lean_workbook_plus_18761

Proved

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

Let $a,b,c>0$ such that $a^2b+b^2c+c^2a+ab^2+bc^2+ca^2=4+2abc.$ Prove that $(a^2+b^2)(b^2+c^2)(c^2+a^2)\geq 8.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_18761 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a * b * c = 1) (h : a^2 * b + b^2 * c + c^2 * a + a * b^2 + b * c^2 + c * a^2 = 4 + 2 * a * b * c) : (a^2 + b^2) * (b^2 + c^2) * (c^2 + a^2) ≥ 8   :=  by sorry

Source

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

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