yiyunliu/sp-eta-postpone
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Add beta and eta rules to syntactic typing

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Yiyun Liu 2025-02-09 16:33:43 -05:00
parent 133968dd23
commit 5b925e3fa1
2 changed files with 42 additions and 3 deletions
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8
theories/logrel.v
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@ -1028,9 +1028,10 @@ Lemma SE_AppEta n Γ (b : PTm n) A B i :
⊨ Γ ->
Γ ⊨ PBind PPi A B ∈ (PUniv i) ->
Γ ⊨ b ∈ PBind PPi A B ->
Γ ⊨ PAbs (PApp (ren_PTm shift b) (VarPTm var_zero)) ∈ PBind PPi A B.
Γ ⊨ PAbs (PApp (ren_PTm shift b) (VarPTm var_zero)) ≡ b ∈ PBind PPi A B.
Proof.
move => hΓ h0 h1. apply : ST_Abs; eauto.
move => hΓ h0 h1. apply SemWt_SemEq; eauto.
apply : ST_Abs; eauto.
have hA : Γ ⊨ A ∈ PUniv i by eauto using SBind_inv1.
eapply ST_App' with (A := ren_PTm shift A)(B:= ren_PTm (upRen_PTm_PTm shift) B). by asimpl.
2 : {
@ -1040,6 +1041,7 @@ Proof.
change (PBind PPi (ren_PTm shift A) (ren_PTm (upRen_PTm_PTm shift) B)) with
(ren_PTm shift (PBind PPi A B)).
apply : weakening_Sem; eauto.
hauto q:on ctrs:rtc,RERed.R.
Qed.
Lemma SE_AppAbs n Γ (a : PTm (S n)) b A B i:
@ -1310,4 +1312,4 @@ Qed.
#[export]Hint Resolve ST_Var ST_Bind ST_Abs ST_App ST_Pair ST_Proj1 ST_Proj2 ST_Univ ST_Conv
SE_Refl SE_Symmetric SE_Transitive SE_Bind SE_Abs SE_App SE_Proj1 SE_Proj2
SE_Conv SSu_Pi_Proj1 SSu_Pi_Proj2 SSu_Sig_Proj1 SSu_Sig_Proj2 SSu_Eq SSu_Transitive SSu_Pi SSu_Sig SemWff_nil SemWff_cons SSu_Univ : sem.
SE_Conv SSu_Pi_Proj1 SSu_Pi_Proj2 SSu_Sig_Proj1 SSu_Sig_Proj2 SSu_Eq SSu_Transitive SSu_Pi SSu_Sig SemWff_nil SemWff_cons SSu_Univ SE_AppAbs SE_ProjPair1 SE_ProjPair2 SE_AppEta SE_PairEta : sem.