reserve n for Nat,
        i,j,i1,i2,i3,i4,i5,i6 for Element of n,
        p,q,r for n-element XFinSequence of NAT;

theorem
  for n being Nat,i being Element of n holds
    {p where p is n-element XFinSequence of NAT: p.i is prime}
     is diophantine Subset of n -xtuples_of NAT
proof let n,i;
  defpred Q[XFinSequence of NAT] means $1.i is prime;
  defpred R[XFinSequence of NAT] means ($1.i-'1)! + 1 mod $1.i = 0 & $1.i > 1;
  A1:Q[q] iff R[q] by NAT_5:22;
   {q: Q[q]} = {r: R[r]} from HILB10_3:sch 2(A1);
  hence thesis by Th3;
end;
