Prove2Me

Binomial coefficient identity #31403

Proved
WorkbookCorrected.plus_31403

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

arithmeticcorrectedelementaryworkbook

The elementary natural-number / rational identity

((325))−((61)∗(225))+((62)∗(125))=55252(\binom{32}{5}) - (\binom{6}{1} * \binom{22}{5}) + (\binom{6}{2} * \binom{12}{5}) = 55252

holds by direct arithmetic evaluation.

Formalization Note: This corrects Lean-Workbook record lean_workbook_plus_31403, 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_31403 (Apache-2.0).

Preamble
import Mathlib.Data.Nat.Choose.Basic
import Mathlib.Tactic.NormNum
Formal statement
theorem WorkbookCorrected.plus_31403 : (Nat.choose 32 5) - ((Nat.choose 6 1) * (Nat.choose 22 5)) + ((Nat.choose 6 2) * (Nat.choose 12 5)) = 55252 := by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook; record lean_workbook_plus_31403; Apache-2.0; corrects Open node ecde47a8-b43f-4c23-98fd-46b797d7e2f5

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