lean_workbook_plus_28024

Proved

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

Let $x,\ y,\ z$ be real numbers such that $|x| \leq 1,\ |y| \leq 1,\ |z| \leq 1$ . Prove that $xyz \geq x + y + z - 2$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_28024 (x y z : ℝ) (hx : abs x ≤ 1) (hy : abs y ≤ 1) (hz : abs z ≤ 1) : x*y*z ≥ x + y + z - 2   :=  by sorry

Source