Prove2Me

Lean-Workbook Plus 32152: Trigonometric inequality

Proved
WorkbookRestored.plus_32152

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

lean-workbookrestored-importssource-checked

For 0<x<π/20<x<\pi/2, 0≤2sin⁡xcos⁡x≤10\le2\sin x\cos x\le1.

Source: Lean-Workbook row lean_workbook_plus_32152 (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_32152 : ∀ x ∈ Set.Ioo 0 (Real.pi / 2), 0 ≤ 2 * Real.sin x * Real.cos x ∧ 2 * Real.sin x * Real.cos x ≤ 1   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_32152; immutable original Prove2Me node c913b54c-0ef6-4b62-a057-db428e6570e8

View graph