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

Lemma Inverses_invr : Group_invr Opposite_map.
Canonical Structure Inverses_group := Build_Group Inverses_invl Inverses_invr.