lean_workbook_plus_3289

Proved

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

Prove for $x,y,z$ positive reals: $x^2y+yz^2+y^2x+zy^2+x^2z+z^2x\geq 6xyz$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_3289 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : x^2*y + y*z^2 + y^2*x + z*y^2 + x^2*z + z^2*x >= 6*x*y*z   :=  by sorry

Source

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

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