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Lean-Workbook Plus 8402: Trigonometric inequality

Proved
WorkbookRestored.plus_8402

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

lean-workbookrestored-importssource-checked

For every real xx, −1≤cos⁡6x−sin⁡4x≤1-1\le\cos^6 x-\sin^4 x\le1. This is the bounding component of the source question about extreme values; attainment is not asserted here.

Source: Lean-Workbook row lean_workbook_plus_8402 (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_8402 (x : ℝ) : (-1 ≤ cos x ^ 6 - sin x ^ 4 ∧ cos x ^ 6 - sin x ^ 4 ≤ 1)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_8402; immutable original Prove2Me node c6545858-932c-41d8-b3b9-419a86b2e771

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