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Relsqui comments on Before you start solving a problem - Less Wrong
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I was taught to approach proofs this way. Figure out what you can derive from what you know. If the proof if is possible, one of those threads must approach the intended conclusion.
It also helps to think of statements from which your goal would directly follow, and work backwards. If one of those back-threads meets a forward-thread, you win. Still, I don't like a mechanical approach like that unless I'm certain I'm at a loss for an intuitive understanding of the problem.
Indeed, to both.