intros n m p H1 H2; replace (p * n)%R with (-(-p * n))%R; auto with real; try ring.
replace (p * m)%R with (-(-p * m))%R; auto with real;try ring.
Qed.

(* Specifications: *)
Theorem Ropp_gt: forall n m, (m > n -> -n > -m)%R.
auto with real.
Theorem Ropp_gt: forall n m, (m > n -> -n > -m)%R.
auto with real.