The use of formal methods provides confidence in the correctness of developments. Yet one may argue about the actual level of confidence obtained when the method itself -- or its implementation -- is not formally checked. We address this question for the B, a widely used formal method that allows for the derivation of correct programs from specifications. Through a deep embedding of the B logic in Coq, we check the B theory but also implement B tools. Both aspects are illustrated by the description of a proved prover for the B logic.