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 Th9:
  n1 >= len p1 implies crossover(p1,p2,n1,n2)=crossover(p1,p2,n2)
proof
  assume
A1: n1 >= len p1;
  then n1 >= len S by Def1;
  then
A2: n1 >= len p2 by Def1;
  crossover(p1,p2,n1,n2) = crossover(p1,crossover(p2,p1,n1),n2) by A1,Th5;
  hence thesis by A2,Th5;
end;
