OrderedType implementation for various numerical datatypes + min/max structures

 - A richer OrderedTypeFull interface : OrderedType + predicate "le"
 - Implementations {Nat,N,P,Z,Q}OrderedType.v, also providing "order" tactics
 - By the way: as suggested by S. Lescuyer, specification of compare is
   now inductive
 - GenericMinMax: axiomatisation + properties of min and max out of
    OrderedTypeFull structures.
 - MinMax.v, {Z,P,N,Q}minmax.v are specialization of GenericMinMax,
    with also some domain-specific results, and compatibility layer
    with already existing results.
 - Some ML code of plugins had to be adapted, otherwise wrong "eq",
   "lt" or simimlar constants were found by functions like coq_constant.
 - Beware of the aliasing problems: for instance eq:=@eq t instead of
   eq:=@eq M.t in Make_UDT made (r)omega stopped working (Z_as_OT.t
   instead of Z in statement of Zmax_spec).
 - Some Morphism declaration are now ambiguous: switch to new syntax
   anyway.
 - Misc adaptations of FSets/MSets
 - Classes/RelationPairs.v: from two relations over A and B, we
   inspect relations over A*B and their properties in terms of classes.

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12461 85f007b7-540e-0410-9357-904b9bb8a0f7

1 files changed, 5 insertions, 6 deletions

diff --git a/theories/FSets/FSetCompat.v b/theories/FSets/FSetCompat.v
index 487b4fc32..f6d5ae1ac 100644
--- a/theories/FSets/FSetCompat.v
+++ b/theories/FSets/FSetCompat.v
@@ -209,11 +209,10 @@ Module Backport_Sets
   Qed.
   Definition compare : forall s s', Compare lt eq s s'.
   Proof.
-   intros s s'. generalize (M.compare_spec s s').
-   destruct (M.compare s s'); simpl; intros.
-   constructor 2; auto.
-   constructor 1; auto.
-   constructor 3; auto.
+   intros s s'.
+   assert (H := M.compare_spec s s').
+   destruct (M.compare s s'); [ apply EQ | apply LT | apply GT ];
+    inversion H; auto.
   Defined.
 
 End Backport_Sets.
@@ -407,7 +406,7 @@ Module Update_Sets
     | GT _ => Gt
    end.
 
-  Lemma compare_spec : forall s s', Cmp eq lt (compare s s') s s'.
+  Lemma compare_spec : forall s s', Cmp eq lt s s' (compare s s').
   Proof. intros; unfold compare; destruct M.compare; auto. Qed.
 
 End Update_Sets.