intros n m p H H1; case (Zle_or_lt n m); auto; intros H2.
absurd (p * n < p * m)%Z; auto with zarith.
apply Zle_not_lt; apply Zmult_le_neg_compat_l; auto with zarith.
Qed.

Theorem Zmult_ge_compat_l_rev:
forall n m p : Z, (p > 0)%Z -> (p * n >= p * m)%Z -> (n >= m)%Z.