lean_workbook_plus_7388

Proved

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

Let $a,b,c>0$ and $abc=1$ . Prove that \n

1+\frac{8}{ (a+b)(1+c)}\ge \frac{9}{a+b+c}

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_7388 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a * b * c = 1) : 1 + 8 / (a + b) * (1 + 1 / c) ≥ 9 / (a + b + c)   :=  by sorry

Source

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

View graph