Prove2Me

Binomial coefficient identity #23470

Proved
WorkbookCorrected.plus_23470

by carlok · Sep 29, 2026 · Mathlib 0df444a (Lean v4.33.1)

arithmeticcorrectedelementaryworkbook

The elementary natural-number / rational identity

9∗(((3520)))=4∗(((3520))+((3516)))9 * ((\binom{35}{20})) = 4 * ((\binom{35}{20}) + (\binom{35}{16}))

holds by direct arithmetic evaluation.

Formalization Note: This corrects Lean-Workbook record lean_workbook_plus_23470, 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_23470 (Apache-2.0).

Preamble
import Mathlib.Data.Nat.Choose.Basic
import Mathlib.Data.Rat.Defs
import Mathlib.Tactic.Ring
import Mathlib.Tactic.NormNum
Formal statement
theorem WorkbookCorrected.plus_23470 : (9:ℚ) * ((Nat.choose 35 20)) = (4:ℚ) * ((Nat.choose 35 20) + (Nat.choose 35 16)) := by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook; record lean_workbook_plus_23470; Apache-2.0; corrects Open node e85f58ab-f331-4b21-b017-c88fa1f7fd6e

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