Section inverses_comp_def.
Variable x y : Inverses_setoid.
Definition Inv_comp_elt_l := Inv_elt_l x +_M Inv_elt_l y.
Definition Inv_comp_elt_r := Inv_elt_r y +_M Inv_elt_r x.
Canonical Structure Inverses_comp : Inverses_setoid :=
Build_Inverses Inv_comp_invs1 Inv_comp_invs2.
End inverses_comp_def.

Lemma Inverses_congl : Map2_congl_law Inverses_comp.