Re: thinking about UPDATE

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"Jan Hidders" <jan.hidders_at_REMOVETHIS.pandora.be> wrote in message news:pan.2004.07.22.18.06.23.604113_at_REMOVETHIS.pandora.be...

> If K is the set of original candidate keys and P is the set of attribute
> on which we project then:
> - Let K' = { k in K | k subset P }
> - If K' is not empty then return K' otherwise { P }

> > Also I note that my post here is simply thinking out the
> > cases, and I have no formalism to back this up. Does anyone
> > have any suggestions as to a formalism to apply to either
> > prove or disprove the above?

> Yep, normalization theory. You can translate the candidate keys to
> functional dependencies and these always also hold for the projection, and
> those that hold for the projection also hold for the original relation. So
> the proof of completeness goes something like this.

> Suppose that in the projection we have a candidate key A that is not in
> K'. Then the FD A->P holds in the projection, but also in the original
> relation. However, the only FDs that hold in the original relation are
> those that are implied by its CKs so A must have already been a CK in the
> original relation. But then A is by definition in K' which leads to a
> contradiction. So the original assumption that the projection has a CK
> that is not in K' must be false. QED

What made you think this:
"However, the only FDs that hold in the original relation are those that are implied by its CKs"

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