A finite binomial convolution

Proved

WorkbookSyntax.plus_44878

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbookrepaired-notationsource-checked

$\sum_{k=0}^{10}\binom{22}{10-k}\binom{15}{k}=348330136$ .

Notation repair: Replaced the obsolete finite-sum binder “in” with the current “∈” notation. The ranges, summands, hypotheses and conclusion are unchanged.

Source: Lean-Workbook record lean_workbook_plus_44878 (Apache-2.0). Original declaration.

Preamble

import Mathlib
open Nat

Formal statement

theorem WorkbookSyntax.plus_44878 (h₁ : 0 < 22) (h₂ : 0 < 15) : ∑ k ∈ Finset.range 11, (Nat.choose 22 (10 - k) * Nat.choose 15 k) = 348330136   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_44878; finite-sum notation repair; Apache-2.0

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