lean_workbook_plus_9209

Proved

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

Let $a,b,c$ be positive real numbers such that $a+b+c=abc+2$ . Prove that \n\n

(a + b)(b + c)(c + a) + 2\geq 2(ab + bc + ca) + 4abc

\n\n $uvw$ kills it immediately.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_9209 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hab : a + b + c = a * b * c + 2) : (a + b) * (b + c) * (c + a) + 2 ≥ 2 * (a * b + b * c + a * c) + 4 * a * b * c   :=  by sorry

Source

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

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