Design patterns capture expert design experience in generic design structure and behavior. A design pattern needs to be instantiated before using. It can be integrated with other patterns as well. The instantiation and integration operations are two important operations when a designer uses a design pattern in a particular application. In this paper, we investigate the commutability of these two operations based on our formal specification framework. We provide rigorous proofs on the conditions when the order of these two operations does not matter. Our results enable the software designers to choose their design processes with assurance of their equivalence.