Revision of the FSetWeak Interface, so that it becomes a precise

subtype of the FSet Interface (and idem for FMapWeak / FMap). 

1) No eq_dec is officially required in FSetWeakInterface.S.E
(EqualityType instead of DecidableType). But of course,
implementations still needs this eq_dec. 

2) elements_3 differs in FSet and FSetWeak (sort vs. nodup). In
FSetWeak we rename it into elements_3w, whereas in FSet we
artificially add elements_3w along to the original elements_3.

Initial steps toward factorization of FSetFacts and FSetWeakFacts, 
and so on...

Even if it's not required, FSetWeakList provides a eq_dec on sets, 
allowing weak sets of weak sets. 





git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10271 85f007b7-540e-0410-9357-904b9bb8a0f7

1 files changed, 7 insertions, 0 deletions

diff --git a/theories/FSets/FMapPositive.v b/theories/FSets/FMapPositive.v
index c3bdc773b..7bf944b85 100644
--- a/theories/FSets/FMapPositive.v
+++ b/theories/FSets/FMapPositive.v
@@ -166,6 +166,7 @@ Qed.
 Module PositiveMap <: S with Module E:=PositiveOrderedTypeBits.
 
   Module E:=PositiveOrderedTypeBits.
+  Module ME:=KeyOrderedType E.
 
   Definition key := positive.
 
@@ -788,6 +789,12 @@ Module PositiveMap <: S with Module E:=PositiveOrderedTypeBits.
   apply xelements_sort; auto.
   Qed.
 
+  Lemma elements_3w : NoDupA eq_key (elements m).
+  Proof.
+  change eq_key with (@ME.eqk A).
+  apply ME.Sort_NoDupA; apply elements_3; auto.
+  Qed.
+
   End FMapSpec.
 
   (** [map] and [mapi] *)