Proving that Android app never uses the internet

If you do not have the INTERNET permission, you should not be able to do any network communications.

So, one proof would be to not have the INTERNET permission. This may require you to specifically remove it via tools:remove or something, as third-party libraries might request it (even if you are not using features of those libraries that require that permission).

If your concern is that the user will not be able to tell that you lack this permission, or may not trust the permission system, or may not trust that the permission is needed for network access, then I do not know that there is much that can be done.

1. Simply stating that your app does not require internet connection, because it does not use it, would be enough (for me at least)
2. You could just redirect user to

this page in settings