280.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

3 declarations, 1 contain sorry, 0 declared as axioms

Erdős Problem 280

References:

erdosproblems.com/280
[ErGr80] Erdős, P. and Graham, R., Old and new problems and results in combinatorial number theory. Monographies de L'Enseignement Mathematique (1980).

Imports (1)

FormalConjecturesUtil

def Erdos280.isCoveredBy The integer m is covered by one of the first k chosen congruence classes line 36 source
Source documentation
The integer m is covered by one of the first k chosen congruence classes.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: Exists, And, Membership.mem, Finset, Finset.Icc, OfNat.ofNat, Eq, HMod.hMod
7 instances, coercions and auxiliary constants left out.
```
def isCoveredBy (n a : ℕ → ℕ) (m k : ℕ) : Prop :=
…
```
def Erdos280.uncoveredCount The number of integers below n k not covered by the first k congruence classes line 40 source
Source documentation
The number of integers below n k not covered by the first k congruence classes.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: Finset.card, Finset.filter, Not, Erdos280.isCoveredBy, Classical.propDecidable, Finset.range
1 instances, coercions and auxiliary constants left out.

Tactic trace: 2 steps
Open to load the checked before-and-after goal states.
```
noncomputable def uncoveredCount (n a : ℕ → ℕ) (k : ℕ) : ℕ := by
…
```
theorem Erdos280.erdos_280 sorry line 54 source
depends on sorry what this means
Statement uses: Iff, False, Nat, StrictMono, LE.le, OfNat.ofNat, LT.lt, Exists, Real, And, GT.gt, HMul.hMul, HAdd.hAdd, Real.log, Not, Filter.Tendsto, HDiv.hDiv, Erdos280.uncoveredCount, Filter.atTop, nhds
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
42 instances, coercions and auxiliary constants left out.

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