Definition Fn_sgroup (F : sgroup) (n : Nat) : SGROUP :=
  Build_sgroup (Build_sgroup_on (Fn_plus_associative (F:=F) (n:=n))).

(* Specifications: *)
Lemma Fn_plus_commutative : forall (F : abelian_sgroup) (n : Nat), commutative (Fn_plus F n).