Definition Fn_abmon (F : abelian_monoid) (n : Nat) : ABELIAN_MONOID :=
  Build_abelian_monoid (Fn_monoid_is_abelian F n).Definition Fn_inv :
  forall (F : group) (n : Nat), Map (Fn_monoid F n) (Fn_monoid F n).

Lemma Fn_inv_is_r_inverse : forall (F : group) (n : Nat), inverse_r (Fn_plus F n) (Fn_zero F n) (Fn_inv F n).