proposition: Theorem mul_le_mono_pos_l : forall n m p, 0 < p -> (n <= m <-> p * n <= p * m).
proof: Proof. intros n m p H; do 2 rewrite lt_eq_cases. rewrite (mul_lt_mono_pos_l p n m) by assumption. now rewrite -> (mul_cancel_l n m p) by (intro H1; rewrite H1 in H; false_hyp H lt_irrefl). Qed.
imports: NZAxioms NZAddOrder