lean_workbook_plus_22764

Open

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

Prove that $e^{-x} > -\frac{2x}{x^2 + 1}$ for $x \in \mathbb{R}^-$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_22764 (x : ℝ) (hx : x < 0) :
  Real.exp (-x) > -2 * x / (x ^ 2 + 1)   :=  by sorry

Source