Technical Lean evidence record
Checked Artifact: Hales–Jewett Theorem (mathlib)
Proof Atlas collected build, no-sorry, axiom, and clean-source evidence directly from the pinned upstream declaration.
ProofAtlas record
What has been checked
These states distinguish upstream identity, local reproduction, review, and Atlas acceptance. This page is part of the public, read-only Mathlib landmark collection.
Mechanical evidence
- Declaration checked
Combinatorics.Line.exists_mono_in_high_dimension- Module
Mathlib.Combinatorics.HalesJewett- Source file checked
Mathlib/Combinatorics/HalesJewett.lean- Package commit
5e932f97dd25535344f80f9dd8da3aab83df0fe6- Build
- passed · transcript retained
- Unfinished proof steps
- None found by the recorded no-sorry scan
- Axiom closure
- Classical.choice, Quot.sound, propext
- Clean collection provenance
- Recorded
Evidence boundary
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 is evidence for the exact formal statement only. It does not establish novelty, transfer a historical acceptance decision, or authorize publication.