apply lt_not_le; apply mult_lt_compat_l; auto.
Qed.

Theorem mult_ge_compat_rev_l: forall n m p : nat, p * n >= p * m -> 0 < p -> n >= m.
intros n m p H H1; case (le_or_lt m n); auto with arith; intros H2; absurd (p * n >= p * m); auto with arith.