363.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, 1 contain sorry, 0 declared as axioms

Erdős Problem 363

References:

erdosproblems.com/363
[BaBe07] Bauer, Mark and Bennett, Michael A., On a question of Erd\H{o}s and Graham. Enseign. Math. (2) (2007), 259--264.
[BeVL12] Bennett, Michael A. and Van Luijk, Ronald, Squares from blocks of consecutive integers: a problem of Erd\H{o}s and Graham. Indag. Math. (N.S.) (2012), 123--127.
[Ul05] Ulas, Maciej, On products of disjoint blocks of consecutive integers. Enseign. Math. (2) (2005), 331--334.

Imports (1)

FormalConjecturesUtil

def Erdos363.IsInterval A finite set of naturals is an interval of naturals line 41 source
Source documentation
A finite set of naturals is an interval of naturals.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Finset, Nat
Proof uses: Exists, Eq, Finset.Icc
2 instances, coercions and auxiliary constants left out.
```
def IsInterval (I : Finset ℕ) : Prop :=
…
```
def Erdos363.IsValidCollection A collection of intervals as in Erdős Problem 363: disjoint intervals of positive integers, each of size at least 4, whose product is a square line 47 source
Source documentation
A collection of intervals as in Erdős Problem 363: disjoint intervals of positive integers, each of size at least 4, whose product is a square. Intervals containing 0 are excluded, since their product is 0, which is a square.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: List, Finset, Nat
Proof uses: And, Membership.mem, Erdos363.IsInterval, LE.le, OfNat.ofNat, Finset.card, Not, List.Pairwise, Disjoint, IsSquare, List.prod, List.map, Finset.prod
10 instances, coercions and auxiliary constants left out.
```
def IsValidCollection (S : List (Finset ℕ)) : Prop :=
…
```
theorem Erdos363.erdos_363 sorry line 67 source
depends on sorry what this means
Statement uses: Iff, False, List, Nat, Set.Finite, Finset, Set.ofPred, And, Erdos363.IsValidCollection, Eq, List.map, Finset.card
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous, OfNat.ofNat
1 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.