lean_workbook_plus_6009

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

The inequality $ab+bc+ca \ge -\frac{1}{2}$ is equivalent to $2(ab+bc+ca)+1 \ge 0$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_6009 (a b c: ℝ) : a * b + b * c + c * a ≥ -1 / 2 ↔ 2 * (a * b + b * c + c * a) + 1 ≥ 0   :=  by sorry

Source