lean_workbook_plus_37219

Proved

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

Prove that there exists a subsequence $(x_{n_k})$ of a Cauchy sequence $(x_n)$ such that for all $k > 0$ , $|x_{n_{k + 1}} - x_{n_k}| < \frac{1}{2^k}$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_37219 (x : ℕ → ℝ) (hx : CauchySeq x) :
    ∃ n : ℕ → ℕ, ∀ k : ℕ, k > 0 → |x (n (k + 1)) - x (n k)| < 1 / 2 ^ k   :=  by sorry

Source

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

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