More detail:
Start with an axiom Aj, use it as data for a LISP expression Rj. A program that computes the value of this expression "B" in AIT has length: Expression + data + self-delimiter or in this case Rj + Aj + Self-delimiter. Like this: P = {Expression(data) + self-delimiter} computes [produces value] "B" If P is the shortest program to do so then it is called elegant and its length is the complexity of "B". In an everywhere elegant cascade each P(i) is longer than P(i -1) because the data for P(i) alone has the same complexity as P(i - 1) then you add the complexity of the expression and the self-delimiter. What is left is to 1) identify "everywhere elegant cascade" = deterministic evolution of the isomorphism and 2) find an upper bound on the complexity of the P(i). Chaitin did the latter by putting an upper limit on the complexity an N-bit FAS could prove an elegant program has i.e. it own complexity plus a constant. But a deterministic cascade is already known to be an everywhere elegant program. A contradiction is established unless the cascade stops but it can not stop. The only way out is a spontaneous increase in the complexity of the FAS. Hal