Prove2Me

Factorial arithmetic identity #35143

Proved
WorkbookCorrected.plus_35143

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

arithmeticcorrectedelementaryworkbook

The elementary natural-number / rational identity

(12!)/((3!∗9!))=220(12!)/((3!*9!)) = 220

holds by direct arithmetic evaluation.

Formalization Note: This corrects Lean-Workbook record lean_workbook_plus_35143, 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_35143 (Apache-2.0).

Preamble
import Mathlib.Data.Nat.Factorial.Basic
import Mathlib.Tactic.NormNum
Formal statement
theorem WorkbookCorrected.plus_35143 : (Nat.factorial 12)/(((Nat.factorial 3)*(Nat.factorial 9))) = 220 := by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook; record lean_workbook_plus_35143; Apache-2.0; corrects Open node 3afe1d63-423f-46f5-861a-088913b9cbca

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