I'm reading this paper http://image.diku.dk/igel/paper/AItRBM-proof.pdf and I got stuck in page 4 with equation (1) that's based on Hammersley–Clifford theorem. I'm not good in reading set theory notation and also I wasn't able to understand the point from the equation.
I couldn't understand what are $x_c$ and $\hat{x}_c$
Here's the section, I'm stuck just at equation (1):