intros p q; case p; case q; simpl in |- *; auto with arith;
try (intros; discriminate); intros q1 p1.
intros H1; rewrite (Pcompare_Eq_eq p1 q1); auto.
unfold Pos.compare.
generalize (Pcompare_Eq_eq p1 q1);
case (Pcompare p1 q1 Datatypes.Eq); simpl in |- *;
intros H H1; try discriminate; rewrite H; auto.
Qed.

Theorem Zlt_Zopp : forall x y : Z, (x < y)%Z -> (- y < - x)%Z.
intros x y; case x; case y; simpl in |- *; auto with zarith; intros p p0;
unfold Zlt in |- *; simpl in |- *; unfold Pos.compare; rewrite <- ZC4;
auto.