Parameter
  surjective_image_full :
    forall (E F : Setoid) (f : MAP E F),
    surjective f -> Equal (image_map f) (full F).

Lemma cardinal_included : forall (E : Setoid) (A : part_set E) (n : nat), cardinal A n -> forall B : part_set E, included B A -> exists m : nat, cardinal B m /\ m <= n.