Fourth powers of pairwise differences bound a mixed correction

Proved

WorkbookSource.base_52673

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

lean-workbooksource-checked

Let $x,y,z \in R$ ,prove that: $(y-z)^4+(z-x)^4+(x-y)^4+\frac{9}{2}yz(y-z)^2\geq 0.$

Source: InternLM Lean-Workbook, record lean_workbook_52673 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_52673 (x y z : ℝ) : (y - z) ^ 4 + (z - x) ^ 4 + (x - y) ^ 4 + (9 / 2) * y * z * (y - z) ^ 2 ≥ 0  :=  by sorry

Source