proposition: Lemma pow_inj_r : forall a b c, 1<a -> 0<=b -> 0<=c -> a^b == a^c -> b == c.
proof: Proof. intros a b c Ha Hb Hc EQ. destruct (lt_trichotomy b c) as [LT|[EQ'|GT]]; trivial. - assert (a^b < a^c) by (apply pow_lt_mono_r; try split; trivial). order. - assert (a^c < a^b) by (apply pow_lt_mono_r; try split; trivial). order. Qed.
imports: NZAxioms NZMulOrder