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I'm working on an exam, and have a solid proof for one of the problems, but it's reliant on a number of theorems left exercises in the textbook which were not assigned as coursework. What, if any convention is there for using those results in later proofs?

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This would be a good question to ask your instructor. –  Robert Israel Dec 16 '11 at 7:54
    
I already have, waiting on a reply. I was just curious to see if there was some established rule here. –  Drew Christianson Dec 16 '11 at 7:59
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Since you basically ask for an opinion, here's mine: I'd expect to see evidence that the exercises were actually solved by you. That is: at least an outline of the solution if not a full proof, or a reference to a different text where proofs are given. –  t.b. Dec 16 '11 at 8:07
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A long time ago, I took a take-home exam (in a graduate course) in which one question was of the form "Prove or disprove: A". One of my fellow students turned in an answer which said "Problem x.yz of our textbook asks us to prove or disprove B. Assuming B is true, the following is a proof that A is true. ..... Assuming B is false, the following is a proof that A is false." He got extra credit (and an A+ grade) for creativity. –  Dilip Sarwate Dec 16 '11 at 13:58
    
you should probably prove it, and since you asked your instructor, s/he probably assumes you havent proven it (else you would have just included a proof) and s/he will make you prove it. –  yoyo Dec 16 '11 at 14:57
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