A shifted quartic product bounds a squared quadratic sum

Proved

WorkbookSource.base_40002

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

lean-workbooksource-checked

Prove that $(b^4 + 3)(c^4 + 3) \ge 3(b^2 + c^2)^2$

Source: InternLM Lean-Workbook, record lean_workbook_40002 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_40002 (b c : ℝ) : (b^4 + 3) * (c^4 + 3) ≥ 3 * (b^2 + c^2)^2  :=  by sorry

Source