Fixpoint digits2_pos (n : positive) : positive :=
  match n with
  | xH => xH
  | xO p => Psucc (digits2_pos p)
  | xI p => Psucc (digits2_pos p)
  end.

(* Specifications: *)
Theorem Zpos_digits2_pos : forall m : positive, Zpos (digits2_pos m) = Zdigits radix2 (Zpos m).