theorem
  n1 >= len p1 & n3 >= len p1 implies crossover(p1,p2,n1,n2,n3) =
  crossover(p1,p2,n2)
proof
  assume that
A1: n1 >= len p1 and
A2: n3 >= len p1;
  crossover(p1,p2,n1,n2,n3) = crossover(p1,p2,n2,n3) by A1,Th18;
  hence thesis by A2,Th10;
end;
