intros n m p H H1; case (Rle_or_lt n m); auto; intros H2.
absurd (p * n < p * m)%R; auto with real.
apply Rle_not_lt; apply Rmult_le_neg_compat_l; auto with real.
Qed.

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