simpl in |- *.
rewrite Z.pos_sub_spec; unfold Pos.compare.
replace (Pcompare p p Datatypes.Eq) with Datatypes.Eq.
auto with *.
elim p.
intros p0; simpl in |- *.
auto with *.
intros p0; simpl in |- *.
auto with *.
simpl in |- *.
auto with *.
Qed.
Hint Resolve ax7 ax6 ax5: algebra.

Lemma nat_to_group_com2 :
forall n m : nat,
Equal (sgroup_law G (nat_to_group n) (nat_to_group m))
(sgroup_law G (nat_to_group m) (nat_to_group n)).