Well, i tried hard to read the converse of the proof and i guess they are using some so-called procedure and tricks to make the proof work. However i can't figure out how it works. Can someone show how the tricks work and explain why it works? thx in advance for your help.
Edited: What i am confused with is starting from the sentence in the proof of the converse "As in the previous example, let girl $m+1$ may personally only know boys.......I don't quite understand they way it prove it with that method.