Completion of a set of rules modulo a set of equations
SIAM Journal on Computing
A mechanical proof of the Church-Rosser theorem
Journal of the ACM (JACM)
Parallel reductions in &lgr;-calculus
Information and Computation
Some Lambda Calculus and Type Theory Formalized
Journal of Automated Reasoning
Five Axioms of Alpha-Conversion
TPHOLs '96 Proceedings of the 9th International Conference on Theorem Proving in Higher Order Logics
A New Approach to Abstract Syntax Involving Binders
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Abstract Syntax and Variable Binding
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
A calculus of transition systems (towards universal coalgebra)
A calculus of transition systems (towards universal coalgebra)
Automating the meta theory of deductive systems
Automating the meta theory of deductive systems
Locus Solum: From the rules of logic to the logic of rules
Mathematical Structures in Computer Science
Nominal Logic: A First Order Theory of Names and Binding
TACS '01 Proceedings of the 4th International Symposium on Theoretical Aspects of Computer Software
Combining Higher Order Abstract Syntax with Tactical Theorem Proving and (Co)Induction
TPHOLs '02 Proceedings of the 15th International Conference on Theorem Proving in Higher Order Logics
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We present the titular proof development which has been implemented in Isabelle/HOL. As a first, the proof is conducted exclusively by the primitive induction principles of the standard syntax and the considered reduction relations: the naive way, so to speak. Curiously, the Barendregt Variable Convention takes on a central technical role in the proof. We also show (i) that our presentation coincides with Curry's and Hindley's when terms are considered equal up-to α and (ii) that the confluence properties of all considered calculi are equivalent.