Lemma

How it is used

Common in university lecture notes and research papers: 'We first prove a lemma', 'By Lemma 2.1, …'. A corollary, by contrast, is a result that follows easily from a theorem. Some famous lemmas, such as Zorn's lemma, are major results in their own right.

Example sentences

1. The proof becomes much shorter if we first prove a lemma about even numbers.

2. By Lemma 3, the sequence is bounded.

Common collocations

• prove a lemma
• by the lemma
• lemma and corollary
• technical lemma

Related terms

• theoremAn important mathematical statement that has been proved to be true, such as the Pythagorean theorem.
• proofA logical argument that shows, step by step from accepted facts, that a mathematical statement is always true.
• QEDShort for the Latin 'quod erat demonstrandum', meaning 'which was to be shown'; written at the end of a proof to show that it is complete.
• it follows thatA linking phrase used in proofs and solutions to show that the next statement is a logical result of what has just been shown.

More terms: Proofs and Mathematical Writing

• let x be
• counterexample
• proof by contradiction
• proof by induction
• without loss of generality