lean_workbook_plus_7381

Proved

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

In $\mathbb{R}^n$ show that $\mid\mid x-y \mid\mid \ \mid\mid x+y \mid\mid \leq \mid\mid x \mid\mid^2 + \mid\mid y \mid\mid^2$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_7381 (x y : ℝ) : ‖x - y‖ * ‖x + y‖ ≤ ‖x‖^2 + ‖y‖^2   :=  by sorry

Source