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As per title, what is a "lemma"? How is it different from "theorem"?

ASAIK, I have to prove a self-proposed theorem in my paper. Do I also have to provide the proof for a self-proposed lemma?

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    $\begingroup$ Sure, unless it is obvious. $\endgroup$ – André Nicolas Oct 1 '13 at 1:20
  • $\begingroup$ Usually you would prove a lemma before the proof of a theorem if using the result from the lemma makes the theorem's proof more elegant and easier to follow. And you can't state the lemma without proof unless it's a well-established result. $\endgroup$ – manthanomen Oct 1 '13 at 1:24
  • $\begingroup$ Another use notion that I have not seen too often is a workhorse lemma. This is a lemma that becomes important because it is needed for lots of theorems. $\endgroup$ – Baby Dragon Oct 1 '13 at 1:35
  • $\begingroup$ I would probably call such a result (the "workhorse lemma" to which Baby Dragon refers) a proposition (or even a theorem). The point to take away here is that while terminology is subjective, any proposed statement must be proved. $\endgroup$ – manthanomen Oct 1 '13 at 1:53
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Short answer, they are the same, and yes, you need to prove it. From Wikipedia

There is no formal distinction between a lemma and a theorem, only one of intention – see Theorem terminology.

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