No. Gödel’s theorem forbids something that in general tells you whether a statement is true or not. (As in, a method which would work for every possible statem

No. Gödel’s theorem forbids something that in general tells you whether a statement is true or not. (As in, a method which would work for every possible statement within a system.) It certainly doesn’t preclude something that checks if a proof is correct, any more than it precludes checking whether some calculation is done correctly (I.e. it doesn’t preclude it at all) . It says that there are statements which the proof system doesn’t have a proof of the statement being true nor of it being false. It doesn’t mean you can’t have a proof system.