(** Primality *)

Inductive prime (p : Z) : Prop :=
    prime_intro :
      (1 < p)%Z -> (forall n : Z, (1 <= n < p)%Z -> rel_prime n p) -> prime p.(** Primality *)

Inductive prime (p : Z) : Prop :=
    prime_intro :
      (1 < p)%Z -> (forall n : Z, (1 <= n < p)%Z -> rel_prime n p) -> prime p.

(* Specifications: *)
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.
Lemma prime_rel_prime : forall p : Z, prime p -> forall a : Z, ~ (p | a)%Z -> rel_prime p a.