Cayley's theorem
In the mathematical field of order theory, an inclusion order is the partial order that arises as the subset-inclusion relation on some collection of objects. In a simple way, every poset "P" = ("X",≤) is (isomorphic to) an inclusion order (just as every group is isomorphic to a permutation group – see Cayley's theorem). To see this, associate to each element "x" of "X" the set