Datasets:

phanerozoic
/

Lean3-Mathlib

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: 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: 124644
  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
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: 124,644
With proof: 124,216 (99.7%)
With docstring: 34,238 (27.5%)
Libraries: 417

By type

Type	Count
lemma	82,758
def	19,312
theorem	14,208
instance	5,867
class	1,010
structure	731
abbreviation	496
inductive	249
definition	10
class inductive	3

Example

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

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

@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}
}