lean_workbook_plus_16641

Proved

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

By AM-GM inequality,\n $x^6z^2+y^6x^2\geq 2x^4y^3z$ \n $\rightarrow$ \n $6\sum_{cyc}x^6z^2\geq 6\sum_{cyc}x^4y^3z$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_16641 (x y z : ℝ) :
  6 * (x ^ 6 * z ^ 2 + y ^ 6 * x ^ 2 + z ^ 6 * y ^ 2) ≥ 6 * (x ^ 4 * y ^ 3 * z + y ^ 4 * z ^ 3 * x + z ^ 4 * x ^ 3 * y)   :=  by sorry

Source

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

View graph