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 Th7:
  crossover(p1,p2,0,n) = crossover(p2,p1,n)
proof
  crossover(p1,p2,0,n) = crossover(p2,crossover(p2,p1,0),n) by Th4
    .= crossover(p2,p1,n) by Th4;
  hence thesis;
end;
