# What is a “lemma”? [duplicate]

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?

• Sure, unless it is obvious. – André Nicolas Oct 1 '13 at 1:20
• – anon Oct 1 '13 at 1:21
• 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. – manthanomen Oct 1 '13 at 1:24
• 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. – Baby Dragon Oct 1 '13 at 1:35
• 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. – manthanomen Oct 1 '13 at 1:53