Definition

Noun: 1. Lemma: In mathematics and logic, a lemma is a proven statement or proposition that is used as a stepping stone to prove a larger, more important theorem. It is a minor, auxiliary result. 2. Subsidiary proposition; auxiliary theorem: A helping theorem or a preliminary proposition that is used in the process of proving a main theorem.

Usage Examples

• Noun:
  • Nhà toán học đã sử dụng một bổ đề quan trọng để chứng minh định lý chính. (The mathematician used an important lemma to prove the main theorem.)
  • Trước khi chứng minh, chúng ta cần thiết lập một vài bổ đề. (Before proving it, we need to establish a few lemmas.)
  • Bạn có thể nhớ lại bổ đề Zorn không? (Can you recall Zorn's lemma?)

Advanced Usage

• "Bổ đề bơm": Pumping Lemma (a specific lemma in the theory of formal languages and automata).
  • Bổ đề bơm được dùng để chứng minh một ngôn ngữ không phải là chính quy. (The Pumping Lemma is used to prove a language is not regular.)
• "Bổ đề Gauss": Gauss's Lemma (a lemma in number theory and polynomial theory).
• "Bổ đề Urysohn": Urysohn's Lemma (a fundamental lemma in topology).

Variants and Related Words

• Định lý (n): Theorem. A major statement that has been proven true based on axioms and other theorems (and often lemmas).
• Hệ quả (n): Corollary. A proposition that follows directly and obviously from a theorem or lemma that has already been proven.
• Mệnh đề (n): Proposition. A declarative statement that is either true or false, often used as a general term for theorems, lemmas, etc.

Synonyms

• Mệnh đề phụ: Subsidiary proposition.
• Định lý phụ: Auxiliary theorem.

Related Phrases / Idioms

(This is a technical academic term, so common idioms or phrasal verbs are not typically associated with it. Its usage is almost exclusively in formal, logical, or mathematical contexts.)

noun

1. Lemma