I would say that software engineering was the engineering discipline, and computer science a mathematical discipline.
My point was that the proof itself is not subsidiary to empirical evidence, only its application is, and in my eyes, there is merit in the proof, free from its application to the "real world", for example as a lemma to another proof. Consider it a form of separation of concerns: whilst I prove a theorem, I am not concerned with how it mirrors the observable world, but in order to apply it, of course I must ensure that its assumptions can be reliably observed. In this way, our "beliefs" are limited and do not taint the logic of the proof itself.
> How do you know that while these proofs reference the infinite, they are actually applicable to the infinite?
Which brings us to your next point: I do not know, I simply believe it to be true because it is convenient to do so. My point is that this belief or its refutation does not affect the worthiness of the proof, only that of its application.
I actually do not believe in the absolute power of proof, I don't think it is something you can get away with believing once presented with all the facts. I hope I've explained myself better in this comment though: I don't think our views are as antipodal as it first seemed.