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)).

(* Specifications: *)
Lemma is_pseries_minus (a b : nat -> V) (x:K) (la lb : V) :
is_pseries a x la -> is_pseries b x lb
-> is_pseries (PS_minus a b) x (plus la (opp lb)).
Lemma ex_pseries_minus (a b : nat -> V) (x : K) :
ex_pseries a x -> ex_pseries b x
-> ex_pseries (PS_minus a b) x.