theorem Th18:
  for F being FinSequence of the_normal_subgroups_of G
  holds F is FinSequence of Subgroups G
proof
  let F be FinSequence of the_normal_subgroups_of G;
  the_normal_subgroups_of G c= Subgroups G by Th17;
  then rng F c= Subgroups G;
  hence thesis by FINSEQ_1:def 4;
end;
