intros H3; absurd (x * y < 0)%R; auto with real.
apply Rle_not_lt;apply Rle_sign_pos_pos; auto with real.
Qed.

Theorem Rlt_sign_neg_pos_rev: forall x y: R, (x < 0 -> x * y < 0 ->  0 < y)%R.
intros x y H1 H2; case (Rle_or_lt y 0); auto with real.