intros p q H'; try assumption.
apply nat_of_P_gt_Gt_compare_complement_morphism.
red in |- *.
apply nat_of_P_lt_Lt_compare_morphism; auto with *.
Qed.
Hint Resolve ax8: algebra.

Lemma Zl4 :
forall p p0 : positive,
Equal (Z_to_group_nat_fun (Zpos p + Zneg p0)%Z)
(sgroup_law G (nat_to_group (nat_of_P p))
(group_inverse G (nat_to_group (nat_of_P p0)))).