lemma-discovery-assistant
From the author
Analyze failed or stuck proofs and propose auxiliary lemmas to help complete the proof in Isabelle/HOL or Coq. Use when encountering proof failures, stuck proof states, unprovable subgoals, or when needing to strengthen induction hypotheses. Identifies missing lemmas, suggests proof strategies, and generates helper lemmas with appropriate statements and proof sketches. Supports inductive proofs, case analysis, rewriting, and complex proof obligations.
Install
npx skills add ArabelaTso/Skills-4-SE --skill lemma-discovery-assistant -a claude-code
Installs to .claude/skills/lemma-discovery-assistant/ · Each command fetches the skill straight from GitHub with the open skills CLI.
Byte-identical to the scanned commit, with the repository’s licence and a SOURCE.txt.
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Similar skills
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- library-advisorArabelaTso/Skills-4-SERecommend relevant Isabelle/HOL or Coq standard library theories, lemmas, and tactics based on proof goals. Use when: (1) Users need library lemmas for their proof, (2) Proof goals match standard library patterns, (3) Users ask what libraries to import, (4) Specific lemmas are needed for list/set/arithmetic operations, (5) Users are stuck and need to know what library support exists, or (6) Guidance on find_theorems/Search commands is needed. Supports both Isabelle/HOL and Coq standard libraries.Planning★ 258
- tactic-suggestion-assistantArabelaTso/Skills-4-SEAnalyze proof states in Isabelle or Coq and suggest applicable tactics to make progress. Use when users need help with: (1) Choosing the next tactic in an interactive proof, (2) Understanding what tactics apply to their current goal, (3) Getting unstuck in a proof, (4) Learning which tactics work for specific goal structures (conjunctions, implications, induction, etc.). Provides 3-5 ranked tactic suggestions with explanations for intermediate-level proofs in both Isabelle/Isar and Coq.Planning★ 258
- proof-failure-explainerArabelaTso/Skills-4-SEAnalyze and explain why Isabelle or Coq proofs fail, identifying the root cause such as type mismatches, missing assumptions, incorrect goals, unification failures, or inapplicable tactics. Use when the user encounters proof failures, error messages in formal verification, stuck proof states, or asks why their Isabelle/Coq proof doesn't work.Other★ 258
- proof-skeleton-generatorArabelaTso/Skills-4-SEGenerate structured proof skeletons with tactics, strategies, and intermediate lemmas for theorems in Isabelle/HOL or Coq. Use when users need to: (1) Create proof outlines for theorem statements, (2) Generate proof structure with tactic placeholders, (3) Identify key lemmas needed for a proof, (4) Plan proof strategies (induction, case analysis, forward/backward reasoning), (5) Scaffold proofs with intermediate steps and subgoals, or (6) Convert theorem statements into detailed proof templates. Supports both Isabelle/HOL and Coq equally.Planning★ 258
- proof-refactoring-assistantArabelaTso/Skills-4-SERestructure and improve Isabelle or Coq proofs to enhance readability, modularity, and maintainability without changing semantics. Use when proofs are long and monolithic, have repeated patterns, use unclear naming, lack documentation, or when the user asks to refactor, clean up, improve, or reorganize their formal proofs.Engineering★ 258
- counterexample-debuggerArabelaTso/Skills-4-SEDebug proof failures using counterexamples from Nitpick (Isabelle) or QuickChick (Coq) to identify specification errors, missing preconditions, and proof strategy issues. Use when: (1) A proof attempt fails and you need to understand why, (2) Counterexamples are generated by Nitpick or QuickChick, (3) Specifications may be incorrect or incomplete, (4) Theorems need validation before proving, (5) Missing preconditions or lemmas need identification, or (6) Proof failures need explanation and correction suggestions. Supports both Isabelle/HOL and Coq equally.Engineering★ 258
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