reserve a,b,k,m,n,s for Nat;
reserve c,c1,c2,c3 for Complex;
reserve i,j,z for Integer;
reserve p for Prime;
reserve x for object;
reserve f,g for complex-valued FinSequence;

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;
