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.
(* Theorem to simplify a hyp x * y ? x * z where ? is < > <= >= *)

(* Specifications: *)
Theorem Rmult_le_compat_l_rev:
forall n m p : R, (0 < p)%R -> (p * n <= p * m)%R -> (n <= m)%R.
Theorem Rmult_le_compat_l_rev:
forall n m p : R, (0 < p)%R -> (p * n <= p * m)%R -> (n <= m)%R.