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

theorem
  A in B iff succ A in succ B
proof
  A in B iff succ A c= B by ORDINAL1:21;
  hence thesis by ORDINAL1:22;
end;
