(** * 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_prod_not_0mod :
forall p : nat, Prime p -> ~ Mod (zproduct (until (pred p))) 0 p.