lean_workbook_plus_38306

Proved

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

Let $a,b,c>0$ and $ab+bc+ca=1$ .Prove that

(a^2+bc)(b^2+ca)(c^2+ab)+ a^2b^2c^2\geq \frac{1}{3}.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_38306 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a * b * c = 1) : (a^2 + b * c) * (b^2 + c * a) * (c^2 + a * b) + a^2 * b^2 * c^2 ≥ 1 / 3   :=  by sorry

Source

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

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