lean_workbook_plus_48583

Proved

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

Prove that if $\lim_{x \to 0}f(x)=L$ then $\lim_{x \to 0}f(cx)=L$ for any nonzero constant c.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_48583 (c : ℝ) (f : ℝ → ℝ) (L : ℝ) (h : c ≠ 0) : (∀ ε > 0, ∃ δ > 0, ∀ x, |x| < δ → |f x - L| < ε) → ∀ ε > 0, ∃ δ > 0, ∀ x, |x| < δ → |f (c * x) - L| < ε   :=  by sorry

Source

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

View graph