Prove2Me

Difference of binomial coefficients

Proved
WorkbookCorrected.plus_6122

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

arithmeticcorrectedelementaryworkbook

The elementary natural-number / rational identity

(164)−(144)=819\binom{16}{4} - \binom{14}{4} = 819

holds by direct arithmetic evaluation.

Formalization Note: This corrects Lean-Workbook record lean_workbook_plus_6122, 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_6122 (Apache-2.0).

Preamble
import Mathlib.Data.Nat.Choose.Basic
import Mathlib.Tactic.NormNum
Formal statement
theorem WorkbookCorrected.plus_6122 : Nat.choose 16 4 - Nat.choose 14 4 = 819 := by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook; record lean_workbook_plus_6122; Apache-2.0; corrects Open node 9f7aef63-d93f-4cf1-a07f-b574acebd9dd

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