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

theorem Th28:
  A in B implies ex C st B = A+^C & C <> {}
proof
  assume
A1: A in B;
  then A c= B by ORDINAL1:def 2;
  then consider C such that
A2: B = A+^C by Th27;
  take C;
  thus B = A+^C by A2;
  assume C = {};
  then B = A by A2,ORDINAL2:27;
  hence contradiction by A1;
end;
