red in |- *.
intros.
simpl in |- *.
red in |- *.
intro i.
simpl in |- *.
apply SGROUP_assoc.
Qed.
Definition Fn_sgroup (F : sgroup) (n : Nat) : SGROUP :=
Build_sgroup (Build_sgroup_on (Fn_plus_associative (F:=F) (n:=n))).
(*****************************************************)
(* And there was an sgroup, and Abel saw it was good *)
(*****************************************************)

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