proposition: Lemma pow_lt_mono_l_iff : forall a b c, 0<=a -> 0<=b -> 0<c -> (a<b <-> a^c < b^c).
proof: Proof. intros a b c Ha Hb Hc. split; intro LT. - apply pow_lt_mono_l; try split; trivial. - destruct (le_gt_cases b a) as [LE|GT]; trivial. assert (b^c <= a^c) by (apply pow_le_mono_l; try split; order). order. Qed.
imports: NZAxioms NZMulOrder