We are currently updating the Lean community website to describe working with Lean 4, but most of the information you will find here today still describes Lean 3.
Pull requests updating this page for Lean 4 are very welcome. There is a link at the bottom of this page.
Please visit the leanprover zulip and ask for whatever help you need during this transitional period!
The website for Lean 3 has been archived. If you need to link to Lean 3 specific resources please link there.
Lean projects
While much Lean development takes place in the mathlib repository, there are many other projects using Lean that are developed and maintained by members of the community. We list here a selection. Many of these projects are designed to be imported as dependencies in other developments. At the bottom of this page, you can see a summary of which projects are compatible with which Lean versions. If two projects both support the same Lean version, you can likely use them together.
To add a project to this list, please see the directions at the leanprovercontrib repository.
This list and the repository that manages it are both works in progress. Please add your own project and report any problems in that repository.
leanliquid
maintained by @jcommelin
Liquid Tensor Experiment is a challenge by Peter Scholze to formalize parts of condensed mathematics, culminating in the main theorem of liquid modules.
flypitch
maintained by @jessemichaelhan @fpvandoorn
The Flypitch project gives a formal proof of the independence of the continuum hypothesis from ZFC. The continuum hypothesis states that there is no cardinality between the smallest infinite cardinal and the cardinality of the continuum. This project also develops a library of firstorder logic, set theory and forcing.
leanperfectoidspaces
maintained by @kbuzzard @jcommelin @PatrickMassot
Perfectoid spaces are sophisticated objects in arithmetic geometry introduced by Peter Scholze in 2012. We formalised enough definitions and theorems in topology, algebra and geometry to define perfectoid spaces in Lean. See also our project webpage and paper.
leangptf
maintained by @jessemichaelhan @jasonrute @tonywu95 @edayers @spolu
Provides an interactive frontend to Lean GPTf, a neural theorem prover which relies on a large Transformer language model to suggest tactics. It can prove nearly 50% of the remaining theorems in a heldout test set. See Jason Rute's talk at Lean Together 2021.
sudoku
maintained by @TwoFx
This is an implementation of sudoku, written in Lean. When you open a level in VS Code, a sudoku board is displayed in the goal view. You can put numbers (and also pencil marks) on the board by adding hypotheses, but you have to prove that the placement of the number follows logically from what is already on the board! There are some tactics to help you with this, and you can also prove theorems to build up your personal library of sudoku theory.
leanmatrixcookbook
maintained by @ericwieser
This project aims to provide the lemmas in The Matrix Cookbook as proofs in the Lean theorem prover. Ideally, every proof in this repository should be a reference to a single lemma in Mathlib; this can be used as an index against (and progress report for) mathlib for standard matrix results.
connf
maintained by @YaelDillies @zeramorphic
A formalisation of the consistency of Quine's New Foundations axiom system, following Randall Holmes' proof. This is arguably the longest standing open question in set theory.
lftcm2020
maintained by @jcommelin @PatrickMassot
This repository contains tutorials about Lean and mathlib that were developed for the workshop Lean for the Curious Mathematician, held in July 2020. The tutorials range from introductory lessons on numbers, logic, and sets to advanced lessons on category theory and manifolds. In addition to the materials found in this repository, we recommend watching the videos of the tutorials and lectures from the workshop.
topos
maintained by @bmehta
This repository contains formal verifications of results in Topos Theory, drawing from "Sheaves in Geometry and Logic" and "Sketches of an Elephant". It currently includes a range of constructions and theorems about both Grothendieck topoi and elementary toposes.
fltregular
maintained by @alexjbest @riccardobrasca @ericrbg @CBirkbeck
The goal of this project is to formalize Kummer's proof of Fermat's Last Theorem for regular prime exponents. This was a landmark 19th century result in algebraic number theory, proving the theorem in many new cases at the time, but is quite different to the final proof of the full theorem, due to WilesTaylor. This project hopes to add more material on algebraic number theory and related topics to mathlib in addition to formalizing a version of Kummer's proof.
leanga
maintained by @ericwieser @utensil
A formalization of parts of Geometric Algebra,
and the source from which most of the clifford_algebra
library graduated to mathlib.
sphereeversion
maintained by @PatrickMassot @fpvandoorn @ocfnash
In this project we formalize the proof of existence of sphere eversions in Lean. More precisely, we aim to formalize the full hprinciple for open and ample first order differential relations, and deduce existence of sphere eversions as a corollary.
mathematica
maintained by @robertylewis @minchaowu
Connects Lean to the computer algebra system Mathematica. This project offers a bidirectional translation between the two systems. From within Lean, you can evaluate Mathematica commands, possibly including translated Lean expressions, and process the results. From Mathematica, you can access a Lean environment.
Examples of calling Mathematica from Lean can be found at robertylewis/mathematica_examples, and examples in the other direction at minchaowu/mmlean. These repositories are not in the contrib list because they depend on Mathematica, which is proprietary software. See also our project webpage with a link to our paper about this project.
rubikscubegroup
maintained by @kendfrey
This project formalizes the Rubik's cube group as a product of corner orientation, corner permutation, edge orientation, and edge permutation.
The solvable subgroup is defined as the the set of positions where both orientations sum to 0 and the permutations have the same sign.
This project includes a widget to visualize elements of the group as physical puzzle states.
leansocialchoice
maintained by @asouther4 @benjamindavidson
Social Choice Theory is a theoretical framework at the intersection of philosophy, political science, and welfare economics. It studies methods for aggregating individual preferences into collective social welfare functions.
This is a library of noteworthy proofs from Social Choice Theory formalized in Lean.
super
maintained by @gebner
Version one of a small superposition prover
written in Lean. This repository introduces
a tactic super
which attempts to solve
problems in first order logic, possibly
given a list of extra hypotheses.
This version is not compatible with community releases of Lean.
unitfractions
maintained by @bmehta @TFBloom
This project formalizes the main results of the preprint On a density conjecture about unit fractions in Lean. One of these results says that any dense set of naturals contains distinct naturals whose reciprocals sum to 1.
leanaclpairs
maintained by @adamtopaz
This project contains formalization of the relationship between socalled acl
pairs and valuation rings.
If K
and F
are two fields, a pair of (group) morphisms f g : Kˣ → F
is called an acl
pair provided that f u * g v = f v * g u
whenever u + v = 1
in K
.
The main result regarding such pairs shows that they essentially always arise from valuation theory, at least when F
is a prime field (such as ℚ
or zmod p
where p
is prime).
The proofs formalized in this repository are based on ideas of BogomolovTschinkel, Efrat, Koenigsmann, and the author.
This repository also formalizes some results about rigid elements and valuation which are due to ArasonElmanJacob.
grammars
maintained by @madvorak
The aim of the project is to formalize the Chomsky hierarchy. So far, the main focus has been to prove closure properties of general (type 0) grammars. We also have some results about contextfree (type 2) grammars.
super2
maintained by @gebner
Version two of a small superposition prover
written in Lean. This repository introduces
a tactic super
which attempts to solve
problems in first order logic, possibly
given a list of extra hypotheses.
Projects by supported Lean versions
If you want to import multiple projects in your own, you should choose a Lean version that is supported by each of these dependencies.

A ✓ in the
x.y.z
column means that the project has aleanx.y.z
branch, all of its dependencies haveleanx.y.z
branches, and the project builds successfully using the most recent commits on all of theseleanx.y.z
branches. 
An × in the
x.y.z
column means that the project has anleanx.y.z
branch but it fails to build. 
No mark in the
x.y.z
column means that the project does not have anx.y.z
branch.
Note that an × does not necessarily mean the project does not compile, just that it does not compile with updated dependencies.