You wouldn't write an Ada contract describing the full system, you would write one describing the local behavior you just described in your TLA+ model. The model ensures that the emergent behavior of the system is correct, and the local contract ensures that the local behavior of the various actors is correct -- and therefore results in that emergent behavior. Combined, that's a fairly solid argument that your system does what you intended.

If you had to implement the full proof in Ada, there would be no point to doing the TLA+ work.