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

Lemma sub_mod_0: forall (a b m: nat), a mod m = 0 -> b mod m = 0 -> (a - b) mod m = 0.