Please bear with my unhelpful typesetting. Link of the FLP paper is below.
https://groups.csail.mit.edu/tds/papers/Lynch/jacm85.pdf
While discussing Lemma 3- authors make an assumption I am unable to understand.
The assumptions are -
1) There exist two neighbour configurations C0 and C1 both from set C (which contains configurations on which event e was never applied). So far so good. Till this part we never discuss about valency of C0 and C1.
2) Next assumption is - From C0 taking e causes to go to D0 while from C1 taking an e causes to go to D1.
3) D0 and D1 do not have same valency. (Both are not 0-valent/1-valent simultaneously)
The proof of lemma goes on and uses commutative property to prove that set D is bivalent.
While I have no problem with rest of proof, I am failing to understand why all three parts of the assumptions should be considered consistent to each other. It is these assumptions (especially 2 and 3) that lead to contradiction. I don't see any
connection between earlier part of proof and these assumptions.
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