An asymmetric quartic inequality on nonnegative variables

Proved

WorkbookSource.base_2222

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

lean-workbooksource-checked

Let $a,b,c \geq 0$ ,prove that:

$c^3a+a^4+b^3c \geq ac(cb+b^2+a^2).$

Source: InternLM Lean-Workbook, record lean_workbook_2222 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_2222 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) : c^3*a + a^4 + b^3*c ≥ a*c*(b*c + b^2 + a^2)  :=  by sorry

Source