From a0cfa4f118023d35b767a999d5a2ac4b082857b4 Mon Sep 17 00:00:00 2001 From: Samuel Mimram Date: Fri, 25 Jul 2008 15:12:53 +0200 Subject: Imported Upstream version 8.2~beta3+dfsg --- theories/Arith/Max.v | 11 +++++++++-- 1 file changed, 9 insertions(+), 2 deletions(-) (limited to 'theories/Arith/Max.v') diff --git a/theories/Arith/Max.v b/theories/Arith/Max.v index e0222e41..95af67f8 100644 --- a/theories/Arith/Max.v +++ b/theories/Arith/Max.v @@ -6,9 +6,9 @@ (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(*i $Id: Max.v 9245 2006-10-17 12:53:34Z notin $ i*) +(*i $Id: Max.v 9883 2007-06-07 18:44:59Z letouzey $ i*) -Require Import Arith. +Require Import Le. Open Local Scope nat_scope. @@ -30,6 +30,13 @@ Proof. auto with arith. Qed. +Theorem max_assoc : forall m n p : nat, max m (max n p) = max (max m n) p. +Proof. + induction m; destruct n; destruct p; trivial. + simpl. + auto using IHm. +Qed. + Lemma max_comm : forall n m, max n m = max m n. Proof. induction n; induction m; simpl in |- *; auto with arith. -- cgit v1.2.3