Prove2Me

Factorial arithmetic identity #7128

Proved
WorkbookCorrected.plus_7128

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

arithmeticcorrectedelementaryworkbook

The elementary natural-number / rational identity

9!/(5∗4∗3∗4∗3∗2∗3∗2∗1)=429! / (5 * 4 * 3 * 4 * 3 * 2 * 3 * 2 * 1) = 42

holds by direct arithmetic evaluation.

Formalization Note: This corrects Lean-Workbook record lean_workbook_plus_7128, 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_7128 (Apache-2.0).

Preamble
import Mathlib.Data.Nat.Factorial.Basic
import Mathlib.Tactic.NormNum
Formal statement
theorem WorkbookCorrected.plus_7128 : (Nat.factorial 9) / (5 * 4 * 3 * 4 * 3 * 2 * 3 * 2 * 1) = 42 := by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook; record lean_workbook_plus_7128; Apache-2.0; corrects Open node 17abcf05-cdbb-4d04-86e3-2e0a2d4b61f3

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