A quartic inequality under a linear difference constraint

Proved

WorkbookSource.base_2945

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

lean-workbooksource-checked

Let $a,b>0$ be such that $2a-b=2$ . Prove that $a^4+(a-b)^4+a^2b \ge a^3+(a-b)^3+ab^2$

Source: InternLM Lean-Workbook, record lean_workbook_2945 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_2945 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) (hab : 2 * a - b = 2) : a ^ 4 + (a - b) ^ 4 + a ^ 2 * b ≥ a ^ 3 + (a - b) ^ 3 + a * b ^ 2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_2945; Apache-2.0

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