Section PS_minus.
Context {K : AbsRing} {V : NormedModule K}.
Definition PS_minus (a b : nat -> V) (n : nat) : V := plus (a n) (opp (b n)).
End PS_minus.
(** ** Abel's theorem for power series *)
(** * Analysis *)
(** ** Continuity *)
(** ** Differentiability *)
Definition PS_derive (a : nat -> R) (n : nat) :=
INR (S n) * a (S n).

Lemma is_derive_PSeries (a : nat -> R) (x : R) :
Rbar_lt (Finite (Rabs x)) (CV_radius a)
-> is_derive (PSeries a) x (PSeries (PS_derive a) x).