lean_workbook_plus_63559

Proved

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

We have a stronger result: $(1 + x^2)(1 + y^2)(1 + z^2) \geq (xy + yz + xz - 1)^2$ is true for all $x, y, z$ real numbers (not just non-negative).

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_63559 (x y z : ℝ) : (1 + x^2) * (1 + y^2) * (1 + z^2) ≥ (x * y + y * z + x * z - 1)^2   :=  by sorry

Source