lean_workbook_plus_64527

Proved

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

From AM-GM, we get that $\frac{x^2y^2+y^2z^2}{2} \geq xy^2z$ $\frac{y^2z^2+z^2x^2}{2} \geq xyz^2$ $\frac{x^2y^2+z^2x^2}{2} \geq x^2yz$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_64527 (x y z : ℝ) :
  (x^2 * y^2 + y^2 * z^2) / 2 ≥ x * y^2 * z ∧
  (y^2 * z^2 + z^2 * x^2) / 2 ≥ x * y * z^2 ∧
  (x^2 * y^2 + z^2 * x^2) / 2 ≥ x^2 * y * z   :=  by sorry

Source

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

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