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Work on the refactoring proof

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Yiyun Liu 2025-03-03 15:50:08 -05:00
parent fe418c2a78
commit 3e8ad2c5bc
3 changed files with 127 additions and 145 deletions
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10
theories/soundness.v
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@ -3,13 +3,13 @@ Require Import fp_red logrel typing.
From Hammer Require Import Tactics.
Theorem fundamental_theorem :
(forall n (Γ : fin n -> PTm n), ⊢ Γ -> ⊨ Γ) /\
(forall n Γ (a A : PTm n), Γ ⊢ a ∈ A -> Γ ⊨ a ∈ A) /\
(forall n Γ (a b A : PTm n), Γ ⊢ a ≡ b ∈ A -> Γ ⊨ a ≡ b ∈ A) /\
(forall n Γ (a b : PTm n), Γ ⊢ a ≲ b -> Γ ⊨ a ≲ b).
(forall Γ, ⊢ Γ -> ⊨ Γ) /\
(forall Γ a A, Γ ⊢ a ∈ A -> Γ ⊨ a ∈ A) /\
(forall Γ a b A, Γ ⊢ a ≡ b ∈ A -> Γ ⊨ a ≡ b ∈ A) /\
(forall Γ a b, Γ ⊢ a ≲ b -> Γ ⊨ a ≲ b).
apply wt_mutual; eauto with sem; [hauto l:on use:SE_Pair].
Unshelve. all : exact 0.
Qed.
Lemma synsub_to_usub : forall n Γ (a b : PTm n), Γ ⊢ a ≲ b -> SN a /\ SN b /\ Sub.R a b.
Lemma synsub_to_usub : forall Γ (a b : PTm), Γ ⊢ a ≲ b -> SN a /\ SN b /\ Sub.R a b.
Proof. hauto lq:on rew:off use:fundamental_theorem, SemLEq_SN_Sub. Qed.