apply Rmult_le_pos; auto with real.
Qed.

Theorem Rle_sign_neg_pos: forall x y, (x <= 0 -> 0 <= y  -> x * y <= 0)%R.
intros x y H1 H2; apply Rle_pos_neg; replace (- (x * y))%R with (-x * y)%R; auto with real; try ring.