(** * 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.