End id_map_def.
(* composition of two Maps *)
Section mcomp.
Variables (A B C : Setoid) (f : Map A B) (g : Map B C).
Definition Comp_fun (x : A) := g (f x).

Lemma Comp_fun_map_law : Map_law Comp_fun.
Canonical Structure Comp_map : Map A C := Comp_fun_map_law.