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Intended for comparison only with #2721 / #2809 by way of offering an 'alternative' (simpler?) design...
NB I'd be very tempted to refactor eg
UpperBoundandMinimalUpperBoundAbovein terms of intersection-closed predicates, ie to develop a theory of objects '≤-minimal such thatP' for predicatesPunder suitable closure conditions, but that's a tale for another day, as well as the theory of 'inclusions' between DC-'subsets' of a given preorder, so that the various lubs/mubs could be compared according to their indexing setsI... etc.UPDATED: definition of Mub might require the additional precondition that
xis a lower bound for the image off, to rule out nonsensical definitions... oops!