Definition func_abmon (A : Setoid) (B : abelian_monoid) : ABELIAN_MONOID :=
  Build_abelian_monoid (func_monoid_is_abelian A B).Definition func_inv :
  forall (A : Setoid) (B : group), Map (func_monoid A B) (func_monoid A B).

Lemma func_inv_is_r_inverse : forall (A : Setoid) (B : group), inverse_r (func_plus A B) (func_zerofun A B) (func_inv A B).