lean_workbook_plus_68965

Proved

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

The inequality $x+y+z-xy-xz-yz\leq 1$ is equivalent to $(1-x)(1-y)(1-z)+xyz\geq 0$ which is obvious for all $0\leq x,y,z\leq 1$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_68965 (x y z : ℝ) : (x + y + z - x * y - x * z - y * z) ≤ 1 ↔ (1 - x) * (1 - y) * (1 - z) + x * y * z ≥ 0   :=  by sorry

Source