Prove2Me

An asymmetric shifted rational product inequality

Proved
WorkbookSource.base_7909

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

lean-workbooksource-checked

Let x,y,z>0x,y,z>0 ,prove that: (2x+z+y)(2z+y+x)2y+x+z+2zyx(x+y)(y+z)≥9zxz+x.\frac{(2x+z+y)(2z+y+x)}{2y+x+z}+\frac{2zyx}{(x+y)(y+z)} \geq \frac{ 9zx}{z+x}.

Source: InternLM Lean-Workbook, record lean_workbook_7909 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_7909 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : (2 * x + z + y) * (2 * z + y + x) / (2 * y + x + z) + 2 * z * y * x / (x + y) / (y + z) ≥ 9 * z * x / (z + x)  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_7909; Apache-2.0

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