theorem Th8:
  crossover(p1,p2,n,0) = crossover(p2,p1,n)
proof
  reconsider q1 = crossover(p1,p2,n) as Individual of S;
  reconsider q2=crossover(p2,p1,n) as Individual of S;
  crossover(p1,p2,n,0) = crossover(q1,q2,0) .= q2 by Th4;
  hence thesis;
end;
