lean_workbook_plus_41976

Proved

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

If $x, y, z>0$ prove that \n $\frac{x}{y}+\frac{y}{z}+\frac{z}{x}+\frac{67xyz}{(x+y)(y+z)(z+x)+4xyz}\ge 9\frac{1}{12}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_41976 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : (x / y + y / z + z / x + 67 * x * y * z / ((x + y) * (y + z) * (z + x) + 4 * x * y * z)) ≥ 9 / 12   :=  by sorry

Source

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

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