proposition: Theorem mul_le_mono_nonneg : forall n m p q, 0 <= n -> n <= m -> 0 <= p -> p <= q -> n * p <= m * q.
proof: Proof. intros n m p q H1 H2 H3 H4. le_elim H2; le_elim H4. - apply lt_le_incl; now apply mul_lt_mono_nonneg. - rewrite <- H4; apply mul_le_mono_nonneg_r; [assumption | now apply lt_le_incl]. - rewrite <- H2; apply mul_le_mono_nonneg_l; [assumption | now apply lt_le_incl]. - rewrite H2; rewrite H4; now apply eq_le_incl. Qed.
imports: NZAxioms NZAddOrder