From 2fe0d3359234a9c51d65a7eaef0fca41797f58b3 Mon Sep 17 00:00:00 2001 From: Yiyun Liu Date: Sun, 29 Dec 2024 22:36:15 -0500 Subject: [PATCH] Minor --- theories/logrel.v | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/theories/logrel.v b/theories/logrel.v index d707dfd..af9d144 100644 --- a/theories/logrel.v +++ b/theories/logrel.v @@ -15,7 +15,7 @@ Inductive InterpExt {n} i (I : forall n, nat -> Tm n -> Prop) : Tm n -> (Tm n -> ⟦ A ⟧ i ;; I ↘ PA -> (forall a, PA a -> exists PB, PF a PB) -> (forall a PB, PF a PB -> ⟦ subst_Tm (scons a VarTm) B ⟧ i ;; I ↘ PB) -> - ⟦ Pi A B ⟧ i ;; I ↘ (ProdSpace PA PF) + ⟦ TBind TPi A B ⟧ i ;; I ↘ (ProdSpace PA PF) | InterpExt_Univ j : j < i -> @@ -86,19 +86,19 @@ Lemma RPar_substone n (a b : Tm (S n)) (c : Tm n): Proof. hauto l:on inv:option use:RPar.substing, RPar.refl. Qed. Lemma InterpExt_Fun_inv n i I (A : Tm n) B P - (h : ⟦ Pi A B ⟧ i ;; I ↘ P) : + (h : ⟦ TBind TPi A B ⟧ i ;; I ↘ P) : exists (PA : Tm n -> Prop) (PF : Tm n -> (Tm n -> Prop) -> Prop), ⟦ A ⟧ i ;; I ↘ PA /\ (forall a, PA a -> exists PB, PF a PB) /\ (forall a PB, PF a PB -> ⟦ subst_Tm (scons a VarTm) B ⟧ i ;; I ↘ PB) /\ P = ProdSpace PA PF. Proof. - move E : (Pi A B) h => T h. + move E : (TBind TPi A B) h => T h. move : A B E. elim : T P / h => //. - hauto l:on. - move => A A0 PA hA hA0 hPi A1 B ?. subst. - elim /RPar.inv : hA => //= _ A2 A3 B0 B1 hA1 hB0 [*]. subst. + elim /RPar.inv : hA => //= _ p A2 A3 B0 B1 hA1 hB0 [*]. subst. hauto lq:on ctrs:InterpExt use:RPar_substone. Qed.