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Finish refactoring substitution lemmas

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Yiyun Liu 2025-03-03 15:22:59 -05:00
parent 896d22ac9b
commit d68adf85f4
4 changed files with 244 additions and 235 deletions
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12
theories/preservation.v
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@ -1,15 +1,15 @@
Require Import Autosubst2.core Autosubst2.fintype Autosubst2.syntax common typing structural fp_red.
Require Import Autosubst2.core Autosubst2.unscoped Autosubst2.syntax common typing structural fp_red.
From Hammer Require Import Tactics.
Require Import ssreflect.
Require Import Psatz.
Require Import Coq.Logic.FunctionalExtensionality.
Lemma App_Inv n Γ (b a : PTm n) U :
Lemma App_Inv Γ (b a : PTm) U :
Γ ⊢ PApp b a ∈ U ->
exists A B, Γ ⊢ b ∈ PBind PPi A B /\ Γ ⊢ a ∈ A /\ Γ ⊢ subst_PTm (scons a VarPTm) B ≲ U.
Proof.
move E : (PApp b a) => u hu.
move : b a E. elim : n Γ u U / hu => n //=.
move : b a E. elim : Γ u U / hu => //=.
- move => Γ b a A B hb _ ha _ b0 a0 [*]. subst.
exists A,B.
repeat split => //=.
@ -18,12 +18,12 @@ Proof.
- hauto lq:on rew:off ctrs:LEq.
Qed.
Lemma Abs_Inv n Γ (a : PTm (S n)) U :
Lemma Abs_Inv Γ (a : PTm) U :
Γ ⊢ PAbs a ∈ U ->
exists A B, funcomp (ren_PTm shift) (scons A Γ) ⊢ a ∈ B /\ Γ ⊢ PBind PPi A B ≲ U.
exists A B, (cons A Γ) ⊢ a ∈ B /\ Γ ⊢ PBind PPi A B ≲ U.
Proof.
move E : (PAbs a) => u hu.
move : a E. elim : n Γ u U / hu => n //=.
move : a E. elim : Γ u U / hu => //=.
- move => Γ a A B i hP _ ha _ a0 [*]. subst.
exists A, B. repeat split => //=.
hauto lq:on use:E_Refl, Su_Eq.