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

theorem Th26:
  for a,b being Element of Z_2, x being Element of bspace(X) holds
  (a+b)*x = (a*x)+(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 \*\ c) \+\ (b \*\ c) by Th18
    .= (a*x)+(b*x) by Lm2;
  hence thesis;
end;
