#[global]
Instance union_ok s1 s2 : forall `(Ok s1, Ok s2), Ok (union s1 s2).
(** * Filter *)

(* Specifications: *)
Lemma filter_spec : forall s x f,
Proper (X.eq==>Logic.eq) f ->
(InT x (filter f s) <-> InT x s /\ f x = true).
Lemma filter_weak_spec : forall s x f,
InT x (filter f s) -> InT x s.