reserve I for non empty set,
  J for ManySortedSet of I,
  S for non void non empty ManySortedSign,
  i for Element of I,
  c for set,
  A for MSAlgebra-Family of I,S,
  EqR for Equivalence_Relation of I,
  U0,U1,U2 for MSAlgebra over S,
  s for SortSymbol of S,
  o for OperSymbol of S,
  f for Function;

theorem Th5:
  the_arity_of o = {} & Result(o,U0) <> {} implies const(o,U0) in Result(o,U0)
proof
  assume that
A1: the_arity_of o = {} and
A2: Result(o,U0) <> {};
  dom Den(o,U0) = Args(o,U0) by A2,FUNCT_2:def 1
    .= {{}} by A1,PRALG_2:4;
  then {} in dom Den(o,U0) by TARSKI:def 1;
  then Den(o,U0).{} in rng Den(o,U0) by FUNCT_1:def 3;
  hence thesis;
end;
