A cyclic quartic bound involving a triple product

Proved

WorkbookSource.base_4868

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

lean-workbooksource-checked

If $x,y,z$ are real numbers, then

$x^4 + y^4 + z^4 + 2xyz(x + y + z)\ge x^3y + y^3z + z^3x$ .

Source: InternLM Lean-Workbook, record lean_workbook_4868 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_4868 (x y z : ℝ) : x ^ 4 + y ^ 4 + z ^ 4 + 2 * x * y * z * (x + y + z) ≥ x ^ 3 * y + y ^ 3 * z + z ^ 3 * x  :=  by sorry

Source