An asymmetric quartic inequality involving a pairwise sum

Proved

WorkbookSource.plus_20152

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

lean-workbooksource-checked

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

$ab(a+b)^2+2c^4 \geq 2abc(b+c+a).$

Source: InternLM Lean-Workbook, record lean_workbook_plus_20152 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_20152 (a b c : ℝ) (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0) : a * b * (a + b) ^ 2 + 2 * c ^ 4 ≥ 2 * a * b * c * (b + c + a)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_20152; Apache-2.0

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