In mathematical logic, for example, saying that A is an elementary substructure of B is equivalent to saying that B is an elementary extension of A. The same wi

In mathematical logic, for example, saying that A is an elementary substructure of B is equivalent to saying that B is an elementary extension of A. The same with subfields and extension fields. Those concepts are opposite. Usually in OOP you extend a class with additional implementation. Intersection of types means union of their members and vice versa. Getting into a situation where extending X gives you a sub-X seems like an unfortunate case of mixing two mental models that behave in a dual manner.