Automated Mathematical Induction

In the 1970s, Boyer and Moore built one of the first automated theorem provers that was capable of proofs by mathematical induction. Today, the Boyer-Moore theorem prover remains the most successful in the field. For a long time, the research on automated mathematical induction was confined to very few people. In recent years, as more people realize the importance of automated inductive reasoning to the use of formal methods of software and hardware development, more automated inductive proof systems have been built. In 1992, the interested researchers in the field formed two consortia on automated inductive reasoning - the MInd consortium in Europe and the IndUS consortium in the United States. The two consortia organized three joint workshops in 1992-1995. There will be another one in 1996. This text documents advances in the understanding of the field and in the power of the theorem provers that can be built. In the first of six papers, the reader is provided with a tutorial study of the Boyer-Moore theorem prover. The other five papers present novel ideas that could be used to build theorem provers more powerful than the Boyer-Moore prover.