reserve G for Group;
reserve A,B for non empty Subset of G;
reserve N,H,H1,H2 for Subgroup of G;
reserve x,a,b for Element of G;

theorem
  N ` (N ` A) c= N ~ (N ~ A)
proof
  N ` A c= N ~ A by Th18;
  then N ` (N ` A) c= N ~ A by Th34;
  hence thesis by Th35;
end;
