User blog comment:Wythagoras/Dollar function formal definition/@comment-5529393-20130619005520/@comment-7484840-20130619190107

a$[0,0]_2 reduces to a$...[[0,0]_1,0]_1...]_1,0]_1 (rule 9). Where did you get yours from? Also, notice that lack of commas in some of the rules (for example [[0][0 is completely different to 0],[0) more variables is a higher level.