Prove2Me

Binomial-factorial identity #33723

Proved
WorkbookCorrected.plus_33723

by carlok · Oct 1, 2026 · Mathlib 0df444a (Lean v4.33.1)

arithmeticcorrectedelementaryworkbook

The elementary natural-number / rational identity

(10050)=100!/(50!∗50!)\binom{100}{50} = 100! / (50! * 50!)

holds by direct arithmetic evaluation.

Formalization Note: This corrects Lean-Workbook record lean_workbook_plus_33723, 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_33723 (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_33723 : (Nat.choose 100 50) = (Nat.factorial 100) / ((Nat.factorial 50) * (Nat.factorial 50)) := by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook; record lean_workbook_plus_33723; Apache-2.0; corrects Open node 540a64e0-d5a9-474e-825a-4dde0e346e3f

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