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license: apache-2.0
task_categories:
- text-generation
- feature-extraction
language:
- en
tags:
- theorem-proving
- formal-methods
- lean
- mathlib
- mathematics
size_categories:
- 10K<n<100K
dataset_info:
features:
- {name: fact, dtype: string}
- {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: line_start, dtype: int64}
- {name: line_end, dtype: int64}
- {name: has_proof, dtype: bool}
- {name: source_url, dtype: string}
- {name: commit, dtype: string}
splits:
- {name: train, num_examples: 133201}
config_name: default
configs:
- config_name: default
data_files:
- split: train
path: data/train-*
---
# Lean3-Mathlib
Declarations from mathlib3, the Lean 3 mathematical library (archived).
## Source
- Repository: https://github.com/leanprover-community/mathlib
- Commit: `65a1391a0106c9204fe45bc73a039f056558cb83`
- Files: 3220
- License: apache-2.0
## Schema
| Column | Type | Description |
|--------|------|-------------|
| fact | string | Verbatim declaration with the leading keyword removed: signature and body/proof joined |
| statement | string | Signature with the leading keyword removed (verbatim slice) |
| proof | string | Verbatim proof/body, empty if 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, null if absent |
| line_start | int | First source line |
| line_end | int | Last source line |
| has_proof | bool | Whether a proof block was captured |
| source_url | string | Upstream repository |
| commit | string | Upstream commit extracted |
## Statistics
- Entries: 133,201
- With proof: 132,770 (99.7%)
- With docstring: 35,100 (26.4%)
- Libraries: 417
### By type
| Type | Count |
|---|---|
| lemma | 83,206 |
| def | 19,387 |
| theorem | 14,273 |
| instance | 13,632 |
| class | 1,010 |
| structure | 732 |
| abbreviation | 496 |
| inductive | 252 |
| example | 199 |
| definition | 10 |
| class inductive | 3 |
| macro | 1 |
## Example
```coq
add_torsor (G : out_param Type*) (P : Type*) [out_param $ add_group G]
extends add_action G P, has_vsub G P :=
[nonempty : nonempty P]
(vsub_vadd' : ∀ (p1 p2 : P), (p1 -ᵥ p2 : G) +ᵥ p2 = p1)
(vadd_vsub' : ∀ (g : G) (p : P), g +ᵥ p -ᵥ p = g)
```
- type: class | symbolic_name: `add_torsor` | src/algebra/add_torsor.lean:48
## Use
Statement and proof are available both joined (`fact`) and split (`statement`, `proof`) for
proof-term modeling, autoformalization, retrieval, and dependency analysis via `deps`.
## Citation
```bibtex
@misc{lean3_mathlib_dataset,
title = {Lean3-Mathlib},
author = {Norton, Charles},
year = {2026},
note = {Extracted from https://github.com/leanprover-community/mathlib, commit 65a1391a0106},
url = {https://huggingface.co/datasets/phanerozoic/Lean3-Mathlib}
}
```
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