A quartic and cubic bound under a zero-sum constraint

Proved

WorkbookSource.base_28147

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

lean-workbooksource-checked

Let $a,b,c$ be real numbers such that $a + b + c = 0.$ Prove that $a^4 + b^4 + c^4 + 6abc + 12\ge3(a^2 + b^2 + c^2).$

Source: InternLM Lean-Workbook, record lean_workbook_28147 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_28147 (a b c : ℝ) (h : a + b + c = 0) : a^4 + b^4 + c^4 + 6*a*b*c + 12 ≥ 3 * (a^2 + b^2 + c^2)  :=  by sorry

Source