lean_workbook_plus_11826

Proved

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

Let $a,b>0$ and $\frac{a}{a+2b+1}+\frac{b}{b+2a+1}= \frac{1}{2}.$ Prove that \n

a^3+b^3\leq 2

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_11826 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) (hab : a / (a + 2 * b + 1) + b / (b + 2 * a + 1) = 1 / 2) : a ^ 3 + b ^ 3 ≤ 2   :=  by sorry

Source

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

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