From 86503800a77326db19412ea1c3e534f79dc5d6d1 Mon Sep 17 00:00:00 2001
From: filliatr
Date: Fri, 19 Apr 2002 08:12:51 +0000
Subject: un thm de plus dans Zdiv; un retour chariot apres un message de la
 tactique FourierR

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@2659 85f007b7-540e-0410-9357-904b9bb8a0f7
---
 theories/ZArith/Zdiv.v | 8 ++++++++
 1 file changed, 8 insertions(+)

(limited to 'theories')

diff --git a/theories/ZArith/Zdiv.v b/theories/ZArith/Zdiv.v
index d3aa637bbb..b7876f3402 100644
--- a/theories/ZArith/Zdiv.v
+++ b/theories/ZArith/Zdiv.v
@@ -181,6 +181,14 @@ Intros.
 Absurd `(NEG p)>0`; [ Generalize (NEG_lt_ZERO p); Omega | Omega ].
 Qed.
 
+Theorem Z_div_mod_eq : (a,b:Z)`b > 0` -> `a = b * (Zdiv a b) + (Zmod a b)`.
+Proof.
+Unfold Zdiv Zmod.
+Intros a b Hb.
+Generalize (Z_div_mod a b Hb).
+Pattern (Zdiv_eucl a b).
+Case (Zdiv_eucl); Tauto.
+Save.
 
 (** Existence theorems *)
 
-- 
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