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- Identify the assumptions and goals of the theorem.
- Understand the implications of each of the assumptions
made. Translate them into mathematical definitions if you can.
- Either try to massage the definitions and theorems that you
identified in (2) into the statement you are trying to
prove, or, if that fails
- Make an assumption about what you are trying to prove and show
that it leads to a proof or a contradiction.
The last two items are the only two possible ways to convert your
assumptions into proof. These and other possible techniques for
proving theorems will be discussed in more detail in the next section.