From e37edc7e31dffb47c312a9421172c19bbb2ec049 Mon Sep 17 00:00:00 2001 From: Robbert Krebbers <mail@robbertkrebbers.nl> Date: Wed, 17 Jan 2018 00:39:29 +0100 Subject: [PATCH] Relate `forallb`/`existsb` to `Forall`/`Exists`. --- theories/list.v | 5 +++++ 1 file changed, 5 insertions(+) diff --git a/theories/list.v b/theories/list.v index b8a79c79..ace7fc83 100644 --- a/theories/list.v +++ b/theories/list.v @@ -2331,6 +2331,11 @@ Section Forall_Exists. end. End Forall_Exists. +Lemma forallb_True (f : A → bool) xs : forallb f xs ↔ Forall f xs. +Proof. split. induction xs; naive_solver. induction 1; naive_solver. Qed. +Lemma existb_True (f : A → bool) xs : existsb f xs ↔ Exists f xs. +Proof. split. induction xs; naive_solver. induction 1; naive_solver. Qed. + Lemma replicate_as_Forall (x : A) n l : replicate n x = l ↔ length l = n ∧ Forall (x =) l. Proof. rewrite replicate_as_elem_of, Forall_forall. naive_solver. Qed. -- GitLab