lean_workbook_plus_30881

Proved

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

If $a,\ b,\ c \geq 1$ , show that $4(abc+1) \geq (a+1)(b+1)(c+1)$ . When do we have equality?

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_30881 (a b c : ℝ) (ha : a ≥ 1) (hb : b ≥ 1) (hc : c ≥ 1) : 4 * (a * b * c + 1) ≥ (a + 1) * (b + 1) * (c + 1)   :=  by sorry

Source

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

View graph