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 Th55:
  N ` H c= N ~ H
proof
A1: N ` H c= carr(H) by Th53;
  carr(H) c= N ~ H by Th54;
  hence thesis by A1;
end;
