intros H3; absurd (x * y <= 0)%Z; auto with zarith.
apply Zlt_not_le;apply Zlt_sign_neg_neg; auto.
Qed.

Theorem Zge_sign_pos_pos_rev: forall x y: Z, (x > 0 -> x * y >= 0 -> y >= 0)%Z.
intros x y H1 H2; apply Z.le_ge; apply Zle_sign_pos_pos_rev with x; auto with zarith.