So in the case where a user has exercised the Right to be Forgotten (in regards to all of their data), that user’s personal data would technically no longer exist on your systems and as such the user would no longer be “identifiable” by you or your systems.
Article 12 of the GDPR states:
"The controller shall facilitate the exercise of data subject rights under Articles 15 to 22. In the cases referred to in Article 11(2), the controller shall not refuse to act on the request of the data subject for exercising his or her rights under Articles 15 to 22, unless the controller demonstrates that it is not in a position to identify the data subject."
This means that data controllers are exempt from the fulfilment of “Users’ Rights”, where the data subject cannot be identified — as in the case where all of the user’s personal data is removed from your systems in the fulfilment of the initial request.
In this situation, there would be no possibility or need to “provide proof” of something that no longer exists in relation to an identifiable person.
In practical terms, the best way to handle such a request would be to clearly inform the user (at the time of the initial request) that in fulfilling the request, all their data will be removed and that it would, therefore, be impossible for them to exercise any further rights in regards to this data as the data will no longer exist on your systems.
Another required (in most cases) and practical way of maintaining proof of your overall compliance is to maintain valid records in regards to your processing activities (like your delete smart campaigns) and acquisition of consent (where applicable). This way, you are better equipped to prove (to the Authority or otherwise) that you have systems in place to facilitate the fulfilment of User’s Rights, even if the data in question is no longer available.