Fixing tauto "special" behavior on singleton types w/ 2 parameters (bug #2680).

- tauto/intuition now works uniformly on and, prod, or, sum, False,
  Empty_set, unit, True (and isomorphic copies of them), iff, ->, and
  on all inhabited singleton types with a no-arguments constructor
  such as "eq t t" (even though the last case goes out of
  propositional logic: this features is so often used that it is
  difficult to come back on it).
- New dtauto and dintuition works on all inductive types with one
  constructors and no real arguments (for instance, they work on
  records such as "Equivalence"), in addition to -> and eq-like types.
- Moreover, both of them no longer unfold inner negations (this is a
  souce of incompatibility for intuition and evaluation of the level
  of incompatibility on contribs still needs to be done).

Incidentally, and amazingly, fixing bug #2680 made that constants
InfA_compat and InfA_eqA in SetoidList.v lost one argument: old tauto
had indeed destructed a section hypothesis "@StrictOrder A ltA@
thinking it was a conjunction, making this section hypothesis
artificially necessary while it was not.

Renouncing to the unfolding of inner negations made auto/eauto
sometimes succeeding more, sometimes succeeding less. There is by the
way a (standard) problem with not in auto/eauto: even when given as an
"unfold hint", it works only in goals, not in hypotheses, so that auto
is not able to solve something like "forall P, (forall x, ~ P x) -> P
0 -> False". Should we automatically add a lemma of type "HYPS -> A ->
False" in the hint database everytime a lemma ""HYPS -> ~A" is
declared (and "unfold not" is a hint), and similarly for all unfold
hints?

At this occasion, also re-did some proofs of Znumtheory.

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@15180 85f007b7-540e-0410-9357-904b9bb8a0f7

2 files changed, 2 insertions, 2 deletions

diff --git a/theories/Classes/EquivDec.v b/theories/Classes/EquivDec.v
index 9f44d4fef..87f86e0d3 100644
--- a/theories/Classes/EquivDec.v
+++ b/theories/Classes/EquivDec.v
@@ -139,7 +139,7 @@ Program Instance list_eqdec `(eqa : EqDec A eq) : ! EqDec (list A) eq :=
       | _, _ => in_right
     end }.
 
-  Next Obligation. destruct y ; intuition eauto. Defined.
+  Next Obligation. destruct y ; unfold not in *; eauto. Defined.
 
   Solve Obligations with unfold equiv, complement in * ; 
     program_simpl ; intuition (discriminate || eauto).
diff --git a/theories/Classes/RelationClasses.v b/theories/Classes/RelationClasses.v
index a8de1ba08..3717e1cb4 100644
--- a/theories/Classes/RelationClasses.v
+++ b/theories/Classes/RelationClasses.v
@@ -130,7 +130,7 @@ Tactic Notation "apply" "*" constr(t) :=
 
 Ltac simpl_relation :=
   unfold flip, impl, arrow ; try reduce ; program_simpl ;
-    try ( solve [ intuition ]).
+    try ( solve [ dintuition ]).
 
 Local Obligation Tactic := simpl_relation.