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I would like to have theorems in my main text with the proof being in the appendix. My idea is to repeat the theorem in the appendix including the proof. However, for that it would be necessary to repeat "Theorem 1" in the Appendix also as "Theorem 1". Does anybody have an idea how to do this in LyX?

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    The thmtools package has the restatable environment for that. See § 1.4, Repeating theorems, p. 6 in the package documentation. – Bernard Dec 9 '19 at 18:07
  • Is there a possibility to do the same in Lyx? – LyxUser12345 Dec 10 '19 at 9:44
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    No real idea, as I'm not a Lyx user, but thmtools has been a well established package for quite a few years, so Lyx should be aware of it. – Bernard Dec 10 '19 at 9:46
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As suggested in Bernard's comment, you can restate the theorem using the thmtools package.

Go to Document > Settings > LaTeX Premable and insert the below and apply.

\usepackage{thmtools}
\newtheorem{thm}{Theorem}

In the document, do Insert > TeX Code to get a TeX code inset. In it, write

\begin{restatable}[Optional-theorem-title]{thm}{theoremname}

Below it, add you theorem statement and end the environment with another TeX code inset containing \end{restatable}.

When you later want to restate the theorem, add a TeX code inset with

\theoremname*

In LyX and compiled:

enter image description here

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