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 Th53:
  N ` H c= carr(H)
proof
  let x be object;
  assume x in N ` H;
  then consider y1 being Element of G such that
A1: y1 = x & y1 * N c= carr(H);
  y1 in y1 * N  by GROUP_2:108;
  hence thesis by A1;
end;
