theorem Th21:
  n1 >= len p1 & n2 >= len p1 implies crossover(p1,p2,n1,n2,n3) =
  crossover(p1,p2,n3)
proof
  assume that
A1: n1 >= len p1 and
A2: n2 >= len p1;
  crossover(p1,p2,n1,n2,n3) = crossover(p1,p2,n2,n3) by A1,Th18;
  hence thesis by A2,Th9;
end;
