Preface 

Concerning the Revised Edition 




1 
A Summary of Mizar 




2 
An Outline of the Mizar Language 




3 
The Structure of the Mizar Article 


3.1 
The Structure of the Mizar 


3.2 
The Environ Section 



3.2.1 
Vocabulary Section 



3.2.2 
Notation Section，Constructors Section 



3.2.3 
Requirements Section 



3.2.4 
Definitions Section 



3.2.5 
Theorems Section 



3.2.6 
Schemes Section 


3.3 
The Main Section 



3.3.1 
Sentences 



3.3.2 
Theorem 






4 
Method for Demonstration 


4.1 
Basic Method for Demonstration 


4.2 
Irrational Method 


4.3 
Dividing the Demonstrations 


4.4 
Demonstration of the Equivalence 


4.5 
Method for Using Now 



4.5.1 
Caution About End 


4.6 
All Symbols 



4.6.1 
When There Are Two Variables 



4.6.2 
Method for Writing With such that 



4.6.3 
Division of Sentences 



4.6.4 
Dividing Sentences With Assume 



4.6.5 
Caution Following that 


4.7 
Existing Symbols 



4.7.1 
Method for Using Consider 



4.7.2 
Method for Using Given 


4.8 
Dividing Into Cases 



4.8.1 
Premise for Dividing Into Cases 



4.8.2 
Labels for Dividing Into Labels 



4.8.3 
Warning About Labels 


4.9 
Method for Using @proof 


4.10 
Introduction of New Variable (Set, reconsider) 


4.11 
About Take 


4.12 
Hereby 






5 
About Mode 


5.1 
Mode 


5.2 
Structure Level 


5.3 
Mode change 


5.4 
Declaration of Mode During a Demonstration 



5.4.1 
Warning About c= 



5.4.2 
Example of Actually Using a Definition 






6 
Definition 


6.1 
Definition 


6.2 
Method for Writing the Vocabulary File 


6.3 
Predicate Definition 


6.4 
Functor Definition 


6.5 
Method for Using Equals 


6.6 
Mode Definition 


6.7 
Cluster Definition 


6.8 
Introduction of structure 






7 
Practice Environment 


7.1 
Installation 



7.1.1 
MSDOS Version 



7.1.2 
Linux Version 


7.2 
Preparation for Using Mizar 


7.3 
Mizar System 


7.4 
The Mizar Usage 



7.4.1 
Accommodate 



7.4.2 
Mizar Checker 



7.4.3 
When There Is An Error 



7.4.4 
Useful Command 






8 
Registering to the Library 


8.1 
Improvement of an Article 



8.1.1 
Improvement of the Main Section 



8.1.2 
Checking the Environ Section 


8.2 
Preparation for Registration 






9 
Useful tools 


9.1 
To find VOC files containing a terminology (findvoc) 


9.2 
To check the contents of the VOC file 


9.3 
To serach for the ABS file which the terminology appears 



9.3.1 
Method for Using grep 



9.3.2 
Method for serach on the Web 






10 
About the version upgrade 






A 
List of Reserved Words 






B 
A Compilation of Mizar Library Theorems 


B.1 
TARSKI 


B.2 
AXIOMS 


B.3 
BOOLE 


B.4 
XBOOL_0 


B.5 
XBOOL_1 


B.6 
REAL_1 


B.7 
NAT_1 


B.8 
FUNCT_1 


B.9 
SUBSET_1 


B.10 
FINSEQ_1 


B.11 
FUNCT_2 


B.12 
SQUARE_1 


B.13 
REAL_2 






C 
C.1 
Contacting the Mizar Society 



C.1.1 
Mizar Society 



C.1.2 
Mizar Society Nagano Circle 


C.2 
Acquisition of Mizar by ftp 


C.3 
How to submit Articles via the Internet 


C.4 
WWW Homepage 


C.5 
Formalized Mathematics 






Conclusion 

Reference 
