lean_workbook_plus_55935

Proved

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

Prove that $(xy+zx+yz)(x^2y+y^2z+z^2x)\geq (x+y+z)^2xyz$ given $x,y,z>0$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_55935 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : (x * y + z * x + y * z) * (x^2 * y + y^2 * z + z^2 * x) ≥ (x + y + z)^2 * x * y * z   :=  by sorry

Source

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

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