Using metrics for proof rules for recursively defined delay-insensitive specifications

An advantage of algebraic specifications of delay insensitive asynchronous processes over most other formalisms is that it allows the recursive definition of processes, and correctness proofs of an implementation through fixpoint induction. On the other hand, proofs by fixpoint induction are intrinsically hard to design and read, which led us to use a much more palatable proof style, using so-called linear proofs and induction. Until now, the intuitive induction rule has never been formalized, and formalizing it, as we do in this paper shows that extreme care has to be taken to phrase the proof rule that is being used. Fortunately, the rules that we derive in this paper validate the proofs that used the intuitive notion, and its formulation is such that it can easily be included in theorem provers and other tools.