(* Ugly tacty to resolve sign condition for R *)
Require Export RGroundTac.
(* Theorems to simplify the goal 0 ? x * y and x * y ? 0 where ? is < > <= >= *)
intros x y H; apply Rmult_le_pos; auto with real.
Qed.
intros x y H1 H2; replace (x * y)%R with (-x * -y)%R; auto with real; try ring.
apply Rmult_le_pos; auto with real.
Qed.

Theorem Rle_pos_neg: forall x, (0 <= -x -> x <= 0)%R.