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

Lemma even_odd_destruct: forall n, (exists a, n = 2 * a) \/ (exists a, n = 2 * a + 1).