User blog comment:Wythagoras/Dollar function formal definition/@comment-5529393-20130619005520

I'm afraid that your notation is circular.

For example, a$[0,2] reduces to a$0,1]_[0,1]_[0,1]..._[0,1],1], which is certainly above a$[0,0]_2.  However, a$[0,0]_2 reduces to a$[0,[0,...[0,a]... which is above a$[0,2] when a is at least 2.

You need to decide which is "higher level" - more variables, or subscripts.