reserve i for Nat,
  j for Element of NAT,
  X,Y,x,y,z for set;

theorem
  {*, non_op} misses Constructors
proof
  assume not thesis;
  then consider x being object such that
A1: x in {*, non_op} and
A2: x in Constructors by XBOOLE_0:3;
  x in Modes \/ Attrs or x in Funcs by A2,XBOOLE_0:def 3;
  then x in Modes or x in Attrs or x in Funcs by XBOOLE_0:def 3;
  then consider Y,Z being set such that
A3: x in [:Y,Z:];
A4: ex y,z being object st ( y in Y)&( z in Z)&( [y,z] = x)
    by A3,ZFMISC_1:def 2;
  reconsider x as set by TARSKI:1;
  x = * or x = non_op by A1,TARSKI:def 2;
  then the_rank_of x = 0 or the_rank_of x = 1 by CLASSES1:73;
  then the_rank_of x c= 1;
  then the_rank_of x in succ succ {} by ORDINAL1:6,12;
  then x in Rank succ succ {} by CLASSES1:66;
  hence thesis by A4,CLASSES1:29,45;
end;
