proposition: Lemma log2_le_mono : forall a b, a<=b -> log2 a <= log2 b.
proof: Proof. intros a b H. destruct (le_gt_cases a 0) as [Ha|Ha]. - rewrite log2_nonpos; order_pos. - assert (Hb : 0 < b) by order. destruct (log2_spec a Ha) as (LEa,_). destruct (log2_spec b Hb) as (_,LTb). apply lt_succ_r, (pow_lt_mono_r_iff 2); order_pos. Qed.
imports: NZAxioms NZMulOrder NZPow