lean_workbook_plus_77111

Proved

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

If $x,y,z>0$ and $xyz=8\;,$ Then prove that $\frac{1}{x^2+2}+\frac{1}{y^2+2}+\frac{1}{z^2+2}\geq \frac{1}{2}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_77111 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) (habc : x * y * z = 8) : 1 / (x ^ 2 + 2) + 1 / (y ^ 2 + 2) + 1 / (z ^ 2 + 2) ≥ 1 / 2   :=  by sorry

Source

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

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