Module Type NZGcdSpec (A : NZOrdAxiomsSig')(B : Gcd A).
Definition divide n m := exists p, m == p*n.
Local Notation "( n | m )" := (divide n m) (at level 0).

Axiom gcd_divide_l : forall n m, (gcd n m | n).
Axiom gcd_divide_r : forall n m, (gcd n m | m).
Axiom gcd_greatest : forall n m p, (p | n) -> (p | m) -> (p | gcd n m).
Axiom gcd_nonneg : forall n m, 0 <= gcd n m.