982.lean`

Explanation legend Lean4 Domain Explanation Language (L4DEL)

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L4DEL: Lean4 Domain Explanation Language

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

1 declarations, 1 contain sorry, 0 declared as axioms

Erdős Problem 982

Reference: erdosproblems.com/982

Imports (1)

FormalConjecturesUtil

theorem Erdos982.erdos_982 If $n$ distinct points in $\mathbb{R}^2$ form a convex polygon then some vertex has at least $\lfloor\frac{n}{2}\rfloor$ different distances to other vertices sorry line 37 source
Source documentation
If $n$ distinct points in $\mathbb{R}^2$ form a convex polygon then some vertex has at least $\lfloor\frac{n}{2}\rfloor$ different distances to other vertices.

depends on sorry what this means
Statement uses: Nat, LE.le, OfNat.ofNat, Fin, EuclideanSpace, Real, Function.Injective, EuclideanGeometry.IsConvexPolygon, ENNReal, Exists, GE.ge, Set.ncard, Set.ofPred, And, Ne, Eq, Dist.dist, HDiv.hDiv
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
60 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_982 (n : ℕ) (hn : 3 ≤ n) (p : Fin n → ℝ²) (hp : Function.Injective p)
    (hp' : EuclideanGeometry.IsConvexPolygon p) :
    ∃ (i : Fin n), { d : ℝ | ∃ j : Fin n, j ≠ i ∧ d = dist (p i) (p j) }.ncard ≥ n / 2 := by
…
```
Mentions: EuclideanGeometry.IsConvexPolygon