A product of three quadratic forms bounds a cube

Proved

WorkbookSource.base_10724

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

It's Holder in the form $(x^2+xy+y^2)(z^2+y^2+yz)(zx+x^2+z^2) \ge (zx+xy+yz)^3$ .

Source: InternLM Lean-Workbook, record lean_workbook_10724 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_10724 {x y z : ℝ} : (x^2 + x*y + y^2)*(z^2 + y^2 + y*z)*(z*x + x^2 + z^2) ≥ (z*x + x*y + y*z)^3  :=  by sorry

Source