lean_workbook_plus_79973

Proved

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

If $x,y \in R$ , then show that: \n $\frac {|x+y|} {1+|x+y|} \le \frac {|x|} {1+|x|}+ \frac {|y|} {1+|y|}$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_79973 (x y : ℝ) : (|x + y| / (1 + |x + y|)) ≤ |x| / (1 + |x|) + |y| / (1 + |y|)   :=  by sorry

Source