reserve I,J for set,i,j,x for object,
  S for non empty ManySortedSign;

theorem Th4:
  for S be non void non empty ManySortedSign, U0 be MSAlgebra over
  S, o be OperSymbol of S st the_arity_of o = {} holds Args(o,U0) = {{}}
proof
  let S be non void non empty ManySortedSign, U0 be MSAlgebra over S, o be
  OperSymbol of S;
  assume
A1: the_arity_of o = {};
  thus Args(o,U0) = product ((the Sorts of U0)*(the_arity_of o)) by Th3
    .= {{}} by A1,CARD_3:10;
end;
