# In any data cube, let C be the collection of all cuboids. Given any L C C, any C C L – Beluw(L) can satisfy both that 1. each cuboid not in C has exactly one descendant in C that is not redundant, and 2. any superset of C must include more than one descendant of some cuboid in Below(L), iff C is the descendant closure of some cuboid c, satisfying that c, is not in Below(L) but all of its ancestors are in Below(L).

In any data cube, let C be the collection of all cuboids. Given any L C C, any C C L – Beluw(L) can satisfy both that 1. each cuboid not in C has exactly one descendant in C that is not redundant, and 2. any superset of C must include more than one descendant of some cuboid in Below(L), iff C is the descendant closure of some cuboid c, satisfying that c, is not in Below(L) but all of its ancestors are in Below(L).