arsinh — Mathlib

English

If f is continuous at a, then arsinh ∘ f is continuous at a.

Русский

Если f непрерывна в точке a, то arsinh(f) непрерывна в a.

LaTeX

$$$\\forall X\\ {\\text{topological space}},\\ f:\\to\\mathbb{R},\\ a:\\mathbb{R},\\ (\\operatorname{ContinuousAt} f a)\\Rightarrow \\operatorname{ContinuousAt}(\\lambda x. \\operatorname{arsinh}(f x)) a.$$$

Lean4

nonrec theorem arsinh (h : ContinuousAt f a) : ContinuousAt (fun x => arsinh (f x)) a :=
  h.arsinh

Похожие утверждения