Definition Fn_absgp (F : abelian_sgroup) (n : Nat) : ABELIAN_SGROUP :=
  Build_abelian_sgroup
    (Build_abelian_sgroup_on (A:=Fn_sgroup F n)
       (Fn_plus_commutative (F:=F) (n:=n))).(******************************************************)
(* It is a monoid, Jim, but... exactly as we know it. *)
(******************************************************)

Definition Fn_zero : forall (F : monoid) (n : Nat), Fn_sgroup F n.

Lemma Fn_zero_is_r_unit : forall (F : monoid) (n : Nat), unit_r (sgroup_law_map (Fn_sgroup F n)) (Fn_zero F n).