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

theorem Th27:
  for a,b being Element of Z_2, x being Element of bspace(X) holds
  (a*b)*x = a*(b*x)
proof
  let a,b be Element of Z_2, x be Element of bspace(X);
  reconsider c = x as Subset of X;
  (a*b)*x = (a*b) \*\ c by Lm2
    .= a \*\ (b \*\ c) by Th20
    .= a*(b*x) by Lm2;
  hence thesis;
end;
