lean_workbook_plus_63196

Disproved

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

$x^2+y^2+z^2 \ge \frac{x+y+z}{2} \ge \frac{3-x-y-z}{2}$ , by proof1 and by Nesbit

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_63196 : ∀ x y z : ℝ, x^2 + y^2 + z^2 ≥ (x + y + z) / 2 ∧ (x + y + z) / 2 ≥ (3 - x - y - z) / 2   :=  by sorry

Source