5. The Rules of the Game

Abstract

This chapter outlines the concepts and techniques that underlie reasoning in Isabelle. Until now, we have proved everything using only induction and simplification, but any serious verification project require more elaborate forms of inference. The chapter also introduces the fundamentals of predicate logic. The first examples in this chapter will consist of detailed, low-level proof steps. Later, we shall see how to automate such reasoning using the methods blast, auto and others. Backward or goal-directed proof is our usual style, but the chapter also introduces forward reasoning, where one theorem is transformed to yield another.