unfold comp_map_map in |- *; simpl in |- *.
unfold Map_eq in |- *; simpl in |- *; auto with algebra.
Qed.
Hint Resolve Id_unit_r: algebra.

Lemma Id_unit_l :
forall (A B : Setoid) (f : MAP A B), Equal (comp_map_map (Id B) f) f.