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

Theorem Rgt_sign_pos_pos_rev: forall x y: R, (x > 0 -> x * y > 0 -> y > 0)%R.
intros x y H1 H2; red; apply Rlt_sign_pos_pos_rev with x; auto with real.