case (Z_gt_le_dec 0 0).
intros z; try assumption.
absurd (0 > 0)%Z; auto with *.
intros z; try assumption.
case (Z_le_lt_eq_dec 0 0 z).
intros z0; try assumption.
absurd (0 < 0)%Z; auto with *.
auto with *.
Qed.
Hint Resolve Zl1: algebra.

Lemma ax3 : forall p : positive, (Zpos p > 0)%Z.
intros p; try assumption.