theorem Th19:
  for I be set, S be non void non empty ManySortedSign, A be
  MSAlgebra-Family of I,S, o be OperSymbol of S for x be Element of Args(o,
product A) holds Den(o,product A).x in product Carrier(A,the_result_sort_of o)
proof
  let I be set, S be non void non empty ManySortedSign, A be MSAlgebra-Family
  of I,S, o be OperSymbol of S;
  let x be Element of Args(o,product A);
  Result(o,product A) = (SORTS A).(the_result_sort_of o) by PRALG_2:3
    .= product Carrier(A,the_result_sort_of o) by PRALG_2:def 10;
  hence thesis;
end;
