Prove2Me

Binomial coefficient identity #35148

Proved
WorkbookCorrected.plus_35148

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

arithmeticcorrectedelementaryworkbook

The elementary natural-number / rational identity

((104))−((64)+(41)∗(63))=115(\binom{10}{4}) - (\binom{6}{4} + \binom{4}{1} * \binom{6}{3}) = 115

holds by direct arithmetic evaluation.

Formalization Note: This corrects Lean-Workbook record lean_workbook_plus_35148, 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_35148 (Apache-2.0).

Preamble
import Mathlib.Data.Nat.Choose.Basic
import Mathlib.Tactic.NormNum
Formal statement
theorem WorkbookCorrected.plus_35148 : (Nat.choose 10 4) - ((Nat.choose 6 4) + (Nat.choose 4 1) * (Nat.choose 6 3)) = 115 := by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook; record lean_workbook_plus_35148; Apache-2.0; corrects Open node c094b4b9-d4e6-46c9-b0c3-9232d164808d

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