Module Type DivideNotation (A:NZOrdAxiomsSig')(B:Gcd A)(C:NZGcdSpec A B).
Notation "( n | m )" := (divide n m) (at level 0).
End DivideNotation.
Module Type NZGcd (A : NZOrdAxiomsSig) := Gcd A <+ NZGcdSpec A.
Module Type NZGcd' (A : NZOrdAxiomsSig) :=
Gcd A <+ NZGcdSpec A <+ DivideNotation A.
(** Derived properties of gcd *)
Module NZGcdProp
(Import A : NZOrdAxiomsSig')
(Import B : NZGcd' A)
(Import C : NZMulOrderProp A).
(** Results concerning divisibility*)
#[global]
Instance divide_wd : Proper (eq==>eq==>iff) divide.

Lemma eq_mul_1_nonneg' : forall n m,
0<=m -> n*m == 1 -> n==1 /\ m==1.