A factored tenth-degree three-variable polynomial is nonnegative

Proved

WorkbookSource.plus_19577

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

lean-workbooksource-checked

prove $(b-c)^2c^2((a-b)^2(a^4+2a^3b+6a^2b^2+2ab^3+b^4-2c^2(a+b)^2)+c^4(a^2+b^2))\geq0$

Source: InternLM Lean-Workbook, record lean_workbook_plus_19577 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_19577 (a b c : ℝ) : (b - c) ^ 2 * c ^ 2 * ((a - b) ^ 2 * (a ^ 4 + 2 * a ^ 3 * b + 6 * a ^ 2 * b ^ 2 + 2 * a * b ^ 3 + b ^ 4 - 2 * c ^ 2 * (a + b) ^ 2) + c ^ 4 * (a ^ 2 + b ^ 2)) ≥ 0   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_19577; Apache-2.0

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