lean_workbook_plus_11835

Proved

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

Let $a,b,c > 0$ and $\frac{1}{a+1}+\frac{1}{b+1}+\frac{1}{c+1}=2$ .

abc\le\frac{1}{8}

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_11835 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (1 / (a + 1) + 1 / (b + 1) + 1 / (c + 1) = 2 → a * b * c ≤ 1 / 8)   :=  by sorry

Source

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

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