A four-variable quartic inequality with rational coefficients

Proved

WorkbookSource.plus_48956

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

lean-workbooksource-checked

prove that: $5.(ab+bc+cd+ad+ac+bd)^2\geq \frac{7}{2}abcd+\frac{65}{32}(a+b+c+d)(acd+abd+abc+bcd)$

Source: InternLM Lean-Workbook, record lean_workbook_plus_48956 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_48956 (a b c d : ℝ) : 5 * (a * b + b * c + c * d + d * a + a * c + b * d) ^ 2 ≥ 7 / 2 * a * b * c * d + 65 / 32 * (a + b + c + d) * (a * c * d + b * c * d + b * a * c + a * b * d)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_48956; Apache-2.0

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