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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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16
theories/common.v
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@ -10,6 +10,12 @@ Inductive lookup : nat -> list PTm -> PTm -> Prop :=
lookup i Γ A ->
lookup (S i) (cons B Γ) (ren_PTm shift A).
Lemma lookup_deter i Γ A B :
lookup i Γ A ->
lookup i Γ B ->
A = B.
Proof. move => h. move : B. induction h; hauto lq:on inv:lookup. Qed.
Lemma here' A Γ U : U = ren_PTm shift A -> lookup 0 (A :: Γ) U.
Proof. move => ->. apply here. Qed.
@ -126,6 +132,14 @@ Definition ishne_ren (a : PTm) (ξ : nat -> nat) :
ishne (ren_PTm ξ a) = ishne a.
Proof. move : ξ. elim : a => //=. Qed.
Lemma renaming_shift Γ (ρ : nat -> PTm) A :
Lemma renaming_shift Γ A :
renaming_ok (cons A Γ) Γ shift.
Proof. rewrite /renaming_ok. hauto lq:on ctrs:lookup. Qed.
Lemma subst_scons_id (a : PTm) :
subst_PTm (scons (VarPTm 0) (funcomp VarPTm shift)) a = a.
Proof.
have E : subst_PTm VarPTm a = a by asimpl.
rewrite -{2}E.
apply ext_PTm. case => //=.
Qed.