proposition: Lemma log2_spec : forall n, 0<n -> 2^(log2 n) <= n /\ n < 2^(succ (log2 n)).
proof: Proof. intros n. zify. change (Z.log2 [n]+1)%Z with (Z.succ (Z.log2 [n])). apply Z.log2_spec. Qed.
imports: ZArith OrdersFacts Nnat NAxioms NSig Lia