225.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

2 declarations, 1 contain sorry, 0 declared as axioms

Erdős Problem 225

References:

erdosproblems.com/225
[Er40b] Erdős, P., Note on some elementary properties of polynomials. Bull. Amer. Math. Soc. (1940), 954-958.
[Er57] Erdős, Paul, Some unsolved problems. Michigan Math. J. (1957), 291-300.
[Er61] Erdős, Paul, Some unsolved problems. Magyar Tud. Akad. Mat. Kutató Int. Közl. (1961), 221-254.
[Ha74] Hayman, W. K., Research problems in function theory: new problems. (1974), 155-180.
[Kr74] Kristiansen, G. K., Proof of an inequality for trigonometric polynomials. Proc. Amer. Math. Soc. (1974), 49-57.
[SaSh74] Saff, E. B. and Sheil-Small, T., Coefficient and integral mean estimates for algebraic and trigonometric polynomials with restricted zeros. J. London Math. Soc. (2) (1974/75), 16-22.
[Kr76] Kristiansen, G. K., Erratum to "Proof of a polynomial conjecture". Proc. Amer. Math. Soc. (1976), 377.

Imports (1)

FormalConjecturesUtil

def Erdos225.trigPoly The trigonometric polynomial $f(z) = \sum_{0\leq k\leq n}c_k e^{ikz}$, as an entire function of $z\in\mathbb{C}$ line 48 source
Source documentation
The trigonometric polynomial $f(z) = \sum_{0\leq k\leq n}c_k e^{ikz}$, as an entire function of $z\in\mathbb{C}$.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat, Complex
Proof uses: Finset.sum, Finset.range, HAdd.hAdd, OfNat.ofNat, HMul.hMul, Complex.exp, Complex.I
8 instances, coercions and auxiliary constants left out.
```
noncomputable def trigPoly (n : ℕ) (c : ℕ → ℂ) (z : ℂ) : ℂ :=
…
```
Mentions: c
theorem Erdos225.erdos_225 sorry line 71 source
depends on sorry what this means
Statement uses: Iff, True, Nat, Complex, LT.lt, OfNat.ofNat, Ne, Eq, Erdos225.trigPoly, Real, Complex.im, Membership.mem, Set, Set.Icc, HMul.hMul, Real.pi, LE.le, Norm.norm, Exists, And and 2 more
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
48 instances, coercions and auxiliary constants left out.

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