lean_workbook_plus_72669

Proved

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

For $a,b>0,\frac{1}{a}+\frac{1}{b}=1.$ Prove that $\frac{1}{a+1}+\frac{2}{2b+1} \leq \frac{3}{4}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_72669 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) (hab : 1 / a + 1 / b = 1) : 1 / (a + 1) + 2 / (2 * b + 1) ≤ 3 / 4   :=  by sorry

Source