  In a 2008 paper, Spekkens improved the traditional notions of non-negativity
of Wigner-style quasi-probability distributions and non-contextuality of
observations. He showed that the two improved notions are equivalent to each
other. Then he proved what he called an even-handed no-go theorem. The paper
contains some minor inaccuracies and one false claim, in the proof of the no-go
theorem. This claim, early in the proof, is used in an essential way in the
rest of the argument. Here we analyze carefully Spekkens's proof of the no-go
theorem, explain the inaccuracies, reduce the task of proving the no-go theorem
to the special case of a single qubit, and then prove the special case. This
gives us a complete proof of Spekkens's no-go theorem.
