ProofAtlas

Lean evidence record

Hook-Length Formula: Lean evidence

This technical record binds the exact theorem statement to its commit-pinned Lean source, checker results, assumptions, and publication-review status.

Read theorem page
Lean buildpassed
Unfinished proof stepsNone
Publication reviewsAccepted

Exact formal proposition

Hypotheses and conclusion

This is the meaningful proposition proved by the checked wrapper declaration. It is extracted from the same commit-pinned Lean source.

def HookLengthFormulaStatement : Prop :=
  ∀ μ : YoungDiagram,
    hookProduct μ * standardTableauCount μ = Nat.factorial μ.card
Definitions used in this proposition

standardTableauCount

noncomputable def standardTableauCount (μ : YoungDiagram) : ℕ :=
  Fintype.card {T : Cell μ → Fin μ.card // IsStandardTableau μ T}

hookProduct

def hookProduct (μ : YoungDiagram) : ℕ :=
  μ.cells.attach.prod fun c ↦ hookLength μ c
Lean wrapper declaration

The checked endpoint names the expanded proposition above. Both come from the same commit-pinned source.

theorem hookLengthFormula : HookLengthFormulaStatement
Open main Lean file

Line counts exclude blank lines; comments and documentation count. The total is the commit-pinned first-party Lean import closure; Mathlib and other third-party dependencies are excluded.

Technical evidence record

Source identity, checker results, and assumptions

Main Lean declaration
hookLengthFormula
Source commit
7e628b6361f2

Mechanical evidence

Lean verification

These fields support the exact Lean declaration, not a broader informal claim.

Artifact ID
artifact.known-hook-length-formula.endpoint.v001
Declarations covered by recorded evidence
AtlasKnownTheorems.HookLengthFormula.hookLengthFormula
AtlasKnownTheorems.HookLengthFormula.HookLengthFormulaStatement
Lean build
passed
Recorded build time
4.3 s one machine-dependent evidence run, not a benchmark
Evidence collected
· clean-source provenance recorded
Unfinished proof check
passed
Lean toolchain
leanprover/lean4:v4.29.1
Recorded source commit
7e628b6361f20e33d6b8214adc608685b9d4da2d
Source SHA-256
sha256:bfcd609759bb37494f274922f11b212beaae2dce56da4e197912ced7915089a6
Statement alignment
accepted

Lean foundations

Standard foundations used by the proof

Lean reports the logical foundations below through Mathlib. They are standard proof-system foundations, not conjectural mathematical assumptions about this theorem. The recorded closure stays within the approved classical_mathlib_standard profile, with no unexpected axiom or unfinished-proof placeholder.

  • Classical.choice
  • Quot.sound
  • propext

Files and machine-readable evidence

Reproduce or inspect the recorded check

Use the complete first-party source bundle for reconstruction, or inspect the exact main file and checker evidence separately. Mathlib and other third-party dependencies are identified but not rebundled.

Complete checked Lean source · 1 Lean file · 1 evidence record · Download ZIPBrowse counted source onlineDownload main Lean fileDownload checker evidence (JSON)Download Apache-2.0 license

Review results

Publication reviews accepted

All four required publication-review gates are accepted for the reviewed presentation of this exact theorem. The review results are separate from the Lean build and do not broaden the formal statement.

Read the publication-review details