Equalising Terms by Diierence Reduction Techniques

In the eld of inductive theorem proving syntactical diierences between the induction hypothesis and induction conclusion are used in order to guide the proof BvHS91, Hut90, Hut]. This method of guiding induction proofs is called rippling / coloring terms and there is considerable evidence of its success on practical examples. For equality reasoning we use these annotated terms to represent syntactical diierences of formulas. Based on these annotations and on hierarchies of function symbols we deene diierent abstractions of formulas which are used for a hierarchical planning of proofs. Also rippling techniques are used to reene single planning steps, e.g. the application of a bridge lemma, on a next planning level.