1030.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 1030

References:

erdosproblems.com/1030
[BEFS89] Burr, S. and Erdős, P. and Faudree, R. J. and Schelp, R. H., On the difference between consecutive Ramsey numbers. Utilitas Math. (1989), 115-118.

Imports (1)

FormalConjecturesUtil

theorem Erdos1030.erdos_1030 Let $R(k,l)$ be the usual Ramsey number: the smallest $n$ such that if the edges of $K_n$ are coloured red and blue then there exists either a red $K_k$ or a blue $K_l$ sorry line 45 source
Source documentation
Let $R(k,l)$ be the usual Ramsey number: the smallest $n$ such that if the edges of $K_n$ are coloured red and blue then there exists either a red $K_k$ or a blue $K_l$.
Prove the existence of some $c>0$ such that $$\lim_{k\to \infty}\frac{R(k+1,k)}{R(k,k)}> 1+c.$$
A problem of Erdős and Sós.

depends on sorry what this means
Statement uses: Exists, Real, And, GT.gt, OfNat.ofNat, Filter.Tendsto, Nat, HDiv.hDiv, SimpleGraph.classicalRamsey, HAdd.hAdd, Filter.atTop, nhds
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
36 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_1030 :
    ∃ c > (0 : ℝ), ∃ L : ℝ,
      Tendsto (fun k : ℕ ↦
        (SimpleGraph.classicalRamsey (k + 1) k : ℝ) /
          (SimpleGraph.classicalRamsey k k : ℝ)) atTop (nhds L) ∧
      L > 1 + c := by
…
```
Mentions: c, SimpleGraph.classicalRamsey