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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

1 declarations, 0 contain sorry, 0 declared as axioms

Divergence of a nonnegative sum over a subset

Mathlib's not_summable_iff_tendsto_nat_atTop_of_nonneg relates ¬ Summable f for f : ℕ → ℝ to divergence of its partial sums. This states the same for a sum restricted to a subset A ⊆ ℕ, in terms of the partial sums over A.

Imports (2)

Imported by 1 file

FormalConjecturesForMathlib.lean

theorem not_summable_subtype_iff_tendsto_sum_indicator For a nonnegative f, the sum over a subset A fails to be summable exactly when the partial sums of f restricted to A diverge line 36 source
Source documentation
For a nonnegative f, the sum over a subset A fails to be summable exactly when the partial sums of f restricted to A diverge.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Set, Nat, Real, LE.le, OfNat.ofNat, Iff, Not, Summable, Membership.mem, SummationFilter.unconditional, Filter.Tendsto, Finset.sum, Finset.range, Set.indicator, Filter.atTop
Proof uses: Eq, Function.comp, Subtype, rfl, Eq.mpr, id, congrArg, propext, summable_subtype_iff_indicator, not_summable_iff_tendsto_nat_atTop_of_nonneg, Set.indicator_nonneg, Iff.rfl
28 instances, coercions and auxiliary constants left out.

Tactic trace: 2 steps
Open to load the checked before-and-after goal states.
```
theorem not_summable_subtype_iff_tendsto_sum_indicator {A : Set ℕ} {f : ℕ → ℝ}
    (hf : ∀ n, 0 ≤ f n) :
    ¬ Summable (fun n : A ↦ f n) ↔
      Tendsto (fun N : ℕ => ∑ n ∈ Finset.range N, A.indicator f n) atTop atTop := by
…
```