312.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 312

Reference: erdosproblems.com/312

Imports (1)

FormalConjecturesUtil

theorem Erdos312.erdos_312 Documented declaration: erdos_312 sorry line 36 source
Source documentation
Does there exist a constant c > 0 such that, for any K > 1, whenever A is a sufficiently large finite multiset of integers with $\sum_{n \in A} 1/n > K$ there exists some $S \subseteq A$ such that $1 - \exp(-(c*K)) < \sum_{n \in S} 1/n \le 1$?

depends on sorry what this means
Statement uses: Iff, True, Exists, Real, And, LT.lt, OfNat.ofNat, Nat, Fin, GE.ge, GT.gt, Finset.sum, Finset.univ, Inv.inv, Finset, HSub.hSub, Real.exp, Neg.neg, HMul.hMul, LE.le
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
35 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_312 :
    answer(sorry) ↔
    ∃ (c : ℝ), 0 < c ∧
      ∀ (K : ℝ), 1 < K →
        ∃ (N₀ : ℕ),
          ∀ (n : ℕ) (a : Fin n → ℕ),
            (n ≥ N₀ ∧ (∑ i : Fin n, (a i : ℝ)⁻¹) > K) →
              ∃ (S : Finset (Fin n)),
                1 - Real.exp (-(c * K)) < (∑ i ∈ S, (a i : ℝ)⁻¹) ∧
                ∑ i ∈ S, (a i : ℝ)⁻¹ ≤ 1 := by
…
```
Mentions: c