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;
