Definition PS_decr_n (a : nat -> V) (n k : nat) : V := a (n + k)%nat.

Lemma ex_pseries_decr_n (a : nat -> V) (n : nat) (x : K) : (x = zero \/ exists y, mult y x = one) -> ex_pseries a x -> ex_pseries (PS_decr_n a n) x.