Lean verification record

Checked Artifact: Łoś's 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: FirstOrder.Language.Ultraproduct.sentence_realize
Module: Mathlib.ModelTheory.Ultraproducts
Source file checked: Mathlib/ModelTheory/Ultraproducts.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 target indexes Mathlib's sentence-level form of Łoś's theorem. For an ultrafilter u and a family M of nonempty L-structures, the ultraproduct satisfies a sentence φ exactly when M a satisfies φ for u-almost every a. “u-almost every” means membership in the ultrafilter; it is not numerical majority, probability, or measure. The selected endpoint does not itself display parameters for formulas with free variables.

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