Program design, test and verification are supported by tailor-made deduction rules for proving Gentzen clauses , which are the most frequently used formulas for expressing requirements and queries to data types. Inductive proofs are built up from simplification, subsumption, resolution, rewriting and narrowing steps in a natural way that permits interaction on various levels. IF prem0 is complete as soon as prem subsumes conc .
Subsumption is a purely syntactical condition on prem and conc that implies conc IF prem .
Testing conc0 means deriving solutions of conc0 . Solutions are identified as the equations in solved form among the goals of conc . When building up front and rear one may interactively modify the underlying specification and add lemmas or induction orderings. The construction of front and rear may be interrupted whereby conc0 IF conc and prem IF prem0 are identified as proved subtheorems and conc IF prem is memorized as the remaining subconjecture. The current induction ordering is transmitted to a later proof of the subconjecture.