Wait, I am missing something here. If the reduction to a true statement is done through operations that can be performed in both direction (which are most of the trivial operations undergrads use) then this is a perfectly fine approach, right?
Even if all facts used in the proof are true "in both directions", it's still a serious breach of modern mathematical style to start with what you're trying to prove.
It's also possible that they don't explicitly note that the facts they're using are "true in both directions". edit: to be explicit, in that case I'd still consider the proof wrong
Anyways, if a student presented a proof like that, I would at least take a couple points off for the awkward style unless it was explicitly justified somehow.
It's also kind of a weird proof technique to start with 0=0 or 1=1 and bother to explicitly state this fact...
It saddens me that so little of what goes in in math papers makes it into textbooks, or math students that do not study original papers themselves.
Obviously, it's a matter of style. I still maintain few mathematicians would write canonical discrete math style induction proofs in reverse order.
But then, a mathematician would totally not write out induction proofs the same way we teach in freshman discrete math courses.
So in some sense the style question is completely irrelevant, and what matters is that the student's answer demonstrates unambiguously an understaning of the concept.
I can't now remember the specifics of a particular paper because I have seen so many, but the main thing is they believed that if they arrive at some fact that happens to be true then their original hypothesis must be true. It is a classic affirming the consequent fallacy, just shrouded in lots of sophisticated symbol manipulations.