(** Convergence theorems *)

(* Specifications: *)
Lemma CV_disk_inside (a : nat -> R) (x : R) :
Rbar_lt (Finite (Rabs x)) (CV_radius a)
-> ex_series (fun n => Rabs (a n * x ^ n)).
Lemma CV_radius_inside (a : nat -> R) (x : R) :
Rbar_lt (Finite (Rabs x)) (CV_radius a)
-> ex_pseries a x.
Lemma CV_disk_outside (a : nat -> R) (x : R) :
Rbar_lt (CV_radius a) (Finite (Rabs x))
-> ~ is_lim_seq (fun n => a n * x ^ n) 0.
Lemma CV_radius_ext (a b : nat -> R) :
(forall n, a n = b n) -> CV_radius a = CV_radius b.