 The order dual is contained in the order bound dual.If the positive cone of an ordered vector space "X" is generating and if for all positive "x" and "y" we have [0, "x"] + [0, "y"] = [0, "x" + "y"], then the order dual is equal to the order bound dual, which is an order complete vector lattice under its canonical ordering.The order dual of a vector lattice is an order complete vector lattice.