lean_workbook_plus_33153

Proved

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

Given $a, b, c > 0$ and $(a+b)(b+c)(c+a) = 8$ , prove that $(a^2+bc)(b^2+ca)(c^2+ab) \le 8(2-abc)^6$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_33153 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a * b * c = 1) (h : (a + b) * (b + c) * (c + a) = 8) : (a^2 + b * c) * (b^2 + c * a) * (c^2 + a * b) ≤ 8 * (2 - a * b * c)^6   :=  by sorry

Source

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

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