A factored sixth-degree polynomial is nonpositive

Proved

WorkbookSource.base_53551

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

lean-workbooksource-checked

Thus, it remains to prove that $4(a+b)^2(a^2+b^2)^2-25(a^2+b^2)(25a^4-4a^3b-31a^2b^2-4ab^3+25b^4)\leq0$ .

Source: InternLM Lean-Workbook, record lean_workbook_53551 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_53551 (a b : ℝ) : 4 * (a + b) ^ 2 * (a ^ 2 + b ^ 2) ^ 2 - 25 * (a ^ 2 + b ^ 2) * (25 * a ^ 4 - 4 * a ^ 3 * b - 31 * a ^ 2 * b ^ 2 - 4 * a * b ^ 3 + 25 * b ^ 4) ≤ 0  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_53551; Apache-2.0

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