Outline compactness proofs for convergent subsequences in Lean 4 templates.
npx skills add https://github.com/bneb/perqed --skill compactness-arguments
Please help me install this Agent Skill. Skill: compactness_arguments Source: https://github.com/bneb/perqed/tree/main/.agents/skills/compactness_arguments Command: npx skills add https://github.com/bneb/perqed --skill compactness-arguments
Compactness arguments let you deduce global conclusions from local properties, enabling proofs that rely on finite subcovers, convergent subsequences, or compactness theorems.
Outline a compactness-based proof that a sequence in a compact set has a convergent subsequence.
High-intent search queries and answers about installing and using this skill.
Structure your convergent subsequence proof by applying sequential compactness to extract limit points, or use Heine-Borel to derive a finite subcover that forces global convergence from local topology.
A compactness argument deduces global conclusions from local properties by extracting finite subcovers or convergent subsequences, enabling proofs for maxima, uniform continuity, and convergence in analysis.
You can use formal templates to structure Lean 4 proofs by applying Heine-Borel and sequential compactness strategies that satisfy formalization requirements for convergence and extraction tasks.
Apply Heine-Borel to a compact domain to extract a finite subcover, translating local topological estimates into global convergence conclusions and maxima extraction for analysis proofs.
You need compactness theorems when proving uniform continuity, extracting maxima, or establishing convergence on compact domains where local estimates must yield global conclusions in analysis and logic.
Sequential compactness works for finding maxima on compact domains by proving a sequence in a compact set has a convergent subsequence, establishing the existence of extreme values.
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