Lean verification record
Checked Artifact: Szemerédi’s Regularity Lemma (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
szemeredi_regularity- Module
Mathlib.Combinatorics.SimpleGraph.Regularity.Lemma- Source file checked
Mathlib/Combinatorics/SimpleGraph/Regularity/Lemma.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
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 effective equipartition form of the finite graph regularity lemma. It assumes ε > 0 and l no larger than the finite vertex count, and it produces a partition of the full vertex set with part sizes differing by at most one, l ≤ #P.parts ≤ SzemerediRegularity.bound ε l, and at most an ε-proportion of ordered distinct part-pairs non-ε-uniform. It does not require every pair to be uniform. This is not Szemerédi’s theorem on arithmetic progressions, a diagonal or degree form of regularity, a counting or removal lemma, or a claim that the bound is optimal, small, or attained.
This checker record does not establish novelty, transfer a historical acceptance decision, or authorize publication.