theorem Th7:
  for N1,N2 being strict normal Subgroup of G holds x in N1 "\/" N2
  iff ex a,b st x = a * b & a in N1 & b in N2
proof
  let N1,N2 be strict normal Subgroup of G;
  N1 * N2 = N2 * N1 by GROUP_3:125;
  hence thesis by Th5;
end;
