I'm having trouble understanding something that was in lectures on set theory. Unfortunately I am not experienced enough in latex to be able to write it out, so have attached a pdf.
(page 10) I am struggling with the theorem:
Theorem 3.1.8. Let A be any set. Then to each equivalence relation R on A there
corresponds a partition PR, and to each partition P of A there corresponds an equivalence relation RP.
If anyone could help me understand the proof I would be most grateful. I get to about line 5 before I just loose track of whats going on completely.