An asymmetric cyclic ratio sum is at least four

Proved

WorkbookSource.base_41900

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

lean-workbooksource-checked

prove that: $\frac{x}{y}+\frac{y}{z}+\frac{2(y+z)}{x+y}\geq 4$ , where $x,y,z>0$

Source: InternLM Lean-Workbook, record lean_workbook_41900 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_41900 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : (x / y + y / z + 2 * (y + z) / (x + y)) ≥ 4  :=  by sorry

Source