In Component-Based Software Engineering programs are constructed from pre-defined software library modules. However, if the library?s subroutines do not exactly match the programmer?s requirements, the subroutines? code must be adapted accordingly. For this process to be acceptable in safety or mission-critical applications, where all code must be proven correct, it must be possible to verify the correctness of the adaptations themselves. In this paper we show how refinement theory can be used to model typical adaptation steps and to define the conditions that must be proven to verify that a library subroutine has been adapted correctly.