(** Scalar multiplication *)
Section PS_scal.
Context {K : AbsRing} {V : NormedModule K}.
Definition PS_scal (c : K) (a : nat -> V) (n : nat) : V := scal c (a n).

(* Specifications: *)
Lemma is_pseries_scal (c : K) (a : nat -> V) (x : K) (l : V) :
mult x c = mult c x -> is_pseries a x l -> is_pseries (PS_scal c a) x (scal c l).
Lemma ex_pseries_scal (c : K) (a : nat -> V) (x : K) :
mult x c = mult c x -> ex_pseries a x -> ex_pseries (PS_scal c a) x.