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

(* Specifications: *)
Theorem Rge_sign_pos_pos_rev: forall x y: R, (x > 0 -> x * y >= 0 -> y >= 0)%R.
intros x y H1 H2; apply Rle_ge; apply Rle_sign_pos_pos_rev with x; auto with real.
Theorem Rge_sign_pos_pos_rev: forall x y: R, (x > 0 -> x * y >= 0 -> y >= 0)%R.
intros x y H1 H2; apply Rle_ge; apply Rle_sign_pos_pos_rev with x; auto with real.