(** * The list of integers between 1 and n (inclusive) *)

Fixpoint until (n : nat) : Zlist :=
  match n with
  | O => Nil Z
  | S n => Cons Z (Z_of_nat (S n)) (until n)
  end.

Lemma until_mapmult_exp : forall (a : Z) (n : nat), zproduct (mapmult a (until n)) = (Exp a n * zproduct (until n))%Z.