Lean verification record
Checked Artifact: Sylow Subgroup Counting 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
card_sylow_modEq_one- Module
Mathlib.GroupTheory.Sylow- Source file checked
Mathlib/GroupTheory/Sylow.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 checked artifact is bound only to Mathlib's counting declaration card_sylow_modEq_one: for prime p and a group G with finitely many Sylow p-subgroups, Nat.card (Sylow p G) is congruent to 1 modulo p. The overview mentions the separate upstream instance Sylow.isPretransitive_of_finite only as mathematical context; that conjugacy declaration is not part of this artifact's recorded declaration set. The checked endpoint does not make a Sylow subgroup unique or canonical, give an exact enumeration formula, include the divisibility-by-index clause sometimes grouped into Sylow III, establish existence or containment from Sylow I, or require G itself to be finite.
This checker record does not establish novelty, transfer a historical acceptance decision, or authorize publication.