This might just be different customs of language usage. But to me, if you say "This is a subset of That", you are saying "every case of This is also a case of T

This might just be different customs of language usage. But to me, if you say "This is a subset of That", you are saying "every case of This is also a case of That". I suppose you are using it to mean "That does not imply This", and honestly I don't think seen it used that way elsewhere.