# Definition:Lemma

## Contents

## 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.

## Linguistic Note

The plural of **lemma** is either **lemmas** or **lemmata**.

## Also see

## Sources

- 1972: A.G. Howson:
*A Handbook of Terms used in Algebra and Analysis*... (previous) ... (next): $\S 1$: Some mathematical language: Axiom systems