544.lean`

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2 declarations, 2 contain sorry, 0 declared as axioms

Erdős Problem 544

References:

erdosproblems.com/544

Imports (1)

FormalConjecturesUtil

theorem Erdos544.erdos_544.parts.i Show that $$R(3,k+1)-R(3,k)\to\infty$$ as $k\to \infty$ sorry line 42 source
Source documentation
Show that $$R(3,k+1)-R(3,k)\to\infty$$ as $k\to \infty$.
A problem of Erdős and Sós. This problem is #8 in Ramsey Theory in the graphs problem collection.

depends on sorry what this means
Statement uses: Filter.Tendsto, Nat, Real, HSub.hSub, SimpleGraph.classicalRamsey, OfNat.ofNat, HAdd.hAdd, Filter.atTop
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_544.parts.i :
    Tendsto (fun k : ℕ ↦ (SimpleGraph.classicalRamsey 3 (k + 1) : ℝ) -
      (SimpleGraph.classicalRamsey 3 k : ℝ)) atTop atTop := by
…
```
Mentions: SimpleGraph.classicalRamsey
theorem Erdos544.erdos_544.parts.ii Similarly, prove or disprove that $$R(3,k+1)-R(3,k)=o(k).$$ sorry line 52 source
Source documentation
Similarly, prove or disprove that $$R(3,k+1)-R(3,k)=o(k).$$

depends on sorry what this means
Statement uses: Iff, True, Asymptotics.IsLittleO, Nat, Real, Filter.atTop, HSub.hSub, SimpleGraph.classicalRamsey, OfNat.ofNat, HAdd.hAdd
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_544.parts.ii : answer(sorry) ↔
    (fun k : ℕ ↦ (SimpleGraph.classicalRamsey 3 (k + 1) : ℝ) -
      (SimpleGraph.classicalRamsey 3 k : ℝ)) =o[atTop] (fun k : ℕ ↦ (k : ℝ)) := by
…
```
Mentions: SimpleGraph.classicalRamsey