591.lean`

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L4DEL: Lean4 Domain Explanation Language

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Credit: The upstream authors and contributors retain credit for the project and mathematics. lean4-explainer only renders their pinned source and adds the separately disclosed explanation layer.

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

1 declarations, 1 contain sorry, 0 declared as axioms

Erdős Problem 591

References:

erdosproblems.com/591
[Sc10] Schipperus, Rene, Countable partition ordinals. Ann. Pure Appl. Logic (2010), 1195-1215.

Imports (1)

FormalConjecturesUtil

theorem Erdos591.erdos_591 Let $α$ be the infinite ordinal $\omega^{\omega^2}$ sorry line 43 source
Source documentation
Let $α$ be the infinite ordinal $\omega^{\omega^2}$. Is it true that any red/blue colouring of the edges of $K_α$ there is either a red $K_α$ or a blue $K_3$?
This is true and was proved independently by Schipperus [Sc10] and Darby.

depends on sorry what this means
Statement uses: Iff, True, OrdinalCardinalRamsey, HPow.hPow, Ordinal, Ordinal.omega0, Nat, OfNat.ofNat, Cardinal
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
20 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_591 : answer(True) ↔ OrdinalCardinalRamsey (ω ^ ω ^ 2) (ω ^ ω ^ 2) 3 := by
…
```
Mentions: OrdinalCardinalRamsey