User blog comment:Mh314159/FOX notation/@comment-39585023-20191205111828/@comment-35470197-20191206112928

But you already have a rule [a]‹S›_n(x) = [[a]‹S›_{n-1}(x)]‹S›(x), don't you? If you meant that you were explaining two candidates of new rules, the iterated subscript can be inductively defined in the following way: Then you do onot have to use α(n), which has ambiguity. (Ellipses are bad, but better than the ambiguous α.)
 * 1) If n = 0, then [a]‹S›_n(x) = [a](x).
 * 2) If n > 0, then [a]‹S›_n(x) = [a]‹T›_{[a]_{n-1}(x)}(x).