ModOne.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, 0 contain sorry, 0 declared as axioms

Imports (1)

Mathlib.Analysis.Real.Cardinality

Imported by 1 file

FormalConjecturesForMathlib.lean

def IsEquidistributed Documented declaration: IsEquidistributed line 29 source
Source documentation
A sequence (s_1, s_2, s_3, ...) of real numbers is said to be equidistributed on an interval [a, b] if for every subinterval [c, d] of [a, b] we have lim_{n→ ∞} |{s_1, ..., s_n} ∩ [c, d]| / n = (d - c)/(b-a)

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Real, Nat
Proof uses: LE.le, Set, Set.Icc, Filter.Tendsto, HDiv.hDiv, Finset.card, Finset.filter, Membership.mem, Finset.range, Filter.atTop, nhds, HSub.hSub
17 instances, coercions and auxiliary constants left out.
```
def IsEquidistributed (a b : ℝ) (s : ℕ → ℝ) : Prop :=
…
```
def IsEquidistributedModuloOne Documented declaration: IsEquidistributedModuloOne line 39 source
Source documentation
A sequence (s_1, s_2, s_3, ...) of real numbers is said to be equidistributed modulo 1 or uniformly distributed modulo 1 if the sequence of the fractional parts of a_n, denoted by (a_n) or by a_n − ⌊a_n⌋, is equidistributed in the interval [0, 1].

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat, Real
Proof uses: IsEquidistributed, OfNat.ofNat, Int.fract
7 instances, coercions and auxiliary constants left out.
```
def IsEquidistributedModuloOne (s : ℕ → ℝ) : Prop :=
…
```