Definition rel_prime_dec: forall a b,
 { rel_prime a b }+{ ~ rel_prime a b }.Definition prime_dec_aux:
 forall p m,
  { forall n, 1 < n < m -> rel_prime n p } +
  { exists n, 1 < n < m  /\ ~ rel_prime n p }.Definition prime_dec: forall p, { prime p }+{ ~ prime p }.

Theorem not_prime_divide: forall p, 1 < p -> ~ prime p -> exists n, 1 < n < p /\ (n | p).