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Add Coquand's algorithm

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Yiyun Liu 2025-02-10 18:40:42 -05:00
parent 8105b5c410
commit bccf6eb860
4 changed files with 169 additions and 35 deletions
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19
theories/admissible.v
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@ -48,3 +48,22 @@ Proof.
move : E_Bind h0 h1; repeat move/[apply].
firstorder.
Qed.
Lemma E_App n Γ (b0 b1 a0 a1 : PTm n) A B :
Γ ⊢ b0 ≡ b1 ∈ PBind PPi A B ->
Γ ⊢ a0 ≡ a1 ∈ A ->
Γ ⊢ PApp b0 a0 ≡ PApp b1 a1 ∈ subst_PTm (scons a0 VarPTm) B.
Proof.
move => h.
have [i] : exists i, Γ ⊢ PBind PPi A B ∈ PUniv i by hauto l:on use:regularity.
move : E_App h. by repeat move/[apply].
Qed.
Lemma E_Proj2 n Γ (a b : PTm n) A B :
Γ ⊢ a ≡ b ∈ PBind PSig A B ->
Γ ⊢ PProj PR a ≡ PProj PR b ∈ subst_PTm (scons (PProj PL a) VarPTm) B.
Proof.
move => h.
have [i] : exists i, Γ ⊢ PBind PSig A B ∈ PUniv i by hauto l:on use:regularity.
move : E_Proj2 h; by repeat move/[apply].
Qed.