In practice, the new setoid rewrite (and the "at" syntax) allows to avoid

using the ad-hoc qsetoid_rewrite. Could QRewrite.v be made completely obsolete ?
For the moment rewrite under fun and exists don't work. 



git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10935 85f007b7-540e-0410-9357-904b9bb8a0f7

4 files changed, 8 insertions, 13 deletions

diff --git a/theories/Numbers/Integer/Abstract/ZLt.v b/theories/Numbers/Integer/Abstract/ZLt.v
index 3d21444ad..8ceecdbf2 100644
--- a/theories/Numbers/Integer/Abstract/ZLt.v
+++ b/theories/Numbers/Integer/Abstract/ZLt.v
@@ -342,7 +342,7 @@ Proof NZgt_wf.
 
 Theorem Zlt_pred_l : forall n : Z, P n < n.
 Proof.
-intro n; pattern n at 2; qsetoid_rewrite <- (Zsucc_pred n); apply Zlt_succ_diag_r.
+intro n; rewrite <- (Zsucc_pred n) at 2; apply Zlt_succ_diag_r.
 Qed.
 
 Theorem Zle_pred_l : forall n : Z, P n <= n.
@@ -362,7 +362,7 @@ Qed.
 
 Theorem Zlt_pred_le : forall n m : Z, P n < m <-> n <= m.
 Proof.
-intros n m; pattern n at 2; qsetoid_rewrite <- (Zsucc_pred n).
+intros n m; rewrite <- (Zsucc_pred n) at 2.
 symmetry; apply Zle_succ_l.
 Qed.
 
diff --git a/theories/Numbers/Integer/Abstract/ZPlus.v b/theories/Numbers/Integer/Abstract/ZPlus.v
index cdafa1ca7..2520d62e1 100644
--- a/theories/Numbers/Integer/Abstract/ZPlus.v
+++ b/theories/Numbers/Integer/Abstract/ZPlus.v
@@ -75,7 +75,7 @@ Proof NZplus_cancel_r.
 Theorem Zplus_pred_l : forall n m : Z, P n + m == P (n + m).
 Proof.
 intros n m.
-pattern n at 2. qsetoid_rewrite <- (Zsucc_pred n).
+rewrite <- (Zsucc_pred n) at 2.
 rewrite Zplus_succ_l. now rewrite Zpred_succ.
 Qed.
 
@@ -104,19 +104,19 @@ Qed.
 
 Theorem Zminus_pred_l : forall n m : Z, P n - m == P (n - m).
 Proof.
-intros n m. pattern n at 2; qsetoid_rewrite <- (Zsucc_pred n).
+intros n m. rewrite <- (Zsucc_pred n) at 2.
 rewrite Zminus_succ_l; now rewrite Zpred_succ.
 Qed.
 
 Theorem Zminus_pred_r : forall n m : Z, n - (P m) == S (n - m).
 Proof.
-intros n m. pattern m at 2; qsetoid_rewrite <- (Zsucc_pred m).
+intros n m. rewrite <- (Zsucc_pred m) at 2.
 rewrite Zminus_succ_r; now rewrite Zsucc_pred.
 Qed.
 
 Theorem Zopp_pred : forall n : Z, - (P n) == S (- n).
 Proof.
-intro n. pattern n at 2; qsetoid_rewrite <- (Zsucc_pred n).
+intro n. rewrite <- (Zsucc_pred n) at 2.
 rewrite Zopp_succ. now rewrite Zsucc_pred.
 Qed.
 
diff --git a/theories/Numbers/Integer/Abstract/ZTimes.v b/theories/Numbers/Integer/Abstract/ZTimes.v
index 7819dc085..2d7ff30f7 100644
--- a/theories/Numbers/Integer/Abstract/ZTimes.v
+++ b/theories/Numbers/Integer/Abstract/ZTimes.v
@@ -73,7 +73,7 @@ Proof NZneq_times_0.
 Theorem Ztimes_pred_r : forall n m : Z, n * (P m) == n * m - n.
 Proof.
 intros n m.
-pattern m at 2; qsetoid_rewrite <- (Zsucc_pred m).
+rewrite <- (Zsucc_pred m) at 2.
 now rewrite Ztimes_succ_r, <- Zplus_minus_assoc, Zminus_diag, Zplus_0_r.
 Qed.
 
diff --git a/theories/Numbers/NumPrelude.v b/theories/Numbers/NumPrelude.v
index 2c221a88e..f2f6b9082 100644
--- a/theories/Numbers/NumPrelude.v
+++ b/theories/Numbers/NumPrelude.v
@@ -11,11 +11,6 @@
 (*i $Id$ i*)
 
 Require Export Setoid.
-(*Require Export Bool.*)
-(* Standard library. Export, not Import, because if a file
-importing the current file wants to use. e.g.,
-Theorem eq_true_or : forall b1 b2 : bool, b1 || b2 <-> b1 \/ b2,
-then it needs to know about bool and have a notation ||. *)
 Require Export QRewrite.
 
 Set Implicit Arguments.
@@ -183,7 +178,7 @@ let x2 := fresh "x" in
 let y2 := fresh "y" in
 let H2 := fresh "H" in
   intros x1 y1 H1 x2 y2 H2;
-  qsetoid_rewrite H1;
+  rewrite H1;
   qiff x2 y2 H2.
 
 (* The tactic solve_relation_wd is not very efficient because qsetoid_rewrite