A cyclic fifth-degree sum bounds a symmetric product

Proved

WorkbookSource.base_47864

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Let $a,b,c>0$ . Show that

a^2(a+b)^3+b^2(b+c)^3+c^2(c+a)^3\geq{\frac{8abc(a+b+c)^2}{3}}.

Source: InternLM Lean-Workbook, record lean_workbook_47864 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_47864 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a^2 * (a + b)^3 + b^2 * (b + c)^3 + c^2 * (c + a)^3 ≥ (8 * a * b * c * (a + b + c)^2) / 3  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_47864; Apache-2.0

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