Fixpoint PS_incr_n (a : nat -> V) (n k : nat) : V :=
  match n with
    | O => a k
    | S n => PS_incr_1 (PS_incr_n a n) k
  end.

Lemma ex_pseries_incr_n (a : nat -> V) (n : nat) (x : K) : ex_pseries a x -> ex_pseries (PS_incr_n a n) x.