94.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

2 declarations, 2 contain sorry, 0 declared as axioms

Ben Green's Open Problem 94

Reference:

Imports (1)

FormalConjecturesUtil

theorem Green94.green_94_outer_measure Let A ⊂ R be a set of positive outer measure sorry line 40 source
Source documentation
Let A ⊂ R be a set of positive outer measure. Does $A$ contain an affine copy of {1, 1/2, 1/4, . . . }?
The answer is "no".

depends on sorry what this means
Statement uses: Iff, False, Set, Real, GT.gt, ENNReal, MeasureTheory.Measure, MeasureTheory.MeasureSpace.volume, OfNat.ofNat, Exists, And, Ne, Nat, Membership.mem, HAdd.hAdd, HMul.hMul, HDiv.hDiv, HPow.hPow
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
58 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem green_94_outer_measure :
   answer(False) ↔ ∀ A : Set ℝ,
   volume A > 0 →
   ∃ a b : ℝ, a ≠ 0 ∧ ∀ n : ℕ, a * (1 / 2^n) + b ∈ A := by
…
```
theorem Green94.green_94 Let A ⊂ R be a set of positive measure sorry line 50 source
Source documentation
Let A ⊂ R be a set of positive measure. Does $A$ contain an affine copy of {1, 1/2, 1/4, . . . }?

depends on sorry what this means
Statement uses: Iff, True, Set, Real, And, MeasurableSet, GT.gt, ENNReal, MeasureTheory.Measure, MeasureTheory.MeasureSpace.volume, OfNat.ofNat, Exists, Ne, Nat, Membership.mem, HAdd.hAdd, HMul.hMul, HDiv.hDiv, HPow.hPow
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 green_94 :
   answer(sorry) ↔ ∀ A : Set ℝ,
   MeasurableSet A ∧ volume A > 0 →
   ∃ a b : ℝ, a ≠ 0 ∧ ∀ n : ℕ, a * (1 / 2^n) + b ∈ A := by
…
```