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 being
  Element of X holds (x\a1)\a2 = x\Product_S<*a1,a2*>
proof
  let X be BCI-Algebra_with_Condition(S);
  let x,a1,a2 be Element of X;
  (x\a1)\a2 = x\(a1 * a2) by Th11;
  hence thesis by Th32;
end;
