reserve fi,psi for Ordinal-Sequence,
  A,A1,B,C,D for Ordinal,
  X,Y for set,
  x,y for object;

theorem Th64:
  (A div^ B)*^B c= A
proof
  now
    per cases;
    suppose
      B <> {};
      then ex C st A = (A div^ B)*^B+^C & C in B by Def6;
      hence thesis by Th24;
    end;
    suppose
      B = {};
      then A div^ B = {} by Def6;
      then (A div^ B)*^B = {} by ORDINAL2:35;
      hence thesis;
    end;
  end;
  hence thesis;
end;
