lean_workbook_plus_14533

Proved

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

Let $x;y;z$ be positive real numbers. Prove that: $(x+y+xy)(y+z+yz)(z+x+xz)\geq xyz(x+2)(y+2)(z+2)$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_14533 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : (x + y + x * y) * (y + z + y * z) * (z + x + z * x) ≥ x * y * z * (x + 2) * (y + 2) * (z + 2)   :=  by sorry

Source

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

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