However, this would make it impossible to associate a ranking with at least one partitioning of S into accepted and rejected subsets contra the assumption that S is shatterable.
if C j is a coordinate in S − {x} that is not W-unique, then, for every partial exclusion that rejects F, under each partitioning of S − {x} into T and F, there is at least one other coordinate C i that fuses to W. C j could be removed from CON while preserving the shatterability of S − {x}.