reserve X1, X2, Y for non empty RelStr,
  f for Function of [:X1, X2:], Y,
  x for Element of X1,
  y for Element of X2;

theorem Th9:
  for R, S, T being non empty RelStr, f being Function of [:R,S:],
T, a being Element of R, b being Element of S holds Proj (f, a). b = Proj (f, b
  ). a
proof
  let R, S, T be non empty RelStr, f be Function of [:R,S:], T, a be Element
  of R, b be Element of S;
  Proj (f, a). b = f.(a, b) by Th7
    .= Proj (f, b). a by Th8;
  hence thesis;
end;
