Strict monotonicity of a rational expression

Proved

WorkbookSource.problem_47039

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

If $x > y > -1$ , prove that $\frac{x}{1+x} > \frac{y}{1+y}$ .

Source: InternLM Lean-Workbook, record lean_workbook_47039; Apache-2.0. Complete source proposition preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_47039 (x y : ℝ) (h : x > y) (h' : y > -1) : (x / (1 + x)) > (y / (1 + y))  :=  by sorry

Source