lean_workbook_plus_45545

Proved

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

Prove that for $a, b, c, d > 0$ , \n $\frac{1}{\frac{1}{a}+\frac{1}{b}}+\frac{1}{\frac{1}{c}+\frac{1}{d}}\le\frac{1}{\frac{1}{a+c}+\frac{1}{b+d}}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_45545 (a b c d : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hd : 0 < d) : (1 / (1 / a + 1 / b) + 1 / (1 / c + 1 / d)) ≤ 1 / (1 / (a + c) + 1 / (b + d))   :=  by sorry

Source

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

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