diff options
Diffstat (limited to 'theories/Reals/Ranalysis4.v')
| -rw-r--r-- | theories/Reals/Ranalysis4.v | 21 |
1 files changed, 8 insertions, 13 deletions
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. |