A quadratic-mean bound for four squared products

Proved

WorkbookSource.problem_17662

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

lean-workbooksource-checked

Using A.M.-G.M. inequality,

\frac{\left((a^2+c^2)+(b^2+d^2)\right)^2}{4} \geq (a^2+c^2)(b^2+d^2) = a^2b^2+b^2c^2+c^2d^2+d^2a^2

Source: InternLM Lean-Workbook, record lean_workbook_17662 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_17662 (a b c d : ℝ) : (a^2 + c^2 + b^2 + d^2)^2 / 4 ≥ a^2 * b^2 + b^2 * c^2 + c^2 * d^2 + d^2 * a^2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_17662; Apache-2.0

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