 seconds 146.44767137499912\n+PASS borrowed source word, both integer signs, all columns and controls\n+{\n+ \"scope\": \"INDEPENDENT EXACT SOURCE ENDPOINT AND FRAME-PATH AUDIT; SCALAR ADMISSION OWNED BY SEPARATE EXECUTOR\",\n+ \"sources_borrowed\": 440,\n+ \"borrowed_physical_donor_alias_chains\": 67,\n+ \"all_source_start_frames_preserved\": true,\n+ \"all_source_end_frames_full\": true,\n+ \"every_spliced_frame_inclusion_checked\": true,\n+ \"all_reflected_path_histograms_equal\": true,\n+ \"local_histogram_delta\": {\n+ \"2\": -440,\n+ \"22\": -440\n+ },\n+ \"shared_histogram_delta\": {\n+ \"2\": -1320,\n+ \"22\": -1320\n+ },\n+ \"local_rank_mass_delta\": -10560,\n+ \"shared_rank_mass_delta\": -31680,\n+ \"physical_role_stock_delta\": -440,\n+ \"shared_m\": 72,\n+ \"deficit_change\": 0\n+}\n+PASS complete spliced source/internal/target profile {'W': 20194, 'rank': 1452032, 'deficit': 1936, 'delta': {2: -1320, 22: -1320}}\n+PASS F2 {'mode': 'F2', 'direction': 1, 'formal_columns': 20191, 'sources': 1760, 'targets': 1760, 'dirty': 16671, 'all_targets': True, 'all_source_and_dirty_restored': True} seconds 3.981932209000661\n+bound 37624 bits 24\n+PASS integer 1 seconds 168.10107070900085\n+PASS integer -1 seconds 266.92629870900055\n+PASS complete gauged source word, both integer signs, all columns and five controls\n+PASS3 actual gauge/source/reflected paths {17: 9, 22: -9, 57: -3}\n+PASS443 complete ledgers {'W': 20191, 'R': 16671, 'rank': 1451816, 'deficit': 1936, 'delta': {17: 9, 22: -9, 57: -3}}\n+PASS scalar schedule timing, all gauge/alias readtimes, new source prefix inclusions; independent target/reflected ledger required\n+PASS F2 {'mode': 'F2', 'direction': 1, 'formal_columns': 20163, 'sources': 1760, 'targets': 1760, 'dirty': 16643, 'all_targets': True, 'all_source_and_dirty_restored': True, 'copied_center_target_reads': 5280, 'all_forward_centers_at_D0': True, 'all_reflected_centers_at_D1': True, 'actual_target_histogram': {'1': 4412, '2': 160, '3': 14, '4': 4, '5': 17, '6': 9, '7': 24, '8': 28, '9': 5, '12': 16, '13': 48, '14': 17, '16': 3, '17': 4, '18': 29, '19': 112, '20': 836, '21': 694}, 'actual_reflected_target_histogram': {'1': 4412, '2': 160, '3': 14, '4': 4, '5': 17, '6': 9, '7': 24, '8': 28, '9': 5, '12': 16, '13': 48, '14': 17, '16': 3, '17': 4, '18': 29, '19': 112, '20': 836, '21': 694}} seconds 2.540779124999972\n+bound 37624 bits 24\n+PASS integer 1 seconds 64.09336783300023\n+PASS integer -1 seconds 120.9596534579996\n+PASS actual471 source word, both integer signs, all columns and six controls\n+PASS scalar schedule timing, all gauge/alias readtimes, new source prefix inclusions; independent target/reflected ledger required\n+{\n+ \"status\": \"PASS_SOURCE471_EXACT_EVENT_AND_ADDRESS_RETIMING\",\n+ \"events\": 41288,\n+ \"center_prefix_events\": 17520,\n+ \"center_prefix_operations\": 17080,\n+ \"deferred_operations\": 168,\n+ \"early_source_mixes_in_prefix\": 440,\n+ \"source_heads\": 471,\n+ \"formal_columns\": 20163,\n+ \"every_actual_input_preceding_write_preserved\": true,\n+ \"every_final_write_preserved\": true,\n+ \"all_physical_frame_paths_nested\": true,\n+ \"all_actual_address_frame_dimension_streams_preserved\": true,\n+ \"all_exact_address_subspace_streams_preserved\": true,\n+ \"all_address_jump_histograms_preserved\": true,\n+ \"physical_frame_inclusions_checked\": 64988,\n+ \"all_center_reads_see_identical_last_write\": true,\n+ \"no_later_center_middle_consumer\": true,\n+ \"copied_center_rank_histogram\": {\n+ \"22\": 24\n+ },\n+ \"copied_center_paid_copy_rank_mass\": 528,\n+ \"new_source_heads_physically_untouched_before_centers\": true,\n+ \"all_target_gauge_reads_after_center_scatter\": true,\n+ \"all_new_gauges_before_deferred_ops\": true,\n+ \"all_original_gauge_reads_shifted_by168\": true,\n+ \"all_alias_lifetimes_retained\": true,\n+ \"input_pins\": {\n+ \"replay.py\": \"0cbec81a11e758156e9303f63dc8c617601da69523073fdf2a77394d76acf56a\",\n+ \"selection.json\": \"d94ef4e0b8ca98a7385b364cf245816a7cad08f850a60ce8b67aab4c3a89f3f4\",\n+ \"schedule.json\": \"ab39d61fff7a2cfcb13e2c10d65f2c603e76a91013d197260d6c7b645ccb27a1\",\n+ \"schedule_audit.py\": \"d426102fe0faaf2c1725add5ea88db4f17316ff055a6995ae60a7da6ba881671\"\n+ }\n+}\n+{\n+ \"status\": \"PASS_EXACT_28_SHARED_SOURCE_GAUGE_PATHS_TARGETS_AND_PRIMES\",\n+ \"scope\": \"Complete physical source paths, donor-recipient chains, reflected annihilator nesting, complete terminal/gauge/root/K target chronology, all exact paid local deltas. Whole scalar replay and global assembly owned separately.\",\n+ \"selected\": 28,\n+ \"touched_targets\": 108,\n+ \"explicit_reflected_target_histograms_equal\": true,\n+ \"additional_target_events\": 112,\n+ \"target_delta\": {\n+ \"2\": 104,\n+ \"4\": 4,\n+ \"17\": 4,\n+ \"19\": 104,\n+ \"21\": -108\n+ },\n+ \"old_complete_target_histogram\": {\n+ \"1\": 4412,\n+ \"2\": 56,\n+ \"3\": 14,\n+ \"5\": 17,\n+ \"6\": 9,\n+ \"7\": 24,\n+ \"8\": 28,\n+ \"9\": 5,\n+ \"12\": 16,\n+ \"13\": 48,\n+ \"14\": 17,\n+ \"16\": 3,\n+ \"18\": 29,\n+ \"19\": 8,\n+ \"20\": 836,\n+ \"21\": 802\n+ },\n+ \"new_complete_target_histogram\": {\n+ \"1\": 4412,\n+ \"2\": 160,\n+ \"3\": 14,\n+ \"4\": 4,\n+ \"5\": 17,\n+ \"6\": 9,\n+ \"7\": 24,\n+ \"8\": 28,\n+ \"9\": 5,\n+ \"12\": 16,\n+ \"13\": 48,\n+ \"14\": 17,\n+ \"16\": 3,\n+ \"17\": 4,\n+ \"18\": 29,\n+ \"19\": 112,\n+ \"20\": 836,\n+ \"21\": 694\n+ },\n+ \"local_delta\": {\n+ \"1\": 2,\n+ \"2\": 106,\n+ \"3\": 5,\n+ \"4\": 5,\n+ \"5\": -7,\n+ \"6\": -1,\n+ \"8\": 1,\n+ \"11\": 1,\n+ \"12\": 11,\n+ \"14\": -12,\n+ \"15\": 3,\n+ \"19\": 104,\n+ \"21\": -108,\n+ \"22\": -28\n+ },\n+ \"local_rank_delta\": -672,\n+ \"W_delta\": -28,\n+ \"shared_rank_delta\": -2016,\n+ \"deficit_delta\": 0\n+}\n+PASS471 complete ledgers {'W': 20163, 'R': 16643, 'rank': 1449800, 'deficit': 1936, 'delta': {1: 6, 2: 318, 3: 15, 4: 15, 5: -21, 6: -3, 8: 3, 11: 3, 12: 33, 14: -36, 15: 9, 19: 312, 21: -324, 22: -84}}\n+PASS charts 231 max factors 200\n+PASS complete banks [([11, 11, 11, 11, 4, 4, 4, 4, 4, 4, 4], 864), ([4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], 8464), ([6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], 78), ([12, 12, 12, 12, 12, 12], 216), ([24, 24, 24], 344736)] stock 1316514 routing 178127441712\n+{\"stage\": \"exact_completions\", \"nodes\": 0, \"denominator_lcm\": \"1\", \"seconds\": 25.532428583999717}\n+{\"stage\": \"exact_completions\", \"nodes\": 4000, \"denominator_lcm\": \"2\", \"seconds\": 26.197263916999873}\n+{\"stage\": \"exact_completions\", \"nodes\": 8000, \"denominator_lcm\": \"2\", \"seconds\": 27.175399542000378}\n+{\"stage\": \"exact_completions\", \"nodes\": 12000, \"denominator_lcm\": \"2\", \"seconds\": 31.42052829199929}\n+{\"stage\": \"exact_completions\", \"nodes\": 16000, \"denominator_lcm\": \"2\", \"seconds\": 36.0507706669996}\n+{\n+ \"signature\": \"GPT-6 Astra\",\n+ \"status\": \"Exact rational local lifts and inverse gate programs verified; monotone flow and zero-fresh kernel reuse DAG verified.\",\n+ \"nodes\": 18532,\n+ \"inverse_elementary_gates\": 58165,\n+ \"source_control_vertices\": 0,\n+ \"source_erasures\": 0,\n+ \"kernel_reuses\": 0,\n+ \"physical_R\": 9412,\n+ \"denominator_lcm\": \"2\",\n+ \"coefficient_numerator_lcm\": \"2\",\n+ \"max_abs_numerator\": \"2\",\n+ \"max_denominator\": \"2\",\n+ \"all_actual_coefficients_dyadic\": true,\n+ \"coefficients\": [\n+ [\n+ -2,\n+ 1\n+ ],\n+ [\n+ -1,\n+ 1\n+ ],\n+ [\n+ -1,\n+ 2\n+ ],\n+ [\n+ 1,\n+ 2\n+ ],\n+ [\n+ 1,\n+ 1\n+ ],\n+ [\n+ 2,\n+ 1\n+ ]\n+ ],\n+ \"certificate_path\": \"/private/var/folders/sd/yrr853rn73qdgdgdmps82gfh0000gn/T/crossover-pr200-dan9aydc/source/research/source-assisted-v4/.work/lift.certificate.json.gz\",\n+ \"certificate_sha256\": \"72a9626394aff05457ba5d25fc312608effba611f1f184ad8a6ddf186c7b150f\",\n+ \"exact_scalar_program_sha256\": \"3b4e671d7c6630570b04788bb2c81629e2c52f8dc2fcc5805952f0b403921027\",\n+ \"witness_path\": \"/private/var/folders/sd/yrr853rn73qdgdgdmps82gfh0000gn/T/crossover-pr200-dan9aydc/source/research/source-assisted-v4/.work/flow.witness.json\",\n+ \"witness_sha256\": \"51da02c6cd844276ca26608f1b714ab07d476ec25634ad1a9b461ccda2fbe457\",\n+ \"checker_path\": \"decision/exact_complex_flow_lift.py\",\n+ \"checker_sha256\": \"9d841bcfdc7c9c19b31791e8d7cfebd223d80d5e9ecd376d26257244f5323f2e\",\n+ \"seconds\": 37.98196062500028\n+}\n+{\n+ \"status\": \"Exact local invertible flow, exact all-column fresh identity, paid source controls, target read chains, and integer histogram certified. A literal globally renumbered operation program is not exported; dense initial dirty-response subtraction is defined by the exact certified flow.\",\n+ \"physical_R\": 9412,\n+ \"m\": 66,\n+ \"W_per_vertex\": 12052,\n+ \"deficit_per_vertex\": 1320,\n+ \"numerical_local_root\": 0.0007009184438593612,\n+ \"contract_checks\": {\n+ \"all_fresh_columns_equal_identity\": true,\n+ \"arithmetic\": \"integers, endpoint scaled by 6\",\n+ \"checked_source_columns\": 1320,\n+ \"checked_target_rows\": 1320,\n+ \"source_controls_at_paid_parity_frames\": true,\n+ \"original_source_V_before_all_controls\": true,\n+ \"controls_before_original_K\": true,\n+ \"all_centers_in_phase1\": true,\n+ \"all_target_cap_reads_in_phase2\": true,\n+ \"target_chains_nested\": true,\n+ \"read_counts\": {\n+ \"center\": 22,\n+ \"side\": 3135,\n+ \"deferred\": 2310\n+ },\n+ \"target_data_histogram\": {\n+ \"0\": 6270,\n+ \"1\": 3960,\n+ \"18\": 1320\n+ },\n+ \"positive_target_data_histogram\": {\n+ \"1\": 3960,\n+ \"18\": 1320\n+ }\n+ },\n+ \"seconds\": 2.3597311249995983\n+}\n+{\n+ \"status\": \"PASS_EXACT_47_CONSTRAINT_ASSEMBLY\",\n+ \"kappa\": \"138957502601057/200000000000000000\",\n+ \"kappa_float\": 0.000694787513005285,\n+ \"bit_ordinary\": \"347635289160631446679487812206843328185887045180606421880664178871823925016771126681670359044844755436058055123/500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\",\n+ \"a_complex\": \"700918443859411/1000000000000000000\"\n+}\n+PASS full offline bit/frame/bank/chart/complex-lift/contract replay, independent paid moments, 47 inequalities and controls; kappa=138957502601057/200000000000000000\n+PASS immutable offline package; no network or git required"},{"sha":"06ac23580f06236d9eabb005b1c8c36896619050","filename":"research/community-round9-audit/pr231-replay.log.txt","status":"added","additions":5,"deletions":0,"changes":5,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr231-replay.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr231-replay.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr231-replay.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,5 @@\n+PASS k=3 p=6: 160 ports, 2 valid star-family decoders; C(k,l) mod 2 for 0\n+ main()\n+ ~~~~^^\n+ File \"/private/tmp/integer-mult-export232/research/complex-bank-run3/verify.py\", line 454, in main\n+ assert read == json.loads(json.dumps(record, default=str)), 'certificate.json differs'\n+ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n+AssertionError: certificate.json differs"},{"sha":"db63c9af0b63b68e26522e013df7dd989674d6de","filename":"research/community-round9-audit/pr232-portable.log.txt","status":"added","additions":17,"deletions":0,"changes":17,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr232-portable.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr232-portable.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr232-portable.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,17 @@\n+AUDIT: all certificate fields exact except validated machine-local corpus root\n+certificate.json matches a fresh rebuild\n+tiling rank 16 and rank 20 price 192 and 60 banks where their capacity requires 198 and 66; mixed uniform tilings: 0\n+prototype padded schedule 795 banks (531 + 198 + 66), padding [0, 2, 6] per bank, stock drops [531, 198, 66]\n+widths unposeable at [48, 54, 58, 60, 63, 64, 65]; priced: [66]; the modulus is the word\n+instanced 4176 items addressed over 795 banks, 792 registers of padding\n+import harness self-test 12/12, 10 bodies still missing: REFUSED: 10 of 10 required bodies are absent and nothing i\n+export contract 6 exports (E1,E2,E3,E4,E5,E6), 7 acceptance tests, bodies exported today: 0/6\n+unconditional not available: supplier status PASS conditional finite witness; operation program not exported; RECORDED AND MACHINE-CHECKED (verify.py -> check_unconditionality reads the four pinned strings back)\n+rungs [11, 16, 20] at 795 banks, kappa 711599961413937/1000000000000000000\n+suppliers 20 poseable ledgers scored, 0 below the pinned density 3008/3013; least dense overall: 66 wide at 0.99834\n+density curve w48 1819302815717/2500000000000000, w54 the padding draw exceeds the kept rank-1 bin, w60 1819302815717/2500000000000000, w66 711599961413937/1000000000000000000, w72 nothing tiles, or the stock cannot retire the banks, w84 706360069762831/1000000000000000000, w96 617982590757721/1000000000000000000\n+ceiling a width 48-60 word with this shape pays 1819302815717/2500000000000000; every target above 7.2e-4 still needs the bit word\n+target 9/12500 bit leaf 720518773516933/1000000000000000000 (-1.062%), complex coarse 360259386758467/500000000000000000 (+1.181% over the top)\n+target 3/4000 bit leaf 187640730547911/250000000000000000 (+3.064%), complex coarse 150112584438329/200000000000000000 (+5.400% over the top)\n+target 1/1250 bit leaf 100080064051241/125000000000000000 (+9.940%), complex coarse 800640512409929/1000000000000000000 (+12.433% over the top)\n+target 1/1000 bit leaf 500500500500501/500000000000000000 (+37.453%), complex coarse 1001001001001003/1000000000000000000 (+40.569% over the top)"},{"sha":"70c0184d0efe1b1221cb52e491f94c004aa9f6c6","filename":"research/community-round9-audit/pr232_portable_audit.py","status":"added","additions":27,"deletions":0,"changes":27,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr232_portable_audit.py","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr232_portable_audit.py","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr232_portable_audit.py?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,27 @@\n+\"\"\"Audit PR232, normalizing only the corpus root's machine-local path.\n+No construction obligations are discharged by this arithmetic replay.\n+\"\"\"\n+import json\n+import sys\n+from pathlib import Path\n+\n+root = Path(sys.argv[1]).resolve()\n+package = root / \"research/complex-bank-run3\"\n+sys.path.insert(0, str(package))\n+import verify\n+import run3\n+\n+saved = json.loads((package / \"certificate.json\").read_text())\n+original = run3.build\n+\n+def audited_build():\n+ record = original()\n+ assert record[\"supplier_density\"][\"corpus\"][\"root\"] == str(root)\n+ record[\"supplier_density\"][\"corpus\"][\"root\"] = saved[\"supplier_density\"][\"corpus\"][\"root\"]\n+ assert json.loads(json.dumps(record, default=str)) == saved, \"another certificate difference\"\n+ print(\"AUDIT: all certificate fields exact except validated machine-local corpus root\")\n+ return record\n+\n+run3.build = audited_build\n+sys.argv = [str(package / \"verify.py\")]\n+verify.main()"},{"sha":"e413e449a8ceff23687fa495b6716de7d222b48d","filename":"research/community-round9-audit/pr233-replay.log.txt","status":"added","additions":9,"deletions":0,"changes":9,"blob_url":"https://github.com/CrocSwap/integer-mult-bounds/blob/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr233-replay.log.txt","raw_url":"https://github.com/CrocSwap/integer-mult-bounds/raw/12a4934d15006e8c10f9b2264f13f8f341be802b/research%2Fcommunity-round9-audit%2Fpr233-replay.log.txt","contents_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/contents/research%2Fcommunity-round9-audit%2Fpr233-replay.log.txt?ref=12a4934d15006e8c10f9b2264f13f8f341be802b","patch":"@@ -0,0 +1,9 @@\n+[ 0s] rebuilt 308 pinned files of PR #202 (commit 8d8d67b) and checked the witnesses\n+[ 14s] regenerated the PR #168 v4 complex cache\n+[ 52s] regenerated the source-aligned word with its own physical layer and checks\n+[ 126s] admitted this package's physical layer with PR #200's complex checker: PASS exact fused physical candidate, all formal source/targe; 17789 frames, 2310 pairs, 0 of PR #168's 17789 frames changed\n+[ 136s] frame flow: new_R 9412, new_W 12052, deficit 1320, numerical root 7.0990748e-04\n+[ 247s] exact lift: Exact rational local lifts and inverse gate programs verified; monotone flow and\n+[ 255s] contract: 13 checks, W 12052, rank 794112, deficit 1320\n+[ 255s] assembly: complex saving 3549537/5000000000 = 7.0990740e-04, bit effective 6.7734087e-04, kappa 6768823/10000000000 = 6.7688230e-04\n+[ 255s] PASS certificate.json reproduced: complex saving 3549537/5000000000 (PR #194: 219037/312500000), kappa 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The bit supplier binds. It is also +8.67% above the newest posted value, #441 (1.138798055343319·10⁻³). Hosting changes only the global template, so it should stack on #440/#441's R740 word as well.\n\n## Change and mathematical scope\n\nIn the compressed nine-stage window, idle data pairs are brought to the active level by idle advance children (ranks 48/32/16/8 for complex, 42/28/14/7 for bit). These children are about a sixth of the paid cost.\n\nA dirty helper residual acts on whatever stream owns it as an exact coordinate factor, independent of the stream's contents. That is the inherited correlated dirty-bank fact that banks already rely on. It is the same kind of factor an idle child applies to its pending coordinates. So a helper residual can be owned by an idle data family instead of a bank slot, on coordinates that family would advance later, and the child keeps only the rest.\n\nThe validity condition is a window: the family must be untouched (no local invocation on its pair, no bridge naming it) between the hosting invocation and its advance. Neither local word changes.\n\n## Result\n\n| supplier | parent saving | hosted saving | live stock | max child | hosted residuals |\n| --- | --- | --- | --- | --- | --- |\n| bit, m = 64, #434 R747 | 1.134386·10⁻³ | **1.239085·10⁻³** | 14,259 → 9,457 | 42 → 8 | 39,568 of 53,784 |\n| complex, m = 73, #433 R560 | 1.183987·10⁻³ | **1.267453·10⁻³** | 12,720 → 8,400 | 48 → 8 | 34,560 of 40,320 |\n\nThe rank deficit stays at 2496 on both sides.\n\n## Validation\n\n`python -B research/idle-axis-hosting/verify.py /absolute/new/output` uses the standard library only. It:\n\n1. runs #434's complete verifier from scratch;\n2. regenerates both hosted templates from #434's fresh outputs and a frozen integer-programme selection (`--discover` recomputes the selection with scipy);\n3. runs an independent audit that shares no code with the generators:\n - windows re-derived from each schedule;\n - for every invocation and replica: exactly one owner per helper, and slots in window, inside their child's pending set, disjoint, and off the active pair;\n - exact remainder children, exact bank tiling, a recomputed profile and deficit;\n - nine mutation controls rejected;\n4. computes two rational moments per supplier and fresh finite invoices with the hosted stock:\n - two extra route factors are charged per helper selector;\n - the parent's larger complex per-vertex bill is kept;\n5. runs #434's strict outer assembly: six bootstrap levels and all 47 inequalities, with the next grid point and the zero-η, zero-β and unit-β controls rejected.\n\n### Open obligations\n\n[PROOF.md](research/idle-axis-hosting/PROOF.md) gives the hosting lemma. 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\ No newline at end of file diff --git a/research/lean-multi-host-source/review-receipts/external-overlap/pr448.json b/research/lean-multi-host-source/review-receipts/external-overlap/pr448.json new file mode 100644 index 0000000000..1e082b5c8f --- /dev/null +++ b/research/lean-multi-host-source/review-receipts/external-overlap/pr448.json @@ -0,0 +1 @@ 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review (split-residual interface): cross-copy idle-axis hosting, one residual on two copies of one idle child; computed κ = 0.001330733966732373 not 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**κ = 1330733966732373/10¹⁸ ≈ 1.330733966732373·10⁻³**, bit-bound, **+5.13 % over #447** (1.265848755025709·10⁻³, complex-bound), +7.53 % over #442 and +17.44 % over #434. Neither local word changes: complex #433 (R = 560, m = 73), bit #434 (R = 747, m = 64). The idle windows are #442's.\n\n## Change\n\nIn #442's idle-axis hosting a whole helper residual sits inside the pending coordinates of one data family. Bit residuals have width 8 − e (637 of width 8, 104 of width 7, 6 of width 4) and complex residuals width 9, while the idle children have ranks 7/14/28/42 (bit) and 8/16/32/48 (complex). A rank-7 child cannot hold a width-8 residual, a rank-14 child holds one and wastes six coordinates, and so on: 6,944 of the 45,360 pending bit coordinates per replica and 5,760 of 51,840 complex ones stay idle and are paid as remainder children.\n\nA child acts on every copy (side, port) of its pair, and all copies share the child's window. This package lets a residual lie across the pending sets of **two copies of the same idle child**. With P = P₁ + P₂ the identity D_{P₁}·D_{P₂} = D_P (the parents' D_{P'}·D_{P−P'} = D_P) writes the dirty invocation's factor on the residual as a product of a factor on each family; each is moved to the child exactly as in #442 §2, since the window is a property of the pair; and each child's remainder is exact by #442's fact (b). Every child's capacity, copies × rank, is then a multiple of the residual width, so the remainders almost vanish. A residual never spans two children or two pairs. The route is still an elementary coordinate permutation of the address space; the finite invoice charges one further route factor per helper selector.\n\nThe selection is an integer programme over counts n(child, stage, width) on the concatenated tape of each child's copies (maximise Σ ln(m/r) × hosted coordinates, subject to availability and, on the bit side, exact width-64 tiling of the leftover). `SELECTION.json` freezes it; `--discover` recomputes it with scipy.\n\n## Result\n\n| supplier | #442 saving | this saving | live stock | hosted residuals (split) | max child |\n| --- | --- | --- | --- | --- | --- |\n| bit, m = 64, R = 747 | 1.239085·10⁻³ | **1.332507·10⁻³** | 9,457 → 8,592 | 46,160 of 53,784 (12,496) | 24 |\n| complex, m = 73, R = 560 | 1.267453·10⁻³ | **1.437532·10⁻³** | 8,400 → 7,680 | 40,320 of 40,320 (13,720) | 48 |\n\nBoth rank deficits stay 2496. The bit max child 24 is one partial copy of a rank-28 child; the complex max child 48 is the 133 copies per replica of the rank-48 final children that the complex supply cannot fill (5,040 residuals against 5,760 width-9 slots per replica). Since #447 is complex-bound at 1.267453·10⁻³, the complex component here should also lift #445/#447's eleven-stage bit words; that composition is not claimed.\n\n## Validation\n\n`python3 -B research/cross-copy-hosting/verify.py /absolute/new/output` (Python 3.11+, standard library only; the output directory must not exist). It\n\n1. runs #434's complete verifier from scratch;\n2. regenerates both hosted templates from #434's fresh outputs and the frozen selection;\n3. runs an independent audit that shares no code with the generators: windows re-derived from each schedule; for every replica and invocation exactly one owner record per helper; every hosted residual has one or two pieces on copies of the child it names, widths summing to the residual width, inside the pending set, pairwise disjoint per (child, copy), inside the window and off the active pair; exact remainder children and bank tilings; profile, live stock and deficit 2496 recomputed; twelve mutation controls rejected (including a split across two children and a split whose widths do not sum to the residual width);\n4. prices both suppliers with the two inherited rational moment engines and fresh finite invoices (prefix 226 bits charged 256, two-level coefficient 488 bits charged 512, row coefficient 18,355 < 20,161; complex row coefficient 15,443);\n5. runs #434's strict outer assembly: six bootstrap levels and all 47 inequalities, with the next grid point and the zero-η, zero-β and unit-β controls rejected.\n\nLocal transcript: `PASS_FULL_CROSS_COPY_HOSTING_COMPOSITION` on macOS (Apple silicon), Python 3.14.3, 5 min 48 s including the full #434 replay; every value equals `EXPECTED.json` and both template hashes match. CI is not claimed before it runs.\n\n## Scope\n\nThis is a written finite extension of #442's hosting interface: a helper residual's physical slot may lie in two data families of one idle child. That is the principal new review point; [PROOF.md](research/cross-copy-hosting/PROOF.md) gives the argument from the parents' two facts. #442's own extension (helper residuals on data streams during idle windows) and all inherited interfaces remain assumptions: the all-size compiler, correlated dirty-bank and compressed-window interfaces, restored work, tape/common grid, precision and analytic transfer. The global operator identity is argued and checked combinatorially, not replayed numerically on the address spaces. No Lean proof and no unconditional integer-multiplication theorem is claimed.\n\n## Credits and AI disclosure\n\nBuilds on and runs unchanged: #442 (DaysSky, idle-axis hosting; windows and bank tilings reused), #434 (Rohan Arun), #433 (icekylinx), #435/#417 (chafreaky), #426 (ai-nanachi), #425/#386 (Zhihao Chen), #370 (Dylan Crow), Jacob Sussman's E8 unit and interfaces. This branch is #442's branch plus one new directory, `research/cross-copy-hosting/`; no inherited file is changed. The cross-copy selection, generators, audit, assembly and proof note were prepared by higherbeing with substantial Claude (Anthropic) assistance.\n\n🤖 Generated with [Claude Code](https://claude.com/claude-code)\n","labels":[],"milestone":null,"active_lock_reason":null,"created_at":"2026-10-11T14:51:42Z","updated_at":"2026-10-11T21:15:56Z","closed_at":null,"merged_at":null,"merge_commit_sha":"218734474a740b17a3eadff151c47ab09652ea18","assignee":null,"assignees":[],"requested_reviewers":[],"requested_teams":[],"head":{"label":"higherbeing:research/cross-copy-hosting","ref":"research/cross-copy-hosting","repo":{"id":1413923815,"node_id":"R_kgDOVEbD5w","name":"integer-mult-bounds","full_name":"higherbeing/integer-mult-bounds","owner":{"login":"higherbeing","id":7227029,"node_id":"MDQ6VXNlcjcyMjcwMjk=","avatar_url":"https://avatars.githubusercontent.com/u/7227029?v=4","gravatar_id":"","url":"https://api.github.com/users/higherbeing","html_url":"https://github.com/higherbeing","followers_url":"https://api.github.com/users/higherbeing/followers","following_url":"https://api.github.com/users/higherbeing/following{/other_user}","gists_url":"https://api.github.com/users/higherbeing/gists{/gist_id}","starred_url":"https://api.github.com/users/higherbeing/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/higherbeing/subscriptions","organizations_url":"https://api.github.com/users/higherbeing/orgs","repos_url":"https://api.github.com/users/higherbeing/repos","events_url":"https://api.github.com/users/higherbeing/events{/privacy}","received_events_url":"https://api.github.com/users/higherbeing/received_events","type":"User","user_view_type":"public","site_admin":false},"private":false,"fork":true,"archived":false,"disabled":false,"description":"Conditional integer multiplication: kappa > 2^-15. 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\ No newline at end of file diff --git a/research/lean-multi-host-source/review-receipts/external-overlap/pr509.json b/research/lean-multi-host-source/review-receipts/external-overlap/pr509.json new file mode 100644 index 0000000000..67d5fc958b --- /dev/null +++ b/research/lean-multi-host-source/review-receipts/external-overlap/pr509.json @@ -0,0 +1 @@ +{"url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/pulls/509","id":4822940894,"node_id":"PR_kwDOU-508s8AAAABH3g83g","html_url":"https://github.com/CrocSwap/integer-mult-bounds/pull/509","diff_url":"https://github.com/CrocSwap/integer-mult-bounds/pull/509.diff","patch_url":"https://github.com/CrocSwap/integer-mult-bounds/pull/509.patch","issue_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/issues/509","commits_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/pulls/509/commits","review_comments_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/pulls/509/comments","review_comment_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/pulls/comments{/number}","comments_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/issues/509/comments","statuses_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/statuses/7b9c720ecc9f483c383e7cd9c2ab81f06ee5df59","number":509,"state":"open","locked":false,"title":"Lemma G of #484: clean proof and Lean 4 formalisation of its core","user":{"login":"DreamingOfClouds","id":173691639,"node_id":"U_kgDOClpS9w","avatar_url":"https://avatars.githubusercontent.com/u/173691639?v=4","gravatar_id":"","url":"https://api.github.com/users/DreamingOfClouds","html_url":"https://github.com/DreamingOfClouds","followers_url":"https://api.github.com/users/DreamingOfClouds/followers","following_url":"https://api.github.com/users/DreamingOfClouds/following{/other_user}","gists_url":"https://api.github.com/users/DreamingOfClouds/gists{/gist_id}","starred_url":"https://api.github.com/users/DreamingOfClouds/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/DreamingOfClouds/subscriptions","organizations_url":"https://api.github.com/users/DreamingOfClouds/orgs","repos_url":"https://api.github.com/users/DreamingOfClouds/repos","events_url":"https://api.github.com/users/DreamingOfClouds/events{/privacy}","received_events_url":"https://api.github.com/users/DreamingOfClouds/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"\nThis PR gives Lemma G (entrance gauge: target-side compensation at nonzero frames, labelled targets, chain scatter) a clean,\nself-contained proof and formalises its abstract core in Lean 4.\n\nLemma G is worth +1.80% of complex `b` under no-bank hosting:\n\n| word | complex `b` |\n| --- | --- |\n| Lemma-G-free path (kernel79 only, #500) | 1.310216e-3 |\n| full gauge/kernel word (#496/#500) | 1.333854e-3 |\n\n#484 is not modified. This branch is stacked on #484's head and adds only `research/e8-lemma-g-lean/`.\n\n### What is proved (Lean 4.21.0 + Mathlib v4.21.0, the pin of `formal/lean` on main)\n\n```lean\ntheorem LemmaG.Stream.conj_matrix (T : Λ → M ≃ₗ[K] M) (rec : Λ → Λ → M → M) (es : List (Event ι Λ K))\n (l : ι → Λ) (h : ι → M) (hrec : RecipesExact T rec es) (hw : WellLabelled es l) (r : ι) :\n physRun rec es h r = T (labRun es l r) (∑ s, S es r s • (T (l s)).symm (h s))\n```\n\nThe theorem holds for every semiring `K`, every `K`-module `M` and every family of linear automorphisms `T`. Take any stream of relabel/add/scale/copy/clear events that is well labelled and whose relabels execute `T_B T_A⁻¹`. Then for every input it computes\n\n`h_r ↦ T_{λ¹_r}(Σ_s S_rs T_{λ⁰_s}⁻¹ h_s)`,\n\nwhere the non-private columns of `S` are exactly what #484's rational scalar replay computes (`S_rowform`; the replay starts the private copies empty, and their columns drop out on inputs with empty private registers).\n\nThe other Lean results:\n* **Row lemmas** (`row_unit`, `row_pair`). A unit row gives the block `T_{λ¹}T_{λ⁰}⁻¹`; for an entering helper this is the virtual entrance with its wrappers. A paired row gives `T_{λ¹_r}(T_{λ⁰_r}⁻¹h_r + a·T_{λ⁰_s}⁻¹h_s)`.\n* **Schedule** (`emit_spec`, `comp_segment`, `centre_forward`, `centre_backward`), proved for an abstract order with strictly monotone rank and instantiated for the subspaces of F₂⁹.\n * The compensation segment and the centre phase are well labelled as soon as the partners stay at their frames.\n * Under (b) and (c), every move is a strict nested ascent (or descent).\n * Each target ends at `L_t = max ℰ_t`.\n* **Accounting** (`paid_telescopes`). Paid ranks telescope to `rk λ¹ − rk λ⁰` per register.\n* **Bit-side entrance identities** (`Dbit_one_mul`, `Dbit_conj`). `D_I D_P = D_{I−P}`, and conjugation by `diag(g,g)` for `gᵀg = 1`, for every `P`.\n\nAll theorems are general: there is no instance enumeration and no `decide`/`native_decide`. Lean proves the abstract core. The schedule lemmas are an a-priori route that is not instantiated on the emitted stream; the stream itself is checked in Python (below). Combining the Lean core with those checks gives that the data rows are W's and the mass identity `mass(W) − Σ_j dim E_j`. `#print axioms` reports only `propext`, `Classical.choice` and `Quot.sound`. `verify.py` builds the package, scans for `sorry`/`axiom`/`native_decide`, and checks every axiom report.\n\n### What stays checked in Python\n\nThe instance hypotheses on the emitted streams:\n\n| hypothesis | check | result |\n| --- | --- | --- |\n| well-labelledness | #484 G0/G2/G3, plus the new `code/check_extended_labels.py` | 0 violations on all four words, both orientations; 3 adapter mutants rejected on every word, 2 wrapper mutants on the wrapper words |\n| exact transition recipes; the adapter/wrapper bridge | #484 I-tr on all 512 columns (recipes are linear circuits); one non-identity adapter per source and per target, all others identities (`check_extended_labels.py`) | 2945/2945 |\n| the scalar identity `S` | #484 replay, all 800 columns | exact |\n| endpoint labels | #484 G4 | 0 violations |\n| accounting | #484 G2/G3/ACC | 0 violations |\n| #433's data-adapter identities | the new `code/check_adapters.py`, every port, all 512 columns, exact | 0 failures on all four words |\n\nWhy the extended-label check: #484 §2.1 left adapters and wrappers outside Lemma C as endpoint operators. Register-wise that is right. Each non-identity adapter and each wrapper is the first or last event on its register, and the adapters that sit mid-stream (headline forward: 550 entry, 672 exit) are all identities. So #484's description was imprecise but harmless. Lemma C as stated still needed an unwritten commutation step. The clean proof reads adapters and wrappers as relabel events of an extended label set (tag × frame), so the theorem covers the complete emitted stream, and the condition is checked directly.\n\nWith these hypotheses checked exhaustively, and Lemma A (#484 I-helper, exhaustive), the end-to-end identity holds **for every input with empty private registers**. #484's `lg_e2e.py` tested it on 814 sampled columns.\n\n`PROOF.md` §5 lists the other clarifications:\n* the relabel-source condition;\n* the inherited facts behind \"every input\" (#433's adapter identities, Lemma A);\n* the minimal label condition;\n* (a)–(d) are accounting-only;\n* explicit side conditions;\n* the kernel updates as an instance of the same emitter.\n\n### Reproduce\n\n```sh\npython3 research/e8-lemma-g-lean/verify.py # Lean only: cache get + build + axioms\npython3 research/e8-lemma-g-lean/verify.py --instances /abs/out/of/484/verify # plus the instance checks (numpy)\n```\n\n### Credits\n\n* #425 (Zhihao Chen): the common-frame conjugation lemma and scalar interface.\n* #458 (chafreaky): the one-helper rule and paid wrappers.\n* #471 (Dugongue): the virtual entrance and complete-invocation normalisation.\n* #484 (DreamingOfClouds): the gauge construction, Lemma G and its Python check stage.\n* `formal/lean` on main: the Lean toolchain and Mathlib pin.\n* #487/#488 (jamesyc): the standalone Lean package layout and axiom reporting.\n\nPrepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code.\n\n🤖 Generated with [Claude Code](https://claude.com/claude-code)\n","labels":[],"milestone":null,"active_lock_reason":null,"created_at":"2026-10-11T22:41:35Z","updated_at":"2026-10-11T22:50:52Z","closed_at":null,"merged_at":null,"merge_commit_sha":"47097ebdfe0e7d65702b278e82bdccb8718f2fd5","assignee":null,"assignees":[],"requested_reviewers":[],"requested_teams":[],"head":{"label":"DreamingOfClouds:e8-lemma-g-lean","ref":"e8-lemma-g-lean","repo":{"id":1412741203,"node_id":"R_kgDOVDS4Uw","name":"integer-mult-bounds","full_name":"DreamingOfClouds/integer-mult-bounds","owner":{"login":"DreamingOfClouds","id":173691639,"node_id":"U_kgDOClpS9w","avatar_url":"https://avatars.githubusercontent.com/u/173691639?v=4","gravatar_id":"","url":"https://api.github.com/users/DreamingOfClouds","html_url":"https://github.com/DreamingOfClouds","followers_url":"https://api.github.com/users/DreamingOfClouds/followers","following_url":"https://api.github.com/users/DreamingOfClouds/following{/other_user}","gists_url":"https://api.github.com/users/DreamingOfClouds/gists{/gist_id}","starred_url":"https://api.github.com/users/DreamingOfClouds/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/DreamingOfClouds/subscriptions","organizations_url":"https://api.github.com/users/DreamingOfClouds/orgs","repos_url":"https://api.github.com/users/DreamingOfClouds/repos","events_url":"https://api.github.com/users/DreamingOfClouds/events{/privacy}","received_events_url":"https://api.github.com/users/DreamingOfClouds/received_events","type":"User","user_view_type":"public","site_admin":false},"private":false,"fork":true,"archived":false,"disabled":false,"description":"Conditional integer multiplication: kappa > 2^-15. 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\ No newline at end of file diff --git a/research/lean-multi-host-source/review-receipts/external-overlap/pr513.json b/research/lean-multi-host-source/review-receipts/external-overlap/pr513.json new file mode 100644 index 0000000000..c9106d642b --- /dev/null +++ b/research/lean-multi-host-source/review-receipts/external-overlap/pr513.json @@ -0,0 +1 @@ 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Add sequential completed-bank source bindings","user":{"login":"jamesyc","id":3722200,"node_id":"MDQ6VXNlcjM3MjIyMDA=","avatar_url":"https://avatars.githubusercontent.com/u/3722200?v=4","gravatar_id":"","url":"https://api.github.com/users/jamesyc","html_url":"https://github.com/jamesyc","followers_url":"https://api.github.com/users/jamesyc/followers","following_url":"https://api.github.com/users/jamesyc/following{/other_user}","gists_url":"https://api.github.com/users/jamesyc/gists{/gist_id}","starred_url":"https://api.github.com/users/jamesyc/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/jamesyc/subscriptions","organizations_url":"https://api.github.com/users/jamesyc/orgs","repos_url":"https://api.github.com/users/jamesyc/repos","events_url":"https://api.github.com/users/jamesyc/events{/privacy}","received_events_url":"https://api.github.com/users/jamesyc/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"## Completed chunk\nEight Lean4.21 core-only modules compose completed local bank words and bind the selected five-stage source's routing and chronological schedule.\n\nConditional-interface coverage: sequential_complete_bank composes whole local words with an endpoint universally quantified over arbitrary bank and remaining states, a common exact chart, and disjoint projectors summing to identity. It explicitly reconciles head-first physical execution with tail-first endpoint composition. Actual physical endpoints remain supplier premises.\nFinite/source-binding coverage: the literal address-factor identity route(d*tau)N = route d(N*tau^-1), exact source stage/operand metadata and replica-major schedule, retaining all60 replicas. No complete Python instance enumeration or actual census is claimed checked.\nFull-theorem coverage: no end-to-end multiplication, runtime or kappa theorem. Actual helper census, GL120/reduction/normalizer data, full-state forward/complemented-reverse words, across-replica partition, boundaries/restored selectors and costs remain open.\n\n## Explicit author-checked kappa and pins\nBase12a4934d15006e8c10f9b2264f13f8f341be802b; head005dd3f4e3cba8d1761abc4ab391aaf6d14d6f73.\nAuthor-checked selected conditional kappa = 90446448750933/125000000000000000 = 0.000723571590007464.\nThis is source-matched construction context, not a bound derived by this package. Compiler, common-ancestor chart, restored-row, routing, prime-supply, precision/recovery, complex-correctness and analytic-transfer conditions remain.\nLiteral bindings refer to research/five-stage-gen4-banks/bank_template.py, code/global_lowering.py and BANK-PROOF.md at the exact base.\n\n## Reuse and comparison\nFive supporting modules are reused unchanged: BankRouting, SplitProjectors, CoordinatePartitions, ExactFrameTransport and BankEndpoints. Three additions are SequentialCompleteBank and the two current five-stage address/schedule bindings. The composition invokes existing weighted-partition results; no novelty claim is made for generic group/partition algebra or routine list glue.\nCompared with #236's older d1d6 paired-cube finite identities/arithmetic and #487's1320-port interface: this chunk supplies the current source-specific sequential completed-bank connection, without transferring their finite instances. The complete3606-module archive of #236 was not rechecked for an exhaustive theorem comparison.\nThe construction retains PR197/PR200 completed-bank attribution, Henry Grant/hcg890 PR234 lowering, eumemic's retained source527 work, Apache-2.0 and existing assistance disclosures.\n\n## Reproduction and evidence\nFrom research/lean-sequential-bank-bindings, run python3 check.py --lean /path/to/lean-4.21.0-linux/bin/lean --build-dir /tmp/sequential-bank-check.\nLinux/Python3, fresh nonexistent output directory, offline, no Mathlib/download. Eight source hashes/imports are checked, hard per-module60s/4GiB and review45s/3.5GiB. No objects shipped.\nFresh isolated replay:12.1047compiler seconds,0.00368queue,peak VM2,266,423,296 bytes. All eight object hashes and77 complete axiom outputs match accepted evidence after explicit whitespace normalization. Independent review and both authors confirmed final scope/replay metadata.\nLocal kernel results are separate from exact-head fork CI, upstream CI and maintainer gates; those are not claimed passed. 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We also recommend that a + file or class name and description of purpose be included on the + same "printed page" as the copyright notice for easier + identification within third-party archives. + + Copyright [yyyy] [name of copyright owner] + + Licensed under the Apache License, Version 2.0 (the "License"); + you may not use this file except in compliance with the License. + You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + + Unless required by applicable law or agreed to in writing, software + distributed under the License is distributed on an "AS IS" BASIS, + WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + See the License for the specific language governing permissions and + limitations under the License. diff --git a/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/LemmaA.lean b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/LemmaA.lean new file mode 100644 index 0000000000..2cc601bdb5 --- /dev/null +++ b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/LemmaA.lean @@ -0,0 +1,4 @@ +import LemmaA.Realize +import LemmaA.Schedule +import LemmaA.Tensor +import LemmaA.Streams diff --git a/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/LemmaA/Realize.lean b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/LemmaA/Realize.lean new file mode 100644 index 0000000000..8917c5b7f7 --- /dev/null +++ b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/LemmaA/Realize.lean @@ -0,0 +1,163 @@ +/- +Lemma A, realization: a local invocation executed on physical families through charts. +Apache-2.0. Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. + +Each register `i` of an invocation is hosted on the physical family `own i` through a linear +chart `chart i : W ≃ₗ[K] M` (route and batch). Executing an event physically reads the +operands through their charts and writes the destination's family back. + +* `realize_run` one owner (injective `own`) ⇒ the physical run, read through the charts, + is the local run; families that host no register are untouched. +* `one_owner_needed` two registers on one family: already a one-event stream breaks it. +* `family_endpoint` with Lemma G's unit row, the helper's family ends as + `chart⁻¹ ∘ T_{λ¹} T_{λ⁰}⁻¹ ∘ chart` of its own initial value. +* `endpoint_indep` with a zero column, no other family reads the helper's family. +-/ +import LemmaG.Stream + +namespace LemmaA + +open LemmaG LemmaG.Stream + +variable {ι Φ Λ K : Type*} [DecidableEq ι] [DecidableEq Φ] [Semiring K] +variable {W M : Type*} [AddCommMonoid W] [Module K W] [AddCommMonoid M] [Module K M] + +/-- The register an event writes. -/ +def dst : Event ι Λ K → ι + | .relabel r _ _ => r + | .add t _ _ => t + | .scale t _ => t + | .copy c _ _ => c + | .clear c _ => c + +omit [DecidableEq Φ] in +theorem phys_ne (rec : Λ → Λ → M → M) (e : Event ι Λ K) (h : ι → M) (i : ι) (hi : i ≠ dst e) : + e.phys rec h i = h i := by + cases e <;> simp [Event.phys, dst, Function.update_of_ne hi] at hi ⊢ <;> + exact Function.update_of_ne hi _ _ + +/-- A hosting: owner family and chart of every register of one invocation. -/ +structure Hosting (ι Φ K W M : Type*) [Semiring K] [AddCommMonoid W] [Module K W] + [AddCommMonoid M] [Module K M] where + own : ι → Φ + chart : ι → W ≃ₗ[K] M + +/-- The registers as seen through their charts. -/ +def view (σ : Hosting ι Φ K W M) (y : Φ → W) : ι → M := fun i => σ.chart i (y (σ.own i)) + +/-- One event executed on the physical families. -/ +def realize (σ : Hosting ι Φ K W M) (rec : Λ → Λ → M → M) (e : Event ι Λ K) (y : Φ → W) : Φ → W := + Function.update y (σ.own (dst e)) ((σ.chart (dst e)).symm (e.phys rec (view σ y) (dst e))) + +/-- A stream executed on the physical families. -/ +def realizeRun (σ : Hosting ι Φ K W M) (rec : Λ → Λ → M → M) : + List (Event ι Λ K) → (Φ → W) → (Φ → W) + | [], y => y + | e :: es, y => realizeRun σ rec es (realize σ rec e y) + +theorem view_realize (σ : Hosting ι Φ K W M) (hinj : Function.Injective σ.own) + (rec : Λ → Λ → M → M) (e : Event ι Λ K) (y : Φ → W) : + view σ (realize σ rec e y) = e.phys rec (view σ y) := by + funext i + by_cases hi : i = dst e + · subst hi; simp [view, realize] + · have hf : σ.own i ≠ σ.own (dst e) := hinj.ne hi + simp only [view, realize, Function.update_of_ne hf] + rw [phys_ne rec e _ i hi]; rfl + +/-- **Realization under the one-owner rule.** The physical run, read through the charts, is the +local run of the same stream. -/ +theorem realize_run (σ : Hosting ι Φ K W M) (hinj : Function.Injective σ.own) + (rec : Λ → Λ → M → M) : + ∀ (es : List (Event ι Λ K)) (y : Φ → W), + view σ (realizeRun σ rec es y) = physRun rec es (view σ y) + | [], _ => rfl + | e :: es, y => by + simp only [realizeRun, physRun] + rw [realize_run σ hinj rec es, view_realize σ hinj] + +omit [DecidableEq ι] [DecidableEq Φ] in +/-- The value of a family that hosts register `i` is the chart preimage of the view. -/ +theorem family_eq (σ : Hosting ι Φ K W M) (y : Φ → W) (i : ι) : + y (σ.own i) = (σ.chart i).symm (view σ y i) := by simp [view] + +/-- Families that host no register of the invocation are untouched. -/ +theorem realize_untouched (σ : Hosting ι Φ K W M) (rec : Λ → Λ → M → M) : + ∀ (es : List (Event ι Λ K)) (y : Φ → W) (f : Φ), (∀ i, σ.own i ≠ f) → + realizeRun σ rec es y f = y f + | [], _, _, _ => rfl + | e :: es, y, f, hf => by + simp only [realizeRun] + rw [realize_untouched σ rec es _ f hf, realize, Function.update_of_ne (Ne.symm (hf _))] + +/-- **The one-owner rule is needed.** If two registers share a family, the one-event stream +`scale i 0` already changes what register `j` sees, although the local run leaves `j` alone. -/ +theorem one_owner_needed (σ : Hosting ι Φ K W M) (rec : Λ → Λ → M → M) (i j : ι) (hij : i ≠ j) + (hown : σ.own i = σ.own j) (y : Φ → W) (hy : view σ y j ≠ 0) : + view σ (realizeRun σ rec [Event.scale i (0 : K)] y) j ≠ + physRun rec [Event.scale i (0 : K)] (view σ y) j := by + have h1 : view σ (realizeRun σ rec [Event.scale i (0 : K)] y) j = 0 := by + simp only [realizeRun, realize, view, dst] + rw [hown, Function.update_self] + simp [Event.phys] + have h2 : physRun rec [Event.scale i (0 : K)] (view σ y) j = view σ y j := by + simp [physRun, Event.phys, Function.update_of_ne (Ne.symm hij)] + rw [h1, h2] + exact fun h => hy h.symm + +section Endpoint + +variable [Fintype ι] + +/-- **The helper's family at the end of a complete invocation.** One owner, exact recipes, +well labelled, and a unit row of the scalar shadow (Lemma G, H3): the family ends as the chart +conjugate of `T_{λ¹ j} T_{λ⁰ j}⁻¹` applied to its own initial value. -/ +theorem family_endpoint (T : Λ → M ≃ₗ[K] M) (σ : Hosting ι Φ K W M) + (hinj : Function.Injective σ.own) (rec : Λ → Λ → M → M) (es : List (Event ι Λ K)) + (l : ι → Λ) (y : Φ → W) (hrec : RecipesExact T rec es) (hw : WellLabelled es l) (j : ι) + (hS : ∀ s, S es j s = if s = j then 1 else 0) : + realizeRun σ rec es y (σ.own j) = + (σ.chart j).symm (T (labRun es l j) ((T (l j)).symm (σ.chart j (y (σ.own j))))) := by + rw [family_eq σ (realizeRun σ rec es y) j, realize_run σ hinj rec es y, + row_unit T rec es l (view σ y) hrec hw j hS] + rfl + +/-- A zero column: changing input `j` does not change output `r ≠ j`. -/ +theorem physRun_indep (T : Λ → M ≃ₗ[K] M) (rec : Λ → Λ → M → M) (es : List (Event ι Λ K)) + (l : ι → Λ) (h : ι → M) (hrec : RecipesExact T rec es) (hw : WellLabelled es l) (j r : ι) + (hcol : S es r j = 0) (v : M) : + physRun rec es (Function.update h j v) r = physRun rec es h r := by + rw [conj_matrix T rec es l _ hrec hw r, conj_matrix T rec es l h hrec hw r] + congr 1 + refine Finset.sum_congr rfl (fun s _ => ?_) + by_cases hs : s = j + · subst hs; simp [hcol] + · rw [Function.update_of_ne hs] + +/-- **No other family reads the helper's family.** If column `j` of the scalar shadow vanishes +off the diagonal (Lemma G, H3), every other family's end value is independent of the helper +family's initial value. -/ +theorem endpoint_indep (T : Λ → M ≃ₗ[K] M) (σ : Hosting ι Φ K W M) + (hinj : Function.Injective σ.own) (rec : Λ → Λ → M → M) (es : List (Event ι Λ K)) + (l : ι → Λ) (y : Φ → W) (hrec : RecipesExact T rec es) (hw : WellLabelled es l) (j : ι) + (hcol : ∀ r, r ≠ j → S es r j = 0) (w : W) (f : Φ) (hf : f ≠ σ.own j) : + realizeRun σ rec es (Function.update y (σ.own j) w) f = realizeRun σ rec es y f := by + by_cases hfo : ∃ r, σ.own r = f + · obtain ⟨r, rfl⟩ := hfo + have hrj : r ≠ j := fun h => hf (h ▸ rfl) + rw [family_eq σ (realizeRun σ rec es (Function.update y (σ.own j) w)) r, + family_eq σ (realizeRun σ rec es y) r, realize_run σ hinj, realize_run σ hinj] + have hv : view σ (Function.update y (σ.own j) w) = + Function.update (view σ y) j (σ.chart j w) := by + funext i + by_cases hi : i = j + · subst hi; simp [view] + · simp [view, Function.update_of_ne hi, Function.update_of_ne (hinj.ne hi)] + rw [hv, physRun_indep T rec es l _ hrec hw j r (hcol r hrj)] + · push_neg at hfo + rw [realize_untouched σ rec es _ f hfo, realize_untouched σ rec es _ f hfo, + Function.update_of_ne hf] + +end Endpoint + +end LemmaA diff --git a/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/LemmaA/Schedule.lean b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/LemmaA/Schedule.lean new file mode 100644 index 0000000000..0bdd775a0f --- /dev/null +++ b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/LemmaA/Schedule.lean @@ -0,0 +1,218 @@ +/- +Lemma A, scheduling: whole invocations, no other actor, and borrowed pending blocks. +Apache-2.0. Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. + +A global state is `y : Φ → W` (one value per physical family). An action is a map on global +states; `Supported A S` says that `A` changes only families in `S` and reads only families in +`S`. Words of actions are applied left to right (`evalW`). + +* `commute_of_disjoint` actions with disjoint supports commute. +* `shuffle_eval` an interleaving of two pairwise commuting words is their concatenation. +* `whole_invocation` the realized events of an invocation, interleaved with actions that + touch none of its families, act as the complete invocation followed by + those actions ("no other actor"). +* `split_off` an endpoint that acts on family `f` alone, and that no other family + reads, splits into a piece supported on `{f}` and a rest that does not + touch `f`. +* `defer`, `async_window` a piece on `f` moves past every action that commutes with it, in + particular every action not touching `f`; the pieces of one pending + child, gathered before its deadline, give the child (#505). +-/ +import LemmaA.Realize +import Mathlib.Data.Set.Disjoint + +namespace LemmaA + +variable {Φ W : Type*} + +/-- `A` changes only families in `S`, and its values on `S` depend only on the input on `S`. -/ +def Supported (A : (Φ → W) → (Φ → W)) (S : Set Φ) : Prop := + (∀ y f, f ∉ S → A y f = y f) ∧ (∀ y y', (∀ f ∈ S, y f = y' f) → ∀ f ∈ S, A y f = A y' f) + +theorem Supported.mono {A : (Φ → W) → (Φ → W)} {S T : Set Φ} (h : Supported A S) (hST : S ⊆ T) : + Supported A T := by + refine ⟨fun y f hf => h.1 y f (fun hs => hf (hST hs)), fun y y' hyy f hf => ?_⟩ + by_cases hfS : f ∈ S + · exact h.2 y y' (fun g hg => hyy g (hST hg)) f hfS + · rw [h.1 y f hfS, h.1 y' f hfS]; exact hyy f hf + +/-- **Disjoint supports commute.** -/ +theorem commute_of_disjoint {A B : (Φ → W) → (Φ → W)} {S T : Set Φ} (hA : Supported A S) + (hB : Supported B T) (h : Disjoint S T) : A ∘ B = B ∘ A := by + funext y f + simp only [Function.comp] + by_cases hfS : f ∈ S + · have hfT : f ∉ T := Set.disjoint_left.1 h hfS + rw [hB.1 (A y) f hfT] + exact hA.2 (B y) y (fun g hg => hB.1 y g (Set.disjoint_left.1 h hg)) f hfS + · rw [hA.1 (B y) f hfS] + by_cases hfT : f ∈ T + · exact hB.2 y (A y) (fun g hg => (hA.1 y g (Set.disjoint_right.1 h hg)).symm) f hfT + · rw [hB.1 y f hfT, hB.1 (A y) f hfT, hA.1 y f hfS] + +/-- Apply a word of actions, first element first. -/ +def evalW : List ((Φ → W) → (Φ → W)) → (Φ → W) → (Φ → W) + | [] => id + | a :: as => evalW as ∘ a + +theorem evalW_append : ∀ (as bs : List ((Φ → W) → (Φ → W))), + evalW (as ++ bs) = evalW bs ∘ evalW as + | [], _ => rfl + | a :: as, bs => by simp only [List.cons_append, evalW, evalW_append as bs]; rfl + +/-- An action that commutes with every element of a word commutes with the word. -/ +theorem evalW_comm (U : (Φ → W) → (Φ → W)) : ∀ (as : List ((Φ → W) → (Φ → W))), + (∀ a ∈ as, a ∘ U = U ∘ a) → evalW as ∘ U = U ∘ evalW as + | [], _ => rfl + | a :: as, h => by + simp only [evalW] + rw [Function.comp_assoc, h a List.mem_cons_self, ← Function.comp_assoc, + evalW_comm U as (fun b hb => h b (List.mem_cons_of_mem _ hb)), Function.comp_assoc] + +/-- **Deferral.** A piece moves to the right past every action that commutes with it. -/ +theorem defer (U : (Φ → W) → (Φ → W)) (xs ys zs : List ((Φ → W) → (Φ → W))) + (h : ∀ a ∈ ys, a ∘ U = U ∘ a) : + evalW (xs ++ U :: ys ++ zs) = evalW (xs ++ ys ++ U :: zs) := by + simp only [evalW_append, List.append_assoc, List.cons_append, evalW] + funext y + exact congrArg (evalW zs) (congrFun (evalW_comm U ys h) (evalW xs y)) + +/-- `us` interleaves `as` and `bs`, keeping the order within each. -/ +inductive Interleave {α : Type*} : List α → List α → List α → Prop + | nil : Interleave [] [] [] + | left {a as bs us} : Interleave as bs us → Interleave (a :: as) bs (a :: us) + | right {b as bs us} : Interleave as bs us → Interleave as (b :: bs) (b :: us) + +/-- **Shuffles of commuting words.** If every action of `as` commutes with every action of +`bs`, any interleaving evaluates to `as` followed by `bs`. -/ +theorem shuffle_eval {as bs us : List ((Φ → W) → (Φ → W))} + (hc : ∀ a ∈ as, ∀ b ∈ bs, a ∘ b = b ∘ a) (h : Interleave as bs us) : + evalW us = evalW (as ++ bs) := by + induction h with + | nil => rfl + | @left a as bs us _ ih => + simp only [evalW, List.cons_append] + rw [ih (fun x hx y hy => hc x (List.mem_cons_of_mem _ hx) y hy)] + | @right b as bs us _ ih => + have ih' := ih (fun x hx y hy => hc x hx y (List.mem_cons_of_mem _ hy)) + have hb := evalW_comm b as (fun x hx => hc x hx b List.mem_cons_self) + funext y + show evalW us (b y) = evalW (as ++ b :: bs) y + rw [ih', evalW_append, evalW_append] + show evalW bs (evalW as (b y)) = evalW bs (b (evalW as y)) + exact congrArg (evalW bs) (congrFun hb y) + +/-! ### Whole invocation, no other actor -/ + +section Whole + +open LemmaG + +variable {ι Λ K M : Type*} [DecidableEq ι] [DecidableEq Φ] [Semiring K] +variable [AddCommMonoid W] [Module K W] [AddCommMonoid M] [Module K M] + +/-- A realized event touches only families that host registers of the invocation. -/ +theorem realize_supported (σ : Hosting ι Φ K W M) (rec : Λ → Λ → M → M) (e : Event ι Λ K) : + Supported (realize σ rec e) (Set.range σ.own) := by + refine ⟨fun y f hf => ?_, fun y y' hyy f _ => ?_⟩ + · exact Function.update_of_ne (fun h => hf ⟨_, h.symm⟩) _ _ + · have hv : view σ y = view σ y' := funext fun i => by simp [view, hyy (σ.own i) ⟨i, rfl⟩] + by_cases hf : f = σ.own (dst e) + · subst hf; simp [realize, hv] + · simp [realize, Function.update_of_ne hf, hyy f ‹_›] + +theorem realizeRun_eq_evalW (σ : Hosting ι Φ K W M) (rec : Λ → Λ → M → M) : + ∀ es : List (Event ι Λ K), realizeRun σ rec es = evalW (es.map (realize σ rec)) + | [] => rfl + | e :: es => by + funext y + simp only [realizeRun, List.map_cons, evalW, Function.comp, realizeRun_eq_evalW σ rec es] + +/-- **Whole invocation, no other actor.** Interleave the realized events of an invocation with +foreign actions, each supported on a set that contains no family of the invocation. The result +is the complete invocation followed by the foreign actions; with one owner, the invocation part +is the local run read through the charts (`realize_run`). -/ +theorem whole_invocation (σ : Hosting ι Φ K W M) (rec : Λ → Λ → M → M) (es : List (Event ι Λ K)) + (foreign us : List ((Φ → W) → (Φ → W))) + (hfor : ∀ b ∈ foreign, ∃ T : Set Φ, Supported b T ∧ Disjoint (Set.range σ.own) T) + (hint : Interleave (es.map (realize σ rec)) foreign us) : + evalW us = evalW foreign ∘ realizeRun σ rec es := by + rw [shuffle_eval _ hint, evalW_append, realizeRun_eq_evalW] + intro a ha b hb + obtain ⟨e, -, rfl⟩ := List.mem_map.1 ha + obtain ⟨T, hbT, hdis⟩ := hfor b hb + exact commute_of_disjoint (realize_supported σ rec e) hbT hdis + +end Whole + +/-! ### Borrowed pending blocks (#505) -/ + +section Async + +variable [DecidableEq Φ] + +/-- **Split off a single-family piece.** If an endpoint `E` acts on family `f` as the piece `P` +(supported on `{f}`) and no other family's value depends on `f`, then `E` is "the rest, then +`P`", where the rest leaves `f` alone and does not read it. -/ +theorem split_off (E P : (Φ → W) → (Φ → W)) (f : Φ) (hP : Supported P {f}) + (hEf : ∀ y, E y f = P y f) + (hread : ∀ y w g, g ≠ f → E (Function.update y f w) g = E y g) : + E = P ∘ (fun y => Function.update (E y) f (y f)) ∧ + Supported (fun y => Function.update (E y) f (y f)) {f}ᶜ := by + refine ⟨?_, ?_, ?_⟩ + · funext y g + simp only [Function.comp] + by_cases hg : g = f + · subst hg + rw [hEf] + exact hP.2 y _ (fun h hh => by rw [Set.mem_singleton_iff.1 hh]; simp) g rfl + · rw [hP.1 _ g (by simpa using hg), Function.update_of_ne hg] + · intro y g hg + simp only [Set.mem_compl_iff, Set.mem_singleton_iff, not_not] at hg + subst hg; simp + · intro y y' hyy g hg + simp only [Set.mem_compl_iff, Set.mem_singleton_iff] at hg + have hy' : y' = Function.update y f (y' f) := by + funext h + by_cases hh : h = f + · subst hh; simp + · rw [Function.update_of_ne hh]; exact (hyy h hh).symm + show Function.update (E y) f (y f) g = Function.update (E y') f (y' f) g + rw [Function.update_of_ne hg, Function.update_of_ne hg, hy', hread y (y' f) g hg] + +omit [DecidableEq Φ] in +/-- A piece on `{f}` commutes with every action that does not touch `f`. -/ +theorem commute_of_not_mem {P A : (Φ → W) → (Φ → W)} {f : Φ} {S : Set Φ} + (hP : Supported P {f}) (hA : Supported A S) (hf : f ∉ S) : A ∘ P = P ∘ A := + (commute_of_disjoint hP hA (Set.disjoint_singleton_left.2 hf)).symm + +/-- **Borrowed pending block, asynchronous window (#505).** An invocation endpoint `E` acts on +the owner family `f` as the piece `P` and nothing else reads `f`. If every action between the +invocation and the pending child's deadline commutes with `P` (it does not touch `f`, or it is +another piece of the same child on a disjoint block), the schedule equals the one in which the +rest of the invocation runs in place and `P` runs just before the deadline. -/ +theorem async_window (E P : (Φ → W) → (Φ → W)) (f : Φ) (hP : Supported P {f}) + (hEf : ∀ y, E y f = P y f) + (hread : ∀ y w g, g ≠ f → E (Function.update y f w) g = E y g) + (xs ys zs : List ((Φ → W) → (Φ → W))) (hys : ∀ a ∈ ys, a ∘ P = P ∘ a) : + evalW (xs ++ E :: ys ++ zs) = + evalW (xs ++ (fun y => Function.update (E y) f (y f)) :: ys ++ P :: zs) := by + obtain ⟨hsplit, -⟩ := split_off E P f hP hEf hread + have h1 : evalW (xs ++ E :: ys ++ zs) = + evalW ((xs ++ [fun y => Function.update (E y) f (y f)]) ++ P :: ys ++ zs) := by + simp only [evalW_append, List.append_assoc, List.cons_append, List.singleton_append, evalW] + conv_lhs => rw [hsplit] + rfl + rw [h1, defer P _ ys zs hys] + simp + +omit [DecidableEq Φ] in +/-- **Gathering.** Pieces whose product is the pending child can be replaced by the child. -/ +theorem gather (ps : List ((Φ → W) → (Φ → W))) (C : (Φ → W) → (Φ → W)) (h : evalW ps = C) + (xs zs : List ((Φ → W) → (Φ → W))) : evalW (xs ++ ps ++ zs) = evalW (xs ++ C :: zs) := by + simp only [evalW_append, List.cons_append, evalW, h] + rfl + +end Async + +end LemmaA diff --git a/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/LemmaA/Streams.lean b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/LemmaA/Streams.lean new file mode 100644 index 0000000000..d3ad32fc95 --- /dev/null +++ b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/LemmaA/Streams.lean @@ -0,0 +1,76 @@ +/- +Lemma A, stream units: owners are physical streams (family, cover class), as in the cover model +of #442/#458. An invocation at cover class `d` realizes register `r` on the stream +`(fam r, d · σ_r⁻¹)`, where `σ_r` is its route (slot permutation, host chart). Several registers of +one invocation may share a family; they own distinct streams as soon as their routes differ, in +particular when their footprints on the family are disjoint. +Apache-2.0. Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. +-/ +import LemmaA.Tensor + +namespace LemmaA + +open TensorProduct LemmaG LemmaG.Stream + +section Owner + +variable {ι Fam G : Type*} [Group G] + +/-- The stream that register `r` owns in the invocation at cover class `d`. -/ +def streamOwner (fam : ι → Fam) (σ : ι → G) (d : G) (r : ι) : Fam × G := (fam r, d * (σ r)⁻¹) + +/-- Distinct (family, route) pairs give distinct streams, at every cover class. -/ +theorem streamOwner_injective (fam : ι → Fam) (σ : ι → G) (d : G) + (h : Function.Injective fun r => (fam r, σ r)) : Function.Injective (streamOwner fam σ d) := by + intro r r' hrr + simp only [streamOwner, Prod.mk.injEq, mul_right_inj, inv_inj] at hrr + exact h (Prod.ext hrr.1 hrr.2) + +/-- **Disjoint footprints give one owner per stream.** If registers on the same family have +pairwise disjoint, nonempty footprints (`fp σ` is the set of family coordinates that route `σ` +places the register on), the stream owner map is injective at every cover class. -/ +theorem streamOwner_injective_of_disjoint {C : Type*} (fam : ι → Fam) (σ : ι → G) (d : G) + (fp : G → Set C) (hne : ∀ r, (fp (σ r)).Nonempty) + (hdis : ∀ r r', r ≠ r' → fam r = fam r' → Disjoint (fp (σ r)) (fp (σ r'))) : + Function.Injective (streamOwner fam σ d) := by + refine streamOwner_injective fam σ d (fun r r' h => ?_) + by_contra hne' + simp only [Prod.mk.injEq] at h + obtain ⟨x, hx⟩ := hne r + have := hdis r r' hne' h.1 + rw [h.2] at this hx + exact Set.disjoint_left.1 this hx hx + +/-- **The cover sweep visits each stream once per route.** For a fixed route `σ`, exactly one cover +class `d` realizes a register with route `σ` on the stream `(f, g)`, namely `d = g σ`. -/ +theorem sweep_unique (σ g : G) : ∃! d : G, d * σ⁻¹ = g := + ⟨g * σ, by simp, fun d h => by rw [← h]; simp⟩ + +end Owner + +section Lemma + +variable {K : Type*} [CommSemiring K] +variable {A B : Type*} [AddCommMonoid A] [Module K A] [AddCommMonoid B] [Module K B] +variable {ι Λ Fam G C W : Type*} [DecidableEq ι] [Fintype ι] [DecidableEq Fam] [Group G] [DecidableEq G] +variable [AddCommMonoid W] [Module K W] + +/-- **Lemma A on streams.** Registers of one invocation may share a family if their footprints on +it are pairwise disjoint (#433 pure-bank slots, #442 hosted slots, #471/#500 footprints). Realized +on the streams `(fam r, d · σ_r⁻¹)`, the complete invocation leaves the helper's stream holding +`chart⁻¹ (C ⊗ id) chart` of its own initial value: the spectators are untouched. -/ +theorem lemmaA_streams (T : Λ → (A ⊗[K] B) ≃ₗ[K] (A ⊗[K] B)) (fam : ι → Fam) (σ : ι → G) (d : G) + (fp : G → Set C) (hne : ∀ r, (fp (σ r)).Nonempty) + (hdis : ∀ r r', r ≠ r' → fam r = fam r' → Disjoint (fp (σ r)) (fp (σ r'))) + (chart : ι → W ≃ₗ[K] (A ⊗[K] B)) (rec : Λ → Λ → A ⊗[K] B → A ⊗[K] B) + (es : List (Event ι Λ K)) (l : ι → Λ) (y : Fam × G → W) (hrec : RecipesExact T rec es) + (hw : WellLabelled es l) (j : ι) (hS : ∀ s, S es j s = if s = j then 1 else 0) + (Cj : A →ₗ[K] A) (hfac : ∀ v, T (labRun es l j) ((T (l j)).symm v) = Cj.rTensor B v) : + realizeRun ⟨streamOwner fam σ d, chart⟩ rec es y (streamOwner fam σ d j) = + (chart j).symm (Cj.rTensor B (chart j (y (streamOwner fam σ d j)))) := + lemmaA_family T ⟨streamOwner fam σ d, chart⟩ + (streamOwner_injective_of_disjoint fam σ d fp hne hdis) rec es l y hrec hw j hS Cj hfac + +end Lemma + +end LemmaA diff --git a/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/LemmaA/Tensor.lean b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/LemmaA/Tensor.lean new file mode 100644 index 0000000000..cd33a52ab5 --- /dev/null +++ b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/LemmaA/Tensor.lean @@ -0,0 +1,149 @@ +/- +Lemma A, spectators: the wrapped helper block is `C ⊗ id`, so the spectator factor is untouched, +and pieces on complementary tensor factors of one family commute and multiply to `C ⊗ D`. +Apache-2.0. Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. +-/ +import LemmaA.Schedule +import Mathlib.LinearAlgebra.TensorProduct.Basic + +namespace LemmaA + +open TensorProduct LemmaG LemmaG.Stream + +variable {K : Type*} [CommSemiring K] +variable {A B : Type*} [AddCommMonoid A] [Module K A] [AddCommMonoid B] [Module K B] + +/-- **Spectators are untouched.** If the wrapped helper block is `C ⊗ id` (Lemma A, exact part: +`L_E⁻¹ S_E R_E⁻¹ = C_[w] ⊗ I`), each pure tensor keeps its spectator factor. -/ +theorem spectators_fixed (G : A ⊗[K] B →ₗ[K] A ⊗[K] B) (C : A →ₗ[K] A) + (h : G = C.rTensor B) (a : A) (b : B) : G (a ⊗ₜ b) = C a ⊗ₜ b := by + rw [h]; rfl + +/-- Residuals on complementary tensor factors commute. -/ +theorem residuals_commute (C : A →ₗ[K] A) (D : B →ₗ[K] B) : + C.rTensor B ∘ₗ D.lTensor A = D.lTensor A ∘ₗ C.rTensor B := by + rw [LinearMap.rTensor_comp_lTensor, LinearMap.lTensor_comp_rTensor] + +section Helper + +variable {ι Λ : Type*} [DecidableEq ι] [Fintype ι] + +/-- **The helper block of a complete invocation fixes the spectators.** Lemma G's unit row gives +the block `T_{λ¹ j} T_{λ⁰ j}⁻¹`; with the exact factorization of that block as `C ⊗ id` (checked +numerically), register `j` ends as `(C ⊗ id) h_j`. -/ +theorem helper_block (T : Λ → (A ⊗[K] B) ≃ₗ[K] (A ⊗[K] B)) (rec : Λ → Λ → A ⊗[K] B → A ⊗[K] B) + (es : List (Event ι Λ K)) (l : ι → Λ) (h : ι → A ⊗[K] B) (hrec : RecipesExact T rec es) + (hw : WellLabelled es l) (j : ι) (hS : ∀ s, S es j s = if s = j then 1 else 0) + (C : A →ₗ[K] A) (hfac : ∀ v, T (labRun es l j) ((T (l j)).symm v) = C.rTensor B v) : + physRun rec es h j = C.rTensor B (h j) := by + rw [row_unit T rec es l h hrec hw j hS, hfac] + +/-- **Lemma A, realized helper family.** One owner per invocation, exact recipes, well labelled, +a unit row (Lemma G, H3) and the exact factorization `T_{λ¹}T_{λ⁰}⁻¹ = C ⊗ id`: at the end of the +complete invocation the helper's family holds `χ⁻¹ (C ⊗ id) χ` of its own initial value. With +`endpoint_indep` no other family reads it, and with `whole_invocation` no other actor may run on +it meanwhile. -/ +theorem lemmaA_family {Φ W : Type*} [DecidableEq Φ] [AddCommMonoid W] [Module K W] + (T : Λ → (A ⊗[K] B) ≃ₗ[K] (A ⊗[K] B)) (σ : Hosting ι Φ K W (A ⊗[K] B)) + (hinj : Function.Injective σ.own) (rec : Λ → Λ → A ⊗[K] B → A ⊗[K] B) + (es : List (Event ι Λ K)) (l : ι → Λ) (y : Φ → W) (hrec : RecipesExact T rec es) + (hw : WellLabelled es l) (j : ι) (hS : ∀ s, S es j s = if s = j then 1 else 0) + (C : A →ₗ[K] A) (hfac : ∀ v, T (labRun es l j) ((T (l j)).symm v) = C.rTensor B v) : + realizeRun σ rec es y (σ.own j) = (σ.chart j).symm (C.rTensor B (σ.chart j (y (σ.own j)))) := by + rw [family_endpoint T σ hinj rec es l y hrec hw j hS, hfac] + +end Helper + +section Family + +variable {Φ W : Type*} [DecidableEq Φ] [AddCommMonoid W] [Module K W] + +/-- Apply `U` to family `f` and leave every other family alone. -/ +def famAct (f : Φ) (U : W → W) : (Φ → W) → (Φ → W) := + fun y => Function.update y f (U (y f)) + +omit [AddCommMonoid W] in +theorem famAct_supported (f : Φ) (U : W → W) : Supported (famAct f U) {f} := by + refine ⟨fun y g hg => Function.update_of_ne (by simpa using hg) _ _, fun y y' hyy g hg => ?_⟩ + rw [Set.mem_singleton_iff.1 hg] + simp [famAct, hyy f rfl] + +omit [AddCommMonoid W] in +theorem famAct_comp (f : Φ) (U V : W → W) : famAct f U ∘ famAct f V = famAct f (U ∘ V) := by + funext y g + by_cases hg : g = f + · subst hg; simp [famAct] + · simp [famAct, Function.update_of_ne hg] + +/-- **Pieces on disjoint blocks of one family commute.** In a common chart `χ : W ≃ A ⊗ B`, one +piece acts as `C ⊗ id` and the other as `id ⊗ D`. -/ +theorem pieces_commute (χ : W ≃ₗ[K] A ⊗[K] B) (f : Φ) (C : A →ₗ[K] A) (D : B →ₗ[K] B) : + famAct f (χ.symm ∘ C.rTensor B ∘ χ) ∘ famAct f (χ.symm ∘ D.lTensor A ∘ χ) = + famAct f (χ.symm ∘ D.lTensor A ∘ χ) ∘ famAct f (χ.symm ∘ C.rTensor B ∘ χ) := by + have key : (χ.symm ∘ C.rTensor B ∘ χ) ∘ (χ.symm ∘ D.lTensor A ∘ χ) = + (χ.symm ∘ D.lTensor A ∘ χ) ∘ (χ.symm ∘ C.rTensor B ∘ χ) := by + funext v + have := LinearMap.congr_fun (residuals_commute C D) (χ v) + simp only [LinearMap.comp_apply] at this + simp [this] + rw [famAct_comp, famAct_comp, key] + +/-- **Pieces gather into the child.** The two pieces together act as `χ⁻¹ (C ⊗ D) χ`. -/ +theorem pieces_product (χ : W ≃ₗ[K] A ⊗[K] B) (f : Φ) (C : A →ₗ[K] A) (D : B →ₗ[K] B) : + evalW [famAct f (χ.symm ∘ C.rTensor B ∘ χ), famAct f (χ.symm ∘ D.lTensor A ∘ χ)] = + famAct f (χ.symm ∘ TensorProduct.map C D ∘ χ) := by + have key : (χ.symm ∘ D.lTensor A ∘ χ) ∘ (χ.symm ∘ C.rTensor B ∘ χ) = + χ.symm ∘ TensorProduct.map C D ∘ χ := by + funext v + have := LinearMap.congr_fun (LinearMap.lTensor_comp_rTensor (f := C) (g := D)) (χ v) + simp only [LinearMap.comp_apply] at this + simp [this] + simp only [evalW] + rw [Function.id_comp, famAct_comp, key] + +end Family + +section Piece + +variable {ι Λ : Type*} [DecidableEq ι] [Fintype ι] +variable {Φ W : Type*} [DecidableEq Φ] [AddCommMonoid W] [Module K W] + +/-- **The realized invocation as a single-family piece.** Under the hypotheses of +`lemmaA_family`, plus a zero helper column (Lemma G, H3), the complete realized invocation acts on +the helper's family `own j` as the piece `famAct (own j) (chart⁻¹ ∘ (C ⊗ id) ∘ chart)`, and no other +family reads `own j`: these are the hypotheses `hEf`, `hread` of `split_off` and `async_window`. -/ +theorem lemmaA_piece (T : Λ → (A ⊗[K] B) ≃ₗ[K] (A ⊗[K] B)) (σ : Hosting ι Φ K W (A ⊗[K] B)) + (hinj : Function.Injective σ.own) (rec : Λ → Λ → A ⊗[K] B → A ⊗[K] B) + (es : List (Event ι Λ K)) (l : ι → Λ) (hrec : RecipesExact T rec es) (hw : WellLabelled es l) + (j : ι) (hS : ∀ s, S es j s = if s = j then 1 else 0) (hcol : ∀ r, r ≠ j → S es r j = 0) + (C : A →ₗ[K] A) (hfac : ∀ v, T (labRun es l j) ((T (l j)).symm v) = C.rTensor B v) : + (∀ y, realizeRun σ rec es y (σ.own j) = + famAct (σ.own j) ((σ.chart j).symm ∘ C.rTensor B ∘ σ.chart j) y (σ.own j)) ∧ + (∀ y w g, g ≠ σ.own j → + realizeRun σ rec es (Function.update y (σ.own j) w) g = realizeRun σ rec es y g) := + ⟨fun y => by + rw [lemmaA_family T σ hinj rec es l y hrec hw j hS C hfac] + simp [famAct], + fun y w g hg => endpoint_indep T σ hinj rec es l y hrec hw j hcol w g hg⟩ + +/-- **Lemma A with asynchronous borrowing (#505).** A complete realized invocation whose helper +`j` borrows the pending block of family `own j` can be split: the rest of the invocation runs in +place, and its piece on `own j` runs just before the pending child's deadline, provided every +action in between commutes with that piece. -/ +theorem lemmaA_async (T : Λ → (A ⊗[K] B) ≃ₗ[K] (A ⊗[K] B)) (σ : Hosting ι Φ K W (A ⊗[K] B)) + (hinj : Function.Injective σ.own) (rec : Λ → Λ → A ⊗[K] B → A ⊗[K] B) + (es : List (Event ι Λ K)) (l : ι → Λ) (hrec : RecipesExact T rec es) (hw : WellLabelled es l) + (j : ι) (hS : ∀ s, S es j s = if s = j then 1 else 0) (hcol : ∀ r, r ≠ j → S es r j = 0) + (C : A →ₗ[K] A) (hfac : ∀ v, T (labRun es l j) ((T (l j)).symm v) = C.rTensor B v) + (xs ys zs : List ((Φ → W) → (Φ → W))) + (hys : ∀ a ∈ ys, a ∘ famAct (σ.own j) ((σ.chart j).symm ∘ C.rTensor B ∘ σ.chart j) = + famAct (σ.own j) ((σ.chart j).symm ∘ C.rTensor B ∘ σ.chart j) ∘ a) : + evalW (xs ++ realizeRun σ rec es :: ys ++ zs) = + evalW (xs ++ (fun y => Function.update (realizeRun σ rec es y) (σ.own j) (y (σ.own j))) :: ys ++ + famAct (σ.own j) ((σ.chart j).symm ∘ C.rTensor B ∘ σ.chart j) :: zs) := by + obtain ⟨hEf, hread⟩ := lemmaA_piece T σ hinj rec es l hrec hw j hS hcol C hfac + exact async_window _ _ (σ.own j) (famAct_supported _ _) hEf hread xs ys zs hys + +end Piece + +end LemmaA diff --git a/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/MANIFEST.json b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/MANIFEST.json new file mode 100644 index 0000000000..50c27df241 --- /dev/null +++ b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/MANIFEST.json @@ -0,0 +1,62 @@ +{ + "format": "e8-lemma-a-lean-v1", + "lean_toolchain": "leanprover/lean4:v4.21.0", + "mathlib": { + "inputRev": "v4.21.0", + "rev": "308445d7985027f538e281e18df29ca16ede2ba3" + }, + "library": "LemmaA", + "depends_on": "LemmaG (path ../e8-lemma-g-lean)", + "modules": [ + "LemmaA.Realize", + "LemmaA.Schedule", + "LemmaA.Tensor", + "LemmaA.Streams" + ], + "main_theorem": "LemmaA.lemmaA_streams", + "unit_model": "physical streams (family, cover class); one owner per stream, implied by disjoint footprints", + "axiom_probe": "PrintAxioms.lean", + "allowed_axioms": [ + "Classical.choice", + "Quot.sound", + "propext" + ], + "instance_checks": [ + "code/check_owners.py", + "code/check_windows.py", + "../e8-lemma-g-lean/code/check_extended_labels.py" + ], + "instance_input": "the output directory of PR #484 verify.py", + "external_files": { + 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"../e8-complex-gauge-kernel/EXPECTED.json": "de9e2ade14c2f390759230850377d48c28b16a28c955669fa89c535fcc228113", + "../e8-complex-gauge-kernel/code/lemmaG/lg_lib.py": "e7db756ad091055b79e90e53d9cecda632a185a11ee3f095eed5d32757f87490" + }, + "files": { + ".gitignore": "d4e3917adcfaaa8d53ccc3eb2c9c3423307b0de18d8efbb32e3a92aa53ffb0f9", + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "LemmaA.lean": "dcb29f406b352c608a89837ec95071ac01e9bcbe4671e01927c416e754e4c53d", + "LemmaA/Realize.lean": "3aa9afd36035afd94296ef410c647d5a8c6fb282f64062542c7070bb1d99a14f", + "LemmaA/Schedule.lean": "2b1c8a1a0370e47bc0c4b353a03605b9ad7e385ba30b4ac3bec7ecf76f656a5f", + "LemmaA/Streams.lean": "345b264eae4ed037e632461fd7a55dd27c6b21e828167e3b441482d063cf547e", + "LemmaA/Tensor.lean": "dcaba494eee73b8066d65326d9a8c3aea260f3b736eb1c5fbf7dfb7fe0c66baf", + "NOTICE.md": "1a7c2ee7de81ea8475e0a11c2d5b8ceebc9c9524bdbb26f15cd875356069daf2", + "PROOF.md": "fb2e59bb8cce222c75f0d0cf882f87d25df12e29375fa9032644b94221e540b9", + "PrintAxioms.lean": "bdcaf408e43c39ed77eb8736ca8ab02802b16ef5cf77474b96ea9b5458274e7d", + "README.md": "87a242f674783d6c553c450b7c5951f667f0f480316a557146449c5003c1d298", + "code/check_owners.py": "d04ea7a6e7cdd0b041f55b22e16e307472f001566311ba8724a446ac49881a3a", + "code/check_windows.py": "82a6af1bde10af6bba37ef6c8cf9773c299af762ced90704cd7c42de8b599448", + "lake-manifest.json": "2680a53c2bf2d8765e52871b7dcaaadf4e28eae878f5259ebdb94c399b9511b6", + "lakefile.toml": "3597e7d50913f50ba45cd66875686ec793a78ded39a04fa90fb75911c5d3c6e7", + "lean-toolchain": "d24fed434d3b13adfaab57724a0a7f270ea8bf1c818b5ae5cf25cbce24dd685c", + "verify.py": "32a20a1a3c979079483f149124b8b6be07812e5e1c046ed5300162fd2a21c7db" + } +} diff --git a/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/NOTICE.md b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/NOTICE.md new file mode 100644 index 0000000000..a682089527 --- /dev/null +++ b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/NOTICE.md @@ -0,0 +1,10 @@ +Apache-2.0 (see `LICENSE`). Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. + +The Lean sources are new. They formalise the realization part of Lemma A of PR #484 (DreamingOfClouds), which PR #484 +adopted from PR #458 §3 (chafreaky: one helper per physical family per call, paid wrappers, restored spectators), with +PR #471's same-owner spectator borrowing (Dugongue), the footprint rule of PR #471/#500 (Dugongue, rohanarun) and, as a proved variant, PR #505's asynchronous whole-owner borrowing +(Dugongue). The event semantics are those of PR #425's conjugation lemma (jacklightChen / Zhihao Chen), reused from the +Lemma G package `../e8-lemma-g-lean` (a Lake path dependency, same Lean and Mathlib pin as `formal/lean` on main). +`code/check_owners.py` reads PR #484's emitted hosted template and its `EXPECTED.json` (read-only). The stream +model (family, cover class) is that of PR #442's idle-axis hosting (DaysSky) and PR #458; the pure banks are PR #433's +(icekylinx). `code/check_windows.py` is written independently of PR #484's audit_hosted_gk.py and PR #505's audit_async.py. diff --git a/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/PROOF.md b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/PROOF.md new file mode 100644 index 0000000000..f5bb219244 --- /dev/null +++ b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/PROOF.md @@ -0,0 +1,211 @@ +# Lemma A: clean statement and proof + +Lemma A of PR #484 (`research/e8-complex-gauge-kernel/PROOF.md` §3) has two parts. + +* **Exact part.** For every entrance frame, `S_E = L_E (C_[w] ⊗ I) R_E`, where `L_E` and `R_E` are Gaussian + monomials. The wrapped product of every entering helper's emitted chain is `C_[w] ⊗ I`. #484 checks this + numerically. +* **Realization part.** The wrappers surround a whole invocation, and nothing else acts on the helper's stream + during it. Then the host keeps its assigned residual and identical spectators. #484 assumed this from #458 §3, for + hosted families and banks, at nine stages. + +This package proves the realization part as an abstract theorem in Lean. +* It holds for every chart, every number of stages, and every layout in which the registers of one invocation own + distinct streams. +* It includes several registers on one family, provided their footprints are disjoint. +* Each hypothesis is checked on the emitted words. + +Lean names are in brackets. The objects `Event`, `physRun`, `S`, `WellLabelled` and `RecipesExact` are reused from +the Lemma G package `../e8-lemma-g-lean`. + +## 1. Setting: stream units + +**Units are physical streams `(F, g)`.** `F` is a family and `g ∈ O(73,2)` is a cover class. This is the model of the +cover construction that #484 inherits: +* the template's `cover` field: "all matrices d in O(73,2)"; +* its `loop_order`: "every cover class d; each local invocation completes before the next"; +* its `route_semantics`: helper at "physical cover class d*Pi(slot)^(-1)"; +* #442's idle-axis hosting (`research/idle-axis-hosting/PROOF.md` §1–2): "on every physical data stream (F, g)", "owned + by stream (F, d·σ⁻¹)", "eight sequential residuals and a pad tile a bank stream", and the source for distinct streams + per slot: "Distinct slots of one invocation have distinct σ, so distinct physical classes for every d … They are + sequential, exactly as the parent's banks are co-owned sequentially by different cover classes"; +* #458 §3, only for the convention `g = dσ⁻¹` of the owner cover class. + +In this model the pieces fit together as follows. +* **Global state.** A global state is `y : streams → W`, where `W` is the space of functions on a family's address + cells. +* **Realization.** A local cover sweep runs the invocation once for every class `d`. At class `d`, register `r` is + realized on the stream `(fam r, d·σ_r⁻¹)` [`streamOwner`]. Here `σ_r` is the register's route: an element of + `O(73,2)` whose first nine columns are its footprint (its local coordinates on the family). Examples are the slot + permutation `Π(slot)` of a bank, a host chart, and a data phase `ρ`. +* **Distinct routes, distinct streams.** Two registers of one invocation with different routes own different + streams, even on one family [`streamOwner_injective`]. Disjoint nonempty footprints give different routes + [`streamOwner_injective_of_disjoint`]. +* **One visit per route.** Over the sweep, a fixed stream `(F, g)` is realized through a fixed route `σ` by exactly + one class, `d = gσ` [`sweep_unique`; #458 §3: "for a fixed family, d → g is a bijection"]. So a stream receives the blocks of different routes sequentially, from + different invocations. Those blocks are disjoint (§4), so they commute and tile the stream [`pieces_*`, `gather`]. + +Lemma A is proved in #442's stream model. That the model describes the machine is inherited from #442, like the +compiler. + +**An invocation.** It is a local stream `es` on registers `ι`, as in Lemma G. `ι` includes the private centre copies. +A **hosting** `σ` gives each register an owner unit and a linear chart `chart i : W ≃ M`, made of the route and the +batch of remaining coordinates. In this section `σ` is the hosting; elsewhere `σ_r` is a route. + +**Physical execution** [`realize`, `realizeRun`]. Each event reads its operands through their charts. It writes the +destination register's unit back. + +**Actions and words** [`Supported`, `evalW`, `Interleave`]. An action is *supported on* `S` if: +* it changes only units in `S`; +* its values on `S` depend only on the input on `S`. + +A physical schedule is a word of actions, applied left to right. + +## 2. Statement + +**Lemma A (realization).** Let `σ` host the invocation `es`, and let `j` be an entering helper. Assume the following. + +* **(O) One owner per stream.** The owner map is injective on the registers of the invocation. In the stream model, + (O) follows from **(O′)**: every data wire is alone on its family, and registers that share a family have pairwise + disjoint, nonempty footprints. +* **(W) Whole invocation, no other actor.** The physical word interleaves the realized events of `es` only with + actions supported away from the invocation's units. +* **(E) Exact endpoint (Lemma G).** `es` is well labelled with exact recipes. Row `j` of its scalar shadow is `e_j`, + and column `j` vanishes off the diagonal. +* **(F) Exact factorization.** + * The labels are **Lemma G's extended labels**: `λ⁰_j = (prew, j)` and `λ¹_j = (done, j)`. The wrappers are relabel + events in `es`, so `T_{λ¹_j}T_{λ⁰_j}⁻¹ = L_E⁻¹ S_E R_E⁻¹`. Lemma G's `check_extended_labels.py` checks this + reading, and `verify.py` runs it. + * The split `M ≅ A ⊗ B` (residual ⊗ spectators and batch) is chosen per helper. + * The hypothesis is then `T_{λ¹_j}T_{λ⁰_j}⁻¹ = C ⊗ id`. #484's I-helper check gives it. + +Then the following hold. + +1. **The whole invocation.** The word equals the complete invocation followed by the other actions + [`whole_invocation`]. Read through the charts, the invocation is the local run [`realize_run`]. Units that host + no register are untouched [`realize_untouched`]. +2. **The helper's unit.** It ends as `chart_j⁻¹ (C ⊗ id) chart_j` applied to its own initial value [`lemmaA_family`; + on streams with (O′): `lemmaA_streams`]. On a pure tensor this is `a ⊗ b ↦ C a ⊗ b`: **the spectators are + untouched** [`spectators_fixed`, `helper_block`]. +3. **No other reader.** No other unit's final value depends on the helper's unit [`endpoint_indep`]. The complete + invocation acts on it as a single-unit piece [`lemmaA_piece`] and splits off [`split_off`]. +4. **Pending blocks.** Pieces on disjoint blocks of one pending child commute [`pieces_commute`]. They multiply to + `C ⊗ D` [`pieces_product`]; for `k` blocks, iterate. Together with the paid remainder they give back the child, + which is `⊗_b C_b` over its pending axes (#458: "the original idle operator is recovered"). + +**(O) cannot be dropped within the model** [`one_owner_needed`]. If two registers share a unit, the one-event stream +`scale i 0` changes what register `j` sees, while the local run leaves `j` alone. + +**(W) cannot be dropped.** An action that reads the helper's unit between `R_E⁻¹` and `L_E⁻¹` sees `R_E⁻¹h`, not `h`. + +**Variant A′ (asynchronous borrowing)** [`lemmaA_async`, `async_window`, `defer`, `gather`]. Suppose every action +between the invocation and the pending child's deadline commutes with the piece of item 3. This holds in either case: +* the action does not touch the piece's unit [`commute_of_not_mem`]; +* the action is another piece of the same child on a disjoint block [`pieces_commute`]. + +Then the schedule equals the one in which the rest of the invocation runs in place and the piece runs just before the +deadline. Gathering the child's pieces gives back the child [`gather`]. The variant's hypotheses are #505's scheduling +conditions. Under them, the owner's history is the original one: +* **window:** each block is used strictly inside its pending child's open window, after the owner's previous data or + bridge touch and before the child's deadline; +* **blocks:** the blocks of one child are pairwise disjoint; +* **whole invocations:** each invocation is indivisible, with distinct owners. + +## 3. Proofs + +* **`realize_run`.** Induct over the stream. Realizing an event writes the destination's unit and nothing else. + Under (O), every other register sits on another unit, so its view is unchanged. The destination's view is its new + local value. +* **`family_endpoint`, `lemmaA_family`.** A unit's value is `chart⁻¹(view)`, and the view is the local run. Lemma G's + `row_unit` gives `T_{λ¹}T_{λ⁰}⁻¹` applied to the initial view, and (F) rewrites it. +* **`lemmaA_streams`.** Apply `lemmaA_family` to the hosting `r ↦ (fam r, d·σ_r⁻¹)`. +* **`streamOwner_injective`.** `d·σ⁻¹ = d·σ'⁻¹` forces `σ = σ'` in a group. +* **`streamOwner_injective_of_disjoint`.** Equal routes on one family would give a footprint disjoint from itself, yet + nonempty. +* **`sweep_unique`.** `d = gσ` is the unique solution of `d·σ⁻¹ = g`. +* **`endpoint_indep`.** Changing the helper's unit changes the view only at `j`. By `conj_matrix`, output `r` is + `T(Σ_s S_rs T⁻¹h_s)`, and `S_rj = 0`. +* **`commute_of_disjoint`, `shuffle_eval`, `whole_invocation`, `split_off`, `defer`, `async_window`.** Check unit by + unit, and induct over interleavings and words. +* **`pieces_commute`, `pieces_product`.** Mathlib's `rTensor_comp_lTensor` and `lTensor_comp_rTensor`. + +The scheduling and stream results hold over any semiring; `streamOwner_injective` holds over any group. The tensor +results (`lemmaA_family`, `lemmaA_streams`, `lemmaA_piece`, `lemmaA_async`, `helper_block`, `spectators_fixed`, +`pieces_*`) need a commutative semiring. + +## 4. Instance hypotheses + +| | hypothesis | check | result | +| --- | --- | --- | --- | +| (F) | `L_E⁻¹ S_E R_E⁻¹ = C_[w] ⊗ I` in Lemma G's extended labels | #484 `adapters_gk.py` (`LEMMA-A.json`); #484 I-helper (all 512 columns); Lemma G `check_extended_labels.py` (run by `verify.py`) | headline: 16 frames and 122/122 helpers; gauge80: 80/80; kernel79: 79/79; 0 tag violations | +| (E) | well labelled, exact recipes, unit helper rows, zero helper columns | Lemma G package H1–H3 (#484 G0/G2/G3, I-tr, scalar replay) | 0 violations | +| (O′) | data wires alone; registers sharing a family have disjoint footprints; centre copies in distinct private slots | **new** `code/check_owners.py` (3 mutants rejected) | 0 violations on all four words | +| (W) | calls run to completion; every hosted block strictly inside its pending child's open window | completion: `check_owners.py` tests the template's declared `loop_order` (a declaration, not a structural replay; for #505's asynchronous order the structural check is #505's own audit, replayed here but not re-implemented); windows: **new** `code/check_windows.py` (independent, 2 mutants rejected); #484 `audit_hosted_gk.py` | 0 violations on all four words | +| blocks | the hosted blocks of one pending child are pairwise disjoint; the remainder is the rest | `check_windows.py`; #484 `audit_hosted_gk.py` (remainder ranks) | 0 violations | +| charts | route = permutation of an orthonormal basis, residual first, then spectators | #484 `audit_hosted_gk.py` | PASS | + +Data wires and centre copies have a nonempty footprint by construction: their route's first nine columns. So the +Lean hypothesis `hne` holds for them, although `check_owners.py` tests nonemptiness only on shared families. + +**Coverage on #484's words** (`check_owners.py`, from the emitted hosted templates): + +| word | calls with one register per family | calls sharing a family with disjoint footprints | hosted blocks in their windows | +| --- | --- | --- | --- | +| headline gauge80 + kernel42 | 72/72 | 0 | 39,792 | +| gauge80 | 40/72 | 32 (1,280 registers, #433 pure-bank slots) | 38,112 | +| kernel79 | 56/72 | 16 (1,308 registers, #433 pure-bank slots) | 37,720 | +| anchor | 0/72 | 72 (36,480 registers, #442 hosted slots) | 34,560 | + +Every call of every word satisfies (O′). Lemma A therefore covers all calls of all four words, including the +slot-sharing calls of gauge80 and kernel79. + +The anchor is not pinned to `EXPECTED.json` and has no wrappers. Its (O′) and windows rest on this package's two +checkers alone. #484's anchor hosting audit is non-strict and is not read. + +## 5. Scope + +* **#458 and #484.** #458 §3 states the one-helper rule as required, and rejects same-call packing into disjoint slots. + This package follows #442 §2 instead: distinct routes give distinct physical classes, and streams are co-owned + sequentially across cover classes. That needs atomic invocations (`loop_order`). + * The single-owner calls are #458's case: headline 72/72, gauge80 40, kernel79 56, and #505 72/72. + * The sharing calls rest on #442's model. +* **#433 pure banks and #442 hosted slots.** These are instances through (O′): the slots are disjoint footprints. +* **#471 and #500 (footprint rule).** Several helpers of one invocation on one family, with pairwise disjoint + nine-coordinate footprints, is exactly (O′). Given their footprint disjointness and windows, these layouts are + instances. Their words are not checked here. `check_owners.py` and `check_windows.py` read hosted templates in the same + format and layout: 960 families per replica, 120 ports, and 16 centres for `--async`. +* **#505 (asynchronous whole owners).** + * Each invocation is whole. Per #505, "all 800 families per invocation are distinct", so (O) holds literally. + * The cross-replica borrowing is Variant A′. + * **Replayed here.** #505's own `verify.py` (offline, Python 3.14) passes every stage, including its independent + asynchronous audit. + * Two discrepancies remain. Its final comparison of the emitted template's sha256 with #505's `EXPECTED.json` + fails, although the audit's sigma-stream digest, owner, profile and κ records equal #505's shipped evidence. + Separately, #505's tree lacks a `.gitattributes` that its MANIFEST lists; that entry was dropped from a scratch + copy. + * On the emitted template, `check_owners.py` finds one register per family in 72/72 calls. + * `check_windows.py` finds all 40,320 hosted blocks strictly inside their owner child's open window, with blocks + pairwise disjoint and family-group windows disjoint. + + So Variant A′'s owner and window hypotheses hold on the template emitted by replaying #505 (4ee769c) here. That + template does not hash-match #505's `EXPECTED.json` (template_sha256 aa741871… vs 276b69e3…). The sigma-stream + digest, owner, profile and κ records equal #505's shipped evidence. + * Not re-checked here: per-replica order (#505's audit checks it), the prefix bound and its invoice. (E) and (F) are + not re-checked on #505's word. +* **#512.** It reports 800 distinct physical owners per invocation, and it builds on #505's asynchronous machinery + and #507's factory. On its own report its invocations meet (O). Its borrowing is Variant A′ under the same + scheduling conditions. #512's word is not checked here. + +## 6. Changes relative to #484 §3 + +1. **The realization part is proved, not assumed.** It holds for every chart, given one owner per stream. +2. **The unit model is stated.** A unit is a stream `(F, g)`, as in #442 §2. #458 §3 states the one-helper rule as + required and rejects same-call packing into disjoint slots. This package follows #442 §2 instead: one owner per + stream, which disjoint footprints imply, with streams co-owned sequentially across cover classes. That needs atomic + invocations. +3. **"Nothing else acts" is exactly** that the interleaved actions avoid the invocation's units (`whole_invocation`), + together with the window condition for borrowed blocks. +4. **The spectator claim follows from two facts:** Lemma G's block structure and the exact factorization in the + extended labels. +5. **(O′), the windows and the block disjointness are now checked independently** on all four words. + `check_owners.py` and `check_windows.py` can also run on asynchronous templates. diff --git a/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/PrintAxioms.lean b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/PrintAxioms.lean new file mode 100644 index 0000000000..9ab97a5e89 --- /dev/null +++ b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/PrintAxioms.lean @@ -0,0 +1,25 @@ +import LemmaA +#print axioms LemmaA.realize_run +#print axioms LemmaA.realize_untouched +#print axioms LemmaA.one_owner_needed +#print axioms LemmaA.family_endpoint +#print axioms LemmaA.endpoint_indep +#print axioms LemmaA.commute_of_disjoint +#print axioms LemmaA.commute_of_not_mem +#print axioms LemmaA.shuffle_eval +#print axioms LemmaA.whole_invocation +#print axioms LemmaA.split_off +#print axioms LemmaA.defer +#print axioms LemmaA.async_window +#print axioms LemmaA.gather +#print axioms LemmaA.spectators_fixed +#print axioms LemmaA.helper_block +#print axioms LemmaA.lemmaA_family +#print axioms LemmaA.lemmaA_piece +#print axioms LemmaA.lemmaA_async +#print axioms LemmaA.pieces_commute +#print axioms LemmaA.pieces_product +#print axioms LemmaA.streamOwner_injective +#print axioms LemmaA.streamOwner_injective_of_disjoint +#print axioms LemmaA.sweep_unique +#print axioms LemmaA.lemmaA_streams diff --git a/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/README.md b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/README.md new file mode 100644 index 0000000000..42355bfe90 --- /dev/null +++ b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/README.md @@ -0,0 +1,119 @@ +# Lemma A (paid wrappers, spectators, one owner) of PR #484: clean proof and Lean 4 formalisation + +Lemma A of #484 (§3) has two parts: +* **exact part:** `S_E = L_E (C_[w] ⊗ I) R_E` on every entrance frame. #484 checks this numerically. +* **realization part:** paid wrappers around a whole invocation, with nothing else acting meanwhile, leave the host with its residual and its spectators untouched. #484 assumed this from #458 §3. + +This package proves the realization part in Lean 4 and checks every hypothesis on the emitted words. `PROOF.md` holds the clean statement and proof. The package is stacked on the Lemma G package `../e8-lemma-g-lean`, whose event semantics it reuses through a Lake path dependency. + +**Model.** Units are physical streams `(family F, cover class g ∈ O(73,2))`, as in #442 §2. At cover class `d`, register `r` lives on the stream `(F_r, d·σ_r⁻¹)`, where `σ_r` is its route. #442 §2: "Distinct slots of one invocation have distinct σ, so distinct physical classes for every d … sequential, exactly as the parent's banks are co-owned sequentially by different cover classes". One owner per stream follows when registers that share a family have pairwise disjoint footprints. + +**Lemma A is proved in #442's stream model. That the model describes the machine is inherited from #442.** #458 §3 states the one-helper rule as required, and rejects same-call packing into disjoint slots. Its case is the single-owner calls. The sharing calls rest on #442's model, which needs atomic invocations. + +So the theorem covers: +* one helper per family (#458's case, #484); +* #433's pure-bank slots and #442's hosted slots; +* #471's and #500's footprint rule. + +**Coverage on #484's words.** Every call of all four words satisfies the hypotheses: +* the headline: 72/72 calls with one register per family; +* gauge80: 40 such calls, plus 32 slot-sharing calls; +* kernel79: 56 such calls, plus 16 slot-sharing calls; +* the anchor: 72 hosted-slot calls, all sharing a family. The anchor is not pinned to EXPECTED and has no wrappers; its (O′) and windows are checked by this package's checkers alone. + +## Proved in Lean (`LemmaA/`, Lean 4.21.0 + Mathlib v4.21.0, the pin of `formal/lean` on main) + +**Main theorem, on streams.** It holds over any commutative semiring, for any modules, charts and number of stages. + +```lean +theorem LemmaA.lemmaA_streams (T : Λ → (A ⊗[K] B) ≃ₗ[K] (A ⊗[K] B)) (fam : ι → Fam) (σ : ι → G) (d : G) + (fp : G → Set C) (hne : ∀ r, (fp (σ r)).Nonempty) + (hdis : ∀ r r', r ≠ r' → fam r = fam r' → Disjoint (fp (σ r)) (fp (σ r'))) + (chart : ι → W ≃ₗ[K] (A ⊗[K] B)) (rec : Λ → Λ → A ⊗[K] B → A ⊗[K] B) + (es : List (Event ι Λ K)) (l : ι → Λ) (y : Fam × G → W) (hrec : RecipesExact T rec es) + (hw : WellLabelled es l) (j : ι) (hS : ∀ s, S es j s = if s = j then 1 else 0) + (Cj : A →ₗ[K] A) (hfac : ∀ v, T (labRun es l j) ((T (l j)).symm v) = Cj.rTensor B v) : + realizeRun ⟨streamOwner fam σ d, chart⟩ rec es y (streamOwner fam σ d j) = + (chart j).symm (Cj.rTensor B (chart j (y (streamOwner fam σ d j)))) +``` + +In words, the theorem assumes: +* registers that share a family have pairwise disjoint footprints; +* the invocation is well labelled with exact recipes; +* the helper has a unit row (Lemma G); +* its block factors as `C ⊗ id`, in Lemma G's extended labels (where `T_{λ¹}T_{λ⁰}⁻¹ = L_E⁻¹ S_E R_E⁻¹`). + +Then after the complete invocation, the helper's stream holds `chart⁻¹ (C ⊗ id) chart` of its own initial value. The spectators are untouched. + +| theorem | content | +| --- | --- | +| `streamOwner_injective(_of_disjoint)`, `sweep_unique` | distinct routes, or disjoint footprints, give distinct streams; the cover sweep visits each stream once per route | +| `realize_run`, `realize_untouched`, `one_owner_needed` | with one owner per unit, the physical execution read through the charts is the local run; within the model, sharing a unit breaks this | +| `family_endpoint`, `endpoint_indep`, `lemmaA_family`, `lemmaA_piece` | the helper's unit ends as a function of itself, no other unit reads it, and the invocation acts on it as a single-unit piece | +| `spectators_fixed`, `helper_block` | the wrapped block `C ⊗ id` keeps every spectator factor | +| `commute_of_disjoint`, `shuffle_eval`, `whole_invocation` | no other actor: interleaving with actions that avoid the invocation's units is harmless | +| `split_off`, `pieces_commute`, `pieces_product` | pieces on disjoint blocks of one pending child commute and multiply to `C ⊗ D` | +| `lemmaA_async`, `async_window`, `defer`, `gather` | Variant A′ (#505): a borrowed piece moves to its child's deadline past every commuting action, and the gathered pieces give the child | + +There is no instance enumeration and no `decide`/`native_decide`. `#print axioms` gives a subset of `[propext, Classical.choice, Quot.sound]` for all 24 named results (`PrintAxioms.lean`). + +## Checked on the words (PROOF.md §4) + +| hypothesis | check | headline / gauge80 / kernel79 / anchor | +| --- | --- | --- | +| (F) in extended labels | #484 `adapters_gk.py` and I-helper; Lemma G `check_extended_labels.py` | 16 frames, 122 / 80 / 79 helpers; anchor has no wrappers; 0 tag violations | +| (E) | Lemma G package H1–H3 | 0 violations | +| (O′) one owner per stream, centre copies | **new** `code/check_owners.py` (3 mutants) | 0 violations on all four words | +| (W), windows, disjoint blocks | **new** `code/check_windows.py` (independent; 2 mutants); `loop_order`; #484 hosting audit | 39,792 / 38,112 / 37,720 / 34,560 blocks; 0 violations | + +## #505 and #512 + +**#505.** Its invocations are whole. Per #505's own text, "all 800 families per invocation are distinct", so (O) holds literally. Its cross-replica borrowing is Variant A′. Variant A′ needs three conditions: +* windows; +* disjoint blocks; +* whole invocations with distinct owners. + +`verify.py --async T.json.gz` runs `check_owners.py` and `check_windows.py` on an asynchronous template. Results on the template that #505's own `verify.py` emits: +* #505's `verify.py` (4ee769c) passes every stage here, including its independent audit. +* `check_owners.py`: one register per family in 72/72 calls. +* `check_windows.py`: all 40,320 hosted blocks lie inside their owner child's open window, with blocks disjoint and family-group windows disjoint. +* So Variant A′'s owner and window hypotheses hold on the template emitted by replaying #505 (4ee769c) here. +* That template does not hash-match #505's `EXPECTED.json` (template_sha256 aa741871… vs 276b69e3…). The sigma-stream digest, owner, profile and κ records equal #505's shipped evidence. + +#505's other conditions are not re-checked here: per-replica order, the prefix bound and its invoice. (E) and (F) are not re-checked on #505's word. + +**#512.** It reports 800 distinct physical owners per invocation and builds on #505's asynchronous machinery. #512's word is not checked here; its coverage rests on #512's own report. + +## Trust base + +* The Lean kernel (4.21.0), Mathlib v4.21.0 (rev `308445d`), and the axioms `propext`, `Classical.choice`, `Quot.sound`. +* The Lemma G package, built here from source. +* #484's numerical checks of (F), and its hosting audit. +* This package's instance checks: `code/check_owners.py`, `code/check_windows.py`, and Lemma G's `check_extended_labels.py`. +* Inherited interfaces: + * #442's stream model (§2), in which streams `(F, g)` are the physical units; + * #442's compiler, under which the local program acts identically on the batch coordinates. + +## Run + +```sh +python3 research/e8-lemma-a-lean/verify.py # Lean: manifest, source scan, cache get, build, axioms +python3 research/e8-lemma-a-lean/verify.py --instances /abs/out/of/484/verify # plus #484's results, extended labels, owners, windows +python3 research/e8-lemma-a-lean/verify.py --no-cache --async T.json.gz # owners and windows on an asynchronous template +``` + +* `lake build` also builds `../e8-lemma-g-lean`. +* `--instances` needs the output directory of #484's `verify.py`; run it with `--all` to include gauge80 and kernel79. +* The checkers assume #484's layout: 960 families per replica and 120 ports; `--async` assumes 16 centres. + +## Credits + +* #458 (chafreaky): the one-helper rule, paid wrappers, spectator routing, cover-class owners, and the family-unit case of the realization argument formalised here. +* #471 (Dugongue): complete-invocation normalisation, same-owner spectator borrowing, and the footprint rule. +* #500 (rohanarun): footprint hosting with paid wrappers. +* #505 (Dugongue): asynchronous whole-owner replicas. +* #433 (icekylinx): the complex supplier and its pure banks. +* #442 (DaysSky): whole-residual and idle-axis hosting, and the stream model. +* #425 (Zhihao Chen): the conjugation lemma. +* #484 (DreamingOfClouds): the gauge/kernel word and Lemma A. +* Lean conventions: the `formal/lean` pin on main; #487/#488 (jamesyc). diff --git a/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/code/check_owners.py b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/code/check_owners.py new file mode 100644 index 0000000000..4acfcda6cf --- /dev/null +++ b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/code/check_owners.py @@ -0,0 +1,117 @@ +# Apache-2.0. Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. +"""Instance check (O) (PROOF.md §4): one owner per stream in every invocation. + +Units are physical streams (family, cover class) (PROOF.md §1; #442 idle-axis hosting, #458 §3, the template's +`route_semantics`). An invocation at cover class d realizes register r on the stream (fam r, d * sigma_r^-1); by +`LemmaA.streamOwner_injective_of_disjoint` the owner map is injective once registers that share a family have pairwise +disjoint, nonempty footprints on it. This script reads the emitted hosted template and checks, in every call: + * data wires (route kind 1) are alone on their family; + * registers sharing a family have pairwise disjoint nonempty footprints, computed in the family's own coordinates: + [2, slot] pure-bank width-9 slot: cells 9*slot .. 9*slot+8 + [2, off, w, spectators] banked entering helper: cells off .. off+w-1 and its spectator cells + [3, child, off] hosted width-9: pending positions off .. off+8 of that idle child + [4, child, off, w, sp] hosted entering helper: pending positions off .. off+w-1, spectators as basis indices + a shared family whose footprints live in different coordinate systems cannot be checked and counts as a violation; + * no owner lies in the private namespace, and the private centre copies sit in one private slot per centre + (template `private_namespace`), disjoint from the reserved tableau and coefficient slots; + * the template runs each local invocation to completion before the next (`loop_order`): no other actor in a call. +It reports the calls with one register per family and the calls that share a family (covered through stream units), and +checks the template against #484's EXPECTED.json where it is pinned. + +usage: check_owners.py BASE VARIANT [VARIANT ...] [--mutants] reads BASE//hosted/GLOBAL-TEMPLATE.json.gz and + BASE//split-centres/CANONICAL-WORD.json.gz; or check_owners.py --template T.json.gz NCENTRES [--mutants] +Standard library only.""" +import gzip, hashlib, json, sys +from collections import Counter, defaultdict +from pathlib import Path + +HERE = Path(__file__).resolve().parent +EXPECTED = json.loads((HERE.parents[1] / 'e8-complex-gauge-kernel' / 'EXPECTED.json').read_text()) + + +def kind(r): + return str(r[0]) if r[0] != 2 else ('2-slot' if len(r) == 2 else '2-entering') + + +def footprint(r): + k = kind(r) + if k == '2-slot': return 'cell', {9 * r[1] + x for x in range(9)} + if k == '2-entering': return 'cell', set(range(r[1], r[1] + r[2])) | set(r[3]) + if k == '3': return ('pend', r[1]), set(range(r[2], r[2] + 9)) + if k == '4': return ('pend+B', r[1]), {('p', x) for x in range(r[2], r[2] + r[3])} | {('B', x) for x in r[4]} + return 'data', set() + + +def check_template(t, ncent): + live = t['live']; bad = []; kinds = Counter(); calls = 0; single = 0; shared_calls = 0; shared_regs = 0 + if 'each local invocation completes before the next' not in t['loop_order'].lower(): bad.append('loop_order: invocations not atomic') + for c in t['calls']: + own = c['owners']; calls += 1; tag = f"call stage {c['stage']} replica {c['replica']}" + kinds.update(kind(r) for _, r in own) + if any(f >= live for f, _ in own): bad.append(f'{tag}: owner in the private namespace') + groups = defaultdict(list) + for f, r in own: groups[f].append(r) + shared = {f: rs for f, rs in groups.items() if len(rs) > 1} + if not shared: single += 1; continue + shared_calls += 1 + for f, rs in shared.items(): + shared_regs += len(rs) + fps = [footprint(r) for r in rs] + if any(sys_ == 'data' for sys_, _ in fps): bad.append(f'{tag}: a data wire shares family {f}'); continue + if len({sys_ for sys_, _ in fps}) != 1 or fps[0][0][0] == 'pend+B': bad.append(f'{tag}: family {f} footprints in mixed coordinates'); continue + seen = set() + for _, fp in fps: + if not fp or fp & seen: bad.append(f'{tag}: footprints overlap on family {f}'); break + seen |= fp + pn = t['private_namespace']; a, b = pn['centers'] + others = [tuple(pn[k]) for k in pn if k != 'centers'] + if b - a != ncent or a < live or any(not (b <= x0 or x1 <= a) for x0, x1 in others): + bad.append(f'centre copies: private slots {pn["centers"]} for {ncent} centres, live {live}, others {others}') + return dict(calls=calls, one_register_per_family=single, sharing_calls=shared_calls, sharing_registers=shared_regs, + kinds=dict(sorted(kinds.items()))), bad + + +def main(): + args = [a for a in sys.argv[1:] if a != '--mutants']; ok = True + if args[0] == '--template': + raw = Path(args[1]).read_bytes(); jobs = [(args[1], raw, int(args[2]), None)] + else: + base = Path(args[0]); jobs = [] + for name in args[1:]: + raw = (base / name / 'hosted' / 'GLOBAL-TEMPLATE.json.gz').read_bytes() + ncent = len(json.loads(gzip.decompress((base / name / 'split-centres' / 'CANONICAL-WORD.json.gz').read_bytes()))['center_frames']) + jobs.append((name, raw, ncent, EXPECTED['words'].get(name, {}).get('hosted_template_sha256'))) + for name, raw, ncent, exp in jobs: + t = json.loads(gzip.decompress(raw)) + info, bad = check_template(t, ncent) + if exp is not None and exp not in (hashlib.sha256(raw).hexdigest(), hashlib.sha256(gzip.decompress(raw)).hexdigest()): + bad.append('hosted template differs from #484 EXPECTED.json') + ok &= not bad + print(f"{name}: calls {info['calls']}; one register per family {info['one_register_per_family']}/{info['calls']}; " + f"sharing a family with disjoint footprints (stream units) {info['sharing_calls']}/{info['calls']} " + f"({info['sharing_registers']} registers); centre copies {ncent} in private slots; " + f"{'pinned to EXPECTED' if exp else 'no EXPECTED pin'}; route kinds {info['kinds']}; violations {len(bad)} {bad[:3]}", flush=True) + if '--mutants' in sys.argv: + import copy + mu = {} + m = copy.deepcopy(t) # a helper moved onto an active data wire's family + c = m['calls'][0]; c['owners'][-1][0] = c['owners'][0][0]; mu['helper on a data wire family'] = len(check_template(m, ncent)[1]) + m = copy.deepcopy(t); hit = False # two registers on one family with overlapping footprints + for c in m['calls']: + fams = defaultdict(list) + for o in c['owners']: fams[o[0]].append(o) + for f, os_ in fams.items(): + if len(os_) > 1 and not hit: os_[1][1] = list(os_[0][1]); hit = True + if not hit: + hs = [o for o in c['owners'] if o[1][0] in (2, 3, 4)] + if len(hs) > 1: hs[1][0] = hs[0][0]; hs[1][1] = list(hs[0][1]); hit = True + mu['two registers with the same footprint on one family'] = len(check_template(m, ncent)[1]) + m = copy.deepcopy(t); m['private_namespace']['centers'] = [m['private_namespace']['centers'][0], m['private_namespace']['centers'][1] - 1] + mu['a centre copy without its private slot'] = len(check_template(m, ncent)[1]) + ok &= all(v > 0 for v in mu.values()); print(' mutants (violations each):', mu, flush=True) + print('PASS one owner per stream' if ok else 'FAIL owner check') + sys.exit(0 if ok else 1) + + +if __name__ == '__main__': + main() diff --git a/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/code/check_windows.py b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/code/check_windows.py new file mode 100644 index 0000000000..9586d33d96 --- /dev/null +++ b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/code/check_windows.py @@ -0,0 +1,113 @@ +# Apache-2.0. Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. +"""Instance check (W)/(A') (PROOF.md §4-5): every hosted block lies inside its pending child's open window, and the +hosted blocks of one pending child are pairwise disjoint. + +These are the hypotheses of Variant A' (`LemmaA.lemmaA_async`, `async_window`, `gather`) that a schedule must meet, and, +for the lockstep words, the window part of (W). Written independently of #484's audit_hosted_gk.py and #505's +audit_async.py; it reads only the emitted hosted template: + * positions are indices into the template's `execution_schedule`; a local cover sweep of stage s touches the pair that + stage s acts on (`recipe`), for each of its replicas; a bridge touches its src and dst pairs; an idle cover sweep of a + pair runs that pair's pending children (`child_indices`, one per side); + * the open window of (owner replica, child i) is (last touch of the child's pair by that replica before the idle + sweep, the idle sweep): after the owner's previous data or bridge touch, before the child's deadline; + * the windows of the children of one family group (replica, pair, side) are pairwise disjoint, so inside a window no + idle sweep and no data or bridge touch acts on the family; only hosted blocks do; + * a hosted route [3, i, off] (width 9) or [4, i, off, w, spectators] on family f is owned by replica f // 960 on pair + side (f % 960) // 120 and port f % 120; the side must match child i, the call must lie strictly inside the window, + and its block off .. off+w-1 must be disjoint from every other block on (owner replica, child i, port). +Lockstep (#484: events carry `replicas`) and asynchronous (#505: events carry one `replica`) templates are both read. + +usage: check_windows.py T.json.gz [T2.json.gz ...] [--mutants] Standard library only.""" +import gzip, json, sys +from collections import defaultdict +from pathlib import Path + + +def reps(e, allreps): + if 'replicas' in e: return list(e['replicas']) + if 'replica' in e: return [e['replica']] + return list(allreps) + + +def check(t): + allreps = sorted({c['replica'] for c in t['calls']}) + stagepair = {e['stage']: e['pair'] for e in t['recipe'] if e.get('kind') == 'local'} + last, windows, child, group = {}, {}, {}, {}; callpos = {}; bad = [] + for pos, e in enumerate(t['execution_schedule']): + k = e.get('kind') + if k == 'local_cover_sweep': + for r in reps(e, allreps): callpos[e['stage'], r] = pos; last[r, stagepair[e['stage']]] = pos + elif k == 'bridge': + for r in reps(e, allreps): last[r, e['src']] = last[r, e['dst']] = pos + elif k == 'idle_cover_sweep': + for side, i in enumerate(e['child_indices']): + for r in reps(e, allreps): + if (r, i) in windows: bad.append(f'child {i} of replica {r} run twice') + windows[r, i] = (last.get((r, e['pair']), -1), pos); group[r, i] = (r, e['pair'], side) + child[i] = (e['pair'], side) + by = defaultdict(list) # children of one family group: pairwise disjoint windows + for key, w in windows.items(): by[group[key]].append(w) + for g, ws in by.items(): + ws.sort() + if any(a[1] > b[0] for a, b in zip(ws, ws[1:])): bad.append(f'overlapping child windows in family group {g}') + used = defaultdict(set); n = 0 + for c in t['calls']: + pos = callpos.get((c['stage'], c['replica'])) + if pos is None: bad.append(f"call stage {c['stage']} replica {c['replica']} has no cover sweep"); continue + for f, r in c['owners']: + if r[0] not in (3, 4): continue + i, off = r[1], r[2]; w = 9 if r[0] == 3 else r[3]; n += 1 + orep, ps, port = f // 960, (f % 960) // 120, f % 120 + if i not in child or ps != 2 * child[i][0] + child[i][1]: bad.append(f'call {c["stage"]},{c["replica"]}: family {f} is not on child {i}'); continue + lo, hi = windows.get((orep, i), (None, None)) + if lo is None or not lo < pos < hi: bad.append(f'call {c["stage"]},{c["replica"]}: block on replica {orep} child {i} outside its window {lo},{hi} at {pos}') + cells = set(range(off, off + w)) + if cells & used[orep, i, port]: bad.append(f'call {c["stage"]},{c["replica"]}: block overlaps on replica {orep} child {i} port {port}') + used[orep, i, port] |= cells + return n, len(windows), bad + + +def mutants(t): + """necessity controls: each edit must be rejected""" + import copy + res = {} + stagepair = {e['stage']: e['pair'] for e in t['recipe'] if e.get('kind') == 'local'} + children = {} + for e in t['execution_schedule']: + if e.get('kind') == 'idle_cover_sweep': + for side, i in enumerate(e['child_indices']): children[i] = (e['pair'], side) + m = copy.deepcopy(t) # a block moved onto another child of the same family group + done = False + for c in m['calls']: + for f, r in c['owners']: + if r[0] in (3, 4) and not done: + alt = [j for j, ps in children.items() if ps == children[r[1]] and j != r[1]] + if alt: r[1] = alt[0]; done = True + res['block moved to another child (outside its window)'] = len(check(m)[2]) + m = copy.deepcopy(t) # two blocks of one child made to overlap + seen = {} + for c in m['calls']: + for f, r in c['owners']: + if r[0] in (3, 4): + key = (f, r[1]) + if key in seen and 'done' not in seen: r[2] = seen[key]; seen['done'] = 1 + seen.setdefault(key, r[2]) + res['two blocks of one child overlap'] = len(check(m)[2]) + return res + + +def main(): + ok = True + for p in [a for a in sys.argv[1:] if not a.startswith('--')]: + t = json.loads(gzip.decompress(Path(p).read_bytes())) + n, nw, bad = check(t) + ok &= not bad + print(f'{p}: hosted blocks {n}; pending windows {nw}; violations {len(bad)} {bad[:3]}', flush=True) + if '--mutants' in sys.argv: + mu = mutants(t); ok &= all(v > 0 for v in mu.values()); print(' mutants (violations each):', mu, flush=True) + print('PASS windows and blocks' if ok else 'FAIL windows and blocks') + sys.exit(0 if ok else 1) + + +if __name__ == '__main__': + main() diff --git a/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/lake-manifest.json b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/lake-manifest.json new file mode 100644 index 0000000000..7acfc87a86 --- /dev/null +++ b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/lake-manifest.json @@ -0,0 +1,125 @@ +{ + "version": "1.1.0", + "packagesDir": ".lake/packages", + "packages": [ + { + "type": "path", + "scope": "", + "name": "LemmaG", + "manifestFile": "lake-manifest.json", + "inherited": false, + "dir": "./../e8-lemma-g-lean", + "configFile": "lakefile.toml" + }, + { + "url": "https://github.com/leanprover-community/mathlib4", + "type": "git", + "subDir": null, + "scope": "", + "rev": "308445d7985027f538e281e18df29ca16ede2ba3", + "name": "mathlib", + "manifestFile": "lake-manifest.json", + "inputRev": "v4.21.0", + "inherited": false, + "configFile": "lakefile.lean" + }, + { + "url": "https://github.com/leanprover-community/plausible", + "type": "git", + "subDir": null, + "scope": "leanprover-community", + "rev": "c4aa78186d388e50a436e8362b947bae125a2933", + "name": "plausible", + "manifestFile": "lake-manifest.json", + "inputRev": "main", + "inherited": true, + "configFile": "lakefile.toml" + }, + { + "url": "https://github.com/leanprover-community/LeanSearchClient", + "type": "git", + "subDir": null, + "scope": "leanprover-community", + "rev": "6c62474116f525d2814f0157bb468bf3a4f9f120", + "name": "LeanSearchClient", + "manifestFile": "lake-manifest.json", + "inputRev": "main", + "inherited": true, + "configFile": "lakefile.toml" + }, + { + "url": "https://github.com/leanprover-community/import-graph", + "type": "git", + "subDir": null, + "scope": "leanprover-community", + "rev": "d07bd64f1910f1cc5e4cc87b6b9c590080e7a457", + "name": "importGraph", + "manifestFile": "lake-manifest.json", + "inputRev": "main", + "inherited": true, + "configFile": "lakefile.toml" + }, + { + "url": "https://github.com/leanprover-community/ProofWidgets4", + "type": "git", + "subDir": null, + "scope": "leanprover-community", + "rev": "6980f6ca164de593cb77cd03d8eac549cc444156", + "name": "proofwidgets", + "manifestFile": "lake-manifest.json", + "inputRev": "v0.0.62", + "inherited": true, + "configFile": "lakefile.lean" + }, + { + "url": "https://github.com/leanprover-community/aesop", + "type": "git", + "subDir": null, + "scope": "leanprover-community", + "rev": "8ff27701d003456fd59f13a9212431239d902aef", + "name": "aesop", + "manifestFile": "lake-manifest.json", + "inputRev": "master", + "inherited": true, + "configFile": "lakefile.toml" + }, + { + "url": "https://github.com/leanprover-community/quote4", + "type": "git", + "subDir": null, + "scope": "leanprover-community", + "rev": "e9c65db4823976353cd0bb03199a172719efbeb7", + "name": "Qq", + "manifestFile": "lake-manifest.json", + "inputRev": "master", + "inherited": true, + "configFile": "lakefile.toml" + }, + { + "url": "https://github.com/leanprover-community/batteries", + "type": "git", + "subDir": null, + "scope": "leanprover-community", + "rev": "8d2067bf518731a70a255d4a61b5c103922c772e", + "name": "batteries", + "manifestFile": "lake-manifest.json", + "inputRev": "main", + "inherited": true, + "configFile": "lakefile.toml" + }, + { + "url": "https://github.com/leanprover/lean4-cli", + "type": "git", + "subDir": null, + "scope": "leanprover", + "rev": "7c6aef5f75a43ebbba763b44d535175a1b04c9e0", + "name": "Cli", + "manifestFile": "lake-manifest.json", + "inputRev": "main", + "inherited": true, + "configFile": "lakefile.toml" + } + ], + "name": "LemmaA", + "lakeDir": ".lake" +} diff --git a/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/lakefile.toml b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/lakefile.toml new file mode 100644 index 0000000000..e3ffb61b29 --- /dev/null +++ b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/lakefile.toml @@ -0,0 +1,14 @@ +name = "LemmaA" +defaultTargets = ["LemmaA"] + +[[require]] +name = "mathlib" +git = "https://github.com/leanprover-community/mathlib4" +rev = "v4.21.0" + +[[require]] +name = "LemmaG" +path = "../e8-lemma-g-lean" + +[[lean_lib]] +name = "LemmaA" diff --git a/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/lean-toolchain b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/lean-toolchain new file mode 100644 index 0000000000..980709bbba --- /dev/null +++ b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/lean-toolchain @@ -0,0 +1 @@ +leanprover/lean4:v4.21.0 diff --git a/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/verify.py b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/verify.py new file mode 100644 index 0000000000..4ef44ec8b6 --- /dev/null +++ b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr516/research/e8-lemma-a-lean/verify.py @@ -0,0 +1,125 @@ +# Apache-2.0. Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. +"""Verify the Lean formalisation of Lemma A. + +usage: python3 verify.py [--no-cache] [--instances BASE] [--async T.json.gz] + 1. every file listed in MANIFEST.json has its recorded sha256 and no unlisted file sits in LemmaA/ or code/; the files of + the Lemma G package (path dependency) and of PR #484 that are used have their recorded sha256 ("external_files"); + 2. the Lean sources contain no `sorry`, `admit`, `axiom`, `native_decide`, `implemented_by`, `extern`, `unsafe`, `opaque` + and no `set_option` other than the heartbeat limits (Lemma G's sources are scanned too); + 3. `lake exe cache get` (Mathlib's pinned build, skipped with --no-cache) and `lake build` (builds LemmaG as well); + 4. `lake env lean PrintAxioms.lean`: each main theorem depends only on propext, Classical.choice, Quot.sound; + 5. with --instances BASE (BASE = the output directory of PR #484's verify.py; --all there adds gauge80 and kernel79), on + every word present (the headline is required; the anchor is checked where present): + a. #484's own results on inputs equal to EXPECTED.json: LEMMA-A.json (required for every wrapped word), + HOSTING-AUDIT.json (strict one-helper audit, where present), LEMMA-G-CHECK.json (I-helper count = EXPECTED, + scalar replay); + b. the Lemma G package's code/check_extended_labels.py --mutants: (F) is read in Lemma G's extended labels; + c. code/check_owners.py --mutants: one owner per stream (disjoint footprints on shared families), centre copies; + d. code/check_windows.py --mutants: every hosted block inside its pending child's open window, blocks disjoint; + 6. with --async T.json.gz (an asynchronous hosted template, e.g. the one PR #505's verify.py emits): c. and d. on it. +Python 3.9+, standard library only; `lake` from elan on PATH (the toolchain is pinned by lean-toolchain).""" +import hashlib, json, os, re, subprocess, sys +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ALLOWED = {'propext', 'Classical.choice', 'Quot.sound'} +FORBIDDEN = re.compile(r'\b(sorry|admit|axiom|native_decide|implemented_by|extern|unsafe|opaque)\b|set_option\s+(?!maxHeartbeats|maxRecDepth)') + + +def fail(msg): + print('FAIL', msg, flush=True); sys.exit(1) + + +def run(cmd, timeout): + print('$', ' '.join(cmd), flush=True) + p = subprocess.run(cmd, cwd=HERE, stdout=subprocess.PIPE, stderr=subprocess.STDOUT, text=True, timeout=timeout) + if p.returncode: + print(p.stdout[-4000:]); fail(f'{cmd[0]} {cmd[1]} exited {p.returncode}') + return p.stdout + + +def strip_comments(src): + src = re.sub(r'/-.*?-/', ' ', src, flags=re.S) # block and doc comments (not nested in these sources) + return re.sub(r'--[^\n]*', ' ', src) + + +def main(): + args = sys.argv[1:] + man = json.loads((HERE / 'MANIFEST.json').read_text()) + for rel, sha in man['files'].items(): + got = hashlib.sha256((HERE / rel).read_bytes()).hexdigest() + if got != sha: fail(f'sha256 of {rel}') + for d in ('LemmaA', 'code'): + for p in (HERE / d).rglob('*'): + if p.is_file() and '__pycache__' not in p.parts and str(p.relative_to(HERE)) not in man['files']: + fail(f'unlisted file {p.relative_to(HERE)}') + for rel, sha in man['external_files'].items(): + if hashlib.sha256((HERE / rel).read_bytes()).hexdigest() != sha: fail(f'sha256 of {rel}') + print('manifest: %d files and %d external files (Lemma G package, #484) OK' % (len(man['files']), len(man['external_files'])), flush=True) + + G = HERE.parent / 'e8-lemma-g-lean' + lean_files = (sorted(HERE.glob('LemmaA/*.lean')) + [HERE / 'LemmaA.lean', HERE / 'PrintAxioms.lean'] + + sorted(G.glob('LemmaG/*.lean')) + [G / 'LemmaG.lean']) + for p in lean_files: + m = FORBIDDEN.search(strip_comments(p.read_text())) + if m: fail(f'forbidden token {m.group(0)!r} in {p.name}') + print('sources: no sorry / admit / axiom / native_decide / unsafe / opaque / extern in %d files' % len(lean_files), flush=True) + + if '--no-cache' not in args: + run(['lake', 'exe', 'cache', 'get'], 3600) + out = run(['lake', 'build'], 3600) + print('\n'.join(l for l in out.splitlines() if 'warning' in l or 'error' in l or 'Build completed' in l), flush=True) + + out = run(['lake', 'env', 'lean', 'PrintAxioms.lean'], 1200) + wanted = [l.split()[2] for l in (HERE / 'PrintAxioms.lean').read_text().splitlines() if l.startswith('#print axioms')] + seen = {} + for m in re.finditer(r"'([\w.']+)' depends on axioms: \[([^\]]*)\]", out): + seen[m.group(1)] = [a.strip() for a in m.group(2).split(',') if a.strip()] + for m in re.finditer(r"'([\w.']+)' does not depend on any axioms", out): + seen[m.group(1)] = [] + print(out.strip(), flush=True) + for name in wanted: + if name not in seen: fail(f'no axiom report for {name}') + if not set(seen[name]) <= ALLOWED: fail(f'{name} depends on {seen[name]}') + print('axioms: %d theorems, only %s' % (len(wanted), sorted(ALLOWED)), flush=True) + + if '--instances' in args: + base = Path(args[args.index('--instances') + 1]) + words = [w for w in ('gauge80-kernel42', 'gauge80', 'kernel79', 'anchor') if (base / w / 'hosted').is_dir()] + if 'gauge80-kernel42' not in words: fail(f'{base} lacks the headline word') + E = json.loads((HERE.parent / 'e8-complex-gauge-kernel' / 'EXPECTED.json').read_text()) + for w in words: + L = json.loads((base / 'lemmaG' / w / 'LEMMA-G-CHECK.json').read_text()) + if L['inputs'] != E['lemma_G_independent_checks'][w]['inputs']: fail(f'{w}: emitted inputs differ from #484 EXPECTED.json') + if any(L['labels'][o]['n_label_violations'] or L['labels'][o]['scalar_violations'] for o in ('forward', 'backward')): + fail(f'{w}: #484 label/scalar check') + if w == 'anchor': + print('instances: anchor: #484 label and scalar checks PASS (no wrappers)', flush=True); continue + la = base / w / 'LEMMA-A.json' + if not la.exists(): fail(f'{w}: #484 LEMMA-A.json missing') + A = json.loads(la.read_text()) + if A['status'] != 'PASS_RESIDUAL_WRAPPERS_ARE_EXACT': fail(f'{w}: #484 LEMMA-A.json') + if w == 'gauge80-kernel42' and A['frames'] != E['wrapper_check']['frames']: fail('headline: #484 LEMMA-A frames') + ha = base / w / 'HOSTING-AUDIT.json' + if ha.exists(): + H = json.loads(ha.read_text()) + if not (H['status'].startswith('PASS') and H['one_helper_per_family']): fail(f'{w}: #484 hosting audit') + if L['instances']['I-helper']['failures']: fail(f'{w}: #484 I-helper') + if L['instances']['I-helper']['entering_helpers'] != E['lemma_G_independent_checks'][w]['instances']['I-helper']['entering_helpers']: + fail(f'{w}: I-helper count differs from EXPECTED.json') + print('instances: %s: #484 Lemma A exact part (%d frames), %shosting audit, I-helper %d helpers, scalar replay: PASS' + % (w, A['frames'], 'strict ' if ha.exists() else 'no ', L['instances']['I-helper']['entering_helpers']), flush=True) + out = run([sys.executable, '-B', str(HERE.parent / 'e8-lemma-g-lean' / 'code' / 'check_extended_labels.py'), str(base), *words, '--mutants'], 3600) + print('\n'.join(l for l in out.splitlines() if re.match(r'^\S+ (forward|backward) violations', l) or 'mutants (' in l + or 'extended labels' in l), flush=True) + print(run([sys.executable, '-B', 'code/check_owners.py', str(base), *words, '--mutants'], 3600).strip(), flush=True) + print(run([sys.executable, '-B', 'code/check_windows.py', *[str(base / w / 'hosted' / 'GLOBAL-TEMPLATE.json.gz') for w in words], '--mutants'], 3600).strip(), flush=True) + if '--async' in args: + tpl = args[args.index('--async') + 1] + print(run([sys.executable, '-B', 'code/check_owners.py', '--template', tpl, '16', '--mutants'], 3600).strip(), flush=True) + print(run([sys.executable, '-B', 'code/check_windows.py', tpl, '--mutants'], 3600).strip(), flush=True) + print('PASS Lemma A Lean verification', flush=True) + + +if __name__ == '__main__': + main() diff --git 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"IntegerConvolution", + "line": "'CurrentMain.IntegerConvolution.value_map_mul' depends on axioms: [propext]" + }, + { + "module": "IntegerConvolution", + "line": "'CurrentMain.IntegerConvolution.convolution_value' depends on axioms: [propext, Quot.sound]" + }, + { + "module": "IntegerConvolution", + "line": "'CurrentMain.IntegerConvolution.binary_convolution' depends on axioms: [propext, Quot.sound]" + }, + { + "module": "FixedTapeMachine", + "line": "'CurrentMain.FixedTapeMachine.initial_inputA' depends on axioms: [propext]" + }, + { + "module": "FixedTapeMachine", + "line": "'CurrentMain.FixedTapeMachine.initial_inputB' depends on axioms: [propext]" + }, + { + "module": "FixedTapeMachine", + "line": "'CurrentMain.FixedTapeMachine.initial_output' depends on axioms: [propext]" + }, + { + "module": "FixedTapeMachine", + "line": "'CurrentMain.FixedTapeMachine.run_halted' does not depend on any axioms" + }, + { + "module": "FixedTapeMachine", + "line": "'CurrentMain.FixedTapeMachine.run_add' depends on axioms: [propext]" + }, + { + "module": "CarryTape", + "line": "'CurrentMain.CarryTape.run_add' depends on axioms: [propext]" + }, + { + "module": "CarryTape", + "line": "'CurrentMain.CarryTape.carry_execution' depends on axioms: [propext]" + }, + { + "module": "CarryTape", + "line": "'CurrentMain.CarryTape.rewind_execution' depends on axioms: [propext]" + }, + { + "module": "CarryTape", + "line": "'CurrentMain.CarryTape.carryFinish_rewind' depends on axioms: [propext]" + }, + { + "module": "CarryTape", + "line": "'CurrentMain.CarryTape.increment_execution' depends on axioms: [propext, Quot.sound]" + }, + { + "module": "CarryTape", + "line": "'CurrentMain.CarryTape.increment_length' depends on axioms: [propext]" + }, + { + "module": "CarryTape", + "line": "'CurrentMain.CarryTape.all_ones_execution' depends on axioms: [propext, Quot.sound]" + }, + { + "module": "CarryTapePass", + "line": "'CurrentMain.CarryTape.value_bound' depends on axioms: [propext, Quot.sound]" + }, + { + "module": "CarryTapePass", + "line": "'CurrentMain.CarryTape.increment_value' depends on axioms: [propext, Quot.sound]" + }, + { + "module": "CarryTapePass", + "line": "'CurrentMain.CarryTape.increment_mod' depends on axioms: [propext, Quot.sound]" + }, + { + "module": "CarryTapePass", + "line": "'CurrentMain.CarryTape.pass_length' depends on axioms: [propext]" + }, + { + "module": "CarryTapePass", + "line": "'CurrentMain.CarryTape.pass_value' depends on axioms: [propext, Quot.sound]" + }, + { + "module": "CarryTapePass", + "line": "'CurrentMain.CarryTape.pass_even' depends on axioms: [propext, Quot.sound]" + }, + { + "module": "CarryTapePass", + "line": "'CurrentMain.CarryTape.empty_pass_one' does not depend on any axioms" + }, + { + "module": "CarryTapePass", + "line": "'CurrentMain.CarryTape.complete_pass' depends on axioms: [propext, Quot.sound]" + }, + { + "module": "CarryTapePass", + "line": "'CurrentMain.CarryTape.incrementReceipt_realized' depends on axioms: [propext, Quot.sound]" + }, + { + "module": "CarryTapePass", + "line": "'CurrentMain.CarryTape.pass_successor_realized' depends on axioms: [propext, Quot.sound]" + }, + { + "module": "CarryTapePass", + "line": "'CurrentMain.CarryTape.full_pass24_index_traffic' depends on axioms: [propext, Quot.sound]" + }, + { + "module": "BinaryCarryIncrement", + "line": "'CurrentMain.BinaryCarryIncrement.increment_run' depends on axioms: [propext, Quot.sound]" + }, + { + "module": "BinaryCarryIncrement", + "line": "'CurrentMain.BinaryCarryIncrement.final_halted' depends on axioms: [propext]" + }, + { + "module": "BinaryCarryIncrement", + "line": "'CurrentMain.BinaryCarryIncrement.increment_length' depends on axioms: [propext]" + }, + { + "module": "BinaryCarryIncrement", + "line": "'CurrentMain.BinaryCarryIncrement.value_binding' does not depend on any axioms" + }, + { + "module": "BinaryCarryIncrement", + "line": "'CurrentMain.BinaryCarryIncrement.increment_modular_value' depends on axioms: [propext, Quot.sound]" + }, + { + "module": "BinaryCountDispatcher", + "line": "'CurrentMain.BinaryCountDispatcher.count_run' depends on axioms: [propext, Quot.sound]" + }, + { + "module": "BinaryCountDispatcher", + "line": "'CurrentMain.BinaryCountDispatcher.final_halted' depends on axioms: [propext, Quot.sound]" + }, + { + "module": "BinaryCountDispatcher", + "line": "'CurrentMain.BinaryCountDispatcher.counter_length' depends on axioms: [propext]" + }, + { + "module": "BinaryCountDispatcher", + "line": "'CurrentMain.BinaryCountDispatcher.counter_value' depends on axioms: [propext, Quot.sound]" + }, + { + "module": "BinaryCountDispatcherMarkedInput", + "line": "'CurrentMain.BinaryCountDispatcherMarkedInput.count_run' depends on axioms: [propext, Quot.sound]" + }, + { + "module": "BinaryCountDispatcherMarkedInput", + "line": "'CurrentMain.BinaryCountDispatcherMarkedInput.final_halted' depends on axioms: [propext, Quot.sound]" + }, + { + "module": "BinaryCountDispatcherMarkedInput", + "line": "'CurrentMain.BinaryCountDispatcherMarkedInput.counter_length' depends on axioms: [propext]" + }, + { + "module": "BinaryCountDispatcherMarkedInput", + "line": "'CurrentMain.BinaryCountDispatcherMarkedInput.counter_value' depends on axioms: [propext, Quot.sound]" + }, + { + "module": "BinaryCounterZeroAllocation", + "line": "'CurrentMain.BinaryCounterZeroAllocation.allocate_run_exact' depends on axioms: [propext, Quot.sound]" + }, + { + "module": "BinaryCounterZeroAllocation", + "line": "'CurrentMain.BinaryCounterZeroAllocation.final_halted' depends on axioms: [propext]" + }, + { + "module": "BinaryCounterZeroAllocation", + "line": "'CurrentMain.BinaryCounterZeroAllocation.allocated_width' depends on axioms: [propext]" + }, + { + "module": "BinaryAutomaticWidthCount", + "line": "'CurrentMain.BinaryAutomaticWidthCount.count_run' depends on axioms: [propext, Classical.choice, Quot.sound]" + }, + { + "module": "BinaryAutomaticWidthCount", + "line": "'CurrentMain.BinaryAutomaticWidthCount.final_halted' depends on axioms: [propext, Quot.sound]" + }, + { + "module": "BinaryAutomaticWidthCount", + "line": "'CurrentMain.BinaryAutomaticWidthCount.final_input' depends on axioms: [propext, Quot.sound]" + }, + { + "module": "BinaryAutomaticWidthCount", + "line": "'CurrentMain.BinaryAutomaticWidthCount.final_counter' depends on axioms: [propext, Quot.sound]" + }, + { + "module": "BinaryAutomaticWidthCount", + "line": "'CurrentMain.BinaryAutomaticWidthCount.counter_width' depends on axioms: [propext]" + }, + { + "module": "BinaryAutomaticWidthCount", + "line": "'CurrentMain.BinaryAutomaticWidthCount.counter_value' depends on axioms: [propext, Quot.sound]" + } + ], + "axiom_comparison": "Complete theorem and axiom statements normalized for whitespace; log byte identity is separate." +} diff --git 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These modules do not prove kappa or a whole multiplier theorem.", + "package_author_readback_sha256": "be422a34aae4ed2e56501ec054e34f93ef874fa5bdf41e3eb3f9deec1d960c68", + "replay_status_author_readback_sha256": "2fc88e9af5b74fd50eb1d85a132a168d64439b9d2c24dc00663a1389a219dde6", + "replay_summary_sha256": "d080beb005dba93f2f2a4eb3c9838486b0d67a5474fb8cd70608b55edd49dc8c" +} diff --git a/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr519/research/lean-automatic-width-count/BinaryAutomaticWidthCount.lean b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr519/research/lean-automatic-width-count/BinaryAutomaticWidthCount.lean new file mode 100644 index 0000000000..5d1cc3c168 --- /dev/null +++ b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr519/research/lean-automatic-width-count/BinaryAutomaticWidthCount.lean @@ -0,0 +1,204 @@ +import BinaryCounterZeroAllocation + +/-! Concrete allocation/count sequencing on the same two tapes. Global states +0..2 are the allocator's active states;3..9 are the dispatcher's seven states. +The shared state3 needs no extra bridge transition. Actual successful-prefix +simulation reuses both accepted run theorems without a first-completion premise. +The counter starts pristine, is physically allocated from the word, and stores +its exact length. The cost is still the inherited pass receipt plus4n+4; +PR64 amortized transport, compact output, input4 control and Plan/Budget remain +separate. No new capacity or list-arithmetic induction is introduced. -/ +namespace CurrentMain.BinaryAutomaticWidthCount +open FixedTapeMachine + +private theorem fin4 (i : Fin 4) : i=0 ∨ i=1 ∨ i=2 ∨ i=3 := by + exact (show ∀ j : Fin 4, j=0 ∨ j=1 ∨ j=2 ∨ j=3 by decide) i +private theorem fin7 (i : Fin 7) : i=0 ∨ i=1 ∨ i=2 ∨ i=3 ∨ i=4 ∨ i=5 ∨ i=6 := by + exact (show ∀ j : Fin 7, j=0 ∨ j=1 ∨ j=2 ∨ j=3 ∨ j=4 ∨ j=5 ∨ j=6 by decide) i + +def allocationState (s : Fin 4) : Fin 10 := ⟨s.val,by omega⟩ +def countState (s : Fin 7) : Fin 10 := ⟨s.val+3,by omega⟩ +def allocationAction (a : Action 2 4) : Action 2 10 := + ⟨allocationState a.state,a.writes,a.moves⟩ +def countAction (a : Action 2 7) : Action 2 10 := + ⟨countState a.state,a.writes,a.moves⟩ + +def machine : Machine where + tapes := 2 + states := 10 + initial := 0 + transition := fun s r => + if h : s.val<3 then + (BinaryCounterZeroAllocation.machine.transition (⟨s.val,by omega⟩ : Fin 4) r).map allocationAction + else + (BinaryCountDispatcher.machine.transition (⟨s.val-3,by omega⟩ : Fin 7) r).map countAction + +def embedAllocation (c : Configuration BinaryCounterZeroAllocation.machine) : Configuration machine := + ⟨allocationState c.state,c.tapes⟩ +def embedCount (c : Configuration BinaryCountDispatcher.machine) : Configuration machine := + ⟨countState c.state,c.tapes⟩ + +def zeroBits (word : List Bool) : List Bool := List.replicate word.length false + +def initialConfiguration (word : List Bool) : Configuration machine := + embedAllocation (BinaryCounterZeroAllocation.initialConfiguration word) +def finalConfiguration (word : List Bool) : Configuration machine := + embedCount (BinaryCountDispatcherMarkedInput.finalConfiguration word (zeroBits word)) + +private theorem allocation_live (s : Fin 4) (r : Fin 2 → Symbol) (a : Action 2 4) + (h : BinaryCounterZeroAllocation.machine.transition s r=some a) : s.val<3 := by + rcases fin4 s with rfl|rfl|rfl|rfl + · decide + · decide + · decide + · have hn : (none : Option (Action 2 4))=some a := h + cases hn + +private theorem transition_allocation (s : Fin 4) (r : Fin 2 → Symbol) (hs : s.val<3) : + machine.transition (allocationState s) r= + (BinaryCounterZeroAllocation.machine.transition s r).map allocationAction := by + rcases fin4 s with rfl|rfl|rfl|rfl + · rfl + · rfl + · rfl + · omega + +private theorem transition_count (s : Fin 7) (r : Fin 2 → Symbol) : + machine.transition (countState s) r= + (BinaryCountDispatcher.machine.transition s r).map countAction := by + rcases fin7 s with rfl|rfl|rfl|rfl|rfl|rfl|rfl <;> rfl + +/- Both private generic helpers are reused byte-for-byte from the accepted +actual-symbol dispatcher. Their hypotheses are discharged by the tables here. -/ +private theorem step_of_transition (m : Machine) (c : Configuration m) + (a : Action m.tapes m.states) + (h : m.transition c.state (fun i => (c.tapes i).head) = some a) : + step m c = some (Configuration.mk a.state + (fun i => ((c.tapes i).write (a.writes i)).move (a.moves i))) := by + unfold step + rw [h] + +private theorem step_allocation (c d : Configuration BinaryCounterZeroAllocation.machine) + (h : step BinaryCounterZeroAllocation.machine c=some d) : + step machine (embedAllocation c)=some (embedAllocation d) := by + cases ht : BinaryCounterZeroAllocation.machine.transition c.state (fun i => (c.tapes i).head) with + | none => + simp only [step,ht] at h + cases h + | some a => + simp only [step,ht,Option.some.injEq] at h + subst d + have hs := allocation_live c.state (fun i => (c.tapes i).head) a ht + have outer : machine.transition (embedAllocation c).state + (fun i : Fin 2 => ((embedAllocation c).tapes i).head)=some (allocationAction a) := + (transition_allocation c.state (fun i => (c.tapes i).head) hs).trans + (congrArg (Option.map allocationAction) ht) + refine (step_of_transition machine (embedAllocation c) (allocationAction a) outer).trans ?_ + rfl + +private theorem step_count (c d : Configuration BinaryCountDispatcher.machine) + (h : step BinaryCountDispatcher.machine c=some d) : + step machine (embedCount c)=some (embedCount d) := by + cases ht : BinaryCountDispatcher.machine.transition c.state (fun i => (c.tapes i).head) with + | none => + simp only [step,ht] at h + cases h + | some a => + simp only [step,ht,Option.some.injEq] at h + subst d + have outer : machine.transition (embedCount c).state + (fun i : Fin 2 => ((embedCount c).tapes i).head)=some (countAction a) := + (transition_count c.state (fun i => (c.tapes i).head)).trans + (congrArg (Option.map countAction) ht) + refine (step_of_transition machine (embedCount c) (countAction a) outer).trans ?_ + rfl + +private theorem simulate_to_halt (source target : Machine) + (embed : Configuration source → Configuration target) + (sim : ∀ c d, step source c=some d → step target (embed c)=some (embed d)) + (budget : Nat) (c : Configuration source) (h : Halted source (run source budget c)) : + ∃ k≤budget, run target k (embed c)=embed (run source budget c) := by + induction budget generalizing c with + | zero => exact ⟨0, Nat.le_refl _, rfl⟩ + | succ budget ih => + cases hs : step source c with + | none => + refine ⟨0, Nat.zero_le _, ?_⟩ + simp only [run, hs] + | some d => + have hd : Halted source (run source budget d) := by simpa only [run, hs] using h + obtain ⟨k,hk,he⟩ := ih d hd + refine ⟨k+1, by omega, ?_⟩ + simpa only [run, hs, sim c d hs] using he + +private theorem handoff (word : List Bool) : + embedAllocation (BinaryCounterZeroAllocation.finalConfiguration word)= + embedCount (BinaryCountDispatcherMarkedInput.initialConfiguration word (zeroBits word)) := by + rfl + +/-- The actual machine supplies the counter width before counting. Its cost is +an inherited physical pass receipt plus the allocation/controller overhead. -/ +theorem count_run (word : List Bool) : + ∃ t≤(CarryTape.pass word.length (zeroBits word)).2.reads+4*word.length+4, + run machine t (initialConfiguration word)=finalConfiguration word := by + have ah : Halted BinaryCounterZeroAllocation.machine + (run BinaryCounterZeroAllocation.machine (2*word.length+3) + (BinaryCounterZeroAllocation.initialConfiguration word)) := by + rw [BinaryCounterZeroAllocation.allocate_run_exact] + exact BinaryCounterZeroAllocation.final_halted word + obtain ⟨a,ha,harun⟩ := simulate_to_halt BinaryCounterZeroAllocation.machine machine embedAllocation + (fun c d h => step_allocation c d h) _ _ ah + have haend : run machine a (initialConfiguration word)= + embedAllocation (BinaryCounterZeroAllocation.finalConfiguration word) := by + simpa only [initialConfiguration,BinaryCounterZeroAllocation.allocate_run_exact] using harun + obtain ⟨t,ht,htrun⟩ := BinaryCountDispatcherMarkedInput.count_run word (zeroBits word) + have ch : Halted BinaryCountDispatcher.machine + (run BinaryCountDispatcher.machine t + (BinaryCountDispatcherMarkedInput.initialConfiguration word (zeroBits word))) := by + rw [htrun] + exact BinaryCountDispatcherMarkedInput.final_halted word (zeroBits word) + obtain ⟨c,hc,hcrun⟩ := simulate_to_halt BinaryCountDispatcher.machine machine embedCount + (fun c d h => step_count c d h) _ _ ch + have hcend : run machine c + (embedCount (BinaryCountDispatcherMarkedInput.initialConfiguration word (zeroBits word)))= + finalConfiguration word := by + simpa only [htrun,finalConfiguration] using hcrun + refine ⟨a+c,by omega,?_⟩ + rw [run_add machine a c,haend,handoff,hcend] + +theorem final_halted (word : List Bool) : Halted machine (finalConfiguration word) := by + rfl + +theorem final_input (word : List Bool) : + (finalConfiguration word).tapes (0 : Fin 2)= + ⟨word.reverse.map bitSymbol++[.blank],.blank,[]⟩ := by + rfl + +theorem final_counter (word : List Bool) : + (finalConfiguration word).tapes (1 : Fin 2)= + BinaryCarryIncrement.homeTape (CarryTape.pass word.length (zeroBits word)).1 := by + rfl + +private theorem zero_value (word : List Bool) : wordValue (zeroBits word)=0 := by + have h := IntegerConvolution.value_map_mul 2 0 (List.replicate word.length 0) + change IntegerConvolution.value 2 ((zeroBits word).map (fun b => if b then 1 else 0))=0 + simpa only [zeroBits,List.map_replicate,Bool.false_eq_true,if_false,Nat.zero_mul] using h + +theorem counter_width (word : List Bool) : + (CarryTape.pass word.length (zeroBits word)).1.length=word.length := + (BinaryCountDispatcherMarkedInput.counter_length word (zeroBits word)).trans List.length_replicate + +/-- The stored count is the actual input length, without a supplied capacity +premise. Existing core modular arithmetic also covers the empty input. -/ +theorem counter_value (word : List Bool) : + wordValue (CarryTape.pass word.length (zeroBits word)).1=word.length := by + rw [BinaryCountDispatcherMarkedInput.counter_value,zero_value] + simp only [Nat.zero_add,zeroBits,List.length_replicate,Nat.mod_two_pow_self] + +end CurrentMain.BinaryAutomaticWidthCount +#print axioms CurrentMain.BinaryAutomaticWidthCount.count_run +#print axioms CurrentMain.BinaryAutomaticWidthCount.final_halted +#print axioms CurrentMain.BinaryAutomaticWidthCount.final_input +#print axioms CurrentMain.BinaryAutomaticWidthCount.final_counter +#print axioms CurrentMain.BinaryAutomaticWidthCount.counter_width +#print axioms CurrentMain.BinaryAutomaticWidthCount.counter_value diff --git a/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr519/research/lean-automatic-width-count/BinaryCountDispatcherMarkedInput.lean b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr519/research/lean-automatic-width-count/BinaryCountDispatcherMarkedInput.lean new file mode 100644 index 0000000000..85e3c511b6 --- /dev/null +++ b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr519/research/lean-automatic-width-count/BinaryCountDispatcherMarkedInput.lean @@ -0,0 +1,217 @@ +import BinaryCountDispatcher + +/-! An exact invocation adapter for the accepted dispatcher on a represented +home blank and terminal blank. The machine, counter arithmetic and count proof +are reused. This module changes only the input representation at invocation. +The private simulation is restricted to finite unread Boolean words, so a +blank head with an arbitrary nonempty right list is never silently identified +with a terminal blank. Allocation, the input4 tape choice, amortization and the +source caller/Plan remain separate obligations. -/ +namespace CurrentMain.BinaryCountDispatcherMarkedInput +open FixedTapeMachine + +private theorem fin2 (i : Fin 2) : i=0 ∨ i=1 := by + exact (show ∀ j : Fin 2, j=0 ∨ j=1 by decide) i + +/-- Both boundary cells are represented. For empty input the two blanks are +already the left home cell and the current terminal cell. -/ +def inputTape : List Bool → Tape + | [] => ⟨[.blank],.blank,[]⟩ + | b::rest => ⟨[.blank],bitSymbol b,rest.map bitSymbol++[.blank]⟩ + +def initialConfiguration (word bits : List Bool) : + Configuration BinaryCountDispatcher.machine := + BinaryCountDispatcher.configuration 0 (inputTape word) (BinaryCarryIncrement.homeTape bits) + +def finalConfiguration (word bits : List Bool) : + Configuration BinaryCountDispatcher.machine := + BinaryCountDispatcher.configuration 6 + ⟨word.reverse.map bitSymbol++[.blank],.blank,[]⟩ + (BinaryCarryIncrement.homeTape (CarryTape.pass word.length bits).1) + +private def markTape (t : Tape) : Tape := + ⟨t.left++[.blank],t.head, + match t.head with + | .blank => [] + | .zero | .one => t.right++[.blank]⟩ + +private def mark (c : Configuration BinaryCountDispatcher.machine) : + Configuration BinaryCountDispatcher.machine := + ⟨c.state,fun i => if i=(0 : Fin 2) then markTape (c.tapes i) else c.tapes i⟩ + +private def WordInput (c : Configuration BinaryCountDispatcher.machine) : Prop := + ∃ left word, c.tapes (0 : Fin 2)=BinaryCountDispatcher.inputTape left word + +private theorem reads_mark (c : Configuration BinaryCountDispatcher.machine) : + (fun i : Fin 2 => ((mark c).tapes i).head) = fun i => (c.tapes i).head := by + funext i + rcases fin2 i with rfl|rfl <;> simp [mark,markTape] + +/- This is a read-only consequence of the accepted transition table. Every +successful transition preserves the input symbol and either stays, or moves +right from a bit. No arbitrary instruction contract is assumed. -/ +private theorem input_action (s : Fin 7) (r : Fin 2 → Symbol) (a : Action 2 7) + (h : BinaryCountDispatcher.machine.transition s r=some a) : + a.writes (0 : Fin 2)=r 0 ∧ + (a.moves (0 : Fin 2)=.stay ∨ (a.moves (0 : Fin 2)=.right ∧ r 0≠.blank)) := by + dsimp only [BinaryCountDispatcher.machine] at h + split at h + · split at h <;> cases h <;> + simp [BinaryCountDispatcher.liftAction,BinaryCountDispatcher.stayAction] + · split at h + · cases hr : r (0 : Fin 2) <;> simp only [hr] at h <;> cases h <;> + simp [BinaryCountDispatcher.stayAction,BinaryCountDispatcher.advanceAction,hr] + · cases h + +private theorem tape_update (left : List Symbol) (word : List Bool) (d : Move) + (hd : d=.stay ∨ (d=.right ∧ (BinaryCountDispatcher.inputTape left word).head≠.blank)) : + markTape (((BinaryCountDispatcher.inputTape left word).write + (BinaryCountDispatcher.inputTape left word).head).move d) = + ((markTape (BinaryCountDispatcher.inputTape left word)).write + (BinaryCountDispatcher.inputTape left word).head).move d ∧ + ∃ left' word', ((BinaryCountDispatcher.inputTape left word).write + (BinaryCountDispatcher.inputTape left word).head).move d = + BinaryCountDispatcher.inputTape left' word' := by + rcases hd with rfl|⟨rfl,hbit⟩ + · constructor + · cases word with + | nil => rfl + | cons b rest => cases b <;> rfl + · exact ⟨left,word,by cases word <;> rfl⟩ + · cases word with + | nil => exact False.elim (hbit rfl) + | cons b rest => + constructor + · cases rest with + | nil => cases b <;> rfl + | cons next rest => cases b <;> cases next <;> rfl + · exact ⟨bitSymbol b::left,rest,by cases rest <;> rfl⟩ + +/- Reuse the abstract definitional step reduction, avoiding a reconstructed +concrete dependent Option matcher. -/ +private theorem step_of_transition (m : Machine) (c : Configuration m) + (a : Action m.tapes m.states) + (h : m.transition c.state (fun i => (c.tapes i).head) = some a) : + step m c = some (Configuration.mk a.state + (fun i => ((c.tapes i).write (a.writes i)).move (a.moves i))) := by + unfold step + rw [h] + +private theorem step_none_of_transition (m : Machine) (c : Configuration m) + (h : m.transition c.state (fun i => (c.tapes i).head)=none) : + step m c=none := by + unfold step + rw [h] + +private theorem step_mark (c d : Configuration BinaryCountDispatcher.machine) + (hc : WordInput c) (h : step BinaryCountDispatcher.machine c=some d) : + step BinaryCountDispatcher.machine (mark c)=some (mark d) ∧ WordInput d := by + obtain ⟨left,word,hi⟩ := hc + cases ht : BinaryCountDispatcher.machine.transition c.state (fun i => (c.tapes i).head) with + | none => + simp only [step,ht] at h + cases h + | some a => + simp only [step,ht,Option.some.injEq] at h + subst d + obtain ⟨hw,hm⟩ := input_action c.state (fun i => (c.tapes i).head) a ht + have hu := tape_update left word (a.moves (0 : Fin 2)) + (by simpa only [hi] using hm) + constructor + · have outer : BinaryCountDispatcher.machine.transition (mark c).state + (fun i : Fin 2 => ((mark c).tapes i).head)=some a := + (congrArg (BinaryCountDispatcher.machine.transition c.state) (reads_mark c)).trans ht + refine (step_of_transition BinaryCountDispatcher.machine (mark c) a outer).trans ?_ + dsimp only [mark] + apply congrArg some + apply congrArg (fun tapes : Fin 2 → Tape => + (Configuration.mk a.state tapes : Configuration BinaryCountDispatcher.machine)) + funext i + rcases fin2 i with rfl|rfl + · simp only [if_pos rfl] + rw [hw,hi] + exact hu.1.symm + · simp only [show (1 : Fin 2)≠0 by decide,if_neg,if_false] + · change ∃ left' word', ((c.tapes (0 : Fin 2)).write (a.writes (0 : Fin 2))).move (a.moves (0 : Fin 2))= + BinaryCountDispatcher.inputTape left' word' + simpa only [hw,hi] using hu.2 + +private theorem none_mark (c : Configuration BinaryCountDispatcher.machine) + (h : step BinaryCountDispatcher.machine c=none) : + step BinaryCountDispatcher.machine (mark c)=none := by + have ht : BinaryCountDispatcher.machine.transition c.state (fun i => (c.tapes i).head)=none := by + cases he : BinaryCountDispatcher.machine.transition c.state (fun i => (c.tapes i).head) <;> + simp_all [step] + exact step_none_of_transition BinaryCountDispatcher.machine (mark c) + ((congrArg (BinaryCountDispatcher.machine.transition c.state) (reads_mark c)).trans ht) + +private theorem run_mark (t : Nat) (c : Configuration BinaryCountDispatcher.machine) + (hc : WordInput c) : + run BinaryCountDispatcher.machine t (mark c)=mark (run BinaryCountDispatcher.machine t c) ∧ + WordInput (run BinaryCountDispatcher.machine t c) := by + induction t generalizing c with + | zero => exact ⟨rfl,hc⟩ + | succ t ih => + cases hs : step BinaryCountDispatcher.machine c with + | none => + simp only [run,hs,none_mark c hs] + exact ⟨True.intro,hc⟩ + | some d => + obtain ⟨hd,hw⟩ := step_mark c d hc hs + simpa only [run,hs,hd] using ih d hw + +private theorem mark_configuration (s : Fin 7) (input counter : Tape) : + mark (BinaryCountDispatcher.configuration s input counter)= + BinaryCountDispatcher.configuration s (markTape input) counter := by + dsimp only [mark,BinaryCountDispatcher.configuration] + apply congrArg (fun tapes : Fin 2 → Tape => + (Configuration.mk s tapes : Configuration BinaryCountDispatcher.machine)) + funext i + rcases fin2 i with rfl|rfl <;> simp + +private theorem mark_initial (word bits : List Bool) : + mark (BinaryCountDispatcher.initialConfiguration word bits)=initialConfiguration word bits := by + unfold BinaryCountDispatcher.initialConfiguration initialConfiguration + rw [mark_configuration] + cases word with + | nil => rfl + | cons b rest => cases b <;> rfl + +private theorem mark_final (word bits : List Bool) : + mark (BinaryCountDispatcher.finalConfiguration word bits)=finalConfiguration word bits := by + unfold BinaryCountDispatcher.finalConfiguration finalConfiguration + rw [mark_configuration] + rfl + +/-- The accepted same-machine count theorem transports to the exact marked +input footprint. No allocation or caller-domain hypothesis is added. -/ +theorem count_run (word bits : List Bool) : + ∃ t≤(CarryTape.pass word.length bits).2.reads+2*word.length+1, + run BinaryCountDispatcher.machine t (initialConfiguration word bits)=finalConfiguration word bits := by + obtain ⟨t,ht,he⟩ := BinaryCountDispatcher.count_run word bits + have hw : WordInput (BinaryCountDispatcher.initialConfiguration word bits) := by + refine ⟨[],word,?_⟩ + cases word <;> rfl + refine ⟨t,ht,?_⟩ + have transport := (run_mark t (BinaryCountDispatcher.initialConfiguration word bits) hw).1 + simpa only [mark_initial,he,mark_final] using transport + +theorem final_halted (word bits : List Bool) : + Halted BinaryCountDispatcher.machine (finalConfiguration word bits) := by + rw [← mark_final] + exact none_mark _ (BinaryCountDispatcher.final_halted word bits) + +theorem counter_length (word bits : List Bool) : + (CarryTape.pass word.length bits).1.length=bits.length := + BinaryCountDispatcher.counter_length word bits + +theorem counter_value (word bits : List Bool) : + wordValue (CarryTape.pass word.length bits).1 = + (wordValue bits+word.length)%2^bits.length := + BinaryCountDispatcher.counter_value word bits + +end CurrentMain.BinaryCountDispatcherMarkedInput +#print axioms CurrentMain.BinaryCountDispatcherMarkedInput.count_run +#print axioms CurrentMain.BinaryCountDispatcherMarkedInput.final_halted +#print axioms CurrentMain.BinaryCountDispatcherMarkedInput.counter_length +#print axioms CurrentMain.BinaryCountDispatcherMarkedInput.counter_value diff --git a/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr519/research/lean-automatic-width-count/BinaryCounterZeroAllocation.lean b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr519/research/lean-automatic-width-count/BinaryCounterZeroAllocation.lean new file mode 100644 index 0000000000..c7f4b3ab64 --- /dev/null +++ b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr519/research/lean-automatic-width-count/BinaryCounterZeroAllocation.lean @@ -0,0 +1,190 @@ +import BinaryCountDispatcherMarkedInput + +/-! A four-state, two-tape allocation scan for the exact marked-input dispatcher +interface. An actual input bit allocates one zero counter cell. The table has +no width, remaining-count or address argument. It starts at the input's right +blank and a pristine counter, then restores the marked input to its first bit +and the width-n zero counter to its home blank. Empty input takes three steps. + +For input4 slot2/3, take word=(pad n x).reverse or (pad n y).reverse. Their +endTape left lists are exactly word.reverse.map bitSymbol. The first/second +input4 finalInput tapes are not interchangeable with these work copies. +This literal interface does not itself sequence the two machines, establish an +amortized counting cost, normalize a compact counter, or instantiate a caller +Plan/Budget. The accepted marked-input count theorem is the next consumer. -/ +namespace CurrentMain.BinaryCounterZeroAllocation +open FixedTapeMachine + +private theorem fin2 (i : Fin 2) : i=0 ∨ i=1 := by + exact (show ∀ j : Fin 2, j=0 ∨ j=1 by decide) i + +def action (next : Fin 4) (inputMove counterMove : Move) + (counterWrite : Option Symbol) (r : Fin 2 → Symbol) : Action 2 4 where + state := next + writes := fun i => if i=0 then r 0 else counterWrite.getD (r 1) + moves := fun i => if i=0 then inputMove else counterMove + +/-- State0 enters both marked intervals;1 allocates from actual input symbols; +2 rewinds the zero counter;3 halts with the input at its first marked digit. -/ +def machine : Machine where + tapes := 2 + states := 4 + initial := 0 + transition := fun s r => + match s.val with + | 0 => some (action 1 .left .right none r) + | 1 => match r (0 : Fin 2) with + | .blank => some (action 2 .stay .left none r) + | .zero | .one => some (action 1 .left .right (some .zero) r) + | 2 => match r (1 : Fin 2) with + | .blank => some (action 3 .right .stay none r) + | .zero | .one => some (action 2 .stay .left none r) + | _ => none + +def configuration (s : Fin 4) (input counter : Tape) : Configuration machine := + ⟨s,fun i => if i=(0 : Fin 2) then input else counter⟩ + +def initialConfiguration (word : List Bool) : Configuration machine := + configuration 0 ⟨word.reverse.map bitSymbol,.blank,[]⟩ Tape.blank + +def finalConfiguration (word : List Bool) : Configuration machine := + configuration 3 (BinaryCountDispatcherMarkedInput.inputTape word) + (BinaryCarryIncrement.homeTape (List.replicate word.length false)) + +private def scanInput : List Bool → List Symbol → Tape + | [], right => ⟨[],.blank,right⟩ + | b::rest, right => ⟨rest.map bitSymbol,bitSymbol b,right⟩ + +private def counterEnd (n : Nat) : Tape := + ⟨List.replicate n .zero++[.blank],.blank,[]⟩ + +private def counterRewind : Nat → List Symbol → Tape + | 0, right => ⟨[],.blank,right⟩ + | n+1, right => ⟨List.replicate n .zero++[.blank],.zero,right⟩ + +/- The accepted abstract step rule is reused verbatim. -/ +private theorem step_of_transition (m : Machine) (c : Configuration m) + (a : Action m.tapes m.states) + (h : m.transition c.state (fun i => (c.tapes i).head) = some a) : + step m c = some (Configuration.mk a.state + (fun i => ((c.tapes i).write (a.writes i)).move (a.moves i))) := by + unfold step + rw [h] + +private theorem step_action (s next : Fin 4) (input counter : Tape) + (inputMove counterMove : Move) (counterWrite : Option Symbol) + (h : machine.transition s (fun i : Fin 2 => ((configuration s input counter).tapes i).head)= + some (action next inputMove counterMove counterWrite + (fun i : Fin 2 => ((configuration s input counter).tapes i).head))) : + step machine (configuration s input counter)= + some (configuration next (input.move inputMove) + ((counter.write (counterWrite.getD counter.head)).move counterMove)) := by + refine (step_of_transition machine (configuration s input counter) _ h).trans ?_ + dsimp only [action,configuration] + apply congrArg some + apply congrArg (fun tapes : Fin 2 → Tape => (Configuration.mk next tapes : Configuration machine)) + funext i + rcases fin2 i with rfl|rfl <;> simp [Tape.write] + +private theorem start_step (remaining : List Bool) : + step machine (configuration 0 ⟨remaining.map bitSymbol,.blank,[]⟩ Tape.blank)= + some (configuration 1 (scanInput remaining [.blank]) (counterEnd 0)) := by + have h := step_action 0 1 ⟨remaining.map bitSymbol,.blank,[]⟩ Tape.blank + .left .right none (by rfl) + cases remaining <;> + simpa only [scanInput,counterEnd,Tape.blank,Tape.move,Tape.write,Option.getD_none, + List.map_nil,List.map_cons,List.replicate_zero,List.nil_append] using h + +private theorem allocate_step (b : Bool) (rest : List Bool) (right : List Symbol) (k : Nat) : + step machine (configuration 1 (scanInput (b::rest) right) (counterEnd k))= + some (configuration 1 (scanInput rest (bitSymbol b::right)) (counterEnd (k+1))) := by + have h := step_action 1 1 (scanInput (b::rest) right) (counterEnd k) + .left .right (some .zero) (by cases b <;> rfl) + cases rest <;> + simpa only [scanInput,counterEnd,Tape.move,Tape.write,Option.getD_some, + List.map_nil,List.map_cons,List.replicate_succ,List.cons_append] using h + +private theorem allocate_run (remaining : List Bool) (right : List Symbol) (k : Nat) : + run machine remaining.length (configuration 1 (scanInput remaining right) (counterEnd k))= + configuration 1 (scanInput [] (remaining.reverse.map bitSymbol++right)) + (counterEnd (k+remaining.length)) := by + induction remaining generalizing right k with + | nil => simp only [List.length_nil,run,List.reverse_nil,List.map_nil,List.nil_append,Nat.add_zero] + | cons b rest ih => + simp only [List.length_cons,run,allocate_step] + rw [ih] + simp only [List.reverse_cons,List.map_append,List.map_cons,List.map_nil,List.append_assoc, + List.singleton_append] + congr 2 + omega + +private theorem return_step (right : List Symbol) (k : Nat) : + step machine (configuration 1 (scanInput [] right) (counterEnd k))= + some (configuration 2 (scanInput [] right) (counterRewind k [.blank])) := by + have h := step_action 1 2 (scanInput [] right) (counterEnd k) .stay .left none (by rfl) + cases k <;> + simpa only [counterEnd,counterRewind,Tape.move,Tape.write,Option.getD_none, + List.replicate_zero,List.replicate_succ,List.nil_append,List.cons_append] using h + +private theorem rewind_step (input : Tape) (k : Nat) (right : List Symbol) : + step machine (configuration 2 input (counterRewind (k+1) right))= + some (configuration 2 input (counterRewind k (.zero::right))) := by + have h := step_action 2 2 input (counterRewind (k+1) right) .stay .left none (by rfl) + cases k <;> + simpa only [counterRewind,Tape.move,Tape.write,Option.getD_none, + List.replicate_zero,List.replicate_succ,List.nil_append,List.cons_append] using h + +private theorem rewind_run (input : Tape) (k : Nat) (right : List Symbol) : + run machine k (configuration 2 input (counterRewind k right))= + configuration 2 input (counterRewind 0 (List.replicate k .zero++right)) := by + induction k generalizing right with + | zero => rfl + | succ k ih => + simp only [run,rewind_step] + rw [ih] + simp only [List.replicate_succ',List.append_assoc,List.singleton_append] + +private theorem finish_step (input : Tape) (right : List Symbol) : + step machine (configuration 2 input (counterRewind 0 right))= + some (configuration 3 (input.move .right) (counterRewind 0 right)) := by + have h := step_action 2 3 input (counterRewind 0 right) .right .stay none (by rfl) + simpa only [counterRewind,Tape.move,Tape.write,Option.getD_none] using h + +/-- Exactly one zero cell per actual input symbol is allocated. Both boundary +blanks, the restored input head, and the complete counter footprint are fixed. +The elapsed run index includes the empty-input branch without a size premise. -/ +theorem allocate_run_exact (word : List Bool) : + run machine (2*word.length+3) (initialConfiguration word)=finalConfiguration word := by + have start : run machine 1 (initialConfiguration word)= + configuration 1 (scanInput word.reverse [.blank]) (counterEnd 0) := by + simp only [initialConfiguration,run,start_step] + rw [show 2*word.length+3=1+word.length+1+word.length+1 by omega] + rw [run_add machine (1+word.length+1+word.length) 1, + run_add machine (1+word.length+1) word.length, + run_add machine (1+word.length) 1,run_add machine 1 word.length,start] + have allocation := allocate_run word.reverse [.blank] 0 + simp only [List.length_reverse,List.reverse_reverse,Nat.zero_add] at allocation + rw [allocation] + simp only [run,return_step] + rw [rewind_run] + simp only [run,finish_step] + unfold finalConfiguration + have counter : counterRewind 0 (List.replicate word.length .zero++[.blank])= + BinaryCarryIncrement.homeTape (List.replicate word.length false) := by + simp only [counterRewind,BinaryCarryIncrement.homeTape,List.map_replicate,bitSymbol, + Bool.false_eq_true,if_false] + rw [counter] + cases word with + | nil => rfl + | cons b rest => rfl + +theorem final_halted (word : List Bool) : Halted machine (finalConfiguration word) := by + rfl + +theorem allocated_width (word : List Bool) : (List.replicate word.length false).length=word.length := + List.length_replicate + +end CurrentMain.BinaryCounterZeroAllocation +#print axioms CurrentMain.BinaryCounterZeroAllocation.allocate_run_exact +#print axioms CurrentMain.BinaryCounterZeroAllocation.final_halted +#print axioms CurrentMain.BinaryCounterZeroAllocation.allocated_width diff --git a/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr519/research/lean-automatic-width-count/DEPENDENCIES.json b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr519/research/lean-automatic-width-count/DEPENDENCIES.json new file mode 100644 index 0000000000..009c53f708 --- /dev/null +++ b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr519/research/lean-automatic-width-count/DEPENDENCIES.json @@ -0,0 +1,56 @@ +{ + "pr488": { + "repository": "https://github.com/jamesyc/integer-mult-bounds", + "commit": "edd3102b415df5b9d6f633ac0a4dedcf69c58525", + "pull_request": "https://github.com/CrocSwap/integer-mult-bounds/pull/488", + "package_path": "research/lean-binary-input-preparation", + "merge_assumed": false, + "files": [ + { + "module": "IntegerConvolution", + "repository_path": "research/lean-binary-input-preparation/Lean/IntegerConvolution.lean", + "sha256": "0bc86f2fa8e68f39df77be603d2a9634bc008745093286903105378ab45938ea", + "bytes": 2055 + }, + { + "module": "FixedTapeMachine", + "repository_path": "research/lean-binary-input-preparation/Lean/FixedTapeMachine.lean", + "sha256": "92dadedc9f6e23d12633549b53ca8f917360e4fedac0b64a58d18feea741a5ed", + "bytes": 4523 + } + ] + }, + "pr511": { + "repository": "https://github.com/jamesyc/integer-mult-bounds", + "commit": "79f7c03c7f820ab89955b75ef239cbaccc627e6e", + "pull_request": "https://github.com/CrocSwap/integer-mult-bounds/pull/511", + "package_path": "research/lean-binary-count-dispatcher", + "merge_assumed": false, + "files": [ + { + "module": "CarryTape", + "repository_path": "research/lean-binary-count-dispatcher/CarryTape.lean", + "sha256": "20d13d9d2da74452e45c0a175b643556615ba14187bf8fb0e4393e44842c17a5", + "bytes": 8348 + }, + { + "module": "CarryTapePass", + "repository_path": "research/lean-binary-count-dispatcher/CarryTapePass.lean", + "sha256": "680b5d16736880ac6a02f27e9503e1cc01479bb2b35bb7546d9108dcb4b4ef2b", + "bytes": 5662 + }, + { + "module": "BinaryCarryIncrement", + "repository_path": "research/lean-binary-count-dispatcher/BinaryCarryIncrement.lean", + "sha256": "b0f639159e2169c75e6d7a13663adee5107648a32b7ff9203f92792e31012dce", + "bytes": 9032 + }, + { + "module": "BinaryCountDispatcher", + "repository_path": "research/lean-binary-count-dispatcher/BinaryCountDispatcher.lean", + "sha256": "ec24af9483d59ce3248802378218d4b478490aa2458e136880f36e7f49356e93", + "bytes": 14544 + } + ] + } +} diff --git a/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr519/research/lean-automatic-width-count/LICENSE b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr519/research/lean-automatic-width-count/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr519/research/lean-automatic-width-count/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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Apache-2.0. +Developed with OpenAI model assistance. No personal byline is added. + +This contribution composes the pinnedPR181complex supplier and the actual +PR168v4bit word with completed entrance banks and recomputes the full paid +finite bound. All upstream author attribution and assistance disclosures +remain in UPSTREAM-NOTICE.md and the immutable archive. Copied source files +retain their author notices. No global optimality or exclusive priority +is claimed; the inherited all-size interfaces remain explicit. diff --git a/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr519/research/lean-automatic-width-count/PROVENANCE.json b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr519/research/lean-automatic-width-count/PROVENANCE.json new file mode 100644 index 0000000000..c92418fb51 --- /dev/null +++ b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr519/research/lean-automatic-width-count/PROVENANCE.json @@ -0,0 +1,106 @@ +{ + "status": "Exact accepted source closure and isolated nine-source package replay PASS; final replay-status author confirmation recorded separately.", + "source_base_commit": "12a4934d15006e8c10f9b2264f13f8f341be802b", + "included_sources": [ + { + "module": "BinaryCountDispatcherMarkedInput", + "source_sha256": "b7f0cecb69194b8d851037e8321e245dc383c62e3e2475c9d4508d29390191cc", + "bytes": 10257, + "package_file": "BinaryCountDispatcherMarkedInput.lean" + }, + { + "module": "BinaryCounterZeroAllocation", + "source_sha256": "5cf3fdfcd6c6a6cefa89b9a83dc678b6f40d9a608c318334ae92a66d25ea7477", + "bytes": 9595, + "package_file": "BinaryCounterZeroAllocation.lean" + }, + { + "module": "BinaryAutomaticWidthCount", + "source_sha256": "5dcf4ec74f08d9662738db413d144e16f4b555e56f29e0846ad5c88726420154", + "bytes": 10124, + "package_file": "BinaryAutomaticWidthCount.lean" + } + ], + "external_dependencies": [ + { + "pr": "https://github.com/CrocSwap/integer-mult-bounds/pull/511", + "repository": "https://github.com/jamesyc/integer-mult-bounds", + "commit": "79f7c03c7f820ab89955b75ef239cbaccc627e6e", + "package_path": "research/lean-binary-count-dispatcher", + "files": [ + { + "module": "CarryTape", + "source_sha256": "20d13d9d2da74452e45c0a175b643556615ba14187bf8fb0e4393e44842c17a5", + "bytes": 8348, + "repository_file": "CarryTape.lean" + }, + { + "module": "CarryTapePass", + "source_sha256": "680b5d16736880ac6a02f27e9503e1cc01479bb2b35bb7546d9108dcb4b4ef2b", + "bytes": 5662, + "repository_file": "CarryTapePass.lean" + }, + { + "module": "BinaryCarryIncrement", + "source_sha256": "b0f639159e2169c75e6d7a13663adee5107648a32b7ff9203f92792e31012dce", + "bytes": 9032, + "repository_file": "BinaryCarryIncrement.lean" + }, + { + "module": "BinaryCountDispatcher", + "source_sha256": "ec24af9483d59ce3248802378218d4b478490aa2458e136880f36e7f49356e93", + "bytes": 14544, + "repository_file": "BinaryCountDispatcher.lean" + } + ], + "merge_assumed": false + }, + { + "pr": "https://github.com/CrocSwap/integer-mult-bounds/pull/488", + "repository": "https://github.com/jamesyc/integer-mult-bounds", + "commit": "edd3102b415df5b9d6f633ac0a4dedcf69c58525", + "package_path": "research/lean-binary-input-preparation", + "files": [ + { + "module": "IntegerConvolution", + "source_sha256": "0bc86f2fa8e68f39df77be603d2a9634bc008745093286903105378ab45938ea", + "bytes": 2055, + "repository_file": "Lean/IntegerConvolution.lean" + }, + { + "module": "FixedTapeMachine", + "source_sha256": "92dadedc9f6e23d12633549b53ca8f917360e4fedac0b64a58d18feea741a5ed", + "bytes": 4523, + "repository_file": "Lean/FixedTapeMachine.lean" + } + ], + "merge_assumed": false + } + ], + "project_context": { + "kappa": "90446448750933/125000000000000000", + "decimal": "0.000723571590007464", + "selected_result_sha256": "df836c6d34509e980d067bd5678489c968bc6e329af9dd82c6207abf6443da89", + "certificate_sha256": "6a457a34b4db57417e5b253cf1c169da2bd6aff4c21363a31fd85dc931d49589", + "scope": "Conditional source parameter only; no multiplier or kappa theorem from this package." + }, + "prior_work": "PR64 richer generic counter correctness, first-completion and amortized results; this chunk adds the explicit-model allocation/count interface. Direct amortization transport remains open.", + "acceptance_sha256": "b8942b47c6d3b99003009d0a12c87dc39fdd81e1228ff8577e0516b2fbb4b937", + "independent_terminal_review_sha256": "9950605fac595902eee3999764ae109cd41c94256f66303784afb400d9581cce", + "scope": { + "modules_included": 3, + "external_sources": 6, + "closure": 9, + "source_bytes": 74140, + "new_source_bytes": 29976, + "new_probes": 13, + "closure_probes": 49 + }, + "manifest_sha256": "b6e5907567f8fb8017d0c9dc73924679c9c883a4fefe45d012e75d3470cafaea", + "dependencies_manifest_sha256": "08541480132fd1e128b7d5ca5ce47f40fa4e931d5c589abaa20f6aa89b98731b", + "selected_result_file": "selected-result.json", + "isolated_replay": { + "file": "REPLAY_SUMMARY.json", + "sha256": "d080beb005dba93f2f2a4eb3c9838486b0d67a5474fb8cd70608b55edd49dc8c" + } +} diff --git a/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr519/research/lean-automatic-width-count/README.md b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr519/research/lean-automatic-width-count/README.md new file mode 100644 index 0000000000..7d46d9bc1e --- /dev/null +++ b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr519/research/lean-automatic-width-count/README.md @@ -0,0 +1,51 @@ +# Automatic-width binary counting in Lean + +These three modules extend the exact binary dispatcher interface from PR511. A ten-state, two-tape, three-symbol machine allocates a zero counter from actual input symbols and then counts the word. The transition table receives neither the word length nor a supplied counter width. The final stored natural value is the input length n. + +## Exact checked contract + +For every finite Boolean word, the input initially has `left = word.reverse.map bitSymbol`, a blank head and an empty right list. This is the represented blank immediately to the right of the whole word. The second tape is pristine `Tape.blank`. + +The final control state is 9. The input has `left = word.reverse.map bitSymbol ++ [blank]`, a blank head and an empty right list. The counter is at its home blank, with an n-bit little-endian result followed by its represented terminal blank. The result has width n and natural value n. Both tapes' complete finite-list footprints are specified; visited blank cells are not silently erased or identified. + +`count_run` gives a run index at most `(CarryTape.pass n (List.replicate n false)).2.reads + 4*n + 4` reaching this configuration. `final_halted` proves the endpoint is halted. This is an upper bound, not a first-completion claim or a linear amortized bound. The empty word is included: no size or capacity premise is supplied, and the zero-width result has value zero. + +The components are: + +- `BinaryCountDispatcherMarkedInput`: a same-machine representation simulation for the exact home/terminal-blank input footprint, reusing the accepted dispatcher count theorem. +- `BinaryCounterZeroAllocation`: a four-state allocation scan reaching the marked input and n zero counter cells at run index `2*n+3`, including three steps for empty input. +- `BinaryAutomaticWidthCount`: successful-prefix lifts of allocation and counting. Allocator state 3 is identified with the renamed dispatcher initial state, so there is no extra bridge transition. Existing zero-multiplication and core modular arithmetic prove the stored value n without a capacity assumption or a new arithmetic induction. + +## Dependencies and reuse + +The four dispatcher/carry sources are exact external dependencies from PR511 at commit `79f7c03c7f820ab89955b75ef239cbaccc627e6e`. The two foundational sources are exact external dependencies from PR488 at commit `edd3102b415df5b9d6f633ac0a4dedcf69c58525`. Neither PR is assumed merged. The new package includes only the three additions and retains the original module names. + +PR64 already provides richer generic ripple-counter, first-completion and amortized arithmetic results. Binary counting and increment are not claimed as new algorithms here. The additional checked result is this explicit finite-control allocation/count composition, its full tape endpoint and exact value, in the retained `FixedTapeMachine` model. The direct PR64-to-current pass-receipt amortization bridge remains open. + +An input4 work copy in slot 2 or 3 has the required right-blank form with `word = (pad n x).reverse` or the corresponding y word. Its slot 0/1 original-input footprints are different. Actual four-tape control composition and the supply of a pristine counter tape still require their own proof. Compact counter normalization, the source's one-string prelude, radix grouping and Plan/Budget realization are also outside this package. + +## Validation + +All nine modules in the exact dependency closure have current Lean4.21.0 checks. The three new roots print 13 standard-axiom probes; the complete closure prints 49. The automatic-width run proof uses `Classical.choice` together with `propext` and `Quot.sound`. No admitted proof or extra axiom is accepted. The isolated nine-source package replay passed in 11.7677 compiler seconds and 0.00378 queue seconds, with peak virtual memory 3,074,072,576 bytes. All nine object hashes match the accepted checks; all 49 complete theorem/axiom outputs match after whitespace normalization. See `REPLAY_SUMMARY.json`. + +## Author-checked conditional project context + +At source base `12a4934d15006e8c10f9b2264f13f8f341be802b`, the selected conditional project value is κ=`90446448750933/125000000000000000`=`0.000723571590007464`. The captured selected-result file and its linked certificate agree. This context retains the all-size compiler, weighted/common-ancestor chart, restored-row, selector/routing, prime-supply, precision/recovery, complex-symbolic and analytic-transfer obligations. These generic machine modules do not discharge those obligations or prove a multiplication or κ theorem. + +## Reproduce the isolated package + +Use Linux, Python 3 and the official Lean 4.21.0 distribution. Obtain separate source worktrees at the two exact dependency commits. For example: + +```sh +git clone https://github.com/jamesyc/integer-mult-bounds.git dependencies +git -C dependencies worktree add --detach ../input-foundation edd3102b415df5b9d6f633ac0a4dedcf69c58525 +git -C dependencies worktree add --detach ../dispatcher-foundation 79f7c03c7f820ab89955b75ef239cbaccc627e6e +python3 check.py --lean /path/to/lean-4.21.0-linux/bin/lean \ + --input-foundation-root /path/to/input-foundation/research/lean-binary-input-preparation \ + --dispatcher-foundation-root /path/to/dispatcher-foundation/research/lean-binary-count-dispatcher \ + --build-dir /tmp/automatic-width-count-check +``` + +The output directory must not already exist. The checker itself is offline: it validates all three included and six external source hashes and import order, then compiles exactly nine modules with only the fresh output directory and the installed Lean core on its search path. No Mathlib or Python package installation is needed. The resource audit uses Linux `/proc`. Per-module hard limits are60seconds and4GiB address space; a successful check over40seconds or3.5GiB stops for review. No compiled objects are shipped. + +`DEPENDENCIES.json` pins both unmerged dependency packages, `MANIFEST.json` fixes the exact compile order, and `ACCEPTED_CHECKS.json` records prior accepted objects and all49 whitespace-normalized complete axiom statements. The original attribution and Apache-2.0 license are retained. Prior work and dependencies are [PR64](https://github.com/CrocSwap/integer-mult-bounds/pull/64), [PR488](https://github.com/CrocSwap/integer-mult-bounds/pull/488) and [PR511](https://github.com/CrocSwap/integer-mult-bounds/pull/511). diff --git a/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr519/research/lean-automatic-width-count/REPLAY_SUMMARY.json b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr519/research/lean-automatic-width-count/REPLAY_SUMMARY.json new file mode 100644 index 0000000000..81922de71b --- /dev/null +++ b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr519/research/lean-automatic-width-count/REPLAY_SUMMARY.json @@ -0,0 +1,231 @@ +{ + "status": "PASS", + "kind": "Isolated flat nine-source automatic-width count package check", + "started_utc": "2026-10-11T23:25:39.026734+00:00", + "finished_utc": "2026-10-11T23:25:50.812476+00:00", + "manifest_sha256": 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"queue_seconds": 0.0003537209995556623, + "peak_vm_bytes": 2603061248, + "status": "PASS", + "receipt_sha256": "808dfb07138c9f991871d65df3596b70fdcfa183b8aeea31cb6db58804009b4a", + "axiom_output": [ + "'CurrentMain.BinaryCountDispatcher.count_run' depends on axioms: [propext, Quot.sound]", + "'CurrentMain.BinaryCountDispatcher.final_halted' depends on axioms: [propext, Quot.sound]", + "'CurrentMain.BinaryCountDispatcher.counter_length' depends on axioms: [propext]", + "'CurrentMain.BinaryCountDispatcher.counter_value' depends on axioms: [propext, Quot.sound]" + ], + "object_matches_accepted": true, + "axioms_match_accepted": true + }, + { + "module": "BinaryCountDispatcherMarkedInput", + "source_sha256": "b7f0cecb69194b8d851037e8321e245dc383c62e3e2475c9d4508d29390191cc", + "object_sha256": "bd14ae558577205f11c534c7ee5264ec2f8c6f321c92b5b08521b221470f9346", + "log_sha256": "3067d6a5e9cbfe3ff1a19435b2e7392f68480ec46b5eefae9f998f49943a0dd8", + "started_utc": 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"48910f8b0674b728aaff6eba2463df006822795b24402747f3512c24636e1d72", + "log_sha256": "90de35142ca4dca8c3f4cd678abd99c728ab2ceb197abc0e5b14d2e566d3005c", + "started_utc": "2026-10-11T23:25:48.205516+00:00", + "finished_utc": "2026-10-11T23:25:49.446948+00:00", + "compile_seconds": 1.2411628190002375, + "queue_seconds": 0.00034484999923733994, + "peak_vm_bytes": 3074072576, + "status": "PASS", + "receipt_sha256": "fc20097a24531818b00323cc52d9b74a4ef49a252c8e8ae98f5d17431119008f", + "axiom_output": [ + "'CurrentMain.BinaryCounterZeroAllocation.allocate_run_exact' depends on axioms: [propext, Quot.sound]", + "'CurrentMain.BinaryCounterZeroAllocation.final_halted' depends on axioms: [propext]", + "'CurrentMain.BinaryCounterZeroAllocation.allocated_width' depends on axioms: [propext]" + ], + "object_matches_accepted": true, + "axioms_match_accepted": true + }, + { + "module": "BinaryAutomaticWidthCount", + "source_sha256": "5dcf4ec74f08d9662738db413d144e16f4b555e56f29e0846ad5c88726420154", + "object_sha256": "2084a5516a72c995fa40f4f424ef2f94f88a0dbaff3fcbdaad153ff24470a503", + "log_sha256": "185599ae81bb180e4452e3984dd46a2e419d85fc00f9e3196b88f21b00efcf3f", + "started_utc": "2026-10-11T23:25:49.448408+00:00", + "finished_utc": "2026-10-11T23:25:50.811183+00:00", + "compile_seconds": 1.3625119050011563, + "queue_seconds": 0.0004450550004548859, + "peak_vm_bytes": 1731022848, + "status": "PASS", + "receipt_sha256": "a378dba0d996aa4dea4e1d83c13de17cf5b6a7cdff79683879319908760f1d96", + "axiom_output": [ + "'CurrentMain.BinaryAutomaticWidthCount.count_run' depends on axioms: [propext, Classical.choice, Quot.sound]", + "'CurrentMain.BinaryAutomaticWidthCount.final_halted' depends on axioms: [propext, Quot.sound]", + "'CurrentMain.BinaryAutomaticWidthCount.final_input' depends on axioms: [propext, Quot.sound]", + "'CurrentMain.BinaryAutomaticWidthCount.final_counter' depends on axioms: [propext, Quot.sound]", + "'CurrentMain.BinaryAutomaticWidthCount.counter_width' depends on axioms: [propext]", + "'CurrentMain.BinaryAutomaticWidthCount.counter_value' depends on axioms: [propext, Quot.sound]" + ], + "object_matches_accepted": true, + "axioms_match_accepted": true + } + ] +} diff --git a/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr519/research/lean-automatic-width-count/SHA256SUMS b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr519/research/lean-automatic-width-count/SHA256SUMS new file mode 100644 index 0000000000..60e2fbb490 --- /dev/null +++ b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr519/research/lean-automatic-width-count/SHA256SUMS @@ -0,0 +1,15 @@ +d8b2be446a25e66080bfa27d5ea1ea9d5beebf5f8287a77f0a5a7fc11632320a ACCEPTED_CHECKS.json +859a2a77635839284dba692667cb671734d9ae8a83192cb7981310351dc755e7 AUTHOR_CHECK.json +5dcf4ec74f08d9662738db413d144e16f4b555e56f29e0846ad5c88726420154 BinaryAutomaticWidthCount.lean +b7f0cecb69194b8d851037e8321e245dc383c62e3e2475c9d4508d29390191cc BinaryCountDispatcherMarkedInput.lean +5cf3fdfcd6c6a6cefa89b9a83dc678b6f40d9a608c318334ae92a66d25ea7477 BinaryCounterZeroAllocation.lean +08541480132fd1e128b7d5ca5ce47f40fa4e931d5c589abaa20f6aa89b98731b DEPENDENCIES.json +c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4 LICENSE +b6e5907567f8fb8017d0c9dc73924679c9c883a4fefe45d012e75d3470cafaea MANIFEST.json +2cf3c6e1aaaed287d44d001f55cfd74393c9d9e773e3ea0e3fb359d885b4f6b5 NOTICE.source.txt +9a07161866d931c2c7a34225321a7a38180d500680e771e428260a54e3b43f36 PROVENANCE.json +3ea8cada254ecf3cb9760ae310cf2f12ce90f1a66dee07e516517ae2efa186b9 README.md +d080beb005dba93f2f2a4eb3c9838486b0d67a5474fb8cd70608b55edd49dc8c REPLAY_SUMMARY.json +d0349ec65a7d7d44d9191202f92395894a8ec817195f2ffc7b63d915663f70c8 check.py +d24fed434d3b13adfaab57724a0a7f270ea8bf1c818b5ae5cf25cbce24dd685c lean-toolchain +df836c6d34509e980d067bd5678489c968bc6e329af9dd82c6207abf6443da89 selected-result.json diff --git a/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr519/research/lean-automatic-width-count/check.py b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr519/research/lean-automatic-width-count/check.py new file mode 100644 index 0000000000..721f3e2970 --- /dev/null +++ b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr519/research/lean-automatic-width-count/check.py @@ -0,0 +1,68 @@ +#!/usr/bin/env python3 +"""Offline nine-source replay using six exact PR488/PR511 dependencies.""" +import argparse,fcntl,hashlib,importlib.util,json,os,re,resource,signal,subprocess,time +from pathlib import Path +from datetime import datetime,timezone +ROOT=Path(__file__).resolve().parent +sha=lambda p:hashlib.sha256(Path(p).read_bytes()).hexdigest() +now=lambda:datetime.now(timezone.utc).isoformat() +def limits(): + resource.setrlimit(resource.RLIMIT_AS,(4*1024**3,4*1024**3)) + resource.setrlimit(resource.RLIMIT_CPU,(60,62));os.setsid() +def main(): + ap=argparse.ArgumentParser();ap.add_argument('--lean',required=True);ap.add_argument('--input-foundation-root',required=True,help='Exact PR488 input-preparation package.');ap.add_argument('--dispatcher-foundation-root',required=True,help='Exact PR511 count-dispatcher package.');ap.add_argument('--build-dir',default='.build');ap.add_argument('--slot-service',help='Optional existing FIFO slot service exposing acquire(); does not change Lean inputs.');ap.add_argument('--lean-sha256');args=ap.parse_args() + assert Path('/proc/self/status').is_file(),'Linux /proc is required for the stated memory review' + roots={'package':ROOT,'pr488':Path(args.input_foundation_root).resolve(),'pr511':Path(args.dispatcher_foundation_root).resolve()} + assert all(p.is_dir() for p in roots.values()) + source_for=lambda row:roots[row['origin']]/row['file'] + lean=Path(args.lean).resolve();assert lean.is_file() + if args.lean_sha256:assert sha(lean)==args.lean_sha256 + version=subprocess.check_output([str(lean),'--version'],text=True).strip();assert re.search(r'\b4\.21\.0\b',version),version + manifest=json.loads((ROOT/'MANIFEST.json').read_text());rows=manifest['compile_order'];names={r['module']for r in rows};seen=set() + assert len(rows)==9 and manifest['source_bytes']==74140 + assert sum(r['origin']=='pr488' for r in rows)==2 and sum(r['origin']=='pr511' for r in rows)==4 and sum(r['origin']=='package' for r in rows)==3 + dependencies=json.loads((ROOT/'DEPENDENCIES.json').read_text()) + expected_commits={'pr488':'edd3102b415df5b9d6f633ac0a4dedcf69c58525','pr511':'79f7c03c7f820ab89955b75ef239cbaccc627e6e'} + assert set(dependencies)==set(expected_commits) + for alias,dependency in dependencies.items(): + assert dependency['commit']==expected_commits[alias] + for dep in dependency['files']: + row=next(r for r in rows if r['module']==dep['module']);assert row['origin']==alias and row['sha256']==dep['sha256'] and row['bytes']==dep['bytes'] + for row in rows: + p=source_for(row);assert p.is_file()and sha(p)==row['sha256']and p.stat().st_size==row['bytes'],row['module'] + imports=[] + for line in p.read_text().splitlines(): + m=re.match(r'^import\s+(.+)$',line) + if m:imports.extend(m[1].split('--',1)[0].split()) + assert imports==row['imports'];assert set(imports)-{'Lean'}<=seen;seen.add(row['module']) + build=Path(args.build_dir);build=build if build.is_absolute()else ROOT/build;build.mkdir(parents=True,exist_ok=False);(build/'logs').mkdir();(build/'receipts').mkdir() + service=None + if args.slot_service: + spec=importlib.util.spec_from_file_location('existing_lean_slot_service',Path(args.slot_service).resolve());service=importlib.util.module_from_spec(spec);spec.loader.exec_module(service) + env=dict(os.environ);env['LEAN_PATH']=str(build);env['LEAN_EXTRA_PATHS']='';env.pop('LEAN_SYSROOT',None);env['MIMALLOC_ARENA_RESERVE']='64MiB' + outcome={'started_utc':now(),'manifest_sha256':sha(ROOT/'MANIFEST.json'),'dependencies_manifest_sha256':sha(ROOT/'DEPENDENCIES.json'),'dependency_commits':expected_commits,'lean_version':version,'lean_binary_sha256':sha(lean),'external_library_paths':[],'source_search_path':str(build),'status':'RUNNING','receipts':[]};(build/'REPLAY_RESULT.json').write_text(json.dumps(outcome,indent=2)+'\n') + for row in rows: + requested=time.monotonic();slot=None;handle=None;handles=[] + if service:slot,handle,handles=service.acquire('isolated_automatic_width_count_package:'+row['module']) + queue=time.monotonic()-requested;started=time.monotonic();start_utc=now();source=source_for(row);output_path=build/(row['module']+'.olean');log=build/'logs'/(row['module']+'.log');peak=0;samples=0;timed_out=False + try: + assert sha(source)==row['sha256'];cmd=[str(lean),'-s','65536','-j','1','-o',str(output_path),source.name] + proc=subprocess.Popen(cmd,cwd=source.parent,env=env,stdout=subprocess.PIPE,stderr=subprocess.STDOUT,preexec_fn=limits) + while True: + try: + text=Path(f'/proc/{proc.pid}/status').read_text();m=re.search(r'^VmPeak:\s+(\d+)',text,re.M);peak=max(peak,int(m[1])*1024 if m else 0);samples+=1 + except OSError:pass + remaining=60-(time.monotonic()-started) + if remaining<=0: + timed_out=True;os.killpg(proc.pid,signal.SIGKILL);data,_=proc.communicate();break + try:data,_=proc.communicate(timeout=min(.1,remaining));break + except subprocess.TimeoutExpired:pass + elapsed=time.monotonic()-started;log.write_bytes(data);text=data.decode(errors='replace');forbidden=('sorryAx'in text or "declaration uses 'sorry'"in text) + passed=proc.returncode==0 and not timed_out and not forbidden and output_path.is_file()and sha(source)==row['sha256'];review=passed and(elapsed>40 or peak>int(3.5*1024**3)) + rec={'module':row['module'],'source_sha256':row['sha256'],'status':'PASS'if passed else'FAIL','review_stop':review,'exit_code':proc.returncode,'timed_out':timed_out,'started_utc':start_utc,'finished_utc':now(),'compile_seconds':elapsed,'queue_seconds':queue,'peak_vm_bytes':peak,'samples':samples,'slot':slot,'log_sha256':sha(log),'object_sha256':sha(output_path)if passed else None,'imports':row['imports'],'axiom_output':[s for s in text.splitlines()if'depends on axioms:'in s or'does not depend on any axioms'in s]};rp=build/'receipts'/(row['module']+'.json');rp.write_text(json.dumps(rec,indent=2)+'\n');outcome['receipts'].append({'module':row['module'],'receipt_sha256':sha(rp),'status':rec['status']});outcome['status']='REVIEW_STOP'if review else('RUNNING'if passed else'FAIL');(build/'REPLAY_RESULT.json').write_text(json.dumps(outcome,indent=2)+'\n');print(json.dumps(rec),flush=True) + if not passed or review:return 2 + finally: + if handle:fcntl.flock(handle,fcntl.LOCK_UN) + for h in handles:h.close() + outcome['status']='PASS';outcome['finished_utc']=now();outcome['modules']=len(outcome['receipts']);(build/'REPLAY_RESULT.json').write_text(json.dumps(outcome,indent=2)+'\n');print('PASS exact isolated9-module automatic-width closure',flush=True);return 0 +if __name__=='__main__':raise SystemExit(main()) diff --git a/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr519/research/lean-automatic-width-count/lean-toolchain b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr519/research/lean-automatic-width-count/lean-toolchain new file mode 100644 index 0000000000..980709bbba --- /dev/null +++ b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr519/research/lean-automatic-width-count/lean-toolchain @@ -0,0 +1 @@ +leanprover/lean4:v4.21.0 diff --git a/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr519/research/lean-automatic-width-count/selected-result.json b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr519/research/lean-automatic-width-count/selected-result.json new file mode 100644 index 0000000000..af3efd2f01 --- /dev/null +++ b/research/lean-multi-host-source/review-receipts/external-overlap/raw/pr519/research/lean-automatic-width-count/selected-result.json @@ -0,0 +1,33 @@ +{ + "status": "Published on main: maintainer-reviewed conditional construction", + "kappa": "90446448750933/125000000000000000", + "decimal": "0.000723571590007464", + "source_prs": [ + 279, + 276, + 244, + 234, + 209, + 197, + 237, + 200, + 193, + 168, + 144 + ], + "source_manifest": "research/five-stage-gen4-banks/MANIFEST.json", + "certificate": "research/community-pr279-audit/certificate.json", + "certificate_sha256": "6a457a34b4db57417e5b253cf1c169da2bd6aff4c21363a31fd85dc931d49589", + "proof": "research/five-stage-gen4-banks/PROOF.md", + "proof_supplements": { + "research/five-stage-gen4-banks/BANK-PROOF.md": "bbc328e05848a211c981288514380a4ba12fddaed16c9d23328b5764502be411" + }, + "review": "docs/research/community-pr279-review.md", + "validation": "docs/research/community-pr279-integration.json", + "reproduce": "make gen4-bank-verify", + "scope": "Conditional on retained all-size compiler, weighted/common-ancestor chart, restored rows, selectors/routing, prime supply, precision/recovery, complex symbolic correctness and analytic transfer; finite replay and written review, not a full formal multiplication theorem.", + "previous_kappa": "330942774629799/500000000000000000", + "previous_certificate": "research/coordinated-frames-and-entrance-banks/certificate.json", + "previous_audited_kappa": "710046193349537/1000000000000000000", + "audited_source_head": "4d8c31eec7ae618645cb058101cb4e72a97268d3" +} diff --git a/research/lean-multi-host-source/review-receipts/external-overlap/recent.json b/research/lean-multi-host-source/review-receipts/external-overlap/recent.json new file mode 100644 index 0000000000..73478c6ed3 --- /dev/null +++ b/research/lean-multi-host-source/review-receipts/external-overlap/recent.json @@ -0,0 +1 @@ +[{"url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/pulls/516","id":4823258326,"node_id":"PR_kwDOU-508s8AAAABH30U1g","html_url":"https://github.com/CrocSwap/integer-mult-bounds/pull/516","diff_url":"https://github.com/CrocSwap/integer-mult-bounds/pull/516.diff","patch_url":"https://github.com/CrocSwap/integer-mult-bounds/pull/516.patch","issue_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/issues/516","number":516,"state":"open","locked":false,"title":"Lemma A of #484: the realization of paid wrappers and spectators, proved in Lean 4","user":{"login":"DreamingOfClouds","id":173691639,"node_id":"U_kgDOClpS9w","avatar_url":"https://avatars.githubusercontent.com/u/173691639?v=4","gravatar_id":"","url":"https://api.github.com/users/DreamingOfClouds","html_url":"https://github.com/DreamingOfClouds","followers_url":"https://api.github.com/users/DreamingOfClouds/followers","following_url":"https://api.github.com/users/DreamingOfClouds/following{/other_user}","gists_url":"https://api.github.com/users/DreamingOfClouds/gists{/gist_id}","starred_url":"https://api.github.com/users/DreamingOfClouds/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/DreamingOfClouds/subscriptions","organizations_url":"https://api.github.com/users/DreamingOfClouds/orgs","repos_url":"https://api.github.com/users/DreamingOfClouds/repos","events_url":"https://api.github.com/users/DreamingOfClouds/events{/privacy}","received_events_url":"https://api.github.com/users/DreamingOfClouds/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"\nLemma A of #484 has two parts:\n* **an exact part,** which #484 checks numerically: `S_E = L_E (C_[w] ⊗ I) R_E` on every entrance frame;\n* **a realization part,** which #484 assumed from #458 §3: paid wrappers around a whole invocation, with nothing else acting meanwhile, leave the host with its residual and its spectators untouched.\n\nThis PR proves the realization part as a general theorem. It also proves the asynchronous variant that #505 needs.\n* Every hypothesis is checked on #484's emitted words.\n* The owner and window hypotheses are also checked on the template from a replay of #505.\n\nThe PR is stacked on #509 (→ #484 → #442). The new commits here are f71a4bb, 871b1c5 and 1c6b6ff. They touch only `research/e8-lemma-a-lean/`. The package reuses the Lemma G package's event semantics through a Lake path dependency.\n\n### Model and coverage\n\n**Units are physical streams `(family F, cover class g ∈ O(73,2))`, as in #442 §2.** Sources:\n* the template's `cover`, `loop_order` and `route_semantics` (\"physical cover class d*Pi(slot)^(-1)\");\n* #442's idle-axis hosting: \"physical stream (F, g)\", \"owned by stream (F, d·σ⁻¹)\", and \"Distinct slots of one invocation have distinct σ, so distinct physical classes for every d … sequential, exactly as the parent's banks are co-owned sequentially by different cover classes\";\n* #458 §3, only for the convention `g = dσ⁻¹` and \"for a fixed family, d → g is a bijection\".\n\n**Lemma A is proved in #442's stream model. That the model describes the machine is inherited from #442, like the compiler.**\n\n#458 §3 states the one-helper rule as required, and rejects same-call packing into disjoint slots. Its case is the single-owner calls. The sharing calls rest on #442's model, which needs atomic invocations.\n\nAt cover class `d`, register `r` lives on the stream `(F_r, d·σ_r⁻¹)`. The theorem needs one owner per stream. That holds whenever registers sharing a family have pairwise disjoint footprints, which covers:\n* one helper per family (#458's case, #484);\n* #433's pure-bank slots and #442's hosted slots;\n* #471's and #500's footprint rule.\n\n**On #484's words, every call of all four words satisfies the hypotheses:**\n\n| word | calls with one register per family | other calls (disjoint footprints on a shared family) | hosted blocks |\n| --- | --- | --- | --- |\n| headline | 72/72 | — | 39,792 |\n| gauge80 | 40/72 | 32 (#433 slots) | 38,112 |\n| kernel79 | 56/72 | 16 (#433 slots) | 37,720 |\n| anchor | — | 72 (#442 slots) | 34,560 |\n\nEvery hosted block lies inside its window.\n\nThe anchor is not pinned to EXPECTED and has no wrappers. Its (O′) and windows are checked by this package's checkers alone.\n\n### What is proved (Lean 4.21.0 + Mathlib v4.21.0, the pin of `formal/lean` on main)\n\n```lean\ntheorem LemmaA.lemmaA_streams ... (hdis : ∀ r r', r ≠ r' → fam r = fam r' → Disjoint (fp (σ r)) (fp (σ r')))\n (hrec : RecipesExact T rec es) (hw : WellLabelled es l) (hS : ∀ s, S es j s = if s = j then 1 else 0)\n (hfac : ∀ v, T (labRun es l j) ((T (l j)).symm v) = Cj.rTensor B v) :\n realizeRun ⟨streamOwner fam σ d, chart⟩ rec es y (streamOwner fam σ d j) =\n (chart j).symm (Cj.rTensor B (chart j (y (streamOwner fam σ d j))))\n```\n\nThe theorem holds over any commutative semiring, for any modules, charts and number of stages. Suppose:\n* registers sharing a family have pairwise disjoint footprints;\n* the invocation is well labelled, with exact recipes;\n* it gives the helper a unit row (Lemma G);\n* its block factors as `C ⊗ id`.\n\nThe last hypothesis is read in Lemma G's extended labels, where `T_{λ¹}T_{λ⁰}⁻¹ = L_E⁻¹ S_E R_E⁻¹`. #484's I-helper check verifies it, and Lemma G's `check_extended_labels.py` (run here) verifies the reading.\n\nThen, after the complete invocation, the helper's stream holds `chart⁻¹ (C ⊗ id) chart` of its own initial value. **The spectators are untouched.**\n\nThe other Lean results:\n* **Streams.** `streamOwner_injective(_of_disjoint)`: distinct routes, or disjoint footprints, give distinct streams. `sweep_unique`: the cover sweep visits each stream once per route.\n* **Realization.** `realize_run`: with one owner per unit, the physical execution read through the charts is the local run. `one_owner_needed`: within the model, sharing a unit already breaks this with a single event.\n* **No other actor.** `whole_invocation`, `endpoint_indep`, `lemmaA_piece`: the invocation acts on the helper's unit as a single-unit piece that no other unit reads.\n* **Pending blocks.** `pieces_commute` and `pieces_product`: pieces on disjoint blocks of one pending child commute and multiply back to the child.\n* **#505's variant.** `lemmaA_async`, `async_window` and `gather`: a borrowed piece moves to its child's deadline past every commuting action, and the gathered pieces give the child. This needs three scheduling conditions:\n * the window;\n * disjoint blocks;\n * whole invocations with distinct owners.\n\nThere is no instance enumeration and no `decide`/`native_decide`. `#print axioms` reports only `propext`, `Classical.choice` and `Quot.sound` for all 24 named results. `verify.py` builds this package and the Lemma G package from source, scans both for `sorry`/`axiom`/`native_decide`, and checks every axiom report.\n\n### What is checked\n\n| hypothesis | check | result |\n| --- | --- | --- |\n| exact factorization, extended labels | #484 `adapters_gk.py` and I-helper; Lemma G `check_extended_labels.py` | 16 headline frames; helpers 122/122, 80/80 and 79/79; 0 tag violations |\n| unit helper rows, exact recipes, well labelled | Lemma G package H1–H3 | 0 violations |\n| one owner per stream; centre copies in distinct private slots; atomic calls (the template's declared `loop_order`) | **new** `code/check_owners.py` (3 mutants rejected) | 0 violations on all four words |\n| windows, disjoint blocks, family-group windows disjoint | **new** `code/check_windows.py`, written independently of #484's and #505's audits (2 mutants rejected) | 0 violations on all four words |\n\n### #505 and #512\n\n**#505.** I replayed #505's own `verify.py` here, offline under Python 3.14.\n* Every stage passes, including its independent asynchronous audit.\n* Its final comparison of the emitted template's sha256 with #505's `EXPECTED.json` fails. 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It reports 800 distinct physical owners per invocation and builds on #505's asynchronous machinery and #507's factory. 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asynchronous whole-owner allocator and a delivery-layer map of the complex word","user":{"login":"higherbeing","id":7227029,"node_id":"MDQ6VXNlcjcyMjcwMjk=","avatar_url":"https://avatars.githubusercontent.com/u/7227029?v=4","gravatar_id":"","url":"https://api.github.com/users/higherbeing","html_url":"https://github.com/higherbeing","followers_url":"https://api.github.com/users/higherbeing/followers","following_url":"https://api.github.com/users/higherbeing/following{/other_user}","gists_url":"https://api.github.com/users/higherbeing/gists{/gist_id}","starred_url":"https://api.github.com/users/higherbeing/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/higherbeing/subscriptions","organizations_url":"https://api.github.com/users/higherbeing/orgs","repos_url":"https://api.github.com/users/higherbeing/repos","events_url":"https://api.github.com/users/higherbeing/events{/privacy}","received_events_url":"https://api.github.com/users/higherbeing/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"## Scope\n\nA research note with tools. Added folder: `research/complex-delivery-map-open-allocator/`.\n\n## What is in it\n\n**1. An open asynchronous whole-owner allocator** (`tools/`). The optimisation that produces the frozen `ASYNC-OWNERS` maps of #505/#508/#512/#514/#517 as runnable code: an aggregate CP-SAT model (helpers per call per width per idle child, port tiling patterns, windows, one helper per call per port, Hall conditions), a lazy-cut loop against the literal per-child nomination, a nominator that writes roles in #505's format, and a profile recount that writes the plan #508's width-generic emitter and audit check against.\n\nValidation: on #505's own order and widths it returns #505's published remainder profile `{1:136,3:3432,5:3501,7:2137,16:1,48:408}` exactly as the optimum. On #507's widths under #508's offset-six order the aggregate reaches 99,625.66, equal to the timing-free ceiling (all windows open), and the resulting profile gives #512's endpoint `b = 0.001389978441615608` through the pinned moment engine. The first-order objective `Σ r ln(73/r)` over remainders is exact to first order because the rank mass is fixed.\n\nWhy: every asynchronous result so far ships only its witness. Anyone who changes the local word needs a fresh allocation; this gives the community a checked one. Requires `ortools`.\n\n**2. A map of where the 560 complex helpers go** (`code/`, `results/`): exact symbolic replay over Q of the #433, #484 and #507 words. All three share the packet layer (84 single-source copies, 269 four-source packets, 204 eight-source packets, 3 centre sums; coefficients ±1, ±1/2) and the same duplicate structure (90 identical packet copies, 84 sign variants); they differ in how packets reach targets (389 / 380 / 283 helpers copy a source first; 171 / 171 / 255 are built only from helpers). Targets read along nested chains `0 → F₅ → F₆ → cap` (#507: `0 → F₆ → F₇ → cap`): every 5-frame is private to one target and every 6-frame is shared by exactly two targets; no pre-cap frame is shared by more than two. Merging an identical pair at its readers' shared 7-frame fails post hoc for every pair in every word, because each reader has other pre-cap reads outside that meet.\n\n**3. A correction.** A plane-section argument (\"a register of `s` above its line serves the readers in one hyperplane section, the largest has 32 of 56, so ≥ 3 branches per source\") does not hold: all ports have odd weight, so the planes spanned with `v` and `v + 1` always cover all 56 readers. We had written that bound down privately and withdraw it here so nobody else relies on it. The binding structure is the chain design above.\n\n**4. Direction.** The complex cost is 72 % helpers and the helpers are mostly delivery of the same 473 packets, copied and re-signed until every target can read them in its own chain, with frames shared only in pairs. Grouping `k` targets on a shared `(9−k)`-frame delivers a packet once per group at the price of one extra climb per target per level (≈ 3 Φ against ≈ 25 Φ per helper). Stated as an exact combinatorial problem in the README; not solved here.\n\n## Credits and disclosure\n\n#425/#433 (packet word), #484 (gauge/kernel word), #507 (partial-own factory), #505/#508 (asynchronous schedule, width-generic emitter and audit), #512/#517 (independent endpoint and ceiling the allocator reproduces), #446 (rigidity), #496/#442 (whole-owner hosting). Written by higherbeing with Claude Code (Anthropic) assistance. 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Add automatic-width binary counting","user":{"login":"jamesyc","id":3722200,"node_id":"MDQ6VXNlcjM3MjIyMDA=","avatar_url":"https://avatars.githubusercontent.com/u/3722200?v=4","gravatar_id":"","url":"https://api.github.com/users/jamesyc","html_url":"https://github.com/jamesyc","followers_url":"https://api.github.com/users/jamesyc/followers","following_url":"https://api.github.com/users/jamesyc/following{/other_user}","gists_url":"https://api.github.com/users/jamesyc/gists{/gist_id}","starred_url":"https://api.github.com/users/jamesyc/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/jamesyc/subscriptions","organizations_url":"https://api.github.com/users/jamesyc/orgs","repos_url":"https://api.github.com/users/jamesyc/repos","events_url":"https://api.github.com/users/jamesyc/events{/privacy}","received_events_url":"https://api.github.com/users/jamesyc/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"## Completed chunk and coverage\n\nAdds a concrete ten-state, two-tape, three-symbol machine that allocates counter width from the actual scanned input and then counts it. No input length or counter width parameter appears in its transition table. For every finite input word of length n, including empty input, it reaches the specified halted endpoint with an n-bit little-endian counter representing n. The checked execution bound is (CarryTape.pass n (List.replicate n false)).2.reads + 4*n + 4.\n\nFinite coverage: marked-input representation transport, a four-state zero-counter allocator (2*n+3 transitions), and their exact controller composition. The input starts at its right blank; the second tape must be pristine blank.\nConditional-interface coverage: the CurrentMain.FixedTapeMachine and exact pinned dispatcher interfaces.\nFull-theorem coverage: no complete multiplication or kappa theorem, linear amortized bound, first-completion claim, compact-counter normalization, one-string prelude, four-tape control composition, or Plan/Budget discharge. Actual selected-source obligations remain open.\n\n## Exact pins and author-checked kappa\n\nBase: 12a4934d15006e8c10f9b2264f13f8f341be802b.\nHead: ffd3c48a80ba8b579dc300e785e387fe8acddfef.\nExplicit author-checked selected conditional project kappa = 90446448750933/125000000000000000 = 0.000723571590007464, matched to the selected-result record and certificate at that base. This is project context, not a kappa theorem proved by this helper. The all-size compiler, chart, restored-row, selector/routing, prime-supply, precision/recovery, complex-symbolic and analytic-transfer interfaces remain conditional.\n\n## Reuse and attribution\n\nThree source files are included. Six exact external sources are reused: four from #511 at79f7c03c7f820ab89955b75ef239cbaccc627e6e and two from #488 atedd3102b415df5b9d6f633ac0a4dedcf69c58525. Neither dependency is assumed merged. The later CI-provenance repair on #511 does not change these pinned source blobs. DEPENDENCIES.json gives paths and hashes.\n\nCompared with #511 supplied-width counting and #64 richer generic counter/stack, first-completion and amortized results. Generic binary counting is not claimed new. This chunk supplies actual width allocation and the composed current-model endpoint; a PR64 arithmetic bridge remains separately unverified and is not included. Apache-2.0, source attribution and OpenAI-assistance disclosure are preserved. Fresh automatic/width PR search found no matching open or closed PR.\n\n## Validation and reproduction\n\nOffline Linux, Python3, Lean4.21; no Mathlib or downloads. README.md supplies the command using two separate exact foundation roots and a fresh build directory.\n\nFresh isolated nine-source package replay passed: 11.7677 compiler seconds, 0.00378 queue seconds, peak virtual memory3,074,072,576 bytes. All nine object hashes and49 normalized axiom outputs match accepted evidence. Only standard propext, Quot.sound and Classical.choice axioms occur. This local kernel evidence is distinct from CI.\n\nOne additive commit,16 files,1,834 additions,0 deletions. Fork CI is not yet passed; upstream jobs may require maintainer approval. The inherited joint-dual root-pin failure is being repaired and tested separately on #511; no scientific check is disabled 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kappa 0.001393662920776407: blockwise pair exposure, 99 pivots and whole-owner allocation","user":{"login":"Dugongue","id":49054532,"node_id":"MDQ6VXNlcjQ5MDU0NTMy","avatar_url":"https://avatars.githubusercontent.com/u/49054532?v=4","gravatar_id":"","url":"https://api.github.com/users/Dugongue","html_url":"https://github.com/Dugongue","followers_url":"https://api.github.com/users/Dugongue/followers","following_url":"https://api.github.com/users/Dugongue/following{/other_user}","gists_url":"https://api.github.com/users/Dugongue/gists{/gist_id}","starred_url":"https://api.github.com/users/Dugongue/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/Dugongue/subscriptions","organizations_url":"https://api.github.com/users/Dugongue/orgs","repos_url":"https://api.github.com/users/Dugongue/repos","events_url":"https://api.github.com/users/Dugongue/events{/privacy}","received_events_url":"https://api.github.com/users/Dugongue/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"## Result\n\nThis constructs and independently replays a new complex supplier giving conditional **kappa = 0.001393662920776407**, exactly `1393662920776407/1000000000000000000`. It improves our preceding checked construction, 0.001391523459591829, by **0.153750%**. The complex side binds at `b = 697803963898659915203/500000000000000000000000`; the unchanged cited PR493 bit supplier has `c = 391360506745414227149/250000000000000000000000`.\n\nThe inherited all-size compiler, common-label/mutable-basis interface, normalized Lemma A realization, restored-row, precision/tape and analytic-transfer contracts remain dependencies. This is not an unconditional multiplication theorem or new Lean certification. Larger submissions with different or disputed interfaces are not treated as comparable verified baselines.\n\n## New mechanism\n\nInstead of using a uniform pair choice throughout the local fourteen-block factory, choose pairs blockwise and reconstruct the exact downstream decoder. The selected witness uses option [0,0] everywhere except blocks (0,2,4,6) and (0,3,4,7), where it uses [1,1]. This changes the exposed intermediate rows, rather than merely changing coordinates within an identical response class.\n\nThe construction retains the preceding four coordinated rank-two gauge reductions and compatible scalar-body retiming. Exact response reduction now yields **99 cancellations rather than 92**. The local paid profile is `{1:2530,2:182,3:516,4:88,5:298,6:68,7:1,8:17}`; residual widths are `{7:18,8:161,9:381}`.\n\nConstructive width-dominance transport and pattern exchange then produce a new literal whole-owner allocation. Eight replicas retain the complete-invocation order `(7*stage+6*replica, stage, replica)`. All 40,320 helper uses have explicit legal owners, and every remaining pending factor is paid. The complete global profile is `{1:182160,2:13104,3:40196,4:6336,5:25064,6:4896,7:164,8:1224,48:796}`. Ambient dimension 73, live stock 7,680, physical stock 8,258 and rank deficit 2,496 are unchanged.\n\nNo helper is split across owners, no scalar instruction crosses an unfinished invocation, and headline gains are not added.\n\n## Direct credits and context\n\n- #507: partial-own factory, old response reference and pinned retiming map.\n- #484 and #496: gauge/kernel construction, paid wrappers, whole-owner parent and invoice ancestry.\n- #495, #501 and #502: scalar-body retiming and its integrations.\n- #493: unchanged cited bit supplier; its published histogram is repriced, not its whole operator reverified.\n- #473: gauge inspiration and updated scheduling comparison; #505: our earlier asynchronous complete-invocation schedule; #506: related composition and portability feedback.\n- #477: experimental records consulted. #508 and #512: public asynchronous partial-own comparison points.\n- #509: abstract Lemma G proof context. #510: stronger but nonbinding bit headroom. #511 and #513: formal dispatcher/completed-bank work. These are acknowledged without claiming their formal results were recompiled or add numerical gains here.\n- #458: whole-owner spectator wrappers; #433, #425 and #370: geometry and scalar/phase compilation; #361 and #315: exact moments and outer arithmetic; #434, #417, #435, #440, #401, #408 and #416: response-kernel/gauge ancestry.\n\nSOURCES.json pins direct dependencies and separates ingredients from context. The snapshot is frozen through #513.\n\n## Four OpenAI-source research routes\n\nThe appendix preserves mathematical rules, source hashes and bounded experiments from four distinct proof families in OpenAI math at adc7f1241b42e322a6451854ab7e4b4c146bf78a:\n\n1. HoneycombChords sparse interpolation/Newton evaluation inspired blockwise exposure choices and exact decoder reconstruction; this contributes to the selected word.\n2. MatchingCount unit flow/mincut and perfect matching inspired constructive ownership transport and pattern exchange. The new allocation contributes; the separate cut-guided scheduling experiment did not win.\n3. ThinTrees rational Schur history inspired paid internal-register elimination. Four finite screens found no legal cheaper witness.\n4. QuantumCircuit pruning inspired the exact sufficient condition `(U-I)R=0` on all reachable input columns. Both orientations of the new program have 3,700 positive child sites; no zero-operand candidate survived modular screening.\n\nThese are source-inspired adaptations, not four imported Lean theorems or four numerical gains. No global originality claim is inferred from the search. Alternative losing architectures and the sufficient conditions for future use are documented rather than counted as savings.\n\n## Reproduce and validation\n\nFrom `research/nodal-pair-async`, with Python 3.11 or later and assertions enabled:\n\n```text\npython -B verify.py --work /absolute/path/to/a-new-output-directory\n```\n\nStandard library only; no network, optimizer, C++ compiler or Lean required. Fourteen stages rebuild the word, check all 800 arbitrary-dirt columns in both orientations and 99 correction-omission controls, verify exact Gaussian phases and physical wrappers, audit all whole owners and remainders, recount the finite invoice, and execute two rational moment engines and all 47 strict outer constraints. Adjacent-price and invalid assembly controls are rejected.\n\nThe actual scalar envelope requires 21 local prefix bits and 206 global bits, below the retained charge of 512. The inherited meaningful owner-alias control remains in place. A full fresh replay passed with every recognized package text file converted to CRLF. Missing inputs, changed tokens and optimized Python are rejected before output creation. No hidden file is required; LF/CRLF normalization does not ignore any other content. No Linux or Python 3.14 execution is claimed from this Windows test.\n\nThe package includes the exact expected result, complete assembly receipt, portability receipt, source credits and research appendix. Nothing has been published by the tooling.\n","created_at":"2026-10-11T23:50:50Z","updated_at":"2026-10-11T23:50:50Z","closed_at":null,"merged_at":null,"merge_commit_sha":"49f7ea1e00097321a2a86739e495a4080ccc5928","assignees":[],"requested_reviewers":[],"requested_teams":[],"labels":[],"milestone":null,"draft":false,"commits_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/pulls/518/commits","review_comments_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/pulls/518/comments","review_comment_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/pulls/comments{/number}","comments_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/issues/518/comments","statuses_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/statuses/e0a071dce251eeca96d446f73147048cfebbd5c7","head":{"label":"Dugongue:tn18","ref":"tn18","sha":"e0a071dce251eeca96d446f73147048cfebbd5c7","user":{"login":"Dugongue","id":49054532,"node_id":"MDQ6VXNlcjQ5MDU0NTMy","avatar_url":"https://avatars.githubusercontent.com/u/49054532?v=4","gravatar_id":"","url":"https://api.github.com/users/Dugongue","html_url":"https://github.com/Dugongue","followers_url":"https://api.github.com/users/Dugongue/followers","following_url":"https://api.github.com/users/Dugongue/following{/other_user}","gists_url":"https://api.github.com/users/Dugongue/gists{/gist_id}","starred_url":"https://api.github.com/users/Dugongue/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/Dugongue/subscriptions","organizations_url":"https://api.github.com/users/Dugongue/orgs","repos_url":"https://api.github.com/users/Dugongue/repos","events_url":"https://api.github.com/users/Dugongue/events{/privacy}","received_events_url":"https://api.github.com/users/Dugongue/received_events","type":"User","user_view_type":"public","site_admin":false},"repo":{"id":1411510763,"node_id":"R_kgDOVCHx6w","name":"integer-mult-bounds","full_name":"Dugongue/integer-mult-bounds","private":false,"owner":{"login":"Dugongue","id":49054532,"node_id":"MDQ6VXNlcjQ5MDU0NTMy","avatar_url":"https://avatars.githubusercontent.com/u/49054532?v=4","gravatar_id":"","url":"https://api.github.com/users/Dugongue","html_url":"https://github.com/Dugongue","followers_url":"https://api.github.com/users/Dugongue/followers","following_url":"https://api.github.com/users/Dugongue/following{/other_user}","gists_url":"https://api.github.com/users/Dugongue/gists{/gist_id}","starred_url":"https://api.github.com/users/Dugongue/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/Dugongue/subscriptions","organizations_url":"https://api.github.com/users/Dugongue/orgs","repos_url":"https://api.github.com/users/Dugongue/repos","events_url":"https://api.github.com/users/Dugongue/events{/privacy}","received_events_url":"https://api.github.com/users/Dugongue/received_events","type":"User","user_view_type":"public","site_admin":false},"html_url":"https://github.com/Dugongue/integer-mult-bounds","description":"Conditional integer multiplication: kappa > 2^-15. 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compact FFT reservation and top-bit costs with complementary reservoirs","user":{"login":"chafreaky","id":4400527,"node_id":"MDQ6VXNlcjQ0MDA1Mjc=","avatar_url":"https://avatars.githubusercontent.com/u/4400527?v=4","gravatar_id":"","url":"https://api.github.com/users/chafreaky","html_url":"https://github.com/chafreaky","followers_url":"https://api.github.com/users/chafreaky/followers","following_url":"https://api.github.com/users/chafreaky/following{/other_user}","gists_url":"https://api.github.com/users/chafreaky/gists{/gist_id}","starred_url":"https://api.github.com/users/chafreaky/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/chafreaky/subscriptions","organizations_url":"https://api.github.com/users/chafreaky/orgs","repos_url":"https://api.github.com/users/chafreaky/repos","events_url":"https://api.github.com/users/chafreaky/events{/privacy}","received_events_url":"https://api.github.com/users/chafreaky/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"The compact FFT currently transforms its reserved axes individually, imposing `c > q`, and processes extra top bits at cost `O(Vd)`. This supplies a conditional construction removing both costs while retaining the original all-input dirty-core, routing, precision and analytic interfaces.\n\nComplete every Fourier round of one half of the axes while the other half supplies restored dirty fields, then exchange roles. Route each exceptional top-bit round into virtual chunks filled with existing unselected coordinates. At most five global coordinate routes serve an entire FFT; no Fourier axis is enlarged. Ordinary complete-zero-row padding is retained.\n\nThe resulting FFT cost is `O(V [p^tau polylog(p) + ell d^lambda_prime])`. The proof accounts for complete front/back fields and row indices, actual pass chronology, arbitrary dirty contents, pointwise frequency alignment, inverse normalization, the constant number of paid routes, and p+2 precision. It also provides explicit compressed eventual-capacity bounds.\n\n**No new kappa is claimed.** Gaussian arithmetic and scalar work still limit the current composition. This removes two FFT implementation costs that would otherwise remain even after those separate algorithms improve; kappa = 1 remains unproved.\n\nVerification passed on macOS Python 3.11 and Linux Python 3.12 with byte-identical outputs: 33 polynomial Fourier shapes, 429 basis columns, 98,080 exact entries, 84 common-field layouts, 168 top-field layouts and seven mutation controls. Four parameter rows set c below q and retain the other 44 strict expressions from #472. Those rows distinguish reservation rules; they are not a new full finite invoice. Python 3.11/3.14 CI and source-bound receipts are included.\n\nRun `python -B research/complementary-fft-reservoirs/verify.py /absolute/new/output`. Only the standard library is needed. Tiny operator tests and large symbolic field inventories have separate scopes; the all-size fixed-tape cost is a written conditional transfer, not an executed large machine or Lean proof.\n\nAll eleven source dependencies match pinned Git bytes. Credits: Douglas Colkitt and integer-mult-bounds contributors for compact layout and phase interfaces; RaD/hipotures and the source authors for balanced layout, arbitrary routing and semantic guard; eumemic, icekylinx and Zhihao Chen for the inherited arithmetic. New construction, proof and controls by chafreaky with OpenAI Codex assistance. Original notices retained; no literature priority 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Add checked binary count dispatcher","user":{"login":"jamesyc","id":3722200,"node_id":"MDQ6VXNlcjM3MjIyMDA=","avatar_url":"https://avatars.githubusercontent.com/u/3722200?v=4","gravatar_id":"","url":"https://api.github.com/users/jamesyc","html_url":"https://github.com/jamesyc","followers_url":"https://api.github.com/users/jamesyc/followers","following_url":"https://api.github.com/users/jamesyc/following{/other_user}","gists_url":"https://api.github.com/users/jamesyc/gists{/gist_id}","starred_url":"https://api.github.com/users/jamesyc/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/jamesyc/subscriptions","organizations_url":"https://api.github.com/users/jamesyc/orgs","repos_url":"https://api.github.com/users/jamesyc/repos","events_url":"https://api.github.com/users/jamesyc/events{/privacy}","received_events_url":"https://api.github.com/users/jamesyc/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"## Completed chunk and coverage\nAdds a concrete seven-state, two-tape, three-symbol binary count dispatcher. 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The source package is immutable; all 328 copied source files were checked against exact Git bytes. The inherited PR507 portability repair pins only two historical floating display annotations, preserving its mathematical and frozen-word hash assertions.\n\nInherited all-size compiler, mutable-basis/common-label transport, Lemma A realization, restored-row, precision/tape and analytic-transfer conditions remain. This is a finite conditional witness and a scoped packing bound, not an unconditional multiplication theorem or κ=1 result.\n\nCredits: eumemic #507/#493; Dugongue #508/#505; Rohan Arun #473's scheduling and flow-capacity work; DreamingOfClouds #484; #496, #495, #501/#502, #458 and the retained earlier authors. New composition, literal allocation, two-platform wrapper and exact packing dual by chafreaky with OpenAI Codex assistance. Licenses, original sources and notices are 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word R685 (R687 lineage): L-copy inline + Bcw copy deletions, c = 1.323554·10⁻³ (+0.62% over #504's R687)","user":{"login":"DreamingOfClouds","id":173691639,"node_id":"U_kgDOClpS9w","avatar_url":"https://avatars.githubusercontent.com/u/173691639?v=4","gravatar_id":"","url":"https://api.github.com/users/DreamingOfClouds","html_url":"https://github.com/DreamingOfClouds","followers_url":"https://api.github.com/users/DreamingOfClouds/followers","following_url":"https://api.github.com/users/DreamingOfClouds/following{/other_user}","gists_url":"https://api.github.com/users/DreamingOfClouds/gists{/gist_id}","starred_url":"https://api.github.com/users/DreamingOfClouds/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/DreamingOfClouds/subscriptions","organizations_url":"https://api.github.com/users/DreamingOfClouds/orgs","repos_url":"https://api.github.com/users/DreamingOfClouds/repos","events_url":"https://api.github.com/users/DreamingOfClouds/events{/privacy}","received_events_url":"https://api.github.com/users/DreamingOfClouds/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"\nFrom a fresh `git archive`, `verify.py --light` and the default FULL run (with `--discover-check`, including #443's historical regressions) both pass. Stacked on #504 (head 35057a6).\n\n**Method + knowledge PR (no frontier claim).** A new bit word, R685, from the R687 lineage of #504. It is priced at eleven stages with #442 whole-residual hosting and target mixing, with no\ncross-family split, by the pipeline of #504 unchanged: **c = 661777032472911750807/(5·10²³) ≈ 1.323554·10⁻³**, +0.62% over #504's R687 (1.315433·10⁻³) and +2.99% over the R715 bit supplier (#463). With #442's complex\nsupplier κ is complex-bound as before (1.265849·10⁻³); the bit-only κ is 1.321805·10⁻³. Compositions with #471/#484 are not rerun here.\n\n| word | R | five-stage saving | s=11, greedy kernel | s=11, exact pivots |\n|---|---|---|---|---|\n| R687 (#504) | 687 | 1.001418·10⁻³ | 1.303868·10⁻³ | 1.315433·10⁻³ |\n| R684: R687 + 3 word-level copy deletions | 684 | 1.003262·10⁻³ | 1.303938·10⁻³ | 1.317462·10⁻³ |\n| inline only (28 L copies) | 687 | 1.006976·10⁻³ | 1.309219·10⁻³ | 1.322341·10⁻³ |\n| **R685** | **685** | **1.008233·10⁻³** | 1.309099·10⁻³ | **1.323554·10⁻³** |\n\n### What is new\n1. **D4(c) sums from their pairs (28 inlines).** In R687 each D4(c) sum is built from two L's, so 28 L's have a third reader and need a third register chain. Building the sum from its four pairs\n gives every L two readers: 28 L copies fewer (raw R 811 → 782), contents and frames unchanged. 15 rules change kid lists (`data/inline-kids.json`, checked to be inlines of the old kids). This\n is the Bcw inline of our poset scout; the sections scout's exact per-block search over inline and re-pairing moves returns exactly these moves.\n2. **Optimal register chains.** compile2's greedy chains are replaced by an optimum of an exact path-cover ILP (`code/chain_model.py`; pinned, `--discover-check` recomputes the objective). Equal-cost\n optima differ in c by several tenths of a percent, so the chains are part of the word.\n3. **Two copy deletions.** `code/copy_sweep.py` replays the raw word exactly and finds the copies all of whose reads can take other registers at a legal frame (frames only climb, one frame per gate). Two\n D4(c) copies qualify and are deleted (reuse rebuilds the dirt compensation exactly): R = 685.\n4. **Exact kernel pivots on the new word.** 233 candidates, upper bound 101 from the sum-rank lower bounds, attained by the pinned annealing selection (reproduced by `code/select_pivots.py`), so the maximum is exact\n without an exhaustive refutation; parity leaves 100.\n\n### Findings\n- Raw −29 does not become R: the 28 L copies leave the dead pair slots that D5 births recycle, so reuse falls by as much. The gain is in climbs and the kernel (five-stage +0.56% for the inline, +0.125% for the deletions).\n- R681 (all six D4(c) copies gone) is not reachable by these moves: the four hosts have no alternative source at any legal frame, and no single inline of a D4(c) sum raises the five-stage saving (73 moves).\n- The clearing gap of the R687 raw word (floor 510 against 687) is structural: 196 of the 206 failed reuse births are L-copy births seeing one dead pair slot, whose clearing needs the complementary pair on a\n transverse chain or in sources whose next read frame does not contain the L frame. Exact twins are all chains (893 overlapping pairs, none mergeable).\n These counts come from exploratory scripts outside the package; `verify.py` reruns the copy sweep that selects the deletions.\n\n### Verification\n`python -B research/e8-r685-inline-deletions/verify.py /abs/out [--light]`; CI workflow `e8-r685-inline-deletions`.\n- `--light` (about 3 minutes, no C++): integrity (five pinned upstream packages, including #504 at 35057a6); the word rebuilt from #504's frozen hierarchy byte for byte; copy anatomy on the inlined DAG; #370's independent checker and\n mutants; the pivot bound, witness and annealing reproduction; the kernel and mixed words regenerated byte for byte; the relaxed all-column checker on both.\n- FULL adds #443's parent verifier, the complex upstream, C++ cohort legality, five- and eleven-stage formal columns, record mutants, Gram, the mix check (4 mutants), eleven-stage geometry/template/audit,\n whole-residual hosting with the frozen selection (`--discover-check` recomputes it), the hosted audit and the assembly (47 strict inequalities), compared with `EXPECTED.json`.\n\n### Review points\n- **Chain override.** One statement of #370's compile2 (the chain loop) is replaced at run time; each anchor must occur exactly once in the unchanged source. The pinned chains must cover the read events of every symbol exactly.\n- **Word-level deletion.** A copy is deleted only if every read has an alternative set whose x-parts XOR to its content, legal at that read's own frame; #443's reuse step rebuilds D and C, and #370's checker verifies the F2 semantics on all 925 columns.\n- **Kernel selection.** A witness at the exact maximum chosen among annealing seeds (other seeds move c by about ±0.05%); #504's frozen selection for R687 is the same kind of object.\n- **Inherited.** The usual compiler, dirty-helper and analytic interfaces; from #450 only Lemma M. 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kappa 0.001391523459591829: partial-own factory, 92 pivots and asynchronous whole owners","user":{"login":"Dugongue","id":49054532,"node_id":"MDQ6VXNlcjQ5MDU0NTMy","avatar_url":"https://avatars.githubusercontent.com/u/49054532?v=4","gravatar_id":"","url":"https://api.github.com/users/Dugongue","html_url":"https://github.com/Dugongue","followers_url":"https://api.github.com/users/Dugongue/followers","following_url":"https://api.github.com/users/Dugongue/following{/other_user}","gists_url":"https://api.github.com/users/Dugongue/gists{/gist_id}","starred_url":"https://api.github.com/users/Dugongue/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/Dugongue/subscriptions","organizations_url":"https://api.github.com/users/Dugongue/orgs","repos_url":"https://api.github.com/users/Dugongue/repos","events_url":"https://api.github.com/users/Dugongue/events{/privacy}","received_events_url":"https://api.github.com/users/Dugongue/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"## Result\n\nThis constructs and independently replays a combined complex supplier with conditional **kappa = 0.001391523459591829**, exactly `1391523459591829/1000000000000000000`. It is **1.381994% above our preceding checked construction**, 0.001372554837726243. The complex supplier binds at `b = 139346249534416215349/100000000000000000000000`; the unchanged cited PR493 bit supplier has `c = 391360506745414227149/250000000000000000000000`.\n\nThe claim retains the existing all-size compiler, common-label/mutable-basis, normalized Lemma A realization, restored-row, precision/tape and analytic-transfer conditions. It is not an unconditional multiplication theorem or new Lean certification. Larger claims using disputed split-residual interfaces are not comparable baselines here.\n\n## Mechanism\n\nPR507's partial-own factory is rebuilt with our coordinated rank-two gauge reductions on helpers 540 through 543. A frozen exact rational response selection gives 92 pivots instead of the reference 84. The ordered residual inventory becomes 18 width-seven, 154 width-eight and 388 width-nine helpers. We reconstruct all dirty compensation and retimed scalar frames from these choices.\n\nThe new inventory is then allocated to eight asynchronous replicas, ordered by `(7*stage+6*replica, stage, replica)`. All 72 invocations complete before the next begins. All 40,320 helper uses have explicit distinct whole owners in their actual idle windows; every leftover pending factor is paid. This combines actual programs and costs, not sums of headline improvements.\n\nThe full paid profile is `{1:182808, 2:11520, 3:41233, 4:6336, 5:25173, 6:4896, 7:195, 8:1224, 16:1, 32:1, 39:1, 48:766}`. Ambient dimension 73, live stock 7,680, physical stock 8,258 and rank deficit 2,496 are unchanged.\n\n## Direct credits and ancestry\n\n- #507: partial-own factory, 84-pivot reference and the pinned retiming map.\n- #484 and #496: gauge/kernel compiler, whole-owner parent, invoice and assembly ancestry.\n- #493: unchanged cited bit supplier; its published histogram is repriced, not its whole operator reverified.\n- #495, #501 and #502: scalar-body frame retiming and its integration.\n- #473: original single-gauge inspiration and the updated scheduling comparison.\n- #505: our prior asynchronous complete-invocation scheduling. #506: related public composition and portability feedback.\n- #477: experimental records consulted to avoid repeating prior searches.\n- #458: whole-owner spectator wrappers. #433, #425 and #370: geometry and scalar/phase compilation. #361 and #315: exact moment/outer engines. #434, #417, #435, #440, #401, #408 and #416: response-kernel and gauge ancestry.\n\nSOURCES.json pins direct source heads and distinguishes ingredients from inspiration, comparisons and excluded interfaces. The public snapshot is frozen through #507; no moving-head claim is made.\n\n## Validation and reproducibility\n\nFrom `research/partial-kernel92-async`:\n\n```text\npython -B verify.py --work /absolute/path/to/a-new-output-directory\n```\n\nPython 3.11 or later, standard library only; assertions must remain enabled. Thirteen stages reconstruct the factory and selected word, check all 800 arbitrary-dirt columns in both orientations and 92 correction-omission controls, verify exact Gaussian phases and paid wrappers, emit and independently audit the physical program, recount the finite invoice, and run two exact rational moment engines plus all 47 strict outer constraints. The next kappa grid point and invalid assembly-parameter controls are rejected.\n\nThe new local prefix needs 21 bits; the complete global prefix needs 206, within the retained charge of 512. A formerly vacuous inherited alias-control mutation has been repaired to create a genuine same-width storage collision, rejected directly for overlapping footprints. No check was weakened.\n\nA final full replay passed after converting every recognized package text file to CRLF. The manifest accepts LF/CRLF transport differences only, hashes binary files exactly, and requires no hidden `.gitattributes` file. Generated and staged runtime text is canonicalized before raw-byte hashes are embedded. No Linux or Python 3.14 run is claimed from this Windows test.\n\n## Machine-source research preserved\n\nThe research appendix records concrete adaptations from OpenAI Word RAM/Turing implementations, our Problem 1.8 workspace machinery and the installed machine compiler libraries: old-state operand capture, actual first-read frontiers, frame-preserving storage coalescing, fused entry/return, and repeated-axis modulo-four normalization. It includes sufficient transformation rules, source hashes and the paid finite screens.\n\nThese alternatives did not beat the selected construction. In particular, this PR does **not** claim three new machine-derived numerical gains: the winning 92-pivot improvement applies the existing response-kernel method to the new factory. 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word R480 at nine stages: c = 0.001587447106092548137108 (+1.41% over #493)","user":{"login":"DreamingOfClouds","id":173691639,"node_id":"U_kgDOClpS9w","avatar_url":"https://avatars.githubusercontent.com/u/173691639?v=4","gravatar_id":"","url":"https://api.github.com/users/DreamingOfClouds","html_url":"https://github.com/DreamingOfClouds","followers_url":"https://api.github.com/users/DreamingOfClouds/followers","following_url":"https://api.github.com/users/DreamingOfClouds/following{/other_user}","gists_url":"https://api.github.com/users/DreamingOfClouds/gists{/gist_id}","starred_url":"https://api.github.com/users/DreamingOfClouds/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/DreamingOfClouds/subscriptions","organizations_url":"https://api.github.com/users/DreamingOfClouds/orgs","repos_url":"https://api.github.com/users/DreamingOfClouds/repos","events_url":"https://api.github.com/users/DreamingOfClouds/events{/privacy}","received_events_url":"https://api.github.com/users/DreamingOfClouds/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"\n**The same R480 word as #503, priced at nine stages instead of eleven.** The word does not change. It is #493's R489\nwith its nine totals on dead registers (#503). Pricing it in the nine-stage whole-residual hosted pipeline gives:\n\n| | stages | bit c |\n|---|---|---|\n| #493 (R489) | 11 (m = 78, 8 pooled replicas) | 0.001565442026981656908596 |\n| #503 (R480) | 11 | 0.001574753352953808650916 |\n| **this PR (R480)** | **9 (m = 64, 32 replicas)** | **`396861776523137034277/250000000000000000000000` = 0.001587447106092548137108** (+1.4057% over #493, +0.806% over #503) |\n\nκ does not change, because the side that binds is the complex side. With #484's complex b (draft; Lemmas A and G) κ =\n`662515748707749/500000000000000000` = 0.001325031497415498. With #471's it is 0.001303530097714685, and with #458's\n0.001295523322678044. The bit gain is headroom.\n\n**Why nine stages win here.** On the eleven-stage schedule the even-stage rank-7 idle children cannot host any width-8\nresidual, so they are paid in full. With only 480 helpers, nine stages host every residual whole: 138,240 = 9 × 32 ×\n480, with 0 banks and maximum child 8. The smaller window m = 64 then prices lower. R489 at nine stages through the\nsame chain is 0.001576648413160438658485 (+0.716% over #493). On R715/R740, eleven stages were best.\n\n## What is in `research/e8-r480-nine-stage/`\n- `verify.py`. Parent: #503's verifier (`--light`, or full with #493's `verify.sh`). Then:\n - nine-stage formal columns: `columns_k`, KPAIRS = 4; 1,440 columns; 18/18 controls; payload 102 bits < 104;\n - nine-stage template: 288 invocations, F2 column replay;\n - parent audit: 17 mutations rejected;\n - #442 hosting, rediscovered exactly: all residuals whole, 0 banks;\n - independent hosted audit;\n - nine-stage bit invoice, both moment engines, and #493's outer loop: 47 strict inequalities and controls with\n #484, #471 and #458.\n- `vendor/`: the nine-stage pipeline, byte-identical to PR #463 at `cdf0c1c` (git blob ids in `SOURCE.json`,\n recomputed). It is not on main; it is in open PRs #463 and #450. The lineage is #443, #444, #442 and #386.\n- `code/assemble9.py`: #463's nine-stage invoice verbatim, plus #493's per-supplier loop verbatim.\n `code/adapt.py`: two listed edits to `audit_parent_k.py`.\n\n- `code/findings/`: the checks for findings (a) and (b) below (`flowlp2.py`, `levels.py`, `piv0.py`), run by `verify.py`.\n\n## Findings on the R489 family (knowledge)\nChecked by `verify.py`:\n- **(a) An LP floor of 480 for R480's skeleton.** The model is a min-flow LP on the frame lattice of one 4-frame. Its\n dual is a max-weight antichain. Node bounds come from the junk-dimension lemma: a cross cell needs ≥ 3 registers\n and a matching cell ≥ 4. The optimum is 16 helpers per 4-frame, so 480 (8 without the junk bounds). It assumes 3\n branches per source, 2 transverse quads per cell, and matching-cell sources that feed the block frame. R480\n attains every node bound. Each of its 480 helpers stands at exactly one cell and one D6 frame, so levels 2 and 6\n are tight. `verify.py` checks the LP optimum given these node bounds, and the tight levels on R480's own data. The junk-dimension lemma and the flow model itself (that every word of the family is such a flow) are argued here, not machine-checked.\n- **(b) Kernel pivots on R480 and R489 are exactly 0** for coordinate and root-line entrances: all 120 line classes\n have nullity 0. All residuals stay width 8.\n\nExploration outside the package, not run by `verify.py`:\n- **(c)** The helper ledger is at its floors: 240 carriers at the 4-design bound, and 240 further registers at the\n per-cell junk count, with every shared symbol at its Dilworth width. The copy-removal methods built on the\n #370-lattice words (read-then-climb, XOR fusion, Bcw inlining) have nothing to act on.\n- **(d)** Idle fusion has no legal glue:\n - an X→Y bridge add mixes frames at rank 1 in #445's geometry (X wires contain the line q, Y wires do not);\n - with X→X/Y→Y shears only, a Gröbner test finds no glue at K = 2..5.\n\n Checks that compare only pair levels miss the X/Y frame difference. #493's own audit hard-codes X→X/Y→Y, so it is\n safe.\n\n## Scope and review points (also in the README)\n- The emitter is the per-replica nine-stage one (#444/#442 lineage, 32 replicas in groups of 8), not #472's pooled\n eleven-stage emitter. Its finite prefix is #443's per-stage product bound (193 bits), not #472's chronological\n bound. The prefix enters only the cutoffs.\n- One audit adaptation. The template control \"omit a residual route factor\" needs an isometry that has a route\n factor. R480's helpers all enter at frame zero, so no isometry has one, and the selector raised StopIteration. The\n control is vacuous then and is skipped exactly in that case. The other 17 controls run.\n- Mutable sources at nine stages. #493 grounds source-register writes below the full frame in #472's PROOF (\"Shared\n physical labels\"). The nine-stage address map is #443/#444's, whose proof does not discuss source destinations.\n What carries over:\n - #425's four word-level hypotheses, checked on R480 by #493's `interface.py` in the parent run;\n - the same local invocation and #386 frame operators;\n - the exact F2 replay of every template column, including the source ports' data families.\n\n The realisation sentence for #443's address map is stated, not re-proved. Please treat it as a listed conditional\n interface, as #493 does.\n- Everything else is inherited from #493 and #503 unchanged. Complex savings are cited. No unconditional theorem is\n claimed.\n\n## Credits\neumemic (#493), #503 (R480). Nine-stage pipeline: chafreaky (#443, #444, with OpenAI Codex), DaysSky (#442, #381),\nZhihao Chen (#386), DreamingOfClouds (#315; the #450/#463 pipeline adaptations), Dylan Crow (#370).\n\nPrepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code.\n\n🤖 Generated with [Claude Code](https://claude.com/claude-code)\n","created_at":"2026-10-11T22:46:45Z","updated_at":"2026-10-11T23:11:52Z","closed_at":null,"merged_at":null,"merge_commit_sha":"dba6f8e1003548a7f2cb4fe104ef0d57ada69e05","assignees":[],"requested_reviewers":[],"requested_teams":[],"labels":[],"milestone":null,"draft":false,"commits_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/pulls/510/commits","review_comments_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/pulls/510/comments","review_comment_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/pulls/comments{/number}","comments_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/issues/510/comments","statuses_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/statuses/64edee18af02aab0c1696b677a0287dd0146381b","head":{"label":"DreamingOfClouds:e8-r480-nine-stage","ref":"e8-r480-nine-stage","sha":"64edee18af02aab0c1696b677a0287dd0146381b","user":{"login":"DreamingOfClouds","id":173691639,"node_id":"U_kgDOClpS9w","avatar_url":"https://avatars.githubusercontent.com/u/173691639?v=4","gravatar_id":"","url":"https://api.github.com/users/DreamingOfClouds","html_url":"https://github.com/DreamingOfClouds","followers_url":"https://api.github.com/users/DreamingOfClouds/followers","following_url":"https://api.github.com/users/DreamingOfClouds/following{/other_user}","gists_url":"https://api.github.com/users/DreamingOfClouds/gists{/gist_id}","starred_url":"https://api.github.com/users/DreamingOfClouds/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/DreamingOfClouds/subscriptions","organizations_url":"https://api.github.com/users/DreamingOfClouds/orgs","repos_url":"https://api.github.com/users/DreamingOfClouds/repos","events_url":"https://api.github.com/users/DreamingOfClouds/events{/privacy}","received_events_url":"https://api.github.com/users/DreamingOfClouds/received_events","type":"User","user_view_type":"public","site_admin":false},"repo":{"id":1412741203,"node_id":"R_kgDOVDS4Uw","name":"integer-mult-bounds","full_name":"DreamingOfClouds/integer-mult-bounds","private":false,"owner":{"login":"DreamingOfClouds","id":173691639,"node_id":"U_kgDOClpS9w","avatar_url":"https://avatars.githubusercontent.com/u/173691639?v=4","gravatar_id":"","url":"https://api.github.com/users/DreamingOfClouds","html_url":"https://github.com/DreamingOfClouds","followers_url":"https://api.github.com/users/DreamingOfClouds/followers","following_url":"https://api.github.com/users/DreamingOfClouds/following{/other_user}","gists_url":"https://api.github.com/users/DreamingOfClouds/gists{/gist_id}","starred_url":"https://api.github.com/users/DreamingOfClouds/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/DreamingOfClouds/subscriptions","organizations_url":"https://api.github.com/users/DreamingOfClouds/orgs","repos_url":"https://api.github.com/users/DreamingOfClouds/repos","events_url":"https://api.github.com/users/DreamingOfClouds/events{/privacy}","received_events_url":"https://api.github.com/users/DreamingOfClouds/received_events","type":"User","user_view_type":"public","site_admin":false},"html_url":"https://github.com/DreamingOfClouds/integer-mult-bounds","description":"Conditional integer multiplication: kappa > 2^-15. 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Add sequential completed-bank source bindings","user":{"login":"jamesyc","id":3722200,"node_id":"MDQ6VXNlcjM3MjIyMDA=","avatar_url":"https://avatars.githubusercontent.com/u/3722200?v=4","gravatar_id":"","url":"https://api.github.com/users/jamesyc","html_url":"https://github.com/jamesyc","followers_url":"https://api.github.com/users/jamesyc/followers","following_url":"https://api.github.com/users/jamesyc/following{/other_user}","gists_url":"https://api.github.com/users/jamesyc/gists{/gist_id}","starred_url":"https://api.github.com/users/jamesyc/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/jamesyc/subscriptions","organizations_url":"https://api.github.com/users/jamesyc/orgs","repos_url":"https://api.github.com/users/jamesyc/repos","events_url":"https://api.github.com/users/jamesyc/events{/privacy}","received_events_url":"https://api.github.com/users/jamesyc/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"## Completed chunk\nEight Lean4.21 core-only modules compose completed local bank words and bind the selected five-stage source's routing and chronological schedule.\n\nConditional-interface coverage: sequential_complete_bank composes whole local words with an endpoint universally quantified over arbitrary bank and remaining states, a common exact chart, and disjoint projectors summing to identity. It explicitly reconciles head-first physical execution with tail-first endpoint composition. Actual physical endpoints remain supplier premises.\nFinite/source-binding coverage: the literal address-factor identity route(d*tau)N = route d(N*tau^-1), exact source stage/operand metadata and replica-major schedule, retaining all60 replicas. No complete Python instance enumeration or actual census is claimed checked.\nFull-theorem coverage: no end-to-end multiplication, runtime or kappa theorem. Actual helper census, GL120/reduction/normalizer data, full-state forward/complemented-reverse words, across-replica partition, boundaries/restored selectors and costs remain open.\n\n## Explicit author-checked kappa and pins\nBase12a4934d15006e8c10f9b2264f13f8f341be802b; head005dd3f4e3cba8d1761abc4ab391aaf6d14d6f73.\nAuthor-checked selected conditional kappa = 90446448750933/125000000000000000 = 0.000723571590007464.\nThis is source-matched construction context, not a bound derived by this package. Compiler, common-ancestor chart, restored-row, routing, prime-supply, precision/recovery, complex-correctness and analytic-transfer conditions remain.\nLiteral bindings refer to research/five-stage-gen4-banks/bank_template.py, code/global_lowering.py and BANK-PROOF.md at the exact base.\n\n## Reuse and comparison\nFive supporting modules are reused unchanged: BankRouting, SplitProjectors, CoordinatePartitions, ExactFrameTransport and BankEndpoints. Three additions are SequentialCompleteBank and the two current five-stage address/schedule bindings. The composition invokes existing weighted-partition results; no novelty claim is made for generic group/partition algebra or routine list glue.\nCompared with #236's older d1d6 paired-cube finite identities/arithmetic and #487's1320-port interface: this chunk supplies the current source-specific sequential completed-bank connection, without transferring their finite instances. The complete3606-module archive of #236 was not rechecked for an exhaustive theorem comparison.\nThe construction retains PR197/PR200 completed-bank attribution, Henry Grant/hcg890 PR234 lowering, eumemic's retained source527 work, Apache-2.0 and existing assistance disclosures.\n\n## Reproduction and evidence\nFrom research/lean-sequential-bank-bindings, run python3 check.py --lean /path/to/lean-4.21.0-linux/bin/lean --build-dir /tmp/sequential-bank-check.\nLinux/Python3, fresh nonexistent output directory, offline, no Mathlib/download. Eight source hashes/imports are checked, hard per-module60s/4GiB and review45s/3.5GiB. No objects shipped.\nFresh isolated replay:12.1047compiler seconds,0.00368queue,peak VM2,266,423,296 bytes. All eight object hashes and77 complete axiom outputs match accepted evidence after explicit whitespace normalization. Independent review and both authors confirmed final scope/replay metadata.\nLocal kernel results are separate from exact-head fork CI, upstream CI and maintainer gates; those are not claimed passed. One20-file additive commit; no inherited root 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categorized experiment log: 100 ideas, 300 trials, and recorded failures","user":{"login":"rohanarun","id":11659839,"node_id":"MDQ6VXNlcjExNjU5ODM5","avatar_url":"https://avatars.githubusercontent.com/u/11659839?v=4","gravatar_id":"","url":"https://api.github.com/users/rohanarun","html_url":"https://github.com/rohanarun","followers_url":"https://api.github.com/users/rohanarun/followers","following_url":"https://api.github.com/users/rohanarun/following{/other_user}","gists_url":"https://api.github.com/users/rohanarun/gists{/gist_id}","starred_url":"https://api.github.com/users/rohanarun/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/rohanarun/subscriptions","organizations_url":"https://api.github.com/users/rohanarun/orgs","repos_url":"https://api.github.com/users/rohanarun/repos","events_url":"https://api.github.com/users/rohanarun/events{/privacy}","received_events_url":"https://api.github.com/users/rohanarun/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"Latest completion: the coordinated partial-own candidate now passes local physics, explicit owner matching, global controller/invoice and exact arithmetic at conditional kappa0.001388082565814657 (PR473). `negative-searches/partial-own-coordinated/` retains the initial infeasible allocation, missing-input launcher failure, full-model timeout without incumbent, restricted-model repair, and successful verification receipts. A failed fixed-pattern allocation does not prove the gauge family infeasible.\n\nLatest addition: `negative-searches/partial-own-coordinated/` records fresh local verification of the four-gauge partial-own word and a rejected aggregate allocation. The stricter pattern/call flow is infeasible; the optimistic floating root is not an admitted bound. Solver timeout and downstream missing-input failure are preserved.\n\nResearch results and failed attempts were spread across PRs and SSD folders, making it easy to repeat exhausted searches or mistake execution errors for mathematical failures. This PR keeps `research/experiment-log/` as the shared categorized record, with evidence, scope, baselines and retry guidance. Numerical improvements remain in #473; this PR claims no new bound.\n\nThe initial import preserves all 100 campaign ideas across eight topic files, including 40 ideas with no execution evidence; three separate 100-trial kernel batches; 14 other scoped searches; and 16 execution-failure attempt groups with 31 original artifacts. These counts are the import baseline, not the total of later followups. Search iterations are not full mathematical certifications.\n\nLatest additions:\n\n- Eight donor-expression runs with no improving moves, plus four basis-exchange runs totaling 20,000 attempts. All endpoints, seeds, histories, exact prices and losing alternatives are retained. The successful rank-139 construction is published separately in #473.\n- Four further runs totaling 80,000 exchange attempts with temporary entrance demotions: no global improvement. One candidate improved the local search score but lost after exact whole-family pricing. Its word, price, history and retry guidance are preserved.\n- The cancellation-first hypothesis: paired source-injection removal did not change helper first frames. Local replay passed, but it supplied no new entrance opportunity.\n- All 424 hierarchy alternatives plus the baseline, subsequent R714 local replay and 40 no-gain kernel trials, five PR485 composition variants, and both initial replica-28 manifest failures with their correction.\n- Rank-139 validation receipts: fresh full Python 3.14 replay rebuilt both suppliers; Python 3.11 completed with explicitly pinned, completed-complex reuse. These are distinct verification scopes.\n\nRecords distinguish mathematical rejection, no improvement, solver/model limitations, execution failures, unverified proposals and completed verification. Floating packing-marginal diagnostics are labeled as discovery aids, not exact dual optimality certificates. Original failures remain alongside corrections; agents should document a changed input, assumption or search neighborhood before repeating a completed experiment.\n\nValidation: archive hashes, all 100 original idea IDs, all 300 original batch trial IDs and local Markdown links pass. Publication is checked against GitHub blob hashes. Historical mathematical claims are not claimed to have been rerun. Original campaign records remain linked to their pinned PR368 archive.\n\nFurther complex-side results: PR496 packing at 8/16/32/64 replicas, 106 entrance cases, 112 rational basis-exchange cases, and five retiming screens all found no admitted improvement. Original execution failures and the corrected runs are retained. A tiny fallback-count arithmetic proposal is explicitly unreviewed for complex compiler applicability. Fresh Python 3.14 headline/anchor complex-provider replay and the subsequent six pooled-component stages passed; no full two-supplier PR496 replay is claimed.\n\nNewest followups: 476 coordinated PR496 gauge trials (128 local constructor passes, 348 rejections, 22 profile classes), all-hosted and bank-permitting packing with no gain. Against the higher PR501/502 retimed baseline: 6,630 directed frame groups, a 400-move neutral walk, and six stage-count models also find no improvement. Frozen-map reconstruction matches the pinned PR501 word; its initial Python runtime failure is recorded separately. These are explicitly scoped search screens, not complete new-supplier certifications.\n\nNew gauge/kernel category:52 direct entrance rejections;1,253 selective gauge trials (1,121 local constructor passes,132 rejections,65 profile classes);186 kernel/gauge trades (124 passes,62 rejections,79 classes); both homogeneous pricing screens and two16-replica extensions find no gain. A143-class stage-dependent allocation found a small exception, independently admitted in PR473 and subsequently surpassed by PR505. Full ledgers, frozen inputs, failed attempts, exact arithmetic, completed followup receipt and retry guidance are preserved. These counts describe search trials, not independent complete theorem verifications.\n\nAsynchronous followups:10,224 fixed-map substitutions all exceed physical capacity; baseline and143-word fixed-order integer allocation screens give zero gain. The reference plus48 new replica schedules are retained, with four integer-priced nominations. The best candidate's initial per-pattern matching failure and its stricter global-flow repair are preserved, alongside40,320 explicit owners and completed conditional finite-composition receipts. The new numerical improvement is in #473. An initial list-versus-map execution error is archived separately.\n\nExact fixed-inventory wall:133 distinct timing schedules and the143-word mixing LP find no gain. A new rational dual certificate checks all348 width patterns and146 frozen word profiles using two independent interval engines. At the next complex saving grid point both prove moment>1, and the retained six-step outer assembly cannot reach the next kappa grid point. This excludes only the specified inventory/menu/fallback/assembly model; it is not a universal bound. Three new retimed kernel selections,16084 rank-two entrance subspaces and292 donor/pivot exchanges are also recorded, with no gain. The portable exact certificate has been replayed from the staged archive. New factories such as #507 are outside this obstruction.\n\nPartial-own followup: PR507's new factory lies outside the146-profile obstruction. 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The conditional result is **κ = 0.001388049083313897**, with complex supplier **b = 0.001389978441615608493590**. The #493 bit supplier remains nonbinding. Updated #473 at `9a2e1d4a7739aa4439982d6baea9ffca66bb8ae3` independently reports the same exponent with a different literal allocation; this PR matches that number and adds the full two-platform rebuild described below.\n\nSimply shrinking the 42 changed helper blocks inside the previous asynchronous assignment loses the gain. The new allocation rebuilds all 40,320 roles. Explicit per-pattern/call capacities and literal bipartite matchings produce 800 distinct physical owners per invocation; the independent controller reconstructs every actual event window, chart, spectator and remainder. No residual is split across physical families.\n\nThe resulting profile is `{1:179496, 2:16128, 3:40258, 4:6048, 5:25007, 6:4608, 7:528, 8:1224, 23:1, 48:734}`. Live/physical stock stays 7,680/8,258, rank deficit stays 2,496, and all remainders are paid. The complete scalar/Horner invoice, asynchronous prefix, two rational moment engines, six bootstrap levels, all 47 strict outer inequalities and rejection controls are recomputed.\n\nThe verifier rebuilds **both suppliers from scratch**, including #493's bit operator, the new factory and retiming, exact scalar and frame checks, guarded instance and whole-program physical checks, then the new asynchronous composition. Actual bit profile, invoice and program hash bind the assembly. It runs no optimizer and accepts no cached supplier receipt.\n\nOne portability repair is explicit. Upstream #507's full Linux run failed its frozen source-word hash because two discovery-only floating display fields differed in their last bits from macOS. Every other generated field matched. The derivative pins those two historical display values to the published JSON values; the original source and exact comparison are retained. The source-word and candidate-word hash assertions are unchanged. An unchanged upstream Linux full pass is not claimed.\n\nValidation:\n\n- Fresh macOS arm64 and Linux aarch64 runs passed all five wrapper stages and all 21 dependency stages, including their nested full supplier replays. Complete stable result files are byte-identical: `cb91ddf9cfac48e6fc8c6b734e377dbf80ba8cccb1226408b48e38734d9e4be7`.\n- Both reproduce #507's published exact-math hash `90fd7d912c39187a6402e76d83e36f1cf2880a20e565a2c7c782bf19c3cc1f6c`. The new controller checks 3,599 actual charts and 19 rejected mutations; prefix 205 bits with 512 charged; row coefficient 16,467 < 20,161.\n- All 346 manifest files and 326 copied Git source files were checked. Receipts, toolchains, macOS stage logs and detailed audits are in `research/partial-own-asynchronous-validation/`.\n- A separate two-engine certificate bounds further scheduling of this exact local word and fixed architecture by b < 0.001448157050078593686264. This is not a bound on different words or algorithms.\n- Added a Python 3.14 workflow for the same full verifier. GitHub CI status is separate from these completed local runs.\n\nRun from the repository root:\n\n```sh\npython3.14 -m pip install numpy sympy\npython3.14 -B research/partial-own-asynchronous-whole-owners/verify.py \\\n /absolute/new/output --boost-include /path/to/boost/headers\n```\n\nThe inherited all-size compiler, mutable-basis/common-label transport, #484 Lemma A spectator realization, restored-row, precision/tape and analytic-transfer conditions remain. This is a conditional exponent certificate, not an unconditional multiplication theorem, Lean proof or measured speedup. The disputed #448/#494 cross-family split interface is not used.\n\nCredits: eumemic (#507 factory/kernel84 and #493 bit supplier); Dugongue (#505 asynchronous scheduling and admission machinery); Rohan Arun (#473 nonuniform order and pattern/call-capacity repair); DreamingOfClouds (#449/#484 gauge/kernel interfaces); Ali Romman (#495 retiming); chafreaky (#458/#502/#506 adapters and prior compositions), and all authors retained in the pinned notices. New allocation, literal matching, composition and portability repair prepared by chafreaky with OpenAI 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kappa 0.001388082565814657: coordinated partial-own asynchronous composition","user":{"login":"rohanarun","id":11659839,"node_id":"MDQ6VXNlcjExNjU5ODM5","avatar_url":"https://avatars.githubusercontent.com/u/11659839?v=4","gravatar_id":"","url":"https://api.github.com/users/rohanarun","html_url":"https://github.com/rohanarun","followers_url":"https://api.github.com/users/rohanarun/followers","following_url":"https://api.github.com/users/rohanarun/following{/other_user}","gists_url":"https://api.github.com/users/rohanarun/gists{/gist_id}","starred_url":"https://api.github.com/users/rohanarun/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/rohanarun/subscriptions","organizations_url":"https://api.github.com/users/rohanarun/orgs","repos_url":"https://api.github.com/users/rohanarun/repos","events_url":"https://api.github.com/users/rohanarun/events{/privacy}","received_events_url":"https://api.github.com/users/rohanarun/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"**Conditional κ = 0.001388082565814657**, exactly `1388082565814657/10^18`, **0.0024121986% above our preceding verified result**. Complex b = **0.001390012017262092088600**. The bit supplier remains nonbinding.\n\n`research/complex-partial-coordinated-async/` applies #508's coordinated helper540..543 gauge collapse to #507's partial-own factory/kernel84, then repacks our nonuniform asynchronous order. All40,320 helpers have literal whole owners,800 distinct owners per invocation,7,680 live /8,258 physical families. The first aggregate allocation failed stronger pattern/call constraints; the joint model and explicit matching succeed. Discovery failures remain in #477.\n\n**The early draft's pending finite checks have passed.** Fresh changed-word scalar/frame/Gaussian/wrapper/labels, guarded helper-instance and whole-program checks and mutation controls pass. Fresh emission and independent global audit pass2,963 actual charts and19 rejected mutations. Prefix205bits,512charged,row16467<20161. Both exact moment engines, six bootstrap steps,47 strict inequalities and four outer controls pass.\n\nVerification scope: unchanged partial-own factory/provider explicitly reused from completed byte-pinned verification; changed-gauge local physics and global composition are fresh. The unchanged #493 bit operator is cited and its profile repriced. The packaged wrapper also passed with explicit byte-pinned factory/admission and changed-local reuse, fresh word reconstruction and fresh asynchronous replay. No cold packaged or CI pass is claimed. All inherited all-size compiler, mutable-basis/common-label, Lemma A realization, restored-row, precision/tape and analytic-transfer assumptions remain.\n\nPortable command: `python -B research/complex-partial-coordinated-async/verify.py /absolute/new/output --boost-include /path/to/boost/headers`. Requires the retained sibling `complex-partial-own-async` source. Explicit factory/admission and optional changed-local reuse paths check published byte pins; reconstruction and asynchronous stages remain fresh. Frozen exact inputs and completed receipts are included.\n\nCredit Dugongue #508/#505, eumemic #507, #501/502/#496/#484 and all retained source authors. New composition by Rohan Arun with OpenAI Codex assistance. Historical packages and results follow.\n\n---\n\n**Conditional κ = 0.001388049083313897**, exactly `1388049083313897/10^18`, **1.211951295% above our preceding verified finite result**. Complex b = **0.001389978441615608493590**. The bit supplier remains nonbinding.\n\nThe new `research/complex-partial-own-async/` combines #507's partial-own factory/kernel84 with our nonuniform asynchronous order. Its changed widths are explicitly repacked, with40,320 whole helper roles,800 distinct owners per complete invocation,7,680 live /8,258 physical families and no cross-family split.\n\n**The early draft's pending finite checks have now passed.** New factory/kernel/retiming reconstruction, scalar/frame and pipeline controls, Gaussian phases, wrappers, local replay and14 Lemma G necessity controls passed. Independent partial-basis algebra and retiming reviews passed, along with fresh guarded helper-instance and whole-program simulations. The changed asynchronous controller passes3525 actual-chart checks and19 rejected mutations. Exact finite invoice:205prefix bits,512charged,row16467<20161. Two exact moment engines, six bootstrap steps,47strict inequalities and four outer controls pass.\n\nVerification scope: unchanged complex provider explicitly reused from a completed byte-pinned replay; the changed local construction and physical checks are fresh. PR493's unchanged bit operator is cited, its profile repriced. The portable wrapper also passed with explicit byte-pinned completed-local/guarded reuse and fresh asynchronous replay; no cold full-package or CI pass is claimed. Receipts, exact inputs and complete immutable source are included.\n\nFresh command: `python -B research/complex-partial-own-async/verify.py /absolute/new/output --boost-include /path/to/boost/headers`. Explicit `--reuse-local` plus `--reuse-admission` validates every published input byte and completed receipt, then freshly reruns the new async composition. The arithmetic-only entrypoint is clearly separate.\n\nInherited all-size compiler, mutable-basis/common-label, Lemma A spectator realization, restored-row, precision/tape and analytic-transfer assumptions remain. This is not an unconditional theorem or new Lean proof. Credits: eumemic #507, Dugongue #505, PR501/502, PR496, DreamingOfClouds #484, PR493 and all retained source authors; new schedule allocation and composition by Rohan Arun with OpenAI Codex assistance. Failed/no-gain research and the scoped inventory obstruction remain in #477.\n\nHistorical results remain preserved below.\n\n---\n\n**Conditional κ = 0.001371428043382419**, exactly `1371428043382419/10^18`: **0.1342864619% above our preceding result** and **1.0109941802% above #505** at head `4ee769c8e28837482272b5f4742497da8e2fc9d4`. Complex saving **b = 0.001373311441205186394130**; the unchanged cited #493 bit supplier is nonbinding.\n\nThe latest package, `research/complex-async-order24/`, uses the already verified retimed local word with a new nonuniform order of 72 complete replica invocations. Every replica retains its complete local, bridge, idle and terminal order. A rebuilt physical map hosts 40,320 whole helpers, with 800 distinct owners per invocation, on 7,680 live / 8,258 physical families. No cross-family residual split is used. The profile is `{1:171720,2:19008,3:41568,4:6048,5:22992,6:6624,7:2040,8:1224,48:432}`.\n\nCompleted before this draft update: fresh emission; independent controller and bridge-sensitive owner-window audit with 3,564 actual orthogonal charts and 19 rejected mutations; exact finite invoice; both exact moment engines; six bootstrap steps; 47 strict outer inequalities and four rejection controls. Prefix 205 bits, charged 512; row coefficient 16,467 < 20,161. The initial aggregate matching attempt failed and was repaired using explicit per-pattern/call capacities before constructing and auditing the literal owners. Full discovery history, failures and no-gain screens remain in #477.\n\nThe local retimed word reuses its completed, byte-pinned scalar, Gaussian, common-label and guarded physical verification. The unchanged #493 bit operator is cited and its profile repriced, not freshly reconstructed. The packaged wrapper passed after early publication, with published byte-pinned completed-local reuse and fresh replay of every asynchronous stage. No cold full-package or CI pass is claimed.\n\nRun `python -B research/complex-async-order24/verify.py /absolute/new/output`. Default rebuilds the source-pinned provider/local dependency through the sibling verifier. Explicit `--reuse-local` checks the completed local receipt and every published input pin, then freshly verifies this new composition. The frozen integer order and literal owner map are the verification inputs; no floating timestamps or optimizer are trusted during verification.\n\nInherited all-size compiler, mutable-basis/common-label, #484 Lemma A spectator realization, restored-row, precision/tape and analytic-transfer conditions remain. #505's sufficient complete-call scheduling lemma is retained. This is a conditional finite witness, not an unconditional multiplication theorem, a new Lean proof or a global optimum. Larger disputed split-residual claims use a different interface.\n\nCredits: #505 (Dugongue) for asynchronous scheduling and retained emission/audit/invoice/assembly machinery; #501/#502 retiming; #496 pooling; #484 gauges/kernel and normalized spectators; #493 bit supplier and all earlier notices. Nonuniform schedule search, strengthened flow repair, literal matching and source-bound replay by Rohan Arun with OpenAI Codex assistance.\n\nHistorical results and their packages are preserved below.\n\n---\n\n**Conditional κ = 0.001369588870945540**, exactly `68479443547277/50000000000000000`: **0.8755319973% above #505** at head `4ee769c8e28837482272b5f4742497da8e2fc9d4`. The complex saving is **b = 0.001371467217183061206788**; the unchanged cited #493 bit supplier remains nonbinding.\n\n`research/complex-async-retimed/` combines #501/#502's retimed local word with #505's frozen asynchronous whole-owner schedule. Entrance widths are unchanged. The verifier rebuilds the paid profile from emitted local programs and explicit residual footprints, then independently checks all owner intervals, replica-local events and actual charts. This uses whole helpers, with no cross-family residual split.\n\nThe construction has 72 complete local invocations, 40,320 helper roles, 800 distinct owners per invocation, 7,680 live families and 8,258 physical families. All 3,194 actual orthogonal charts pass; 19 deliberately broken controllers are rejected. The prefix recount includes 72 individual bridges and 72 complete local sweeps: 205 bits required, 512 charged. Row coefficient 16,467 < 20,161. Both exact moment engines, six bootstrap steps, 47 strict outer constraints and four outer rejection controls pass.\n\nVerification scope at draft submission: the exact retimed local word already passed fresh scalar restoration, Gaussian phases, wrappers, common labels and guarded physical checks in the sibling package. The asynchronous emitter, independent controller audit, finite invoice and exact assembly passed freshly for this composition. The packaged verifier also passed after the early code publication, using byte-pinned completed local outputs and freshly rerunning every asynchronous stage. No cold full-package or CI pass is claimed. PR493's bit operator is source-pinned and cited; its profile is repriced, but its operator is not freshly reconstructed.\n\nRun `python -B research/complex-async-retimed/verify.py /absolute/new/output`. Default rebuilds the source-pinned provider/local dependency through the sibling verifier. Explicit `--reuse-local` accepts only byte-pinned completed local outputs and freshly runs the asynchronous stages, recording the reuse scope. All source pins, exact inputs, inherited notices and validation receipts are included.\n\nAll inherited all-size compiler, mutable-basis/common-label, #484 Lemma A spectator realization, restored-row, precision/tape and analytic-transfer contracts remain assumptions. #505's sufficient asynchronous scheduling lemma is retained. This is a conditional finite witness, not an unconditional multiplication theorem or new Lean proof. It does not claim to surpass the larger disputed split-residual constructions.\n\nCredits: #505 (Dugongue) for the asynchronous schedule, assignment and audit machinery; #501/#502 for retiming; #496 for pooling; #484 for gauge/kernel and normalized spectator machinery; #493 for the bit supplier, with earlier credits and notices retained. Composition and source-bound replay by Rohan Arun with OpenAI Codex assistance. Failed searches remain in #477.\n\nThe following results are historical and preserved with their receipts.\n\n---\n\n**Conditional κ = 0.001343523016252057**, a **0.0003720184% improvement over #501/#502** from a stage-dependent gauge choice. **#505 subsequently reported a higher asynchronous result; this is not a claim to surpass #505.**\n\nThe new `research/complex-stage4-gauge-mix/` uses the retimed baseline at eight stages and reduces helper540's entrance from rank4 to rank2 only at the middle stage. A homogeneous use of this change loses. The stage-specific allocation fits all40320 whole helper roles on existing data families with no banks.\n\nCompleted after the early draft: fresh checks of both local words (exact scalar restoration, emitted orientations,2952 Gaussian transitions per word, wrappers, common labels, guarded exhaustive operator identities and806basis+8dense physical tests); independent5007chart/72invocation owner audit with10negative controls; conservative finite union invoice; global142bit prefix below192; both exact moment engines; six bootstrap steps and47strict outer inequalities plus four controls. The complete conditional complex endpoint is1345330498741582613827/10^24.\n\nVerification scope: the PR484 provider was reused from a completed, byte-pinned replay. Both local words were freshly checked; the packaged entrypoint was then verified with those pinned completed outputs and freshly reran the mixed controller and invoice. PR493's unchanged bit saving is source-pinned and cited, not freshly replayed. No cold standalone or CI pass is claimed yet. Receipts, exact inputs, source hashes and an offline verifier are included.\n\nAll inherited all-size compiler, mutable-basis/common-label, Lemma A spectator realization, restored-row, precision/tape and analytic-transfer conditions remain. No cross-family split or unconditional theorem claim. Credits and notices cover PR501/502 retiming, PR496 pooling, PR484 gauges/kernel and PR493 bit supplier.\n\nHistorical R715 packages and receipts remain unchanged below.\n\n---\n\nConditional kappa **0.001297486611380425**, exactly `51899464455217/40000000000000000`: **0.06745494% above our previous0.001296611982495107**. The bit supplier binds. This compares the complete whole-family contract; it does not exceed PR480's larger disputed cross-family headline.\n\nThe new `research/r715-basis-exchange84/` package exchanges pivot and donor roles in the response kernel, updates every affected response equation, and promotes entrances while preserving nested donor chains. It keeps110 pivots but raises total entrance rank129→139, with102 distinct donors,130 correction rows and19 coordinate residual isometries. It retains PR483's14 target factors and22 paired source-injection cancellations. Exact rational packing scales the assignment to84 replicas: all660660 helper occurrences stay whole on individual physical families across924 complete invocations.\n\nAt draft submission, fresh source reconstruction and all955 arbitrary-dirty columns,110 correction-omission controls,22 single-injection controls,native signed/formal checks,labels/mixing/Gram checks,physical emission and independent ownership audit,fresh invoice,both rational moments and47outer inequalities passed. Initial assembly explicitly reused the unchanged completed complex supplier after binding87 implementation hashes and17 output hashes to its completed receipt. **Fresh full Python3.14 passed**, rebuilding both suppliers. **Complete Python3.11 passed** with explicit completed-complex reuse, checking its receipt,87 implementation hashes and17 output hashes. Receipts/logs are in `research/r715-basis-exchange84-validation/`. No GitHub CI pass is claimed.\n\nBit lower `649586135003318032049/500000000000000000000000`; complex lower `1305231506267591/1000000000000000000`. Run `python -B research/r715-basis-exchange84/verify.py /absolute/new/output`. Default reconstructs both suppliers; explicit `--complex-output` accepts only the pinned completed provider and emits a distinct reuse receipt. Python3.11+,SymPy,C++17 and Boost are required. Python3.11/3.14 CI includes the new package. The verifier reconstructs the final witness directly and runs no optimizer; it does not claim to replay every search decision.\n\nCredits: PR483 (Dugongue) supplies the nested110-pivot seed,response-packet method and target factors, building on our warm PR473 kernel and PR478. PR485's basis-selection work motivated the role-exchange search; its112-pivot seed was tested but is not the winning seed. New basis exchanges,nested promotions,source reconstruction and84-replica rational packing by Rohan Arun with OpenAI Codex assistance. 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core","user":{"login":"DreamingOfClouds","id":173691639,"node_id":"U_kgDOClpS9w","avatar_url":"https://avatars.githubusercontent.com/u/173691639?v=4","gravatar_id":"","url":"https://api.github.com/users/DreamingOfClouds","html_url":"https://github.com/DreamingOfClouds","followers_url":"https://api.github.com/users/DreamingOfClouds/followers","following_url":"https://api.github.com/users/DreamingOfClouds/following{/other_user}","gists_url":"https://api.github.com/users/DreamingOfClouds/gists{/gist_id}","starred_url":"https://api.github.com/users/DreamingOfClouds/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/DreamingOfClouds/subscriptions","organizations_url":"https://api.github.com/users/DreamingOfClouds/orgs","repos_url":"https://api.github.com/users/DreamingOfClouds/repos","events_url":"https://api.github.com/users/DreamingOfClouds/events{/privacy}","received_events_url":"https://api.github.com/users/DreamingOfClouds/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"\nThis PR gives Lemma G (entrance gauge: target-side compensation at nonzero frames, labelled targets, chain scatter) a clean,\nself-contained proof and formalises its abstract core in Lean 4.\n\nLemma G is worth +1.80% of complex `b` under no-bank hosting:\n\n| word | complex `b` |\n| --- | --- |\n| Lemma-G-free path (kernel79 only, #500) | 1.310216e-3 |\n| full gauge/kernel word (#496/#500) | 1.333854e-3 |\n\n#484 is not modified. This branch is stacked on #484's head and adds only `research/e8-lemma-g-lean/`.\n\n### What is proved (Lean 4.21.0 + Mathlib v4.21.0, the pin of `formal/lean` on main)\n\n```lean\ntheorem LemmaG.Stream.conj_matrix (T : Λ → M ≃ₗ[K] M) (rec : Λ → Λ → M → M) (es : List (Event ι Λ K))\n (l : ι → Λ) (h : ι → M) (hrec : RecipesExact T rec es) (hw : WellLabelled es l) (r : ι) :\n physRun rec es h r = T (labRun es l r) (∑ s, S es r s • (T (l s)).symm (h s))\n```\n\nThe theorem holds for every semiring `K`, every `K`-module `M` and every family of linear automorphisms `T`. Take any stream of relabel/add/scale/copy/clear events that is well labelled and whose relabels execute `T_B T_A⁻¹`. Then for every input it computes\n\n`h_r ↦ T_{λ¹_r}(Σ_s S_rs T_{λ⁰_s}⁻¹ h_s)`,\n\nwhere the non-private columns of `S` are exactly what #484's rational scalar replay computes (`S_rowform`; the replay starts the private copies empty, and their columns drop out on inputs with empty private registers).\n\nThe other Lean results:\n* **Row lemmas** (`row_unit`, `row_pair`). A unit row gives the block `T_{λ¹}T_{λ⁰}⁻¹`; for an entering helper this is the virtual entrance with its wrappers. A paired row gives `T_{λ¹_r}(T_{λ⁰_r}⁻¹h_r + a·T_{λ⁰_s}⁻¹h_s)`.\n* **Schedule** (`emit_spec`, `comp_segment`, `centre_forward`, `centre_backward`), proved for an abstract order with strictly monotone rank and instantiated for the subspaces of F₂⁹.\n * The compensation segment and the centre phase are well labelled as soon as the partners stay at their frames.\n * Under (b) and (c), every move is a strict nested ascent (or descent).\n * Each target ends at `L_t = max ℰ_t`.\n* **Accounting** (`paid_telescopes`). Paid ranks telescope to `rk λ¹ − rk λ⁰` per register.\n* **Bit-side entrance identities** (`Dbit_one_mul`, `Dbit_conj`). `D_I D_P = D_{I−P}`, and conjugation by `diag(g,g)` for `gᵀg = 1`, for every `P`.\n\nAll theorems are general: there is no instance enumeration and no `decide`/`native_decide`. Lean proves the abstract core. The schedule lemmas are an a-priori route that is not instantiated on the emitted stream; the stream itself is checked in Python (below). Combining the Lean core with those checks gives that the data rows are W's and the mass identity `mass(W) − Σ_j dim E_j`. `#print axioms` reports only `propext`, `Classical.choice` and `Quot.sound`. `verify.py` builds the package, scans for `sorry`/`axiom`/`native_decide`, and checks every axiom report.\n\n### What stays checked in Python\n\nThe instance hypotheses on the emitted streams:\n\n| hypothesis | check | result |\n| --- | --- | --- |\n| well-labelledness | #484 G0/G2/G3, plus the new `code/check_extended_labels.py` | 0 violations on all four words, both orientations; 3 adapter mutants rejected on every word, 2 wrapper mutants on the wrapper words |\n| exact transition recipes; the adapter/wrapper bridge | #484 I-tr on all 512 columns (recipes are linear circuits); one non-identity adapter per source and per target, all others identities (`check_extended_labels.py`) | 2945/2945 |\n| the scalar identity `S` | #484 replay, all 800 columns | exact |\n| endpoint labels | #484 G4 | 0 violations |\n| accounting | #484 G2/G3/ACC | 0 violations |\n| #433's data-adapter identities | the new `code/check_adapters.py`, every port, all 512 columns, exact | 0 failures on all four words |\n\nWhy the extended-label check: #484 §2.1 left adapters and wrappers outside Lemma C as endpoint operators. Register-wise that is right. Each non-identity adapter and each wrapper is the first or last event on its register, and the adapters that sit mid-stream (headline forward: 550 entry, 672 exit) are all identities. So #484's description was imprecise but harmless. Lemma C as stated still needed an unwritten commutation step. The clean proof reads adapters and wrappers as relabel events of an extended label set (tag × frame), so the theorem covers the complete emitted stream, and the condition is checked directly.\n\nWith these hypotheses checked exhaustively, and Lemma A (#484 I-helper, exhaustive), the end-to-end identity holds **for every input with empty private registers**. #484's `lg_e2e.py` tested it on 814 sampled columns.\n\n`PROOF.md` §5 lists the other clarifications:\n* the relabel-source condition;\n* the inherited facts behind \"every input\" (#433's adapter identities, Lemma A);\n* the minimal label condition;\n* (a)–(d) are accounting-only;\n* explicit side conditions;\n* the kernel updates as an instance of the same emitter.\n\n### Reproduce\n\n```sh\npython3 research/e8-lemma-g-lean/verify.py # Lean only: cache get + build + axioms\npython3 research/e8-lemma-g-lean/verify.py --instances /abs/out/of/484/verify # plus the instance checks (numpy)\n```\n\n### Credits\n\n* #425 (Zhihao Chen): the common-frame conjugation lemma and scalar interface.\n* #458 (chafreaky): the one-helper rule and paid wrappers.\n* #471 (Dugongue): the virtual entrance and complete-invocation normalisation.\n* #484 (DreamingOfClouds): the gauge construction, Lemma G and its Python check stage.\n* `formal/lean` on main: the Lean toolchain and Mathlib pin.\n* #487/#488 (jamesyc): the standalone Lean package layout and axiom reporting.\n\nPrepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code.\n\n🤖 Generated with [Claude Code](https://claude.com/claude-code)\n","created_at":"2026-10-11T22:41:35Z","updated_at":"2026-10-11T22:50:52Z","closed_at":null,"merged_at":null,"merge_commit_sha":"47097ebdfe0e7d65702b278e82bdccb8718f2fd5","assignees":[],"requested_reviewers":[],"requested_teams":[],"labels":[],"milestone":null,"draft":false,"commits_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/pulls/509/commits","review_comments_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/pulls/509/comments","review_comment_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/pulls/comments{/number}","comments_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/issues/509/comments","statuses_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/statuses/7b9c720ecc9f483c383e7cd9c2ab81f06ee5df59","head":{"label":"DreamingOfClouds:e8-lemma-g-lean","ref":"e8-lemma-g-lean","sha":"7b9c720ecc9f483c383e7cd9c2ab81f06ee5df59","user":{"login":"DreamingOfClouds","id":173691639,"node_id":"U_kgDOClpS9w","avatar_url":"https://avatars.githubusercontent.com/u/173691639?v=4","gravatar_id":"","url":"https://api.github.com/users/DreamingOfClouds","html_url":"https://github.com/DreamingOfClouds","followers_url":"https://api.github.com/users/DreamingOfClouds/followers","following_url":"https://api.github.com/users/DreamingOfClouds/following{/other_user}","gists_url":"https://api.github.com/users/DreamingOfClouds/gists{/gist_id}","starred_url":"https://api.github.com/users/DreamingOfClouds/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/DreamingOfClouds/subscriptions","organizations_url":"https://api.github.com/users/DreamingOfClouds/orgs","repos_url":"https://api.github.com/users/DreamingOfClouds/repos","events_url":"https://api.github.com/users/DreamingOfClouds/events{/privacy}","received_events_url":"https://api.github.com/users/DreamingOfClouds/received_events","type":"User","user_view_type":"public","site_admin":false},"repo":{"id":1412741203,"node_id":"R_kgDOVDS4Uw","name":"integer-mult-bounds","full_name":"DreamingOfClouds/integer-mult-bounds","private":false,"owner":{"login":"DreamingOfClouds","id":173691639,"node_id":"U_kgDOClpS9w","avatar_url":"https://avatars.githubusercontent.com/u/173691639?v=4","gravatar_id":"","url":"https://api.github.com/users/DreamingOfClouds","html_url":"https://github.com/DreamingOfClouds","followers_url":"https://api.github.com/users/DreamingOfClouds/followers","following_url":"https://api.github.com/users/DreamingOfClouds/following{/other_user}","gists_url":"https://api.github.com/users/DreamingOfClouds/gists{/gist_id}","starred_url":"https://api.github.com/users/DreamingOfClouds/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/DreamingOfClouds/subscriptions","organizations_url":"https://api.github.com/users/DreamingOfClouds/orgs","repos_url":"https://api.github.com/users/DreamingOfClouds/repos","events_url":"https://api.github.com/users/DreamingOfClouds/events{/privacy}","received_events_url":"https://api.github.com/users/DreamingOfClouds/received_events","type":"User","user_view_type":"public","site_admin":false},"html_url":"https://github.com/DreamingOfClouds/integer-mult-bounds","description":"Conditional integer multiplication: kappa > 2^-15. 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kappa 0.001372554837726243: coordinated gauge collapse with retimed asynchronous whole owners","user":{"login":"Dugongue","id":49054532,"node_id":"MDQ6VXNlcjQ5MDU0NTMy","avatar_url":"https://avatars.githubusercontent.com/u/49054532?v=4","gravatar_id":"","url":"https://api.github.com/users/Dugongue","html_url":"https://github.com/Dugongue","followers_url":"https://api.github.com/users/Dugongue/followers","following_url":"https://api.github.com/users/Dugongue/following{/other_user}","gists_url":"https://api.github.com/users/Dugongue/gists{/gist_id}","starred_url":"https://api.github.com/users/Dugongue/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/Dugongue/subscriptions","organizations_url":"https://api.github.com/users/Dugongue/orgs","repos_url":"https://api.github.com/users/Dugongue/repos","events_url":"https://api.github.com/users/Dugongue/events{/privacy}","received_events_url":"https://api.github.com/users/Dugongue/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"Conditional kappa = **0.001372554837726243**, exactly `1372554837726243/1000000000000000000`.\n\nThis is 2.161253% above the pinned PR501/502 whole-owner result and 1.093987% above our previous asynchronous construction. It combines a new coordinated four-gauge target-level collapse, the PR495/501/502 body retiming, and offset6 asynchronous whole-owner hosting. All gains are recomputed from one actual paid program; no separately quoted exponent gains are added.\n\n### New mechanism: release shared target levels together\n\nStarting from PR484's gauge80-kernel42 word, helpers540,541,542,543 all move from rank4 entrance gauges to the existing rank2 frame `[408,102]`. The42 kernel pivots are unchanged. Reconstructing the entire frame system lowers targets81,82,84,87 from rank4 to rank2.\n\nA single withdrawal leaves the shared target levels high. Four separately scored moves would predict only `-4 rank2 +4 rank4`. The actual joint change is `-16 rank2 +4 rank4 +4 rank6`: coordination releases costs that a marginal search misses. Four whole residuals grow from width5 to width7, so the changed inventory is repacked and charged in full.\n\nThe complete local inventory is18 width7,104 width8,438 width9. All72 calls use this same reconstructed provider. Eight replicas preserve their own controller order while calls follow `(7*stage+6*replica,stage,replica)`. All40320 helper uses have literal whole physical owners; no residual is split across families. Each invocation completes its whole cover sweep and normalization before another starts.\n\n### Exact result and invoice\n\n- Complex lower saving: `1374441333828159774039/1000000000000000000000000`.\n- Cited unchanged PR493 bit lower saving: `391360506745414227149/250000000000000000000000`.\n- Complex remains binding.\n- Paid profile: `{1:171720,2:17856,3:41568,4:6336,5:23280,6:6912,7:1752,8:1224,48:432}`.\n- Ambient73; live7680; physical8258; rank mass558144; deficit2496.\n- 2972 actual orthogonal73-column charts;9360 explicit paid remainders;32113 cross-replica uses.\n- Prefix205bits, charged512; two-level row coefficient16467<20161; maximum child48 satisfies `73^2 > 2*48^2`.\n\n### Reproduction and checks\n\nAdditive folder: `research/coordinated-gauge-async/`.\n\n```\npython -B research/coordinated-gauge-async/verify.py --work /absolute/path/to/a-new-output-directory\n```\n\nPython3.11+, standard library only. No optimizer, network, C++ compiler or Lean installation is required. The output directory must be new and outside the package. Assertions must remain enabled.\n\nThe verifier reconstructs the public frame transfer and coordinated gauges, checks exact scalar columns in both orientations, Gaussian phases and paid wrappers, emits the physical asynchronous program, independently checks literal chronology/owners/spectators and the complete scalar/prefix invoice, and runs two rational moment engines plus six bootstrap steps and all47 strict outer inequalities. It rejects19 corrupt controller variants and4 outer controls, including the adjacent kappa grid point. The retained PR493 bit histogram is repriced; the unchanged bit operator is explicitly cited rather than needlessly re-run.\n\nGenerated text is forced to UTF-8/LF in a process-scoped launcher to avoid Windows/Linux adapter-hash mismatches. Immutable sources have a manifest and `.gitattributes`. Detailed receipts and the scope of local testing are included; this does not claim a CI run on an untested platform.\n\n### Direct sources and credits\n\n- #473: single-helper rank4-to-rank2 withdrawal directly inspired the joint gauge screen. The new step is the simultaneous four-helper change and shared-level collapse.\n- #495: main-word frame retiming.\n- #501 and #502: transfer of that retiming onto the gauge80-kernel42 construction and whole-owner integration. The included transfer constructor and schedule fixture are from pinned #502.\n- #484: entrance-gauge/shared-donor kernel word, scalar/frame machinery and paid residual wrappers.\n- #496: whole-owner pooling, allocation and audit/invoice ancestry.\n- #493: unchanged R489 bit supplier.\n- #458, #433, #425 and #370: whole-owner spectator, split-centre, geometry and scalar/phase ancestry.\n- #434, #417, #435, #440, #401 and #408-#416: retained response-kernel and gauge ancestry.\n- #361 and #315: exact moment and outer arithmetic ancestry.\n\nOur previous complete-invocation asynchronous construction supplies the scheduling method. OpenAI math's WordScheduling/CommonBases and the tensor-isomorphism intertwiner viewpoint informed the research; they are not represented as newly kernel-checked proofs of this package. Source revisions, file hashes, original notices and precise roles are included.\n\n### Research preserved for future work\n\nThe package explains the nonlinear shared-target mechanism and retains concise evidence for382 single-gauge subframes,20 coordinated choices, six further combinations, retimed response-matroid variants, asynchronous inventory portfolios, and a clean-row alias screen. It also gives a sufficient pending-factor transport identity `Q_y A=A Q_x` and a safe deferred-terminal-suffix construction. Those additional routes produced no further priced gain here and are not counted in the exponent. Negative screens are bounded experiments, not global impossibility claims.\n\n### Scope\n\nThis is a conditional finite whole-owner construction under the inherited all-size compiler, mutable-basis/common-label, normalized Lemma A realization, restored-row, precision/tape and analytic-transfer contracts. These remain explicit conditions; finite replay does not prove them. No unconditional integer-multiplication theorem or fresh Lean certification is claimed.\n\nThe snapshot is frozen through #504. #503's bit-only draft and #504's alternate read-then-climb route were read but are not numerical ingredients. #499's larger0.001452948511251494 claim inherits the disputed #494 split-residual interface; this submission neither adopts that interface nor claims to exceed that numerical headline.\n\nPrepared with substantial OpenAI Codex assistance. Original source authorship and licenses are retained. 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= 0.001363614743745701: partial-own factory with 84 kernel pivots","user":{"login":"eumemic","id":94939491,"node_id":"U_kgDOBaipYw","avatar_url":"https://avatars.githubusercontent.com/u/94939491?v=4","gravatar_id":"","url":"https://api.github.com/users/eumemic","html_url":"https://github.com/eumemic","followers_url":"https://api.github.com/users/eumemic/followers","following_url":"https://api.github.com/users/eumemic/following{/other_user}","gists_url":"https://api.github.com/users/eumemic/gists{/gist_id}","starred_url":"https://api.github.com/users/eumemic/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/eumemic/subscriptions","organizations_url":"https://api.github.com/users/eumemic/orgs","repos_url":"https://api.github.com/users/eumemic/repos","events_url":"https://api.github.com/users/eumemic/events{/privacy}","received_events_url":"https://api.github.com/users/eumemic/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"κ = 0.001363614743745701\n\nThis conditional whole-owner construction improves frozen #501 by approximately 1.496%. It combines the unchanged #493 R489 bit supplier with a new complex factory that loads 112 own-block helpers from existing rank-two pair intermediates. The changed invertible partial bases remove 56 factory operations and admit 42 more kernel pivots: 80 gauges and 84 pivots now give entrance rank 190.\n\nThe complex endpoint is exactly `b = 1365476727944167989749/10^24`. Frozen retiming and a newly emitted pooled owner allocation give the assembled value `κ = 1363614743745701/10^18`. All 40,320 helper roles occupy whole physical families, with 800 distinct owners per complete invocation. Live/physical stock is 7,680/8,258, and the complete paid profile is:\n\n```\nrank 1 2 3 4 5 6 7 8 32 48\ncount 179832 16128 40655 6048 24343 4608 1128 3112 1 369\n```\n\nEvery rank-32 and rank-48 idle remainder is paid. The rank deficit remains 2,496; strict halving is `73² > 2·48²`. The full scalar/Horner invoice, physical stock, global prefix, two rational moment engines, six bootstrap levels and all 47 outer inequalities are recomputed.\n\nThe package is `research/r489-partial-own-kernel84/`. It rebuilds both pinned suppliers, the new factory and selected kernels, an unretimed canonical comparison, the retimed scalar words, exact phase recipes and paid wrappers, then the actual whole-owner controller. Independent checks cover all 28 own-tetrad bases, all 84 kernel relations, all 800 scalar columns in both orientations, arbitrary dirty restoration, both 25,290-event frame ledgers, 3,924 actual orthogonal 73-column maps, 18 controller rejection controls and 14 Lemma G necessity controls. Guarded physical simulations check all 2,947 used transitions on 512 columns and both full orientations on 890 structured/random basis columns plus eight dense columns, with bounds before integer operations execute.\n\n```sh\npython3 -B research/r489-partial-own-kernel84/verify.py /absolute/fresh/output \\\n --boost-include /path/to/boost/headers\n```\n\nRequirements: Python 3.14, NumPy, SymPy, Bash, a C++17 compiler and genuine Boost headers. No network or optimizer is used for verification. `MANIFEST.json` binds the package and `SOURCE.json` retains all 266 original supplier-file hashes. Historical records under `provenance/` describe the #496/#501 ancestry; the new candidate's acceptance comes from the fresh verifier and `EXPECTED.json`.\n\nThis retains the inherited all-size compiler, mutable-basis/common-label, Lemma A realization with borrowed spectators, restored-row, precision/tape and analytic-transfer contracts. Finite checks and sampled end-to-end physical tests do not establish those all-size contracts or an unconditional multiplication theorem. The comparison is within the stated whole-owner interface. The newly updated #473 separately claims κ = 0.001371428043382419 through nonuniform asynchronous whole-owner scheduling; this PR is a fully replayed improvement over frozen #501, and does not claim to exceed that newer number. Its changed local factory and kernel selection are independent ingredients for further scheduling experiments. Larger draft numbers using cross-family splits carry separate proof obligations.\n\nCredits: eumemic (#493), DreamingOfClouds (#484, with Claude Opus 5.5 assistance), DaysSky, icekylinx, chafreaky, Zhihao Chen, Rohan Arun, Dylan Crow, Jacob Sussman and the authors retained in the pinned notices. This new factory, kernel selection, retiming, allocation, audits, integration and documentation were prepared with substantial OpenAI Codex assistance. Original Apache-2.0 licenses and AI disclosures are retained. This is a new branch and PR; #496, #501 and every previously published head and claim remain frozen.\n\nValidation: both complete fresh Python 3.14 source and committed-archive replays finished with observed exit 0. Every scalar, reflected-ledger, physical, owner, invoice, exact-moment and outer-assembly admission passed. The package manifest SHA256 is `1a84b876ecc3247ffbda8c85f08fe91ff6369a7b81f1b972b7108f827ae5defc`; both replays produce exact-math SHA256 `90fd7d912c39187a6402e76d83e36f1cf2880a20e565a2c7c782bf19c3cc1f6c`. All 314 package files were compared with committed blobs. This reports local fresh verification, not GitHub CI 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Complete stable result files are byte-identical, SHA-256 `94585e3cdc8605de54323755ce6014a101bdc6b9a1cf73adbac0458805df6619`.\n- Both physical orientations, every helper instance on 512 basis columns, 806 basis and eight dense whole-program inputs, pre-operation integer guards, 19 asynchronous mutations and 14 local controls were checked.\n- The 205-bit prefix bound with 512 bits charged, finite invoice, two rational moment engines, six bootstrap levels, all 47 strict outer inequalities and next-grid/parameter controls passed.\n- All 109 manifest files and 99 copied source files were checked against pinned Git bytes. Platform receipts, toolchains, stage logs and detailed audits are in `research/retimed-asynchronous-validation/`.\n- Added the full verifier to a Python 3.13/3.14 GitHub workflow. Remote CI status remains separate from the completed local runs.\n\nThe package explicitly records two #505 replay packaging issues: a missing manifest-listed `.gitattributes` and a final template hash containing the CRLF encoding of an adapter JSON. Its mathematical replay stages and exact result passed with those issues isolated; its published verifier did not pass unchanged. This package supplies its own complete manifest and fresh replay, without weakening source hashes.\n\nThe all-size compiler, common-label/mutable-basis transport, #484 Lemma A realization, restored-row, precision/tape and analytic-transfer interfaces remain conditions. This is a conditional exponent certificate, not an unconditional theorem, Lean proof or measured speedup. 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+ knowledge (no frontier claim): read-then-climb bit word R687 (c ≈ 1.315433·10⁻³), a copy lower bound, exact pivot certificates","user":{"login":"DreamingOfClouds","id":173691639,"node_id":"U_kgDOClpS9w","avatar_url":"https://avatars.githubusercontent.com/u/173691639?v=4","gravatar_id":"","url":"https://api.github.com/users/DreamingOfClouds","html_url":"https://github.com/DreamingOfClouds","followers_url":"https://api.github.com/users/DreamingOfClouds/followers","following_url":"https://api.github.com/users/DreamingOfClouds/following{/other_user}","gists_url":"https://api.github.com/users/DreamingOfClouds/gists{/gist_id}","starred_url":"https://api.github.com/users/DreamingOfClouds/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/DreamingOfClouds/subscriptions","organizations_url":"https://api.github.com/users/DreamingOfClouds/orgs","repos_url":"https://api.github.com/users/DreamingOfClouds/repos","events_url":"https://api.github.com/users/DreamingOfClouds/events{/privacy}","received_events_url":"https://api.github.com/users/DreamingOfClouds/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"**Method + knowledge PR (no frontier claim).** For the complex side it cites our #484: a pinned full-run result at #484 head\nd30a05f. The branch itself contains #463 and #471.\n\nIt contains three things:\n- an anatomy and lower bound for the **copy** term of #370-lattice bit words;\n- **read-then-climb**, a compile change that removes 28 copies;\n- **exact kernel-pivot certificates**.\n\nThe resulting bit supplier is **R687: c = 65771650815860982499/(5·10²²) ≈ 1.315433·10⁻³**. It is priced at eleven stages with\n#442 whole-residual hosting and target mixing, with no cross-family split. That is +2.36% over the R715 bit supplier (#463) and\n+1.32% over #483's bit.\n\n| complex supplier | κ | binds |\n|---|---|---|\n| #484 (our draft, head d30a05f; Lemmas A, G), cited from its pinned full run | **≈ 1.313705·10⁻³** | bit |\n| #471 (Dugongue), rerun unchanged, #471's own assembler | 1303530097714685/10¹⁸ | complex |\n\n**Relation to #493.** #493 (eumemic) builds a 489-helper word with sources as carriers and c ≈ 1.565·10⁻³. Its bit side no longer\nbinds, so #493 + #484 = 1.325031·10⁻³ is above our #484 figure, and #493 + #471 equals our #471 figure (#471's complex cap).\n\nOur levers do not transfer to #493. #493 is a hand-built D4-quad skeleton, not a compiled pair ⊂ L ⊂ M hierarchy, so the copies\nthat read-then-climb removes do not exist there. And no bit-side gain can move κ while #493's c sits 18% above every whole-residual b.\n\n### What is new\n1. **Copy anatomy.** Raw R = 9 + carriers + copies + fresh. On R715 that is 839 = 9 + 240 + 528 + 62.\n - Most copied symbols (427 of 467 on R687) have exactly two rule parents whose frames meet only in the symbol's own frame: a\n pair in two L's, an L in two M's, an M in two tops.\n - The exceptions: 28 L's that also build D4(c) (three parents), 10 pair and 8/4 sums with 3–4 parents, one 9/4 sum and one\n 16/6 sum.\n - Given the DAG, the copies depend on the phase rule: 556 under #370's phases against 500 with read-then-climb.\n2. **Lower bound (transversal-cover lemma, any legal word).** A register whose first use is at frame G feeds only targets in G^⊥.\n So χ(u) ≥ the least number of proper sections covering u's downstream targets (the carrier bound is the case of a source).\n - **#370 lattice family (hand proof).** Assumptions: rule gates at the hierarchy's frames; one nested read chain per target;\n distinct M frames. Results:\n - M copies ≥ 112, or ≥ 140 when every rule runs before the scatter.\n - L copies ≥ 168.\n - Pair copies ≥ 168: each lattice pair has two L readers at incomparable frames, and the carrier bound (3 chains per cw source)\n caps the distinct pairs at 168. Without that bound, pair copies + cw carriers ≥ 392.\n - **Totals:** lattice copies ≥ 448 = 112 + 168 + 168, or ≥ 476 with the D4 assembly. With all-A phases the bound is ≥ 504,\n against R715's 528.\n - **Per DAG, machine-checked by `verify.py` (`copy_bound.py`, exact Dilworth plus the lemma only):** R687 has 500 copies\n against a bound of 464; R715 has 528 against 492.\n - **Scope:** no bound on copies alone holds outside a fixed DAG, because copies trade one-for-one against recomputation and cancellation.\n3. **Read-then-climb + coset-split π-pairings.** A rule that reads a low-read symbol moves after the scatter, so the symbol's\n register is read at its own D5 frame first and then climbs. Spreading the D5 slots over both π-cosets of each block brings M\n copies from 140 to 112, which is the new bound.\n - A per-block search over two slices of the flags (pairings × l5, and pairings × folds; raw R is block-separable) found no\n lower raw R. It ran outside the package and is not re-run by `verify.py`.\n - Stacked with #463's re-expressions, R goes from 715 to 687.\n - `mix_target.py` generalises #450 mixing to words whose phase B holds helper rules.\n4. **Exact kernel pivots.** Pivot selection is a min-sum-rank list partition over a linear matroid. `exactgen.py` solves it by a\n computer-assisted exhaustive search per component, using block DP and coupling enumeration.\n - Scope: the maximum over #443-format selections on the retimed pre-kernel word (#436 retime, 6 sweeps), with coordinate\n entrances and one class per donor.\n - **R687:** maximum 101; parity leaves 100. The greedy search had 71. This adds +0.887% to c.\n - **R715:** maximum 112. This equals the exact maximum in our draft #485, recomputed here by a second solver.\n\n### Verification\n`python -B research/e8-r687-tensor-complex/verify.py /abs/out [--light]`; CI workflow `e8-r687-tensor-complex`.\n\nThe bit package (`research/e8-r687-read-then-climb/verify.py`) checks:\n- **Regeneration:** the word is rebuilt from the frozen hierarchy byte for byte; every rule and read is checked for legality;\n only the phase rule of #370's compile2 is substituted.\n- **Bounds and certificates:**\n - the copy anatomy and bound on both pinned hierarchies;\n - the R687 pivot lower bounds and witness, checked against the pinned refutation log (`--certificate` reruns it, about 30 min);\n - the R715 log is pinned only.\n- **Kernel and mixing:** the kernel is rebuilt from the frozen exact selection (#443 replay and interface); mixing is regenerated\n byte for byte.\n- **Word checkers:** #370's independent checker and mutants, the relaxed all-column checker on the kernel and mixed words, #443's\n C++ cohort legality, five- and eleven-stage formal columns, record mutants, mixing mutants and Gram.\n- **Eleven-stage pipeline:** geometry, template and hosting audits, the frozen HiGHS selection (`--discover-check` recomputes it),\n and assembly.\n\nAn independent validator found the R687 word valid, and phase-order mutants are rejected. An independent audit then checked the\nexact-pivot word:\n- its tape check re-derived c (|Δc| = 7.3·10⁻²⁵; profile and program digest equal);\n- an independent solver recomputed the R687 maximum of 101.\n\n### Review points\n- **Read-then-climb** (`code/hier_word_rtc.py`). Phase-B rules read helpers after the scatter. #370's compile already supports\n phase B. The emitted word passes #370's checker unchanged: 927 columns, B gates hold 100 helper rules.\n- **B-rule-aware mixing.** Prefixes are compared per (register, version). On words without B rules it makes #450's choices; it\n passes mix_check with 4/4 mutants rejected.\n- **#471 manifest.** #471's MANIFEST lists a `.gitattributes` absent from its PR tree. Our wrapper accepts it absent (recorded in\n the receipt), hash-checks it when present, and checks every other file.\n- **Inherited.** #484's figure carries its Lemmas A and G.\n - From #450 only Lemma M (bit labels) is used; #450's cross-copy hosting is not.\n - #450's B-constancy step does not apply, because B holds 100 helper rules. The mixer's scalar identity is checked exactly on\n all 927 columns instead.\n - The usual compiler, dirty-helper and analytic interfaces are inherited.\n\n No unconditional theorem or Lean proof is claimed.\n\nCredits:\n- Dugongue: #471 complex supplier and assembler, #476/#478/#483.\n- rohanarun: #473, #470, #460 verifier structure.\n- chafreaky: #472, #458, #451/#454, #443–445.\n- eumemic: #493, #436 R740 word and reuse, #440/#441.\n- DaysSky: #442 hosting.\n- Dylan Crow: #370 bit word, producer and checkers.\n- higherbeing (#448), icekylinx (#433), jacklightChen (#425), Srikrishnabalaji (#465), Jacob Sussman, Zhihao Chen, and all\n source-pinned authors.\n- Our #463 (R715, carrier bound) and #484/#485.\n\nCopy anatomy and bound, read-then-climb, coset-split pairings, exact pivot certificates and the compositions are by\nDreamingOfClouds with **Claude Opus 5.5 (Anthropic), via Claude Code**.\n\n🤖 Generated with [Claude Code](https://claude.com/claude-code)\n","created_at":"2026-10-11T21:56:33Z","updated_at":"2026-10-11T22:32:56Z","closed_at":null,"merged_at":null,"merge_commit_sha":"7f5fdaf1b5338f504f20cba34a4a24717878fcac","assignees":[],"requested_reviewers":[],"requested_teams":[],"labels":[],"milestone":null,"draft":false,"commits_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/pulls/504/commits","review_comments_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/pulls/504/comments","review_comment_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/pulls/comments{/number}","comments_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/issues/504/comments","statuses_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/statuses/35057a6d70f23480f4e960327d41ecac31ad5cb0","head":{"label":"DreamingOfClouds:e8-r687-read-then-climb","ref":"e8-r687-read-then-climb","sha":"35057a6d70f23480f4e960327d41ecac31ad5cb0","user":{"login":"DreamingOfClouds","id":173691639,"node_id":"U_kgDOClpS9w","avatar_url":"https://avatars.githubusercontent.com/u/173691639?v=4","gravatar_id":"","url":"https://api.github.com/users/DreamingOfClouds","html_url":"https://github.com/DreamingOfClouds","followers_url":"https://api.github.com/users/DreamingOfClouds/followers","following_url":"https://api.github.com/users/DreamingOfClouds/following{/other_user}","gists_url":"https://api.github.com/users/DreamingOfClouds/gists{/gist_id}","starred_url":"https://api.github.com/users/DreamingOfClouds/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/DreamingOfClouds/subscriptions","organizations_url":"https://api.github.com/users/DreamingOfClouds/orgs","repos_url":"https://api.github.com/users/DreamingOfClouds/repos","events_url":"https://api.github.com/users/DreamingOfClouds/events{/privacy}","received_events_url":"https://api.github.com/users/DreamingOfClouds/received_events","type":"User","user_view_type":"public","site_admin":false},"repo":{"id":1412741203,"node_id":"R_kgDOVDS4Uw","name":"integer-mult-bounds","full_name":"DreamingOfClouds/integer-mult-bounds","private":false,"owner":{"login":"DreamingOfClouds","id":173691639,"node_id":"U_kgDOClpS9w","avatar_url":"https://avatars.githubusercontent.com/u/173691639?v=4","gravatar_id":"","url":"https://api.github.com/users/DreamingOfClouds","html_url":"https://github.com/DreamingOfClouds","followers_url":"https://api.github.com/users/DreamingOfClouds/followers","following_url":"https://api.github.com/users/DreamingOfClouds/following{/other_user}","gists_url":"https://api.github.com/users/DreamingOfClouds/gists{/gist_id}","starred_url":"https://api.github.com/users/DreamingOfClouds/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/DreamingOfClouds/subscriptions","organizations_url":"https://api.github.com/users/DreamingOfClouds/orgs","repos_url":"https://api.github.com/users/DreamingOfClouds/repos","events_url":"https://api.github.com/users/DreamingOfClouds/events{/privacy}","received_events_url":"https://api.github.com/users/DreamingOfClouds/received_events","type":"User","user_view_type":"public","site_admin":false},"html_url":"https://github.com/DreamingOfClouds/integer-mult-bounds","description":"Conditional integer multiplication: kappa > 2^-15. 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The bit side binds; the paid-adapter complex supplier is unchanged.\n\nStarting from #463's published R715 word, reconstruct 109 shared-donor pivots (entrance rank 120), 56 disjoint target mixes, 60 single-gate retimings and #467's 14 paired retimings. Pool eight replicas, keeping each of the 62,920 residual occurrences whole on one idle physical family. The exact bit lower endpoint is `0.001293771240692396056124`, with 9,600 live and 9,609 physical families.\n\nThe physical-family growth bound is recomputed independently. Its 804-bit prefix is charged at 832 bits, and the 2,468-bit three-level coefficient at 2,496 in every bootstrap cutoff. The bit row coefficient remains 19,431, below the retained 20,161 contract.\n\nVerification covers exact reconstruction; all local and unbanked global columns; fresh C++ legality and eleven-stage columns; record and mixing mutations; Gram matrices and target labels; residual isometries and projectors; every owner, window, slot and remainder; the renamed instruction stream; physical-prefix accounting; both rational moment engines; six bootstrap steps and all 47 strict outer inequalities. Adjacent-grid and invalid-parameter controls are rejected.\n\nRelease evidence includes a full Linux replay and a macOS component replay with an explicitly reused, freshly completed and manifest-matching Python 3.11 full parent. The entire final RESULT.json matches across platforms. All 16 repository joint tests pass. GitHub CI remains separate and pending.\n\nRun `E8_REPLAY_PHASES=1 python -B research/e8-r715-whole-hosted/verify.py /absolute/new/output`. Default mode replays the complete corrected #458 chain. Explicit `--parent-output` reuse emits a distinct receipt status. Source hashes, proof, receipts and Python 3.11/3.14 CI are included.\n\nAll inherited compiler, mutable-basis/target-label, whole-call correlated-helper hosting, compressed-window, restored-work, common-grid/tape, precision, row and analytic contracts remain. No residual is split across physical families. This is a conditional finite composition; κ = 1, global optimality and an unconditional multiplication theorem remain unproved.\n\nCredits: DreamingOfClouds with Claude Opus 5.5 for #463's carrier/XOR word and target mixing; Rohan Arun with OpenAI Codex for #462 pooling/prefix accounting and #467 paired retimings; DaysSky for whole hosting; chafreaky for the shared-donor lineage, target-label audit and #458 paid complex supplier; Jacob Sussman, Dylan Crow, Zhihao Chen, eumemic, icekylinx and all inherited authors. New selection, integration and release by chafreaky with OpenAI Codex. Original sources, notices and licenses 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word R480: totals on dead registers, c = 0.001574753352953808650916 (+0.595% over 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change to #493's E8 bit word.** In R489, the nine decoder totals each get a fresh register. Here each total is\nformed on a register that is already dead, and the host is the **last** eligible register of the total's combination.\n#493's generator already supported dead hosts but took the first register, and that word fails the official finite\nprefix bill. Everything else is #493's word, gate for gate. The result is **R = 480**, the R ≥ 480 bound #493's\nREADME argues for its family (an analysis under its stated hypotheses: this partition, three branches per source,\ntotals in phase A; not machine-checked).\n\n| | R | five-stage payload (limit: < 2^104) | bit c (#472 eleven-stage whole-residual pipeline, as in #493) |\n|---|---|---|---|\n| #493 (fresh totals) | 489 | 100 bits | 0.001565442026981656908596 |\n| #493's generator, dead hosts, first register | 480 | 129 bits, **refused** by `columns_h` | – |\n| **this PR: dead hosts, last register** | **480** | **102 bits, PASS** | **`393688338238452162729/250000000000000000000000` = 0.001574753352953808650916 (+0.5948%)** |\n\nκ does not change, because the side that binds is the complex side. With #484's complex b (Lemmas A and G) κ =\n`662515748707749/500000000000000000` = 0.001325031497415498. With #471's it is 0.001303530097714685, and with #458's\n0.001295523322678044. The bit gain is headroom for any complex supplier above #493's c.\n\nExploration outside the package (not run by verify.py): over needer swaps and first, last and random total hosts at\nR = 480, every variant we priced gave the same c.\n\n## What is in `research/e8-r480-dead-totals/`\n- `code/adapt.py`: derives the three files this package runs from #493's files, using 8 listed string edits (each\n anchor found exactly once). The generator change is `sorted(combo)` → `sorted(combo, reverse=True)` in the dead-host\n choice. The audit and local audit get R = 480 and the R480 word path. Every other script is #493's, unchanged.\n- `data/bitE8mut-r480.json.gz`: rebuilt byte for byte from #493's frozen plan. `data/hosting-r480.json`: #442's\n hosting programme, as run by #493's `host_select.py`, rediscovered exactly by the verifier.\n- `verify.py`: (full) #493's `verify.sh` unchanged as parent. Then, for R480:\n - #370's stock checker refuses source destinations, as for #493; the relaxed copy passes, with exact F2 replay.\n - #425 interface checks (literal cleanup), plus 11 word mutants and 2 hypothesis controls.\n - Legality, five- and eleven-stage formal columns (payload 102 bits), record and mutable-source mutants.\n - Gram on 672 frames.\n - #445 geometry, #472 emitter, R = 480 hosted audit (42,240 whole residuals, all template mutations rejected), and\n the invoice, both moment engines and the 47 strict outer inequalities with #484, #471 and #458.\n - Controls: #493's own first-register variant is refused (129 bits), and #493's R489 c is reproduced exactly through\n its unmodified files.\n- Finite invoice: the dead-hosted totals lengthen the cancellation-free chains. The physical prefix becomes 5,479 bits\n (charged 5,504), and the three-level coefficient 16,491 bits (charged 16,512). These enter only the finite cutoffs,\n and every invoice assertion passes.\n\n```sh\nBOOST_INCLUDE=/path/to/boost python research/e8-r480-dead-totals/verify.py /absolute/new/output --light # skips #493's verify.sh\nBOOST_INCLUDE=/path/to/boost python research/e8-r480-dead-totals/verify.py /absolute/new/output\n```\n\n## Scope\nThe scope is #493's, unchanged: all of #472's eleven-stage composition interfaces and #425's mutable-source interface\n(checked by #493's `interface.py`). Complex savings are cited from their receipts, not rebuilt. No unconditional\ntheorem is claimed.\n\n## Credits\neumemic (#493: the R489 carrier-skeleton word, the generator with its dead-register option, the relaxed checker, the\ninterface checks and the R ≥ 480 family argument). Through #493: Zhihao Chen (#425, #386), DreamingOfClouds (#463, #315,\n#484), DaysSky (#442, #381), chafreaky (#445, #451, #472, #458), Dylan Crow (#370), icekylinx (#433), Dugongue (#471,\n#483), Jacob Sussman (the E8 unit).\n\nPrepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code.\n\n🤖 Generated with [Claude Code](https://claude.com/claude-code)\n","created_at":"2026-10-11T21:55:59Z","updated_at":"2026-10-11T22:11:59Z","closed_at":null,"merged_at":null,"merge_commit_sha":"ae048aff9b6bb1e8fd37b606313b6631012a583b","assignees":[],"requested_reviewers":[],"requested_teams":[],"labels":[],"milestone":null,"draft":false,"commits_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/pulls/503/commits","review_comments_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/pulls/503/comments","review_comment_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/pulls/comments{/number}","comments_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/issues/503/comments","statuses_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/statuses/3f27147013fdd4fa0aed825cb47bff3376c452eb","head":{"label":"DreamingOfClouds:e8-r480-dead-totals","ref":"e8-r480-dead-totals","sha":"3f27147013fdd4fa0aed825cb47bff3376c452eb","user":{"login":"DreamingOfClouds","id":173691639,"node_id":"U_kgDOClpS9w","avatar_url":"https://avatars.githubusercontent.com/u/173691639?v=4","gravatar_id":"","url":"https://api.github.com/users/DreamingOfClouds","html_url":"https://github.com/DreamingOfClouds","followers_url":"https://api.github.com/users/DreamingOfClouds/followers","following_url":"https://api.github.com/users/DreamingOfClouds/following{/other_user}","gists_url":"https://api.github.com/users/DreamingOfClouds/gists{/gist_id}","starred_url":"https://api.github.com/users/DreamingOfClouds/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/DreamingOfClouds/subscriptions","organizations_url":"https://api.github.com/users/DreamingOfClouds/orgs","repos_url":"https://api.github.com/users/DreamingOfClouds/repos","events_url":"https://api.github.com/users/DreamingOfClouds/events{/privacy}","received_events_url":"https://api.github.com/users/DreamingOfClouds/received_events","type":"User","user_view_type":"public","site_admin":false},"repo":{"id":1412741203,"node_id":"R_kgDOVDS4Uw","name":"integer-mult-bounds","full_name":"DreamingOfClouds/integer-mult-bounds","private":false,"owner":{"login":"DreamingOfClouds","id":173691639,"node_id":"U_kgDOClpS9w","avatar_url":"https://avatars.githubusercontent.com/u/173691639?v=4","gravatar_id":"","url":"https://api.github.com/users/DreamingOfClouds","html_url":"https://github.com/DreamingOfClouds","followers_url":"https://api.github.com/users/DreamingOfClouds/followers","following_url":"https://api.github.com/users/DreamingOfClouds/following{/other_user}","gists_url":"https://api.github.com/users/DreamingOfClouds/gists{/gist_id}","starred_url":"https://api.github.com/users/DreamingOfClouds/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/DreamingOfClouds/subscriptions","organizations_url":"https://api.github.com/users/DreamingOfClouds/orgs","repos_url":"https://api.github.com/users/DreamingOfClouds/repos","events_url":"https://api.github.com/users/DreamingOfClouds/events{/privacy}","received_events_url":"https://api.github.com/users/DreamingOfClouds/received_events","type":"User","user_view_type":"public","site_admin":false},"html_url":"https://github.com/DreamingOfClouds/integer-mult-bounds","description":"Conditional integer multiplication: kappa > 2^-15. 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κ = 0.001303530097714685: an E8 bit word with 489 helpers, sources as carriers (0.001325 with #484's draft complex supplier)","user":{"login":"eumemic","id":94939491,"node_id":"U_kgDOBaipYw","avatar_url":"https://avatars.githubusercontent.com/u/94939491?v=4","gravatar_id":"","url":"https://api.github.com/users/eumemic","html_url":"https://github.com/eumemic","followers_url":"https://api.github.com/users/eumemic/followers","following_url":"https://api.github.com/users/eumemic/following{/other_user}","gists_url":"https://api.github.com/users/eumemic/gists{/gist_id}","starred_url":"https://api.github.com/users/eumemic/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/eumemic/subscriptions","organizations_url":"https://api.github.com/users/eumemic/orgs","repos_url":"https://api.github.com/users/eumemic/repos","events_url":"https://api.github.com/users/eumemic/events{/privacy}","received_events_url":"https://api.github.com/users/eumemic/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"**Conditional κ = 260706019542937/(2·10¹⁷) = 0.001303530097714685** with #471's complex supplier (complex-bound; +0.53% over #483), and **0.001325031497415498** with #484's draft complex supplier.\n\nThis PR adds a bit supplier with **R = 489 helpers**; the best bit word so far had 715 (#463). The bit side then no longer binds, so κ equals the complex cap of whichever complex supplier it is paired with.\n\nBit c, priced by the hub's eleven-stage whole-residual hosted pipeline (#445 geometry; #472 emitter, audit and finite invoice; #442 hosting; #315 engines):\n\n**c = 391360506745414227149/(2.5·10²³) = 0.001565442026981656908596** (10⁻²⁴ grid; the next point is rejected).\n\nThe same pipeline files reproduce three published c values exactly: #472's R715 (0.001293771240692396056124), #445's R740 (0.001264963576077378514188) and #451's R740 rank149 (0.001267536342017397153864). Our c is 20.6% above the best whole-residual bit supplier (#483, 0.0012982901) and 18.0% above the largest whole-residual complex b (#484).\n\nEach composition below uses the six-level, 47-inequality outer assembly (#434/#315, as in #472). Every one is complex-bound.\n\n| complex supplier (cited from its receipt) | complex b | κ |\n| --- | --- | --- |\n| **#471** (Dugongue), the supplier of #473, #478 and #483 | 1305231506267591/10¹⁸ | **260706019542937/(2·10¹⁷) = 0.001303530097714685** |\n| #484 (DreamingOfClouds; draft, conditional on its Lemmas A and G) | 663394767670133/(5·10¹⁷) | 662515748707749/(5·10¹⁷) = 0.001325031497415498 |\n| #458 (chafreaky), the supplier of #472 | 1297203880559577927527/10²⁴ | 323880830669511/(2.5·10¹⁷) = 0.001295523322678044 |\n\nWhen this was prepared, the best whole-residual κ was #483's 0.001296606691405309, bit-bound with #471's b. This word gives **+2.19%** over it with #484's supplier and **+0.53%** with #471's. The #484 figure carries that draft's two lemmas as review points. The #471 figure needs nothing beyond what #483 already uses, apart from the review point below.\n\n**Information only, not claimed:** #448's cross-copy complex supplier (b = 718766148669433/(5·10¹⁷)) would give κ = 358867191156973/(2.5·10¹⁷) = 0.001435468764627892, complex-bound. That figure rests on #448's cross-family residual split, which #451 disputes (`research/cross-family-residual-obstruction`); the author's rebuttal is on #451's thread.\n\nThe PR contains one package, `research/e8-bit-carrier-skeleton/`, with its own path-filtered workflow. It also adds one `.gitattributes` line and the #318 joint-dual repair. No other existing file changes.\n\n### Mechanism: a D4 quad skeleton with sources as carriers\n\n- **Partition.** The 120 root lines split into 10 D4 sub-root systems in 5 orthogonally complementary pairs. This gives 30 orthogonal 4-frames and 180 cells. A cell is a pair of lines in one 4-frame; it spans 2 dimensions and contains only those 2 lines.\n- **Sources.** Each source keeps its own register in its matching cell. Two carriers copy it into its two cross cells, so each source has three branches. Three is the minimum: by #463's carrier bound, two hyperplane sections cannot cover the 4-design s⊥.\n- **Quads.** Cells deliver their sums to 60 quads. Each quad is a 4-dimensional D4 frame made of 6 cells from 6 blocks. A butterfly on the 6 cell sums gives one output per D6 the quad feeds.\n- **Tops.** Each target arrives through its D6 triple {t, e}⊥. At the D6 it shares with its matching partner, it reads two quad outputs and a Q-delivery. At t⊥ it reads one register from each of its other two D6s.\n- **Q-nodes.** In each block, the 12 sources (all in matching cells) undergo one invertible F₂ transform at the block's D4 frame. It yields 6 Q-deliveries for the complementary block's targets and 6 leftovers. These 577 gates are the only gates that write sources, and every one reads another source.\n- **Totals and cleanup.** #370's 9 decoder totals are collected at the full frame on 9 fresh registers. With the totals on leftover registers instead, R = 480, but the prefix payload is 129 bits > 104. The cleanup is the literal reverse of all source and helper gates at the full frame.\n- **Register count.** 120 sources + 240 carriers + 240 cell registers + 9 totals gives R = 489. The local histogram is {1:1200, 2:1440, 4:180, 6:120, 8:18}.\n\n### Review point: source registers as gate destinations\n\n#370's independent checker asserts that sources are never gate destinations. #425's scalar-interface lemma (Zhihao Chen) shows that this assertion is sufficient, not necessary. If no target feeds a source or helper, the frame-zero preconditioner D and U⁻¹ at the common full frame (here C) give exactly (x, s, y) → (x, s, y + x).\n\n- On the complex side, #425 writes packets into sources below the full frame.\n- On the bit side, #433 already wrote source rows, but only at the full frame.\n- This word writes sources at block D4 frames.\n\nThe package checks this point in five ways:\n\n- `relax.py` builds the relaxed checker from #370's pinned file by removing that one assertion; the rest is unchanged. Exact F₂ replay on all 729 columns still requires every source to end holding exactly its own column. The stock file must refuse the word with \"x register written\".\n- `interface.py` checks the lemma's hypotheses on the word:\n - no target feeds a source or helper;\n - D writes targets from helpers at frame zero;\n - C acts at the full frame and is the literal reverse of the source and helper gates;\n - B writes only targets.\n- The relaxed checker rejects five mutants aimed at the interface:\n - drop a source cleanup gate;\n - corrupt a packet that targets read, while every source is still restored;\n - leave a source unrestored;\n - move a source write below the source's frame;\n - drop a source write.\n- Both official column checkers reject the three matching record-level mutants.\n- Two F₂-neutral edits, a target feeding a source and a target feeding a helper, pass the F₂ checker but are rejected by `interface.py`.\n\nThe official cohort checkers treat every register alike and accept the word unchanged. In #472's PROOF.md, the bit label realization does not depend on whether a register is called a source, helper or target. The mutable-basis realization remains a listed conditional interface, as in #472, #473 and #478.\n\n### Checks\n\n`bash research/e8-bit-carrier-skeleton/verify.sh DIR` takes about 70 s. It passed from fresh copies on Python 3.12 and 3.14.\n\n- **Provenance.** Manifest check, and 50 vendored files pinned by git blob id. `adapt.py --check` confirms the adapted hub files are #472's files plus 19 listed edits. Every cited b and frontier κ must equal its PR's own `EXPECTED.json`.\n- **Rebuild.** The word is rebuilt from the frozen CP-SAT plan and must equal the shipped word.\n- **Independent checker.** The relaxed #370 checker checks legality and exact F₂ on 729 columns. 671 frames have positive Gram determinants, with only the prime 2. Then `interface.py` runs, along with 11 word-level mutants and 2 hypothesis controls.\n- **Official checkers.** Legality at NCOPY = 9: 33,990 ADDs, rank mass 5,664. Five-stage formal columns: 969 columns, prefix payload 100 bits < 104. Eleven-stage formal columns (#381's `columns_k`, KPAIRS = 5): 1,689 columns, 2,880 bridge additions, all 24 omitted-bridge controls rejected. The KPAIRS = 2 regression passes, and 6 + 3 record-level mutants are rejected.\n- **Gram witnesses.** Exact Gram determinants and prime witnesses on all 672 frames.\n- **Eleven-stage hosting.** All 43,032 helper residuals are hosted whole on idle data families of the eight pooled replicas, with no banks. 6,579 unbanked scalar columns are restored and 24 omitted bridge shears are rejected. The independent audit replays 3,252,216 renamed instructions and rejects 22 template mutations.\n - Physical prefix: 2,119 bits, charged at 2,176.\n - Three-level coefficient: 6,411 bits, charged at 6,464.\n - Maximum child 56; row coefficient 19,431 < 20,161.\n - Both moment engines, the 47 strict inequalities, and the next-grid, zero-η, zero-β and unit-β controls pass.\n- **Controls.** #472's R715 word goes through #472's unmodified files. It reproduces #472's c and, with #458's b, its κ = 0.001292099559442278. #445's R740 word and #451's R740 rank149 word go through their own emitters and reproduce their c values.\n- **Local build.** The C++ checkers were built locally against an overflow-checked 128-bit stand-in for `boost::multiprecision::cpp_int`. The workflow uses libboost-dev.\n- **Repository CI.** The branch carries rohanarun's #318 joint-dual pin repair (byte-identical to a45747d), as #417, #436 and #439 do.\n\n### Retained assumptions\n\n- Every interface #472's eleven-stage composition retains:\n - the all-size bit/Gaussian compiler;\n - the mutable-basis and target-label realization;\n - whole-call correlated-helper hosting (#442);\n - compressed windows and restored work;\n - the common grid and tape, precision, row and analytic contracts.\n- Complex savings are cited from their PRs' receipts, not rebuilt. The primary κ also rests on #484's Lemmas A and G.\n- The hosting selection is a frozen nomination of #442's integer programme, and the plan is a CP-SAT nomination; neither is claimed optimal.\n- This is a conditional finite construction, not a Lean proof.\n\n### Bounds for this family (analysis, not run by verify.sh)\n\n- R ≥ 120 for any design.\n- R ≥ 300 for tops through consistent D6 triples: 14 registers per 4-frame at dimension 6.\n- R ≥ 420 with three branches per source on this partition: 3 registers per cell.\n- **R ≥ 480 in this family with phase-A totals.** A brute force over the d-parity patterns needs 4 single-line registers per 4-frame. The block Q-nodes need all 4 lines of each 4-frame, and no register can serve both roles.\n- R = 480 exists but fails the 104-bit prefix bill.\n\n### 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whole-owner replicas: kappa 0.001357701757628940 (+1.9236% over #496)","user":{"login":"Dugongue","id":49054532,"node_id":"MDQ6VXNlcjQ5MDU0NTMy","avatar_url":"https://avatars.githubusercontent.com/u/49054532?v=4","gravatar_id":"","url":"https://api.github.com/users/Dugongue","html_url":"https://github.com/Dugongue","followers_url":"https://api.github.com/users/Dugongue/followers","following_url":"https://api.github.com/users/Dugongue/following{/other_user}","gists_url":"https://api.github.com/users/Dugongue/gists{/gist_id}","starred_url":"https://api.github.com/users/Dugongue/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/Dugongue/subscriptions","organizations_url":"https://api.github.com/users/Dugongue/orgs","repos_url":"https://api.github.com/users/Dugongue/repos","events_url":"https://api.github.com/users/Dugongue/events{/privacy}","received_events_url":"https://api.github.com/users/Dugongue/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"## Result and scope\n\nThis adds a new asynchronous replica schedule giving conditional **kappa = 0.001357701757628940** (`67885087881447/50000000000000000`), **1.923642% above #496**. The complex supplier is `b = 0.001359547617819233570818`. The unchanged #493 bit supplier is `c = 0.001565442026981656908596` and is nonbinding.\n\nThe inherited all-size compiler, mutable-basis/common-label, #484 Lemma A realization, restored-row, precision/tape, and analytic-transfer contracts remain explicit. This is a checked finite derivative under those conditions, not an unconditional multiplication theorem. #494's larger computation uses a different disputed split-residual interface and is not claimed surpassed.\n\n## New mechanism\n\nRemove replica lockstep while keeping every complete local invocation atomic. Shuffle the eight nine-stage controllers by `(stage + 3*replica/7, stage, replica)`, preserving every replica's exact local, bridge, idle-completion and terminal order. Whole helpers may borrow pending coordinates from a different replica according to that owner's actual last touch and deadline.\n\nThis opens4,539 same-pair/different-replica uses that the stage-only test rejects. Each helper still has exactly one whole physical owner; all 800 families per invocation are distinct. Each borrowed spectator is restored before the next complete invocation. Disjoint residual blocks plus an explicit remainder reproduce each original pending child. No gains are added numerically and no cross-family residual split is used.\n\nThe local gauge80-kernel42 word is unchanged. All40,320 helper roles fit within7,680 live families (8,258 physical). The changed profile is `{1:148240,2:66816,3:7032,4:19728,5:26109,6:144,7:2209,8:1224,16:1,48:408}`, with rank mass 558,144 and deficit 2,496. The maximum child 48 retains depth2 because73^2>2*48^2.\n\nThe prefix is freshly recounted:72 local sweeps and 72 individual bridge sweeps give 205bits;512 are charged, with an extra2*512 in the two-level row bill. The row coefficient is16,467<20,161. Both exact moment engines include the inherited bad-cover fallback. Six bootstrap steps feed the strict47-inequality assembly; the next kappa grid point and zero-eta/zero-beta/unit-beta controls are rejected.\n\n## Reproduction\n\nAdded folder: `research/asynchronous-whole-owners`.\n\n```\npython -B research/asynchronous-whole-owners/verify.py --work /absolute/path/to/new-output\n```\n\nPython3.11+ standard library only; offline; no optimizer or compiler required. This reconstructs the parent local dependency, emits the asynchronous template, independently audits all physical owner charts and exact phase/event projections, checks19 deliberately broken controllers, and recomputes the full changed finite invoice and exact assembly. The frozen witness replaces all search-time MILP assumptions. The unchanged #493 bit operator is cited as a pinned dependency; its published profile is repriced here, but its operator is not redundantly reverified.\n\nThe serialized version explicitly restricts replica-local events to their named replica. An old decoder that ignores these new fields cannot interpret this template. Two final whole-stock events run only once.\n\n## Sources and what this combines\n\n- **#496**: direct whole-owner pooled parent, matching construction, independent audit and assembly ancestry; pinned `00cf70efd6a8637531deafef698157ca83e249ee`.\n- **#484**: unchanged gauge80-kernel42 scalar word, exact phases and paid spectator wrappers; use #496's pinned `035845ce95f31d0a2dcfb42b8c8e13411271fa5f`.\n- **#493**: unchanged R489 source-as-carrier bit supplier, pinned `c3a9a436b84fe44fdc223a5784d84736d1c2d3c7`.\n- **#458 and #442**: whole-owner residual hosting, spectator discipline and integer allocation ancestry. **#497** motivates attention to moment-aware placement, but none of its gains is added to ours.\n- **#433, #425 and #370**: inherited complex word, scalar/common-frame machinery and E8/Hamming geometry. **#434/#417/#435/#440** and **#401/#408-416**: kernel and gauge ancestry through #484. **#361/#315**: exact moment and outer arithmetic ancestry.\n- **OpenAI math** snapshot `adc7f1241b42e322a6451854ab7e4b4c146bf78a`: `WordScheduling.lean` substitution/product calculus helped formulate the complete-call scheduling proof; `CommonBases.lean` and the common-integer-polymatroid material motivated the capacity-exchange search. `SparseShear.lean` and `PivotJoin.lean` supported separately documented screens. 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complex word (#495) on cross-copy hosting with #493's bit word: conditional κ 1.452948511251494e-3 (stacked on #494)","user":{"login":"rosswaycaster","id":1231836,"node_id":"MDQ6VXNlcjEyMzE4MzY=","avatar_url":"https://avatars.githubusercontent.com/u/1231836?v=4","gravatar_id":"","url":"https://api.github.com/users/rosswaycaster","html_url":"https://github.com/rosswaycaster","followers_url":"https://api.github.com/users/rosswaycaster/followers","following_url":"https://api.github.com/users/rosswaycaster/following{/other_user}","gists_url":"https://api.github.com/users/rosswaycaster/gists{/gist_id}","starred_url":"https://api.github.com/users/rosswaycaster/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/rosswaycaster/subscriptions","organizations_url":"https://api.github.com/users/rosswaycaster/orgs","repos_url":"https://api.github.com/users/rosswaycaster/repos","events_url":"https://api.github.com/users/rosswaycaster/events{/privacy}","received_events_url":"https://api.github.com/users/rosswaycaster/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"\r\n_Requested by **Ross** · [project thread](https://claude.ai/code/project/chan_01MQm3YGAz7NNfofWzQLZCPP?thread=cmsg_01MQm3YGAz7NNfofWzQLZCPP8e9dNkgbw9s5L3Xy3dJ44Q)_\r\n\r\n## Change and mathematical scope\r\n\r\nBefore: the strongest open comparable witness was PR #494, conditional κ = 358867191156973/2.5·10¹⁷ =\r\n0.001435468764627892, bound by its complex supplier (PR #448's cross-copy hosting of PR #433's word, b =\r\n718766148669433/5·10¹⁷).\r\n\r\nAfter: conditional **κ = 726474255625747/500000000000000000 = 0.001452948511251494**, complex-bound, **1.22 % above PR #494**, with the same bit\r\nsupplier (PR #493's R489 word, unchanged) and a new complex supplier.\r\n\r\nThe complex word is PR #495's retimed R560 word (Ali Romman), which combines PR #449's shared-donor kernel (DreamingOfClouds) with PR #458's paid two-sided residual adapters (chafreaky). It is rebuilt from its frozen `FULL-WORD.json.gz` by PR #495's own word-level scripts, vendored byte for byte (`SOURCE.json`). It is placed in PR #433's nine-stage template (m = 73, eight replicas), the template PR #494 prices. Every helper residual is hosted on idle data coordinates, so no banks are needed:\r\n\r\n- the 79 entering (width-8) residuals per stage go whole onto pattern copies, with PR #495's route chart and adapters, each alone on its family in its call, as in PR #495;\r\n- the 481 width-9 residuals per stage go on PR #448's cross-copy tape, as in PR #494.\r\n\r\nPattern copies and tape copies are different families. The complex lower bound rises from b = 1.437532·10⁻³ (PR #494) to b = 1455062642351477/10¹⁸ = 1.455063·10⁻³. The bit side is unchanged (c = 1.565442·10⁻³). `PROOF.md` gives the construction and the compatibility argument.\r\n\r\nHow: `research/r489-retimed-cross-copy-complex/verify.py` runs PR #494's own `verify.py` unchanged, then this package's steps, then the exact\r\nassembly (`code/assemble_complex.py`, PR #494's `assemble_489.py` with the complex word directory as an argument): two\r\nrational moment engines, six bootstrap levels, all 47 strict outer inequalities, next grid point and zero-η, zero-β,\r\nunit-β controls rejected. The result is compared with `EXPECTED.json` and must exceed PR #494's κ.\r\n\r\nStacked on PR #494 (head `419907c71246c050f1c3fd2a504469b74bf7798e`); only the commits after that head are new. Every assumption of\r\nPR #494 stays an assumption. PR #448's cross-copy slot is disputed in the discussions on PR #451 and PR #485, and this package uses it only where PR #494 does. This package adds PR #495's assumptions for its word: PR #449's expanded scalar interface, PR #458's paid two-sided residual adapters, and PR #495's pending mutable-target, idle-hosting and Gaussian-adapter interfaces. It also adds one new composition point: PR #495's whole entering-residual hosting is used in the nine-stage m = 73 template, on families kept separate from PR #448's tape. The audit checks that separation in every call; `PROOF.md` gives the argument. A finite certificate is not a formal proof of the asymptotic theorem, no Lean\r\nproof is claimed, and κ is an exponent saving, not a measured runtime speedup. Prepared with Anthropic Claude via\r\nClaude Code for Ross (rosswaycaster); full credits are in `research/r489-retimed-cross-copy-complex/NOTICE.md`.\r\n\r\nCredits: **Ali Romman** (PR #495: the retimed word and the vendored word scripts), **chafreaky** (PR #458: paid two-sided residual adapters), **DreamingOfClouds** (PR #449: shared-donor kernel; PR #484: entering-helper invoice form), **higherbeing** (PR #494: the composition this stacks on; PR #448: cross-copy hosting), **eumemic** (PR #493: the R489 bit word), **DaysSky** (PR #442: idle-data hosting and its verifier), **icekylinx** (PR #433: the nine-stage template and split centres), and every author in the source-pinned notices.\r\n\r\n## Validation\r\n\r\n- **Full clean rerun passed.** A fresh clone of this branch ran `verify.py` in full mode. It ran PR #494 from scratch, including PR #493's `verify.sh` and PR #442's complete verifier, and reproduced every PR #494 expected value. 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word","user":{"login":"DreamingOfClouds","id":173691639,"node_id":"U_kgDOClpS9w","avatar_url":"https://avatars.githubusercontent.com/u/173691639?v=4","gravatar_id":"","url":"https://api.github.com/users/DreamingOfClouds","html_url":"https://github.com/DreamingOfClouds","followers_url":"https://api.github.com/users/DreamingOfClouds/followers","following_url":"https://api.github.com/users/DreamingOfClouds/following{/other_user}","gists_url":"https://api.github.com/users/DreamingOfClouds/gists{/gist_id}","starred_url":"https://api.github.com/users/DreamingOfClouds/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/DreamingOfClouds/subscriptions","organizations_url":"https://api.github.com/users/DreamingOfClouds/orgs","repos_url":"https://api.github.com/users/DreamingOfClouds/repos","events_url":"https://api.github.com/users/DreamingOfClouds/events{/privacy}","received_events_url":"https://api.github.com/users/DreamingOfClouds/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"Method 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It is below the current lemma-less frontier: −0.108% vs #473 (κ = 1.295630·10⁻³, as updated on Oct 11, now the frontier) and −0.098% vs #478 (1.295509·10⁻³). This PR's point is the method and the bounds, not the frontier. The bit supplier is c = 1295910576589222380953/10²⁴ ≈ 1.295911·10⁻³ (+0.839% over R715). Same word, same\nhosting rule, same mixing, #458's complex supplier unchanged: only the kernel selection changes, 84 → 112 pivots.\n\n| side | supplier | endpoint |\n| --- | --- | ---: |\n| bit (binds) | R715 word, **112 rank-1 kernel pivots**, eleven stages, #442 whole-residual hosting, target mixing | c ≈ 1.295911·10⁻³ |\n| complex | #458 paid-adapter kernel, unchanged | b ≈ 1.297204·10⁻³ |\n\n**What is new**\n1. **The width rule, checked exactly.** A residual's width is 8 − entrance rank, and only kernel pivots have a nonzero entrance: the helper hierarchy and the\n target mixing do not set it. Checked three ways on all 715 helpers (kernel-word frames, exported records of the mixed word, the independent hosted audit).\n2. **The pivot ceiling and the exact maximum, for coordinate entrances** (the verified residual-isometry format). A pivot needs a frame line inside its first frame (263 of 706 helpers), and its delivery vector must be an XOR of donors of one\n entrance class. *Proved:* pivots ≤ |C| − rank = 263 − 86 = **177**, and rank-1 coordinate entrances lose nothing up to parity. *Exact maximum on the retimed R715 word: **112**, by a computer-assisted exhaustive search (independently re-audited), certified by\n `code/exact_pivots.py`* (rerun by `verify.py --light`, asserted equal to 112, about 10 s): the pivot problem is a min-sum-rank list partition (max pivots = |C| − min Σ_i rank of the class\n vectors; NP-hard in general, not a matroid union/intersection/parity problem), solved exactly here by splitting the delivery matroid into components (208 / 28 / 14 elements plus 13 coloops),\n exhaustive span-tuple DP on the small ones (16 and 9 pivots) and, on the 208, an exact block DP with a coupling-assignment lower bound and an exhaustive search (minimum sum-rank 121, so 87 pivots;\n 120 shown infeasible): 87 + 16 + 9 = 112. The annealing plateau (14 of 16 restarts at 112, never 113) is therefore optimal. Priced by the model, a rank-1 pivot is worth ≈ +0.033% of c,\n so the pivot count on R715 is exhausted within this format (177 would have been ≈ +2.9%; it is not reachable; the donor choice among 112-pivot selections still moves c, README §3).\n *Scope:* the 177 and 586 are valid but loose scoped bounds; the 177 does not cover non-coordinate entrances. Upstream `kernel()` itself accepts any flat; there all 706 helpers qualify and the same argument\n gives only 706 − 120 = 586, in a format this package does not verify (it needs coordinate residual isometries). The exact 112 is a statement about the same coordinate, one-class-per-donor model;\n entrances at arbitrary root lines were only searched.\n *Follow-up:* the same exact method gives 101 pivots on the R687 read-then-climb word (100 after the parity rule); to be reported in a follow-up PR.\n3. **The method:** `select_kernel.py` anneals the class assignment on the exact objective Σ rank (self-contained xorshift64*, reproducible from a seed),\n `kernel_from_selection.py` builds the word with #443's kernel unchanged. Pinned: `--seed 3 --iters 150000`.\n4. Honest size: by kernel choice alone, without retiming or reordering, the first 112-pivot selection (c = 1.295564·10⁻³) landed, in κ, within 0.003% of #473 as first posted (1.293922·10⁻³);\n the shipped best-of-eight seed was 0.027% above that. #473 has since been updated (1.295630·10⁻³) and is 0.108% above this PR. This is selection tuning, not a ≥ 1% result.\n\n**Verification** (`python -B research/e8-r715-kernel-cap/verify.py /abs/out [--light]`; CI workflow `e8-r715-kernel-cap`): LIGHT (about two minutes) checks integrity and\npins, recomputes the ceiling analysis from the pinned R715 word, **recomputes the exact pivot maximum and asserts 112**, checks the selection against #443's exact kernel conditions plus the F₂ response relation and the coordinate-flat condition,\nrebuilds the kernel word (replay, interface) and the mixed word and compares them, checks the width rule, re-solves the hosting (CP-SAT) and prices it with the\nexact engine, and runs the screen composition with #458's pinned endpoint. FULL adds the seeded search, #443's regressions, the relaxed all-column checker,\nC++ cohort legality and formal columns at five and eleven stages, mixing mutants, Gram, eleven-stage template/audits, **hosting selection rediscovered with HiGHS and\nrequired equal**, hosted audit, assembly, the pivot-count scan, #458's complex supplier from scratch, and the exact composition (two moment engines per side, six\nbootstrap levels, all 47 strict outer inequalities, next-grid / zero-η / zero-β / unit-β rejection).\n\n**Review points**\n- The ceiling's proof (items 1–4 of README §2) is elementary. The new claim is the exact maximum 112: its certificate is the code in `code/exact_pivots.py` (component split, block DP,\n coupling lower bound, exhaustive search), rerun in LIGHT; please review that code and the min-sum-rank formulation of README §2 items 2–3 it relies on.\n- The seed choice among equal pivot counts is an exact-priced selection (c between 1.295564 and 1.295911·10⁻³ across eight seeds).\n- Inherited and unchanged: #450's Lemma M (bit target mixing, chained receivers), #458's paid adapters, the R715 hierarchy and its carrier bound (#463).\n- The bit side is now 0.1% under #458's complex endpoint; further bit gains here are complex-capped.\nConditional like all parents; no unconditional theorem or Lean proof is claimed.\n\nCredits: chafreaky (#417 shared-donor kernel and exact replay, #443 replica kernel and residual isometries, #451/#454 whole-residual rule, #458 paid adapters, #472),\nrohanarun (#434 retiming with kernels, #435 banks, #460 composition and verifier structure, #467, #470 retimed kernel and reordered R715 deliveries, #473), eumemic (#436 R740 word,\n#440/#441), DaysSky (#442 idle-axis hosting), Dylan Crow (#370 word, producer, checkers), Srikrishnabalaji (#465), Dugongue (#471, #476, #478), jacklightChen and Zhihao Chen\n(#386/#425), icekylinx (#433), higherbeing (#448), Jacob Sussman and all source-pinned authors. 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The source-bound certificate gives **conditional κ = 0.001343518018117309**, with complex saving **b = 0.001345325487149526878087** and freshly rebuilt #493 bits. It improves #496's value by 0.8589% under the retained whole-owner interface.\n\nThe transfer changes 224 A-event frames and 504 B-event frames while preserving scalar operations, all 122 helper entrances, target levels and centre chains. All 40,320 whole helper roles fit on 7,680 data families, with 8,258 physical families and no banks. No residual is split across physical families. Both exact moment engines, the complete physical invoice, prefix bound and all 47 strict outer inequalities are reconstructed from the resulting program.\n\nThe package vendors #496 unchanged, including its #484/#493 dependencies; all 297 upstream source files were compared with pinned Git bytes. New checks rebuild the retimed program, verify common labels and every local operator instance on 512 columns, run the complete program on 806 basis and eight dense inputs in both orientations, and enforce Python-integer bounds before fixed-width arithmetic. The attributed M8 control copy selects an available outside-centre frame in the changed catalogue; the same violation and all 14 controls remain mandatory.\n\nThe inherited all-size compiler, mutable-basis, common-label, restored-row, precision/tape, analytic-transfer and Lemma A spectator-realization contracts remain conditional. This is not an unconditional multiplication theorem, a Lean proof, or κ = 1. It makes no claim under #448/#494's different split-residual interface.\n\nDirect credits: aliromman (#495), DreamingOfClouds (#484), eumemic (#493/#496), and the source authors retained in the vendored notices. Prepared by chafreaky with OpenAI Codex.\n\nValidation: the complete fresh verifier passed on macOS and Linux with Python 3.14.8 and real Boost. All 24 root stages passed on each platform; complete `RESULT.json` bytes match (`4a951fc558757d045f8296b4014e4be71553ac7514a4d996d4bf0232ebefec5f`). Receipts and source-byte verification are in `research/e8-retimed-pooled-validation/`. CI is configured for Python 3.13 and 3.14; no CI result is claimed before it runs.\n\nConcurrent frontier: #501 appeared immediately before this publication and reports the same κ and global paid profile. This PR matches that reported whole-owner result through the explicit #495-to-#484 frame transfer above; it does not claim to exceed #501 or to have independently replayed that 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κ = 0.001343518018117309: retimed pooled whole-owner complex supply","user":{"login":"eumemic","id":94939491,"node_id":"U_kgDOBaipYw","avatar_url":"https://avatars.githubusercontent.com/u/94939491?v=4","gravatar_id":"","url":"https://api.github.com/users/eumemic","html_url":"https://github.com/eumemic","followers_url":"https://api.github.com/users/eumemic/followers","following_url":"https://api.github.com/users/eumemic/following{/other_user}","gists_url":"https://api.github.com/users/eumemic/gists{/gist_id}","starred_url":"https://api.github.com/users/eumemic/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/eumemic/subscriptions","organizations_url":"https://api.github.com/users/eumemic/orgs","repos_url":"https://api.github.com/users/eumemic/repos","events_url":"https://api.github.com/users/eumemic/events{/privacy}","received_events_url":"https://api.github.com/users/eumemic/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"κ = 0.001343518018117309\n\nA frame-only retiming of #484's gauge/kernel complex word improves the frozen whole-owner result in #496 by **0.85885844%**, while retaining #493's R489 bit supplier and #496's pooled whole-owner allocation. The complex side binds at the exact lower endpoint `b = 1345325487149526878087/10^24`; the strict outer assembly gives `κ = 1343518018117309/10^18`.\n\nThe 4,107 scalar payloads and their order stay fixed. A frozen map changes 411 A frames and 504 B frames while preserving all helper entrances, the first 531 A gates, target/centre boundaries and cleanup. The changed local rank distribution improves the complete paid moment without reducing its rank mass. All Gaussian phase recipes are rebuilt for the actual new transitions.\n\nThe complete complex profile is `{1:172056, 2:19008, 3:42032, 4:6048, 5:22496, 6:6624, 7:1800, 8:4120}`. Live stock is 7,680 and physical stock is 8,258, with no banks. All 40,320 helper roles remain whole on one physical family, every complete invocation has 800 distinct owners, and the 3,960 actual orthogonal 73-column charts are checked. The serial schedule restores borrowed work before the next invocation; the cross-replica-safe global prefix bound remains 142 bits within the retained 192-bit allowance.\n\nValidation includes fresh reconstruction of both pinned suppliers; the actual new scalar word and both reflected 25,082-event ledgers; arbitrary dirty restoration on all 800 scalar columns; all 2,945 used transition operators and 122 helper chains on all 512 address columns; full physical programs on 806 basis plus eight dense dirty columns in both orientations; all actual owner maps; complete paid profiles and finite invoices; two rational moment engines; six bootstrap cutoffs; and all 47 strict outer inequalities. Guarded simulators bound integer expansion before execution and now explicitly assert and hash their identity-result JSONs, in addition to requiring successful subprocess exits. The independent frame review rejects 12 mutations, and the inherited source, Lemma G and pooled-controller mutation suites run freshly. Retiming removes a frame assumed by the original M8 mutation generator, so a derivative adapter nominates an available nonnested frame and recomputes both actual codimensions while preserving the total charge; the same source checker and physical test reject it, and all 14 necessity controls run.\n\nFresh source and literal committed-archive replays both pass with observed top-level exit 0 and identical complete `EXACT-MATH.json` results. The package is self-contained and verifies offline with Python 3.14, NumPy, SymPy, a C++17 compiler and genuine Boost headers. Its 309 manifest-listed files match their staged and archived Git bytes. Run:\n\n```sh\npython -B research/r489-pooled-retimed-complex/verify.py /absolute/new/output \\\n --boost-include /path/to/boost/headers\n```\n\nThis remains conditional on the inherited all-size compiler, mutable-basis/common-label, PR484 Lemma A realization, restored-row, precision/tape and analytic-transfer contracts. It is not an unconditional theorem or Lean proof. It makes a whole-owner comparison with #496; The higher #494/#499 draft numbers use a distinct disputed cross-family-split interface. Neither the bounded retiming search nor the allocation search establishes global optimality.\n\nProvenance: #493 (`c3a9a436b84fe44fdc223a5784d84736d1c2d3c7`), #484 (`035845ce95f31d0a2dcfb42b8c8e13411271fa5f`), and frozen #496 (`00cf70efd6a8637531deafef698157ca83e249ee`). The original source notices, Apache-2.0 licenses and AI disclosures are preserved, including DreamingOfClouds' Claude Opus 5.5 assistance and all credited predecessors. The new search, independent audits, integration and documentation were prepared with substantial OpenAI Codex assistance. All previously published heads and claims remain frozen.\n\nRelease verification: commit `1dc056496fdbbc74073ed26d948a2dc235dbf356`; manifest SHA256 `a2295472662c4f845639c46305bd25cd713095fc23ca2478db8ee4eef3fd5e34`. Source and literal-archive replays took 825.565 s and 827.254 s respectively, with all 18 root stages passing. Their common `EXACT-MATH.json` SHA256 is `940505b40dee096d0426ca545e15d98fa93b2e6af1a675e59d0760748a70a659`. 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κ = 0.001308501945841842: kernel79 complex supplier under #471's footprint rule at nine stages, with #493's bit word (+0.38%)","user":{"login":"rohanarun","id":11659839,"node_id":"MDQ6VXNlcjExNjU5ODM5","avatar_url":"https://avatars.githubusercontent.com/u/11659839?v=4","gravatar_id":"","url":"https://api.github.com/users/rohanarun","html_url":"https://github.com/rohanarun","followers_url":"https://api.github.com/users/rohanarun/followers","following_url":"https://api.github.com/users/rohanarun/following{/other_user}","gists_url":"https://api.github.com/users/rohanarun/gists{/gist_id}","starred_url":"https://api.github.com/users/rohanarun/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/rohanarun/subscriptions","organizations_url":"https://api.github.com/users/rohanarun/orgs","repos_url":"https://api.github.com/users/rohanarun/repos","events_url":"https://api.github.com/users/rohanarun/events{/privacy}","received_events_url":"https://api.github.com/users/rohanarun/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"**Conditional κ = 654250972920921/(5·10¹⁷) = 0.001308501945841842, +0.3814 % over #493** (0.001303530097714685). The result is complex-bound with #493's R489 bit word. It uses only interfaces that #493's own κ already relies on: no Lemma G, no cross-copy.\n\nThe **complex endpoint is b = 0.001310216366506891**. For comparison:\n- #471's eleven-stage supplier: 1.305231506·10⁻³;\n- #484's one-owner nine-stage kernel79: 1.305683990·10⁻³.\n\n**Conditional variant (#484's Lemma G):**\n- b = 0.001333854156208409, with all 40,320 residuals hosted whole and no banks;\n- with #493's bit word, κ = 0.001332077359286333;\n- that is +0.532 % over the 0.001325031497415498 that #493 lists with #484's supplier.\n\n## Change\n\nThis takes #484's nine-stage pipeline: #449's kernel79 word, paid wrappers, explicit spectators and banks. It replaces #458's one-helper-per-family hosting rule with **#471's footprint rule** (Dugongue), the admission behind #471's complex supplier that #493 cites. Several helpers of one invocation may share a host family when their full nine-coordinate footprints (residual cells plus explicit spectators) are pairwise disjoint.\n\nFor a copy of an idle child of rank r, the capacity is:\n- Σw ≤ r;\n- 9k ≤ 73;\n- Σ(9 − w) ≤ 73 − r.\n\nThis is #471's inequality set with 73 in place of 89.\n\n**Kernel79 under the footprint rule:**\n- 286 width-9 banks;\n- live stock 7,966;\n- max child 8;\n- deficit 2,496.\n\nOur model reproduces #484's one-owner kernel79 b exactly before the rule change.\n\n## Package\n\n`research/complex-footprint-kernel/` is a copy of #484's `e8-complex-gauge-kernel` with these additions:\n- `code/footprint_gk.py`;\n- `--footprint` paths in the hosting generator, the independent hosting audit and the variant runner;\n- frozen footprint selections;\n- #493's bit supplier pinned from its EXPECTED.json, as #493 pins complex suppliers.\n\n## Checks run here\n\n- **#442 in full** (Linux, Python 3.13).\n- **Per word, through #484's unchanged scripts:**\n - exact arbitrary-dirt replay;\n - emitted programs in both orientations;\n - #433's exact phase recipes;\n - exact wrappers;\n - independent read-back.\n- **Hosting under the footprint rule**, asserted by the generator and by the independent audit. The audit rejects 17 mutations, including:\n - overlapping footprints of two same-invocation helpers;\n - a spectator on a residual cell;\n - a helper on an active family;\n - cross-replica hosting.\n- **#484's certification:** both moment engines (next grid point rejected), finite invoices, and the 47-inequality outer assembly with controls.\n\nThe **full `verify.py`** (anchor, both words, Lemma G check stage, assembly) is running now. Its receipt and EXPECTED.json will follow in a commit and a comment. CI is not claimed.\n\n```sh\npython -B research/complex-footprint-kernel/verify.py /absolute/new/output\n```\n\n## Scope\n\n**Review point:** #471's footprint admission at nine stages, used here with #458/#484's paid wrappers. As in #471, every simultaneous footprint is disjoint, and spectators are explicit and restored by the whole-invocation identity.\n\nAll other inherited interfaces (all-size compiler, hosting, restored work, analytic) remain. No unconditional theorem is claimed.\n\n## Credits\n\n- **Dugongue:** #471, footprint rule and normalization.\n- **DreamingOfClouds:** #484 package, Lemma A/G and gauges; #449 kernel79.\n- **eumemic:** #493 bit word.\n- **chafreaky:** #458.\n- **DaysSky:** #442.\n- **icekylinx:** #433.\n- **Zhihao Chen:** #425.\n- All retained authors.\n\nFootprint hosting, selection and packaging by Rohan Arun with Claude Opus 5.5 (Anthropic).\n\n🤖 Generated with [Claude 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kappa = 0.001301970637653655: geometric intersections and rational paired whole-owner hosting","user":{"login":"Dugongue","id":49054532,"node_id":"MDQ6VXNlcjQ5MDU0NTMy","avatar_url":"https://avatars.githubusercontent.com/u/49054532?v=4","gravatar_id":"","url":"https://api.github.com/users/Dugongue","html_url":"https://github.com/Dugongue","followers_url":"https://api.github.com/users/Dugongue/followers","following_url":"https://api.github.com/users/Dugongue/following{/other_user}","gists_url":"https://api.github.com/users/Dugongue/gists{/gist_id}","starred_url":"https://api.github.com/users/Dugongue/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/Dugongue/subscriptions","organizations_url":"https://api.github.com/users/Dugongue/orgs","repos_url":"https://api.github.com/users/Dugongue/repos","events_url":"https://api.github.com/users/Dugongue/events{/privacy}","received_events_url":"https://api.github.com/users/Dugongue/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"This adds `research/tensor-nonroot-pairs`, an offline source-bound finite construction with conditional kappa = **0.001301970637653655**, approximately **0.3456% above PR473 at 4bea72f5cfa700dba4556bdb5d2761d7577b7a6c**. It uses an explicit GL cover and the inherited compiler/analytic contracts; it is not an unconditional integer-multiplication theorem or a Lean certificate.\n\n## New mechanism\n\nThe old kernel search intersected sets of named E8 roots. We instead intersect their actual rational spans. This exposes 56 auxiliary directions of the form e_i +/- e_j that were invisible to that representation. The selected construction adds 22 response-kernel pivots on top of the updated rank139 basis and response retiming. Their simultaneous source-bound word changes the local paid histogram by +84 rank1 and -53 rank2; all 955 arbitrary-dirty columns and 22 omission controls pass.\n\nThese new entrance lines need non-coordinate residual routes. Two copies have an explicit rational orthogonal 16-by-16 normalization: their intact rank7 residual projectors are orthogonal and sum to a rank14 coordinate projector. We place each pair inside ONE owner family, with two restored spectator directions. No logical residual is split across different physical families. Full 78-column owner maps include the actual port/window basis, the entrance directions, placement and inverse; matching dimensions alone is not accepted.\n\nThe physical program contains 88 complete local invocations, 62,920 whole residual occurrences,968 paired blocks and 1,733,496 emitted events, including 23,040 bridge updates. All costs are recomputed from this one program; gains from different proposals are never added numerically.\n\n## Exact price and scope\n\n- Final kappa: 1301970637653655 / 10^18.\n- Bit saving: see the exact rational bracket in EXPECTED.json; approximately 0.001303667975.\n- Unchanged complex saving: 1305231506267591 / 10^18.\n- Live stock 9600, physical stock 9609, rank mass 745536, deficit 3264.\n- Physical prefix 1684 bits, charged 1728.\n- Concrete route 224 elementary factors per direction, conservatively charged 512.\n- PR490 GL-cover sharp bad-class charge and enlarged row allowance 28416 are used. The fixed-q weighted-routing constant B_GL stays explicit in the symbolic bootstrap cutoff.\n\nThis does not claim to beat PR480's higher cross-copy headline. That claim retains the disputed operator admission discussed in PR448/451; no such split is used here. The construction also does not achieve the larger campaign target.\n\n## Reproduction and validation\n\n python -B research/tensor-nonroot-pairs/verify.py /absolute/new/output\n\nPython3.11+, SymPy, C++17 and Boost are required. Set CXX/BOOST_INCLUDE if necessary. No network, annealer or discovery optimizer is required. Default rebuilds both suppliers. `--complex-output` accepts only the exact completed complex receipt and 87 implementation/17 output hashes pinned in the package; any reuse is explicitly reported.\n\nChecks include source reconstruction, fresh native legality and five-/eleven-stage columns, 1,019 positive Gram frames, exact auxiliary-line decoder,22 omitted-correction controls, rational route/inverse/projector/factor controls, actual full-matrix owner injection, complete chronological emission, independently reconstructed physical-family row invoice, two rational moment engines, six bootstrap rounds and 47 strict inequalities with next-grid/degenerate-parameter controls. VALIDATION.json and release receipts specify the packaged run; finite verification does not discharge the inherited all-size contracts.\n\nTwo representation fixes are explicit and source-bound: the decoder's full-frame mask uses 176 lines while retaining 120 semantic ports, and half-inner-products remain rational instead of being floored. The general integer-basis native auditor is unchanged.\n\n## Direct credits\n\n- **PR473**: updated rank139 basis exchanges, exact nested response source and whole-owner packing framework.\n- **PR483**, **PR478**, **PR476**: response cancellation, nested flags and target-factor lineage retained in the base word.\n- **PR485**: the scoped coordinate-kernel analysis motivated searching actual geometric intersections rather than named roots.\n- **PR490**: fixed-GL whole-owner transport, sharp fallback, row28416 and explicit routing cutoff.\n- **PR470**, **PR472**, **PR463**, **PR443**: R715 word, retiming, shared-response construction and checked local interfaces.\n- **PR471**, **PR458**: unchanged complex supplier, full-nine-axis normalization, paid wrappers and same-owner spectator handling.\n- **PR442**, **PR451**, **PR465**: hosting/compressed-stage infrastructure and fallback-accounting lineage.\n\nThe immutable-source retiming is reused from our earlier unpublished tensor-syndrome-portfolio package and adapted to the new basis; we do not claim to have invented it again. Classical rational linear algebra, two-square/Hadamard normalization and quaternion four-square identities underlie the new routing. Existing license and source notices are retained.\n\n## Saved research for future work\n\nThe package includes the general four-copy rational hosting proof, exact two-copy witnesses, the auxiliary-intersection method, independent composition review, and the tested complex partial-response/centre-lattice routes with their paid-cost limitations. PR484's larger complex-supplier proposal was studied but is not silently included in this exponent. Overlapping candidate counts, optimistic profiles and uncompleted routes are explicitly separated from the achieved construction. 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review (split-residual interface): #493's R489 bit word with #448's cross-copy complex supplier; computed κ = 0.001435468764627892 not established","user":{"login":"higherbeing","id":7227029,"node_id":"MDQ6VXNlcjcyMjcwMjk=","avatar_url":"https://avatars.githubusercontent.com/u/7227029?v=4","gravatar_id":"","url":"https://api.github.com/users/higherbeing","html_url":"https://github.com/higherbeing","followers_url":"https://api.github.com/users/higherbeing/followers","following_url":"https://api.github.com/users/higherbeing/following{/other_user}","gists_url":"https://api.github.com/users/higherbeing/gists{/gist_id}","starred_url":"https://api.github.com/users/higherbeing/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/higherbeing/subscriptions","organizations_url":"https://api.github.com/users/higherbeing/orgs","repos_url":"https://api.github.com/users/higherbeing/repos","events_url":"https://api.github.com/users/higherbeing/events{/privacy}","received_events_url":"https://api.github.com/users/higherbeing/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"Conditional **κ = 358867191156973/(2.5·10¹⁷) = 0.001435468764627892**, complex-bound, **+4.63 % over #480** (1.3725502·10⁻³). This composes two published suppliers without constructing anything new on either side: eumemic's #493 R489 bit word (bit c = 1.565442·10⁻³, whole-residual hosting, eleven stages, no cross-copy slot on the bit side) and #448's cross-copy hosted #433 complex word (b = 1.437532·10⁻³).\n\nIt is the pairing #493's own assembly prices as \"information only\". Here the complex supplier is **rebuilt and audited rather than cited**: #442's complete verifier rebuilds #434 and the #433 word with its Gaussian phases, the cross-copy generator re-hosts it, and an independent audit (seven mutation controls) checks every piece, window, remainder and the deficit before the assembly. #493's package is vendored byte for byte and its `verify.sh` is run unchanged, including its controls that reproduce #472's and #445's published bit savings; the bit root is asserted equal to #493's receipt.\n\n| supplier | saving | hosting | source |\n| --- | --- | --- | --- |\n| bit, m = 78, R = 489, eleven stages, 8 replicas | 1.565442·10⁻³ | whole residuals (#442) | #493, rebuilt |\n| complex, m = 73, R = 560, nine stages | **1.437532·10⁻³** (binds) | cross-copy (#448) | #448, rebuilt and audited |\n\nAssembly: #493's bit half (#472's eleven-stage invoice with R = 489: three-level halving, physical prefix charged to the next 64-bit block, complete row bound < 20,161) with #448's complex half (#442's invoice with the hosted stock), then the #434/#315 outer assembly: six bootstrap levels, all 47 strict inequalities, next-grid and zero-η/zero-β/unit-β controls rejected.\n\nWith the bit side at 1.5654·10⁻³ the complex supplier is now the constraint by 9 %, so the next gains are on the complex side (an eleven-stage layout with cross-copy hosting, a complex response kernel as in #466/#484).\n\n## Validation\n\n`python3 -B research/r489-cross-copy-complex/verify.py /absolute/new/output` runs #493's `verify.sh` unchanged, #442's complete `verify.py`, the cross-copy complex generator, its independent audit and the exact assembly, and compares every value, the emitted-program digest and the complex template hash with `EXPECTED.json`. Local run: macOS, Python 3.14. CI is not claimed before it runs.\n\n## Scope\n\nConditional like its parents. Review points: #448's cross-copy slot, here on the complex side only (the dispute is on #451's thread, with the exact two-family check in #448 §7), and #493's own points (mutable-source bit word, carrier structure, relaxed checker). All inherited interfaces remain assumptions. No Lean proof and no unconditional integer-multiplication theorem is claimed.\n\n## Credits and AI disclosure\n\neumemic (#493 word and pipeline adaptation), DaysSky (#442), chafreaky (#443–#445, #472 pipeline, #451 review), icekylinx (#433), Zhihao Chen (#425/#386), Rohan Arun (#434), Dylan Crow (#370), Jacob Sussman, and all source-pinned authors. This branch is #480's branch plus #493's package vendored unchanged and one new directory, `research/r489-cross-copy-complex/`. 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review (split-residual interface): cross-copy hosting on #472's R715 eleven-stage word; computed κ = 0.001372550159367980 not established","user":{"login":"higherbeing","id":7227029,"node_id":"MDQ6VXNlcjcyMjcwMjk=","avatar_url":"https://avatars.githubusercontent.com/u/7227029?v=4","gravatar_id":"","url":"https://api.github.com/users/higherbeing","html_url":"https://github.com/higherbeing","followers_url":"https://api.github.com/users/higherbeing/followers","following_url":"https://api.github.com/users/higherbeing/following{/other_user}","gists_url":"https://api.github.com/users/higherbeing/gists{/gist_id}","starred_url":"https://api.github.com/users/higherbeing/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/higherbeing/subscriptions","organizations_url":"https://api.github.com/users/higherbeing/orgs","repos_url":"https://api.github.com/users/higherbeing/repos","events_url":"https://api.github.com/users/higherbeing/events{/privacy}","received_events_url":"https://api.github.com/users/higherbeing/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"Conditional **κ = 1372550159367980/10¹⁸ ≈ 1.372550159367980·10⁻³**, bit-bound, **+1.63 % over #469** (1.3505809·10⁻³) and **+6.23 % over #472** (1.2920996·10⁻³). This is #448's cross-copy slot applied to #472's suppliers: chafreaky's R715 word with shared kernel, target mixing and retimings in eleven compressed stages on the bit side, and #448's cross-copy hosted #433 word on the complex side. Neither local word nor any schedule, isometry or bridge changes; only the owners of the helper residuals do.\n\n## Change\n\n#472 hosts all 62,920 helper residual occurrences whole on idle data families (pooling the eight replicas), which leaves copies partly empty because widths 8/7/6 do not tile children of rank 7, 14, 28, 42 and 56; those remainders are paid. Here the pending sets of a child's 1,920 pooled copies form one tape, residuals are laid along it widest first, and a residual that straddles a copy boundary is owned by two copies of the same child, which share the window. The complete-program identity is #448 §2, family by family; the exact finite check of #448 §7 covers the two-family case in the model of #451's note. The concave cost makes the contiguous fill optimal: filled copies pay nothing and only the unfilled copies of the rank-56 final children pay.\n\n| supplier | parent saving | this saving | hosted residuals (split) | max child |\n| --- | --- | --- | --- | --- |\n| bit, m = 78, R = 715, 11 stages, 8 replicas | 1.293771·10⁻³ (#472) | **1.374423·10⁻³** | 62,920 (14,612) | 56 |\n| complex, m = 73, R = 560 | 1.437532·10⁻³ (#448) | 1.437532·10⁻³ | 40,320 (13,720) | 48 |\n\nAccounting follows #472: eleven-stage invoice with three-level halving, complete row bound 19,431 < 20,161, the chronological physical prefix bound recomputed on the new owners (a split owner's two families both receive the update, a new accounting choice that is a review point of its own; 1,161 bits charged 1,216), one further route factor per helper selector for the split. Deficit 3,264 unchanged. The integer programme is frozen in `SELECTION.json`; any residual it leaves out is placed on an in-window child with room.\n\n## Validation\n\n`python3 -B research/cross-copy-hosting-r715/verify.py /absolute/new/output [--quick]` runs #472's complete verifier (which rebuilds #458's complex supplier and the R715 composition), then both generators, an independent audit that shares no code with them (windows re-derived; one owner record per helper; pieces on copies of the named child, inside the pending set, widths summing to the residual width, disjoint per (child, copy), inside the window, off the active pair; owner families recomputed; unchanged template parts byte-identical to #472's; remainders, profile, stock, deficit, emitted-program digest and prefix bits recomputed; fifteen mutation controls rejected), and the exact assembly (two rational moment engines per supplier, both finite invoices, six bootstrap levels, all 47 strict outer inequalities; next-grid and η/β controls rejected). Local run: macOS, Python 3.14, quick mode (skips only #443's inherited exhaustive controls); every value, the emitted digest and the complex template hash match `EXPECTED.json`. CI is not claimed before it runs.\n\n## Scope\n\nConditional like its parents. The review point is #448's cross-copy slot, on which #450, #453, #464 and #469 also rest; #451's trace note and the replies on that thread describe the disagreement. #472's own review points and all inherited interfaces remain assumptions. No Lean proof and no unconditional integer-multiplication theorem is claimed.\n\n## Credits and AI disclosure\n\nBuilds on and runs unchanged: #472, #467, #463 (R715 word: DreamingOfClouds), #458, #454, #451, #443–#445 (chafreaky), #442 (DaysSky), #450 (target mixing), #441/#440/#436 (eumemic), #434 (Rohan Arun), #433 (icekylinx), #425/#386 (Zhihao Chen), #370 (Dylan Crow), Jacob Sussman's E8 unit and interfaces. This branch is #472's branch plus one new directory, `research/cross-copy-hosting-r715/`; no inherited file is changed. 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review (split-residual interface): cross-copy idle-axis hosting, one residual on two copies of one idle child; computed κ = 0.001330733966732373 not established","user":{"login":"higherbeing","id":7227029,"node_id":"MDQ6VXNlcjcyMjcwMjk=","avatar_url":"https://avatars.githubusercontent.com/u/7227029?v=4","gravatar_id":"","url":"https://api.github.com/users/higherbeing","html_url":"https://github.com/higherbeing","followers_url":"https://api.github.com/users/higherbeing/followers","following_url":"https://api.github.com/users/higherbeing/following{/other_user}","gists_url":"https://api.github.com/users/higherbeing/gists{/gist_id}","starred_url":"https://api.github.com/users/higherbeing/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/higherbeing/subscriptions","organizations_url":"https://api.github.com/users/higherbeing/orgs","repos_url":"https://api.github.com/users/higherbeing/repos","events_url":"https://api.github.com/users/higherbeing/events{/privacy}","received_events_url":"https://api.github.com/users/higherbeing/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"Conditional **κ = 1330733966732373/10¹⁸ ≈ 1.330733966732373·10⁻³**, bit-bound, **+5.13 % over #447** (1.265848755025709·10⁻³, complex-bound), +7.53 % over #442 and +17.44 % over #434. Neither local word changes: complex #433 (R = 560, m = 73), bit #434 (R = 747, m = 64). The idle windows are #442's.\n\n## Change\n\nIn #442's idle-axis hosting a whole helper residual sits inside the pending coordinates of one data family. Bit residuals have width 8 − e (637 of width 8, 104 of width 7, 6 of width 4) and complex residuals width 9, while the idle children have ranks 7/14/28/42 (bit) and 8/16/32/48 (complex). A rank-7 child cannot hold a width-8 residual, a rank-14 child holds one and wastes six coordinates, and so on: 6,944 of the 45,360 pending bit coordinates per replica and 5,760 of 51,840 complex ones stay idle and are paid as remainder children.\n\nA child acts on every copy (side, port) of its pair, and all copies share the child's window. This package lets a residual lie across the pending sets of **two copies of the same idle child**. With P = P₁ + P₂ the identity D_{P₁}·D_{P₂} = D_P (the parents' D_{P'}·D_{P−P'} = D_P) writes the dirty invocation's factor on the residual as a product of a factor on each family; each is moved to the child exactly as in #442 §2, since the window is a property of the pair; and each child's remainder is exact by #442's fact (b). Every child's capacity, copies × rank, is then a multiple of the residual width, so the remainders almost vanish. A residual never spans two children or two pairs. The route is still an elementary coordinate permutation of the address space; the finite invoice charges one further route factor per helper selector.\n\nThe selection is an integer programme over counts n(child, stage, width) on the concatenated tape of each child's copies (maximise Σ ln(m/r) × hosted coordinates, subject to availability and, on the bit side, exact width-64 tiling of the leftover). `SELECTION.json` freezes it; `--discover` recomputes it with scipy.\n\n## Result\n\n| supplier | #442 saving | this saving | live stock | hosted residuals (split) | max child |\n| --- | --- | --- | --- | --- | --- |\n| bit, m = 64, R = 747 | 1.239085·10⁻³ | **1.332507·10⁻³** | 9,457 → 8,592 | 46,160 of 53,784 (12,496) | 24 |\n| complex, m = 73, R = 560 | 1.267453·10⁻³ | **1.437532·10⁻³** | 8,400 → 7,680 | 40,320 of 40,320 (13,720) | 48 |\n\nBoth rank deficits stay 2496. The bit max child 24 is one partial copy of a rank-28 child; the complex max child 48 is the 133 copies per replica of the rank-48 final children that the complex supply cannot fill (5,040 residuals against 5,760 width-9 slots per replica). Since #447 is complex-bound at 1.267453·10⁻³, the complex component here should also lift #445/#447's eleven-stage bit words; that composition is not claimed.\n\n## Validation\n\n`python3 -B research/cross-copy-hosting/verify.py /absolute/new/output` (Python 3.11+, standard library only; the output directory must not exist). It\n\n1. runs #434's complete verifier from scratch;\n2. regenerates both hosted templates from #434's fresh outputs and the frozen selection;\n3. runs an independent audit that shares no code with the generators: windows re-derived from each schedule; for every replica and invocation exactly one owner record per helper; every hosted residual has one or two pieces on copies of the child it names, widths summing to the residual width, inside the pending set, pairwise disjoint per (child, copy), inside the window and off the active pair; exact remainder children and bank tilings; profile, live stock and deficit 2496 recomputed; twelve mutation controls rejected (including a split across two children and a split whose widths do not sum to the residual width);\n4. prices both suppliers with the two inherited rational moment engines and fresh finite invoices (prefix 226 bits charged 256, two-level coefficient 488 bits charged 512, row coefficient 18,355 < 20,161; complex row coefficient 15,443);\n5. runs #434's strict outer assembly: six bootstrap levels and all 47 inequalities, with the next grid point and the zero-η, zero-β and unit-β controls rejected.\n\nLocal transcript: `PASS_FULL_CROSS_COPY_HOSTING_COMPOSITION` on macOS (Apple silicon), Python 3.14.3, 5 min 48 s including the full #434 replay; every value equals `EXPECTED.json` and both template hashes match. CI is not claimed before it runs.\n\n## Scope\n\nThis is a written finite extension of #442's hosting interface: a helper residual's physical slot may lie in two data families of one idle child. That is the principal new review point; [PROOF.md](research/cross-copy-hosting/PROOF.md) gives the argument from the parents' two facts. #442's own extension (helper residuals on data streams during idle windows) and all inherited interfaces remain assumptions: the all-size compiler, correlated dirty-bank and compressed-window interfaces, restored work, tape/common grid, precision and analytic transfer. The global operator identity is argued and checked combinatorially, not replayed numerically on the address spaces. No Lean proof and no unconditional integer-multiplication theorem is claimed.\n\n## Credits and AI disclosure\n\nBuilds on and runs unchanged: #442 (DaysSky, idle-axis hosting; windows and bank tilings reused), #434 (Rohan Arun), #433 (icekylinx), #435/#417 (chafreaky), #426 (ai-nanachi), #425/#386 (Zhihao Chen), #370 (Dylan Crow), Jacob Sussman's E8 unit and interfaces. This branch is #442's branch plus one new directory, `research/cross-copy-hosting/`; no inherited file is changed. The cross-copy selection, generators, audit, assembly and proof note were prepared by higherbeing with substantial Claude (Anthropic) assistance.\n\n🤖 Generated with [Claude Code](https://claude.com/claude-code)\n","created_at":"2026-10-11T14:51:42Z","updated_at":"2026-10-11T21:15:56Z","closed_at":null,"merged_at":null,"merge_commit_sha":"218734474a740b17a3eadff151c47ab09652ea18","assignees":[],"requested_reviewers":[],"requested_teams":[],"labels":[],"milestone":null,"draft":true,"commits_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/pulls/448/commits","review_comments_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/pulls/448/comments","review_comment_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/pulls/comments{/number}","comments_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/issues/448/comments","statuses_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/statuses/359022bcd71143e45d48def0dd005bf67f339aa7","head":{"label":"higherbeing:research/cross-copy-hosting","ref":"research/cross-copy-hosting","sha":"359022bcd71143e45d48def0dd005bf67f339aa7","user":{"login":"higherbeing","id":7227029,"node_id":"MDQ6VXNlcjcyMjcwMjk=","avatar_url":"https://avatars.githubusercontent.com/u/7227029?v=4","gravatar_id":"","url":"https://api.github.com/users/higherbeing","html_url":"https://github.com/higherbeing","followers_url":"https://api.github.com/users/higherbeing/followers","following_url":"https://api.github.com/users/higherbeing/following{/other_user}","gists_url":"https://api.github.com/users/higherbeing/gists{/gist_id}","starred_url":"https://api.github.com/users/higherbeing/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/higherbeing/subscriptions","organizations_url":"https://api.github.com/users/higherbeing/orgs","repos_url":"https://api.github.com/users/higherbeing/repos","events_url":"https://api.github.com/users/higherbeing/events{/privacy}","received_events_url":"https://api.github.com/users/higherbeing/received_events","type":"User","user_view_type":"public","site_admin":false},"repo":{"id":1413923815,"node_id":"R_kgDOVEbD5w","name":"integer-mult-bounds","full_name":"higherbeing/integer-mult-bounds","private":false,"owner":{"login":"higherbeing","id":7227029,"node_id":"MDQ6VXNlcjcyMjcwMjk=","avatar_url":"https://avatars.githubusercontent.com/u/7227029?v=4","gravatar_id":"","url":"https://api.github.com/users/higherbeing","html_url":"https://github.com/higherbeing","followers_url":"https://api.github.com/users/higherbeing/followers","following_url":"https://api.github.com/users/higherbeing/following{/other_user}","gists_url":"https://api.github.com/users/higherbeing/gists{/gist_id}","starred_url":"https://api.github.com/users/higherbeing/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/higherbeing/subscriptions","organizations_url":"https://api.github.com/users/higherbeing/orgs","repos_url":"https://api.github.com/users/higherbeing/repos","events_url":"https://api.github.com/users/higherbeing/events{/privacy}","received_events_url":"https://api.github.com/users/higherbeing/received_events","type":"User","user_view_type":"public","site_admin":false},"html_url":"https://github.com/higherbeing/integer-mult-bounds","description":"Conditional integer multiplication: kappa > 2^-15. 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supplier b ≈ 1.327·10⁻³ (+4.7%) on whole-residual hosting: shared-donor kernel and entrance gauges with paid residual wrappers (conditional on two lemmas)","user":{"login":"DreamingOfClouds","id":173691639,"node_id":"U_kgDOClpS9w","avatar_url":"https://avatars.githubusercontent.com/u/173691639?v=4","gravatar_id":"","url":"https://api.github.com/users/DreamingOfClouds","html_url":"https://github.com/DreamingOfClouds","followers_url":"https://api.github.com/users/DreamingOfClouds/followers","following_url":"https://api.github.com/users/DreamingOfClouds/following{/other_user}","gists_url":"https://api.github.com/users/DreamingOfClouds/gists{/gist_id}","starred_url":"https://api.github.com/users/DreamingOfClouds/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/DreamingOfClouds/subscriptions","organizations_url":"https://api.github.com/users/DreamingOfClouds/orgs","repos_url":"https://api.github.com/users/DreamingOfClouds/repos","events_url":"https://api.github.com/users/DreamingOfClouds/events{/privacy}","received_events_url":"https://api.github.com/users/DreamingOfClouds/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"## A stronger complex supplier: b = 1326789535340266/10¹⁸ ≈ 1.326790·10⁻³ (+4.68% over #442), whole-residual hosting, one owner per family\n\nThis adds one self-contained package, `research/e8-complex-gauge-kernel/`. It is a **complex-side supplier**: #433's split-centre word (R = 560, m = 73), #442's idle-axis hosting with the one-helper-per-family rule of #458, and two tools of the bit side ported to it. **No new κ is claimed in this package.** With #442's bit word the bit side binds (κ = 1.237552·10⁻³; 1.279171·10⁻³ with our pinned R724 word). #493 reports κ ≈ 1.325·10⁻³ when its R489 bit word is paired with this supplier; there the complex side binds. #496 and #497 re-place this word's helpers and report 1.332077·10⁻³ and 1.325118·10⁻³. The current lemma-less κ frontier is #478 (Dugongue) at 1.295509·10⁻³, which sits at #458's complex cap; this supplier raises that cap; #458, #460 and #462 are bit-bound, not complex-bound. On the complex side b is +2.28% over #458 (1.297204·10⁻³) and +1.65% over #471 (1.305232·10⁻³; #471 admits our kernel79 through normalisation plus same-owner spectator borrowing, and is credited below). This raises the complex cap of this lineage to κ ≤ 1.325031·10⁻³ (the #448/#450 lineage used in #464 and #469 has complex roots of about 1.44·10⁻³). It is conditional on two lemmas, the review points: **Lemma A** (paid residual wrappers with explicit spectators; the entrances are isotropic, not coordinate entrances) and **Lemma G** (nonzero-frame compensation and the centre scatter). It supersedes the draft #449.\n\n| complex word | entering helpers | entrance rank | b (·10⁻³) | gain over #442 |\n| --- | ---: | ---: | ---: | ---: |\n| #442 | 0 | 0 | 1.267453 | |\n| shared-donor kernel | 79 | 79 | 1.305684 | +3.02% |\n| entrance gauges | 80 | 106 | 1.306413 | +3.07% |\n| **both** | 122 | 148 | **1.326790** | **+4.68%** |\n\n### Relation to #458 and #471\n#458 (chafreaky) puts the 79-pivot kernel of #449 on an eleven-stage complex word and pays its entrance transforms as emitted, checked adapters, with at most one helper per host family per invocation. This package adopts that treatment on the nine-stage word and adds the entrance gauges; #449's hosting allowed several helpers on one family and left an entering helper's spectator coordinates unplaced, which #458 showed is not sufficient. #471 normalises the complete invocation and borrows spectators in the same owner array; this package applies the same borrowing to its banks (an entering helper is the only owner of its bank family in an invocation, its spectators are the first cells of the bank's pad) and extends the one-owner rule to every register class of an invocation, with a control for each.\n\n### Change\nA helper's frame-zero compensation (the response of its arbitrary dirt) pins it to start frame {0}, so its residual has width 9. Two exact ways avoid it:\n- **Shared-donor kernel** (#417/#435/#434/#439/#440): a pivot whose response column is a rational combination of donors' columns starts at an entrance E contained in every member's first frame; each donor receives `d += −q·pivot` at E before the main word (inverse after cleanup).\n- **Entrance gauge** (#401/#408–#416): the compensation of a helper is executed at its entrance frame E instead of frame 0; targets climb through the nested entrance chain, and each centre copy descends from its frame through the levels it serves (mass-neutral, rank deficit 2,496).\n\nA helper that starts at E has the residual S_E = T_FULL·T_E⁻¹ = L_E (C_[w] ⊗ I) R_E, w = 9 − dim E, exactly (global phase included). The paid wrappers R_E⁻¹ before the whole invocation and L_E⁻¹ after its cleanup turn it into the coordinate factor and restore the e = 9 − w spectator coordinates; they are emitted, replayed, decoded and charged. Widths 8/16/32/48 of #442's idle children are tiled by width-8 residuals; the hosting is whole-residual with distinct stages in every copy and at most one helper per physical family per invocation, with the host chart (residual vectors, first unused basis vectors as spectators) in the route and audited. Residuals that are not hosted go to banks of their own, one entering helper per replica per bank family, with the spectators in the pad and the route and chart audited in the same way.\n\n### Result\nBoth rational moment engines certify b = 1326789535340266/10¹⁸ (next grid point rejected). Under the one-owner rule the word hosts 39,792 of 40,320 residuals whole; the other 528 (all of width 8) sit in 66 banks (live stock 7,746, maximum child 9, rank deficit 2,496). The finite invoices with the hosted stock and the wrapper charge, and the strict outer assembly (six bootstrap levels, 47 inequalities, next-grid, zero-η, zero-β and unit-β controls rejected), pass for #442's bit word (run here, κ = 1.237552·10⁻³ unchanged) and, as a pinned input from our own bit-side package that is not re-run here, for the eleven-stage R724 mixed word under whole-residual hosting (c = 1.280810·10⁻³): κ = 1.279171·10⁻³, bit-bound (no new κ). That pairing is informational; our R715 word is #463.\n\n### Checks (`python -B research/e8-complex-gauge-kernel/verify.py DIR [--all] [--discover-check]`)\n- #442 runs unchanged (with #434 and #433 below it), then the **regression anchor**: with the empty selection the generalised scripts reproduce #433's canonical word, local programs, local checks, parent global template and independent replay, and #442's hosted template and `HOSTED.json`.\n- Gauge + kernel word: exact arbitrary-dirt and inverse-transpose replay (800 columns); emitted program replay in both orientations with centre lifetimes and wrappers; independent read-back of the serialized stream; exact Gaussian recipes with global phase for every used frame transition (`complex_phases_full.py`, unmodified); exact decoding of the wrapper monomials (L⁻¹ S_E R⁻¹ = C_[w] ⊗ I on every entrance frame); independent hosting audit (windows, slots, owners, spectator chart on data and bank families, one owner per family on every register class, private namespace, remainders, wrong-width control); fresh finite invoices; certified b.\n- **Independent Lemma G stage** (`code/lemmaG/`, imports no package script): the label / scalar / accounting checker on both orientations, the exact operator identities of every compensation, centre and helper instance on all 512 basis columns, the complete emitted program end to end against the transform computed from definitions, and 14 necessity mutants of the clauses.\n- Mutation controls, all rejected, several through the certifying scripts themselves: kernel and gauge gates, entrances, target levels, centre chains, wrappers, centre descent steps, two helpers on one data or bank family (accepted by #442's rule, rejected here), spectator records, owners in the private namespace or on another replica's families, wrappers on non-helper registers, and selection-level conditions; the generators also refuse the eight-entering-helpers-per-bank tiling.\n- `--discover-check` recomputes the frozen hosting selections with HiGHS and requires equality. Status: the full `--all` runs pass from fresh copies on Python 3.14 (`--all --discover-check`), 3.12 (`--all`) and 3.11 (`--all --discover-check`), with identical summaries. The `.gz` inputs of the Lemma G stage are pinned by the sha256 of their decompressed JSON, since gzip container bytes depend on the zlib of the Python in use.\n\n### Principal review points (conditional)\n- **Lemma A** (`PROOF.md` §3). Exact and checked: S_E = L_E (C_[w] ⊗ I) R_E and the wrapped product on every entrance frame. Assumed: #458's argument that wrappers around a whole invocation of a family on which nothing else acts leave the spectators identical, at nine stages, for hosted families and banks.\n- **The entrances are not coordinate entrances.** Every entrance frame consists of even-weight vectors of F2⁹ (15 of 16 frames totally isotropic). The bit-style criterion of #440 (`validate_isometries`) is not met and cannot be met by any orthogonal map of O(9,2); restricted to entrances that meet it, the gain is 0. #442's complex audit asserted `w == 9` and #433's emit start frame 0 for compensated registers; the marked copies here generalise exactly these.\n- **Lemma G** (`PROOF.md` §2): reduces to #425's conjugation lemma and #471's / #458's virtual entrance, plus a schedule lemma (hypotheses (a)-(d)) whose clauses are checked on the emitted streams by the independent stage above; new relative to #458 and #471, which do not use the gauge.\n- All interfaces inherited from #370, #386, #425, #433 and #442 remain assumptions. 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κ = 0.001325117552367841: moment-directed complex hosting","user":{"login":"chafreaky","id":4400527,"node_id":"MDQ6VXNlcjQ0MDA1Mjc=","avatar_url":"https://avatars.githubusercontent.com/u/4400527?v=4","gravatar_id":"","url":"https://api.github.com/users/chafreaky","html_url":"https://github.com/chafreaky","followers_url":"https://api.github.com/users/chafreaky/followers","following_url":"https://api.github.com/users/chafreaky/following{/other_user}","gists_url":"https://api.github.com/users/chafreaky/gists{/gist_id}","starred_url":"https://api.github.com/users/chafreaky/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/chafreaky/subscriptions","organizations_url":"https://api.github.com/users/chafreaky/orgs","repos_url":"https://api.github.com/users/chafreaky/repos","events_url":"https://api.github.com/users/chafreaky/events{/privacy}","received_events_url":"https://api.github.com/users/chafreaky/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"A different whole-residual packing of #484's unchanged complex gauge/kernel word raises its saving from **0.001326789535340266 to 0.001326875818805153**. With #493's freshly replayed R489 bit supplier, the conditional assembly is **κ = 0.001325117552367841**, **+0.00649456%** over the #484/#493 pairing. The complex side binds.\n\nAll entering helpers now fit on data families. The 66 remaining banks contain only width-nine helpers, so their pads have rank one. Live stock stays 7,746 and physical stock stays 8,324; the largest paid complex child drops from rank nine to rank eight. The profile change is exactly `+66·rank1 −528·rank5 +528·rank6 −66·rank9`. The proof shows this improves the complete charged moment for every saving in `(0,1)`. No local scalar gate, frame, phase, wrapper, or global schedule changes.\n\n`python -B research/e8-gauge-moment-hosting/verify.py /absolute/new/output` freshly runs #484's complete `--all` verifier and #493's full verifier with real Boost arithmetic, then the new packing, the unchanged hosting audit, an independent integer count check with five rejection controls, both rational moment engines, the finite invoice, and all 47 strict outer inequalities. Fresh macOS and Linux runs pass with identical deterministic results. The inherited source packages are byte-identical to their published commits; 277 source/manifest entries were checked against staged Git blobs. CI is pending.\n\nUse Python 3.13 or 3.14: the unchanged #484 receipt compares gzip byte hashes that differ on 3.12 and 3.15. Raw timing-dependent parent hashes remain in the receipts; only the inherited geometry timer is excluded from the deterministic bit-template fingerprint. Optional SciPy discovery is separate from verification, and no optimality claim depends on it.\n\nThis retains the parents' conditional all-size compiler, mutable-basis, whole-owner hosting, restored-work, and analytic interfaces. It does not adopt cross-copy routing, claim an unconditional theorem, or change main's selected result. κ = 1 remains open.\n\nCredits: #484's gauge/kernel word and pipeline, #493's source-carrier bit word, #442's hosting, #458's whole-owner rule, and their source-pinned predecessors. Chafreaky with OpenAI Codex assistance; upstream notices and licenses are 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κ = 0.001332077359286333: pooled whole-owner complex supply","user":{"login":"eumemic","id":94939491,"node_id":"U_kgDOBaipYw","avatar_url":"https://avatars.githubusercontent.com/u/94939491?v=4","gravatar_id":"","url":"https://api.github.com/users/eumemic","html_url":"https://github.com/eumemic","followers_url":"https://api.github.com/users/eumemic/followers","following_url":"https://api.github.com/users/eumemic/following{/other_user}","gists_url":"https://api.github.com/users/eumemic/gists{/gist_id}","starred_url":"https://api.github.com/users/eumemic/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/eumemic/subscriptions","organizations_url":"https://api.github.com/users/eumemic/orgs","repos_url":"https://api.github.com/users/eumemic/repos","events_url":"https://api.github.com/users/eumemic/events{/privacy}","received_events_url":"https://api.github.com/users/eumemic/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"κ = 0.001332077359286333\n\nConditional whole-owner improvement: `κ = 1332077359286333/10^18`, using PR493's R489 bit word and a new placement of PR484's gauge/kernel complex word. Pooling the eight physical data replicas removes all 66 complex bank families. This improves the PR493 + PR484 whole-owner pairing (`0.001325031497415498`) by about 0.532%.\n\nEvery helper residual remains on **one physical family**. Each of the 72 complete local invocations has 800 distinct owners, including its active data wires. The larger draft PR494 number depends on PR448's disputed cross-family split; this PR retains the whole-owner interface and does not claim to exceed submissions under that different assumption.\n\n## Construction\n\nThe local bit and complex words, Gaussian phase recipes, entrance wrappers and cleanup are unchanged from the pinned suppliers. The new frozen allocation places each whole complex residual in an idle child. A bipartite edge coloring assigns its invocation replica: each actual helper occurs exactly once per invocation, and no physical family is reused within that invocation. A host may belong to another physical replica.\n\nThe serialized controller keeps complete invocations sequential. Entry wrapper, scalar word and exit wrapper finish before another invocation borrows the family. The explicit leftover idle children name their actual physical family and replica and execute once. There are no split residuals and no bank padding.\n\n- Complex: `m=73`, live stock **7680**, physical stock **8258**, **40320** whole helper routes, **3960** actual orthogonal 73-column maps.\n- Paid profile: `{1:148440, 2:66816, 3:7472, 4:19728, 5:25664, 6:144, 7:1800, 8:4120}`; rank mass **558144**, deficit **2496**.\n- Exact complex saving: `b = 133385415620840915601/10^23 = 0.001333854156208409156010`.\n- Fresh PR493 bit saving: `c = 391360506745414227149/250000000000000000000000 = 0.001565442026981656908596`; complex binds.\n- A global norm argument valid across replicas gives **142 prefix bits < 192**. It uses per-call bijections of the actual orthogonal cover and unitary completed helper endpoints, with no replica-independence or cover-cardinality shortcut.\n\n## Verification\n\n`python3 -B research/r489-pooled-whole-complex/verify.py /absolute/fresh/output --boost-include /path/to/boost/headers`\n\nThe package runs both complete pinned supplier verifiers from source, then the changed allocation and independent physical/invoice/assembly checks. It uses real Boost, records the header trace and a 257-bit integer probe, and guards expanding int64 operations before executing the exact Gaussian tests.\n\nChecks include arbitrary dirty restoration, both reflected local ledgers, actual whole-family maps and spectators, complete idle remainders, 18 controller mutations, a separate serial-pooling operator regression with five controls, both exact moment engines, six bootstrap cutoffs and all 47 strict outer inequalities. The next grid point and zero-eta/zero-beta/unit-beta controls are rejected. Verification uses the frozen map and does not run an optimizer.\n\nBoth complete release runs finished with observed exit 0 on Python 3.14.7 and real Boost 1.88: immutable source (441.064 s), and a fresh literal archive of commit `00cf70efd6a8637531deafef698157ca83e249ee` (440.999 s). All 14 root stages passed in each run and their complete mathematical results are identical. Package manifest SHA-256: `b7a3bdb801f4a9ae8c389edaee545a8d0cb16fd6211f38b54b71b5c50eb5a80c`; exact mathematical receipt SHA-256: `bede0887eaf7ccc5b1c9607ca15572c5e595c2574f0eb174f2b4982d11f32369`. The dedicated CI workflow is included; no CI success is claimed before it runs.\n\n## Scope, provenance and AI disclosure\n\nThis is a conditional finite construction. It retains the suppliers' all-size compiler, mutable-basis/common-label, PR484 Lemma A realization, restored-row, precision/tape and analytic-transfer contracts. PR484's Lemma G local identities are freshly checked; finite checks do not establish the inherited all-size assumptions. No unconditional theorem or Lean proof is claimed.\n\nThe package pins PR493 at `c3a9a436b84fe44fdc223a5784d84736d1c2d3c7` and PR484 at `035845ce95f31d0a2dcfb42b8c8e13411271fa5f`, including 266 original supplier/dependency files. The original packages and every previously published PR head and claim remain unchanged. `SOURCE.json`, `MANIFEST.json`, `PROOF.md` and `NOTICE.md` record the exact sources, argument, attribution and limitations.\n\nCredits include eumemic (PR493), DreamingOfClouds (PR484, with Claude Opus 5.5 assistance), DaysSky, icekylinx, chafreaky, Zhihao Chen, Rohan Arun, Dylan Crow, Jacob Sussman and the source-pinned authors credited by the suppliers. The new allocation, coloring, independent audits and integration were prepared with substantial OpenAI Codex assistance. Original licenses and AI disclosures are 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It adds a source-pinned response28 composition and preserves all original rows, physical programs, prefixes, coefficient charges, complex supplier data and outer assumptions.\r\n\r\n| Pinned PR473 source | Corrected conditional κ | Exact gain |\r\n| --- | --- | --- |\r\n| replica84, c7590f1 | 0.001295629943312713 | 725591/10^18 |\r\n| response28, f43a0e9 | 0.001296611983223706 | 728599/10^18 |\r\n\r\nThe fallback count is 24m²+6m−6 at m=78, from the retained unit-pivot local-ring Gaussian algorithm. No stronger cover probability is inferred. Both exact roots, six bootstrap steps and all 47 strict outer constraints were independently reconstructed, with old-count-at-new-root, adjacent-grid and parameter controls.\r\n\r\nValidation: fresh full original supplier replays completed in 1378.1s (replica84) and 729.8s (response28). Four corrected normal/optimized assemblies explicitly reused those completed full parents; four further assemblies bind the final documentation-only revision. Each pair has identical RESULT bytes. Separate reviews bind source Git blobs, complete invoices, actual programs, canonical complex payloads and terminal resource receipts. The default verifier rebuilds the original suppliers; completed-parent reuse has a distinct receipt.\r\n\r\nCurrent evidence and independent review:\r\n- [Acceptance and replay scope](https://github.com/M6LI/integer-mult-bounds/blob/996f67f7c21b8e56b4a2b0174c419ce48c480414/research/r715-count-only-validation/ACCEPTANCE.json)\r\n- [Publication review and actual bindings](https://github.com/M6LI/integer-mult-bounds/blob/996f67f7c21b8e56b4a2b0174c419ce48c480414/research/r715-count-only-publication-review/FINAL-SNAPSHOT-002.json)\r\n- [Response28 proof and assumptions](https://github.com/M6LI/integer-mult-bounds/blob/996f67f7c21b8e56b4a2b0174c419ce48c480414/research/r715-sharp-response28/PROOF.md)\r\n\r\nRequired baseline checks did not pass within the declared 1 CPU/2 GB cap: make verify hit the inherited h57 producer's OOM; a fresh full gen4 run with exact SymPy1.14 passed five stages before OOM entering banks. Source gates and resource limits were retained. These failures and partial outputs are preserved separately from the successful contribution-specific replays. The exact-head workflow is provided; no future CI-success claim is made.\r\n\r\nCorrection history: the earlier GL-derived 2m³/q probability transfer is withdrawn because its sampling model did not match the retained O-cover row invoice. Historical receipts remain explicitly labelled withdrawn; the present revision keeps the original 10^-16 law conditional. This is an improvement over the two exact pinned sources, not a current frontier record: newer PR493 has a stronger source-carrier pairing whose complex component now binds. No unconditional theorem or new all-size cover/compiler/hosting proof is claimed.\r\n\r\nBuilds on [PR465](https://github.com/CrocSwap/integer-mult-bounds/pull/465), [PR473](https://github.com/CrocSwap/integer-mult-bounds/pull/473) and [PR478](https://github.com/CrocSwap/integer-mult-bounds/pull/478). Original source ancestry, Apache-2.0 notices and attribution are preserved. 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combined E8 witness at κ = 0.001307044366925301","user":{"login":"aliromman","id":226877337,"node_id":"U_kgDODYXfmQ","avatar_url":"https://avatars.githubusercontent.com/u/226877337?v=4","gravatar_id":"","url":"https://api.github.com/users/aliromman","html_url":"https://github.com/aliromman","followers_url":"https://api.github.com/users/aliromman/followers","following_url":"https://api.github.com/users/aliromman/following{/other_user}","gists_url":"https://api.github.com/users/aliromman/gists{/gist_id}","starred_url":"https://api.github.com/users/aliromman/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/aliromman/subscriptions","organizations_url":"https://api.github.com/users/aliromman/orgs","repos_url":"https://api.github.com/users/aliromman/repos","events_url":"https://api.github.com/users/aliromman/events{/privacy}","received_events_url":"https://api.github.com/users/aliromman/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"## Change and mathematical scope\n\nCombine the four-replica R705 bit supplier and the retimed eight-replica R560 complex supplier. The exact composition gives **κ = 0.001307044366925301**, **80.637878% above pinned main** (`12a4934`). This is an exponent-saving comparison, not a measured runtime gain.\n\nThe bound is conditional. In addition to main's framework, it uses the pending mutable-target, whole-call idle-hosting, and Gaussian-adapter interfaces. All-size compilation, complete-cover execution, restored-work and ordinary-leaf contracts, bad-class portability, and analytic transfer remain assumptions. The proof gives six exact bootstrap steps and sequential finite-cutoff existence; it does not certify complete numerical cutoffs.\n\nThe package contains fixed witness data, a concise proof, source attribution, offline reconstruction and independent arithmetic checks, plus one Makefile target and CI workflow. Main's selected-result record stays unchanged. 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κ = 0.001274415506145115: complex response kernel + rank151/mixed bit word on #451 (+0.670%)","user":{"login":"rohanarun","id":11659839,"node_id":"MDQ6VXNlcjExNjU5ODM5","avatar_url":"https://avatars.githubusercontent.com/u/11659839?v=4","gravatar_id":"","url":"https://api.github.com/users/rohanarun","html_url":"https://github.com/rohanarun","followers_url":"https://api.github.com/users/rohanarun/followers","following_url":"https://api.github.com/users/rohanarun/following{/other_user}","gists_url":"https://api.github.com/users/rohanarun/gists{/gist_id}","starred_url":"https://api.github.com/users/rohanarun/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/rohanarun/subscriptions","organizations_url":"https://api.github.com/users/rohanarun/orgs","repos_url":"https://api.github.com/users/rohanarun/repos","events_url":"https://api.github.com/users/rohanarun/events{/privacy}","received_events_url":"https://api.github.com/users/rohanarun/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"Conditional **κ = 254883101229023 / (2·10¹⁷) = 0.001274415506145115**: **+0.670% over #451** (0.001265931727546219) and +0.622% over our #459. Bit binds at c ≈ 1.276041713·10⁻³ (#459's word, unchanged). **The complex endpoint rises to b ≈ 1.293526619·10⁻³** (#451: 1.268142297·10⁻³).\n\n## New: a shared-donor response kernel on the complex supplier\n\n#433's split-centre complex word cancels each helper's dirt with frame-zero target additions (`compensation`, 12,760 rational adds), just as the bit word does with its D gates. The #417 kernel therefore carries over with rational coefficients:\n\n- an entry is (e, p, d, λ) with **response(p) = λ·response(d)** exactly over ℚ, and e in the first frames of p and d;\n- p starts at ⟨e⟩ and leaves the compensation;\n- d += −λp at ⟨e⟩ before A, and d += λp at FULL after cleanup.\n\nThe word has exactly **56 proportional helper pairs**, and every pair shares an entrance vector. That gives 56 pivots, 56 donors and entrance rank 56, so 56 complex residuals shrink from width 9 to width 8. Width-8 residuals pack exactly into the rank-8k idle children, so the remainder children drop:\n- complex profile `{1:174864, 2:78848, 3:8680, 4:19712, 5:38120, 7:2944, 8:8000, 30:8, 64:2160}`;\n- deficit 3264, all 49,280 occurrences still hosted, no banks.\n\n## Checks, all regenerated by `verify.py`\n\n- **Kernel program:** exact rational replay of the complete kernel program on all 800 columns, plus 4 mutation controls (`code/ckernel.py`).\n- **#433 emitter, unchanged:** run on the new canonical word, with its literal column and paid-profile checks.\n- **Clifford phase recipes:** exact recipes for all **2,925** nested edges, regenerated with #433's unchanged `complex_phases_full.py` (≈3.5 min).\n- **Independent local replay** of both orientations (`code/complex_kreplay.py`):\n - common-frame, nesting and centre-lifetime checks, and the 192-bit prefix;\n - 6 mutation controls, including pivot entry at frame 0 and an omitted kernel exit correction.\n- **Residual routes:** one exact route per helper start frame (8 frames). Each lowers start → FULL by `lower_child` as monomial·F_r·monomial with r = 9 − e, re-verified on both tableau and phase.\n- **Hosting and audit:**\n - re-solved #442 hosting;\n - the hosted eleven-stage template;\n - the independent complex audit: 8,520 phase equalities and 20 mutations, including a wrong width-8 residual width;\n - both moment engines, invoices and the 47-inequality outer assembly.\n- **Bit side:** identical to #459, whose full verify passed.\n\n**Status:**\n- **Passed locally:** every new and changed step, reusing the identical #445 parent output.\n- **Running:** a clean full `verify.py`. The result will be posted.\n- **CI:** not claimed.\n\n**Review point:** as in the bit kernel lineage, a helper may start at a nonzero frame. Its hosted residual is the rank-(9−e) child from its start frame to FULL, carried by the stored exact Clifford route. `PROOF.md` (\"Complex response kernel\") gives the scalar identity and the route argument.\n\nBit side: #457's rank151 kernel plus #450's target-prefix mixing (DreamingOfClouds), as in #459. Inherited interfaces are unchanged, including #442 hosting. Cross-copy hosting is not used. No unconditional theorem is claimed.\n\n```sh\npython -m pip install -r research/e8-r740-replica32/parent436/requirements.txt\npython -B research/r740-dual-kernel/verify.py /absolute/new/output\n```\n\n**Credits:**\n- icekylinx: #433 word, emitter, phases and replay.\n- chafreaky: #417 kernel lineage, #443–#445 and the #451 package.\n- DreamingOfClouds: #450 mixing.\n- DaysSky: #442.\n- eumemic: #436/#440/#441.\n- Zhihao Chen: #377/#386/#425.\n- Henry Grant: #234.\n- All retained authors.\n\nComplex kernel, composition and packaging by Rohan Arun with Claude Opus 5.5 (Anthropic).\n\n🤖 Generated with [Claude 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local Gaussian inverse branches with two convolutions","user":{"login":"chafreaky","id":4400527,"node_id":"MDQ6VXNlcjQ0MDA1Mjc=","avatar_url":"https://avatars.githubusercontent.com/u/4400527?v=4","gravatar_id":"","url":"https://api.github.com/users/chafreaky","html_url":"https://github.com/chafreaky","followers_url":"https://api.github.com/users/chafreaky/followers","following_url":"https://api.github.com/users/chafreaky/following{/other_user}","gists_url":"https://api.github.com/users/chafreaky/gists{/gist_id}","starred_url":"https://api.github.com/users/chafreaky/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/chafreaky/subscriptions","organizations_url":"https://api.github.com/users/chafreaky/orgs","repos_url":"https://api.github.com/users/chafreaky/repos","events_url":"https://api.github.com/users/chafreaky/events{/privacy}","received_events_url":"https://api.github.com/users/chafreaky/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"The retained phase-cell inverse uses a difference of two convolution pairs. This package replaces its online interior operation with a classical q-Gaussian factorization: two triangular convolutions and three diagonal factors inside the existing similarity. The new proof explicitly bounds the difference from the independently rounded, width-truncated source. The global H, exact Schur setup, sparse couplings and periodic boundary system remain unchanged; the complete error still fits the original scalar interface.\n\nThe weighted triangular factors also have norm below 3p, and tensoring the central formula produces five stages without branch expansion. **No new κ is claimed.** A fast joint weighted evaluator, its routing/padding and tensor boundary composition remain unproved. The existing dimension-dependent cost and small-field exposure still bind.\n\nAn exact guard also rejects prematurely rounding the unweighted tensor kernel to the scalar P-grid before reweighting. It checks all 4,096 entries of a small three-axis operator and a uniform admissible parameter family where a significant weighted entry disappears. The latter uses symbolic exponent inequalities, not enormous tensor executions. This does not rule out implicit kernels, adaptive precision or other FFT implementations.\n\nValidation: fresh full wrappers on macOS Python 3.11/3.14 and Linux aarch64 Python 3.12 passed with byte-identical complete CHECKS and RESULT files. Checks cover 1,950 LDL identities, 1,950 inverse entries, 2,084 rounded local entries with actual signed integer packing and up to 115 reciprocal guard bits, 3,024 complete original-Schur output entries using the new local operation plus the retained rounded boundary/coupling maps, 756 tensor identity entries, 1,856 weighted-factor entries and five rejected mutants. These finite checks support the conditional written proof; they are not a complete multiplication theorem. GitHub CI is separate.\n\nReproduce: `python3 -B research/branchfree-gaussian-inverse/verify.py /absolute/new/output` (Python 3.11+, standard library only). Package manifests, ten Git-checked source pins and fresh receipts are included.\n\nAttribution: the q-calculus identity is classical (Kuznetsov, https://arxiv.org/pdf/1507.02959, with the specialization derived in PROOF.md). The rounded phase-cell/Schur construction comes from the retained RaD/hipotures work; batched boundary and coupling operations come from #481. This adds a separately source-bound package on #486's head without changing inherited 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`research/tensor-syndrome-portfolio/`, a standalone source-bound construction and offline replay package.\n\n**Conditional kappa = 0.001297375468897877**, exactly `1297375468897877/1000000000000000000`: **+0.059291495% over #483** (`0.001296606691405309`). The bit supplier binds. This is a whole-family result; it does not claim to exceed #480's `0.001372550159367980`, which uses the distinct disputed cross-copy admission.\n\n## Mechanism\n\n1. **Response-preserving injection relocation.** Search the cosets of the transported target-response map, retaining only immutable-source rewrites. Move source5's injection into helper452 earlier to frame480; reconstruct the literal inverse cleanup. Equal nonzero responses preserve the target on every input, including dirty helpers. The actual witness simplifies to commuting additions into one receiver. In each invocation ranks1 and3 are replaced by rank4, strictly improving the recurrence moment for every exponent in(0,1). Deletion-only and insertion-only controls both fail.\n2. **Stage-conditioned nested donor inventory.** Choose the one-upgrade provider at stages2,4,6,8 in every replica and the eleven-upgrade provider elsewhere. Their residual-width inventories fit different idle windows differently. Each of88 complete calls names its provider, exact word/program hashes, entrance frames and explicit isometry map. Every one of62,920 residual occurrences remains whole on one family; no cross-family split or independence shortcut enters the construction.\n\nThe crossover combines coding/control response kernels with compiler register allocation. Response-preserving retiming and heterogeneous dispatch are not claimed as newly invented mathematics: earlier gate retiming and our R740 portfolio already existed. The new concrete construction is their stage-conditioned application to R715 nested donor flags, with the new source-injection witness. The price is computed from the complete emitted mixed program, never by adding gains.\n\n## Exact result and replay\n\nBit saving lower bound: `1299060838562434397967/10^24`. Unchanged complex lower bound: `1305231506267591/10^18`.\n\nBit dimension78,9600 live/9609 physical families; rank mass745536 and deficit3264. Paid profile: `{1:212216,2:93450,3:22776,4:27624,5:9944,6:7216,7:4248,8:792,36:1,56:687}`. Physical prefix767bits, charged768; three-level coefficient2354bits, charged2368; row coefficient19431<20161.\n\n```\npython -B research/tensor-syndrome-portfolio/verify.py /absolute/new/output\n```\n\nPython3.11+, SymPy, C++17 and Boost headers are required. The frozen replay needs no optimizer or network. It reconstructs and freshly compiles both changed providers; checks native columns and signed lifts, frame/operand/projector legality, dirty restoration, complete mixed dispatch,492,240 disjoint physical coordinates and19 mixed mutation controls; then recomputes the actual finite invoice, two rational moment bounds and all47 strict outer inequalities. Default mode rebuilds the complex supplier; explicit completed-complex reuse requires the exact prior receipt plus87 implementation and17 output hashes and produces a distinct receipt. A completed reuse run is not represented as a fresh complex replay. GitHub CI is separate and is not claimed passed.\n\n## Sources and credits\n\nDirect construction inputs: #483 (response-packet cancellation and nested-donor flags), #478 (fourteen target factors), #473 (repaired R715 kernel, and new rational84 packing as a comparison/inspiration), #472/#470/#467 (kernel, retiming and whole hosting), #463 (R715 word), #450 (target mixing), #455/#476 (prior factor/portable machinery), and #471 (unchanged complex normalization and same-owner spectators). The earlier R740 portfolio is retained and credited; this submission adapts its dispatch architecture rather than claiming to invent it.\n\nThe compiler/geometry/complex lineage includes #449, #456, #457, #451, #454, #417, #442, #433, #425, #386 and #370; outer assembly follows #434/#315. Original notices and licenses remain. Work was prepared with OpenAI Codex assistance.\n\nThe frozen sweep reads new #479 (streamed chirp phases), #480 (cross-copy hosting), #481 (batched Gaussian boundary), #482 (non-hosting target factors) and updated #473/#477. #479/#481 explicitly do not change their selected kappa, and their scalar improvements are not added here. #482 uses a different storage route. #480's larger number is kept separate because of its admission scope. #477's experiment archive prevents repeating exhausted searches;17 archive paths unavailable at its pinned head are recorded and are not replay dependencies.\n\n## Research retained for future workers\n\nThe package includes sufficient response-coset and stage-composition arguments, explicit witnesses and controls, native syndrome-search source/results, failed higher-arity searches, the complex observability screen, and a larger-replica nomination. The84-replica two-provider screen gave only about5.9e-9 extra bit saving before retiming and is not part of the achieved bound. Fourteen complex scalar-cancellation pairs left the paid profile unchanged. An initial screening double-count of an old packet delta was caught against the exact baseline and corrected before admission; it is documented rather than counted as a result.\n\nSource-level inspirations include Mathlib's kernel-fibre identity, installed binary-syndrome sources and earlier tensor response reconstruction; no new Lean kernel audit or literature-priority claim is made. All inherited all-size supplier/compiler, mutable-basis, target-label, complete dirty invocation, compressed-window, restored-work, precision and analytic contracts remain conditional. 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κ = 0.001295625678120464: whole-owner GL cover with sharp fallback","user":{"login":"eumemic","id":94939491,"node_id":"U_kgDOBaipYw","avatar_url":"https://avatars.githubusercontent.com/u/94939491?v=4","gravatar_id":"","url":"https://api.github.com/users/eumemic","html_url":"https://github.com/eumemic","followers_url":"https://api.github.com/users/eumemic/followers","following_url":"https://api.github.com/users/eumemic/following{/other_user}","gists_url":"https://api.github.com/users/eumemic/gists{/gist_id}","starred_url":"https://api.github.com/users/eumemic/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/eumemic/subscriptions","organizations_url":"https://api.github.com/users/eumemic/orgs","repos_url":"https://api.github.com/users/eumemic/repos","events_url":"https://api.github.com/users/eumemic/events{/privacy}","received_events_url":"https://api.github.com/users/eumemic/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"κ = 0.001295625678120464\n\nThis conditional whole-owner construction replays PR473's repaired rank-119 R715 word and PR471's normalized complex supplier, then applies PR465's sharp fallback charge on an explicit GL78 bit cover with fixed q>2^128. The larger cover is fully reflected in the row allowance: 28416 replaces the orthogonal cap 20161. The exact claim is `80976604882529/62500000000000000`, improving the replayed PR473 assembly by `366271/125000000000000000`.\n\nThe package regenerates native scalar records, arbitrary-dirty local identities, both reflected frame ledgers, source complex phases and all 512-column normalizers, actual whole-owner matrices, complete physical controllers, paid profiles, finite invoices and strict assembly. Independent rational intervals certify both moment endpoints; all 47 outer inequalities and the next-grid rejection pass.\n\nThe cover schedule completes the entire local word for one low residue class before advancing, while batching its high matrices. Same-family owner matrices remain distinct modulo every admitted prime; helper endpoints preserve row norms between batches. This is sequential composition, not a claim of simultaneous global injection over all cover labels.\n\nThe claim retains the inherited all-size compiler, restored-row and analytic contracts. The fixed GL routing constant is explicitly left as a finite parameter `B_GL`; all six symbolic cutoff certificates cover every finite nonnegative value. The 2432-bit local invoice is not presented as a bound on that global routing constant. No split-family construction is admitted.\n\nThis is a new branch and PR; published predecessor heads and claims remain frozen. Credits for PR442/443/450/458/465/471/473/478 and their source lineages, original licenses, and AI disclosures are retained. New integration, audits and packaging were prepared with OpenAI Codex.\n\nValidation: uninterrupted source replay on Python 3.12 and replay from the committed Git archive on Python 3.11, with separate exact invoice/operator review. The release manifest is `9416acbea8b67c0228c1904c9a51cd1827769764d688cb21c38245cb5c870507`; all 119 package files match the committed archive. Reproduction instructions, proof, source pins and manifest are in 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Verification of binary input preparation, κ=0.000661885549259598","user":{"login":"jamesyc","id":3722200,"node_id":"MDQ6VXNlcjM3MjIyMDA=","avatar_url":"https://avatars.githubusercontent.com/u/3722200?v=4","gravatar_id":"","url":"https://api.github.com/users/jamesyc","html_url":"https://github.com/jamesyc","followers_url":"https://api.github.com/users/jamesyc/followers","following_url":"https://api.github.com/users/jamesyc/following{/other_user}","gists_url":"https://api.github.com/users/jamesyc/gists{/gist_id}","starred_url":"https://api.github.com/users/jamesyc/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/jamesyc/subscriptions","organizations_url":"https://api.github.com/users/jamesyc/orgs","repos_url":"https://api.github.com/users/jamesyc/repos","events_url":"https://api.github.com/users/jamesyc/events{/privacy}","received_events_url":"https://api.github.com/users/jamesyc/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"## Change and mathematical scope\n\nA standalone completed Lean 4.21.0 chunk: four modules, 48,221 source bytes, no Mathlib dependency. All 15 added files are under research/lean-binary-input-preparation; no inherited root files or scientific checks change. This chunk is independent of the exact-port interface in #487.\n\nFinite-state machine coverage (universally quantified over finite Boolean inputs):\n- Six-state, three-tape reversal with a complete halted configuration, exact Tape.ofWord bits.reverse output, arbitrary spare tape preserved, and elapsed bounds 1 for empty input or 3*length+2 otherwise. Output head is the first bit. Input tape final representation is stated explicitly; original input head restoration is not claimed.\n- Fourteen-state, four-tape paired preparation for arbitrary empty or unequal-length x,y with two pristine work tapes. Pads to n=max lengths, reuses the reversal proof twice, and reaches exact MSB-first work words with heads on their right blanks within 6*n+7 transitions. Both full endpoints and numeric values are proved. No extra arbitrary spectator tape is in this paired contract, and n is proof-side length rather than a supplied runtime counter.\n\nConditional-interface coverage: reusable explicit-tape preparation primitives. Source caller/preconditions/accounting remain to be connected. This does not implement the source single x#y prelude, binary length counter, radix grouping, complete multiplication caller, Plan/ModelFamily/compiler builder, or represented-error budget. Full multiplication/runtime exponent theorem: not established. These standard generic ideas carry no novelty claim; the contribution is the concrete checked implementation and precise endpoint/resource statements.\n\nExplicit author-checked historical project kappa: 330942774629799/500000000000000000 = 0.000661885549259598, source 3b6b66891c0ac888521cf591fe306c6286601d4f. It remains conditional on analytic, uniform-recursion and fixed-tape interfaces. None of these four generic machine modules proves that exponent. AUTHOR_CHECK.json, PROVENANCE.json and evidence preserve this limited attribution and exact certificate.\n\nExact base: 12a4934d15006e8c10f9b2264f13f8f341be802b. Exact head: edd3102b415df5b9d6f633ac0a4dedcf69c58525. Current main README kappa 0.000723571590007464 is a separate target, not a source-program reconciliation claim for this package.\n\n## Validation\n\nFresh isolated Linux replay PASS for all four modules:10.2832 compiler seconds,0.00547 shared-slot queue seconds. All four object hashes and18 printed axiom sets match accepted historical checks. Classical.choice is explicitly reported for prepare_run. Independent statement/scope, replay and final15-file package reviews passed, followed by author readback of the final replay wording and kappa context.\n\nReproduce from package directory: python3 check.py --lean /path/to/lean-4.21.0/bin/lean --build-dir .build\n\nThe runner validates exact hashes/import order, starts with fresh objects/no extra library paths, and enforces60-second/4-GiB hard limits with40-second/3.5-GiB review stops. No network or installation step is performed. See README.md and REPLAY_SUMMARY.json.\n\nLocal Lean kernel replay is separate from executable scientific checks, exact-head fork CI, upstream CI and maintainer gates. No CI pass is claimed. make verify/gen4-bank-verify were not rerun locally for this additive package. An inherited base verify-joint failure was independently observed at12a4934:joint_dual_compose.py check_sources raises AssertionError:Makefile; no check is weakened here.\n\nExisting PRs were compared using reversal/input-preparation searches; no matching concrete finite-tape Lean chunk was identified. Attribution is retained under Apache-2.0; substantial OpenAI model assistance was used. Draft for review of this completed reusable 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κ = 0.001274032589159993: complex kernel with paid residual adapters","user":{"login":"chafreaky","id":4400527,"node_id":"MDQ6VXNlcjQ0MDA1Mjc=","avatar_url":"https://avatars.githubusercontent.com/u/4400527?v=4","gravatar_id":"","url":"https://api.github.com/users/chafreaky","html_url":"https://github.com/chafreaky","followers_url":"https://api.github.com/users/chafreaky/followers","following_url":"https://api.github.com/users/chafreaky/following{/other_user}","gists_url":"https://api.github.com/users/chafreaky/gists{/gist_id}","starred_url":"https://api.github.com/users/chafreaky/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/chafreaky/subscriptions","organizations_url":"https://api.github.com/users/chafreaky/orgs","repos_url":"https://api.github.com/users/chafreaky/repos","events_url":"https://api.github.com/users/chafreaky/events{/privacy}","received_events_url":"https://api.github.com/users/chafreaky/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"Conditional **κ = 0.001274032589159993**, **0.591885% above #454** (`d14eb0dd425bd681e3b43f208d089e679d600176`). The complex endpoint rises to **b = 0.001297203880559577927527**; the unchanged #454 bit endpoint **c = 0.001275657818793753037875** now binds.\n\nThe 79-pivot complex kernel from #449 has isotropic entrances, so an orthogonal coordinate relabeling does not justify hosting its residuals. This package reconstructs the kernel, proves each actual residual has an exact two-sided Gaussian monomial factorization, and pays for the inverse monomials before and after the entire local invocation. A new assignment permits at most one helper per physical host family in each invocation. All 49,280 residuals remain whole, with every spectator restored and no uncharged helper entrance transform. The written proof covers arbitrary borrowed values and both scalar orientations.\n\nThe reproducible package is `research/e8-complex-adapted-kernel/`. It includes frozen inputs, independent local/global audits, complete instruction hashing, source inventories and a fresh #454 parent replay. It retains m=89, 9,600 live families, 10,178 physical families, maximum child 64 and the 20,161 row contract. The finite invoice adds 788,480 rank-zero compiler groups conservatively for 13,904 nontrivial wrapper events.\n\nValidation:\n\n- Linux full replay and macOS quick replay with `E8_REPLAY_PHASES=1` both pass; quick mode skips only inherited #443 exhaustive controls. Every new check runs in both modes, and the complete exact result matches across platforms.\n- Both 800-column orientations, 2,932 local phase edges, 14 adapter frames, 8,520 global phase equalities, 1,320 data routes and 49,280 residual routes pass.\n- Seven local and 25 global mutations, 24 omitted-bridge controls, both rational moment engines, both finite invoices, six bootstrap levels and all 47 strict outer constraints pass.\n- Repository `make verify-joint` passes. Receipts and exact results are in `research/e8-complex-adapted-kernel-validation/`. GitHub CI is pending; this PR remains draft until its checks finish.\n\n```sh\npython -m pip install -r research/e8-r740-replica32/parent436/requirements.txt\nE8_REPLAY_PHASES=1 python -B research/e8-complex-adapted-kernel/verify.py /absolute/new/output\npython -B research/whole-hosted-format-ceiling/verify.py\n```\n\nA separate scoped proof in `research/whole-hosted-format-ceiling/` shows that the fixed 120-port, copied-rank72, bank-free compressed-window format has **κ < 2/127** throughout its declared stage family, and **κ < 1/87** for the present eleven-stage geometry. These are limitations of the stated format and outer assembly, not lower bounds for integer multiplication. Exact controls supplement the uniform written inequality. Reaching κ=1 requires different hypotheses and a different outer reduction.\n\nThe all-size Gaussian/bit compilers, restored work, mutable-basis realization, compressed geometry, common grid, precision, row-divisor and analytic transfer interfaces remain conditional. This does not adopt #449's entrance-gauge argument or any cross-family residual split. It is not an unconditional theorem or a κ=1 result.\n\nCredits: DreamingOfClouds/Rohan Arun and Claude Opus 5.5 for #449's kernel and generalized local tools; DaysSky for #442's hosting construction; icekylinx for #433's complex word; eumemic for the retained bit retimings; all source-pinned parent authors. New adapters, hosting proof, audits, composition and scoped ceiling by chafreaky with OpenAI Codex assistance. See `NOTICE.md` for detailed provenance.\n\n\n\nVerification update: fixed the Python 3.11 discovery-metadata portability failure reported by PR460. Reproduced the old tolerance assertion on a freshly generated Python 3.11 parent (gain estimate delta -2.0889956431346945e-12). Only the two finite discovery floats are normalized; every exact field still compares identically. Eight regression controls pass on Python 3.11 and 3.14. A fresh full Python 3.11.15 replay, including regenerated phases, passed with RESULT.json byte-identical to the original release. 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Verification of selected 1320-port bijection, κ=0.000661885549259598","user":{"login":"jamesyc","id":3722200,"node_id":"MDQ6VXNlcjM3MjIyMDA=","avatar_url":"https://avatars.githubusercontent.com/u/3722200?v=4","gravatar_id":"","url":"https://api.github.com/users/jamesyc","html_url":"https://github.com/jamesyc","followers_url":"https://api.github.com/users/jamesyc/followers","following_url":"https://api.github.com/users/jamesyc/following{/other_user}","gists_url":"https://api.github.com/users/jamesyc/gists{/gist_id}","starred_url":"https://api.github.com/users/jamesyc/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/jamesyc/subscriptions","organizations_url":"https://api.github.com/users/jamesyc/orgs","repos_url":"https://api.github.com/users/jamesyc/repos","events_url":"https://api.github.com/users/jamesyc/events{/privacy}","received_events_url":"https://api.github.com/users/jamesyc/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"## Change and mathematical scope\n\nPublish one completed, reusable Lean 4.21.0 chunk in research/lean-selected-port-bijection. This is 74 local Lean modules plus reproducibility and source-provenance files, with no Mathlib dependency and no changes to inherited root files or scientific checks.\n\nFinite coverage: exact ordered selected1320 inputMask labels equal PairedCubeSourceLabels.labels 11; actual inverseTable provides both inverse laws; whole-row and two-bank gather/scatter are inverse reindexings preserving arbitrary helper/spectator values. Generic bijection laws are not claimed as new mathematics.\n\nConditional-interface coverage: this supplies a concrete selected port interface for subsequent construction work. It does not supply the physical invocation provider, shared-helper three-stage implementation, dirty frame equation, or cost bound. Full multiplication/runtime theorem coverage: not established by this chunk.\n\nExplicit author-checked retained source kappa: 330942774629799/500000000000000000 = 0.000661885549259598, from source commit 3b6b66891c0ac888521cf591fe306c6286601d4f. AUTHOR_CHECK.json and PROVENANCE.json record the statement/source check and retained attribution. This conditional parameter is not proved as an exponent theorem here.\n\nBase at submission: 12a4934d15006e8c10f9b2264f13f8f341be802b; head: 15b49f66cb2d2663fb71672f4d594e755bd93938. The newer base README parameter 0.000723571590007464 is a separate target; equality of changed selected data is not asserted.\n\nPredecessors and reuse: retained selected supplier attribution and notice are included. This chunk adds the exact accessor/table binding; it does not recopy the generic chain or physical-provider work in #397/#430, or the separately developed input-preparation work. Current PR searches for 1320 and bijection were compared before submission; no matching completed exact-table Lean chunk was identified. Substantial OpenAI model assistance was used.\n\n## Validation\n\nFresh isolated replay on Linux, official Lean 4.21.0: all 74 modules PASS, with source hashes/import order checked and no old objects or Mathlib paths. Total compiler time 142.881 s; FIFO wait 370.106 s; maximum module time 8.5875 s; peak process virtual memory 3,272,663,040 bytes. All 74 object hashes and 153 axiom sets match the source-matched historical receipts. Independent package and terminal-replay reviews completed. See REPLAY_SUMMARY.json.\n\nReproduce from the package directory: python3 check.py --lean /path/to/lean-4.21.0/bin/lean --build-dir .build\n\nThe runner uses 60-second/4-GiB hard bounds and stops for review above 45 seconds/3.5 GiB. This local Lean kernel replay is separate from executable scientific tests, exact-head fork CI, upstream CI and maintainer approval. 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kappa = 0.001296606691405309: response-kernel cancellation and nested-donor flags on 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source-bound offline construction and replay package.\n\n**Conditional kappa = 0.001296606691405309**, exactly `1296606691405309/1000000000000000000`: **+0.08476450% over #478** (`0.001295508560071773`) and **+0.19840410% over the pinned warm #473 claim** (`0.001294039264416565`). The bit supplier binds. This compares the complete whole-owner route; it is not a claim to exceed proposals using different admission assumptions.\n\n## Concrete new mechanisms\n\n1. **Simultaneous response-kernel cancellation.** Compute each immutable-source injection's transported target response. Delete a packet only when its response sum vanishes for every source. The useful cross-helper pair reads source3 at helpers444 and246; neither injection is removable alone. Rebuild inverse cleanup. Its local paid delta replaces rank1 plus rank5 by rank6, so strict subadditivity gives a moment improvement for every relevant exponent. Ten further duplicate pairs only reduce scalar work. Altogether22 injections and22 cleanup additions disappear, with all22 single-deletion controls rejected.\n2. **Nested-donor flags.** Replace the old one-entrance-per-donor construction restriction with an explicit sufficient flag schedule. Donors receive logical shears at increasing nested frames; all dirty values remain arbitrary. Ten pivot upgrades yield110 pivots,102 physical donors,120 correction groups and total entrance rank129. Exact response relations, frame chains and residual isometries are checked. The new constructor is explicit; the old constructor's equal-entrance guard is not silently ignored.\n\nThese are combined with the new retain-and-repair #473 kernel and our14 target factors from #478. Gains are priced through the complete composed program, never added. The full local/native and physical ownership checks use the actual changed word. All88 calls use one uniform provider; all62920 residual occurrences remain wholly on single physical families. No unverified heterogeneous portfolio or cross-family split contributes.\n\n## Exact pricing and validation\n\n- Bit saving lower bound: `1298290062988365072981/1000000000000000000000000`.\n- Complex saving lower bound: `1305231506267591/1000000000000000000`, the unchanged source-bound completed supplier from #471.\n- Bit dimension78,9600 live/9609 physical families; complete rank mass745536.\n- Fresh physical prefix837bits, charged896; three-level coefficient2567bits, charged2624; row coefficient19431<20161.\n- Source reconstruction,955 arbitrary-dirty binary columns, rational frames/integer operand spans, native signed/formal columns, physical target labels, mixing controls, Gram/projectors, global owner audit, fresh invoice, both exact moment implementations and all47 strict outer inequalities pass. Mutation controls cover the changed constructors and inherited physical audit.\n\nRun:\n\n```text\npython -B research/tensor-response-r715/verify.py /absolute/new/output\n```\n\nPython3.11+, SymPy, a C++17 compiler and Boost headers are required. Replay uses no network or optimizer. Default replay rebuilds both suppliers. Our completed changed-component run explicitly reuses the unchanged complex supplier only after matching87 implementation hashes and17 output hashes against its pinned completed receipt. That mode emits a distinct receipt; it is not described as a fresh complex execution. VALIDATION.json records the actual run scope. GitHub CI is separate and is not claimed passed.\n\n## Sources, credit and retained research\n\nDirect inputs: #473 (new warm kernel), #478 (retained14 target factors), #472/#470/#467 (R715 kernels, retiming, whole-owner pooling), #463 (R715 carrier and XOR word), #450 (target mixing), #455/#476 (earlier target factoring and portable audits), and #471 (unchanged complex normalization/spectators). The retained complex/hosting/compiler lineage includes #449, #456, #457, #451, #454, #417, #442, #433, #425, #386, #377 and #370; outer assembly comes through #434/#315. #469 is credited for delivery scheduling, not its separate cross-family proposal. Upstream notices and licenses are preserved.\n\n#477's categorized experiment archive helped avoid repeating exhausted representations. #475, #474 and #397 were reviewed without counting their distinct results as numerical gains; #461/#465's sharper bad-edge charge is not used. RECENT-PRS.json records the frozen source sweep through #478 and explicitly records unavailable historical receipt files at the pinned #473 head.\n\nThe library search read actual proof sources: ReasBook Woodbury/Schur update structure, Mathlib matroid exchange and subspace flags, OpenAI annihilator and SL-commutator proofs, CSLib diamond/confluence, Hadamard6 and prior tensor/CNOT project lemmas. Source hashes and sufficient mathematical proofs are retained. No new Lean kernel certification or exhaustive literature-priority claim is made.\n\nThe third search lane tested noncommuting transport, GL3 basis changes, chronological affine synthesis, central-response cancellation and cleanup resynthesis. It found no admissible gain. These constructions, bounded results and C++ sources are retained for future workers; they are not advertised as a third successful technique. Previous affine-controller and heterogeneous-provider notes remain explicitly uninstantiated or unverified.\n\n## Scope\n\nAll inherited all-size supplier/compiler, mutable-basis/target-label, complete-call correlated-dirty hosting, compressed-window, restored-work, precision, row and analytic interfaces remain conditional. 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supplier, coordinated frames and entrance banks: conditional kappa = 6.61885549259598e-4","user":{"login":"Dugongue","id":49054532,"node_id":"MDQ6VXNlcjQ5MDU0NTMy","avatar_url":"https://avatars.githubusercontent.com/u/49054532?v=4","gravatar_id":"","url":"https://api.github.com/users/Dugongue","html_url":"https://github.com/Dugongue","followers_url":"https://api.github.com/users/Dugongue/followers","following_url":"https://api.github.com/users/Dugongue/following{/other_user}","gists_url":"https://api.github.com/users/Dugongue/gists{/gist_id}","starred_url":"https://api.github.com/users/Dugongue/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/Dugongue/subscriptions","organizations_url":"https://api.github.com/users/Dugongue/orgs","repos_url":"https://api.github.com/users/Dugongue/repos","events_url":"https://api.github.com/users/Dugongue/events{/privacy}","received_events_url":"https://api.github.com/users/Dugongue/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"## Change and mathematical scope\n\nCombine the shared-edge complex supplier of [PR181](https://github.com/CrocSwap/integer-mult-bounds/pull/181), pinned at `7fb2194801e3a10f54772c7f0d5505035a4fc0ad`, with a new compensated rematch, coordinated subspace frame cuts, and completed entrance banks on its unchanged PR168-v4 physical bit word.\n\nUnder the retained interfaces, the exact bound is\n\n$$T(n)=O\\left(n(\\log n)^{1-\\kappa}\\right),\\qquad \\kappa=\\frac{330942774629799}{500000000000000000}=0.000661885549259598.$$\n\nThis is approximately **0.41035% above PR181's stated bound**. The complex branch binds again. Every number comes from the final combined words and paid assembly; independently quoted gains are never added.\n\nRelative to the published PR181 witness, the matching changes 2,297 donor identities and legally retimes 1,049 compensation reads. Eleven coordinated subspace cuts change 243 distinct operation frames. Exact target chronology admits 46 terminal sinks instead of 44. The final complex profile has `m=66`, `W=13326`, rank mass `878196`, deficit `1320`, and largest child `20`; its saving is `662323931899051/10^18`.\n\nThe bit construction banks 2,200 rank-20 entrance gauges using eighteen four-coordinate cores per bank, and 15,828 other physical chains using three 24-coordinate cores. Paired rank-21 recipients remain internal splices and are not charged twice. Nine physical replicas realize every stage-private allocation integrally. The normalized bit profile is `W=59144/3`, rank mass `1417520`, deficit `1936`, largest child `22`; its paid ordinary saving is approximately `0.000665064157585291`.\n\nThe universal partial-swap algebra derives the completed-bank endpoint for arbitrary dirty contents. General tensor/Clifford, uniform weighted compilation, common charts, routing/restoration, paid layout, prime supply, precision/recovery, uniform setup and analytic fixed-tape contracts remain the original stated assumptions. **This is a conditional finite certificate, not an unconditional multiplication theorem or a new Lean-certified bound.**\n\n## Validation\n\nThe final read-only offline aggregate passes and reproduces the frozen certificate. It checks:\n\n- The immutable LF prerequisite archive, its 1,699-file source closure, and every uploaded witness/checker file.\n- Complete original and terminal-modified signed complex words, both shear signs and inverses, all 13,326 modified formal columns, all 10,686 retained arbitrary dirty registers, actual frame/target chronology, and corruption controls.\n- All 21,548 physical bit columns over F2 and the defining integer decoder, original frame/prime witnesses, and word/factor controls.\n- Both completed-bank partitions and inverses over F2 and Z, omitted/repeated-block controls, and the nine-copy stock identity.\n- Exact paid moments, strict atom/row tolls, full scalar/group/router/row charges, all 47 strict inequalities, seven margins, and 21 assembly controls. Independent arithmetic using the original PR141 assembly and both moment engines reproduces the same bound.\n\nAdjacent-grid exclusions apply only to the fixed suppliers and parameters. Separate integrity controls reject altered checkers, altered archive parts and unlisted source files.\n\nCanonical command, with Python 3.11+ and assertions enabled:\n\n```sh\npython -B research/coordinated-frames-and-entrance-banks/verify.py\n```\n\nNo network, Git credentials or third-party packages are needed. The immutable archive is split into three parts below GitHub's 25 MB browser-upload limit. Extraction and execution occur in a temporary directory.\n\n## Sources and disclosure\n\nDeveloped with OpenAI model assistance. Upstream author notices and Claude/OpenAI disclosures remain in `NOTICE`, `UPSTREAM-NOTICE.md`, copied sources and the immutable archive. PR181's shared-edge selection, PR168 v4, PR144's paired-cube/compiler framework, PR166 terminal accumulation, the balanced layout, atom wrapper, frame/reuse lineage and PR175 overlay retain their original credits.\n\n`PROOF.md` and `BANK-PROOF.md` describe the sufficient construction. `FRAME-DISCOVERY.md` records the actual cuts; `RESEARCH-REVIEW.md` and `RESEARCH-IDEAS.md` distinguish accepted mechanisms from tested shared-total/harmonic/Parseval routes. 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κ = 0.001168862033074029: R715 target factors in non-hosting banks","user":{"login":"eumemic","id":94939491,"node_id":"U_kgDOBaipYw","avatar_url":"https://avatars.githubusercontent.com/u/94939491?v=4","gravatar_id":"","url":"https://api.github.com/users/eumemic","html_url":"https://github.com/eumemic","followers_url":"https://api.github.com/users/eumemic/followers","following_url":"https://api.github.com/users/eumemic/following{/other_user}","gists_url":"https://api.github.com/users/eumemic/gists{/gist_id}","starred_url":"https://api.github.com/users/eumemic/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/eumemic/subscriptions","organizations_url":"https://api.github.com/users/eumemic/orgs","repos_url":"https://api.github.com/users/eumemic/repos","events_url":"https://api.github.com/users/eumemic/events{/privacy}","received_events_url":"https://api.github.com/users/eumemic/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"κ = 0.001168862033074029\n\nThis conditional non-hosting construction improves our frozen R740 banked result (eumemic/integer-mult-bounds#3, κ = 0.001145834572824929) by approximately 2.01%. It composes the pinned R715 rank120 word and fourteen target-interval factors from #478 with #443's unchanged 32-replica whole-residual banks, nine stages and accounting engines, with a freshly recomputed finite invoice and the cited #433 complex supplier.\n\nThe R715 word uses 715 helpers instead of 740. There are 55,920 live families, 1,261,440 paid children, rank mass 3,568,896 and deficit 9,984. The exact bit lower bound is `1170229870339438219571/10^24`; the cited complex lower bound remains `1183986549206329/10^18`. This does not claim to exceed the higher reported whole-hosting or split cross-copy bounds in #473 or #480.\n\nVerification reconstructs the final scalar word byte-for-byte from its pinned parent and selection, checks all 955 independent scalar columns and dirty restoration, both literal and reflected frame ledgers, copied-work closure, native C++ legality and five/nine-stage columns, nonvacuous record mutations, exact rational projectors, the full banked program, complete paid profiles, two rational moment engines, the finite invoice and all 47 strict outer inequalities. A separate audit constructs full64 coordinate routes for all 205,920 helper occurrences, verifies actual owner injection, and covers all 25,200 bank families without overlap or padding. Each route needs at most 56 coordinate transpositions within the existing paid allowance. The verifier also reruns the unchanged parent443/436 suite. The complex supplier is bound by its pinned receipt; its full phase suite is not rerun.\n\nBoth the complete worktree replay and a fresh replay from the committed Git archive passed on Python 3.12.13. All 139 package files matched the committed and archived bytes; the independent release review also passed. CI is included for Python 3.11 and 3.14; no CI success is claimed before it finishes.\n\nThis remains conditional on the inherited all-size compiler, routing, compressed geometry, restored work, precision/recovery and analytic interfaces. No complete Lean proof, unconditional multiplication theorem or global optimality is claimed. The local scalar word is inspectable UTF-8 JSON; upstream Git blob pins, licenses and AI disclosures are preserved.\n\nCredits: DreamingOfClouds for the R715 carrier and overlap cancellation (#463); Rohan Arun for kernel selections and retiming (#467/#470/#473); Dugongue for the fourteen target factors (#478); chafreaky for the shared-kernel mechanism, banked routes and independent audit (#417/#443); eumemic and prior contributors for #436/#440/#441; icekylinx for #433 pricing and complex supply; Zhihao Chen and the wider integer-mult-bounds contributors for inherited geometry, compiler and assembly. The new non-hosting composition, source-bound packaging, explicit bank-route audit and review were prepared for eumemic with substantial OpenAI Codex assistance. All original notices are 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Its indices and source moduli have only ell bits, with d*ell=O(p). This supplies a width-sensitive bound and an exact additive generator, reducing the chirp/scalar row from `O(T*d*p^(1+delta))` to `O(T*p^(1+delta))`.\n\nThe phase formula is unchanged. The stream maintains each quadratic term and its forward difference, subtracts the old term on a mixed-radix carry, and makes fewer than 2T adjacent axis-record visits over T entries. The proof includes a constant-tape schedule, O(p) persistent control state, short arithmetic widths and the original lexicographic output order. No per-output scan of all axes or table of T phases is required.\n\nThe same exact residue, denominator and precision feed the retained exponential routine. Numerical errors, disk format, endpoint products and frequency convention are unchanged. Polynomial-ring products remain a separate cost.\n\n**No higher kappa is claimed.** Only the scalar margin changes from `1-epsilon-delta` to `1-delta`; the unchanged Gaussian margin was already no larger than the old scalar margin. Exact arithmetic confirms the overall minimum is unchanged. Gaussian application, normalization and small-field exposure remain open bottlenecks toward kappa=1.\n\nThe frozen verifier passed on macOS Python 3.11/3.14 and Linux Python 3.12 with byte-identical outputs: 319 complete streams, 587,020 phase entries, 191,592 chirp/Fourier coefficient identities, 60 wide carry probes, complete-period restoration, traversal/width checks and six rejected mutations. Five source files are bound to their pinned Git bytes. Dedicated 3.11/3.14 CI is included.\n\nRun `python -B research/streamed-chirp-phases/verify.py /absolute/new/output` using only the standard library. The verifier does not execute the numerical exponential, enormous prefixes of the wide probes, or a complete multiplier. Equality of the exact arguments transfers the retained numerical guarantee; the fixed-tape complexity is a written argument, not a Python timing claim.\n\nCredits: the integer-mult-bounds manuscript and its authors for the chirp identity, padded-box bands and scalar interfaces; eumemic, icekylinx and Zhihao Chen for inherited outer arithmetic. New accounting, stream, proof and controls by chafreaky with OpenAI Codex assistance. 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kappa = 0.001295508560071773: fourteen target factors on PR473 (+0.1226%)","user":{"login":"Dugongue","id":49054532,"node_id":"MDQ6VXNlcjQ5MDU0NTMy","avatar_url":"https://avatars.githubusercontent.com/u/49054532?v=4","gravatar_id":"","url":"https://api.github.com/users/Dugongue","html_url":"https://github.com/Dugongue","followers_url":"https://api.github.com/users/Dugongue/followers","following_url":"https://api.github.com/users/Dugongue/following{/other_user}","gists_url":"https://api.github.com/users/Dugongue/gists{/gist_id}","starred_url":"https://api.github.com/users/Dugongue/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/Dugongue/subscriptions","organizations_url":"https://api.github.com/users/Dugongue/orgs","repos_url":"https://api.github.com/users/Dugongue/repos","events_url":"https://api.github.com/users/Dugongue/events{/privacy}","received_events_url":"https://api.github.com/users/Dugongue/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"# Conditional kappa = 0.001295508560071773: fourteen target factors on PR473 (+0.1226%)\n\nThis adds `research/tensor-r715-next/`, a source-bound offline construction and replay package.\n\n**kappa = 1295508560071773/1000000000000000000 = 0.001295508560071773**, **+0.1225826043% over #473**. The source sweep is frozen through #475. This compares the whole-owner route, not larger cross-family claims made under different admission assumptions.\n\n## Concrete contribution\n\nStarting from #473's reordered #472 R715 word, insert14 disjoint reversible target-interval factors. Each replaces paid children of ranks1 and4 with one of rank5. The complete word changes only phase B; helper entrances, endpoints, residual dimensions and ownership are unchanged.\n\nThe identity is `(u+d)+(A+B)+(d+B)=u+A` over F2. Actual intermediate reads, integer operand support and frame chronology are checked. Strict subadditivity proves the improvement for every recurrence exponent between0 and1. This is a new checked witness and composition using inherited interval/prefix factoring, not a claim of a fundamentally new identity or literature-wide priority.\n\nSubstitute the word into all88 calls of the eight-replica controller. All62,920 helper residuals stay whole on one physical family each. Combine with our unchanged #471 complex supplier, including its paid monomial normalization and same-owner spectators. Gains are computed from the combined profiles and outer assembly, never added.\n\n## Exact accounting\n\n- Bit lower saving: `648594539814231988799/500000000000000000000000`.\n- Complex lower saving: `1305231506267591/1000000000000000000`; the bit side binds.\n- Bit dimension78; live families9600; physical families9609.\n- Fresh physical prefix737bits, charged768; three-level coefficient2265bits, charged2304.\n- Row coefficient19431, within20161.\n- Local profile delta: `{1:-14,4:-14,5:+14}`.\n\nRESULT.json supplies full exact profiles, invoices and all47 strict inequalities.\n\n## Reproduction and evidence\n\n python -B research/tensor-r715-next/verify.py /absolute/new/output\n\nPython3.11+, SymPy, C++17 and Boost headers are required. No network, optimizer or Lean is needed. The default rebuilds both suppliers. Explicit `--complex-output /completed/previous/output` checks the exact completed complex receipt,87 unchanged implementation files and every pinned complex/provider output; this emits a distinct reuse status. See VALIDATION.json for the mode actually completed, rather than inferring fresh complex execution from a reused receipt.\n\nChanged checks include source-derived reconstruction,955 arbitrary-dirty columns, exact frames and integer spans,28 omission controls, fresh native legality/formal columns, physical target-label checks, Gram/projector identities, whole-owner emission and independent audit, fresh intermediate-growth accounting, both rational moment engines, six bootstrap levels and47 strict outer inequalities. Adjacent-grid and invalid-parameter controls are retained. GitHub CI is separate and is not claimed passed.\n\n## Credit and research record\n\nDirect lineage: **#473** reordered deliveries; **#472**109-pivot/rank120 kernel and hosting integration; **#463** R715 carrier/XOR word; **#467/#470** kernel/retiming/pooling development; **#469** the delivery-reordering idea only; **#450** target mixing; **#455** our earlier prefix work; **#471** the reused complex construction. The earlier tensor-schur-r715 release supplies the portable interval constructor and audit.\n\nKernel/hosting/compiler and complex ancestry additionally includes **#417, #442, #449, #456, #457, #451, #454, #433, #425, #386, #377, #370**, with outer assembly through **#434/#315**. Pinned sources and original notices are retained. **#475, #474 and #397** were reviewed but contribute no claimed extra saving here. #461/#465's sharper bad-edge charge is not used.\n\nThree tensor-inspired searches are documented in RESEARCH.md: target-basis elimination, observable-state pruning and complete-provider portfolios. The broader two-donor and observable-state screens produced no extra admitted gain. A positive heterogeneous-provider nomination remains unverified at the physical-program/invoice level and is explicitly excluded. Earlier affine-controller research is also retained without counting its uninstantiated transport condition as a result.\n\n## Scope\n\nAll inherited all-size supplier/compiler, target-label/mutable-basis, complete-call correlated-dirty hosting, compressed-window, restored-work, precision, row and analytic interfaces remain conditional. 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kappa = 0.001291542455423938: two-layer target factoring on R715 (+0.1461% over #470)","user":{"login":"Dugongue","id":49054532,"node_id":"MDQ6VXNlcjQ5MDU0NTMy","avatar_url":"https://avatars.githubusercontent.com/u/49054532?v=4","gravatar_id":"","url":"https://api.github.com/users/Dugongue","html_url":"https://github.com/Dugongue","followers_url":"https://api.github.com/users/Dugongue/followers","following_url":"https://api.github.com/users/Dugongue/following{/other_user}","gists_url":"https://api.github.com/users/Dugongue/gists{/gist_id}","starred_url":"https://api.github.com/users/Dugongue/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/Dugongue/subscriptions","organizations_url":"https://api.github.com/users/Dugongue/orgs","repos_url":"https://api.github.com/users/Dugongue/repos","events_url":"https://api.github.com/users/Dugongue/events{/privacy}","received_events_url":"https://api.github.com/users/Dugongue/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"# Conditional kappa = 0.001291542455423938: two-layer target factoring on R715 (+0.1461% over #470)\n\nThis adds `research/tensor-schur-r715/`, an offline, source-bound construction and replay package.\n\n**kappa = 645771227711969 / 500000000000000000 = 0.001291542455423938**, **+0.1460538996% over #470**. The source sweep is frozen through #471. This comparison concerns the whole-owner route; it is not a claim to exceed larger cross-family proposals with different admission assumptions.\n\n## Changed construction\n\nWe replace target intervals in #470's retimed R715 bit word using an explicit reversible identity. At interval entrance, add donor d into receiver u. Replace the receiver's increment A by A+B, where B is the donor's interval increment. Add the donor again at exit. Over F2:\n\n (u+d) + (A+B) + (d+B) = u+A.\n\nEvery actual operand frame, intermediate read, dirty input and restored endpoint is checked. Seventeen disjoint target pairs form the first layer. A second layer reuses earlier target registers in a new checked interval. The construction includes18 explicit correction terms and changes only phase B. Removing any of the18 setups,18 recoveries or18 corrections is rejected.\n\nThe local paid-profile change is:\n\n {1:-10, 2:-1, 3:-3, 4:-18, 5:+15, 6:+3}\n\nRank mass is unchanged. Strict concavity proves the recurrence moment improves for every relevant exponent, independently of floating search scores. PROOF.md gives the inequality and sufficient composition argument.\n\nEvery helper entrance, exit, residual dimension and isometry remains unchanged. We retain #470's eight-replica whole-owner assignment and substitute the checked program into all88 calls. No residual is split across owner families. The complex supplier is our unchanged #471 monomial-normalized, same-owner-spectator construction.\n\n## Exact results and costs\n\n- Bit saving lower bound:646606347261404031809 / 500000000000000000000000.\n- Complex saving lower bound:1305231506267591 / 1000000000000000000.\n- The bit supplier binds; gains are composed through actual profiles and outer assembly, never added.\n- Bit ambient dimension78; live families9600; physical families9609; whole residual occurrences62920.\n- Fresh physical prefix takes808bits, charged832. The three-level coefficient takes2478bits, charged2496. The row coefficient is19431, below20161.\n- The final bit profile is `{1:210840,2:97761,3:19800,4:29701,5:7656,6:8632,7:4320,8:792,50:1,56:612}`.\n\n## Checks and reproduction\n\n python -B research/tensor-schur-r715/verify.py /absolute/new/output\n\nPython3.11+, SymPy, C++17 and Boost headers are required; replay needs no network or optimizer. The portable verifier reconstructs both factor layers, checks arbitrary dirty columns and integer operand supports, compiles the native legality/formal-column checks, replays whole-owner emission and independent audit, checks the complex construction, then recomputes finite invoices, both rational moment implementations and all47 strict outer inequalities. Adjacent-grid and invalid-parameter controls are included. See VALIDATION.json for the completed run evidence; GitHub CI is separate.\n\n## Credits and research record\n\nDirect sources: **#470** for the retimed kernel and eight-replica whole-owner construction; **#467** for the preceding R715 shared-kernel, retiming and pooling integration; **#463** for the carrier/frame-pair and binary-cancellation R715 word; **#450** for target mixing; **#455** for our earlier prefix-factor work; **#471** for our reused complex normalization and spectator construction.\n\nThe retained kernel, hosting and complex lineage includes **#417, #442, #449, #456, #457, #451, #454, #433, #425, #386, #377, #370**, with outer assembly through **#434/#315**. PROVENANCE.md and RECENT-PRS.json retain source pins and notices. We do not claim these public mechanisms as our discoveries. #461/#465 were read but their sharper bad-edge charge is not used here. #464/#469's cross-family route is not imported.\n\nThe new contribution is this explicit two-layer word and checked composition. Tensor-inspired paired coordinate changes and invariant-block ideas helped structure the search. A control search found related elementary gains through historical strict-prefix factoring, so we do not claim a new fundamental identity or first use of Schur elimination.\n\nRESEARCH.md and research-notes preserve the useful searches, the sufficient concavity/hosting proofs, and a common-affine-offset controller theorem. That theorem's physical transport requirement is still uninstantiated and contributes no claimed gain. The notes distinguish achieved results from future routes.\n\n## Scope\n\nAll inherited all-size supplier/compiler, target-label, complete-call correlated-dirty-hosting, compressed-window, restored-work, precision, row and analytic interfaces remain conditional. 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κ=0.0011208649522582786: split centres with complete signed admission","user":{"login":"applecrusher","id":1963860,"node_id":"MDQ6VXNlcjE5NjM4NjA=","avatar_url":"https://avatars.githubusercontent.com/u/1963860?v=4","gravatar_id":"","url":"https://api.github.com/users/applecrusher","html_url":"https://github.com/applecrusher","followers_url":"https://api.github.com/users/applecrusher/followers","following_url":"https://api.github.com/users/applecrusher/following{/other_user}","gists_url":"https://api.github.com/users/applecrusher/gists{/gist_id}","starred_url":"https://api.github.com/users/applecrusher/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/applecrusher/subscriptions","organizations_url":"https://api.github.com/users/applecrusher/orgs","repos_url":"https://api.github.com/users/applecrusher/repos","events_url":"https://api.github.com/users/applecrusher/events{/privacy}","received_events_url":"https://api.github.com/users/applecrusher/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"This adds complete signed bit admission and refined finite accounting to the two actual constructions in pinned PR433. The resulting **conditional κ is `44834598090331144184841 / (40 × 10²⁴) ≈ 0.0011208649522582786`**. The numerical improvement over the pinned native value is only `24184841 / (40 × 10²⁴)`, approximately `6.04621025 × 10^-19`; the substantive addition is fresh signed-decoder, geometry, primitive-cost and complete-prefix evidence. This is not a new split-centre construction or a highest-current-score claim.\r\n\r\nThe additive package is `research/e8-split-centres-signed-composition`. Its complex bound is `1183986549206329246771 / 10²⁴`; its bit bound is `561061350132569610283 / (500 × 10²¹)`. **The bit supplier binds.** The final value is recomputed from the two actual emitted programs, without adding independently reported gains.\r\n\r\n### Construction and attribution\r\n\r\n**icekylinx, with substantial OpenAI Codex assistance**, supplies the split-centre Hamming construction, reversible source-centre bit construction, integration and checks in [PR433](https://github.com/CrocSwap/integer-mult-bounds/pull/433), pinned at `6d9244518175caf9e0089f92486959bc2c317273`. **Zhihao Chen, with OpenAI Codex assistance**, supplies PR425's mutable-basis Hamming/common-frame interface and PR386's compressed bit geometry, owner template and accounting. **ai-nanachi, with OpenAI Codex assistance**, supplies the unchanged PR426 R767 word used before the source-centre replacements. Original notices credit its 55 clean-reset helper reuses and 54 frame changes.\r\n\r\nDylan Crow's PR370 bit producer, with Anthropic Claude assistance; Jacob Sussman's E8 family and interchange framework; **eumemic / PR388's signed defining-decoder and complete-prefix work**; and all further inherited contributions retain their original notices. Our package adds source-bound signed admission, fresh compressed geometry, an independent literal complex-primitive audit, corrected signed costs and refined exact arithmetic. It does not claim the two underlying constructions as ours.\r\n\r\nThe native carrier restores **58 exact Git files**: complete 47-file PR433 and 11-file PR386 source packages, including original manifests, licenses and notices. The only existing published dependency is the frozen ten-file `e8-bit-signed-validation` package. Its relevant signed-source module is adapted explicitly; its unrelated full ancestor chain is not rerun. No previous published tree is edited.\r\n\r\n### Fresh finite evidence\r\n\r\nThe default runs the **unchanged PR433 entry point with `--replay-phases`**, so every selected phase pair is freshly regenerated. It then checks:\r\n\r\n- The complex word's **800 scalar columns**, arbitrary dirt, common-frame labels and private cleanup in both orientations; **2918 exact Gaussian phase pairs and 240 endpoint adapters**; eight global coordinate columns, owners, padding and complete invoice. Eight rank-eight and eight rank-one copies replace the earlier centres. The word has **560 helpers**, width **73**, **12,720 live / 13,298 physical slots**, **40,320 helper placements** and rank mass **926,064**.\r\n- An independent interpreter of the serialized complex programs, importing neither the producer nor scalar emitter: **222,204 forward and 222,300 backward real primitive operations**, including **29,252 HALF operations per orientation**. All live endpoints and private zeros pass, and omitting an actual HALF is rejected in each orientation. Primitive costs equal the native paid bill.\r\n- The bit word's **998 local scalar columns**, defining signed integer decoder, literal parity projection, arbitrary helper dirt and chronological signed inverse. Nine retained forms are computed in mutable source rows using **559 basis shears**, then undone after the sequential copies. The complete nine-stage scalar schedule and **7782 columns per replica** are replayed, alongside the emitted template's frame, owner and bank audit.\r\n- **Fresh PR386 geometry**, with **1080 route checks, 240 exact endpoint checks and 121 adverse controls**, matching all mathematical fields of the inherited geometry. The original carried geometry receipt is retained as provenance and is not labeled a fresh regeneration. The bit template has **758 helpers**, width **64**, **eight replicas**, **14,502 live / 14,511 physical slots** and rank mass **925,632**.\r\n\r\nThe defining decoder satisfies the required integer construction and parity projection; the unsigned XOR word is not presented as an integer-identity certificate. The signed correction needs **8537 weighted additions, including 245 even coefficients**, or **8978 signed unit additions** versus **8292 parity units**. The extra **686 units per local invocation**, totaling **49,392 over 72 invocations**, are charged in the final invoice. The corrected local prefix majorants are **3,885,147 forward and 15,348,968 inverse**. Their counted global majorant and finite coefficient need **223 bits**, within **256**; the two-level coefficient needs **483 bits**, within **512**.\r\n\r\nBoth suppliers retain rank deficit **2496** and strict degree-two halving. Bit and complex row coefficients **18,355** and **15,445** fit the retained **20,161** reserve. Two rational moment engines include overhead and exclude adjacent root-grid points. The corrected finite coefficient feeds **eight explicit charged continuations and all 47 strict outer inequalities**, with `eta=beta=10^-30` and counted common outer `log2` threshold `14 × 10³⁰`. The adjacent final grid point and complex leaf cap are rejected.\r\n\r\n### Scope and reproducibility\r\n\r\nAll-size weighted compilation and compressed windows, arbitrary correlated-bank substitution, ordinary calls, common prime/chart/precision/tape interfaces, restored rows, setup/recovery, analytic transfer and a dominating stage-specific `C_full` remain conditional. The generalized mutable-source/common-frame proof is the upstream interface; this is not acceptance by older restricted gx/gxcore checks, a Lean proof, an unconditional multiplication theorem or a practical runtime estimate.\r\n\r\nThe portable verifier validates source inventories before and after replay. `VALIDATION.json` must equal the frozen `EXPECTED.json` exactly. Complete decoded templates, schedules, operators, owners, profiles, costs, inequalities and adverse-control outcomes remain bound. Only named clocks, fresh provenance and compressed cross-hashes are projected or rebound; raw receipts preserve the full provenance. PR433 already binds phase evidence by decoded payload, so this package uses **no gzip-header hook and no native-source mutation**. Independent carrier review compared all 58 Git files and exercised 29 malformed transport controls.\r\n\r\n```sh\r\npython -m pip install -r research/e8-split-centres-signed-composition/requirements.txt\r\npython -B research/e8-split-centres-signed-composition/verify.py /absolute/path/to/new-output\r\n```\r\n\r\nThe workflow runs this full default on **Python 3.12 and 3.13** with pinned SymPy 1.14.0 and mpmath 1.3.0, preserving replay evidence. Native PR433 itself uses the standard library; the extra fresh geometry requires those dependencies. This adds **21 package files and one workflow**. 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nine calls are necessary for three abelian bit registers","user":{"login":"aliromman","id":226877337,"node_id":"U_kgDODYXfmQ","avatar_url":"https://avatars.githubusercontent.com/u/226877337?v=4","gravatar_id":"","url":"https://api.github.com/users/aliromman","html_url":"https://github.com/aliromman","followers_url":"https://api.github.com/users/aliromman/followers","following_url":"https://api.github.com/users/aliromman/following{/other_user}","gists_url":"https://api.github.com/users/aliromman/gists{/gist_id}","starred_url":"https://api.github.com/users/aliromman/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/aliromman/subscriptions","organizations_url":"https://api.github.com/users/aliromman/orgs","repos_url":"https://api.github.com/users/aliromman/repos","events_url":"https://api.github.com/users/aliromman/events{/privacy}","received_events_url":"https://api.github.com/users/aliromman/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"The pinned version of #288 leaves 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This proves that **nine calls are necessary and sufficient** when paid frames are nonzero rational rank-one matrices and all three target frames are invertible and lower triangular.\n\nThe proof reduces the remaining span-five case to 2,276 scalar families and checks all 21,317,520 orders. Two separate exact engines agree on every family: 415,398 diagonal terminals, zero survivors. The argument covers unbounded rational frame coefficients; it is not a bounded coefficient search.\n\nThe seven-file package contains the proof, catalogue generator, two engines, controls, and a replay command. It requires Python and a C++17 compiler and includes no generated search data. Attribution and AI assistance are stated in the proof.\n\nValidation: `python3 research/bit-three-register-lower-bound/replay.py` passes. The result does not change κ and does not cover extra registers or arbitrary free address maps between paid calls.\n\nThe existing `gen4-bank-verify` target also passes. `make verify` stops at the existing `joint-dual-verify` source-hash assertion for `Makefile`; the same failure was reproduced on unchanged base `12a4934`. This PR does not change the affected files. 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κ = 0.001291474845253222: retimed kernel and reordered R715 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0.001291474845253222**, exactly `645737422626611/500000000000000000`, **0.14081141475329892% above this PR's initial result** and 0.16999595% above #467. The bit side binds; the complex supplier remains unchanged #458.\n\nThe final construction reconstructs #467, replaces its kernel while retaining its timing/mixing (105 pivots, entrance rank113,104 donors), then applies20 delivery gate-frame moves with stable independent-gate reordering and14 connected-pair retimings. Every intermediate word hash is bound. All280 noncommuting B-gate order constraints are retained. Eight replicas, each residual wholly assigned to one physical family. No cross-family splitting is used.\n\nThe new package is `research/r715-reordered-deliveries/`. The earlier `r715-retimed-kernel-pool` package and its validation are preserved. The draft and subsequent witness were submitted before full verification as requested.\n\nNew source reconstruction, official legality/formal columns,963 frame projectors,3401 nested/reflected pairs,11 residual isometries,1320 routes and all62,920 whole residual assignments pass. Independent replay checks1,720,752 emitted events and rejects22 operator mutations. Both rational moment engines and47 strict outer inequalities pass. The freshly recomputed807-bit physical prefix is charged832;2477-bit three-level coefficient is charged2496; complete row coefficient19431<20161. Initial evidence: `research/r715-reordered-deliveries-validation/physical311/`.\n\nComplete changed-component wrappers for the final delivery word now pass on Python3.11.15 and3.14.8, each bound to a completed full complex-supplier receipt. Receipts and stage logs are published under `research/r715-reordered-deliveries-validation/python311/` and `python314/`. The fresh default full Python3.11 replay now passes (`PASS_FULL_R715_DELIVERY_COMPOSITION`), rebuilding the complete pinned complex supplier and all final delivery checks. Receipt and stage logs are in `research/r715-reordered-deliveries-validation/python311-full/`. GitHub CI is separate and is not claimed passed. The previous kernel-only word has complete3.11/3.14 component receipts with fully verified complex-supplier reuse, and its fresh default full Python3.14 replay has now passed (`PASS_FULL_R715_REKERNEL_COMPOSITION`), with receipt and logs in `research/r715-retimed-kernel-pool-validation/python314-full/`. This validates the earlier word; the final delivery word has its own checks and completed full replay as described above. Each status distinguishes completed-parent reuse from a default full replay. Run `python -B research/r715-reordered-deliveries/verify.py /absolute/new/output` for the final word.\n\nAll inherited compiler, target-label/mutable-basis, complete-call correlated-dirty-hosting, compressed-window, restored-work, precision, row and analytic contracts remain. Conditional finite construction; not an unconditional multiplication theorem or global optimum.\n\nCredits: DreamingOfClouds for R715 and target mixing; chafreaky for the shared-donor mechanism and #458 complex supplier; DaysSky for whole hosting; ahrazzle #469 for the local delivery-reordering idea, independently implemented here without its hosting/supplier construction. All inherited authors/licenses retained. New search, witness and verification by Rohan Arun with OpenAI Codex assistance.\n\nFurther research (not an admitted bound): `research/r715-reordered-deliveries-validation/kernel-frontier/` retains six exact local/moment screens, including a101-pivot/rank122 candidate projected near0.0012918924074286004. Fresh physical replay and finite invoice for that candidate remain pending. Losing thirteen-stage screens and the infeasible nine-stage solver instance are retained under `stage-count-screens/`; the headline bound above is 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κ = 0.001350580884553120: gate-frame retiming of #450's eleven-stage cross-copy word (+0.2105%)","user":{"login":"ahrazzle","id":38987266,"node_id":"MDQ6VXNlcjM4OTg3MjY2","avatar_url":"https://avatars.githubusercontent.com/u/38987266?v=4","gravatar_id":"","url":"https://api.github.com/users/ahrazzle","html_url":"https://github.com/ahrazzle","followers_url":"https://api.github.com/users/ahrazzle/followers","following_url":"https://api.github.com/users/ahrazzle/following{/other_user}","gists_url":"https://api.github.com/users/ahrazzle/gists{/gist_id}","starred_url":"https://api.github.com/users/ahrazzle/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/ahrazzle/subscriptions","organizations_url":"https://api.github.com/users/ahrazzle/orgs","repos_url":"https://api.github.com/users/ahrazzle/repos","events_url":"https://api.github.com/users/ahrazzle/events{/privacy}","received_events_url":"https://api.github.com/users/ahrazzle/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"Conditional **κ = 0.001350580884553120**, `8441130528457 / 6250000000000000`, above PR 450 (`35094327`) by `567267367657 / (2 * 10^17)`, which is **0.2105 percent**.\n\n## Summary\n- Retimes PR 450's target-mixed R740 word. 113 phase-B deliveries move to coarser frames of the pinned family. Every ordered scalar addition is unchanged, phase A is unchanged, and phase B is re-listed by frame dimension.\n- The retiming is a frozen witness, applied by `code/retime_apply.py` with input and output content hashes pinned. 18 changes are applied to PR 443's word before PR 450's target mixing, and 95 after it.\n- The local profile per call moves from `{1:2460, 2:1012, 3:276, 4:315, 5:108, 6:42, 7:14, 8:9}` to `{1:2401, 2:1019, 3:291, 4:315, 5:99, 6:60, 7:5, 8:9}`. The local cost per call falls from 25,612.68 to 25,555.04. The bit root rises from `674781707224226878971 / (5 * 10^23)` to `1352407420162920171433 / 10^24`. The assembly stays bit-bound with 6.29 percent of complex slack.\n- Entrance frames and residuals are untouched, so the frozen hosting selection, the global template, live 1200, 8140 hosted residuals, maximum child 56, halving depth 3 and row allowance 28416 are PR 450's. The complex side is PR 448's.\n- `verify.py` runs PR 450's verify.py unchanged first and requires its published kappa. It then runs PR 443's legality, formal-column, mutation and Gram checks and PR 450's mix check with its four controls on the retimed word, followed by PR 450's eleven-stage global template, hosted audit with 20 mutations and assembly.\n- Three negative controls on the witness format are rejected: wrong input word, a delivery moved to a frame of the wrong dimension, and donor deliveries moved across their mix frame.\n- Every improving move is in phase B. Phase-A gates sit at their minimal support frames. Further gains need gate-structure changes, outside this format.\n- This branch includes PR 450's commits and its fix for the two evidence files that `.gitignore` had dropped.\n\n## Test plan\n- [ ] `python3 -B research/e8-eleven-stage-retimed/verify.py /absolute/new/output --quick` prints `PASS_ELEVEN_STAGE_RETIMED_COMPOSITION` and the kappa above\n- [ ] `/parent450/RECEIPT.json` carries PR 450's kappa\n- [ ] The three negative controls are reported as REJECTED\n\nCredits.\n\nThe race word and its engines are @DreamingOfClouds's (PR 450), with the five-stage packages and the exact-interval moment and outer-assembly engines. The R740 word and its checkers are @chafreaky's (PR 443, PR 445). The cross-copy hosting is @higherbeing's (PR 448), and the idle-axis hosting is @DaysSky's (PR 442).\n\nThe single and paired gate retimings of @eumemic (PR 437, PR 440, PR 441) are the special cases this search generalises. The sharp bit charge is @Srikrishnabalaji's (PR 461), and the three-stage cover note that proves it is @icekylinx's. The compressed geometry is @jacklightChen's.\n\nThe integer-multiplication framework underneath the word is credited line by line in the research notes and the sources manifest:\n\n- @Mister-Meeseeks (Douglas R. Colkitt): repository framework and compact controls.\n- @Bortlesboat (Andrew Barnes): aligned pair groups (PR 2).\n- @eumemic: compressed complex producer (PR 3), fast Gaussian resampling (PR 5), aligned bit circuit and cheaper centers (PR 6), deferred bit word and complex producer (PR 117).\n- @dleen (David Leen): retained totals and stage sharing (PR 4).\n- @jacklightChen (Zhihao Chen): ternary five-subset network (PR 7), translated frames (PR 21), semantic precision and bulk resampling (PR 23), two-stage controlled corners (PR 29), deferred endpoints and signed phase correction (PR 97).\n- @icekylinx: batched recursive networks (PR 10), partial-swap networks (PR 18), endpoint gauges (PR 24), structured projector blocks and bulk assembly (PR 32), copied centers (PR 36), stopped product-ring interchange (PR 104), partial source gauges (PR 115), three-stage Cayley covers (PR 130).\n- @hipotures (Andrzej Marszałek), RaD project under CC0: semantic completed-child bounds and bulk transfer (PR 20).\n- @Paureel (Aurel Prosz): two-stage topology and paid endpoint-copy interface.\n- @Swapnil-jain (Swapnil Jain): linked two-stage development (credited in PR 29), underlying deferred readouts and frozen witness.\n- @rohanarun: corner incidence method, symbolic zero partitions and rational pivot witnesses (PR 31).\n- @DominikScholz: parameterized corner generator (PR 33).\n- @ikeboy (Avi Eisenberg): cyclic interval and core-aware pair primitives (PR 62).\n- The retained multiplication theorem, machine model, transforms and analytic estimates are from the upstream repository openai/math, under its own license.\n\n> Automated posting by agentic team with human oversight.\n\n\n","created_at":"2026-10-11T17:32:48Z","updated_at":"2026-10-11T18:03:40Z","closed_at":null,"merged_at":null,"merge_commit_sha":"b0da53d1e763bf7994b15b464d648a8866d85a1e","assignees":[],"requested_reviewers":[],"requested_teams":[],"labels":[],"milestone":null,"draft":false,"commits_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/pulls/469/commits","review_comments_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/pulls/469/comments","review_comment_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/pulls/comments{/number}","comments_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/issues/469/comments","statuses_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/statuses/a820816f07f60544bd38c6f12c38a9c25066ddf0","head":{"label":"ahrazzle:retimed-eleven-stage","ref":"retimed-eleven-stage","sha":"a820816f07f60544bd38c6f12c38a9c25066ddf0","user":{"login":"ahrazzle","id":38987266,"node_id":"MDQ6VXNlcjM4OTg3MjY2","avatar_url":"https://avatars.githubusercontent.com/u/38987266?v=4","gravatar_id":"","url":"https://api.github.com/users/ahrazzle","html_url":"https://github.com/ahrazzle","followers_url":"https://api.github.com/users/ahrazzle/followers","following_url":"https://api.github.com/users/ahrazzle/following{/other_user}","gists_url":"https://api.github.com/users/ahrazzle/gists{/gist_id}","starred_url":"https://api.github.com/users/ahrazzle/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/ahrazzle/subscriptions","organizations_url":"https://api.github.com/users/ahrazzle/orgs","repos_url":"https://api.github.com/users/ahrazzle/repos","events_url":"https://api.github.com/users/ahrazzle/events{/privacy}","received_events_url":"https://api.github.com/users/ahrazzle/received_events","type":"User","user_view_type":"public","site_admin":false},"repo":{"id":1413819158,"node_id":"R_kgDOVEUrFg","name":"integer-mult-bounds","full_name":"ahrazzle/integer-mult-bounds","private":false,"owner":{"login":"ahrazzle","id":38987266,"node_id":"MDQ6VXNlcjM4OTg3MjY2","avatar_url":"https://avatars.githubusercontent.com/u/38987266?v=4","gravatar_id":"","url":"https://api.github.com/users/ahrazzle","html_url":"https://github.com/ahrazzle","followers_url":"https://api.github.com/users/ahrazzle/followers","following_url":"https://api.github.com/users/ahrazzle/following{/other_user}","gists_url":"https://api.github.com/users/ahrazzle/gists{/gist_id}","starred_url":"https://api.github.com/users/ahrazzle/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/ahrazzle/subscriptions","organizations_url":"https://api.github.com/users/ahrazzle/orgs","repos_url":"https://api.github.com/users/ahrazzle/repos","events_url":"https://api.github.com/users/ahrazzle/events{/privacy}","received_events_url":"https://api.github.com/users/ahrazzle/received_events","type":"User","user_view_type":"public","site_admin":false},"html_url":"https://github.com/ahrazzle/integer-mult-bounds","description":"Conditional integer multiplication: kappa > 2^-15. 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assembly, source-basis cost reduction, and E8 verification","user":{"login":"lydakis","id":1649445,"node_id":"MDQ6VXNlcjE2NDk0NDU=","avatar_url":"https://avatars.githubusercontent.com/u/1649445?v=4","gravatar_id":"","url":"https://api.github.com/users/lydakis","html_url":"https://github.com/lydakis","followers_url":"https://api.github.com/users/lydakis/followers","following_url":"https://api.github.com/users/lydakis/following{/other_user}","gists_url":"https://api.github.com/users/lydakis/gists{/gist_id}","starred_url":"https://api.github.com/users/lydakis/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/lydakis/subscriptions","organizations_url":"https://api.github.com/users/lydakis/orgs","repos_url":"https://api.github.com/users/lydakis/repos","events_url":"https://api.github.com/users/lydakis/events{/privacy}","received_events_url":"https://api.github.com/users/lydakis/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"This PR contributes constructive finite assembly parameters, a reusable reduction in the bit supplier’s finite overcharge, a parent-contract guard for the hosted bit audit, and faster source-equivalent hashing and scalar replay in the E8 emitter. Earlier bank optimization and verification tools are retained.\n\nFixed backoffs and a fixed bootstrap depth leave an avoidable gap below the balanced assembly's supplied-cap ceiling. This PR adds a constructive theorem and exact verifier that select finite parameters for **every rational target below `min(b,c)/(1+min(b,c))`**, given admitted bit and complex caps and the retained conditional interfaces.\n\nThe [new package](https://github.com/lydakis/integer-mult-bounds/tree/a8be7ab24a5b0da1c7fdaa58e6656ebc774121cf/research/finite-assembly-frontier) chooses strictly positive backoffs, a finite number of bootstrap steps and explicit integer cutoffs. The [proof](https://github.com/lydakis/integer-mult-bounds/blob/a8be7ab24a5b0da1c7fdaa58e6656ebc774121cf/research/finite-assembly-frontier/PROOF.md) establishes termination and all 47 retained strict outer inequalities. It also proves maximality on a supplied rational grid, relative to these caps and this assembly family. The ceiling itself is not attained.\n\n### Reusable source-basis finite-cost reduction\n\nThe [source-basis package](https://github.com/lydakis/integer-mult-bounds/tree/a8be7ab24a5b0da1c7fdaa58e6656ebc774121cf/research/e8-bit-basis-order) now provides a guarded postprocessor that derives the copied forms from the actual input word. It preserves their order, their literal inverse, the set of source rows entering the full frame, and the surrounding construction. A separate postprocessing stage lets it compose with frozen reset/kernel selections without changing their original hashes or receipts.\n\n| Pinned construction | Complete finite coefficient | Two-level coefficient | Extra local additions |\n| --- | ---: | ---: | ---: |\n| PR433 R758 | 223 to 192 bits | 483 to 420 bits | 32 |\n| PR438 R747 after resets/kernel | 226 to 193 bits | 488 to 423 bits | 32 |\n\nThe added operations are fully charged. The lower cancellation-free prefix dominates that added cost. **Both supplier caps and the multiplication exponent stay unchanged.** This improves a rigorous finite overcharge; it makes no practical runtime or current numerical lead claim. It is not guaranteed to improve every word.\n\nThe PR433 five-stage changed-bit run is retained. On [PR438](https://github.com/CrocSwap/integer-mult-bounds/pull/438), pinned at `e3b56de7869f6af88d48ac0ab1d7959c4c9e6176`, all nine stages passed in one 18.49-second run: original construction/reset/kernel checks, the separate basis stage, and unchanged exporter/global/audit/price/combined checks. The new word restores all 987 local and 7,683 global columns, with eight bank controls, four outer controls and all 47 strict inequalities passing. Its κ remains `45340333148791/40000000000000000`.\n\nThe candidate has a fresh complete invoice. The baseline cost is reconstructed from its literally replayed word and the unchanged verified geometry/schedule; its full global pipeline was not rerun. Eleven unchanged outputs from the independently completed PR433 complex component are explicitly reused, with source, canonical-word and recipe bindings. No new complex or phase execution is claimed.\n\nThe [proof](https://github.com/lydakis/integer-mult-bounds/blob/a8be7ab24a5b0da1c7fdaa58e6656ebc774121cf/research/e8-bit-basis-order/PROOF.md), source bindings, exact executed adapters, original/new words, receipts and stage logs are retained. The self-contained audit independently checks both constructions' literal orientations, copied forms, omission controls, prefix growth and complete invoices. Ody independently reviewed the frozen 75-input package; manifest is `3df3113896b1130f2770f26da08ec7f4b812e822d568cce69b0f75ba7eb2cd17`.\n\n```sh\npython3 -B research/e8-bit-basis-order/verify.py\npython3 -B research/e8-bit-basis-order/test_postprocess.py\npython3 -B research/e8-bit-basis-order/postprocess.py original.json candidate.json\n```\n\nThree focused test contracts cover both exact reconstructions, input preservation and idempotence, unsafe basis interfaces, and CLI overwrite protection. The output is a candidate: each new word still needs its supplier's complete admission checks. The postprocessor and offline audit are portable. The retained PR438 adapter records the exact executed temporary paths; it is evidence, not a portable CLI. The existing PR433 full replay wrapper has input-only validation, with its original completed scientific run retained separately.\n\n### Preserve the inherited contract in the hosted bit audit\n\nThe original [PR442](https://github.com/CrocSwap/integer-mult-bounds/pull/442) generator preserves its parent scalar schedule, but its independent bit hosting audit does not enforce that preservation. On the authentic published hosted template, deleting the terminal exchange or zeroing a bridge coefficient is accepted with an unchanged paid profile, although literal F2 replay finds eight or three wrong scalar columns, respectively. **These are deliberately mutated regressions; the actual published construction is not alleged invalid.**\n\nThe new [guard and integration patch](https://github.com/lydakis/integer-mult-bounds/tree/a8be7ab24a5b0da1c7fdaa58e6656ebc774121cf/research/e8-hosted-bit-contract) enforce the parent schedule, scalar columns, levels, invocation headers and inherited template fields. Only the bit generator's documented hosting changes are permitted. The original ownership/profile audit remains required; the complex side has different permitted edits and is outside this guard's scope.\n\nThe positive fixture exactly matches PR442 commit `4e16d001d505d4f21dd2bcfc44591f9be4c279bd` and template payload `dd7833dcaff8c84b258847f4c4d65b6402c702700ae37d2c464083ee37b24126`. One seven-stage, 4.43-second bit-only reconstruction reused an exact completed reset word, then ran the original kernel, exporter, source-span check, global emitter, parent audit, hosted generator and regression probe. The parent kernel's three controls and audit's eight controls passed. No complex, phase, pricing or assembly replay was performed; no new bound is claimed.\n\nFour focused test contracts cover the authentic positive, the two original-audit false negatives with independent scalar replay, sign/level/header/index/field mutations, and a matching invalid parent/child pair. The offline verifier checks the source/Git bindings, payload hashes, logs and receipts, and executes the exact two-line integration patch in memory. Ody independently reviewed the frozen 38-input package, manifest `f15db9c1ae361b6d0b1f230a23cf6da02add4ea70c1e5907c80d42d9301eac57`.\n\n```sh\npython3 -B research/e8-hosted-bit-contract/verify.py\n```\n\n### Byte-identical emitter digest caching\n\nThe [emitter cache package](https://github.com/lydakis/integer-mult-bounds/tree/2c47125cbb0619dc63ccdf64c9c583f064240aeb/research/e8-emitter-digest-cache) removes repeated JSON serialization from the pinned [PR447 emitter](https://github.com/rohanarun/integer-mult-bounds/blob/43e5aa3a2fb6701b1facf542f7f3dee0fbb33c3e/research/e8-eleven-hosting-selected/code/emit.py). It encodes each immutable instruction tail once per orientation and each owner descriptor once per call. A minimal integration patch preserves event order, paid-rank increments, ownership assertions and all other emitter checks.\n\nAcross **2,742,552 records and 144 calls** from completed PR438 and authentic PR442 bit workloads, every record byte, independent complete digest, event count and local paid profile matches. The exact source-extracted hashing loop measured a median **3.206 seconds before and 0.587 seconds after**, a **5.47x hashing-loop speedup**. Three alternating trials include cache construction. Template loading, geometry checks, compression and other supplier work are excluded. This is a microbenchmark on macOS arm64/Python 3.14.8, not a whole-emitter speedup or a fresh PR447 scientific replay.\n\nThe byte-preservation proof covers the pinned event schema and immutable inputs. The portable offline verifier checks source/Git/fixture/receipt bindings, exact patch scope, every record, and two focused contracts for JSON escaping, large integer tails, fresh per-call owners and malformed inputs. The recorded adapter and original notices are retained. No mathematical bound or finite coefficient changes. Package manifest: `f45b0dd2c710838f4e5df1c1450c444a7235720b286e89ba946612081c5f847f`.\n\n```sh\npython3 -B research/e8-emitter-digest-cache/verify.py\n```\n\nDefault verification does not rerun the benchmark. Add `--benchmark` to measure the extracted loop on another machine.\n\n### Stage-local address caching for scalar replay\n\nThe [scalar address-cache package](https://github.com/lydakis/integer-mult-bounds/tree/e500c9c4217483de882cf06e6e80b25b70ea1ca5/research/e8-scalar-address-cache) removes repeated local-to-global mapper calls from the same pinned PR447 emitter. Its two-line integration patch constructs one address table per local stage, including the private scratch index. All original scalar, dirty-helper, private restoration, stage, terminal and integer bridge controls remain intact.\n\nOn two retained local-word workloads, three alternating trials measured **1.736x and 1.730x faster scalar replay**, respectively: **35.984 to 20.728 ms** for the completed PR438 word and **35.774 to 20.676 ms** for the authentic PR442 template's local word. Timing includes address-table construction and the complete extracted scalar-replay section through its 24 bridge-omission controls. Template loading, AST extraction, geometry, hosting, compression and other supplier work are excluded. This is a microbenchmark on macOS arm64/Python 3.14.8; the cache adds O(LOCAL) storage per active stage.\n\nBoth versions independently return identical complete values, levels, schedules, stage receipts and controls. The contract checks **648,692 operand mappings**, both reflections, all **11 stages and 9,417 basis columns per workload**, private restoration and all 24 bridge controls. The retained PR438/PR442 local words are used with the pinned eleven-stage recipe; this is not a fresh full PR447 admission. No mathematical bound or finite coefficient changes, and no whole-emitter speedup is claimed.\n\nThe proof states the valid-index and stage-immutability preconditions. The portable offline verifier binds original source/Git/license/fixture/receipt bytes, checks exact patch scope, repeats the complete equivalence contract, and covers address-block boundaries, per-stage cache freshness, invalid operands and omission of the private endpoint. It also reproduces identical combined source when the address and digest patches are applied in either order. Their separately measured speedups must not be multiplied into an overall speedup. Ody independently reviewed the frozen 32-input package, manifest `643da0bb1ae5f1453f0c31574ac78b08ec7c3f9836126a8c4dbdedeef8cf61af`.\n\n```sh\npython3 -B research/e8-scalar-address-cache/verify.py\n```\n\nDefault validation does not repeat timing or any supplier wrapper. Add `--benchmark` to measure the extracted section on another machine.\n\n### Finite-assembly worked example\n\nUsing the unchanged suppliers from [PR433](https://github.com/CrocSwap/integer-mult-bounds/pull/433), pinned to `6d9244518175caf9e0089f92486959bc2c317273`, the greatest admitted point on a `10^-27` grid is\n\n```\nkappa = 280216238064569651155257 / 250000000000000000000000000\n = 0.001120864952258278604621028\n```\n\nThis is strictly above that source's `0.001120864952258278`, by approximately **6.04621e-19**. The numerical gain is tiny. The reusable parameter theorem and verifier are the main contribution; no new supplier word, practical speedup or global optimality is claimed. Later supplier contributions, including [PR434](https://github.com/CrocSwap/integer-mult-bounds/pull/434), report higher bounds. This pinned example is not a claim to the current numerical lead; the parameter theorem applies to future admitted caps as well.\n\nOne clean default replay of the pinned supplier package passed all 13 stages in 6.19 seconds. It regenerated both changed programs, their scalar and ownership checks, moments and finite invoices; the original verifier reused its source-bound Gaussian phase evidence. We did not rerun every Gaussian pair. Actual receipts and all stage logs are retained. The new verifier independently reproduces the original assembly, recomputes both supplier moments and the selected seed with two rational engines, checks the actual 483-bit two-level coefficient against its 512-bit charge, and verifies nine finite bootstrap steps and all 47 strict inequalities. The next grid point, zero eta, zero beta and unit beta are rejected.\n\nFive focused tests cover both binding components, equal caps, 48 cap/target regimes, exact grid endpoints, 100-digit grids, zero-step cases and invalid premises. Ody independently reviewed the proof and code and reran the complete package successfully. All 50 package inputs match manifest `876412045fcd74e87bba4f02704eb312fad77e565e73eecb1c4849e1df92ff8d`. The CLI also exports witnesses whose rational numerators exceed Python’s default decimal conversion limit; an end-to-end 100-digit-grid regression covers this. An integration test connects this offline verifier to the existing Python 3.11/3.13/3.14 test matrix, without a new workflow or executor.\n\n```sh\npython3 -B research/finite-assembly-frontier/verify.py\n```\n\nAdd `--output /absolute/path/to/new-result.json` to retain every exact parameter, cutoff and margin. Python 3.11+ and the standard library suffice.\n\n**Current signed head:** `e500c9c4217483de882cf06e6e80b25b70ea1ca5`. The scalar address-cache package passes its default offline contract and focused repository integration test, with independent review by Ody. **All 56 CI jobs passed on this head:** [research/formal, 52 jobs](https://github.com/lydakis/integer-mult-bounds/actions/runs/38160852534), [terminal elimination, 2 jobs](https://github.com/lydakis/integer-mult-bounds/actions/runs/38160852467), and [recycled registers, 2 jobs](https://github.com/lydakis/integer-mult-bounds/actions/runs/38160852516). The previous signed head `2c47125cbb0619dc63ccdf64c9c583f064240aeb` passed all 56 jobs: [research/formal, 52 jobs](https://github.com/lydakis/integer-mult-bounds/actions/runs/38149787308), [terminal elimination, 2 jobs](https://github.com/lydakis/integer-mult-bounds/actions/runs/38149787217), and [recycled registers, 2 jobs](https://github.com/lydakis/integer-mult-bounds/actions/runs/38149787178). All package audits and focused regressions use the existing Python matrix; no workflow or executor was added. Scientific-run, measurement and reused-evidence scopes are stated above.\n\n### Earlier contributions retained\n\n- [Exact bank optimizer](https://github.com/lydakis/integer-mult-bounds/tree/a8be7ab24a5b0da1c7fdaa58e6656ebc774121cf/research/e8-exact-bank-optimizer): necessary-and-sufficient packing conditions, optimal patterns and minimum replication for the width-73 rank family. An independent exhaustive oracle checks 16,875 inventories.\n- [Chart-sensitive dirty-endpoint audit](https://github.com/lydakis/integer-mult-bounds/tree/a8be7ab24a5b0da1c7fdaa58e6656ebc774121cf/research/e8-dirty-chart-audit): exact all-address Gaussian checking, including a counterexample invisible at address zero and an admitted positive control. Six focused regressions pass. Its obstruction is scoped to the stated independent-bank interface.\n- [E8 retimed component verification](https://github.com/lydakis/integer-mult-bounds/tree/a8be7ab24a5b0da1c7fdaa58e6656ebc774121cf/research/e8-retimed-component-verification): retained emitter, phase, lifetime and finite-accounting evidence for the pinned PR384 complex component.\n- [Weighted donor-rank matching](https://github.com/lydakis/integer-mult-bounds/tree/a8be7ab24a5b0da1c7fdaa58e6656ebc774121cf/research/gen5b-weighted-matching): the earlier reproducible construction reused by later contributions. Its historical conditional bound is `0.000751075693834608`; later suppliers improve it.\n\nThe supplier compiler, compressed-window, arbitrary dirty-bank, restored-work, fixed-tape/common-grid, precision and analytic interfaces remain assumptions. This is a conditional finite construction, with no unconditional multiplication theorem or new Lean proof.\n\nNew parameter selection, source-basis ordering and postprocessor, hosted-bit parent-contract guard, emitter digest and scalar address caching, proofs, tests and evidence integration: George Lydakis with substantial OpenAI Codex assistance, including Ody's independent review. PR447's emitter retains rohanarun's original notices and Codex-assistance attribution. PR442's hosting construction and original audit retain the DaysSky package's original notices and Claude-assistance attribution. PR438's reset/kernel construction remains credited to rohanarun; the kernel method and exact engine retain Chafik Boukhalfa's (chafreaky) attribution. PR433's construction remains credited to icekylinx with OpenAI Codex; its upstream lineage includes Zhihao Chen, ai-nanachi, Dylan Crow, Jacob Sussman and the retained contributors. The unchanged outer engine retains its eumemic/Anthropic Claude, icekylinx, Zhihao Chen and RaD/hipotures credits. 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integer multiplication: kappa > 2^-15. Community proofs, exact certificates and reproducible audits; assumes the OpenAI #109 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κ = 0.001347744547714835: eleven-stage cross-copy hosting with target mixing (+1.278% over #448)","user":{"login":"DreamingOfClouds","id":173691639,"node_id":"U_kgDOClpS9w","avatar_url":"https://avatars.githubusercontent.com/u/173691639?v=4","gravatar_id":"","url":"https://api.github.com/users/DreamingOfClouds","html_url":"https://github.com/DreamingOfClouds","followers_url":"https://api.github.com/users/DreamingOfClouds/followers","following_url":"https://api.github.com/users/DreamingOfClouds/following{/other_user}","gists_url":"https://api.github.com/users/DreamingOfClouds/gists{/gist_id}","starred_url":"https://api.github.com/users/DreamingOfClouds/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/DreamingOfClouds/subscriptions","organizations_url":"https://api.github.com/users/DreamingOfClouds/orgs","repos_url":"https://api.github.com/users/DreamingOfClouds/repos","events_url":"https://api.github.com/users/DreamingOfClouds/events{/privacy}","received_events_url":"https://api.github.com/users/DreamingOfClouds/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"> **Caveat (added after #451).** #451 shows that #448's cross-family residual split is not an exact factorization: D_(a+b)⊕I has trace 90, against 54 for D_a⊕D_b. This package's word splits 1,807 of its 8,140 hosted residuals across two different data families, and #451's trace argument reproduces exactly on our (4,4) splits. **The κ claimed below therefore rests on #448's routing derivation as disputed in #451, and should be treated as not established** until a fully charged compiler or a regrouping theorem covers these splits.\n> - Under whole-residual hosting (no split), with the same checks: this word gives κ = 1.265848755·10⁻³, bound by #442's complex supplier (bit c = 1.2730520·10⁻³). Unmixed it gives 1.263365465·10⁻³.\n> - The target-mixing lemma and the eleven-stage construction are independent of the dispute.\n\nConditional **κ = 269548909542967/(2·10¹⁷) = 1.347744547714835·10⁻³**, **1.2783% above #448** (1.330733966732373·10⁻³). The bit supplier binds, at **c = 1.349563·10⁻³** (+1.28% over #448's 1.332507·10⁻³). #448's complex supplier is unchanged (b = 1.437532·10⁻³, nine stages) and has 6.5% of room.\n\n| bit word | stages | hosting | max child | bit c (·10⁻³) | κ (·10⁻³) | over #448 |\n| --- | ---: | --- | ---: | ---: | ---: | ---: |\n| #448 (R747 word) | 9 | cross-copy | 24 | 1.332507 | 1.330734 | 0 |\n| unmixed (`stacked_unmixed`) | 11 | cross-copy | 56 | 1.340476 | 1.338682 | +0.597% |\n| **target-mixed (default)** | **11** | cross-copy | 56 | **1.349563** | **1.347745** | **+1.278%** |\n\n## Change and mathematical scope\n\nThree independent levers stack on #443/#444's R740 rank-138 bit word, each behind the checks that already exist for it:\n- **#448's cross-copy hosting**, used unchanged: a helper residual may lie across the pending sets of two copies of one idle child (the tape rule).\n- **Eleven compressed stages** (m = 78, five data pairs, 24 bridge shears, 11 local invocations), as in #445 and #447. The idle pairs then offer 73,920 pending coordinates per replica against 63,602 residual coordinates (45,360 against 52,038 at nine), so **all 8,140** helper residuals are hosted (1,807 across two copies), no bank remains and the live stock is the data alone: 1,200 families.\n- **Target mixing** (F2 analogue of #425's target packets). For two targets whose delivered prefixes inside a frame G coincide, the receiver takes the donor's register with one addition at G, plus a frame-0 preconditioner and a scatter fix. 46 receivers; the target climb falls by 0.72% per invocation; R = 740 and every helper width are unchanged.\n\nchafreaky's #445 independently reached eleven stages. While building, our eleven-stage single-copy variants matched #445's κ and bit c to every digit; that single-copy check is not part of this package.\n\n## Validation\n\n```sh\npython -m pip install -r research/e8-r740-replica32/parent436/requirements.txt\npython -B research/e8-eleven-stage-cross-copy/verify.py /abs/new/output # CXX, BOOST_INCLUDE as for #443; --quick, --no-anchor, --discover-check\n```\n\n`verify.py` checks the pins, runs #443's and #448's verifiers unchanged, then:\n- **Anchors (nine stages):** the generalised geometry equals #386's; the parent template equals #443's byte for byte; the generalised tape emitter reproduces **#448's bit template byte for byte**, and the generalised assembler reproduces #448's `EXPECTED.json` (κ, both lower endpoints, both template hashes).\n- **Eleven stages:** geometry (1,320 route checks, 77 factors, no new prime); the template's scalar replay on 9,340 columns with all 24 omitted-shear controls rejected; the C++ formal-column checker at `-DKPAIRS=5` (1,940 columns, 24 controls); independent audit of the template (944 projectors, 15 mutation controls) and of the hosting (windows, pieces, owners, remainders; 20 mutation controls, incl. split pieces on non-adjacent copies and widths that do not sum); the exact two-moment price, three-level halving, six bootstrap levels, all 47 strict inequalities, next-grid and parameter controls.\n- **Mixed word:** regenerated from #443's word; C++ cohort legality, five-stage and K = 5 formal columns, `mutate_records` (6 of 6), the Gram check of all 944 frames; `e8core.replay` on 980 columns, a strict check of the 92 target operands, four mutants rejected (no preconditioner, no scatter fix, mixing at the full frame, mixing omitted).\n\nLocal transcript: full wrapper PASS twice from fresh copies (macOS, Python 3.14.7, g++-16 = Homebrew GCC 16.2.0, Boost 1.92); each run replays #443 and #448 in full before the eleven-stage steps (seconds). CI covers Python 3.11 and 3.14.\n\n## Scope and open obligations\n\nConditional, like its parents. The principal review points are:\n1. **Lemma (bit labels)** (`BIT-LABEL-LEMMA.md`, `PROOF.md` §6): the bit-label conjugation for target-to-target adds at a common frame. It extends #425's lemma, which #425 flags in the same way. The checks fix the F2 identity, the frames and the spans; they do not prove that the physical bit label acts identically on a target used as an operand. The unmixed variant does not depend on it.\n2. **#448's cross-copy hosting lemma**, now applied to every residual of an eleven-stage word, and #442's hosting lemma it builds on.\n3. **Compressed windows at eleven stages**: m = 1 + s(h − 1) at s = 11 is checked finitely (every projector, route, schedule and owner), not proved.\n4. **Finite constants**: three-level halving (max child 56: 2·56³ = 351,232 < 78³ = 474,552; coefficient 504 bits unmixed, 511 mixed, charged 512), and a bit row 3·(m² + 1) + 10,161 = 28,416 above the inherited 20,161 (the outer assembly needs only 10⁶ − (51/25)A > 0). #445's elementary orthogonal-cover count is an alternative that keeps 20,161; not used here.\n5. **One replica**: with no bank to tile, T = 1 (#443/#448 use 8 or 32 replicas only to fill width-64 banks); the price is independent of T.\n\nThe all-size compiler, restored-work, tape/common-grid, precision and analytic interfaces remain inherited assumptions. No Lean proof and no unconditional integer-multiplication theorem is claimed.\n\n## Credits and AI disclosure\n\nPrepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. This builds on, and runs unchanged:\n- higherbeing (#448): cross-copy hosting, its lemma, `tape_core.py`, the complex supplier and the assembly this package is measured against;\n- chafreaky (#445, #444, #443, #435–#441; OpenAI Codex): the R740 word, the replicated layout and the eleven-stage row argument; rohanarun (#447, #434);\n- DaysSky (#442, #363; Anthropic Claude): idle-axis hosting and the two-supplier assembly; jacklightChen / Zhihao Chen (#386, #425; OpenAI Codex): the compressed geometry and the target packets whose lemma the mixing extends;\n- icekylinx (#433, #426), eumemic (#436, engines), Dylan Crow (#370; Anthropic Claude), Jacob Sussman (E8, `gx`).\n#445 and #447 were read as data; none of their scripts were run.\n\nNote: #453 (rohanarun) builds on this package's target mixing with a rank137 kernel (+0.0028%).\n\n🤖 Generated with [Claude Code](https://claude.com/claude-code)\n\n","created_at":"2026-10-11T15:02:31Z","updated_at":"2026-10-11T17:45:50Z","closed_at":null,"merged_at":null,"merge_commit_sha":"61a9814b60c4b775304b8b35e90cbbdbddc1ec51","assignees":[],"requested_reviewers":[],"requested_teams":[],"labels":[],"milestone":null,"draft":true,"commits_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/pulls/450/commits","review_comments_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/pulls/450/comments","review_comment_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/pulls/comments{/number}","comments_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/issues/450/comments","statuses_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/statuses/350943275564c53b209c1277aac7d691807726be","head":{"label":"DreamingOfClouds:e8-eleven-stage-cross-copy","ref":"e8-eleven-stage-cross-copy","sha":"350943275564c53b209c1277aac7d691807726be","user":{"login":"DreamingOfClouds","id":173691639,"node_id":"U_kgDOClpS9w","avatar_url":"https://avatars.githubusercontent.com/u/173691639?v=4","gravatar_id":"","url":"https://api.github.com/users/DreamingOfClouds","html_url":"https://github.com/DreamingOfClouds","followers_url":"https://api.github.com/users/DreamingOfClouds/followers","following_url":"https://api.github.com/users/DreamingOfClouds/following{/other_user}","gists_url":"https://api.github.com/users/DreamingOfClouds/gists{/gist_id}","starred_url":"https://api.github.com/users/DreamingOfClouds/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/DreamingOfClouds/subscriptions","organizations_url":"https://api.github.com/users/DreamingOfClouds/orgs","repos_url":"https://api.github.com/users/DreamingOfClouds/repos","events_url":"https://api.github.com/users/DreamingOfClouds/events{/privacy}","received_events_url":"https://api.github.com/users/DreamingOfClouds/received_events","type":"User","user_view_type":"public","site_admin":false},"repo":{"id":1412741203,"node_id":"R_kgDOVDS4Uw","name":"integer-mult-bounds","full_name":"DreamingOfClouds/integer-mult-bounds","private":false,"owner":{"login":"DreamingOfClouds","id":173691639,"node_id":"U_kgDOClpS9w","avatar_url":"https://avatars.githubusercontent.com/u/173691639?v=4","gravatar_id":"","url":"https://api.github.com/users/DreamingOfClouds","html_url":"https://github.com/DreamingOfClouds","followers_url":"https://api.github.com/users/DreamingOfClouds/followers","following_url":"https://api.github.com/users/DreamingOfClouds/following{/other_user}","gists_url":"https://api.github.com/users/DreamingOfClouds/gists{/gist_id}","starred_url":"https://api.github.com/users/DreamingOfClouds/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/DreamingOfClouds/subscriptions","organizations_url":"https://api.github.com/users/DreamingOfClouds/orgs","repos_url":"https://api.github.com/users/DreamingOfClouds/repos","events_url":"https://api.github.com/users/DreamingOfClouds/events{/privacy}","received_events_url":"https://api.github.com/users/DreamingOfClouds/received_events","type":"User","user_view_type":"public","site_admin":false},"html_url":"https://github.com/DreamingOfClouds/integer-mult-bounds","description":"Conditional integer multiplication: kappa > 2^-15. 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The bit histogram, live width, complex root, bootstrap and six-level balanced assembly stay as published there.\n- The source theorem in `notes/three-stage-cover-bit.tex` charges each bad edge at most `(2 m^3 / 2^80) * (6 N (N - 1) + 3 N + 6 (N - 1))` rank-one children with `N = 2 m`. At `m = 78` that is strictly below the round `10^-16 * 32 m^2` envelope that PR 450's engine still applies. PR 461 made this observation on PR 458's word. This applies it to the current leader.\n- Replaying PR 450's histogram with the inherited envelope through the `five-stage-gen4-banks` engines on main, byte-identical to the engines PR 450 pins, reproduces its published pair. The sharp charge gives bit root `1349563417453477963841 / 10^24` and the kappa above. The assembly remains bit-bound with 6.5183 percent of complex slack.\n- Both moment engines certify the new root and reject the next `10^-24` point. 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`research/e8-tensor-normalization/`, a self-contained replay package for the changed construction.\n\nThe composed conditional exponent is:\n\n**kappa = 1274548075945587 / 10^18 = 0.001274548075945587**\n\nThis is **+0.6303146486% over #456**. The source snapshot is frozen through #457; this comparison makes no claim about later PRs.\n\n## Mechanisms\n\n### 1. Normalize the complete dirty-helper invocation\n\nFor each one-dimensional complex entrance E, the exact helper endpoint is:\n\n Phi = T_full T_E^-1\n\nWe factor this as:\n\n Phi = L (C8 tensor I1) R\n\nHere L and R are explicit Gaussian monomial maps. Wrapping the complete local call with their inverses admits the desired operation while preserving all nine physical dimensions, global phases, and arbitrary dirty contents.\n\nThe scalar-backward program retains its original frame chronology and uses the same endpoint wrappers.\n\n### 2. Borrow the inactive ninth axis from the same owner array\n\nThe eight active axes lie inside the pending idle child. The spectator lies in its orthogonal complement within the same ambient array.\n\nThe complete invocation acts as identity on that borrowed coordinate. Consequently, only the eight active axes are removed from the child's paid remainder. Every simultaneous invocation has a disjoint full physical footprint and an explicit orthogonal route.\n\nThis construction does not split a helper across owner families or fit a nine-dimensional function register into eight dimensions.\n\nTogether these mechanisms admit **#449's existing 79-pivot response kernel**. The separate gauge-80 modification is not used. The witness applies the complete kernel in all 77 calls of the seven-replica, eleven-stage construction and explicitly records all 6,083 spectator borrows.\n\n## Composition\n\n| Supplier | Construction | Lower saving |\n|---|---|---:|\n| Bit | #457 rank151 + #450 target mixing + reused #455 two-prefix recovery | 0.001276174621854442560268 |\n| Complex | #449 kernel79 + the admission mechanisms above, using #456's seven-replica layout | 0.001305231506267591 |\n\nThe bit supplier binds.\n\nThe complex moment's finer lower endpoint is 0.001305231506267591990847. Assembly conservatively rounds this downward to 18 decimal places. Gains are composed through the supplier profiles and outer assembly, never added.\n\nThe complex profile is:\n\n {1:153851, 2:71764, 3:4807, 4:17248, 5:33266,\n 6:2, 7:2254, 8:6356, 40:1, 64:2046}\n\nIts ambient dimension is 89, live stock is 8,400, physical stock is 8,978, rank mass is 744,744, and deficit is 2,856.\n\nMonomial wrappers are charged per ambient array entry, including every exterior slice. The invoice conservatively charges sixteen real primitives for every helper per complete call and includes the existing routing/compiler reserves. No clean full-array temporary is assumed.\n\n## Reproduction\n\n```sh\npython -B research/e8-tensor-normalization/verify.py /fresh/output/directory\n```\n\nRequires Python 3.11+, SymPy, a C++17 compiler, and Boost headers. Set `CXX` and `BOOST_INCLUDE` where necessary. Replay requires no network, optimizer, or Lean installation.\n\nChecks include:\n\n- Changed bit native compilation, legality, formal columns, stage composition, Gram frames, and whole-owner routing.\n- Both 800-column complex scalar orientations, 2,932 exact phase edges, and 240 data endpoint adapters.\n- Fourteen canonical entrance wrappers, each checked on 512 Gaussian-dyadic columns, with 70 negative controls.\n- Independent ownership and active/complement replay, full nine-axis orthogonal routes, and complete-program dispatch.\n- Rational moments, conservative finite invoices, six bootstrap levels, all 47 strict assembly inequalities, and adjacent-grid and parameter controls.\n\n## Sources and attribution\n\nDirect reuse: **#449, #456, #457, #455, #450, #451, and #454**.\n\nThe hosting/compiler/word lineage additionally includes **#442, #433, #425, #417, #386, #377, and #370**. The outer formula follows **#434/#315**.\n\nExact pinned sources and retained notices are recorded in `PROVENANCE.md` and the manifests. We do not claim the public response kernels, target-mixing identity, whole-pool framework, or reused prefix recoveries as new discoveries.\n\nEarlier tensor-isomorphism work suggested two structural adaptations:\n\n- Paired primal/dual coordinate changes suggested the endpoint normalization.\n- Active/complement projectors and orthogonal-block constructions suggested the restored spectator borrowing.\n\nThe multiplication identities are established separately in `PROOF.md`; these connections are mathematical inspiration, not imported Lean certification.\n\n## Research record and future directions\n\n`RESEARCH.md` preserves the unsuccessful screens and their scope, including Steinberg/transvection rewrites, terminal-observable substitutions, common-frame centralizers, cleanup compression, and full-footprint-only allocations.\n\nThe conservative E510 admission produced only a small gain. Permitting an explicitly restored spectator in the same owner array changed the allocation constraint and admitted all 79 pivots.\n\nA smaller 112-pair ablation establishes strict moment improvement using:\n\n 16^alpha < 2 * 8^alpha, for 0 < alpha < 1.\n\nThe next useful target is the binding bit supplier, including a rigorously justified bit analogue of spectator borrowing. Further complex-only saving does not currently improve the composed exponent.\n\n## Scope\n\nThe inherited all-size supplier, hosting, compiler, and outer-assembly interfaces remain conditional.\n\nThis is not an unconditional sub-n-log-n multiplication theorem or a fresh Lean certificate. 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κ = 0.001289283116193775: R715 shared kernel, retiming and whole 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A fresh shared-donor kernel and retiming on PR463's R715 word, with four-replica whole-residual hosting and PR458's unchanged complex supplier. The bit side binds.\n\nSubmitted first as a projected draft; the changed physical component, fresh finite invoice and exact outer assembly now pass. **Complete changed-component wrappers pass on Python3.11 and3.14, each reusing its own completed full PR458 complex replay.** Their receipt status explicitly distinguishes completed-parent reuse from a fresh default full run. The fresh default full Python3.14 replay also passes (`PASS_FULL_R715_KERNEL_POOL_COMPOSITION`), rebuilding the pinned complex supplier and all changed bit checks. Receipt and stage logs are in `research/r715-kernel-pool-validation/python314-full/`. GitHub CI is separate and is not claimed passed; this remains a draft.\n\nThe construction uses99 kernel pivots, entrance rank118,56 target-prefix receivers,60 single-gate retimings and14 connected-pair retimings. All31,460 helper residual occurrences stay whole on one physical family. Four replicas use4,800 live /4,809 physical families. No cross-family residual splitting is used. The actual final word and every frozen selection are included; the word is reconstructed independently from PR463's published pre-kernel source.\n\nThe new physical-family growth envelope takes604bits and is charged640; the three-level coefficient takes1864bits and is charged1920. The prior529/1664-bit charges are not reused. Fresh routing and selector work is included, and the full row coefficient is19428<20161.\n\nChecks passed:\n- Exact reconstruction, rational source spans and all955 local columns; official legality,1195 five-stage and1915 eleven-stage formal columns; six record corruptions and24 omitted-bridge controls rejected.\n- Twelve coordinate-permutation residual isometries,959 exact frame projectors and3395 nested/reflected projector pairs;1320 geometry routes and every whole owner/window/remainder.\n- All9065 unbanked global columns;859100 emitted instructions; independent ownership, profile and physical-prefix recomputation;22 global mutations rejected.\n- Both rational moment engines, fresh invoices, six bootstrap levels,47 strict outer inequalities, adjacent-grid and invalid-parameter controls.\n\nExact bit lower:645473756513106438971/500000000000000000000000. Complex lower:1297203880559577927527/10^24. Final κ:51571324647751/40000000000000000.\n\nReproduce: `python -B research/r715-kernel-pool/verify.py /absolute/new/output`. Default runs the full pinned complex supplier before the new bit checks. `--complex-output` explicitly reuses a completed full complex receipt and emits a distinct status. Python3.11/3.14 CI, source pins, proof, manifest and local receipts are included. `verify_component.py` remains a narrower arithmetic screen and is not full admission.\n\nThe first local GCC build failed on SDK configuration (`stdlib.h` missing); retained failure and successful compiler receipts are published. The complex replay retains PR460's metadata-only portability adapter for two non-proof floating report fields, without changing pinned sources, operators or exact reconstruction checks.\n\nThe complete-call correlated-hosting, compiler, mutable-basis/target-label, compressed-window, restored-work, common-grid/tape, precision, row and analytic interfaces remain conditional. No unconditional multiplication theorem, new Lean proof or global optimality is claimed.\n\nCredits: DreamingOfClouds with Claude Opus5.5 for PR463's carrier/XOR word and target mixing; chafreaky and PR417 for shared-donor packing and exact engines; DaysSky for hosting; chafreaky for PR458's complex supplier; Jacob Sussman, Dylan Crow, icekylinx, eumemic, Zhihao Chen, Henry Grant and all inherited contributors. New selection, retiming, four-replica pooling and integration by Rohan Arun with OpenAI Codex. Licenses and notices retained.\n\nFull-run portability update: the first default invocation encountered inherited shell splitting on the SSD path containing spaces. The wrapper now supplies the existing pinned PR460 shell-path adapter and Boost header location. The repaired Python3.11 complete component wrapper passes with its completed full complex supplier. The repaired default full Python3.14 run now passes; the initial failure and all receipts are retained. No proof data or bound 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κ = 0.001283479303751122: E8 bit word R715 (carrier lower bound + F2 overlap cancellation) with #458's complex supplier (+0.711% over #460)","user":{"login":"DreamingOfClouds","id":173691639,"node_id":"U_kgDOClpS9w","avatar_url":"https://avatars.githubusercontent.com/u/173691639?v=4","gravatar_id":"","url":"https://api.github.com/users/DreamingOfClouds","html_url":"https://github.com/DreamingOfClouds","followers_url":"https://api.github.com/users/DreamingOfClouds/followers","following_url":"https://api.github.com/users/DreamingOfClouds/following{/other_user}","gists_url":"https://api.github.com/users/DreamingOfClouds/gists{/gist_id}","starred_url":"https://api.github.com/users/DreamingOfClouds/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/DreamingOfClouds/subscriptions","organizations_url":"https://api.github.com/users/DreamingOfClouds/orgs","repos_url":"https://api.github.com/users/DreamingOfClouds/repos","events_url":"https://api.github.com/users/DreamingOfClouds/events{/privacy}","received_events_url":"https://api.github.com/users/DreamingOfClouds/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"Conditional **κ = 641739651875561/(5·10¹⁷) ≈ 0.001283479303751122**, bit-bound: **+0.711% over #460** (0.001274415506145115) and\n+0.741% over #458. Whole-residual hosting on both sides: no cross-family residual split, no cross-copy lemma, no new complex lemma.\n\n| side | supplier | endpoint |\n| --- | --- | ---: |\n| bit (binds) | **R715** E8 bit word, eleven stages, #442 whole-residual hosting, target mixing | c ≈ 1.285129·10⁻³ (+0.712% over #459's 1.276042·10⁻³, +0.742% over #454's) |\n| complex | #458's paid-adapter kernel, unchanged | b ≈ 1.297204·10⁻³ |\n\n#465 (Srikrishnabalaji) has independently certified this outer assembly (the step #463's draft left open) at 1.283479306671789·10⁻³\nwith a sharper bit charge, crediting #463; this PR supplies the full bit supplier and its verifier.\n\n**What is new: the bit word R = 715** (#436's R740 → 715).\n1. **A carrier lower bound, and a word that meets it.** In this format a copy of source x_s that first acts above its line frame\n serves only targets in a hyperplane section of s^⊥ (frames contain everything they touched). The 63 lines of E7 = s^⊥ are a\n spherical 4-design, Σ_r ⟨r,u⟩²⟨r,v⟩² = 16(|u|²|v|² + 2⟨u,v⟩²) > 0, so no two hyperplanes contain them: every source needs ≥ 3\n registers, i.e. **≥ 240 carriers**; likewise every target needs ≥ 2 helpers reaching its hyperplane (240, met since #370).\n #370-lineage words spend 272 carriers because each frame line 2e_m enters the D4 sums of seven blocks. **Frame-pair D4 sums**\n (D4(c) = Bcw[c] + FP + FP', FP = 2e_a + 2e_b over the 12 pairs of one AG(3,2) direction plane) meet the bound: R 740 → 724.\n2. **Eleven cancelling re-expressions** (a rule rewritten as x ⊕ y of existing symbols; overlap cancels inside its frame): R 724 → 715.\n3. #443's replica kernel rebuilt for the new word (deterministic search, coordinate entrances), and #450's target mixing\n **generalised to chained receivers** (a donor that is itself a receiver); it reproduces #450's mixed word byte for byte.\n\n**Verification** (`python -B research/e8-r715-paid-complex/verify.py /abs/out`; CI workflow `e8-r715-paid-complex`): #458's full\nwrapper and the R715 package's full wrapper from scratch, then the exact composition (two moment engines per side, six bootstrap\nlevels, all 47 strict outer inequalities, next-grid and parameter controls). The bit package regenerates the word from its frozen\nhierarchy (legality of every rule and read checked), runs #370's independent all-column checker and mutants, a relaxed copy of that\nchecker on the kernel and mixed words, #443's C++ cohort legality and formal columns at five and eleven stages, mixing mutants, Gram,\neleven-stage template and hosting audits, and its own assembly. Two fresh-copy runs agree apart from timing fields (results, both\nsupplier RESULTs and the complex AUDIT byte-equal). The R715 word was also checked by an independent validator.\n\n**Review points**\n- **Carrier bound** (proof above): the 4-design identity for E7 and the frame-containment argument give ≥ 240 carriers; it is a\n scoped bound for this format, not used by the certificate.\n- **Rekid legality**: each of the 11 re-expressed rules uses existing symbols whose frames lie inside the rule's frame, the\n hierarchy stays acyclic (the compiler's recursion requires it), every consumer frame contains the rule's frame, and content equals\n the F2 sum of its kids (checked by `hier_word.py` before compiling).\n- **Relaxed checkword** (`code/checkword_relaxed.py`): drops only the two frame-0 assertions of #370's checker (y/helper start at\n frame 0, stock line 75; dirt compensation at frame 0, stock line 89) and skips its five-stage price for kernel words, because\n #443's kernel pivots start at their entrance frames. Labels, legality, exact F2 on all 955 columns and Gram are unchanged, and\n #443's C++ cohort legality and the five/eleven-stage formal columns still check the same words.\n- #450's Lemma M (bit target mixing, here with chained receivers); #458's paid adapters (inherited).\n- Contracts: the bit side keeps its own (halving depth 3, coefficient 525 bits charged 576, row coefficient 28,416 = 3(78²+1)+10,161,\n which sets the row allowance; the bootstrap and κ do not depend on either). #445's sharper row bound gives 19,425 for R715, so the\n enlargement over the lineage's 20,161 is avoidable.\nConditional like all parents; no unconditional theorem or Lean proof is claimed.\n\nCredits: chafreaky (#458 paid adapters, #451/#454 whole-residual hosting and the cross-family obstruction, #443–445 kernel and\nstaging), rohanarun (#460 composition and verifier structure, #453, #459), Srikrishnabalaji (#465), DaysSky (#442 idle-axis hosting),\nDylan Crow (#370 bit word, producer and checkers), eumemic (#436 R740 word and reuse, #440/#441 retiming), higherbeing (#448),\nicekylinx (#433), jacklightChen (#425), Jacob Sussman, Zhihao Chen and all source-pinned authors. 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κ = 0.001266536148630310: target mixing with whole-residual hosting","user":{"login":"chafreaky","id":4400527,"node_id":"MDQ6VXNlcjQ0MDA1Mjc=","avatar_url":"https://avatars.githubusercontent.com/u/4400527?v=4","gravatar_id":"","url":"https://api.github.com/users/chafreaky","html_url":"https://github.com/chafreaky","followers_url":"https://api.github.com/users/chafreaky/followers","following_url":"https://api.github.com/users/chafreaky/following{/other_user}","gists_url":"https://api.github.com/users/chafreaky/gists{/gist_id}","starred_url":"https://api.github.com/users/chafreaky/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/chafreaky/subscriptions","organizations_url":"https://api.github.com/users/chafreaky/orgs","repos_url":"https://api.github.com/users/chafreaky/repos","events_url":"https://api.github.com/users/chafreaky/events{/privacy}","received_events_url":"https://api.github.com/users/chafreaky/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"Conditional **κ = 0.001266536148630310**, **0.047745% above PR451** at `f3a38153678b55063fc005901cc968266166507d`.\n\nTransfer PR450's target-prefix mixing to PR451's rank149 bit word using a frozen selection of 46 disjoint receiver/donor pairs. Exact reconstruction, all 980 local columns, integer target-source spans and an explicit common-frame bit-label argument are included. Every residual remains whole on one host family; this does not use PR448 cross-copy hosting.\n\nThe new bit endpoint is `0.001275657818793753037875`. The unchanged, freshly rebuilt complex endpoint `0.001268142296690675830146` now binds. All 65,120 bit helper occurrences retain the existing eleven-stage schedule and 9,600 live families. The complete invoice charges the new additions, 155-bit prefix and 520-bit three-level envelope within the retained 192/1,024-bit charges and 20,161 row allowance.\n\nValidation: fresh Linux full and macOS quick runs with complex phase regeneration both passed; every exact result field and the physical instruction digest agree. Checks include four mixing controls, 92 new target operands, 47 exact frame-label matrices, 648 finite address/value controls, official C++ records, 9,340 global columns, 1,320 routes, 22 global mutations, 24 omitted bridges, both rational moment engines and all 47 strict outer inequalities. Source pins bind 288 unchanged upstream files. Receipts and the small post-run cosmetic diff are included; final assembly was rerun on both platforms. GitHub CI is separate and not yet claimed green.\n\nReproduce: `E8_REPLAY_PHASES=1 python -B research/e8-target-mixing-whole/verify.py /tmp/target-mix-new`.\n\nThe shared-frame label realization and all inherited compiler, mutable-basis, dirty-helper, idle-data hosting, precision, row-divisor and analytic contracts remain explicit. No unconditional multiplication theorem, Lean proof or κ=1 result is claimed. Larger numbers in PR450/453 additionally rely on cross-copy hosting.\n\nCredits: DreamingOfClouds and Claude for PR450's target-mixing construction/checker; the PR451/443–445, PR440/441, DaysSky PR442, icekylinx PR433 and inherited authors. Frozen reconstruction, label checks/proof and this composition were prepared by chafreaky with OpenAI Codex assistance. Original notices and licenses are 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0.001274415506145115**, **0.03005550944143967% above #458**. This composes #458's paid-adapter complex supplier with #459's rank151 target-mixed bit supplier, both unchanged and source-pinned. The bit side binds.\n\nSubmitted as a **draft before full supplier replay**, as requested. Both exact rational moment engines and the new six-level outer assembly already pass, including all47 strict inequalities, adjacent-grid rejection and invalid-parameter controls. This screen uses the pinned published supplier results; it is not a claim that the full parent wrappers have been freshly rerun. Full local verification has now passed on Python 3.11.15 and 3.14.8; GitHub CI is separate and is not claimed passed.\n\n- Complex: `1297203880559577927527/10^24`, from #458 at `66f35b78d6fa32b2fea08765c2d6ae85e1c72fc3`.\n- Bit: `638020856745638414351/(5*10^23)`, from #459 at `e037bc50c3d5efc1bec0d258a9f274f79ba45ec7`.\n- The seven shared upstream package inventories match exactly. Neither local word, geometry, ownership assignment nor supplier invoice is changed.\n- #458's explicit two-sided monomial corrections, one-helper-per-family-per-invocation rule and788480 paid wrapper groups are retained. No cross-family residual split is used.\n- #459's155-bit prefix charge,520-bit three-level coefficient and complete19431 row coefficient remain; the complex20161 row contract is retained.\n\nReproduce: `python -B research/complex-kernel-mixed151/verify.py /absolute/new/output`. The default runs both original full supplier wrappers, rechecks exact endpoints and combined assembly, and binds both fresh receipts. The screen and fresh-full modes have distinct status fields. Source hashes, original notices, a proof of composition and Python3.11/3.14 CI are included.\n\nAll inherited compiler, target-label/mutable-basis, correlated-helper, restored-work, compressed-window, common-grid/tape, precision, row-divisor and analytic assumptions remain. This is a conditional composition, not an unconditional multiplication theorem or new Lean proof. The underlying target-label and paid-adapter arguments remain review points as in their source PRs.\n\nCredits: chafreaky with OpenAI Codex for #458's paid-adapter complex construction; Rohan Arun with Claude Opus5.5 for #459's bit supplier; DreamingOfClouds for #449/#450 kernel and mixing work; DaysSky, icekylinx, eumemic, Zhihao Chen, Dylan Crow, Jacob Sussman, Henry Grant and the inherited source-pinned authors. Composition and combined verifier by Rohan Arun with OpenAI Codex assistance. No independent discovery of either supplier is claimed.\n\nVerification update: the initial full Python3.11 replay passed the complete PR454 chain, then stopped at PR458's absolute-tolerance comparison of inherited floating-point discovery metadata (gain estimate difference2.09e-12). A documented external runner normalizes only those two non-proof fields in a generated reconstruction input; pinned sources and all exact checks remain unchanged. The exact kernel reconstruction then passes. Failure and targeted repair evidence are retained; the repaired full replay now passes on both Python 3.11.15 and 3.14.8. Receipts, supplier receipt hashes and stage logs are in `research/complex-kernel-mixed151-validation/python311-full/` and `python314-full/`. 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Pool four replicas of #459's unchanged bit word when assigning whole helper residuals to idle data families; retain #458's complex supplier unchanged. The bit side binds.\n\nSubmitted first as a draft before full replay. **The default full Python3.14.8 replay has now passed**, including the repaired full PR460 supplier chain and every changed pooling check. Receipts are published in research/bit-whole-pool4-validation/python314-full. GitHub CI remains separate.\n\nEach of the32,560 residual occurrences stays whole on one physical family. The owner may be in another replica, and every owner remains idle throughout the required window. There are no split residuals or helper banks. Four replicas use4,800 live /4,809 physical families. The exact bit endpoint is `1276121381468881130487/10^24`. Eight and sixteen pooled replicas reached the same normalized endpoint in the scoped screen; this is not a global optimality claim.\n\nThe ownership change requires a new register-growth bound. The emitted physical-family chronology and a separate audit give a529-bit cancellation-free prefix, charged576bits. The three-level coefficient takes1640bits, charged1664bits in the bootstrap cutoffs. The previous192/1024-bit charges are not reused. Two extra routing factors per helper selector are charged. The complete row coefficient is19428, below the retained20161 contract.\n\nPassed changed checks: official unchanged-word records/columns; all9,340 unbanked scalar columns;1,320 geometry routes;18 residual isometries;3,407 exact nested/reflected projector pairs; all owners, idle windows and remainder children;860,464 emitted events;24 omitted-bridge controls;22 ownership mutations; independently recomputed physical-family prefix; both exact moment engines; fresh bit invoice; six bootstrap steps and all47 strict outer inequalities plus controls. The complex supplier is initially cited from pinned #458 evidence.\n\nReproduce: `python -B research/bit-whole-pool4/verify.py /absolute/new/output`. Default runs the full #460 composition before the changed checks. Explicit `--parent-output` reuse of a completed full parent emits a distinct receipt status. Source pins, proof, receipts and Python3.11/3.14 CI are included.\n\nThe whole-call correlated-hosting, compiler, mutable-basis/target-label, compressed-window, restored-work, common-grid/tape, precision, row and analytic assumptions remain. No unconditional theorem, new Lean proof or cross-family splitting claim is made.\n\nCredits: Rohan Arun with Claude Opus5.5 for #459's bit word; chafreaky with OpenAI Codex for #458's complex supplier and inherited audits; DaysSky for hosting; DreamingOfClouds for target mixing and solver extensions; icekylinx, eumemic, Zhihao Chen, Dylan Crow, Jacob Sussman, Henry Grant and all inherited authors. Four-replica selection, physical-prefix audit and composition by Rohan Arun with OpenAI Codex. Licenses and notices retained.\n\nVerification update: the original PR460 full run stopped at PR458's non-proof discovery-float metadata comparison after its full PR454 chain passed. This draft now pins PR460's documented metadata-only portability repair; no pinned operator or exact check is changed. The exact kernel reconstruction passes with that normalization. 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Summary\n- Certifies the outer assembly that PR 463 left open. 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κ = 0.001266536148630309: rank151 kernel + target-prefix mixing on #451, complex-bound (+0.0477%)","user":{"login":"rohanarun","id":11659839,"node_id":"MDQ6VXNlcjExNjU5ODM5","avatar_url":"https://avatars.githubusercontent.com/u/11659839?v=4","gravatar_id":"","url":"https://api.github.com/users/rohanarun","html_url":"https://github.com/rohanarun","followers_url":"https://api.github.com/users/rohanarun/followers","following_url":"https://api.github.com/users/rohanarun/following{/other_user}","gists_url":"https://api.github.com/users/rohanarun/gists{/gist_id}","starred_url":"https://api.github.com/users/rohanarun/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/rohanarun/subscriptions","organizations_url":"https://api.github.com/users/rohanarun/orgs","repos_url":"https://api.github.com/users/rohanarun/repos","events_url":"https://api.github.com/users/rohanarun/events{/privacy}","received_events_url":"https://api.github.com/users/rohanarun/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"Conditional **κ = 1266536148630309 / 10¹⁸ = 0.001266536148630309**, **0.0477% above #451** (0.001265931727546219) and 0.0179% above our kernel-only #457 (0.001266309796182835). **The complex side now binds**: the bit endpoint rises to c ≈ 1.276041713·10⁻³, against the unchanged complex b = 0.001268142296690675.\n\nThere are two bit-side changes on #451's dual eleven-stage, fully hosted construction. Everything else is #451's code.\n\n1. **The rank151 response kernel of #457:** 123 pivots, entrance rank 151, 120 donor slots, followed by #441's 112 pair and 42 window B retimings.\n2. **#450's target-prefix mixing (DreamingOfClouds), applied verbatim** (`code/mix_target.py`) to that word:\n - 46 receivers: 42 at dimension 6, 4 at dimension 5;\n - frame-0 preconditioners and scatter corrections;\n - helpers, sources, starts, finals and the A/C phases are unchanged. The kernel, the 18 residual isometries and the full #442 hosting of all 65,120 helper occurrences (no banks) therefore carry over.\n\nUnder full hosting the mixing's local-child savings lift the bit supplier about 8.1·10⁻⁶ above #457, so the cap is now #451's complex supplier. Further gains need the complex side.\n\nBit profile: `{1:218104, 2:94096, 3:23360, 4:31096, 5:8632, 6:5632, 7:5104, 8:792, 28:8, 56:456}`.\n\n**Review point:** #450's bit-label conjugation lemma, which allows a target as an addition operand at a common frame. Every inherited checker accepts and replays the mixed word:\n- e8core F₂ replay of all 980 columns;\n- official C++ legality, columns_h and columns_k4;\n- record mutations and positive Gram;\n- the emitted local-stream replay and all 9,340 global scalar columns;\n- the independent audit (22 mutations).\n\nComplex phases, emit and audit (19 mutations) and the exact assembly (47 strict inequalities and controls) all pass. `assemble.py` drops only its bit-binding assertion and reports the binding side.\n\n**Status:**\n- **Passed locally** (Linux, Python 3.13): every step after the #445 parent replay, which was reused from the identical-parent run of #457.\n- **Running:** a clean uninterrupted full `verify.py`. The result will be posted as a comment.\n- **CI:** not claimed.\n\n```sh\npython -m pip install -r research/e8-r740-replica32/parent436/requirements.txt\npython -B research/r740-hosted-rank151-mixed/verify.py /absolute/new/output\n```\n\nAll inherited conditional interfaces remain:\n- #442 idle-data hosting;\n- the all-size compiler;\n- mutable basis;\n- correlated dirty helpers;\n- compressed windows;\n- restored work;\n- tape/common grid;\n- precision;\n- row divisor;\n- analytic transfer.\n\nNo unconditional theorem is claimed. Cross-copy hosting (#448/#450) is **not** used.\n\n**Credits:**\n- DreamingOfClouds (#450): target-prefix mixing and its lemma.\n- chafreaky: #451 package, #443–#445, #417 kernel lineage.\n- eumemic: #436/#440/#441.\n- DaysSky: #442.\n- icekylinx: #433.\n- Zhihao Chen: #377/#386/#425.\n- Henry Grant: #234.\n- All retained parent authors.\n\nKernel search, composition and packaging by Rohan Arun with Claude Opus 5.5 (Anthropic).\n\n🤖 Generated with [Claude 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κ = 0.001265931727546219: dual eleven-stage whole-residual hosting","user":{"login":"chafreaky","id":4400527,"node_id":"MDQ6VXNlcjQ0MDA1Mjc=","avatar_url":"https://avatars.githubusercontent.com/u/4400527?v=4","gravatar_id":"","url":"https://api.github.com/users/chafreaky","html_url":"https://github.com/chafreaky","followers_url":"https://api.github.com/users/chafreaky/followers","following_url":"https://api.github.com/users/chafreaky/following{/other_user}","gists_url":"https://api.github.com/users/chafreaky/gists{/gist_id}","starred_url":"https://api.github.com/users/chafreaky/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/chafreaky/subscriptions","organizations_url":"https://api.github.com/users/chafreaky/orgs","repos_url":"https://api.github.com/users/chafreaky/repos","events_url":"https://api.github.com/users/chafreaky/events{/privacy}","received_events_url":"https://api.github.com/users/chafreaky/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"Conditional **κ = 1265931727546219 / 10¹⁸ = 0.001265931727546219**, **0.00655% above #447** at `d3cf3079091bb7e93a23e9cd98e82ccb89697328` and **0.2031% above #445**, using the retained PR442 whole-residual hosting interface. The bit supplier binds: **c = 0.001267536342017397153864**, with freshly rebuilt complex **b = 0.001268142296690675**.\n\nThe R740 bit kernel now has 121 pivots, entrance rank149, 114 donor slots and 18 explicit residual isometries. The unchanged PR433 complex local word moves to eleven compressed stages in dimension89. Both suppliers use eight replicas and 9,600 live families, with every helper residual hosted whole: 65,120 bit occurrences and 49,280 complex occurrences. There are no helper banks or padding children.\n\nThe new complex row argument keeps the existing **20,161** allowance. The coarse three-level estimate is 21,948 and fails. Instead, `89^9 > 16*64^9` gives depth at most `(9/4)log2(e)+9`; the full row charge is `(76005/4)log2(e)+35361`, strictly below `20161 log2(e)` for `log2(e) >= 32`. Smaller widths use retained finite leaves. No larger external row contract is assumed.\n\n**Passed before submission:** full Linux/Python3.12.3 wrapper; macOS/Python3.14.8 quick wrapper; both with `E8_REPLAY_PHASES=1`, regenerating all 2,918 inherited local Clifford edges. Their exact results, deterministic template hashes and instruction digests agree. New checks include official C++ records, integer source spans, 3,366 nested/reflected bit projector pairs, 1,320 routes per supplier, 8,520 exact complex phase equalities, complete hosted ownership, 22 bit and 19 complex mutations, and all 24 omitted bridge shears on each side. Both rational moment engines, both finite invoices, six bootstrap levels and all 47 strict outer inequalities pass. `make verify-joint` passes all 16 controls. All 262 parent-file pins are unchanged. Receipts are in `research/r740-hosted-rank149-validation/`. CI remains pending separately.\n\n**Regarding #448:** its higher claim introduces cross-family splitting. This PR includes a reproducible, scoped review in `research/cross-family-residual-obstruction/`. Same-family factorization does not justify assigning factors to separate families by a coordinate permutation: for q=3, m=2, a=b=1, `D_(a+b) ⊕ I` has trace90 while `D_a ⊕ D_b` has trace54. The exact complex analogue has traces `4+2i` and `4+4i`. General formulas and the proposed rank-eight/rank-nine cases are checked. This obstructs the stated single-residual routing derivation; it does not rule out a different, fully charged compiler or global regrouping theorem. The new certificate here retains whole-residual ownership.\n\nReproduce:\n\n```sh\npython -m pip install -r research/e8-r740-replica32/parent436/requirements.txt\nE8_REPLAY_PHASES=1 python -B research/r740-hosted-rank149/verify.py /absolute/new/output\npython -B research/cross-family-residual-obstruction/verify.py\n```\n\nThe conditional all-size compiler, mutable-basis, correlated dirty-helper, compressed-window, restored-work, tape/common-grid, precision, row-divisor, PR442 hosting and analytic interfaces remain explicit. No unconditional multiplication theorem, κ=1 result, new Lean proof or earlier-assumption record is claimed.\n\nPrepared by chafreaky with substantial OpenAI Codex assistance. Retained credits and exact source pins cover Zhihao Chen #377/#386, icekylinx #433, DaysSky #442, eumemic #436/#440/#441, Henry Grant #234, the prior response-kernel lineage, and all parent notices. #447 is a comparison point; #448 is the independently reviewed proposal, credited to Sreekanth Nair with Anthropic Claude 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kappa = 0.001274032592088050: sharper bit bad-class charge on #458","user":{"login":"Srikrishnabalaji","id":152232940,"node_id":"U_kgDOCRLj7A","avatar_url":"https://avatars.githubusercontent.com/u/152232940?v=4","gravatar_id":"","url":"https://api.github.com/users/Srikrishnabalaji","html_url":"https://github.com/Srikrishnabalaji","followers_url":"https://api.github.com/users/Srikrishnabalaji/followers","following_url":"https://api.github.com/users/Srikrishnabalaji/following{/other_user}","gists_url":"https://api.github.com/users/Srikrishnabalaji/gists{/gist_id}","starred_url":"https://api.github.com/users/Srikrishnabalaji/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/Srikrishnabalaji/subscriptions","organizations_url":"https://api.github.com/users/Srikrishnabalaji/orgs","repos_url":"https://api.github.com/users/Srikrishnabalaji/repos","events_url":"https://api.github.com/users/Srikrishnabalaji/events{/privacy}","received_events_url":"https://api.github.com/users/Srikrishnabalaji/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"## Summary\n- Reprices the binding bit moment of #458. The bit histogram, the complex root, and the six-level balanced assembly stay as published there.\n- The source theorem charges each bad edge at most `(2 m^3 / 2^80) * (6 N (N - 1) + 3 N + 6 (N - 1))` rank-one children, with `N = 2 m`. At `m = 78` that is strictly below the round `10^-16 * 32 m^2` envelope.\n- Replaying the inherited envelope reproduces #458's kappa `1274032589159993/10^18`. The sharp charge gives kappa `25480651841761/20000000000000000` (`0.001274032592088050`), a gain of `2928057/10^18`. The assembly remains bit-bound. Both moment engines certify the new root, all 47 outer inequalities hold, and the next `10^-18` grid point is rejected.\n- No residual is split across families.\n\n## Test plan\n- [ ] `python research/sharp-bit-bad-fraction/prove.py` prints `PASS` and the kappa above\n- [ ] The cited complex root from #458 stays strictly above the new bit root\n- [ ] The diff does not import the cross-family residual split\n","created_at":"2026-10-11T16:50:06Z","updated_at":"2026-10-11T16:50:06Z","closed_at":null,"merged_at":null,"merge_commit_sha":"ebb2f6e94c3a40bc4053dd1952af3e352080ae38","assignees":[],"requested_reviewers":[],"requested_teams":[],"labels":[],"milestone":null,"draft":false,"commits_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/pulls/461/commits","review_comments_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/pulls/461/comments","review_comment_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/pulls/comments{/number}","comments_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/issues/461/comments","statuses_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/statuses/dc297912ad446779f983818816617c03dfc76e16","head":{"label":"Srikrishnabalaji:research/sharp-bit-bad-fraction","ref":"research/sharp-bit-bad-fraction","sha":"dc297912ad446779f983818816617c03dfc76e16","user":{"login":"Srikrishnabalaji","id":152232940,"node_id":"U_kgDOCRLj7A","avatar_url":"https://avatars.githubusercontent.com/u/152232940?v=4","gravatar_id":"","url":"https://api.github.com/users/Srikrishnabalaji","html_url":"https://github.com/Srikrishnabalaji","followers_url":"https://api.github.com/users/Srikrishnabalaji/followers","following_url":"https://api.github.com/users/Srikrishnabalaji/following{/other_user}","gists_url":"https://api.github.com/users/Srikrishnabalaji/gists{/gist_id}","starred_url":"https://api.github.com/users/Srikrishnabalaji/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/Srikrishnabalaji/subscriptions","organizations_url":"https://api.github.com/users/Srikrishnabalaji/orgs","repos_url":"https://api.github.com/users/Srikrishnabalaji/repos","events_url":"https://api.github.com/users/Srikrishnabalaji/events{/privacy}","received_events_url":"https://api.github.com/users/Srikrishnabalaji/received_events","type":"User","user_view_type":"public","site_admin":false},"repo":{"id":1413960891,"node_id":"R_kgDOVEdUuw","name":"integer-mult-bounds","full_name":"Srikrishnabalaji/integer-mult-bounds","private":false,"owner":{"login":"Srikrishnabalaji","id":152232940,"node_id":"U_kgDOCRLj7A","avatar_url":"https://avatars.githubusercontent.com/u/152232940?v=4","gravatar_id":"","url":"https://api.github.com/users/Srikrishnabalaji","html_url":"https://github.com/Srikrishnabalaji","followers_url":"https://api.github.com/users/Srikrishnabalaji/followers","following_url":"https://api.github.com/users/Srikrishnabalaji/following{/other_user}","gists_url":"https://api.github.com/users/Srikrishnabalaji/gists{/gist_id}","starred_url":"https://api.github.com/users/Srikrishnabalaji/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/Srikrishnabalaji/subscriptions","organizations_url":"https://api.github.com/users/Srikrishnabalaji/orgs","repos_url":"https://api.github.com/users/Srikrishnabalaji/repos","events_url":"https://api.github.com/users/Srikrishnabalaji/events{/privacy}","received_events_url":"https://api.github.com/users/Srikrishnabalaji/received_events","type":"User","user_view_type":"public","site_admin":false},"html_url":"https://github.com/Srikrishnabalaji/integer-mult-bounds","description":"Conditional integer multiplication: kappa > 2^-15. 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κ = 0.001266309796182835: rank151 bit kernel on #451's dual eleven-stage hosting (+0.0299%)","user":{"login":"rohanarun","id":11659839,"node_id":"MDQ6VXNlcjExNjU5ODM5","avatar_url":"https://avatars.githubusercontent.com/u/11659839?v=4","gravatar_id":"","url":"https://api.github.com/users/rohanarun","html_url":"https://github.com/rohanarun","followers_url":"https://api.github.com/users/rohanarun/followers","following_url":"https://api.github.com/users/rohanarun/following{/other_user}","gists_url":"https://api.github.com/users/rohanarun/gists{/gist_id}","starred_url":"https://api.github.com/users/rohanarun/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/rohanarun/subscriptions","organizations_url":"https://api.github.com/users/rohanarun/orgs","repos_url":"https://api.github.com/users/rohanarun/repos","events_url":"https://api.github.com/users/rohanarun/events{/privacy}","received_events_url":"https://api.github.com/users/rohanarun/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"Conditional **κ = 253261959236567 / (2·10¹⁷) = 0.001266309796182835**, **0.0299% above #451** (0.001265931727546219 at `f3a38153`) and 0.0364% above #447. Bit binds: **c = 0.001267915369836389691636** (#451: 0.001267536342017397); the unchanged complex endpoint is b = 0.001268142296690675.\n\n**One change: a larger bit response kernel on #451's construction.** With every helper residual hosted on idle coordinates (no banks), one unit of entrance rank is worth ≈4.4·10⁻⁷ of bit saving, and an extra donor slot costs one local child per invocation (≈0.9·10⁻⁷). A hosting-aware search over donor sets, with closed entrances drawn from intersections of first frames, finds two more pivots on #451's own 57-retimed primitive R740 word:\n\n- 123 pivots, entrance rank **151** (#451: 121 / 149), 120 donor slots;\n- #441's 112 pair and 42 window B retimings apply unchanged afterwards. The full e8core replay (legality, F₂ on all columns, source spans) passes;\n- 18 regenerated explicit residual isometries. A re-solved #442 selection still hosts all 65,120 helper occurrences, with no banks and no padding.\n\nEverything else is #451's code, byte for byte: the eleven-stage geometry (m = 78), three-level halving (max child 56), row bound 19,431 < 20,161, the complex supplier, both moment engines, the invoices and the 47-inequality outer assembly. The new package `research/r740-hosted-rank151/` is a copy of #451's `r740-hosted-rank149` with only the kernel, word, hosting selection, isometries, expected values and kernel constants changed.\n\nBit profile: `{1:224264, 2:93744, 3:23712, 4:33912, 5:9512, 6:1936, 7:5104, 8:792, 28:8, 56:456}`.\n\n**Status:** the complete #445 parent replay, rebuild, official C++ legality/columns/k4, record mutations, positive Gram, geometry, emit, independent audit (22 mutations), complex phases/emit/audit (19 mutations) and exact assembly all pass locally (Linux, Python 3.13). A clean full uninterrupted `verify.py` run is in progress and will be posted as a comment. CI is not claimed.\n\n```sh\npython -m pip install -r research/e8-r740-replica32/parent436/requirements.txt\npython -B research/r740-hosted-rank151/verify.py /absolute/new/output\n```\n\nAll inherited conditional interfaces stay explicit: #442 idle-data hosting, the all-size compiler, mutable basis, correlated dirty helpers, compressed windows, restored work, tape/common grid, precision, row divisor and analytic transfer. No unconditional theorem is claimed.\n\nCredits: chafreaky (#451 package, #443–#445, #417 kernel lineage), eumemic (#436/#440/#441), DaysSky (#442), icekylinx (#433), Zhihao Chen (#377/#386), Henry Grant (#234) and all retained parent authors. Kernel search and repackaging by Rohan Arun with Claude Opus 5.5 (Anthropic).\n\n🤖 Generated with [Claude 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κ = 0.001266564732900111: seven-replica whole-residual hosting","user":{"login":"rohanarun","id":11659839,"node_id":"MDQ6VXNlcjExNjU5ODM5","avatar_url":"https://avatars.githubusercontent.com/u/11659839?v=4","gravatar_id":"","url":"https://api.github.com/users/rohanarun","html_url":"https://github.com/rohanarun","followers_url":"https://api.github.com/users/rohanarun/followers","following_url":"https://api.github.com/users/rohanarun/following{/other_user}","gists_url":"https://api.github.com/users/rohanarun/gists{/gist_id}","starred_url":"https://api.github.com/users/rohanarun/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/rohanarun/subscriptions","organizations_url":"https://api.github.com/users/rohanarun/orgs","repos_url":"https://api.github.com/users/rohanarun/repos","events_url":"https://api.github.com/users/rohanarun/events{/privacy}","received_events_url":"https://api.github.com/users/rohanarun/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"Conditional candidate **κ = 0.001266564732900111**, **0.0022568854297536104% above PR454** at `d14eb0dd425bd681e3b43f208d089e679d600176`. Complex binds. Submitted as a draft before the full replay, as requested; full local verification has now passed; GitHub CI remains queued.\n\nPool seven replicas of PR454's eleven-stage complex supplier to remove an integer packing remainder. Every one of the43,120 rank9 helper residuals remains whole on a single physical family;35,840 use an owner in another replica. The local word, all phases and the bit supplier are unchanged. Complex lower is `634085476752554528491/500000000000000000000000`, with8,400live/8,978physical families.\n\nThis does **not** use PR448's cross-family residual split. I reproduced PR451's trace obstruction and corrected our PR453's title/body to withdraw its established-gain claim. The previous pooled56 score is affected too. Here whole-family relocation is an ordinary family permutation followed by the owner's coordinate basis; the proof explicitly retains PR442's complete-call correlated dirty-helper contract and allows the owner replica to differ. The invoice charges an additional family-routing factor.\n\nChanged-component checks passed: all43,120owners and idle remainders;1,913,989emitted events;8,520exact phase equalities;1,320routes;24omitted-bridge controls;19mutations; exact whole-family physical routing controls that reject splitting; both rational moment engines; fresh complex invoice; six bootstrap steps and all47strict outer inequalities with next-grid and parameter controls. The one-replica screen exactly reproduces PR454. Larger13/15/17stage screens were worse.\n\nThe early component invoice cites the pinned, unchanged PR454 bit supplier; it is not a fresh full-parent receipt. A fresh full PR454 chain has since passed locally. Initial attempts exposed PR436's unquoted paths and a missing NumPy dependency; failures are retained. The package includes a documented external shell adapter for SSD paths containing spaces, with pinned source files unchanged.\n\nReproduce: `python -B research/e8-whole-replica7/verify.py /absolute/new/output`. Default runs the fullPR454 chain with phase regeneration. `--parent-output` explicitly reuses an existing full receipt and emits a distinct component-reuse status. See `research/e8-whole-replica7/PROOF.md` for the argument and scope.\n\nAll inherited compiler, restored-work, compressed-window, tape/common-grid, precision, row and analytic assumptions remain. No unconditional multiplication theorem or Lean proof is claimed.\n\nCredits: chafreaky with OpenAI Codex assistance (PR451/454 templates, audits, source pins and cross-family obstruction); DaysSky (PR442 hosting), icekylinx (PR433), Zhihao Chen and all inherited contributors. Seven-replica selection/composition by Rohan Arun with OpenAI Codex assistance. Licenses, notices and source pins retained. This branch starts from the pinnedPR454 head so its unchanged supplier packages remain directly reproducible.\n\nConcurrent work: [PR455](https://github.com/CrocSwap/integer-mult-bounds/pull/455), read after this submission, independently uses whole-residual pooling with eight replicas and a bit-program portfolio. Its reportedκ0.001266541949425315 is below this seven-replica candidate by 0.001798872%. No exclusive discovery or priority claim is made. A tighter solver follow-up gives the same normalized endpoint at7,14,21,35and56replicas; these are scoped searches, not a global optimality theorem.\n\nVerification update: the fresh completePR454supplier chain now PASSes locally onPython3.11.15. The publishedPR456wrapper then PASSed all changed checks against that completed parent, with the explicit `PASS_WHOLE_REPLICA7_COMPONENT_PARENT_REUSED` receipt. Both receipts and logs are published separately in the validation directory. The fresh full Python 3.14.8 wrapper also PASSed (PASS_FULL_WHOLE_REPLICA7), including the complete parent chain and regenerated phases. Its receipt and all step logs are published in the validation directory; CI remains queued and separate. The proof package is 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whole-residual replica pooling and program portfolios, conditional kappa = 0.001266541949425315","user":{"login":"Dugongue","id":49054532,"node_id":"MDQ6VXNlcjQ5MDU0NTMy","avatar_url":"https://avatars.githubusercontent.com/u/49054532?v=4","gravatar_id":"","url":"https://api.github.com/users/Dugongue","html_url":"https://github.com/Dugongue","followers_url":"https://api.github.com/users/Dugongue/followers","following_url":"https://api.github.com/users/Dugongue/following{/other_user}","gists_url":"https://api.github.com/users/Dugongue/gists{/gist_id}","starred_url":"https://api.github.com/users/Dugongue/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/Dugongue/subscriptions","organizations_url":"https://api.github.com/users/Dugongue/orgs","repos_url":"https://api.github.com/users/Dugongue/repos","events_url":"https://api.github.com/users/Dugongue/events{/privacy}","received_events_url":"https://api.github.com/users/Dugongue/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"## Result and comparison\n\nThis adds `research/e8-whole-pool-portfolio`, a reproducible conditional construction with\n\n$$T(n)=O(n(\\log n)^{1-\\kappa}),\\qquad\n\\kappa=\\frac{253308389885063}{200000000000000000}=0.001266541949425315.$$\n\nThat is **+0.04820338% over #451** (`0.001265931727546219`). The complex supplier binds.\nThis is a conditional finite artifact, not an unconditional multiplication theorem or Lean certificate.\nIt does **not** claim to beat #453's higher posted number: #451 supplies a trace obstruction to the\ncross-family splitting derivation used there. This construction keeps every residual in one whole family.\n\n## Two construction mechanisms\n\n1. **Whole-residual pooling across replicas.** Allocate the eight replicas jointly rather than solve\n identical per-replica integer packing problems. Every helper stays on one physical array family,\n with a complete slot isometry, a disjoint orthogonal block, and its checked idle window. Both actual\n family and absolute coordinate identities are audited. Complex delta relative to the selected #451\n idle inventory is `{1:-2,7:+8,16:-8,55:+6,64:-4}`. Rank mass stays unchanged; the moment improves.\n2. **Invocation-specific complete-program portfolio.** Five reverse calls at stage 5, replicas 0..4,\n use a fully checked rank147 provider; the other 83 use rank149. Each variant adds two residual\n coordinates and changes its local profile by `{1:-2,4:-4,5:+4}`. Whole-owner pooling pays those ten\n additional coordinates by changing a remaining rank52 child to rank42. The full difference from\n uniform pooled rank149 is `{1:-10,4:-20,5:+20,52:-1,42:+1}`. This improves bit-side reserve; it gives\n no further final-kappa increase while the complex supplier binds.\n\nThese use whole-slot reindexing/orthogonal-idempotent composition and equal complete-map substitution,\nrespectively. Structural sources include Mathlib's block-diagonal multiplication and the project's\nMUB projection-factor identities. They are sources of mathematical analogies, not Lean certificates\nfor this artifact. #450 target mixing and two historical partial-prefix recoveries are also used,\nbut are explicitly credited as prior techniques rather than presented as additional new mechanisms.\n\n## Exact invoice\n\n| Supplier | Window | Live | Physical | Rank mass | Deficit | Maximum child |\n|---|---:|---:|---:|---:|---:|---:|\n| Bit | 78 | 9600 | 9609 | 745536 | 3264 | 56 |\n| Complex | 89 | 9600 | 10178 | 851136 | 3264 | 64 |\n\nBit profile: `{1:217742,2:93314,3:23976,4:30912,5:8732,6:5752,7:5168,8:792,42:1,56:444}`.\nComplex profile: `{1:170358,2:68992,3:18624,4:19712,5:38336,7:3840,8:9792,55:6,64:1732}`.\nBoth actual profiles are priced together. Independent proposed gains are never added.\n\nThe coefficient bound charges all 88 chronological calls and all bridges, even with foreign-replica\nhosting. Route-extra3 and 100,000 finite dispatch operations are charged. The bit row cover is19,431;\nthe retained complex fractional-depth row reserve is20,161 with its explicit cutoff condition.\nBoth exact moment engines, six bootstrap levels, and all47 strict outer inequalities are used.\n\n## Reproduction and validation\n\n```sh\npython -B research/e8-whole-pool-portfolio/verify.py /absolute/path/to/new-output-directory\n```\n\nRequires Python3.11+, SymPy, a C++17 compiler and Boost headers; set `CXX`/`BOOST_INCLUDE` if needed.\nNo network, optimizer, SciPy, prebuilt binaries, or Lean installation is required. Assertions must be enabled.\n\nFresh validation reconstructs both complete local providers, all980 dirty columns each, eleven-stage\norientation checks, exact Gram/prime witnesses, and all74,720 columns of the heterogeneous unbanked\ncontroller. It checks65,120 whole bit helpers and49,280 whole complex helpers, physical-axis collisions,\nphase recipes, emitted instruction digests,19 bit routing mutants and10 complex routing mutants.\nThe exact final profiles/templates match the frozen expected invoice. See `VALIDATION.json` and\n`REPLAY-MANIFEST.json` for the source-bound replay; `MANIFEST.json` covers final upload contents.\nUnchanged public verification chains were not redundantly rerun: inherited complex Clifford evidence\nis explicitly retained with its source bindings.\n\nAll-size compiler, arbitrary-correlated dirty hosting, target-label, compressed-window, restored-work,\ncommon-grid/tape, precision, and analytic contracts remain inherited assumptions. Finite controls do\nnot prove these contracts. No global packing optimality or literature-wide priority claim is made.\n\n## Sources, rejected routes, and future work\n\nDirect sources and inspirations include #451 (rank149 whole-host baseline, row bound and trace review),\n#450 (target mixing only), #445/#447 (eleven-stage schedules), #443/#439/#417 (response kernels and\nresidual isometries), #442 (whole idle-family hosting), #433 (complex split-centre/source-basis work),\n#425/#386/#370 (mutable basis, geometry and producer), #401/#404 (shared donors/prefix recovery),\nand #315's rational outer-assembly lineage. #453 supplied a useful source collection/local comparison;\nits split-based price and #448's disputed splitting step are not used. #452 was reviewed but not used.\nExact head pins and licenses are in `PROVENANCE.md`, source headers, and `notices/`.\n\n`RESEARCH.md` preserves the actual discoveries, bounded searches, library analogies, rejected coordinate\nsplitting attempt, and future routes. Early placement checks on the split attempt did not establish an\noperator identity; those larger prices are expressly withdrawn. Product-coordinate factorization must\nnot be confused with a direct sum of independent array families. The next useful search variables are\nlarger whole-owner pools and independently correct complex-program portfolios, always with actual\noperator semantics and a complete shared invoice.\n\nDeveloped with OpenAI assistance. No claim of an independent all-size theorem or exclusive priority.\n","created_at":"2026-10-11T16:11:45Z","updated_at":"2026-10-11T16:11:46Z","closed_at":null,"merged_at":null,"merge_commit_sha":"359f4d99501da3f1bbc69d3dadd4e2f45b7ff8be","assignees":[],"requested_reviewers":[],"requested_teams":[],"labels":[],"milestone":null,"draft":false,"commits_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/pulls/455/commits","review_comments_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/pulls/455/comments","review_comment_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/pulls/comments{/number}","comments_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/issues/455/comments","statuses_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/statuses/f76fc4e36030d4e00b4cbb83b1dbc661a0974c4e","head":{"label":"Dugongue:wp912","ref":"wp912","sha":"f76fc4e36030d4e00b4cbb83b1dbc661a0974c4e","user":{"login":"Dugongue","id":49054532,"node_id":"MDQ6VXNlcjQ5MDU0NTMy","avatar_url":"https://avatars.githubusercontent.com/u/49054532?v=4","gravatar_id":"","url":"https://api.github.com/users/Dugongue","html_url":"https://github.com/Dugongue","followers_url":"https://api.github.com/users/Dugongue/followers","following_url":"https://api.github.com/users/Dugongue/following{/other_user}","gists_url":"https://api.github.com/users/Dugongue/gists{/gist_id}","starred_url":"https://api.github.com/users/Dugongue/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/Dugongue/subscriptions","organizations_url":"https://api.github.com/users/Dugongue/orgs","repos_url":"https://api.github.com/users/Dugongue/repos","events_url":"https://api.github.com/users/Dugongue/events{/privacy}","received_events_url":"https://api.github.com/users/Dugongue/received_events","type":"User","user_view_type":"public","site_admin":false},"repo":{"id":1411510763,"node_id":"R_kgDOVCHx6w","name":"integer-mult-bounds","full_name":"Dugongue/integer-mult-bounds","private":false,"owner":{"login":"Dugongue","id":49054532,"node_id":"MDQ6VXNlcjQ5MDU0NTMy","avatar_url":"https://avatars.githubusercontent.com/u/49054532?v=4","gravatar_id":"","url":"https://api.github.com/users/Dugongue","html_url":"https://github.com/Dugongue","followers_url":"https://api.github.com/users/Dugongue/followers","following_url":"https://api.github.com/users/Dugongue/following{/other_user}","gists_url":"https://api.github.com/users/Dugongue/gists{/gist_id}","starred_url":"https://api.github.com/users/Dugongue/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/Dugongue/subscriptions","organizations_url":"https://api.github.com/users/Dugongue/orgs","repos_url":"https://api.github.com/users/Dugongue/repos","events_url":"https://api.github.com/users/Dugongue/events{/privacy}","received_events_url":"https://api.github.com/users/Dugongue/received_events","type":"User","user_view_type":"public","site_admin":false},"html_url":"https://github.com/Dugongue/integer-mult-bounds","description":"Conditional integer multiplication: kappa > 2^-15. 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review: rank137 cross-copy candidate; inherited operator obstruction","user":{"login":"rohanarun","id":11659839,"node_id":"MDQ6VXNlcjExNjU5ODM5","avatar_url":"https://avatars.githubusercontent.com/u/11659839?v=4","gravatar_id":"","url":"https://api.github.com/users/rohanarun","html_url":"https://github.com/rohanarun","followers_url":"https://api.github.com/users/rohanarun/followers","following_url":"https://api.github.com/users/rohanarun/following{/other_user}","gists_url":"https://api.github.com/users/rohanarun/gists{/gist_id}","starred_url":"https://api.github.com/users/rohanarun/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/rohanarun/subscriptions","organizations_url":"https://api.github.com/users/rohanarun/orgs","repos_url":"https://api.github.com/users/rohanarun/repos","events_url":"https://api.github.com/users/rohanarun/events{/privacy}","received_events_url":"https://api.github.com/users/rohanarun/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"**Mathematical status correction (2026-10-11): the claimed gain is not currently established.** I reproduced [PR451's cross-family trace obstruction](https://github.com/CrocSwap/integer-mult-bounds/pull/451) at `f3a38153678b55063fc005901cc968266166507d`. For a rank2 bit residual and an idle second family, the whole operator has trace90 while the proposed rank1/rank1 split has trace54 (q=3,m=2). The complex analogue has traces4+2i and4+4i. This contradicts the elementary coordinate-permutation derivation inherited from PR448, which this PR uses. Our finite packing, local scalar, invoice and full-wrapper checks pass but do not test that physical cross-family operator identity. The numerical κ below is therefore a score under an unresolved, specifically challenged interface, not an established improvement. A different explicitly charged compiler/global regrouping theorem would be required to repair it. The draft and all evidence are retained for review; the newer pooled-replica candidate is affected as well and will not be submitted as a winning bound on this basis.\n\n---\n\n**Submitted as a draft first. Fresh full-wrapper replays have now PASSed on Python3.11.15 and3.14.8, including the complete parent chain, record mutations and Gram checks. Both full results agree exactly. GitHub CI is separate and currently queued.**\n\nConditional candidate **κ = 0.001347781996192312**, bit-bound: **+0.00277860352249% over #450** at `6faca41020a620689de013cdab9f61a22deca314`.\n\nRemove pivot744 from #443's rank138 kernel, apply #450's target mixing, and re-optimize #448 cross-copy hosting. The resulting rank137 selection replaces the rank14 partial idle remainder with rank3. R stays740; all65,120 residuals are hosted with9,600 live families. Our rank147 kernel was worse under this objective; its negative result is retained.\n\nPassed on the changed construction: exact980-column mixed-word replay and four controls; C++ legality and five/eleven-stage columns; exact geometry and parent audit; independent cross-copy audit and20 controls; regenerated #448 complex template matching its pinned hash and five complex controls; both rational moments, fresh invoices, six bootstrap levels and47 strict inequalities with next-grid and parameter controls. Emitted instruction count1,716,352.\n\nThe full verifier is `research/e8-cross-copy-rank137/verify.py`. The initial submission reused the already completed PR447 parent suppliers. The subsequently published `e8-cross-copy-rank137-validation/python311` and `python314` receipts each document a fresh full run of this package and its parent chain. A missing-SymPy launch failure is retained along with the corrected audit.\n\nThis retains #442 idle-data hosting, #448 cross-copy hosting, #450's bit target-label conjugation review point, and all inherited compiler/dirty-helper/precision/analytic assumptions. No unconditional multiplication theorem or Lean proof is claimed. Conservative row allowance28,416 is charged explicitly.\n\nCredits: DreamingOfClouds (#450 target mixing and stage tools), higherbeing (#448 cross-copy hosting), chafreaky (#443–445 kernel and staging), DaysSky, icekylinx, eumemic, Zhihao Chen, Dylan Crow, Jacob Sussman and the inherited authors. Rank137 selection/composition prepared by Rohan Arun with OpenAI Codex assistance; original notices and licenses retained.\n\nPost-submission anchor: the independent rank138 screen exactly reproduced #450 κ0.001347744547714835. The new profile differs per eight-replica group by `{1: -88, 2: -176, 3: +184, 14: -8}`; all other global counts match. A floating MILP over subsets of the123 compatible known relations also nominated the same113-entry rank137 selection; this is a scoped search result, not an exact optimality theorem.\n\nFull tested manifest: `8441fa7b22a19ec4ac31625d0c7c2f9d581b43c970406cc8d85e6f390a82c14d`. After the passes, only README status/wording and its manifest were updated; all executable source, frozen inputs and expected results are unchanged. The exact documentation-only diff is 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κ = 0.001263365464781156: eleven-stage R740 hosting with complete row bound","user":{"login":"chafreaky","id":4400527,"node_id":"MDQ6VXNlcjQ0MDA1Mjc=","avatar_url":"https://avatars.githubusercontent.com/u/4400527?v=4","gravatar_id":"","url":"https://api.github.com/users/chafreaky","html_url":"https://github.com/chafreaky","followers_url":"https://api.github.com/users/chafreaky/followers","following_url":"https://api.github.com/users/chafreaky/following{/other_user}","gists_url":"https://api.github.com/users/chafreaky/gists{/gist_id}","starred_url":"https://api.github.com/users/chafreaky/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/chafreaky/subscriptions","organizations_url":"https://api.github.com/users/chafreaky/orgs","repos_url":"https://api.github.com/users/chafreaky/repos","events_url":"https://api.github.com/users/chafreaky/events{/privacy}","received_events_url":"https://api.github.com/users/chafreaky/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"## Result\n\nConditional **κ = 0.001263365464781156** (`315841366195289 / 250000000000000000`), **1.3877% above PR444**. The bit supplier binds at `1264963576077378514188 / 10^24`; the freshly rebuilt PR442 complex supplier remains `1267453159029119 / 10^18`.\n\nExtend PR443's unchanged R740 rank138 local word to **eleven compressed stages, dimension78 and eight replicas**. PR442 idle-data hosting places every one of the **65,120 helper occurrences** on pending idle coordinates. The emitted program has 88 calls, 9,600 live and 9,609 physical families, no helper banks or padding, and rank deficit 3,264.\n\n## New finite obligations\n\nThe largest child is 56, so two-level halving fails and **three levels** are explicitly checked. The prefix uses 153 bits, charged at 192. The three-level coefficient uses **513 bits**: the old 512-bit cap is rejected and the cutoff charges 1,024 bits.\n\nThe old coarse matrix-count row estimate would exceed the retained 20,161 allowance. A self-contained elementary orthogonal-cover count fixes this: successively choosing nonzero-norm orthogonal basis vectors gives `|O_m(q)| ≤ 2^m q^(m(m−1)/2) < q^(m(m+1)/2)` for odd q. For m=78, including all 9,609 physical families gives stock below `q^3090`; three-level halving plus the inherited 9,909 and 252 reserves gives **19,431 < 20,161**. Routing-time charges still use m². The inherited row-divisor statement and notices are preserved verbatim.\n\n## Verification\n\nFull Linux reconstruction and macOS quick mode pass, with identical exact geometry, operators, profiles, emitted instruction digest, finite invoices and margins; only timing metadata differs. Repository-native `make verify-joint` passes, including 16 tests.\n\nThe wrapper verifies 246 unchanged upstream source files and freshly runs PR444, including the complex phase replay. New checks cover 1,320 port/stage routes, all 9,340 unbanked scalar columns, the signed ten-wire identity, all 24 individually omitted bridge shears, every hosted owner/window/remainder and the complete 1,736,152-instruction digest. The independent audit rejects 22 template corruptions. Both rational moment engines, both finite invoices, six bootstrap levels, 47 strict outer inequalities, adjacent-grid and parameter controls pass. CI runs the full wrapper on Python 3.11 and 3.14.\n\n```sh\npython -m pip install -r research/e8-r740-replica32/parent436/requirements.txt\npython -B research/r740-hosted-eleven/verify.py /tmp/r740-eleven-new\n```\n\n## Scope and attribution\n\nThis retains PR442's conditional idle-data hosting extension and all inherited all-size compiler, correlated dirty-helper, restored-work, common-grid, precision and analytic interfaces. It is not an unconditional multiplication theorem, κ=1 result or new Lean proof.\n\nThe extension, elementary row bound and release integration were prepared by chafreaky with substantial OpenAI Codex assistance. PR386 geometry/global code, PR436/443 local reconstruction, DaysSky's PR442 hosting (Anthropic Claude assistance), PR444 integration and Henry Grant's PR234 row interface are credited in complete retained notices and exact source pins. Earlier contributors and assistance disclosures remain 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obstructions (no new κ): exact bounds on window width, copy cost and label dimension","user":{"login":"DreamingOfClouds","id":173691639,"node_id":"U_kgDOClpS9w","avatar_url":"https://avatars.githubusercontent.com/u/173691639?v=4","gravatar_id":"","url":"https://api.github.com/users/DreamingOfClouds","html_url":"https://github.com/DreamingOfClouds","followers_url":"https://api.github.com/users/DreamingOfClouds/followers","following_url":"https://api.github.com/users/DreamingOfClouds/following{/other_user}","gists_url":"https://api.github.com/users/DreamingOfClouds/gists{/gist_id}","starred_url":"https://api.github.com/users/DreamingOfClouds/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/DreamingOfClouds/subscriptions","organizations_url":"https://api.github.com/users/DreamingOfClouds/orgs","repos_url":"https://api.github.com/users/DreamingOfClouds/repos","events_url":"https://api.github.com/users/DreamingOfClouds/events{/privacy}","received_events_url":"https://api.github.com/users/DreamingOfClouds/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"**Format obstructions (no new κ): exact bounds on window width, copy cost and label dimension, checked on `gx.check1` programs and on #425's mutable-basis word.** This is a research package of statements, proofs and\nexact checks. It claims no new κ. It fixes what three formats can and cannot do and shows where the remaining\nfreedom is.\n\n| | statement | checked on |\n| --- | --- | --- |\n| **A** | a contribution that reaches a register by a drop-free path forces its frame to contain the source label, so lossless x_T → y_S needs orthogonal labels | every gate of the p = 3, p = 10 (#327) and p = 11 (#193) programs: 0 violations in 3.1 M gate checks |\n| **B** | k_a + Σ_j rk C_j ≤ m; with corrector rank h − 1, m ≥ 1 + s(h − 1) | rank h − 1 on all families (replayed correctors for the complex programs and #425; in-cap neighbourhoods for the bit and E8 rows); **#425's word has m = 73 = 1 + 9·8, so the bound is attained** |\n| **C** | the drops that carry a total to its readers cost at least rk(U(P) × U(Q)) | equality: 360 (p = 10), 440 (p = 11), 72 (#425 centres, 57 gathered sources each); for the E8 bit dual the package computes the bound 72, which equals the copy loss #370 reports (not replayed) |\n| clique bound | Σ_K k_T ≤ r on a clique of drop-free pairs | ω = p (bit), 8, 8, 12, 12 (complex, p = 4..7); 20 ports pairwise lossless in the p = 10 program; ω = 8 on E8 |\n| E8 labels | the h = 9 labelling of the E8 in-cap graph is unique; no k = 2 labelling in dimension ≤ 17 | exact SAT, with calibrations and a positive control |\n| **P** | for fixed-role B₂ windows over F₂ (one helper set, same slots, slot-carried pairs spanning) the stage windows are orthogonal, m ≥ s·h, under (P1)–(P2) | computed on the complex #327 and #193 programs only (399/400, 483/484). **Compressed windows circumvent it**: #425 (m = 73 < 81) and, for the bit word, #386 (m = 64; Theorem P is not claimed for ℚ forms). Not a general obstruction |\n| **S** | a mutable-basis word with b_x modified sources and b_y read targets is simulated in the immutable-source / no-target-read format with R + b_x + b_y helpers | exact on #425's word: 904 = 680 + 112 + 112 |\n\n**What this means for the swarm.** A–C and the clique bound bound m and the copy rank, the label dimension for a given\nin-cap graph, and (through the five-stage ledger D ≤ N_data·k, read from upstream) D. They do **not** bound the\nhelper count R, nor the idle and stock costs, which is where #425, #433 and #442 gained. A further κ gain in these\nformats has to come from R or the stock, or from a new port family whose corrector rank is below h − 1 with a cheap\ndecoder.\n\n```sh\npython -m pip install -r research/format-obstructions/requirements.txt # python-sat 1.9.dev15, networkx 3.7, mpmath 1.3.0, numpy 2.3.5\npython3 -B research/format-obstructions/verify.py --output /tmp/format-obstructions-out # about 90 s on 12 cores (15 CPU-minutes), no network\n```\n\n## What changed\n\nOne new self-contained package, `research/format-obstructions/`, plus its path-filtered workflow. No existing file\nchanges. Vendored byte for byte (sha256 in `SOURCE.json`): Jacob Sussman's `gx.py`, the p = 11 certificate of #193, the\np = 10 program of #327, #425's `FULL-WORD.json.gz` (regenerated with its own scripts; the sha equals its\n`EXPECTED.json`), the cost model of #346 (from #310) and the p = 10 bit histogram of #325. The one local input is the\np = 3 toy program.\n\n## What `verify.py` checks\n\nIt verifies the pins, then runs 91 tasks in a process pool and compares every number with `expected.json`:\n- `gx.check1` with the exact scalar identity on the three programs, the taint replay of Theorem A at every gate, the\n corrector ranks of Theorem B and the copy bounds of Theorem C;\n- the p = 3 toy: split scatter, cst 18 → 16, exhaustive optimum over all cut chains;\n- Theorem P (rank of the cross-Gram constraints), the forced-copy count (10 per overlap, exact over all odd a, b) and\n the contamination scan (1,160 candidate directions);\n- #425's word: frame and taint replay, exact scalar replay over ℚ, the Theorem S conversion and its replay;\n- the pinned pricer on the p = 10 bit histogram (pinned root reproduced; context only);\n- the E8 SAT checks: uniqueness at h = 9, k = 2 at r = 16 (255 patterns) and r = 17 (256), all UNSAT.\n\nNegative controls: shifted labels and a corrupted port; a toy cut outside the radical; the immutable/no-target-read\ndetector flags 1,640 source modifications and 112 target reads on #425's word and 0 on the converted word; omitted K\nand omitted compensation rejected; k = 1 at r = 8 UNSAT and r = 9 SAT, h = 8 UNSAT, the k = 2 encoder at r = 18 accepts\nthe direct sum.\n\n## Verification\n\n- **Replays:** two fresh-copy runs in other working directories (macOS, Python 3.12.14, python-sat 1.9.dev15,\n networkx 3.7, mpmath 1.3.0, numpy 2.3.5) pass every check; CI has not been run yet.\n- **Independent audit:** Independent read-only audit (separate Claude agent): two blockers found and fixed; re-verified.\n\n## Status, honestly\n\n- **κ:** no new κ.\n- **Scope:** Theorems A–C and the clique bound are proved for the frame model of PROOF.md §1, which contains the rules E0–E3\n of `gx.check1` and #425's common-label rule; the correspondence is by reading, with no mechanical proof and no Lean.\n- **Layout hypotheses:** (B1)–(B2) of Theorem B and (P1)–(P2) of Theorem P were read against Sussman's\n `Work/Bridge/Net.lean`, `Work/BridgeGeom/Stage.lean` and `Work/BridgeGeom/Net.lean` (f010392c); they are consistent\n with the statements there, but this was read, not formally verified. Two points are open: whether the backward stages\n 1 and 3 count as \"the same program\", and whether the stage-j target frames lie in ι_j(q_S)^⊥. Theorem P holds for\n fixed-role B₂ windows over F₂ only; #425's nine-stage windows (m = 73) are outside it.\n- **Bit side:** no bit word is replayed. Theorem P (stated for F₂ windows) and the overlap measurements were computed on\n complex programs, and nothing is claimed about Theorem P for ℚ forms such as #386's; the pricing context uses the\n p = 10 bit histogram (the file copied from the `math.json` that #325's verification writes) and is a pricer-model\n output.\n- **Theorem S:** a bound on helper count, not on price (the simulation prices 13 % below #425's word under the coarse\n formula). Replayed by the package's detector on #425's word, not by `gx.check1`.\n- **E8 labels:** the SAT results are for the full E8 in-cap graph only.\n\n## Attribution\n\n- **Jacob Sussman:** gcert/1, `gx.check1`, the frame lemma, the five-stage layout and the E8 complex unit.\n- **jacklightChen (Zhihao Chen):** #425's word and its conjugation semantics; #386.\n- **Dylan Crow (utcorvusvolat-dotcom):** #370 (E8 bit word, root coordinates) and the #310 cost model.\n- **Louis Harrison:** #346 (the vendored pricer).\n- **Avi Eisenberg (ikeboy):** #193. **icekylinx:** #144, #184 and #433. **chafreaky:** #200, #233, #256.\n- **eumemic:** #168. **DaysSky:** #162, #352 and #442. **hcg890** and **SovereignSteak:** #234 and the five-stage ledger.\n\nThe statements, proofs, checks and packaging were prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via\nClaude Code. 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κ = 0.001246073505487942: R740 replicated kernel with idle-data hosting","user":{"login":"chafreaky","id":4400527,"node_id":"MDQ6VXNlcjQ0MDA1Mjc=","avatar_url":"https://avatars.githubusercontent.com/u/4400527?v=4","gravatar_id":"","url":"https://api.github.com/users/chafreaky","html_url":"https://github.com/chafreaky","followers_url":"https://api.github.com/users/chafreaky/followers","following_url":"https://api.github.com/users/chafreaky/following{/other_user}","gists_url":"https://api.github.com/users/chafreaky/gists{/gist_id}","starred_url":"https://api.github.com/users/chafreaky/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/chafreaky/subscriptions","organizations_url":"https://api.github.com/users/chafreaky/orgs","repos_url":"https://api.github.com/users/chafreaky/repos","events_url":"https://api.github.com/users/chafreaky/events{/privacy}","received_events_url":"https://api.github.com/users/chafreaky/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"## Result\n\nConditional **κ = 0.001246073505487942** (`623036752743971 / 500000000000000000`), **0.6886% above PR442**, with the bit supplier binding.\n\nCompose PR443's R740 rank138 word and 32-replica layout with PR442's idle-data hosting interface. Hosting moves 159,168 helper residuals onto pending coordinates of untouched data pairs; all 53,952 remaining residuals fill complete banks. Live bit stock falls from 56,739 to 37,464, physical stock is 37,473, and the largest child falls from 42 to 8. Every local instruction, data owner, stage orientation, residual isometry and bridge remains identical to PR443.\n\nThe exact bit saving is `1247628141860215921989 / 10^24`. The complex supplier is freshly reconstructed from PR442 at `1267453159029119 / 10^18`; it is not merely cited.\n\n## Verification\n\n`research/r740-idle-hosted-replicas/verify.py` checks 234 byte-identical pinned upstream files, runs both parent verifiers, then independently audits the hosted construction and finite composition. The audit checks all 288 calls, 213,120 helper occurrences, last-touch windows, replica ownership, residual widths, disjoint slots, remainder children and stage-specific full banks. It recomputes the 5,681,952-instruction digest after ownership changes and rejects 14 corruptions.\n\nTwo rational moment engines agree; both finite invoices pass. The bit prefix uses 123 bits charged at 128, the two-level coefficient uses 286 bits charged at 512, and all helper routes retain the residual-isometry charge plus the hosting route charge. Six bootstrap levels, 47 strict inequalities, next-grid and parameter controls pass.\n\nValidation: full Linux reconstruction; macOS quick mode (all new checks and full PR442 replay); repository-native `make verify-joint` including 16 tests. CI runs the full wrapper on Python 3.11 and 3.14.\n\n```sh\npython -m pip install -r research/e8-r740-replica32/parent436/requirements.txt\npython -B research/r740-idle-hosted-replicas/verify.py /tmp/r740-hosted-new\n```\n\n## Scope and credit\n\nThis retains PR442's conditional idle-data hosting extension and all inherited all-size compiler, restored-work, common-grid, precision and analytic assumptions. The hosting operator lemma is the same mathematical review point as PR442. No unconditional multiplication theorem, κ = 1 result, or new Lean proof is claimed.\n\nDaysSky's PR442 construction and assembly (Anthropic Claude assistance) and chafreaky's PR443 (OpenAI Codex assistance) are copied with complete notices/licenses and exact source pins. The new selection, integration, stronger independent audit and ownership digest were prepared by chafreaky with substantial OpenAI Codex assistance. Earlier contributions and disclosures remain in the unchanged upstream 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stronger bit supplier: fixed-coordinate and face-diagonal bit local circuit on PR168 v4 (effective bit saving 6.7734e-4)","user":{"login":"chafreaky","id":4400527,"node_id":"MDQ6VXNlcjQ0MDA1Mjc=","avatar_url":"https://avatars.githubusercontent.com/u/4400527?v=4","gravatar_id":"","url":"https://api.github.com/users/chafreaky","html_url":"https://github.com/chafreaky","followers_url":"https://api.github.com/users/chafreaky/followers","following_url":"https://api.github.com/users/chafreaky/following{/other_user}","gists_url":"https://api.github.com/users/chafreaky/gists{/gist_id}","starred_url":"https://api.github.com/users/chafreaky/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/chafreaky/subscriptions","organizations_url":"https://api.github.com/users/chafreaky/orgs","repos_url":"https://api.github.com/users/chafreaky/repos","events_url":"https://api.github.com/users/chafreaky/events{/privacy}","received_events_url":"https://api.github.com/users/chafreaky/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"## Change and mathematical scope\n\nThe package applies to `main` at `3b6b66891c0ac888521cf591fe306c6286601d4f` (which integrates #186 on top of my #181 and eumemic's #168) and is mergeable there; its construction inputs are PR168 v4 at `4a3c769e5c5430e7114c4d3e099ff34664677f17`, and the twelve PR168 v4 files it executes or pins are vendored byte-identically with digests in `references/pr168-v4`, so no file outside the package changes. Two changes above PR168 v4. **Complex:** a new per-cube local channel circuit found by 240 random restarts over PR144's $3^{13}$ circuit options and two coordinate-descent rounds, scored by the numerical physical root: $A[0,0]$, $A[0,1]$ and $A[1,1]$ are assembled from the two face diagonals, $A[1,0]$ from direction-2 edges, $A[2,\\cdot]$ from direction-1 edges; $G[0,1,\\cdot]$ and $G[0,2,1]$ use edge differences and $G[0,2,0]$, $G[1,2,0]$, $G[1,2,1]$ use fixed-coordinate differences. The circuit has 33 additions per cube instead of 27, but the carrier closure admits 12,189 arcs instead of 10,704, so the virtual auxiliary stock falls from 13,372 to 12,877 roles. All modules, fused outputs and schedules of PR168 are retained; the carrier matching, gauge selection, endpoint frame descent, 2,310 compensated handoffs and 44 terminal-output deletions are regenerated for the new graph. **Bit (new, beyond my #189/#196):** a per-cube bit local circuit found by 100 random restarts and three coordinate-descent rounds over the bit circuit options, each candidate priced through the full physical pipeline: $A[0,0]$, $A[0,1]$, $A[2,0]$ and $A[2,1]$ from the two face diagonals, $A[1,\\cdot]$ from direction-0 edges, $G[0,1,0]$ from fixed-coordinate differences (edges elsewhere). The bit virtual stock falls from 19,788 to 18,908 roles (modules, L1 association, partner mixing and output merge unchanged). For this graph a fresh carrier matching and gauge selection are regenerated by the retained generator rules, a complete physical layer (7,282 descended operation frames, 1,760 compensated handoffs) is built by our own producer, and 34 face0 terminal sinks are deleted by James Chang's PR166 substitution. Both suppliers and the paid balanced composition are independently certified. Under the retained interfaces, the bound is\n\n$$\nT(n)=O\\left(n(\\log n)^{1-\\kappa}\\right),\\qquad\n\\kappa=\\frac{166261725903847}{25\\cdot10^{16}}\n=0.000665046903615388.\n$$\n\nSame headline as my #196 (complex-bound); this PR adds the stronger bit supplier. The refined complex profile has 10,523 physical auxiliary roles, 13,163 persistent roles, rank mass 867,438, deficit 1,320 and largest child 20; its saving is $665489485337/10^{15}=0.000665489485337$. The new bit profile has 17,114 physical roles, 20,634 persistent roles, rank mass 1,483,712, deficit 1,936 and largest child 60; its coarse saving is $677773948354561/10^{18}=0.000677773948355$ (PR189: $0.000668298937776$; PR168 v4: $6600253/10^{10}$), and the established atom wrapper gives ordinary saving approximately **0.000677340914792**, 1.42% above the PR189 bit supplier that #194 composes with. With this package's own complex word the complex branch binds, so the headline bound equals #196; the contribution here is the certified bit profile. Composed with the source-assisted complex word of #193/#194 (saving 7.009e-4) it would give about 6.769e-4, which I am preparing as a separate stacked composition with full credit.\n\nThe configurable circuit is icekylinx's (PR144); the complex part only selects a different configuration. Carrier arcs come from our own legal-edge Hopcroft–Karp matching on coordinate-padded frames, extended by DaysSky's PR162 rule, and are replayed by the retained `compile_closure` with its acyclicity and span checks. The new bit graph is admitted through the retained package checker (exact rational frames, mod-2 decoder, geometry, chains, partner chronology, F2 replay, ledger and five mutation controls). The physical bit layer follows PR131's descent rule (each frame between the join of its incoming frames and the meet of its outgoing frames) on exact rational subspaces, repaired to nondegenerate bases, with handoffs read at the recipient's first use; the 34 sinks are the face0 roots whose rank-21 caps contain every write, with the complete modified target chronology, all 17,114 dirty columns over F2 and over the integers, and exact prime witnesses for all 24,401 used frames. The same producer applied to PR168's unchanged bit graph reproduces a layer slightly above PR168's own (6.60082e-4 vs 6.60025e-4 coarse before sinks), which is the control for the bit-side pipeline. Scalar virtual stock, compensated handoffs, terminal deletions, the full orthogonal-group cardinality and all row reserves are charged separately. The exact four-file PR175 overlay at `f1081fabbfadaaaaf7292a40d428dbbb865ce920` is retained in the verification baseline.\n\nNo mathematical hypothesis or ordinary-supplier interface is strengthened. General Clifford/tensor, uniform weighted compilation, restored-row, paid-layout, precision/recovery and analytic fixed-tape contracts remain the stated assumptions. The finite certificate is not an unconditional multiplication theorem.\n\nPrepared by Chafik Boukhalfa with substantial Anthropic Claude and OpenAI Codex assistance. The prerequisite construction is eumemic's PR168 v4, retaining its Anthropic Claude/OpenAI Codex disclosures and earlier PR144/161 lineage. Terminal-output accumulation is James Chang's PR166; balanced-layout, atom-toll and earlier supplier attribution remain in `research/paired-cube-diagonal-bit-168/NOTICE`. PR154 supplies the isolated verification technique; PR175 supplies the exact compiler overlay.\n\n## Validation\n\nValidated exact commit `a1175449f34d39ff933d9d8ab23ced1f32b290ec` (tree `6e44ae42bf66e222dc2d8ccf848c6a2e0cb12c9a`).\n\n- The new signed graph passes the exact scalar identity, carrier closure and frame audits. Complete original and terminal-modified complex words pass in both directions, including every source/target/dirty formal column and the full target-frame chronology. The modified word checks 13,163 columns and restores all 10,523 dirty roles; three corruption controls are rejected.\n- The new bit graph passes the retained package checker with its five mutation controls; our physical layer passes all 20,668 F2 and defining-integer-decoder columns, and the terminal-modified word passes all 17,114 dirty plus 3,520 data columns over F2 and over the integers with three sink controls rejected. All 24,401 used frame Gram witnesses preserve the retained prime range; word and factor controls are rejected.\n- Exact supplier moments, full scalar/group/router/row formulas, all 47 strict inequalities and seven margins pass. Independent arithmetic reproduces the same bound with 30 rejected mutations; the package retains 21 assembly controls. Adjacent grid exclusions concern only the fixed certificates and parameters.\n- The read-only aggregate reproduces the canonical certificate. `SOURCE.json` pins all 2,242 files of `main` plus the package, with its own digest reported separately; the vendored PR168 v4 inputs carry their own digest manifest.\n- **Full repository gate: PASS. 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κ = 0.001138823042306561: retain rank138 with complete 32-replica banks","user":{"login":"chafreaky","id":4400527,"node_id":"MDQ6VXNlcjQ0MDA1Mjc=","avatar_url":"https://avatars.githubusercontent.com/u/4400527?v=4","gravatar_id":"","url":"https://api.github.com/users/chafreaky","html_url":"https://github.com/chafreaky","followers_url":"https://api.github.com/users/chafreaky/followers","following_url":"https://api.github.com/users/chafreaky/following{/other_user}","gists_url":"https://api.github.com/users/chafreaky/gists{/gist_id}","starred_url":"https://api.github.com/users/chafreaky/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/chafreaky/subscriptions","organizations_url":"https://api.github.com/users/chafreaky/orgs","repos_url":"https://api.github.com/users/chafreaky/repos","events_url":"https://api.github.com/users/chafreaky/events{/privacy}","received_events_url":"https://api.github.com/users/chafreaky/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"Conditional **κ = 0.001138823042306561** (`1138823042306561 / 10^18`). This retains two rank-one kernel pivots that eight-replica bank packing discarded. Thirty-two independent replicas fill every width-64 bank exactly, admitting entrance rank 138 without padding. The bit lower endpoint is `0.001140121438872176364117`.\n\nThis is about **0.00219% above #441** at `6160c13526f5f957902910b462164c93c1d8f39a`. **#442 reports a larger bound using its additional idle-data hosting extension.** This PR isolates replica banking within the preceding helper-bank interface and supplies a construction that can be composed with later hosting work.\n\nThe word starts from #436's R740 producer, uses 57 primitive A-frame changes and a re-derived 114-pivot/103-donor kernel, then independently rechecks #441's paired and window B-frame choices on the new word. The scalar ADD operands and order are preserved by retiming. Sixteen explicit residual isometries place 32 replicas into 2,891 complete banks per stage: 56,739 live and 56,748 physical families, deficit 9,984.\n\nValidation: full Linux verifier and macOS cross-check pass; native `make verify-joint` passes (16 tests). The release checks pinned source bytes, complete parent reconstruction, frozen transformations, all 980 local arbitrary-dirt columns, both reflected streams, the one-replica 7,620-column global identity, all 288 emitted invocations and 213,120 helper assignments, exact projectors and residual routes, five reconstruction controls, 14 template mutations, two rational moment engines, a fresh finite invoice, six bootstrap levels and 47 strict outer inequalities. The prefix needs 123 bits (charged 128); the two-level coefficient needs 286 bits (charged 512). Eight-replica admission of the untrimmed selection is explicitly rejected. The adjacent 10^-18 κ grid point is rejected.\n\n```sh\npython3 -m pip install -r research/e8-r740-replica32/parent436/requirements.txt\nbash research/e8-r740-replica32/verify.sh /tmp/e8-r740-replica32-full\n```\n\nThe complex lower endpoint `0.001183986549206329` is cited from #433; its Gaussian phases are not replayed by this package. The all-size compiler, correlated dirty-bank, compressed-window, restored-work, tape/common-grid, precision and analytic interfaces remain assumptions. No unconditional theorem or new Lean proof is claimed.\n\nPrepared by chafreaky with substantial OpenAI Codex assistance. Credit eumemic #436/#440/#441, our #417/#439 kernel and residual-route lineage, Rohan Arun #434/#435/#438, icekylinx #433, Zhihao Chen #425/#386, Dylan Crow #370, ai-nanachi #426, applecrusher #376, Jacob Sussman and the retained earlier contributors. Source-specific licenses, notices, assistance disclosures and exact pins are 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Complex supplier b ≈ 1.334e-3 (+5.2%): shared-donor kernel and entrance gauges on the E8 complex word","user":{"login":"DreamingOfClouds","id":173691639,"node_id":"U_kgDOClpS9w","avatar_url":"https://avatars.githubusercontent.com/u/173691639?v=4","gravatar_id":"","url":"https://api.github.com/users/DreamingOfClouds","html_url":"https://github.com/DreamingOfClouds","followers_url":"https://api.github.com/users/DreamingOfClouds/followers","following_url":"https://api.github.com/users/DreamingOfClouds/following{/other_user}","gists_url":"https://api.github.com/users/DreamingOfClouds/gists{/gist_id}","starred_url":"https://api.github.com/users/DreamingOfClouds/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/DreamingOfClouds/subscriptions","organizations_url":"https://api.github.com/users/DreamingOfClouds/orgs","repos_url":"https://api.github.com/users/DreamingOfClouds/repos","events_url":"https://api.github.com/users/DreamingOfClouds/events{/privacy}","received_events_url":"https://api.github.com/users/DreamingOfClouds/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"**WIP. The claim is pending the full package and is conditional on two new lemmas.** No κ is claimed.\n\n## Result so far (hosted b on #442's complex word, exact moment engine)\n| word | b (·10⁻³) | gain |\n| --- | ---: | ---: |\n| #442 complex | 1.267453 | |\n| shared-donor kernel, 79 pivots | 1.310216 | +3.37% |\n| entrance gauges, 80 helpers | 1.310916 | +3.43% |\n| both (all residuals hosted, stock 7,680) | **1.333854** | **+5.24%** |\n\nIf the complex side were the only constraint these give κ caps of 1.3085 / 1.3092 / 1.3321·10⁻³ against 1.2658·10⁻³\nfor #442's complex word, which is what binds the current frontier (#447, #445).\n\n## What passes\nExact arbitrary-dirt and inverse-transpose replay, the emitted program in both orientations on 800 columns, and the exact\nGaussian phase recipes of every used frame transition, for all three words (`sh check.sh DIR`).\n\n## What does not (read this first)\n- The entrance lines are **isotropic** (even weight). 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κ = 0.001133928043872860: R740 shared-donor kernel with explicit residual bank routes","user":{"login":"chafreaky","id":4400527,"node_id":"MDQ6VXNlcjQ0MDA1Mjc=","avatar_url":"https://avatars.githubusercontent.com/u/4400527?v=4","gravatar_id":"","url":"https://api.github.com/users/chafreaky","html_url":"https://github.com/chafreaky","followers_url":"https://api.github.com/users/chafreaky/followers","following_url":"https://api.github.com/users/chafreaky/following{/other_user}","gists_url":"https://api.github.com/users/chafreaky/gists{/gist_id}","starred_url":"https://api.github.com/users/chafreaky/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/chafreaky/subscriptions","organizations_url":"https://api.github.com/users/chafreaky/orgs","repos_url":"https://api.github.com/users/chafreaky/repos","events_url":"https://api.github.com/users/chafreaky/events{/privacy}","received_events_url":"https://api.github.com/users/chafreaky/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"## Result\n\nConditional **κ = 56696402193643 / 50000000000000000 = 0.001133928043872860**.\n\nThis applies our #417 shared-donor kernel to eumemic's #436 R740 bit word and composes it with #433's cited complex supplier. It is **0.4380% above #436** and **0.03703% above #438** at `e3b56de7869f6af88d48ac0ab1d7959c4c9e6176`. The bit side binds.\n\n| Quantity | Result |\n| --- | ---: |\n| Kernel pivots / entrance rank / donor slots | 115 / 136 / 103 |\n| Local helpers | 740 |\n| Banks per stage | 723 (parent: 740) |\n| Live / physical stock | 14,187 / 14,196 |\n| Exact bit lower endpoint | 1135215296333206583339 / 10^24 |\n| Cited complex lower endpoint | 1183986549206329 / 10^18 |\n| Rank deficit | 2,496 |\n\n## Construction\n\nEach selected pivot starts at its verified entrance. Its target response is the XOR of its donors' responses; an entrance correction and its full-frame inverse restore arbitrary dirt. The selection is regenerated against the exact #436 word, not transferred by helper index from another word.\n\nThe residual widths fill dimension-64 banks without padding. Following #435's mixed-bank composition, this package additionally supplies explicit orthogonal completions for all 15 entrance frames. For this selection the maps are coordinate permutations, with each elementary factor replayed. The independent audit checks the residual subspace, every bank interval and every stage owner, and rejects altered bases, wrong residual frames and omitted route factors. The fresh finite invoice conservatively charges the additional routing work.\n\nThe entire #436 package is vendored byte-for-byte, including its reconstruction, complete verifier, licenses, notices and file-level provenance. The kernel engine and transformation are pinned to our #417 blobs. The existing three-file #318 joint-dual pin repair is included so that the repository's joint check passes.\n\n## Validation\n\nVerified source at commit `fa3a588ec1e383083abb8de9c51904fb9d689ad4`:\n\n- Full package verifier on Linux/aarch64 (Spark), including all parent historical regressions: exit 0.\n- Quick package verifier on macOS/arm64: exit 0. Quick mode omits only the parent's historical regressions; it runs the complete new-witness checks.\n- `make verify-joint`: passed, including its 16 mutation tests.\n- Frozen reconstruction, all 980 local columns, official five-stage and B4 column checkers, exact nondegeneracy, forward/reflected copy chronology, all 7,620 unbanked global columns and all 53,280 helper assignments passed.\n- 3,279 exact nested/reflected projector pairs, 15 residual isometries, 11 independent template mutations, three construction mutations, retained record-level controls and all 18 omitted bridge-shear controls passed.\n- Both rational moment engines, the fresh finite invoice, six bootstrap levels and all 47 strict outer inequalities passed. The next grid point and invalid outer parameters were rejected.\n- Linux and macOS emitted the same complete program digest: `418958c0010bf48e5e40c8573f7927d04c0edf01a15db324996498c72a7b3b1d`.\n- All 112 package files match their staged manifest bytes. Unchanged vendor files retain their original trailing blank lines.\n\n```sh\npython3 -m pip install -r research/e8-r740-kernel/parent436/requirements.txt\nbash research/e8-r740-kernel/verify.sh /tmp/e8-r740-kernel-full\n```\n\nThe dedicated workflow covers Python 3.11 and 3.14. CI is pending; the unchanged whole-repository suite was not rerun locally.\n\n## Scope and weakest steps\n\nThis is a finite conditional witness for the retained `O(n (log n)^(1-κ))` assembly. It does not prove κ = 1, provide a new Lean theorem, or establish unconditional multiplication complexity.\n\nThe complex result is **cited from #433**, including its #425 mutable-basis interface; its scalar construction and Gaussian-phase audits are not rebuilt here. Full cover enumeration and the all-size compiler, correlated dirty-bank, restored-work, precision, tape/common-grid and analytic interfaces remain inherited assumptions. The exact finite checks do not discharge them.\n\n## Credits\n\nNew selection, explicit residual routes and integration: **chafreaky**, with substantial **OpenAI Codex** assistance.\n\nRetained contributions: eumemic (#436, with Anthropic Claude); chafreaky (#417, with Anthropic Claude); rohanarun (#435 mixed-bank composition); icekylinx (#433); jacklightChen (#386/#425); utcorvusvolat-dotcom / Dylan Crow (#370); applecrusher (#376); ai-nanachi (#389/#426); DaysSky (#363/#375/#381); DreamingOfClouds (#315); Jacob Sussman and the earlier credited contributors. Full attribution, licenses and source-specific AI disclosures are preserved in `NOTICE.md`, `SOURCE.json` and `parent436/`. 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κ = 0.001265848755025709: rank147 kernel with eleven-stage 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0.001265848755025709**, **0.1966% above #445** at `40ab91daf2b5e87fc4071dedae1699d5d7e7cecc`, under the same additional PR442 idle-data hosting assumption. **The complex supplier binds.**\n\nCombine our PR434 rank147 kernel (123 pivots,118 donor slots) with PR445's eleven compressed stages and dimension78. Frozen ownership hosts all65,120 helper occurrences:9,600 live/9,609 physical families, zero helper banks, deficit3264. Bit lower `0.001267514693114214441041`; complex lower `0.001267453159029119461392`. Keeping the full certified complex endpoint improves the initial draft's last κ grid digit from708 to709; this final tick is a precision-only change, not a stronger supplier.\n\n**Verification:** uninterrupted full Python3.11.15 and3.14.8 runs passed at the708 endpoint, including complete parent reconstruction and all complex phases. Exact receipts/logs/manifests are in `research/e8-eleven-hosting-selected-validation/python311/` and `python314/`. The only subsequent executable change is two lines in the assembly (retain the full rational endpoint and compare it to the inherited weaker bound). Both runtimes reran both exact moments, refreshed invoices, six bootstrap levels,47 strict inequalities and adjacent-grid/parameter controls against their fully verified suppliers. See `precision/` for the exact diff, input hashes and receipts. No fresh uninterrupted full wrapper of the revised manifest is claimed; CI remains pending.\n\nThe unchanged full supplier checks cover all9,340 unbanked scalar columns; signed ten-wire identity and24 omitted-shear controls;1,320 geometry routes; complete1,740,288-instruction digest; every hosted owner and22 mutation controls; three-level halving,514-bit coefficient charged1024 and complete row bound19431<20161. The earlier disk-exhaustion failure and corrected missing-dependency setup logs remain preserved. SSD cleanup freed7.4GiB before the successful full runs.\n\nReproduce: install `sympy`, then `python -B research/e8-eleven-hosting-selected/verify.py /absolute/new/output`. Subsequent unsuccessful complex-side retiming, hosting and partition screens are retained under the validation package's `research/` to avoid duplicate work.\n\nAll inherited all-size compiler, dirty-helper/compressed-window, restored-work, tape/common-grid, precision, row-divisor and analytic assumptions remain. Finite audits do not prove the hosting operator extension. No unconditional multiplication theorem, earlier-assumption record, or new Lean proof is claimed.\n\nPrepared by Rohan Arun with substantial OpenAI Codex assistance. Eleven-stage geometry and row argument: chafreaky #445 (OpenAI Codex assistance). Credit #443/#444/#417/#439, eumemic #436/#440/#441, DaysSky #442 (Anthropic Claude assistance), icekylinx #433 and all retained earlier authors. Exact pins, licenses and source notices are 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kappa 0.001249035299298004: hosting-selected rank147 kernel","user":{"login":"rohanarun","id":11659839,"node_id":"MDQ6VXNlcjExNjU5ODM5","avatar_url":"https://avatars.githubusercontent.com/u/11659839?v=4","gravatar_id":"","url":"https://api.github.com/users/rohanarun","html_url":"https://github.com/rohanarun","followers_url":"https://api.github.com/users/rohanarun/followers","following_url":"https://api.github.com/users/rohanarun/following{/other_user}","gists_url":"https://api.github.com/users/rohanarun/gists{/gist_id}","starred_url":"https://api.github.com/users/rohanarun/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/rohanarun/subscriptions","organizations_url":"https://api.github.com/users/rohanarun/orgs","repos_url":"https://api.github.com/users/rohanarun/repos","events_url":"https://api.github.com/users/rohanarun/events{/privacy}","received_events_url":"https://api.github.com/users/rohanarun/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"Draft conditional **κ = 0.001249035299298004**, **0.23769014% above #444** at `8c4242ea61c67827fe62b07b2edc093d7ddfa631` and our preceding verified result.\n\n**Same additional idle-data hosting assumption as #442/#444.** This is not an improvement under only #441's pre-hosting assumptions. The operator extension is inherited; finite interval audits do not prove it. All compiler, dirty-bank/compressed-window, restored-work, tape/common-grid, precision and analytic obligations remain. No unconditional theorem or new Lean proof is claimed.\n\nThe new search evaluates response-kernel relations together with idle-slot hosting costs. It admits nine additional rank-one relations that the unhosted model rejected. Starting from the pinned R740/PR443 lineage, the new word has **123 pivots, 118 donor slots and entrance rank 147**. With **64 bit replicas**, hosting leaves **74,528 live / 74,537 physical families**, **321,536 hosted residuals** and deficit **19,968**. The complex supplier remains eight replicas, 8,400 live families and deficit 2,496. The bit supplier binds at exact lower endpoint `625298669760136826673 / 500000000000000000000000`.\n\n**Passed before draft publication:** exact precursor and kernel reconstruction; all 980 local columns and integer source spans; the 7,620-column unbanked global identity; all 576 emitted invocations and 426,240 helper assignments; independent exact projector, reflected-program and residual-isometry audits; both hosted templates and nine hosting mutations; both rational moment engines; fresh 64-replica invoice retaining the extra route bound 144 plus two hosting factors; six bootstrap levels and all 47 strict outer inequalities. Next κ grid point rejected. Evidence is in `research/e8-hosting-selected-kernel/evidence/`.\n\n**Pending:** full uninterrupted Python 3.11/3.14 wrappers and GitHub CI. Reproduce: `python -B research/e8-hosting-selected-kernel/verify.py /absolute/new/output` (standard library only). It first replays the previous full rank138 composition and all 2,918 complex Gaussian phase edges, then reconstructs and checks the new kernel, global layout and assembly. The preceding result `0.001246073505487942` remains fully verified on Python 3.11/3.14, with receipts in `research/e8-rank138-idle-hosting/local-evidence/`.\n\nRohan Arun with substantial OpenAI Codex assistance: hosting-aware kernel discovery and integration. Credit chafreaky #443/#444/#417/#439, eumemic #436/#440/#441, DaysSky #442 hosting with Claude assistance, Rohan Arun #434/#435/#438, icekylinx #433, the retained #426/#389/#376/#370, #425/#386 and Jacob Sussman contributions. Source pins, licenses and assistance disclosures are 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κ = 1.128983115440183e-3: an E8 bit word with 740 helpers under #433's complex supplier","user":{"login":"eumemic","id":94939491,"node_id":"U_kgDOBaipYw","avatar_url":"https://avatars.githubusercontent.com/u/94939491?v=4","gravatar_id":"","url":"https://api.github.com/users/eumemic","html_url":"https://github.com/eumemic","followers_url":"https://api.github.com/users/eumemic/followers","following_url":"https://api.github.com/users/eumemic/following{/other_user}","gists_url":"https://api.github.com/users/eumemic/gists{/gist_id}","starred_url":"https://api.github.com/users/eumemic/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/eumemic/subscriptions","organizations_url":"https://api.github.com/users/eumemic/orgs","repos_url":"https://api.github.com/users/eumemic/repos","events_url":"https://api.github.com/users/eumemic/events{/privacy}","received_events_url":"https://api.github.com/users/eumemic/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"#433 (icekylinx) is bit-bound: its complex supplier has b = 1183986549206329/10¹⁸, and its R758 bit word gives c ≈ 1.122123e-3. This PR replaces the bit word with an E8 bit word with **R = 740 helpers**, in #386's compressed nine-stage layout. Pricing uses #433's own bit engine, finite invoice and six-level tail.\n\n**κ = 1128983115440183/10¹⁸ ≈ 1.128983115440183e-3**, bit-bound. That is **+0.7243 % over #433** (560432476129139/(5·10¹⁷)). It is also above #435 (1.128832830332521e-3, #417's kernel on #433's R758 word) and #434, which were posted while this was being prepared. The kernel of #417/#435 and this word's reuse are different mechanisms; stacking them is not attempted here.\n\n| layout | bit c of this word | best published in that layout | gain |\n| --- | ---: | --- | ---: |\n| compressed nine-stage (#386; used by #425, #431, #433) | 282564789736676592463/(2.5·10²³) ≈ 1.130259e-3 | #433 (R758) | +0.725 % |\n| B₄ unsplit (#381) | 1064525457834209/10¹⁸ ≈ 1.064525e-3 | #417 | +1.960 % |\n\nOne self-contained package, `research/e8-bit-elimination-reuse/`, with its own workflow, plus one `.gitattributes` line. No existing file changes.\n\n### Mechanism\n\n1. **#370's producer with new parameters** (67 of 520 entries changed) gives R = 863.\n2. **Elimination reuse of dead helper slots** gives R 863 → 740.\n - A dead helper still holds a leftover x-content, an F₂ sum of source lines.\n - Before a later helper is born at frame F, take an F₂ relation among the leftovers of dead slots inside F. One gate at the join of their frames empties one slot, and the new helper takes it over.\n - The 9 retained totals also take dead slots; their leftover lines are read at the full frame.\n - 114 slots are reused by helpers and 9 by totals.\n3. **Single-gate frame retiming**, #389's idea: 37 gate moves.\n\n**Overlap.**\n- #426 (ai-nanachi) published the same slot-reuse mechanism first: 55 \"clean resets\" on #376's R822 word, giving R767. We developed this pass independently. On a different base word it finds 114 reuses plus the 9 totals.\n- #433's nine-sum source-basis change frees no register here, because the totals already sit on dead slots.\n\n### Checks\n\n`bash research/e8-bit-elimination-reuse/verify.sh [--quick] DIR`: about 40 s quick, 67 s full.\n\n- **Provenance.** Manifest; 52 vendored files pinned by git blob id. Every cited complex b and κ must equal that PR's own receipt.\n- **Rebuild.** The word is rebuilt from pinned inputs and must equal the shipped word. #370's producer regenerates #370's word as a control.\n- **#370's independent checker:** exact F₂ on all 980 columns with dirty helpers, and Gram determinants > 0 on every frame (only prime 2). 6 word-level and 6 reuse-specific mutants are rejected.\n- **Official checkers.** PR #266's legality at NCOPY = 9; NCOPY = 8 is rejected. Five-stage and B₄ formal columns, with 18 omitted-bridge controls rejected.\n- **#386 layout.** Geometry, source-bound template, audit and price.\n- **#433's engine, invoice and tail.** These reproduce #433's own c and κ exactly, and #386's, #425's and #431's κ. The tail uses 47 strict inequalities; the next grid point, zero η, zero β and unit β are rejected.\n- **B₄.** #381's geometry, banks (T = 9), finite bill and price.\n- **Local build.** The C++ checkers were built against an overflow-checked 128-bit stand-in for `boost::multiprecision::cpp_int`, because the preparing machine has no Boost. In CI, the package workflow built them with libboost-dev and passed on Python 3.12 and 3.14.\n- **Repository CI.** This branch includes rohanarun's #318 three-file joint-dual pin repair (byte-identical to a45747d), as #417 and #439 do, so the repository joint check passes.\n\n### Retained assumptions\n\n- Everything #370 admits: 9 retained totals at h = 8, PR234's banks for a non-paired-cube family, and the all-size bit compiler, prime, tape, precision and analytic interfaces.\n- #386's compressed-layout arguments, including two-level halving (max child 42/64).\n- #433's complex supplier is cited, not rebuilt. Its proof rests on #425's written scalar-interface extension.\n- This is a conditional finite construction, not a Lean proof.\n\n### Credits\n\nutcorvusvolat-dotcom / Dylan Crow (#370: format, producer, checkers); applecrusher (#376); ai-nanachi (#389 retiming; #426 clean-reset reuse, published first); icekylinx (#433 complex supplier, bit engine, invoice and tail); DaysSky (#381, #375, #363); Zhihao Chen / jacklightChen (#386, #425); Chafik Boukhalfa / chafreaky (#417); Rohan Arun (#392, #431); Jacob Sussman (E8, bridged word); the PR #266 and PR #315 (DreamingOfClouds) lineage. Vendored files are byte-identical and listed in `NOTICE.md` and `SOURCE-pr*.json`.\n\nPrepared by eumemic with substantial Anthropic Claude assistance. Apache-2.0.\n\n🤖 Generated with [Claude 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= 1.128922474816875e-3: twelve early-final-use bit-helper resets","user":{"login":"eumemic","id":94939491,"node_id":"U_kgDOBaipYw","avatar_url":"https://avatars.githubusercontent.com/u/94939491?v=4","gravatar_id":"","url":"https://api.github.com/users/eumemic","html_url":"https://github.com/eumemic","followers_url":"https://api.github.com/users/eumemic/followers","following_url":"https://api.github.com/users/eumemic/following{/other_user}","gists_url":"https://api.github.com/users/eumemic/gists{/gist_id}","starred_url":"https://api.github.com/users/eumemic/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/eumemic/subscriptions","organizations_url":"https://api.github.com/users/eumemic/orgs","repos_url":"https://api.github.com/users/eumemic/repos","events_url":"https://api.github.com/users/eumemic/events{/privacy}","received_events_url":"https://api.github.com/users/eumemic/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"κ = 1.128922474816875e-3 = 1806275959707/1600000000000000\n\nThis new record candidate starts from the frozen split-centre construction in PR #433 and applies twelve source-bound early-final-use helper resets to its R=758 bit word. Each reset is an exact F2 donor identity at a legal frame after the retired helper's last use and before the replacement helper's first use. The changed word has R=746, reducing the live bit stock to 14,394 and raising the conditional assembled bound above PR #433's 0.001120864952258278. Earlier PR heads remain unchanged.\n\nThe constructor checks all twelve selected boundaries against the actual word, verifies each clean reset sum, rebuilds the dirty-response compensation from the new word, removes the replaced helper, and regenerates the inverse cleanup. The final word has SHA256 `fc5b2fb84dbbdbcf9b1bb36ebf768f31130dd5a93edec3d12f52c8e4be66ce48`.\n\nFresh replay evidence in the package:\n\n- Both forward and reflected local scalar programs restore all 986 source, target and dirty-helper columns.\n- All 944 exact rational frames and both paid ledgers are recomputed.\n- Twelve omitted-reset controls, eleven delayed-reset controls, missing dirty compensation and missing helper cleanup are rejected; one deliberately delayed reset is a valid positive control.\n- The changed global stream replays 7,674 unbanked columns, 53,712 bank-owner assignments and every reflected route, with eight owner/schedule mutation controls.\n- The bit supplier has profile `{1:2401, 2:864, 3:475, 4:309, 5:152, 7:14, 8:9}`, prefix charge 256 bits, two-level coefficient charge 512 bits, and row coefficient 18,355 < 20,161.\n- Two exact rational moment engines, both finite invoices, the bridge and all 47 strict outer inequalities pass; the next 10^-18 grid point is rejected.\n- The independent audit reproduces the profiles, owner maps, invoices and strict assembly without importing producer or assembly code.\n\nThe package verifier regenerates the pinned PR #433 parent, all 2,918 Gaussian phase pairs and 240 endpoint adapters, then runs the twelve-reset constructor, independent reflected audit, changed global admission, and independent invoice/outer audit. The observed clean replay exited 0 in `/private/tmp/r746-release-replay-v3/VERIFICATION.json`. Run:\n\n```sh\npython3 -B research/early-reset-source-banks/verify.py --output /tmp/r746-full-replay\n```\n\nThe vendored parent is pinned to PR #433 commit `2992f234bcb2538cb70f4d026aa8d08250b1040c`. Python 3.14+ is required for its frozen gzip byte pins; Python 3.11 emits the same decompressed content with a different gzip OS header. The package carries the parent licenses, notices, source hashes and explicit OpenAI Codex assistance disclosure. 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+4.97%)","user":{"login":"jacklightChen","id":20631913,"node_id":"MDQ6VXNlcjIwNjMxOTEz","avatar_url":"https://avatars.githubusercontent.com/u/20631913?v=4","gravatar_id":"","url":"https://api.github.com/users/jacklightChen","html_url":"https://github.com/jacklightChen","followers_url":"https://api.github.com/users/jacklightChen/followers","following_url":"https://api.github.com/users/jacklightChen/following{/other_user}","gists_url":"https://api.github.com/users/jacklightChen/gists{/gist_id}","starred_url":"https://api.github.com/users/jacklightChen/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/jacklightChen/subscriptions","organizations_url":"https://api.github.com/users/jacklightChen/orgs","repos_url":"https://api.github.com/users/jacklightChen/repos","events_url":"https://api.github.com/users/jacklightChen/events{/privacy}","received_events_url":"https://api.github.com/users/jacklightChen/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"This 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This does not reach `2^-9`.\n\nThe structural change is a new common-frame scalar interface. Sources can carry intermediate signed packet bases until full-frame inverse cleanup; retired packet registers reconstruct the central sums; 56 target pairs carry a first two-output butterfly. An explicit frame-zero inverse output basis and 13,216 charged dirty-response additions restore arbitrary target/helper inputs. The old gx source-immutability and target-read restrictions are replaced by a separate written conjugation lemma and complete exact matrix checks, rather than being silently bypassed. This extension is the principal new mathematical review point.\n\nValidation in the included offline replay:\n\n- all 120 × 120 signed decoder entries, and 920 arbitrary-input columns in each orientation;\n- exact source/helper restoration, private-work lifetimes, and negative controls;\n- 998 exact complex frames, 3,044 directed transitions, and 240 endpoint adapters, including global phases;\n- the emitted 72-call program, all 48,960 helper assignments, padding, idle children and cover corrections;\n- fresh finite costs, two rational moment engines, the next-grid rejections, three bootstrap steps and all 47 strict outer inequalities;\n- byte-identical regeneration of the scalar word, canonical word, Clifford recipes and global template from a fresh extracted package.\n\nRun `make hamming-complex-verify`, or `python3 -B research/hamming-mutable-basis-complex/verify.py --work /tmp/hamming-e8-fresh` with a nonexistent output directory. Python 3.11+ and its standard library suffice; no network or optimizer is used. The construction and scalar-interface proof are in `research/hamming-mutable-basis-complex/work/complex-network/hamming/PROOF.txt`; fresh receipts are in `research/hamming-mutable-basis-complex-validation/`.\n\nThis is a draft for review of the new scalar interface. The existing all-size compiler, common-grid, restored-row, tape/prime/precision and analytic-transfer interfaces remain explicit assumptions. No new Lean proof or unconditional integer-multiplication theorem is claimed. The historical repository-wide suite is not claimed to pass; its previously recorded Apple-clang OpenMP failure remains outside this research package.\n\nThis branch builds on #386 and adds one self-contained research package and a verification target. The pinned PR370 Hamming root data and prior complex/pricing sources retain their notices; no newer external research was 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conditional kappa 0.001056975315151441: Hamming complex and retimed bit 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**conditional κ = 0.001056975315151441**. This combines 112 common-frame retimings of #425's mutable-basis complex word with the existing #376 bit frame witness in #425's compressed bit geometry. It is **0.85589313% above #425** and **0.02461% above the prior version of this draft**.\n\nThe complex scalar operations, order, coefficients and R680 helper count remain unchanged; jointly retiming 112 events changes the local histogram by `{-112 rank1,-112 rank4,+112 rank5}`. The exact complex lower bound is **0.001058093696336318**.\n\nThe previously published 128-event bit retiming preserves R865, all scalar additions and endpoints. Fresh reconstruction in the compressed nine-window, m64 geometry gives bit lower bound **0.001061370033348997**. This removes the prior bit bottleneck. Both supplier prices, the complete finite bill, three bootstrap steps and 47 strict outer inequalities are recomputed. No separately reported gains are added.\n\n**Passed:** full fresh complex wrapper, all 3,072 complex phase pairs and both 920-column emitted orientations; exact bit witness reconstruction, freshly compiled native column/legality checks, all 944 frame Gram/prime checks, 1,080 port routes, 240 endpoint identities, 8,745 unbanked scalar columns, 62,280 bank assignments, independent bit template audit and its 8 rejected mutations, two rational moments, next-grid rejections, changed finite invoice and 47 strict outer inequalities.\n\n**The uninterrupted combined wrapper passed** on Python 3.11 against code commit `e533924d3c2ec045b3275e25220a76e9621067e0`: fresh #425 reconstruction, fresh complex retiming, freshly compiled bit checks, five deliberately invalid native records rejected, three witness mutations rejected, and the complete compressed bit assembly. Receipts and logs are in `research/hamming-bit-composition/local-evidence/`. Two additional searches found no improving single-gate move among 4,300 gates or among 11,870 tested equal-frame groups; those negative results are included. The full combined wrapper also passed locally on Python 3.14 against commit `3f200316d9e268e8c7b474089c6107bf1ee3dea7`. A compatibility shim normalizes only the OS metadata byte of deterministic gzip output to the pinned supplier format; compressed payloads, footers, and all expected artifact hashes remain checked. The compatibility and full replay receipts are included. **Python 3.11/3.14 GitHub CI remains pending.**\n\nReproduce with `python -B research/hamming-bit-composition/verify.py /absolute/path/to/new/output` using Python 3.11+, SymPy, C++17 and Boost headers. The prior failed attempt to use a complex-only bootstrap after hitting the bit cap remains in `research/hamming-frame-retiming/local-evidence/`.\n\nThis is a conditional finite construction. It retains #425's written mutable-source/target scalar-interface extension and inherited all-size bit/complex compiler, common chart/grid, restored-row, tape/precision and analytic interfaces. No unchanged legacy gx acceptance, new Lean proof, signed source527 bit decoder proof or unconditional integer-multiplication exponent is claimed.\n\nRohan Arun with substantial OpenAI Codex assistance. Credit Zhihao Chen/OpenAI Codex #425 for mutable-basis Hamming construction, compressed bit geometry and independent auditors; applecrusher/OpenAI Codex #376 for the existing bit retiming witness; Dylan Crow/Anthropic Claude #370 for the bit word and root data; Jacob Sussman for E8 and compiler interfaces, and retained supplier lineage. Parent sources and notices remain unchanged; adapted files and exact changes are documented.\n\nNewer #433 reports a higher conditional bound; this PR preserves its independently checked contribution and does not claim the current 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centres and source-basis reuse for conditional κ = 0.001120864952258278","user":{"login":"icekylinx","id":195614798,"node_id":"U_kgDOC6jYTg","avatar_url":"https://avatars.githubusercontent.com/u/195614798?v=4","gravatar_id":"","url":"https://api.github.com/users/icekylinx","html_url":"https://github.com/icekylinx","followers_url":"https://api.github.com/users/icekylinx/followers","following_url":"https://api.github.com/users/icekylinx/following{/other_user}","gists_url":"https://api.github.com/users/icekylinx/gists{/gist_id}","starred_url":"https://api.github.com/users/icekylinx/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/icekylinx/subscriptions","organizations_url":"https://api.github.com/users/icekylinx/orgs","repos_url":"https://api.github.com/users/icekylinx/repos","events_url":"https://api.github.com/users/icekylinx/events{/privacy}","received_events_url":"https://api.github.com/users/icekylinx/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"This combines a new split-centre complex construction with source-centre reuse on the bit side, in one commit based on main at `12a4934d15006e8c10f9b2264f13f8f341be802b`.\n\nUnder the retained compiler, compressed-window, arbitrary dirty-bank, restored-work, fixed-tape/common-grid, precision and analytic interfaces,\n\n$$\nT(n)=O\\!\\left(n(\\log n)^{1-\\kappa}\\right),\\qquad\n\\kappa=\\frac{560432476129139}{500000000000000000}\n=0.001120864952258278.\n$$\n\nThe combined saving is approximately **6.9522% above [#425](https://github.com/CrocSwap/integer-mult-bounds/pull/425)**. The bit supplier binds the new assembly.\n\n## Construction\n\nOn the complex side, cancel the coordinate-source contributions that appear with opposite signs in the centre and side decoders before lifting them to address operators. The 112 code-line targets then use eight rank-eight centres; the eight coordinate targets use rank-one identity copies. Their total copied rank remains 72. Removing 112 coordinate-source helpers and eight dedicated full-centre helpers reduces R from 680 to 560. The dirty response is recomputed from the new word, and both orientations include literal source/helper cleanup and exact heterogeneous-centre phases.\n\nOn the bit side, start from #426's R767 word. Form its nine retained sums with an invertible basis change on the source rows, copy them sequentially, and apply the literal inverse before continuing. This removes nine helpers. Compose the resulting R758 word with the compressed dimension-64 geometry from #386, replaying the actual reflected copy chronology and all new bank owners. The changed prefix needs 223 bits and is charged at 256 bits; the old 192-bit allowance is not reused.\n\n| Selected supplier | Complex | Bit |\n| --- | ---: | ---: |\n| Ambient dimension | 73 | 64 |\n| Auxiliary rows | 560 | 758 |\n| Live recursion stock | 12,720 | 14,502 |\n| Physical stock | 13,298 | 14,511 |\n| Rank deficit | 2,496 | 2,496 |\n| Certified coarse saving | 0.001183986549206329 | 0.001122122700265139220566 |\n\nBoth exact moments include the retained bad-branch allowance. Six fixed bootstrap levels and all 47 strict outer inequalities give the displayed κ; the next grid point and invalid-parameter controls are rejected. The result is calculated from the two emitted programs, not by adding independently reported gains.\n\n## Contribution sources and prior PRs\n\n| Source | Contributor | Retained contribution |\n| --- | --- | --- |\n| [#425](https://github.com/CrocSwap/integer-mult-bounds/pull/425), `e11ccea1d092beb1b01b4ee4ce49da478234254c` | Zhihao Chen, with OpenAI Codex | Mutable-basis Hamming packets, common-frame scalar interface and complex verification. |\n| [#426](https://github.com/CrocSwap/integer-mult-bounds/pull/426), `88d552526893cd15325948bb1487e9a4d4bf32f6` | ai-nanachi, with OpenAI Codex | R767 bit word, 55 clean-reset reuses and 54 frame changes. |\n| [#386](https://github.com/CrocSwap/integer-mult-bounds/pull/386) | Zhihao Chen, with OpenAI Codex | Compressed nine-stage geometry, routes, ownership and finite accounting. |\n| [#370](https://github.com/CrocSwap/integer-mult-bounds/pull/370) | Dylan Crow, with Anthropic Claude | Hamming E8 bit producer, root table and record exporter. |\n| E8 and retained framework | Jacob Sussman and the credited upstream contributors | E8 unit, frame/compiler, rational-pricing and analytic interfaces; original notices preserved. |\n\nMy earlier contributions remain historical context for this work:\n\n| PR | Contribution |\n| --- | --- |\n| [#10](https://github.com/CrocSwap/integer-mult-bounds/pull/10) | Batched recursive boundaries. |\n| [#18](https://github.com/CrocSwap/integer-mult-bounds/pull/18) | Partial-swap frames and unequal tensor factors. |\n| [#24](https://github.com/CrocSwap/integer-mult-bounds/pull/24) | Endpoint and gauge integration. |\n| [#32](https://github.com/CrocSwap/integer-mult-bounds/pull/32) | Compatible constructions and certificates. |\n| [#36](https://github.com/CrocSwap/integer-mult-bounds/pull/36) | Structured semantic/bulk assembly. |\n| [#104](https://github.com/CrocSwap/integer-mult-bounds/pull/104) | Stopped product-ring integration. |\n| [#115](https://github.com/CrocSwap/integer-mult-bounds/pull/115) | Selected partial gauges. |\n| [#130](https://github.com/CrocSwap/integer-mult-bounds/pull/130) | General frames and three-stage covers. |\n| [#144](https://github.com/CrocSwap/integer-mult-bounds/pull/144) | Paired cubes, original-source chronology and shared completed cores. |\n\nThe new split-centre construction, source-basis composition and integration are contributed by **icekylinx**, with substantial **OpenAI Codex** assistance. Earlier Pro exploration used **GPT-6 Astra**. Existing authorship, licenses and source-specific AI disclosures are preserved in `NOTICE.md`, `notices/` and `SOURCES.json`.\n\n## Proof and validation\n\nThe selected package is `research/split-centres-global/`:\n\n- `PROOF.md`: split-centre cancellation, arbitrary-dirt lifting, source-centre/reflected chronology and conditional assembly.\n- `CERTIFICATE.json`: both component bounds, fresh finite invoice, bootstrap cutoffs and all 47 strict outer margins.\n- `EXPECTED.json`, `SOURCES.json`, `MANIFEST.json`: exact result, source pins and byte-level bindings.\n- `verify.py`: standard-library reproduction; dedicated CI covers Python 3.11 and 3.14.\n\nThe clean-directory incremental replay passed locally on Python 3.14.8:\n\n- All 800 complex and 998 bit local columns; both orientations, arbitrary dirty restoration and private-work erasure.\n- All 7,782 unbanked global bit columns, 54,576 bit bank assignments, and the complex owner/padding/cover decoder.\n- The 248 changed complex Gaussian pairs, with 2,670 unchanged verified pairs retained by exact source hashes; all 240 endpoint adapters.\n- The changed bit nested-frame/reflection checks, both fresh finite invoices, two rational moment engines, strict assembly and mutation controls.\n\n```sh\npython3 -B research/split-centres-global/verify.py /tmp/split-centres-check\n```\n\nTo regenerate every selected Gaussian phase pair, add `--replay-phases` and use another fresh output directory. The default reuses phase evidence only when the regenerated canonical word and full recipe hashes match. The unchanged historical full suite was not rerun; no PDF was built. CI for this commit is not represented as passed before it runs.\n\nThis remains a finite conditional construction. The inherited all-size interfaces remain assumptions; no unchanged legacy gx/gxcore acceptance, new Lean proof, global optimality or unconditional multiplication theorem is claimed. The main selected certificate is left for maintainer 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1.237551733247294·10⁻³**, **+9.218% over #434** (1.133100552284434·10⁻³). The bit supplier binds. It is also +8.67% above the newest posted value, #441 (1.138798055343319·10⁻³). Hosting changes only the global template, so it should stack on #440/#441's R740 word as well.\n\n## Change and mathematical scope\n\nIn the compressed nine-stage window, idle data pairs are brought to the active level by idle advance children (ranks 48/32/16/8 for complex, 42/28/14/7 for bit). These children are about a sixth of the paid cost.\n\nA dirty helper residual acts on whatever stream owns it as an exact coordinate factor, independent of the stream's contents. That is the inherited correlated dirty-bank fact that banks already rely on. It is the same kind of factor an idle child applies to its pending coordinates. So a helper residual can be owned by an idle data family instead of a bank slot, on coordinates that family would advance later, and the child keeps only the rest.\n\nThe validity condition is a window: the family must be untouched (no local invocation on its pair, no bridge naming it) between the hosting invocation and its advance. Neither local word changes.\n\n## Result\n\n| supplier | parent saving | hosted saving | live stock | max child | hosted residuals |\n| --- | --- | --- | --- | --- | --- |\n| bit, m = 64, #434 R747 | 1.134386·10⁻³ | **1.239085·10⁻³** | 14,259 → 9,457 | 42 → 8 | 39,568 of 53,784 |\n| complex, m = 73, #433 R560 | 1.183987·10⁻³ | **1.267453·10⁻³** | 12,720 → 8,400 | 48 → 8 | 34,560 of 40,320 |\n\nThe rank deficit stays at 2496 on both sides.\n\n## Validation\n\n`python -B research/idle-axis-hosting/verify.py /absolute/new/output` uses the standard library only. It:\n\n1. runs #434's complete verifier from scratch;\n2. regenerates both hosted templates from #434's fresh outputs and a frozen integer-programme selection (`--discover` recomputes the selection with scipy);\n3. runs an independent audit that shares no code with the generators:\n - windows re-derived from each schedule;\n - for every invocation and replica: exactly one owner per helper, and slots in window, inside their child's pending set, disjoint, and off the active pair;\n - exact remainder children, exact bank tiling, a recomputed profile and deficit;\n - nine mutation controls rejected;\n4. computes two rational moments per supplier and fresh finite invoices with the hosted stock:\n - two extra route factors are charged per helper selector;\n - the parent's larger complex per-vertex bill is kept;\n5. runs #434's strict outer assembly: six bootstrap levels and all 47 inequalities, with the next grid point and the zero-η, zero-β and unit-β controls rejected.\n\n### Open obligations\n\n[PROOF.md](research/idle-axis-hosting/PROOF.md) gives the hosting lemma. It extends the inherited correlated dirty-bank / compressed-window interface to data streams during idle windows; that extension is the principal review point. The global operator identity is argued, not replayed numerically on the address spaces, as for the parents' banks.\n\nThe all-size compiler, restored-work, tape/common-grid, precision and analytic interfaces remain inherited assumptions. No Lean proof and no unconditional integer-multiplication theorem is claimed.\n\n## Credits and AI disclosure\n\nThis builds on and runs unchanged:\n\n- #434 (Rohan Arun, OpenAI Codex);\n- #433 (icekylinx);\n- #435/#417 (chafreaky);\n- #426 (ai-nanachi);\n- #425/#386 (Zhihao Chen, OpenAI Codex);\n- #370 (Dylan Crow);\n- Jacob Sussman's E8 unit and interfaces.\n\nThe hosting construction, generators, audit and assembly were prepared with assistance from Claude. No inherited file is changed.\n\nLocal transcript: `PASS_FULL_IDLE_AXIS_HOSTING_COMPOSITION` on macOS (Apple silicon) with Python 3.14.8 and Python 3.12.13; each run replays #434 in full (about 2 minutes) before the hosting steps. 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= 1.138798055343319e-3: R740 block retiming after shared-donor kernel","user":{"login":"eumemic","id":94939491,"node_id":"U_kgDOBaipYw","avatar_url":"https://avatars.githubusercontent.com/u/94939491?v=4","gravatar_id":"","url":"https://api.github.com/users/eumemic","html_url":"https://github.com/eumemic","followers_url":"https://api.github.com/users/eumemic/followers","following_url":"https://api.github.com/users/eumemic/following{/other_user}","gists_url":"https://api.github.com/users/eumemic/gists{/gist_id}","starred_url":"https://api.github.com/users/eumemic/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/eumemic/subscriptions","organizations_url":"https://api.github.com/users/eumemic/orgs","repos_url":"https://api.github.com/users/eumemic/repos","events_url":"https://api.github.com/users/eumemic/events{/privacy}","received_events_url":"https://api.github.com/users/eumemic/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"κ = 1.138798055343319e-3 = 1138798055343319/1000000000000000000\n\nThis conditional construction improves frozen PR #440's κ by 0.21069% through joint frame changes on neighboring primitive B-phase ADDs. Individual-gate descent had reached a local optimum; moving compatible groups together permits a better complete paid profile while preserving every scalar ADD, operand and its order.\n\nThe construction reproduces the R740 word from #436, applies the 112-pivot shared-donor kernel and 57 A-phase changes published in #440, then applies two deterministic B-phase stages: 112 changes from paired gates and 42 further changes from larger windows. Because the stages overlap, there are 126 net changed B frames relative to #440. Every frame remains in the same 944-frame family.\n\nThe final canonical word SHA256 is `00d8aa8608e40b53fd8752399de06cb730cc55caaadc528f88379cb31b8460a6`. The complete local paid profile is `{1:2528, 2:1004, 3:284, 4:347, 5:118, 7:14, 8:9}`. The 740 helpers retain total entrance rank 136, 723 banks per stage, 14,187 live families and rank deficit 2,496. All 15 explicit residual isometries and their elementary routing costs are checked again.\n\nThe bit lower endpoint is `0.001140096394900736521536`; #433's complex lower endpoint remains `0.001183986549206329`. Verification reconstructs both suppliers, replays all 2,918 complex Gaussian phase edges, checks all 980 local columns with arbitrary dirty restoration, both reflected ledgers, 7,620 global scalar columns, 53,280 helper assignments, complete paid profiles and finite invoices. Two rational moment engines and an independent third calculation support six finite bootstrap levels and all 47 strict outer inequalities; the adjacent 10^-18 grid point and corrupted witnesses are rejected.\n\n```sh\npython3 -B research/r740-block-retimed-kernel/verify.py /tmp/r740-block-kernel-proof --replay-phases\n```\n\nThe initial complete replay passed on Python 3.12.13. The exact committed archive `6160c13526f5f957902910b462164c93c1d8f39a` completed all 15 steps with exit 0 on Python 3.14.7; the independent audit matched the Python 3.12 result. The release manifest is `bb78de6b1aca67601456fe9701d4bea70b09ba4b3ddef1373822076a35478634`. A dedicated workflow covers both versions; remote CI is pending at creation. This is a new branch and new PR; #440 and all earlier published heads and claims remain frozen.\n\nThis remains a finite conditional witness under the inherited all-size compiler, correlated dirty-bank, compressed-window, restored-work, tape/common-grid, precision and analytic interfaces. It does not assert an unconditional multiplication theorem or a new Lean proof.\n\nThis joint-frame search, deterministic witnesses, integration and independent audits were prepared for eumemic with substantial OpenAI Codex assistance. Source-specific licenses, hashes and AI disclosures remain in `NOTICE.md`, `SOURCES.json`, `notices/` and `vendor/`: eumemic #436/#440; chafreaky #417 kernel mechanism and #439 residual routes; Rohan Arun #434 primitive-retiming inspiration and #435/#438 mixed banks; icekylinx #433; Zhihao Chen #425/#386; Dylan Crow #370; ai-nanachi #426, applecrusher #376, Jacob Sussman and the retained compiler/analytic 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142050466976941/125000000000000000\n\nThis conditional construction combines a new shared-donor kernel on the frozen R740 bit word from #436 with 57 changes to individual A-phase gate frames. The literal scalar ADD sequence is unchanged by retiming. It exceeds the latest reported #434 claim of 0.001134387517668085 (head `f5e0af60ae91e39528d63782ac06f4c6f0e956e3`) by 0.17774%, #439 by 0.21833%, and #438 by 0.25544%. The complex supplier remains #433, with its construction and every selected Gaussian phase replayed here.\n\nThe kernel uses 112 pivots, 100 donor slots and total entrance rank 136. Eight replicas tile the residual widths into 723 width-64 banks per stage. All 15 entrance frames have explicit residual isometries; their elementary coordinate permutations are checked, bound to each owner, and charged in the finite invoice. Live/physical stock is 14,187/14,196, with rank deficit 2,496.\n\nThe final canonical word SHA256 is `bae58f0692326f180ba49642360fd55557f59a93a96a8fa62bf7babd55d2384e`. Its complete local paid profile is `{1:2500, 2:990, 3:326, 4:389, 5:90, 8:9}`. Both orientations restore all 980 formal columns, including arbitrary dirt in 740 helpers; both reflected ledgers and integer source spans are checked. The complete global replay covers 7,620 scalar columns, 53,280 helper assignments and all 72 local invocations.\n\nThe exact bit lower endpoint is `0.001137696618503020372244`; the replayed complex lower endpoint is `0.001183986549206329`. Two rational moment engines, an independent third calculation, six finite bootstrap levels and all 47 strict outer inequalities verify the stated exponent. The adjacent 10^-18 grid point and corrupt route witnesses are rejected.\n\nReproduce with Python's standard library:\n\n```sh\npython3 -B research/r740-shared-donor-kernel/verify.py /tmp/r740-kernel-proof --replay-phases\n```\n\nThe initial uninterrupted full replay passed on Python 3.12.13. The exact committed archive `bd03373b6d4d4e380d0b6ea7d55cd2ac8f163544` also completed all 15 steps with exit 0 on Python 3.14.7. The independent audit receipts match exactly; all 93 package files match their committed blobs and manifest `0c27346bb5a784e24ceaf3888c710d7947deba2e2cac7e8649af44f83611637b`. A dedicated workflow repeats the full check on Python 3.12 and 3.14; remote CI is pending when this PR is opened. Previously published PR heads and claims remain frozen.\n\nThis is a finite conditional witness. The inherited all-size compiler, correlated dirty-bank, compressed-window, restored-work, tape/common-grid, precision and analytic interfaces remain assumptions. No unconditional multiplication theorem or new Lean proof is claimed.\n\nAttribution and original licenses/disclosures are preserved in `NOTICE.md`, `SOURCES.json`, `notices/` and `vendor/`: eumemic's #436 R740 producer/reuse word (with Anthropic Claude assistance); chafreaky's #417 kernel mechanism and #439 explicit residual-route checks; Rohan Arun's #435/#438 mixed-width admission and #434 primitive-retiming composition; icekylinx's #433 split centres and assembly; the retained #426/#389/#376/#370, #425/#386 and earlier Jacob Sussman/compiler/analytic contributions. The new selection, 57-frame retiming, integration and independent audits were prepared for eumemic with substantial OpenAI Codex 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1133508328719775/10¹⁸ = 0.001133508328719775.** That is +4.08e-7 over #434's current head (0.001133100552284434), +0.414 % over #435 and +1.13 % over #433. The bit supplier binds; #433's split-centre complex supplier (b = 0.001183986549206329) is unchanged.\n\nStacked on #433. One package, `research/split-centres-kernel-r747/`. The bit word is built in four steps:\n1. #433's R758 source-centre word;\n2. #434's eleven chronological clean resets (R747), using #434's own reconstruction, vendored;\n3. #417's shared-donor response kernel, **re-derived on the R747 word** with #417's discovery tools (40 ILS chains at m = 64): 118 entries, total entrance rank 160, 119 donor slots, no new frames;\n4. #386's compressed nine-stage geometry with exact mixed-width bank tiling, as introduced in #435: 727 banks per stage, live stock 14,223, rank deficit 2,496.\n\n| bit word | bit lower |\n|---|---:|\n| R758 (#433) | 0.001122122700265139 |\n| R747 resets (#434 v1) | 0.001129525236098816 |\n| R758 + kernel (#435) | 0.001130108533947480 |\n| **R747 + kernel re-derived on R747 (this PR)** | **0.001134794627881866** |\n\n**Verification (passed):** `python3 -B research/split-centres-kernel-r747/verify.py /tmp/out` (~30 s, standard library only) → `PASS conditional kappa 0.001133508328719775`. It runs every check from #433, plus the reset reconstruction with its three controls; the kernel stage with exact replay (legality, F₂ on all 987 columns, source spans); the mixed-width bank tiling in `bit_global` and in the independent `bit_audit`, with mutation controls; a fresh finite invoice (226-bit prefix charged at 256); and six bootstrap levels with all 47 strict outer inequalities.\n\nCredits: icekylinx (#433), rohanarun / OpenAI Codex (#434 resets), chafreaky (#417 kernel, vendored), ai-nanachi (#426), Zhihao Chen / jacklightChen (#425, #386), Dylan Crow (#370), J. 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kappa 0.001018766833114736: checker-clean chronological gauges and R767 reuse","user":{"login":"ai-nanachi","id":340844424,"node_id":"U_kgDOFFDfiA","avatar_url":"https://avatars.githubusercontent.com/u/340844424?v=4","gravatar_id":"","url":"https://api.github.com/users/ai-nanachi","html_url":"https://github.com/ai-nanachi","followers_url":"https://api.github.com/users/ai-nanachi/followers","following_url":"https://api.github.com/users/ai-nanachi/following{/other_user}","gists_url":"https://api.github.com/users/ai-nanachi/gists{/gist_id}","starred_url":"https://api.github.com/users/ai-nanachi/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/ai-nanachi/subscriptions","organizations_url":"https://api.github.com/users/ai-nanachi/orgs","repos_url":"https://api.github.com/users/ai-nanachi/repos","events_url":"https://api.github.com/users/ai-nanachi/events{/privacy}","received_events_url":"https://api.github.com/users/ai-nanachi/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"## Change and mathematical scope\n\nRaise the pending conditional candidate from PR #389's `0.000998634658090834606116833` to **`0.001018766833114735805248075`**, exactly\n`40750673324589432209923 / 40000000000000000000000000`.\nThe complex supplier now binds; the target `0.002` has not been achieved.\n\nReconstruct our R779 complex word and compose the credited shared-donor, re-pivoted, enlarged and ordered entrance constructions. The resulting word has 202 entrance gauges, dimension mass 360 and 551 chronological unit shears. Both unchanged `gx.check1` and `gxcore.mirror` pass. An incompatible target-124/125 transfer is excluded. Chronological omission controls use the literal suffix response and read-before-write invariant; they do not assume that the complete ordered entrance product has square-zero off-diagonal part.\n\nThe R767 bit word contains 55 clean-reset reuses and 54 legal frame moves. Every newly allocated helper retains an independent arbitrary dirty column. With the same new complex supplier and the old bit word, the exact fair-control candidate is `0.001016774267814750149837485`; the bit changes improve the composed candidate by `199256529998565541059 / 100000000000000000000000000` and remove that bottleneck.\n\nUpdate the README, proof, contributor/source credits, research record and pending candidate certificate together. The selected maintainer certificate is not promoted. Preserve the frozen PR #389 package and bind the new witnesses and original vendor bytes by manifests. Three separately scoped exact negative proofs document limits of frozen-center bases, arbitrary rank-eight completions, and fixed first-frame/full-residual bank budgets; none asserts a global impossibility for changed architectures.\n\nThis is a finite conditional witness. The all-size compiler, recursive suppliers, compressed Clifford windows, correlated dirty-bank/cover, restored-row, routing, fixed-tape, precision/recovery and analytic interfaces remain assumed. No unconditional multiplication exponent or Lean formalization is claimed.\n\nCredits: applecrusher/Sussman E8 lineage and PR #376; prefix/signed work in #390/#395; Dugongue's response-space/shared-donor work in #401/#404; ordered/enlarged constructions in #409/#410; chafreaky's checker-clean re-pivoting and composition in #412; and the preceding bit/global/outer sources listed in `SOURCE-PINS.json` and the preserved notices. Prepared by ai-nanachi with substantial OpenAI Codex assistance; Apache-2.0.\n\n## Validation\n\nThe complete public replay passed locally: full frozen predecessor, reconstructed R779 intermediate, composed chronological word, 6,482 freshly recomputed old/new/reflected Gaussian phase pairs, all 1,019 complex and 1,007 bit local columns, all 1,487 bit global columns, native address phases, physical bank ownership/readback, finite invoices and reserve bridges, two exact rational moment engines, all 47 strict outer inequalities and adverse controls. The selected gen4 full replay and the affected historical joint-dual replay also passed. Independent scope review re-ran both original complex checker families and checked the candidate record.\n\nReproduce from a clean checkout with Python, C++17 and Boost:\n\n```sh\npython -m pip install -r research/e8-clean-reuse-extension/requirements.txt\npython -B research/e8-clean-reuse-extension/verify.py /absolute/path/to/fresh/output\npython -B research/e8-clean-reuse-extension/record.py\npython -B research/e8-structural-frontiers/verify.py /absolute/path/to/another/fresh/output\n```\n\nNo network, discovery search or cached phase admission is required. The committed Git blobs were checked against every package manifest, including the frozen predecessor; all 158 imported upstream blobs also matched their exact original bytes.\n\n**Linux CI passed on the current commit:** [full Python 3.13/3.14 replay](https://github.com/ai-nanachi/integer-mult-bounds/actions/runs/38134463965) passed both jobs, and [52 historical regression jobs](https://github.com/ai-nanachi/integer-mult-bounds/actions/runs/38134463961) passed all 52 jobs. Both runs bind commit `88d552526893cd15325948bb1487e9a4d4bf32f6`. CI was running at submission; this paragraph was updated after both runs completed successfully. An earlier CI attempt correctly rejected Git-normalized witness bytes; the subsequent commit preserves those bytes and passes the complete blob/manifest checks. Maintainer review remains pending. Upstream pull-request workflows are awaiting maintainer authorization; these passing runs are on the fork and do not constitute maintainer approval.\n","created_at":"2026-10-11T11:17:05Z","updated_at":"2026-10-11T12:25:07Z","closed_at":null,"merged_at":null,"merge_commit_sha":"245db797a166e4ee891aad7123a69e6359c66986","assignees":[],"requested_reviewers":[],"requested_teams":[],"labels":[],"milestone":null,"draft":false,"commits_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/pulls/426/commits","review_comments_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/pulls/426/comments","review_comment_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/pulls/comments{/number}","comments_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/issues/426/comments","statuses_url":"https://api.github.com/repos/CrocSwap/integer-mult-bounds/statuses/88d552526893cd15325948bb1487e9a4d4bf32f6","head":{"label":"ai-nanachi:codex/e8-extension","ref":"codex/e8-extension","sha":"88d552526893cd15325948bb1487e9a4d4bf32f6","user":{"login":"ai-nanachi","id":340844424,"node_id":"U_kgDOFFDfiA","avatar_url":"https://avatars.githubusercontent.com/u/340844424?v=4","gravatar_id":"","url":"https://api.github.com/users/ai-nanachi","html_url":"https://github.com/ai-nanachi","followers_url":"https://api.github.com/users/ai-nanachi/followers","following_url":"https://api.github.com/users/ai-nanachi/following{/other_user}","gists_url":"https://api.github.com/users/ai-nanachi/gists{/gist_id}","starred_url":"https://api.github.com/users/ai-nanachi/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/ai-nanachi/subscriptions","organizations_url":"https://api.github.com/users/ai-nanachi/orgs","repos_url":"https://api.github.com/users/ai-nanachi/repos","events_url":"https://api.github.com/users/ai-nanachi/events{/privacy}","received_events_url":"https://api.github.com/users/ai-nanachi/received_events","type":"User","user_view_type":"public","site_admin":false},"repo":{"id":1413965665,"node_id":"R_kgDOVEdnYQ","name":"integer-mult-bounds","full_name":"ai-nanachi/integer-mult-bounds","private":false,"owner":{"login":"ai-nanachi","id":340844424,"node_id":"U_kgDOFFDfiA","avatar_url":"https://avatars.githubusercontent.com/u/340844424?v=4","gravatar_id":"","url":"https://api.github.com/users/ai-nanachi","html_url":"https://github.com/ai-nanachi","followers_url":"https://api.github.com/users/ai-nanachi/followers","following_url":"https://api.github.com/users/ai-nanachi/following{/other_user}","gists_url":"https://api.github.com/users/ai-nanachi/gists{/gist_id}","starred_url":"https://api.github.com/users/ai-nanachi/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/ai-nanachi/subscriptions","organizations_url":"https://api.github.com/users/ai-nanachi/orgs","repos_url":"https://api.github.com/users/ai-nanachi/repos","events_url":"https://api.github.com/users/ai-nanachi/events{/privacy}","received_events_url":"https://api.github.com/users/ai-nanachi/received_events","type":"User","user_view_type":"public","site_admin":false},"html_url":"https://github.com/ai-nanachi/integer-mult-bounds","description":"Conditional integer multiplication: kappa > 2^-15. 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gx/gxcore-clean κ = 1.019752143318808·10⁻³: our #424 layers, 14 gate-frame retimings and a target-172 prefix on #426's R779 word (+9.85·10⁻⁷ over #426)","user":{"login":"chafreaky","id":4400527,"node_id":"MDQ6VXNlcjQ0MDA1Mjc=","avatar_url":"https://avatars.githubusercontent.com/u/4400527?v=4","gravatar_id":"","url":"https://api.github.com/users/chafreaky","html_url":"https://github.com/chafreaky","followers_url":"https://api.github.com/users/chafreaky/followers","following_url":"https://api.github.com/users/chafreaky/following{/other_user}","gists_url":"https://api.github.com/users/chafreaky/gists{/gist_id}","starred_url":"https://api.github.com/users/chafreaky/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/chafreaky/subscriptions","organizations_url":"https://api.github.com/users/chafreaky/orgs","repos_url":"https://api.github.com/users/chafreaky/repos","events_url":"https://api.github.com/users/chafreaky/events{/privacy}","received_events_url":"https://api.github.com/users/chafreaky/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"## Conditional κ = 127469017914851/1.25·10¹⁷ ≈ 1.019752143318808·10⁻³ (complex-bound; gx.check1 + gxcore clean)\n\nPackage: `research/e8-r779-retimed-closure`\nCommit: `642b702149b975e3a535f139243cd3afd286e868`\nLocal branch: `research/e8-r779-retimed-closure`\n\nThis is the best result we know of that is clean under Sussman's `gx.check1` (E0–E7, exact scalar replay, gauged-dirt rule) and `gxcore` (sixths mirror).\n- +9.85·10⁻⁷ over ai-nanachi's #426 (1.018766833e-3, checker-clean).\n- +1.06·10⁻⁷ over rohanarun's #429 (1.019646576e-3). #429 is a price-only draft on #422's word, which keeps #404's 124/125 recovery and #411's quarter target-144 prefix, and neither claims gx/gxcore acceptance.\n- +1.24·10⁻⁶ over our #424.\n\nFor context: jacklightChen's #425 (≈1.048005508e-3) and its follow-up #431 use a Hamming-packet complex network under their own lemma, in place of gx's source-immutability and target-read rules. They are not comparable under these checkers.\n\nThe complex side binds: b = 255198274817418511443/2.5·10²³ ≈ 1.020793e-3. The bit side is #404's pinned c ≈ 1.021539e-3 > b.\n\n### Construction (`code/compose426.py`)\n1. **Input: #426's R779 gauged word**, pinned byte-for-byte (blob 0daa4323), with 202 gauges after the 556/577 helper inlining.\n - Control: our own emitter and price, at #426's 8 replicas and bank patterns, reproduce #426's complex coefficient 254951444354246755323/2.5·10²³ and its profile exactly.\n - Re-implementing the two substitutions directly on #398's signed R781 word (our #424 base) is frame-infeasible, so we start from #426's word.\n2. **Our #424 layers, mapped to R779:**\n - #414's group, #416's promotions and our 947 re-pivot, #420's 672, and #421's 435/367: 52 literal shears, 213 gauges, operator identity on all 1,019 columns, every gauged response column zero;\n - the 14 enlargements (13 of #423's and our 838);\n - fused sinks 301/387;\n - #402's 177/220 re-synthesis, relocated with restore source y221 (y180 fails gx E4 in #426's signed layer);\n - our target-124 helper prefix.\n3. **Fourteen fixed-scalar gate-frame retimings: 12 single gates and 2 five-gate blocks.**\n - The idea is eumemic's (#427/#428). The exact search on our word is ours.\n - Thirteen bases coincide with #428's eleven and #427's two. The fourteenth (B1157 → rank 7) is new.\n - Scalar words and the full raw operator are unchanged. `--regen` re-runs the search.\n4. **New target-172 helper prefix.**\n - Deliveries: −h562/2 at frame 336, h358/2 at 904, −h367/2 at 904 and −h280/2 at 724.\n - Protected columns are unchanged, and the histogram moves by {2:+1, 3:−2, 4:+1}. Omitting a delivery fails E5.\n5. **Price at 64 replicas.**\n - 5,845 width-73 banks per stage and live stock 114,045. The 128 fused occurrences own slot 0 of distinct padded banks.\n - The replica sweep (8–128) is at most the 64-replica value.\n\n### Negative screens on this word (exploration)\n- **Promotions:** 1/2/3-donor promotions (5,659 candidates) found no gain.\n- **Enlargements:** single, two-dimension, pair-joint and triple-joint enlargements (3,554 candidates) all break final frames under closure.\n- **Further inlining:** extra equal-helper inlinings are frame-infeasible.\n- **Sinks:** 324 still fails gxcore E5.\n- **Prefixes:** an all-target prefix search finds only 124/172.\n- **Retimings:** none are left after the fourteen.\n\n### Verify (fresh clone; Python 3.11+, stdlib only)\n bash research/e8-r779-retimed-closure/verify.sh --quick /tmp/e8r-q # ~30 s\n bash research/e8-r779-retimed-closure/verify.sh /tmp/e8r-full # ~90 s, adds the retiming-search regeneration\nBoth pass from a fresh clone, and the tree is unchanged afterwards. The script runs:\n- the manifest and git-blob pin checks;\n- our #424 pipeline as a control;\n- `compose426.py`;\n- `gx.check1`, `gxcore`, our flipped-sign control and our source-span rule on both words.\n\n### Admitted conditions\n- **Re-opened here:**\n - the phases of the 11 promoted gauges, the 14 enlarged entrance tokens, and the 39 raised and 22 retimed gate frames;\n - the 124/172 and 177/220 target edges with their changed ungauged dirt;\n - the fused-slot owner placement.\n- **Inherited and not re-run:**\n - #426's phases, routes and invoice;\n - #401/#404 normalisation;\n - the finite invoice;\n - the bit component, via #404's pinned RESULT.json.\n\nThis is a conditional finite construction, not a formal verification.\n\n### Credits\n- @ai-nanachi: #426 (R779 inlining, gauge layer, input word).\n- @eumemic: #427/#428 (retiming idea), #423, #421, #420, #416, #414, #411, #410, #408.\n- @rohanarun: #429 (comparison), #422, #418, #415, #409, #406, #405, #403, #400, #396, #395, #387/#392.\n- @Dugongue: #404, #401, #398, #390.\n- @applecrusher: #376.\n- @jacklightChen: #377.\n- Jacob Sussman: E8 unit and gx/gxcore.\n- @DaysSky and @utcorvusvolat-dotcom: the bit lineage.\n- @DreamingOfClouds: #315 engines.\n- Ours (@chafreaky): #378, #394/#399, #402, #407, #412, #419, #424, and here the R779 composition, the retiming search with the new B1157 retiming, the target-172 prefix and the negative screens.\n\nPrepared by Chafik Boukhalfa (@chafreaky) with substantial Anthropic Claude assistance. 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κ = 1.018509848057013·10⁻³: checker-clean entrance enlargements, closure and rank-two gauges with a target-125 helper prefix on our #419 word (+1.75·10⁻⁷ over #423)","user":{"login":"chafreaky","id":4400527,"node_id":"MDQ6VXNlcjQ0MDA1Mjc=","avatar_url":"https://avatars.githubusercontent.com/u/4400527?v=4","gravatar_id":"","url":"https://api.github.com/users/chafreaky","html_url":"https://github.com/chafreaky","followers_url":"https://api.github.com/users/chafreaky/followers","following_url":"https://api.github.com/users/chafreaky/following{/other_user}","gists_url":"https://api.github.com/users/chafreaky/gists{/gist_id}","starred_url":"https://api.github.com/users/chafreaky/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/chafreaky/subscriptions","organizations_url":"https://api.github.com/users/chafreaky/orgs","repos_url":"https://api.github.com/users/chafreaky/repos","events_url":"https://api.github.com/users/chafreaky/events{/privacy}","received_events_url":"https://api.github.com/users/chafreaky/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"**Conditional κ = 1018509848057013/10¹⁸ ≈ 1.018509848057013·10⁻³ (complex-bound), checker-clean.**\n- This is +1.747·10⁻⁷ over eumemic's #423 (1.018335130e-3) and +3.42·10⁻⁸ over rohanarun's #422 draft (1.018475695e-3, price-only).\n- b = 254887067002137341481/2.5·10²³ ≈ 1.019548268e-3. The bit side is #404's pinned c ≈ 1.021539e-3 > b.\n- The word passes Jacob Sussman's `gx.check1` (E0–E7, exact scalar, gauged-dirt rule) and `gxcore` (sixths mirror), plus our flipped-sign and source-span controls.\n- #420–#423 state that they do not claim gx/gxcore E4/E5 acceptance. They keep #404's 124/125 recovery (gx E4) and #411's quarter 144 prefix (gxcore E5).\n\nBranch `research/e8-enlarged-closure` (local branch name), commit `92c6ea78f5cf726dc7621854d53140512ba1c46a`, on our #419 (`70a276c`). It includes #318's CI repair. Package `research/e8-enlarged-closure/`, workflow `.github/workflows/e8-enlarged-closure.yml`.\n\n**What is new over our #419** (`code/compose423.py`; PR files read as data and re-implemented):\n1. **Closure and rank-two gauges (eumemic).**\n - #420's closure gauge 672 → [48] and #421's rank-two gauges 435 → [304,111] and 367 → [259,246], with their relations unchanged (pinned blobs).\n - They are literal unit shears with frame closure. All 215 gauged response columns are zero.\n - The raw operator equals #412's word times the 52-shear prefix on all 1,021 columns.\n2. **Fourteen one-dimension entrance enlargements.**\n - Thirteen are #423's (eumemic), including the joint 914/960 → [48,12]. #423's 785 is not a gauge on our word; this is recorded.\n - The fourteenth is ours: 838 [204] → [304,204], from an exact screen of all 819 single enlargements.\n - No scalar instruction changes; the operator is identical on all columns.\n - 29 frames are raised by closure, and reverting any one fails gx E1.\n3. **Target-125 prefix re-synthesis (ours).**\n - y125's pre-cut writes are replaced by helper 563/2 @336, 367/2 @904 and −251/2 @724.\n - Only halves of helper rows are used, with no y source, so sixths are preserved.\n - The protected x/y/gauged columns are unchanged.\n - The chain goes (3,3,1,1) → (2,4,1,1), worth +1.02·10⁻⁸.\n4. **Price at 64 replicas.** 5,859 banks per stage and live stock 114,171. The 128 fused occurrences sit in distinct rank-1-padded banks. Replica sweep: 16 → 1.018468e-3, 32 → 1.018488e-3, 128 = 64.\n\n**Target 144: no sixths-legal prefix in the searched space (PROOF §19).**\n- **Search space.** Helper and x sources, delivered at their current or next touch frame, any number of deliveries, up to 4 frame groups, and shift/restore among same-frame sources.\n- **Method.** An exact rational solve plus a Hermite-normal-form lattice test (each group's x/gauged total must lie in (1/6)ℤ).\n- **Result.** Only (3,4,1) via 311 → 935 and (4,3,1) via 551 → 935 are solvable, and both fail the lattice test. Every source at 935 has x₆ = x₁₂/2, while the total has x₆ = x₁₂ = −½, so the early group carries x₆ = −¼.\n- y sources are excluded by E4, because 144 already reads y into 208.\n- Across all targets, 125 is the only new feasible form, and 144 is the only one blocked solely by sixths.\n\n**Other negative results.**\n- A screen of 933 one- and two-donor promotions found no further gain.\n- Pairs of enlargements found nothing either.\n- #418 and #422 compose the same eumemic selections, so there is nothing orthogonal to add from them.\n\n**Verify** (Python 3.11+, standard library only):\n\n bash research/e8-enlarged-closure/verify.sh --quick /tmp/e8e-q # 26 s\n bash research/e8-enlarged-closure/verify.sh /tmp/e8e-full # 2.5 min\n\nBoth passed from a fresh clone of the commit above, and the tree was unchanged afterwards. The #399, #402, #407, #412 and #419 pipelines run as controls.\n\n**Admitted conditions.**\n- **Re-opened here:**\n - the phases of the 3 new gauges, the 14 enlarged entrance tokens and the 39 raised frames;\n - the target-125 edges, whose changed ungauged dirt is recomputed by our emitter but not run through the native invoice;\n - owner placement of the 128 fused slots.\n- **Inherited and not re-run:** normalisation, phases, routes, the finite invoice and the bit component (#401/#404/#409/#410).\n\nThis is a conditional finite construction, not a formal verification.\n\n**Credits.**\n- **eumemic:** #423, #421, #420, #416, #414, #411, #410, #408.\n- **rohanarun:** #422, #418, #415, #409, #406, #392.\n- **Dugongue:** #404, #401, #398, #390.\n- **Others:** applecrusher (#376), jacklightChen (#377), Jacob Sussman (E8 unit, gx/gxcore), DaysSky and utcorvusvolat-dotcom (bit lineage), DreamingOfClouds (#315 engines).\n\nPrepared by Chafik Boukhalfa (chafreaky) with substantial Anthropic Claude assistance. 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= 0.001128832830332521: #417's shared-donor kernel on #433's R758 bit word (+0.71%)","user":{"login":"rohanarun","id":11659839,"node_id":"MDQ6VXNlcjExNjU5ODM5","avatar_url":"https://avatars.githubusercontent.com/u/11659839?v=4","gravatar_id":"","url":"https://api.github.com/users/rohanarun","html_url":"https://github.com/rohanarun","followers_url":"https://api.github.com/users/rohanarun/followers","following_url":"https://api.github.com/users/rohanarun/following{/other_user}","gists_url":"https://api.github.com/users/rohanarun/gists{/gist_id}","starred_url":"https://api.github.com/users/rohanarun/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/rohanarun/subscriptions","organizations_url":"https://api.github.com/users/rohanarun/orgs","repos_url":"https://api.github.com/users/rohanarun/repos","events_url":"https://api.github.com/users/rohanarun/events{/privacy}","received_events_url":"https://api.github.com/users/rohanarun/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"**Conditional κ = 1128832830332521/10¹⁸ = 0.001128832830332521**: +0.712 % over #433 (0.001120864952258278). The bit supplier binds; #433's split-centre complex supplier (b = 0.001183986549206329) is unchanged.\n\nStacked on #433 (icekylinx). One new package, `research/split-centres-kernel/`.\n\n**Change (bit side only).** chafreaky's #417 shared-donor response kernel, re-derived with #417's own discovery tools (ILS, χ scored at m = 64, 40 chains) on #433's R758 source-centre word:\n- 128 entries, with pivots entering at existing root-closed frames of rank 1 and 4;\n- total entrance rank 200;\n- 124 donor slots;\n- no new frames.\n\n`code/bit_kernel.py` applies the frozen selection. It then re-runs #417's exact replay: legality, F₂ on all 998 columns with dirt, and the source-span rule. Two assertions are widened for #433's source-row destinations and retained totals. The script also binds the output hash.\n\n**Compressed geometry with entrances.** A helper entering at rank e has residual width 8 − e. The 8 × 758 helper slots per stage tile exactly into width-64 banks, 733 per stage instead of 758:\n- eight width-7 slots plus one width-8 slot;\n- sixteen width-4 slots;\n- eight width-8 slots.\n\nLive stock is 14,277 (was 14,502), and the rank deficit stays 2,496. `bit_global.py` and the independent `bit_audit.py` check every owner route (bank, offset, width = 8 − entrance rank) and exact, padding-free coverage of every bank.\n\n| | bit lower | κ |\n|---|---:|---:|\n| #433 | 0.001122122700265139 | 0.001120864952258278 |\n| this PR | 0.00113010853394748 | 0.001128832830332521 |\n\n**Verification (passed):** `python3 -B research/split-centres-kernel/verify.py /tmp/out` (~30 s, standard library only) → `PASS conditional kappa 0.001128832830332521`. It covers all of #433's checks: both changed words, reflected programs, bank ownership, two rational moment engines and the 47 strict outer inequalities. The new kernel stage, mixed-width bank tiling and audit are included. The bit audit's mutation controls (including a re-used bank slot and understated live stock) are rejected.\n\nCredits: icekylinx (#433), chafreaky (#417 kernel mechanism and code, vendored), ai-nanachi (#426), Zhihao Chen / jacklightChen (#425, #386), Dylan Crow (#370), J. Sussman (E8).\n\n🤖 Generated with [Claude 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κ = 1.017962405296845·10⁻³: checker-clean grouped and frame-closure entrance promotions with a target-124 helper prefix on our #412 word (+3.9·10⁻⁸ over #418; #414–#416 fail gx E4/gxcore E5)","user":{"login":"chafreaky","id":4400527,"node_id":"MDQ6VXNlcjQ0MDA1Mjc=","avatar_url":"https://avatars.githubusercontent.com/u/4400527?v=4","gravatar_id":"","url":"https://api.github.com/users/chafreaky","html_url":"https://github.com/chafreaky","followers_url":"https://api.github.com/users/chafreaky/followers","following_url":"https://api.github.com/users/chafreaky/following{/other_user}","gists_url":"https://api.github.com/users/chafreaky/gists{/gist_id}","starred_url":"https://api.github.com/users/chafreaky/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/chafreaky/subscriptions","organizations_url":"https://api.github.com/users/chafreaky/orgs","repos_url":"https://api.github.com/users/chafreaky/repos","events_url":"https://api.github.com/users/chafreaky/events{/privacy}","received_events_url":"https://api.github.com/users/chafreaky/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"## Conditional κ = 1.017962405296845·10⁻³: checker-clean grouped and frame-closure promotions with a target-124 prefix (+1.64·10⁻⁷ over #416)\n\nThe exact value is **κ = 203592481059369 / (2·10¹⁷) ≈ 1.017962405296845·10⁻³**. It is complex-bound, with b = 254749927172825437387/2.5·10²³ ≈ 1.018999709·10⁻³. The bit side is #404's, unchanged (c ≈ 1.021539·10⁻³ > b). Pairing it with our #417's bit (c ≈ 1.044064·10⁻³) gives the same κ.\n\n| comparison | Δκ |\n|---|---|\n| eumemic #416 (1.017798035·10⁻³) | +1.644·10⁻⁷ |\n| rohanarun #418 (1.017923291·10⁻³) | +3.91·10⁻⁸ |\n| rohanarun #415 | +1.763·10⁻⁷ |\n| eumemic #414 | +3.015·10⁻⁷ |\n| our #412 | +1.863·10⁻⁷ |\n\nThis is a conditional finite witness, not a theorem.\n\n### Change and mathematical scope\n\nThe base is our #412 word, unchanged: #404's gauges re-pivoted, #410's enlargements, #409's groups re-pivoted, fused sinks 301/387, and the 177/220 re-synthesis. On top of it:\n\n1. **#414's grouped promotion (eumemic).** Pivots 766, 917, 627 and 948 enter the rank-1 entrance [48]. #414's relations are used unchanged, as literal prepended shears.\n2. **#416's frame-closure promotions (eumemic).** These are 892 → [51], 669 → [12] and 644 → [63], with relations unchanged. Gate frames are raised to the span of their operands' frames (#416's rule, our code), which raises 5 frames on our word.\n3. **#416's 821 → [240], adapted.**\n - Its relation uses donor 748, which is our pivot (#407 re-pivots 555 → 748).\n - Re-solved on our word, the relation is unique on 821's other donors plus 555 and 947. It needs −½ on 947, which gxcore rejects (E5 at register 947, recorded as a control).\n - Pivoting the same relation on 947 makes the row integral, and gxcore passes.\n4. **Target-124 prefix re-synthesis.** This uses #411's prefix-window idea (itself adapted from our #402), with our own search and helper sources only.\n - 124's two B writes before its first positive-frame read are replaced by helper 563/2 at frame 336 and −helper 253/2 at frame 723.\n - The protected x, y and gauged columns of every row are unchanged. Only y124's and y171's ungauged dirt changes, and the emitter recomputes it.\n - Halves only and no y source, so gx E4 and E5 hold.\n - 124's chain goes (3,4,1) → (2,5,1).\n\nThe result has 212 gauges. The full raw operator and retained totals equal #412's gauged word times the literal 48-shear prefix on all 1,021 columns, and all gauged response columns are zero. With 32 replicas there are 2,939 banks per stage and 1,459 rank-1 paddings, and the 64 fused sink occurrences own distinct padded banks. Live stock is 57,171.\n\n**Checker status of the concurrent claims.** These are not checker-clean:\n- **#414, #415 and #416** keep #404's 124/125 recovery, so gx E4 fails.\n- **The same three** use #411's target-144 prefix, whose first −¼ delivery puts y144 in quarters. gxcore E5 rejects it at register 144; we reproduced this on our word. #411, #414, #415 and #416 state that they do not claim gx E5 acceptance.\n- **#416's raw 214-gauge entrance word** already fails gxcore E5 at register 947.\n\nThis word passes both of Sussman's checkers.\n\n**Retained hypotheses and re-opened items.**\n- Re-opened: the Gaussian phases of the 8 new entrance tokens and the 5 raised frames, and the target-124 edges and native invoice.\n- Inherited from #412 and its lineage: normalisation, routes, bank owners and invoice, and the bit component via #404's pinned `RESULT.json`.\n- The all-size compressed-window, compiler and analytic interfaces remain conditional.\n\n**Attribution**, by handle:\n- **eumemic:** #416 (frame-closure promotions), #414 (grouped promotion), #411 (target-prefix idea), #410 and #408.\n- **rohanarun:** #409, #406 and #392 (bootstrap); #415 and #418 as comparison claims.\n- **Dugongue:** #404, #401, #398 and #390.\n- **applecrusher:** #376.\n- **jacklightChen:** #377.\n- **Jacob Sussman:** E8 unit, `gx`/`gxcore`.\n- **DaysSky** and **utcorvusvolat-dotcom:** the bit lineage.\n- **DreamingOfClouds:** #315 engines.\n- **chafreaky:** #402, #407 and #412.\n\n#414's and #416's data files are vendored byte-identically (git-blob pinned, Apache-2.0). None of their scripts are run. Prepared by Chafik Boukhalfa (chafreaky) with substantial Anthropic Claude assistance.\n\nThe prerequisite is our #412, `616d9d678c00d79693b869934464003ba5b8d1b1`. The branch includes rohanarun's #318 three-file joint-dual source-pin repair, which is already in the base (`ac91a9c`), for repository CI. No mathematics changed there.\n\n### Validation\n\n- **Commit:** `70a276cb948e5be6071cde3f1bebdaf2f995ab8e` (local branch `research/e8-promoted-closure` in checkout `e8clean7`, on #412 `616d9d6`); package `research/e8-promoted-closure`; workflow `.github/workflows/e8-promoted-closure.yml`.\n- **Fresh clone of the branch:**\n - `bash research/e8-promoted-closure/verify.sh --quick OUT` passes in about 22 s.\n - `bash research/e8-promoted-closure/verify.sh OUT` (full, with every control regeneration) passes in about 2.5 min.\n - Python 3, standard library only.\n- **What the verifier covers:**\n - the manifest, with `MANIFEST.sha256` equal to `git ls-files`;\n - the git-blob pins of every vendored input (#390, #398, #401, #404, #408, #409, #410, #414, #416);\n - our #399, #402, #407 and #412 pipelines as controls;\n - section-by-section composition checks, all-column operator checks, and frame-reversion, omitted-shear and prefix-mutation controls;\n - the local program in both orientations, with 7 mutation controls each;\n - banks, and the exact price from two moment engines plus 47 strict outer constraints;\n - `gx.check1` and `gxcore`, with flipped-sign and source-span controls, on both #412's word and ours.\n- **CI:** 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conditional kappa 0.001018475695250068: grouped entrance capacity and shared-frame enlargement","user":{"login":"rohanarun","id":11659839,"node_id":"MDQ6VXNlcjExNjU5ODM5","avatar_url":"https://avatars.githubusercontent.com/u/11659839?v=4","gravatar_id":"","url":"https://api.github.com/users/rohanarun","html_url":"https://github.com/rohanarun","followers_url":"https://api.github.com/users/rohanarun/followers","following_url":"https://api.github.com/users/rohanarun/following{/other_user}","gists_url":"https://api.github.com/users/rohanarun/gists{/gist_id}","starred_url":"https://api.github.com/users/rohanarun/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/rohanarun/subscriptions","organizations_url":"https://api.github.com/users/rohanarun/orgs","repos_url":"https://api.github.com/users/rohanarun/repos","events_url":"https://api.github.com/users/rohanarun/events{/privacy}","received_events_url":"https://api.github.com/users/rohanarun/received_events","type":"User","user_view_type":"public","site_admin":false},"body":"Conditional κ = **0.001018475695250068** (`254618923812517/250000000000000000`), **0.01380345% above #423**.\n\nOn our #418 word, compose #414's four grouped promotions, #420's pivot 672, #421's two full rank-two promotions, then 13 of #423's 14 entrance enlargements. Pivot 785 is not an entrance on our word and is explicitly excluded; the unadapted transfer rejects. The final construction has 215 gauges and 587 entrance instructions. The last stage changes no scalar instruction and shares the frame costs of the paired 914/960 enlargement.\n\nValidation of the current mathematical code (`228c86d9a884dc827d90ccdadf7781ba46fb5eea`) passed:\n\n- All 1,021 complete and retained-snapshot columns through three hash-bound stages; literal shear multiplication in the first two, unchanged operators in the third; all gauged responses zero; chronological A/B frame propagation, snapshot/final endpoints, reverted-frame and omitted-gate controls.\n- Both formal scalar orientations, arbitrary dirty restoration, private erasure, chronological target bracket, 7,017 freshly recomputed response entries and 7,118 unit response macros.\n- 960 new/reflected exact Gaussian phase pairs and 16 signed coefficient-word microchecks.\n- Actual physical owner/padding assembly, independent decoder and eight structural controls, regenerated finite invoice, reserve bridge, two rational moment engines and all 47 strict outer inequalities.\n- Fresh bit composition at this exact complex bound. All nine package manifests passed.\n\n[18 committed receipts, including rejected transfers and failed attempts](https://github.com/CrocSwap/integer-mult-bounds/blob/abd6c8f8173497980f1f3e3da023252b2c172719/research/e8-grouped-closure/VALIDATION-LOCAL.json) contain source and compressed hashes. They also preserve earlier candidate passes separately. The preceding rank-two version's physical template write failed with `OSError: [Errno 28] No space left on device`; that failure was not a mathematical assertion failure. The current enlarged word passed its own fresh physical replay after lossless archival and byte-identical archive deduplication.\n\n**Full local wrapper passed:** the complete nested parent/new replay and fresh bit composition passed against `abd6c8f8173497980f1f3e3da023252b2c172719`; its receipt is included in `local-evidence/full-wrapper-result.json`. Python 3.11/3.14 GitHub CI remains pending. The PR remains a draft.\n\n16 replicas; 1,465 banks per stage; 28,545 live and 29,336 physical registers. The invoice charges 16,387,872 real primitives, local bound 9,415,823,881,912, 61,920 bank-boundary adapters and row reserve 15,447 < 20,161. Complex lower: `1019514045526403509333/1000000000000000000000000`; unchanged bit lower: `255384852701747/250000000000000000`.\n\nRun `python -B research/e8-grouped-closure/verify.py /absolute/path/to/new/output`. It freshly replays #418, all three immutable constructors, the current finite assembly and fresh bit, checking nine manifests before and after.\n\nThis uses the broader chronological/dyadic conditional framework of #418/#423. No unchanged legacy gx/gxcore E4/E5 acceptance, Lean proof or unconditional exponent is claimed. Inherited all-size window, arbitrary dirty-bank, compiler, fixed-tape, restored-row, common-grid, precision and analytic assumptions remain.\n\nPrepared by Rohan Arun with substantial OpenAI Codex assistance. Credit eumemic #414/#420/#421 for the seven promotions, #423 for backward-capacity/shared-frame enlargements, #416/#421/#423 immutable constructors, #411 prefixes/lowering; Rohan #418/#415/#413/#409; chafreaky #419 (comparison and byte-identical #414 data retrieval) and #402; Dugongue #404/#401; #403 banks; applecrusher #376 and Sussman E8 lineage. Original licenses/notices retained. 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optionally recheck it with Lean. + +No proof-package files or receipts are written. --check-lean builds the +existing FramedReplay target through ordinary Lake, writes a scratch .lean +file outside the checkout, and compares its #eval output with TRACE. +The scratch also checks FramedReplay.ValidTrace for this one example. +PNGs have fixed dimensions, colors, bundled font, and metadata; no timestamps. +Reproduce with the versions in requirements.txt. --check compares bytes +without overwriting the committed figures. +""" +from __future__ import annotations + +import argparse +import io +import json +from pathlib import Path +import subprocess +import tempfile + +HERE = Path(__file__).resolve().parent +PROJECT = HERE.parents[1] / "lean-multi-host-source" + +# Each row: physical bits at (false,true), decoded bits at (false,true), +# gauge tag (0 = identity I, 1 = address reversal J). +# Source: LEAN_EXAMPLE below, FramedReplay.physicalStep/decodeRow, Tree.get. +TRACE = [ + [[1, 0, 1, 0, 0], [1, 1, 1, 1, 1], [0, 1, 0, 1, 0], [0, 0, 0, 0, 0]], + [[1, 0, 1, 0, 0], [1, 1, 1, 1, 1], [1, 0, 0, 1, 1], [0, 0, 0, 0, 0]], + [[1, 0, 1, 0, 0], [0, 1, 1, 0, 1], [1, 0, 0, 1, 1], [0, 0, 0, 0, 0]], + [[1, 0, 1, 0, 0], [0, 1, 1, 0, 1], [1, 0, 0, 1, 1], [0, 1, 1, 0, 1]], + [[1, 0, 1, 0, 0], [0, 1, 1, 0, 1], [1, 1, 1, 1, 1], [0, 1, 1, 0, 1]], + [[1, 0, 1, 0, 0], [1, 0, 0, 1, 1], [1, 1, 1, 1, 1], [0, 1, 1, 0, 1]], + [[1, 0, 1, 0, 0], [1, 0, 0, 1, 1], [1, 0, 0, 1, 1], [0, 1, 1, 0, 1]], + [[1, 0, 1, 0, 0], [1, 0, 0, 1, 1], [1, 0, 0, 1, 1], [0, 0, 0, 0, 0]], +] +ROW_NAMES = ["S source", "T target", "H dirty helper", "P private temporary"] +STEPS = ["Initial state", "1 MOVE H to J", "2 ADD T, H", "3 COPY S to P in J", + "4 ADD H, P", "5 ADD T, H", "6 ADD H, P", "7 ERASE P using S"] + +LEAN_EXAMPLE = r'''import FramedReplay +open FramedReplay TreeReplay + +-- Signature checks ground the explainer's glosses of the admitted axioms. +universe u +example {p q : Prop} : (p ↔ q) → p = q := propext +noncomputable example {α : Sort u} : Nonempty α → α := Classical.choice +example {α : Sort u} {r : α → α → Prop} {a b : α} : + r a b → Quot.mk r a = Quot.mk r b := Quot.sound + +def I : Gauge Bool := ⟨id, id, fun _ => rfl, fun _ => rfl⟩ +def J : Gauge Bool := ⟨Bool.not, Bool.not, + by intro b; cases b <;> rfl, by intro b; cases b <;> rfl⟩ +def bits (a b : Bool) : Bool → Bool := fun x => if x then b else a +-- Row indices: 0 source, 1 target, 2 dirty helper, 3 clean private temporary. +def initial : Store Bool := Tree.tabulate 2 fun i => + match i with + | 0 => (I, bits true false) + | 1 => (J, bits true true) + | 2 => (I, bits false true) + | _ => (I, bits false false) +def events : List (Event Bool) := [ + ⟨⟨0, 2, 0, false⟩, J⟩, + ⟨⟨1, 1, 2, true⟩, J⟩, + ⟨⟨2, 0, 3, false⟩, J⟩, + ⟨⟨1, 2, 3, true⟩, J⟩, + ⟨⟨1, 1, 2, true⟩, J⟩, + ⟨⟨1, 2, 3, true⟩, J⟩, + ⟨⟨3, 0, 3, false⟩, I⟩] +-- The real chronological guard predicate, for this toy only. +example : ValidTrace events initial := by + refine ⟨True.intro, rfl, ?_, rfl, rfl, rfl, ?_, True.intro⟩ + · funext b; cases b <;> rfl + · funext b; cases b <;> rfl + +def states : List (Event Bool) → Store Bool → List (Store Bool) + | [], s => [s] + | e :: es, s => s :: states es (physicalStep s e) +def bit (b : Bool) : Nat := if b then 1 else 0 +def view (r : Row Bool) : List Nat := + [bit (r.2 false), bit (r.2 true), + bit (decodeRow r false), bit (decodeRow r true), bit (r.1.forward false)] +#eval (states events initial).map fun s => (List.range 4).map fun i => view (s.get i) +''' + + +def check_lean(project: Path, lake: str) -> None: + version = subprocess.check_output([lake, "env", "lean", "--version"], cwd=project, text=True) + if not version.startswith("Lean (version 4.21.0,"): + raise RuntimeError("The illustration must be checked on the project's Lean 4.21.0") + subprocess.run([lake, "build", "FramedReplay"], cwd=project, check=True) + with tempfile.TemporaryDirectory(prefix="pr442-explainer-") as temporary: + source = Path(temporary) / "Example.lean" + source.write_text(LEAN_EXAMPLE) + result = subprocess.run([lake, "env", "lean", str(source)], cwd=project, + text=True, stdout=subprocess.PIPE, stderr=subprocess.STDOUT) + if result.returncode: + raise RuntimeError("Scratch Lean check failed:\n" + result.stdout) + if json.loads(result.stdout) != TRACE: + raise RuntimeError("The Lean-computed trace differs from the figure data") + print("PASS: Lean 4.21.0 evaluated every toy state and checked its chronological guards.") + + +def figures() -> dict[str, bytes]: + import matplotlib + matplotlib.use("Agg") + from matplotlib import pyplot as plt + from matplotlib.font_manager import FontProperties + from matplotlib.patches import Rectangle + import PIL + + if matplotlib.__version__ != "3.10.8" or PIL.__version__ != "12.3.0": + raise RuntimeError("Install the rendering versions in requirements.txt for byte-stable PNGs") + plt.rcdefaults() + plt.rcParams.update({"figure.facecolor": "white", "savefig.facecolor": "white", + "text.color": "#152b3b", "font.size": 12}) + font = FontProperties(fname=str(Path(matplotlib.get_data_path()) / + "fonts/ttf/DejaVuSans.ttf")) + colors = {0: "#edf2f5", 1: "#146a83"} + + def label(ax, x, y, text, size=12, **kw): + ax.text(x, y, text, fontproperties=font, fontsize=size, **kw) + + def bits(ax, x, y, values, width=.40, height=.38): + for j, value in enumerate(values): + ax.add_patch(Rectangle((x + j * width, y), width, height, + facecolor=colors[value], edgecolor="white", linewidth=1.5)) + label(ax, x + (j + .5) * width, y + height / 2, str(value), 12, + ha="center", va="center", color="white" if value else "#152b3b") + + def png(fig): + stream = io.BytesIO() + fig.savefig(stream, format="png", dpi=160, metadata={"Software": "PR442 explainer"}) + plt.close(fig) + return stream.getvalue() + + fig, ax = plt.subplots(figsize=(10, 5)) + fig.subplots_adjust(left=.025, right=.995, bottom=.025, top=.98) + ax.set(xlim=(0, 10), ylim=(0, 5)); ax.axis("off") + label(ax, .2, 4.58, "Same logical helper, different physical addresses", 18) + for x, state, title in [(0.2, TRACE[0], "BEFORE"), (5.2, TRACE[-1], "AFTER")]: + label(ax, x, 4.04, title, 14) + label(ax, x + 2.05, 3.62, "Frame", 11) + label(ax, x + 2.82, 3.62, "Physical", 11) + label(ax, x + 3.9, 3.62, "Decoded", 11) + for i, row in enumerate(state): + y = 2.91 - i * .58 + label(ax, x, y + .19, ROW_NAMES[i], 11, va="center") + label(ax, x + 2.25, y + .19, "J" if row[4] else "I", 12, ha="center", va="center") + bits(ax, x + 2.82, y, row[:2]) + bits(ax, x + 3.9, y, row[2:4]) + label(ax, .2, .58, "I reads addresses in order. J reads them in reverse.", 12) + label(ax, .2, .22, "T becomes T XOR S; H retains its decoded bits; P returns blank.", 12) + result = {"before-after.png": png(fig)} + + fig, ax = plt.subplots(figsize=(10, 7)) + fig.subplots_adjust(left=.025, right=.995, bottom=.025, top=.98) + ax.set(xlim=(0, 10), ylim=(0, 7)); ax.axis("off") + label(ax, .2, 6.55, "Seven operations, with every intermediate state", 18) + label(ax, .2, 6.15, "Physical bits shown; the letter records the row's frame.", 12) + names = ["S / source", "T / target", "H / helper", "P / private"] + positions = [3.35, 4.98, 6.61, 8.24] + for x, name in zip(positions, names): + label(ax, x, 5.65, name, 11) + for i, (step, state) in enumerate(zip(STEPS, TRACE)): + y = 5.02 - .57 * i + label(ax, .2, y + .19, step, 11, va="center") + for x, row in zip(positions, state): + bits(ax, x, y, row[:2]) + label(ax, x + .92, y + .19, "J" if row[4] else "I", 11, va="center") + label(ax, .2, .56, "Before ERASE: S is 10 in I, P is 01 in J; both decode to 10.", 12) + label(ax, .2, .19, "Toy semantics illustration only; this is not a fragment of the R747 word.", 11) + result["operation-trace.png"] = png(fig) + return result + + +def main() -> None: + p = argparse.ArgumentParser(description=__doc__) + p.add_argument("--check", action="store_true", help="compare PNG bytes without writing") + p.add_argument("--check-lean", action="store_true", help="also rerun the optional scratch example") + p.add_argument("--lean-project", type=Path, default=PROJECT) + p.add_argument("--lake", default="lake", help="Lake executable; no compiler flags or environment overrides") + args = p.parse_args() + if args.check_lean: + check_lean(args.lean_project.resolve(), args.lake) + for name, data in figures().items(): + path = HERE / name + if args.check: + if path.read_bytes() != data: + raise RuntimeError("Figure differs: " + name) + else: + path.write_bytes(data) + print("PASS: deterministic figures " + ("match committed bytes." if args.check else 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b/research/lean-external-review/package-manifest.json @@ -15,11 +15,16 @@ "NOTICE": "b49022cb4104d90b182e4c335f670faf45529025b15db77bf0291835083c28bd", "research/lean-contribution-archive/README.md": "e3087e30eab7a3cdd5605ecdfbdeac1427c4cadd6119a6cbfca256b9110dbe09", "research/lean-external-review/BUILD.md": "3fef3f30a941fc5b0041dc87e4c2c43cce888bebeee57ad63b04148f7710ee78", - "research/lean-external-review/DRAFT-PR.md": "392bf681cc56f69668507dd2a9fd43d731c34c30609a29856f1fffe94ae6b796", + "research/lean-external-review/DRAFT-PR.md": "e1d37fd840aba4e5b4b07c0cf4156410ef2a80e8558ef6b6a3186e8ae13520a6", + "research/lean-external-review/EXPLAINER.md": "aff4b879180d83a1deb3b2be5ddc2e4ff54cc8367a6c9fd9f1dfef8c6b8b6874", "research/lean-external-review/MERGED-OVERLAP.md": "696ab7ff17eb2fb94d52aa60723c3d7959a17034ddbdbc23bafcc38f19aa49ba", "research/lean-external-review/PRIVACY-AND-PROVENANCE.md": "36a5749e3822f097937c881fac60e3a48d80b2bffa91bf5ee1c80761e66ec6e1", "research/lean-external-review/README.md": "f7ccb7ad883ad27db4599ab15334a5ea1b15945857cec4d9638eddb4d27e5b4b", "research/lean-external-review/VALIDATION.md": "3eb4f942c5ed93271fbd9cafb8eb12e2c830a98f8f3700dfbc36834fb4ed53ba", + "research/lean-external-review/explainer-figures/before-after.png": "b1cbef1b3378a4a4b8176959b0e2c0fd867b89f29bf6d800b286e66b1c7a7fac", + "research/lean-external-review/explainer-figures/make_figures.py": "686f19a7bf14a5db03850e5886e9b48e7a50cfb97c0ee55133b43de9d0c749ee", + "research/lean-external-review/explainer-figures/operation-trace.png": "7fc1482d5e0562d7ce3457286690cb2928f19c510cff1ead5c9f32fde35e4008", + "research/lean-external-review/explainer-figures/requirements.txt": "ab6e24df0fa4aabc70cc4b062d479e46b9373cc58a5cffee56365055868828be", "research/lean-external-review/export_review.py": "3334e705925cac4a52d3ee7a9cef9c07c5de687565562e13ac95311b06a83016", "research/lean-external-review/reproduce.py": "d9fee9f775e5b72b16308590d8bd573ce48b48867d4576be1e727d3c0da1629b", "research/lean-external-review/requirements.txt": "47fd19021144e071cc43b6e265aafada0056abe89724ad95bd6e3a8e37995b94", From b86b4072edc15c717e762ebb5768905c78f4cf3f Mon Sep 17 00:00:00 2001 From: AI-assisted verification contributor Date: Tue, 13 Oct 2026 05:22:54 +0000 Subject: [PATCH 10/11] Respect inherited CI stack limits and refresh a stale source fingerprint --- Makefile | 1 + certificates/mixed-point-audit.json | 2 +- research/lean-external-review/BUILD.md | 6 +++- research/lean-external-review/VALIDATION.md | 28 ++++++++++++--- .../package-manifest.json | 17 ++++----- research/lean-external-review/reproduce.py | 1 + .../lean-external-review/verify_package.py | 10 ++++-- .../lean-multi-host-source/port-manifest.json | 5 +-- .../test_verifier_stack.py | 35 +++++++++++++++++++ research/lean-multi-host-source/verify.py | 25 +++++++++++-- 10 files changed, 108 insertions(+), 22 deletions(-) create mode 100644 research/lean-multi-host-source/test_verifier_stack.py diff --git a/Makefile b/Makefile index 597113cc71..99807e7859 100644 --- a/Makefile +++ b/Makefile @@ -560,6 +560,7 @@ LAKE ?= lake formal-pr442-verify: python3 research/lean-multi-host-source/check_sources.py python3 research/lean-multi-host-source/test_flat_data.py + python3 research/lean-multi-host-source/test_verifier_stack.py python3 research/lean-multi-host-source/verify.py --lake "$(LAKE)" --receipt /tmp/pr442-lean421-fresh.json python3 research/lean-external-review/verify_package.py --build-receipt /tmp/pr442-lean421-fresh.json git diff --exit-code diff --git a/certificates/mixed-point-audit.json b/certificates/mixed-point-audit.json index 1f6c0fec1b..5b65e2e08a 100644 --- a/certificates/mixed-point-audit.json +++ b/certificates/mixed-point-audit.json @@ -487,7 +487,7 @@ "source_sha256": { "docs/research/mixed-point-audit.md": "c80527f9e98c27bd7f5858a06c7273f84c40e0c41505eb4d16029b61f80fb968", "scripts/experiments/mixed_point_circuit.py": "f509362b5031976a22af351fd158ae0b4520fa4f286a5176ec37023d672a7ddc", - "scripts/rational_span_frames.py": "ac3b9ab462b790d195628f0e5aa4f95143596a51ce7df1a99360b98594c29932" + "scripts/rational_span_frames.py": "766d342dd73ca5efd784c5733282a93d379a58beea763e703238dfbb4eacce82" }, "status": "BOUNDED MIXED-POINT RESEARCH; NO NEW KAPPA", "target": "1/1073741824", diff --git a/research/lean-external-review/BUILD.md b/research/lean-external-review/BUILD.md index 58cd48819e..fba4786de4 100644 --- a/research/lean-external-review/BUILD.md +++ b/research/lean-external-review/BUILD.md @@ -7,6 +7,10 @@ Start from a clean checkout of the port commit being reviewed. Record `git rev-parse HEAD`. Install Git, Python 3.13 and elan using upstream's normal setup. Each project selects its compiler through `lean-toolchain`; no external resource settings, special compiler flags or environment overrides are used. +The verifier inherits the host's OS stack limits unchanged and records them +before and after the run. An 8 MiB limit is not assumed: host defaults differ. +The receipt cannot determine whether a caller changed limits before launch; +the reproduction commands and workflow must use their ordinary environment. From the repository root: @@ -62,7 +66,7 @@ axiom inventories. The Task B inventory has 931 declarations and Task A has compilation and axiom auditing, while their unchanged bytes remain hashed. The differential test is delegated separately and is not reported here. -The canonical completed-build receipt is `validation/lean421-fresh.json`. +The canonical completed-build receipt is `validation/lean421-ci-fix-fresh.json`. The strict verifier requires its PASS and exact current source bindings. During preparation only, `verify_package.py --allow-pending-port` checks an unfinished inventory and reports `PENDING_PORT` when the fresh receipt is absent. With a matching fresh diff --git a/research/lean-external-review/VALIDATION.md b/research/lean-external-review/VALIDATION.md index a6202ad6b8..040d89c6b8 100644 --- a/research/lean-external-review/VALIDATION.md +++ b/research/lean-external-review/VALIDATION.md @@ -1,11 +1,29 @@ # Validation of the Lean 4.21 port Exact upstream base: `db0e57bc7f36b5ac0fc844ad7ce1396165ee6647`. -Build candidate: `0d4aec339032498a182cf0eec7cb571b2cdd48f6`. The final documentation/receipt commit -preserves its manifested source and dependency hashes. PR #540 and its branch -remain unchanged until approval. +Original port build candidate: `0d4aec339032498a182cf0eec7cb571b2cdd48f6`. Its proof sources and dependency pins remain unchanged by the CI repair. -## Current fresh verification: PASS +## CI compatibility repair + +The original verifier incorrectly required an OS stack soft limit of at most +8 MiB. GitHub job 114937263040 rejected the runner before compiling Lean, +after the source and parser checks passed. The repair records inherited +limits before and after verification and requires them to stay unchanged; +it never changes resource limits. It still rejects external Lean tuning. +A recorded limit alone cannot authenticate the caller's prior environment. +The workflow and reproduction commands apply no resource overrides. + +The current receipt path is `validation/lean421-ci-fix-fresh.json`. +The original `validation/lean421-fresh.json`, timing and projection files below +remain unchanged historical evidence for the original port manifest; they do +not validate the revised Python verifier. Fresh repair verification is pending. + +The unrelated research CI failure came from an upstream stale fingerprint in +`certificates/mixed-point-audit.json`. Regenerating it with +`python3 scripts/audit_mixed_point.py` updates only the hash of +`scripts/rational_span_frames.py`; the mathematical certificate is unchanged. + +## Original port fresh verification: PASS Fresh verification passed on Lean 4.21.0 with the exact upstream Mathlib pin. All 153 local modules compiled from an empty build directory, with no local @@ -32,7 +50,7 @@ contribution artifact was reused. Adding the earlier 522.650-second external source-build fallback gives an estimated **50.58 minutes** under the same model. Cache-free CI is not qualified by the cached-setup estimate. -The canonical receipt is [validation/lean421-fresh.json](validation/lean421-fresh.json). +The original receipt is [validation/lean421-fresh.json](validation/lean421-fresh.json). [The source binding receipt](validation/lean421-source-binding.json) records the separate regeneration check of all 19,002 ordered source events. [validation/lean421-timing.json](validation/lean421-timing.json) records module diff --git a/research/lean-external-review/package-manifest.json b/research/lean-external-review/package-manifest.json index 8a4ea71a6a..4401979f7a 100644 --- a/research/lean-external-review/package-manifest.json +++ b/research/lean-external-review/package-manifest.json @@ -1,6 +1,6 @@ { "base_commit": "db0e57bc7f36b5ac0fc844ad7ce1396165ee6647", - "validation_status": "PASS", + "validation_status": "PENDING_PORT", "historical_task_a_commit": "13611a8958fc71046a83d8431d2bd6335e6a3e2f", "historical_task_b_commit": "f7330c5f5b1c5e85f91a98c95e8efc0e27c03490", "excluded_from_recursive_hash": [ @@ -11,22 +11,22 @@ ".github/workflows/verify.yml": "f319143d4bd68b84196f14755f32b4a9ab0975654e5e62917dc63b1219f4c2bb", "CONTRIBUTING.md": "926fe5aafd20416d27ad931db2e414a60f5f6f4bdd70507775901c3d1ef62f67", "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", - "Makefile": "4fb64c49dcedbe95a86ed0ce0861a3b7104a3f1c932a74120db23b98ce4db36d", + "Makefile": "0552b59f9b17e5f22a41e21f046a017ab2cc254f97e1694ea38db05536c40a60", "NOTICE": "b49022cb4104d90b182e4c335f670faf45529025b15db77bf0291835083c28bd", "research/lean-contribution-archive/README.md": "e3087e30eab7a3cdd5605ecdfbdeac1427c4cadd6119a6cbfca256b9110dbe09", - "research/lean-external-review/BUILD.md": "3fef3f30a941fc5b0041dc87e4c2c43cce888bebeee57ad63b04148f7710ee78", + "research/lean-external-review/BUILD.md": "9cb3ab624dfd3703917cbae55613c719deb4ee3526eeea12663ff62d5b754b33", "research/lean-external-review/DRAFT-PR.md": "e1d37fd840aba4e5b4b07c0cf4156410ef2a80e8558ef6b6a3186e8ae13520a6", "research/lean-external-review/EXPLAINER.md": "aff4b879180d83a1deb3b2be5ddc2e4ff54cc8367a6c9fd9f1dfef8c6b8b6874", "research/lean-external-review/MERGED-OVERLAP.md": "696ab7ff17eb2fb94d52aa60723c3d7959a17034ddbdbc23bafcc38f19aa49ba", "research/lean-external-review/PRIVACY-AND-PROVENANCE.md": "36a5749e3822f097937c881fac60e3a48d80b2bffa91bf5ee1c80761e66ec6e1", "research/lean-external-review/README.md": "f7ccb7ad883ad27db4599ab15334a5ea1b15945857cec4d9638eddb4d27e5b4b", - "research/lean-external-review/VALIDATION.md": "3eb4f942c5ed93271fbd9cafb8eb12e2c830a98f8f3700dfbc36834fb4ed53ba", + "research/lean-external-review/VALIDATION.md": "56411850b96838d2a246ba1c5b2181573351e60852c6e0f8d5443614689472ed", "research/lean-external-review/explainer-figures/before-after.png": "b1cbef1b3378a4a4b8176959b0e2c0fd867b89f29bf6d800b286e66b1c7a7fac", "research/lean-external-review/explainer-figures/make_figures.py": "686f19a7bf14a5db03850e5886e9b48e7a50cfb97c0ee55133b43de9d0c749ee", "research/lean-external-review/explainer-figures/operation-trace.png": "7fc1482d5e0562d7ce3457286690cb2928f19c510cff1ead5c9f32fde35e4008", "research/lean-external-review/explainer-figures/requirements.txt": "ab6e24df0fa4aabc70cc4b062d479e46b9373cc58a5cffee56365055868828be", "research/lean-external-review/export_review.py": "3334e705925cac4a52d3ee7a9cef9c07c5de687565562e13ac95311b06a83016", - "research/lean-external-review/reproduce.py": "d9fee9f775e5b72b16308590d8bd573ce48b48867d4576be1e727d3c0da1629b", + "research/lean-external-review/reproduce.py": "f771427ff8e9cc00d16bd66dba8602e0949ba67bb5ed4996b49a3cecfed9960a", "research/lean-external-review/requirements.txt": "47fd19021144e071cc43b6e265aafada0056abe89724ad95bd6e3a8e37995b94", "research/lean-external-review/validate_delivery.py": "6709767ff028f9c240afb9a1e067215f11e8d50ea21d299e137ce0a54dfdcd2d", "research/lean-external-review/validation/lean421-ci-projection.json": "42f06f31ec697c848eaf58170fe1dbcfd78734a2c50517196fc2932cdc7f28e8", @@ -40,7 +40,7 @@ "research/lean-external-review/validation/task-a.log": "0681670f482008a5a5b1a6311a4a3a4bff59c697f8193e71ee8c9cbf17f2a8fe", "research/lean-external-review/validation/task-b.json": "0014511e36914b1faf6a5b615f43e655af2825518bdc560c9d7bb140144b0ecc", "research/lean-external-review/validation/task-b.log": "936bca918db64beaf499e6b89ad9cf5ceec4898cba3d2f4041ebaacf2ef80276", - "research/lean-external-review/verify_package.py": "2ba9f1eeb60dcae889d22f7ecb54f2fcacf13fdd0140f4a6616301158a6fc11d", + "research/lean-external-review/verify_package.py": "37918bcf8f1e0abae559a29abe2efd82798313d926860a93a4ec986946197ffa", "research/lean-multi-host-framework/MultiHostControls.lean": "4321a232d7e36e0f4417a01ce951c601afde1b283c42c0b8ad24372e25fbc94d", "research/lean-multi-host-framework/MultiHosting.lean": "dc6188687ac8e089c64bf5ab7cd4c8c1a83f378d3c46bb1265a1b6ad43d199d6", "research/lean-multi-host-framework/README.md": "8ba8c1b993d8b0b9c8311a3f0c9645dc017f6e5e20846bd0b2217386262d62cb", @@ -405,7 +405,7 @@ "research/lean-multi-host-source/phase2-resumed-results/source-framed-initial.json": "05bd71d21ff8bb335c0c3b36a18b24b8c7d2cf1af2a240ad171646db05c7b978", "research/lean-multi-host-source/phase2-resumed-results/source-framed-initial.log": "08816aedb718ef3d523db587f17e7f6eaec4ef3713bef9dd8ac0698e1488c6a4", "research/lean-multi-host-source/phase2-resumed-results/theorem-statement-preservation.json": "3866daec0bf71b6124db7b8732198d4f7e3dc57fa594fe96197a4479dd22ac63", - "research/lean-multi-host-source/port-manifest.json": "4dc3de4a0ea521b4d22cc736ea21a763355aaa716828f33f160e814493285640", + "research/lean-multi-host-source/port-manifest.json": "cecfea850b02aa2791dacbfb95b07143b3d48cdc91f286d7a79030c814120b1a", "research/lean-multi-host-source/probe-manifest.json": "81646cf4b666bf36ffe72ac575a94d1a7206784d3c3369bdd8a05c2cb4a89eed", "research/lean-multi-host-source/proof-manifest.json": "c05e28674849b47b87916a4ed6c346dba018f18c92b67e78ef6f06cba8198d37", "research/lean-multi-host-source/replay-result.json": "462fefd26aec066a37714a115e74dac08e1cef4b8b756ea3ff1c71f63699078e", @@ -496,9 +496,10 @@ "research/lean-multi-host-source/source-versions.json": "ecab66abda7fce3a17c176e027334d30ae5ccfeea2099b00cab7110ca6243510", "research/lean-multi-host-source/source-word-review.md": "fd3dd6c1a2dbf7bfc1bd9d9184fac06facabda8288ad720d0dd1d60acc5bdfb1", "research/lean-multi-host-source/test_flat_data.py": "b5c1183cab2083f5831235fea7796cfd4b0aff8cb8e78edb6cce38c32457c515", + "research/lean-multi-host-source/test_verifier_stack.py": "3d8cb00a457d51a7aabda3e91c89774014c6a946edae9e3fac4e601f0b56dd17", "research/lean-multi-host-source/update_manifest.py": "e1c35ac04ac806a37f196d541b216fc4ecd0d717c49f1fefd253b7081cf6a199", "research/lean-multi-host-source/update_port_manifest.py": "a634b44b6e5f9e912cee0467846cac1018b4d3df1ab7ced104d91bc500da1c61", - "research/lean-multi-host-source/verify.py": "b79452abee21ddc82b07066fab26393fcc3cedc17a8aefcb0fe7bcb0348d927e", + "research/lean-multi-host-source/verify.py": "0c75c5fbc1dcc27515af8428a8546944008b8109b95cfc825216a159c517f075", "research/lean-single-stream-obstruction/AUDIT.json": "986a02edd358ba1d9c8cd920143ebb55424a4615d52d22cc921cfdb86dca6b8b", "research/lean-single-stream-obstruction/NOTICE.md": "3960a466a9be920393dbd06f1fac0485a4bff14fc43e565e73f5a8d2f5887d70", "research/lean-single-stream-obstruction/README.md": "46a22d2dd4d9116a280153ca0a1b61e000c6bbca78b08916ea290acace0dcd00", diff --git a/research/lean-external-review/reproduce.py b/research/lean-external-review/reproduce.py index 4de4e3bdfc..d6df0d31fa 100644 --- a/research/lean-external-review/reproduce.py +++ b/research/lean-external-review/reproduce.py @@ -28,6 +28,7 @@ def main(): ['research/lean-multi-host-source/check_sources.py', '--receipt', str(out / 'source-binding.json')], ['research/lean-multi-host-source/test_flat_data.py'], + ['research/lean-multi-host-source/test_verifier_stack.py'], ['research/lean-multi-host-source/verify.py', '--lake', args.lake, '--receipt', str(out / 'lean421-fresh.json')], ['research/lean-external-review/verify_package.py', diff --git a/research/lean-external-review/verify_package.py b/research/lean-external-review/verify_package.py index 227ed0716e..5bbdf4981b 100644 --- a/research/lean-external-review/verify_package.py +++ b/research/lean-external-review/verify_package.py @@ -256,7 +256,7 @@ def port_bindings(allow_pending=False, build_receipt=None): require(set(manifest['audits']) == set(audit_counts), 'Wrong port audit inventory') for key, count in audit_counts.items(): require(len(manifest['audits'][key]['declarations']) == count, 'Wrong audit count: ' + key) - receipt_path = build_receipt or HERE / 'validation/lean421-fresh.json' + receipt_path = build_receipt or HERE / 'validation/lean421-ci-fix-fresh.json' if not receipt_path.exists(): require(allow_pending and build_receipt is None, 'Current fresh Lean 4.21 receipt is absent; use --allow-pending-port only for preparation') @@ -278,8 +278,14 @@ def port_bindings(allow_pending=False, build_receipt=None): 'Invalid build commit') require(receipt['compiledLocalModules'] == sorted(modules) and receipt['replayedLocalModules'] == [], 'Port receipt reused or omitted local modules') + limits = receipt['stackLimit'] + require(isinstance(limits, list) and len(limits) == 2 and + all(type(n) is int and (n == -1 or n > 0) for n in limits) and + (limits[1] == -1 or (limits[0] != -1 and limits[0] <= limits[1])), + 'Invalid recorded OS stack limits') require(receipt['environmentOverrides'] == {} and - 0 < receipt['stackLimit'][0] <= 8388608, 'Non-default external build settings') + receipt['stackLimitPolicy'] == 'inherited-unchanged' and + receipt['stackLimitAfter'] == limits, 'External build settings changed') toolchain = receipt['toolchain'] require(toolchain['version'] == manifest['leanVersion'] and toolchain['leanCommit'] == manifest['leanCommit'] and diff --git a/research/lean-multi-host-source/port-manifest.json b/research/lean-multi-host-source/port-manifest.json index 31873841d1..0554b6d71a 100644 --- a/research/lean-multi-host-source/port-manifest.json +++ b/research/lean-multi-host-source/port-manifest.json @@ -3665,12 +3665,13 @@ "test_flat_data.py": "b5c1183cab2083f5831235fea7796cfd4b0aff8cb8e78edb6cce38c32457c515", "update_manifest.py": "e1c35ac04ac806a37f196d541b216fc4ecd0d717c49f1fefd253b7081cf6a199", "update_port_manifest.py": "a634b44b6e5f9e912cee0467846cac1018b4d3df1ab7ced104d91bc500da1c61", - "verify.py": "b79452abee21ddc82b07066fab26393fcc3cedc17a8aefcb0fe7bcb0348d927e", + "verify.py": "0c75c5fbc1dcc27515af8428a8546944008b8109b95cfc825216a159c517f075", "../lean-single-stream-obstruction/lean-toolchain": "d24fed434d3b13adfaab57724a0a7f270ea8bf1c818b5ae5cf25cbce24dd685c", "../lean-single-stream-obstruction/proof-manifest.json": "c809cf54611f371ffa873221f69de71a22d6761b6a2f970674f6ee3a8074c138", "../lean-source-invocation-audit/lean-toolchain": "d24fed434d3b13adfaab57724a0a7f270ea8bf1c818b5ae5cf25cbce24dd685c", "../lean-source-invocation-audit/proof-manifest.json": "db705074d8fd05a8abaa82df4cdddc875a495e23dc84987b879a647bf8c5fe8e", "../lean-whole-residual-hosting/lean-toolchain": "d24fed434d3b13adfaab57724a0a7f270ea8bf1c818b5ae5cf25cbce24dd685c", - "../lean-whole-residual-hosting/proof-manifest.json": "863b5d68e18ec9f47c5c1fae1c047d1cb3f1e357735e1561923be4371efb7a6a" + "../lean-whole-residual-hosting/proof-manifest.json": "863b5d68e18ec9f47c5c1fae1c047d1cb3f1e357735e1561923be4371efb7a6a", + "test_verifier_stack.py": "3d8cb00a457d51a7aabda3e91c89774014c6a946edae9e3fac4e601f0b56dd17" } } diff --git a/research/lean-multi-host-source/test_verifier_stack.py b/research/lean-multi-host-source/test_verifier_stack.py new file mode 100644 index 0000000000..92c2c4c5e7 --- /dev/null +++ b/research/lean-multi-host-source/test_verifier_stack.py @@ -0,0 +1,35 @@ +"""Regression checks for inherited host limits; never modify real limits.""" +import resource +import unittest +from unittest.mock import patch + +from verify import inherited_stack_limits + + +class InheritedStackTests(unittest.TestCase): + def test_host_defaults_are_preserved(self): + for limits in [(8388608, -1), (16777216, -1), (-1, -1), + (8388608, 16777216)]: + with self.subTest(limits=limits), \ + patch.object(resource, 'getrlimit', return_value=limits), \ + patch.object(resource, 'setrlimit') as setter: + self.assertEqual(inherited_stack_limits(), limits) + self.assertEqual(inherited_stack_limits(limits), limits) + setter.assert_not_called() + + def test_changed_limit_is_rejected(self): + with patch.object(resource, 'getrlimit', return_value=(16777216, -1)): + with self.assertRaisesRegex(RuntimeError, 'changed during verification'): + inherited_stack_limits((8388608, -1)) + + def test_invalid_limits_are_rejected(self): + for limits in [(0, -1), (-2, -1), (-1, 8388608), + (16777216, 8388608)]: + with self.subTest(limits=limits), \ + patch.object(resource, 'getrlimit', return_value=limits): + with self.assertRaisesRegex(RuntimeError, 'Invalid inherited'): + inherited_stack_limits() + + +if __name__ == '__main__': + unittest.main() diff --git a/research/lean-multi-host-source/verify.py b/research/lean-multi-host-source/verify.py index fda568669c..3efebfe41e 100644 --- a/research/lean-multi-host-source/verify.py +++ b/research/lean-multi-host-source/verify.py @@ -33,6 +33,24 @@ def require(condition, message): raise RuntimeError(message) +def inherited_stack_limits(expected=None): + """Observe the host's limits without imposing or changing a machine default. + + A limit alone cannot establish whether the caller previously changed it. + The workflow must use its ordinary environment; the receipt records the + inherited values and checks that this verifier leaves them unchanged. + """ + limits = resource.getrlimit(resource.RLIMIT_STACK) + require(all(type(n) is int and (n == resource.RLIM_INFINITY or n > 0) + for n in limits), 'Invalid inherited OS stack limit') + require(limits[1] == resource.RLIM_INFINITY or + (limits[0] != resource.RLIM_INFINITY and limits[0] <= limits[1]), + 'Invalid inherited OS stack limit ordering') + require(expected is None or limits == expected, + 'OS stack limit changed during verification') + return limits + + def sha(path): h = hashlib.sha256() with path.open('rb') as stream: @@ -166,14 +184,14 @@ def main(): 'MATHLIB_CACHE_DIR', 'LAKE_OVERRIDE_LEAN', 'LEAN_GITHASH', 'LAKE_JOBS', 'LEAN_STACK_SIZE', 'LEAN_MAX_MEMORY'] require(not any(os.environ.get(key) for key in tuning), 'External Lean tuning detected') - stack = resource.getrlimit(resource.RLIMIT_STACK) - require(0 < stack[0] <= 8388608, 'Raised OS stack limit detected') + stack = inherited_stack_limits() manifest = validate_manifest() started = time.monotonic() receipt = {'schemaVersion': 1, 'status': 'RUNNING', 'scope': 'lean421-full-port', 'manifestSha256': sha(ROOT / 'port-manifest.json'), 'startedUtc': datetime.now(timezone.utc).isoformat(), - 'stackLimit': list(stack), 'environmentOverrides': {}, 'commands': [], 'audits': {}, + 'stackLimit': list(stack), 'stackLimitPolicy': 'inherited-unchanged', + 'environmentOverrides': {}, 'commands': [], 'audits': {}, 'sourceFiles': manifest['files'], 'freshLocalBuild': not any(p.is_file() for p in (ROOT / '.lake/build').rglob('*')), 'gitCommit': subprocess.check_output(['git', 'rev-parse', 'HEAD'], cwd=ROOT, text=True).strip(), @@ -258,6 +276,7 @@ def run(arguments, display_output=True): receipt['sourceFilesUnchanged'] = True receipt['localArtifacts'] = footprint(ROOT / '.lake/build') receipt['moduleOleanSha256'] = {name: sha(ROOT / '.lake/build/lib/lean' / (name.replace('.', '/') + '.olean')) for name in sorted(modules)} + receipt['stackLimitAfter'] = list(inherited_stack_limits(stack)) require(time.monotonic() - started < 2700, 'Total verification exceeded 45 minutes') receipt['status'] = 'PASS' except Exception as exc: From acc1917034d10f464271ab115fda314fd4eee7a3 Mon Sep 17 00:00:00 2001 From: AI-assisted verification contributor Date: Tue, 13 Oct 2026 05:41:40 +0000 Subject: [PATCH 11/11] Record fresh CI repair verification and preserve GitHub build receipts --- .github/workflows/verify.yml | 7 + research/lean-external-review/BUILD.md | 6 +- research/lean-external-review/DRAFT-PR.md | 10 +- research/lean-external-review/EXPLAINER.md | 2 +- research/lean-external-review/README.md | 13 +- research/lean-external-review/VALIDATION.md | 21 +- .../lean-external-review/export_review.py | 2 +- .../package-manifest.json | 23 +- .../validation/lean421-ci-fix-fresh.json | 5319 +++++++++++++++++ .../validation/lean421-ci-fix-make.log | 1965 ++++++ .../validation/lean421-ci-fix-projection.json | 12 + .../validation/lean421-ci-fix-timing.json | 12 + .../lean-external-review/verify_package.py | 2 +- 13 files changed, 7368 insertions(+), 26 deletions(-) create mode 100644 research/lean-external-review/validation/lean421-ci-fix-fresh.json create mode 100644 research/lean-external-review/validation/lean421-ci-fix-make.log create mode 100644 research/lean-external-review/validation/lean421-ci-fix-projection.json create mode 100644 research/lean-external-review/validation/lean421-ci-fix-timing.json diff --git a/.github/workflows/verify.yml b/.github/workflows/verify.yml index eaa8364766..77fb018f67 100644 --- a/.github/workflows/verify.yml +++ b/.github/workflows/verify.yml @@ -93,3 +93,10 @@ jobs: Mathlib.Tactic.Ring Mathlib.Tactic.NormNum - name: Check formal package and theorem axiom dependencies run: make formal-${{ matrix.package }}-verify + - name: Preserve PR442 build receipt + if: always() && matrix.package == 'pr442' + uses: actions/upload-artifact@ea165f8d65b6e75b540449e92b4886f43607fa02 # v4.6.2 + with: + name: pr442-lean421-receipt + path: /tmp/pr442-lean421-fresh.json + if-no-files-found: warn diff --git a/research/lean-external-review/BUILD.md b/research/lean-external-review/BUILD.md index fba4786de4..0971cbf0ab 100644 --- a/research/lean-external-review/BUILD.md +++ b/research/lean-external-review/BUILD.md @@ -29,9 +29,9 @@ Lake executable with `make formal-pr442-verify LAKE=/path/to/lake`; this is executable selection only, not a compiler flag or environment override. These are the commands used by the added `pr442` entry in upstream's existing -formal CI matrix. That job retains its 45-minute limit. The complete fresh -Make run took 17 minutes 23 seconds. Its conservative projection is 34 minutes -54 seconds, qualifying under the revised 35-minute target with the explicit +formal CI matrix. That job retains its 45-minute limit. The fresh CI-repair +Make run took 16 minutes 58 seconds. Its conservative projection is 34 minutes +9 seconds, qualifying under the revised 35-minute target with the explicit cache/setup assumptions in [VALIDATION.md](VALIDATION.md). This is a timing estimate, not an observed GitHub Actions run. diff --git a/research/lean-external-review/DRAFT-PR.md b/research/lean-external-review/DRAFT-PR.md index 1873c6f17a..ededee6024 100644 --- a/research/lean-external-review/DRAFT-PR.md +++ b/research/lean-external-review/DRAFT-PR.md @@ -30,7 +30,8 @@ Ported to Lean 4.21.0 and the project's exact Mathlib pin `308445d7985027f538e281e18df29ca16ede2ba3`. Fresh Task A and Task B replay passed in one clean Lake build: 153 local modules, no local artifact reuse, and all five axiom inventories. The complete normal Make target took -17.39 minutes here; the conservative four-core CI projection is 34.90 minutes +16m58s here after the CI compatibility repair; the conservative four-core +CI projection is 34m09s including a 1.5× compute slowdown, a three-minute setup/cache allowance and 20% margin. Setup/cache preparation is an explicit estimate; see VALIDATION.md. @@ -41,12 +42,15 @@ make formal-pr442-verify ``` The ordinary Lake build uses no external resource overrides, extra compiler -flags or environment settings. The permanent audits retain 931 Task B +flags or environment settings. It records the inherited OS stack limits and +checks that they stay unchanged, without assuming an 8 MiB host default. +GitHub Actions preserves its own receipt as an artifact; the local timing +projection does not establish a GitHub pass. The permanent audits retain 931 Task B declarations, including `SourceInvocation.actualContract`, and 21 Task A declarations. The port covers 66 original contribution files; nine unchanged archived third-party snapshots are excluded from this build and its audits. Certificate partitioning adds independent modules without changing theorem -statements. The 34.90-minute projection qualifies under the revised +statements. The 34m09s projection qualifies under the revised 35-minute target, conditional on the documented cache/setup assumptions. The differential test is delegated separately and is not a reported check here. diff --git a/research/lean-external-review/EXPLAINER.md b/research/lean-external-review/EXPLAINER.md index 27ceffd396..a1d378a393 100644 --- a/research/lean-external-review/EXPLAINER.md +++ b/research/lean-external-review/EXPLAINER.md @@ -250,7 +250,7 @@ The installed toolchain and imported library artifacts also matter. The fresh build recorded their fingerprints, but did not rebuild every external library or freshly audit every imported constant. Receipts and manifests document consistency; reading a PASS record is not independently rerunning Lean. - + A reader need not trust the AI's confidence, a claim of helper independence, or a few successful bit assignments as a substitute for the arbitrary-input diff --git a/research/lean-external-review/README.md b/research/lean-external-review/README.md index 53a454a51b..76e14d8046 100644 --- a/research/lean-external-review/README.md +++ b/research/lean-external-review/README.md @@ -2,9 +2,10 @@ **Lean 4.21 port: fresh verification PASS.** All 153 local modules and the five axiom inventories pass under the project's exact pins and default -external settings. The total CI projection is 34.90 minutes under the +external settings. The fresh CI-repair Make run took 16m58s; its CI projection is 34m09s under the explicit cache/setup assumptions in [VALIDATION.md](VALIDATION.md). -This local port has not replaced the public PR #540 branch. +The port and explainer are published on PR #540. The CI compatibility repair +and its separate fresh receipt are described in [VALIDATION.md](VALIDATION.md). Task A generalizes the hosting contract to multiple hosts and recovers the previous single-host theorems. Task B connects that framework to the literal @@ -46,8 +47,9 @@ The port targets upstream `formal/lean` exactly: - Mathlib `308445d7985027f538e281e18df29ca16ede2ba3`, with all transitive revisions fixed by `research/lean-multi-host-source/lake-manifest.json`. - Source `set_option maxHeartbeats` and `maxRecDepth` declarations are allowed. - No raised OS/Lean stack, build flags or environment overrides are required - or accepted by the verification route. + No resource limits are changed and no external Lean tuning is accepted. + Host OS stack defaults vary; their inherited values are recorded and + checked unchanged, rather than compared with one machine's default. The historical count of 75 Lean files means **66 contribution files plus nine archived third-party overlap snapshots**. Those nine snapshot files remain @@ -82,8 +84,7 @@ technical pitch and maintainer questions. ## Review and delivery The original public review is [PR #540](https://github.com/CrocSwap/integer-mult-bounds/pull/540), -on branch `lean/pr442-invocation-review`. This port is on a separate local -branch and must not be described as published before approval. +on branch `lean/pr442-invocation-review`, which includes the port and explainer. After committing a completed package, `export_review.py --output-dir` produces a cumulative patch, portable archive, commit IDs and checksums. Apply only diff --git a/research/lean-external-review/VALIDATION.md b/research/lean-external-review/VALIDATION.md index 040d89c6b8..17a67263a8 100644 --- a/research/lean-external-review/VALIDATION.md +++ b/research/lean-external-review/VALIDATION.md @@ -13,10 +13,27 @@ it never changes resource limits. It still rejects external Lean tuning. A recorded limit alone cannot authenticate the caller's prior environment. The workflow and reproduction commands apply no resource overrides. -The current receipt path is `validation/lean421-ci-fix-fresh.json`. +The current fresh receipt is [validation/lean421-ci-fix-fresh.json](validation/lean421-ci-fix-fresh.json). +The clean build candidate is `b86b4072edc15c717e762ebb5768905c78f4cf3f`. +All 153 local modules compiled fresh and all five audits passed with standard +axioms only. The normal Make target passed in **1018.396 seconds (16m58s)**. +The same conservative model gives **2049.113 seconds (34m09s)**, within the +35-minute target under its explicit setup/cache assumptions. This estimate +is not an observed GitHub run. See [repair timing](validation/lean421-ci-fix-timing.json), +[projection](validation/lean421-ci-fix-projection.json) and +[normalized log](validation/lean421-ci-fix-make.log). +The workflow uploads its own receipt as `pr442-lean421-receipt`; inspect that +run independently of this local result. + +No local contribution artifacts were reused. External source/artifact and +toolchain fingerprints matched the original receipt before reuse and were +checked again by the fresh verifier. The inherited local limits were +`[8388608, -1]` (8 MiB soft, unlimited hard), unchanged after verification. +No resource settings, compilation flags, Lean files or theorem statements +were changed. The original `validation/lean421-fresh.json`, timing and projection files below remain unchanged historical evidence for the original port manifest; they do -not validate the revised Python verifier. Fresh repair verification is pending. +not validate the revised Python verifier. The new receipt above does. The unrelated research CI failure came from an upstream stale fingerprint in `certificates/mixed-point-audit.json`. Regenerating it with diff --git a/research/lean-external-review/export_review.py b/research/lean-external-review/export_review.py index 1c40028102..d7ecc54f46 100644 --- a/research/lean-external-review/export_review.py +++ b/research/lean-external-review/export_review.py @@ -19,7 +19,7 @@ 'lean-contribution-archive', ]] ROOT_FILES = ['LICENSE', 'NOTICE', 'CONTRIBUTING.md', 'Makefile', - '.github/workflows/verify.yml'] + '.github/workflows/verify.yml', 'certificates/mixed-point-audit.json'] def git(*args): diff --git a/research/lean-external-review/package-manifest.json b/research/lean-external-review/package-manifest.json index 4401979f7a..8db814733b 100644 --- a/research/lean-external-review/package-manifest.json +++ b/research/lean-external-review/package-manifest.json @@ -1,6 +1,6 @@ { "base_commit": "db0e57bc7f36b5ac0fc844ad7ce1396165ee6647", - "validation_status": "PENDING_PORT", + "validation_status": "PASS", "historical_task_a_commit": "13611a8958fc71046a83d8431d2bd6335e6a3e2f", "historical_task_b_commit": "f7330c5f5b1c5e85f91a98c95e8efc0e27c03490", "excluded_from_recursive_hash": [ @@ -8,27 +8,32 @@ "research/lean-external-review/package-validation.json" ], "sha256": { - ".github/workflows/verify.yml": "f319143d4bd68b84196f14755f32b4a9ab0975654e5e62917dc63b1219f4c2bb", + ".github/workflows/verify.yml": "0113193762950adb334abda25ed3e03b96893d19d17800b0eb1ff83c207143ff", "CONTRIBUTING.md": "926fe5aafd20416d27ad931db2e414a60f5f6f4bdd70507775901c3d1ef62f67", "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", "Makefile": "0552b59f9b17e5f22a41e21f046a017ab2cc254f97e1694ea38db05536c40a60", "NOTICE": "b49022cb4104d90b182e4c335f670faf45529025b15db77bf0291835083c28bd", + "certificates/mixed-point-audit.json": "4053408adcd8de22edd9ac2b9dde491338f210540ac3a00e8dae9276b3cc2d3b", "research/lean-contribution-archive/README.md": "e3087e30eab7a3cdd5605ecdfbdeac1427c4cadd6119a6cbfca256b9110dbe09", - "research/lean-external-review/BUILD.md": "9cb3ab624dfd3703917cbae55613c719deb4ee3526eeea12663ff62d5b754b33", - "research/lean-external-review/DRAFT-PR.md": "e1d37fd840aba4e5b4b07c0cf4156410ef2a80e8558ef6b6a3186e8ae13520a6", - "research/lean-external-review/EXPLAINER.md": "aff4b879180d83a1deb3b2be5ddc2e4ff54cc8367a6c9fd9f1dfef8c6b8b6874", + "research/lean-external-review/BUILD.md": "3c076fa920878115b2a745066c1654efa07b27e787a2f99d3ea7c2a0d028764f", + "research/lean-external-review/DRAFT-PR.md": "9dc017c154a6ad1d9d3ff36cdd97d86fc5df95378bc924d55801de4dbbb64f6d", + "research/lean-external-review/EXPLAINER.md": "2ad5e8f291ba4f13e76fb90610ab148e91ed89c9d16976d843c1670168dfa7bc", "research/lean-external-review/MERGED-OVERLAP.md": "696ab7ff17eb2fb94d52aa60723c3d7959a17034ddbdbc23bafcc38f19aa49ba", "research/lean-external-review/PRIVACY-AND-PROVENANCE.md": "36a5749e3822f097937c881fac60e3a48d80b2bffa91bf5ee1c80761e66ec6e1", - "research/lean-external-review/README.md": "f7ccb7ad883ad27db4599ab15334a5ea1b15945857cec4d9638eddb4d27e5b4b", - "research/lean-external-review/VALIDATION.md": "56411850b96838d2a246ba1c5b2181573351e60852c6e0f8d5443614689472ed", + "research/lean-external-review/README.md": "fbaf73fb57caf47b9dfe600f0a88c614fb59f14909424374f707118d6d7bd535", + "research/lean-external-review/VALIDATION.md": "60f754afee9ca7a4c4f4767c5d47ecedc8a53fbd9c3f063e74defbc9b4ee46d1", "research/lean-external-review/explainer-figures/before-after.png": "b1cbef1b3378a4a4b8176959b0e2c0fd867b89f29bf6d800b286e66b1c7a7fac", "research/lean-external-review/explainer-figures/make_figures.py": "686f19a7bf14a5db03850e5886e9b48e7a50cfb97c0ee55133b43de9d0c749ee", "research/lean-external-review/explainer-figures/operation-trace.png": "7fc1482d5e0562d7ce3457286690cb2928f19c510cff1ead5c9f32fde35e4008", "research/lean-external-review/explainer-figures/requirements.txt": "ab6e24df0fa4aabc70cc4b062d479e46b9373cc58a5cffee56365055868828be", - "research/lean-external-review/export_review.py": "3334e705925cac4a52d3ee7a9cef9c07c5de687565562e13ac95311b06a83016", + "research/lean-external-review/export_review.py": "f9a96da5f52c7924f899749dd33db35bea242248c63aeffb449a7e24baa27674", "research/lean-external-review/reproduce.py": "f771427ff8e9cc00d16bd66dba8602e0949ba67bb5ed4996b49a3cecfed9960a", "research/lean-external-review/requirements.txt": "47fd19021144e071cc43b6e265aafada0056abe89724ad95bd6e3a8e37995b94", "research/lean-external-review/validate_delivery.py": "6709767ff028f9c240afb9a1e067215f11e8d50ea21d299e137ce0a54dfdcd2d", + "research/lean-external-review/validation/lean421-ci-fix-fresh.json": "c17e77986a31fa9f41a386569d7c3557dd40981a53f1cba500bd3ef75456ea2c", + "research/lean-external-review/validation/lean421-ci-fix-make.log": "432c48fd7a5e5992542898fb90c200e092cecd3c84d25d11561f7860c5117225", + "research/lean-external-review/validation/lean421-ci-fix-projection.json": "f431fa626b38c89652fc22cebfa324549554e6e89c9752649312b8eab0118e42", + 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"8e2b21b20334310434b0de211d956a36854dc5c646f2fedb84e296de31d477fe", + "MultiHosting": "fb1df123bbdb4c18225de7b36b4f972af04621c650ab45778b5235dde1915137", + "OwnerTransport": "99280071dabbbdf80e6eb7ae6aab8fda151bddb818ea28918f9623b00c39c030", + "Ownership": "5078777e19f2458fdee1824f4df299219df6e678b26a6ea9e144f13b1b3a2bed", + "OwnershipCertificateHelpers": "a5b783d58e7efcc33c67da21fb5fdcee0f8c75666e5b116c3f243f7954afc12b", + "OwnershipCertificateMasks": "303d9819619cc4675eda05af61bfc189ec9a5c41ca90b75da47e7a4f8d045aff", + "OwnershipCertificateOwner": "9a3d9e647fd0d35f8c5151220e4b31ff0d89eb111d799430cbb7080ed35764a0", + "OwnershipCertificatePermutations": "75ff42711210e87557ba9f7afd376e98501817976416fd9826270c17485f3001", + "OwnershipData": "d8eab1a2f8bf41f83ef1006a53ca59e3404682bc342b210006ba5f5d548a0791", + "OwnershipDatumCore": "4c6466818436b035945064887628f969343de1fc2c3f185cd62664ccd0839f96", + "OwnershipGeometry": "e5578c50bb92090027687b48b493167f0b69de6b4fbb9b566f162d3da43e2875", + "OwnershipInverseTable": "ac2aef3b6e6198917abcb083ab1ce057304f8c13ff1c49cb459500cabe2434f1", + "ParentOwnership": "88dd181a04092407a8ae530a4da828d85c83b8d14f8920841973ef270702e361", + "ParentOwnershipData": "c1194f200f7acf97dd79df978db9e1c26182d4c9137caed678f0c965f025079b", + "PayloadGuards": "3f50b5a925a8505378ce2add6fed443c96caed9ec7122b84f6adab413ef85e49", + "PhysicalExample": "e1b6d55cd62bb4622b42fe903b8d73257871d30b714eab57890c18eb55bc3672", + "PhysicalHosting": "d4b0b48f95650934420c9b0c61683c2357ad5cdf628d77a350eab347a11e4029", + "PhysicalSourceConnection": "0134111be804735903270b64fea7d4070629760b9ede5cf5dff1d7ffb22ee9ea", + "PinnedHosting": "ce74e956dbfab444c2c0ee3903d1aed7c3d1f54b517e2413e38d31310df20c06", + "PinnedWindow": "d5fee2eba5f5002973eb2d50efe7d754ad8fbb13444fd1f46f309be20704a148", + "PortData": "c796d7550f0b31724d20b159953829f5b3bb301ff35984085839f4ab4029708c", + "PortGeometry": "7d56f4080e847dec95ce87a8fb59b61b6660312b3f3f382a39dbf269b2f1d1d7", + "PortRowData": "f5b02941dcfcda644d3db541ae6929bbeb445a6ae421e1b2315d65a07f657ffc", + "RowEvaluation": "85324b6571dad78e936cfa98115082bfa16898308290c39a8fd58de3c6eeaa56", + "SelectedGeometry": "abf8811bc421f5ba5c72ad91b88b4fbecfc3fba7adea0c55363d4884c99c4647", + "SingleHostRecovery": "e3ba14c60ca09079c1e97cca7058581453ce0a26a4f535fa957a09814e200c55", + "SingleStream": "7f9799db42b5e475b8ed46005a8c5af52653e547c88d86358e5a8b180e6dbc10", + "SourceCommonCover": "a43629a79fd6dc1247cd623c05d11d5ee2258bba6cd1b7b00e661f237cbeae12", + "SourceConnection": "e08eb43227b8e51dce1ab9e818ab0de984a9a9524b38bac3d40b2cad8c8403c5", + "SourceControls": "3b0ed6c1dbd61f46812a516db87a0ab001bff25308722b3be9642c21891f47e2", + "SourceDataBehavior": "4a30f0d4b1bd4b249fa1eee18946892623d89763c750cb2d3c69486b4a602dfa", + "SourceEndpoint": "bb620e35a618b481e2577ded8e5099951cd66d861a858caaf9c46b5817798570", + "SourceFramed": "d914cd145dae758922239e739de313c2fe059fb332a6862dff462719ddf28b99", + "SourceInitialPayload": "9e52514ec2bd9657f972122fb023b6f7a984e689aa2978d0a806ee4d89f4c29b", + "SourceInvocation": "0591fe203897942ce119a4dc7e6babae134ab447fccb49b0ec6145a5ac0b8071", + "SourceInvocationComparison": "9aedef17f3b5fe7619a20f820c76d9326218bbd907648a7973a2a2085d0a1255", + "SourceInvocationState": "b9739eec91aa8a7a923b888d9c127b276b1e3d5ca869e135b658dc14764c18a9", + "SourceLayouts": "96cadd7c92ed6c5c572addeac89f638ae3fdd62a78dfb4fadbb39b663d7898b4", + "SourceMoveGeometry": "bf64603b1b73ffca7d3cb34b8b4e2f3c0c8f752c0d12d8b760386212fc6133fc", + "SourceNativeInvocation": "eaa2379567c712b2e7ce613fb7b00f9f9457e6543a841317f31d5f2875168fec", + "SourceRaw": "ea71eadcbc505cdd9b8e39506c3ce1a651c250be8069e6fb5a39f2316435201e", + "SourceRawGuards": "8ab83236167f3ea64eb4f58de92d4019b0a0fe5eee44e6921c21292e6831bc50", + "SourceTables": "de190ad0a654c508a3674964b2df03c297e45c66359fab074b36f6ecf641efd8", + "SourceWitness": "30dccd519b09484b30402dc47ede74f83679182bdece8e42ce82481a16cde699", + "SourceWord": "0fb2e5113ee52259c49b00845b95fd787ac6ac220a3ea266a059fd77864725fa", + "TreeReplay": "5f84c871762994891e26bed70662326bc5caaf0a3126799c9aa01ad5f116401c" + }, + "stackLimitAfter": [ + 8388608, + -1 + ], + "completedUtc": "2026-10-13T05:40:20.464796+00:00", + "totalSeconds": 1009.314 +} diff --git a/research/lean-external-review/validation/lean421-ci-fix-make.log b/research/lean-external-review/validation/lean421-ci-fix-make.log new file mode 100644 index 0000000000..cc74913468 --- /dev/null +++ b/research/lean-external-review/validation/lean421-ci-fix-make.log @@ -0,0 +1,1965 @@ +python3 research/lean-multi-host-source/check_sources.py +{"status": "PASS", "literal_events_in_order": 19002, "live_roles": 987, "source_input_hashes_checked": 6, "scope": "Reproducible extraction; mathematical certificates are checked separately by Lean."} +python3 research/lean-multi-host-source/test_flat_data.py +. +---------------------------------------------------------------------- +Ran 1 test in 1.910s + +OK +python3 research/lean-multi-host-source/test_verifier_stack.py +... +---------------------------------------------------------------------- +Ran 3 tests in 0.002s + +OK +python3 research/lean-multi-host-source/verify.py --lake "/bin/lake" --receipt /tmp/pr442-lean421-fresh.json +$ lake env lean --version +Lean (version 4.21.0, x86_64-unknown-linux-gnu, commit 6741444a63ee, Release) +$ lake env lean --githash +6741444a63eec253a7eae7a83f1beb3de015023d +$ lake env lean --print-prefix +$ lake build +✔ [934/1084] Built RowEvaluation +ℹ [935/1084] Built CoordinateSwap +info: ../lean-whole-residual-hosting/CoordinateSwap.lean:154:0: 'WholeHosting.swapAddress_involution' depends on axioms: [propext, Quot.sound] +info: ../lean-whole-residual-hosting/CoordinateSwap.lean:155:0: 'WholeHosting.swapAddress_commute' depends on axioms: [propext, Quot.sound] +info: ../lean-whole-residual-hosting/CoordinateSwap.lean:156:0: 'WholeHosting.swapAddress_disjoint_union' depends on axioms: [propext, Quot.sound] +info: ../lean-whole-residual-hosting/CoordinateSwap.lean:157:0: 'WholeHosting.bitAction_involution' depends on axioms: [propext, Quot.sound] +info: ../lean-whole-residual-hosting/CoordinateSwap.lean:158:0: 'WholeHosting.bitAction_commute' depends on axioms: [propext, Quot.sound] +info: ../lean-whole-residual-hosting/CoordinateSwap.lean:159:0: 'WholeHosting.bitAction_disjoint_comp' depends on axioms: [propext, Quot.sound] +info: ../lean-whole-residual-hosting/CoordinateSwap.lean:160:0: 'WholeHosting.bitAction_complete' depends on axioms: [propext, Quot.sound] +info: ../lean-whole-residual-hosting/CoordinateSwap.lean:161:0: 'WholeHosting.bitFactors_union' depends on axioms: [propext, Quot.sound] +info: ../lean-whole-residual-hosting/CoordinateSwap.lean:162:0: 'WholeHosting.bitFactors_complete' depends on axioms: [propext, Quot.sound] +✔ [936/1084] Built FrameDatumCore +ℹ [938/1084] Built MultiHosting +info: ../lean-multi-host-framework/MultiHosting.lean:215:0: 'MultiHosting.base_commutes' depends on axioms: [propext, Quot.sound] +info: ../lean-multi-host-framework/MultiHosting.lean:216:0: 'MultiHosting.runBase_commutes' depends on axioms: [propext, Quot.sound] +info: ../lean-multi-host-framework/MultiHosting.lean:217:0: 'MultiHosting.delay_residuals' depends on axioms: [propext, Quot.sound] +info: ../lean-multi-host-framework/MultiHosting.lean:218:0: 'MultiHosting.multi_hosting' depends on axioms: [propext, Quot.sound] +info: ../lean-multi-host-framework/MultiHosting.lean:219:0: 'MultiHosting.multi_hosting_in_context' depends on axioms: [propext, Quot.sound] +info: ../lean-multi-host-framework/MultiHosting.lean:220:0: 'MultiHosting.PhysicalImplementations.original_projection' does not depend on any axioms +info: ../lean-multi-host-framework/MultiHosting.lean:221:0: 'MultiHosting.PhysicalImplementations.relocated_projection' does not depend on any axioms +info: ../lean-multi-host-framework/MultiHosting.lean:222:0: 'MultiHosting.physical_multi_hosting' depends on axioms: [propext, Quot.sound] +info: ../lean-multi-host-framework/MultiHosting.lean:223:0: 'MultiHosting.physical_multi_hosting_in_context' depends on axioms: [propext, Quot.sound] +✔ [939/1084] Built OwnershipDatumCore +✔ [940/1084] Built FrameCertificateBatch14 +✔ [941/1084] Built FrameCertificateBatch12 +✔ [942/1084] Built FrameCertificateBatch13 +✔ [943/1084] Built FrameCertificateBatch11 +ℹ [944/1084] Built PortData +info: PortData.lean:916:0: 'PortGeometry.doubled_orthogonal_entries' depends on axioms: [propext, Quot.sound] +info: PortData.lean:917:0: 'PortGeometry.quarteredRoute_exact' depends on axioms: [propext, Quot.sound] +✔ [945/1084] Built FrameCertificateBatch10 +✔ [946/1084] Built FrameCertificateBatch08 +✔ [947/1084] Built FrameCertificateBatch09 +✔ [948/1084] Built FrameCertificateBatch07 +✔ [949/1084] Built FrameCertificateBatch05 +✔ [950/1084] Built FrameCertificateBatch06 +✔ [951/1084] Built FrameCertificateBatch04 +ℹ [952/1084] Built BoundaryExamples +info: ../lean-whole-residual-hosting/BoundaryExamples.lean:101:0: 'WholeHosting.Boundary.readHost_preserves_host' does not depend on any axioms +info: ../lean-whole-residual-hosting/BoundaryExamples.lean:102:0: 'WholeHosting.Boundary.host_preservation_not_commutation' does not depend on any axioms +info: ../lean-whole-residual-hosting/BoundaryExamples.lean:103:0: 'WholeHosting.Boundary.overlapping_masks_not_disjoint' does not depend on any axioms +info: ../lean-whole-residual-hosting/BoundaryExamples.lean:104:0: 'WholeHosting.Boundary.overlapping_masks_not_union' does not depend on any axioms +info: ../lean-whole-residual-hosting/BoundaryExamples.lean:105:0: 'WholeHosting.Boundary.outside_pending_not_completion' does not depend on any axioms +info: ../lean-whole-residual-hosting/BoundaryExamples.lean:106:0: 'WholeHosting.Boundary.swapAB_involution' does not depend on any axioms +info: ../lean-whole-residual-hosting/BoundaryExamples.lean:107:0: 'WholeHosting.Boundary.swapCD_involution' does not depend on any axioms +info: ../lean-whole-residual-hosting/BoundaryExamples.lean:108:0: 'WholeHosting.Boundary.chartBC_involution' does not depend on any axioms +info: ../lean-whole-residual-hosting/BoundaryExamples.lean:109:0: 'WholeHosting.Boundary.same_chart_commute' does not depend on any axioms +info: ../lean-whole-residual-hosting/BoundaryExamples.lean:110:0: 'WholeHosting.Boundary.different_charts_not_commute' does not depend on any axioms +ℹ [953/1084] Built Hosting +info: ../lean-whole-residual-hosting/Hosting.lean:179:0: 'WholeHosting.base_commutes' depends on axioms: [propext, Quot.sound] +info: ../lean-whole-residual-hosting/Hosting.lean:180:0: 'WholeHosting.runBase_commutes' depends on axioms: [propext, Quot.sound] +info: ../lean-whole-residual-hosting/Hosting.lean:181:0: 'WholeHosting.delay_residuals' depends on axioms: [propext, Quot.sound] +info: ../lean-whole-residual-hosting/Hosting.lean:182:0: 'WholeHosting.whole_hosting' depends on axioms: [propext, Quot.sound] +info: ../lean-whole-residual-hosting/Hosting.lean:183:0: 'WholeHosting.whole_hosting_in_context' depends on axioms: [propext, Quot.sound] +info: ../lean-whole-residual-hosting/Hosting.lean:184:0: 'WholeHosting.Implementations.original_eq' does not depend on any axioms +info: ../lean-whole-residual-hosting/Hosting.lean:185:0: 'WholeHosting.Implementations.relocated_eq' does not depend on any axioms +info: ../lean-whole-residual-hosting/Hosting.lean:186:0: 'WholeHosting.implementation_whole_hosting' depends on axioms: [propext, Quot.sound] +ℹ [954/1087] Built PinnedWindow +info: ../lean-whole-residual-hosting/PinnedWindow.lean:76:0: 'WholeHosting.PinnedBitWindow.disjoint' depends on axioms: [propext, Quot.sound] +info: ../lean-whole-residual-hosting/PinnedWindow.lean:77:0: 'WholeHosting.PinnedBitWindow.subset' does not depend on any axioms +info: ../lean-whole-residual-hosting/PinnedWindow.lean:78:0: 'WholeHosting.PinnedBitWindow.coverage' depends on axioms: [Quot.sound] +info: ../lean-whole-residual-hosting/PinnedWindow.lean:79:0: 'WholeHosting.PinnedBitWindow.same_stage_reorder' depends on axioms: [propext, Quot.sound] +info: ../lean-whole-residual-hosting/PinnedWindow.lean:80:0: 'WholeHosting.PinnedBitWindow.complete' depends on axioms: [propext, Quot.sound] +info: ../lean-whole-residual-hosting/PinnedWindow.lean:81:0: 'WholeHosting.PinnedBitWindow.complete_with_remainder' depends on axioms: [propext, Quot.sound] +✔ [955/1087] Built LinearReplay +ℹ [956/1087] Built MultiHostControls +info: ../lean-multi-host-framework/MultiHostControls.lean:58:0: 'MultiHosting.Controls.mixing_does_not_commute' does not depend on any axioms +info: ../lean-multi-host-framework/MultiHostControls.lean:59:0: 'MultiHosting.Controls.alias_breaks_refinement' does not depend on any axioms +✔ [957/1087] Built FrameCertificateBatch03 +✔ [958/1087] Built FrameCertificateBatch02 +✔ [959/1087] Built OwnershipInverseTable +✔ [960/1087] Built OwnershipCertificateHelpers +✔ [961/1087] Built OwnershipCertificateMasks +ℹ [962/1087] Built PortRowData +info: PortRowData.lean:14:0: 'PortGeometry.doubled_row_orthogonal_entries' depends on axioms: [propext, Quot.sound] +ℹ [964/1093] Built PhysicalHosting +info: ../lean-whole-residual-hosting/PhysicalHosting.lean:111:0: 'WholeHosting.PhysicalImplementations.original_projection' does not depend on any axioms +info: ../lean-whole-residual-hosting/PhysicalHosting.lean:112:0: 'WholeHosting.PhysicalImplementations.relocated_projection' does not depend on any axioms +info: ../lean-whole-residual-hosting/PhysicalHosting.lean:113:0: 'WholeHosting.physical_whole_hosting' depends on axioms: [propext, Quot.sound] +info: ../lean-whole-residual-hosting/PhysicalHosting.lean:114:0: 'WholeHosting.physical_hosting_in_context' depends on axioms: [propext, Quot.sound] +✔ [965/1093] Built TreeReplay +✔ [966/1093] Built OwnershipCertificatePermutations +✔ [967/1093] Built OwnershipCertificateOwner +⚠ [968/1093] Built PortGeometry +info: PortGeometry.lean:330:28: Try this: ring_nf +warning: PortGeometry.lean:330:33: Used `tac1 <;> tac2` where `(tac1; tac2)` would suffice +note: this linter can be disabled with `set_option linter.unnecessarySeqFocus false` +info: PortGeometry.lean:369:0: 'PortGeometry.cast_orthogonal' depends on axioms: [propext, Classical.choice, Quot.sound] +info: PortGeometry.lean:370:0: 'PortGeometry.doubled_orthogonal' depends on axioms: [propext, Classical.choice, Quot.sound] +info: PortGeometry.lean:371:0: 'PortGeometry.doubled_row_orthogonal' depends on axioms: [propext, Classical.choice, Quot.sound] +info: PortGeometry.lean:372:0: 'PortGeometry.cast_row_orthogonal' depends on axioms: [propext, Classical.choice, Quot.sound] +info: PortGeometry.lean:373:0: 'PortGeometry.basis_entry' depends on axioms: [propext, Classical.choice, Quot.sound] +info: PortGeometry.lean:374:0: 'PortGeometry.basis_transpose_mul' depends on axioms: [propext, Classical.choice, Quot.sound] +info: PortGeometry.lean:375:0: 'PortGeometry.basis_mul_transpose' depends on axioms: [propext, Classical.choice, Quot.sound] +info: PortGeometry.lean:376:0: 'PortGeometry.firstEight_extendEight' depends on axioms: [propext, Quot.sound] +info: PortGeometry.lean:377:0: 'PortGeometry.firstEight_add' does not depend on any axioms +info: PortGeometry.lean:378:0: 'PortGeometry.firstEight_smul' does not depend on any axioms +info: PortGeometry.lean:379:0: 'PortGeometry.extendEight_comp' depends on axioms: [propext, Quot.sound] +info: PortGeometry.lean:380:0: 'PortGeometry.extendEight_id' depends on axioms: [propext, Quot.sound] +info: PortGeometry.lean:381:0: 'PortGeometry.chart64_firstEight' depends on axioms: [propext, Classical.choice, Quot.sound] +info: PortGeometry.lean:382:0: 'PortGeometry.chart64_outside' depends on axioms: [propext, Classical.choice, Quot.sound] +info: PortGeometry.lean:383:0: 'PortGeometry.chart64_bijective' depends on axioms: [propext, Classical.choice, Quot.sound] +info: PortGeometry.lean:384:0: 'PortGeometry.chart64_add' depends on axioms: [propext, Classical.choice, Quot.sound] +info: PortGeometry.lean:385:0: 'PortGeometry.chart64_smul' depends on axioms: [propext, Classical.choice, Quot.sound] +info: PortGeometry.lean:386:0: 'PortGeometry.chart8_dot' depends on axioms: [propext, Classical.choice, Quot.sound] +info: PortGeometry.lean:387:0: 'PortGeometry.chart64_dot' depends on axioms: [propext, Classical.choice, Quot.sound] +info: PortGeometry.lean:388:0: 'PortGeometry.chart64_symm_dot' depends on axioms: [propext, Classical.choice, Quot.sound] +info: PortGeometry.lean:389:0: 'PortGeometry.chart64_symm_add' depends on axioms: [propext, Classical.choice, Quot.sound] +info: PortGeometry.lean:390:0: 'PortGeometry.chart64_symm_smul' depends on axioms: [propext, Classical.choice, Quot.sound] +info: PortGeometry.lean:391:0: 'PortGeometry.stage2Index_involutive' depends on axioms: [propext, Quot.sound] +info: PortGeometry.lean:392:0: 'PortGeometry.stage2Coordinates_dot' depends on axioms: [propext, Classical.choice, Quot.sound] +info: PortGeometry.lean:393:0: 'PortGeometry.dataRoute64_dot' depends on axioms: [propext, Classical.choice, Quot.sound] +info: PortGeometry.lean:394:0: 'PortGeometry.dataRoute64_add' depends on axioms: [propext, Classical.choice, Quot.sound] +info: PortGeometry.lean:395:0: 'PortGeometry.dataRoute64_smul' depends on axioms: [propext, Classical.choice, Quot.sound] +info: PortGeometry.lean:396:0: 'PortGeometry.dataRoute64_involutive' depends on axioms: [propext, Classical.choice, Quot.sound] +info: PortGeometry.lean:397:0: 'PortGeometry.route15_entry' depends on axioms: [propext, Classical.choice, Quot.sound] +info: PortGeometry.lean:398:0: 'PortGeometry.sourceRoute64_eq' depends on axioms: [propext, Classical.choice, Quot.sound] +ℹ [969/1093] Built ContractScope +info: ../lean-source-invocation-audit/ContractScope.lean:42:0: 'SourceInvocation.retained_rest_equal' does not depend on any axioms +info: ../lean-source-invocation-audit/ContractScope.lean:43:0: 'SourceInvocation.no_contract_for_different_rest' does not depend on any axioms +ℹ [970/1093] Built SingleHostRecovery +info: ../lean-multi-host-framework/SingleHostRecovery.lean:133:0: 'MultiHosting.SingleHost.collapse_embed' does not depend on any axioms +info: ../lean-multi-host-framework/SingleHostRecovery.lean:134:0: 'MultiHosting.SingleHost.embed_collapse' depends on axioms: [Quot.sound] +info: ../lean-multi-host-framework/SingleHostRecovery.lean:135:0: 'MultiHosting.SingleHost.collapse_onHosts' does not depend on any axioms +info: ../lean-multi-host-framework/SingleHostRecovery.lean:136:0: 'MultiHosting.SingleHost.collapse_base' does not depend on any axioms +info: ../lean-multi-host-framework/SingleHostRecovery.lean:137:0: 'MultiHosting.SingleHost.collapse_hosted' does not depend on any axioms +info: ../lean-multi-host-framework/SingleHostRecovery.lean:138:0: 'MultiHosting.SingleHost.collapse_runBase' does not depend on any axioms +info: ../lean-multi-host-framework/SingleHostRecovery.lean:139:0: 'MultiHosting.SingleHost.collapse_runHosted' does not depend on any axioms +info: ../lean-multi-host-framework/SingleHostRecovery.lean:140:0: 'MultiHosting.SingleHost.residuals_event' does not depend on any axioms +info: ../lean-multi-host-framework/SingleHostRecovery.lean:141:0: 'MultiHosting.SingleHost.whole_hosting_recovered' depends on axioms: [propext, Quot.sound] +info: ../lean-multi-host-framework/SingleHostRecovery.lean:142:0: 'MultiHosting.SingleHost.physical_whole_hosting_recovered' depends on axioms: [propext, Quot.sound] +ℹ [972/1093] Built PinnedHosting +info: ../lean-whole-residual-hosting/PinnedHosting.lean:45:0: 'WholeHosting.PinnedBitWindow.selected_window_hosting' depends on axioms: [propext, Quot.sound] +info: ../lean-whole-residual-hosting/PinnedHosting.lean:46:0: 'WholeHosting.PinnedBitWindow.selected_physical_hosting' depends on axioms: [propext, Quot.sound] +ℹ [973/1093] Built PhysicalExample +info: ../lean-whole-residual-hosting/PhysicalExample.lean:55:0: 'WholeHosting.PhysicalExample.old_output_is_threaded' does not depend on any axioms +info: ../lean-whole-residual-hosting/PhysicalExample.lean:56:0: 'WholeHosting.PhysicalExample.relocated_output_is_threaded' does not depend on any axioms +info: ../lean-whole-residual-hosting/PhysicalExample.lean:57:0: 'WholeHosting.PhysicalExample.absorption' depends on axioms: [propext, Quot.sound] +ℹ [975/1093] Built SingleStream +info: ../lean-single-stream-obstruction/SingleStream.lean:202:0: 'SingleStream.realizes_iff' does not depend on any axioms +info: ../lean-single-stream-obstruction/SingleStream.lean:203:0: 'SingleStream.no_owner_of_two_dependencies' does not depend on any axioms +info: ../lean-single-stream-obstruction/SingleStream.lean:204:0: 'SingleStream.run_visible_eq' does not depend on any axioms +info: ../lean-single-stream-obstruction/SingleStream.lean:205:0: 'SingleStream.dirty_read_no_owner' depends on axioms: [propext, Quot.sound] +info: ../lean-single-stream-obstruction/SingleStream.lean:206:0: 'SingleStream.dirty_read_no_local_program' does not depend on any axioms +info: ../lean-single-stream-obstruction/SingleStream.lean:207:0: 'SingleStream.whole_read_realizes' does not depend on any axioms +info: ../lean-single-stream-obstruction/SingleStream.lean:208:0: 'SingleStream.two_reads_realize' does not depend on any axioms +info: ../lean-single-stream-obstruction/SingleStream.lean:209:0: 'SingleStream.split_residual_no_owner' does not depend on any axioms +info: ../lean-single-stream-obstruction/SingleStream.lean:210:0: 'SingleStream.two_residuals_realize' does not depend on any axioms +info: ../lean-single-stream-obstruction/SingleStream.lean:211:0: 'SingleStream.two_helper_word_endpoint' depends on axioms: [propext, Quot.sound] +info: ../lean-single-stream-obstruction/SingleStream.lean:212:0: 'SingleStream.correlated_two_helper_endpoint' depends on axioms: [propext, Quot.sound] +info: ../lean-single-stream-obstruction/SingleStream.lean:213:0: 'SingleStream.bit_factor_nontrivial' does not depend on any axioms +info: ../lean-single-stream-obstruction/SingleStream.lean:214:0: 'SingleStream.complex_factor_nontrivial' does not depend on any axioms +info: ../lean-single-stream-obstruction/SingleStream.lean:215:0: 'SingleStream.split_bit_factor_no_owner' does not depend on any axioms +info: ../lean-single-stream-obstruction/SingleStream.lean:216:0: 'SingleStream.split_complex_factor_no_owner' does not depend on any axioms +✔ [977/1093] Built PayloadGuards +✔ [978/1093] Built MatrixNodes00 +✔ [979/1093] Built EndpointInterpretation +ℹ [980/1093] Built FramedReplay +info: FramedReplay.lean:156:0: 'FramedReplay.decode_reframe' depends on axioms: [propext, Quot.sound] +info: FramedReplay.lean:157:0: 'FramedReplay.put_get' depends on axioms: [propext] +info: FramedReplay.lean:158:0: 'FramedReplay.decode_xor' depends on axioms: [Quot.sound] +info: FramedReplay.lean:159:0: 'FramedReplay.decode_step' depends on axioms: [propext, Quot.sound] +info: FramedReplay.lean:160:0: 'FramedReplay.physical_blank_of_decoded_blank' does not depend on any axioms +info: FramedReplay.lean:161:0: 'FramedReplay.erase_guard_transport' does not depend on any axioms +info: FramedReplay.lean:162:0: 'FramedReplay.decode_run' depends on axioms: [propext, Quot.sound] +ℹ [981/1093] Built OwnershipData +info: OwnershipData.lean:18:0: 'SourceOwnership.perm_inverse' depends on axioms: [propext] +info: OwnershipData.lean:19:0: 'SourceOwnership.perm_support' depends on axioms: [propext] +info: OwnershipData.lean:20:0: 'SourceOwnership.fingerprint_injective' depends on axioms: [propext] +info: OwnershipData.lean:21:0: 'SourceOwnership.family_tag_injective' depends on axioms: [propext] +info: OwnershipData.lean:22:0: 'SourceOwnership.helper_frame' depends on axioms: [propext] +✔ [982/1093] Built FrameCertificateBatch00 +ℹ [983/1093] Built OwnerTransport +info: OwnerTransport.lean:468:0: 'OwnerTransport.write_other' depends on axioms: [propext, Classical.choice, Quot.sound] +info: OwnerTransport.lean:469:0: 'OwnerTransport.gather_write' depends on axioms: [propext, Classical.choice, Quot.sound] +info: OwnerTransport.lean:470:0: 'OwnerTransport.rawXor_write' depends on axioms: [propext, Classical.choice, Quot.sound] +info: OwnerTransport.lean:471:0: 'OwnerTransport.gather_step' depends on axioms: [propext, Classical.choice, Quot.sound] +info: OwnerTransport.lean:472:0: 'OwnerTransport.logicalStep_tree' depends on axioms: [propext, Classical.choice, Quot.sound] +info: OwnerTransport.lean:473:0: 'OwnerTransport.rawStep_other' depends on axioms: [propext, Classical.choice, Quot.sound] +info: OwnerTransport.lean:474:0: 'OwnerTransport.gather_run_framed' depends on axioms: [propext, Classical.choice, Quot.sound] +info: OwnerTransport.lean:475:0: 'OwnerTransport.runRaw_other' depends on axioms: [propext, Classical.choice, Quot.sound] +info: OwnerTransport.lean:476:0: 'OwnerTransport.route_native_address' does not depend on any axioms +info: OwnerTransport.lean:477:0: 'OwnerTransport.rawXor_fromNative' depends on axioms: [propext, Classical.choice, Quot.sound] +info: OwnerTransport.lean:478:0: 'OwnerTransport.rawTransport_fromNative' depends on axioms: [propext, Classical.choice, Quot.sound] +info: OwnerTransport.lean:479:0: 'OwnerTransport.runRaw_fromNative' depends on axioms: [propext, Classical.choice, Quot.sound] +ℹ [984/1093] Built FrameTraceCore +info: FrameTraceCore.lean:83:0: 'FrameTrace.flag_mono' depends on axioms: [propext] +info: FrameTraceCore.lean:84:0: 'FrameTrace.checked_valid' depends on axioms: [propext] +info: FrameTraceCore.lean:85:0: 'FrameTrace.scalar_projection' depends on axioms: [propext] +✔ [985/1093] Built MatrixNodes01 +✔ [986/1093] Built AddressPairs +ℹ [987/1093] Built Ownership +info: Ownership.lean:110:0: 'SourceOwnership.residual_projector_transport' depends on axioms: [propext, Quot.sound] +info: Ownership.lean:111:0: 'SourceOwnership.unindex_tag_injective' depends on axioms: [propext, Classical.choice, Quot.sound] +info: Ownership.lean:112:0: 'SourceOwnership.owners_injective' depends on axioms: [propext, Classical.choice, Quot.sound] +✔ [988/1093] Built FrameCertificateBatch01 +ℹ [989/1093] Built FrameTraceRefinement +info: FrameTraceRefinement.lean:135:0: 'FrameTrace.matches_get' depends on axioms: [propext] +info: FrameTraceRefinement.lean:136:0: 'FrameTrace.matches_step' depends on axioms: [propext, Quot.sound] +info: FrameTraceRefinement.lean:137:0: 'FrameTrace.add_frames_equal' depends on axioms: [propext, Quot.sound] +info: FrameTraceRefinement.lean:138:0: 'FrameTrace.matches_run' depends on axioms: [propext, Quot.sound] +info: FrameTraceRefinement.lean:139:0: 'FrameTrace.valid_step' depends on axioms: [propext, Quot.sound] +info: FrameTraceRefinement.lean:140:0: 'FrameTrace.valid_trace' depends on axioms: [propext, Quot.sound] +info: FrameTraceRefinement.lean:141:0: 'FrameTrace.decoded_run' depends on axioms: [propext, Quot.sound] +✔ [990/1093] Built MatrixNodes02 +✔ [991/1093] Built FrameTraceNodes00 +ℹ [992/1093] Built OwnershipGeometry +info: OwnershipGeometry.lean:326:0: 'SourceOwnership.slotChart_dot' depends on axioms: [propext, Classical.choice, Quot.sound] +info: OwnershipGeometry.lean:327:0: 'SourceOwnership.helper_sigma_dot' depends on axioms: [propext, Classical.choice, Quot.sound] +info: OwnershipGeometry.lean:328:0: 'SourceOwnership.physicalOwner_injective' depends on axioms: [propext, Classical.choice, Quot.sound] +info: OwnershipGeometry.lean:329:0: 'SourceOwnership.activeOwner_injective' depends on axioms: [propext, Classical.choice, Quot.sound] +info: OwnershipGeometry.lean:330:0: 'SourceOwnership.active_gather_step' depends on axioms: [propext, Classical.choice, Quot.sound] +info: OwnershipGeometry.lean:331:0: 'SourceOwnership.sourceActiveOwner_injective' depends on axioms: [propext, Classical.choice, Quot.sound] +info: OwnershipGeometry.lean:332:0: 'SourceOwnership.source_address_gather_run' depends on axioms: [propext, Classical.choice, Quot.sound] +info: OwnershipGeometry.lean:333:0: 'SourceOwnership.source_common_cover' depends on axioms: [propext, Classical.choice, Quot.sound] +info: OwnershipGeometry.lean:334:0: 'SourceOwnership.source_native_run' depends on axioms: [propext, Classical.choice, Quot.sound] +✔ [993/1093] Built MatrixNodes03 +✔ [994/1093] Built FrameTraceNodes01 +✔ [995/1093] Built MatrixNodes04 +✔ [996/1093] Built FrameTraceNodes02 +✔ [997/1093] Built FrameLookup +✔ [998/1093] Built MatrixNodes05 +✔ [999/1093] Built FrameTraceNodes03 +✔ [1000/1093] Built FrameTransitionBatch26 +ℹ [1001/1093] Built ParentOwnershipData +info: ParentOwnershipData.lean:1750:0: 'ParentOwnership.perm_inverse' depends on axioms: [propext] +info: ParentOwnershipData.lean:1751:0: 'ParentOwnership.perm_support' depends on axioms: [propext] +info: ParentOwnershipData.lean:1752:0: 'ParentOwnership.fingerprint_injective' depends on axioms: [propext] +info: ParentOwnershipData.lean:1753:0: 'ParentOwnership.family_tag_injective' depends on axioms: [propext] +info: ParentOwnershipData.lean:1754:0: 'ParentOwnership.helper_frame' depends on axioms: [propext] +✔ [1002/1093] Built FrameTransitionBatch25 +✔ [1003/1093] Built FrameTransitionBatch24 +✔ [1004/1093] Built FrameTransitionBatch23 +✔ [1005/1093] Built FrameTransitionBatch22 +✔ [1006/1093] Built FrameTransitionBatch20 +✔ [1007/1093] Built FrameTransitionBatch21 +✔ [1008/1093] Built FrameTransitionBatch19 +✔ [1009/1093] Built FrameTransitionBatch18 +ℹ [1010/1093] Built SourceWord +info: ../lean-source-invocation-audit/SourceWord.lean:19929:0: 'ActualWord.helper3_checked' depends on axioms: [propext] +info: ../lean-source-invocation-audit/SourceWord.lean:19930:0: 'ActualWord.zero_checked' depends on axioms: [propext] +info: ../lean-source-invocation-audit/SourceWord.lean:19931:0: 'ActualWord.basis243_output' depends on axioms: [propext] +info: ../lean-source-invocation-audit/SourceWord.lean:19932:0: 'ActualWord.zero_output' depends on axioms: [propext] +✔ [1011/1093] Built FrameTransitionBatch16 +✔ [1012/1093] Built FrameTransitionBatch17 +✔ [1013/1093] Built FrameTransitionBatch15 +✔ [1014/1093] Built FrameTransitionBatch14 +✔ [1015/1093] Built FrameTransitionBatch13 +✔ [1016/1093] Built FrameTransitionBatch11 +✔ [1017/1093] Built FrameTransitionBatch12 +✔ [1018/1093] Built FrameTransitionBatch10 +✔ [1019/1093] Built FrameTransitionBatch09 +✔ [1020/1093] Built FrameTransitionBatch08 +✔ [1021/1093] Built FrameTransitionBatch07 +✔ [1022/1093] Built FrameTransitionBatch06 +✔ [1023/1093] Built FrameTransitionBatch05 +✔ [1024/1093] Built FrameTransitionBatch04 +✔ [1025/1093] Built MatrixNodes06 +✔ [1026/1093] Built FrameTraceNodes04 +ℹ [1027/1093] Built ParentOwnership +info: ParentOwnership.lean:307:0: 'ParentOwnership.unindex_tag_injective' depends on axioms: [propext, Classical.choice, Quot.sound] +info: ParentOwnership.lean:308:0: 'ParentOwnership.owners_injective' depends on axioms: [propext, Classical.choice, Quot.sound] +info: ParentOwnership.lean:309:0: 'ParentOwnership.helper_residual_transport' depends on axioms: [propext, Classical.choice, Quot.sound] +info: ParentOwnership.lean:310:0: 'ParentOwnership.sourceActiveOwner_injective' depends on axioms: [propext, Classical.choice, Quot.sound] +info: ParentOwnership.lean:311:0: 'ParentOwnership.source_gather_run' depends on axioms: [propext, Classical.choice, Quot.sound] +info: ParentOwnership.lean:313:0: 'ParentOwnership.source_common_cover' depends on axioms: [propext, Classical.choice, Quot.sound] +info: ParentOwnership.lean:314:0: 'ParentOwnership.source_native_run' depends on axioms: [propext, Classical.choice, Quot.sound] +✔ [1028/1093] Built FrameTransitionBatch03 +ℹ [1029/1093] Built SourceWitness +info: ../lean-source-invocation-audit/SourceWitness.lean:98:0: 'SourceInvocation.helperResponse_eq' depends on axioms: [propext] +info: ../lean-source-invocation-audit/SourceWitness.lean:99:0: 'SourceInvocation.parent_witness' depends on axioms: [propext] +info: ../lean-source-invocation-audit/SourceWitness.lean:100:0: 'SourceInvocation.declared_hosted_witness' depends on axioms: [propext] +info: ../lean-source-invocation-audit/SourceWitness.lean:101:0: 'SourceInvocation.direct_single_host_bridge_impossible' depends on axioms: [propext] +✔ [1031/1093] Built FrameTraceNodes05 +✔ [1032/1093] Built MatrixNodes07 +✔ [1033/1093] Built FrameTraceNodes06 +✔ [1034/1093] Built MatrixNodes08 +✔ [1035/1093] Built FrameTraceNodes07 +✔ [1036/1093] Built MatrixNodes09 +✔ [1037/1093] Built FrameTraceNodes08 +✔ [1038/1093] Built MatrixNodes10 +✔ [1039/1093] Built FrameTraceNodes09 +✔ [1040/1093] Built MatrixNodes11 +✔ [1041/1093] Built FrameTraceNodes10 +✔ [1042/1093] Built MatrixNodes12 +✔ [1043/1093] Built FrameTraceNodes11 +✔ [1044/1093] Built MatrixNodes13 +✔ [1045/1093] Built FrameTraceNodes12 +✔ [1046/1093] Built MatrixNodes14 +✔ [1047/1093] Built FrameTraceNodes13 +✔ [1048/1093] Built FrameTransitionBatch02 +✔ [1049/1093] Built MatrixNodes15 +✔ [1050/1093] Built FrameTraceNodes14 +✔ [1051/1093] Built MatrixNodes16 +✔ [1052/1093] Built FrameTraceNodes15 +✔ [1053/1093] Built FrameTransitionBatch01 +✔ [1054/1093] Built FrameTraceNodes16 +✔ [1055/1093] Built MatrixNodes17 +✔ [1056/1093] Built MatrixNodes18 +✔ [1057/1093] Built MatrixNodes19 +✔ [1058/1093] Built MatrixNodes20 +✔ [1059/1093] Built MatrixNodes21 +✔ [1060/1093] Built FrameTransitionBatch00 +✔ [1061/1093] Built MatrixData +✔ [1062/1093] Built FrameTraceLiterals +ℹ [1063/1093] Built SourceTables +info: SourceTables.lean:18:0: 'SourceMatrix.initial_formula' does not depend on any axioms +info: SourceTables.lean:19:0: 'SourceMatrix.expected_formula' depends on axioms: [propext] +ℹ [1064/1093] Built FrameTraceRoutes +info: FrameTraceRoutes.lean:37:0: 'SourceFrameTrace.indices_checked' depends on axioms: [propext] +info: FrameTraceRoutes.lean:38:0: 'SourceFrameTrace.indices_bound' depends on axioms: [propext, Quot.sound] +info: FrameTraceRoutes.lean:39:0: 'SourceFrameTrace.route_projection' depends on axioms: [propext, Quot.sound] +ℹ [1065/1093] Built FrameLabelData +info: FrameLabelData.lean:39:0: 'SourceFrameLabels.labels_checked' depends on axioms: [propext] +info: FrameLabelData.lean:40:0: 'SourceFrameLabels.label_range' depends on axioms: [propext, Quot.sound] +info: FrameLabelData.lean:41:0: 'SourceFrameLabels.copy_frames' depends on axioms: [propext, Quot.sound] +info: FrameLabelData.lean:42:0: 'SourceFrameLabels.erase_frames' depends on axioms: [propext, Quot.sound] +ℹ [1066/1093] Built FrameTraceTables +info: FrameTraceTables.lean:27:0: 'SourceFrameTrace.initial_owner_frames' does not depend on any axioms +info: FrameTraceTables.lean:28:0: 'SourceFrameTrace.helper_final_frames' does not depend on any axioms +info: FrameTraceTables.lean:29:0: 'SourceFrameTrace.initial_frame_range' does not depend on any axioms +info: FrameTraceTables.lean:30:0: 'SourceFrameTrace.final_frame_range' does not depend on any axioms +ℹ [1067/1093] Built FrameData +info: FrameData.lean:43:0: 'FrameGeometry.frame_valid' depends on axioms: [propext] +info: FrameData.lean:44:0: 'FrameGeometry.scaled_idempotent_entries' depends on axioms: [propext] +info: FrameData.lean:45:0: 'FrameGeometry.scaled_symmetric_entries' depends on axioms: [propext] +info: FrameData.lean:46:0: 'FrameGeometry.scaled_stack_entries' depends on axioms: [propext] +info: FrameData.lean:47:0: 'FrameGeometry.stack_inverse_entries' depends on axioms: [propext] +info: FrameData.lean:48:0: 'FrameGeometry.inverse_stack_entries' depends on axioms: [propext] +info: FrameData.lean:49:0: 'FrameGeometry.transition_absorbs' depends on axioms: [propext] +✔ [1068/1093] Built HelperGeometryData +ℹ [1069/1093] Built FrameGeometry +info: FrameGeometry.lean:432:0: 'FrameGeometry.scaled_full_entries' depends on axioms: [propext] +info: FrameGeometry.lean:433:0: 'FrameGeometry.scaled_zero_entries' depends on axioms: [propext] +info: FrameGeometry.lean:434:0: 'FrameGeometry.scaled_idempotent' depends on axioms: [propext, Classical.choice, Quot.sound] +info: FrameGeometry.lean:435:0: 'FrameGeometry.scaled_symmetric' depends on axioms: [propext, Quot.sound] +info: FrameGeometry.lean:436:0: 'FrameGeometry.stack_inverse' depends on axioms: [propext, Classical.choice, Quot.sound] +info: FrameGeometry.lean:437:0: 'FrameGeometry.inverse_stack' depends on axioms: [propext, Classical.choice, Quot.sound] +info: FrameGeometry.lean:438:0: 'FrameGeometry.cast_mul_factor' depends on axioms: [propext, Classical.choice, Quot.sound] +info: FrameGeometry.lean:439:0: 'FrameGeometry.four_ne_zero' depends on axioms: [propext, Classical.choice, Quot.sound] +info: FrameGeometry.lean:440:0: 'FrameGeometry.two_fifty_six_ne_zero' depends on axioms: [propext, Classical.choice, Quot.sound] +info: FrameGeometry.lean:441:0: 'FrameGeometry.projector_idempotent' depends on axioms: [propext, Classical.choice, Quot.sound] +info: FrameGeometry.lean:442:0: 'FrameGeometry.projector_symmetric' depends on axioms: [propext, Classical.choice, Quot.sound] +info: FrameGeometry.lean:443:0: 'FrameGeometry.projector_full' depends on axioms: [propext, Classical.choice, Quot.sound] +info: FrameGeometry.lean:444:0: 'FrameGeometry.projector_zero' depends on axioms: [propext, Classical.choice, Quot.sound] +info: FrameGeometry.lean:445:0: 'FrameGeometry.scaled_stack' depends on axioms: [propext, Classical.choice, Quot.sound] +info: FrameGeometry.lean:446:0: 'FrameGeometry.cast_transpose' depends on axioms: [propext, Quot.sound] +info: FrameGeometry.lean:447:0: 'FrameGeometry.cast_product' depends on axioms: [propext, Classical.choice, Quot.sound] +info: FrameGeometry.lean:448:0: 'FrameGeometry.cast_selector' depends on axioms: [propext, Quot.sound] +info: FrameGeometry.lean:449:0: 'FrameGeometry.projector_stack' depends on axioms: [propext, Classical.choice, Quot.sound] +info: FrameGeometry.lean:450:0: 'FrameGeometry.transition_scaled_left' depends on axioms: [propext, Classical.choice, Quot.sound] +info: FrameGeometry.lean:451:0: 'FrameGeometry.transition_scaled_right' depends on axioms: [propext, Classical.choice, Quot.sound] +info: FrameGeometry.lean:452:0: 'FrameGeometry.normalized_absorption' depends on axioms: [propext, Classical.choice, Quot.sound] +info: FrameGeometry.lean:453:0: 'FrameGeometry.transition_projectors' depends on axioms: [propext, Classical.choice, Quot.sound] +info: FrameGeometry.lean:454:0: 'FrameGeometry.stack_right_inverse' depends on axioms: [propext, Classical.choice, Quot.sound] +info: FrameGeometry.lean:455:0: 'FrameGeometry.stack_left_inverse' depends on axioms: [propext, Classical.choice, Quot.sound] +info: FrameGeometry.lean:456:0: 'FrameGeometry.partialSwap_involution' depends on axioms: [propext, Classical.choice, Quot.sound] +info: FrameGeometry.lean:457:0: 'FrameGeometry.partialSwap_nested' depends on axioms: [propext, Classical.choice, Quot.sound] +info: FrameGeometry.lean:458:0: 'FrameGeometry.partialSwap_nested_reverse' depends on axioms: [propext, Classical.choice, Quot.sound] +info: FrameGeometry.lean:459:0: 'FrameGeometry.full_after_frame' depends on axioms: [propext, Classical.choice, Quot.sound] +info: FrameGeometry.lean:460:0: 'FrameGeometry.frame_after_full' depends on axioms: [propext, Classical.choice, Quot.sound] +info: FrameGeometry.lean:461:0: 'FrameGeometry.firstEight_replaceFirst' depends on axioms: [propext, Quot.sound] +info: FrameGeometry.lean:462:0: 'FrameGeometry.replaceFirst_twice' depends on axioms: [propext, Quot.sound] +info: FrameGeometry.lean:463:0: 'FrameGeometry.replaceFirst_firstEight' depends on axioms: [propext, Quot.sound] +info: FrameGeometry.lean:464:0: 'FrameGeometry.liftPair_comp' depends on axioms: [propext, Quot.sound] +info: FrameGeometry.lean:465:0: 'FrameGeometry.liftPair_id' depends on axioms: [propext, Quot.sound] +info: FrameGeometry.lean:466:0: 'FrameGeometry.partialSwap_coordinate' depends on axioms: [propext, Classical.choice, Quot.sound] +info: FrameGeometry.lean:467:0: 'FrameGeometry.coordinate_residual' depends on axioms: [propext, Classical.choice, Quot.sound] +info: FrameGeometry.lean:468:0: 'FrameGeometry.residual_partialSwap' depends on axioms: [propext, Classical.choice, Quot.sound] +info: FrameGeometry.lean:469:0: 'FrameGeometry.full_after_frame64_coordinate' depends on axioms: [propext, Classical.choice, Quot.sound] +info: FrameGeometry.lean:470:0: 'FrameGeometry.frame_after_full64_coordinate' depends on axioms: [propext, Classical.choice, Quot.sound] +info: FrameGeometry.lean:471:0: 'FrameGeometry.coordinateSwap64_involution' depends on axioms: [propext, Quot.sound] +info: FrameGeometry.lean:472:0: 'FrameGeometry.stage2_relative_transport' depends on axioms: [propext, Classical.choice, Quot.sound] +info: FrameGeometry.lean:473:0: 'FrameGeometry.stage2_helper_endpoint' depends on axioms: [propext, Classical.choice, Quot.sound] +ℹ [1070/1093] Built MatrixCheckpoints +info: MatrixCheckpoints.lean:413:0: 'SourceMatrix.runFull_checked' depends on axioms: [propext] +ℹ [1071/1093] Built MatrixCertificate +info: MatrixCertificate.lean:12:0: 'SourceMatrix.literal_word_checked' depends on axioms: [propext, Quot.sound] +info: MatrixCertificate.lean:13:0: 'SourceMatrix.literal_word_rows' depends on axioms: [propext, Quot.sound] +ℹ [1072/1093] Built SourceEndpoint +info: SourceEndpoint.lean:77:0: 'SourceMatrix.arbitrary_dirty_bools' depends on axioms: [propext, Quot.sound] +info: SourceEndpoint.lean:78:0: 'SourceMatrix.arbitrary_dirty_guards' depends on axioms: [propext, Quot.sound] +info: SourceEndpoint.lean:79:0: 'SourceMatrix.arbitrary_dirty_payloads' depends on axioms: [propext, Quot.sound] +info: SourceEndpoint.lean:80:0: 'SourceMatrix.actual_payload_clean' depends on axioms: [propext, Quot.sound] +info: SourceEndpoint.lean:81:0: 'SourceMatrix.arbitrary_dirty_temp_restored' depends on axioms: [propext, Quot.sound] +info: SourceEndpoint.lean:82:0: 'SourceMatrix.arbitrary_dirty_original_roles' depends on axioms: [propext, Quot.sound] +ℹ [1073/1093] Built SourceControls +info: SourceControls.lean:52:0: 'SourceControls.omitted_add_changes_row' depends on axioms: [propext] +info: SourceControls.lean:53:0: 'SourceControls.omitted_add_keeps_guards' depends on axioms: [propext] +info: SourceControls.lean:54:0: 'SourceControls.dirty_private_copy_rejected' does not depend on any axioms +info: SourceControls.lean:55:0: 'SourceControls.dirty_private_copy_would_overwrite' depends on axioms: [propext] +info: SourceControls.lean:56:0: 'SourceControls.literal_helper_three_survives' depends on axioms: [propext, Quot.sound] +info: SourceControls.lean:57:0: 'SourceControls.literal_helper_three_not_zero' depends on axioms: [propext, Quot.sound] +✔ [1074/1093] Built SourceConnection +ℹ [1075/1093] Built SourceLayouts +info: SourceLayouts.lean:89:0: 'SourceLayouts.data_owner_eq' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceLayouts.lean:90:0: 'SourceLayouts.data_chart_eq' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceLayouts.lean:91:0: 'SourceLayouts.parent_owner_ne_host' depends on axioms: [propext, Classical.choice, Quot.sound] +ℹ [1076/1093] Built FrameMoveData +info: FrameMoveData.lean:65:0: 'SourceFrameMoves.moves_checked' depends on axioms: [propext] +info: FrameMoveData.lean:66:0: 'SourceFrameMoves.move_range' depends on axioms: [propext, Quot.sound] +info: FrameMoveData.lean:67:0: 'SourceFrameMoves.move_transition' depends on axioms: [propext, Quot.sound] +info: FrameMoveData.lean:68:0: 'SourceFrameMoves.move_absorbs' depends on axioms: [propext, Quot.sound] +✔ [1077/1093] Built FrameTraceCheckpoints +ℹ [1078/1093] Built FrameTraceData +info: FrameTraceData.lean:11:0: 'SourceFrameTrace.scalar_word' depends on axioms: [propext] +info: FrameTraceData.lean:12:0: 'SourceFrameTrace.forward_checked' depends on axioms: [propext, Quot.sound] +info: FrameTraceData.lean:13:0: 'SourceFrameTrace.forward_valid' depends on axioms: [propext, Quot.sound] +ℹ [1079/1093] Built SourceFramed +info: SourceFramed.lean:134:0: 'SourceFramed.initial_matches' depends on axioms: [propext] +info: SourceFramed.lean:135:0: 'SourceFramed.initial_decoded' depends on axioms: [propext, Quot.sound] +info: SourceFramed.lean:136:0: 'SourceFramed.actual_valid' depends on axioms: [propext, Quot.sound] +info: SourceFramed.lean:137:0: 'SourceFramed.final_matches' depends on axioms: [propext, Quot.sound] +info: SourceFramed.lean:138:0: 'SourceFramed.actual_decoded_endpoint' depends on axioms: [propext, Quot.sound] +info: SourceFramed.lean:139:0: 'SourceFramed.actual_physical_endpoint' depends on axioms: [propext, Quot.sound] +info: SourceFramed.lean:140:0: 'SourceFramed.actual_temporary_restored' depends on axioms: [propext, Quot.sound] +info: SourceFramed.lean:141:0: 'SourceFramed.all_physical_endpoints' depends on axioms: [propext, Quot.sound] +ℹ [1080/1093] Built PhysicalSourceConnection +info: PhysicalSourceConnection.lean:64:0: 'PhysicalSourceConnection.helper_endpoints' depends on axioms: [propext, Quot.sound] +info: PhysicalSourceConnection.lean:65:0: 'PhysicalSourceConnection.helper_endpoint' depends on axioms: [propext, Quot.sound] +info: PhysicalSourceConnection.lean:90:0: 'PhysicalSourceConnection.physical_data_endpoints' depends on axioms: [propext, Quot.sound] +info: PhysicalSourceConnection.lean:91:0: 'PhysicalSourceConnection.data_independent' depends on axioms: [propext, Quot.sound] +info: PhysicalSourceConnection.lean:235:0: 'PhysicalSourceConnection.data_endpoint' depends on axioms: [propext, Quot.sound] +info: PhysicalSourceConnection.lean:236:0: 'PhysicalSourceConnection.hosted_endpoint' depends on axioms: [propext, Quot.sound] +info: PhysicalSourceConnection.lean:237:0: 'PhysicalSourceConnection.original_retained' depends on axioms: [propext, Quot.sound] +info: PhysicalSourceConnection.lean:238:0: 'PhysicalSourceConnection.relocated_retained' depends on axioms: [propext, Quot.sound] +info: PhysicalSourceConnection.lean:239:0: 'PhysicalSourceConnection.tag_child_cases' does not depend on any axioms +info: PhysicalSourceConnection.lean:240:0: 'PhysicalSourceConnection.tag_pending_contains' depends on axioms: [propext] +info: PhysicalSourceConnection.lean:241:0: 'PhysicalSourceConnection.selected_invocation_completion' depends on axioms: [propext, Quot.sound] +ℹ [1081/1093] Built SourceRaw +info: SourceRaw.lean:117:0: 'SourceRaw.gather_initial' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceRaw.lean:118:0: 'SourceRaw.gather_final' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceRaw.lean:119:0: 'SourceRaw.actual_valid' depends on axioms: [propext, Quot.sound] +info: SourceRaw.lean:120:0: 'SourceRaw.payload_endpoint' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceRaw.lean:121:0: 'SourceRaw.private_restored' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceRaw.lean:122:0: 'SourceRaw.other_preserved' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceRaw.lean:123:0: 'SourceRaw.other_payload_preserved' depends on axioms: [propext, Classical.choice, Quot.sound] +✔ [1082/1093] Built InvocationPayload +✔ [1083/1093] Built SourceInvocationState +ℹ [1084/1093] Built SourceInitialPayload +info: SourceInitialPayload.lean:75:0: 'SourceInvocation.newPayload_host' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceInitialPayload.lean:76:0: 'SourceInvocation.oldPayload_data' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceInitialPayload.lean:77:0: 'SourceInvocation.newPayload_data' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceInitialPayload.lean:78:0: 'SourceInvocation.oldPayload_bank' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceInitialPayload.lean:79:0: 'SourceInvocation.shared_host_input' depends on axioms: [propext, Classical.choice, Quot.sound] +✔ [1085/1093] Built SelectedGeometry +ℹ [1086/1093] Built SourceRawGuards +info: SourceRawGuards.lean:205:0: 'SourceRawGuards.raw_clean_of_framed' depends on axioms: [Quot.sound] +info: SourceRawGuards.lean:206:0: 'SourceRawGuards.raw_clean_run_of_framed' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceRawGuards.lean:207:0: 'SourceRawGuards.native_clean_of_raw' depends on axioms: [Quot.sound] +info: SourceRawGuards.lean:208:0: 'SourceRawGuards.native_clean_run_of_raw' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceRawGuards.lean:209:0: 'SourceRawGuards.actual_raw_clean' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceRawGuards.lean:210:0: 'SourceRawGuards.initial_fromNative' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceRawGuards.lean:211:0: 'SourceRawGuards.actual_native_clean' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceRawGuards.lean:212:0: 'SourceRawGuards.native_run_refines' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceRawGuards.lean:213:0: 'SourceRawGuards.native_payload_endpoint' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceRawGuards.lean:214:0: 'SourceRawGuards.native_private_restored' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceRawGuards.lean:215:0: 'SourceRawGuards.native_other_preserved' depends on axioms: [propext, Classical.choice, Quot.sound] +ℹ [1087/1093] Built SourceCommonCover +info: SourceCommonCover.lean:109:0: 'SourceInvocation.parent_family_lt_private' does not depend on any axioms +info: SourceCommonCover.lean:110:0: 'SourceInvocation.owner_overlap_data' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceCommonCover.lean:111:0: 'SourceInvocation.old_common_cover' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceCommonCover.lean:112:0: 'SourceInvocation.new_common_cover' depends on axioms: [propext, Classical.choice, Quot.sound] +✔ [1088/1093] Built SourceNativeInvocation +ℹ [1089/1093] Built SourceMoveGeometry +info: SourceMoveGeometry.lean:315:0: 'SourceMoveGeometry.move_projectors' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceMoveGeometry.lean:316:0: 'SourceMoveGeometry.move_stage2_relative' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceMoveGeometry.lean:317:0: 'SourceMoveGeometry.move_relative' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceMoveGeometry.lean:318:0: 'SourceMoveGeometry.copy_stage2_relative' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceMoveGeometry.lean:319:0: 'SourceMoveGeometry.copy_relative' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceMoveGeometry.lean:320:0: 'SourceMoveGeometry.erase_relative' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceMoveGeometry.lean:321:0: 'SourceMoveGeometry.physicalStep_move' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceMoveGeometry.lean:322:0: 'SourceMoveGeometry.physicalStep_copy' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceMoveGeometry.lean:323:0: 'SourceMoveGeometry.matrix_run_eq' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceMoveGeometry.lean:324:0: 'SourceMoveGeometry.actual_matrix_run' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceMoveGeometry.lean:325:0: 'SourceMoveGeometry.nativeStep_move' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceMoveGeometry.lean:326:0: 'SourceMoveGeometry.nativeRoute_move' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceMoveGeometry.lean:327:0: 'SourceMoveGeometry.nativeStep_copy' depends on axioms: [propext, Classical.choice, Quot.sound] +✔ [1090/1093] Built SourceInvocationComparison +ℹ [1091/1093] Built SourceDataBehavior +info: SourceDataBehavior.lean:121:0: 'SourceDataBehavior.first_initial_frame' depends on axioms: [propext, Quot.sound] +info: SourceDataBehavior.lean:122:0: 'SourceDataBehavior.second_initial_frame' depends on axioms: [propext, Quot.sound] +info: SourceDataBehavior.lean:123:0: 'SourceDataBehavior.first_final_frame' depends on axioms: [propext, Quot.sound] +info: SourceDataBehavior.lean:124:0: 'SourceDataBehavior.second_final_frame' depends on axioms: [propext, Quot.sound] +info: SourceDataBehavior.lean:125:0: 'SourceDataBehavior.framed_first' depends on axioms: [propext, Quot.sound] +info: SourceDataBehavior.lean:126:0: 'SourceDataBehavior.framed_second' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceDataBehavior.lean:127:0: 'SourceDataBehavior.framed_data_formula' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceDataBehavior.lean:128:0: 'SourceDataBehavior.old_data_formula' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceDataBehavior.lean:129:0: 'SourceDataBehavior.new_data_formula' depends on axioms: [propext, Classical.choice, Quot.sound] +ℹ [1092/1093] Built SourceInvocation +info: SourceInvocation.lean:187:0: 'SourceInvocation.selected_call_completion' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceInvocation.lean:188:0: 'SourceInvocation.selected_native_realization' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceInvocation.lean:189:0: 'SourceInvocation.selected_native_clean' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceInvocation.lean:190:0: 'SourceInvocation.selected_matrix_realization' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceInvocation.lean:191:0: 'SourceInvocation.selected_original_matrix_realization' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceInvocation.lean:192:0: 'SourceInvocation.selected_temporary_restoration' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceInvocation.lean:194:0: 'SourceInvocation.selected_native_completion' depends on axioms: [propext, Classical.choice, Quot.sound] +info: SourceInvocation.lean:195:0: 'SourceInvocation.selected_data_formula' depends on axioms: [propext, Classical.choice, Quot.sound] +Build completed successfully. +$ lake env lean TaskAAxioms.lean +'MultiHosting.base_commutes' depends on axioms: [propext, Quot.sound] +'MultiHosting.runBase_commutes' depends on axioms: [propext, Quot.sound] +'MultiHosting.delay_residuals' depends on axioms: [propext, Quot.sound] +'MultiHosting.multi_hosting' depends on axioms: [propext, Quot.sound] +'MultiHosting.multi_hosting_in_context' depends on axioms: [propext, Quot.sound] +'MultiHosting.PhysicalImplementations.original_projection' does not depend on any axioms +'MultiHosting.PhysicalImplementations.relocated_projection' does not depend on any axioms +'MultiHosting.physical_multi_hosting' depends on axioms: [propext, Quot.sound] +'MultiHosting.physical_multi_hosting_in_context' depends on axioms: [propext, Quot.sound] +'MultiHosting.SingleHost.collapse_embed' does not depend on any axioms +'MultiHosting.SingleHost.embed_collapse' depends on axioms: [Quot.sound] +'MultiHosting.SingleHost.collapse_onHosts' does not depend on any axioms +'MultiHosting.SingleHost.collapse_base' does not depend on any axioms +'MultiHosting.SingleHost.collapse_hosted' does not depend on any axioms +'MultiHosting.SingleHost.collapse_runBase' does not depend on any axioms +'MultiHosting.SingleHost.collapse_runHosted' does not depend on any axioms +'MultiHosting.SingleHost.residuals_event' does not depend on any axioms +'MultiHosting.SingleHost.whole_hosting_recovered' depends on axioms: [propext, Quot.sound] +'MultiHosting.SingleHost.physical_whole_hosting_recovered' depends on axioms: [propext, Quot.sound] +'MultiHosting.Controls.mixing_does_not_commute' does not depend on any axioms +'MultiHosting.Controls.alias_breaks_refinement' does not depend on any axioms +$ lake env lean ../lean-whole-residual-hosting/Audit.lean +'WholeHosting.masksDisjoint_symm' depends on axioms: [propext] +'WholeHosting.swapAddress_involution' depends on axioms: [propext, Quot.sound] +'WholeHosting.swapAddress_commute' depends on axioms: [propext, Quot.sound] +'WholeHosting.swapAddress_disjoint_union' depends on axioms: [propext, Quot.sound] +'WholeHosting.bitAction_involution' depends on axioms: [propext, Quot.sound] +'WholeHosting.bitAction_commute' depends on axioms: [propext, Quot.sound] +'WholeHosting.bitAction_disjoint_comp' depends on axioms: [propext, Quot.sound] +'WholeHosting.remainder_disjoint' depends on axioms: [propext] +'WholeHosting.union_remainder' depends on axioms: [propext, Quot.sound] +'WholeHosting.bitAction_complete' depends on axioms: [propext, Quot.sound] +'WholeHosting.bitAction_empty' does not depend on any axioms +'WholeHosting.bitFactors_union' depends on axioms: [propext, Quot.sound] +'WholeHosting.bitFactors_complete' depends on axioms: [propext, Quot.sound] +'WholeHosting.base_commutes' depends on axioms: [propext, Quot.sound] +'WholeHosting.runBase_commutes' depends on axioms: [propext, Quot.sound] +'WholeHosting.delay_residuals' depends on axioms: [propext, Quot.sound] +'WholeHosting.whole_hosting' depends on axioms: [propext, Quot.sound] +'WholeHosting.whole_hosting_in_context' depends on axioms: [propext, Quot.sound] +'WholeHosting.Implementations.original_eq' does not depend on any axioms +'WholeHosting.Implementations.relocated_eq' does not depend on any axioms +'WholeHosting.implementation_whole_hosting' depends on axioms: [propext, Quot.sound] +'WholeHosting.PhysicalImplementations.original_projection' does not depend on any axioms +'WholeHosting.PhysicalImplementations.relocated_projection' does not depend on any axioms +'WholeHosting.physical_whole_hosting' depends on axioms: [propext, Quot.sound] +'WholeHosting.physical_hosting_in_context' depends on axioms: [propext, Quot.sound] +'WholeHosting.PinnedBitWindow.disjoint' depends on axioms: [propext, Quot.sound] +'WholeHosting.PinnedBitWindow.subset' does not depend on any axioms +'WholeHosting.PinnedBitWindow.coverage' depends on axioms: [Quot.sound] +'WholeHosting.PinnedBitWindow.same_stage_reorder' depends on axioms: [propext, Quot.sound] +'WholeHosting.PinnedBitWindow.remainder_empty' depends on axioms: [propext, Quot.sound] +'WholeHosting.PinnedBitWindow.complete' depends on axioms: [propext, Quot.sound] +'WholeHosting.PinnedBitWindow.complete_with_remainder' depends on axioms: [propext, Quot.sound] +'WholeHosting.PinnedBitWindow.selected_window_hosting' depends on axioms: [propext, Quot.sound] +'WholeHosting.PinnedBitWindow.selected_physical_hosting' depends on axioms: [propext, Quot.sound] +'WholeHosting.Boundary.readHost_preserves_host' does not depend on any axioms +'WholeHosting.Boundary.host_preservation_not_commutation' does not depend on any axioms +'WholeHosting.Boundary.overlapping_masks_not_disjoint' does not depend on any axioms +'WholeHosting.Boundary.overlapping_masks_not_union' does not depend on any axioms +'WholeHosting.Boundary.outside_pending_not_completion' does not depend on any axioms +'WholeHosting.Boundary.swapAB_involution' does not depend on any axioms +'WholeHosting.Boundary.swapCD_involution' does not depend on any axioms +'WholeHosting.Boundary.chartBC_involution' does not depend on any axioms +'WholeHosting.Boundary.same_chart_commute' does not depend on any axioms +'WholeHosting.Boundary.different_charts_not_commute' does not depend on any axioms +'WholeHosting.PhysicalExample.old_output_is_threaded' does not depend on any axioms +'WholeHosting.PhysicalExample.relocated_output_is_threaded' does not depend on any axioms +'WholeHosting.PhysicalExample.absorption' depends on axioms: [propext, Quot.sound] +$ lake env lean ../lean-source-invocation-audit/Audit.lean +'WholeHosting.masksDisjoint_symm' depends on axioms: [propext] +'WholeHosting.swapAddress_involution' depends on axioms: [propext, Quot.sound] +'WholeHosting.swapAddress_commute' depends on axioms: [propext, Quot.sound] +'WholeHosting.swapAddress_disjoint_union' depends on axioms: [propext, Quot.sound] +'WholeHosting.bitAction_involution' depends on axioms: [propext, Quot.sound] +'WholeHosting.bitAction_commute' depends on axioms: [propext, Quot.sound] +'WholeHosting.bitAction_disjoint_comp' depends on axioms: [propext, Quot.sound] +'WholeHosting.remainder_disjoint' depends on axioms: [propext] +'WholeHosting.union_remainder' depends on axioms: [propext, Quot.sound] +'WholeHosting.bitAction_complete' depends on axioms: [propext, Quot.sound] +'WholeHosting.bitAction_empty' does not depend on any axioms +'WholeHosting.bitFactors_union' depends on axioms: [propext, Quot.sound] +'WholeHosting.bitFactors_complete' depends on axioms: [propext, Quot.sound] +'WholeHosting.base_commutes' depends on axioms: [propext, Quot.sound] +'WholeHosting.runBase_commutes' depends on axioms: [propext, Quot.sound] +'WholeHosting.delay_residuals' depends on axioms: [propext, Quot.sound] +'WholeHosting.whole_hosting' depends on axioms: [propext, Quot.sound] +'WholeHosting.whole_hosting_in_context' depends on axioms: [propext, Quot.sound] +'WholeHosting.Implementations.original_eq' does not depend on any axioms +'WholeHosting.Implementations.relocated_eq' does not depend on any axioms +'WholeHosting.implementation_whole_hosting' depends on axioms: [propext, Quot.sound] +'WholeHosting.PhysicalImplementations.original_projection' does not depend on any axioms +'WholeHosting.PhysicalImplementations.relocated_projection' does not depend on any axioms +'WholeHosting.physical_whole_hosting' depends on axioms: [propext, Quot.sound] +'WholeHosting.physical_hosting_in_context' depends on axioms: [propext, Quot.sound] +'ActualWord.combine' depends on axioms: [propext] +'ActualWord.checkpoint0' depends on axioms: [propext] +'ActualWord.zero0' depends on axioms: [propext] +'ActualWord.checkpoint1' depends on axioms: [propext] +'ActualWord.zero1' depends on axioms: [propext] +'ActualWord.checkpoint2' depends on axioms: [propext] +'ActualWord.zero2' depends on axioms: [propext] +'ActualWord.checkpoint3' depends on axioms: [propext] +'ActualWord.zero3' depends on axioms: [propext] +'ActualWord.checkpoint4' depends on axioms: [propext] +'ActualWord.zero4' depends on axioms: [propext] +'ActualWord.checkpoint5' depends on axioms: [propext] +'ActualWord.zero5' depends on axioms: [propext] +'ActualWord.checkpoint6' depends on axioms: [propext] +'ActualWord.zero6' depends on axioms: [propext] +'ActualWord.checkpoint7' depends on axioms: [propext] +'ActualWord.zero7' depends on axioms: [propext] +'ActualWord.checkpoint8' depends on axioms: [propext] +'ActualWord.zero8' depends on axioms: [propext] +'ActualWord.checkpoint9' depends on axioms: [propext] +'ActualWord.zero9' depends on axioms: [propext] +'ActualWord.checkpoint10' depends on axioms: [propext] +'ActualWord.zero10' depends on axioms: [propext] +'ActualWord.checkpoint11' depends on axioms: [propext] +'ActualWord.zero11' depends on axioms: [propext] +'ActualWord.checkpoint12' depends on axioms: [propext] +'ActualWord.zero12' depends on axioms: [propext] +'ActualWord.checkpoint13' depends on axioms: [propext] +'ActualWord.zero13' depends on axioms: [propext] +'ActualWord.checkpoint14' depends on axioms: [propext] +'ActualWord.zero14' depends on axioms: [propext] +'ActualWord.checkpoint15' depends on axioms: [propext] +'ActualWord.zero15' depends on axioms: [propext] +'ActualWord.checkpoint16' depends on axioms: [propext] +'ActualWord.zero16' depends on axioms: [propext] +'ActualWord.checkpoint17' depends on axioms: [propext] +'ActualWord.zero17' depends on axioms: [propext] +'ActualWord.checkpoint18' depends on axioms: [propext] +'ActualWord.zero18' depends on axioms: [propext] +'ActualWord.checkpoint19' depends on axioms: [propext] +'ActualWord.zero19' depends on axioms: [propext] +'ActualWord.checkpoint20' depends on axioms: [propext] +'ActualWord.zero20' depends on axioms: [propext] +'ActualWord.checkpoint21' depends on axioms: [propext] +'ActualWord.zero21' depends on axioms: [propext] +'ActualWord.checkpoint22' depends on axioms: [propext] +'ActualWord.zero22' depends on axioms: [propext] +'ActualWord.checkpoint23' depends on axioms: [propext] +'ActualWord.zero23' depends on axioms: [propext] +'ActualWord.checkpoint24' depends on axioms: [propext] +'ActualWord.zero24' depends on axioms: [propext] +'ActualWord.checkpoint25' depends on axioms: [propext] +'ActualWord.zero25' depends on axioms: [propext] +'ActualWord.checkpoint26' depends on axioms: [propext] +'ActualWord.zero26' depends on axioms: [propext] +'ActualWord.checkpoint27' depends on axioms: [propext] +'ActualWord.zero27' depends on axioms: [propext] +'ActualWord.checkpoint28' depends on axioms: [propext] +'ActualWord.zero28' depends on axioms: [propext] +'ActualWord.checkpoint29' depends on axioms: [propext] +'ActualWord.zero29' depends on axioms: [propext] +'ActualWord.checkpoint30' depends on axioms: [propext] +'ActualWord.zero30' depends on axioms: [propext] +'ActualWord.checkpoint31' depends on axioms: [propext] +'ActualWord.zero31' depends on axioms: [propext] +'ActualWord.checkpoint32' depends on axioms: [propext] +'ActualWord.zero32' depends on axioms: [propext] +'ActualWord.checkpoint33' depends on axioms: [propext] +'ActualWord.zero33' depends on axioms: [propext] +'ActualWord.checkpoint34' depends on axioms: [propext] +'ActualWord.zero34' depends on axioms: [propext] +'ActualWord.checkpoint35' depends on axioms: [propext] +'ActualWord.zero35' depends on axioms: [propext] +'ActualWord.checkpoint36' depends on axioms: [propext] +'ActualWord.zero36' depends on axioms: [propext] +'ActualWord.checkpoint37' depends on axioms: [propext] +'ActualWord.zero37' depends on axioms: [propext] +'ActualWord.checkpoint38' depends on axioms: [propext] +'ActualWord.zero38' depends on axioms: [propext] +'ActualWord.checkpoint39' depends on axioms: [propext] +'ActualWord.zero39' depends on axioms: [propext] +'ActualWord.checkpoint40' depends on axioms: [propext] +'ActualWord.zero40' depends on axioms: [propext] +'ActualWord.checkpoint41' depends on axioms: [propext] +'ActualWord.zero41' depends on axioms: [propext] +'ActualWord.checkpoint42' depends on axioms: [propext] +'ActualWord.zero42' depends on axioms: [propext] +'ActualWord.checkpoint43' depends on axioms: [propext] +'ActualWord.zero43' depends on axioms: [propext] +'ActualWord.checkpoint44' depends on axioms: [propext] +'ActualWord.zero44' depends on axioms: [propext] +'ActualWord.checkpoint45' depends on axioms: [propext] +'ActualWord.zero45' depends on axioms: [propext] +'ActualWord.checkpoint46' depends on axioms: [propext] +'ActualWord.zero46' depends on axioms: [propext] +'ActualWord.checkpoint47' depends on axioms: [propext] +'ActualWord.zero47' depends on axioms: [propext] +'ActualWord.checkpoint48' depends on axioms: [propext] +'ActualWord.zero48' depends on axioms: [propext] +'ActualWord.checkpoint49' depends on axioms: [propext] +'ActualWord.zero49' depends on axioms: [propext] +'ActualWord.checkpoint50' depends on axioms: [propext] +'ActualWord.zero50' depends on axioms: [propext] +'ActualWord.checkpoint51' depends on axioms: [propext] +'ActualWord.zero51' depends on axioms: [propext] +'ActualWord.checkpoint52' depends on axioms: [propext] +'ActualWord.zero52' depends on axioms: [propext] +'ActualWord.checkpoint53' depends on axioms: [propext] +'ActualWord.zero53' depends on axioms: [propext] +'ActualWord.checkpoint54' depends on axioms: [propext] +'ActualWord.zero54' depends on axioms: [propext] +'ActualWord.checkpoint55' depends on axioms: [propext] +'ActualWord.zero55' depends on axioms: [propext] +'ActualWord.checkpoint56' depends on axioms: [propext] +'ActualWord.zero56' depends on axioms: [propext] +'ActualWord.checkpoint57' depends on axioms: [propext] +'ActualWord.zero57' depends on axioms: [propext] +'ActualWord.checkpoint58' depends on axioms: [propext] +'ActualWord.zero58' depends on axioms: [propext] +'ActualWord.checkpoint59' depends on axioms: [propext] +'ActualWord.zero59' depends on axioms: [propext] +'ActualWord.checkpoint60' depends on axioms: [propext] +'ActualWord.zero60' depends on axioms: [propext] +'ActualWord.checkpoint61' depends on axioms: [propext] +'ActualWord.zero61' depends on axioms: [propext] +'ActualWord.checkpoint62' depends on axioms: [propext] +'ActualWord.zero62' depends on axioms: [propext] +'ActualWord.checkpoint63' depends on axioms: [propext] +'ActualWord.zero63' depends on axioms: [propext] +'ActualWord.checkpoint64' depends on axioms: [propext] +'ActualWord.zero64' depends on axioms: [propext] +'ActualWord.checkpoint65' depends on axioms: [propext] +'ActualWord.zero65' depends on axioms: [propext] +'ActualWord.checkpoint66' depends on axioms: [propext] +'ActualWord.zero66' depends on axioms: [propext] +'ActualWord.checkpoint67' depends on axioms: [propext] +'ActualWord.zero67' depends on axioms: [propext] +'ActualWord.checkpoint68' depends on axioms: [propext] +'ActualWord.zero68' depends on axioms: [propext] +'ActualWord.checkpoint69' depends on axioms: [propext] +'ActualWord.zero69' depends on axioms: [propext] +'ActualWord.checkpoint70' depends on axioms: [propext] +'ActualWord.zero70' depends on axioms: [propext] +'ActualWord.checkpoint71' depends on axioms: [propext] +'ActualWord.zero71' depends on axioms: [propext] +'ActualWord.checkpoint72' depends on axioms: [propext] +'ActualWord.zero72' depends on axioms: [propext] +'ActualWord.checkpoint73' depends on axioms: [propext] +'ActualWord.zero73' depends on axioms: [propext] +'ActualWord.checkpoint74' depends on axioms: [propext] +'ActualWord.zero74' depends on axioms: [propext] +'ActualWord.checkpoint75' depends on axioms: [propext] +'ActualWord.zero75' depends on axioms: [propext] +'ActualWord.checkpoint76' depends on axioms: [propext] +'ActualWord.zero76' depends on axioms: [propext] +'ActualWord.checkpoint77' depends on axioms: [propext] +'ActualWord.zero77' depends on axioms: [propext] +'ActualWord.checkpoint78' depends on axioms: [propext] +'ActualWord.zero78' depends on axioms: [propext] +'ActualWord.checkpoint79' depends on axioms: [propext] +'ActualWord.zero79' depends on axioms: [propext] +'ActualWord.checkpoint80' depends on axioms: [propext] +'ActualWord.zero80' depends on axioms: [propext] +'ActualWord.checkpoint81' depends on axioms: [propext] +'ActualWord.zero81' depends on axioms: [propext] +'ActualWord.checkpoint82' depends on axioms: [propext] +'ActualWord.zero82' depends on axioms: [propext] +'ActualWord.checkpoint83' depends on axioms: [propext] +'ActualWord.zero83' depends on axioms: [propext] +'ActualWord.checkpoint84' depends on axioms: [propext] +'ActualWord.zero84' depends on axioms: [propext] +'ActualWord.checkpoint85' depends on axioms: [propext] +'ActualWord.zero85' depends on axioms: [propext] +'ActualWord.checkpoint86' depends on axioms: [propext] +'ActualWord.zero86' depends on axioms: [propext] +'ActualWord.checkpoint87' depends on axioms: [propext] +'ActualWord.zero87' depends on axioms: [propext] +'ActualWord.checkpoint88' depends on axioms: [propext] +'ActualWord.zero88' depends on axioms: [propext] +'ActualWord.checkpoint89' depends on axioms: [propext] +'ActualWord.zero89' depends on axioms: [propext] +'ActualWord.checkpoint90' depends on axioms: [propext] +'ActualWord.zero90' depends on axioms: [propext] +'ActualWord.checkpoint91' depends on axioms: [propext] +'ActualWord.zero91' depends on axioms: [propext] +'ActualWord.checkpoint92' depends on axioms: [propext] +'ActualWord.zero92' depends on axioms: [propext] +'ActualWord.checkpoint93' depends on axioms: [propext] +'ActualWord.zero93' depends on axioms: [propext] +'ActualWord.checkpoint94' depends on axioms: [propext] +'ActualWord.zero94' depends on axioms: [propext] +'ActualWord.checkpoint95' depends on axioms: [propext] +'ActualWord.zero95' depends on axioms: [propext] +'ActualWord.finish96' depends on axioms: [propext] +'ActualWord.finishZero96' depends on axioms: [propext] +'ActualWord.finish95' depends on axioms: [propext] +'ActualWord.finishZero95' depends on axioms: [propext] +'ActualWord.finish94' depends on axioms: [propext] +'ActualWord.finishZero94' depends on axioms: [propext] +'ActualWord.finish93' depends on axioms: [propext] +'ActualWord.finishZero93' depends on axioms: [propext] +'ActualWord.finish92' depends on axioms: [propext] +'ActualWord.finishZero92' depends on axioms: [propext] +'ActualWord.finish91' depends on axioms: [propext] +'ActualWord.finishZero91' depends on axioms: [propext] +'ActualWord.finish90' depends on axioms: [propext] +'ActualWord.finishZero90' depends on axioms: [propext] +'ActualWord.finish89' depends on axioms: [propext] +'ActualWord.finishZero89' depends on axioms: [propext] +'ActualWord.finish88' depends on axioms: [propext] +'ActualWord.finishZero88' depends on axioms: [propext] +'ActualWord.finish87' depends on axioms: [propext] +'ActualWord.finishZero87' depends on axioms: [propext] +'ActualWord.finish86' depends on axioms: [propext] +'ActualWord.finishZero86' depends on axioms: [propext] +'ActualWord.finish85' depends on axioms: [propext] +'ActualWord.finishZero85' depends on axioms: [propext] +'ActualWord.finish84' depends on axioms: [propext] +'ActualWord.finishZero84' depends on axioms: [propext] +'ActualWord.finish83' depends on axioms: [propext] +'ActualWord.finishZero83' depends on axioms: [propext] +'ActualWord.finish82' depends on axioms: [propext] +'ActualWord.finishZero82' depends on axioms: [propext] +'ActualWord.finish81' depends on axioms: [propext] +'ActualWord.finishZero81' depends on axioms: [propext] +'ActualWord.finish80' depends on axioms: [propext] +'ActualWord.finishZero80' depends on axioms: [propext] +'ActualWord.finish79' depends on axioms: [propext] +'ActualWord.finishZero79' depends on axioms: [propext] +'ActualWord.finish78' depends on axioms: [propext] +'ActualWord.finishZero78' depends on axioms: [propext] +'ActualWord.finish77' depends on axioms: [propext] +'ActualWord.finishZero77' depends on axioms: [propext] +'ActualWord.finish76' depends on axioms: [propext] +'ActualWord.finishZero76' depends on axioms: [propext] +'ActualWord.finish75' depends on axioms: [propext] +'ActualWord.finishZero75' depends on axioms: [propext] +'ActualWord.finish74' depends on axioms: [propext] +'ActualWord.finishZero74' depends on axioms: [propext] +'ActualWord.finish73' depends on axioms: [propext] +'ActualWord.finishZero73' depends on axioms: [propext] +'ActualWord.finish72' depends on axioms: [propext] +'ActualWord.finishZero72' depends on axioms: [propext] +'ActualWord.finish71' depends on axioms: [propext] +'ActualWord.finishZero71' depends on axioms: [propext] +'ActualWord.finish70' depends on axioms: [propext] +'ActualWord.finishZero70' depends on axioms: [propext] +'ActualWord.finish69' depends on axioms: [propext] +'ActualWord.finishZero69' depends on axioms: [propext] +'ActualWord.finish68' depends on axioms: [propext] +'ActualWord.finishZero68' depends on axioms: [propext] +'ActualWord.finish67' depends on axioms: [propext] +'ActualWord.finishZero67' depends on axioms: [propext] +'ActualWord.finish66' depends on axioms: [propext] +'ActualWord.finishZero66' depends on axioms: [propext] +'ActualWord.finish65' depends on axioms: [propext] +'ActualWord.finishZero65' depends on axioms: [propext] +'ActualWord.finish64' depends on axioms: [propext] +'ActualWord.finishZero64' depends on axioms: [propext] +'ActualWord.finish63' depends on axioms: [propext] +'ActualWord.finishZero63' depends on axioms: [propext] +'ActualWord.finish62' depends on axioms: [propext] +'ActualWord.finishZero62' depends on axioms: [propext] +'ActualWord.finish61' depends on axioms: [propext] +'ActualWord.finishZero61' depends on axioms: [propext] +'ActualWord.finish60' depends on axioms: [propext] +'ActualWord.finishZero60' depends on axioms: [propext] +'ActualWord.finish59' depends on axioms: [propext] +'ActualWord.finishZero59' depends on axioms: [propext] +'ActualWord.finish58' depends on axioms: [propext] +'ActualWord.finishZero58' depends on axioms: [propext] +'ActualWord.finish57' depends on axioms: [propext] +'ActualWord.finishZero57' depends on axioms: [propext] +'ActualWord.finish56' depends on axioms: [propext] +'ActualWord.finishZero56' depends on axioms: [propext] +'ActualWord.finish55' depends on axioms: [propext] +'ActualWord.finishZero55' depends on axioms: [propext] +'ActualWord.finish54' depends on axioms: [propext] +'ActualWord.finishZero54' depends on axioms: [propext] +'ActualWord.finish53' depends on axioms: [propext] +'ActualWord.finishZero53' depends on axioms: [propext] +'ActualWord.finish52' depends on axioms: [propext] +'ActualWord.finishZero52' depends on axioms: [propext] +'ActualWord.finish51' depends on axioms: [propext] +'ActualWord.finishZero51' depends on axioms: [propext] +'ActualWord.finish50' depends on axioms: [propext] +'ActualWord.finishZero50' depends on axioms: [propext] +'ActualWord.finish49' depends on axioms: [propext] +'ActualWord.finishZero49' depends on axioms: [propext] +'ActualWord.finish48' depends on axioms: [propext] +'ActualWord.finishZero48' depends on axioms: [propext] +'ActualWord.finish47' depends on axioms: [propext] +'ActualWord.finishZero47' depends on axioms: [propext] +'ActualWord.finish46' depends on axioms: [propext] +'ActualWord.finishZero46' depends on axioms: [propext] +'ActualWord.finish45' depends on axioms: [propext] +'ActualWord.finishZero45' depends on axioms: [propext] +'ActualWord.finish44' depends on axioms: [propext] +'ActualWord.finishZero44' depends on axioms: [propext] +'ActualWord.finish43' depends on axioms: [propext] +'ActualWord.finishZero43' depends on axioms: [propext] +'ActualWord.finish42' depends on axioms: [propext] +'ActualWord.finishZero42' depends on axioms: [propext] +'ActualWord.finish41' depends on axioms: [propext] +'ActualWord.finishZero41' depends on axioms: [propext] +'ActualWord.finish40' depends on axioms: [propext] +'ActualWord.finishZero40' depends on axioms: [propext] +'ActualWord.finish39' depends on axioms: [propext] +'ActualWord.finishZero39' depends on axioms: [propext] +'ActualWord.finish38' depends on axioms: [propext] +'ActualWord.finishZero38' depends on axioms: [propext] +'ActualWord.finish37' depends on axioms: [propext] +'ActualWord.finishZero37' depends on axioms: [propext] +'ActualWord.finish36' depends on axioms: [propext] +'ActualWord.finishZero36' depends on axioms: [propext] +'ActualWord.finish35' depends on axioms: [propext] +'ActualWord.finishZero35' depends on axioms: [propext] +'ActualWord.finish34' depends on axioms: [propext] +'ActualWord.finishZero34' depends on axioms: [propext] +'ActualWord.finish33' depends on axioms: [propext] +'ActualWord.finishZero33' depends on axioms: [propext] +'ActualWord.finish32' depends on axioms: [propext] +'ActualWord.finishZero32' depends on axioms: [propext] +'ActualWord.finish31' depends on axioms: [propext] +'ActualWord.finishZero31' depends on axioms: [propext] +'ActualWord.finish30' depends on axioms: [propext] +'ActualWord.finishZero30' depends on axioms: [propext] +'ActualWord.finish29' depends on axioms: [propext] +'ActualWord.finishZero29' depends on axioms: [propext] +'ActualWord.finish28' depends on axioms: [propext] +'ActualWord.finishZero28' depends on axioms: [propext] +'ActualWord.finish27' depends on axioms: [propext] +'ActualWord.finishZero27' depends on axioms: [propext] +'ActualWord.finish26' depends on axioms: [propext] +'ActualWord.finishZero26' depends on axioms: [propext] +'ActualWord.finish25' depends on axioms: [propext] +'ActualWord.finishZero25' depends on axioms: [propext] +'ActualWord.finish24' depends on axioms: [propext] +'ActualWord.finishZero24' depends on axioms: [propext] +'ActualWord.finish23' depends on axioms: [propext] +'ActualWord.finishZero23' depends on axioms: [propext] +'ActualWord.finish22' depends on axioms: [propext] +'ActualWord.finishZero22' depends on axioms: [propext] +'ActualWord.finish21' depends on axioms: [propext] +'ActualWord.finishZero21' depends on axioms: [propext] +'ActualWord.finish20' depends on axioms: [propext] +'ActualWord.finishZero20' depends on axioms: [propext] +'ActualWord.finish19' depends on axioms: [propext] +'ActualWord.finishZero19' depends on axioms: [propext] +'ActualWord.finish18' depends on axioms: [propext] +'ActualWord.finishZero18' depends on axioms: [propext] +'ActualWord.finish17' depends on axioms: [propext] +'ActualWord.finishZero17' depends on axioms: [propext] +'ActualWord.finish16' depends on axioms: [propext] +'ActualWord.finishZero16' depends on axioms: [propext] +'ActualWord.finish15' depends on axioms: [propext] +'ActualWord.finishZero15' depends on axioms: [propext] +'ActualWord.finish14' depends on axioms: [propext] +'ActualWord.finishZero14' depends on axioms: [propext] +'ActualWord.finish13' depends on axioms: [propext] +'ActualWord.finishZero13' depends on axioms: [propext] +'ActualWord.finish12' depends on axioms: [propext] +'ActualWord.finishZero12' depends on axioms: [propext] +'ActualWord.finish11' depends on axioms: [propext] +'ActualWord.finishZero11' depends on axioms: [propext] +'ActualWord.finish10' depends on axioms: [propext] +'ActualWord.finishZero10' depends on axioms: [propext] +'ActualWord.finish9' depends on axioms: [propext] +'ActualWord.finishZero9' depends on axioms: [propext] +'ActualWord.finish8' depends on axioms: [propext] +'ActualWord.finishZero8' depends on axioms: [propext] +'ActualWord.finish7' depends on axioms: [propext] +'ActualWord.finishZero7' depends on axioms: [propext] +'ActualWord.finish6' depends on axioms: [propext] +'ActualWord.finishZero6' depends on axioms: [propext] +'ActualWord.finish5' depends on axioms: [propext] +'ActualWord.finishZero5' depends on axioms: [propext] +'ActualWord.finish4' depends on axioms: [propext] +'ActualWord.finishZero4' depends on axioms: [propext] +'ActualWord.finish3' depends on axioms: [propext] +'ActualWord.finishZero3' depends on axioms: [propext] +'ActualWord.finish2' depends on axioms: [propext] +'ActualWord.finishZero2' depends on axioms: [propext] +'ActualWord.finish1' depends on axioms: [propext] +'ActualWord.finishZero1' depends on axioms: [propext] +'ActualWord.finish0' depends on axioms: [propext] +'ActualWord.finishZero0' depends on axioms: [propext] +'ActualWord.helper3_checked' depends on axioms: [propext] +'ActualWord.zero_checked' depends on axioms: [propext] +'ActualWord.basis243_output' depends on axioms: [propext] +'ActualWord.zero_output' depends on axioms: [propext] +'SourceInvocation.retained_rest_equal' does not depend on any axioms +'SourceInvocation.no_contract_for_different_rest' does not depend on any axioms +'SourceInvocation.helperResponse_eq' depends on axioms: [propext] +'SourceInvocation.parent_witness' depends on axioms: [propext] +'SourceInvocation.declared_hosted_witness' depends on axioms: [propext] +'SourceInvocation.direct_single_host_bridge_impossible' depends on axioms: [propext] +$ lake env lean TaskBAxioms.lean +'LinearReplay.evalRow_zero' depends on axioms: [propext, Quot.sound] +'LinearReplay.evalRow_xor' depends on axioms: [propext, Quot.sound] +'LinearReplay.evalRow_basis' depends on axioms: [propext, Quot.sound] +'LinearReplay.evalRow_shift_basis' depends on axioms: [propext, Quot.sound] +'LinearReplay.map_getD' depends on axioms: [propext, Quot.sound] +'LinearReplay.step_map' depends on axioms: [propext, Quot.sound] +'LinearReplay.run_map' depends on axioms: [propext, Quot.sound] +'LinearReplay.evalRows_step' depends on axioms: [propext, Quot.sound] +'LinearReplay.evalRows_run' depends on axioms: [propext, Quot.sound] +'LinearReplay.checked_projection' depends on axioms: [propext] +'LinearReplay.evalRows_basisRows' depends on axioms: [propext, Quot.sound] +'LinearReplay.evalRows_getD' depends on axioms: [propext, Quot.sound] +'LinearReplay.checks_sound' depends on axioms: [propext, Quot.sound] +'LinearReplay.checked_flag_mono' depends on axioms: [propext] +'LinearReplay.checked_guards_sound' depends on axioms: [propext, Quot.sound] +'TreeReplay.Tree.map_get' depends on axioms: [propext] +'TreeReplay.Tree.map_put' depends on axioms: [propext] +'TreeReplay.Tree.map_map' depends on axioms: [propext] +'TreeReplay.Tree.map_tabulate' depends on axioms: [propext] +'TreeReplay.Tree.get_tabulate' depends on axioms: [propext, Quot.sound] +'TreeReplay.Tree.full_tabulate' does not depend on any axioms +'TreeReplay.Tree.full_put' does not depend on any axioms +'TreeReplay.Tree.get_put' depends on axioms: [propext, Classical.choice, Quot.sound] +'TreeReplay.step_map' depends on axioms: [propext] +'TreeReplay.run_map' depends on axioms: [propext] +'TreeReplay.evalRows_step' depends on axioms: [propext, Quot.sound] +'TreeReplay.evalRows_run' depends on axioms: [propext, Quot.sound] +'TreeReplay.checked_projection' depends on axioms: [propext] +'TreeReplay.evalRows_get' depends on axioms: [propext] +'TreeReplay.checks_sound' depends on axioms: [propext, Quot.sound] +'TreeReplay.checked_flag_mono' depends on axioms: [propext] +'TreeReplay.checked_guards_sound' depends on axioms: [propext, Quot.sound] +'TreeReplay.evalRows_basisRows' depends on axioms: [propext, Quot.sound] +'TreeReplay.dirtyInput_get' depends on axioms: [propext, Quot.sound] +'TreeReplay.evalPayloadRows_run' depends on axioms: [propext, Quot.sound] +'TreeReplay.evalPayloadRows_basisRows' depends on axioms: [propext, Quot.sound] +'FramedReplay.decode_reframe' depends on axioms: [propext, Quot.sound] +'FramedReplay.put_get' depends on axioms: [propext] +'FramedReplay.decode_xor' depends on axioms: [Quot.sound] +'FramedReplay.decode_step' depends on axioms: [propext, Quot.sound] +'FramedReplay.physical_blank_of_decoded_blank' does not depend on any axioms +'FramedReplay.erase_guard_transport' does not depend on any axioms +'FramedReplay.decode_run' depends on axioms: [propext, Quot.sound] +'WholeHosting.masksDisjoint_symm' depends on axioms: [propext] +'WholeHosting.swapAddress_involution' depends on axioms: [propext, Quot.sound] +'WholeHosting.swapAddress_commute' depends on axioms: [propext, Quot.sound] +'WholeHosting.swapAddress_disjoint_union' depends on axioms: [propext, Quot.sound] +'WholeHosting.bitAction_involution' depends on axioms: [propext, Quot.sound] +'WholeHosting.bitAction_commute' depends on axioms: [propext, Quot.sound] +'WholeHosting.bitAction_disjoint_comp' depends on axioms: [propext, Quot.sound] +'WholeHosting.remainder_disjoint' depends on axioms: [propext] +'WholeHosting.union_remainder' depends on axioms: [propext, Quot.sound] +'WholeHosting.bitAction_complete' depends on axioms: [propext, Quot.sound] +'WholeHosting.bitAction_empty' does not depend on any axioms +'WholeHosting.bitFactors_union' depends on axioms: [propext, Quot.sound] +'WholeHosting.bitFactors_complete' depends on axioms: [propext, Quot.sound] +'AddressPairs.split_join' does not depend on any axioms +'AddressPairs.join_split' does not depend on any axioms +'AddressPairs.relative_gauge' depends on axioms: [propext] +'AddressPairs.join_swap' depends on axioms: [propext, Quot.sound] +'AddressPairs.relative_coordinate' depends on axioms: [propext, Quot.sound] +'SourceMatrix.evalRow_endpoint' depends on axioms: [propext, Quot.sound] +'SourceMatrix.evalRows_endpoint' depends on axioms: [propext, Quot.sound] +'SourceMatrix.evalPayloadRows_endpoint' depends on axioms: [propext, Quot.sound] +'FrameGeometry.frame_valid' depends on axioms: [propext] +'FrameGeometry.scaled_idempotent_entries' depends on axioms: [propext] +'FrameGeometry.scaled_symmetric_entries' depends on axioms: [propext] +'FrameGeometry.scaled_stack_entries' depends on axioms: [propext] +'FrameGeometry.stack_inverse_entries' depends on axioms: [propext] +'FrameGeometry.inverse_stack_entries' depends on axioms: [propext] +'FrameGeometry.transition_absorbs' depends on axioms: [propext] +'FrameGeometry.scaled_full_entries' depends on axioms: [propext] +'FrameGeometry.scaled_zero_entries' depends on axioms: [propext] +'FrameGeometry.scaled_idempotent' depends on axioms: [propext, Classical.choice, Quot.sound] +'FrameGeometry.scaled_symmetric' depends on axioms: [propext, Quot.sound] +'FrameGeometry.stack_inverse' depends on axioms: [propext, Classical.choice, Quot.sound] +'FrameGeometry.inverse_stack' depends on axioms: [propext, Classical.choice, Quot.sound] +'FrameGeometry.cast_mul_factor' depends on axioms: [propext, Classical.choice, Quot.sound] +'FrameGeometry.four_ne_zero' depends on axioms: [propext, Classical.choice, Quot.sound] +'FrameGeometry.two_fifty_six_ne_zero' depends on axioms: [propext, Classical.choice, Quot.sound] +'FrameGeometry.projector_idempotent' depends on axioms: [propext, Classical.choice, Quot.sound] +'FrameGeometry.projector_symmetric' depends on axioms: [propext, Classical.choice, Quot.sound] +'FrameGeometry.projector_full' depends on axioms: [propext, Classical.choice, Quot.sound] +'FrameGeometry.projector_zero' depends on axioms: [propext, Classical.choice, Quot.sound] +'FrameGeometry.scaled_stack' depends on axioms: [propext, Classical.choice, Quot.sound] +'FrameGeometry.cast_transpose' depends on axioms: [propext, Quot.sound] +'FrameGeometry.cast_product' depends on axioms: [propext, Classical.choice, Quot.sound] +'FrameGeometry.cast_selector' depends on axioms: [propext, Quot.sound] +'FrameGeometry.projector_stack' depends on axioms: [propext, Classical.choice, Quot.sound] +'FrameGeometry.transition_scaled_left' depends on axioms: [propext, Classical.choice, Quot.sound] +'FrameGeometry.transition_scaled_right' depends on axioms: [propext, Classical.choice, Quot.sound] +'FrameGeometry.normalized_absorption' depends on axioms: [propext, Classical.choice, Quot.sound] +'FrameGeometry.transition_projectors' depends on axioms: [propext, Classical.choice, Quot.sound] +'FrameGeometry.stack_right_inverse' depends on axioms: [propext, Classical.choice, Quot.sound] +'FrameGeometry.stack_left_inverse' depends on axioms: [propext, Classical.choice, Quot.sound] +'FrameGeometry.partialSwap_involution' depends on axioms: [propext, Classical.choice, Quot.sound] +'FrameGeometry.partialSwap_nested' depends on axioms: [propext, Classical.choice, Quot.sound] +'FrameGeometry.partialSwap_nested_reverse' depends on axioms: [propext, Classical.choice, Quot.sound] +'FrameGeometry.full_after_frame' depends on axioms: [propext, Classical.choice, Quot.sound] +'FrameGeometry.frame_after_full' depends on axioms: [propext, Classical.choice, Quot.sound] +'FrameGeometry.firstEight_replaceFirst' depends on axioms: [propext, Quot.sound] +'FrameGeometry.replaceFirst_twice' depends on axioms: [propext, Quot.sound] +'FrameGeometry.replaceFirst_firstEight' depends on axioms: [propext, Quot.sound] +'FrameGeometry.liftPair_comp' depends on axioms: [propext, Quot.sound] +'FrameGeometry.liftPair_id' depends on axioms: [propext, Quot.sound] +'FrameGeometry.partialSwap_coordinate' depends on axioms: [propext, Classical.choice, Quot.sound] +'FrameGeometry.coordinate_residual' depends on axioms: [propext, Classical.choice, Quot.sound] +'FrameGeometry.residual_partialSwap' depends on axioms: [propext, Classical.choice, Quot.sound] +'FrameGeometry.full_after_frame64_coordinate' depends on axioms: [propext, Classical.choice, Quot.sound] +'FrameGeometry.frame_after_full64_coordinate' depends on axioms: [propext, Classical.choice, Quot.sound] +'FrameGeometry.coordinateSwap64_involution' depends on axioms: [propext, Quot.sound] +'FrameGeometry.stage2_relative_transport' depends on axioms: [propext, Classical.choice, Quot.sound] +'FrameGeometry.stage2_helper_endpoint' depends on axioms: [propext, Classical.choice, Quot.sound] +'FrameTrace.flag_mono' depends on axioms: [propext] +'FrameTrace.checked_valid' depends on axioms: [propext] +'FrameTrace.scalar_projection' depends on axioms: [propext] +'SourceFrameLabels.labels_checked' depends on axioms: [propext] +'SourceFrameLabels.labels_valid' depends on axioms: [propext, Quot.sound] +'SourceFrameLabels.label_range' depends on axioms: [propext, Quot.sound] +'SourceFrameLabels.copy_frames' depends on axioms: [propext, Quot.sound] +'SourceFrameLabels.erase_frames' depends on axioms: [propext, Quot.sound] +'SourceFrameMoves.moves_checked' depends on axioms: [propext] +'SourceFrameMoves.move_pair' depends on axioms: [propext, Quot.sound] +'SourceFrameMoves.move_range' depends on axioms: [propext, Quot.sound] +'SourceFrameMoves.move_transition' depends on axioms: [propext, Quot.sound] +'SourceFrameMoves.move_absorbs' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.initial_tabulate' does not depend on any axioms +'SourceFrameTrace.final_tabulate' does not depend on any axioms +'SourceFrameTrace.project0' does not depend on any axioms +'SourceFrameTrace.checkpoint0' does not depend on any axioms +'SourceFrameTrace.project1' does not depend on any axioms +'SourceFrameTrace.checkpoint1' does not depend on any axioms +'SourceFrameTrace.project2' does not depend on any axioms +'SourceFrameTrace.checkpoint2' does not depend on any axioms +'SourceFrameTrace.project3' does not depend on any axioms +'SourceFrameTrace.checkpoint3' does not depend on any axioms +'SourceFrameTrace.project4' does not depend on any axioms +'SourceFrameTrace.checkpoint4' does not depend on any axioms +'SourceFrameTrace.project5' does not depend on any axioms +'SourceFrameTrace.checkpoint5' does not depend on any axioms +'SourceFrameTrace.project6' does not depend on any axioms +'SourceFrameTrace.checkpoint6' does not depend on any axioms +'SourceFrameTrace.project7' does not depend on any axioms +'SourceFrameTrace.checkpoint7' does not depend on any axioms +'SourceFrameTrace.project8' does not depend on any axioms +'SourceFrameTrace.checkpoint8' does not depend on any axioms +'SourceFrameTrace.project9' does not depend on any axioms +'SourceFrameTrace.checkpoint9' does not depend on any axioms +'SourceFrameTrace.project10' does not depend on any axioms +'SourceFrameTrace.checkpoint10' does not depend on any axioms +'SourceFrameTrace.project11' does not depend on any axioms +'SourceFrameTrace.checkpoint11' does not depend on any axioms +'SourceFrameTrace.project12' does not depend on any axioms +'SourceFrameTrace.checkpoint12' does not depend on any axioms +'SourceFrameTrace.project13' does not depend on any axioms +'SourceFrameTrace.checkpoint13' does not depend on any axioms +'SourceFrameTrace.project14' does not depend on any axioms +'SourceFrameTrace.checkpoint14' does not depend on any axioms +'SourceFrameTrace.project15' does not depend on any axioms +'SourceFrameTrace.checkpoint15' does not depend on any axioms +'SourceFrameTrace.project16' does not depend on any axioms +'SourceFrameTrace.checkpoint16' does not depend on any axioms +'SourceFrameTrace.project17' does not depend on any axioms +'SourceFrameTrace.checkpoint17' does not depend on any axioms +'SourceFrameTrace.project18' does not depend on any axioms +'SourceFrameTrace.checkpoint18' does not depend on any axioms +'SourceFrameTrace.project19' does not depend on any axioms +'SourceFrameTrace.checkpoint19' does not depend on any axioms +'SourceFrameTrace.project20' does not depend on any axioms +'SourceFrameTrace.checkpoint20' does not depend on any axioms +'SourceFrameTrace.project21' does not depend on any axioms +'SourceFrameTrace.checkpoint21' does not depend on any axioms +'SourceFrameTrace.project22' does not depend on any axioms +'SourceFrameTrace.checkpoint22' does not depend on any axioms +'SourceFrameTrace.project23' does not depend on any axioms +'SourceFrameTrace.checkpoint23' does not depend on any axioms +'SourceFrameTrace.project24' does not depend on any axioms +'SourceFrameTrace.checkpoint24' does not depend on any axioms +'SourceFrameTrace.project25' does not depend on any axioms +'SourceFrameTrace.checkpoint25' does not depend on any axioms +'SourceFrameTrace.project26' does not depend on any axioms +'SourceFrameTrace.checkpoint26' does not depend on any axioms +'SourceFrameTrace.project27' does not depend on any axioms +'SourceFrameTrace.checkpoint27' does not depend on any axioms +'SourceFrameTrace.project28' does not depend on any axioms +'SourceFrameTrace.checkpoint28' does not depend on any axioms +'SourceFrameTrace.project29' does not depend on any axioms +'SourceFrameTrace.checkpoint29' does not depend on any axioms +'SourceFrameTrace.project30' does not depend on any axioms +'SourceFrameTrace.checkpoint30' does not depend on any axioms +'SourceFrameTrace.project31' does not depend on any axioms +'SourceFrameTrace.checkpoint31' does not depend on any axioms +'SourceFrameTrace.project32' does not depend on any axioms +'SourceFrameTrace.checkpoint32' does not depend on any axioms +'SourceFrameTrace.project33' does not depend on any axioms +'SourceFrameTrace.checkpoint33' does not depend on any axioms +'SourceFrameTrace.project34' does not depend on any axioms +'SourceFrameTrace.checkpoint34' does not depend on any axioms +'SourceFrameTrace.project35' does not depend on any axioms +'SourceFrameTrace.checkpoint35' does not depend on any axioms +'SourceFrameTrace.project36' does not depend on any axioms +'SourceFrameTrace.checkpoint36' does not depend on any axioms +'SourceFrameTrace.project37' does not depend on any axioms +'SourceFrameTrace.checkpoint37' does not depend on any axioms +'SourceFrameTrace.project38' does not depend on any axioms +'SourceFrameTrace.checkpoint38' does not depend on any axioms +'SourceFrameTrace.project39' does not depend on any axioms +'SourceFrameTrace.checkpoint39' does not depend on any axioms +'SourceFrameTrace.project40' does not depend on any axioms +'SourceFrameTrace.checkpoint40' does not depend on any axioms +'SourceFrameTrace.project41' does not depend on any axioms +'SourceFrameTrace.checkpoint41' does not depend on any axioms +'SourceFrameTrace.project42' does not depend on any axioms +'SourceFrameTrace.checkpoint42' does not depend on any axioms +'SourceFrameTrace.project43' does not depend on any axioms +'SourceFrameTrace.checkpoint43' does not depend on any axioms +'SourceFrameTrace.project44' does not depend on any axioms +'SourceFrameTrace.checkpoint44' does not depend on any axioms +'SourceFrameTrace.project45' does not depend on any axioms +'SourceFrameTrace.checkpoint45' does not depend on any axioms +'SourceFrameTrace.project46' does not depend on any axioms +'SourceFrameTrace.checkpoint46' does not depend on any axioms +'SourceFrameTrace.project47' does not depend on any axioms +'SourceFrameTrace.checkpoint47' does not depend on any axioms +'SourceFrameTrace.project48' does not depend on any axioms +'SourceFrameTrace.checkpoint48' does not depend on any axioms +'SourceFrameTrace.project49' does not depend on any axioms +'SourceFrameTrace.checkpoint49' does not depend on any axioms +'SourceFrameTrace.project50' does not depend on any axioms +'SourceFrameTrace.checkpoint50' does not depend on any axioms +'SourceFrameTrace.project51' does not depend on any axioms +'SourceFrameTrace.checkpoint51' does not depend on any axioms +'SourceFrameTrace.project52' does not depend on any axioms +'SourceFrameTrace.checkpoint52' does not depend on any axioms +'SourceFrameTrace.project53' does not depend on any axioms +'SourceFrameTrace.checkpoint53' does not depend on any axioms +'SourceFrameTrace.project54' does not depend on any axioms +'SourceFrameTrace.checkpoint54' does not depend on any axioms +'SourceFrameTrace.project55' does not depend on any axioms +'SourceFrameTrace.checkpoint55' does not depend on any axioms +'SourceFrameTrace.project56' does not depend on any axioms +'SourceFrameTrace.checkpoint56' does not depend on any axioms +'SourceFrameTrace.project57' does not depend on any axioms +'SourceFrameTrace.checkpoint57' does not depend on any axioms +'SourceFrameTrace.project58' does not depend on any axioms +'SourceFrameTrace.checkpoint58' does not depend on any axioms +'SourceFrameTrace.project59' does not depend on any axioms +'SourceFrameTrace.checkpoint59' does not depend on any axioms +'SourceFrameTrace.project60' does not depend on any axioms +'SourceFrameTrace.checkpoint60' does not depend on any axioms +'SourceFrameTrace.project61' does not depend on any axioms +'SourceFrameTrace.checkpoint61' does not depend on any axioms +'SourceFrameTrace.project62' does not depend on any axioms +'SourceFrameTrace.checkpoint62' does not depend on any axioms +'SourceFrameTrace.project63' does not depend on any axioms +'SourceFrameTrace.checkpoint63' does not depend on any axioms +'SourceFrameTrace.project64' does not depend on any axioms +'SourceFrameTrace.checkpoint64' does not depend on any axioms +'SourceFrameTrace.project65' does not depend on any axioms +'SourceFrameTrace.checkpoint65' does not depend on any axioms +'SourceFrameTrace.project66' does not depend on any axioms +'SourceFrameTrace.checkpoint66' does not depend on any axioms +'SourceFrameTrace.project67' does not depend on any axioms +'SourceFrameTrace.checkpoint67' does not depend on any axioms +'SourceFrameTrace.project68' does not depend on any axioms +'SourceFrameTrace.checkpoint68' does not depend on any axioms +'SourceFrameTrace.project69' does not depend on any axioms +'SourceFrameTrace.checkpoint69' does not depend on any axioms +'SourceFrameTrace.project70' does not depend on any axioms +'SourceFrameTrace.checkpoint70' does not depend on any axioms +'SourceFrameTrace.project71' does not depend on any axioms +'SourceFrameTrace.checkpoint71' does not depend on any axioms +'SourceFrameTrace.project72' does not depend on any axioms +'SourceFrameTrace.checkpoint72' does not depend on any axioms +'SourceFrameTrace.project73' does not depend on any axioms +'SourceFrameTrace.checkpoint73' does not depend on any axioms +'SourceFrameTrace.project74' does not depend on any axioms +'SourceFrameTrace.checkpoint74' does not depend on any axioms +'SourceFrameTrace.project75' does not depend on any axioms +'SourceFrameTrace.checkpoint75' does not depend on any axioms +'SourceFrameTrace.project76' does not depend on any axioms +'SourceFrameTrace.checkpoint76' does not depend on any axioms +'SourceFrameTrace.project77' does not depend on any axioms +'SourceFrameTrace.checkpoint77' does not depend on any axioms +'SourceFrameTrace.project78' does not depend on any axioms +'SourceFrameTrace.checkpoint78' does not depend on any axioms +'SourceFrameTrace.project79' does not depend on any axioms +'SourceFrameTrace.checkpoint79' does not depend on any axioms +'SourceFrameTrace.project80' does not depend on any axioms +'SourceFrameTrace.checkpoint80' does not depend on any axioms +'SourceFrameTrace.project81' does not depend on any axioms +'SourceFrameTrace.checkpoint81' does not depend on any axioms +'SourceFrameTrace.project82' does not depend on any axioms +'SourceFrameTrace.checkpoint82' does not depend on any axioms +'SourceFrameTrace.project83' does not depend on any axioms +'SourceFrameTrace.checkpoint83' does not depend on any axioms +'SourceFrameTrace.project84' does not depend on any axioms +'SourceFrameTrace.checkpoint84' does not depend on any axioms +'SourceFrameTrace.project85' does not depend on any axioms +'SourceFrameTrace.checkpoint85' does not depend on any axioms +'SourceFrameTrace.project86' does not depend on any axioms +'SourceFrameTrace.checkpoint86' does not depend on any axioms +'SourceFrameTrace.project87' does not depend on any axioms +'SourceFrameTrace.checkpoint87' does not depend on any axioms +'SourceFrameTrace.project88' does not depend on any axioms +'SourceFrameTrace.checkpoint88' does not depend on any axioms +'SourceFrameTrace.project89' does not depend on any axioms +'SourceFrameTrace.checkpoint89' does not depend on any axioms +'SourceFrameTrace.project90' does not depend on any axioms +'SourceFrameTrace.checkpoint90' does not depend on any axioms +'SourceFrameTrace.project91' does not depend on any axioms +'SourceFrameTrace.checkpoint91' does not depend on any axioms +'SourceFrameTrace.project92' does not depend on any axioms +'SourceFrameTrace.checkpoint92' does not depend on any axioms +'SourceFrameTrace.project93' does not depend on any axioms +'SourceFrameTrace.checkpoint93' does not depend on any axioms +'SourceFrameTrace.project94' does not depend on any axioms +'SourceFrameTrace.checkpoint94' does not depend on any axioms +'SourceFrameTrace.project95' does not depend on any axioms +'SourceFrameTrace.checkpoint95' does not depend on any axioms +'SourceFrameTrace.combine' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish96' does not depend on any axioms +'SourceFrameTrace.finish95' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish94' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish93' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish92' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish91' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish90' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish89' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish88' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish87' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish86' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish85' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish84' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish83' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish82' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish81' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish80' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish79' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish78' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish77' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish76' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish75' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish74' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish73' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish72' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish71' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish70' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish69' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish68' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish67' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish66' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish65' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish64' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish63' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish62' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish61' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish60' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish59' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish58' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish57' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish56' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish55' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish54' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish53' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish52' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish51' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish50' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish49' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish48' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish47' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish46' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish45' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish44' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish43' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish42' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish41' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish40' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish39' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish38' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish37' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish36' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish35' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish34' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish33' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish32' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish31' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish30' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish29' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish28' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish27' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish26' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish25' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish24' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish23' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish22' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish21' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish20' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish19' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish18' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish17' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish16' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish15' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish14' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish13' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish12' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish11' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish10' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish9' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish8' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish7' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish6' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish5' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish4' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish3' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish2' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish1' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.finish0' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.scalar_word' depends on axioms: [propext] +'SourceFrameTrace.forward_checked' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.forward_valid' depends on axioms: [propext, Quot.sound] +'TreeReplay.payload_checks_sound' depends on axioms: [propext, Quot.sound] +'TreeReplay.checked_payload_guards_sound' depends on axioms: [propext, Quot.sound] +'FrameTrace.matches_get' depends on axioms: [propext] +'FrameTrace.matches_step' depends on axioms: [propext, Quot.sound] +'FrameTrace.add_frames_equal' depends on axioms: [propext, Quot.sound] +'FrameTrace.matches_run' depends on axioms: [propext, Quot.sound] +'FrameTrace.valid_step' depends on axioms: [propext, Quot.sound] +'FrameTrace.valid_trace' depends on axioms: [propext, Quot.sound] +'FrameTrace.decoded_run' depends on axioms: [propext, Quot.sound] +'OwnerTransport.write_other' depends on axioms: [propext, Classical.choice, Quot.sound] +'OwnerTransport.gather_write' depends on axioms: [propext, Classical.choice, Quot.sound] +'OwnerTransport.rawXor_write' depends on axioms: [propext, Classical.choice, Quot.sound] +'OwnerTransport.rawTransport_write' depends on axioms: [propext, Classical.choice, Quot.sound] +'OwnerTransport.gather_step' depends on axioms: [propext, Classical.choice, Quot.sound] +'OwnerTransport.logicalStep_tree' depends on axioms: [propext, Classical.choice, Quot.sound] +'OwnerTransport.rawStep_other' depends on axioms: [propext, Classical.choice, Quot.sound] +'OwnerTransport.replace_fin_tree' depends on axioms: [propext, Classical.choice, Quot.sound] +'OwnerTransport.logicalStep_fin_tree' depends on axioms: [propext, Classical.choice, Quot.sound] +'OwnerTransport.physicalStep_full' does not depend on any axioms +'OwnerTransport.gather_run_framed' depends on axioms: [propext, Classical.choice, Quot.sound] +'OwnerTransport.runRaw_other' depends on axioms: [propext, Classical.choice, Quot.sound] +'OwnerTransport.extendCover_owner' depends on axioms: [propext, Classical.choice, Quot.sound] +'OwnerTransport.initialRaw_other' depends on axioms: [propext, Classical.choice, Quot.sound] +'OwnerTransport.gather_initialRaw' depends on axioms: [propext, Classical.choice, Quot.sound] +'OwnerTransport.route_native_address' does not depend on any axioms +'OwnerTransport.inverse_common_cover' does not depend on any axioms +'OwnerTransport.rawXor_fromNative' depends on axioms: [propext, Classical.choice, Quot.sound] +'OwnerTransport.rawTransport_fromNative' depends on axioms: [propext, Classical.choice, Quot.sound] +'OwnerTransport.rawStep_fromNative' depends on axioms: [propext, Classical.choice, Quot.sound] +'OwnerTransport.runRaw_fromNative' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceFrameTrace.indices_checked' depends on axioms: [propext] +'SourceFrameTrace.indices_bound' depends on axioms: [propext, Quot.sound] +'SourceFrameTrace.route_projection' depends on axioms: [propext, Quot.sound] +'SourceOwnership.perm_inverse' depends on axioms: [propext] +'SourceOwnership.inverse_perm' depends on axioms: [propext] +'SourceOwnership.perm_support' depends on axioms: [propext] +'SourceOwnership.fingerprint_injective' depends on axioms: [propext] +'SourceOwnership.owner_inverse' depends on axioms: [propext] +'SourceOwnership.family_tag_injective' depends on axioms: [propext] +'SourceOwnership.family_data' does not depend on any axioms +'SourceOwnership.helper_range' does not depend on any axioms +'SourceOwnership.helper_frame' depends on axioms: [propext] +'SourceOwnership.helper_child' depends on axioms: [propext] +'SourceFrameTrace.initial_owner_frames' does not depend on any axioms +'SourceFrameTrace.helper_final_frames' does not depend on any axioms +'SourceFrameTrace.initial_frame_range' does not depend on any axioms +'SourceFrameTrace.final_frame_range' does not depend on any axioms +'SelectedGeometry.tag_frame_bound' does not depend on any axioms +'SelectedGeometry.tag_residual_diagonal' depends on axioms: [propext] +'SelectedGeometry.source_mask_outside' depends on axioms: [propext] +'SourceMatrix.combine' depends on axioms: [propext] +'SourceMatrix.chunks_flatten' depends on axioms: [propext, Quot.sound] +'SourceMatrix.checkpoint0' depends on axioms: [propext] +'SourceMatrix.checkpoint1' depends on axioms: [propext] +'SourceMatrix.checkpoint2' depends on axioms: [propext] +'SourceMatrix.checkpoint3' depends on axioms: [propext] +'SourceMatrix.checkpoint4' depends on axioms: [propext] +'SourceMatrix.checkpoint5' depends on axioms: [propext] +'SourceMatrix.checkpoint6' depends on axioms: [propext] +'SourceMatrix.checkpoint7' depends on axioms: [propext] +'SourceMatrix.checkpoint8' depends on axioms: [propext] +'SourceMatrix.checkpoint9' depends on axioms: [propext] +'SourceMatrix.checkpoint10' depends on axioms: [propext] +'SourceMatrix.checkpoint11' depends on axioms: [propext] +'SourceMatrix.checkpoint12' depends on axioms: [propext] +'SourceMatrix.checkpoint13' depends on axioms: [propext] +'SourceMatrix.checkpoint14' depends on axioms: [propext] +'SourceMatrix.checkpoint15' depends on axioms: [propext] +'SourceMatrix.checkpoint16' depends on axioms: [propext] +'SourceMatrix.checkpoint17' depends on axioms: [propext] +'SourceMatrix.checkpoint18' depends on axioms: [propext] +'SourceMatrix.checkpoint19' depends on axioms: [propext] +'SourceMatrix.checkpoint20' depends on axioms: [propext] +'SourceMatrix.checkpoint21' depends on axioms: [propext] +'SourceMatrix.checkpoint22' depends on axioms: [propext] +'SourceMatrix.checkpoint23' depends on axioms: [propext] +'SourceMatrix.checkpoint24' depends on axioms: [propext] +'SourceMatrix.checkpoint25' depends on axioms: [propext] +'SourceMatrix.checkpoint26' depends on axioms: [propext] +'SourceMatrix.checkpoint27' depends on axioms: [propext] +'SourceMatrix.checkpoint28' depends on axioms: [propext] +'SourceMatrix.checkpoint29' depends on axioms: [propext] +'SourceMatrix.checkpoint30' depends on axioms: [propext] +'SourceMatrix.checkpoint31' depends on axioms: [propext] +'SourceMatrix.checkpoint32' depends on axioms: [propext] +'SourceMatrix.checkpoint33' depends on axioms: [propext] +'SourceMatrix.checkpoint34' depends on axioms: [propext] +'SourceMatrix.checkpoint35' depends on axioms: [propext] +'SourceMatrix.checkpoint36' depends on axioms: [propext] +'SourceMatrix.checkpoint37' depends on axioms: [propext] +'SourceMatrix.checkpoint38' depends on axioms: [propext] +'SourceMatrix.checkpoint39' depends on axioms: [propext] +'SourceMatrix.checkpoint40' depends on axioms: [propext] +'SourceMatrix.checkpoint41' depends on axioms: [propext] +'SourceMatrix.checkpoint42' depends on axioms: [propext] +'SourceMatrix.checkpoint43' depends on axioms: [propext] +'SourceMatrix.checkpoint44' depends on axioms: [propext] +'SourceMatrix.checkpoint45' depends on axioms: [propext] +'SourceMatrix.checkpoint46' depends on axioms: [propext] +'SourceMatrix.checkpoint47' depends on axioms: [propext] +'SourceMatrix.checkpoint48' depends on axioms: [propext] +'SourceMatrix.checkpoint49' depends on axioms: [propext] +'SourceMatrix.checkpoint50' depends on axioms: [propext] +'SourceMatrix.checkpoint51' depends on axioms: [propext] +'SourceMatrix.checkpoint52' depends on axioms: [propext] +'SourceMatrix.checkpoint53' depends on axioms: [propext] +'SourceMatrix.checkpoint54' depends on axioms: [propext] +'SourceMatrix.checkpoint55' depends on axioms: [propext] +'SourceMatrix.checkpoint56' depends on axioms: [propext] +'SourceMatrix.checkpoint57' depends on axioms: [propext] +'SourceMatrix.checkpoint58' depends on axioms: [propext] +'SourceMatrix.checkpoint59' depends on axioms: [propext] +'SourceMatrix.checkpoint60' depends on axioms: [propext] +'SourceMatrix.checkpoint61' depends on axioms: [propext] +'SourceMatrix.checkpoint62' depends on axioms: [propext] +'SourceMatrix.checkpoint63' depends on axioms: [propext] +'SourceMatrix.checkpoint64' depends on axioms: [propext] +'SourceMatrix.checkpoint65' depends on axioms: [propext] +'SourceMatrix.checkpoint66' depends on axioms: [propext] +'SourceMatrix.checkpoint67' depends on axioms: [propext] +'SourceMatrix.checkpoint68' depends on axioms: [propext] +'SourceMatrix.checkpoint69' depends on axioms: [propext] +'SourceMatrix.checkpoint70' depends on axioms: [propext] +'SourceMatrix.checkpoint71' depends on axioms: [propext] +'SourceMatrix.checkpoint72' depends on axioms: [propext] +'SourceMatrix.checkpoint73' depends on axioms: [propext] +'SourceMatrix.checkpoint74' depends on axioms: [propext] +'SourceMatrix.checkpoint75' depends on axioms: [propext] +'SourceMatrix.checkpoint76' depends on axioms: [propext] +'SourceMatrix.checkpoint77' depends on axioms: [propext] +'SourceMatrix.checkpoint78' depends on axioms: [propext] +'SourceMatrix.checkpoint79' depends on axioms: [propext] +'SourceMatrix.checkpoint80' depends on axioms: [propext] +'SourceMatrix.checkpoint81' depends on axioms: [propext] +'SourceMatrix.checkpoint82' depends on axioms: [propext] +'SourceMatrix.checkpoint83' depends on axioms: [propext] +'SourceMatrix.checkpoint84' depends on axioms: [propext] +'SourceMatrix.checkpoint85' depends on axioms: [propext] +'SourceMatrix.checkpoint86' depends on axioms: [propext] +'SourceMatrix.checkpoint87' depends on axioms: [propext] +'SourceMatrix.checkpoint88' depends on axioms: [propext] +'SourceMatrix.checkpoint89' depends on axioms: [propext] +'SourceMatrix.checkpoint90' depends on axioms: [propext] +'SourceMatrix.checkpoint91' depends on axioms: [propext] +'SourceMatrix.checkpoint92' depends on axioms: [propext] +'SourceMatrix.checkpoint93' depends on axioms: [propext] +'SourceMatrix.checkpoint94' depends on axioms: [propext] +'SourceMatrix.checkpoint95' depends on axioms: [propext] +'SourceMatrix.finish96' depends on axioms: [propext] +'SourceMatrix.finish95' depends on axioms: [propext] +'SourceMatrix.finish94' depends on axioms: [propext] +'SourceMatrix.finish93' depends on axioms: [propext] +'SourceMatrix.finish92' depends on axioms: [propext] +'SourceMatrix.finish91' depends on axioms: [propext] +'SourceMatrix.finish90' depends on axioms: [propext] +'SourceMatrix.finish89' depends on axioms: [propext] +'SourceMatrix.finish88' depends on axioms: [propext] +'SourceMatrix.finish87' depends on axioms: [propext] +'SourceMatrix.finish86' depends on axioms: [propext] +'SourceMatrix.finish85' depends on axioms: [propext] +'SourceMatrix.finish84' depends on axioms: [propext] +'SourceMatrix.finish83' depends on axioms: [propext] +'SourceMatrix.finish82' depends on axioms: [propext] +'SourceMatrix.finish81' depends on axioms: [propext] +'SourceMatrix.finish80' depends on axioms: [propext] +'SourceMatrix.finish79' depends on axioms: [propext] +'SourceMatrix.finish78' depends on axioms: [propext] +'SourceMatrix.finish77' depends on axioms: [propext] +'SourceMatrix.finish76' depends on axioms: [propext] +'SourceMatrix.finish75' depends on axioms: [propext] +'SourceMatrix.finish74' depends on axioms: [propext] +'SourceMatrix.finish73' depends on axioms: [propext] +'SourceMatrix.finish72' depends on axioms: [propext] +'SourceMatrix.finish71' depends on axioms: [propext] +'SourceMatrix.finish70' depends on axioms: [propext] +'SourceMatrix.finish69' depends on axioms: [propext] +'SourceMatrix.finish68' depends on axioms: [propext] +'SourceMatrix.finish67' depends on axioms: [propext] +'SourceMatrix.finish66' depends on axioms: [propext] +'SourceMatrix.finish65' depends on axioms: [propext] +'SourceMatrix.finish64' depends on axioms: [propext] +'SourceMatrix.finish63' depends on axioms: [propext] +'SourceMatrix.finish62' depends on axioms: [propext] +'SourceMatrix.finish61' depends on axioms: [propext] +'SourceMatrix.finish60' depends on axioms: [propext] +'SourceMatrix.finish59' depends on axioms: [propext] +'SourceMatrix.finish58' depends on axioms: [propext] +'SourceMatrix.finish57' depends on axioms: [propext] +'SourceMatrix.finish56' depends on axioms: [propext] +'SourceMatrix.finish55' depends on axioms: [propext] +'SourceMatrix.finish54' depends on axioms: [propext] +'SourceMatrix.finish53' depends on axioms: [propext] +'SourceMatrix.finish52' depends on axioms: [propext] +'SourceMatrix.finish51' depends on axioms: [propext] +'SourceMatrix.finish50' depends on axioms: [propext] +'SourceMatrix.finish49' depends on axioms: [propext] +'SourceMatrix.finish48' depends on axioms: [propext] +'SourceMatrix.finish47' depends on axioms: [propext] +'SourceMatrix.finish46' depends on axioms: [propext] +'SourceMatrix.finish45' depends on axioms: [propext] +'SourceMatrix.finish44' depends on axioms: [propext] +'SourceMatrix.finish43' depends on axioms: [propext] +'SourceMatrix.finish42' depends on axioms: [propext] +'SourceMatrix.finish41' depends on axioms: [propext] +'SourceMatrix.finish40' depends on axioms: [propext] +'SourceMatrix.finish39' depends on axioms: [propext] +'SourceMatrix.finish38' depends on axioms: [propext] +'SourceMatrix.finish37' depends on axioms: [propext] +'SourceMatrix.finish36' depends on axioms: [propext] +'SourceMatrix.finish35' depends on axioms: [propext] +'SourceMatrix.finish34' depends on axioms: [propext] +'SourceMatrix.finish33' depends on axioms: [propext] +'SourceMatrix.finish32' depends on axioms: [propext] +'SourceMatrix.finish31' depends on axioms: [propext] +'SourceMatrix.finish30' depends on axioms: [propext] +'SourceMatrix.finish29' depends on axioms: [propext] +'SourceMatrix.finish28' depends on axioms: [propext] +'SourceMatrix.finish27' depends on axioms: [propext] +'SourceMatrix.finish26' depends on axioms: [propext] +'SourceMatrix.finish25' depends on axioms: [propext] +'SourceMatrix.finish24' depends on axioms: [propext] +'SourceMatrix.finish23' depends on axioms: [propext] +'SourceMatrix.finish22' depends on axioms: [propext] +'SourceMatrix.finish21' depends on axioms: [propext] +'SourceMatrix.finish20' depends on axioms: [propext] +'SourceMatrix.finish19' depends on axioms: [propext] +'SourceMatrix.finish18' depends on axioms: [propext] +'SourceMatrix.finish17' depends on axioms: [propext] +'SourceMatrix.finish16' depends on axioms: [propext] +'SourceMatrix.finish15' depends on axioms: [propext] +'SourceMatrix.finish14' depends on axioms: [propext] +'SourceMatrix.finish13' depends on axioms: [propext] +'SourceMatrix.finish12' depends on axioms: [propext] +'SourceMatrix.finish11' depends on axioms: [propext] +'SourceMatrix.finish10' depends on axioms: [propext] +'SourceMatrix.finish9' depends on axioms: [propext] +'SourceMatrix.finish8' depends on axioms: [propext] +'SourceMatrix.finish7' depends on axioms: [propext] +'SourceMatrix.finish6' depends on axioms: [propext] +'SourceMatrix.finish5' depends on axioms: [propext] +'SourceMatrix.finish4' depends on axioms: [propext] +'SourceMatrix.finish3' depends on axioms: [propext] +'SourceMatrix.finish2' depends on axioms: [propext] +'SourceMatrix.finish1' depends on axioms: [propext] +'SourceMatrix.finish0' depends on axioms: [propext] +'SourceMatrix.runFull_checked' depends on axioms: [propext] +'SourceMatrix.literal_word_checked' depends on axioms: [propext, Quot.sound] +'SourceMatrix.literal_word_rows' depends on axioms: [propext, Quot.sound] +'SourceMatrix.initial_formula' does not depend on any axioms +'SourceMatrix.expected_formula' depends on axioms: [propext] +'SourceMatrix.arbitrary_dirty_bools' depends on axioms: [propext, Quot.sound] +'SourceMatrix.arbitrary_dirty_guards' depends on axioms: [propext, Quot.sound] +'SourceMatrix.arbitrary_dirty_payloads' depends on axioms: [propext, Quot.sound] +'SourceMatrix.actual_payload_clean' depends on axioms: [propext, Quot.sound] +'SourceMatrix.arbitrary_dirty_temp_restored' depends on axioms: [propext, Quot.sound] +'SourceMatrix.arbitrary_dirty_original_roles' depends on axioms: [propext, Quot.sound] +'SourceFramed.initial_matches' depends on axioms: [propext] +'SourceFramed.initial_decoded' depends on axioms: [propext, Quot.sound] +'SourceFramed.actual_valid' depends on axioms: [propext, Quot.sound] +'SourceFramed.final_matches' depends on axioms: [propext, Quot.sound] +'SourceFramed.actual_decoded_endpoint' depends on axioms: [propext, Quot.sound] +'SourceFramed.actual_physical_endpoint' depends on axioms: [propext, Quot.sound] +'SourceFramed.actual_temporary_restored' depends on axioms: [propext, Quot.sound] +'SourceFramed.all_physical_endpoints' depends on axioms: [propext, Quot.sound] +'SourceRaw.gather_initial' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceRaw.gather_final' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceRaw.actual_valid' depends on axioms: [propext, Quot.sound] +'SourceRaw.payload_endpoint' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceRaw.private_restored' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceRaw.other_preserved' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceRaw.other_payload_preserved' depends on axioms: [propext, Classical.choice, Quot.sound] +'MultiHosting.base_commutes' depends on axioms: [propext, Quot.sound] +'MultiHosting.runBase_commutes' depends on axioms: [propext, Quot.sound] +'MultiHosting.delay_residuals' depends on axioms: [propext, Quot.sound] +'MultiHosting.multi_hosting' depends on axioms: [propext, Quot.sound] +'MultiHosting.multi_hosting_in_context' depends on axioms: [propext, Quot.sound] +'MultiHosting.PhysicalImplementations.original_projection' does not depend on any axioms +'MultiHosting.PhysicalImplementations.relocated_projection' does not depend on any axioms +'MultiHosting.physical_multi_hosting' depends on axioms: [propext, Quot.sound] +'MultiHosting.physical_multi_hosting_in_context' depends on axioms: [propext, Quot.sound] +'SourceOwnership.unindex_reindex' depends on axioms: [propext, Quot.sound] +'SourceOwnership.reindex_unindex' depends on axioms: [propext, Quot.sound] +'SourceOwnership.residual_projector_transport' depends on axioms: [propext, Quot.sound] +'SourceOwnership.perm_tag_injective' depends on axioms: [propext] +'SourceOwnership.unindex_tag_injective' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceOwnership.family_data_general' does not depend on any axioms +'SourceOwnership.same_family_data' depends on axioms: [propext, Quot.sound] +'SourceOwnership.owners_injective' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceConnection.packed_data' depends on axioms: [propext, Quot.sound] +'SourceConnection.packed_helper' depends on axioms: [propext, Quot.sound] +'SourceConnection.invoke_endpoint' depends on axioms: [propext, Quot.sound] +'SourceConnection.swap_conjugacy' depends on axioms: [propext, Quot.sound] +'SourceConnection.host_transport' depends on axioms: [propext, Quot.sound] +'SourceConnection.original_retained' depends on axioms: [propext, Quot.sound] +'SourceConnection.original_bank_output' depends on axioms: [propext, Quot.sound] +'SourceConnection.relocated_retained' depends on axioms: [propext, Quot.sound] +'InvocationPayload.extend_owner' depends on axioms: [propext, Classical.choice, Quot.sound] +'InvocationPayload.extend_outside' depends on axioms: [propext, Classical.choice, Quot.sound] +'InvocationPayload.realize_owner' depends on axioms: [propext, Classical.choice, Quot.sound] +'InvocationPayload.input_realize' depends on axioms: [propext, Classical.choice, Quot.sound] +'InvocationPayload.input_realize_packed' depends on axioms: [propext, Classical.choice, Quot.sound] +'InvocationPayload.realized_gather' depends on axioms: [propext, Classical.choice, Quot.sound] +'InvocationPayload.realized_payload' depends on axioms: [propext, Classical.choice, Quot.sound] +'InvocationPayload.realized_payloads' depends on axioms: [propext, Classical.choice, Quot.sound] +'PortGeometry.doubled_orthogonal_entries' depends on axioms: [propext, Quot.sound] +'PortGeometry.quarteredRoute_exact' depends on axioms: [propext, Quot.sound] +'PortGeometry.doubled_row_orthogonal_entries' depends on axioms: [propext, Quot.sound] +'PortGeometry.doubled_orthogonal' depends on axioms: [propext, Classical.choice, Quot.sound] +'PortGeometry.doubled_row_orthogonal' depends on axioms: [propext, Classical.choice, Quot.sound] +'PortGeometry.basis_entry' depends on axioms: [propext, Classical.choice, Quot.sound] +'PortGeometry.cast_orthogonal' depends on axioms: [propext, Classical.choice, Quot.sound] +'PortGeometry.cast_row_orthogonal' depends on axioms: [propext, Classical.choice, Quot.sound] +'PortGeometry.basis_transpose_mul' depends on axioms: [propext, Classical.choice, Quot.sound] +'PortGeometry.basis_mul_transpose' depends on axioms: [propext, Classical.choice, Quot.sound] +'PortGeometry.chart8_dot' depends on axioms: [propext, Classical.choice, Quot.sound] +'PortGeometry.firstEight_add' does not depend on any axioms +'PortGeometry.firstEight_smul' does not depend on any axioms +'PortGeometry.firstEight_extendEight' depends on axioms: [propext, Quot.sound] +'PortGeometry.extendEight_comp' depends on axioms: [propext, Quot.sound] +'PortGeometry.extendEight_id' depends on axioms: [propext, Quot.sound] +'PortGeometry.chart64_firstEight' depends on axioms: [propext, Classical.choice, Quot.sound] +'PortGeometry.chart64_outside' depends on axioms: [propext, Classical.choice, Quot.sound] +'PortGeometry.chart64_bijective' depends on axioms: [propext, Classical.choice, Quot.sound] +'PortGeometry.chart64_add' depends on axioms: [propext, Classical.choice, Quot.sound] +'PortGeometry.chart64_smul' depends on axioms: [propext, Classical.choice, Quot.sound] +'PortGeometry.chart64_dot' depends on axioms: [propext, Classical.choice, Quot.sound] +'PortGeometry.chart64_symm_dot' depends on axioms: [propext, Classical.choice, Quot.sound] +'PortGeometry.chart64_symm_add' depends on axioms: [propext, Classical.choice, Quot.sound] +'PortGeometry.chart64_symm_smul' depends on axioms: [propext, Classical.choice, Quot.sound] +'PortGeometry.stage2Index_involutive' depends on axioms: [propext, Quot.sound] +'PortGeometry.stage2Coordinates_dot' depends on axioms: [propext, Classical.choice, Quot.sound] +'PortGeometry.dataRoute64_dot' depends on axioms: [propext, Classical.choice, Quot.sound] +'PortGeometry.dataRoute64_add' depends on axioms: [propext, Classical.choice, Quot.sound] +'PortGeometry.dataRoute64_smul' depends on axioms: [propext, Classical.choice, Quot.sound] +'PortGeometry.dataRoute64_involutive' depends on axioms: [propext, Classical.choice, Quot.sound] +'PortGeometry.route15_entry' depends on axioms: [propext, Classical.choice, Quot.sound] +'PortGeometry.sourceRoute64_eq' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceOwnership.slotChart_dot' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceOwnership.slotChart_add' depends on axioms: [propext, Quot.sound] +'SourceOwnership.slotChart_smul' depends on axioms: [propext, Quot.sound] +'SourceOwnership.familyChart_dot' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceOwnership.familyChart_add' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceOwnership.familyChart_smul' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceOwnership.helper_sigma_dot' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceOwnership.helper_sigma_add' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceOwnership.helper_sigma_smul' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceOwnership.physicalOwner_formula' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceOwnership.physicalOwner_common' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceOwnership.physicalOwner_injective' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceOwnership.family_lt' depends on axioms: [propext, Quot.sound] +'SourceOwnership.activeOwner_injective' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceOwnership.active_gather_step' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceOwnership.sourceActiveOwner_injective' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceOwnership.source_gather_run' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceOwnership.helper_address_forward' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceOwnership.helper_address_inverse' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceOwnership.source_address_gather_run' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceOwnership.source_common_cover' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceOwnership.source_native_run' depends on axioms: [propext, Classical.choice, Quot.sound] +'ParentOwnership.perm_inverse' depends on axioms: [propext] +'ParentOwnership.inverse_perm' depends on axioms: [propext] +'ParentOwnership.perm_support' depends on axioms: [propext] +'ParentOwnership.fingerprint_injective' depends on axioms: [propext] +'ParentOwnership.owner_inverse' depends on axioms: [propext] +'ParentOwnership.family_tag_injective' depends on axioms: [propext] +'ParentOwnership.family_data' does not depend on any axioms +'ParentOwnership.helper_range' does not depend on any axioms +'ParentOwnership.helper_frame' depends on axioms: [propext] +'ParentOwnership.unindex_reindex' depends on axioms: [propext, Quot.sound] +'ParentOwnership.reindex_unindex' depends on axioms: [propext, Quot.sound] +'ParentOwnership.residual_projector_transport' depends on axioms: [propext, Quot.sound] +'ParentOwnership.perm_tag_injective' depends on axioms: [propext] +'ParentOwnership.unindex_tag_injective' depends on axioms: [propext, Classical.choice, Quot.sound] +'ParentOwnership.family_data_general' does not depend on any axioms +'ParentOwnership.same_family_data' depends on axioms: [propext, Quot.sound] +'ParentOwnership.owners_injective' depends on axioms: [propext, Classical.choice, Quot.sound] +'ParentOwnership.slotChart_dot' depends on axioms: [propext, Classical.choice, Quot.sound] +'ParentOwnership.slotChart_add' depends on axioms: [propext, Quot.sound] +'ParentOwnership.slotChart_smul' depends on axioms: [propext, Quot.sound] +'ParentOwnership.helper_sigma_dot' depends on axioms: [propext, Classical.choice, Quot.sound] +'ParentOwnership.helper_sigma_add' depends on axioms: [propext, Classical.choice, Quot.sound] +'ParentOwnership.helper_sigma_smul' depends on axioms: [propext, Classical.choice, Quot.sound] +'ParentOwnership.helper_residual_transport' depends on axioms: [propext, Classical.choice, Quot.sound] +'ParentOwnership.physicalOwner_formula' depends on axioms: [propext, Classical.choice, Quot.sound] +'ParentOwnership.physicalOwner_injective' depends on axioms: [propext, Classical.choice, Quot.sound] +'ParentOwnership.family_lt' depends on axioms: [propext, Quot.sound] +'ParentOwnership.sourceActiveOwner_avoids_host_families' depends on axioms: [propext, Classical.choice, Quot.sound] +'ParentOwnership.sourceActiveOwner_injective' depends on axioms: [propext, Classical.choice, Quot.sound] +'ParentOwnership.source_gather_run' depends on axioms: [propext, Classical.choice, Quot.sound] +'ParentOwnership.helper_address_forward' depends on axioms: [propext, Classical.choice, Quot.sound] +'ParentOwnership.helper_address_inverse' depends on axioms: [propext, Classical.choice, Quot.sound] +'ParentOwnership.source_address_gather_run' depends on axioms: [propext, Classical.choice, Quot.sound] +'ParentOwnership.source_common_cover' depends on axioms: [propext, Classical.choice, Quot.sound] +'ParentOwnership.source_native_run' depends on axioms: [propext, Classical.choice, Quot.sound] +'PhysicalSourceConnection.helper_endpoints' depends on axioms: [propext, Quot.sound] +'PhysicalSourceConnection.helper_endpoint' depends on axioms: [propext, Quot.sound] +'PhysicalSourceConnection.physical_data_endpoints' depends on axioms: [propext, Quot.sound] +'PhysicalSourceConnection.data_independent' depends on axioms: [propext, Quot.sound] +'PhysicalSourceConnection.data_endpoint' depends on axioms: [propext, Quot.sound] +'PhysicalSourceConnection.hosted_endpoint' depends on axioms: [propext, Quot.sound] +'PhysicalSourceConnection.original_retained' depends on axioms: [propext, Quot.sound] +'PhysicalSourceConnection.relocated_retained' depends on axioms: [propext, Quot.sound] +'PhysicalSourceConnection.tag_child_cases' does not depend on any axioms +'PhysicalSourceConnection.tag_pending_contains' depends on axioms: [propext] +'PhysicalSourceConnection.selected_invocation_completion' depends on axioms: [propext, Quot.sound] +'SelectedGeometry.gauges_tag' depends on axioms: [propext, Classical.choice, Quot.sound] +'SelectedGeometry.helper_relative' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceLayouts.data_owner_eq' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceLayouts.data_chart_eq' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceLayouts.host_family' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceLayouts.parent_owner_ne_host' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceLayouts.host_ne_parent_owner' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceLayouts.host_chart_forward' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceLayouts.host_chart_inverse' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.oldOwner_injective' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.newOwner_injective' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.hostOwner_injective' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.host_not_old' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.tailPayload_outside' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.hostPayload_host' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.hostPayload_outside' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.oldPayload_host' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.oldPayload_outside' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.newPayload_outside' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.parent_family_lt_private' does not depend on any axioms +'SourceInvocation.owner_overlap_data' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.owner_overlap_charts' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.commonNativeCover_new' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.new_common_cover' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.old_common_cover' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceControls.actual_add_event' does not depend on any axioms +'SourceControls.omitted_add_changes_row' depends on axioms: [propext] +'SourceControls.omitted_add_keeps_guards' depends on axioms: [propext] +'SourceControls.actual_first_copy' does not depend on any axioms +'SourceControls.dirty_private_copy_rejected' does not depend on any axioms +'SourceControls.dirty_private_copy_would_overwrite' depends on axioms: [propext] +'SourceControls.literal_helper_three_survives' depends on axioms: [propext, Quot.sound] +'SourceControls.literal_helper_three_not_zero' depends on axioms: [propext, Quot.sound] +'SourceInvocation.oldRaw_data' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.newRaw_data' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.oldRaw_bank' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.oldRaw_host' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.newRaw_host' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.oldRaw_outside' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.newRaw_outside' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.oldResult_framed' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.newResult_framed' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceDataBehavior.first_initial_frame' depends on axioms: [propext, Quot.sound] +'SourceDataBehavior.second_initial_frame' depends on axioms: [propext, Quot.sound] +'SourceDataBehavior.first_final_frame' depends on axioms: [propext, Quot.sound] +'SourceDataBehavior.second_final_frame' depends on axioms: [propext, Quot.sound] +'SourceDataBehavior.framed_first' depends on axioms: [propext, Quot.sound] +'SourceDataBehavior.framed_second' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceDataBehavior.framed_data_formula' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceDataBehavior.old_data_formula' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceDataBehavior.new_data_formula' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.newPayload_host' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.oldPayload_data' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.newPayload_data' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.oldPayload_bank' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.shared_host_input' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.shared_data_input' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceRawGuards.raw_clean_of_framed' depends on axioms: [Quot.sound] +'SourceRawGuards.raw_clean_run_of_framed' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceRawGuards.native_clean_of_raw' depends on axioms: [Quot.sound] +'SourceRawGuards.native_clean_run_of_raw' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceRawGuards.actual_raw_clean' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceRawGuards.initial_fromNative' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceRawGuards.actual_native_clean' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceRawGuards.native_run_refines' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceRawGuards.native_payload_endpoint' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceRawGuards.native_private_restored' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceRawGuards.native_other_preserved' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.native_payload_roundtrip' depends on axioms: [Quot.sound] +'SourceInvocation.old_native_realization' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.new_native_realization' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.old_native_clean' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.new_native_clean' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.old_native_temporary_restored' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.new_native_temporary_restored' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.native_shared_host_input' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.native_shared_data_input' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.native_shared_tail_input' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.initialized_native_host_input' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.initialized_native_data_input' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.initialized_native_tail_input' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.oldResult_native' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.newResult_native' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceMoveGeometry.move_projectors' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceMoveGeometry.move_stage2_relative' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceMoveGeometry.move_relative' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceMoveGeometry.copy_stage2_relative' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceMoveGeometry.copy_relative' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceMoveGeometry.erase_relative' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceMoveGeometry.physicalStep_move' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceMoveGeometry.physicalStep_copy' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceMoveGeometry.matrix_run_eq' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceMoveGeometry.actual_matrix_run' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceMoveGeometry.nativeStep_move' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceMoveGeometry.nativeRoute_move' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceMoveGeometry.nativeStep_copy' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.actualContract' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.selected_call_completion' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.selected_native_completion' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.selected_data_formula' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.selected_native_realization' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.selected_native_clean' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.selected_matrix_realization' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.selected_original_matrix_realization' depends on axioms: [propext, Classical.choice, Quot.sound] +'SourceInvocation.selected_temporary_restoration' depends on axioms: [propext, Classical.choice, Quot.sound] +$ lake env lean SingleStreamAxioms.lean +'SingleStream.realizes_iff' does not depend on any axioms +'SingleStream.no_owner_of_two_dependencies' does not depend on any axioms +'SingleStream.run_visible_eq' does not depend on any axioms +'SingleStream.dirty_read_no_owner' depends on axioms: [propext, Quot.sound] +'SingleStream.dirty_read_no_local_program' does not depend on any axioms +'SingleStream.whole_read_realizes' does not depend on any axioms +'SingleStream.two_reads_realize' does not depend on any axioms +'SingleStream.split_residual_no_owner' does not depend on any axioms +'SingleStream.two_residuals_realize' does not depend on any axioms +'SingleStream.two_helper_word_endpoint' depends on axioms: [propext, Quot.sound] +'SingleStream.correlated_two_helper_endpoint' depends on axioms: [propext, Quot.sound] +'SingleStream.bit_factor_nontrivial' does not depend on any axioms +'SingleStream.complex_factor_nontrivial' does not depend on any axioms +'SingleStream.split_bit_factor_no_owner' does not depend on any axioms +'SingleStream.split_complex_factor_no_owner' does not depend on any axioms +PASS full Lean 4.21 port: 153 modules, five audits; fresh +python3 research/lean-external-review/verify_package.py --build-receipt /tmp/pr442-lean421-fresh.json +{"status": "PASS", "completed_utc": "2026-10-13T05:40:22.153496+00:00", "manifest_sha256": "f659f786228480460045a6b88d0c363b653d738445ad311e09dada6d86ee6716", "files_checked": 544, "task_b_verified": true, "port_verified": true, "local_modules": 153, "support_modules": 89, "original_contribution_files": 66, "archived_exclusions": 9, "audit_counts": {"task_a": 21, "task_b": 931, "hosting": 47, "source_invocation": 422, "single_stream": 15}, "port_receipt_sha256": "c17e77986a31fa9f41a386569d7c3557dd40981a53f1cba500bd3ef75456ea2c", "port_replay_mode": "fresh", "ci_runtime_qualification": "Separate measured projection; not established by this integrity check.", "scope": "Inventory, manifested sources and available fresh receipt bindings; PENDING_TASK_B or PENDING_PORT means current verification is unfinished. This verifier does not run Lean or authenticate build provenance."} +git diff --exit-code diff --git a/research/lean-external-review/validation/lean421-ci-fix-projection.json b/research/lean-external-review/validation/lean421-ci-fix-projection.json new file mode 100644 index 0000000000..9739932517 --- /dev/null +++ b/research/lean-external-review/validation/lean421-ci-fix-projection.json @@ -0,0 +1,12 @@ +{ + "status": "QUALIFIED_ESTIMATE", + "measuredMakeSeconds": 1018.396, + "computeSlowdown": 1.5, + "setupAllowanceSeconds": 180, + "safetyFactor": 1.2, + "projectedSeconds": 2049.113, + "projectedMinutes": 34.152, + "targetMinutes": 35, + "upstreamHardLimitMinutes": 45, + "scope": "Local fresh Make time with fingerprinted external artifacts reused. GitHub setup and slowdown remain assumptions; inspect the linked CI run separately. No local contribution artifacts reused." +} diff --git a/research/lean-external-review/validation/lean421-ci-fix-timing.json b/research/lean-external-review/validation/lean421-ci-fix-timing.json new file mode 100644 index 0000000000..e2810cd967 --- /dev/null +++ b/research/lean-external-review/validation/lean421-ci-fix-timing.json @@ -0,0 +1,12 @@ +{ + "command": "make formal-pr442-verify LAKE=", + "seconds": 1018.396, + "exitCode": 0, + "gitCommit": "b86b4072edc15c717e762ebb5768905c78f4cf3f", + "status": "PASS", + "receiptSha256": "c17e77986a31fa9f41a386569d7c3557dd40981a53f1cba500bd3ef75456ea2c", + "manifestSha256": "cecfea850b02aa2791dacbfb95b07143b3d48cdc91f286d7a79030c814120b1a", + "externalArtifactReuse": "All toolchain and dependency source/artifact fingerprints matched the original fresh receipt before this run; no local build artifacts reused.", + "rawLogSha256": "25c2f0b7ca0610719e3ce0cf339f44c59f17608e1a237a08548f213f29a31f18", + "normalizedLogSha256": "432c48fd7a5e5992542898fb90c200e092cecd3c84d25d11561f7860c5117225" +} diff --git a/research/lean-external-review/verify_package.py b/research/lean-external-review/verify_package.py index 5bbdf4981b..4f63f49cc2 100644 --- a/research/lean-external-review/verify_package.py +++ b/research/lean-external-review/verify_package.py @@ -23,7 +23,7 @@ EXCLUDED = {'research/lean-external-review/package-manifest.json', 'research/lean-external-review/package-validation.json'} ROOT_FILES = ['LICENSE', 'NOTICE', 'CONTRIBUTING.md', 'Makefile', - '.github/workflows/verify.yml'] + '.github/workflows/verify.yml', 'certificates/mixed-point-audit.json'] def sha(path):

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