Mathlib theorem · Existing formal mathematics

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

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 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.