Lean verification record

Checked Artifact: Hales–Jewett Theorem (mathlib)

Proof Atlas collected build, no-sorry, axiom, and clean-source evidence directly from the pinned upstream declaration.

Verification result

The recorded Lean checks passed

Build replaypassed with retained transcript
Unfinished stepsNone found
Source identityPinned commit and file recorded
Dependency profileAxiom closure recorded

Reproducibility details

What the checker recorded

Declaration checked: Combinatorics.Line.exists_mono_in_high_dimension
Module: Mathlib.Combinatorics.HalesJewett
Source file checked: Mathlib/Combinatorics/HalesJewett.lean
Package commit: 5e932f97dd25535344f80f9dd8da3aab83df0fe6
Build transcript: passed · retained with this record
Unfinished proof steps: None found by the recorded no-sorry scan
Axiom closure: Classical.choice, Quot.sound, propext
Collection provenance: Clean source state recorded

ProofAtlas record

What has been checked

Upstream indexedPinned source bytes verified locally

Locally reproducedExact upstream declaration replayed

Reviewed pageCurrent public presentation reviewed

Accepted Atlas resultNot recorded for the preferred artifact

Mathlib is the source of the theorem; the local Lean replay and page review are separate.

Evidence boundary

Exact formal statement only

This page indexes Mathlib’s combinatorial-line form of the Hales–Jewett theorem for arbitrary finite types α and κ. It produces some finite coordinate type ι before quantifying over every coloring C : (ι → α) → κ. A line fixes some coordinates and varies one nonempty set of coordinates together through a common letter. The selected declaration supplies no effective or least dimension, canonical choice, coloring-independent line, or algorithm, and it is not the separate multidimensional subspace theorem or the Van der Waerden corollary.

This checker record does not establish novelty, transfer a historical acceptance decision, or authorize publication.