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Prove PairEta

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Yiyun Liu 2025-04-19 00:24:09 -04:00
parent 8e083aad4b
commit 0e04a7076b
3 changed files with 98 additions and 77 deletions
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6
theories/algorithmic.v
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@ -608,13 +608,12 @@ Proof.
have /regularity_sub0 [i' hPi0] := hPi.
have : Γ ⊢ PAbs (PApp (ren_PTm shift u) (VarPTm var_zero)) ≡ u ∈ PBind PPi A2 B2.
apply : E_AppEta; eauto.
hauto l:on use:regularity.
apply T_Conv with (A := A);eauto.
eauto using Su_Eq.
move => ?.
suff : Γ ⊢ PAbs a ≡ PAbs (PApp (ren_PTm shift u) (VarPTm var_zero)) ∈ PBind PPi A2 B2
by eauto using E_Transitive.
apply : E_Abs; eauto. hauto l:on use:regularity.
apply : E_Abs; eauto.
apply iha.
move /Su_Pi_Proj2_Var in hPi'.
apply : T_Conv; eauto.
@ -666,7 +665,7 @@ Proof.
have hA02 : Γ ⊢ A0 ≲ A2 by sfirstorder use:Su_Sig_Proj1.
have hu' : Γ ⊢ u ∈ PBind PSig A2 B2 by eauto using T_Conv_E.
move => [:ih0'].
apply : E_Transitive; last (apply E_Symmetric; apply : E_PairEta).
apply : E_Transitive; last (apply : E_PairEta).
apply : E_Pair; eauto. hauto l:on use:regularity.
abstract : ih0'.
apply ih0. apply : T_Conv; eauto.
@ -679,7 +678,6 @@ Proof.
move /E_Symmetric in ih0'.
move /regularity_sub0 in hA'.
hauto l:on use:bind_inst.
hauto l:on use:regularity.
eassumption.
(* Same as before *)
- move {hAppL}.