lean_workbook_plus_73842

Proved

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

If $x,y,z>0$ , then $\frac{1}{x+y}+\frac{1}{y+z}+\frac{1}{z+x}\le \frac{3\left( x+y+z \right)}{2\left( xy+yz+zx \right)}$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_73842 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : (1 / (x + y) + 1 / (y + z) + 1 / (z + x)) ≤ (3 * (x + y + z)) / (2 * (x*y + y*z + z*x))   :=  by sorry

Source

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

View graph