theorem Th16:
  for F being FinSequence of the_normal_subgroups_of G
  for j st j in dom F holds F.j is strict normal Subgroup of G
proof
  let F be FinSequence of the_normal_subgroups_of G;
  let j;
  assume j in dom F;
  then F.j in rng F by FUNCT_1:3;
  hence thesis by Def1;
end;
