A mixed sixth-degree polynomial inequality

Proved

WorkbookSource.base_43462

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

lean-workbooksource-checked

Let $a,b,c$ are real numbers,prove that: $a^2(c^2a^2+a^2b^2+ac^2b+c^4)+2b^4c^2 \geq ac(a^2+2b^2)(ab+c^2).$

Source: InternLM Lean-Workbook, record lean_workbook_43462 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_43462 (a b c : ℝ) : a^2 * (c^2 * a^2 + a^2 * b^2 + a * c^2 * b + c^4) + 2 * b^4 * c^2 ≥ a * c * (a^2 + 2 * b^2) * (a * b + c^2)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_43462; Apache-2.0

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