Single word to describe thing-a which can either contain thing-b or *be* thing-b

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"?"

• A huge part of your problem is the very odd beginning, Like "has-or-is": the logical test is…. not in English, it isn't, and prolly not in any other human as opposed to logical language. In logic as taught to who - 12 year olds? - there might be. If you could drag together some combination of is or contains and equal to or greater than you might be getting there but not in English. Did you ask a search engine about sets or Venn diagrams, please? Commented Oct 10, 2017 at 22:47
• Sorry @RobbieGoodwin, it's a slightly difficult thing to explain, and "has-or-is" seemed like a succinct way of putting it. There may be words from formal logic, or set theory, which fit this, but I'm looking for a word which would be recognised by most people, rather than just mathematicians. Commented Oct 11, 2017 at 9:39
• Max, since so few of us seem to follow this, could you explain what this is for, please? If there were a nice, short, single word for this don’t you think we would all have been taught it as part of our introduction to sets, Venn diagrams and Boolean logic? I’ve no idea where that comes in today’s school syllabus; I happen to have been among the first-contact group, as it were, aged about 10. How sure are you that has-or-is translates to Does this thing contain, or is it the same as the other thing? Would that not require has to mean, quite specifically contain… and does it? Commented Oct 11, 2017 at 19:47
• @RobbieGoodwin - as someone once said, "There are two difficult problems in computer science: naming things, cache invalidation, and off-by-one errors". It's for a function name. I know I could call it anything but it made me curious about whether there was a word. If you don't know, personally, that's fine, but you don't need to question the whole educational system. Commented Oct 12, 2017 at 8:16
• Uh… thanks Max and sadly, the point here is that it's you who questions the whole system. There is no such term, let alone word, and there will not be, however much you want one, until someone - who might be you - invents it, and then justifies his invention. Apart from anything else, how were you describing a function, please? Commented Oct 12, 2017 at 23:15