Inductive Proofs with Sets, and Some Applications in Process Algebra

We formalise proofs by structural induction on sets, speciied as an algebraic data type. The core idea is that the standard scheme for constructor induction can be used for the derivation of alternative schemes. This way, considerable exibility can be obtained for proofs in the inductive theory for the sets. For more general purposes we formulate a rule for`hybrid' induction, which allows a variety of induction schemes. A number of examples is provided, most of which contain well-known and intuitively clear facts about sets that are nevertheless not always easy to prove. We also use our material on sets for proving some interesting properties of two special processes that have sets as a parameter, speciied in CRL style, representing generalised alternative and parallel compositions of processes. We moreover demonstrate how our generalised parallel composition can be used for a speciication of broadcasting.