A sextic and quadratic product bounds a mixed quartic square

Proved

WorkbookSource.base_36864

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

lean-workbooksource-checked

Applying CS, $\left( a^4b^2+a^2b^4+b^4c^2+b^2c^4+c^4a^2+c^2a^4+2a^2b^2c^2\right)(b^2+a^2+c^2+b^2+a^2+c^2+2)\geq \left(2\sum_{cyc} a^2b^2+2abc \right) ^2$

Source: InternLM Lean-Workbook, record lean_workbook_36864 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_36864 {a b c : ℝ} : (a^4 * b^2 + a^2 * b^4 + b^4 * c^2 + b^2 * c^4 + c^4 * a^2 + c^2 * a^4 + 2 * a^2 * b^2 * c^2) * (b^2 + a^2 + c^2 + b^2 + a^2 + c^2 + 2) ≥ (2 * (a^2 * b^2 + b^2 * c^2 + a^2 * c^2) + 2 * a * b * c)^2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_36864; Apache-2.0

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