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

Lemma mod2sub: forall a b, b <= a -> mod2 (a - b) = xorb (mod2 a) (mod2 b).