reserve D for non empty set;
reserve f1,f2 for FinSequence of D;
reserve i,n,n1,n2,n3,n4,n5,n6 for Element of NAT;
reserve S for Gene-Set;
reserve p1,p2 for Individual of S;

theorem
  n2 >= len p1 & n3 >= len p1 implies crossover(p1,p2,n1,n2,n3) =
  crossover(p1,p2,n1)
proof
  assume that
A1: n2 >= len p1 and
A2: n3 >= len p1;
  crossover(p1,p2,n1,n2,n3) = crossover(p1,p2,n1,n3) by A1,Th19;
  hence thesis by A2,Th10;
end;
