lean_workbook_plus_10862

Proved

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

For $x,y,z$ positive real numbers, prove that $(2x - y - z)\cdot\frac {x + y}{y + z} + (2y - z - x)\cdot\frac {y + z}{z + x} + (2z - x - y)\cdot\frac {z + x}{x + y}\geq0$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_10862 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : (2*x - y - z)*(x + y)/(y + z) + (2*y - z - x)*(y + z)/(z + x) + (2*z - x - y)*(z + x)/(x + y) ≥ 0   :=  by sorry

Source

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

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