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

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