Definition CV_radius (a : nat -> R) : Rbar :=
  Lub_Rbar (CV_disk a).

Lemma CV_radius_Reals_2 (a : nat -> R) (x : R) : Rbar_lt (Finite (Rabs x)) (CV_radius a) -> exists r : posreal, CVU (fun n x => sum_f_R0 (fun k => a k * x ^ k) n) (PSeries a) x r.