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/FMapAVL.v b/theories/FSets/FMapAVL.v
index 6e4c4b26f..b7947cddd 100644
--- a/theories/FSets/FMapAVL.v
+++ b/theories/FSets/FMapAVL.v
@@ -1070,6 +1070,10 @@ Proof.
 Qed.
 Hint Resolve elements_sort.
 
+Lemma elements_nodup : forall s : t elt, bst s -> NoDupA eqk (elements s).
+Proof.
+ intros; apply Sort_NoDupA; auto.
+Qed.
 
 (** * Fold *)
 
@@ -1816,6 +1820,9 @@ Module IntMake (I:Int)(X: OrderedType) <: S with Module E := X.
  Lemma elements_3 : forall m, sort lt_key (elements m).  
  Proof. intros m; exact (@Raw.elements_sort elt m.(this) m.(is_bst)). Qed.
 
+ Lemma elements_3w : forall m, NoDupA eq_key (elements m).  
+ Proof. intros m; exact (@Raw.elements_nodup elt m.(this) m.(is_bst)). Qed.
+
  Definition Equal cmp m m' := 
    (forall k, In k m <-> In k m') /\ 
    (forall k e e', MapsTo k e m -> MapsTo k e' m' -> cmp e e' = true).