lean_workbook_plus_78148

Proved

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

x^2+y^2\ge 2xy and ditto for the other two cases, all by AM-GM or noticing that $x^2+y^2-2xy=(x-y)^2\ge 0$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_78148 : ∀ x y : ℝ, x^2 + y^2 ≥ 2 * x * y   :=  by sorry

Source