lean_workbook_plus_52653

Proved

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

Prove that $-1<(x-1)(y-1)(z-1)<0$ for $0<x,y,z<1$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_52653 (x y z : ℝ) (hx : 0 < x ∧ x < 1) (hy : 0 < y ∧ y < 1) (hz : 0 < z ∧ z < 1) : -1 < (x - 1) * (y - 1) * (z - 1) ∧ (x - 1) * (y - 1) * (z - 1) < 0   :=  by sorry

Source

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

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