FLP86's famous proof regarding impossibility of solving consensus in a asynchronous distributed system (even with only a single failure) assumes, in the proof of the third lemma, the existence of an event e', such that the neighbor configurations C0 and C1 can be related as C1 = e'(C0).
I don't get how this is possible, as this seems to me like e' carries out a state transition from a 0-valent configuration to a 1-valent configuration. Further, the proof of case 1 of lemma 3 clearly states that any successor of any 0-valent configuration has to be a 0-valent configuration. What am I missing here?
The answers to this question do not answer the above question. That other question is relates to the proof of existence of C0 and C1 and not that of e'.
