An asymmetric quartic inequality with a squared-difference correction

Proved

WorkbookSource.base_28649

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

lean-workbooksource-checked

Let $x,y,z \in R$ ,prove that: $x^4+y^4+z^4-(x+y+z)xyz+\frac{1}{2}yz(y-z)^2\geq 0.$

Source: InternLM Lean-Workbook, record lean_workbook_28649 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_28649 (x y z : ℝ) :  x^4 + y^4 + z^4 - (x + y + z) * x * y * z + (1 / 2) * y * z * (y - z)^2 ≥ 0  :=  by sorry

Source