In this article, we propose a coq formalization of the relational data model which underlies relational database systems. More precisely, we present and formalize the data definition part of the model including integrity constraints. We model two different query language formalisms: relational algebra and conjunctive queries. The former is the basis of We also present logical query optimization and prove the main ''database theorems'': algebraic equivalences, the homomorphism theorem and conjunctive query minimization.