716.lean`

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Project sources: Pinned project documentation, Formal Conjectures paper, arXiv v1

1 declarations, 1 contain sorry, 0 declared as axioms

Erdős Problem 716

References:

erdosproblems.com/716
[BES73] Brown, W. G. and Erdős, P. and S'os, V. T., Some extremal problems on {$r$}-graphs. (1973), 53--63.
[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.

Imports (1)

FormalConjecturesUtil

theorem Erdos716.erdos_716 Let $\mathcal{F}$ be the family of all $3$-uniform hypergraphs with $6$ vertices and $3$ $3$-edges sorry line 46 source
Source documentation
Let $\mathcal{F}$ be the family of all $3$-uniform hypergraphs with $6$ vertices and $3$ $3$-edges. Is it true that $$\mathrm{ex}_3(n,\mathcal{F})=o(n^2)?$$
The answer is yes, proved by Ruzsa and Szemerédi [RuSz78] (this is known as the Ruzsa-Szemerédi problem).

depends on sorry what this means
Statement uses: Iff, True, Asymptotics.IsLittleO, Nat, Real, Filter.atTop, Hypergraph.configurationExtremalNumber, OfNat.ofNat, HPow.hPow
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
18 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_716 :
    answer(True) ↔
    (fun n ↦ (Hypergraph.configurationExtremalNumber n 3 6 3 : ℝ)) =o[atTop]
      (fun n ↦ (n : ℝ) ^ 2) := by
…
```
Mentions: Hypergraph.configurationExtremalNumber