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Dedukti is a Logical Framework based on the $\lambda$$\Pi$-Calculus ModuloTheory. We show that many theories can be expressed in Dedukti: constructiveand classical predicate logic, Simple type theory, programming languages, Puretype systems, the Calculus of inductive constructions with universes, etc. andthat permits to used it to check large libraries of proofs developed in otherproof systems: Zenon, iProver, FoCaLiZe, HOL Light, and Matita.

Dedukti: a Logical Framework based on the $\lambda$$\Pi$-Calculus Modulo Theory