 reserve n,i,k,m for Nat;
 reserve p for Prime;

theorem
  for n being non zero Nat
  for x being object st x in bool SetPrimes n holds
    x is finite Subset of SetPrimes
  proof
    let n be non zero Nat;
    let x be object;
    assume G1: x in bool SetPrimes n;
    reconsider g1 = x as Subset of SetPrimes n by G1;
    SetPrimes n c= SetPrimes by XBOOLE_1:17; then
    g1 c= SetPrimes;
    hence thesis;
  end;
