Three scaled quadratic factors bound a squared pairwise sum

Proved

WorkbookSource.base_35375

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

lean-workbooksource-checked

For all reals $x$ , $y$ and $z$ prove that: $(2x^2+1)(2y^2+1)(2z^2+1)\geq3(xy+xz+yz)^2$

Source: InternLM Lean-Workbook, record lean_workbook_35375 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_35375 (x y z : ℝ) : (2 * x ^ 2 + 1) * (2 * y ^ 2 + 1) * (2 * z ^ 2 + 1) ≥ 3 * (x * y + x * z + y * z) ^ 2  :=  by sorry

Source