intros p; try assumption.
unfold Z_to_group_nat_fun in |- *.
case (Z_gt_le_dec (Zneg p) 0); intros z.
absurd (Zneg p > 0)%Z; auto with *.
case (Z_le_lt_eq_dec (Zneg p) 0 z); intros.
simpl in |- *; auto with *.
inversion e.
Qed.
Hint Resolve Zl3: algebra.

Lemma ax5 :
forall p q : positive,
(Zpos p > Zpos q)%Z -> (Zpos p + Zneg q)%Z = Zpos (p - q).