From 7293e063458a0e449e2de10f7ea5f243b01e0cf7 Mon Sep 17 00:00:00 2001 From: Robbert Krebbers <mail@robbertkrebbers.nl> Date: Wed, 28 Sep 2016 13:44:55 +0200 Subject: [PATCH] Prove always_if_pure. --- algebra/upred.v | 3 +++ 1 file changed, 3 insertions(+) diff --git a/algebra/upred.v b/algebra/upred.v index d41a5adec..e9a83061b 100644 --- a/algebra/upred.v +++ b/algebra/upred.v @@ -1081,6 +1081,9 @@ Lemma always_if_elim p P : □?p P ⊢ P. Proof. destruct p; simpl; auto using always_elim. Qed. Lemma always_elim_if p P : □ P ⊢ □?p P. Proof. destruct p; simpl; auto using always_elim. Qed. + +Lemma always_if_pure p φ : □?p ■φ ⊣⊢ ■φ. +Proof. destruct p; simpl; auto using always_pure. Qed. Lemma always_if_and p P Q : □?p (P ∧ Q) ⊣⊢ □?p P ∧ □?p Q. Proof. destruct p; simpl; auto using always_and. Qed. Lemma always_if_or p P Q : □?p (P ∨ Q) ⊣⊢ □?p P ∨ □?p Q. -- GitLab