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Home -> Community -> Usenet -> comp.databases.theory -> Re: completeness of the relational lattice
On 30 jun, 00:00, Vadim Tropashko <vadimtro_inva..._at_yahoo.com> wrote:
> On Jun 29, 1:40 pm, Jan Hidders <hidd..._at_gmail.com> wrote:
>
>
>
> > On 29 jun, 18:20, Vadim Tropashko <vadimtro_inva..._at_yahoo.com> wrote:
>
> > > On Jun 28, 3:41 pm, Jan Hidders <hidd..._at_gmail.com> wrote:
>
> > > > > > I invite you to challenge me to show that it can prove an equation
> > > > > > that holds. Of course you should also check if all these equations can
> > > > > > be derived by you.
>
> > > One more challenge:
>
> > > <xy> + S + Q = <xy> + S
>
> > > where S * [] = [z], and Q header is unconstrained. (I don't see axioms
> > > about the lattice bottom element:-)
>
> > Sorry. The rules axiomatize the algebra for relations with finite
> > headers. [...]
>
> I'm OK with no W.
Ok. I misunderstood "unconstrained". You mean it is an arbitrary header.
It seems I forgot a rule :-( (it turns out I needed it in a part of
the proof I had no worked out yet)
This rule is of course:
(62) r + <> = <>
And then it is easy:
<xy> + S + Q
(20) = <xy> + S + (S * []) + Q (22) = <xy> + S + [z] + Q (26) = <> + S + Q (62) = <> (62) = <> + S (26) = <xy> + S + [z] (22) = <xy> + S + (S * []) (20) = <xy> + S