303.lean`

Explanation legend Lean4 Domain Explanation Language (L4DEL)

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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 303

References:

erdosproblems.com/303
[BrRo91] Brown, Tom C. and Rödl, Voijtech, Monochromatic solutions to equations with unit fractions. Bull. Austral. Math. Soc. (1991), 387-392.

Imports (1)

FormalConjecturesUtil

theorem Erdos303.erdos_303 Is it true that in any finite colouring of the integers there exists a monochromatic solution to $\frac 1 a = \frac 1 b + \frac 1 c$ with distinct $a, b, c$? sorry line 42 source
Source documentation
Is it true that in any finite colouring of the integers there exists a monochromatic solution to $\frac 1 a = \frac 1 b + \frac 1 c$ with distinct $a, b, c$?
This is true, as proved by Brown and Rödl [BrRo91].
This was formalized in Lean by Yuan using Seed-Prover.

depends on sorry what this means
Statement uses: Iff, True, Int, Set.Finite, Set.range, Exists, And, List.Nodup, List.cons, OfNat.ofNat, List.nil, Eq, Real, HDiv.hDiv, HAdd.hAdd, Set.Subsingleton, Set.image, Insert.insert, Set, Singleton.singleton
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous, Nat
25 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_303 :
    answer(True) ↔
    -- For any finite colouring of the integers
    ∀ (𝓒 : ℤ → ℤ), (Set.range 𝓒).Finite →
      -- There exists integers `a, b, c`
      ∃ (a b c : ℤ),
      -- that are non-zero and distinct.
      [a, b, c, 0].Nodup ∧
      -- `a, b, c` satisfy the equation
      (1/a : ℝ) = 1/b + 1/c ∧
      -- `a, b, c` have the same color
      (𝓒 '' {a, b, c}).Subsingleton := by
…
```
Mentions: c