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

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