Deduction Modulo is a theoretical framework that allows the introduction of computational steps in deductive systems. This approach is well suited to automated theorem proving. We describe a proof-search method based upon tableaux for Gentzen’s intuitionistic LJ extended with rewrite rules on propositions and terms . We prove its completeness with respect to Kripke structures. We then give a soundness proof with respect to cut-free LJ modulo. This yields a constructive proof of semantic cut elimination, which we use to characterize the relation between tableaux methods and cut elimination in the intuitionistic case.
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