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 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;
