lean_workbook_plus_4292

Proved

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

For any positive numbers $a, b, c$ prove the inequalities \n $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\ge \frac{2}{a+b}+\frac{2}{b+c}+\frac{2}{c+a}\ge \frac{9}{a+b+c}.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_4292 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (1 / a + 1 / b + 1 / c) ≥ (2 / (a + b) + 2 / (b + c) + 2 / (c + a)) ∧ (2 / (a + b) + 2 / (b + c) + 2 / (c + a)) ≥ 9 / (a + b + c)   :=  by sorry

Source

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

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