lean_workbook_plus_70936

Proved

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

Let $a,b,c \geq 1$ such that $abc=3$ . Prove that \n\n

(a+1)(b+1)(c+1) \geq 8(a-1)(b-1)(c-1).

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_70936 (a b c : ℝ) (habc : a * b * c = 3) (ha : a ≥ 1) (hb : b ≥ 1) (hc : c ≥ 1) : (a + 1) * (b + 1) * (c + 1) ≥ 8 * (a - 1) * (b - 1) * (c - 1)   :=  by sorry

Source

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

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