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You got my meaning. I have a bad habit of under-explaining things.

As far as the second part goes, I'm wary of the math. While I would imagine that your argument would tend to work out much of the time, it certainly isn't a proof, and Bayes' Theorem doesn't deal with the respective complexity of the canonical events A and B except to say that they are each more probable individually than separately. Issues of what is meant by the complexity of the events also arise. I suspect that if your assertion was easy to prove, then it would have been proven by now and mentioned in the main entry.

Thus, while Occam's razor may follow from Bayes' theorem in certain cases, I am far from satisfied that it does for all cases.

No, because you can't say anything about the relationship of P(A) in comparison to P(C|D)

"Those who find this confusing may find it helpful to study mathematical logic, which trains one to make very sharp distinctions between the proposition P, a proof of P, and a proof that P is provable"

This is a bit of a side question, but wouldn't a proof that P is provable be a proof of P? In fact, it sounds like a particularly elegant form of proof.