773.lean`

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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 773

References:

erdosproblems.com/773
[AlEr85] Alon, Noga and Erdős, P., An application of graph theory to additive number theory. European J. Combin. (1985), 201-203.
[Er80] Erdős, Paul, A survey of problems in combinatorial number theory. Ann. Discrete Math. (1980), 89-115.
[LeTh95] Lefmann, Hanno and Thiele, Torsten, Point sets with distinct distances. Combinatorica (1995), 379--408.

Imports (1)

FormalConjecturesUtil

theorem Erdos773.erdos_773 What is the size of the largest Sidon subset $A\subseteq\{1,2^2,\ldots,N^2\}$? sorry line 43 source
Source documentation
What is the size of the largest Sidon subset $A\subseteq\{1,2^2,\ldots,N^2\}$? Is it $N^{1-o(1)}$?

depends on sorry what this means
Statement uses: Iff, True, Real, GT.gt, OfNat.ofNat, Filter.Eventually, Nat, LE.le, HPow.hPow, HSub.hSub, Finset.maxSidonSubsetCard, Finset.image, Finset.Icc, Filter.atTop
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
40 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_773 : answer(sorry) ↔
    ∀ ε > (0 : ℝ), ∀ᶠ N : ℕ in atTop,
      (N : ℝ) ^ (1 - ε) ≤
        (Finset.maxSidonSubsetCard
          (Finset.image (fun n : ℕ => n ^ 2) (Finset.Icc 1 N)) : ℝ) := by
…
```
Mentions: Finset.maxSidonSubsetCard