Prove2Me

Factorial arithmetic identity #37901

Proved
WorkbookCorrected.plus_37901

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

arithmeticcorrectedelementaryworkbook

The elementary natural-number / rational identity

(10!/(2!∗3!))−(9!/(2!∗2!))=211680(10!/(2!*3!))-(9!/(2!*2!)) = 211680

holds by direct arithmetic evaluation.

Formalization Note: This corrects Lean-Workbook record lean_workbook_plus_37901, 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_37901 (Apache-2.0).

Preamble
import Mathlib.Data.Nat.Factorial.Basic
import Mathlib.Tactic.NormNum
Formal statement
theorem WorkbookCorrected.plus_37901 : ((Nat.factorial 10)/((Nat.factorial 2)*(Nat.factorial 3)))-((Nat.factorial 9)/((Nat.factorial 2)*(Nat.factorial 2))) = 211680 := by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook; record lean_workbook_plus_37901; Apache-2.0; corrects Open node 38182c5f-a0f9-4928-ad1a-1b62ec344a00

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