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Lean 4 theorem proving toolkit: search lemmas, verify proofs, repair/simplify code, and get LLM-assisted informal proofs
用 Codex 或 Claude 帮你安装 复制这段 Prompt，粘贴到 Codex、Claude 或其他助手里，让它检查 Skill 页面并帮你完成安装。
基于 SOC 职业分类
A no-op skill used only by the agent-capability tests to confirm a harness can mount and invoke a skill. Has no real behavior; invoke it when asked to during a capability probe.
Use when editing .lean files, debugging Lean 4 builds (type mismatch, sorry, failed to synthesize instance, axiom warnings, lake build errors), searching mathlib for lemmas, formalizing mathematics in Lean, or learning Lean 4 concepts. Also trigger when the user asks for help with Lean 4, mathlib, or lakefile. Do NOT trigger for Coq/Rocq, Agda, Isabelle, HOL4, Mizar, Idris, Megalodon, or other non-Lean theorem provers.
Code transformation tools for repairing, simplifying, and extracting Lean proofs
LLM-assisted tools for informal proofs, proof strategy discussion, and code simplification
Search tools for finding Lean theorems, lemmas, and definitions in Mathlib
Isolates failing proof steps by replacing them with `sorry` and extracting them into standalone lemmas to modularize and decouple complex Lean 4 proofs.
| name | numina-lean-agent |
| description | Lean 4 theorem proving toolkit: search lemmas, verify proofs, repair/simplify code, and get LLM-assisted informal proofs |
| Skill | Description |
|---|---|
| search | Search tools: leanexplore, loogle, leanfinder, leansearch, state-search, hammer-premise |
| verification | Verification: lean-check, verify-proof, disprove |
| code-transform | Code transforms: repair-proofs, simplify-theorems, sorry2lemma, extract-theorems |
| llm | LLM tools: informal_prover, discussion_partner, code_golf |
GEMINI_API_KEY — informal_prover (gemini generation, gemini verifier, gemini refinement), code_golf, discussion_partner (gemini)OPENAI_API_KEY — informal_prover (gpt generation, gpt verifier), discussion_partner (gpt)ANTHROPIC_API_KEY — informal_prover (claude verifier)AXLE_API_KEY — axle commands (verify-proof, disprove, sorry2lemma, etc.)