Prove2Me

Applying Pascal’s recurrence twice

Proved
WorkbookRestored.plus_9465

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

lean-workbookrestored-importssource-checked

For every natural number nn,

(n+24)=(n2)+2(n3)+(n4).\binom{n+2}4=\binom n2+2\binom n3+\binom n4.

This restores the missing imports or namespaces of the original node, retaining its formal proposition. Source: Lean-Workbook row lean_workbook_plus_9465 (Apache-2.0).

Preamble
import Mathlib.Data.Nat.Choose.Basic
open Nat
Formal statement
theorem WorkbookRestored.plus_9465 (n : ℕ) : choose (n + 2) 4 = choose n 2 + 2 * choose n 3 + choose n 4   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_9465; original Prove2Me node 2919d552-4766-4c5f-b650-f0bbec90ff33; Apache-2.0

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