Prove2Me

Binomial-factorial identity #55641

Proved
WorkbookCorrected.plus_55641

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

arithmeticcorrectedelementaryworkbook

The elementary natural-number / rational identity

(7!∗4!∗70)=(7!∗4!∗choose(4+5−1)(5−1))(7! * 4! * 70) = (7! * 4! * choose (4+5-1) (5-1))

holds by direct arithmetic evaluation.

Formalization Note: This corrects Lean-Workbook record lean_workbook_plus_55641, 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_55641 (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_55641 : ((Nat.factorial 7) * (Nat.factorial 4) * 70) = ((Nat.factorial 7) * (Nat.factorial 4) * (Nat.choose (4+5-1) (5-1))) := by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook; record lean_workbook_plus_55641; Apache-2.0; corrects Open node 25320e62-d1a0-4054-9dfc-9abcb2037f40

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