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Add extensional version of pair equality rules

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Yiyun Liu 2025-04-17 15:15:58 -04:00
parent ef8feb63c3
commit a367591e9a
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16
theories/logrel.v
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@ -1521,6 +1521,22 @@ Proof.
rewrite /DJoin.R. hauto lq:on ctrs:rtc,RERed.R. rewrite /DJoin.R. hauto lq:on ctrs:rtc,RERed.R.
Qed. Qed.
Lemma SE_PairExt Γ (a b : PTm) A B i :
Γ ⊨ PBind PSig A B ∈ PUniv i ->
Γ ⊨ a ∈ PBind PSig A B ->
Γ ⊨ b ∈ PBind PSig A B ->
Γ ⊨ PProj PL a ≡ PProj PL b ∈ A ->
Γ ⊨ PProj PR a ≡ PProj PR b ∈ subst_PTm (scons (PProj PL a) VarPTm) B ->
Γ ⊨ a ≡ b ∈ PBind PSig A B.
Proof.
move => h0 ha hb h1 h2.
suff h : Γ ⊨ a ≡ PPair (PProj PL a) (PProj PR a) ∈ PBind PSig A B /\
Γ ⊨ PPair (PProj PL b) (PProj PR b) ≡ b ∈ PBind PSig A B /\
Γ ⊨ PPair (PProj PL a) (PProj PR a) ≡ PPair (PProj PL b) (PProj PR b) ∈ PBind PSig A B
by decompose [and] h; eauto using SE_Transitive, SE_Symmetric.
eauto 20 using SE_PairEta, SE_Symmetric, SE_Pair.
Qed.
Lemma SE_FunExt Γ (a b : PTm) A B i : Lemma SE_FunExt Γ (a b : PTm) A B i :
Γ ⊨ PBind PPi A B ∈ PUniv i -> Γ ⊨ PBind PPi A B ∈ PUniv i ->
Γ ⊨ a ∈ PBind PPi A B -> Γ ⊨ a ∈ PBind PPi A B ->