lean_workbook_plus_6687

Proved

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

Prove that $a>0,b>0,c>0$ and $ab+bc+ca+2abc=1\Longrightarrow 1+2(a+b+c)\geqq 32abc$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_6687 (a b c : ℝ) (ha : a > 0) (hb : b > 0) (hc : c > 0) (habc : a * b * c = 1) (h : a * b + b * c + c * a + 2 * a * b * c = 1) : 1 + 2 * (a + b + c) ≥ 32 * a * b * c   :=  by sorry

Source

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

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