(** * 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 untiln_prod_not_0modp : forall p n : nat, 0 < n -> n < p -> Prime p -> ~ Mod (zproduct (until n)) 0 p.