A proof checker that encounters a non-provable statement like those constructed in Goedel’s proof of Incompleteness while evaluating a proof would declare that proof to be invalid. A valid proof would not contain any such statement, which it obviously has not proved.
A proof checker that encounters a non-provable statement like those constructed in Goedel’s proof of Incompleteness while evaluating a proof would declare that proof to be invalid. A valid proof would not contain any such statement, which it obviously has not proved.