reserve x,y for set,
  G for Group,
  A,B,H,H1,H2 for Subgroup of G,
  a,b,c for Element of G,
  F,F1 for FinSequence of the carrier of G,
  I,I1 for FinSequence of INT,
  i,j for Element of NAT;

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;
