lean_workbook_plus_68292

Proved

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

$(a+b+c)^2\le 3(a^2+b^2+c^2)\Leftrightarrow (a-b)^2+(b-c)^2+(c-a)^2\ge 0$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_68292 (a b c : ℝ) : (a+b+c)^2 ≤ 3*(a^2+b^2+c^2) ↔ (a-b)^2+(b-c)^2+(c-a)^2 ≥ 0   :=  by sorry

Source