We extend classic union and intersection type systems with a type-case construction and show that the combination of the union elimination rule of the former and the typing rules for type-cases of our extension encompasses occurrence typing. The latter is a typing technique that takes into account the result of type tests to assign different types to the same expression when it occurs in different branchings of the test. To apply this system in practice, we define a canonical form for the expressions of our extension, called MSC-form. We show that an expression of the extension is typable if and only if its MSC-form is, and reduce the problem of typing the latter to the one of reconstructing annotations for that term. We provide a sound algorithm that performs this reconstruction and a proof-of-concept implementation.