theorem :: Problem 168
  for S being positive Nat holds
  the set of all f where f is Solution_of_Sierp168 of S is infinite
  proof
    let S be positive Nat;
    set F = Solutions_of_Sierp168(the Solution_of_Sierp168 of S);
A1: dom F = NATPLUS by PARTFUN1:def 2;
    rng F c= the set of all f where f is Solution_of_Sierp168 of S by Th72;
    hence thesis by A1,CARD_1:59;
  end;
