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

Lemma finite_surjective_injective : forall (E F : Setoid) (f : MAP E F) (n : nat), cardinal (full E) n -> cardinal (full F) n -> surjective f -> injective f.