This is a real baby proof, but I'm not sure I'm doing the well ordering proof right, as its my first attempt.
Is this the basic structure of a well ordering proof?
Thanks in advance.
I feel as though you are way overdoing it. Let . Assume that , then by the well-ordering principle has a least element . Thus, . Dividing both sides we see that . This contradicts the minimality of and thus it follows that .