lean_workbook_plus_55963

Proved

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

Let $a,b,c$ be positive real numbers. Prove that \n $\frac{a^{2}b^{2}(b-c)}{a+b}+\frac{b^{2}c^{2}(c-a)}{b+c}+\frac{c^{2}a^{2}(a-b)}{c+a}\ge 0$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_55963 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^2 * b^2 * (b - c)) / (a + b) + (b^2 * c^2 * (c - a)) / (b + c) + (c^2 * a^2 * (a - b)) / (c + a) ≥ 0   :=  by sorry

Source

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

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