A strong restriction of the inductive completion procedure
International Colloquium on Automata, Languages and Programming on Automata, languages and programming
CADE-10 Proceedings of the tenth international conference on Automated deduction
Testing for inductive (Co)-reducibility
CAAP '90 Proceedings of the fifteenth colloquium on CAAP'90
Handbook of theoretical computer science (vol. B)
On proving inductive properties of abstract data types
POPL '80 Proceedings of the 7th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
SPIKE, an Automatic Theorem Prover
LPAR '92 Proceedings of the International Conference on Logic Programming and Automated Reasoning
A Mechanizable Induction Principle for Equational Specifications
Proceedings of the 9th International Conference on Automated Deduction
Canonical Conditional Rewrite Systems
Proceedings of the 9th International Conference on Automated Deduction
Extensions to the Rippling-Out Tactic for Guiding Inductive Proofs
Proceedings of the 10th International Conference on Automated Deduction
Implementing Contextual Rewriting
CTRS '92 Proceedings of the Third International Workshop on Conditional Term Rewriting Systems
Conditional Rewriting in Focus
Proceedings of the 2nd International CTRS Workshop on Conditional and Typed Rewriting Systems
Strategic Issues, Problems and Challenges in Inductive Theorem Proving
Electronic Notes in Theoretical Computer Science (ENTCS)
Automating coinduction with case analysis
ICFEM'10 Proceedings of the 12th international conference on Formal engineering methods and software engineering
Contextual Rewriting In Automated Reasoning
Fundamenta Informaticae
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We propose a new procedure for proof by induction in conditional theories where case analysis is simulated by term rewriting. This technique reduces considerably the number of variables of a conjecture to be considered for applying induction schemes (inductive positions). Our procedure is presented as a set of inference rules whose correctness has been formally proved. Moreover, when the axioms are ground convergent and the defined functions are completely defined over free constructors, it is possible to apply the system for refuting conjectures. The procedure is even refutationally complete for conditional equations with boolean preconditions (under the same hypotheses). The method is entirely implemented in the prover SPIKE. This system has proved interesting examples in a completely automatic way, that is, without interaction with the user and without ad-hoc heuristics. It has also proved the challenging Gilbreath card trick, with only 5 easy lemmas.