lean_workbook_plus_19505

Proved

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

Prove that for all positive real numbers $x$ , $y$ , and $z$ , the following inequality holds:\n $\sum\frac{xy^{2}}{y+z}\ge \frac{xy+yz+zx}{2}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_19505 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : (x * y ^ 2 / (y + z) + y * z ^ 2 / (z + x) + z * x ^ 2 / (x + y)) ≥ (x * y + y * z + z * x) / 2   :=  by sorry

Source

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

View graph