A four-variable quadratic sum bounds three mixed products

Proved

WorkbookSource.base_46341

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

lean-workbooksource-checked

Prove that $a^2+b^2+c^2+d^2 \geq d(a+b+c)$ for all real numbers $a, b, c, d$ .

Source: InternLM Lean-Workbook, record lean_workbook_46341 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_46341 (a b c d : ℝ) : a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2 ≥ d * (a + b + c)  :=  by sorry

Source