296.lean`

Explanation legend Lean4 Domain Explanation Language (L4DEL)

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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

3 declarations, 1 contain sorry, 0 declared as axioms

Erdős Problem 296

References:

erdosproblems.com/296
[Bl21] Bloom, T. F., On a density conjecture about unit fractions. arXiv:2112.03726 (2021).

Imports (1)

FormalConjecturesUtil

def Erdos296.recipSum The reciprocal sum of a finite set of natural numbers, as a rational number line 36 source
Source documentation
The reciprocal sum of a finite set of natural numbers, as a rational number.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Finset, Nat, Rat
Proof uses: Finset.sum, HDiv.hDiv, OfNat.ofNat
6 instances, coercions and auxiliary constants left out.
```
def recipSum (A : Finset ℕ) : ℚ :=
…
```
def Erdos296.HasDisjointUnitDecomps There are k pairwise disjoint subsets of {1, ..., N} with reciprocal sum 1 line 40 source
Source documentation
There are k pairwise disjoint subsets of {1, ..., N} with reciprocal sum 1.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: Exists, Fin, Finset, And, LE.le, Finset.Icc, OfNat.ofNat, Eq, Rat, Erdos296.recipSum, Ne, Disjoint
8 instances, coercions and auxiliary constants left out.
```
def HasDisjointUnitDecomps (N k : ℕ) : Prop :=
…
```
theorem Erdos296.erdos_296 sorry line 54 source
depends on sorry what this means
Statement uses: And, Nat, Erdos296.HasDisjointUnitDecomps, LE.le, Rat, Erdos296.recipSum, Finset.Icc, OfNat.ofNat, Real, LT.lt, Filter.Eventually, Nat.floor, HMul.hMul, HSub.hSub, Real.log, Filter.atTop
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
44 instances, coercions and auxiliary constants left out.

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