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/Reals/Ranalysis4.v | 21 ++++++++-------------
 1 file changed, 8 insertions(+), 13 deletions(-)

(limited to 'theories/Reals/Ranalysis4.v')

diff --git a/theories/Reals/Ranalysis4.v b/theories/Reals/Ranalysis4.v
index 661bc8c7..94f1757a 100644
--- a/theories/Reals/Ranalysis4.v
+++ b/theories/Reals/Ranalysis4.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 Rbase.
@@ -130,15 +132,8 @@ Proof.
   intro; exists (mkposreal (- x) H1); intros.
   rewrite (Rabs_left x).
   rewrite (Rabs_left (x + h)).
-  rewrite Rplus_comm.
-  rewrite Ropp_plus_distr.
-  unfold Rminus; rewrite Ropp_involutive; rewrite Rplus_assoc;
-    rewrite Rplus_opp_l.
-  rewrite Rplus_0_r; unfold Rdiv.
-  rewrite Ropp_mult_distr_l_reverse.
-  rewrite <- Rinv_r_sym.
-  rewrite Ropp_involutive; rewrite Rplus_opp_l; rewrite Rabs_R0; apply H0.
-  apply H2.
+  replace ((-(x + h) - - x) / h - -1) with 0 by now field.
+  rewrite Rabs_R0; apply H0.
   destruct (Rcase_abs h) as [Hlt|Hgt].
   apply Ropp_lt_cancel.
   rewrite Ropp_0; rewrite Ropp_plus_distr; apply Rplus_lt_0_compat.
-- 
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