Lean verification record

Checked Artifact: Binomial Theorem (mathlib)

Proof Atlas collected build, no-sorry, axiom, and clean-source evidence directly from the pinned upstream declaration.

Verification result

The recorded Lean checks passed

Build replaypassed with retained transcript
Unfinished stepsNone found
Source identityPinned commit and file recorded
Dependency profileAxiom closure recorded

Reproducibility details

What the checker recorded

Declaration checked: add_pow
Module: Mathlib.Data.Nat.Choose.Sum
Source file checked: Mathlib/Data/Nat/Choose/Sum.lean
Package commit: 5e932f97dd25535344f80f9dd8da3aab83df0fe6
Build transcript: passed · retained with this record
Unfinished proof steps: None found by the recorded no-sorry scan
Axiom closure: Classical.choice, Quot.sound, propext
Collection provenance: Clean source state recorded

ProofAtlas record

What has been checked

Upstream indexedPinned source bytes verified locally

Locally reproducedExact upstream declaration replayed

Reviewed pageCurrent public presentation reviewed

Accepted Atlas resultNot recorded for the preferred artifact

Mathlib is the source of the theorem; the local Lean replay and page review are separate.

Evidence boundary

Exact formal statement only

This page indexes Mathlib's commutative-semiring binomial theorem add_pow. For x and y in a commutative semiring and n in ℕ, it gives one finite sum indexed by range (n + 1), with summand x ^ m * y ^ (n - m) * n.choose m. It is not an analytic infinite-series statement, does not extend the exponent beyond natural numbers, and does not claim the formula for arbitrary noncommuting elements.

This checker record does not establish novelty, transfer a historical acceptance decision, or authorize publication.