In academic writing, it is common to refer to or prove properties about the main object of an article.
If I prove a property for (some object), I know I can use the phrase:
Property X holds for the object Y.
But, can an object hold a property?
Furthermore, object Y holds some additional properties.
It always sounded "natural" to me (I'm not a native speaker), but now that I'm trying to verify my sentence construction using Google, I just can't seem to find anything useful.