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

Theorem mod2_pow2_twice: forall n, mod2 (pow2 n + (pow2 n + 0)) = false.