I have to find a really bad example where you cannot apply Heaths Theorem because of a missing functional dependency.
But am I right, that every relation has at least one functional dependency?
Or can anyone of you come up with an example table with at least 3 Sets of Attributes to project it and then join it together. The result should of course be different from the original table to proof Heath's Theorem right (no FD -> no lossless decompositions)
It does not matter, wheter it is an sql example or an abstract one.