theorem Th13:
  for a,b,i1 holds
    {p: a* p.i1 = b} is diophantine Subset of n -xtuples_of NAT
proof
  let a,b be Integer,i1;
  set i2 = the Element of n;
  defpred P[XFinSequence of NAT] means a*($1.i1) = b;
  defpred Q[XFinSequence of NAT] means a*($1.i1) = 0 * ($1.i2)+b;
  A1:for p holds P[p] iff Q[p];
  {p: P[p]} = {q:Q[q]} from Eq(A1);
  hence thesis by Th6;
end;
