Binomial coefficient identity #10935

Proved

WorkbookCorrected.plus_10935

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

arithmeticcorrectedelementaryworkbook

The elementary natural-number / rational identity

(2 * \binom{12}{2} + 6 * \binom{6}{2}) / \binom{60}{2} = 37 / 295

holds by direct arithmetic evaluation.

Formalization Note: This corrects Lean-Workbook record lean_workbook_plus_10935, 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_10935 (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_10935 : ((2:ℚ) * (Nat.choose 12 2) + 6 * (Nat.choose 6 2)) / (Nat.choose 60 2) = (37:ℚ) / 295 := by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook; record lean_workbook_plus_10935; Apache-2.0; corrects Open node a7567ab9-fce1-4e4e-80fb-bedf6abce4b4

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