Qed.
(* Theorems to simplify the goal 0 ? x * y and x * y ? 0 where ? is < > <= >= *)

(* Specifications: *)
Theorem Zle_sign_pos_pos: forall x y: Z, (0 <= x -> 0 <= y  -> 0 <= x * y)%Z.
auto with zarith.
Theorem Rle_sign_pos_pos: forall x y, (0 <= x -> 0 <= y  -> 0 <= x * y)%R.
intros x y H; apply Rmult_le_pos; auto with real.