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| author | Chloe Brown <chloe.brown.00@outlook.com> | 2022-07-07 22:20:39 +0100 |
|---|---|---|
| committer | Chloe Brown <chloe.brown.00@outlook.com> | 2022-07-07 22:20:39 +0100 |
| commit | fd8eed040d6c567f85c9f7509bce60c6ed1c4cce (patch) | |
| tree | 7e6d123f460bc8151eab6f76fe9054a36ec084e0 | |
| parent | 027d42676f98282b9d50f5c31118c7a868ca104b (diff) | |
Prove alpha equivalence is transitive.
| -rw-r--r-- | src/Data/Type/Properties.agda | 10 |
1 files changed, 10 insertions, 0 deletions
diff --git a/src/Data/Type/Properties.agda b/src/Data/Type/Properties.agda index 28667fa..16f6d8e 100644 --- a/src/Data/Type/Properties.agda +++ b/src/Data/Type/Properties.agda @@ -252,3 +252,13 @@ free-≈ (all {α} {A} {β} {B} A≈B) = begin ≈-sym unit = unit ≈-sym (bin A≈C B≈D) = bin (≈-sym A≈C) (≈-sym B≈D) ≈-sym (all A≈B) = all (λ γ∉∀β∙B γ∉∀α∙A → ≈-sym (A≈B γ∉∀α∙A γ∉∀β∙B)) + +≈-trans : Transitive _≈_ +≈-trans (var α) (var .α) = var α +≈-trans unit unit = unit +≈-trans (bin A≈B A₁≈B₁) (bin B≈C B₁≈C₁) = + bin (≈-trans A≈B B≈C) (≈-trans A₁≈B₁ B₁≈C₁) +≈-trans (all A≈B) (all B≈C) = + all (λ δ∉∀α∙A δ∉∀γ∙C → + ≈-trans (A≈B δ∉∀α∙A (P.subst (_ ∉_) (free-≈ (all A≈B)) δ∉∀α∙A)) + (B≈C (P.subst (_ ∉_) (sym (free-≈ (all B≈C))) δ∉∀γ∙C) δ∉∀γ∙C)) |