Just addressing some recent posts:
You can't sign either Thomas or Bradley (or really anyone) and still sign Hayward. Even if you renounce literally everyone and get Yabu to agree to stay in China, you will not have enough space for Hayward and another $20+ million player (unless you think team friendly is like $12 million and then ok, but it's not happening with those guys). This is also why they aren't going to be keeping Olynyk if they go after Hayward. To re-sign the rotation players you need their Bird rights to kick in. To sign Hayward, you have to trade Bradley (for a lower salary) or Rozier (for no salary) and renounce everyone. Then after you sign Hayward you can use the exemption to add one decent guy (probably bring Amir back - I don't think you can use the exemption on an RFA (Olynyk)) and after that vet minimum guys.
You aren't getting a top 10, and probably not a lottery pick, for a year of Bradley. Who's close enough that could use him for just next year? Remember that you also need his salary cleared, so if you trade him it needs to be to a team under the cap, or you are also getting back a player with a salary you then need to clear. This gets pretty complicated, and I'm not sure anyone who has space is going to want to use it for Avery Bradley before FA really even begins (which needs to happen in order to properly clear the room for Hayward).
If the Celtics sign Hayward, the most likely scenario is that one of Bradley, Thomas, and Smart is allowed to go for nothing, and another is traded for not as much as people expect. This doesn't have to happen for a year, but it will have to happen.