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Lean-Workbook Plus 41922: Trigonometric inequality

Proved
WorkbookRestored.plus_41922

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

lean-workbookrestored-importssource-checked

For every real xx, cos⁡3x−cos⁡2x=cos⁡2x(cos⁡x−1)≤0\cos^3x-\cos^2x=\cos^2x(\cos x-1)\le0.

Source: Lean-Workbook row lean_workbook_plus_41922 (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_41922 : ∀ x : ℝ, (cos x)^3 - (cos x)^2 = (cos x)^2 * (cos x - 1) ∧ (cos x)^2 * (cos x - 1) ≤ 0   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_41922; immutable original Prove2Me node 1d232657-78c6-4098-8bbb-18805f970767

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