536.lean`

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L4DEL: Lean4 Domain Explanation Language

Annotation provenance. This overlay contains 10 curated AI-written annotations and 7190 mechanical source-derived annotations. They have not been human-reviewed as explanations; treat them as unverified and not mathematical authority. Retained generation history: The 71 original curated annotations were produced in a Claude Sonnet 5.5 session at medium effort; Claude Opus 5.5 is recorded in that session as the advisor model, not the direct author. The bulk source-derived expansion was generated mechanically from pinned source comments by tooling developed in a GPT-5.6 Sol session at ultra reasoning; GPT-5.6 Sol did not originate the quoted source prose. On 2026-10-17 the mechanically generated source-comment annotations of the Formal Conjectures, Carleson, FLT, PFR, CompFiles, Mathematics in Lean and Theorem Proving in Lean overlays were regenerated by the same generator after three corrections made in a Claude Sonnet 5.5 session: titles no longer cut a sentence inside mathematics or end on a dangling word, workflow markers are removed from the quoted prose, and declaration names follow the scanner's namespace resolution. The boilerplate step line was dropped, and comments that were only a row of dashes no longer yield annotations. No new prose was written and no human review is claimed.

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 536

Reference: erdosproblems.com/536

Imports (1)

FormalConjecturesUtil

theorem Erdos536.erdos_536 Let $\epsilon>0$ and $N$ be sufficiently large sorry line 39 source
Source documentation
Let $\epsilon>0$ and $N$ be sufficiently large. Is it true that if $A\subseteq \{1,\ldots,N\}$ has size at least $\epsilon N$ then there must be distinct $a,b,c\in A$ such that $$[a, b]=[b, c]=[a, c],$$ where $[\cdot, \cdot]$ denotes the least common multiple?

depends on sorry what this means
Statement uses: Iff, True, Real, GT.gt, OfNat.ofNat, Filter.Eventually, Nat, Finset, LE.le, Finset.Icc, HMul.hMul, Finset.card, Exists, And, Membership.mem, Eq, Insert.insert, Singleton.singleton, Nat.lcm, Filter.atTop
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
38 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_536 :
    answer(sorry) ↔ ∀ᵉ (ε > (0: ℝ)), ∀ᶠ N in atTop,
    ∀ (A : Finset ℕ), A ⊆ Icc 1 N → (ε * (N : ℝ)) ≤ (A.card : ℝ) →
    ∃ᵉ  (a ∈ A) (b ∈ A) (c ∈ A),
    # {a, b, c} = 3 ∧ a.lcm b = b.lcm c ∧ b.lcm c = a.lcm c := by
…
```
Mentions: c