Imported Upstream version 8.4dfsgupstream/8.4dfsg

1 files changed, 17 insertions, 17 deletions

diff --git a/plugins/fourier/Fourier_util.v b/plugins/fourier/Fourier_util.v
index 3d16f189..b10c304c 100644
--- a/plugins/fourier/Fourier_util.v
+++ b/plugins/fourier/Fourier_util.v
@@ -1,6 +1,6 @@
 (************************************************************************)
 (*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
-(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010     *)
+(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2012     *)
 (*   \VV/  **************************************************************)
 (*    //   *      This file is distributed under the terms of the       *)
 (*         *       GNU Lesser General Public License Version 2.1        *)
@@ -16,7 +16,7 @@ intros; apply Rmult_lt_compat_l; assumption.
 Qed.
 
 Lemma Rfourier_le : forall x1 y1 a:R, x1 <= y1 -> 0 < a -> a * x1 <= a * y1.
-red in |- *.
+red.
 intros.
 case H; auto with real.
 Qed.
@@ -63,19 +63,19 @@ Lemma Rfourier_le_le :
    x1 <= y1 -> x2 <= y2 -> 0 < a -> x1 + a * x2 <= y1 + a * y2.
 intros x1 y1 x2 y2 a H H0 H1; try assumption.
 case H0; intros.
-red in |- *.
+red.
 left; try assumption.
 apply Rfourier_le_lt; auto with real.
 rewrite H2.
 case H; intros.
-red in |- *.
+red.
 left; try assumption.
 rewrite (Rplus_comm x1 (a * y2)).
 rewrite (Rplus_comm y1 (a * y2)).
 apply Rplus_lt_compat_l.
 try exact H3.
 rewrite H3.
-red in |- *.
+red.
 right; try assumption.
 auto with real.
 Qed.
@@ -84,7 +84,7 @@ Lemma Rlt_zero_pos_plus1 : forall x:R, 0 < x -> 0 < 1 + x.
 intros x H; try assumption.
 rewrite Rplus_comm.
 apply Rle_lt_0_plus_1.
-red in |- *; auto with real.
+red; auto with real.
 Qed.
 
 Lemma Rlt_mult_inv_pos : forall x y:R, 0 < x -> 0 < y -> 0 < x * / y.
@@ -101,12 +101,12 @@ Qed.
 Lemma Rle_zero_pos_plus1 : forall x:R, 0 <= x -> 0 <= 1 + x.
 intros x H; try assumption.
 case H; intros.
-red in |- *.
+red.
 left; try assumption.
 apply Rlt_zero_pos_plus1; auto with real.
 rewrite <- H0.
 replace (1 + 0) with 1.
-red in |- *; left.
+red; left.
 exact Rlt_zero_1.
 ring.
 Qed.
@@ -114,28 +114,28 @@ Qed.
 Lemma Rle_mult_inv_pos : forall x y:R, 0 <= x -> 0 < y -> 0 <= x * / y.
 intros x y H H0; try assumption.
 case H; intros.
-red in |- *; left.
+red; left.
 apply Rlt_mult_inv_pos; auto with real.
 rewrite <- H1.
-red in |- *; right; ring.
+red; right; ring.
 Qed.
 
 Lemma Rle_zero_1 : 0 <= 1.
-red in |- *; left.
+red; left.
 exact Rlt_zero_1.
 Qed.
 
 Lemma Rle_not_lt : forall n d:R, 0 <= n * / d -> ~ 0 < - n * / d.
-intros n d H; red in |- *; intros H0; try exact H0.
+intros n d H; red; intros H0; try exact H0.
 generalize (Rgt_not_le 0 (n * / d)).
 intros H1; elim H1; try assumption.
 replace (n * / d) with (- - (n * / d)).
 replace 0 with (- -0).
 replace (- (n * / d)) with (- n * / d).
 replace (-0) with 0.
-red in |- *.
+red.
 apply Ropp_gt_lt_contravar.
-red in |- *.
+red.
 exact H0.
 ring.
 ring.
@@ -162,7 +162,7 @@ ring.
 Qed.
 
 Lemma Rnot_lt_lt : forall x y:R, ~ 0 < y - x -> ~ x < y.
-unfold not in |- *; intros.
+unfold not; intros.
 apply H.
 apply Rplus_lt_reg_r with x.
 replace (x + 0) with x.
@@ -173,7 +173,7 @@ ring.
 Qed.
 
 Lemma Rnot_le_le : forall x y:R, ~ 0 <= y - x -> ~ x <= y.
-unfold not in |- *; intros.
+unfold not; intros.
 apply H.
 case H0; intros.
 left.
@@ -188,7 +188,7 @@ rewrite H1; ring.
 Qed.
 
 Lemma Rfourier_gt_to_lt : forall x y:R, y > x -> x < y.
-unfold Rgt in |- *; intros; assumption.
+unfold Rgt; intros; assumption.
 Qed.
 
 Lemma Rfourier_ge_to_le : forall x y:R, y >= x -> x <= y.