intros E R p; try assumption.
red in |- *.
intros y; exists y; try assumption.
simpl in |- *.
elim p.
intros H'; red in H'.
unfold app_rel in H'.
auto with algebra.
Qed.
Section Maps1_3.
Comments "We define the composition of maps:".
Variable E F G : Setoid.
Variable g : MAP F G.
Variable f : MAP E F.
Comments
"First, we define the composition of the functions associated to two maps:"
f "and" g.
Definition comp_map_fun (x : E) := g (f x).
Comments "Then, we proof that the result is compatible with equality:".

(* Specifications: *)
Lemma comp_map_fun_compatible : fun_compatible comp_map_fun.
red in |- *.