A fifth-degree product bound involving symmetric sums

Proved

WorkbookSource.base_28299

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Prove that the following inequality is also true. Let $a, b, c>0$ . Prove that $(a+b+c)^2(a+b)(b+c)(c+a)\le4(a^3+b^3+c^3+3abc)(ab+bc+ca)$

Source: InternLM Lean-Workbook, record lean_workbook_28299 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_28299 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a + b + c) ^ 2 * (a + b) * (b + c) * (c + a) ≤ 4 * (a ^ 3 + b ^ 3 + c ^ 3 + 3 * a * b * c) * (a * b + b * c + c * a)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_28299; Apache-2.0

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