This paper formalizes an incremental approach to design flow-control oriented hardware devices described by Moore machines. The method is based on successive additions of new behaviours to a simple device in order to build a more complex one. The new behaviours added must not override the previous ones. A set of CTL formulae is assigned to each step of the design. The links between the formulae of two consecutive design steps are formalized as a set of formula-transformations F, stating that: for all CTL formula f with atomic propositions related to step i, f is satisfied on a design at step i, iff F(f) is satisfied on the design extended at step i + 1. This result extends the classical CTL property preservation results in a particular context. Moreover, it simplifies the writing of properties for a new device. This approach has been applied in the design of bus protocol converters and the transformations were useful to perform non-regression analysis. It could also be applied in order to simplify both system and formulae in particular cases.