---
name: lean-theorem-proving-guide-ada4b9f66707
description: "LLM agent for formal theorem proving in Lean 4"
metadata:
  openclaw:
    emoji: "📐"
    category: "domains"
    subcategory: "math"
    keywords: ["Lean 4", "theorem proving", "formal verification", "LLM math", "proof assistant", "LeanAgent"]
    source: "https://github.com/lean-dojo/LeanAgent"
---

# 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 timeout
```

## Usage

```python
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

```python
# 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

```lean
-- 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

```python
# 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

1. **Automated proving**: Prove mathematical theorems formally
2. **Proof assistance**: Suggest tactics during manual proving
3. **Verification**: Formally verify mathematical claims
4. **Education**: Learn Lean 4 tactics with AI guidance
5. **Research**: Explore new proof techniques

## References

- [LeanAgent GitHub](https://github.com/lean-dojo/LeanAgent)
- [Lean 4](https://lean-lang.org/)
- [Mathlib4](https://leanprover-community.github.io/mathlib4_docs/)
- [LeanDojo](https://leandojo.org/)


---
Source attribution: wentorai
Original project: https://github.com/wentorai/research-plugins/blob/bf44b3cd617fa94c8a1b254c5d1987142ca3d631/skills/domains/math/lean-theorem-proving-guide/SKILL.md
License: MIT
License information: https://opensource.org/license/mit
Original upstream instructions; downloaded from Mega AI Hub.

## Upstream license notice

MIT License

Copyright (c) 2026 Wentor AI

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.



# Mega AI Hub resource metadata

Creator / publisher: wentorai
Original project: https://github.com/wentorai/research-plugins/blob/bf44b3cd617fa94c8a1b254c5d1987142ca3d631/skills/domains/math/lean-theorem-proving-guide/SKILL.md
Attribution basis: Source repository record

Fields of work: Data & Analytics, Development & Engineering, Education & Research
Roles: Data Scientist, ML / AI Engineer, Researcher
Specialties: API
Tools: Anthropic, Lean4
Country applicability: Country not specified
Classification basis: Source catalog labels
Instruction SHA-256: 8bf647cad684b7f96fb4387371a9a2f6def41ff472cc2b3d5d16dcfc274476cb