(** * 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_allex : forall (p : nat) (a : Z), Prime p -> ~ Mod a 0 p -> allex p (until (pred p)) (mapmult a (until (pred p))).