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|  HOL CASE STUDY: Modular Arithmetic				      |
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AUTHOR
  Elsa L. Gunter
  Department of Computer and Information Science
  University of Pennsylvania
  200 South 33rd Street
  Philadelphia, PA 19104, USA
  Telephone: (1) 215-898-9514
  Email: elsa@linc.cis.upenn.edu


CONCEPTS ILLUSTRATED
  Application of abstract group theory, use of specialized tactics for group
  theory and for the integers, interactive proof, tactics.

PREREQUISITES
  At least as much knowledge of HOL as is given in "Getting started with
  HOL".  Knowledge of the definitions of a group and a subgroup


SUPPORTING FILES
  In the directories hol/Training/studies/int_mod and hol/Library/int_mod.


ABSTRACT 
  The development of the basic group theory of the integers, including
  basic modular arithmetic, is described in three sections.  This case
  study is intended to give the user extensive hands-on experience proving
  facts using theorems and tactics from group theory and the theory of
  the integers, applying and developing abstract theories, and working
  through large proofs.  The material presented in this case study in
  graded in difficulty, with increases in difficulty occurring mainly
  from section to section.  This study is intended to be worked through
  in an interactive fashion.  While substantial benefit should be obtainable
  by simply reading this case study, the full benefit can only be had
  by executing the commands here outline as they are read.  At the end
  of the second and third sections, projects have been suggested for those
  who wish to further test their understanding of the concepts studied
  in those sections.

LATEX FILES
  The top-level TeX file for the case study is tutorial.tex.

