intros.
intro.
unfold pointwise in |- *.
simpl in |- *.
apply Ap_comp; auto with algebra.
Qed.

(* Specifications: *)
Lemma pointwise_comp :
forall (n : Nat) (B C D : Setoid) (op op' : Map (cart B C) D)
(f f' : seq n B) (g g' : seq n C),
op =' op' in MAP _ _ ->
f =' f' in _ -> g =' g' in _ -> pointwise op f g =' pointwise op' f' g' in _.