https://maximummathematics.com/books/foundational-mathematics/set-theory/proof-technique-casework/index.htmlPreviously, we talked about a proof technique where we examine every single element of a finite set. In a sense, we examined multiple cases, and verified some result for each of those cases. An exhaustive proof is a special kind of proof by casework. Sometimes, we may have trouble demonstrating that some result holds for a set of elements. However, if we partition the set into groups that have their own special traits, and those traits make it easy to show the desired result holds, a proof by casework can be used to establish the desired result for the entire set.Hugoen-US