Technical Lean evidence 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.
ProofAtlas record
What has been checked
These states distinguish upstream identity, local reproduction, review, and Atlas acceptance. This page is part of the public, read-only Mathlib landmark collection.
Mechanical evidence
- Declaration checked
szemeredi_regularity- Module
Mathlib.Combinatorics.SimpleGraph.Regularity.Lemma- Source file checked
Mathlib/Combinatorics/SimpleGraph/Regularity/Lemma.lean- Package commit
5e932f97dd25535344f80f9dd8da3aab83df0fe6- Build
- passed · transcript retained
- Unfinished proof steps
- None found by the recorded no-sorry scan
- Axiom closure
- Classical.choice, Quot.sound, propext
- Clean collection provenance
- Recorded
Evidence boundary
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 is evidence for the exact formal statement only. It does not establish novelty, transfer a historical acceptance decision, or authorize publication.