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;

theorem Th47:
  for f,g being non empty len-total homogeneous to-naturals NAT*-defined
    Function st arity f = 0 & arity g = 0 & f.{} = g.{} holds f = g
proof
  let f,g be non empty len-total homogeneous to-naturals NAT*-defined
  Function;
A1: g is non empty quasi_total Element of HFuncs NAT by Th28;
  f is non empty quasi_total Element of HFuncs NAT by Th28;
  hence thesis by A1,Th46;
end;
