reserve X for non empty BCIStr_1;
reserve d for Element of X;
reserve n,m,k for Nat;
reserve f for sequence of  the carrier of X;

theorem
  for X being BCI-Algebra_with_Condition(S) holds for x,a1,a2,a3 being
  Element of X holds ((x\a1)\a2)\a3 = x\Product_S<*a1,a2,a3*>
proof
  let X be BCI-Algebra_with_Condition(S);
  let x,a1,a2,a3 be Element of X;
  ((x\a1)\a2)\a3 = (x\(a1 * a2))\a3 by Th11
    .= x\(a1 * a2 * a3) by Th11;
  hence thesis by Th33;
end;
