lean_workbook_plus_16865

Proved

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

Let $x,y,z$ be non-negative numbers. Prove that $\frac{2}{x+y+z+1}-\frac{1}{(x+1)(y+1)(z+1)}\leq 1$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_16865 (x y z : ℝ) (hx : 0 ≤ x) (hy : 0 ≤ y) (hz : 0 ≤ z) : (2 / (x + y + z + 1) - 1 / (x + 1) / (y + 1) / (z + 1)) ≤ 1   :=  by sorry

Source

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

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