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

@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}
}