lean_workbook_plus_78261

Proved

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

If $x,y,z>0$ and $xy+yz+zx \le xyz$ , prove that $x^2 y^2 + y^2 z^2+ z^2 x^2 \ge 9 (xy+yz+zx)$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_78261 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) (h : x * y + y * z + z * x ≤ x * y * z) : x^2 * y^2 + y^2 * z^2 + z^2 * x^2 ≥ 9 * (x * y + y * z + z * x)   :=  by sorry

Source

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

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