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;
