apply divides_le; auto.
apply sym_not_eq; auto with arith.
Qed.
(********************************************************************)
Inductive prime : nat -> Prop :=
primeDef :
forall a : nat,
a <> 1 -> (forall b : nat, divides b a -> b <> 1 -> a = b) -> prime a.

Lemma not_prime_1 : ~ prime 1.
Hint Resolve div_ref all_divides_O SO_divides_all not_prime_O not_prime_1.