lean_workbook_plus_21142

Proved

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

Let $a,b$ be positive real numbers . Prove that $\frac{1}{1+a}-\frac{1}{1+b}+\frac{a}{a+b}< 1.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_21142 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) : 1 / (1 + a) - 1 / (1 + b) + a / (a + b) < 1   :=  by sorry

Source