This project is currently an implementation of a proof-checker. But it is planned to be extended; for example, to support algorithm extraction from intuitionistic proofs, which is considered to be an interesting feature.
Possible later some PA-proofs can be translated to ZFC ones in some automated way, though I don't see this opportunity right now, using current methods
Just like current peano.h -- it is not hard and not that connected with other parts of the project