lean_workbook_plus_19328

Proved

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

Prove that $\frac{ax}{a+x}+\frac{by}{b+y} \leq \frac{(a+b)(x+y)}{a+b+x+y}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_19328 (a b x y : ℝ) (ha : 0 < a) (hb : 0 < b) (hx : 0 < x) (hy : 0 < y) : (a * x / (a + x) + b * y / (b + y)) ≤ (a + b) * (x + y) / (a + b + x + y)   :=  by sorry

Source

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

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