Implementing Class With Chain Of Inheritances

Usually, if I make a class that has an implementation and also inherits a class with same method signatures, then I do not need to manually add implementation code. For example, if I create a class that inherits List(of Double) and Implements IList(of Double), then I do not need to add any code to make this compile, since the program realizes that the inheritance covers all the methods of the implementation. (Even though VB will auto-generate methods you can remove them no problem).

Now I'm trying do to something more complicated, using an implementation on top of IList, with a class that has a chain of inheritances, and the program won't accept it. See this example:

Interface ICustomList
Inherits IList(Of Double)
Sub TestSub()
End Interface
Class BaseList
[Code] .....

The final item, CustomList, is not compiling. The program says 'TestSub' must be implemented, but by inheriting BaseList, the class has a TestSub (and it is recognized by intellisense)! All the subs exist, they are functional, so why is the implementation not valid? (I know I can get rid of this error by manually creating an (overloading) TestSub in CustomList and specifying that it is an implementation. However, this should not be necessary since it already exists, and if I am going to be building a chain of classes inheriting each other, this could potentially become time-consuming and annoying.)