A pair-square sum bounds the triple product at total three

Proved

WorkbookSource.base_7240

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Let real numbers $x,y,z$ such that $x+y+z=3$ ,please do this:

$y^2z^2+z^2x^2+x^2y^2 \geq 3xyz$

Source: InternLM Lean-Workbook, record lean_workbook_7240 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_7240 (x y z : ℝ) (h : x + y + z = 3) : y ^ 2 * z ^ 2 + z ^ 2 * x ^ 2 + x ^ 2 * y ^ 2 ≥ 3 * x * y * z  :=  by sorry

Source