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

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