Prove2Me

Ten factorial over two and eight factorial

Proved
WorkbookCorrected.plus_48564

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

arithmeticcorrectedelementaryworkbook

The elementary natural-number / rational identity

10!2! 8!=45\frac{10!}{2!\,8!} = 45

holds by direct arithmetic evaluation.

Formalization Note: This corrects Lean-Workbook record lean_workbook_plus_48564, 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_48564 (Apache-2.0).

Preamble
import Mathlib.Data.Nat.Factorial.Basic
import Mathlib.Tactic.NormNum
Formal statement
theorem WorkbookCorrected.plus_48564 : Nat.factorial 10 / (Nat.factorial 2 * Nat.factorial 8) = 45 := by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook; record lean_workbook_plus_48564; Apache-2.0; corrects Open node 2734dbc5-8bd6-4bdb-8214-68e76922be31

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