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Factorial arithmetic identity #81110

Proved
WorkbookCorrected.plus_81110

by carlok · Sep 29, 2026 · Mathlib 0df444a (Lean v4.33.1)

arithmeticcorrectedelementaryworkbook

The elementary natural-number / rational identity

8∗10!∗2!=8∗10!∗2!8 * 10! * 2! = 8 * 10! * 2!8∗10!∗2!=8∗10!∗2!

holds by direct arithmetic evaluation.

Formalization Note: This corrects Lean-Workbook record lean_workbook_plus_81110, 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_81110 (Apache-2.0).

Preamble
import Mathlib.Data.Nat.Factorial.Basic
import Mathlib.Tactic.NormNum
Formal statement
theorem WorkbookCorrected.plus_81110 : 8 * (Nat.factorial 10) * (Nat.factorial 2) = 8 * (Nat.factorial 10) * (Nat.factorial 2) := by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook; record lean_workbook_plus_81110; Apache-2.0; corrects Open node b0979d85-c32d-4aef-bc4c-053b7a644ab9

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