A sixth-degree product bound involving three quadratic factors

Proved

WorkbookSource.plus_10841

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

lean-workbooksource-checked

For $a,b,c$ positive reals prove that $(\sum a^3)(a+b)(b+c)(c+a) \geq 3(a^2+bc)(b^2+ca)(c^2+ab)$

Source: InternLM Lean-Workbook, record lean_workbook_plus_10841 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_10841 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^3 + b^3 + c^3)*(a + b)*(b + c)*(c + a) ≥ 3 * (a^2 + b * c)*(b^2 + c * a)*(c^2 + a * b)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_10841; Apache-2.0

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