lean_workbook_plus_10938

Proved

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

Prove that $a^2 + b^2 + c^2 - ab - bc - ca = \frac {1}{2}((a - b)^2 + (a - c)^2 + (b - c)^2) \geq 0$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_10938 (a b c : ℝ) : a^2 + b^2 + c^2 - (a * b + b * c + c * a) = 1 / 2 * ((a - b)^2 + (a - c)^2 + (b - c)^2)   :=  by sorry

Source