#[global]
Instance filter_ok s f `(H : Ok s) : Ok (filter f s).

(* Specifications: *)
Lemma partition_spec1' s f : (partition f s)#1 = filter f s.
Lemma partition_spec2' s f : (partition f s)#2 = filter (fun x => negb (f x)) s.
Lemma partition_spec1 s f : Proper (X.eq==>Logic.eq) f -> Equal (partition f s)#1 (filter f s).
Lemma partition_spec2 s f : Proper (X.eq==>Logic.eq) f -> Equal (partition f s)#2 (filter (fun x => negb (f x)) s).