Now one can go even further and define orders where arbitrary joins distribute over arbitrary meets. Such structures are called completely distributive lattices. However, expressing this requires formulations that are a little more technical. Consider a doubly indexed family {"x""j","k" | "j" in "J", "k" in "K"("j")} of elements of a complete lattice, and let "F" be the set of choice functions "f" choosing for each index "j" of "J" some index "f"("j") in "K"("j"). A complete lattice is completely distributive if for all such data the following statement holds: