Definition:Lemma

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 take 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), but they are still categorised as second-class citizens in the aristocracy of mathematics.

"Always the lemma, never the theorem."