intros F n.
red in |- *.
intro.
simpl in |- *.
red in |- *.
intro i.
simpl in |- *.
auto with algebra.
Qed.
Definition Fn_group (F : group) (n : Nat) : GROUP :=
Build_group
(Build_group_on (group_inverse_map:=Fn_inv F n)
(Fn_inv_is_r_inverse (F:=F) (n:=n))
(Fn_inv_is_l_inverse (F:=F) (n:=n))).
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(* Once more, Abel spoke... *)
(****************************)

Lemma Fn_group_is_abelian :
forall (F : abelian_group) (n : Nat), abelian_group_on (Fn_group F n).