Prove2Me

Binomial-factorial identity #62975

Proved
WorkbookCorrected.plus_62975

by carlok · Sep 22, 2026 · Mathlib 0df444a (Lean v4.33.1)

arithmeticcorrectedelementaryworkbook

The elementary natural-number / rational identity

(94)∗(5!/(2!∗2!))=9!/(2!∗2!∗4!)\binom{9}{4} * (5! / (2! * 2!)) = 9! / (2! * 2! * 4!)

holds by direct arithmetic evaluation.

Formalization Note: This corrects Lean-Workbook record lean_workbook_plus_62975, which omitted a compilable colon/type annotation and/or used a preamble of only Mathlib.Analysis.Complex.Basic.

Source: InternLM Lean-Workbook, record lean_workbook_plus_62975 (Apache-2.0).

Preamble
import Mathlib.Data.Nat.Choose.Basic
import Mathlib.Data.Nat.Factorial.Basic
import Mathlib.Tactic.NormNum
Formal statement
theorem WorkbookCorrected.plus_62975 : (Nat.choose 9 4) * ((Nat.factorial 5) / ((Nat.factorial 2) * (Nat.factorial 2))) = (Nat.factorial 9) / ((Nat.factorial 2) * (Nat.factorial 2) * (Nat.factorial 4)) := by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook; record lean_workbook_plus_62975; Apache-2.0; corrects Open node c0214a64-eade-4916-898c-54a662b4f115

View graph