#### 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:GivenA,f, and φ as defined in FUNC, then, for an arbitrary real numberb:prob[v(f(A))^{|φ>}=b] = prob[f(v(A))^{|φ>}=b]