(** * 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))).