1178.lean`

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L4DEL: Lean4 Domain Explanation Language

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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 1178

References:

erdosproblems.com/1178
[BES73] Brown, W. G. and Erdős, P. and S'os, V. T., Some extremal problems on {$r$}-graphs. (1973), 53--63.
[CGLS23] Conlon, David and Gishboliner, Lior and Levanzov, Yevgeny and Shapira, Asaf, A new bound for the {B}rown-{E}rd\H os-S'os problem. J. Combin. Theory Ser. B (2023), 1--35.
[EFR86] Erdős, P. and Frankl, P. and Rödl, V., The asymptotic number of graphs not containing a fixed subgraph and a problem for hypergraphs having no exponent. Graphs Combin. (1986), 113-121.
[Er75b] Erdős, Paul, Problems and results in combinatorial number theory. Journ'{e}es Arithm'{e}tiques de Bordeaux (Conf., Univ. Bordeaux, Bordeaux, 1974) (1975), 295-310.
[RuSz78] Ruzsa, I. Z. and Szemer'{e}di, E., Triple systems with no six points carrying three triangles. Combinatorics (Proc. Fifth Hungarian Colloq., Keszthely, 1976), Vol. II (1978), 939-945.
[SaSe05] Sárk"ozy, Gábor N. and Selkow, Stanley, An extension of the {R}uzsa-Szemer'edi theorem . Combinatorica (2005), 77--84.
[SoSo17] Solymosi, David and Solymosi, Jozsef, Small cores in 3-uniform hypergraphs. J. Combin. Theory Ser. B (2017), 897--910.

Imports (1)

FormalConjecturesUtil

theorem Erdos1178.erdos_1178 Documented declaration: erdos_1178 sorry line 56 source
Source documentation
For $r\geq 3$ let $d_r(e)$ be the minimal $d$ such that $$\mathrm{ex}_r(n,\mathcal{F})=o(n^2),$$ where $\mathcal{F}$ is the family of $r$-uniform hypergraphs on $d$ vertices with $e$ edges. Prove that $$d_r(e)=(r-2)e+3$$ for all $r,e\geq 3$.

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

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_1178 :
    ∀ r e : ℕ, 3 ≤ r → 3 ≤ e →
    Hypergraph.sparseConfigurationThreshold r e = (((r - 2) * e + 3 : ℕ) : ℕ∞) := by
…
```
Mentions: Hypergraph.sparseConfigurationThreshold