Module Type NZDivSpec (Import A : NZOrdAxiomsSig')(Import B : DivMod' A).
Declare Instance div_wd : Proper (eq==>eq==>eq) div.
Declare Instance mod_wd : Proper (eq==>eq==>eq) modulo.

Axiom div_mod : forall a b, b ~= 0 -> a == b*(a/b) + (a mod b).
Axiom mod_bound_pos : forall a b, 0<=a -> 0<b -> 0 <= a mod b < b.