lean_workbook_plus_66419

Proved

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

Let $a, b>0$ and $a+b \leq 1 .$ Prove that \n

\left(a+\frac{1}{b}\right)\left(b+\frac{1}{a}\right) \geq \frac{25}{4}

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_66419 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) (hab : a + b ≤ 1) : (a + 1 / b) * (b + 1 / a) ≥ 25 / 4   :=  by sorry

Source