927.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 927

References:

erdosproblems.com/927
[MoMo65] Moon, J. W. and Moser, L., On cliques in graphs. Israel J. Math. (1965), 23-28.
[Er66b] Erdős, P., On cliques in graphs. Israel J. Math. (1966), 233--234.
[Er69b] Erdős, P., Problems and results in chromatic graph theory. Proof Techniques in Graph Theory (Proc. Second Ann Arbor Graph Theory Conf., Ann Arbor, Mich., 1968) (1969), 27-35.
[Er71] Erdős, P., Some unsolved problems in graph theory and combinatorial analysis. Combinatorial Mathematics and its Applications (Proc. Conf., Oxford, 1969) (1971), 97-109.
[Sp71] Spencer, J. H., On cliques in graphs. Israel J. Math. (1971), 419-421.

Imports (1)

FormalConjecturesUtil

def Erdos927.g g n is the maximum number of different sizes of cliques (maximal complete subgraphs) of a graph on n vertices line 43 source
Source documentation
g n is the maximum number of different sizes of cliques (maximal complete subgraphs) of a graph on n vertices.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: Finset.sup, SimpleGraph, Fin, Finset.univ, Set.ncard, SimpleGraph.cliqueSizes
6 instances, coercions and auxiliary constants left out.

Tactic trace: 2 steps
Open to load the checked before-and-after goal states.
```
noncomputable def g (n : ℕ) : ℕ := by
…
```
theorem Erdos927.erdos_927 sorry line 67 source
depends on sorry what this means
Statement uses: Iff, False, Exists, Nat, Filter.Eventually, And, LE.le, HAdd.hAdd, Erdos927.g, Nat.log, OfNat.ofNat, Nat.iteratedLog, Filter.atTop
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
10 instances, coercions and auxiliary constants left out.

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