intros p; try assumption.
unfold Z_to_group_nat_fun in |- *.
case (Z_gt_le_dec (Zpos p) 0); intros z.
simpl in |- *; auto with *.
case (Z_le_lt_eq_dec (Zpos p) 0 z); intros.
absurd (Zpos p < 0)%Z; auto with *.
inversion e.
Qed.
Hint Resolve Zl2: algebra.

(* Specifications: *)
Lemma ax4 : forall p : positive, ~ (Zneg p > 0)%Z.
intros p; red in |- *.