reserve a,b,r for non unit non zero Real;
reserve X for non empty set,
        x for Tuple of 4,X;

theorem
  pi_13(pi_23(pi_13(x))) = pi_12(x) &
  pi_12(pi_34(pi_23(pi_13(x)))) = pi_34(pi_23(x)) &
  pi_23(pi_24(pi_14(pi_23(pi_13(x))))) = pi_14(x);
