- Fix bug in unification not taking into account the right meta

substitution. Makes unification succeed a bit more often, hence auto
works better in some cases.
- Backtrack the changes of auto using Hint Unfold to do more delta and add
a new tactic "new auto" which does that, for compatibility.

The first fix may have a big impact on the contribs, whereas the second
should make them compile again... we'll see.


git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10855 85f007b7-540e-0410-9357-904b9bb8a0f7

5 files changed, 9 insertions, 29 deletions

diff --git a/theories/Ints/num/NMake.v b/theories/Ints/num/NMake.v
index ab7b4a2549..5cc8f0284a 100644
--- a/theories/Ints/num/NMake.v
+++ b/theories/Ints/num/NMake.v
@@ -5177,9 +5177,6 @@ Qed.
    rewrite H1; simpl Z_of_nat; change (2^1) with (2).
    unfold base.
    apply Zpower_le_monotone; split; auto with zarith.
-   rewrite Zmult_comm; repeat rewrite <- Zmult_assoc.
-     repeat rewrite <- Zpos_xO.
-   refine (Zle_refl _).
  intros n; case n; clear n.
  intros H1; rewrite spec_reduce_2; unfold to_Z.
  apply (znz_of_pos_correct w2_spec).
@@ -5187,19 +5184,13 @@ Qed.
    rewrite H1; simpl Z_of_nat; change (2^2) with (2 * 2).
    unfold base.
    apply Zpower_le_monotone; split; auto with zarith.
-   rewrite Zmult_comm; repeat rewrite <- Zmult_assoc.
-     repeat rewrite <- Zpos_xO.
-   refine (Zle_refl _).
  intros n; case n; clear n.
  intros H1; rewrite spec_reduce_3; unfold to_Z.
  apply (znz_of_pos_correct w3_spec).
  apply Zlt_le_trans with (1 := pheight_correct x).
    rewrite H1; simpl Z_of_nat; change (2^3) with (2 * 2 * 2).
    unfold base.
-   apply Zpower_le_monotone; split; auto with zarith.
-   rewrite Zmult_comm; repeat rewrite <- Zmult_assoc.
-     repeat rewrite <- Zpos_xO.
-   refine (Zle_refl _).
+   apply Zpower_le_monotone; split; auto with zarith. 
  intros n; case n; clear n.
  intros H1; rewrite spec_reduce_4; unfold to_Z.
  apply (znz_of_pos_correct w4_spec).
@@ -5207,9 +5198,6 @@ Qed.
    rewrite H1; simpl Z_of_nat; change (2^4) with (2 * 2 * 2 * 2).
    unfold base.
    apply Zpower_le_monotone; split; auto with zarith.
-   rewrite Zmult_comm; repeat rewrite <- Zmult_assoc.
-     repeat rewrite <- Zpos_xO.
-   refine (Zle_refl _).
  intros n; case n; clear n.
  intros H1; rewrite spec_reduce_5; unfold to_Z.
  apply (znz_of_pos_correct w5_spec).
@@ -5217,9 +5205,6 @@ Qed.
    rewrite H1; simpl Z_of_nat; change (2^5) with (2 * 2 * 2 * 2 * 2).
    unfold base.
    apply Zpower_le_monotone; split; auto with zarith.
-   rewrite Zmult_comm; repeat rewrite <- Zmult_assoc.
-     repeat rewrite <- Zpos_xO.
-   refine (Zle_refl _).
  intros n; case n; clear n.
  intros H1; rewrite spec_reduce_6; unfold to_Z.
  apply (znz_of_pos_correct w6_spec).
@@ -5227,9 +5212,6 @@ Qed.
    rewrite H1; simpl Z_of_nat; change (2^6) with (2 * 2 * 2 * 2 * 2 * 2).
    unfold base.
    apply Zpower_le_monotone; split; auto with zarith.
-   rewrite Zmult_comm; repeat rewrite <- Zmult_assoc.
-     repeat rewrite <- Zpos_xO.
-   refine (Zle_refl _).
  intros n.
  intros H1; rewrite spec_reduce_n; unfold to_Z.
  simpl minus; rewrite <- minus_n_O.
diff --git a/theories/Lists/List.v b/theories/Lists/List.v
index 5ab27cfc7d..78a2db5347 100644
--- a/theories/Lists/List.v
+++ b/theories/Lists/List.v
@@ -686,8 +686,7 @@ Section ListOps.
     rewrite app_nth1; auto.
     rewrite (minus_plus_simpl_l_reverse (length l) n 1).
     replace (1 + length l) with (S (length l)); auto with arith.
-    rewrite <- minus_Sn_m; auto with arith; simpl.
-    apply IHl; auto.
+    rewrite <- minus_Sn_m; auto with arith.
     rewrite rev_length; auto.
   Qed.
 
@@ -1363,7 +1362,6 @@ End Fold_Right_Recursor.
       destruct n; destruct d; simpl; auto.
       destruct a; destruct (split l); simpl; auto.
       destruct a; destruct (split l); simpl in *; auto.
-      rewrite IHl; simpl; auto.
     Qed.
 
     Lemma split_length_l : forall (l:list (A*B)),
diff --git a/theories/Sets/Powerset_Classical_facts.v b/theories/Sets/Powerset_Classical_facts.v
index ac36640549..8116045b69 100644
--- a/theories/Sets/Powerset_Classical_facts.v
+++ b/theories/Sets/Powerset_Classical_facts.v
@@ -101,6 +101,7 @@ Section Sets_as_an_algebra.
     intros X x H'; red in |- *.
     intros x0 H'0; try assumption.
     elim (classic (x = x0)); intro K; auto with sets.
+    elim K; auto with sets.
   Qed.
   
   Lemma add_soustr_1 :
diff --git a/theories/Strings/String.v b/theories/Strings/String.v
index 4057ba022e..6826e0c51f 100644
--- a/theories/Strings/String.v
+++ b/theories/Strings/String.v
@@ -110,8 +110,8 @@ Proof.
 intros s1; elim s1; simpl in |- *; auto.
 intros s2 n; rewrite plus_comm; simpl in |- *; auto.
 intros a s1' Rec s2 n; case n; simpl in |- *; auto.
-generalize (Rec s2 0); simpl in |- *; auto.
-intros n0; rewrite <- Plus.plus_Snm_nSm; auto.
+generalize (Rec s2 0); simpl in |- *; auto. intros.
+rewrite <- Plus.plus_Snm_nSm; auto.
 Qed.
 
 (** *** Substrings *)
diff --git a/theories/ZArith/Zpow_facts.v b/theories/ZArith/Zpow_facts.v
index b862d663b8..9524bd44f5 100644
--- a/theories/ZArith/Zpow_facts.v
+++ b/theories/ZArith/Zpow_facts.v
@@ -171,12 +171,11 @@ Qed.
 Theorem Zpower_ge_0: forall x y, 0 <= x -> 0 <= x^y. 
 Proof.
   intros x y; case y; auto with zarith.
-  simpl; auto with zarith.
   intros p H1; assert (H: 0 <= Zpos p); auto with zarith.
-  generalize H; pattern (Zpos p); apply natlike_ind; auto.
-  intros p1 H2 H3 _; unfold Zsucc; rewrite Zpower_exp; simpl; auto with zarith.
-  apply Zmult_le_0_compat; auto with zarith.
-  generalize H1; case x; compute; intros; auto; discriminate.
+  generalize H; pattern (Zpos p); apply natlike_ind; auto with zarith.
+  intros p1 H2 H3 _; unfold Zsucc; rewrite Zpower_exp; simpl; auto with zarith. 
+  apply Zmult_le_0_compat; auto with zarith.  
+  generalize H1; case x; compute; intros; auto; try discriminate.
 Qed.
 
 Theorem Zpower_le_monotone2: