lean_workbook_plus_25829

Proved

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

Let $a,b,c\geq 0$ . Prove that $\sum a^2(a-b)(a-c)\geq 0$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_25829 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) : a^2 * (a - b) * (a - c) + b^2 * (b - a) * (b - c) + c^2 * (c - a) * (c - b) ≥ 0   :=  by sorry

Source

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

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