We present a way to enjoy the power of SAT and SMT provers in Coq without compromising soundness. This requires these provers to return not only a yes/no answer, but also a proof witness that can beâ€¦ (More)

We define a generic notion of cut that applies to many first-order theories. We prove a generic cut elimination theorem showing that the cut elimination property holds for all theories having aâ€¦ (More)

The system Coq (Dowek et al., 1991) is an environment for proof development based on the Calculus of Constructions (Coquand, 1985) (Coquand and Huet, 1985) enhanced with inductive definitionsâ€¦ (More)

We present a new scheme to translate mathematical developments from HOL Light to Coq, where they can be re-used and rechecked. By relying on a carefully chosen embedding of Higher-Order Logic intoâ€¦ (More)

We present constructive arithmetic in Deduction modulo with rewrite rules only. In natural deduction and in sequent calculus, the cut elimination theorem and the analysis of the structure of cut freeâ€¦ (More)

It is well-known that the Calculus of Constructions (CC) bears a simple set-theoretical model in which proof-terms are mapped onto a single objectâ€”a property which is known as proof-irrelevance. Inâ€¦ (More)