(** Primality *)
Inductive prime (p : Z) : Prop :=
prime_intro :
(1 < p)%Z -> (forall n : Z, (1 <= n < p)%Z -> rel_prime n p) -> prime p.
(** The sole divisors of a prime number [p] are [-1], [1], [p] and [-p]. *)

Lemma prime_divisors :
forall p : Z,
prime p ->
forall a : Z, (a | p)%Z -> a = (-1)%Z \/ a = 1%Z \/ a = p \/ a = (- p)%Z.