From 7a7e1d220d502f80601a1681de69efc21a194944 Mon Sep 17 00:00:00 2001 From: Robbert Krebbers <mail@robbertkrebbers.nl> Date: Thu, 17 May 2018 23:47:57 +0200 Subject: [PATCH] =?UTF-8?q?Prove=20`=E2=96=A1=20False=20=E2=8A=A3=E2=8A=A2?= =?UTF-8?q?=20False`.?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- theories/bi/derived_laws_bi.v | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/theories/bi/derived_laws_bi.v b/theories/bi/derived_laws_bi.v index e62306783..1b5b013b5 100644 --- a/theories/bi/derived_laws_bi.v +++ b/theories/bi/derived_laws_bi.v @@ -988,6 +988,8 @@ Proof. by rewrite /bi_intuitionistically -persistently_True_emp persistently_pure affinely_True_emp affinely_emp. Qed. +Lemma intuitionistically_False : □ False ⊣⊢ False. +Proof. by rewrite /bi_intuitionistically persistently_pure affinely_False. Qed. Lemma intuitionistically_True_emp : □ True ⊣⊢ emp. Proof. rewrite -intuitionistically_emp /bi_intuitionistically @@ -1179,6 +1181,8 @@ Proof. destruct p; simpl; auto using intuitionistically_intro'. Qed. Lemma intuitionistically_if_emp p : □?p emp ⊣⊢ emp. Proof. destruct p; simpl; auto using intuitionistically_emp. Qed. +Lemma intuitionistically_if_False p : □?p False ⊣⊢ False. +Proof. destruct p; simpl; auto using intuitionistically_False. Qed. Lemma intuitionistically_if_and p P Q : □?p (P ∧ Q) ⊣⊢ □?p P ∧ □?p Q. Proof. destruct p; simpl; auto using intuitionistically_and. Qed. Lemma intuitionistically_if_or p P Q : □?p (P ∨ Q) ⊣⊢ □?p P ∨ □?p Q. -- GitLab