From c630fdf04db508d5d877a6b1fd93145893377287 Mon Sep 17 00:00:00 2001
From: letouzey
Date: Fri, 8 Jan 2010 14:44:45 +0000
Subject: Init/Logic: commutativity and associativity of /\ and \/

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12643 85f007b7-540e-0410-9357-904b9bb8a0f7
---
 theories/Init/Logic.v | 20 ++++++++++++++++++++
 1 file changed, 20 insertions(+)

diff --git a/theories/Init/Logic.v b/theories/Init/Logic.v
index e1bb443a63..4fca1d1dbb 100644
--- a/theories/Init/Logic.v
+++ b/theories/Init/Logic.v
@@ -112,6 +112,16 @@ Proof.
 intros; tauto.
 Qed.
 
+Theorem and_comm : forall A B : Prop, A /\ B <-> B /\ A.
+Proof.
+intros; tauto.
+Qed.
+
+Theorem and_assoc : forall A B C : Prop, (A /\ B) /\ C <-> A /\ B /\ C.
+Proof.
+intros; tauto.
+Qed.
+
 Theorem or_cancel_l : forall A B C : Prop,
   (B -> ~ A) -> (C -> ~ A) -> ((A \/ B <-> A \/ C) <-> (B <-> C)).
 Proof.
@@ -124,6 +134,16 @@ Proof.
 intros; tauto.
 Qed.
 
+Theorem or_comm : forall A B : Prop, (A \/ B) <-> (B \/ A).
+Proof.
+intros; tauto.
+Qed.
+
+Theorem or_assoc : forall A B C : Prop, (A \/ B) \/ C <-> A \/ B \/ C.
+Proof.
+intros; tauto.
+Qed.
+
 (** Backward direction of the equivalences above does not need assumptions *)
 
 Theorem and_iff_compat_l : forall A B C : Prop,
-- 
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