No misunderstanding about NP here for sure. As I said, this is about as much of a thesis as Church Turing is about what can be computed.
I have no clue about CiC, lean and whatnot. It was never my field and I don't doubt there can be some very weird things you can do with some fancy logic models that are rarely discussed by non logicians.
What I'm claiming is that anything a human could prove without a computer could be done by a non deterministic machine in poly time under a very reasonable assumption of proof length. I'm baking in the assumption of proof length, so I can claim something about NP...
Let me put it this way: if you can write a paper with your proof and I can check it with only my brain without a computer helping me, then a poly time algorithm could also check that proof. Unless you believe something exotic about how the brain computes, how would it not be the case?
I have no clue about CiC, lean and whatnot. It was never my field and I don't doubt there can be some very weird things you can do with some fancy logic models that are rarely discussed by non logicians.
What I'm claiming is that anything a human could prove without a computer could be done by a non deterministic machine in poly time under a very reasonable assumption of proof length. I'm baking in the assumption of proof length, so I can claim something about NP...
Let me put it this way: if you can write a paper with your proof and I can check it with only my brain without a computer helping me, then a poly time algorithm could also check that proof. Unless you believe something exotic about how the brain computes, how would it not be the case?