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 Th38:
  W is Tarski implies Rank card W is Tarski
proof
  assume
A1: W is Tarski;
  set B = Rank card W;
  thus for X,Y holds X in B & Y c= X implies Y in B by CLASSES1:41;
  now
A2: card W is limit_ordinal by A1,Th19;
    assume
A3: W <> {};
    thus for X holds X in B implies bool X in B
    proof
      let X;
      assume X in B;
      then consider A such that
A4:   A in card W and
A5:   X in Rank A by A3,A2,CLASSES1:31;
A6:   bool X in Rank succ A by A5,CLASSES1:42;
      succ A in card W by A2,A4,ORDINAL1:28;
      hence thesis by A2,A6,CLASSES1:31;
    end;
  end;
  hence thesis by A1,Th36,CLASSES1:29;
end;
