From b95c0bc7677747aa38d2644124df8df3e393d37b Mon Sep 17 00:00:00 2001 From: Robbert Krebbers <mail@robbertkrebbers.nl> Date: Sat, 2 Jul 2016 12:02:29 +0200 Subject: [PATCH] Add lemma pure_iff. --- algebra/upred.v | 2 ++ 1 file changed, 2 insertions(+) diff --git a/algebra/upred.v b/algebra/upred.v index 73d521139..607214971 100644 --- a/algebra/upred.v +++ b/algebra/upred.v @@ -564,6 +564,8 @@ Proof. intros ->; apply iff_refl. Qed. Lemma pure_mono φ1 φ2 : (φ1 → φ2) → ■φ1 ⊢ ■φ2. Proof. intros; apply pure_elim with φ1; eauto using pure_intro. Qed. +Lemma pure_iff φ1 φ2 : (φ1 ↔ φ2) → ■φ1 ⊣⊢ ■φ2. +Proof. intros [??]; apply (anti_symm _); auto using pure_mono. Qed. Lemma and_mono P P' Q Q' : (P ⊢ Q) → (P' ⊢ Q') → P ∧ P' ⊢ Q ∧ Q'. Proof. auto. Qed. Lemma and_mono_l P P' Q : (P ⊢ Q) → P ∧ P' ⊢ Q ∧ P'. -- GitLab