Question: Type checking for a kind of set

This question is related to the Question Why is this type check not working?

I am trying to add this to my type list in a package, but cannot get it to work.

TypeTools:-AddType(_L3DP, set(satisfies(s -> type(s, [algebraic $ 3])),'Vector[column](3, algebraic)'));

when I test with this I get an error.

 type({[7,8,9],<1,2,3>},:-_L3DP);
Error, testing against an invalid type

or this 

type({[7,8,9],<1,2,3>},set(satisfies(s -> type(s, [algebraic $ 3])),'Vector[column](3, algebraic)'));
Error, testing against an invalid type
Please Wait...