A four-variable quartic bound involving the square of a sum

Proved

WorkbookSource.plus_79113

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

lean-workbooksource-checked

Prove that $3(a^2+b^2+c^2+d^2)^2+4(a^2+d^2)(b^2+c^2) \geq (a^2+b^2+c^2+d^2)(a+b+c+d)^2$

Source: InternLM Lean-Workbook, record lean_workbook_plus_79113 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_79113 (a b c d : ℝ) : 3 * (a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2) ^ 2 + 4 * (a ^ 2 + d ^ 2) * (b ^ 2 + c ^ 2) ≥ (a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2) * (a + b + c + d) ^ 2   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_79113; Apache-2.0

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