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 Th17:
  the_normal_subgroups_of G c= Subgroups G
proof
  let x be object;
  assume x in the_normal_subgroups_of G;
  then x is strict normal Subgroup of G by Def1;
  hence thesis by GROUP_3:def 1;
end;
