lean_workbook_plus_23472

Proved

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

Prove that $\frac{1}{a+b}+\frac{1}{b+c}+\frac{1}{c+a} \leq \frac{{(a+b+c)}^{2}}{6abc}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_23472 {a b c : ℝ} (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : 1 / (a + b) + 1 / (b + c) + 1 / (c + a) ≤ (a + b + c) ^ 2 / (6 * a * b * c)   :=  by sorry

Source

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

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