Follow-up concerning eqb / ltb / leb comparisons

 - All statement using reflect are made transparent.
   (Otherwise, since reflect isn't in Prop, extraction
    complains now about opaque Type definition).

 - remove two local Peqb_spec and Neqb_spec, now provided
   globally as Pos.eqb_spec and N.eqb_spec.

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14232 85f007b7-540e-0410-9357-904b9bb8a0f7

3 files changed, 5 insertions, 5 deletions

diff --git a/theories/Bool/Bool.v b/theories/Bool/Bool.v
index 437ce5726..d5d11ceaa 100644
--- a/theories/Bool/Bool.v
+++ b/theories/Bool/Bool.v
@@ -791,7 +791,7 @@ Qed.
 Lemma iff_reflect : forall P b, (P<->b=true) -> reflect P b.
 Proof.
  destr_bool; intuition.
-Qed.
+Defined.
 
 (** It would be nice to join [reflect_iff] and [iff_reflect]
     in a unique [iff] statement, but this isn't allowed since
@@ -802,7 +802,7 @@ Qed.
 Lemma reflect_dec : forall P b, reflect P b -> {P}+{~P}.
 Proof.
  destruct 1; auto.
-Qed.
+Defined.
 
 (** Reciprocally, from a decidability, we could state a
     [reflect] as soon as we have a [bool_of_sumbool]. *)
diff --git a/theories/Structures/Equalities.v b/theories/Structures/Equalities.v
index 933c4ea0e..eb5373859 100644
--- a/theories/Structures/Equalities.v
+++ b/theories/Structures/Equalities.v
@@ -196,7 +196,7 @@ Qed.
 Lemma eqb_spec x y : reflect (x==y) (x =? y).
 Proof.
 apply iff_reflect. symmetry. apply eqb_eq.
-Qed.
+Defined.
 
 (** Negated form of [eqb_eq] *)
 
diff --git a/theories/Structures/OrdersFacts.v b/theories/Structures/OrdersFacts.v
index a447e8fb5..2e9c0cf56 100644
--- a/theories/Structures/OrdersFacts.v
+++ b/theories/Structures/OrdersFacts.v
@@ -365,7 +365,7 @@ Include CompareBasedOrderFacts E C O.
 Lemma leb_spec0 x y : reflect (x<=y) (x<=?y).
 Proof.
  apply iff_reflect. symmetry. apply leb_le.
-Qed.
+Defined.
 
 Lemma leb_spec x y : BoolSpec (x<=y) (y<x) (x<=?y).
 Proof.
@@ -376,7 +376,7 @@ Qed.
 Lemma ltb_spec0 x y : reflect (x<y) (x<?y).
 Proof.
  apply iff_reflect. symmetry. apply ltb_lt.
-Qed.
+Defined.
 
 Lemma ltb_spec x y : BoolSpec (x<y) (y<=x) (x<?y).
 Proof.