Fixpoint int_of_one_bits' (l: list Int.int) : int :=
  match l with
  | nil => zero
  | a :: b => add (shl' one a) (int_of_one_bits' b)
  end.

Theorem mul_pow2': forall x n logn, is_power2' n = Some logn -> mul x n = shl' x logn.