reserve i, j, k, c, m, n for Nat,
  a, x, y, z, X, Y for set,
  D, E for non empty set,
  R for Relation,
  f, g for Function,
  p, q for FinSequence;
reserve f1, f2 for non empty homogeneous to-naturals NAT*-defined Function,
  e1, e2 for homogeneous to-naturals NAT*-defined Function,
  p for Element of (arity f1+1)-tuples_on NAT;
reserve P for primitive-recursively_closed non empty Subset of HFuncs NAT;

theorem Th78:
  for f1 be 1-ary len-total to-naturals homogeneous NAT*-defined Function,
      f2 be non empty to-naturals homogeneous NAT*-defined Function holds
  primrec(f1,f2,2).<*i,0*> = f1.<*i*>
proof
  let f1 be 1-ary len-total to-naturals homogeneous NAT*-defined Function,
  f2 be non empty to-naturals homogeneous NAT*-defined Function;
  reconsider i1=i as Element of NAT by ORDINAL1:def 12;
  arity f1 = 1 by Def21;
  then reconsider p = <*i1,0*> as Element of (arity f1 +1)-tuples_on NAT
  by FINSEQ_2:101;
  len p = 2 by FINSEQ_1:44;
  then
A1: 2 in dom p by FINSEQ_3:25;
  p+*(2,0) = p by Th1;
  hence primrec(f1,f2,2).<*i,0*> = f1.Del(p,2) by A1,Th59
    .= f1.<*i*> by WSIERP_1:19;
end;
