unfold comp_map_map in |- *; simpl in |- *.
unfold Map_eq in |- *; simpl in |- *; auto with algebra.
unfold comp_map_fun in |- *.
auto with algebra.
Qed.
Hint Resolve comp_map_comp: algebra.
Comments "Composition is associative:".

Lemma comp_map_assoc :
forall (A B C D : Setoid) (f : MAP A B) (g : MAP B C) (h : MAP C D),
Equal (comp_map_map h (comp_map_map g f))
(comp_map_map (comp_map_map h g) f).