Lean4-Stdlib

Structured dataset of definitions and theorems from the Lean 4 standard library (Init + Std).

Source

• Repository: https://github.com/leanprover/lean4
• Commit: d265d1ca745e7741a7e7f7366c22ce9c9dda57b6
• Files: 1071
• 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: 52,970
• With proof: 51,596 (97.4%)
• With docstring: 7,626 (14.4%)
• Libraries: 165

By type

Type	Count
theorem	42,996
def	7,688
abbrev	441
structure	426
opaque	383
instance	349
class	313
inductive	184
macro	172
axiom	15
class inductive	2
class abbrev	1

Example

apply_dite (f : α → β) (P : Prop) [Decidable P] (x : P → α) (y : ¬P → α) :
    f (dite P x y) = dite P (fun h => f (x h)) (fun h => f (y h))
by
  by_cases h : P <;> simp [h]

• type: theorem | symbolic_name: apply_dite | src/Init/ByCases.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_stdlib_dataset,
  title  = {Lean4-Stdlib},
  author = {Norton, Charles},
  year   = {2026},
  note   = {Extracted from https://github.com/leanprover/lean4, commit d265d1ca745e},
  url    = {https://huggingface.co/datasets/phanerozoic/Lean4-Stdlib}
}