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;
reserve N1,N2 for Subgroup of G;

theorem
  N1 is Subgroup of N2 implies N2 ` N1 c= N1 ` N2
proof
  assume
A1: N1 is Subgroup of N2; then
A2: N2 ` N1 c= N2 ` N2 by Th59;
    N2 ` N2 c= N1 ` N2 by A1,Th60;
  hence thesis by A2;
end;
