52.lean`

Explanation legend Lean4 Domain Explanation Language (L4DEL)

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L4DEL: Lean4 Domain Explanation Language

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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 52

Reference: erdosproblems.com/52

Imports (1)

FormalConjecturesUtil

theorem Erdos52.erdos_52 Let $A$ be a finite set of integers sorry line 37 source
Source documentation
Let $A$ be a finite set of integers. Is it true that for every $\epsilon>0$ $\max( \lvert A+A\rvert,\lvert AA\rvert)\gg_\epsilon \lvert A\rvert^{2-\epsilon}?$

depends on sorry what this means
Statement uses: Iff, True, Real, LT.lt, OfNat.ofNat, Exists, And, Finset, Int, GE.ge, Max.max, Finset.card, HAdd.hAdd, HMul.hMul, HPow.hPow, HSub.hSub, Nat
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
50 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_52 : answer(sorry) ↔ ∀ (ε : ℝ), 0 < ε → ε < 1 → ∃ (C : ℝ), 0 < C ∧ ∀ (A : Finset ℤ),
    (max (A + A).card (A * A).card : ℝ) ≥ C * (A.card : ℝ) ^ (2 - ε) := by
…
```