lean_workbook_plus_29547

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Let $a,b\geq 0$ and $a^3+b^3=a-b.$ Prove that $(a-b)^4\leq (1-4ab)(1-ab)^2.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_29547 {a b : ℝ} (ha : 0 ≤ a) (hb : 0 ≤ b) (hab : a^3 + b^3 = a - b) : (a - b)^4 ≤ (1 - 4 * a * b) * (1 - a * b)^2   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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