Like "has-or-is": the logical test is "Does this thing contain the other thing, or is it the same as the other thing?". Is there a nice, short, single word for this?
Imagine different sized boxes, with labels, which nest inside one another. I pick up a box, and I want to know if it has the label "foo" on it, or contains a box with the label "foo" on it. I might say "Does this box
<insert word here> "foo"?"