yiyunliu/sp-eta-postpone
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity Actions

Finish indzero and indsuc rules

Browse source
This commit is contained in:
Yiyun Liu 2025-02-25 15:46:22 -05:00
parent 890f97365c
commit 4dd2cd7cd8
2 changed files with 50 additions and 1 deletions
Download patch file Download diff file Expand all files Collapse all files

32
theories/logrel.v
View file

@ -1513,6 +1513,36 @@ Proof.
apply smorphing_ext; eauto using smorphing_ok_refl.
Qed.
Lemma SE_IndZero n Γ P i (b : PTm n) c :
funcomp (ren_PTm shift) (scons PNat Γ) ⊨ P ∈ PUniv i ->
Γ ⊨ b ∈ subst_PTm (scons PZero VarPTm) P ->
funcomp (ren_PTm shift)(scons P (funcomp (ren_PTm shift) (scons PNat Γ))) ⊨ c ∈ ren_PTm shift (subst_PTm (scons (PSuc (VarPTm var_zero)) (funcomp VarPTm shift) ) P) ->
Γ ⊨ PInd P PZero b c ≡ b ∈ subst_PTm (scons PZero VarPTm) P.
Proof.
move => hP hb hc.
apply SemWt_SemEq; eauto using ST_Zero, ST_Ind.
apply DJoin.FromRRed0. apply RRed.IndZero.
Qed.
Lemma SE_IndSuc s Γ P (a : PTm s) b c i :
funcomp (ren_PTm shift) (scons PNat Γ) ⊨ P ∈ PUniv i ->
Γ ⊨ a ∈ PNat ->
Γ ⊨ b ∈ subst_PTm (scons PZero VarPTm) P ->
funcomp (ren_PTm shift)(scons P (funcomp (ren_PTm shift) (scons PNat Γ))) ⊨ c ∈ ren_PTm shift (subst_PTm (scons (PSuc (VarPTm var_zero)) (funcomp VarPTm shift) ) P) ->
Γ ⊨ PInd P (PSuc a) b c ≡ (subst_PTm (scons (PInd P a b c) (scons a VarPTm)) c) ∈ subst_PTm (scons (PSuc a) VarPTm) P.
Proof.
move => hP ha hb hc.
apply SemWt_SemEq; eauto using ST_Suc, ST_Ind.
set Δ := (X in X ⊨ _ ∈ _) in hc.
have : smorphing_ok Γ Δ (scons (PInd P a b c) (scons a VarPTm)).
apply smorphing_ext. apply smorphing_ext. apply smorphing_ok_refl.
done. eauto using ST_Ind.
move : morphing_SemWt hc; repeat move/[apply].
by asimpl.
apply DJoin.FromRRed0.
apply RRed.IndSuc.
Qed.
Lemma SE_ProjPair1 n Γ (a b : PTm n) A B i :
Γ ⊨ PBind PSig A B ∈ (PUniv i) ->
Γ ⊨ a ∈ A ->
@ -1692,4 +1722,4 @@ 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 SE_AppAbs SE_ProjPair1 SE_ProjPair2 SE_AppEta SE_PairEta : 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 ST_Nat ST_Ind ST_Suc ST_Zero SE_IndCong SE_SucCong : sem.

19
theories/typing.v
View file

@ -42,6 +42,25 @@ Inductive Wt : forall {n}, (fin n -> PTm n) -> PTm n -> PTm n -> Prop :=
⊢ Γ ->
Γ ⊢ PUniv i : PTm n ∈ PUniv (S i)
| T_Nat n Γ i :
⊢ Γ ->
Γ ⊢ PNat : PTm n ∈ PUniv i
| T_Zero n Γ :
⊢ Γ ->
Γ ⊢ PZero : PTm n ∈ PNat
| T_Suc n Γ (a : PTm n) :
Γ ⊢ a ∈ PNat ->
Γ ⊢ PSuc a ∈ PNat
| T_Ind s Γ P (a : PTm s) b c i :
funcomp (ren_PTm shift) (scons PNat Γ) ⊢ P ∈ PUniv i ->
Γ ⊢ a ∈ PNat ->
Γ ⊢ b ∈ subst_PTm (scons PZero VarPTm) P ->
funcomp (ren_PTm shift)(scons P (funcomp (ren_PTm shift) (scons PNat Γ))) ⊢ c ∈ ren_PTm shift (subst_PTm (scons (PSuc (VarPTm var_zero)) (funcomp VarPTm shift) ) P) ->
Γ ⊢ PInd P a b c ∈ subst_PTm (scons a VarPTm) P
| T_Conv n Γ (a : PTm n) A B :
Γ ⊢ a ∈ A ->
Γ ⊢ A ≲ B ->