That description is really only valid for Ffestiniog mines, or mines where the angle of the vein supports that method.
In the Corris area mines, where the vein is nearly vertical, the method is very different. This is my understanding:
A shaft is dug between two levels, and a crane erected at the top to allow material to be lowered. A working floor is opened out around the top of the shaft, and gradually worked down. When it reached the bottom of the shaft, a new shaft was dug, and the process repeated. In this way you get huge vertical chambers descending many hundreds of feet, with pulley blocks hung from the ceilings in what now appear to be the most inacessible places!
Chris.
P.S. I stand to be corrected.