lean_workbook_plus_15896

Proved

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

Prove that for any three positive real numbers $a,b,c, \frac{1}{a+b}+\frac{1}{b+c}+\frac{1}{c+a} \ge \frac{9}{2} \cdot \frac{1}{a+b+c}$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_15896 : ∀ a b c : ℝ, a > 0 ∧ b > 0 ∧ c > 0 → 1 / (a + b) + 1 / (b + c) + 1 / (c + a) ≥ 9 / 2 * (1 / (a + b + c))   :=  by sorry

Source

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

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