From 9043add656177eeac1491a73d2f3ab92bec0013c Mon Sep 17 00:00:00 2001
From: Benjamin Barenblat <bbaren@debian.org>
Date: Sat, 29 Dec 2018 14:31:27 -0500
Subject: Imported Upstream version 8.8.2

---
 theories/Numbers/Integer/Abstract/ZDivTrunc.v | 18 ++++++++++++++----
 1 file changed, 14 insertions(+), 4 deletions(-)

(limited to 'theories/Numbers/Integer/Abstract/ZDivTrunc.v')

diff --git a/theories/Numbers/Integer/Abstract/ZDivTrunc.v b/theories/Numbers/Integer/Abstract/ZDivTrunc.v
index 04301077..31e42738 100644
--- a/theories/Numbers/Integer/Abstract/ZDivTrunc.v
+++ b/theories/Numbers/Integer/Abstract/ZDivTrunc.v
@@ -1,9 +1,11 @@
 (************************************************************************)
-(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
-(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016     *)
+(*         *   The Coq Proof Assistant / The Coq Development Team       *)
+(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
+(* <O___,, *       (see CREDITS file for the list of authors)           *)
 (*   \VV/  **************************************************************)
-(*    //   *      This file is distributed under the terms of the       *)
-(*         *       GNU Lesser General Public License Version 2.1        *)
+(*    //   *    This file is distributed under the terms of the         *)
+(*         *     GNU Lesser General Public License Version 2.1          *)
+(*         *     (see LICENSE file for the text of the license)         *)
 (************************************************************************)
 
 Require Import ZAxioms ZMulOrder ZSgnAbs NZDiv.
@@ -622,6 +624,14 @@ Proof.
  apply quot_rem; order.
 Qed.
 
+Lemma rem_quot: forall a b, b~=0 ->
+ a rem b ÷ b == 0.
+Proof.
+ intros a b Hb.
+ rewrite quot_small_iff by assumption.
+ auto using rem_bound_abs.
+Qed.
+
 (** A last inequality: *)
 
 Theorem quot_mul_le:
-- 
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