FormalConjectures/ErdosProblems/653.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 653

Reference: erdosproblems.com/653

Imports (1)
  1. theorem Erdos653.erdos_653 Documented declaration: erdos_653 sorry line 38 source

    Source documentation

    Let $x_1,\ldots,x_n\in \mathbb{R}^2$ and let $R(x_i)=\#\{ \lvert x_j-x_i\rvert : j\neq i\}$, where the points are ordered such that $$R(x_1)\leq \cdots \leq R(x_n).$$ Let $g(n)$ be the maximum number of distinct values the $R(x_i)$ can take. Is it true that $g(n) \geq (1-o(1))n$?

    depends on sorry what this means

    Statement uses: Iff, True, Exists, Nat, Real, And, Asymptotics.IsLittleO, Filter.atTop, OfNat.ofNat, Filter.Eventually, LE.le, HMul.hMul, HSub.hSub, EuclideanGeometry.maximalDistinctDistancesFrom

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

    25 instances, coercions and auxiliary constants left out.

    Tactic trace: 1 steps

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

    theorem erdos_653 : answer(sorry) ↔ ∃ o : ℕ → ℝ, o =o[atTop] (1 : ℕ → ℝ) ∧
    ∀ᶠ n in atTop, (1 - o n) * n ≤ maximalDistinctDistancesFrom n := by
…