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\title{Abstract Completeness}
\author{Jasmin Christian Blanchette, Andrei Popescu, and Dmitriy Traytel}

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\begin{abstract}
  This is a formalization of an abstract property of possibly infinite
  derivation trees (modeled by a codatatype), that represents the core of a
  Beth--Hintikka-style proof of the first-order logic completeness theorem and
  is independent of the concrete syntax or inference rules. This work is
  described in detail in a publication by the authors \cite{bla-compl}.

  The abstract proof can be instantiated for a wide range of Gentzen and tableau
  systems as well as various flavors of FOL---e.g., with or without predicates,
  equality, or sorts. Here, we give only a toy example instantiation with
  classical propositional logic. A more serious instance---many-sorted FOL with
  equality---is described elsewhere \cite{bla-mech}.
\end{abstract}

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