apply Rmult_lt_0_compat; auto with real.
Qed.

(* Specifications: *)
Theorem Rlt_pos_neg: forall x, (0 < -x -> x < 0)%R.
intros x H; rewrite <- (Ropp_involutive 0);  rewrite <- (Ropp_involutive x); auto with real.
Theorem Rge_sign_neg_neg: forall x y, (0 >= x -> 0 >= y  -> x * y >= 0)%R.
intros; apply Rle_ge; apply Rle_sign_neg_neg; auto with real.
Theorem Rlt_pos_neg: forall x, (0 < -x -> x < 0)%R.
intros x H; rewrite <- (Ropp_involutive 0);  rewrite <- (Ropp_involutive x); auto with real.
Theorem Rge_sign_neg_neg: forall x y, (0 >= x -> 0 >= y  -> x * y >= 0)%R.
intros; apply Rle_ge; apply Rle_sign_neg_neg; auto with real.