Notation pow2 := (Nat.pow 2).Fixpoint Npow2 (n : nat) : N :=
  match n with
    | O => 1
    | S n' => 2 * Npow2 n'
  end%N.

Lemma Zabs_of_nat: forall n, Z.abs (Z.of_nat n) = Z.of_nat n.