lean_workbook_plus_8987

Proved

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

If 0<x,y,z<1 .Prove that\n $x(1-y)+y(1-z)+z(1-x)<1$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_8987 (x y z : ℝ) (hx : 0 < x ∧ x < 1) (hy : 0 < y ∧ y < 1) (hz : 0 < z ∧ z < 1) : x * (1 - y) + y * (1 - z) + z * (1 - x) < 1   :=  by sorry

Source

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

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