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Julius
2026-04-21 20:44:15 +02:00
parent 077d91a485
commit 5cbf679c0c
2 changed files with 56 additions and 12 deletions
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SubjectReduction/Confluence.agda
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@@ -556,6 +556,12 @@ par-triangle (ξ-· (ξ-, l l₁) r) = ξ-· (ξ-, (par-triangle l) (par-triangl
par-triangle (ξ-· (ξ-subst t e₁ e₂) r) = ξ-· (par-triangle (ξ-subst t e₁ e₂)) (par-triangle r)
par-triangle (ξ-· s@(β-subst l) r) = ξ-· (par-triangle s) (par-triangle r)
par-triangle (ξ-· ξ-refl r) = ξ-· ξ-refl (par-triangle r)
par-triangle (ξ-· (ξ-Setω l) r) = ξ-· (ξ-Setω (par-triangle l)) (par-triangle r)
par-triangle (ξ-· (ξ-Setn l) r) = ξ-· (ξ-Setn (par-triangle l)) (par-triangle r)
par-triangle (ξ-· ξ-Level r) = ξ-· ξ-Level (par-triangle r)
par-triangle (ξ-· ξ-lzero r) = ξ-· ξ-lzero (par-triangle r)
par-triangle (ξ-· (ξ-lsuc l) r) = ξ-· (ξ-lsuc (par-triangle l)) (par-triangle r)
par-triangle (ξ-· (ξ-⊔ l l₁) r) = ξ-· (ξ-⊔ (par-triangle l) (par-triangle l₁)) (par-triangle r)
par-triangle (β-proj₁ e) = par-triangle e
par-triangle (β-proj₂ e) = par-triangle e
par-triangle (ξ-proj₁ ξ-`) = ξ-proj₁ ξ-`
@@ -607,6 +613,12 @@ par-triangle (ξ-subst e (ξ-, e₁ e₃) e₂) = ξ-subst (par-triangle e) (ξ-
par-triangle (ξ-subst e (ξ-subst e₁ e₃ e₄) e₂) = ξ-subst (par-triangle e) (par-triangle (ξ-subst e₁ e₃ e₄)) (par-triangle e₂)
par-triangle (ξ-subst e (β-subst e₁) e₂) = ξ-subst (par-triangle e) (par-triangle e₁) (par-triangle e₂)
par-triangle (ξ-subst e ξ-refl e₂) = β-subst (par-triangle e₂)
par-triangle (ξ-subst e (ξ-Setω e₁) e₂) = ξ-subst (par-triangle e) (ξ-Setω (par-triangle e₁)) (par-triangle e₂)
par-triangle (ξ-subst e (ξ-Setn e₁) e₂) = ξ-subst (par-triangle e) (ξ-Setn (par-triangle e₁)) (par-triangle e₂)
par-triangle (ξ-subst e ξ-Level e₂) = ξ-subst (par-triangle e) ξ-Level (par-triangle e₂)
par-triangle (ξ-subst e ξ-lzero e₂) = ξ-subst (par-triangle e) ξ-lzero (par-triangle e₂)
par-triangle (ξ-subst e (ξ-lsuc e₁) e₂) = ξ-subst (par-triangle e) (ξ-lsuc (par-triangle e₁)) (par-triangle e₂)
par-triangle (ξ-subst e (ξ-⊔ e₁ e₃) e₂) = ξ-subst (par-triangle e) (ξ-⊔ (par-triangle e₁) (par-triangle e₃)) (par-triangle e₂)
par-triangle (ξ-proj₁ (ξ-Setω x)) = ξ-proj₁ (ξ-Setω (par-triangle x))
par-triangle (ξ-proj₁ (ξ-Setn x)) = ξ-proj₁ (ξ-Setn (par-triangle x))
par-triangle (ξ-proj₁ ξ-Level) = ξ-proj₁ ξ-Level
@@ -619,18 +631,13 @@ par-triangle (ξ-proj₂ ξ-Level) = ξ-proj₂ ξ-Level
par-triangle (ξ-proj₂ ξ-lzero) = ξ-proj₂ (par-triangle ξ-lzero)
par-triangle (ξ-proj₂ (ξ-lsuc x)) = ξ-proj₂ (ξ-lsuc (par-triangle x))
par-triangle (ξ-proj₂ (ξ-⊔ x x₁)) = ξ-proj₂ (ξ-⊔ (par-triangle x) (par-triangle x₁))
par-triangle (ξ-· x x₁) = {! !}
par-triangle (ξ-subst x x₁ x₂) = {! !}
-- New
par-triangle (ξ-Setω x) = ξ-Setω (par-triangle x)
par-triangle (ξ-Setn x) = ξ-Setn (par-triangle x)
par-triangle ξ-Level = ξ-Level
par-triangle ξ-lzero = ξ-lzero
par-triangle (ξ-lsuc x) = ξ-lsuc (par-triangle x)
par-triangle (ξ-⊔ x x₁) = ξ-⊔ (par-triangle x) (par-triangle x₁)
-- par-triangle (ξ-proj₁ ξ-Set) = ξ-proj₁ ξ-Set
-- par-triangle (ξ-proj₂ ξ-Set) = ξ-proj₂ ξ-Set
-- par-triangle (ξ-· ξ-Set r) = ξ-· ξ-Set (par-triangle r)
-- par-triangle (ξ-subst e ξ-Set e₂) = ξ-subst (par-triangle e) ξ-Set (par-triangle e₂)
1→* : ∀ {m} {e e' : Term m} → e ↪ₚ e' → (e ↪ₚ* e')
1→* e↪ₚe' = ↪ₚ*-step e↪ₚe' ↪ₚ*-refl