Leanstral Formal Verification

A skill for formal verification using Lean 4 + Mathlib + the Leanstral model (labs-leanstral-2603) from Mistral AI to mathematically prove code properties.

🔑 Requires a Mistral API key. Set via MISTRAL_API_KEY environment variable. The Leanstral model is available for free via Mistral's API as of 2026-05-17. Get a key at: https://console.mistral.ai/api-keys

export MISTRAL_API_KEY="your-key-here"

⚠️ When using this skill:

• Theorem statements and code are sent to Mistral's API. Do not include confidential code, secrets, or proprietary protocol details in prompts.
• Generated .lean files are untrusted code — verify.sh rejects proof holes (sorry/admit) and compiles in an isolated project directory.
• Always review the generated theorem statements. Lean verifies that the proof is valid, not that the theorem matches your intent.

About the Model

Leanstral is Mistral AI's first open-source code agent for Lean 4 (released March 2026). It is specialized for theorem proving — it generates proofs, and Lean 4 verifies them mechanically. When a proof passes, correctness is a mathematical fact, not a probability.

Why Leanstral beats general-purpose LLMs at proofs

General-purpose LLMs (GPT, Claude, etc.) write code and hope it works — they test a few inputs but miss edge cases. Leanstral writes code and proves it correct for all inputs. When Lean 4 accepts the proof, correctness is guaranteed mathematically.

FLTEval Benchmarks

Pass@16 beats Sonnet at 1/2 the cost, approaches Opus at 1/6 the cost.

Quick Start — Direct API Call

The primary way to use this skill: call the Mistral API directly.

curl -X POST "https://api.mistral.ai/v1/chat/completions" \
  -H "Authorization: Bearer $MISTRAL_API_KEY" \
  -H "Content-Type: application/json" \
  -d '{
    "model": "labs-leanstral-2603",
    "temperature": 1.0,
    "max_tokens": 32000,
    "messages": [{
      "role": "user",
      "content": "Prove the following theorem in Lean 4:\n\ntheorem add_comm (a b : Nat) : a + b = b + a := by\n  sorry"
    }]
  }'

Or with Python:

from openai import OpenAI

client = OpenAI(
    api_key="***",
    base_url="https://api.mistral.ai/v1"
)

response = client.chat.completions.create(
    model="labs-leanstral-2603",
    temperature=1.0,
    max_tokens=32000,
    messages=[{"role": "user", "content": "Prove that..."}],
)
print(response.choices[0].message.content)

Recommended API Parameters

Pass@N Strategy

Leanstral improves significantly with multiple attempts. If a proof fails on the first try, call the API again — the model explores different proof strategies each time. pass@2 adds +4.4 points to the score. For automated workflows, loop with retry logic:

for i in 1 2 3; do
  curl -s -X POST "https://api.mistral.ai/v1/chat/completions" \
    -H "Authorization: Bearer $MISTRAL_API_KEY" \
    -H "Content-Type: application/json" \
    -d "{\"model\":\"labs-leanstral-2603\",\"temperature\":1.0,\"max_tokens\":32000,\"messages\":[{\"role\":\"user\",\"content\":\"$(cat proof_request.txt | jq -Rs .)\"}]}" \
    | jq -r '.choices[0].message.content' > proof_attempt_$i.lean
  # Verify with Lean 4
  bash verify.sh proof_attempt_$i.lean && break
done

Prerequisites

Before using this skill, set up a Lean 4 project on your machine:

1. Install elan (Lean version manager)
2. Create a Lean project: lake new formal-verification
3. Add Mathlib as a dependency in lakefile.lean
4. Run lake build once to build the Mathlib cache (~500MB, one-time cost)
5. Create a verify.sh script in the project root (see below)

verify.sh template

#!/bin/bash
# verify.sh — compile and check a Lean 4 proof file
# Usage: bash verify.sh /path/to/proof.lean
set -e
export PATH="$HOME/.elan/bin:$PATH"
PROJECT_DIR="<your-lean-project-dir>"
cp "$1" "$PROJECT_DIR/Proof.lean"
cd "$PROJECT_DIR"
lake build

When to use

Use cases:

• Proving that a code fix satisfies the intended properties
• Formal verification of security properties
• Proving the correctness of algorithms
• Verifying the safety of protocols
• Proving that multiple conditional branches are exhaustive
• Providing formal assurance that "this change does not break existing behavior"

Do not use:

• When simple unit tests are sufficient
• When you want to check runtime behavior (test by actually running it)
• For unprovable subjective properties (UX, design, etc.)
• For I/O-heavy code (file systems, network, databases — Lean 4 is for pure functions)
• For entire large codebases — focus on the critical core, not 100% coverage

Workflow Patterns

Pattern 1: Verify an existing code fix

1. Write the code + specification in Lean 4
2. Call Leanstral API: "Prove this implementation satisfies the specification"
3. Compile the returned proof with verify.sh
4. Pass → correctness guaranteed. Fail → failure point is the bug location.

Pattern 2: Spec-driven development

1. Write the specification in Lean 4 first (what "correct" means)
2. Call Leanstral to generate both implementation AND proof
3. Compile — when the proof passes, development is complete. No tests needed.

Pattern 3: Root-cause a bug

1. Observe the bug's symptoms
2. Write the "correct behavior" specification in Lean 4
3. Call Leanstral to prove the current implementation satisfies it
4. The point where the proof fails = the bug's root cause
5. Fix, then re-prove to confirm

Pattern 4: Safe refactoring

1. Write the pre- and post-refactoring code
2. Define equivalence as a specification
3. Call Leanstral to prove they are equivalent
4. Proof passes → refactoring is mathematically safe

Pattern 5: State machine / concurrency verification

1. Model the state machine as an inductive proposition in Lean 4
2. Formulate properties: "no deadlocks", "no unreachable states", etc.
3. Call Leanstral to prove them
→ Catches concurrency bugs exhaustively, not probabilistically

Verification Flow

Step 1: Identify the properties to be verified

Clearly state the properties to be proven in natural language. For example, when verifying a code change that adds a new boolean guard condition:

• "When the user cancels, the side effect does not fire."
• "During system-generated timeouts, the side effect fires as before (unchanged)."
• "The guard flag only becomes true on user-initiated operations."

Step 2: Build a formal model

Convert the natural language properties into Lean 4 types and theorems:

-- Model the relevant boolean conditions as variables
variable (timedOut compactDuring timeExecuting userAborted : Bool)

-- Condition BEFORE the change
def triggerOld : Bool := timedOut && !compactDuring && !timeExecuting

-- Condition AFTER the change (adds userAborted guard)
def triggerNew : Bool := timedOut && !compactDuring && !timeExecuting && !userAborted

Step 3: Call Leanstral to generate proofs

Send the model + theorems to the Leanstral API with a prompt like:

Prove the following theorems in Lean 4 using Mathlib.
Use only the tactics: simp, tauto, rw, cases, rfl, constructor.

[paste your model + theorems here]

Step 4: Save output and compile

# Save Leanstral's response to a .lean file
echo "$LEANSTRAL_OUTPUT" > FormalVerification.lean

# Compile and verify
bash <lean-project-dir>/verify.sh FormalVerification.lean

• Success: Build completed successfully → Proof completed
• Failure: Read the error message → Send the error back to Leanstral → Retry

Step 5: Report the results

• List of proven theorems
• Compilation output (success message)
• Which real-world properties each theorem corresponds to

Prompt Strategy

When instructing Leanstral via the API, always provide:

[Context]
- Lean 4 version in use
- Dependencies (Mathlib, specific modules)
- The code/specification to verify

[Instruction]
- What property to prove
- Optional: suggested tactics or approach
- Any constraints (e.g., "only use simp and tauto")

Concrete Example: Algorithm Correctness

-- Define the specification FIRST
def sorted_correct (arr : Array Nat) : Prop :=
  ∀ i j, i < j → j < arr.size → arr[i]! ≤ arr[j]!

-- Send to Leanstral: "Prove that bubbleSort satisfies sorted_correct"
def bubbleSort (arr : Array Nat) : Array Nat := by
  sorry -- implementation

theorem bubbleSort_correct (arr : Array Nat) :
  sorted_correct (bubbleSort arr) := by
  sorry -- Leanstral generates this proof

Using as an OpenClaw Sub-Agent (Optional)

If you have already configured a Leanstral sub-agent in your OpenClaw gateway (this is separate setup — see the gateway's agent configuration), you can delegate proof generation to it:

sessions_spawn:
  agentId: <your-leanstral-agent-id>
  task: |
    You are a Lean 4 formal verification expert.

    ## Context
    [Description of the verification target and properties to prove]

    ## Environment
    Lean 4 is available on the HOST. To compile:
    ```bash
    export PATH="$HOME/.elan/bin:$PATH"
    bash <lean-project-dir>/verify.sh /workspace/your-file.lean
    ```

    ## Task
    1. Identify the properties to be verified
    2. Build a formal model in Lean 4
    3. Write and prove theorems
    4. Verify compilation using verify.sh (mandatory)
    5. If it fails, read the error, fix the proof, and recompile
    6. Report the final compilation output

    Save to: /workspace/FormalVerification.lean

Recommended sub-agent parameters (if configuring one):

Best Practices

✅ DO

1. Write the specification first. Define "correct" before implementing.
2. Prove in small steps. Break large theorems into lemmas.
3. Set reasoning_effort="high". Essential for non-trivial proofs.
4. Use pass@N. If the first API call fails, retry — each attempt explores different strategies.
5. Feed Lean errors back to Leanstral. The error message tells exactly what failed.
6. Leverage Mathlib. Use existing proven lemmas — don't re-prove everything from scratch.
7. Keep proofs small and focused. One property per verification task.

❌ DON'T

1. Use for I/O-heavy code. Lean 4 is for pure functions. File I/O, networking, databases are impractical to formalize.
2. Formalize an entire large codebase. Pick the critical 5% — the core logic that must never be wrong.
3. Confuse "proof passes" with "spec is correct." Lean verifies that the implementation matches the spec. The spec's correctness is a human judgment.
4. Use Leanstral for general tasks. It's specialized for Lean 4 proofs — not for Python web apps, general chat, or code generation in other languages.
5. Trust proofs blindly. Lean's verification is trustworthy, but rare hallucinations (non-existent theorems/tactics) are caught by the compiler.

Important Notes

Lean on the host

Lean 4 with Mathlib requires ~500MB of cached dependencies. Run it directly on your machine — containerizing it is impractical. The verify.sh script compiles .lean files using the host's Lean installation.

Timeout management

The Leanstral model can take minutes to generate proofs. Countermeasures:

• Set generous API timeouts (600–1200s)
• Use pass@N: retry with fresh API calls if the first proof fails
• Divide complex proofs into smaller lemmas

Applications in Other Fields

Application procedure

1. Define the property in natural language — "If X, then Y must always hold"
2. Build a formal model — Variables, types, functions that model the system
3. Write theorems — Express properties using theorem
4. Call Leanstral API — Send the model + theorems and request proofs
5. Compile and verify — lake build checks the proofs

Basic proof tactics

Limitations

Error Handling

Compilation errors

error: unknown identifier 'foo'

→ The definition does not exist. Define it with def or add an import.

error: type mismatch

→ Type mismatch. Check the variable type declaration.

error: tactic 'simp' failed

→ simp cannot prove it. Use more specific tactics (cases, rw).

Pass@N retry loop

# Basic retry loop: try up to 3 times, stop on first success
for i in 1 2 3; do
  echo "Attempt $i..."
  curl -s ... | python3 -c "import sys,json; print(json.load(sys.stdin)['choices'][0]['message']['content'])" > proof.lean
  if bash verify.sh proof.lean 2>/dev/null; then
    echo "✅ Proof verified on attempt $i"
    break
  fi
  echo "❌ Attempt $i failed, retrying..."
done

Reference Links

• Leanstral blog: https://mistral.ai/news/leanstral
• Model (HuggingFace): https://huggingface.co/mistralai/Leanstral-2603
• API docs: https://docs.mistral.ai/models/leanstral-26-03
• Lean 4: https://github.com/leanprover/lean4
• Mathlib: https://github.com/leanprover-community/mathlib4
• Lean AI leaderboard: https://lean-lang.org/eval/