Prove2Me

Lean-Workbook Plus 14089: Trigonometric inequality

Proved
WorkbookRestored.plus_14089

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

lean-workbookrestored-importssource-checked

Prove that 2sin⁡(α)2+2sin⁡(β)2+2≥2sin⁡(α)+2sin⁡(β)+2sin⁡(α)sin⁡(β)2\sin(\alpha)^2+2\sin(\beta)^2+2 \geq 2\sin(\alpha)+2\sin(\beta)+2\sin(\alpha)\sin(\beta)

Source: Lean-Workbook row lean_workbook_plus_14089 (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_14089 (α β : ℝ) : 2 * sin α ^ 2 + 2 * sin β ^ 2 + 2 ≥ 2 * sin α + 2 * sin β + 2 * sin α * sin β   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_14089; immutable original Prove2Me node a8c28f94-dcc6-4f3c-8208-2146be26388d

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