lean_workbook_plus_6168

Proved

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

Prove that $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}+\frac{1}{d}>\frac{1}{a+b+c+d}$ for all positive $a, b, c$ and $d$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_6168 (a b c d : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hd : 0 < d) : 1 / a + 1 / b + 1 / c + 1 / d > 1 / (a + b + c + d)   :=  by sorry

Source

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

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