# Is it possible to reference Lemmas inside another Lemma?

number0

## Homework Statement

Is it possible to reference Lemmas inside another Lemma?

That is, while you are trying to prove a lemma, you refer to another lemma you have just proven. Is this accepted?

None.

None.

## Answers and Replies

Homework Helper
Yes, its fine. If it's happening too much though, you might want to reconsider what you are calling theorems and what are lemmas, as the lemmas are meant to be the simpler, preliminary results to be used for the proofs of theorems.

Staff Emeritus
Gold Member
Math books use the terms "proposition", "theorem", "lemma" and "corollary", but they all refer to theorems. They're just used in slightly different contexts.

Lemma: A theorem that isn't particularly interesting on its own, but is used in the proof of a more interesting theorem.

Theorem: Sometimes reserved for theorems of a greater significance than most.

Proposition: What most theorems are called if the author likes to use the word "theorem" only for the fancy ones.

Corollary: A theorem that's easy to prove if we use the theorem(s) we just proved.