lean_workbook_plus_22669

Proved

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

Given the inequalities $1 - xy \geq 0$ , $1 - xz \geq 0$ , and $1 - yz \geq 0$ , prove that $(1 - xy)(1 - yz)(1 - zx) \geq 0$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_22669 (x y z : ℝ) (h1 : 1 - x*y ≥ 0) (h2 : 1 - x*z ≥ 0) (h3 : 1 - y*z ≥ 0) : (1 - x*y) * (1 - y*z) * (1 - z*x) ≥ 0   :=  by sorry

Source

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

View graph