Most serious places you officially download from will provide you with proof of purchase/invoices. So keeping those in an administrative system is handy.
If you are playing out, they won’t be too concerned about your tracks being bought officially (although they might investigate if they don’t trust things. They will be more concerned with whether or not your right to play tracks in public is legit. Depending on the country you live in the legislation on this will vary. There have been some previous posts on the subject, so I suggest using the search function to find out more.
Generally this means you or the venue needs a license to play music in public. If that is in order, I am gonna guess they will go home satisfied (again if you don’t have 50.000 tracks in your collection, in which case they might take a closer look).