CompareSpec: a slight generalization/reformulation of CompSpec

 CompareSpec expects 3 propositions Peq Plt Pgt instead of 2 relations
 eq lt and 2 points x y. For the moment, we still always use (Peq=eq x y),
 (Plt=lt x y) (Pgt=lt y x), but this may not be always the case,
 especially for Pgt. The former CompSpec is now defined in term of
 CompareSpec. Compatibility is preserved (except maybe a rare unfold
 or red to break the CompSpec definition).

 Typically, CompareSpec looks nicer when we have infix notations, e.g.

  forall x y, CompareSpec (x=y) (x<y) (y<x) (x?=x)

 while CompSpec is shorter when we directly refer to predicates:

  forall x y, CompSpec eq lt x y (compare x y)

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13914 85f007b7-540e-0410-9357-904b9bb8a0f7

3 files changed, 3 insertions, 3 deletions

diff --git a/theories/Numbers/Integer/SpecViaZ/ZSigZAxioms.v b/theories/Numbers/Integer/SpecViaZ/ZSigZAxioms.v
index cf38adf3a..fe0e6567e 100644
--- a/theories/Numbers/Integer/SpecViaZ/ZSigZAxioms.v
+++ b/theories/Numbers/Integer/SpecViaZ/ZSigZAxioms.v
@@ -138,7 +138,7 @@ Qed.
 
 (** Order *)
 
-Lemma compare_spec : forall x y, CompSpec eq lt x y (compare x y).
+Lemma compare_spec : forall x y, CompareSpec (x==y) (x<y) (y<x) (compare x y).
 Proof.
  intros. zify. destruct (Zcompare_spec [x] [y]); auto.
 Qed.
diff --git a/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v b/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v
index cef8c3819..bff52fb37 100644
--- a/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v
+++ b/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v
@@ -126,7 +126,7 @@ Qed.
 
 (** Order *)
 
-Lemma compare_spec : forall x y, CompSpec eq lt x y (compare x y).
+Lemma compare_spec : forall x y, CompareSpec (x==y) (x<y) (y<x) (compare x y).
 Proof.
  intros. zify. destruct (Zcompare_spec [x] [y]); auto.
 Qed.
diff --git a/theories/Numbers/Rational/SpecViaQ/QSig.v b/theories/Numbers/Rational/SpecViaQ/QSig.v
index a4f0dbce1..29e1e795a 100644
--- a/theories/Numbers/Rational/SpecViaQ/QSig.v
+++ b/theories/Numbers/Rational/SpecViaQ/QSig.v
@@ -135,7 +135,7 @@ Program Instance power_wd : Proper (eq==>Logic.eq==>eq) power.
 
 (** Let's implement [HasCompare] *)
 
-Lemma compare_spec : forall x y, CompSpec eq lt x y (compare x y).
+Lemma compare_spec : forall x y, CompareSpec (x==y) (x<y) (y<x) (compare x y).
 Proof. intros. qify. destruct (Qcompare_spec [x] [y]); auto. Qed.
 
 (** Let's implement [TotalOrder] *)