intros H3; absurd (x * y <= 0)%R; auto with real.
apply Rlt_not_le;apply Rlt_sign_pos_pos; auto.
Qed.

(* Specifications: *)
Theorem Rle_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 0 y); auto with real.
Theorem Rle_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 0 y); auto with real.