lean_workbook_plus_15592

Proved

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

Prove that for all real numbers $a, b$ . We have : $\frac{|a+b|}{1+|a+b|} \le \frac{|a|}{1+|a|} + \frac{|b|}{1 + |b|}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_15592 (a b : ℝ) :  |a+b| / (1 + |a+b|) ≤ |a| / (1 + |a|) + |b| / (1 + |b|)   :=  by sorry

Source