Prove2Me

An asymmetric pairwise ratio sum has a lower bound

Proved
WorkbookSource.base_4224

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

x,y,z>0,prove that:

xy+z+2yz+x+2zx+y+xx+y≥52+zz+x.\frac{x}{y+z}+\frac{2y}{z+x}+\frac{2z}{x+y}+\frac{x}{x+y}\geq \frac{5}{2}+\frac{z}{z+x}.

Source: InternLM Lean-Workbook, record lean_workbook_4224 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_4224 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : (x / (y + z) + 2 * y / (z + x) + 2 * z / (x + y) + x / (x + y)) ≥ 5 / 2 + z / (z + x)  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_4224; Apache-2.0

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