diff options
Diffstat (limited to 'theories/Reals/Rsqrt_def.v')
| -rw-r--r-- | theories/Reals/Rsqrt_def.v | 12 |
1 files changed, 5 insertions, 7 deletions
diff --git a/theories/Reals/Rsqrt_def.v b/theories/Reals/Rsqrt_def.v index f2095982..7c3b4699 100644 --- a/theories/Reals/Rsqrt_def.v +++ b/theories/Reals/Rsqrt_def.v @@ -1,13 +1,11 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2011 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(*i $Id: Rsqrt_def.v 14641 2011-11-06 11:59:10Z herbelin $ i*) - Require Import Sumbool. Require Import Rbase. Require Import Rfunctions. @@ -15,7 +13,7 @@ Require Import SeqSeries. Require Import Ranalysis1. Open Local Scope R_scope. -Boxed Fixpoint Dichotomy_lb (x y:R) (P:R -> bool) (N:nat) {struct N} : R := +Fixpoint Dichotomy_lb (x y:R) (P:R -> bool) (N:nat) {struct N} : R := match N with | O => x | S n => @@ -56,7 +54,7 @@ Proof. assumption. unfold Rdiv in |- *; apply Rmult_le_reg_l with 2. prove_sup0. - pattern 2 at 3 in |- *; rewrite Rmult_comm. + rewrite Rmult_comm. rewrite Rmult_assoc; rewrite <- Rinv_l_sym; [ idtac | discrR ]. rewrite Rmult_1_r. rewrite double. @@ -95,7 +93,7 @@ Proof. case (P ((Dichotomy_lb x y P n + Dichotomy_ub x y P n) / 2)). unfold Rdiv in |- *; apply Rmult_le_reg_l with 2. prove_sup0. - pattern 2 at 3 in |- *; rewrite Rmult_comm. + rewrite Rmult_comm. rewrite Rmult_assoc; rewrite <- Rinv_l_sym; [ idtac | discrR ]. rewrite Rmult_1_r. rewrite double. @@ -120,7 +118,7 @@ Proof. assumption. unfold Rdiv in |- *; apply Rmult_le_reg_l with 2. prove_sup0. - pattern 2 at 3 in |- *; rewrite Rmult_comm. + rewrite Rmult_comm. rewrite Rmult_assoc; rewrite <- Rinv_l_sym; [ rewrite Rmult_1_r | discrR ]. rewrite double; apply Rplus_le_compat. assumption. |