Prove2Me

Lean-Workbook Plus 11215: Trigonometric inequality

Proved
WorkbookRestored.plus_11215

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

lean-workbookrestored-importssource-checked

prove that : 3(cos⁡2x+cos⁡2y+cos⁡2z)≥(cos⁡x+cos⁡y+cos⁡z)2 3(\cos^2x+\cos^2y+\cos^2z) \geq ( \cos x+ \cos y+ \cos z)^2

Source: Lean-Workbook row lean_workbook_plus_11215 (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_11215 (x y z: ℝ) : 3 * (Real.cos x ^ 2 + Real.cos y ^ 2 + Real.cos z ^ 2) ≥ (Real.cos x + Real.cos y + Real.cos z) ^ 2   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_11215; immutable original Prove2Me node aa330e17-9bf4-4ae0-a35a-c7c7dbc46574

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