Definition PS_plus (a b : nat -> V) (n : nat) : V := plus (a n)  (b n).

(* Specifications: *)
Lemma is_pseries_plus (a b : nat -> V) (x :K) (la lb : V) : is_pseries a x la -> is_pseries b x lb -> is_pseries (PS_plus a b) x (plus la lb).
Lemma ex_pseries_plus (a b : nat -> V) (x : K) : ex_pseries a x -> ex_pseries b x -> ex_pseries (PS_plus a b) x.
Lemma PSeries_plus (a b : nat -> R) (x : R) : ex_pseries a x -> ex_pseries b x -> PSeries (PS_plus a b) x = PSeries a x + PSeries b x.
Lemma CV_disk_plus (a b : nat -> R) (x : R) : (CV_disk a x) -> (CV_disk b x) -> (CV_disk (PS_plus a b) x).
Lemma CV_radius_plus (a b : nat -> R) : Rbar_le (Rbar_min (CV_radius a) (CV_radius b)) (CV_radius (PS_plus a b)).