  The key ingredients of the KS theorem are the constraints on value assignments spelled out in (2): the Sum Rule and Product Rule. They can be derived from a more general principle, called the Functional Composition Principle  (FUNC).[11]  The principle trades on the mathematical fact that for a self-adjoint operator A operating on a Hilbert space, and an arbitrary function f:  R→R (where R is the set of the real numbers), we can define f(A) and show that it also is a self-adjoint operator (hence, we write f(A)). If we further assume that to every self-adjoint operator there corresponds a QM observable, then the principle can be formulated thus: