Module MP:= WProperties_fun 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 remove_Subtract : forall x s, !!(remove x s) === Subtract _ (!!s) x.