lean_workbook_plus_31610

Proved

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

Let $a,b,c$ be positive real numbers . Prove that \n\n

(a+1)^2 (b+1)^2 (c+1)^2\geq 4(a+b+c+1)(ab+bc+ca+abc)

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_31610 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a + 1) ^ 2 * (b + 1) ^ 2 * (c + 1) ^ 2 ≥ 4 * (a + b + c + 1) * (a * b + b * c + c * a + a * b * c)   :=  by sorry

Source

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

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