A symmetric fifth-degree inequality with a triple-product correction

Proved

WorkbookSource.plus_22420

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

lean-workbooksource-checked

Prove that for positive numbers a, b, and c, the following inequality holds: $\sum (a^4b+a^4c)+2abc(\sum ab)\ge \sum (a^3b^2+a^3c^2)+2abc(\sum a^2)$

Source: InternLM Lean-Workbook, record lean_workbook_plus_22420 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_22420 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a^4 * b + a^4 * c + b^4 * c + b^4 * a + c^4 * a + c^4 * b + 2 * a * b * c * (a * b + b * c + c * a) ≥ a^3 * b^2 + a^3 * c^2 + b^3 * c^2 + b^3 * a^2 + c^3 * a^2 + c^3 * b^2 + 2 * a * b * c * (a^2 + b^2 + c^2)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_22420; Apache-2.0

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