Lean Formalize
wanshuiyin/Auto-claude-code-research-in-sleep
Develop and verify a mathematical proof in Lean, continue an incomplete Lean project, or audit whether it proves the original statement.
LLM agent for formal theorem proving in Lean 4. An agent skill from wentorai/research-plugins.
MITAuto-check passed
Install Lean Theorem Proving Guide
$ npx skills add wentorai/research-plugins --skill lean-theorem-proving-guide -a claude-codeProject install by default; add -g for ~/.claude/skills/.
$ gh skill install wentorai/research-plugins lean-theorem-proving-guide --agent claude-codeProject scope by default; add --scope user for a personal install. Needs GitHub CLI 2.90.0 or later (public preview).
$ git clone --depth 1 https://github.com/wentorai/research-plugins.git skills-src && mkdir -p .claude/skills && cp -r skills-src/skills/domains/math/lean-theorem-proving-guide .claude/skills/lean-theorem-proving-guide && rm -rf skills-srcUse ~/.claude/skills/ instead of .claude/skills for a personal install. The folder must contain SKILL.md.
Claude Code skills documentation · loads skills from .claude/skills/
Install the "lean-theorem-proving-guide" agent skill from https://github.com/wentorai/research-plugins/tree/main/skills/domains/math/lean-theorem-proving-guide into .claude/skills/lean-theorem-proving-guide/ in this project. Copy the whole folder (SKILL.md and every file beside it), keep the folder name "lean-theorem-proving-guide", then confirm the skill loads.Claude Code copies the folder itself, the same result as the manual copy. Check what it changed before you commit it.
$skill-installer install https://github.com/wentorai/research-plugins/tree/main/skills/domains/math/lean-theorem-proving-guideType this inside Codex. $skill-installer <name> installs a curated skill from openai/skills. The installer writes to $CODEX_HOME/skills (default ~/.codex/skills). Restart Codex if the skill does not show up.
$ npx skills add wentorai/research-plugins --skill lean-theorem-proving-guide -a codexProject install goes to .agents/skills/; add -g for ~/.codex/skills/.
$ gh skill install wentorai/research-plugins lean-theorem-proving-guide --agent codexProject scope by default (.agents/skills/); add --scope user for a personal install.
$ git clone --depth 1 https://github.com/wentorai/research-plugins.git skills-src && mkdir -p .agents/skills && cp -r skills-src/skills/domains/math/lean-theorem-proving-guide .agents/skills/lean-theorem-proving-guide && rm -rf skills-srcUse ~/.agents/skills/ instead of .agents/skills for a personal install.
Codex skills documentation · loads skills from .agents/skills/
Install the "lean-theorem-proving-guide" agent skill from https://github.com/wentorai/research-plugins/tree/main/skills/domains/math/lean-theorem-proving-guide into .agents/skills/lean-theorem-proving-guide/ in this project. Copy the whole folder (SKILL.md and every file beside it), keep the folder name "lean-theorem-proving-guide", then confirm the skill loads.Codex copies the folder itself, the same result as the manual copy. Check what it changed before you commit it.
$ npx skills add wentorai/research-plugins --skill lean-theorem-proving-guide -a cursorProject install goes to .agents/skills/; add -g for ~/.cursor/skills/.
$ gh skill install wentorai/research-plugins lean-theorem-proving-guide --agent cursorProject scope by default (.agents/skills/); add --scope user for a personal install.
$ git clone --depth 1 https://github.com/wentorai/research-plugins.git skills-src && mkdir -p .cursor/skills && cp -r skills-src/skills/domains/math/lean-theorem-proving-guide .cursor/skills/lean-theorem-proving-guide && rm -rf skills-srcUse ~/.cursor/skills/ instead of .cursor/skills for a personal install.
Cursor skills documentation · loads skills from .cursor/skills/, .agents/skills/, .claude/skills/, .codex/skills/
Install the "lean-theorem-proving-guide" agent skill from https://github.com/wentorai/research-plugins/tree/main/skills/domains/math/lean-theorem-proving-guide into .cursor/skills/lean-theorem-proving-guide/ in this project. Copy the whole folder (SKILL.md and every file beside it), keep the folder name "lean-theorem-proving-guide", then confirm the skill loads.Cursor copies the folder itself, the same result as the manual copy. Check what it changed before you commit it.
$ gemini skills install https://github.com/wentorai/research-plugins.git --path skills/domains/math/lean-theorem-proving-guide--scope user (default) or --scope workspace; --path is the subfolder of the repo that holds the skill; --consent skips the security confirmation prompt.
$ npx skills add wentorai/research-plugins --skill lean-theorem-proving-guide -a gemini-cliProject install goes to .agents/skills/; add -g for ~/.gemini/skills/.
$ gh skill install wentorai/research-plugins lean-theorem-proving-guide --agent gemini-cliProject scope by default (.agents/skills/); add --scope user for a personal install.
$ git clone --depth 1 https://github.com/wentorai/research-plugins.git skills-src && mkdir -p .gemini/skills && cp -r skills-src/skills/domains/math/lean-theorem-proving-guide .gemini/skills/lean-theorem-proving-guide && rm -rf skills-srcUse ~/.gemini/skills/ instead of .gemini/skills for a personal install, then run /skills reload.
Gemini CLI skills documentation · loads skills from .gemini/skills/, .agents/skills/
Install the "lean-theorem-proving-guide" agent skill from https://github.com/wentorai/research-plugins/tree/main/skills/domains/math/lean-theorem-proving-guide into .gemini/skills/lean-theorem-proving-guide/ in this project. Copy the whole folder (SKILL.md and every file beside it), keep the folder name "lean-theorem-proving-guide", then confirm the skill loads.Gemini CLI copies the folder itself, the same result as the manual copy. Check what it changed before you commit it.
$ gh skill install wentorai/research-plugins lean-theorem-proving-guideInstalls for Copilot at project scope by default; add --scope user for a personal install. Preview a skill first with gh skill preview. Needs GitHub CLI 2.90.0 or later (public preview).
$ npx skills add wentorai/research-plugins --skill lean-theorem-proving-guide -a github-copilotProject install goes to .agents/skills/; add -g for ~/.copilot/skills/.
$ git clone --depth 1 https://github.com/wentorai/research-plugins.git skills-src && mkdir -p .github/skills && cp -r skills-src/skills/domains/math/lean-theorem-proving-guide .github/skills/lean-theorem-proving-guide && rm -rf skills-srcUse ~/.copilot/skills/ instead of .github/skills for a personal install. Commit .github/skills so cloud agent and code review can use it.
GitHub Copilot skills documentation · loads skills from .github/skills/, .claude/skills/, .agents/skills/
Install the "lean-theorem-proving-guide" agent skill from https://github.com/wentorai/research-plugins/tree/main/skills/domains/math/lean-theorem-proving-guide into .github/skills/lean-theorem-proving-guide/ in this project. Copy the whole folder (SKILL.md and every file beside it), keep the folder name "lean-theorem-proving-guide", then confirm the skill loads.GitHub Copilot copies the folder itself, the same result as the manual copy. Check what it changed before you commit it.
$ npx skills add wentorai/research-plugins --skill lean-theorem-proving-guide -a opencodeOpenCode documents no install command of its own. Project install goes to .agents/skills/; add -g for ~/.config/opencode/skills/.
$ gh skill install wentorai/research-plugins lean-theorem-proving-guide --agent opencodeProject scope by default (.agents/skills/); add --scope user for a personal install.
$ git clone --depth 1 https://github.com/wentorai/research-plugins.git skills-src && mkdir -p .opencode/skills && cp -r skills-src/skills/domains/math/lean-theorem-proving-guide .opencode/skills/lean-theorem-proving-guide && rm -rf skills-srcUse ~/.config/opencode/skills/ instead of .opencode/skills for a personal install.
OpenCode skills documentation · loads skills from .opencode/skills/, .claude/skills/, .agents/skills/
Install the "lean-theorem-proving-guide" agent skill from https://github.com/wentorai/research-plugins/tree/main/skills/domains/math/lean-theorem-proving-guide into .opencode/skills/lean-theorem-proving-guide/ in this project. Copy the whole folder (SKILL.md and every file beside it), keep the folder name "lean-theorem-proving-guide", then confirm the skill loads.OpenCode copies the folder itself, the same result as the manual copy. Check what it changed before you commit it.
Facts
- Skill name
lean-theorem-proving-guide- GitHub stars
- 298
- Used in
- 1 other repo
- Token cost
- ~921 tokens
- SKILL.md length
- 114 words
- Files
- 1
- Skills in repo
- 405
- Repo updated
- First seen
- Licence
- MIT
At a glance
LLM agent for formal theorem proving in Lean 4. An agent skill from wentorai/research-plugins.
- Works in 5 steps: Automated proving: Prove mathematical… → Proof assistance: Suggest tactics during… → Verification: Formally verify… → …
- SKILL.md covers Overview, Architecture, Usage and Proof Search Strategies, plus 4 more sections
- Instructions only: no scripts, shell commands, URLs or credentials in SKILL.md
What it does
Lean Theorem Proving Guide is an agent skill from wentorai/research-plugins. LLM agent for formal theorem proving in Lean 4
Its SKILL.md is about 920 tokens, which your agent loads only when the skill is triggered. It is a single SKILL.md file with no bundled scripts.
The repository describes itself as: 350+ academic research skills, MCP configs, and plugins for Research-Claw and AI agents. The licence is MIT.
Example prompts
- “/lean-theorem-proving-guide”
Requirements
- Python 3
Workflow steps
5 steps, taken from the first numbered list in SKILL.md.
- Automated proving: Prove mathematical theorems formally
- Proof assistance: Suggest tactics during manual proving
- Verification: Formally verify mathematical claims
- Education: Learn Lean 4 tactics with AI guidance
- Research: Explore new proof techniques
What it can do on your machine
Read from SKILL.md and the folder at commit bf44b3c. It shows what the files ask for, not the result of running them.
Tool permissions
Pre-approves nothing: there is no allowed-tools line, so your agent's usual permission prompts apply.
From allowed-tools in the SKILL.md frontmatter.
Runs code
No scripts in the folder and no shell commands in SKILL.md (its code samples are python and lean).
From the folder's file list and the shell code blocks in SKILL.md.
Network
Links to these hosts (documentation or services it may open):
github.comlean-lang.orgleanprover-community.github.ioleandojo.org
From URLs in SKILL.md, links to its own repository left out.
Credentials
Names no API keys, tokens, secrets or passwords.
From names ending in _API_KEY, _TOKEN, _SECRET, _KEY or _PASSWORD in SKILL.md.
Context cost
Lean Theorem Proving Guide loads about 921 tokens when it runs. Until then it costs about 18 tokens; SKILL.md has 114 words of instructions outside code blocks.
Estimates: characters ÷ 4, the usual rule of thumb; real counts depend on the model's tokenizer. Scripts and assets cost tokens only if the agent reads them.
Safety
Auto-check passed
The automated check found no risky patterns in SKILL.md.
Automated static check — not a guarantee. Review scripts before installing. It scans the text of SKILL.md for risky patterns (piping downloads into a shell, reading credential files, hidden Unicode, destructive commands); files beside SKILL.md are not scanned.
SKILL.md
The full file from wentorai/research-plugins at commit bf44b3c, republished under its MIT licence (© wentorai). 114 words, ~921 tokens.
Download SKILL.mdSave it as
.claude/skills/lean-theorem-proving-guide/SKILL.md (or your agent's skills folder).- name
- lean-theorem-proving-guide
- description
- LLM agent for formal theorem proving in Lean 4
Lean Theorem Proving Agent Guide
Overview
LeanAgent is an LLM-based agent for automated theorem proving in Lean 4, a modern proof assistant. It combines LLM reasoning with formal verification — proposing proof steps that are verified by Lean's type checker. Can prove novel theorems, not just benchmarks, by exploring proof strategies, backtracking on failures, and learning from successful proofs.
Architecture
Theorem Statement (Lean 4)
↓
Goal Analysis Agent (understand proof obligations)
↓
Tactic Suggestion Agent (propose proof steps)
↓
Lean 4 Verification (check tactic correctness)
↓
Backtracking (if tactic fails, try alternatives)
↓
Proof or timeoutUsage
from lean_agent import LeanAgent
agent = LeanAgent(
llm_provider="anthropic",
lean_path="/path/to/lean4",
)
# Prove a theorem
result = agent.prove(
theorem="""
theorem add_comm (m n : Nat) : m + n = n + m := by
sorry
""",
max_attempts=50,
timeout=120,
)
if result.proved:
print("Proof found!")
print(result.proof)
else:
print(f"Failed. Best attempt:\n{result.best_attempt}")
print(f"Remaining goals: {result.remaining_goals}")Proof Search Strategies
# Configure search strategy
agent = LeanAgent(
search_config={
"strategy": "best_first", # best_first, bfs, dfs
"max_depth": 20, # Max proof steps
"beam_width": 5, # Tactics to try per step
"temperature": 0.7, # LLM sampling temp
"backtrack_on_fail": True,
},
)
# Interactive proof mode
session = agent.interactive_prove(
theorem="theorem my_thm : ∀ n : Nat, n + 0 = n := by"
)
while not session.done:
print(f"Current goals:\n{session.goals}")
tactics = session.suggest_tactics(k=5)
for i, t in enumerate(tactics):
print(f" {i}: {t.tactic} (confidence: {t.score:.2f})")
# Agent automatically picks best tactic
session.step()Lean 4 Tactic Library
-- Common tactics LeanAgent uses:
-- intro, apply, exact, rfl, simp, omega
-- induction, cases, constructor, ext
-- rw, calc, have, let, show
-- Example theorem + proof
theorem list_append_nil (l : List α) : l ++ [] = l := by
induction l with
| nil => simp
| cons h t ih => simp [ih]Batch Proving
# Prove multiple theorems
theorems = [
"theorem t1 : 1 + 1 = 2 := by sorry",
"theorem t2 (n : Nat) : n + 0 = n := by sorry",
"theorem t3 (n m : Nat) : n + m = m + n := by sorry",
]
results = agent.prove_batch(
theorems=theorems,
parallel=True,
timeout_per=60,
)
for thm, result in zip(theorems, results):
status = "PROVED" if result.proved else "FAILED"
print(f"[{status}] {thm[:50]}...")Use Cases
- Automated proving: Prove mathematical theorems formally
- Proof assistance: Suggest tactics during manual proving
- Verification: Formally verify mathematical claims
- Education: Learn Lean 4 tactics with AI guidance
- Research: Explore new proof techniques
References
© wentorai, MIT. Rendered from Markdown: HTML in the file is shown as text, images as links, and headings moved down two levels. Raw file
Files
Just SKILL.md in skills/domains/math/lean-theorem-proving-guide of wentorai/research-plugins.
Open the folder on GitHubat commit bf44b3c
Used in 1 other repository
We found 1 copy of this SKILL.md (exact, near-identical or edited) in other folders, from 1 other GitHub owner. This page covers the copy in wentorai/research-plugins, which our catalogue first saw on October 7, 2026.
Compare with similar skills
Lean Theorem Proving Guide next to the 5 skills that share the most tags, products or categories with it. Stars are the repository's; “used in” counts other GitHub owners with a copy.
| Skill | Stars | Used in | Tokens | Auto-check | Licence | Repo updated |
|---|---|---|---|---|---|---|
| Lean Theorem Proving Guide this skillwentorai/research-plugins | 298 | 1 repos | ~921 | Automated safety check: Pass | MIT | |
| Lean Formalizewanshuiyin/Auto-claude-code-research-in-sleep | 17k | — | ~5.4k | Automated safety check: Notes | MIT | |
| Lean4 Theorem Provingbenchflow-ai/skillsbench | 1.8k | — | ~2.2k | Automated safety check: Pass | Apache-2.0 | |
| Math Formalizationtradecatlabs/vibe-coding-cn | 17k | — | ~717 | Automated safety check: Pass | MIT | |
| Lean Canvasphuryn/pm-skills | 27k | — | ~1.2k | Automated safety check: Pass | MIT | |
| Lean BuildJuliusBrussee/caveman | 110k | 1 repos | ~273 | Automated safety check: Pass | Apache-2.0 |
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Questions about Lean Theorem Proving Guide
What does Lean Theorem Proving Guide do?
LLM agent for formal theorem proving in Lean 4. An agent skill from wentorai/research-plugins. Lean Theorem Proving Guide is an agent skill from wentorai/research-plugins.
How do I install Lean Theorem Proving Guide in Claude Code?
Run `npx skills add wentorai/research-plugins --skill lean-theorem-proving-guide -a claude-code`. Or copy the skill folder (skills/domains/math/lean-theorem-proving-guide in wentorai/research-plugins) into .claude/skills/lean-theorem-proving-guide in your project. Claude Code loads it when a task matches its description.
How do I install Lean Theorem Proving Guide in Codex?
Run `npx skills add wentorai/research-plugins --skill lean-theorem-proving-guide -a codex`. Or copy the skill folder (skills/domains/math/lean-theorem-proving-guide in wentorai/research-plugins) into .agents/skills/lean-theorem-proving-guide in your project. Codex loads it when a task matches its description.
Can I use Lean Theorem Proving Guide in Cursor, Gemini CLI or GitHub Copilot?
Cursor, Gemini CLI, GitHub Copilot and OpenCode also load SKILL.md folders. With the skills CLI, run `npx skills add wentorai/research-plugins --skill lean-theorem-proving-guide -a cursor` (or -a gemini-cli, github-copilot or opencode for the others). To copy it by hand, put the folder in .cursor/skills/lean-theorem-proving-guide, .gemini/skills/lean-theorem-proving-guide, .github/skills/lean-theorem-proving-guide and .opencode/skills/lean-theorem-proving-guide in your project.
What does Lean Theorem Proving Guide need to run?
SKILL.md names no scripts, command-line tools or credentials: Lean Theorem Proving Guide is instructions for the agent only. Our summary lists: Python 3.
Does Lean Theorem Proving Guide access the network?
SKILL.md names 4 domains. As links in the text: github.com, lean-lang.org, leanprover-community.github.io and leandojo.org. This is read from the text; nothing was executed.
Is Lean Theorem Proving Guide safe to install?
Our automated static check of SKILL.md found no risky patterns, such as piping downloads into a shell, reading credential files or hidden Unicode. It is not a guarantee. Review the folder before installing.
What licence does Lean Theorem Proving Guide use?
Lean Theorem Proving Guide is published under the MIT licence (the repository's licence). It allows redistribution, so the full SKILL.md is shown on this page.
How many tokens does Lean Theorem Proving Guide use?
About 921 tokens (SKILL.md is roughly 3.7k characters). Agents keep only the skill's name and description in context until a task matches; then they load SKILL.md in full.
What are the alternatives to Lean Theorem Proving Guide?
Skills that share tags, products or a category with Lean Theorem Proving Guide: Lean Formalize (wanshuiyin/Auto-claude-code-research-in-sleep, 17k stars), Lean4 Theorem Proving (benchflow-ai/skillsbench, 1.8k stars), Math Formalization (tradecatlabs/vibe-coding-cn, 17k stars) and Lean Canvas (phuryn/pm-skills, 27k stars). The comparison table on this page puts their stars, adoption, token cost, safety result and licence side by side.
Who maintains Lean Theorem Proving Guide?
wentorai (a GitHub user) maintains it in wentorai/research-plugins, which has 298 GitHub stars. The repository holds 405 skills in this directory. The repository was last updated on June 19, 2026.
Source: wentorai/research-plugins on GitHub. Facts on this page come from the repository at the commit we read; the author's words are quoted as theirs.