616.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

1 declarations, 1 contain sorry, 0 declared as axioms

Erdős Problem 616

References:

erdosproblems.com/616
[EHT91] Erdős, Paul and Hajnal, András and Tuza, Zsolt, Local constraints ensuring small representing sets. J. Combin. Theory Ser. A (1991), 78-84.

Imports (1)

FormalConjecturesUtil

theorem Erdos616.erdos_616 Let $r\geq 3$ sorry line 42 source
Source documentation
Let $r\geq 3$. For an $r$-uniform hypergraph $G$ let $\tau(G)$ denote the covering number (or transversal number), the minimum size of a set of vertices which includes at least one from each edge in $G$. Determine the best possible $t$ such that, if $G$ is an $r$-uniform hypergraph $G$ where every subgraph $G'$ on at most $3r-3$ vertices has $\tau(G')\leq 1$, we have $\tau(G)\leq t$.

depends on sorry what this means
Statement uses: Nat, ENat, sorryAx, Bool.false, LE.le, OfNat.ofNat, Eq, Hypergraph.localTransversalBound, HSub.hSub, HMul.hMul
Proof uses: Lean.Name, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
12 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_616 :
    let f : ℕ → ℕ∞ := answer(sorry)
…
```