theorem
  for a,i1,i2,i3 holds
    {p: p.i1 = a*p.i2*p.i3} is diophantine Subset of n -xtuples_of NAT
proof
  let a,i1,i2,i3;
  defpred Q1[XFinSequence of NAT] means 1*$1.i1 = a*$1.i2*$1.i3;
  defpred Q2[XFinSequence of NAT] means $1.i1 = a*$1.i2*$1.i3;
A1:for p holds Q1[p] iff Q2[p];
  {p:Q1[p]} = {q:Q2[q]} from HILB10_3:sch 2(A1);
  hence thesis by HILB10_3:9;
end;
