intros H'; try assumption.
inversion H'.
intros p H'; try assumption.
replace 0%Z with (- (0))%Z.
apply Zlt_gt; auto with algebra.
auto with algebra.
intros p H'; try assumption.
replace 0%Z with (- (0))%Z.
apply Zlt_gt; auto with algebra.
auto with algebra.
Qed.
Hint Resolve Zopp1: algebra.

Lemma Zopp2 : forall n : Z, (n > 0)%Z -> (- n < 0)%Z.
simple induction n.