lean_workbook_plus_55536

Proved

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

Prove that $\dfrac{1}{2}\left(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}\right)\ge \dfrac{1}{a+b}+\dfrac{1}{a+c}+\dfrac{1}{b+c}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_55536 {a b c : ℝ} (ha : a > 0) (hb : b > 0) (hc : c > 0) : (1 / 2) * (1 / a + 1 / b + 1 / c) ≥ 1 / (a + b) + 1 / (a + c) + 1 / (b + c)   :=  by sorry

Source

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

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