Start with the official Lean 4 extension for Visual Studio Code and its guided setup. Then learn the proof basics in a beginner resource, create a Lake project when you need more than a scratch file, and add Mathlib when your work calls for its mathematical library. Lean checks formal proof terms as you edit, giving you immediate feedback on whether a proof follows from its definitions and assumptions.
What Lean does in formal proof verification
Lean is both a functional programming language and a theorem prover. You express definitions and propositions in Lean’s type theory, then construct proofs—directly as terms or with tactics that help build those terms. Lean checks the result against the proposition. This is verification in a precise, formal sense: the system checks the proof you have written, not whether an informal argument merely sounds convincing.
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The official tutorial introduces dependent type theory, propositions and proofs, quantifiers, equality, and tactics. Its authors describe its purpose this way: “This book is designed to teach you to develop and verify proofs in Lean.” Theorem Proving in Lean 4
Install Lean 4 with the recommended editor setup
- Install Visual Studio Code if it is not already on your computer.
- Install the official Lean 4 extension from the VS Code Extensions view.
- Follow the extension’s guided setup, then create and save a file with the
.leanextension. - Allow the toolchain setup to finish before diagnosing missing Lean editor features. The official installation page recommends VS Code as the best-supported setup route; a manual installation guide is available if you prefer terminal-based steps, but some instructions may need adapting to your operating system.
As you edit a Lean file, the editor provides continuous feedback. Treat errors and unsolved goals as part of the working loop: make a small change, inspect what Lean reports, and revise. The official Lean 4 documentation introduces this interactive workflow.
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The official setup pages reviewed do not specify minimum hardware requirements, so they do not support a particular computer recommendation. A computer able to run VS Code is the practical starting point.
Choose a first learning resource
Pick a resource based on what you already know and what you want to do. The official Lean learning catalog lists these complementary starting points:
| Resource | Best fit | Focus |
|---|---|---|
| Natural Number Game | Beginners who want to learn by working through exercises | Proof construction through an interactive game |
| Theorem Proving in Lean | Learners focused on Lean’s proof language and tactics | Lean foundations and proof development |
| Mathematics in Lean | Mathematicians and others aiming to formalize mathematics | Mathematical formalization using Mathlib |
| Functional Programming in Lean | Programmers starting from a programming background | Functional programming in Lean |
The catalog does not give a comparative completion time or difficulty rating, so choose by subject matter rather than an assumed ranking. You can move between resources as your goal changes.
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Move from a scratch file to a Lake project
A saved .lean file is enough to begin experimenting. When you need a repeatable project with dependencies, use Lake, Lean’s project and build tool. For work that depends on Mathlib, follow the official manual guide’s Mathlib project instructions; the initial dependency download can take time.
- Use the project’s setup instructions to create or enter the project rather than treating a single file as the whole environment.
- Keep the project’s
lean-toolchainand dependency revision aligned with the instructions for that project. - Let Lake fetch and build dependencies, then open the project files in VS Code so the editor works with the project’s configured toolchain.
Lean and Mathlib versions are not interchangeable by assumption. An existing project’s lean-toolchain and dependency instructions take precedence over installing an unpinned latest release. At the time the official Theorem Proving in Lean 4 page was reviewed, it identified Lean 4.33.0 as the assumed version; the online page can change, so check it alongside the version pinned by your project.
When to add Mathlib
Mathlib is the mathematical library used by resources such as Mathematics in Lean. If your goal is to formalize mathematics using that library, start with its Mathlib-oriented learning material and a project configured for the required dependency. If you are learning Lean’s proof language or functional programming, begin with a suitable resource before adding a Mathlib dependency you do not yet need.
Keeping Lean’s toolchain and Mathlib revision in sync is part of project setup, not a detail to fix after proofs stop compiling. When joining an existing project, follow its pinned versions instead of changing them casually.
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A practical first-session checklist
- Confirm the guided VS Code setup has completed and Lean feedback appears for a saved
.leanfile. - Choose one learning path that matches your background: interactive exercises, proof foundations, Mathlib formalization, or functional programming.
- Work through examples in small edits, using Lean’s feedback to understand the current proof state and errors.
- Start a Lake-managed project when you need dependencies or a reusable project structure; add Mathlib only when the work requires it.
- For an existing project, preserve its declared toolchain and dependency versions.
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