Proof: Assume round n is the first time where O violates E, that is, he references some round n−i such that i≠ 1. Assume further that this is the first time that round n−i has been referenced. Now, look at round (n−i)+1. What move does O reference here? If it is not n−i, then, contra assumption, round n is not the first round where E has been violated. If it is n−i, then, contra assumption, round n is not the first round where n−i is referenced. QED.
Thursday, June 23, 2011
Proof of BC 1
I was pretty sure that I had an easy way to prove Bold Conjecture #1, and I ran it by Jesse; all I had to say was "induction + pigeonhole principle" and he essentially rattled off the rest, which was good confirmation for me that my intuition was right. I should probably still write it up in full detail, but essentially, it is this: