@@ -234,7 +234,7 @@ about `M` and can therefore use `⊥` for the value of `M`.
234234
235235Previously we showed that renaming variables preserves meaning. Now
236236we prove the opposite, that it reflects meaning. That is,
237- if ` δ ⊢ rename ρ M ↓ v ` , then ` γ ⊢ M ↓ v ` , where ` (δ ∘ ρ) ` ⊑ γ`.
237+ if ` δ ⊢ rename ρ M ↓ v ` , then ` γ ⊢ M ↓ v ` , where `` (δ ∘ ρ) `⊑ γ ` ` .
238238
239239First, we need a variant of a lemma given earlier.
240240``` agda
@@ -355,7 +355,7 @@ same-const-env : ∀{Γ} {x : Γ ∋ ★} {v} → (const-env x v) x ≡ v
355355same-const-env {x = x} rewrite var≟-refl x = refl
356356```
357357
358- and ` const-env x v ` maps ` y ` to ` ⊥, so long as ` x ≢ y`.
358+ and ` const-env x v ` maps ` y ` to ` ⊥ ` , so long as ` x ≢ y ` .
359359
360360``` agda
361361diff-const-env : ∀{Γ} {x y : Γ ∋ ★} {v}
@@ -378,7 +378,7 @@ Now to finish the two cases of the proof.
378378
379379* In the case where ` x ≡ y ` , we need to show
380380 that ` γ ⊢ σ y ↓ v ` , but that's just our premise.
381- * In the case where ` x ≢ y, ` we need to show
381+ * In the case where ` x ≢ y ` , we need to show
382382 that ` γ ⊢ σ y ↓ ⊥ ` , which we do via rule ` ⊥-intro ` .
383383
384384Thus, we have completed the variable case of the proof that
@@ -500,7 +500,7 @@ subst-reflect (sub d lt) eq
500500... | ⟨ δ , ⟨ subst-δ , m ⟩ ⟩ = ⟨ δ , ⟨ subst-δ , sub m lt ⟩ ⟩
501501```
502502
503- * Case ` var ` : We have subst ` σ M ≡ y ` , so ` M ` must also be a variable, say ` x ` .
503+ * Case ` var ` : We have ` subst σ M ≡ y ` , so ` M ` must also be a variable, say ` x ` .
504504 We apply the lemma ` subst-reflect-var ` to conclude.
505505
506506* Case ` ↦-elim ` : We have ` subst σ M ≡ L₁ · L₂ ` . We proceed by cases on ` M ` .
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