lean_workbook_plus_17544

Proved

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

Let $x,y,z$ be positive real numbers. Prove that $(x^{2}+y^{2})(y^{2}+z^{2})(z^{2}+x^{2})\geq(x^{2}+2y^{2}-z^{2})(y^{2}+2z^{2}-x^{2})(z^{2}+2x^{2}-y^{2})$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_17544 (x y z : ℝ) : (x ^ 2 + y ^ 2) * (y ^ 2 + z ^ 2) * (z ^ 2 + x ^ 2) ≥ (x ^ 2 + 2 * y ^ 2 - z ^ 2) * (y ^ 2 + 2 * z ^ 2 - x ^ 2) * (z ^ 2 + 2 * x ^ 2 - y ^ 2)   :=  by sorry

Source

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

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