A fifth-degree product comparison of symmetric expressions

Proved

WorkbookSource.base_56863

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

lean-workbooksource-checked

Prove that for all a,b,c >0. we have $(a^{2}+b^{2}+c^{2})(a+b)(b+c)(c+a)\geq{(a^{3}+b^{3}+c^{3}+5abc)(ab+bc+ca)}$

Source: InternLM Lean-Workbook, record lean_workbook_56863 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_56863 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^2 + b^2 + c^2) * (a + b) * (b + c) * (c + a) ≥ (a^3 + b^3 + c^3 + 5 * 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_56863; Apache-2.0

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