lean_workbook_plus_64113

Proved

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

It is known that $a,b,c>0$ , $\frac{1}{a^3+1}+\frac{1}{b^3+1}+\frac{1}{c^3+1}=1$ .Prove that: $abc{\ge}2$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_64113 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a * b * c = 1) (h : (1 / (a^3 + 1)) + (1 / (b^3 + 1)) + (1 / (c^3 + 1)) = 1) : a * b * c ≥ 2   :=  by sorry

Source

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

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