Getting rid of Default Document Content Type from a document Set

When I attempted to get rid of the default document type from the allowed content types for a set of document, a message coming from the web page appears right before my eyes and it also says this type of content is in use.

Message from web page
Content Type in use
I don’t have an idea what this error was all about. I would appreciate it if somebody would be so nice to provide some ideas on how to repair this.
