reserve m for Cardinal,
  A,B,C for Ordinal,
  x,y,z,X,Y,Z,W for set,
  f for Function;
reserve f,g for Function,
  L for Sequence,
  F for Cardinal-Function;

theorem Th27:
  W is Tarski implies Rank card W c= W
proof
  assume
A1: W is Tarski;
  now
    assume
A2: W <> {};
    thus thesis
    proof
A3:   card W is limit_ordinal by A1,Th19;
      let x be object;
      assume x in Rank card W;
      then consider A such that
A4:   A in card W and
A5:   x in Rank A by A2,A3,CLASSES1:31;
      A in On W by A1,A4,Th9;
      then Rank A c= W by A1,Th7,Th25;
      hence thesis by A5;
    end;
  end;
  hence thesis by CLASSES1:29;
end;
