857.lean`

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L4DEL: Lean4 Domain Explanation Language

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

2 declarations, 1 contain sorry, 0 declared as axioms

Erdős Problem 857

Reference: erdosproblems.com/857

For fixed n, k, let m(n, k) be minimal such that every family of subsets of [n] of size at least m(n, k) contains a k-sunflower. The problem asks to estimate m(n, k), ideally asymptotically.

Imports (1)

FormalConjecturesUtil

def Erdos857.m m(n, k): minimal sunflower-forcing family size in the non-uniform [n] model line 39 source
Source documentation
m(n, k): minimal sunflower-forcing family size in the non-uniform [n] model.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: InfSet.sInf, Set.ofPred, Set, Fin, LE.le, Set.ncard, Exists, And, Eq, IsSunflower
3 instances, coercions and auxiliary constants left out.
```
noncomputable def m (n k : ℕ) : ℕ :=
…
```
theorem Erdos857.erdos_857 Estimate m(n,k), or better give an asymptotic formula sorry line 47 source
Source documentation
Estimate m(n,k), or better give an asymptotic formula.

depends on sorry what this means
Statement uses: Nat, Real, sorryAx, Bool.false, LE.le, OfNat.ofNat, Filter.Tendsto, HDiv.hDiv, Erdos857.m, Filter.atTop, nhds
Proof uses: Lean.Name, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
26 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_857 :
    let f : ℕ → ℕ → ℝ := answer(sorry)
…
```