lean_workbook_plus_76663

Proved

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

Let $a,b>0$ and $ab=1 .$ Prove that \n

\frac{1}{a^2+b }+\frac{1}{b+1} \leq 1

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_76663 (a b : ℝ) (hab : a * b = 1) (ha : 0 < a) (hb : 0 < b) : 1 / (a ^ 2 + b) + 1 / (b + 1) ≤ 1   :=  by sorry

Source