A four-variable cyclic quartic inequality with a bilinear correction

Proved

WorkbookSource.plus_35952

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

lean-workbooksource-checked

prove that:

$(ac+bd)^2+\frac{3}{4}(a^2+c^2+b^2+d^2)^2 \geq (a+b+c+d)(ab^2+bc^2+cd^2+a^2d)$

$a,b,c,d \in R$

Source: InternLM Lean-Workbook, record lean_workbook_plus_35952 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_35952 (a b c d : ℝ) : (a * c + b * d) ^ 2 + (3 / 4) * (a ^ 2 + c ^ 2 + b ^ 2 + d ^ 2) ^ 2 ≥ (a + b + c + d) * (a * b ^ 2 + b * c ^ 2 + c * d ^ 2 + a ^ 2 * d)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_35952; Apache-2.0

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