GraphConjecture176.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

Written on the Wall II - Conjecture 176

Reference: E. DeLaVina, Written on the Wall II, Conjectures of Graffiti.pc

The conjecture is false for the graph D₇, formed from two triangles by joining distinguished vertices with a path of seven edges. It has at most four leaves in a spanning tree and largest induced bipartite subgraph order ten. The two maximum-degree vertices of its square are at distance five in the original graph, so the claimed inequality would give 14 ≥ 17.

Imports (1)

FormalConjecturesUtil

def WrittenOnTheWallII.GraphConjecture176.squareMaximumDegreeVertices The maximum-degree vertices of G², presented using finite graph distance line 41 source
Source documentation
The maximum-degree vertices of G², presented using finite graph distance.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Fintype, DecidableEq, SimpleGraph, DecidableRel, SimpleGraph.Adj, Set
Proof uses: Nat, Finset.card, Finset.filter, And, Ne, LE.le, SimpleGraph.computable_dist, OfNat.ofNat, Eq, Finset.univ, Set.ofPred, Finset.sup
8 instances, coercions and auxiliary constants left out.
```
def squareMaximumDegreeVertices {V : Type} [Fintype V] [DecidableEq V]
    (G : SimpleGraph V) [DecidableRel G.Adj] : Set V :=
…
```
theorem WrittenOnTheWallII.GraphConjecture176.conjecture176 sorry line 55 source
depends on sorry what this means
Statement uses: Iff, False, Fintype, DecidableEq, Nontrivial, SimpleGraph, DecidableRel, SimpleGraph.Adj, SimpleGraph.Connected, GE.ge, Real, HAdd.hAdd, SimpleGraph.Ls, SimpleGraph.b, Fintype.card, SimpleGraph.distMin, WrittenOnTheWallII.GraphConjecture176.squareMaximumDegreeVertices
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous, OfNat.ofNat, Nat
11 instances, coercions and auxiliary constants left out.

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