Members of the rdfs:ContainerMembershipProperty class

I would like to ask about the use of the class 
rdfs:ContainerMembershipProperty class.

In the RDF Schema document 
(http://www.w3.org/TR/rdf-schema/#ch_containermembershipproperty)
is mentioned that:

> The |rdfs:ContainerMembershipProperty| class has as members the 
> property |rdfs:member| and the properties |_1, _2, _3 ...| that can be 
> used to indicate membership of Bag, Seq and Alt containers. 
> |rdfs:ContainerMembershipProperty| is a subclass of |rdf:Property|. 
> Each container membership property is a |rdfs:subPropertyOf| the 
> |rdfs:member| property.
>
However, in the RDF Model Theory document 
(http://www.w3.org/TR/rdf-mt/#rdfs_entail)
the 2nd rule of the /rdfs-closure/ of an RDF graph states that the 
following triples are true:

> |[rdf:_1] [rdf:type] [rdfs:Property] .
> [rdf:_2] [rdf:type] [rdfs:Property] .|
> ...
>
> |[rdf:_1] [rdfs:subPropertyOf] [rdfs:member] .
> [rdf:_2]| |[rdfs:subPropertyOf] [rdfs:member] .|
> ...
>
However, since rdf:_XXX properties are members of the class 
 rdfs:ContainerMembershipProperty the first group
of the above triples shouldn't better be as follows?

|[rdf:_1] [rdf:type] [rdfs:ContainerMembershipProperty||] .
[rdf:_2] [rdf:type] ||[rdfs:ContainerMembershipProperty||] .|
...

Of course, rdfs:ContainerMembershipProperty is a subclass of 
rdfs:Property, therefore the latter
implies the former. However, if the latter is missing, then 
 rdfs:ContainerMembershipProperty will
contain no members and it'll be useless.

Nick

-- 
**************************************************************
* Dr. Nick Bassiliades                                       *
*                                                            *
* Programming Languages And Software Engineering (PLASE) Lab *
* Logic Programming and Intelligent Systems (LPIS) Group     *
*                                                            *
* Dept. of Informatics, Aristotle University of Thessaloniki *
* 54006 Thessaloniki, Greece                                 *
*                                                            *
* Tel: +30310998418    E-mail: nbassili@csd.auth.gr          *
* Fax: +30310998419    URL:    http://www.csd.auth.gr/~nick  *
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