FormalConjectures/ErdosProblems/66.lean

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Explanation legend Lean4 Domain Explanation Language (L4DEL)

L4DEL explanations are a separate layer. They do not change the Lean source. Intuition is explanatory prose; numbered items are a reading path; sources link the wording back to evidence.

L4DEL
Lean4 Domain Explanation Language

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 66

Reference: erdosproblems.com/66

Imports (1)
  1. theorem Erdos66.erdos_66 Is there and $A \subset \mathbb{N}$ is such that $$\lim_{n\to \infty}\frac{1_A\ast 1_A(n)}{\log n}$$ exists and is $\ne 0$? sorry line 40 source

    Source documentation

    Is there and $A \subset \mathbb{N}$ is such that $$\lim_{n\to \infty}\frac{1_A\ast 1_A(n)}{\log n}$$ exists and is $\ne 0$?

    depends on sorry what this means

    Statement uses: Iff, True, Exists, Set, Nat, Real, And, Ne, OfNat.ofNat, Filter.Tendsto, HDiv.hDiv, AdditiveCombinatorics.sumRep, Real.log, Filter.atTop, nhds

    Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous

    23 instances, coercions and auxiliary constants left out.

    Tactic trace: 1 steps

    Open to load the checked before-and-after goal states.

    theorem erdos_66 : answer(sorry) ↔ ∃ (A : Set ℕ) (c : ℝ), c ≠ 0 ∧
    Tendsto (fun n ↦ (sumRep A n : ℝ) / Real.log n) atTop (𝓝 c) := by
…

    Mentions: c