
theorem Th1:
  for S being non empty non void ManySortedSign for A being
  MSAlgebra over S for o being OperSymbol of S, a being set st a in Args(o,A)
  holds a is Function
proof
  let S be non empty non void ManySortedSign;
  let A be MSAlgebra over S;
  let o be OperSymbol of S;
  let x be set;
  assume x in Args(o,A);
  then x in product((the Sorts of A)*the_arity_of o) by PRALG_2:3;
  then ex f being Function st x = f & dom f = dom ((the Sorts of A)*
  the_arity_of o) &
for y be object st y in dom ((the Sorts of A)*the_arity_of o)
  holds f.y in ((the Sorts of A)*the_arity_of o).y by CARD_3:def 5;
  hence thesis;
end;
