1158.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

1 declarations, 1 contain sorry, 0 declared as axioms

Erdős Problem 1158

References:

erdosproblems.com/1158
[Er64f] Erdős, P., On extremal problems of graphs and generalized graphs. Israel J. Math. (1964), 183--190.

Imports (1)

FormalConjecturesUtil

theorem Erdos1158.erdos_1158 Let $K_{t}(r)$ be the complete $t$-partite $t$-uniform hypergraph with $r$ vertices in each class sorry line 42 source
Source documentation
Let $K_{t}(r)$ be the complete $t$-partite $t$-uniform hypergraph with $r$ vertices in each class. Is it true that $$\mathrm{ex}_t(n,K_t(r)) \geq n^{t-r^{1-t}-o(1)}$$ for all $t,r\geq 2$? The restriction $r\geq 2$ excludes forbidding a single edge.

depends on sorry what this means
Statement uses: Iff, True, Nat, LE.le, OfNat.ofNat, Real, LT.lt, Filter.Eventually, HPow.hPow, HSub.hSub, Hypergraph.partiteExtremalNumber, Filter.atTop
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
30 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_1158 :
    answer(sorry) ↔ ∀ t r : ℕ, 2 ≤ t → 2 ≤ r →
    ∀ ε : ℝ, 0 < ε → ∀ᶠ n : ℕ in atTop,
      (n : ℝ) ^ ((t : ℝ) - (r : ℝ) ^ (1 - (t : ℝ)) - ε) ≤
        (Hypergraph.partiteExtremalNumber n t r : ℝ) := by
…
```
Mentions: Hypergraph.partiteExtremalNumber