(** We show F(J)=A\Img(B\Imf(J))=J *)
(** First left-to-right inclusion *)
(** Lemma: J_is_in_FJ (Included U J (F J))  *)

(** Then right-to-left inclusion *)
(** Lemma: FJ_is_in_J (Included U (F J) J)  *)
Lemma FJ_is_in_J : Included U (F J) J.
Inductive h (x y : U) : Prop :=
| hl_intro : In U J x -> f x y -> h x y
| hr_intro : Setminus U B (Imf J) y -> g y x -> h x y.