Prove2Me

Lean-Workbook Plus 12542: Trigonometric inequality

Proved
WorkbookRestored.plus_12542

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

lean-workbookrestored-importssource-checked

For all real r1,r2,θr_1,r_2,\theta, (1−cos⁡θ)(r1−r2)2≥0(1-\cos\theta)(r_1-r_2)^2\ge0.

Source: Lean-Workbook row lean_workbook_plus_12542 (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_12542 (r₁ r₂ : ℝ) (θ : ℝ) : (1 - Real.cos θ) * (r₁ - r₂) ^ 2 ≥ 0   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_12542; immutable original Prove2Me node b017fc35-9fc8-4bff-ba6d-bdad1e5bb6d8

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