Prove2Me

lean_workbook_plus_67327

Proved

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

Given that −1<x,y<1-1 < x, y < 1 , show that −1<x+y1+xy<1-1 < \frac{x + y}{1 + xy} < 1 .

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_67327 (x y : ℝ) (hx : -1 < x ∧ x < 1) (hy : -1 < y ∧ y < 1) : -1 < (x + y) / (1 + x * y) ∧ (x + y) / (1 + x * y) < 1   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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