reserve X,Y for set, x,y,z for object, i,j,n for natural number;

theorem Th4:
  for S being non empty non void ManySortedSign
  for o being OperSymbol of S, r being SortSymbol of S,
      T being MSAlgebra over S holds
  o is_of_type {},r implies {} in Args(o,T)
  proof
    let S be non empty non void ManySortedSign;
    let o be OperSymbol of S;
    let r be SortSymbol of S;
    let T be MSAlgebra over S;
    assume A1: (the Arity of S).o = {} & (the ResultSort of S).o = r;
    Args(o,T) = product ((the Sorts of T)*the_arity_of o) by PRALG_2:3
    .= {{}} by A1,CARD_3:10;
    hence {} in Args(o,T) by TARSKI:def 1;
  end;
