(* Ugly tacty to resolve sign condition for Z *)
Require Export NatGroundTac.
intros n m p H H1; repeat rewrite (mult_comm p); apply mult_lt_compat_r; auto.
Qed.
intros n m p H; auto with arith.
Qed.

Theorem mult_gt_compat_l: forall n m p : nat, n > m -> p > 0 -> p * n > p * m.