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 Th10:
  n2 >= len p1 implies crossover(p1,p2,n1,n2)=crossover(p1,p2,n1)
proof
  assume n2 >= len p1;
  then n2 >= len S by Def1;
  then
A1: n2 >= len crossover(p1,p2,n1) by Def1;
  crossover(p1,p2,n1,n2) = crossover(crossover(p1,p2,n1),crossover(p2,p1,
  n1),n2);
  hence thesis by A1,Th5;
end;
