An asymmetric quartic bound on nonnegative variables

Proved

WorkbookSource.plus_436

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

lean-workbooksource-checked

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

$b^3a+a^4+c^4 \geq abc(c+b)+a^3c.$

Source: InternLM Lean-Workbook, record lean_workbook_plus_436 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_436 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) : b^3 * a + a^4 + c^4 ≥ a * b * c * (c + b) + a^3 * c   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_436; Apache-2.0

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