arsinh — Mathlib

English

If f is continuous on s, then arsinh ∘ f is continuous on s.

Русский

Если f непрерывна на множестве s, то arsinh(f) непрерывна на s.

LaTeX

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

Lean4

theorem arsinh (h : ContinuousOn f s) : ContinuousOn (fun x => arsinh (f x)) s := fun x hx => (h x hx).arsinh

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