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/QArith/Qabs.v | 25 +++++++++++++++++--------
 1 file changed, 17 insertions(+), 8 deletions(-)

(limited to 'theories/QArith/Qabs.v')

diff --git a/theories/QArith/Qabs.v b/theories/QArith/Qabs.v
index c60d0451..31eb41bc 100644
--- a/theories/QArith/Qabs.v
+++ b/theories/QArith/Qabs.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 Export QArith.
@@ -26,8 +28,8 @@ intros [xn xd] [yn yd] H.
 simpl.
 unfold Qeq in *.
 simpl in *.
-change (' yd)%Z with (Z.abs (' yd)).
-change (' xd)%Z with (Z.abs (' xd)).
+change (Zpos yd)%Z with (Z.abs (Zpos yd)).
+change (Zpos xd)%Z with (Z.abs (Zpos xd)).
 repeat rewrite <- Z.abs_mul.
 congruence.
 Qed.
@@ -86,8 +88,8 @@ unfold Qplus.
 unfold Qle.
 simpl.
 apply Z.mul_le_mono_nonneg_r;auto with *.
-change (' yd)%Z with (Z.abs (' yd)).
-change (' xd)%Z with (Z.abs (' xd)).
+change (Zpos yd)%Z with (Z.abs (Zpos yd)).
+change (Zpos xd)%Z with (Z.abs (Zpos xd)).
 repeat rewrite <- Z.abs_mul.
 apply Z.abs_triangle.
 Qed.
@@ -100,6 +102,13 @@ rewrite Z.abs_mul.
 reflexivity.
 Qed.
 
+Lemma Qabs_Qinv : forall q, Qabs (/ q) == / (Qabs q).
+Proof.
+  intros [n d]; simpl.
+  unfold Qinv.
+  case_eq n; intros; simpl in *; apply Qeq_refl.
+Qed.
+  
 Lemma Qabs_Qminus x y: Qabs (x - y) = Qabs (y - x).
 Proof.
  unfold Qminus, Qopp. simpl.
-- 
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