Revert "Tentative to fix bug #2628 by not letting intuition break records. Might be too much of a backwards-incompatible change"

Indeed it is breaking too many scripts.
This reverts commit 47e9afaaa4c08aca97d4f4b5a89cb40da76bd850.

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14956 85f007b7-540e-0410-9357-904b9bb8a0f7

6 files changed, 14 insertions, 29 deletions

diff --git a/theories/Classes/Equivalence.v b/theories/Classes/Equivalence.v
index 87316cda9..d9e9fe257 100644
--- a/theories/Classes/Equivalence.v
+++ b/theories/Classes/Equivalence.v
@@ -115,12 +115,6 @@ Section Respecting.
 
   Next Obligation.
   Proof.
-    unfold respecting in *. program_simpl. transitivity (y y0); auto. symmetry; apply H. reflexivity.
-  Qed.
-
-
-  Next Obligation.
-  Proof.
     unfold respecting in *. program_simpl. transitivity (y y0); auto. apply H0. reflexivity.
   Qed.
 
@@ -128,13 +122,10 @@ End Respecting.
 
 (** The default equivalence on function spaces, with higher-priority than [eq]. *)
 
-Hint Extern 0 => reflexivity : relations.
-Hint Extern 1 => solve [symmetry; auto] : relations.
-
 Program Instance pointwise_equivalence {A} `(eqb : Equivalence B eqB) :
   Equivalence (pointwise_relation A eqB) | 9.
 
   Next Obligation.
   Proof.
-    transitivity (y a); auto with relations.
+    transitivity (y a) ; auto.
   Qed.
diff --git a/theories/Classes/Morphisms.v b/theories/Classes/Morphisms.v
index 30d82822a..8e491b1b8 100644
--- a/theories/Classes/Morphisms.v
+++ b/theories/Classes/Morphisms.v
@@ -146,13 +146,6 @@ Program Instance respectful_per `(PER A R, PER B R') : PER (R ==> R').
   Next Obligation.
   Proof with auto.
     assert(R x0 x0).
-    transitivity y0... symmetry... 
-    symmetry... apply H1. now symmetry.
-  Qed.
-
-  Next Obligation.
-  Proof with auto.
-    assert(R x0 x0).
     transitivity y0... symmetry...
     transitivity (y x0)...
   Qed.
diff --git a/theories/FSets/FMapFacts.v b/theories/FSets/FMapFacts.v
index db24a417f..0c1448c9b 100644
--- a/theories/FSets/FMapFacts.v
+++ b/theories/FSets/FMapFacts.v
@@ -18,13 +18,12 @@ Require Export FMapInterface.
 Set Implicit Arguments.
 Unset Strict Implicit.
 
+Hint Extern 1 (Equivalence _) => constructor; congruence.
+
 (** * Facts about weak maps *)
 
 Module WFacts_fun (E:DecidableType)(Import M:WSfun E).
 
-Module UEq := Equalities.UpdateEq(E)(E).
-Import UEq.
-
 Notation eq_dec := E.eq_dec.
 Definition eqb x y := if eq_dec x y then true else false.
 
@@ -1185,7 +1184,7 @@ Module WProperties_fun (E:DecidableType)(M:WSfun E).
     Equal m m' -> cardinal m = cardinal m'.
   Proof.
   intros; do 2 rewrite cardinal_fold.
-  apply fold_Equal with (eqA:=eq); compute; auto. apply _.
+  apply fold_Equal with (eqA:=eq); compute; auto.
   Qed.
 
   Lemma cardinal_1 : forall m : t elt, Empty m -> cardinal m = 0.
@@ -1198,7 +1197,7 @@ Module WProperties_fun (E:DecidableType)(M:WSfun E).
   Proof.
   intros; do 2 rewrite cardinal_fold.
   change S with ((fun _ _ => S) x e).
-  apply fold_Add with (eqA:=eq); compute; auto. apply _.
+  apply fold_Add with (eqA:=eq); compute; auto.
   Qed.
 
   Lemma cardinal_inv_1 : forall m : t elt,
@@ -1545,7 +1544,7 @@ Module WProperties_fun (E:DecidableType)(M:WSfun E).
   setoid_replace (fold f m 0) with (fold f m1 (fold f m2 0)).
   rewrite <- cardinal_fold.
   apply fold_rel with (R:=fun u v => u = v + cardinal m2); simpl; auto.
-  apply Partition_fold with (eqA:=eq); repeat red; auto. apply _.
+  apply Partition_fold with (eqA:=eq); repeat red; auto.
   Qed.
 
   Lemma Partition_partition : forall m m1 m2, Partition m m1 m2 ->
@@ -1695,7 +1694,7 @@ Module WProperties_fun (E:DecidableType)(M:WSfun E).
  Proof.
   intros m1 m1' Hm1 m2 m2' Hm2.
   setoid_replace (update m1 m2) with (update m1' m2); unfold update.
-  apply fold_Equal with (eqA:=Equal); auto. apply _.
+  apply fold_Equal with (eqA:=Equal); auto.
   intros k k' Hk e e' He m m' Hm; rewrite Hk,He,Hm; red; auto.
   intros k k' e e' i Hneq x.
   rewrite !add_o; do 2 destruct eq_dec; auto. elim Hneq; eauto.
@@ -1713,7 +1712,7 @@ Module WProperties_fun (E:DecidableType)(M:WSfun E).
    intros k e i i' H Hii' x.
    pattern (mem k m2); rewrite Hm2. (* UGLY, see with Matthieu *)
    destruct mem; rewrite Hii'; auto.
-  apply fold_Equal with (eqA:=Equal); auto. apply _.
+  apply fold_Equal with (eqA:=Equal); auto.
    intros k k' Hk e e' He m m' Hm; simpl in *.
    pattern (mem k m2); rewrite Hk. (* idem *)
    destruct mem; rewrite ?Hk,?He,Hm; red; auto.
@@ -1732,7 +1731,7 @@ Module WProperties_fun (E:DecidableType)(M:WSfun E).
    intros k e i i' H Hii' x.
    pattern (mem k m2); rewrite Hm2. (* idem *)
    destruct mem; simpl; rewrite Hii'; auto.
-  apply fold_Equal with (eqA:=Equal); auto. apply _.
+  apply fold_Equal with (eqA:=Equal); auto.
    intros k k' Hk e e' He m m' Hm; simpl in *.
    pattern (mem k m2); rewrite Hk. (* idem *)
    destruct mem; simpl; rewrite ?Hk,?He,Hm; red; auto.
diff --git a/theories/FSets/FSetEqProperties.v b/theories/FSets/FSetEqProperties.v
index 3a2de94b5..755bc7dd0 100644
--- a/theories/FSets/FSetEqProperties.v
+++ b/theories/FSets/FSetEqProperties.v
@@ -920,6 +920,8 @@ Lemma sum_compat :
   forall s, (forall x, In x s -> f x=g x) -> sum f s=sum g s.
 intros.
 unfold sum; apply (fold_compat _ (@Logic.eq nat)); auto with *.
+intros x x' Hx y y' Hy. rewrite Hx, Hy; auto.
+intros x x' Hx y y' Hy. rewrite Hx, Hy; auto.
 Qed.
 
 End Sum.
diff --git a/theories/Structures/OrderedType.v b/theories/Structures/OrderedType.v
index beb10a833..f84cdf32c 100644
--- a/theories/Structures/OrderedType.v
+++ b/theories/Structures/OrderedType.v
@@ -223,7 +223,7 @@ Lemma Inf_lt : forall l x y, lt x y -> Inf y l -> Inf x l.
 Proof. exact (InfA_ltA lt_strorder). Qed.
 
 Lemma Inf_eq : forall l x y, eq x y -> Inf y l -> Inf x l.
-Proof. exact (InfA_eqA eq_equiv lt_compat). Qed.
+Proof. exact (InfA_eqA eq_equiv lt_strorder lt_compat). Qed.
 
 Lemma Sort_Inf_In : forall l x a, Sort l -> Inf a l -> In x l -> lt a x.
 Proof. exact (SortA_InfA_InA eq_equiv lt_strorder lt_compat). Qed.
@@ -396,7 +396,7 @@ Module KeyOrderedType(O:OrderedType).
   Qed.
 
   Lemma Inf_eq : forall l x x', eqk x x' -> Inf x' l -> Inf x l.
-  Proof. exact (InfA_eqA eqk_equiv ltk_compat). Qed.
+  Proof. exact (InfA_eqA eqk_equiv ltk_strorder ltk_compat). Qed.
 
   Lemma Inf_lt : forall l x x', ltk x x' -> Inf x' l -> Inf x l.
   Proof. exact (InfA_ltA ltk_strorder). Qed.
diff --git a/theories/Structures/OrdersLists.v b/theories/Structures/OrdersLists.v
index 059992f5b..f83b63779 100644
--- a/theories/Structures/OrdersLists.v
+++ b/theories/Structures/OrdersLists.v
@@ -32,7 +32,7 @@ Lemma Inf_lt : forall l x y, lt x y -> Inf y l -> Inf x l.
 Proof. exact (InfA_ltA lt_strorder). Qed.
 
 Lemma Inf_eq : forall l x y, eq x y -> Inf y l -> Inf x l.
-Proof. exact (InfA_eqA eq_equiv lt_compat). Qed.
+Proof. exact (InfA_eqA eq_equiv lt_strorder lt_compat). Qed.
 
 Lemma Sort_Inf_In : forall l x a, Sort l -> Inf a l -> In x l -> lt a x.
 Proof. exact (SortA_InfA_InA eq_equiv lt_strorder lt_compat). Qed.