  The reason is the following. Recall that the derivation of FUNC established uniqueness of the new observable f(Q) only in its final step (via NC). It is this uniqueness which guarantees that one operator represents exactly one observable so that observables (and thereby their values) in different contexts can be equated. This allows one to establish indirect connections between different incompatible observables. Without this final step, FUNC must be viewed as holding relative to different contexts, the connection is broken and FUNC is restricted to one set of observables which are all mutually compatible.  Then indeed FUNC, the Sum Rule and the Product Rule become trivial, and empirical testing in these cases would be a pointless   question.[16]  It is NC that does all the work and deserves to be tested via checking whether for incompatible P, Q such that f(Q)=g(P) it is true that v(f(Q))=v(g(P)). However, though QM and a noncontextual HV theory contradict each other for a single system, this contradiction involves incompatible observables and, thus, is untestable (as we have just seen from Kochen and Specker’s own proposal). Physicists have, however, made ingenious proposals for overcoming this obstacle. It is well-known that the consideration of two-particle systems and products of spin components leads to very simple KS-type proofs (Mermin 1990b). Cabello and Garcìa-Alcaine (1998) have shown that for such systems QM and a noncontextual HV theory make different predictions for every single case. Their reasoning makes no reference to locality considerations, but as it requires two particles, such considerations might creep in. Simon et al. (2000), have mapped the Cabello/Garcìa-Alcaine scheme onto a combination of position and spin observables for a single particle. Their experiment has been carried out and has confirmed the QM predictions (Huang et al. 2003; see also more recently Huang et al. 2013). All the mentioned authors consider their experimental proposals to be empirical refutations of NC, but this has been doubted (Barrett and Kent 2004), for reasons considered in the next paragraph.