Parameterized Metareasoning in Membership Equational Logic

Basin, Clavel, and Meseguer showed in [1] that membership equational logic is a good metalogical framework because of its initial models and support of reflective reasoning. A development and an application of those ideas was presented later in [4]. Here we further extend the metalogical reasoning principles proposed there to consider classes of parameterized theories and apply this reflective methodology to the proof of different parameterized versions of the deduction theorem for minimal logic of implication.