# Lean Copilot: Large Language Models as Copilots for Theorem Proving in Lean

Peiyang Song 1, Kaiyu Yang1, Anima Anandkumar1
1California Institute of Technology
Published: International Conference on Neuro-symbolic Systems (NeuS) 2025
arXiv Code

## Abstract

Lean Copilot addresses the grand challenge of human-AI collaboration in formal theorem proving by introducing large language models as intelligent assistants within the Lean proof environment. This system bridges the gap between human mathematical intuition and machine computational power, enabling seamless collaboration in formal proof development.

The system provides real-time assistance through tactic suggestion, premise selection, and automated proof search, fundamentally transforming how mathematicians interact with formal proof systems and accelerating the formalization of mathematical knowledge.

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## Technical Architecture

Lean Copilot implements a sophisticated human-in-the-loop architecture that seamlessly integrates large language models with the Lean theorem prover:

### Intelligent Tactic Suggestion

Context-aware tactic recommendations based on current proof state and mathematical context, leveraging deep understanding of Lean's tactic language and proof patterns.

### Dynamic Premise Selection

Automated identification and retrieval of relevant theorems and lemmas from Lean's extensive mathematical library using semantic similarity and logical relevance.

### Guided Proof Search

Advanced search algorithms that combine human guidance with automated exploration to discover complete proofs efficiently.

## Human-AI Collaboration Paradigm

Lean Copilot pioneered a new paradigm of human-AI collaboration in formal mathematics, where AI serves as an intelligent assistant rather than a replacement for human mathematical reasoning:

#### Interactive Assistance

Real-time suggestions and guidance that adapt to the mathematician's proof strategy and style, maintaining human agency in the proof development process.

#### Flexible Deployment

Support for local, cloud, and custom model deployment options, enabling researchers to choose the configuration that best fits their privacy and performance requirements.

#### Extensible Framework

Modular architecture that allows integration of new models and techniques, fostering continued innovation in AI-assisted theorem proving.

## Getting Started

To get started with Lean Copilot, visit our GitHub repository for installation instructions and usage examples.