Here are the definitions and theorems without proofs in postscript . The complete Mizar text in postscript . In the second version of the Mizar specification I make use of some types available in Mizar. The initial data base is a family of empty functions. Next seat .
Invariants There is almost nothing to prove as the required invariants follow from typing.
This is the main gain from using richer types. The invariants of operations are expressed in the type of their result. There is a guarantee that we do not forget to prove an invariant for an operation as it must be done when the operation is defined. Putative theorems have been proven, they are expressed slightly differently than in Version 0. Here are the definitions and theorems without proofs in postscript .