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Factorial arithmetic identity #45515

Disproved
WorkbookCorrected.plus_45515

by carlok · Sep 30, 2026 · Mathlib 0df444a (Lean v4.33.1)

arithmeticcorrectedelementaryworkbook

The elementary natural-number / rational identity

10!/(2!3)=4500010! / (2!^3) = 4500010!/(2!3)=45000

holds by direct arithmetic evaluation.

Formalization Note: This corrects Lean-Workbook record lean_workbook_plus_45515, 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_45515 (Apache-2.0).

Preamble
import Mathlib.Tactic.NormNum
Formal statement
theorem WorkbookCorrected.plus_45515 : (Nat.factorial 10) / ((Nat.factorial 2) ^ 3) = 45000 := by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook; record lean_workbook_plus_45515; Apache-2.0; corrects Open node 98b03b61-4abc-42fa-9765-632061114120

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