lean_workbook_plus_43471

Proved

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

Prove that if $a, b, c > 0$ and $\frac{1}{1+a} + \frac{1}{1+b} + \frac{1}{1+c} = 1$ , then $abc \ge 8$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_43471 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a * b * c = 1) : 1 / (1 + a) + 1 / (1 + b) + 1 / (1 + c) = 1 → a * b * c ≥ 8   :=  by sorry

Source

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

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