lean_workbook_plus_19905

Proved

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

Let $x,y,z>0$ Prove that : $x^4+y^4+z^4+xyz\left( x+y+z\right)\ge \frac{2}{3}\left( xy+yz+zx\right)^2$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_19905 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : x^4 + y^4 + z^4 + x*y*z*(x + y + z) ≥ (2/3)*(x*y + y*z + z*x)^2   :=  by sorry

Source

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

View graph