4.lean`

Explanation legend Lean4 Domain Explanation Language (L4DEL)

L4DEL explanations are a separate layer. They do not change the Lean source. Intuition is explanatory prose; numbered items are a reading path; sources link the wording back to evidence.

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

3 declarations, 2 contain sorry, 0 declared as axioms

Erdős Problem 4

Reference: erdosproblems.com/4

Imports (1)

FormalConjecturesUtil

def Erdos4.Erdos4For line 32 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Real
Proof uses: Set.Infinite, Nat, Set.ofPred, GT.gt, HSub.hSub, Nat.nth, Nat.Prime, HAdd.hAdd, OfNat.ofNat, HMul.hMul, HDiv.hDiv, Real.log, HPow.hPow
17 instances, coercions and auxiliary constants left out.
theorem Erdos4.erdos_4 Is it true that, for any $C > 0$, there infinitely many $n$ such that: $$ p_{n + 1} - p_n > C \frac{\log\log n\log\log\log\log n}{(\log\log\log n) ^ 2}\log n $$ sorry line 43 source
Source documentation
Is it true that, for any $C > 0$, there infinitely many $n$ such that: $$ p_{n + 1} - p_n > C \frac{\log\log n\log\log\log\log n}{(\log\log\log n) ^ 2}\log n $$

depends on sorry what this means
Statement uses: Iff, True, Real, GT.gt, OfNat.ofNat, Erdos4.Erdos4For
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous, Nat
7 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_4 : answer(True) ↔ (∀ C > 0, Erdos4For C) := by
…
```
Mentions: Erdos4.Erdos4For
theorem Erdos4.erdos_4.variants.rankin Rankin's theorem: there exists a positive constant $C$ such that Erdos4For C holds sorry line 48 source
Source documentation
Rankin's theorem: there exists a positive constant $C$ such that Erdos4For C holds.

depends on sorry what this means
Statement uses: Exists, Real, And, GT.gt, OfNat.ofNat, Erdos4.Erdos4For
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous, Nat
7 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_4.variants.rankin :
    ∃ C > 0, Erdos4For C := by
…
```
Mentions: Erdos4.Erdos4For