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

Lemma minus_minus: forall a b c, c <= b <= a -> a - (b - c) = a - b + c.