lean_workbook_plus_61757

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

For $x\in (-1,0)$ we have $e^x<1<\frac{1}{1+x}$ and for $x\in (0,\infty )$ we have $e^x>1>\frac{1}{1+x}$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_61757 : ∀ x ∈ Set.Ioo (-1 : ℝ) 0, exp x < 1 ∧ 1 < 1 / (1 + x) ∧ ∀ x ∈ Set.Ioi 0, exp x > 1 ∧ 1 > 1 / (1 + x)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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