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.
Lemma PSeries_scal (c : R) (a : nat -> R) (x : R) : PSeries (PS_scal c a) x = c * PSeries a x.
Lemma CV_disk_scal (c : R) (a : nat -> R) (x : R) : (CV_disk a x) -> (CV_disk (PS_scal c a) x).
Lemma CV_radius_scal (c : R) (a : nat -> R) : c <> 0 -> (CV_radius (PS_scal c a)) = (CV_radius a).