lean_workbook_plus_56306

Proved

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

$\frac{(a+b)(b+c)(c+a)}{abc} - \frac{24(a^2+b^2+c^2)}{(a+b+c)^2} = \sum \frac{(a+b-3c)^2(a-b)^2}{ab(a+b+c)^2} \geqslant 0$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_56306 {a b c : ℝ} (ha : a > 0) (hb : b > 0) (hc : c > 0) (hab : a + b > c) (hbc : b + c > a) (hca : a + c > b) : (a + b) * (b + c) * (c + a) / a / b / c - 24 * (a ^ 2 + b ^ 2 + c ^ 2) / (a + b + c) ^ 2 = (a + b - 3 * c) ^ 2 * (a - b) ^ 2 / (a * b * (a + b + c) ^ 2) + (b + c - 3 * a) ^ 2 * (b - c) ^ 2 / (b * c * (a + b + c) ^ 2) + (c + a - 3 * b) ^ 2 * (c - a) ^ 2 / (c * a * (a + b + c) ^ 2)   :=  by sorry

Source

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

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