lean_workbook_plus_65607

Proved

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

Let $x,y,z\geq 0$ ,prove that: $(x^2+y^2+z^2)(y^2z^2+z^2x^2+x^2y^2)\geq (x^2y+y^2z+z^2x)^2.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_65607 (x y z : ℝ) : (x^2 + y^2 + z^2) * (y^2 * z^2 + z^2 * x^2 + x^2 * y^2) ≥ (x^2 * y + y^2 * z + z^2 * x)^2   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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