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In set theory, the terms "contains" and "belongs" have well-established, non-overlapping standard meanings. The predicate "contains" () is strictly a relation between two subsets of the same set: "A contains B" means "B is a subset of A". The relationship between a set and its elements () is read either "belongs" or "is in": "x belongs to A" is the same as "x is an element of A". The symmetric predicate () is rarely used, and may be read "has" or "owns", never "contains". So, to avoid conflict with the mathematical tradition, methinks that the best choice for the abstract set type operations would be
I would suggest to remove the part about bunches and packing, at least from the introduction. As far as I can tell this are no widely used concepts and I could only find the one paper cited as reference from 2001, A theory of bunches, that introduced the concepts.