theorem Th30:
  for x being Element of G st x in N ~ (N ` (N ~ A))
  holds x * N meets N ` (N ~ A)
proof
  let x be Element of G;
  assume x in N ~ (N ` (N ~ A));
  then ex x1 being Element of G st x = x1 & x1 * N meets N ` (N ~ A);
  hence thesis;
end;
