Recently on Marilyn's discussion boards...

From Gofer:

"So the lemma actually reduces to the case of B=T."
" No, it really doesn't."

Yes it really does, because we can split B into two cases: B=T and B is a proper subset of T, where, for the second one, the lemma follows immediately due to the definition of a proper subset.

So in this case, it turns out that proof by negation (not contradiction) and proof by contrapostive are actually one and the same.