25.lean`

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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 25: Logarithmic density of size-dependent congruences

Reference: erdosproblems.com/25

Imports (1)

FormalConjecturesUtil

theorem Erdos25.erdos_25 Let $n_1 < n_2 < \dots$ be an arbitrary sequence of integers, each with an associated residue class $a_i \pmod{n_i}$ sorry line 39 source
Source documentation
Let $n_1 < n_2 < \dots$ be an arbitrary sequence of integers, each with an associated residue class $a_i \pmod{n_i}$. Let $A$ be the set of integers $n$ such that for every $i$ either $n < n_i$ or $n \not\equiv a_i \pmod{n_i}$. Must the logarithmic density of $A$ exist?

depends on sorry what this means
Statement uses: Iff, True, Nat, Int, LT.lt, OfNat.ofNat, StrictMono, Exists, Real, Set.HasLogDensity, Set.ofPred, Or, Not, Int.ModEq
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
12 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_25 : answer(sorry) ↔
    ∀ (seq_n : ℕ → ℕ) (seq_a : ℕ → ℤ), (∀ i, 0 < seq_n i) → StrictMono seq_n →
      ∃ d, Set.HasLogDensity
        { x : ℕ | ∀ i, (x : ℤ) < seq_n i ∨ ¬((x : ℤ) ≡ seq_a i [ZMOD seq_n i]) } d := by
…
```
Mentions: Set.HasLogDensity