John, you wrote
> $$ \Phi(x,y) = I \otimes \mathcal{X}(x,x) \le \mathcal{X}(x,x) \otimes \Phi(x,y) $$
in your proof of the last Lemma. Did you actually mean
$$ \Phi(x,y) = I \otimes \Phi(x,y) \le \mathcal{X}(x,x) \otimes \Phi(x,y) $$
or is there something I'm missing?
> $$ \Phi(x,y) = I \otimes \mathcal{X}(x,x) \le \mathcal{X}(x,x) \otimes \Phi(x,y) $$
in your proof of the last Lemma. Did you actually mean
$$ \Phi(x,y) = I \otimes \Phi(x,y) \le \mathcal{X}(x,x) \otimes \Phi(x,y) $$
or is there something I'm missing?
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