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Yiyun Liu 2025-02-09 17:05:36 -05:00
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6
theories/structural.v
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@ -84,6 +84,7 @@ Lemma T_Proj2' n Γ (a : PTm n) A B U :
Proof. move => ->. apply T_Proj2. Qed. Proof. move => ->. apply T_Proj2. Qed.
Lemma E_Bind' n Γ i p (A0 A1 : PTm n) B0 B1 : Lemma E_Bind' n Γ i p (A0 A1 : PTm n) B0 B1 :
Γ ⊢ A0 ∈ PUniv i ->
Γ ⊢ A0 ≡ A1 ∈ PUniv i -> Γ ⊢ A0 ≡ A1 ∈ PUniv i ->
funcomp (ren_PTm shift) (scons A0 Γ) ⊢ B0 ≡ B1 ∈ PUniv i -> funcomp (ren_PTm shift) (scons A0 Γ) ⊢ B0 ≡ B1 ∈ PUniv i ->
Γ ⊢ PBind p A0 B0 ≡ PBind p A1 B1 ∈ PUniv i. Γ ⊢ PBind p A0 B0 ≡ PBind p A1 B1 ∈ PUniv i.
@ -113,6 +114,9 @@ Proof.
- move => n Γ a A B ha iha m Δ ξ hΔ hξ. apply : T_Proj2'; eauto. by asimpl. - move => n Γ a A B ha iha m Δ ξ hΔ hξ. apply : T_Proj2'; eauto. by asimpl.
- hauto lq:on ctrs:Wt,LEq. - hauto lq:on ctrs:Wt,LEq.
- hauto lq:on ctrs:Eq. - hauto lq:on ctrs:Eq.
- move => n Γ i p A0 A1 B0 B1 hΓ _ hA ihA hB ihB m Δ ξ hΔ hξ. - move => n Γ i p A0 A1 B0 B1 hΓ _ hA ihA hA' ihA' hB ihB m Δ ξ hΔ hξ.
apply E_Bind'; eauto. apply E_Bind'; eauto.
apply ihB; last by hauto l:on use:renaming_up. apply ihB; last by hauto l:on use:renaming_up.
hauto lq:on ctrs:Wff,Wt use:renaming_up.
- move => n Γ a b A B i hP ihP ha iha m Δ ξ hΔ hξ.
apply : E_Abs; eauto. apply iha; last by hauto l:on use:renaming_up.