Lean-Workbook Plus 5163: Trigonometric inequality

Proved

WorkbookRestored.plus_5163

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

lean-workbookrestored-importssource-checked

Prove $\sin(x) * \cos(x) \leq \frac{1}{2}$ .

Source: Lean-Workbook row lean_workbook_plus_5163 (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_5163 : ∀ x : ℝ, sin x * cos x ≤ 1 / 2   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_5163; immutable original Prove2Me node eca5186c-207c-420d-a68a-1f4c6e7c85e8

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