This is a logically, well, trivial statement since if A and B are the two sets that were ambiguous (i.e. they intersects), you can always make two new sets A’ and B’ by assign the intersection of A and B to A.
In another word, (repeat almost exactly what I’ve said above) just because you can make an unambiguous definition on top of an ambiguous one does not means the ambiguity is not there. If it is allowed to add arbitrary qualifiers to the condition (i.e. adding non-type condition of fieldnames on values) then ambiguity will never be a valid argument for anything, ever. Since this doesn’t seem to be what you suggest, you have to use the original definition of A and B (that do not have arbitrary qualifier applied) and in that case they are clearly ambiguous.