Proof: Assume roundnis the first time where O violates E, that is, he references some roundn−isuch thati≠ 1. Assume further that this is the first time that roundn−ihas been referenced. Now, look at round (n−i)+1. What move does O reference here? If it is notn−i, then, contra assumption, round n is not the first round where E has been violated. If it isn−i, then, contra assumption, roundnis not the first round wheren−iis 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:

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