reserve S for 1-sorted,
  i for Element of NAT,
  p for FinSequence,
  X for set;

theorem Th31:
  for X being non empty set, x being Element of X holds (<*>(
  bspace(X)))@x = <*>Z_2
proof
  let X be non empty set, x be Element of X;
  set V = bspace(X);
  set L = (<*>V)@x;
  len L = len <*>V by Def9
    .= 0;
  hence thesis;
end;
