Prove2Me

Binomial-factorial identity #45071

Proved
WorkbookCorrected.plus_45071

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

arithmeticcorrectedelementaryworkbook

The elementary natural-number / rational identity

3!∗((42))∗((62))=5403! * (\binom{4}{2}) * (\binom{6}{2}) = 540

holds by direct arithmetic evaluation.

Formalization Note: This corrects Lean-Workbook record lean_workbook_plus_45071, 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_45071 (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_45071 : (Nat.factorial 3) * (Nat.choose 4 2) * (Nat.choose 6 2) = 540 := by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook; record lean_workbook_plus_45071; Apache-2.0; corrects Open node e9cd02f9-38db-48f6-9379-cfc550cb15d6

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