Mine shafts on earth are limited in how deep they can go by two things, internal heat and rock pressure. The deepest mine on Earth currently is just under 4 kilometers.

There is internal heat on the moon caused by tidal pressures, but it is very deep. The motion core is a tiny portion of the whole compared to the earth. With ⅙th G gravity, I wonder how deep you could go before rock pressure got higher than the compressive strength of the rock? I'm guessing pretty far.
My question is; how deep could a lunar mine go before heat or rock pressure made it impractical?