 As we said before, some properties of systems are local properties, with only some of the components of the systems being relevant in determining whether they hold or not. That a monitoring situation is one where the plane is moving North depends only on the plane, not on the screen. In general, if a property is completely determined by subset of components \(\mathbf{x}\) then, in what concerns that property, any two global states that agree on \(\mathbf{x}\) should be indistinguishable. In fact, each such \(\mathbf{x}\) induces an equivalence relation of local property determination so that for every two global states \(\mathbf{s}, \mathbf{t}\): 