In this paper branching for attacking MILP is investigated. Under certain circumstances branches can be done concurrently. By introducing a new calculus it is shown there are restrictions for certain dual values and reduced costs. As a second unexpected result of this study a new class of cuts for MILP is found, which are defined by those values. This class is a superclass of all other classes of cuts. Furthermore the restrictions of the dual values and the reduced costs can be used for studying the addition of arbitraries inequalities.