lean_workbook_plus_20877

Proved

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

Let $a,b,c>0$ and $\frac{a}{b+1}+\frac{b}{c+1}+\frac{c}{a+1}=1.$ Prove that

abc\leq \frac{1}{8}

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_20877 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a * b * c = 1) (h : a / (b + 1) + b / (c + 1) + c / (a + 1) = 1) : a * b * c ≤ 1 / 8   :=  by sorry

Source

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

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