34.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

2 declarations, 1 contain sorry, 0 declared as axioms

Erdős Problem 34

References:

erdosproblems.com/34
[Er77c] Erdős, Paul, Problems and results on combinatorial number theory. III. Number theory day (Proc. Conf., Rockefeller Univ., New York, 1976) (1977), 43-72.
[ErGr80] Erdős, P. and Graham, R., Old and new problems and results in combinatorial number theory. Monographies de L'Enseignement Mathematique (1980).
[He86] Hegyvári, N., On consecutive sums in sequences. Acta Math. Hungar. (1986), 193--200.
[Ko15] Konieczny, J., On consecutive sums in permutations. arXiv:1504.07156 (2015).

Imports (1)

FormalConjecturesUtil

def Erdos34.consecutiveSums The set of consecutive sums of a permutation p of {1,…,n}, where position k holds the value p k + 1: the sums ∑_{u ≤ k ≤ v} (p k + 1) line 42 source
Source documentation
The set of consecutive sums of a permutation p of {1,…,n}, where position k holds the value p k + 1: the sums ∑_{u ≤ k ≤ v} (p k + 1).

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat, Equiv.Perm, Fin, Finset
Proof uses: Finset.image, Prod, Finset.sum, Finset.Icc, Prod.fst, Prod.snd, HAdd.hAdd, OfNat.ofNat, Finset.filter, LE.le, Finset.univ
16 instances, coercions and auxiliary constants left out.
```
def consecutiveSums (n : ℕ) (p : Equiv.Perm (Fin n)) : Finset ℕ :=
…
```
theorem Erdos34.erdos_34 sorry line 57 source
depends on sorry what this means
Statement uses: Iff, False, Real, LT.lt, OfNat.ofNat, Exists, Nat, GE.ge, Equiv.Perm, Fin, Finset.card, Erdos34.consecutiveSums, HMul.hMul, HPow.hPow
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
26 instances, coercions and auxiliary constants left out.

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