(* 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.
intros n m p H H1; red; apply mult_lt_compat_l; auto.
Qed.

Theorem mult_lt_compat_rev_l1: forall n m p : nat, p * n < p * m -> 0 < p.