lean_workbook_plus_47215

Proved

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

Prove that if $a,b,c$ are positive real numbers, then:\n\n $\frac{9}{a+b+c} \le 2 \left( \frac{1}{a+b}+\frac{1}{b+c}+\frac{1}{c+a} \right) \le \frac{1}{a}+\frac{1}{b}+\frac{1}{c}.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_47215 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (9 / (a + b + c) : ℝ) ≤ 2 * (1 / (a + b) + 1 / (b + c) + 1 / (c + a)) ∧ (2 * (1 / (a + b) + 1 / (b + c) + 1 / (c + a)) : ℝ) ≤ (1 / a + 1 / b + 1 / c)   :=  by sorry

Source

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

View graph