theorem
  (G is negative or G is next) implies the_argument_of G is_subformula_of G
proof
  assume G is negative or G is next;
  then the_argument_of G is_immediate_constituent_of G by Th20,Th21;
  then the_argument_of G is_proper_subformula_of G by Th29;
  hence thesis;
end;
