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 Th5:
  n >= len p1 implies crossover(p1,p2,n) = p1
proof
  assume
A1: n >= len p1;
  then n >= len S by Def1;
  then
A2: n >= len p2 by Def1;
  crossover(p1,p2,n) = p1^(p2/^n) by A1,FINSEQ_1:58
    .= p1^{} by A2,FINSEQ_5:32
    .= p1 by FINSEQ_1:34;
  hence thesis;
end;
