lean_workbook_plus_62123

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_62123 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (9 / (a + b + c)) ≤ (2 * (1 / (a + b) + 1 / (b + c) + 1 / (c + a))) ∧ (2 * (1 / (a + b) + 1 / (b + c) + 1 / (c + a))) ≤ (1 / a + 1 / b + 1 / c)   :=  by sorry

Source

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

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