Module NZGcdProp
(Import A : NZOrdAxiomsSig')
(Import B : NZGcd' A)
(Import C : NZMulOrderProp A).
(** Results concerning divisibility*)
Instance divide_wd : Proper (eq==>eq==>iff) divide.
Instance divide_reflexive : Reflexive divide | 5 := divide_refl.
Instance divide_transitive : Transitive divide | 5 := divide_trans.
(** Due to sign, no general antisymmetry result *)
(** Basic properties of gcd *)

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.