An out-of-range odd binomial coefficient vanishes

Proved

WorkbookRestored.plus_40829

by wamlart · Sep 12, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

lean-workbookrestored-importssource-checked

For natural $n,j$ with $2j+1>n$ , $\binom n{2j+1}=0$ .

This restores the missing imports or namespaces of the original node, retaining its formal proposition. Source: Lean-Workbook row lean_workbook_plus_40829 (Apache-2.0).

Preamble

import Mathlib.Analysis.Complex.Basic
import Mathlib.Data.Nat.Choose.Basic
open Nat

Formal statement

theorem WorkbookRestored.plus_40829 (n j : ℕ) (h₁ : 2 * j + 1 > n) : choose n (2 * j + 1) = 0   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_40829; original Prove2Me node 456a017f-aa8d-4451-88dd-99ba7457eb39; Apache-2.0

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