85.lean`

Explanation legend Lean4 Domain Explanation Language (L4DEL)

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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 85

Reference: erdosproblems.com/85

Imports (1)

FormalConjecturesUtil

def Erdos85.f Let $f(n)$ be the smallest integer for which every graph on $n$ vertices with minimal degree $\geq f(n)$ contains a $C_4$ line 36 source
Source documentation
Let $f(n)$ be the smallest integer for which every graph on $n$ vertices with minimal degree $\geq f(n)$ contains a $C_4$.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: InfSet.sInf, Set.ofPred, SimpleGraph, Fin, GE.ge, SimpleGraph.minDegree, Classical.propDecidable, SimpleGraph.Adj, SimpleGraph.IsContained, OfNat.ofNat, SimpleGraph.cycleGraph
4 instances, coercions and auxiliary constants left out.
```
noncomputable def f (n : ℕ) : ℕ :=
…
```
theorem Erdos85.erdos_85 Is it true that, for all large $n$, $f(n + 1) \ge f(n)$? sorry line 44 source
Source documentation
Is it true that, for all large $n$, $f(n + 1) \ge f(n)$?

depends on sorry what this means
Statement uses: Iff, True, Filter.Eventually, Nat, LE.le, Erdos85.f, HAdd.hAdd, OfNat.ofNat, Filter.atTop
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
10 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_85 : answer(sorry) ↔ ∀ᶠ n in atTop, f n ≤ f (n + 1) := by
…
```
Mentions: Erdos85.f