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-rw-r--r--theories/Reals/Rsqrt_def.v12
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.