lean_workbook_plus_12649

Proved

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

Prove that $xy^2 + yz^2 + zx^2 + xyz \geq 0$ given $x, y, z \geq 0$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_12649 (x y z : ℝ) (hx : x ≥ 0) (hy : y ≥ 0) (hz : z ≥ 0) : x * y ^ 2 + y * z ^ 2 + z * x ^ 2 + x * y * z ≥ 0   :=  by sorry

Source

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

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