lean_workbook_plus_41503

Proved

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

Let $a,b,x,y$ be real numbers with ${0<y\leq\3x}.$ Prove the inequality $x(a^{4}+b^{4})+2ya^{2}b^{2}\ge\ (x+y)(a^{3}b+ab^{3}).$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_41503 (a b x y : ℝ) (h₀ : 0 < y) (h₁ : y ≤ 3 * x) :  x * (a^4 + b^4) + 2 * y * a^2 * b^2 ≥ (x + y) * (a^3 * b + a * b^3)   :=  by sorry

Source

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

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