A cyclic quartic bound with a symmetric correction

Proved

WorkbookSource.base_24124

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

lean-workbooksource-checked

prove that $2(a^4+b^4+c^4)+abc(a+b+c)\ge 3(a^3b+b^3c+c^3a)$ (arqady)

Source: InternLM Lean-Workbook, record lean_workbook_24124 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_24124 (a b c : ℝ) : 2 * (a ^ 4 + b ^ 4 + c ^ 4) + a * b * c * (a + b + c) ≥ 3 * (a ^ 3 * b + b ^ 3 * c + c ^ 3 * a)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_24124; Apache-2.0

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