1021.lean`

Explanation legend Lean4 Domain Explanation Language (L4DEL)

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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

3 declarations, 2 contain sorry, 0 declared as axioms

Erdős Problem 1021

References:

erdosproblems.com/1021
[Er71] Erdős, P., Some unsolved problems in graph theory and combinatorial analysis. Combinatorial Mathematics and its Applications (Proc. Conf., Oxford, 1969) (1971), 97-109.
[Er74c] Erdős, Paul, Extremal problems on graphs and hypergraphs. (1974), 75-84.
[CoLe21] Conlon, David and Lee, Joonkyung, On the extremal number of subdivisions. Int. Math. Res. Not. IMRN (2021), 9122--9145.
[Ja19] Janzer, Oliver, Improved bounds for the extremal number of subdivisions. Electron. J. Combin. (2019), Paper No. 3.3, 6.

Imports (1)

FormalConjecturesUtil

def Erdos1021.cliqueSubdivision Documented declaration: cliqueSubdivision line 44 source
Source documentation
The graph G_k: the bipartite graph between {y_1, …, y_k} (the elements of Fin k) and {z_1, …, z_{k choose 2}} (the two-element subsets of Fin k), each z being joined to the two elements of the corresponding pair. This is the 1-subdivision of K_k.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat, SimpleGraph, Sum, Fin, Finset, Set.powersetCard, OfNat.ofNat
Proof uses: SimpleGraph.mk, Erdos1021.cliqueSubdivision.match_1, Membership.mem, Set, False
10 instances, coercions and auxiliary constants left out.

Tactic trace: 9 steps
Open to load the checked before-and-after goal states.
```
def cliqueSubdivision (k : ℕ) : SimpleGraph (Fin k ⊕ Set.powersetCard (Fin k) 2) where
…
```
theorem Erdos1021.erdos_1021 sorry line 72 source
depends on sorry what this means
Statement uses: Iff, True, Nat, LE.le, OfNat.ofNat, Exists, Real, And, LT.lt, Asymptotics.IsBigO, Filter.atTop, SimpleGraph.extremalNumber, Sum, Fin, Finset, Set.powersetCard, Erdos1021.cliqueSubdivision, HPow.hPow, HSub.hSub, HDiv.hDiv
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
40 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem Erdos1021.erdos_1021.variants.janzer sorry line 81 source
depends on sorry what this means
Statement uses: Nat, LE.le, OfNat.ofNat, Asymptotics.IsBigO, Real, Filter.atTop, SimpleGraph.extremalNumber, Sum, Fin, Finset, Set.powersetCard, Erdos1021.cliqueSubdivision, HPow.hPow, HSub.hSub, HDiv.hDiv, HMul.hMul
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
42 instances, coercions and auxiliary constants left out.

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