proposition: Lemma bijective_comp : forall (A B : Setoid) (f f' : MAP A B), bijective f -> Equal f f' -> bijective f'.
proof: Proof. unfold bijective in |- *. intros A B f f' H' H'0; try assumption. split; [ try assumption | idtac ]. elim H'; intros H'1 H'2; try exact H'1; clear H'. apply injective_comp with (f := f); auto with algebra. elim H'; intros H'1 H'2; try exact H'2; clear H'. apply surjective_comp with (f := f); auto with algebra. Qed.