A lemma is a small theorem. It is proved true, but its main purpose is to help prove something larger. Lemmas are the scaffolding of mathematical arguments. They break a big proof into manageable pieces.

Euclid's lemma states that if a prime divides a product of two integers, it divides at least one of them. That lemma is essential for proving the fundamental theorem of arithmetic. Zorn's lemma, a more advanced example, is used to prove the existence of maximal ideals and bases in infinite-dimensional spaces.

Sometimes a lemma becomes famous in its own right. Gauss's lemma, Fatou's lemma, and Urysohn's lemma all carry names and appear in textbooks. The distinction between lemma, proposition, theorem, and corollary is partly stylistic. A lemma is a helper; a theorem is the main result.

• Proven statement used to prove a theorem
• Breaks large proofs into steps
• Examples: Euclid's lemma, Zorn's lemma
• Sometimes becomes famous independently