theorem Th45:
  for k,s being Nat st k < s holds
  Product PrimeNumbersFS(s) / primenumber(k) is Nat
  proof
    let k,s be Nat;
    assume k < s;
    then PrimeNumbersFS(s).(k+1) = primenumber(k) by Th43;
    hence thesis;
  end;
