1139.lean`

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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 1139

Reference: erdosproblems.com/1139

Imports (1)

FormalConjecturesUtil

theorem Erdos1139.erdos_1139 Let $1\leq u_1 < u_2 < \cdots$ be the sequence of integers with at most $2$ prime factors sorry line 38 source
Source documentation
Let $1\leq u_1 < u_2 < \cdots$ be the sequence of integers with at most $2$ prime factors. Is it true that $$\limsup_{k \to \infty} \frac{u_{k+1}-u_k}{\log k}=\infty?$$

depends on sorry what this means
Statement uses: Iff, True, Eq, EReal, Filter.limsup, Nat, HDiv.hDiv, HSub.hSub, Real, Nat.nth, And, LT.lt, OfNat.ofNat, LE.le, ArithmeticFunction, ArithmeticFunction.cardFactors, HAdd.hAdd, Real.log, Filter.atTop, Top.top
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
56 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_1139 :
    answer(sorry) ↔
      letI u := Nat.nth (fun n ↦ 0 < n ∧ Ω n ≤ 2)
…
```