selecting nodes where all (dynamically created) items in a series match attributes - xpath

Question

In the following XML (using Xquery):
let $xml :=
(<list xml:id="first">
<item corresp="a"/>
</list>,
<list xml:id="second">
<item corresp="a"/>
<item corresp="b"/>
</list>,
<list xml:id="third">
<item corresp="b"/>
</list>,
<list xml:id="third">
<item corresp="c"/>
</list>,
<list xml:id="forth">
<item corresp="b"/>
<item corresp="c"/>
</list>)
I am trying to return <list> where #corresp has both a and b (this is a series that is dynamically constructed, from 1 - 15 items). However this:
return $xml[./item[#corresp=("a","b")]]
Returns
<list xml:id="first">
<item corresp="a"/>
</list>
<list xml:id="second">
<item corresp="a"/>
<item corresp="b"/>
</list>
<list xml:id="third">
<item corresp="b"/>
</list>
<list xml:id="forth">
<item corresp="b"/>
<item corresp="c"/>
</list>
When I am looking for this result
<list xml:id="second">
<item corresp="a"/>
<item corresp="b"/>
</list>
Additionally, the parameters contained in ("a","b")are dynamically constructed. Therefore I am trying to identify a solution that can take any number/combination of parameters in a series, anywhere between 1 and 15.
I'm not sure how to build the predicate to return the expected result.
Thanks in advance.

Answer 1

You can use every in your predicates, to specify that every key in your sequence must satisfies being the value of a corresp attribute, for a candidate list element.
The expression looks like: every $v in $seq satisfies $v, which returns true if the expression on the right-hand side of satisfies returns true for every value in $seq. It returns false otherwise.
So in your example:
<lists>
<list xml:id="first">
<item corresp="a"/>
</list>
<list xml:id="second">
<item corresp="a"/>
<item corresp="b"/>
</list>
<list xml:id="third">
<item corresp="b"/>
</list>
<list xml:id="third">
<item corresp="c"/>
</list>
<list xml:id="forth">
<item corresp="b"/>
<item corresp="c"/>
</list>
</lists>
/list[every $k in $keys satisfies item/#corresp = $k]
FYI, you also have any, that you use the same way as every, but which returns true if, you got it, the expression returns true for any item in the sequence.

Answer 2

Just change your request to
return $xml[item[#corresp="a"] and item[#corresp="b"]]
which will return the desired output
<list xml:id="second">
<item corresp="a"/>
<item corresp="b"/>
</list>
You have to make separate predicates for each <item> match.
I guess you were trying to simplify things too much, because you were selecting by an OR rather than an AND, because your predicate was checking if item[#corresp...] is contained in the set ("a","b").