The program used to check the validity of a proof is called a kernel. It just need to check one step at a time and the possible steps can be taken are just basic logic rules. People can gain more confidence on its validity by:
- Reading it very carefully (doable since it's very small)
- Having multiple independent implementations and compare the results
- Proving it in some meta-theory. Here the result is not correctness per se, but relative consistency. (Although it can be argued all other points are about relative consistency as well.)
The program used to check the validity of a proof is called a kernel. It just need to check one step at a time and the possible steps can be taken are just basic logic rules. People can gain more confidence on its validity by:
- Reading it very carefully (doable since it's very small)
- Having multiple independent implementations and compare the results
- Proving it in some meta-theory. Here the result is not correctness per se, but relative consistency. (Although it can be argued all other points are about relative consistency as well.)