intros H'; try assumption.
inversion H'.
intros p H'; try assumption.
replace 0%Z with (- (0))%Z.
apply Zgt_lt; auto with algebra.
auto with algebra.
intros p H'; try assumption.
replace 0%Z with (- (0))%Z.
apply Zgt_lt; auto with algebra.
auto with algebra.
Qed.
Hint Resolve Zopp2: algebra.

Lemma pos_abs_comp :
forall (x : Z) (p p' : (x > 0)%Z), pos_abs p = pos_abs p'.