In the context of interactive theorem provers based on a dependent type theory, automation tactics (dedicated decision procedures, call of automated solvers, ...) are often limited to goals which are exactly in some expected logical fragment. This very often prevents users from applying these tactics in other contexts, even similar ones.This paper discusses the design and the implementation of pre-processing operations for automating formal proofs in the Coq proof assistant. It presents the implementation of a wide variety of predictible, atomic goal transformations, which can be composed in various ways to target different backends. A gallery of examples illustrates how it helps to expand significantly the power of automation engines.

The power of modern automated theorem provers can be put at the service of interactive theorem proving. But this requires in particular bridging the expressivity gap between the logics these provers are respectively based on. This paper presents the implementation of a modular suite of pre-processing transformations, which incrementally bring certain formulas expressed in the Calculus of Inductive Constructions closer to the first-order logic of Satifiability Modulo Theory solvers. These transformations address issues related to the axiomatization of inductive types, to polymorphic definitions or to the different implementations of a same theory signature. This suite is implemented as a plugin for the Coq proof assistant, and integrated to the SMTCoq toolchain.