Prove2Me

Factorial arithmetic identity #9037

Proved
WorkbookCorrected.plus_9037

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

arithmeticcorrectedelementaryworkbook

The elementary natural-number / rational identity

10!/(8!∗2!)∗(4!/(2!∗2!))∗(4!/(2!∗2!))=162010! / (8! * 2!) * (4! / (2! * 2!)) * (4! / (2! * 2!)) = 1620

holds by direct arithmetic evaluation.

Formalization Note: This corrects Lean-Workbook record lean_workbook_plus_9037, 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_9037 (Apache-2.0).

Preamble
import Mathlib.Data.Nat.Factorial.Basic
import Mathlib.Tactic.NormNum
Formal statement
theorem WorkbookCorrected.plus_9037 : (Nat.factorial 10) / ((Nat.factorial 8) * (Nat.factorial 2)) * ((Nat.factorial 4) / ((Nat.factorial 2) * (Nat.factorial 2))) * ((Nat.factorial 4) / ((Nat.factorial 2) * (Nat.factorial 2))) = 1620 := by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook; record lean_workbook_plus_9037; Apache-2.0; corrects Open node 51d2ccd9-03ec-4cd1-8a2d-f201a738a662

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