The first proof shows T is provable from S ; this is an ordinary mathematical proof along with a justification that it can be carried out in the system S .
To show that a system S is required to prove a theorem T , two proofs are required .
The first proof shows theorem T is provable from S ; this is an ordinary mathematical proof along with a justification that it can be carried out in the system S .
To show that a system S is required to prove a theorem T , two proofs are required .