192.lean`

Explanation legend Lean4 Domain Explanation Language (L4DEL)

L4DEL explanations are a separate layer. They do not change the Lean source. Intuition is explanatory prose; numbered items are a reading path; sources link the wording back to evidence.

L4DEL: Lean4 Domain Explanation Language

Annotation provenance. This overlay contains 10 curated AI-written annotations and 7190 mechanical source-derived annotations. They have not been human-reviewed as explanations; treat them as unverified and not mathematical authority. Retained generation history: The 71 original curated annotations were produced in a Claude Sonnet 5.5 session at medium effort; Claude Opus 5.5 is recorded in that session as the advisor model, not the direct author. The bulk source-derived expansion was generated mechanically from pinned source comments by tooling developed in a GPT-5.6 Sol session at ultra reasoning; GPT-5.6 Sol did not originate the quoted source prose. On 2026-10-17 the mechanically generated source-comment annotations of the Formal Conjectures, Carleson, FLT, PFR, CompFiles, Mathematics in Lean and Theorem Proving in Lean overlays were regenerated by the same generator after three corrections made in a Claude Sonnet 5.5 session: titles no longer cut a sentence inside mathematics or end on a dangling word, workflow markers are removed from the quoted prose, and declaration names follow the scanner's namespace resolution. The boilerplate step line was dropped, and comments that were only a row of dashes no longer yield annotations. No new prose was written and no human review is claimed.

Credit: The upstream authors and contributors retain credit for the project and mathematics. lean4-explainer only renders their pinned source and adds the separately disclosed explanation layer.

Project sources: Pinned project documentation, Formal Conjectures paper, arXiv v1

2 declarations, 1 contain sorry, 0 declared as axioms

Erdős Problem 192

References:

erdosproblems.com/192
[ErGr79] Erdős, P. and Graham, R., Old and new problems and results in combinatorial number theory: van der Waerden's theorem and related topics. Enseign. Math. (1979), 325-344.
[ErGr80] Erdős, P. and Graham, R., Old and new problems and results in combinatorial number theory. Monographies de L'Enseignement Mathematique (1980).
[Ke92] Keränen, Veikko, Abelian squares are avoidable on $4$ letters. Automata, languages and programming (Vienna, 1992) (1992), 41-52.
[FiPu23] Fici, Gabriele and Puzynina, Svetlana, Abelian combinatorics on words: a survey. Comput. Sci. Rev. (2023), Paper No. 100532, 21.

Imports (1)

FormalConjecturesUtil

def Erdos192.IsPositiveUnitWalk A sequence $a_1, a_2, \ldots \in \mathbb{R}^d$ such that every difference $a_{i+1}-a_i$ is a positive unit vector $(0,\ldots,0,1,0,\ldots,0)$ line 41 source
Source documentation
A sequence $a_1, a_2, \ldots \in \mathbb{R}^d$ such that every difference $a_{i+1}-a_i$ is a positive unit vector $(0,\ldots,0,1,0,\ldots,0)$.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat, Fin, Real
Proof uses: Exists, Eq, HAdd.hAdd, OfNat.ofNat, ite
9 instances, coercions and auxiliary constants left out.
```
def IsPositiveUnitWalk {d : ℕ} (a : ℕ → Fin d → ℝ) : Prop :=
…
```
theorem Erdos192.erdos_192 sorry line 67 source
depends on sorry what this means
Statement uses: Eq, Set, Nat, Set.ofPred, Fin, Real, Erdos192.IsPositiveUnitWalk, Exists, And, Membership.mem, Set.range, Ne, HAdd.hAdd, HMul.hMul, OfNat.ofNat, Set.Iic
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
22 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.