unfold injective in |- *.
intros A B f f' H' H'0 x y H'1; try assumption.
apply H'.
apply Trans with (Ap f' x); auto with algebra.
apply Trans with (Ap f' y); auto with algebra.
Qed.

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