lean_workbook_plus_76556

Proved

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

Prove that, if $x,$ and $z$ are non-negative and $xyz \geq 1$ , then $(x+1)(y+1)(z+1) \geq 8$ . Is the converse true?

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_76556 (x y z : ℝ) (hx : x ≥ 0) (hy : y ≥ 0) (hz : z ≥ 0) (h : x*y*z ≥ 1) : (x + 1) * (y + 1) * (z + 1) ≥ 8   :=  by sorry

Source