lean_workbook_plus_75892

Proved

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

Given $a, b, c > 0$ and $\frac{1}{1 + a} + \frac{1}{1 + b} + \frac{1}{1 + c} = 2$ , prove that $abc \le \frac{9}{64}$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_75892 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (1 / (1 + a) + 1 / (1 + b) + 1 / (1 + c) = 2) → a * b * c ≤ 9 / 64   :=  by sorry

Source

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

View graph