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 *)

Lemma Abel (a : nat -> R) :
Rbar_lt 0 (CV_radius a) -> Rbar_lt (CV_radius a) p_infty
-> ex_pseries a (CV_radius a)
-> filterlim (PSeries a) (at_left (CV_radius a)) (locally (PSeries a (CV_radius a))).