Fin.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 9 curated AI-written annotations and 485 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, Polynomial Freiman-Ruzsa proof paper, arXiv v2

1 declarations, 0 contain sorry, 0 declared as axioms

Imports (1)

Mathlib.Algebra.BigOperators.Fin

Imported by 2 files

lemma Fin.sum_univ_castSucc' TODO: Rename Fin.sum_univ_castSucc to Fin.sum_univ_eq_castSucc line 12 source
Source comment
TODO: Rename `Fin.sum_univ_castSucc` to `Fin.sum_univ_eq_castSucc`

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: AddCommMonoid, Nat, Fin, HAdd.hAdd, OfNat.ofNat, Eq, Finset.sum, Finset.univ, Fin.castSucc, Finset.Iio, Fin.last
Proof uses: Eq.mpr, Finset.image, eq_of_heq, HEq, Eq.refl, HEq.refl, Eq.symm, Finset.sum_congr, Finset.coe_injective, Set.ext, Finset, of_eq_true, Iff, Membership.mem, Set, Eq.trans, LT.lt, True, congr, congrArg and 24 more
35 instances, coercions and auxiliary constants left out.

Tactic trace: 4 steps
Open to load the checked before-and-after goal states.
```
lemma Fin.sum_univ_castSucc' (f : Fin (n + 1) → M) :
    ∑ i : Fin n, f i.castSucc = ∑ i ∈ .Iio (.last _), f i := by
…
```