lean_workbook_plus_41864

Proved

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

Let $a,b,c$ be positive real numbers. Prove the inequality \n $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}+\frac{3}{a+b+c}\ge \frac{4(a+b+c)}{ab+bc+ca}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_41864 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : 1 / a + 1 / b + 1 / c + 3 / (a + b + c) ≥ 4 * (a + b + c) / (a * b + b * c + a * c)   :=  by sorry

Source

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

View graph