Prove2Me

Partial sum of binomial coefficients

Proved
WorkbookCorrected.plus_8968

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

arithmeticcorrectedelementaryworkbook

The elementary natural-number / rational identity

(30)+(41)+(52)=(62)\binom{3}{0}+\binom{4}{1}+\binom{5}{2}=\binom{6}{2}

holds by direct arithmetic evaluation.

Formalization Note: This corrects Lean-Workbook record lean_workbook_plus_8968, 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_8968 (Apache-2.0).

Preamble
import Mathlib.Data.Nat.Choose.Basic
import Mathlib.Tactic.NormNum
Formal statement
theorem WorkbookCorrected.plus_8968 : Nat.choose 3 0 + Nat.choose 4 1 + Nat.choose 5 2 = Nat.choose 6 2 := by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook; record lean_workbook_plus_8968; Apache-2.0; corrects Open node aff26194-f2bc-4d1c-980c-fca599f3bcc2

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