unfold surjective in |- *.
intros A B f f' H' H'0 y; try assumption.
elim (H' y); intros x E; try exact E.
exists x; try assumption.
apply Trans with (Ap f x); auto with algebra.
Qed.

Lemma bijective_comp :
forall (A B : Setoid) (f f' : MAP A B),
bijective f -> Equal f f' -> bijective f'.