lean_workbook_plus_44082

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Prove the inequality: $x^2z+y^2z+z^2y+xyz>0$ for $x\geq y\geq z>0$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_44082 (x y z : ℝ) (hx : x ≥ y) (hy : y ≥ z) (hz : z > 0) : x^2 * z + y^2 * z + z^2 * y + x * y * z > 0   :=  by sorry

Source