A four-variable quartic bound with rational coefficients

Proved

WorkbookSource.base_36379

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

lean-workbooksource-checked

prove that: $2.(a+b+c+d)^4+(ab+bc+cd+ad+ac+bd)^2 \geq 3abcd+\frac{289}{96}(a+b+c+d)^2(ab+bc+cd+ad+ac+bd)$

Source: InternLM Lean-Workbook, record lean_workbook_36379 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_36379 (a b c d : ℝ) : 2 * (a + b + c + d) ^ 4 + (a * b + b * c + c * d + d * a + a * c + b * d) ^ 2 ≥ 3 * a * b * c * d + 289 / 96 * (a + b + c + d) ^ 2 * (a * b + b * c + c * d + d * a + a * c + b * d)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_36379; Apache-2.0

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