lean_workbook_plus_21878

Proved

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

Let $a, b\geq0$ and $a^3+b^3= 2$ . Prove that

a^2+b^2\le a^5+b^5\le 2(a^2+b^2)

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_21878 (a b : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hab : a^3 + b^3 = 2) : a^2 + b^2 ≤ a^5 + b^5 ∧ a^5 + b^5 ≤ 2 * (a^2 + b^2)   :=  by sorry

Source

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

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