Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: König's lemma | Statement: [Julius König, notableWork, König's lemma]

Target entity: König's lemma
Context triple: [Julius König, notableWork, König's lemma]

• A. Kruskal's tree theorem
  Kruskal's tree theorem is a fundamental result in combinatorics and mathematical logic stating that finite trees are well-quasi-ordered under homeomorphic embedding, with deep implications in proof theory and computer science.
• B. Ky Fan’s lemma
  Ky Fan’s lemma is a combinatorial topological result that generalizes Tucker’s lemma and provides conditions guaranteeing the existence of certain balanced or fully labeled simplices in labeled triangulations of spheres or simplices.
• C. Bailey lemma
  The Bailey lemma is a key result in the theory of basic hypergeometric series that provides a systematic method for generating Rogers–Ramanujan-type identities and other q-series relations.
• D. Robbins lemma
  Robbins lemma is a result in probability theory that provides a bound on the expected maximum of partial sums of independent random variables, named after mathematician Herbert Robbins.
• E. Knaster–Kuratowski–Mazurkiewicz lemma
  The Knaster–Kuratowski–Mazurkiewicz lemma is a fundamental result in combinatorial topology that guarantees the existence of a point common to a family of closed sets covering a simplex under certain intersection conditions, and underlies several fixed-point theorems.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: König's lemma
Target entity description: König's lemma is a fundamental result in graph theory and logic stating that every finitely branching infinite tree has an infinite path.

• A. Kruskal's tree theorem
  Kruskal's tree theorem is a fundamental result in combinatorics and mathematical logic stating that finite trees are well-quasi-ordered under homeomorphic embedding, with deep implications in proof theory and computer science.
• B. Ky Fan’s lemma
  Ky Fan’s lemma is a combinatorial topological result that generalizes Tucker’s lemma and provides conditions guaranteeing the existence of certain balanced or fully labeled simplices in labeled triangulations of spheres or simplices.
• C. Bailey lemma
  The Bailey lemma is a key result in the theory of basic hypergeometric series that provides a systematic method for generating Rogers–Ramanujan-type identities and other q-series relations.
• D. Robbins lemma
  Robbins lemma is a result in probability theory that provides a bound on the expected maximum of partial sums of independent random variables, named after mathematician Herbert Robbins.
• E. Knaster–Kuratowski–Mazurkiewicz lemma
  The Knaster–Kuratowski–Mazurkiewicz lemma is a fundamental result in combinatorial topology that guarantees the existence of a point common to a family of closed sets covering a simplex under certain intersection conditions, and underlies several fixed-point theorems.
• F. None of above. chosen