# Definition:Lemma

## Definition

A lemma is a statement which is proven during the course of reaching the proof of a theorem.

Logically there is no qualitative difference between a lemma and a theorem.

They are both statements whose value is either true or false.

However, a lemma is seen more as a stepping-stone than a theorem in itself (and frequently takes a lot more work to prove than the theorem to which it leads).

Some lemmas are famous enough to be named after the mathematician who proved them (for example: Abel's Lemma and Urysohn's Lemma), but they are still categorised as second-class citizens in the aristocracy of mathematics.

Always the lemma, never the theorem.

## Linguistic Note

The plural of lemma is either lemmas or lemmata.