(** * Operations *)
(** Addition of two power series *)
Section PS_plus.
Context {K : AbsRing} {V : NormedModule K}.
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.