352.lean`

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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 352

Reference: erdosproblems.com/352

Imports (1)

FormalConjecturesUtil

theorem Erdos352.erdos_352 Is there some $c > 0$ such that every measurable $A \subseteq \mathbb{R}^2$ of measure $\geq c$ contains the vertices of a triangle of area 1? sorry line 38 source
Source documentation
Is there some $c > 0$ such that every measurable $A \subseteq \mathbb{R}^2$ of measure $\geq c$ contains the vertices of a triangle of area 1?

depends on sorry what this means
Statement uses: Iff, True, Exists, Real, And, GT.gt, OfNat.ofNat, Set, EuclideanSpace, Fin, Nat, MeasurableSet, ENNReal, GE.ge, EReal, MeasureTheory.Measure, MeasureTheory.MeasureSpace.volume, Affine.Triangle, Membership.mem, Affine.Simplex.points and 3 more
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
166 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_352 :
    answer(sorry) ↔ ∃ c > (0: ℝ), ∀ A : Set ℝ², MeasurableSet A → ℙ A ≥ c.toEReal
       → (∃ t : Affine.Triangle ℝ ℝ²,
           (∀ p : Fin 3, t.points p ∈ A) ∧
           EuclideanGeometry.triangle_area (t.points 0) (t.points 1) (t.points 2) = 1) := by
…
```
Mentions: c, EuclideanGeometry.triangle_area