Binomial-factorial identity #9273

Proved

WorkbookCorrected.plus_9273

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

arithmeticcorrectedelementaryrepairedworkbook

The elementary natural-number identity

(\binom{8}{4} * 7! * 4!) = 8467200

holds by direct arithmetic evaluation.

Formalization Note: This corrects Lean-Workbook record lean_workbook_plus_9273, 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 90720).

Source: InternLM Lean-Workbook, record lean_workbook_plus_9273 (Apache-2.0).

Preamble

import Mathlib.Data.Nat.Choose.Basic
import Mathlib.Data.Nat.Factorial.Basic
import Mathlib.Tactic.NormNum

Formal statement

theorem WorkbookCorrected.plus_9273 : ((Nat.choose 8 4) * (Nat.factorial 7) * (Nat.factorial 4)) = 8467200 := by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook; record lean_workbook_plus_9273; Apache-2.0; corrects Open node 6a7ac830-d8c4-48d1-abf2-9374c4e9a78d

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