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 Th1:
   for i holds {p: p.i > 1} is diophantine Subset of n -xtuples_of NAT
proof
  let i;
  defpred Q[XFinSequence of NAT] means 1* $1 . i > 0*$1.i+1;
  defpred R[XFinSequence of NAT] means $1 . i > 1;
  A1:Q[q] iff R[q];
  {q: Q[q]} = {r: R[r]} from HILB10_3:sch 2(A1);
  hence thesis by HILB10_3:7;
end;
