lean_workbook_plus_6294

Proved

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

Let $x,y,z\in\mathbb{R}^+$ . Prove that $(x+y)(y+z)(z+x)\ge\frac{8}{9}(x+y+z)(xy+yz+zx)$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_6294 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : (x + y) * (y + z) * (z + x) ≥ (8 / 9) * (x + y + z) * (x * y + y * z + z * x)   :=  by sorry

Source

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

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