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 Th20:
  n3 >= len p1 implies crossover(p1,p2,n1,n2,n3) = crossover(p1,p2 ,n1,n2)
proof
  assume n3 >= len p1;
  then n3 >= len S by Def1;
  then
A1: n3 >= len crossover(p1,p2,n1,n2) by Def1;
  crossover(p1,p2,n1,n2,n3) = crossover(crossover(p1,p2,n1,n2),crossover(
  p2,p1,n1,n2),n3);
  hence thesis by A1,Th5;
end;
