lean_workbook_plus_39869

Proved

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

$\frac{1}{\frac{1}{a}+\frac{1}{b}}+\frac{1}{\frac{1}{c}+\frac{1}{d}} \leq \frac{a+b+c+d}{4}.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_39869 {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) ≤ (a + b + c + d) / 4   :=  by sorry

Source

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

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