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).

Lemma add_Add : forall x s, !!(add x s) === Add _ (!!s) x.