Prove2Me

Nine factorial over mixed factorials

Proved
WorkbookCorrected.plus_39046

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

arithmeticcorrectedelementaryworkbook

The elementary natural-number / rational identity

9!2! 2! 4!=3780\frac{9!}{2!\,2!\,4!} = 3780

holds by direct arithmetic evaluation.

Formalization Note: This corrects Lean-Workbook record lean_workbook_plus_39046, 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_39046 (Apache-2.0).

Preamble
import Mathlib.Data.Nat.Factorial.Basic
import Mathlib.Tactic.NormNum
Formal statement
theorem WorkbookCorrected.plus_39046 : Nat.factorial 9 / (Nat.factorial 2 * Nat.factorial 2 * Nat.factorial 4) = 3780 := by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook; record lean_workbook_plus_39046; Apache-2.0; corrects Open node 42c8db8f-c49c-4431-9e87-93e95dfeae63

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