A quartic lower bound with linear and cyclic cubic terms

Proved

WorkbookSource.base_48806

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

lean-workbooksource-checked

For reals $a,b,c$ , prove that: a^4+b^4+c^4+4a+4b+4c+12 \ge 3a^2+3b^2+3c^2+2ab^2+2bc^2+2ca^2

Source: InternLM Lean-Workbook, record lean_workbook_48806 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_48806 (a b c : ℝ) : a^4+b^4+c^4+4*a+4*b+4*c+12 ≥ 3*a^2+3*b^2+3*c^2+2*a*b^2+2*b*c^2+2*c*a^2  :=  by sorry

Source