Supplement to The Kochen-Specker Theorem
STAT FUNC from FUNC
Indeed, STAT FUNC follows immediately from FUNC. Given A, f, and |φ> as defined in FUNC, we have:
v(f(A))|φ> = f(v(A))|φ>,
where f(A) is a new observable. Now, by the statistical algorithm:
STAT FUNC: Given A, f, and φ as defined in FUNC, then, for an arbitrary real number b:prob[v(f(A))|φ> = b] = prob[f(v(A))|φ> = b]