An asymmetric quartic inequality on nonnegative variables

Proved

WorkbookSource.base_26591

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

lean-workbooksource-checked

Let $x,y,z\geq 0$ ,prove that: $-(x+y+z)xyz+x^4+yz(y^2+z^2)\geq 0$

Source: InternLM Lean-Workbook, record lean_workbook_26591 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_26591 (x y z : ℝ) (hx : 0 ≤ x) (hy : 0 ≤ y) (hz : 0 ≤ z) : -(x + y + z)*x*y*z + x^4 + y*z*(y^2 + z^2) ≥ 0  :=  by sorry

Source