theorem
  n1 >= len p1 & n2 >= len p1 implies crossover(p1,p2,n1,n2)=p1
proof
  assume that
A1: n1 >= len p1 and
A2: n2 >= len p1;
  crossover(p1,p2,n1,n2) = crossover(p1,p2,n2) by A1,Th9;
  hence thesis by A2,Th5;
end;
