Definition:Lemma

Definition

A lemma (plural: lemmas or lemmata) 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."

Also see

Not to be confused with Lemmy, who would not be classed as a second-class citizen in the aristocracy of anything.