User blog comment:Wythagoras/All my stuff/@comment-7484840-20130708083606/@comment-5529393-20130708171802

You don't need (a+b)[n] = (a + b[n]), as the rules can just operate on the rightmost term. All you need is a + 0 = a;  if you say that requires a rule, okay, but make sure your own notational rules handle every possible corner case as well!

You don't need a rule for multiplication as it doesn't appear in Cantor Normal Form. You don't need a rule for exponentiation except for w^a, and that is handled in my above rules.