lean_workbook_plus_20288

Proved

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

Demonstrate the inequality $(b-c)^2+(c-a)^2\ge\frac12(a-b)^2$ using the inequality $x^2+y^2\ge\frac12(x+y)^2$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_20288 (a b c : ℝ) : (b - c) ^ 2 + (c - a) ^ 2 ≥ 1 / 2 * (a - b) ^ 2   :=  by sorry

Source