Module MP:= WPropertiesOn U M.
Definition mkEns : M.t -> Ensemble M.elt :=
fun s x => M.In x s.
Notation " !! " := mkEns.
Notation " a === b " := (Same_set M.elt a b) (at level 70, no associativity).
(** we can even build a function from Finite Ensemble to MSet ... at least in Prop. *)

Lemma Ens_to_MSet : forall e : Ensemble M.elt, Finite _ e ->
exists s:M.t, !!s === e.