Definition
Plain language
A small helper result proved on the way to proving a bigger one.
As stated in the literature
An auxiliary proposition established as a stepping stone toward a main theorem; automated proof-search systems decompose a hard goal into lemmas they can close and reassemble.
Also called: lemmas
Why it matters: Breaking a hard proof into provable lemmas makes it tractable, which is exactly how automated proof systems tackle difficult goals.
For example, before proving a big theorem, a mathematician might first prove a small lemma that a certain quantity is always positive.
Heard on the show
“The system produced a clean proof of a lemma he needed, and his reaction was that the aesthetic style of the proofs was the best he'd gotten from any model.”Episode 029 — Why Forty-Eight Percent on FrontierMath Isn't the Real Story in DeepMind's New Math Paper