The text introduces in a very progressive way the different notations and concepts required for developing the case study; it analyzes the case study and extracts informations for constructing a first skeleton of B event-based model. The B event-based modeling technique is introduced by writing an event~~B model. The first invoice case study model is given in section~4 and it completes the skeleton of the section~2. Section~5 defines the refinement of a event~~B model and it is used in the section~6 for deriving the second case study model; a refinement of this model is proposed and introduces an ordering over invoices. Sections~7 and 8 conclude our proof-based development of B event-based models for the case study. The complete B models are given in three figures.