(* 2 at the n *)
(**************)

Fixpoint two_power (m : nat) : nat :=
  match m with
  | O => 1
  | S n => two * two_power n
  end.

Lemma holes_in_powers : forall n z : nat, two_power n < z -> z < two_power (S n) -> forall p : nat, z <> two_power p.