A pair of squared quadratic sums bounds a mixed eighth-degree term

Proved

WorkbookSource.base_8693

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

lean-workbooksource-checked

Let $x,y,z \in R$ ,prove that: $B.(y^2+z^2)^2(z^2+x^2)^2\geq 4z^4(y+x)^2xy.$

Source: InternLM Lean-Workbook, record lean_workbook_8693 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_8693 (x y z : ℝ) : (y^2 + z^2)^2 * (z^2 + x^2)^2 ≥ 4 * z^4 * (y + x)^2 * x * y  :=  by sorry

Source