theorem
  Rank n is finite
proof
  defpred P[Nat] means Rank $1 is finite;
A1: P[0] by CLASSES1:29;
A2: for n st P[n] holds P[n+1] by Lm7;
  for n holds P[n] from NAT_1:sch 2(A1,A2);
  hence thesis;
end;
