lean_workbook_plus_26754

Proved

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

By AM-GM, we have $\displaystyle \frac{x^2+y^2}{2}\geq xy$ , $\displaystyle \frac{x^2+z^2}{2}\geq xz$ , $\displaystyle \frac{y^2+z^2}{2}\geq yz$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_26754 (x y z: ℝ) : (x^2 + y^2) / 2 ≥ x * y ∧ (x^2 + z^2) / 2 ≥ x * z ∧ (y^2 + z^2) / 2 ≥ y * z   :=  by sorry

Source