lean_workbook_plus_31799

Proved

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

Prove that $a^3+b^3+c^3+1\ge 4(abc)^3$ given $a,b,c > 0$ and $ab+ac+bc = 3$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_31799 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a * b * c = 1) : a ^ 3 + b ^ 3 + c ^ 3 + 1 ≥ 4 * (a * b * c) ^ 3   :=  by sorry

Source

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

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