diff options
Diffstat (limited to 'theories/Reals/Ranalysis2.v')
| -rw-r--r-- | theories/Reals/Ranalysis2.v | 9 |
1 files changed, 5 insertions, 4 deletions
diff --git a/theories/Reals/Ranalysis2.v b/theories/Reals/Ranalysis2.v index b070cdaa..eb646913 100644 --- a/theories/Reals/Ranalysis2.v +++ b/theories/Reals/Ranalysis2.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2014 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) @@ -9,6 +9,7 @@ Require Import Rbase. Require Import Rfunctions. Require Import Ranalysis1. +Require Import Omega. Local Open Scope R_scope. (**********) @@ -432,17 +433,17 @@ Proof. unfold IZR; unfold INR, Pos.to_nat; simpl; intro; elim (Rlt_irrefl 1 (Rlt_trans _ _ _ H13 H12)). apply IZR_lt; omega. - unfold Rabs; case (Rcase_abs (/ 2)); intro. + unfold Rabs; case (Rcase_abs (/ 2)) as [Hlt|Hge]. assert (Hyp : 0 < 2). prove_sup0. - assert (H11 := Rmult_lt_compat_l 2 _ _ Hyp r); rewrite Rmult_0_r in H11; + assert (H11 := Rmult_lt_compat_l 2 _ _ Hyp Hlt); rewrite Rmult_0_r in H11; rewrite <- Rinv_r_sym in H11; [ idtac | discrR ]. elim (Rlt_irrefl 0 (Rlt_trans _ _ _ Rlt_0_1 H11)). reflexivity. apply (Rabs_pos_lt _ H0). ring. assert (H6 := Req_dec x0 (x0 + h)); elim H6; intro. - intro; rewrite <- H7; unfold dist, R_met; unfold R_dist; + intro; rewrite <- H7. unfold R_met, dist; unfold R_dist; unfold Rminus; rewrite Rplus_opp_r; rewrite Rabs_R0; apply Rabs_pos_lt. unfold Rdiv; apply prod_neq_R0; |