# difference between theorem, lemma and corollary

Can anybody explain what is the basic difference between theorem, lemma and corollary. We have been using it for a long time but I never paid any attention. I am just curious to know.Thanks a lot.

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Lemmas are smaller results to be used in a bigger (more important) result. The big result is usually a theorem. Corollaries are special cases of theorems. –  Cameron Williams Aug 9 '13 at 5:23
@CameronWilliams... Oh.... thanks a lot. Your reply in few words cleared my doubt :) –  monalisa Aug 9 '13 at 5:24
I'm glad I could help :) –  Cameron Williams Aug 9 '13 at 5:25
@Cameron is, of course, correct but let me add that lemmas needn't always be small results. Typically, they are but some results such as Urysohn's lemma could also be referred to as theorems. See, e.g., math.stackexchange.com/questions/111428/lemma-vs-theorem for additional discussion. –  Amitesh Datta Aug 9 '13 at 5:33

Lemma is generally used to describe a "helper" fact that is used in the proof of a more significant result.

Significant results are frequently called theorems.

Short, easy results of theorems are called corollaries.

But the words aren't exactly that set in stone.

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@T.Bongers... thanks a lot for clearing it in a very efficient way. –  monalisa Aug 9 '13 at 5:26

A lot of authors like to use lemma to mean "small theorem." Often a group of lemmas are used to prove a larger result, a "theorem."

A corollary is something that follows trivially from any one of a theorem, lemma, or other corollary.

However, when it boils down to it, all of these things are equivalent as they denote the truth of a statement.

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Thanks a lot for timely reply. –  monalisa Aug 9 '13 at 5:26
I want to stress that calling something a lemma, theorem, or corollary is purely a choice made for organizational purposes. That's probably the most important thing to take away from my answer: a lemma is just as true as a theorem! –  par Aug 9 '13 at 5:27
thanks for making it very clear to me –  monalisa Aug 9 '13 at 5:33

A lemma are those minor results which are used into proving a definite results of a theorem.

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