A 'Theory' Mechanism for a Proof-Verifier Based on First-Order Set Theory

We propose classical set theory as the core of an automated proof-verifier and outline a version of it, designed to assist in proof development, which is indefinitely expansible with function symbols generated by Skolemization and embodies a modularization mechanism named 'theory'. Through several examples, centered on the finite summation operation, we illustrate the potential utility in large-scale proof-development of the 'theory' mechanism: utility which stems in part from the power of the underlying set theory and in part from Skolemization.

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