Definition PS_scal_r (c : R) (a : nat -> R) (n : nat) : R :=
a n * c.

(* Specifications: *)
Lemma PSeries_scal_r (c : R) (a : nat -> R) (x : R) :
PSeries (PS_scal_r c a) x = PSeries a x * c.
Lemma CV_disk_scal_r (c : R) (a : nat -> R) (x : R) :
(CV_disk a x)
-> (CV_disk (PS_scal_r c a) x).
Lemma CV_radius_scal_r (c : R) (a : nat -> R) : c <> 0 ->
(CV_radius (PS_scal_r c a)) = (CV_radius a).