A quartic sum bound under a cyclic relation

Proved

WorkbookSource.base_45693

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

lean-workbooksource-checked

Let $a,$ $b,$ $c$ are real numbers, such that $a^3b+b^3c+c^3a=0.$ Prove that $3(a^4+b^4+c^4)+2abc(a+b+c)\geq0.$

Source: InternLM Lean-Workbook, record lean_workbook_45693 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_45693 (a b c : ℝ) (h : a^3 * b + b^3 * c + c^3 * a = 0) :
  3 * (a^4 + b^4 + c^4) + 2 * a * b * c * (a + b + c) ≥ 0  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_45693; Apache-2.0

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