lean_workbook_plus_46630

Proved

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

Where $a^2+b^2+c^2\ge \frac{1}{3}(a+b+c)^2\iff a^2+b^2+c^2\ge bc+ca+ab$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_46630 : ∀ a b c : ℝ, a^2 + b^2 + c^2 ≥ (1 / 3) * (a + b + c)^2 ↔ a^2 + b^2 + c^2 ≥ b * c + c * a + a * b   :=  by sorry

Source