lean_workbook_plus_12710

Proved

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

Prove that for positive real numbers $a$ , $b$ , and $c$ , the following inequality holds:\n

(b^{2}-bc+c^{2})(b-c)^{2}+(c^{2}-ca+a^{2})(c-a)^{2}+(a^{2}-ab+b^{2})(a-b)^{2}\geq 0

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_12710 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (b^2 - b*c + c^2)*(b - c)^2 + (c^2 - c*a + a^2)*(c - a)^2 + (a^2 - a*b + b^2)*(a - b)^2 ≥ 0   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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