lean_workbook_plus_25391

Proved

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

Prove that for $x,y,z\geq 0$ , \n $(xy+xz+yz)(xy^2+yz^2+x^2z)-(x+y+z)^2xyz\geq 0$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_25391 (x y z : ℝ) (hx : x ≥ 0) (hy : y ≥ 0) (hz : z ≥ 0) : (x * y + x * z + y * z) * (x * y ^ 2 + y * z ^ 2 + x ^ 2 * z) - (x + y + z) ^ 2 * x * y * z ≥ 0   :=  by sorry

Source

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

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