lean_workbook_plus_27320

Proved

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

Given the $x, y, z \in \mathbb{R}$ such that $0 < x, y, z < 1$ and $xyz = (1 - x)(1 - y)(1 - z)$ . Show that at least one of the numbers $(1 - x)y, (1 - y)z, (1 - z)x$ is greater than or equal to $\frac{1}{4}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_27320 (x y z : ℝ) (hx : 0 < x ∧ x < 1) (hy : 0 < y ∧ y < 1) (hz : 0 < z ∧ z < 1) (h : x * y * z = (1 - x) * (1 - y) * (1 - z)) : (1 - x) * y ≥ 1 / 4 ∨ (1 - y) * z ≥ 1 / 4 ∨ (1 - z) * x ≥ 1 / 4   :=  by sorry

Source

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

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