A four-variable quartic bound for two pairwise sums

Proved

WorkbookSource.base_1076

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

lean-workbooksource-checked

Note that for any reals $a, b, c, d$ we have $(a^2+b^2+c^2+d^2)^2+16abcd\geq 2(a+c)^2(b+d)^2$

Source: InternLM Lean-Workbook, record lean_workbook_1076 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_1076 (a b c d : ℝ) : (a^2+b^2+c^2+d^2)^2+16*a*b*c*d ≥ 2*(a+c)^2*(b+d)^2  :=  by sorry

Source