lean_workbook_plus_63825

Proved

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

Prove that for positive numbers a, b, c, and d, the following inequality holds: $\frac{ab}{a+b}+\frac{cd}{c+d}\leq \frac{(a+c)(b+d)}{a+b+c+d}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_63825 (a b c d : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hd : 0 < d) : (a * b / (a + b) + c * d / (c + d)) ≤ (a + c) * (b + d) / (a + b + c + d)   :=  by sorry

Source

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

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