intros p q H'; red in H'.
simpl in H'.
simpl in |- *.
rewrite Z.pos_sub_spec.
rewrite H'.
auto with *.
Qed.

(* Specifications: *)
Lemma ax6 :
forall p q : positive,
(Zpos p < Zpos q)%Z -> (Zpos p + Zneg q)%Z = Zneg (q - p).
Lemma ax7 : forall p : positive, (Zpos p + Zneg p)%Z = 0%Z.
intros p; try assumption.