lean_workbook_plus_45201

Proved

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

Given $a,b,c>0$ . Prove that $\frac{1}{a(b+1)}+\frac{1}{b(c+1)}+\frac{1}{c(a+1)}\ge \frac{3}{1+abc}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_45201 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (1 / (a * (b + 1)) + 1 / (b * (c + 1)) + 1 / (c * (a + 1))) ≥ 3 / (1 + a * b * c)   :=  by sorry

Source

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

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