#[global]
Instance divide_reflexive : Reflexive divide | 5 := divide_refl.#[global]
Instance divide_transitive : Transitive divide | 5 := divide_trans.

Lemma gcd_unique : forall n m p, 0<=p -> (p|n) -> (p|m) -> (forall q, (q|n) -> (q|m) -> (q|p)) -> gcd n m == p.