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Factorial arithmetic identity #31931

Proved
WorkbookCorrected.plus_31931

by carlok · Oct 6, 2026 · Mathlib 0df444a (Lean v4.33.1)

arithmeticcorrectedelementaryrepairedworkbook

The elementary natural-number identity

10∗8∗6∗4/4!=8010 * 8 * 6 * 4 / 4! = 8010∗8∗6∗4/4!=80

holds by direct arithmetic evaluation.

Formalization Note: This corrects Lean-Workbook record lean_workbook_plus_31931, which omitted a compilable colon/type annotation and/or used a preamble of only Mathlib.Analysis.Complex.Basic, and whose stated right-hand side did not match the evaluated left-hand side. The repaired statement keeps the combinatorial/arithmetic left-hand side and uses the evaluated integer right-hand side (original RHS was 240).

Source: InternLM Lean-Workbook, record lean_workbook_plus_31931 (Apache-2.0).

Preamble
import Mathlib.Data.Nat.Factorial.Basic
import Mathlib.Tactic.NormNum
Formal statement
theorem WorkbookCorrected.plus_31931 : 10 * 8 * 6 * 4 / (Nat.factorial 4) = 80 := by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook; record lean_workbook_plus_31931; Apache-2.0; corrects Open node 3f35d5b7-85c1-433a-87da-e811ae350f70

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