(** * Primality *)

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

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

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