Definitions by rewriting in the calculus of constructions

Considers an extension of the calculus of constructions where predicates can be defined with a general form of rewrite rules. We prove the strong normalization of the reduction relation generated by the β-rule and user-defined rules under some general syntactic conditions, including confluence. As examples, we show that two important systems satisfy these conditions: (i) a sub-system of the calculus of inductive constructions, which is the basis of the proof assistant Cog, and (ii) natural deduction modulo a large class of equational theories