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Lean-Workbook Plus 35328: Trigonometric identity

Proved
WorkbookRestored.plus_35328

by wamlart · Sep 12, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

lean-workbookrestored-importssource-checked

Lean-Workbook Plus 35328: Arithmetic identity involving pi

Assuming π⋅82=64π\pi\cdot8^2=64\pi, 12⋅12⋅28−12π⋅82=168−32π\tfrac12\cdot12\cdot28-\tfrac12\pi\cdot8^2=168-32\pi.

Source: Lean-Workbook row lean_workbook_plus_35328 (Apache-2.0). The unchanged proposition comes from the original record; its missing mathematical imports and namespaces are restored here.

Preamble
import Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic
open Real
Formal statement
theorem WorkbookRestored.plus_35328 (h₁ : π * 8^2 = 64 * π) : 1 / 2 * 12 * 28 - 1 / 2 * π * 8^2 = 168 - 32 * π   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_35328; immutable original Prove2Me node cc3dafd9-10a1-4cec-9b5f-b10e58be8420

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