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license: apache-2.0
task_categories:
- text-generation
- feature-extraction
language:
- en
tags:
- theorem-proving
- formal-methods
- lean4
- mathlib
- mathematics
size_categories:
- 100K<n<1M
dataset_info:
features:
- {name: statement, dtype: string}
- {name: proof, dtype: string}
- {name: type, dtype: string}
- {name: symbolic_name, dtype: string}
- {name: library, dtype: string}
- {name: filename, dtype: string}
- {name: imports, list: string}
- {name: deps, list: string}
- {name: docstring, dtype: string}
- {name: source_url, dtype: string}
- {name: commit, dtype: string}
splits:
- {name: train, num_examples: 232431}
config_name: default
configs:
- config_name: default
data_files:
- split: train
path: data/train-*
---
# Lean4-Mathlib
Structured dataset of mathematical formalizations from the Mathlib4 library for Lean 4.
## Source
- Repository: https://github.com/leanprover-community/mathlib4
- Commit: `b9f14353520df73472ae3825fb53f86559a01319`
- Files: 8170
- License: apache-2.0
## Schema
| Column | Type | Description |
|--------|------|-------------|
| statement | string | Declaration signature/claim with the leading keyword removed (verbatim slice); the full declaration minus its proof |
| proof | string | Verbatim proof/body, empty if the declaration has none |
| type | string | Declaration keyword |
| symbolic_name | string | Declaration identifier |
| library | string | Sub-library |
| filename | string | Repository-relative source path |
| imports | list[string] | File-level `Require`/`Import` modules |
| deps | list[string] | Intra-corpus identifiers referenced |
| docstring | string | Preceding documentation comment, empty if absent |
| source_url | string | Upstream repository |
| commit | string | Upstream commit extracted |
## Statistics
- Entries: 232,431
- With proof: 228,818 (98.4%)
- With docstring: 67,814 (29.2%)
- Libraries: 1103
### By type
| Type | Count |
|---|---|
| theorem | 125,463 |
| lemma | 56,488 |
| def | 31,961 |
| instance | 10,971 |
| abbrev | 3,379 |
| class | 1,937 |
| structure | 1,580 |
| inductive | 326 |
| elab | 168 |
| macro | 147 |
| class inductive | 6 |
| class abbrev | 3 |
| opaque | 2 |
## Example
```
infinite_of_charZero (R A : Type*) [CommRing R] [Ring A] [Algebra R A]
[CharZero A] : { x : A | IsAlgebraic R x }.Infinite
by
letI := MulActionWithZero.nontrivial R A
exact infinite_of_injective_forall_mem Nat.cast_injective isAlgebraic_nat
```
- type: theorem | symbolic_name: `Algebraic.infinite_of_charZero` | Mathlib/Algebra/AlgebraicCard.lean
## Use
Each declaration is split into a `statement` (signature/claim) and a `proof` (body) that are disjoint
and together form the complete declaration, for proof modeling, autoformalization, retrieval, and
dependency analysis via `deps`.
## Citation
```bibtex
@misc{lean4_mathlib_dataset,
title = {Lean4-Mathlib},
author = {Norton, Charles},
year = {2026},
note = {Extracted from https://github.com/leanprover-community/mathlib4, commit b9f14353520d},
url = {https://huggingface.co/datasets/phanerozoic/Lean4-Mathlib}
}
```
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