From 971a4e00a56cb142fb5fb2ef1fe3b87a14f488b6 Mon Sep 17 00:00:00 2001
From: herbelin
Date: Wed, 14 May 2003 00:11:56 +0000
Subject: Deplacement lemmes sur fact de Reals vers Arith

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@4014 85f007b7-540e-0410-9357-904b9bb8a0f7
---
 theories/Arith/Factorial.v | 15 +++++++++++++++
 1 file changed, 15 insertions(+)

(limited to 'theories/Arith')

diff --git a/theories/Arith/Factorial.v b/theories/Arith/Factorial.v
index 4963379e68..71cef55ce4 100644
--- a/theories/Arith/Factorial.v
+++ b/theories/Arith/Factorial.v
@@ -9,7 +9,10 @@
 (*i $Id$ i*)
 
 Require Plus.
+Require Mult.
 Require Lt.
+V7only [Import nat_scope.].
+Open Local Scope nat_scope.
 
 (** Factorial *)
 
@@ -32,3 +35,15 @@ Apply lt_O_neq.
 Apply lt_O_fact.
 Qed.
 
+Lemma fact_growing : (m,n:nat) (le m n) -> (le (fact m) (fact n)).
+Proof.
+NewInduction 1.
+Apply le_n.
+Assert (le (mult (S O) (fact m)) (mult (S m0) (fact m0))).
+Apply le_mult_mult.
+Apply lt_le_S; Apply lt_O_Sn.
+Assumption.
+Simpl (mult (S O) (fact m)) in H0.
+Rewrite <- plus_n_O in H0.
+Assumption.
+Qed.
-- 
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