FormalConjectures/ErdosProblems/213.lean

GitHub source file

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

3 declarations, 2 contain sorry, 0 declared as axioms

Erdős Problem 213

Reference: erdosproblems.com/213

Imports (1)
  1. def Erdos213.Erdos213For The predicate (on $n$) that there exist $n$ points in $\mathbb{R}^2$, no three on a line and no four on a circle, such that all pairwise distances are integers line 37 source

    Source documentation

    The predicate (on $n$) that there exist $n$ points in $\mathbb{R}^2$, no three on a line and no four on a circle, such that all pairwise distances are integers.

    standard axioms: Classical.choice, Quot.sound, propext what this means

    Statement uses: Nat

    Proof uses: Exists, Set, EuclideanSpace, Real, Fin, OfNat.ofNat, And, Set.Finite, Eq, Set.ncard, EuclideanGeometry.NonTrilinear, ENNReal, LE.le, Not, EuclideanGeometry.Cospherical, Set.Pairwise, Membership.mem, Set.range, Int, Dist.dist

    29 instances, coercions and auxiliary constants left out.

    def Erdos213For (n : ℕ) : Prop := ∃ S : Set ℝ², S.Finite ∧ S.ncard = n ∧
…
  2. theorem Erdos213.erdos_213 Let $n \geq 4$ sorry line 47 source

    Source documentation

    Let $n \geq 4$. Are there $n$ points in $\mathbb{R}^2$, no three on a line and no four on a circle, such that all pairwise distances are integers?

    depends on sorry what this means

    Statement uses: Iff, True, Nat, GE.ge, OfNat.ofNat, Erdos213.Erdos213For

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

    4 instances, coercions and auxiliary constants left out.

    Tactic trace: 1 steps

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

    theorem erdos_213 : answer(sorry) ↔ ∀ n : ℕ, n ≥ 4 → Erdos213For n := by sorry
…

    Mentions: Erdos213.Erdos213For

  3. theorem Erdos213.erdos_213.variants.KK08 The best construction to date, due to Kreisel and Kurz, has $n = 7$ sorry line 53 source

    Source documentation

    The best construction to date, due to Kreisel and Kurz, has $n = 7$.

    depends on sorry what this means

    Statement uses: Erdos213.Erdos213For, OfNat.ofNat, Nat

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

    2 instances, coercions and auxiliary constants left out.

    Tactic trace: 1 steps

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

    theorem erdos_213.variants.KK08 : Erdos213For 7 := by sorry
…

    Mentions: Erdos213.Erdos213For