Diagonalization and Type Rewriting in Clam

In this paper, we show an implementation of Cantor's Diagonalization Process in the Oyster-Clam theorem proving system. To achieve that, we have extended the Oyster logic with comparison and induction on types, and developed a method and some rewrite rules. The rewrite rules deal with types, what was not supported yet in the Oyster-Clam system, and some modifications were done to make that possible.