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/Rtrigo_reg.v | 24 ++++++++++--------------
 1 file changed, 10 insertions(+), 14 deletions(-)

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

diff --git a/theories/Reals/Rtrigo_reg.v b/theories/Reals/Rtrigo_reg.v
index eed612d9..456fb6a7 100644
--- a/theories/Reals/Rtrigo_reg.v
+++ b/theories/Reals/Rtrigo_reg.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.
@@ -251,6 +253,7 @@ Proof.
   exists delta; intros.
   rewrite Rplus_0_l; replace (cos h - cos 0) with (-2 * Rsqr (sin (h / 2))).
   unfold Rminus; rewrite Ropp_0; rewrite Rplus_0_r.
+  change (-2) with (-(2)).
   unfold Rdiv; do 2 rewrite Ropp_mult_distr_l_reverse.
   rewrite Rabs_Ropp.
   replace (2 * Rsqr (sin (h * / 2)) * / h) with
@@ -266,7 +269,7 @@ Proof.
   apply Rabs_pos.
   assert (H9 := SIN_bound (h / 2)).
   unfold Rabs; case (Rcase_abs (sin (h / 2))); intro.
-  pattern 1 at 3; rewrite <- (Ropp_involutive 1).
+  rewrite <- (Ropp_involutive 1).
   apply Ropp_le_contravar.
   elim H9; intros; assumption.
   elim H9; intros; assumption.
@@ -395,15 +398,8 @@ Proof.
   apply Rlt_le_trans with alp.
   apply H7.
   unfold alp; apply Rmin_l.
-  rewrite sin_plus; unfold Rminus, Rdiv;
-    repeat rewrite Rmult_plus_distr_r; repeat rewrite Rmult_plus_distr_l;
-      repeat rewrite Rmult_assoc; repeat rewrite Rplus_assoc;
-        apply Rplus_eq_compat_l.
-  rewrite (Rplus_comm (sin x * (-1 * / h))); repeat rewrite Rplus_assoc;
-    apply Rplus_eq_compat_l.
-  rewrite Ropp_mult_distr_r_reverse; rewrite Ropp_mult_distr_l_reverse;
-    rewrite Rmult_1_r; rewrite Rmult_1_l; rewrite Ropp_mult_distr_r_reverse;
-      rewrite <- Ropp_mult_distr_l_reverse; apply Rplus_comm.
+  rewrite sin_plus.
+  now field.
   unfold alp; unfold Rmin; case (Rle_dec alp1 alp2); intro.
   apply (cond_pos alp1).
   apply (cond_pos alp2).
-- 
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