It is not without importance to emphasize that an alternate way of proving Theorem 4.2 is to establish that conditions of (EVPm) are fulfilled over (X,_; d) and '.
By the developments above, we have the chain of implications: (DC) [??] (BB)[??] (BBm) [??] (EVP), (BB) [??] (EVPm) [??] (EVP), (BBm) [??] (GTZ) [??] (EVPv) [??] (EVP).
So, the maximal/variational principles (BB), (BBm), (EVPm), (EVP), (GTZ) and (EVPv) are all equivalent with (DC); hence, mutually equivalent.