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Sniffnoy comments on Beauty quips, "I'd shut up and multiply!" - Less Wrong
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Lemma 1 is wrong. -h=(-1/2)m, m=2h. So your two lemmas are just saying the same thing.
I agree. I should have used a computer algebra program ;) I've revised my post so that it's correct. It's funny to me that I let slip a computation error that happened to accidentally give me the result I expected.