lean_workbook_plus_4157

Proved

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

prove $x^2+y^2+z^2 \geq \frac{3}{4}$ given $x,y,z \geqslant 0$ and $x+y^2+z^3=1$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_4157 (x y z : ℝ) (hx : x ≥ 0) (hy : y ≥ 0) (hz : z ≥ 0) (h : x + y^2 + z^3 = 1) : x^2 + y^2 + z^2 ≥ 3 / 4   :=  by sorry

Source