Proof by induction using test sets
Proc. of the 8th international conference on Automated deduction
Sufficient completeness, term rewriting systems and “anti-unification”
Proc. of the 8th international conference on Automated deduction
A strong restriction of the inductive completion procedure
Journal of Symbolic Computation
Principles of automated theorem proving
Principles of automated theorem proving
The Z notation: a reference manual
The Z notation: a reference manual
Rippling: a heuristic for guiding inductive proofs
Artificial Intelligence
Handbook of logic in artificial intelligence and logic programming
Handbook of logic in artificial intelligence and logic programming
On proving inductive properties of abstract data types
POPL '80 Proceedings of the 7th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Derivation and Use of Induction Schemes in Higher-Order Logic
TPHOLs '97 Proceedings of the 10th International Conference on Theorem Proving in Higher Order Logics
A Mechanizable Induction Principle for Equational Specifications
Proceedings of the 9th International Conference on Automated Deduction
Proceedings of the 10th International Conference on Automated Deduction
Proceedings of the 10th International Conference on Automated Deduction
Lazy Generation of Induction Hypotheses
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
Termination of Algorithms over Non-freely Generated Data Types
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
ZUM '98 Proceedings of the 11th International Conference of Z Users on The Z Formal Specification Notation
Type Synthesis in B and the Translation of B to PVS
ZB '02 Proceedings of the 2nd International Conference of B and Z Users on Formal Specification and Development in Z and B
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Selecting appropriate induction cases is one of the major problems in proof by induction. Heuristic strategies often use the recursive pattern of definitions and lemmas in making these selections. In this paper, we describe a general framework, based upon unification, that encourages and supports the use of such heuristic strategies within a Z-based proof system. The framework is general in that it is not bound to any particular selection strategies and does not rely on conjectures being in a \normal form" such as equations. We illustrate its generality with proofs using different strategies, including a simultaneous proof of two theorems concerning mutually-defined relations; these theorems are expressed in a non-equational form, involving both universal and existential quantifiers.