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

theorem Th22:
  bspace(X) is add-associative
proof
  let x,y,z be Element of bspace(X);
  reconsider A = x, B = y, C = z as Subset of X;
  x+(y+z) = A \+\ (B \+\ C) by Lm1
    .= (A \+\ B) \+\ C by XBOOLE_1:91
    .= (x+y)+z by Lm1;
  hence thesis;
end;
