Canonical Structure Inverses_Monoid :=
  Build_Monoid Mass_Inverses Midl_Inverses Midr_Inverses.(* opposite operation *)

Definition Opposite (x : Inverses_setoid) : Inverses_setoid :=
  Build_Inverses (Prf_invs2 x) (Prf_invs1 x).

Lemma Opposite_map_law : Map_law Opposite.