TS: Why isn't union type in object field extracted to out of the object?

I think these type should be equal:

  { a: string | undefined }
  { a: string } | { a: undefined }

These mean same set of values. And if these are equals, the following works:

  Exclude<{ a: string | undefined }, { a: string }>   // => { a: undefined }

But it don't work as I expected. Because { a: string | undefined } is not { a: string } | { a: undefined }.

If it works, Exclude could be considered as subtraction of set in mathematical context. I think there is big deals if these types are equals. Why not? And please tell me related GitHub issues if you know.