lean_workbook_plus_14989

Proved

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

Given $f(x) = \frac{1}{1+x^2}$ , find $\delta$ such that for all $x, y \in \mathbb{R}$ , if $|x - y| < \delta$ , then $|f(x) - f(y)| < \epsilon$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_14989 (f : ℝ → ℝ) (ε : ℝ) (hε : ε > 0) : ∃ δ, ∀ x y, abs (x - y) < δ → abs (f x - f y) < ε   :=  by sorry

Source